ALBERT

Description: Uncertainties in calculating precipitation climatology in East Asia Hydrology and Earth System Sciences Discussions, 12, 7765-7783, 2015 Author(s): J. Kim and S. K. Park This study examines the uncertainty in calculating the fundamental climatological characteristics of precipitation in the East Asia region from multiple fine-resolution gridded analysis datasets based on in-situ rain gauge observations. Five observation-based gridded precipitation datasets are used to derive the long-term means, standard deviations in lieu of interannual variability and linear trends over the 28-year period from 1980 to 2007. Both the annual and summer (June–July–August) mean precipitation is examined. The agreement amongst these precipitation datasets are examined using multiple metrics including the signal-to-noise ratio (SNR) defined as the ratio between long-term means and the corresponding standard deviations, and Taylor diagrams which allows examinations of the pattern correlation, the standard deviation, and the centered root mean square error. It is found that the five gauge-based precipitation analysis datasets agree well in the long-term mean and interannual variability in most of the East Asia region including eastern China, Manchuria, South Korea, and Japan, which are densely populated and have fairly high density observation networks. The regions of large inter-dataset variations include Tibetan Plateau, Mongolia, northern Indo-China, and North Korea. The regions of large uncertainties are typically lightly populated and are characterized by severe terrain and/or extreme high elevations. Unlike the long-term mean and interannual variability, agreements between datasets in the linear trend is weak, both for the annual and summer mean values. In most of the East Asia region, the SNR for the linear trend is below 0.5, i.e., the inter-dataset variability exceeds the multi-data ensemble mean. The uncertainty in the spatial distribution of long-term means among these datasets occurs both in the spatial pattern and variability, but the uncertainty for the interannual variability and time trend is much larger in the variability than in the pattern correlation. Thus, care must be taken in using long-term trends calculated from gridded precipitation analysis data for climate studies over the East Asia region.

Description: Nonlinear effects of locally heterogeneous hydraulic conductivity fields on regional stream–aquifer exchanges Hydrology and Earth System Sciences Discussions, 12, 7727-7764, 2015 Author(s): J. Zhu, C. L. Winter, and Z. Wang Computational experiments are performed to evaluate the effects of locally heterogeneous conductivity fields on regional exchanges of water between stream and aquifer systems in the Middle Heihe River Basin (MHRB) of northwestern China. The effects are found to be nonlinear in the sense that simulated discharges from aquifers to streams are systematically lower than discharges produced by a base model parameterized with relatively coarse effective conductivity. A similar, but weaker, effect is observed for stream leakage. The study is organized around three hypotheses: (H1) small-scale spatial variations of conductivity significantly affect regional exchanges of water between streams and aquifers in river basins, (H2) aggregating small-scale heterogeneities into regional effective parameters systematically biases estimates of stream–aquifer exchanges, and (H3) the biases result from slow-paths in groundwater flow that emerge due to small-scale heterogeneities. The hypotheses are evaluated by comparing stream–aquifer fluxes produced by the base model to fluxes simulated using realizations of the MHRB characterized by local (grid-scale) heterogeneity. Levels of local heterogeneity are manipulated as control variables by adjusting coefficients of variation. All models are implemented using the MODFLOW simulation environment, and the PEST tool is used to calibrate effective conductivities defined over 16 zones within the MHRB. The effective parameters are also used as expected values to develop log-normally distributed conductivity ( K ) fields on local grid scales. Stream-aquifer exchanges are simulated with K fields at both scales and then compared. Results show that the effects of small-scale heterogeneities significantly influence exchanges with simulations based on local-scale heterogeneities always producing discharges that are less than those produced by the base model. Although aquifer heterogeneities are uncorrelated at local scales, they appear to induce coherent slow-paths in groundwater fluxes that in turn reduce aquifer–stream exchanges. Since surface water–groundwater exchanges are critical hydrologic processes in basin-scale water budgets, these results also have implications for water resources management.

Description: Near–surface air temperature and snow skin temperature comparison from CREST-SAFE station data with MODIS land surface temperature data Hydrology and Earth System Sciences Discussions, 12, 7665-7687, 2015 Author(s): C. L. Pérez Díaz, T. Lakhankar, P. Romanov, J. Muñoz, R. Khanbilvardi, and Y. Yu Land Surface Temperature (LST) is a key variable (commonly studied to understand the hydrological cycle) that helps drive the energy balance and water exchange between the Earth's surface and its atmosphere. One observable constituent of much importance in the land surface water balance model is snow. Snow cover plays a critical role in the regional to global scale hydrological cycle because rain-on-snow with warm air temperatures accelerates rapid snow-melt, which is responsible for the majority of the spring floods. Accurate information on near-surface air temperature ( T -air) and snow skin temperature ( T -skin) helps us comprehend the energy and water balances in the Earth's hydrological cycle. T -skin is critical in estimating latent and sensible heat fluxes over snow covered areas because incoming and outgoing radiation fluxes from the snow mass and the air temperature above make it different from the average snowpack temperature. This study investigates the correlation between MODerate resolution Imaging Spectroradiometer (MODIS) LST data and observed T -air and T -skin data from NOAA-CREST-Snow Analysis and Field Experiment (CREST-SAFE) for the winters of 2013 and 2014. LST satellite validation is imperative because high-latitude regions are significantly affected by climate warming and there is a need to aid existing meteorological station networks with the spatially continuous measurements provided by satellites. Results indicate that near-surface air temperature correlates better than snow skin temperature with MODIS LST data. Additional findings show that there is a negative trend demonstrating that the air minus snow skin temperature difference is inversely proportional to cloud cover. To a lesser extent, it will be examined whether the surface properties at the site are representative for the LST properties within the instrument field of view.

Description: Does drought alter hydrological functions in forest soils? An infiltration experiment Hydrology and Earth System Sciences Discussions, 12, 7689-7725, 2015 Author(s): K. F. Gimbel, H. Puhlmann, and M. Weiler The water cycle is expected to change in future and severely affect precipitation patterns across central Europe and in other parts of the world, leading to more frequent and severe droughts. Usually, it is assumed that system properties, like soil properties, remain stable and will not be affected by drought events. To study if this assumption is appropriate, we address the effects of drought on the infiltration behavior of forest soils using dye tracer experiments on six sites in three regions across Germany, which were forced into drought conditions. The sites cover clayey, loamy and sandy textured soils. In each region, we compared a deciduous and a coniferous forest stand to address differences between the main tree species. The results of the dye tracer experiments show clear evidence for changes in infiltration behavior at the sites. The infiltration changed at the clayey plots from regular and homogeneous flow to fast preferential flow. Similar behavior was observed at the loamy plots, where large areas in the upper layers remained dry, displaying signs of strong water repellency. This was confirmed by WDPT tests, which revealed, in all except one plot, moderate to severe water repellency. Water repellency was also accountable for the change of regular infiltration to fingered flow in the sandy soils. The results of this study suggest that the "drought-history" or generally the climatic conditions in the past of a soil are more important than the actual antecedent soil moisture status regarding hydrophobicity and infiltration behavior; and also, that drought effects on infiltration need to be considered in hydrological models to obtain realistic predictions concerning water quality and quantity in runoff and groundwater recharge.

Description: Does the Budyko curve reflect a maximum power state of hydrological systems? A backward analysis Hydrology and Earth System Sciences Discussions, 12, 7821-7842, 2015 Author(s): M. Westhoff, E. Zehe, P. Archambeau, and B. Dewals Almost all catchments plot within a small envelope around the Budyko curve. This apparent behaviour suggests that organizing principles may play a role in the evolution of catchments. In this paper we applied the thermodynamic principle of maximum power as the organizing principle. In a top-down approach we derived mathematical formulations of the relation between relative wetness and gradients driving runoff and evaporation for a simple one-box model. We did this in such a way that when the conductances are optimized with the maximum power principle, the steady state behaviour of the model leads exactly to a point on the Budyko curve. Subsequently we derived gradients that, under constant forcing, resulted in a Budyko curve following the asymptotes closely. With these gradients we explored the sensitivity of dry spells and dynamics in actual evaporation. Despite the simplicity of the model, catchment observations compare reasonably well with the Budyko curves derived with dynamics in rainfall and evaporation. This indicates that the maximum power principle may be used (i) to derive the Budyko curve and (ii) to move away from the empiricism in free parameters present in many Budyko functions. Future work should focus on better representing the boundary conditions of real catchments and eventually adding more complexity to the model.

Description: Impacts of land use change and climate variations on annual inflow into Miyun Reservoir, Beijing, China Hydrology and Earth System Sciences Discussions, 12, 7785-7819, 2015 Author(s): J. K. Zheng, G. Sun, W. H. Li, X. X. Yu, C. Zhang, Y. B. Gong, and L. H. Tu Miyun reservoir, the only surface water source for Beijing city, has experienced water supply decline in recent decades. Previous studies suggest that both land use change and climate contributes the changes of water supply in this critical watershed. However, the specific causes of the decline in Miyun reservoir are debatable in a non-stationary climate in the past four decades. The central objective of this study was to quantify the separate and collective contributions of land use change and climate variability to the decreasing inflow into Miyun reservoir during 1961–2008. Different from previous studies, this work objectively identified breakpoints by analyzing the long-term historical hydrometeorology and land cover records. To effectively study the different impacts of the climate variation and land cover change during different sub-periods, annual water balance model (AWB), climate elasticity model (CEM), and rainfall–runoff model (RRM) were employed to conduct attribution analysis synthetically. We found a significant decrease in annual streamflow ( p 〈 0.01), a significant positive trend in annual potential evapotranspiration ( p 〈 0.01), and an insignificant negative trend in annual precipitation ( p 〉 0.1) during 1961–2008. Combined with historical records, we identified two breakpoints as in 1983 and 1999 for the period 1961–2008 by the sequential Mann–Kendall Test and Double Mass Curve. Climate variability alone did not explain the decrease in inflow to Miyun reservoir. Reduction of water yield was closely related to increase in evapotranspiration rates due to the expansion of forestlands and reduction in cropland and grassland, and was likely exacerbated by increased water consumption for domestic and industrial uses in the basin. Our study found that the contribution to the observed streamflow decline from land use change fell from 64–92 % during 1984–1999 to 36–58 % during 2000–2008, whereas the contribution from climate variation climbed from 8–36 % during the 1984–1999 to 42–64 % during 2000–2008. Model uncertainty analysis further demonstrated that climate warming played a dominant role in streamflow reduction in the 2000s. We conclude that future climate change and variability will further challenge the goal of water supply of Miyun reservoir to meet water demand. A comprehensive watershed management strategy needs to consider the climate variations besides vegetation management.

Description: Acoustic localization is an essential technique in speech capturing, speech enhancement, video conferencing, and human–robot interaction. However, in practical situations, localization has to be performed in abominable environments, where the presence of reverberation and noise degrades the performance of available position estimates. Besides, the designed systems should be adaptive to locomotion of targets with low computational complexity. In the context, this paper introduces a robust hierarchical acoustic localization method via time-delay compensation (TDC) and interaural matching filter (IMF). Firstly, interaural time-delay (ITD) and interaural level difference (ILD), which are cues involved in first two layers, respectively, are yielded by TDC all at once. Then, a novel feature named IMF, which can eliminate the difference between binaural signals, is proposed in the third layer. The final decision making is based on a Bayesian rule. The relationships among the three layers are that the former layer provides candidate directions for later ones such that the searching space becomes gradually smaller to reduce matching time. Experiments using both a public database and a real scenario verify that TDC and IMF are robust for acoustic localization, and hierarchical system has less consumption time.

Description: Canonical correlation analysis (CCA) is a widely used data analysis tool that allows to assess the correlation between two distinct sets of signals. It computes optimal linear combinations of the signals in both sets such that the resulting signals are maximally correlated. The weight vectors defining these optimal linear combinations are referred to as “principal CCA directions”. In addition to this particular type of data analysis, CCA is also often used as a blind source separation (BSS) technique, i.e., under certain assumptions, the principal CCA directions have certain demixing properties. In this paper, we propose a distributed CCA (DCCA) algorithm that can operate in wireless sensor networks (WSNs) with a fully connected or a tree topology. The algorithm estimates the $Q$ principal CCA directions from the sensor signal observations collected by the different nodes in the WSN and extracts the corresponding sources. These network-wide principal CCA directions are estimated in a time-recursive fashion without explicitly constructing the corresponding network-wide correlation matrices, i.e., without the need for data centralization. Instead, each node locally computes smaller CCA problems and only transmits compressed sensor signal observations (of dimension $Q$ ), which significantly reduces the bit rate over the wireless links of the WSN. We prove convergence and optimality of the DCCA algorithm, and we demonstrate its performance by means of numerical simulations in a blind source separation scenario.

Description: Future changes in flash flood frequency and intensity of the Tha Di River (Thailand) based on rainfall–runoff modeling and advanced delta change scaling Hydrology and Earth System Sciences Discussions, 12, 7327-7352, 2015 Author(s): S. Hilgert, A. Wagner, and S. Fuchs As a consequence of climate change, extreme and flood-causing precipitation events are expected to increase in magnitude and frequency, especially in today's high-precipitation areas. During the north-east monsoon seasons, Nakhon Si Thammarat in southern Thailand is flash-flooded every 2.22 years on average. This study investigates frequency and intensity of harmful discharges of the Tha Di River regarding the IPCC emission scenarios A2 and B2. The regional climate model (RCM) PRECIS was transformed using the advanced delta change (ADC) method. The hydrologic response model HBV-Light was calibrated to the catchment and supplied with ADC-scaled daily precipitation and temperature data for 2010–2089. Under the A2 (B2) scenario, the flood threshold exceedance frequency on average increases by 133 % (decreases by 10 %), average flood intensity increases by 3 % (decreases by 2 %) and the annual top five discharge peaks intensities increase by 46 % (decrease by 5 %). Yearly precipitation sums increase by 30 % (10 %) towards the end of the century. The A2 scenario predicts a precipitation increase during the rainy season, which intensifies flood events; while increases projected exclusively for the dry season are not expected to cause floods. Retention volume demand of past events was calculated to be up to 12 × 10 6 m 3 . Flood risks are staying at high levels under the B2 scenario or increase dramatically under the A2 scenario. Results show that the RCM scaling process is inflicted with systematic biases but is crucial to investigate small, mountainous catchments. Improvement of scaling techniques should therefore accompany the development towards high-resolution climate models.

Description: Multiscale evaluation of the standardized precipitation index as a groundwater drought indicator Hydrology and Earth System Sciences Discussions, 12, 7405-7436, 2015 Author(s): R. Kumar, J. L. Musuuza, A. F. Van Loon, A. J. Teuling, R. Barthel, J. Ten Broek, J. Mai, L. Samaniego, and S. Attinger The lack of comprehensive groundwater observations at regional and global scales has promoted the use of alternative proxies and indices to quantify and predict groundwater droughts. Among them, the Standardized Precipitation Index (SPI) is commonly used to characterize droughts in different compartments of the hydro-meteorological system. In this study, we explore the suitability of the SPI to characterize local and regional scale groundwater droughts using observations at more than 2000 groundwater wells in geologically different areas in Germany and the Netherlands. A multiscale evaluation of the SPI is performed using the station data and their corresponding 0.5° gridded estimates to analyze the local and regional behavior of groundwater droughts, respectively. The standardized anomalies in the groundwater heads (SGI) were correlated against SPIs obtained using different accumulation periods. The accumulation periods to achieve maximum correlation exhibited high spatial variability (ranges 3 to 36 months) at both scales, leading to the conclusion that an a priori selection of the accumulation period (for computing the SPI) would result in inadequate characterization of groundwater droughts. The application of the uniform accumulation periods over the entire domain significantly reduced the correlation between SPI and SGI (≈ 21–66 %) indicating the limited applicability of SPI as a proxy for groundwater droughts even at long accumulation times. Furthermore, the low scores of the hit rate (0.3–0.6) and high false alarm ratio (0.4–0.7) at the majority of the wells and grid cells demonstrated the low reliability of groundwater drought predictions using the SPI. The findings of this study highlight the pitfalls of using the SPI as a groundwater drought indicator at both local and regional scales, and stress the need for more groundwater observations and accounting for regional hydrogeological characteristics in groundwater drought monitoring.

Description: Comparing the Ensemble and Extended Kalman Filters for in situ soil moisture assimilation with contrasting soil conditions Hydrology and Earth System Sciences Discussions, 12, 7353-7403, 2015 Author(s): D. Fairbairn, A. L. Barbu, J.-F. Mahfouf, J.-C. Calvet, and E. Gelati Two data assimilation methods are compared for their ability to produce a deterministic soil moisture analysis on the Météo-France land surface model: (i) SEKF, a Simplified Extended Kalman Filter, which uses a climatological background-error covariance, (ii) EnSRF, the Ensemble Square Root Filter, which uses an ensemble background-error covariance and approximates random forcing errors stochastically. The accuracy of the deterministic analysis is measured on 12 sites with in situ observations and various soil textures in Southwest France (SMOSMANIA network). In the experiments with real observations, the two methods perform similarly and improve on the open loop. Both methods suffer from incorrect linear assumptions which are particularly degrading to the analysis during water-stressed conditions: the EnSRF by a dry bias and the SEKF by an over-sensitivity of the model Jacobian between the surface and the root zone layers. These problems are less severe for sandy soils than clay soils because sandy soils are less sensitive to perturbations in the initial conditions. A simple bias correction technique is tested on the EnSRF. Although this reduces the bias, it also suppresses the ensemble spread, which degrades the analysis performance. However, the EnSRF flow-dependent background-error covariance evidently captures seasonal variability in the soil moisture errors and should exploit planned improvements in the model physics. Synthetic experiments demonstrate that when there is only a random component in the precipitation forcing errors, the correct stochastic representation of these errors enables the EnSRF to perform better than the SEKF. But in the real experiments the same rainfall error specification does not improve the EnSRF analysis. It is likely that the actual rainfall errors are underestimated and that other sources of errors could limit the usefulness of this information. More comprehensive ways of representing the rainfall errors are suggested, which might improve the EnSRF performance.

Description: There has been much research on shrinkage methods for real-valued covariance matrices and their inverses (precision matrices). In spectral analysis of $p$ -vector-valued time series, complex-valued spectral matrices and precision matrices arise, and good shrinkage methods are often required, most notably when the estimated complex-valued spectral matrix is singular. As an improvement on the Ledoit-Wolf (LW) type of spectral matrix estimator we use random matrix theory to derive a Rao-Blackwell estimator for a spectral matrix, its inverse being a Rao–Blackwellized estimator for the spectral precision matrix. A random matrix method has previously been proposed for complex-valued precision matrices. It was implemented by very costly simulations. We formulate a fast, completely analytic approach. Moreover, we derive a way of selecting an important parameter using predictive risk methodology. We show that both the Rao–Blackwell estimator and the random matrix estimator of the precision matrix can substantially outperform the inverse of the LW estimator in a time series setting. Our new methodology is applied to EEG-derived time series data where it is seen to work well and deliver substantial improvements for precision matrix estimation.

Description: In this paper, the state estimation problem for discrete-time linear systems influenced by multiplicative and time-correlated additive measurement noises is considered where the multiplicative noises are zero-mean white noise sequences, and the time-correlated additive noise is described by a linear system model with white noise. An optimal linear estimator for the system under consideration is proposed, which does not require computing the inverse of state transition matrix. The proposed estimator has a recursive structure, and has time-independent computation and storage load. Computer simulations are carried out to demonstrate the performance of the proposed estimator. The simulation results show the superiority of the proposed estimator.

Description: In this paper, we start with the standard support vector machine (SVM) formulation and extend it by considering a general SVM formulation with normalized margin. This results in a unified convex framework that allows many different variations in the formulation with very diverse numerical performance. The proposed unified framework can capture the existing methods, i.e., standard soft-margin SVM, $ell_{1}$ -SVM, and SVMs with standardization, feature selection, scaling, and many more SVMs, as special cases. Furthermore, our proposed framework can not only provide us with more insights on different SVMs from the “energy” and “penalty” point of views, which help us understand the connections and differences between them in a unified way, but also enable us to propose more SVMs that outperform the existing ones under some scenarios.

Description: Morphological dynamics of an englacial channel Hydrology and Earth System Sciences Discussions, 12, 7615-7664, 2015 Author(s): G. Vatne and T. D. L. Irvine-Fynn Despite an interest in the hydraulic functioning of supraglacial and englacial channels over the last four decades, the processes and forms of such ice-bounded streams have remained poorly documented. Recent glaciological research has demonstrated the potential significance of so-called "cut and closure" streams, where englacial or subglacial flowpaths are created from the long-term incision of supraglacial channels. These flowpaths are reported to exhibit step-pool morphology, comprising knickpoints and/or knickzones, albeit exaggerated in dimensions in comparison to their supraglacial channel counterparts. However, little is known of the development of such channels' morphology. Here, we examine the spatial organization of step-pools and the upstream migration of steps, many of which form knickzones, with repeated surveys over a 10 year period in an englacial conduit in cold-based Austre Brøggerbreen, Svalbard. The observations show upstream knickpoint recession to be the dominant process for channel evolution. This is paralleled by an increase in average step height and conduit gradient over time. Characteristic channel reach types and step-riser forms are consistently observed in each of the morphological surveys reported. We suggest that the formation of steps has a hydrodynamic origin, where step-pool geometry is more efficient for energy dissipation than meanders, and that the englacial channel system is one in rapid transition rather than in dynamic equilibrium. The evolution and recession of knickzones reported here result in the formation of a 37 m moulin, suggesting over time the englacial channel may evolve towards a stable end-point characterised by a singular vertical descent to the local hydraulic base level. In light of this, our observations highlight the need to further examine the adjustment processes in cut-and-closure channels to better understand their coupling to supraglacial meltwater sources and role and potential significance in cold-based glacier hydrology and ice dynamics.

Description: The impact of near-surface soil moisture assimilation at subseasonal, seasonal, and inter-annual time scales Hydrology and Earth System Sciences Discussions, 12, 7971-8004, 2015 Author(s): C. Draper and R. Reichle Nine years of Advanced Microwave Scanning Radiometer – Earth Observing System (AMSR-E) soil moisture retrievals are assimilated into the Catchment land surface model at four locations in the US. The assimilation is evaluated using the unbiased Mean Square Error (ubMSE) relative to watershed-scale in situ observations, with the ubMSE separated into contributions from the subseasonal (SM short ), mean seasonal (SM seas ) and inter-annual (SM long ) soil moisture dynamics. For near-surface soil moisture, the average ubMSE for Catchment without assimilation was (1.8 × 10 −3 m 3 m −3 ) 2 , of which 19 % was in SM long , 26 % in SM seas , and 55 % in SM short . The AMSR-E assimilation significantly reduced the total ubMSE at every site, with an average reduction of 33 %. Of this ubMSE reduction, 37 % occurred in SM long , 24 % in SM seas , and 38 % in SM short . For root-zone soil moisture, in situ observations were available at one site only, and the near-surface and root-zone results were very similar at this site. These results suggest that, in addition to the well-reported improvements in SM short , assimilating a sufficiently long soil moisture data record can also improve the model representation of important long term events, such as droughts. The improved agreement between the modeled and in situ SM seas is harder to interpret, given that mean seasonal cycle errors are systematic, and systematic errors are not typically targeted by (bias-blind) data assimilation. Finally, the use of one year subsets of the AMSR-E and Catchment soil moisture for estimating the observation-bias correction (rescaling) parameters is investigated. It is concluded that when only one year of data is available, the associated uncertainty in the rescaling parameters should not greatly reduce the average benefit gained from data assimilation, but locally and in extreme years there is a risk of increased errors.

Description: We consider multiple-antenna signal detection of primary user transmission signals by a secondary user receiver in cognitive radio networks. The optimal detector is analyzed for the scenario where the number of primary user signals is no less than the number of receive antennas at the secondary user. We first derive exact expressions for the moments of the generalized likelihood ratio test (GLRT) statistic, yielding approximations for the false alarm and detection probabilities. We then show that the normalized GLRT statistic converges in distribution to a Gaussian random variable when the number of antennas and observations grow large at the same rate. Further, using results from large random matrix theory, we derive expressions to compute the detection probability without explicit knowledge of the channel, and then particularize these expressions for two scenarios of practical interest: 1) a single primary user sending spatially multiplexed signals, and 2) multiple spatially distributed primary users. Our analytical results are finally used to obtain simple design rules for the signal detection threshold.

Description: A rainfall design method for spatial flood risk assessment: considering multiple flood sources Hydrology and Earth System Sciences Discussions, 12, 8005-8033, 2015 Author(s): X. Jiang and H. Tatano Information about the spatial distribution of flood risk is important for integrated urban flood risk management. Focusing on urban areas, spatial flood risk assessment must reflect all risk information derived from multiple flood sources: rivers, drainage, coastal flooding etc. that may affect the area. However, conventional flood risk assessment deals with each flood source independently, which leads to an underestimation of flood risk in the floodplain. Even in floodplains that have no risk from coastal flooding, flooding from river channels and inundation caused by insufficient drainage capacity should be considered simultaneously. For integrated flood risk management, it is necessary to establish a methodology to estimate flood risk distribution across a floodplain. In this paper, a rainfall design method for spatial flood risk assessment, which considers the joint effects of multiple flood sources, is proposed. The concept of critical rainfall duration determined by the concentration time of flooding is introduced to connect response characteristics of different flood sources with rainfall. A copula method is then adopted to capture the correlation of rainfall amount with different critical rainfall durations. Rainfall events are designed taking advantage of the copula structure of correlation and marginal distribution of rainfall amounts within different critical rainfall durations. A case study in the Otsu River Basin, Osaka prefecture, Japan was conducted to demonstrate this methodology.

Description: This paper presents an optimized low-complexity and high-throughput MIMO signal detector core for detecting spatially multiplexed data streams. The core architecture supports various layer configurations up to 4, while achieving near-optimal performance, and configurable modulation constellations up to 256-QAM on each layer. The core is capable of operating as a soft-input soft-output log-likelihood ratio (LLR) MIMO detector which can be used in the context of iterative detection and decoding. High area-efficiency is achieved via algorithmic and architectural optimizations performed at two levels. First, distance computations and slicing operations for an optimal 2-layer maximum a posteriori MIMO detector are optimized to eliminate use of multipliers and reduce the overhead of slicing in the presence of soft-input LLRs. We show that distances can be easily computed using elementary addition operations, while optimal slicing is done via efficient comparisons with soft decision boundaries, resulting in a simple feed-forward pipelined architecture. Second, to support more layers, an efficient channel decomposition scheme is presented that reduces the detection of multiple layers into multiple 2-layer detection subproblems, which map onto the 2-layer core with a slight modification using a distance accumulation stage and a post-LLR processing stage. Various architectures are accordingly developed to achieve a desired detection throughput and run-time reconfigurability by time-multiplexing of one or more component cores. The proposed core is applied also to design an optimal multiuser MIMO detector for LTE. The core occupies an area of 1.58 MGE and achieves a throughput of 733 Mbps for 256-QAM when synthesized in 90-nm CMOS.

Description: We study a tandem of agents who make decisions about an underlying binary hypothesis, where the distribution of the agent observations under each hypothesis comes from an uncertainty class defined by a 2-alternating capacity. We investigate both decentralized detection rules, where agents collaborate to minimize the error probability of the final agent, and social learning rules, where each agent minimizes its own local minimax error probability. We then extend our results to the infinite tandem network, and derive necessary and sufficient conditions on the uncertainty classes for the minimax error probability to converge to zero when agents know their positions in the tandem. On the other hand, when agents do not know their positions in the network, we study the cases where agents collaborate to minimize the asymptotic minimax error probability, and where agents seek to minimize their worst-case minimax error probability (over all possible positions in the tandem). We show that asymptotic learning of the true hypothesis is no longer possible in these cases, and derive characterizations for the minimax error performance.

Description: Various blind synchronization methods built on the maximum likelihood (ML) principle have been proposed, where the addressed scenarios include additive white Gaussian noise (AWGN), single-path fading, and multipath fading channels. We consider ML blind synchronization over wide-sense stationary uncorrelated scattering (WSSUS) channels. Different from existing studies, we exploit a more complete signal correlation function and find the carrier frequency offset estimate to be the solution of a quartic equation, rather than the phase angle of a complex number. As the truly ML synchronizer (dubbed MLE) is very complicated, we also derive a reduced-complexity alternative (dubbed RCE). It is found that the RCE yields indistinguishable performance from the MLE, at a somewhat lower complexity than an existing rival. We also present an in-depth theoretical analysis and comparison of the performance of various methods. Simulations show that the proposed methods yield rather robust performance in modeling errors of the fading rate and the channel power-delay profile (PDP).

Description: Technical Note: Testing an improved index for analysing storm nutrient hysteresis Hydrology and Earth System Sciences Discussions, 12, 7875-7892, 2015 Author(s): C. E. M. Lloyd, J. E. Freer, P. J. Johnes, and A. L. Collins Analysis of hydrochemical behaviour in extreme flow events can provide new insights into the process controls on nutrient transport in catchments. The examination of storm behaviours using hysteresis analysis has increased in recent years, partly due to the increased availability of high temporal resolution datasets for discharge and nutrient parameters. A number of these analyses involve the use of an index to describe the characteristics of a hysteresis loop in order to compare different storm behaviours both within and between catchments. This technical note reviews the methods for calculation of the hysteresis index (HI) and explores a new more effective methodology. Each method is systematically tested and the impact of the chosen calculation on the results is examined. Recommendations are made regarding the most effective method of calculating a HI which can be used for comparing data between storms and between different parameters and catchments.

Description: In this paper, the performance of cloud radio access networks (CRANs) where spatially distributed remote radio heads (RRHs) aid the macro base station (MBS) in transmission is analysed. In order to reflect a realistic scenario, the MBS and the RRHs are assumed to be equipped with multiple antennas and distributed according to a Poisson point process. Both, the MBS and the RRHs, are assumed to employ maximal ratio transmission (MRT) or transmit antenna selection (TAS). Considering downlink transmission, the outage performance of three schemes is studied; first is the selection transmission (ST) scheme, in which the MBS or the RRH with the best channel is selected for transmission. In the second scheme, all the RRHs participate (ARP) and transmit the signal to the user, whereas in the third scheme, a minimal number of RRHs, to attain a desired data-rate, participate in transmission (MRP). Exact closed-form expression for the outage probability is derived for the ST scheme. For the ARP and MRP schemes, analytical approximations of the outage probability are derived which are tight at high signal-to-noise ratios. In addition, for the MRP scheme, the minimal number of RRHs required to meet a target data rate is also calculated which can be useful in characterizing the system complexity. Furthermore, the derived expressions are validated through numerical simulation. It is shown that the average diversity gains of these schemes are independent of the intensity/number of RRHs and only depend on the number of antennas on the MBS. Furthermore, the ARP scheme outperforms the ST scheme when the MBS/RRHs transmit with maximum power. However, in case of a sum power constraint and equal power allocation, the ST scheme outperforms the ARP scheme.

Description: This paper proposes a dynamic resource allocation scheme to exploit the mixed timescale channel state information (CSI) knowledge structure in a multi-antenna base station-assisted device-to-device (D2D) network. The short-term multi-antenna beamforming control at each transmit device is adaptive to the local real-time CSI. The long-term routing and flow control is adaptive to the global topology and the long-term global CSI statistics of the D2D network. The design objective is to maximize a network utility function subject to the average transmit power constraint, the flow balance constraints and the instantaneous physical layer capacity constraints. The mixed timescale problem can be decomposed into a short-term beamforming control problem and a long-term flow and routing control problem. Using the stochastic cutting plane, we propose a low complexity, self-learning algorithm, which converges to the global optimal solution without explicit knowledge of the channel statistics. Simulation illustrates performance gains with several baselines.

Description: This paper considers the estimation of multi-scale multi-lag (MSML) channels. The MSML channel model is a good representation for wideband communication channels, such as underwater acoustic communication and radar. This model is characterized by a limited number of paths, each parameterized by a delay, Doppler scale, and attenuation factor. Herein, it is shown that an OFDM signal after passing through the MSML channel exhibits a low rank representation. This feature can be exploited to improve the channel estimation. By characterizing the received signal, it is shown that the MSML channel estimation problem can be adapted to a structured spectral estimation problem. The challenge is that the unknown frequencies are very close to each other due to the small values of Doppler scales. This feature can be employed to show that the data matrix is approximately low-rank. By exploiting structural features of the received signal, the Prony algorithm is modified to estimate the Doppler scales (close frequencies), delays and channel gains. Two strategies using convex and no-convex regularizers to remove noise from the corrupted signal are proposed. These algorithms are iterative based on the alternating direction method of multipliers. A bound on the reconstruction of the noiseless received signal provides guidance on the selection of the relaxation parameter in the optimizations. The performance of the proposed estimation strategies are investigated via numerical simulations, and it is shown that the proposed non-convex method offers up to 7 dB improvement in low SNR and the convex method offers up to 5 dB improvement in high SNR over prior methods for the MSML channel estimation.

Description: Soil storage influences climate–evapotranspiration interactions in three western United States catchments Hydrology and Earth System Sciences Discussions, 12, 7893-7931, 2015 Author(s): E. S. Garcia and C. L. Tague In the winter-wet, summer-dry forests of the western United States, total annual evapotranspiration (ET) varies with precipitation and temperature. Geologically mediated drainage and storage properties, however, may strongly influence these relationships between climate and ET. We use a physically based process model to evaluate how soil available water capacity (AWC) and rates of drainage influence model estimates of ET-climate relationships for three snow-dominated, mountainous catchments with differing precipitation regimes. Model estimates show that total annual precipitation is a primary control on inter-annual variation in ET across all catchments and that the timing of recharge is a second order control. Low soil AWC, however, increases the sensitivity of annual ET to these climate drivers by three to five times in our two study basins with drier summers. ET–climate relationships in our Colorado basin receiving summer precipitation are more stable across subsurface drainage and storage characteristics. Climate driver-ET relationships are most sensitive to soil AWC and soil drainage parameters related to lateral redistribution in the relatively dry Sierra site that receives little summer precipitation. Our results demonstrate that uncertainty in geophysically mediated storage and drainage properties can strongly influence model estimates of watershed scale ET responses to climate variation and climate change. This sensitivity to uncertainty in geophysical properties is particularly true for sites receiving little summer precipitation. A parallel interpretation of this parameter sensitivity is that spatial variation in soil properties are likely to lead to substantial within-watershed plot scale differences in forest water use and drought stress.

Description: Sub-daily runoff simulations with parameters inferred at the daily time scale Hydrology and Earth System Sciences Discussions, 12, 7437-7467, 2015 Author(s): J. E. Reynolds, S. Halldin, C. Y. Xu, J. Seibert, and A. Kauffeldt Concentration times in small and medium-sized watersheds (~ 100–1000 km 2 ) are commonly less than 24 h. Flood-forecasting models then require data at sub-daily time scales, but time-series of input and runoff data with sufficient lengths are often only available at the daily time scale, especially in developing countries. This has led to a search for time-scale relationships to infer parameter values at the time scales where they are needed from the time scales where they are available. In this study, time-scale dependencies in the HBV-light conceptual hydrological model were assessed within the generalized likelihood uncertainty estimation (GLUE) approach. It was hypothesised that the existence of such dependencies is a result of the numerical method or time-stepping scheme used in the models rather than a real time-scale-data dependence. Parameter values inferred showed a clear dependence on time scale when the explicit Euler method was used for modelling at the same time steps as the time scale of the input data (1–24 h). However, the dependence almost fully disappeared when the explicit Euler method was used for modelling in 1 h time steps internally irrespectively of the time scale of the input data. In other words, it was found that when an adequate time-stepping scheme was implemented, parameter sets inferred at one time scale (e.g., daily) could be used directly for runoff simulations at other time scales (e.g., 3 or 6 h) without any time scaling and this approach only resulted in a small (if any) model performance decrease, in terms of Nash–Sutcliffe and volume-error efficiencies. The overall results of this study indicated that as soon as sub-daily driving data can be secured, flood forecasting in watersheds with sub-daily concentration times is possible with model-parameter values inferred from long time series of daily data, as long as an appropriate numerical method is used.

Description: Analysis of three-dimensional groundwater flow toward a radial collector well in a finite-extent unconfined aquifer Hydrology and Earth System Sciences Discussions, 12, 7503-7540, 2015 Author(s): C.-S. Huang, J.-J. Chen, and H.-D. Yeh This study develops a three-dimensional mathematical model for describing transient hydraulic head distributions due to pumping at a radial collector well (RCW) in a rectangular confined or unconfined aquifer bounded by two parallel streams and no-flow boundaries. The governing equation with a point-sink term is employed. A first-order free surface equation delineating the water table decline induced by the well is considered. The head solution for the point sink is derived by applying the methods of double-integral transform and Laplace transform. The head solution for a RCW is obtained by integrating the point-sink solution along the laterals of the RCW and then dividing the integration result by the sum of lateral lengths. On the basis of Darcy's law and head distributions along the streams, the solution for the stream depletion rate (SDR) can also be developed. With the aid of the head and SDR solutions, the sensitivity analysis can then be performed to explore the response of the hydraulic head to the change in a specific parameter such as the horizontal and vertical hydraulic conductivities, streambed permeability, specific storage, specific yield, lateral length and well depth. Spatial head distributions subject to the anisotropy of aquifer hydraulic conductivities are analyzed. A quantitative criterion is provided to identify whether groundwater flow at a specific region is 3-D or 2-D without the vertical component. In addition, another criterion is also given to allow the neglect of vertical flow effect on SDR. Conventional 2-D flow models can be used to provide accurate head and SDR predictions if satisfying these two criteria.

Description: Effects of cultivation and reforestation on suspended sediment concentrations: a case study in a mountainous catchment in China Hydrology and Earth System Sciences Discussions, 12, 7583-7614, 2015 Author(s): N. F. Fang, F. X. Chen, H. Y. Zhang, Y. X. Wang, and Z. H. Shi Understanding how sediment concentrations vary with land use/cover is critical for evaluating the current and future impacts of human activities on river systems. This paper presents suspended sediment concentration (SSC) dynamics and the relationship between SSC and discharge ( Q ) in the 8973 km 2 Du catchment and its sub-catchment (4635 km 2 ). In the Du catchment and its sub-catchment, 4235 and 3980 paired Q -SSC samples, respectively, were collected over 30 years. Under the influence of the "Household Contract Responsibility System" and Grain-for-Green projects in China, three periods were designated, the original period (1980s), cultivation period (1990s), and reforestation period (2000s). The results of a Mann–Kendall test showed that rainfall slightly increased during the study years; however, the annual discharge and sediment load significantly decreased. The annual suspended sediment yield of the Du catchment varied between 4 and 332 kg s −1 , and that of the sub-catchment varied between 2 and 135 kg s −1 . The SSCs in the catchment and sub-catchment fluctuated between 1 and 22 400 g m −3 and between 1 and 31 800 g m −3 , respectively. The mean SSC of the Du catchment was relatively stable during the three periods (±83 g m −3 ). ANOVA indicated that the SSC did not significantly change under cultivation for low and moderate flows, but was significantly different under high flow during reforestation of the Du catchment. The SSC in the sub-catchment was more variable, and the mean-SSC in the sub-catchment varied from 1058 g m −3 in the 1980s to 1256 g m −3 in the 1990s and 891 g m −3 in the 2000s. Reforestation significantly decreased the SSCs during low and moderate flows, whereas cultivation increased the SSCs during high flow. The sediment rating curves showed a stable relationship between the SSC and Q in the Du catchment during the three periods. However, the SSC- Q of the sub-catchment exhibited scattered relationships during the original and cultivation periods and a more linear relationship during the reforestation period.

Description: Distributed processing over networks relies on in-network processing and cooperation among neighboring agents. Cooperation is beneficial when agents share a common objective. However, in many applications, agents may belong to different clusters that pursue different objectives. Then, indiscriminate cooperation will lead to undesired results. In this paper, we propose an adaptive clustering and learning scheme that allows agents to learn which neighbors they should cooperate with and which other neighbors they should ignore. In doing so, the resulting algorithm enables the agents to identify their clusters and to attain improved learning and estimation accuracy over networks. We carry out a detailed mean-square analysis and assess the error probabilities of Types I and II, i.e., false alarm and misdetection, for the clustering mechanism. Among other results, we establish that these probabilities decay exponentially with the step-sizes so that the probability of correct clustering can be made arbitrarily close to one.

Description: Robust Chinese remainder theorem (CRT) has been recently investigated for both integers and real numbers, where the folding integers are accurately recovered from erroneous remainders. In this paper, we consider the CRT problem for real numbers with noisy remainders that follow wrapped Gaussian distributions. We propose the maximum-likelihood estimation (MLE) based CRT when the remainder noises may not necessarily have the same variances. Furthermore, we present a fast algorithm for the MLE based CRT algorithm that only needs to search for the solution among $L$ elements, where $L$ is the number of remainders. Then, a necessary and sufficient condition on the remainder errors for the MLE CRT to be robust is obtained, which is weaker than the existing result. Finally, we compare the performances of the newly proposed algorithm and the existing algorithm in terms of both theoretical analysis and numerical simulations. The results demonstrate that the proposed algorithm not only has a better performance especially when the remainders have different error levels/variances, but also has a much lower computational complexity.

Description: Sparse signal restoration is usually formulated as the minimization of a quadratic cost function $Vert { mbi { y}} - { mbi { A}} { mbi { x}} Vert_{2}^{2}$ where $ { mbi { A}} $ is a dictionary and $ { mbi { x}} $ is an unknown sparse vector. It is well-known that imposing an $ell _{0}$ constraint leads to an NP-hard minimization problem. The convex relaxation approach has received considerable attention, where the $ell _{0}$ -norm is replaced by the $ell _{1}$ -norm. Among the many effective $ell _{1}$ solvers, the homotopy algorithm minimizes $Vert { mbi { y}} - { mbi { A}} { mbi { x}} Vert_{2}^{2}+lambda Vert { mbi { x}} Vert _{1}$ with respect to $ { mbi { x}} $ for a continuum of $lambda $ ’s. It is inspired by the piecewise regularity of the $ell _{1}$ -regularization path, also referred to as the homotopy path. In this paper, we address the minimization problem $Vert { mbi { y}} - { mbi { A}} { mbi { x}} Vert_{2}^{2}+lambda Vert { mbi { x}} Vert _{0}$ for a continuum of $lambda $ ’s and propose two heuristic search algorithms for $ell _{0}$ -homotopy. Continuation Single Best Replacement is a forward–backward greedy strategy extending the Single Best Replacement algorithm, previously proposed for $ell _{0}$ -minimization at a given $lambda $ . The adaptive search of the $lambda $ -values is inspired by $ell _{1}$ -homotopy. $ell _{0}$ Regularization Path Descent is a more complex algorithm exploiting the structural properties of the $ell _{0}$ -regularization path, which is piecewise constant with respect to $lambda $ . Both algorithms are empirically evaluated for difficult inverse problems involving ill-conditioned dictionaries. Finally, we show that they can be easily coupled with usual methods of model order selection.

Description: In recent work, robust Principal Components Analysis (PCA) has been posed as a problem of recovering a low-rank matrix ${bf L}$ and a sparse matrix ${bf S}$ from their sum, ${bf M}:= {bf L} + {bf S}$ and a provably exact convex optimization solution called PCP has been proposed. This work studies the following problem. Suppose that we have partial knowledge about the column space of the low rank matrix ${bf L}$ . Can we use this information to improve the PCP solution, i.e., allow recovery under weaker assumptions? We propose here a simple but useful modification of the PCP idea, called modified-PCP, that allows us to use this knowledge. We derive its correctness result which shows that, when the available subspace knowledge is accurate, modified-PCP indeed requires significantly weaker incoherence assumptions than PCP. Extensive simulations are also used to illustrate this. Comparisons with PCP and other existing work are shown for a stylized real application as well. Finally, we explain how this problem naturally occurs in many applications involving time series data, i.e., in what is called the online or recursive robust PCA problem. A corollary for this case is also given.

Description: Phased array is widely used in radar systems with its beam steering fixed in one direction for all ranges. Therefore, the range of a target cannot be determined within a single pulse when range ambiguity exists. In this paper, an unambiguous approach for joint range and angle estimation is devised for multiple-input multiple-output (MIMO) radar with frequency diverse array (FDA). Unlike the traditional phased array, FDA is capable of employing a small frequency increment across the array elements. Because of the frequency increment, the transmit steering vector of the FDA-MIMO radar is a function of both range and angle. As a result, the FDA-MIMO radar is able to utilize degrees-of-freedom in the range-angle domains to jointly determine the range and angle parameters of the target. In addition, the Cramér–Rao bounds for range and angle are derived, and the coupling between these two parameters is analyzed. Numerical results are presented to validate the effectiveness of the proposed approach.

Description: Identification of spatiotemporal patterns of biophysical droughts in semi-arid region – a case study of the Karkheh river basin in Iran Hydrology and Earth System Sciences Discussions, 12, 5187-5217, 2015 Author(s): B. Kamali, K. C. Abbaspour, A. Lehmann, B. Wehrli, and H. Yang This study aims at identifying historical patterns of meteorological, hydrological, and agricultural (inclusively biophysical) droughts in the Karkheh River Basin (KRB), one of the nine benchmark watersheds of the CGIAR Challenge Program on Water and Food. Standardized precipitation index (SPI), standardized runoff index (SRI), and soil moisture deficit index (SMDI) were used to represent the above three types of droughts, respectively. The three drought indices were compared across temporal and spatial dimensions. Variables required for calculating the indices were obtained from the Soil and Water Assessment Tool (SWAT) constructed for the region. The model was calibrated based on monthly runoff and yearly wheat yield using the Sequential Uncertainty Fitting (SUFI-2) algorithm. Five meteorological drought events were identified in the studied period (1980–2004), of which four corresponded with the hydrological droughts with 1–3 month lag. The meteorological droughts corresponded well with the agricultural droughts during dry months (May–August), while the latter lasted for a longer period of time. Analysis of drought patterns showed that southern parts of the catchment were more prone to agricultural drought, while less influenced by hydrological drought. Our analyses highlighted the necessity for monitoring all three aspects of drought for a more effective watershed management. The analysis on different types of droughts in this study provides a framework for assessing their possible impacts under future climate change in semi-arid areas.

Description: Long-term effects of climate and land cover change on freshwater provision in the tropical Andes Hydrology and Earth System Sciences Discussions, 12, 5219-5250, 2015 Author(s): A. Molina, V. Vanacker, E. Brisson, D. Mora, and V. Balthazar Andean headwater catchments play a pivotal role to supply fresh water for downstream water users. However, few long-term studies exist on the relative importance of climate change and direct anthropogenic perturbations on flow regimes. In this paper, we assess multi-decadal change in freshwater provision based on long time series (1974–2008) of hydrometeorological data and land cover reconstructions for a 282 km 2 catchment located in the tropical Andes. Three main land cover change trajectories can be distinguished: (1) rapid decline of native vegetation in montane forest and páramo ecosystems in ~1/5 or 20% of the catchment area, (2) expansion of agricultural land by 14% of the catchment area, (3) afforestation of 12% of native páramo grasslands with exotic tree species in recent years. Given the strong temporal variability of precipitation and streamflow data related to El Niño–Southern Oscillation, we use empirical mode decomposition techniques to detrend the time series. The long-term increasing trend in rainfall is remarkably different from the observed changes in streamflow that exhibit a decreasing trend. Hence, observed changes in streamflow are not the result of long-term climate change but very likely result from direct anthropogenic disturbances after land cover change. Partial water budgets for montane cloud forest and páramo ecosystems suggest that the strongest changes in evaporative water losses are observed in páramo ecosystems, where progressive colonization and afforestation of high alpine grasslands leads to a strong increase in transpiration losses.

Description: In this paper, we propose a novel single-group multicasting relay beamforming scheme. We assume a source that transmits common messages via multiple amplify-and-forward relays to multiple destinations. To increase the number of degrees of freedom in the beamforming design, the relays process two received signals jointly and transmit the Alamouti space-time block code over two different beams. Furthermore, in contrast to the existing relay multicasting scheme of the literature, we take into account the direct links from the source to the destinations. We aim to maximize the lowest received quality-of-service by choosing the proper relay weights and the ideal distribution of the power resources in the network. To solve the corresponding optimization problem, we propose an iterative algorithm which solves sequences of convex approximations of the original non-convex optimization problem. Simulation results demonstrate significant performance improvements of the proposed methods as compared with the existing relay multicasting scheme of the literature and an algorithm based on the popular semidefinite relaxation technique.

Description: In this paper, we propose a new class of iteratively re-weighted least squares (IRLS) for sparse recovery problems. The proposed methods are inspired by constrained maximum-likelihood estimation under a Gaussian scale mixture (GSM) distribution assumption. In the noise-free setting, we provide sufficient conditions ensuring the convergence of the sequences generated by these algorithms to the set of fixed points of the maps that rule their dynamics and derive conditions verifiable a posteriori for the convergence to a sparse solution. We further prove that these algorithms are quadratically fast in a neighborhood of a sparse solution. We show through numerical experiments that the proposed methods outperform classical IRLS for $ell_{tau}$ -minimization with $tauin(0,1]$ in terms of speed and of sparsity-undersampling tradeoff and are robust even in presence of noise. The simplicity and the theoretical guarantees provided in this paper make this class of algorithms an attractive solution for sparse recovery problems.

Description: We consider the problem of approximating optimal in the Minimum Mean Squared Error (MMSE) sense nonlinear filters in a discrete time setting, exploiting properties of stochastically convergent state process approximations. More specifically, we consider a class of nonlinear, partially observable stochastic systems, comprised by a (possibly nonstationary) hidden stochastic process (the state), observed through another conditionally Gaussian stochastic process (the observations). Under general assumptions, we show that, given an approximating process which, for each time step, is stochastically convergent to the state process, an approximate filtering operator can be defined, which converges to the true optimal nonlinear filter of the state in a strong and well defined sense. In particular, the convergence is compact in time and uniform in a completely characterized set of probability measure almost unity. The results presented in this paper can form a common basis for the analysis and characterization of a number of popular but heuristic approaches for approximating optimal nonlinear filters, such as approximate grid based techniques.

Description: A standard assumption for consistent estimation in the errors-in-variables setting is persistency of excitation of the noise-free input signal. We relax this assumption by considering data from multiple experiments. Consistency is obtained asymptotically as the number of experiments tends to infinity. The main theoretical and algorithmic difficulties are related to the growing number of to-be-estimated initial conditions. The method proposed in the paper is based on analytic elimination of the initial conditions and optimization over the remaining parameters. The resulting estimator is consistent; however, achieving asymptotically efficiency is an open problem.

Description: Bayesian filtering aims at estimating sequentially a hidden process from an observed one. In particular, sequential Monte Carlo (SMC) techniques propagate in time weighted trajectories which represent the posterior probability density function (pdf) of the hidden process given the available observations. On the other hand, conditional Monte Carlo (CMC) is a variance reduction technique which replaces the estimator of a moment of interest by its conditional expectation given another variable. In this paper, we show that up to some adaptations, one can make use of the time recursive nature of SMC algorithms in order to propose natural temporal CMC estimators of some point estimates of the hidden process, which outperform the associated crude Monte Carlo (MC) estimator whatever the number of samples. We next show that our Bayesian CMC estimators can be computed exactly, or approximated efficiently, in some hidden Markov chain (HMC) models; in some jump Markov state-space systems (JMSS); as well as in multitarget filtering. Finally our algorithms are validated via simulations.

Description: In this paper, cooperative sensor localization using asynchronous time-of-arrival measurements is investigated. It is well known that localization performance in wireless networks using time-based ranging or pseudo-ranging methods is greatly affected by the accuracy of the timing synchronization between the nodes involved in the estimation. Commonly, the original estimation problem is broken down into two subproblems, the synchronization problem and the localization problem, in what is known as a two-step approach. However, in this paper, the joint synchronization and localization problem is considered and examined for use in cooperative networks. It is discussed that the cooperation between the source nodes eliminates the need for high anchor node densities and improves localization performance significantly. Furthermore, the Cramér-Rao lower bounds (CRLB) and the maximum likelihood (ML) estimator are derived. It is shown that the ML estimator is highly nonlinear and nonconvex and must, therefore, be solved by using computationally complex algorithms. In order to reduce the complexity of the estimation, a novel semidefinite programming (SDP) relaxation method is developed by relaxing the original nonconvex ML problem, in such a way as to reformulate the estimation problem as a convex problem. The performance of the proposed SDP method is shown through computer simulations to nearly equal that of the ML estimator. The approach is also applied to the noncooperative case where it is found to be superior in performance than the previously proposed suboptimal estimators. Finally, complexity analyses are included for the estimators under consideration.

Description: Estimating evapotranspiration with thermal UAV data and two source energy balance models Hydrology and Earth System Sciences Discussions, 12, 7469-7502, 2015 Author(s): H. Hoffmann, H. Nieto, R. Jensen, R. Guzinski, P. J. Zarco-Tejada, and T. Friborg Estimating evapotranspiration is important when managing water resources and cultivating crops. Evapotranspiration can be estimated using land surface heat flux models and remotely sensed land surface temperatures (LST) which recently have become obtainable in very high resolution using Unmanned Aerial Vehicles (UAVs). Very high resolution LST can give insight into e.g. distributed crop conditions within cultivated fields. In this study evapotranspiration is estimated using LST retrieved with a UAV and the physically-based, two source energy balance models: the Priestley–Taylor TSEB (TSEB-PT) and the Dual-Temperature-Difference (DTD). A fixed-wing UAV was flown over a barley field in western Denmark during the spring and summer in 2014 and retrieved images of LST is successfully processed into thermal mosaics which serve as model input for both TSEB-PT and DTD. The aim is to assess whether a lightweight thermal camera mounted on a UAV is able to provide data of sufficient quality to obtain high spatial and temporal resolution surface energy heat fluxes. Furthermore, this study evaluates the performance of the two source energy balance (TSEB) model scheme during cloudy and overcast weather conditions. This is feasible due to the low data retrieval altitude compared to satellite thermal data that are only available during clear skies and sunny conditions. Flux estimates from TSEB-PT and DTD are compared and validated against field data collected using an eddy covariance system located at same site at which the UAV flights were conducted. Furthermore, spatially distributed evapotranspiration patterns are evaluated using known irrigation patterns. Evapotranspiration is well estimated by both TSEB-PT and DTD with DTD as the best predictor. The DTD model provides results comparable to studies estimating evapotranspiration with satellite retrieved LST and physical land-surface models. This study shows that the UAV platform and the lightweight thermal camera provide high spatial and temporal resolution data valid for model input and for other potential applications requiring high resolution and consistent LST. Lastly, this study explicates thermal UAV data processing and the mosaicking of images into ortho-photos suited for model input.

Description: In this paper, we consider the problem of parameter estimation over sensor networks in the presence of quantized data and directed communication links. We propose a two-stage distributed algorithm aiming at achieving the centralized sample mean estimate in a distributed manner. Different from the existing algorithms, a running average technique is utilized in the proposed algorithm to smear out the randomness caused by the probabilistic quantization scheme. With the running average technique, it is shown that the centralized sample mean estimate can be achieved both in the mean square and almost sure senses, which is not observed in the standard consensus algorithms. In addition, the rates of convergence are given to quantify the mean square and almost sure performances. Finally, simulation results are presented to illustrate the effectiveness of the proposed algorithm and highlight the improvements by using running average technique.

Description: This paper studies a pilot-assisted physical layer data fusion technique known as Distributed Co-Phasing (DCP). In this two-phase scheme, the sensors first estimate the channel to the fusion center (FC) using pilots sent by the latter; and then they simultaneously transmit their common data by pre-rotating them by the estimated channel phase, thereby achieving physical layer data fusion. First, by analyzing the symmetric mutual information of the system, it is shown that the use of higher order constellations (HOC) can improve the throughput of DCP compared to the binary signaling considered heretofore. Using an HOC in the DCP setting requires the estimation of the composite DCP channel at the FC for data decoding. To this end, two blind algorithms are proposed: 1) power method, and 2) modified $K$ -means algorithm. The latter algorithm is shown to be computationally efficient and converges significantly faster than the conventional $K$ -means algorithm. Analytical expressions for the probability of error are derived, and it is found that even at moderate to low SNRs, the modified $K$ -means algorithm achieves a probability of error comparable to that achievable with a perfect channel estimate at the FC, while requiring no pilot symbols to be transmitted from the sensor nodes. Also, the problem of signal corruption due to imperfect DCP is investigated, and constellation shaping to minimize the probability of signal corruption is proposed and analyzed. The analysis is validated, and the promising performance of DCP for energy-efficient physical layer data fusion is illustrated, using Monte Carlo simulations.

Description: In this paper we propose a fast and efficient Jacobi-like approach named JET (Joint Eigenvalue decomposition based on Triangular matrices) for the Joint EigenValue Decomposition (JEVD) of a set of real or complex non-defective matrices based on the LU factorization of the matrix of eigenvectors. Contrarily to classical Jacobi-like JEVD methods, the iterative procedure of the JET approach can be reduced to the search for only one of the two triangular matrices involved in the factorization of the matrix of eigenvectors, hence decreasing the numerical complexity. Two variants of the JET technique, namely JET-U and JET-O, which correspond to the optimization of two different cost functions are described in detail and these are extended to the complex case. Numerical simulations show that in many practical cases the JET approach provides more accurate estimation of the matrix of eigenvectors than its competitors and that the lowest numerical complexity is consistently achieved by the JET-U algorithm. In addition, we illustrate in the ICA context the interest of being able to solve efficiently the (non-orthogonal) JEVD problem. More particularly, based on our JET-U algorithm, we propose a more robust version of an existing ICA method, named MICAR-U. The identifiability of the latter is studied and proved under some conditions. Computer results given in the context of brain interfaces show the better ability of MICAR-U to denoise simulated electrocortical data compared to classical ICA techniques for low signal to noise ratio values.

Description: A new design for successive interference cancellation (SIC) detection for multiple-input multiple-output systems is introduced, and it is developed on the basis of the method of normal equations commonly used to solve the linear least squares problem. On the basis of this design, optimal-ordered and suboptimal-ordered SIC detection algorithms are derived. It is shown that the proposed optimal-ordered SIC detection algorithm offers a complexity reduction ratio of 1.11–1.25 compared to the fastest known optimal-ordered SIC detection algorithm for intermediate and large numbers of antennas and in terms of the average complexity. On the other hand, the proposed suboptimal-ordered SIC detection algorithm requires a lower complexity than the proposed optimal-ordered one and provides a bit-error-rate performance close to that of the optimal-ordered one and better than those of the other suboptimal-ordered SIC detection algorithms.

Description: We consider the problem of signal recovery on graphs. Graphs model data with complex structure as signals on a graph. Graph signal recovery recovers one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We formulate graph signal recovery as an optimization problem, for which we provide a general solution through the alternating direction methods of multipliers. We show how signal inpainting, matrix completion, robust principal component analysis, and anomaly detection all relate to graph signal recovery and provide corresponding specific solutions and theoretical analysis. We validate the proposed methods on real-world recovery problems, including online blog classification, bridge condition identification, temperature estimation, recommender system for jokes, and expert opinion combination of online blog classification.

Description: In this paper, we investigate the network power minimization problem for the multicast cloud radio access network (Cloud-RAN) with imperfect channel state information (CSI). The key observation is that network power minimization can be achieved by adaptively selecting active remote radio heads (RRHs) via controlling the group-sparsity structure of the beamforming vector. However, this yields a non-convex combinatorial optimization problem, for which we propose a three-stage robust group sparse beamforming algorithm. In the first stage, a quadratic variational formulation of the weighted mixed $ell_1/ell_2$ -norm is proposed to induce the group-sparsity structure in the aggregated beamforming vector, which indicates those RRHs that can be switched off. A perturbed alternating optimization algorithm is then proposed to solve the resultant non-convex group-sparsity inducing optimization problem by exploiting its convex substructures. In the second stage, we propose a PhaseLift technique based algorithm to solve the feasibility problem with a given active RRH set, which helps determine the active RRHs. Finally, the semidefinite relaxation (SDR) technique is adopted to determine the robust multicast beamformers. Simulation results will demonstrate the convergence of the perturbed alternating optimization algorithm, as well as, the effectiveness of the proposed algorithm to minimize the network power consumption for multicast Cloud-RAN.

Description: Many machine learning frameworks, such as resource-allocating networks, kernel-based methods, Gaussian processes, and radial-basis-function networks, require a sparsification scheme in order to address the online learning paradigm. For this purpose, several online sparsification criteria have been proposed to restrict the model definition on a subset of samples. The most known criterion is the (linear) approximation criterion, which discards any sample that can be well represented by the already contributing samples, an operation with excessive computational complexity. Several computationally efficient sparsification criteria have been introduced in the literature with the distance and the coherence criteria. This paper provides a unified framework that connects these sparsification criteria in terms of approximating samples, by establishing theoretical bounds on the approximation errors. Furthermore, the error of approximating any pattern is investigated, by proposing upper bounds on the approximation error for each of the aforementioned sparsification criteria. Two classes of fundamental patterns are described in detail, the centroid (i.e., empirical mean) and the principal axes in the kernel principal component analysis. Experimental results show the relevance of the theoretical results established in this paper.

Description: The radix- $2^{k}$ algorithm plays a crucial role in the pipelined implementation of fast Fourier transform (FFT). This paper presents a fixed-point analysis and hardware evaluation of radix- $2^{k}$ FFT under the framework of the single-path delay feedback (SDF) and multi-path delay commutator (MDC) pipelined structure. The investigation is carried out with variable operating word-lengths to ensure the generality. Furthermore, the main streams to fulfill FFT coefficients weighting, namely, the approach using complex multipliers and the one adopting memoryless CORDIC units, are both considered in the analysis. Based on these derivations, a joint optimization of radix- $2^{k}$ algorithm and operating word-length is discussed to achieve a reasonable trade-off between computational accuracy and hardware expenditure. Simulations and experiments indicates that the derived SQNR is reliable to unfold the quantization effects of fixed-point radix- $2^{k}$ FFT. In addition, the proposed joint optimization strategy is capable of providing better solutions to implement the radix- $2^{k}$ FFT processor efficiently.

Description: In this paper, the quickest change detection problem is studied in two-state hidden Markov models (HMM), where the vector parameter $theta$ of the HMM changes from $theta_{0}$ to $theta_{1}$ at some unknown time, and one wants to detect the true change as quickly as possible while controlling the false alarm rate. It turns out that the generalized likelihood ratio (GLR) scheme, while theoretically straightforward, is generally computationally infeasible for the HMM. To develop efficient but computationally simple schemes for the HMM, we first discuss a subtlety in the recursive form of the generalized likelihood ratio (GLR) scheme for the HMM. Then we show that the recursive CUSUM scheme proposed in Fuh (Ann. Statist., 2003) can be regarded as a quasi-GLR scheme for pseudo post-change hypotheses with certain dependence structure between pre- and postchange observations. Next, we extend the quasi-GLR idea to propose recursive score schemes in the scenario when the postchange parameter $theta_{1}$ of the HMM involves a real-valued nuisance parameter. Finally, the Kullback-Leibler (KL) divergence plays an essential role in the quickest change detection problem and many other fields, however it is rather challenging to numerically compute it in HMMs. Here we develop a non-Monte Carlo method that computes the KL divergence of two-state HMMs via the underlying invariant probability measure, which is characterized by the Fredholm integral equation. Numerical study demonstrates an unusual property of the KL divergence for HMM that implies the severe effects of misspecifying the postchange parameter for the HMM.

Description: Convex optimization is a powerful tool for resource allocation and signal processing in wireless networks. As the network density is expected to drastically increase in order to accommodate the exponentially growing mobile data traffic, performance optimization problems are entering a new era characterized by a high dimension and/or a large number of constraints, which poses significant design and computational challenges. In this paper, we present a novel two-stage approach to solve large-scale convex optimization problems for dense wireless cooperative networks, which can effectively detect infeasibility and enjoy modeling flexibility. In the proposed approach, the original large-scale convex problem is transformed into a standard cone programming form in the first stage via matrix stuffing, which only needs to copy the problem parameters such as channel state information (CSI) and quality-of-service (QoS) requirements to the prestored structure of the standard form. The capability of yielding infeasibility certificates and enabling parallel computing is achieved by solving the homogeneous self-dual embedding of the primal-dual pair of the standard form. In the solving stage, the operator splitting method, namely, the alternating direction method of multipliers (ADMM), is adopted to solve the large-scale homogeneous self-dual embedding. Compared with second-order methods, ADMM can solve large-scale problems in parallel with modest accuracy within a reasonable amount of time. Simulation results will demonstrate the speedup, scalability, and reliability of the proposed framework compared with the state-of-the-art modeling frameworks and solvers.

Description: Crop-specific seasonal estimates of irrigation water demand in South Asia Hydrology and Earth System Sciences Discussions, 12, 7843-7873, 2015 Author(s): H. Biemans, C. Siderius, A. Mishra, and B. Ahmad Especially in the Himalayan headwaters of the main rivers in South Asia, shifts in runoff are expected as a result of a rapidly changing climate. In recent years, our insight in these shifts and their impact on water availability has increased. However, a similar detailed understanding of the seasonal pattern in water demand is surprisingly absent. This hampers a proper assessment of water stress and ways to cope and adapt. In this study, the seasonal pattern of irrigation water demand resulting from the typical practice of multiple-cropping in South Asia was accounted for by introducing double-cropping with monsoon-dependent planting dates in a hydrology and vegetation model. Crop yields were calibrated to the latest subnational statistics of India, Pakistan, Bangladesh and Nepal. The representation of seasonal land use and more accurate cropping periods lead to lower estimates of irrigation water demand compared to previous model-based studies, despite the net irrigated area being higher. Crop irrigation water demand differs sharply between seasons and regions; in Pakistan, winter (Rabi) and summer (Kharif) irrigation demands are almost equal, whereas in Bangladesh the Rabi demand is ~ 100 times higher. Moreover, the relative importance of irrigation supply vs. rain decreases sharply from west to east. Given the size and importance of South Asia, improved regional estimates of food production and its irrigation water demand will also affect global estimates. In models used for global water resources and food-security assessments, processes like multiple-cropping and monsoon-dependent planting dates should not be ignored.

Description: The discrete cosine transform (DCT) is known to be asymptotically equivalent to the Karhunen-Loève transform (KLT) of Gaussian first-order auto-regressive (AR(1)) processes. Since being uncorrelated under the Gaussian hypothesis is synonymous with independence, it also yields an independent-component analysis (ICA) of such signals. In this paper, we present a constructive non-Gaussian generalization of this result: the characterization of the optimal orthogonal transform (ICA) for the family of symmetric- $alpha$ -stable AR(1) processes. The degree of sparsity of these processes is controlled by the stability parameter $0 〈 alphaleq2$ with the only non-sparse member of the family being the classical Gaussian AR(1) process with $alpha=2$ . Specifically, we prove that, for $alpha 〈 2$ , a fixed family of operator-like wavelet bases systematically outperforms the DCT in terms of compression and denoising ability. The effect is quantified with the help of two performance criteria (one based on the Kullback-Leibler divergence, and the other on Stein’s formula for the minimum estimation error) that can also be viewed as statistical measures of independence. Finally, we observe that, for the sparser kind of processes with $0 〈 alphaleq 1$ , the operator-like wavelet basis, as dictated by linear system theory, is undistinguishable from the ICA solution obtained through numerical optimization. Our framework offers a unified view that encompasses sinusoidal transforms such as the DCT and a family of orthogonal Haar-like wavelets that is linked analytically to the underlying signal model.

Description: MUSIC is a popular algorithm for estimating the direction of arrival (DOA) in array signal processing applications. In this paper, we analyze the performance of the MUSIC algorithm for a single source system, in the presence of noisy and missing data (when only a random subset of the entries in the data matrix are observed). We prove consistency of the DOA estimate when signal from a single source is impinging on low coherence arrays, and derive an analytic expression for the mean-squared-error (MSE) performance of MUSIC for the case of uniform linear arrays, in the large array and relatively large sample setting. Our analysis is mathematically justified in both the sample rich and deficient regimes. The expression for the MSE is a simple function of array geometry, signal-to-noise ratio (SNR), the fraction of entries observed, and the ratio of the number of sensors to number of snapshots. We derive a phase transition threshold which separates a regime where MUSIC is consistent from a regime where MUSIC is inconsistent. This threshold depends upon the SNR, the probability of observing entries in the data matrix, and number of sensors and snapshots in a simple manner which we make explicit.

Description: Phase retrieval problems involve solving linear equations, but with missing sign (or phase, for complex numbers) information. More than four decades after it was first proposed, the seminal error reduction algorithm of Gerchberg and Saxton and Fienup is still the popular choice for solving many variants of this problem. The algorithm is based on alternating minimization; i.e., it alternates between estimating the missing phase information, and the candidate solution. Despite its wide usage in practice, no global convergence guarantees for this algorithm are known. In this paper, we show that a (resampling) variant of this approach converges geometrically to the solution of one such problem—finding a vector $bf x$ from ${bf y}, {bf A}$ , where ${bf y} = vert {bf A}^T{bf x}vert$ and $vert{bf z}vert$ denotes a vector of element-wise magnitudes of ${bf z}$ —under the assumption that $ {bf A}$ is Gaussian. Empirically, we demonstrate that alternating minimization performs similar to recently proposed convex techniques for this problem (which are based on “lifting” to a convex matrix problem) in sample complexity and robustness to noise. However, it is much more efficient and can scale to large problems. Analytically, for a resampling version of alternating minimization, we show geometric convergence to the solution, and sample complexity that is off by log factors from obvious lower bounds. We also establish close to optimal scaling for the case when the unknown vector is sparse. Our work represents the first theoretical guarantee for al- ernating minimization (albeit with resampling) for any variant of phase retrieval problems in the non-convex setting.

Description: We consider Bayesian blind deconvolution (BD) of an unknown sparse sequence convolved with an unknown pulse. Our goal is to detect the positions where the sparse input sequence is nonzero and to estimate the corresponding amplitudes as well as the pulse shape. For this task, we propose a novel evolution of the single most likely replacement (SMLR) algorithm. Our method uses a modified Bernoulli-Gaussian prior that incorporates a minimum temporal distance constraint. This prior simultaneously induces sparsity and enforces a prescribed minimum distance between the pulse centers. The minimum distance constraint provides an effective way to avoid overfitting (i.e., spurious detected pulses) and improve resolution. The proposed BD method overcomes certain weaknesses of the traditional SMLR-based BD method, which is verified experimentally to result in improved detection/estimation performance and reduced computational complexity. Our simulation results also demonstrate performance and complexity advantages relative to the iterated window maximization (IWM) algorithm and a recently proposed partially collapsed Gibbs sampler method.

Description: Evaluation of global fine-resolution precipitation products and their uncertainty quantification in ensemble discharge simulations Hydrology and Earth System Sciences Discussions, 12, 9337-9391, 2015 Author(s): W. Qi, C. Zhang, G. T. Fu, C. Sweetapple, and H. C. Zhou The applicability of six fine-resolution precipitation products, including precipitation radar, infrared, microwave and gauge-based products using different precipitation computation recipes, is comprehensively evaluated using statistical and hydrological methods in a usually-neglected area (northeastern China), and a framework quantifying uncertainty contributions of precipitation products, hydrological models and their interactions to uncertainties in ensemble discharges is proposed. The investigated precipitation products include TRMM3B42, TRMM3B42RT, GLDAS/Noah, APHRODITE, PERSIANN and GSMAP-MVK+. Two hydrological models of different complexities, i.e., a water and energy budget-based distributed hydrological model and a physically-based semi-distributed hydrological model, are employed to investigate the influence of hydrological models on simulated discharges. Results show APHRODITE has high accuracy at a monthly scale compared with other products, and the cloud motion vectors used by GSMAP-MVK+ show huge advantage. These findings could be very useful for validation, refinement and future development of satellite-based products (e.g., NASA Global Precipitation Measurement). Although significant uncertainty exists in heavy precipitation, hydrological models contribute most of the uncertainty in extreme discharges. Interactions between precipitation products and hydrological models contribute significantly to uncertainty in discharge simulations and a better precipitation product does not guarantee a better discharge simulation because of interactions. It is also found that a good discharge simulation depends on a good coalition of a hydrological model and a precipitation product, suggesting that, although the satellite-based precipitation products are not as accurate as the gauge-based product, they could have better performance in discharge simulations when appropriately combined with hydrological models. This information is revealed for the first time and very beneficial for precipitation product applications.

Description: Technical Note: Application of artificial neural networks in groundwater table forecasting – a case study in Singapore swamp forest Hydrology and Earth System Sciences Discussions, 12, 9317-9336, 2015 Author(s): Y. Sun, D. Wendi, D. E. Kim, and S.-Y. Liong Accurate prediction of groundwater table is important for the efficient management of groundwater resources. Despite being the most widely used tools for depicting the hydrological regime, numerical models suffer from formidable constraints, such as extensive data demanding, high computational cost and inevitable parameter uncertainty. Artificial neural networks (ANNs), in contrast, can make predictions on the basis of more easily accessible variables, rather than requiring explicit characterization of the physical systems and prior knowledge of the physical parameters. This study applies ANN to predict the groundwater table in a swamp forest of Singapore. A standard multilayer perceptron (MLP) is selected, trained with the Levenberg–Marquardt (LM) algorithm. The inputs to the network are solely the surrounding reservoir levels and rainfall. The results reveal that ANN is able to produce accurate forecast with a leading time up to 7 days, whereas the performance slightly decreases when leading time increases.

Description: Using geochemical tracers to distinguish groundwater and parafluvial inflows in rivers (the Avon Catchment, SE Australia) Hydrology and Earth System Sciences Discussions, 12, 9205-9246, 2015 Author(s): I. Cartwright and H. Hofmann Understanding the location and magnitude of groundwater inflows to rivers is important for the protection of riverine ecosystems and the management of connected groundwater and surface water systems. Downstream trends in 222 Rn activities and Cl concentrations in the Avon River, southeast Australia, implies that it contains alternating gaining and losing reaches. 222 Rn activities of up to 3690 Bq m −3 imply that inflows are locally substantial (up to 3.1 m 3 m −1 day −1 ). However, if it assumed that these inflows are solely from groundwater, the net groundwater inflows during low-flow periods exceed the measured increase in streamflow along the Avon River by up to 490 %. Uncertainties in the 222 Rn activities of groundwater, the gas transfer coefficient, and the degree of hyporheic exchange cannot explain this discrepancy. It is proposed that a significant volume of the total calculated inflows into the Avon River represents water that exfiltrates from the river, flows through parafluvial sediments, and subsequently re-enters the river in the gaining reaches. This returning parafluvial flow has high 222 Rn activities due to 222 Rn emanations from the alluvial sediments. The riffle sections of the Avon River commonly have steep longitudinal gradients and may transition from losing at their upstream end to gaining at the downstream end and parafluvial flow through the sediment banks on meanders and point bars may also occur. Parafluvial flow is likely to be important in rivers with coarse-grained alluvial sediments on their floodplains and failure to quantify the input of 222 Rn from parafluvial flow will result in overestimating groundwater inflows to rivers.

Description: Subsurface flow mixing in coarse, braided river deposits Hydrology and Earth System Sciences Discussions, 12, 9295-9316, 2015 Author(s): E. Huber and P. Huggenberger Coarse, braided river deposits show a large hydraulic heterogeneity at the metre scale. One of the main depositional elements found in such deposits is a trough structure filled with open-framework–bimodal gravel couplet cross-beds. Several studies investigated the impact of the highly permeable open-framework gravel texture mainly in terms of concentration breakthrough curves. However, although the trough fills are expected to be significant mixing agents for the subsurface flow, their impact on the three-dimensional flow field has not draw much attention. This study aims to evaluate the subsurface flow mixing caused by overlapping trough fills embedded in a poorly-sorted gravel matrix. Below the river bed of the Tagliamento River (northeast Italy), trough fills were identified with ground-penetrating radar (GPR) probing. Based on field observations of coarse, braided river deposits, a simple three-dimensional geometrical model with associated hydraulic properties was fitted to the interpreted GPR reflectors. Then, steady-state subsurface flow and advective transport simulations were performed on the small-scale, high-resolution model (size: 45 m × 50 m × 10.26 m). The impact of trough fills on the flow field is visualised by the injection of a conservative tracer at three different depths.

Description: Sustainability of water uses in managed hydrosystems: human- and climate-induced changes for the mid-21st century Hydrology and Earth System Sciences Discussions, 12, 9247-9293, 2015 Author(s): J. Fabre, D. Ruelland, A. Dezetter, and B. Grouillet This paper assesses the sustainability of planned water uses in mesoscale river basins under multiple climate change scenarios, and contributes to determining the possible causes of unsustainability. We propose an assessment grounded in real-world water management issues, with water management scenarios built in collaboration with local water agencies. Furthermore we present an analysis through indicators that relate to management goals and present the implications of climate uncertainty for our results, furthering the significance of our study for water management. A modeling framework integrating hydro-climatic and human dynamics and accounting for interactions between resource and demand was developed and applied in two basins of different scales and with contrasting water uses: the Herault (2500 km 2 , France) and the Ebro (85 000 km 2 , Spain) basins. Natural streamflow was evaluated using a conceptual hydrological model. A demand-driven reservoir management model was designed to account for streamflow regulations from the main dams. Human water demand was estimated from time series of demographic, socio-economic and climatic data. Environmental flows were accounted for by defining streamflow thresholds under which withdrawals were strictly limited. Finally indicators comparing water availability to demand at strategic resource and demand nodes were computed. This framework was applied under different combinations of climatic and water use scenarios for the mid-21st century to differentiate the impacts of climate- and human-induced changes on streamflow and water balance. Results showed that objective monthly environmental flows would be guaranteed in current climate conditions in both basins, yet in several areas this could imply limiting human water uses more than once every five years. The impact of the tested climate projections on both water availability and demand could question the water allocations and environmental requirements currently planned for the coming decades. Water shortages for human use could become more frequent and intense, and the pressure on water resources and aquatic ecosystems could intensify. The causes of unsustainability vary across sub-basins and scenarios, and in most areas results are highly dependent on the climate change scenario.

Description: Investigation of hydrological time series using copulas for detecting catchment characteristics and anthropogenic impacts Hydrology and Earth System Sciences Discussions, 12, 9157-9203, 2015 Author(s): T. Sugimoto, A. Bárdossy, G. S. S. Pegram, and J. Cullmann Global climate change can have impacts on characteristics of rainfall-runoff events and subsequently on the hydrological regime. Meanwhile, the catchment itself changes due to anthropogenic influences. In this context, it can be meaningful to detect the temporal changes of catchments independent from climate change by investigating existing long term discharge records. For this purpose, a new stochastic system based on copulas for time series analysis is introduced. While widely used time series models are based on linear combinations of correlations assuming a Gaussian behavior of variables, a statistical tool like copula has the advantage to scrutinize the dependence structure of the data in the uniform domain independent of the marginal. Two measures in the copula domain are introduced herein: 1. Copula asymmetry is defined for copulas and calculated for discharges; this measure describes the non symmetric property of the dependence structure and differs from one catchment to another due to the intrinsic nature of both runoff and catchment. 2. Copula distance is defined as Cramér-von Mises type distance calculated between two copula densities of different time scales. This measure describes the variability and interdependency of dependence structures similar to variance and covariance, which can assist in identifying the catchment changes. These measures are calculated for 100 years of daily discharges for the Rhine rivers. Comparing the results of copula asymmetry and copula distance between an API and simulated discharge time series by a hydrological model we can show the interesting signals of systematic modifications along the Rhine rivers in the last 30 years.

Description: We address the problem of super-resolution frequency recovery using prior knowledge of the structure of a spectrally sparse, undersampled signal. In many applications of interest, some structure information about the signal spectrum is often known. The prior information might be simply knowing precisely some signal frequencies or the likelihood of a particular frequency component in the signal. We devise a general semidefinite program to recover these frequencies using theories of positive trigonometric polynomials. Our theoretical analysis shows that, given sufficient prior information, perfect signal reconstruction is possible using signal samples no more than thrice the number of signal frequencies. Numerical experiments demonstrate great performance enhancements using our method. We show that the nominal resolution necessary for the grid-free results can be improved if prior information is suitably employed.

Description: This paper addresses the behavior of a classical multiantenna GLRT test that allows to detect the presence of a known signal corrupted by a multipath propagation channel and by an additive temporally white Gaussian noise with unknown spatial covariance matrix. The paper is focused on the case where the number of sensors $M$ is large, and of the same order of magnitude as the sample size $N$ , a context which is modeled by the large system asymptotic regime $M rightarrow +infty $ , $N rightarrow +infty $ in such a way that $M/N rightarrow c$ for $c in (0,+infty )$ . The purpose of this paper is to study the behaviour of a GLRT statistics in this regime, and to show that the corresponding theoretical analysis allows to accurately predict the performance of the test when $M$ and $N$ are of the same order of magnitude.

Description: This paper derives an asymptotic generalized likelihood ratio test (GLRT) and an asymptotic locally most powerful invariant test (LMPIT) for two hypothesis testing problems: 1) Is a vector-valued random process cyclostationary (CS) or is it wide-sense stationary (WSS)? 2) Is a vector-valued random process CS or is it nonstationary? Our approach uses the relationship between a scalar-valued CS time series and a vector-valued WSS time series for which the knowledge of the cycle period is required. This relationship allows us to formulate the problem as a test for the covariance structure of the observations. The covariance matrix of the observations has a block-Toeplitz structure for CS and WSS processes. By considering the asymptotic case where the covariance matrix becomes block-circulant we are able to derive its maximum likelihood (ML) estimate and thus an asymptotic GLRT. Moreover, using Wijsman’s theorem, we also obtain an asymptotic LMPIT. These detectors may be expressed in terms of the Loève spectrum, the cyclic spectrum, and the power spectral density, establishing how to fuse the information in these spectra for an asymptotic GLRT and LMPIT. This goes beyond the state-of-the-art, where it is common practice to build detectors of cyclostationarity from ad-hoc functions of these spectra.

Description: The impulse response of wireless channels between the $N_t$ transmit and $N_r$ receive antennas of a MIMO-OFDM system are group approximately sparse (ga-sparse), i.e., the $N_tN_r$ channels have a small number of significant paths relative to the channel delay spread and the time-lags of the significant paths between transmit and receive antenna pairs coincide. Often, wireless channels are also group approximately cluster-sparse (gac-sparse), i.e., every ga-sparse channel consists of clusters, where a few clusters have all strong components while most clusters have all weak components. In this paper, we cast the problem of estimating the ga-sparse and gac-sparse block-fading and time-varying channels in the sparse Bayesian learning (SBL) framework and propose a bouquet of novel algorithms for pilot-based channel estimation, and joint channel estimation and data detection, in MIMO-OFDM systems. The proposed algorithms are capable of estimating the sparse wireless channels even when the measurement matrix is only partially known. Further, we employ a first-order autoregressive modeling of the temporal variation of the ga-sparse and gac-sparse channels and propose a recursive Kalman filtering and smoothing (KFS) technique for joint channel estimation, tracking, and data detection. We also propose novel, parallel-implementation based, low-complexity techniques for estimating gac-sparse channels. Monte Carlo simulations illustrate the benefit of exploiting the gac-sparse structure in the wireless channel in terms of the mean square error (MSE) and coded bit error rate (BER) performance.

Description: One-dimensional (1-D) and two-dimensional (2-D) frequency estimation for a single complex sinusoid in white Gaussian noise is a classic signal processing problem with numerous applications. It is revisited here through a new unitary principal-singular-vector utilization modal analysis (PUMA) approach, which is realized in terms of real-valued computations. The 2-D unitary PUMA is first formulated as an iteratively weighted least squares optimization problem. Recognizing that only one iteration is sufficient when 2-D unitary PUMA is initialized using least squares, a computationally attractive closed-form solution is then obtained. A variant of 2-D unitary PUMA is also developed for the 1-D case. Due to the real-valued computations and closed-form expression for the frequency estimate, the unitary PUMA is more computationally efficient than a number of state-of-the-art methods. Furthermore, the asymptotic variances of 1-D and 2-D unitary PUMA estimators are theoretically derived, and numerical results are included to demonstrate the effectiveness of the proposed methods.

Description: Distributed estimation over sensor networks has received a lot of attention due to its great promise for broad applicability. In many cases, sensors have constraints on the range of data they can measure. This may cause that the measurements or observations are censored, and hence the value of a measurement or observation could be only partially known. This paper focuses on distributed censored regression over networks and develops a diffusion-based algorithm for the censored regression. The proposed algorithm first adopts an adaptive bias-corrected estimator based on a probit regression model to reduce the adverse effect of censoring on estimation results, and afterwards carries out the least squares procedure to find the estimate of the parameter of interest in a collaborative manner between every node and its neighbors. The theoretical study of convergence in the mean and mean-square sense reveals that the proposed algorithm is asymptotically unbiased and stable under some conditions. Moreover, simulation results show the effectiveness of the proposed algorithm.

Description: Computational load remains a major concern when processing signals by means of sliding transforms. In this paper, we present an efficient algorithm for the fast computation of one-dimensional and two-dimensional sliding discrete Tchebichef moments. To do so, we first establish the relationships that exist between the Tchebichef moments of two neighboring windows taking advantage of Tchebichef polynomials’ properties. We then propose an original way to fast compute the moments of one window by utilizing the moment values of its previous window. We further theoretically establish the complexity of our fast algorithm and illustrate its interest within the framework of digital forensics and more precisely the detection of duplicated regions in an audio signal or an image. Our algorithm is used to extract local features of such a signal tampering. Experimental results show that its complexity is independent of the window size, validating the theory. They also exhibit that our algorithm is suitable to digital forensics and beyond to any applications based on sliding Tchebichef moments.

Description: In this paper, we describe a model for maximum likelihood estimation (MLE) of the relative abundances of different conformations of a protein in a heterogeneous mixture from small angle X-ray scattering (SAXS) intensities. To consider cases where the solution includes intermediate or unknown conformations, we develop a subset selection method based on k-means clustering and the Cramér-Rao bound on the mixture coefficient estimation error to find a sparse basis set that represents the space spanned by the measured SAXS intensities of the known conformations of a protein. Then, using the selected basis set and the assumptions on the model for the intensity measurements, we show that the MLE model can be expressed as a constrained convex optimization problem. Employing the adenylate kinase (ADK) protein and its known conformations as an example, and using Monte Carlo simulations, we demonstrate the performance of the proposed estimation scheme. Here, although we use 45 crystallographically determined experimental structures and we could generate many more using, for instance, molecular dynamics calculations, the clustering technique indicates that the data cannot support the determination of relative abundances for more than 5 conformations. The estimation of this maximum number of conformations is intrinsic to the methodology we have used here.

Description: Tensor factorization has proven useful in a wide range of applications, from sensor array processing to communications, speech and audio signal processing, and machine learning. With few recent exceptions, all tensor factorization algorithms were originally developed for centralized, in-memory computation on a single machine; and the few that break away from this mold do not easily incorporate practically important constraints, such as non-negativity. A new constrained tensor factorization framework is proposed in this paper, building upon the Alternating Direction Method of Multipliers (ADMoM). It is shown that this simplifies computations, bypassing the need to solve constrained optimization problems in each iteration; and it naturally leads to distributed algorithms suitable for parallel implementation. This opens the door for many emerging big data-enabled applications. The methodology is exemplified using non-negativity as a baseline constraint, but the proposed framework can incorporate many other types of constraints. Numerical experiments are encouraging, indicating that ADMoM-based non-negative tensor factorization (NTF) has high potential as an alternative to state-of-the-art approaches.

Description: A method for authorship attribution based on function word adjacency networks (WANs) is introduced. Function words are parts of speech that express grammatical relationships between other words but do not carry lexical meaning on their own. In the WANs in this paper, nodes are function words and directed edges from a source function word to a target function word stand in for the likelihood of finding the latter in the ordered vicinity of the former. WANs of different authors can be interpreted as transition probabilities of a Markov chain and are therefore compared in terms of their relative entropies. Optimal selection of WAN parameters is studied and attribution accuracy is benchmarked across a diverse pool of authors and varying text lengths. This analysis shows that, since function words are independent of content, their use tends to be specific to an author and that the relational data captured by function WANs is a good summary of stylometric fingerprints. Attribution accuracy is observed to exceed the one achieved by methods that rely on word frequencies alone. Further combining WANs with methods that rely on word frequencies, results in larger attribution accuracy, indicating that both sources of information encode different aspects of authorial styles.

Description: Greed is good. However, the tighter you squeeze, the less you have. In this paper, a less greedy algorithm for sparse signal reconstruction in compressive sensing, named orthogonal matching pursuit with thresholding is studied. Using the global 2-coherence, which provides a “bridge” between the well known mutual coherence and the restricted isometry constant, the performance of orthogonal matching pursuit with thresholding is analyzed and more general results for sparse signal reconstruction are obtained. It is also shown that given the same assumption on the coherence index and the restricted isometry constant as required for orthogonal matching pursuit, the thresholding variation gives exactly the same reconstruction performance with significantly less complexity.

Description: In multiobject inference, the multiobject probability density captures the uncertainty in the number and the states of the objects as well as the statistical dependence between the objects. Exact computation of the multiobject density is generally intractable and tractable implementations usually require statistical independence assumptions between objects. In this paper we propose a tractable multiobject density approximation that can capture statistical dependence between objects. In particular, we derive a tractable Generalized Labeled Multi-Bernoulli (GLMB) density that matches the cardinality distribution and the first moment of the labeled multiobject distribution of interest. It is also shown that the proposed approximation minimizes the Kullback–Leibler divergence over a special tractable class of GLMB densities. Based on the proposed GLMB approximation we further demonstrate a tractable multiobject tracking algorithm for generic measurement models. Simulation results for a multiobject Track-Before-Detect example using radar measurements in low signal-to-noise ratio (SNR) scenarios verify the applicability of the proposed approach.

Description: With bandwidths on the order of a gigahertz in emerging wireless systems, high-resolution analog-to-digital convertors (ADCs) become a power consumption bottleneck. One solution is to employ low resolution one-bit ADCs. In this paper, we analyze the flat fading multiple-input multiple-output (MIMO) channel with one-bit ADCs. Channel state information is assumed to be known at both the transmitter and receiver. For the multiple-input single-output channel, we derive the exact channel capacity. For the single-input multiple-output and MIMO channel, the capacity at infinite signal-to-noise ratio (SNR) is found. We also derive upper bound at finite SNR, which is tight when the channel has full row rank. In addition, we propose an efficient method to design the input symbols to approach the capacity achieving solution. We incorporate millimeter wave channel characteristics and find the bounds on the infinite SNR capacity. The results show how the number of paths and number of receive antennas impact the capacity.

Description: Based on the biorthogonal analysis approach, a multiwindow real-valued discrete Gabor transform (M-RDGT) for periodic sequences is presented to efficiently analyze the dynamic time-frequency content of a signal containing components with multiple and/or time-varying frequencies. The M-RDGT offers a computationally efficient implementation as well as a real-valued formulation of the multiwindow complex-valued discrete Gabor transform (M-CDGT). The completeness condition of the M-RDGT is proved to be equivalent to its biorthogonality constraint between analysis windows and synthesis windows. The M-RDGT can utilize the fast discrete Hartley transform algorithms for fast computation and has a simple relationship with the M-CDGT such that its coefficients can be directly computed from the M-RDGT coefficients. Therefore, the M-RDGT offers an efficient method to compute the M-CDGT. Since the analyzed sequence, analysis and synthesis windows in the existing M-CDGT must have an equal period, if the period of a sequence is very long, solving its windows requires a huge amount of computation and memory and could lead to numerical instability. To overcome this problem, a modified M-RDGT for long-periodic (or even infinite) sequences is presented and its corresponding biorthogonality constraint between analysis windows and synthesis windows is modified, in which the period of the analysis and synthesis windows is independent of the period of a analyzed sequence so that one can apply short windows to process any long-periodic (or even in finite) sequence. Finally, the multirate-based parallel implementation of the M-RDGT is presented, which has shown to be effective and fast for time-frequency analysis.

Description: In this paper, we present a Bayesian approach for spectral unmixing of multispectral Lidar (MSL) data associated with surface reflection from targeted surfaces composed of several known materials. The problem addressed is the estimation of the positions and area distribution of each material. In the Bayesian framework, appropriate prior distributions are assigned to the unknown model parameters and a Markov chain Monte Carlo method is used to sample the resulting posterior distribution. The performance of the proposed algorithm is evaluated using synthetic MSL signals, for which single and multi-layered models are derived. To evaluate the expected estimation performance associated with MSL signal analysis, a Cramer-Rao lower bound associated with model considered is also derived, and compared with the experimental data. Both the theoretical lower bound and the experimental analysis will be of primary assistance in future instrument design.

Description: This paper is concerned with Gaussian approximations to the posterior probability density function (PDF) in the update step of Bayesian filtering with nonlinear measurements. In this setting, sigma-point approximations to the Kalman filter (KF) recursion are widely used due to their ease of implementation and relatively good performance. In the update step, these sigma-point KFs are equivalent to linearizing the nonlinear measurement function by statistical linear regression (SLR) with respect to the prior PDF. In this paper, we argue that the measurement function should be linearized using SLR with respect to the posterior rather than the prior to take into account the information provided by the measurement. The resulting filter is referred to as the posterior linearization filter (PLF). In practice, the exact PLF update is intractable but can be approximated by the iterated PLF (IPLF), which carries out iterated SLRs with respect to the best available approximation to the posterior. The IPLF can be seen as an approximate recursive Kullback-Leibler divergence minimization procedure. We demonstrate the high performance of the IPLF in relation to other Gaussian filters in two numerical examples.

Description: Optimal queueing control of multihop networks remains a challenging problem even in the simplest scenarios. In this paper, we consider a two-hop half-duplex relaying system with random channel connectivity. The relay is equipped with a finite buffer. We focus on stochastic link selection and transmission rate control to maximize the average system throughput subject to a half-duplex constraint. We formulate this stochastic optimization problem as an infinite horizon average cost Markov decision process (MDP), which is well known to be a difficult problem. By using sample-path analysis and exploiting the specific problem structure, we first obtain an equivalent Bellman equation with reduced state and action spaces. By using relative value iteration algorithm, we analyze the properties of the value function of the MDP. Then, we show that the optimal policy has a threshold-based structure by characterizing the supermodularity in the optimal control. Based on the threshold-based structure and Markov chain theory, we further simplify the original complex stochastic optimization problem to a static optimization problem over a small discrete feasible set and propose a low-complexity algorithm to solve the simplified static optimization problem by making use of its special structure. Furthermore, we obtain the closed-form optimal threshold for the symmetric case. The analytical results obtained in this paper also provide design insights for two-hop relaying systems with multiple relays equipped with finite relay buffers.

Description: This paper studies noise enhanced (NE) estimators, which are constructed from an original estimator by artificially adding noise to the observation and computing the expected estimator output. By this expectation operation, we take into account the neighbourhood of an observation and the resulting NE estimator often has a smaller Bayes risk than the original one. We derive some general properties of this estimator and also present a method to obtain a suitable approximation of the optimal NE estimator which can be computed numerically by solving a constrained optimization problem. Finally, we study two examples to show the Bayes risk improvement that we can obtain from the NE estimator and we compare it to the stochastic resonance estimator.

Description: Soil–aquifer phenomena affecting groundwater under vertisols: a review Hydrology and Earth System Sciences Discussions, 12, 9571-9598, 2015 Author(s): D. Kurtzman, S. Baram, and O. Dahan Vertisols are cracking clayey soils that: (i) usually form in alluvial lowlands where normally, groundwater pools into aquifers, (ii) have different types of voids (due to cracking) which make flow and transport of water, solutes and gas complex, and (iii) are regarded as fertile soils in many areas. The combination of these characteristics results in the unique soil–aquifer phenomena that are highlighted and summarized in this review. The review is divided into the following four sections: (1) soil cracks as preferential pathways for water and contaminants; in this section lysimeter- to basin-scale observations that show the significance of cracks as preferential flow paths in vertisols which bypass matrix blocks in the unsaturated zone are summarized. Relatively fresh-water recharge and groundwater contamination from these fluxes and their modeling are reviewed, (2) soil cracks as deep evaporators and unsaturated-zone salinity; deep sediment samples under uncultivated vertisols in semiarid regions reveal a dry (immobile), saline matrix, partly due to enhanced evaporation through soil cracks. Observations of this phenomenon are compiled in this section and the mechanism of evapoconcentration due to air flow in the cracks is discussed, (3) impact of cultivation on flushing of the unsaturated zone and aquifer salinization; the third section examines studies reporting that land-use change of vertisols from native land to cropland promotes greater fluxes through the saline unsaturated-zone matrix, eventually flushing salts to the aquifer. Different degrees of salt flushing are assessed as well as aquifer salinization on different scales, and a comparison is made with aquifers under other soils, (4) relatively little nitrate contamination in aquifers under vertisols; In this section we turn the light on observations showing that aquifers under cultivated vertisols are somewhat resistant to groundwater contamination by nitrate (the major agriculturally related groundwater problem). Denitrification is probably the main mechanism supporting this resistance, whereas a certain degree of anion-exchange capacity may have a retarding effect as well.

Description: A framework for testing the use of electric and electromagnetic data to reduce the prediction error of groundwater models Hydrology and Earth System Sciences Discussions, 12, 9599-9653, 2015 Author(s): N. K. Christensen, S. Christensen, and T. P. A. Ferre Despite geophysics is being used increasingly, it is still unclear how and when the integration of geophysical data improves the construction and predictive capability of groundwater models. Therefore, this paper presents a newly developed HY drogeophysical TE st- B ench (HYTEB) which is a collection of geological, groundwater and geophysical modeling and inversion software wrapped to make a platform for generation and consideration of multi-modal data for objective hydrologic analysis. It is intentionally flexible to allow for simple or sophisticated treatments of geophysical responses, hydrologic processes, parameterization, and inversion approaches. It can also be used to discover potential errors that can be introduced through petrophysical models and approaches to correlating geophysical and hydrologic parameters. With HYTEB we study alternative uses of electromagnetic (EM) data for groundwater modeling in a hydrogeological environment consisting of various types of glacial deposits with typical hydraulic conductivities and electrical resistivities covering impermeable bedrock with low resistivity. It is investigated to what extent groundwater model calibration and, often more importantly, model predictions can be improved by including in the calibration process electrical resistivity estimates obtained from TEM data. In all calibration cases, the hydraulic conductivity field is highly parameterized and the estimation is stabilized by regularization. For purely hydrologic inversion (HI, only using hydrologic data) we used Tikhonov regularization combined with singular value decomposition. For joint hydrogeophysical inversion (JHI) and sequential hydrogeophysical inversion (SHI) the resistivity estimates from TEM are used together with a petrophysical relationship to formulate the regularization term. In all cases, the regularization stabilizes the inversion, but neither the HI nor the JHI objective function could be minimized uniquely. SHI or JHI with regularization based on the use of TEM data produced estimated hydraulic conductivity fields that bear more resemblance to the reference fields than when using HI with Tikhonov regularization. However, for the studied system the resistivities estimated by SHI or JHI must be used with caution as estimators of hydraulic conductivity or as regularization means for subsequent hydrological inversion. Much of the lack of value of the geophysical data arises from a mistaken faith in the power of the petrophysical model in combination with geophysical data of low sensitivity, thereby propagating geophysical estimation errors into the hydrologic model parameters. With respect to reducing model prediction error, it depends on the type of prediction whether it has value to include geophysical data in the model calibration. It is found that all calibrated models are good predictors of hydraulic head. When the stress situation is changed from that of the hydrologic calibration data, then all models make biased predictions of head change. All calibrated models turn out to be a very poor predictor of the pumping well's recharge area and groundwater age. The reason for this is that distributed recharge is parameterized as depending on estimated hydraulic conductivity of the upper model layer which tends to be underestimated. Another important insight from the HYTEB analysis is thus that either recharge should be parameterized and estimated in a different way, or other types of data should be added to better constrain the recharge estimates.

Description: Co-evolution of volcanic catchments in Japan Hydrology and Earth System Sciences Discussions, 12, 9655-9700, 2015 Author(s): T. Yoshida and P. A. Troch Present day landscapes have evolved over time through interactions between the prevailing climates and geological settings. Understanding the linkage between spatial patterns of landforms, soils, and vegetation in landscapes and their hydrological response is critical to make quantitative predictions in ungaged basins. Catchment co-evolution is a theoretical framework that seeks to formulate hypotheses about the mechanisms and conditions that determine the historical development of catchments and how such evolution affects their hydrological response. In this study, we selected 14 volcanic catchments of different ages (from 0.225 to 82.2 Ma) in Japan. We derived indices of landscape properties (drainage density) as well as hydrological response (annual water balance, baseflow index, and flow duration curves) and examined their relation with catchment age and climate (through the aridity index). We found significant correlation between drainage density and baseflow index with age, but not with climate. The age of the catchments was also significantly related to intra-annual flow variability. Younger catchments tend to have lower peak flows and higher low flows, while older catchments exhibit more flashy runoff. The decrease of baseflow with catchment age confirms previous studies that hypothesized that in volcanic landscapes the major flow pathways have changed over time, from deep groundwater flow to shallow subsurface flow. The drainage density of our catchments decreased with age, contrary to previous findings in similar volcanic catchments but of significant younger age than the ones explored here. In these younger catchments, an increase in drainage density with age was observed, and it was hypothesized that this was because of more landscape incision due to increasing near-surface lateral flow paths in more mature catchments. Our results suggests two hypotheses on the evolution of drainage density in matured catchments. One is that as catchments further evolve, hydrologically active channels retreat as less recharge leads to lower average aquifer levels and less baseflow; the other is that it does not significantly change after catchments reached maturity in terms of surface dissection.

Description: Identifying hydrological responses of micro-catchments under contrasting land use in the Brazilian Cerrado Hydrology and Earth System Sciences Discussions, 12, 9915-9975, 2015 Author(s): R. L. B. Nobrega, A. C. Guzha, G. N. Torres, K. Kovacs, G. Lamparter, R. S. S. Amorim, E. Couto, and G. Gerold In recent decades, the Brazilian Cerrado biome has been affected by intense land-use change, particularly the conversion of natural forest to agricultural land. Understanding the environmental impacts of this land-use change on landscape hydrological dynamics is one of the main challenges in the Amazon agricultural frontier, where part of the Brazilian Cerrado biome is located and where most of the deforestation has occurred. This study uses empirical data from field measurements to characterize controls on hydrological processes from three first-order micro-catchments 〈 1 km 2 in the Cerrado biome. These micro-catchments were selected on the basis of predominant land use including native cerrado vegetation, pasture grass with cattle ranching, and cash crop land. We continuously monitored precipitation, streamflow, soil moisture, and meteorological variables from October 2012 to September 2014. Additionally, we determined the physical and hydraulic properties of the soils, and conducted topographic surveys. We used these data to quantify the water balance components of the study catchments and to relate these water fluxes to land use, catchment physiographic parameters, and soil hydrophysical properties. The results of this study show that runoff coefficients were 0.27, 0.40, and 0.16 for the cerrado, pasture, and cropland catchments, respectively. Baseflow is shown to play a significant role in streamflow generation in the three study catchments, with baseflow index values of more than 0.95. The results also show that evapotranspiration was highest in the cerrado (986 mm yr −1 ) compared to the cropland (828 mm yr −1 ) and the pasture (532 mm yr −1 ). However, discharges in the cropland catchment were unexpectedly lower than that of the cerrado catchment. The normalized discharge was 55 % higher and 57 % lower in the pasture and cropland catchments, respectively, compared with the cerrado catchment. We attribute this finding to the differences in soil type and topographic characteristics, and low-till farming techniques in the cropland catchment, additionally to the buffering effect of the gallery forests in these catchments. Although the results of this study provide a useful assessment of catchment rainfall–runoff controls in the Brazilian Cerrado landscape, further research is required to include quantification of the influence of the gallery forests on both hydrological and hydrochemical fluxes, which are important for watershed management and ecosystem services provisioning.

Description: Stochastic or statistic? Comparing flow duration curve models in ungauged basins and changing climates Hydrology and Earth System Sciences Discussions, 12, 9765-9811, 2015 Author(s): M. F. Müller and S. E. Thompson The prediction of flow duration curves (FDCs) in ungauged basins remains an important task for hydrologists given the practical relevance of FDCs for water management and infrastructure design. Predicting FDCs in ungauged basins typically requires spatial interpolation of statistical or model parameters. This task is complicated if climate becomes non-stationary, as the prediction challenge now also requires extrapolation through time. In this context, process-based models for FDCs that mechanistically link the streamflow distribution to climate and landscape factors may have an advantage over purely statistical methods to predict FDCs. This study compares a stochastic (process-based) and statistical method for FDC prediction in both stationary and non-stationary contexts, using Nepal as a case study. Under contemporary conditions, both models perform well in predicting FDCs, with Nash–Sutcliffe coefficients above 0.80 in 75 % of the tested catchments. The main drives of uncertainty differ between the models: parameter interpolation was the main source of error for the statistical model, while violations of the assumptions of the process-based model represented the main source of its error. The process-based approach performed better than the statistical approach in numerical simulations with non-stationary climate drivers. The predictions of the statistical method under non-stationary rainfall conditions were poor if (i) local runoff coefficients were not accurately determined from the gauge network, or (ii) streamflow variability was strongly affected by changes in rainfall. A Monte Carlo analysis shows that the streamflow regimes in catchments characterized by a strong wet-season runoff and a rapid, strongly non-linear hydrologic response are particularly sensitive to changes in rainfall statistics. In these cases, process-based prediction approaches are strongly favored over statistical models.

Description: Reviving the "Ganges Water Machine": where and how much? Hydrology and Earth System Sciences Discussions, 12, 9741-9763, 2015 Author(s): L. Muthuwatta, U. A. Amarasinghe, A. Sood, and S. Lagudu Surface runoff generated in the monsoon months in the upstream parts of the Ganges River Basin contributes substantially to downstream floods, while water shortages in the dry months affect agricultural production in the basin. This paper examines the parts (sub-basins) of the Ganges that have the potential for augmenting subsurface storage (SSS), increase the availability of water for agriculture and other uses, and mitigate the floods in the downstream areas. The Soil and Water Assessment Tool (SWAT) is used to estimate sub-basin-wise water availability. The water availability estimated is then compared with the sub-basin-wise un-met water demand for agriculture. Hydrological analyses revealed that five sub-basins produced more than 10 billion cubic meters (B m 3 ) of annual surface runoff consistently during the simulation period. In these sub-basins, less than 50 % of the annual surface runoff is sufficient to irrigate all irrigable land in both the \textit{Rabi} (November to March) and summer (April to May) seasons. Further, for most of the sub-basins, there is sufficient water to meet the un-met water demand, provided that it is possible to capture the surface runoff during the wet season. It is estimated that the average flow to Bihar State from the upstream of the Ganges, a downstream basin location, is 277 ± 121 B m 3 , which is more than double the rainfall in the state alone. Strong relationships between outflows from the upstream sub-basins and the inflows to Bihar State suggested that flood inundation in the state could be reduced by capturing a portion of the upstream flows during the peak runoff periods.

Description: Monitoring infiltration processes with high-resolution surface-based Ground-Penetrating Radar Hydrology and Earth System Sciences Discussions, 12, 12215-12246, 2015 Author(s): P. Klenk, S. Jaumann, and K. Roth In this study, we present a series of high resolution Ground-Penetrating Radar (GPR) measurements monitoring two artificially induced infiltration pulses into two different sands with dual-frequency ground-based GPR. After the application of the second infiltration pulse, the water table in the subsoil was raised by pumping in water from below. The longterm relaxation of the system was then monitored over the course of several weeks. We focused on the capillary fringe reflection and on observed variations in soil water content as derived from direct wave travel times. We discuss the advantages of this dual-frequency approach and show the attainable precision in longterm monitoring of such relaxation processes. Reaching a relative precision of better than 0.001 [–] in water content, we can clearly discern the relaxation of the two investigated sands.

Description: Macropore flow at the field scale: predictive performance of empirical models and X-ray CT analyzed macropore characteristics Hydrology and Earth System Sciences Discussions, 12, 12089-12120, 2015 Author(s): M. Naveed, P. Moldrup, M. Schaap, M. Tuller, R. Kulkarni, H.-J. Vögel, and L. Wollesen de Jonge Predictions of macropore flow is important for maintaining both soil and water quality as it governs key related soil processes e.g. soil erosion and subsurface transport of pollutants. However, macropore flow currently cannot be reliably predicted at the field scale because of inherently large spatial variability. The aim of this study was to perform field scale characterization of macropore flow and investigate the predictive performance of (1) current empirical models for both water and air flow, and (2) X-ray CT derived macropore network characteristics. For this purpose, 65 cylindrical soil columns (6 cm diameter and 3.5 cm height) were extracted from the topsoil (5 to 8.5 cm depth) in a 15 m × 15 m grid from an agricultural loamy field located in Silstrup, Denmark. All soil columns were scanned with an industrial CT scanner (129 μm resolution) and later used for measurements of saturated water permeability, air permeability and gas diffusivity at −30 and −100 cm matric potentials. Distribution maps for both water and air permeabilities and gas diffusivity reflected no spatial correlation irrespective of the soil texture and organic matter maps. Empirical predictive models for both water and air permeabilities showed poor performance as they were not able to realistically capture macropore flow because of poor correlations with soil texture and bulk density. The tested empirical model predicted well gas diffusivity at −100 cm matric potential, but relatively failed at −30 cm matric potential particularly for samples with biopore flow. Image segmentation output of the four employed methods was nearly the same, and matched well with measured air-filled porosity at −30 cm matric potential. Many of the CT derived macropore network characteristics were strongly interrelated. Most of the macropore network characteristics were also strongly correlated with saturated water permeability, air permeability, and gas diffusivity. The correlations between macropore network characteristics and macropore flow parameters were further improved on dividing soil samples into samples with biopore and matrix flow. Observed strong correlations between macropore network characteristics and macropore flow highlighted the need of further research on numerical simulations of macropore flow based on X-ray CT images. This could pave the way for the digital soil physics laboratory in the future.

Description: Identification of the main attribute of river flow temporal variations in the Nile Basin Hydrology and Earth System Sciences Discussions, 12, 12167-12214, 2015 Author(s): C. Onyutha and P. Willems Temporal variation of monthly flows was investigated at 18 Discharge Measurement Stations (DMS) within the Nile Basin in Africa. The DMS were grouped using a clustering procedure based on the similarity in the flow variation patterns. The co-variation of the rainfall and flow was assessed in each group. To investigate the possible change in catchment behavior, which may interfere with the flow–rainfall relationship, three rainfall–runoff models were applied to the major catchment in each group based on the data time period falling within 1940–2003. The co-occurrence of the changes in the observed and simulated overland flow was examined using the cumulative rank difference (CRD) technique and the quantile perturbation method (QPM). Two groups of the DMS were obtained. Group 1 comprises the DMS from the equatorial region and/or South Sudan, while those in Sudan, Ethiopia and Egypt form group 2. In the selected catchment of each group, the patterns of changes in terms of the CRD sub-trends and QPM anomalies for both the observed and simulated flows were in a close agreement. These results indicate that change in catchment behavior due to anthropogenic influence in the Nile basin over the selected time period was minimal. Thus, the overall rainfall–runoff generation processes of the catchments were not impacted upon in a significant way. The temporal flow variations could be attributed mainly to the rainfall variations.

Description: The socio-ecohydrology of rainwater harvesting in India: understanding water storage and release dynamics at tank and catchment scales Hydrology and Earth System Sciences Discussions, 12, 12121-12165, 2015 Author(s): K. J. Van Meter, N. B. Basu, D. L. McLaughlin, and M. Steiff Rainwater harvesting (RWH), the small-scale collection and storage of runoff for irrigated agriculture, is recognized as a sustainable strategy for ensuring food security, especially in monsoonal landscapes in the developing world. In south India, these strategies have been used for millennia to mitigate problems of water scarcity. However, in the past 100 years many traditional RWH systems have fallen into disrepair due to increasing dependence on groundwater. This dependence has contributed to an accelerated decline in groundwater resources, which has in turn led to increased efforts at the state and national levels to revive older RWH systems. Critical to the success of such efforts is an improved understanding of how these ancient systems function in contemporary landscapes with extensive groundwater pumping and shifted climatic regimes. Knowledge is especially lacking regarding the water-exchange dynamics of these RWH "tanks" at tank and catchment scales, and how these exchanges regulate tank performance and catchment water balances. Here, we use fine-scale water-level variation to quantify daily fluxes of groundwater, evapotranspiration (ET), and sluice outflows in four tanks over the 2013 northeast monsoon season in a tank cascade that covers a catchment area of 28 km 2 . At the tank scale, our results indicate that groundwater recharge and irrigation outflows comprise the largest fractions of the tank water budget, with ET accounting for only 13–22 % of the outflows. At the scale of the cascade, we observe a distinct spatial pattern in groundwater-exchange dynamics, with the frequency and magnitude of groundwater inflows increasing down the cascade of tanks. The significant magnitude of return flows along the tank cascade leads to the most downgradient tank in the cascade having an outflow-to capacity ratio greater than 2. The presence of tanks in the landscape dramatically alters the catchment water balance, with runoff decreasing by nearly 75 %, and recharge increasing by more than 40 %. Finally, while water from the tanks directly satisfies ~40 % of the crop water requirement across the northeast monsoon season via surface water irrigation, a large fraction of the tank water is "wasted," and more efficient management of sluice outflows could lead to tanks meeting a higher fraction of crop water requirements.

Description: Analytical approach for determining the mean water level profile in an estuary with substantial fresh water discharge Hydrology and Earth System Sciences Discussions, 12, 8381-8417, 2015 Author(s): H. Cai, H. H. G. Savenije, C. Jiang, L. Zhao, and Q. Yang Although modestly, the mean water level in estuaries rises in landward direction induced by a combination of the salinity gradient, the tidal asymmetry, and the backwater effect. The water level slope is increased by the fresh water discharge. However, the interactions between tide and river flow and their individual contributions to the rise of the mean water level along the estuary are not yet completely understood. In this study, we adopt an analytical approach to describe the tidal wave propagation under the influence of fresh water discharge, in which the friction term is approximated by a Chebyshev polynomials approach. The analytical model is used to quantify the contributions made by tide, river, and tide–river interaction to the water level slope along the estuary. Subsequently, the method is applied to the Yangtze estuary under a wide range of river discharge conditions and the influence of tidal amplitude and fresh water discharge on the longitudinal variation of mean water level is explored. The proposed method is particularly useful for accurately predicting water levels and the frequency of extreme high water, relevant for water management and flood control.

Description: Trends in West African floods: a comparative analysis with rainfall and vegetation indices Hydrology and Earth System Sciences Discussions, 12, 5083-5121, 2015 Author(s): B. N. Nka, L. Oudin, H. Karambiri, J. E. Paturel, and P. Ribstein After the drought of the 1970s in West Africa, the variability of rainfall and land use changes affected mostly flow, and recently flooding has been said to be an increasingly common occurrence throughout the whole of West Africa. These changes raised many questions about the impact of climate change on the flood regimes in West African countries. This paper investigates whether floods are becoming more frequent or more severe, and to what extent climate patterns have been responsible for these changes. We analyzed the trends in the floods occurring in 14 catchments within West Africa's main climate zone. The methodology includes two methods for sampling flood events, namely the AM (annual maximum) method and the POT (peak over threshold), and two perspectives of analysis are presented: long-term analysis based on two long flood time series, and a regional perspective involving 14 catchments with shorter series. The Mann–Kendall trend test and the Pettitt break test were used to assess time series stationarity. The trends detected in flood time series were compared to the rainfall index trends and vegetation indices using contingency tables, in order to identify the main driver of change in flood magnitude and flood frequency. The relation between the flood index and the physiographic index was evaluated through a success criterion and the Cramer criterion calculated from the contingency tables. The results point out the existence of trends in flood magnitude and flood frequency time series with two main patterns. Sahelian floods show increasing flood trends and some Sudanian catchments present decreasing flood trends. For the overall catchments studied, the maximum 5 day consecutive rainfall index (Rx5d) seems to follow the flood trend, while the NDVI indices do not show a significant link with the flood trends, meaning that this index has no impact in the behavior of floods in the region.

Description: Evaluation of a multi-satellite soil moisture product and the Community Land Model 4.5 simulation in China Hydrology and Earth System Sciences Discussions, 12, 5151-5186, 2015 Author(s): B. Jia, J. Liu, and Z. Xie Twenty years of in situ soil moisture data from more than 300 stations located in China are used to perform an evaluation of two surface soil moisture datasets: a microwave-based multi-satellite product (ECV-SM) and the land surface model simulation from the Community Land Model 4.5 (CLM4.5). Both soil moisture products generally show a good agreement with in situ observations. The ECV-SM product has a low bias, with a root mean square difference (RMSD) of 0.075 m 3 m -3 , but shows a weak correlation with in situ observations ( R = 0.41). In contrast, the CLM4.5 simulation, forced by an observation-based atmospheric forcing data, produces better temporal variation of surface soil moisture ( R = 0.52), but shows a clear overestimation (bias = 0.05 m 3 m -3 ) and larger RMSD (0.09 m 3 m -3 ), especially in eastern China, caused by inaccurate descriptions of soil characteristics. The ECV-SM product is more likely to be superior in semi-arid regions, mainly because of the accurate retrievals and high observation density, but inferior over areas covered by dense vegetation. Furthermore, it shows a stable to slightly increasing performance in China, except for a decrease during the 2007–2010 blending period. Results from this study can provide comprehensive insight into the performances of the two soil moisture datasets in China, which will be useful for their improvements in merging algorithms or model simulations and for applications in soil moisture data assimilation.

Description: Optimality and inference in hydrology from entropy production considerations: synthetic hillslope numerical experiments Hydrology and Earth System Sciences Discussions, 12, 5123-5149, 2015 Author(s): S. J. Kollet In this study, entropy production optimization and inference principles are applied to a synthetic semi-arid hillslope in high-resolution, physics-based simulations. The results suggest that entropy or power is indeed maximized, because of the strong nonlinearity of variably saturated flow and competing processes related to soil moisture fluxes, the depletion of gradients, and the movement of a free water table. Thus, it appears that the maximum entropy production (MEP) principle may indeed be applicable to hydrologic systems. In the application to hydrologic system, the free water table constitutes an important degree of freedom in the optimization of entropy production and may also relate the theory to actual observations. In an ensuing analysis, an attempt is made to transfer the complex, "microscopic" hillslope model into a macroscopic model of reduced complexity using the MEP principle as an interference tool to obtain effective conductance coefficients and forces/gradients. The results demonstrate a new approach for the application of MEP to hydrologic systems and may form the basis for fruitful discussions and research in future.

Description: Creating long term gridded fields of reference evapotranspiration in Alpine terrain based on a re-calibrated Hargreaves method Hydrology and Earth System Sciences Discussions, 12, 5055-5082, 2015 Author(s): K. Haslinger and A. Bartsch A new approach for the construction of high resolution gridded fields of reference evapotranspiration for the Austrian domain on a daily time step is presented. Forcing fields of gridded data of minimum and maximum temperatures are used to estimate reference evapotranspiration based on the formulation of Hargreaves. The calibration constant in the Hargreaves equation is recalibrated to the Penman–Monteith equation, which is recommended by the FAO, in a monthly and station-wise assessment. This ensures on one hand eliminated biases of the Hargreaves approach compared to the formulation of Penman–Monteith and on the other hand also reduced root mean square errors and relative errors on a daily time scale. The resulting new calibration parameters are interpolated in time to a daily temporal resolution for a standard year of 365 days. The overall novelty of the approach is the conduction of surface elevation as a predictor to estimate the re-calibrated Hargreaves parameter in space. A third order spline is fitted to the re-calibrated parameters against elevation at every station and yields the statistical model for assessing these new parameters in space by using the underlying digital elevation model of the temperature fields. Having newly calibrated parameters for every day of year and every grid point, the Hargreaves method is applied to the temperature fields, yielding reference evapotranspiration for the entire grid and time period from 1961–2013. With this approach it is possible to generate high resolution reference evapotranspiration fields starting when only temperature observations are available but re-calibrated to meet the requirements of the recommendations defined by the FAO.

Description: Assessing the quality of Digital Elevation Models obtained from mini-Unmanned Aerial Vehicles for overland flow modelling in urban areas Hydrology and Earth System Sciences Discussions, 12, 5629-5670, 2015 Author(s): J. P. Leitão, M. Moy de Vitry, A. Scheidegger, and J. Rieckermann Precise and detailed Digital Elevation Models (DEMs) are essential to accurately predict overland flow in urban areas. Unfortunately, traditional sources of DEM remain a bottleneck for detailed and reliable overland flow models, because the resulting DEMs are too coarse to provide DEMs of sufficient detail to inform urban overland flows. Interestingly, technological developments of Unmanned Aerial Vehicles (UAVs) suggest that they have matured enough to be a competitive alternative to satellites or airplanes. However, this has not been tested so far. In this this study we therefore evaluated whether DEMs generated from UAV imagery are suitable for urban drainage overland flow modelling. Specifically, fourteen UAV flights were conducted to assess the influence of four different flight parameters on the quality of generated DEMs: (i) flight altitude, (ii) image overlapping, (iii) camera pitch and (iv) weather conditions. In addition, we compared the best quality UAV DEM to a conventional Light Detection and Ranging (LiDAR)-based DEM. To evaluate both the quality of the UAV DEMs and the comparison to LiDAR-based DEMs, we performed regression analysis on several qualitative and quantitative metrics, such as elevation accuracy, quality of object representation (e.g., buildings, walls and trees) in the DEM, which were specifically tailored to assess overland flow modelling performance, using the flight parameters as explanatory variables. Our results suggested that, first, as expected, flight altitude influenced the DEM quality most, where lower flights produce better DEMs; in a similar fashion, overcast weather conditions are preferable, but weather conditions and other factors influence DEM quality much less. Second, we found that for urban overland flow modelling, the UAV DEMs performed competitively in comparison to a traditional LiDAR-based DEM. An important advantage of using UAVs to generate DEMs in urban areas is their flexibility that enables more frequent, local and affordable elevation data updates, allowing, for example, to capture different tree foliage conditions.

Description: Joint inference of groundwater-recharge and hydraulic-conductivity fields from head data using the Ensemble-Kalman filter Hydrology and Earth System Sciences Discussions, 12, 5565-5599, 2015 Author(s): D. Erdal and O. A. Cirpka Regional groundwater flow strongly depends on groundwater recharge and hydraulic conductivity. Both are spatially variable fields, and their estimation is an ongoing topic in groundwater research and practice. In this study, we use the Ensemble Kalman filter as an inversion method to jointly estimate spatially variable recharge and conductivity fields from head observations. The success of the approach strongly depends on the assumed prior knowledge. If the structural assumptions underlying the initial ensemble of the parameter fields are correct, both estimated fields resemble the true ones. However, erroneous prior knowledge may not be corrected by the data. In the worst case, the estimated recharge field resembles the true conductivity field, resulting in a model that meets the observations but has very poor predictive power. The study exemplifies the importance of prior knowledge in the joint estimation of parameters from ambiguous measurements.

Description: Previous studies have confirmed the adverse impact of fading correlation on the mutual information (MI) of two-dimensional (2D) multiple-input multiple-output (MIMO) systems. More recently, the trend is to enhance the system performance by exploiting the channels degrees of freedom in the elevation, which necessitates the derivation and characterization of three-dimensional (3D) channels in the presence of spatial correlation. In this paper, an exact closed-form expression for the Spatial Correlation Function (SCF) is derived for 3D MIMO channels. The proposed method resorts to the spherical harmonic expansion (SHE) of plane waves and the trigonometric expansion of Legendre and associated Legendre polynomials. The resulting expression depends on the underlying arbitrary angular distributions and antenna patterns through the Fourier Series (FS) coefficients of power azimuth and elevation spectrums. The novelty of the proposed method lies in the SCF being valid for any 3D propagation environment. The developed SCF determines the covariance matrices at the transmitter and the receiver that form the Kronecker channel model. In order to quantify the effects of correlation on system performance, the information-theoretic deterministic equivalents of the MI for the Kronecker model are utilized in both mono-user and multi-user cases. Numerical results validate the proposed analytical expressions and elucidate the dependence of the system performance on azimuth and elevation angular spreads and antenna patterns. Some useful insights into the behavior of MI as a function of downtilt angles are provided. The derived model will help evaluate the performance of correlated 3D MIMO channels in the future.