ALBERT

Description: We strongly concur with most of Morgan’s points regarding expert knowledge elicitation (EKE) for policy making (1); however, we contest the somewhat idealistic tone of Morgan’s paper, which we believe counters the goal of better policy making otherwise promoted. Furthermore, we disagree on two specific issues raised by Morgan that...

Description: In a recent issue of PNAS, Daniel et al. (1) attempted to advance the integration of cultural values and cultural ecosystem services (ES) into the ES framework. Although I agree with the authors that cultural values are of eminent importance, I see two flaws in their argument.The range of cultural...

Description: We thank Thomas Kirchhoff (1) for agreeing that cultural values are important. As is explicit in our paper (2), we also agree that not all cultural values can be fit into the ecosystems services framework; however, we chose to focus on those that can. We are nonetheless considerably more optimistic...

Description: Steward et al. (1) assess the hydrologic and agricultural future of the High Plains Aquifer. We have many concerns about hydrologic aspects of their study and describe the most significant here. The authors state “…the lines of recharge plus storage in Fig. 1C very closely approximate the recent data points...

Description: In their letter (1), López et al. propose “control-based” accounting of air pollution that assigns pollution to countries according to the nationality of corporations producing the pollution. For example, pollution produced in China by US corporations would be assigned to the United States regardless of where the related goods are...

Description: Lin et al. (1) measure pollution embodied in Chinese–US international trade using an atmospheric chemical transport model and find that moving manufacturing offshore to China had an overall beneficial effect on public health in the United States but at the expense of air quality over the western region of the...

Description: We propose to test if gravimetry can prove useful in discriminating different models of long-term deep crustal processes in the case of the Taiwan mountain belt. We discuss two existing tectonic models that differ in the deep processes proposed to sustain the long-term growth of the orogen. One model assumes underplating of the uppermost Eurasian crust with subduction of the deeper part of the crust into the mantle. The other one suggests the accretion of the whole Eurasian crust above crustal-scale ramps, the lower crust being accreted into the collisional orogen. We compute the temporal gravity changes caused only by long-term rock mass transfers at depth for each of them. We show that the underplating model implies a rate of gravity change of –6 x 10 –2 μGal yr –1 , a value that increases to 2 x 10 –2 μGal yr –1 if crustal subduction is neglected. If the accretion of the whole Eurasian crust occurs, a rate of 7 x 10 –2 μGal yr –1 is obtained. The two models tested differ both in signal amplitude and spatial distribution. The yearly gravity changes expected by long-term deep crustal mass processes in Taiwan are two orders of magnitude below the present-day uncertainty of land-based gravity measurements. Assuming that these annually averaged long-term gravity changes will linearly accumulate with ongoing mountain building, multidecadal time-series are needed to identify comparable rates of gravity change. However, as gravity is sensitive to any mass redistribution, effects of short-term processes such as seismicity and surface mass transfers (erosion, sedimentation, ground-water) may prevent from detecting any long-term deep signal. This study indicates that temporal gravity is not appropriate for deciphering the long-term deep crustal processes involved in the Taiwan mountain belt.

Description: The computation of quasi-static deformation for axisymmetric viscoelastic structures on a gravitating spherical earth is addressed using the spectral element method (SEM). A 2-D spectral element domain is defined with respect to spherical coordinates of radius and angular distance from a pole of symmetry, and 3-D viscoelastic structure is assumed to be azimuthally symmetric with respect to this pole. A point dislocation source that is periodic in azimuth is implemented with a truncated sequence of azimuthal order numbers. Viscoelasticity is limited to linear rheologies and is implemented with the correspondence principle in the Laplace transform domain. This leads to a series of decoupled 2-D problems which are solved with the SEM. Inverse Laplace transform of the independent 2-D solutions leads to the time-domain solution of the 3-D equations of quasi-static equilibrium imposed on a 2-D structure. The numerical procedure is verified through comparison with analytic solutions for finite faults embedded in a laterally homogeneous viscoelastic structure. This methodology is applicable to situations where the predominant structure varies in one horizontal direction, such as a structural contrast across (or parallel to) a long strike-slip fault.

Description: The geodetic rates for the gravity variation and vertical uplift in polar regions subject to past and present-day ice-mass changes (PDIMCs) provide important insight into the rheological structure of the Earth. We provide an update of the rates observed at Ny-Ålesund, Svalbard. To do so, we extract and remove the significant seasonal content from the observations. The rate of gravity variations, derived from absolute and relative gravity measurements, is –1.39 ± 0.11 μGal yr –1 . The rate of vertical displacements is estimated using GPS and tide gauge measurements. We obtain 7.94 ± 0.21 and 8.29 ± 1.60 mm yr –1 , respectively. We compare the extracted signal with that predicted by GLDAS/Noah and ERA-interim hydrology models. We find that the seasonal gravity variations are well-represented by local hydrology changes contained in the ERA-interim model. The phase of seasonal vertical displacements are due to non-local continental hydrology and non-tidal ocean loading. However, a large part of the amplitude of the seasonal vertical displacements remains unexplained. The geodetic rates are used to investigate the asthenosphere viscosity and lithosphere/asthenosphere thicknesses. We first correct the updated geodetic rates for those induced by PDIMCs in Svalbard, using published results, and the sea level change due to the melting of the major ice reservoirs. We show that the latter are at the level of the geodetic rate uncertainties and are responsible for rates of gravity variations and vertical displacements of –0.29 ± 0.03 μGal yr –1 and 1.11 ± 0.10 mm yr –1 , respectively. To account for the late Pleistocene deglaciation, we use the global ice evolution model ICE-3G. The Little Ice Age (LIA) deglaciation in Svalbard is modelled using a disc load model with a simple linear temporal evolution. The geodetic rates at Ny-Ålesund induced by the past deglaciations depend on the viscosity structure of the Earth. We find that viscous relaxation time due to the LIA deglaciation in Svalbard is more than 60 times shorter than that due to the Pleistocene deglaciation. We also find that the response to past and PDIMCs of an Earth model with asthenosphere viscosities ranging between 1.0 and 5.5 x 10 18 Pa s and lithosphere (resp. asthenosphere) thicknesses ranging between 50 and 100 km (resp. 120 and 170 km) can explain the rates derived from geodetic observations.

Description: The conclusions of a recent study by Wright and Wimberly (1) suggesting that corn/soy cultivation in the Western Corn Belt (WCB) “threatens grasslands” are questionable because of the methods and data used. The study (1) compared National Agricultural Statistics Service (NASS) Cropland Data Layer (CDL) for 2006 with CDL for...

Description: The 2 principle and the unbiased predictive risk estimator are used to determine optimal regularization parameters in the context of 3-D focusing gravity inversion with the minimum support stabilizer. At each iteration of the focusing inversion the minimum support stabilizer is determined and then the fidelity term is updated using the standard form transformation. Solution of the resulting Tikhonov functional is found efficiently using the singular value decomposition of the transformed model matrix, which also provides for efficient determination of the updated regularization parameter each step. Experimental 3-D simulations using synthetic data of a dipping dike and a cube anomaly demonstrate that both parameter estimation techniques outperform the Morozov discrepancy principle for determining the regularization parameter. Smaller relative errors of the reconstructed models are obtained with fewer iterations. Data acquired over the Gotvand dam site in the south-west of Iran are used to validate use of the methods for inversion of practical data and provide good estimates of anomalous structures within the subsurface.

Description: Global navigation satellite systems (GNSSs) have revealed that a mega-thrust earthquake that occurs in an island-arc trench system causes post-seismic crustal deformation. Such crustal deformation data have been interpreted by combining three mechanisms: afterslip, poroelastic rebound and viscoelastic relaxation. It is seismologically important to determine the contribution of each mechanism because it provides frictional properties between the plate boundaries and viscosity estimates in the asthenosphere which are necessary to evaluate the stress behaviour during earthquake cycles. However, the observation sites of GNSS are mostly deployed over land and can detect only a small part of the large-scale deformation, which precludes a clear separation of the mechanisms. To extend the spatial coverage of the deformation area, recent studies started to use satellite gravity data that can detect long-wavelength deformations over the ocean. To date, compared with theoretical models for calculating the post-seismic crustal deformation, a few models have been proposed to interpret the corresponding gravity variations. Previous approaches have adopted approximations for the effects of compressibility, sphericity and self-gravitation when computing gravity changes. In this study, a new spectral-finite element approach is presented to consider the effects of material compressibility for Burgers viscoelastic earth model with a laterally heterogeneous viscosity distribution. After the basic principles are explained, it is applied to the 2004 Sumatra–Andaman earthquake. For this event, post-seismic deformation mechanisms are still a controversial topic. Using the developed approach, it is shown that the spatial patterns of gravity change generated by the above three mechanisms clearly differ from one another. A comparison of the theoretical simulation results with the satellite gravity data obtained from the Gravity Recovery and Climate Experiment reveals that both afterslip and viscoelastic relaxation are occurring. Considering the spatial patterns in satellite gravity fields is an effective method for investigating post-seismic deformation mechanisms.

Description: We thank Metson et al. (1) for their addition to our paper (2). These authors raise an important point, and are definitely right in pointing out the global importance of phosphorous and the dominant role of the livestock industry in its use. Our omission of phosphorous from our calculations, which...

Description: Eshel et al. (1) quantify the land, irrigation water, and reactive nitrogen demands of feed production, and calculate a full life cycle of greenhouse gas emission estimates for each of the five major animal-based categories in the United States diet: dairy, beef, poultry, pork, and eggs. The authors find that...

Description: A recent paper (1) states that a cultural shift and a transformative change is needed that changes consumption patterns to reduce human pressure on the environment (the environmental footprint of humanity), keeping it within planetary boundaries. The excellent paper of Santi et al. (2) addresses one of the new forms...

Description: We strongly concur with Brush et al. (1) regarding the urgency for a new generation of studies (2), but reject claims that our findings are unsupported and our comparisons false, a misperception that could delay adequate academic and policy responses. First, spurious or not, it is not our interpretation that...

Description: Some of the major geothermal anomalies in central Europe are linked to tectonic structures within the top of crystalline basement, which modify strongly the top of this basement. Their assessment is a major challenge in exploration geophysics. Gravity has been proven to be suitable for the detection of mainly large scale lithological and structural inhomogeneities. Indeed, it is well known and proven by different wells that, for example, in northern Switzerland extended negative anomalies are linked to such structures. Due to depth limitation of wells, there vertical extension is often unknown. In this study, we have investigated the potential of gravity for the geometrical characterization of such basement structures. Our approach consists in the combination of the series of Butterworth filters, geological modelling and best-fitting between observed and computed residual anomalies. In this respect, filters of variable wavelength are applied to observed and computed gravity data. The geological model is discretized into a finite element mesh. Near-surface anomalies and the effect of the sedimentary cover were eliminated using cut-off wavelength of 10 km and geological and seismic information. We analysed the potential of preferential Butterworth filtering in a sensitivity study and applied the above mentioned approach to part of the Swiss molasses basin. Sensitivity analyses reveal that such sets of residual anomalies represents a pseudo-tomography revealing the distribution of different structures with depth. This finding allows for interpreting negative anomalies in terms of 3-D volumes. Best-fitting then permits determination of the most likely 3-D geometries of such basement structures. Our model fits both, geological observations and gravity: among 10 deep boreholes in the studied area, six reach the respective units and confirm our distribution of the negative (and positive) anomalies.

Description: Our fundamental message (1) is that under intense forms of intermittent flooding—a technique used to reduce methane emissions from rice farms (2)—emissions of nitrous oxide (N2O), a long-term climate forcer (Fig. 1), can be very high. Fig. 1. General understanding of climate impacts of rice farms under continuous flooding or...

Description: In PNAS, Kritee et al. (1) report extremely high nitrous oxide (N2O) fluxes from rice paddy fields with intermittent irrigation and alternate wetting and drying (AWD) and conclude that N2O can be reduced by up to 90%—with nitrogen management not playing a central role. However, we believe that this conclusion...

Description: Karplus et al. (1) raise the concern of potential data manipulation by coal-fired power plants in China by comparing Continuous Emissions Monitoring Systems (CEMS) data with NASA satellite data. Since the two sources of data are not directly comparable, the comparison in the paper is empowered by a policy shock...

Description: The central concern in ref. 1 that the “timing of the policy shock is incorrect for key regions” is false. We received confirmation from the Ministry of Environmental Protection’s representative who authored the policy document issued on February 27, 2013. We confirmed that by July 1, 2014, in the key...

Description: In PNAS, Meyer et al. (1) analyze whether exclusion devices in trawl nets contributed to New Zealand sea lion (NZSL; Phocarctos hookeri) population decline at the Auckland Islands. We refute the primary conclusion from their correlative assessment: that annual pup production changes (as a measure of population size) were primarily...

Description: In Meyer et al. (1), we fitted a Bayesian state-space Gompertz population model to assess whether the implementation of sea lion exclusion devices (SLEDs) in trawl fisheries has served to protect New Zealand sea lions (NZSLs) or obscured ongoing mortality. We found strong evidence of obscured ongoing mortality. Roberts et...

Description: A new analytical method for the computation of a truncated series of solid spherical harmonic coefficients (HCs) from data on a spheroid (i.e. an oblate ellipsoid of revolution) is derived, using a transformation between surface and solid spherical HCs. A two-step procedure is derived to extend this transformation beyond degree and order (d/o) 520. The method is compared to the Hotine–Jekeli transformation in a numerical study based on the EGM2008 global gravity model. Both methods are shown to achieve submicrometre precision in terms of height anomalies for a model to d/o 2239. However, both methods result in spherical harmonic models that are different by up to 7.6 mm in height anomalies and 2.5 mGal in gravity disturbances due to the different coordinate system used. While the Hotine–Jekeli transformation requires the use of an ellipsoidal coordinate system, the new method uses only spherical polar coordinates. The Hotine–Jekeli transformation is numerically more efficient, but the new method can more easily be extended to cases where (a linear combination of) normal derivatives of the function under consideration are given on the surface of the spheroid. It therefore provides a solution to many types of ellipsoidal boundary-value problems in the spectral domain.

Description: We explore Earth's elastic deformation response to ocean tidal loading (OTL) using kinematic Global Positioning System (GPS) observations and forward-modelled predictions across South America. Harmonic coefficients are extracted from up to 14 yr of GPS-inferred receiver locations, which we estimate at 5 min intervals using precise point positioning. We compare the observed OTL-induced surface displacements against predictions derived from spherically symmetric, non-rotating, elastic and isotropic (SNREI) Earth models. We also compare sets of modelled predictions directly for various ocean-tide and Earth-model combinations. The vector differences between predicted displacements computed using separate ocean-tide models reveal uniform-displacement components common to all stations in the South America network. Removal of the network-mean OTL-induced displacements from each site substantially reduces the vector differences between observed and predicted displacements. We focus on the dominant astronomical tidal harmonics from three distinct frequency bands: semidiurnal (M 2 ), diurnal (O 1 ) and fortnightly (M f ). In each band, the observed OTL-induced surface displacements strongly resemble the modelled displacement-response patterns, and the residuals agree to about 0.3 mm or better. Even with the submillimetre correspondence between observations and predictions, we detect regional-scale spatial coherency in the final set of residuals, most notably for the M 2 harmonic. The spatial coherency appears relatively insensitive to the specific choice of ocean-tide or SNREI-Earth model. Varying the load model or 1-D elastic structure yields predicted OTL-induced displacement differences of order 0.1 mm or less for the network. Furthermore, estimates of the observational uncertainty place the noise level below the magnitude of the residual displacements for most stations, supporting our interpretation that random errors cannot account for the entire misfit. Therefore, the spatially coherent residuals may reveal deficiencies in the a priori SNREI Earth models. In particular, the residuals may indicate sensitivity to regional deviations from standard globally averaged Earth structure due to the presence of the South American craton.

Description: Tessum et al. (1) use state-of-the-art spatial models to evaluate electric vehicle (EV) environmental impacts. Unfortunately, in my view, the article’s assumptions and framing lead readers toward misguided conclusions. I believe that the decision to compare air quality with climate change dollar-for-dollar, invokes an inappropriate framing of competing with each...

Description: Planar faults are widely adopted during inversions to determine slip distributions and fault geometries using geodetic observations; however, little research has been conducted with respect to curved faults. We attribute this to the lack of an appropriate parameterized modelling method. In this paper, we present a curved-fault modelling method (CFMM) that describes a curved fault according to specific parameters, and we also develop a corresponding hybrid iterative inversion algorithm (HIIA) to perform inversions for parametric curved-fault geometries and slips. The results of the strike-component and dip-component synthetic tests show that a complex S-shaped fault surface and a circular slip distribution are successfully recovered, indicating the strong performance of the CFMM and HIIA methods. In addition, we describe and verify a scenario for determining the number of necessary geometrical parameters for the HIIA and examine the case study of the Wenchuan earthquake, which occurred on a complex listric fault surface. During the iteration process of the HIIA, both the fault geometry and slip distribution of the Beichuan and Pengguan faults converge to optimal values, indicating a Beichuan fault (BCF) model with a continuous listric shape and gradual steepening from the southwest to the northeast, which is highly consistent with geological survey results. Both the synthetic and real-world case studies show that the HIIA and the CMFF are superior to the conventional fault modelling method based on rectangular planes and that these models have the potential for use in more integrated research involving inversion studies, such as joint slip/curved-fault-geometry inversions that take into account data resolving power.

Description: A recent article in PNAS contained shocking assertions that carbon emissions “already have exceeded the critical level” for New Orleans (1). In this letter, we challenge how the analysis was applied to New Orleans and point out that this latest in a series of “New Orleans is doomed” reports actually...

Description: Globally gridded estimates of monthly-mean anomalies of terrestrial water storage (TWS) are estimated from the most recent GRACE release 05a of GFZ Potsdam in order to provide non-geodetic users a convenient access to state-of-the-art GRACE monitoring data. We use an ensemble of five global land model simulations with different physics and different atmospheric forcing to obtain reliable gridded scaling factors required to correct for spatial leakage introduced during data processing. To allow for the application of this data-set for large-scale monitoring tasks, model validation efforts, and subsequently also data assimilation experiments, globally gridded estimates of TWS uncertainties that include (i) measurement, (ii) leakage and (iii) re-scaling errors are provided as well. The results are generally consistent with the gridded data provided by Tellus, but deviate in some basins which are largely affected by the uncertainties of the model information required for re-scaling, where the approach based on the median of a small ensemble of global land models introduced in this paper leads to more robust results.

Description: Regional recovery of the disturbing gravitational potential in the area of Central Europe from satellite gravitational gradients data is discussed in this contribution. The disturbing gravitational potential is obtained by inverting surface integral formulas which transform the disturbing gravitational potential onto disturbing gravitational gradients in the spherical local north-oriented frame. Two numerical approaches that solve the inverse problem are considered. In the first approach, the integral formulas are rigorously decomposed into two parts, that is, the effects of the gradient data within near and distant zones. While the effect of the near zone data is sought as an inverse problem, the effect of the distant zone data is synthesized from the global gravitational model GGM05S using spectral weights given by truncation error coefficients up to the degree 150. In the second approach, a reference gravitational field up to the degree 180 is applied to reduce and smooth measured gravitational gradients. In both cases we recovered the disturbing gravitational potential from each of the four well-measured gravitational gradients of the GOCE satellite separately as well as from their combination. Obtained results are compared with the EGM2008, DIR-r2, TIM-r2 and SPW-r2 global gravitational models. The best fit was achieved for EGM2008 and the second approach combining all four well-measured gravitational gradients with rms of 1.231 m 2  s –2 .

Description: We present efficient Fourier-domain algorithms for modelling gravity effects due to topographic masses. The well-known Parker's formula originally based on the standard fast Fourier transform (FFT) algorithm is modified by applying the Gauss–FFT method instead. Numerical precision of the forward and inverse Fourier transforms embedded in Parker's formula and its extended forms are significantly improved by the Gauss–FFT method. The topographic model is composed of two major aspects, the geometry and the density. Versatile geometric representations, including the mass line model, the mass prism model, the polyhedron model and smoother topographic models interpolated from discrete data sets using high-order splines or pre-defined by analytical functions, in combination with density distributions that vary both laterally and vertically in rather arbitrary ways following exponential or general polynomial functions, now can be treated in a consistent framework by applying the Gauss–FFT method. The method presented has been numerically checked by space-domain analytical and hybrid analytical/numerical solutions already established in the literature. Synthetic and real model tests show that both the Gauss–FFT method and the standard FFT method run much faster than space-domain solutions, with the Gauss–FFT method being superior in numerical accuracy. When truncation errors are negligible, the Gauss–FFT method can provide forward results almost identical to space-domain analytical or semi-numerical solutions in much less time.

Description: The gravity gradient tensor (GGT) has been increasingly used in practical applications, but the advantages and the disadvantages of the analysis of GGT components versus the analysis of the vertical component of the gravity field are still debated. We analyse the performance of joint inversion of GGT components versus separate inversion of the gravity field alone, or of one tensor component. We perform our analysis by inspection of the Picard Plot, a Singular Value Decomposition tool, and analyse both synthetic data and gradiometer measurements carried out at the Vredefort structure, South Africa. We show that the main factors controlling the reliability of the inversion are algebraic ambiguity (the difference between the number of unknowns and the number of available data points) and signal-to-noise ratio. Provided that algebraic ambiguity is kept low and the noise level is small enough so that a sufficient number of SVD components can be included in the regularized solution, we find that: (i) the choice of tensor components involved in the inversion is not crucial to the overall reliability of the reconstructions; (ii) GGT inversion can yield the same resolution as inversion with a denser distribution of gravity data points, but with the advantage of using fewer measurement stations.

Description: With development and stability teetering in many African and western Asian countries, new insights into barriers to development are always welcome. However, this field is full of false leads. One example is the recent claim of Cumming and von Cramon-Taubadel (1) that countries are attracted to one of two equilibrium...

Description: O’Sullivan (1) both misunderstands and misrepresents our analysis (2). We tested, and found support for, the hypothesis that national economies tend toward one of two attractors because of complex feedbacks among ecosystem services, economic growth, and population growth. We then explored the possible consequences of alternative feedback loops for global...

Description: Hoekstra and Mekonnen (1) offered a comprehensive assessment of global water use from the perspective of national production, consumption, and international trade. This study highlighted the often neglected fact that it is the demand for everyday goods and services that places the most pressure on the world’s freshwater systems. As such, strategies based on sustainable consumption and production are needed to reduce humanity’s burden on freshwater and to complement those strategies that operate at the watershed or water resource level.That said, environmental relevance must be taken into consideration if water footprints are to inform wise decision making and policy development....

Description: In their paper in PNAS, Rose et al. (1) applied a statistical model to estimate hurricane wind losses to wind turbines over a 20-y typical wind farm lifetime. They combined a county annual landfall frequency probability density function with a generalized extreme value (GEV) fit of maximum wind speeds to model the expected 20-y losses attributable to hurricane activity at four hypothetical offshore wind farm sites.We found one error and three major flaws in this approach, which lead to an order of magnitude overestimation of risk:i) The GEV fit parameters used by Rose et al. (1) can only be reproduced...

Description: This paper compares GRACE (Gravity Recovery and Climate Experiment) and ICESat (Ice, Cloud and land Elevation Satellite) observations to confirm whether the observed gravity increase in the Tibetan Plateau (TP) was primarily caused by lake storage gain, and comprehensively analyses the changing pattern of lake level over 2003–2009. An improved automated method was used to obtain lake-level changes and the underestimation of lake water storage was considered due to lake area expansion and lake density. The result demonstrates that GRACE recorded a mass gain (16.43 ± 1.65/11.79 ± 1.25 gt a –1 ) in the total/inner TP, of which lake storage increase accounts for (8.78 ± 0.75/7.53 ± 0.56 gt a –1 ) based on ICESat. The northwestern residual may be stored in new lakes and soil moisture as a result of net precipitation gain. According to the character of the lake-level changes, we divide the TP into four subregions. Generally, the changing pattern of lake level concurs with the distribution of precipitation, which is increasing in the inner TP and decreasing in the upstream area of the Indus and Brahmaputra Rivers. An excess of rainfall in the northeastern TP in the summer of 2005 and 2009 caused a simultaneous large increase in water level in many lakes. The correlation of lake changes with precipitation demonstrates that precipitation rather than glacial melt is the main cause of lake-level change in most places. Nonetheless, the meltwater is a considerable supplement for lakes near glaciers such as Selin Co and Nam Co, which partly explains why GRACE indicates a much weaker signal in this region.

Description: Reinmann and Hutyra (1) measured an increase in aboveground forest growth and biomass at temperate oak forest edges (0–10 m) compared with the interior (20–30 m). When scaling their results up to the region of southern New England, they obtained an increase in aboveground carbon (C) uptake (13%) and C...

Description: Despite the heavily fragmented nature of the world’s forests (1), the response of forest carbon (C) and nitrogen (N) dynamics to edge effects is understudied. Contrasting our findings that edge effects did not alter soil C and N storage of temperate forests within residential landscapes in New England (2), Remy...

Description: Traditional processing of Global Navigation Satellite System (GNSS) data using dedicated scientific software has provided the highest levels of positional accuracy, and has been used extensively in geophysical deformation studies. To achieve these accuracies a significant level of understanding and training is required, limiting their availability to the general scientific community. Various online GNSS processing services, now freely available, address some of these difficulties and allow users to easily process their own GNSS data and potentially obtain high quality results. Previous research into these services has focused on Continually Operating Reference Station (CORS) GNSS data. Less research exists on the results achievable with these services using large campaign GNSS data sets, which are inherently noisier than CORS data. Even less research exists on the quality of velocity fields derived from campaign GNSS data processed through online precise point positioning services. Particularly, whether they are suitable for geodynamic and deformation studies where precise and reliable velocities are needed. In this research, we process a very large campaign GPS data set (spanning 10 yr) with the online Jet Propulsion Laboratory Automated Precise Positioning Service. This data set is taken from a GNSS network specifically designed and surveyed to measure deformation through the central North Island of New Zealand. This includes regional CORS stations. We then use these coordinates to derive a horizontal and vertical velocity field. This is the first time that a large campaign GPS data set has been processed solely using an online service and the solutions used to determine a horizontal and vertical velocity field. We compared this velocity field to that of another well utilized GNSS scientific software package. The results show a good agreement between the CORS positions and campaign station velocities obtained from the two approaches. We discuss the implications of these results for how future GNSS campaign field surveys might be conducted and how their data might be processed.

Description: We have developed a method to estimate the geometry, location and densities of anomalies coming from 2-D gravity data based on compact gravity inversion technique. Compact gravity inversion is simple, fast and user friendly but severely depends on the number of model parameters, that is, by increasing the model parameters, the anomalies tend to concentrate near the surface. To overcome this ambiguity new weighting functions based on density contrast, depth, and compactness models have been introduced. Variable compactness factors have been defined here to get either a sharp or a smooth model based on the depth of the source or existence of prior information. Depth weighting derived from one station of gravity data whereas the effect of gravity data is 2-D and 3-D. To compensate this limitation an innovating weighting function namely kernel function has been introduced which multiplies with weight and compactness matrixes to yield a general model weighting function. The method is tested using three different sets of synthetic examples: a body at various depths (20, 40, 80 and 140 m), two bodies at the same depth but various distances to estimate lateral resolution and three bodies with negative and positive density contrast in different depths. The method is also applied to three real gravity data of Woodlawn massive sulphide body, sulphides mineralization of British Colombia and iron ore body of Missouri. The method produces solutions consistent with the known geologic attributes of the gravity sources, illustrating its potential practicality.

Description: This paper resurrects a version of Poisson's Partial Differential Equation (PDE) associated with the gravitational field at the Earth's surface and illustrates how the PDE possesses a capability to extract the mass density of Earth's topography from land-based gravity data. Herein, first we propound a theorem which mathematically introduces this version of Poisson's PDE adapted for the Earth's surface and then we use this PDE to develop a method of approximating the terrain mass density. Also, we carry out a real case study showing how the proposed approach is able to be applied to a set of land-based gravity data. In the case study, the method is summarized by an algorithm and applied to a set of gravity stations located along a part of the north coast of the Persian Gulf in the south of Iran. The results were numerically validated via rock-samplings as well as a geological map. Also, the method was compared with two conventional methods of mass density reduction. The numerical experiments indicate that the Poisson PDE at the Earth's surface has the capability to extract the mass density from land-based gravity data and is able to provide an alternative and somewhat more precise method of estimating the terrain mass density.

Description: Evaluating the significance of protected areas for biodiversity and ecosystem services is important for nature conservation. In a recent issue of PNAS, Xu et al. (1) present valuable information on provision of biodiversity and ecosystem services by China’s nature reserves. They conclude that reserves serve bird populations moderately well. However,...

Description: We thank Yang et al. (1) for their perspective. We are aware of the importance of coastal wetland protection for endangered migratory birds. Our paper in PNAS (2) focuses on the general representation of protected areas for endangered species (e.g., endangered birds) and ecosystem services. Thus, we did not emphasize...

Description: Blackman et al. (1) assess the forest cover impacts of providing indigenous Peruvian communities with formal title to land they have long inhabited. We applaud the authors’ use of high-quality forest change data and rigorous causal methods; both are critical gaps in the land tenure and forest change literature (2)....

Description: We thank Robinson et al. (1) for their thoughtful comments on our article (2). We agree with their main point, which is that our findings about the link between titling and forest cover change are context- and time-specific, and do not necessarily generalize to other countries and other periods. However,...

Description: Flores et al. (1) suggest that large Amazonian floodplains are vulnerable to fire and that a future, drier climate will trigger wide-spread conversion of floodplain forests into fire-dominated savanna. Furthermore, the authors argue that fires in fluvial networks will cascade through nonflooded communities and spearhead fire-induced change in the wider...

Description: Our recent findings that floodplain ecosystems harbor the most fragile forests of the Amazon (1) was seen by Schöngart et al. (2) as an oversimplification of a complex ecosystem. They argue that the majority of floodplain forests are associated with fertile soils, and should therefore be highly resilient. Indeed, the...

Description: Miller and Kleidon (1) study future global deployment of wind turbines. They use a general circulation model (GCM) with 2.8° resolution to simulate the electricity generation for different wind-power deployments using global constant installed capacity densities. Results from the simulations with the maximum electricity generation over land and over water...

Description: Badger and Volker (1) claim that our paper (2) incorrectly estimates the wind energy resource and underestimates it by more than 50%. However, a detailed reading of their work (3) reveals that their estimates are consistent with ours (and others; table 2 of ref. 2), yet their extrapolation to larger...

Description: By generating soil phytolith and charcoal data from a region of geoglyph construction in southwest Amazonia, Watling et al. (1) provide important evidence on a current debate over the scale and intensity of pre-Columbian modification of Amazonia (e.g., refs. 2–6). The clear evidence for human activity in their study region...

Description: The Moho surface can be determined according to isostatic theories, and among them, the recent Vening Meinesz-Moritz (VMM) theory of isostasy has been successfully applied for this purpose. In this paper, this method is studied from a theoretical prospective and its connection to the Airy–Heiskanen (AH) and Vening Meinesz original theories are presented. Jeffrey's inverse solution to isostasy is developed according to the recent developments of the VMM method and both are compared in similar situations. It is shown that they are generalizations of the AH model in a global and continuous domain. In the VMM spherical harmonic solution for Moho depth, the mean Moho depth contributes only to the zero-degree term of the series, while in Jeffrey's solution it contributes to all frequencies. In addition, the VMM spherical harmonic series is improved further so that the mean Moho can contribute to all frequencies of the solution. This modification makes the VMM global solution superior to the Jeffrey one, but in a global scale, the difference between both solutions is less than 3 km. Both solutions are asymptotically convergent and we present two methods to obtain smooth solutions for Moho from them.

Description: In a pioneering study, Wahr & Bergen developed the widely adopted, pseudo-normal mode framework for predicting the impact of anelastic effects on the Earth's body tides. Lau et al. have recently derived an extended normal mode treatment of the problem (as well as a minor variant of the theory known as the direct solution method) that makes full use of theoretical developments in free oscillation seismology spanning the last quarter century and that avoids a series of assumptions and approximations adopted in the traditional theory for predicting anelastic effects. There are two noteworthy differences between these two theories: (1) the traditional theory only considers perturbations to the eigenmodes of an elastic Earth, whereas the new theory augments this set of modes to include the relaxation modes that arise in anelastic behaviour; and (2) the traditional theory approximates the complex perturbation to the tidal Love number as a scaled version of the complex perturbation to the elastic moduli, whereas the new theory computes the full complex perturbation to each eigenmode. In this study, we highlight the above differences using a series of synthetic calculations, and demonstrate that the traditional theory can introduce significant error in predictions of the complex perturbation to the Love numbers due to anelasticity and the related predictions of tidal lag angles. For the simplified Earth models we adopt, the computed lag angles differ by ~20 per cent. The assumptions in the traditional theory have important implications for previous studies that use model predictions to correct observables for body tide signals or that analyse observations of body tide deformation to infer mantle anelastic structure. Finally, we also highlight the fundamental difference between apparent attenuation (i.e. attenuation inferred from observations or predicted using the above theories) and intrinsic attenuation (i.e. the material property investigated through experiments), where both are often expressed in terms of lag angles or Q –1 . In particular, we demonstrate the potentially significant (factor of two or more) bias introduced in estimates of Q –1 and its frequency dependence in studies that have treated Q –1 determined from tidal phase lags or measured experimentally as being equal. The observed or theoretically predicted lag angle (or apparent Q –1 ) differs from the intrinsic, material property due to inertia, self-gravity and effects associated with the energy budget. By accounting for these differences we derive, for a special case, an expression that accurately maps apparent attenuation predicted using the extended normal mode formalism of Lau et al. into intrinsic attenuation. The theory allows for more generalized mappings which may be used to robustly connect observations and predictions of tidal lag angles to results from laboratory experiments of mantle materials.

Description: We consider a new approach to both the forward and inverse problems in post-seismic deformation. We present a method for forward modelling post-seismic deformation in a self-gravitating, heterogeneous and compressible earth with a variety of linear and nonlinear rheologies. We further demonstrate how the adjoint method can be applied to the inverse problem both to invert for rheological structure and to calculate the sensitivity of a given surface measurement to changes in rheology or time-dependence of the source. Both the forward and inverse aspects are illustrated with several numerical examples implemented in a spherically symmetric earth model.

Description: The Seiland Igneous Province (SIP) is the largest complex of mafic and ultramafic intrusions in northern Fennoscandia intruded at ca . 580–560 Ma. The depth extent and the deep structure of the SIP are mainly unknown apart from three profiles modelled by gravity and refraction seismic data. Utilizing 3-D gravity modelling, a complex model of the deep subsurface structure of the SIP has been developed. The structure is presented in a multiprofile model ranging from the surface to the Moho. The mafic/ultramafic rocks of the SIP are modelled with densities of 3100 and 3300 kg m –3 , the surrounding rocks by densities of 2700 and 2900 kg m –3 for upper and lower crust, respectively. This density model explains the pronounced positive Bouguer gravity anomaly of up to 100 mGal above background. Its minimum volume is estimated from the subsurface model to 17 000 km 3 and as such we revise downwards the earlier estimations of 25 000 km 3 . The new subsurface model suggests that most of the SIP has a thickness between 2 and 4 km. An area with roots in an annular pattern is found and two deep-reaching roots have been identified located below the islands of Seiland and Sørøy. The depth of these roots is estimated to approximatively 9 km. The SIP is presently interpreted to be in the Caledonian Kalak Nappe Complex and the roots depth constrains its minimum thickness which is larger than earlier estimated. Furthermore, the rather undisturbed shape of the annular root pattern indicates that the SIP has not been subjected to strong tectonic reworking during the Caledonian orogeny.

Description: On 2008 October 5, a magnitude 6.6 earthquake struck the eastern termination of the intermontane Alai valley between the southern Tien Shan and the northern Pamir of Kyrgyzstan. The shallow thrust earthquake occurred in the footwall of the Main Pamir thrust, where the Pamir orogen is colliding with the southern Tien Shan mountains. We measure the coseismic surface displacements using SAR (Synthetic Aperture RADAR) data; the results show clear gradients in the vertical and horizontal directions along a complex pattern of surface ruptures and active faults. To integrate and to interpret these observations in the context of the regional tectonics, we complement the SAR data analysis with seismological data and geological field observations. While the main moment release of the Nura earthquake appears to be on the Pamir Frontal thrust, the main surface displacements and surface rupture occurred in the footwall along the NE–SW striking Irkeshtam fault. With InSAR data from ascending and descending tracks along with pixel offset measurements, we model the Nura earthquake source as a segmented rupture. One fault segment corresponds to high-angle brittle faulting at the Pamir Frontal thrust and two more fault segments show moderate-angle and low-friction thrusting at the Irkeshtam fault. Our integrated analysis of the coseismic deformation argues for rupture segmentation and strain partitioning associated to the earthquake. It possibly activated an orogenic wedge in the easternmost segment of the Pamir-Alai collision zone. Further, the style of the segmentation may be associated with the presence of Palaeogene evaporites.

Description: The terrestrial reference frame is a cornerstone for modern geodesy and its applications for a wide range of Earth sciences. The underlying assumption for establishing a terrestrial reference frame is that the motion of the solid Earth's figure centre relative to the mass centre of the Earth system on a multidecadal timescale is linear. However, past international terrestrial reference frames (ITRFs) showed unexpected accelerated motion in their translation parameters. Based on this underlying assumption, the inconsistency of relative origin motions of the ITRFs has been attributed to data reduction imperfection. We investigated the impact of surface mass loading from atmosphere, ocean, snow, soil moisture, ice sheet, glacier and sea level from 1983 to 2008 on the geocentre variations. The resultant geocentre time-series display notable trend acceleration from 1998 onward, in particular in the z -component. This effect is primarily driven by the hydrological mass redistribution in the continents (soil moisture, snow, ice sheet and glacier). The acceleration is statistically significant at the 99 per cent confidence level as determined using the Mann–Kendall test, and it is highly correlated with the satellite laser ranging determined translation series. Our study, based on independent geophysical and hydrological models, demonstrates that, in addition to systematic errors from analysis procedures, the observed non-linearity of the Earth-system behaviour at interannual timescales is physically driven and is able to explain 42 per cent of the disparity between the origins of ITRF2000 and ITRF2005, as well as the high level of consistency between the ITRF2005 and ITRF2008 origins.

Description: The article by Simonit and Perrings (1) describes development of a spatially explicit model of ecosystem service flows associated with reforestation of the Panama Canal watershed. Critical to their study are estimates of water flows, particularly during dry seasons. We have two concerns. First, we agree with Ogden and Stallard’s...

Description: This paper presents a novel mathematical reformulation of the theory of the free wobble/nutation of an axisymmetric reference earth model in hydrostatic equilibrium, using the linear momentum description. The new features of this work consist in the use of (i) Clairaut coordinates (rather than spherical polars), (ii) standard spherical harmonics (rather than generalized spherical surface harmonics), (iii) linear operators (rather than J-square symbols) to represent the effects of rotational and ellipticity coupling between dependent variables of different harmonic degree and (iv) a set of dependent variables all of which are continuous across material boundaries. The resulting infinite system of coupled ordinary differential equations is given explicitly, for an elastic solid mantle and inner core, an inviscid outer core and no magnetic field. The formulation is done to second order in the Earth's ellipticity. To this order it is shown that for wobble modes (in which the lowest harmonic in the displacement field is degree 1 toroidal, with azimuthal order m  = ±1), it is sufficient to truncate the chain of coupled displacement fields at the toroidal harmonic of degree 5 in the solid parts of the earth model. In the liquid core, however, the harmonic expansion of displacement can in principle continue to indefinitely high degree at this order of accuracy. The full equations are shown to yield correct results in three simple cases amenable to analytic solution: a general earth model in rigid rotation, the tiltover mode in a homogeneous solid earth model and the tiltover and Chandler periods for an incompressible homogeneous solid earth model. Numerical results, from programmes based on this formulation, are presented in part II of this paper.

Description: Numerical solutions are presented for the formulation of the linear momentum description of Earth's dynamics using Clairaut coordinates. We have developed a number of methods to integrate the equations of motion, including starting at the Earth's centre of mass, starting at finite radius and separating the displacement associated with the primary rigid rotation. We include rotation and ellipticity to second order up to spherical harmonic T $_5^m$ , starting with the primary displacement T $_1^m$ with m  = ±1. We are able to confirm many of the previous results for models PREM (with no surface ocean) and 1066A, both in their original form and with neutrally stratified liquid cores. Our period search ranges from the near-seismic band [0.1 sidereal days (sd)] to 3500 sd, within which we have identified the four well-known wobble-nutation modes: the Free Core Nutation (retrograde) at –456 sd, the Free Inner Core Nutation (FICN, prograde) at 468 sd, the Chandler Wobble (prograde) at 402 sd, and the Inner Core Wobble (ICW, prograde) at about 2842 sd (7.8 yr) for neutral PREM. The latter value varies significantly with earth model and integration method. In addition we have verified to high accuracy the tilt-over mode at 1 sd within a factor 10 –6 . In an exhaustive search we found no additional near-diurnal wobble modes that could be identified as nutations. We show that the eigenfunctions for the as-yet-unidentified ICW are extremely sensitive to the details of the earth model, especially the core stability profile and there is no well-defined sense of its wobble relative to the mantle. Calculations are also done for a range of models derived from PREM with homogeneous layers, as well as with incompressible cores. For this kind of model the ICW ceases to have just a simple IC rigid motion when the fluid compressibility is either unchanged or multiplied by a factor 10; in this case the outer core exhibits oscillations that arise from an unstable fluid density stratification. For the FICN our results for the truncation at harmonic T 5 show less change from the T 3 truncation than a similar result reported elsewhere. Finally, we give a thorough discussion of the complete spectrum of the characteristic determinant including the location of poles and non-wobble gravity modes, and discuss in general the dynamics of the inviscid core at periods short compared to those involved in the geodynamo.

Description: Considering the drawback of existing global weighted mean temperature model, this paper uses 2006–2012 NCEP reanalysis data to establish global empirical model for mapping zenith wet delays onto precipitable water—GTm_N, takes the influence of half-year periodicity of Tm into account when modelling and estimate the initial phase of each cycle. In order to evaluate the precision of GTm_N, we use three different Tm data sets from the NCEP during 2013, 650 radiosonde stations and COSMIC occultation in 2011 to test this model. The results show that GTm_N has higher precision in both ocean and continental area in every moment of every day. The accuracy of GTm_N is higher than Bevis formulas and GTm_II models. In addition, the actual surface temperature is not required in GTm_N model, and it will have wide application in GPS meteorology.

Description: As a result of Powell and Cocke’s letter (1) regarding our paper on the hurricane risk to offshore wind turbines (2), we have reviewed and updated some of our analysis. However, our conclusion remains that wind turbines in hurricane-prone areas face extreme wind conditions significantly different from those for which offshore wind turbines are currently designed; some of this risk can be mitigated through engineered mechanisms:i) Powell and Cocke (1) observe that we interpreted the “maximum sustained wind speed” of US hurricanes as 10-minute averages when they are actually 1-min averages. We recalculated our results with this correction and have...

Description: In their letter, Leifeld et al. (1) argue that our metaanalysis to identify differences in soil organic carbon (SOC) between organic (OF) and nonorganic farming [conventional farming (CF)] (2) selected CF systems that were nonrepresentative. This was not the case. We included data from all available pairwise field comparisons between...

Description: Agricultural management strongly affects soil organic carbon (C), as shown by numerous long-term experiments (1). Practices known to increase soil C include adding organic manures and including grassland in crop rotations. Their effect on C is related to the net primary productivity of the agroecosystem and the fraction of organic...

Description: Kline et al. (1) pose a series of “what-if” scenarios intended to cast doubt on our (2) findings. These scenarios arise from a critical misreading of our paper and misinterpretation of the US Department of Agriculture’s Cropland Data Layer (CDL). First, we did not include alfalfa (Medicago sativa), a perennial...

Description: Simonit and Perrings (1) endeavor to assess effects of land use decisions on hydrological behavior of the Panama Canal watershed. Although this is a worthy study topic, the authors used the US Department of Agriculture–Natural Resources Conservation Service Curve Number (CN) model to predict hydrologic response. Modeling of land-management effects...

Description: We absolutely and unequivocally refute the criticisms of Steward et al. (1) by Butler et al. (2) from the Kansas Geological Survey (KGS), which are based on several apparent misconceptions that are straightforward to address.i)Groundwater use rates continue: The letter states that “There is a systematic deviation (authors’ calculated use...

Description: Ogden and Stallard (1) argue that our estimates of the effect of reforestation on runoff in the Panama Canal watershed (2) are invalid because we use a particular phenomenological runoff model: the US Department of Agriculture–Natural Resources Conservation Service Curve Number (CN) model. The authors claim that the CN model,...

Description: White and Hall (1) suggest that removing animals from US agriculture would create a food supply incapable of supporting the United States population’s nutritional requirements and increase nutritional deficiencies compared with the current food system. However, their analysis suffers from an uncritical use of nutritional values and optimization algorithms, and...

Description: White and Hall (1) recently assessed the contribution of animal-based agriculture to greenhouse gas emissions (GHGE) and nutrient provision of the United States society. Unfortunately, their study provides a misleading message. Reducing animal-based food is needed to meet climate goals and future global food demands (2). Hence, it is important...

Description: In “Nutritional and greenhouse gas impacts of removing animals from US agriculture,” White and Hall (1) imagine a future without animal agriculture but fail to address perhaps the single most influential aspect of livestock on US agriculture: land use for feed crops. The authors unrealistically assume that without livestock, Americans...

Description: Letters by Van Meerbeek and Svenning (1), Emery (2), and Springmann et al. (3), regarding the study by White and Hall (4), express concerns regarding assumptions of land allocation and proposed dietary characteristics. The authors (1–3) also present individual, diverse concerns. We attempt to address each concern below. Land Allocation...

Description: Carleton (1) established that high temperature has caused 59,300 suicides during 1987–2013 in India and for temperatures above 20 °C, a 1 °C increase in a single day’s temperature causes ∼70 suicides in the country. The author argues that high temperature stimulates suicides through a crop-damaging agricultural channel as the...

Description: In Carleton (1) I demonstrate that increases in growing-season temperatures in India contribute to rising suicide rates. In secondary analysis, I show correlational evidence of an agricultural channel, in which heat damages crops and crop losses induce suicide. The concerns raised by Murari et al. (2), Das (3), and Plewis...

Description: Arguments about the causes of Indian farmer suicides have been widely aired in recent years, both in the media and in academic papers. It is plausible to suppose, as Carleton (1) does, that climate change has an indirect causal effect on the farmer suicide rate via reduced crop yields and...

Description: Estimating the relief of the Moho from gravity data is a computationally intensive nonlinear inverse problem. What is more, the modelling must take the Earths curvature into account when the study area is of regional scale or greater. We present a regularized nonlinear gravity inversion method that has a low computational footprint and employs a spherical Earth approximation. To achieve this, we combine the highly efficient Bott's method with smoothness regularization and a discretization of the anomalous Moho into tesseroids (spherical prisms). The computational efficiency of our method is attained by harnessing the fact that all matrices involved are sparse. The inversion results are controlled by three hyperparameters: the regularization parameter, the anomalous Moho density-contrast, and the reference Moho depth. We estimate the regularization parameter using the method of hold-out cross-validation. Additionally, we estimate the density-contrast and the reference depth using knowledge of the Moho depth at certain points. We apply the proposed method to estimate the Moho depth for the South American continent using satellite gravity data and seismological data. The final Moho model is in accordance with previous gravity-derived models and seismological data. The misfit to the gravity and seismological data is worse in the Andes and best in oceanic areas, central Brazil and Patagonia, and along the Atlantic coast. Similarly to previous results, the model suggests a thinner crust of 30–35 km under the Andean foreland basins. Discrepancies with the seismological data are greatest in the Guyana Shield, the central Solimões and Amazonas Basins, the Paraná Basin, and the Borborema province. These differences suggest the existence of crustal or mantle density anomalies that were unaccounted for during gravity data processing.

Description: Geophysical parameters of the deep Earth's interior can be evaluated through the resonance effects associated with the core and inner-core wobbles on the forced nutations of the Earth's figure axis, as observed by very long baseline interferometry (VLBI), or on the diurnal tidal waves, retrieved from the time-varying surface gravity recorded by superconducting gravimeters (SGs). In this paper, we inverse for the rotational mode parameters from both techniques to retrieve geophysical parameters of the deep Earth. We analyse surface gravity data from 15 SG stations and VLBI delays accumulated over the last 35 yr. We show existing correlations between several basic Earth parameters and then decide to inverse for the rotational modes parameters. We employ a Bayesian inversion based on the Metropolis–Hastings algorithm with a Markov-chain Monte Carlo method. We obtain estimates of the free core nutation resonant period and quality factor that are consistent for both techniques. We also attempt an inversion for the free inner-core nutation (FICN) resonant period from gravity data. The most probable solution gives a period close to the annual prograde term (or S 1 tide). However the 95 per cent confidence interval extends the possible values between roughly 28 and 725 d for gravity, and from 362 to 414 d from nutation data, depending on the prior bounds. The precisions of the estimated long-period nutation and respective small diurnal tidal constituents are hence not accurate enough for a correct determination of the FICN complex frequency.

Description: We evaluate the benefit of different global geophysical loading products on the internal scatter of GPS position time-series from 240 globally distributed sites. We focus on the non-tidal atmospheric pressure loading predicted from NASA's Modern-Era Retrospective Analysis for Research and Applications (MERRA-NATML) and the European Center for Medium-Range Weather Forecasts operational model (ECMWF-NATML), non-tidal ocean loading predicted from the Ocean Model for Circulation and Tides model (OMCT-NTOL), and the continental water storage loading predicted from the MERRA model (MERRA-CWSL) and the GFZ's Land Surface Discharge Model (LSDM-CWSL), respectively. The result shows that the root mean square (RMS) discrepancy of different CWSL models is larger than that of NATML models in the vertical component due to the varying model parameters and input data choices. We discuss the performance of different loading models and their combination to reduce the weighted RMS of GPS up-coordinates. MERRA-NATML & OMCT-NTOL & MERRA-CWSL reduced the weighted RMS (WRMS) in 96 per cent (JPL solutions) and 86 per cent (SOPAC solutions) of the cases, and ECMWF-NATML & OMCT-NTOL & LSDM-CWSL reduced the WRMS in 95 per cent (JPL solutions) and 88 per cent (SOPAC solutions) of the cases. The result shows that local effects and technical uncertainties in GPS time-series hamper the meaningful comparison between GPS observations and mass loading models. Hence, simply using the RMS of the time-series as the assessment criteria may lead to biased comparison results. Nonetheless, we give a detailed comparison (differences in phase and amplitude at seasonal timescales) for eight representative stations located adjacent to great rivers, lakes and reservoirs. We find that LSDM can provide a complementary model to study the small-scale hydrological loading like loading extremes along river channels. However, such small-scale hydrological loading effects are still instable to be modelled in some regions with its current accuracy. Finally, we discuss the impacts of mass loading corrections on the velocity and noise estimates. The noise reductions have the consistent performance as WRMS reductions for most sites, whereas some sites have their noise increased even though GPS signal WRMS is decreased there, suggesting that our posterior correction is potentially feasible, but not sufficient.

Description: Although an amount of hydrocarbon has been discovered in the West Korea Bay Basin (WKBB), located in the North Korean offshore area, geophysical investigations associated with these hydrocarbon reservoirs are not permitted because of the current geopolitical situation. Interpretation of satellite-derived potential field data can be alternatively used to image the 3-D density distribution in the sedimentary basin associated with hydrocarbon deposits. We interpreted the TRIDENT satellite-derived gravity field data to provide detailed insights into the spatial distribution of sedimentary density structures in the WKBB. We used 3-D forward density modelling for the interpretation that incorporated constraints from existing geological and geophysical information. The gravity data interpretation and the 3-D forward modelling showed that there are two modelled areas in the central subbasin that are characterized by very low density structures, with a maximum density of about 2000 kg m –3 , indicating some type of hydrocarbon reservoir. One of the anticipated hydrocarbon reservoirs is located in the southern part of the central subbasin with a volume of about 250 km 3 at a depth of about 3000 m in the Cretaceous/Jurassic layer. The other hydrocarbon reservoir should exist in the northern part of the central subbasin, with an average volume of about 300 km 3 at a depth of about 2500 m.

Description: We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/ r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.

Description: Moment accumulation rate (also referred to as moment deficit rate) is a fundamental quantity for evaluating seismic hazard. The conventional approach for evaluating moment accumulation rate of creeping faults is to invert for the slip distribution from geodetic measurements, although even with perfect data these slip-rate inversions are non-unique. In this study, we show that the slip-rate versus depth inversion is not needed because moment accumulation rate can be estimated directly from surface geodetic data. We propose an integral approach that uses dense geodetic observations from Interferometric Synthetic Aperture Radar (InSAR) and the Global Positioning System (GPS) to constrain the moment accumulation rate. The moment accumulation rate is related to the integral of the product of the along-strike velocity and the distance from the fault. We demonstrate our methods by studying the Creeping Section of the San Andreas fault observed by GPS and radar interferometry onboard the ERS and ALOS satellites. Along-strike variation of the moment accumulation rate is derived in order to investigate the degree of partial locking of the Creeping Section. The central Creeping Segment has a moment accumulation rate of 0.25–3.1  x  10 15 Nm yr –1 km –1 . The upper and lower bounds of the moment accumulation rates are derived based on the statistics of the noise. Our best-fitting model indicates that the central portion of the Creeping Section is accumulating seismic moment at rates that are about 5 per cent to 23 per cent of the fully locked Carrizo segment that will eventually be released seismically. A cumulative moment budget calculation with the historical earthquake catalogue ( M  〉 5.5) since 1857 shows that the net moment deficit at present is equivalent to a M w 6.3 earthquake.

Description: Sibhatu et al. (1) elegantly show how access to markets influences the relationship between production and consumption diversity at the household level. This confirms similar findings from other recent studies (2) but lacks discussion of three major points: (i) landscape diversity and local markets, (ii) multifunctionality of diversity, and (iii)...

Description: The increasing availability of geophysical models of the Earth's lithosphere and mantle has generated renewed interest in computation of theoretical gravity effects at global and regional scales. At the same time, the increasing availability of gravity gradient anomalies derived from satellite measurements, such as those provided by GOCE satellite, requires mathematical methods that directly model the gravity gradient anomalies in the same reference frame as GOCE gravity gradients. Our main purpose is to interpret these anomalies in terms of source and density distribution. Numerical integration methods for calculating gravity gradient values are generally based on a mass discretization obtained by decomposing the Earth's layers into a finite number of elementary solid bodies. In order to take into account the curvature of the Earth, spherical prisms or ‘tesseroids’ have been established unequivocally as accurate computation tools for determining the gravitational effects of large-scale structures. The question which then arises from, is whether gravity calculation methods using spherical prisms remain valid when factoring in the ellipticity of the Earth. In the paper, we outline a comprehensive method to numerically compute the complete gravity field with the help of the Gauss–Legendre quadrature involving ellipsoidal shaped prisms. The assessment of this new method is conducted by comparison between the gravity gradient values of simple sources obtained by means of numerical and analytical calculations, respectively. A comparison of the gravity gradients obtained from PREM and LITHO1.0 models using spherical- and ellipsoidal-prism-based methods is also presented. Numerical results indicate that the error on gravity gradients, caused by the use of the spherical prism instead of its ellipsoidal counterpart to describe an ellipsoidally shaped Earth, is useful for a joint analysis with those deduced from GOCE satellite measurements. Provided that a suitable scaling of prism densities has been performed, the spherical approximation error at GOCE height hardly reaches 1 mE for the entire Earth's lithosphere. The error attains 6 mE at a peak for a complete modeling of the Earth, from the crust down to the internal core.

Description: In their letter, Remans et al. (1) argue that our study (2) on the relationship between farm production diversity and household dietary diversity confirms earlier research but lacks discussion of scale and environmental aspects. Indeed, our findings are largely consistent with recent case studies from particular settings, but they challenge...

Description: This paper presents efficient numerical schemes for 3-D gravity field inversion. We propose a 2-D multilayer model to approximate a 3-D density distribution, and prove that the solution of the multilayer model will converge to the discretized 3-D solution. Differed from the conventional fast Fourier transform (FFT) based methods in which FFT is applied to the kernel, the proposed approach directly generates the Block-Toeplitz Toeplitz-Block (BTTB) structure by discretizing the multilayer model and the BTTB matrix is embedded into a Block-Circulant Circulant-Block (BCCB) matrix such that FFT can be utilized. In this approach, both regularization and optimal pre-conditioning operator can be constructed in the form of BTTB matrix. Consequently, very efficient solvers can be developed, and tremendous reduction in storage requirement and computing time can be achieved. To validate the new approach, numerical simulations using synthetic and real field data are reported, and numerical analysis is carried out for the inversion problems. Based on this study, we conclude that the proposed methods are capable of performing large-scale 3-D density inversions with a modest computing resource.

Description: In this study, we propose a method to determine dislocation Love numbers using co-seismic gravity changes from GRACE measurements. First, we present an observation equation to model GRACE observations taking into account the effect of ocean water mass redistribution. The L-curve method was used to determine the regulation parameter in the inversion of the geopotential dislocation Love numbers constrained by an a priori preliminary reference Earth (PREM) model. Then, the GRACE data error was estimated in the study area to evaluate the uncertainty of our inversion, and our inverted Love numbers are significantly deviated from the PREM ones even the uncertainty is considered. Finally, GRACE data observed for the 2011 Tohoku-Oki earthquake ( M w  = 9.0) were used to estimate the gravity dislocation Love numbers, considering three different fault-slip models. The results show that the inverted dislocation Love numbers deviate from PREM model, especially for $k_{l1}^{32}$ and $k_{l0}^{33} - k_{l0}^{22}$ , which indicates that the inverted dislocation Love numbers can reflect the local structure that is different from the global average. This inconsistency is possibly because that the cold denser oceanic slab dives from the Japanese Trench into the softer asthenosphere, and then changes the local density here higher than the global average. And with these sets of Love numbers, we can invert for more accurate fault model and analyse focal rupture mechanism when some other earthquake in this area occurs in the future. This study provides a new approach to invert for dislocation Love numbers linked with local geological information.

Description: The intra-plate deformation of the Upper Rhine Graben (URG) located in Central Europe is investigated using geodetic measurement techniques. We present a new approach to calculate a combined velocity field from InSAR, levelling and GNSS measurements. As the expected tectonic movements in the URG area are small (less than 1 mm a –1 ), the best possible solutions for linear velocity rates from single-technique analyses are estimated in a first step. Second, we combine the velocity rates obtained from InSAR (line of sight velocity rates in ascending and descending image geometries), levelling (vertical velocity rates) and GNSS (horizontal velocity rates) using least-squares adjustment (LSA). Focusing on the Northern URG area, we analyse SAR data on four different image stacks (ERS ascending, ERS descending, Envisat ascending, Envisat descending) using the Persistent Scatterer (PS) approach. The linear velocity rates in ascending and descending image geometries, respectively, are estimated in an LSA from joint time-series analysis of ERS and Envisat data. Vertical velocity rates from levelling are obtained from a consistent adjustment of more than 40 000 measured height differences using a kinematic displacement model. Horizontal velocity rates in east and north direction are calculated from a time-series analysis of daily coordinate estimates at 76 permanently operating GNSS sites in the URG region. As the locations, at which the measurement data of PS-InSAR, levelling and GNSS reside, do not coincide, spatial interpolation is needed during several steps of the rigorous processing. We use Ordinary Kriging to interpolate from a given set of data points to the locations of interest with a special focus on the modeling and propagation of errors. The final 3-D velocity field is calculated at a 200 m grid, which carries values only close to the location of PS points, resulting in a mean horizontal and vertical precision of 0.30 and 0.13 mm a –1 , respectively. The vertical component of the combined velocity field shows a significant subsidence of about 0.5 mm a –1 in the northern part of the graben coinciding with a well-known quaternary basin structure. Horizontal displacement rates of up to 0.8 mm a –1 in southeast direction are observed outside the graben, in reasonable alignment with the average direction of maximum horizontal stress. Within the graben, the velocity directions rotate toward east in the non-subsiding part, while an opposite trend is observed in the subsiding part of the graben. The complexities of the observed velocity field are compatible to the geomechanical situation in our investigation area which is characterized by a transition from a restraining to a releasing bend setting. Glacial isostatic adjustment is another potential source influencing the observed velocity field, as well as anthropogenic signals due to mining, oil exploration and groundwater usage that have been identified in some places.

Description: The measurement of ongoing ice-mass loss and associated melt water contribution to sea-level change from regions such as West Antarctica is dependent on a combination of remote sensing methods. A key method, the measurement of changes in Earth's gravity via the GRACE satellite mission, requires a potentially large correction to account for the isostatic response of the solid Earth to ice-load changes since the Last Glacial Maximum. In this study, we combine glacial isostatic adjustment modelling with a new GPS dataset of solid Earth deformation for the southern Antarctic Peninsula to test the current understanding of ice history in this region. A sufficiently complete history of past ice-load change is required for glacial isostatic adjustment models to accurately predict the spatial variation of ongoing solid Earth deformation, once the independently-constrained effects of present-day ice mass loss have been accounted for. Comparisons between the GPS data and glacial isostatic adjustment model predictions reveal a substantial misfit. The misfit is localized on the southwestern Weddell Sea, where current ice models under-predict uplift rates by approximately 2 mm yr –1 . This under-prediction suggests that either the retreat of the ice sheet grounding line in this region occurred significantly later in the Holocene than currently assumed, or that the region previously hosted more ice than currently assumed. This finding demonstrates the need for further fieldwork to obtain direct constraints on the timing of Holocene grounding line retreat in the southwestern Weddell Sea and that GRACE estimates of ice sheet mass balance will be unreliable in this region until this is resolved.

Description: Oron (1) argues that our study (2) uses “inappropriate” methods and is framed in a way that leads “readers toward misguided conclusions.” Both of these arguments are misplaced and seem more focused on some media coverage of our article than on our article itself. Oron’s (1) specific critiques do not...

Description: Density is a key driver of tectonic processes, but it is a difficult property to define well in the lithosphere because the gravity method is non-unique, and because converting to density from seismic velocity models, themselves non-unique, is also highly uncertain. Here we use a new approach to define the lithospheric density field of Australia, covering from 100°E to 165°E, from 5°N to 55°S and from the crust surface to 300 km depth. A reference model was derived primarily from the recently released Australian Seismological Reference Model, and refined further using additional models of sedimentary basin thickness and crustal thickness. A novel form of finite-element method based deterministic gravity inversion was applied in geodetic coordinates, implemented within the open-source escript modelling environment. Three spatial resolutions were modelled: half-, quarter- and eighth-degree in latitude and longitude, with vertical resolutions of 5, 2.5 and 1.25 km, respectively. Parameter sweeps for the key inversion regularization parameters show that parameter selection is not scale dependent. The sweep results also show that finer resolutions are more sensitive to the uppermost crust, but less sensitive to the mid- to lower-crust and uppermost mantle than lower resolutions. All resolutions show similar sensitivity below about 100 km depth. The final density model shows that Australia's lithospheric density field is strongly layered but also has large lateral density contrasts at all depths. Within the continental crust, the structure of the middle and lower crust differs significantly from the crystalline upper crust, suggesting that the tectonic processes or events preserved in the deep crust differ from those preserved in the shallower crust. The lithospheric mantle structure is not extensively modified from the reference model, but the results reinforce the systematic difference between the density of the oceanic and continental domains, and help identify subdivisions within each. The lithospheric static pressure field was resolved in 3D from the gravity and density fields. The pressure field model also highlights the fundamental difference between the oceanic and continental domains, with the former possessing lower pressure through most of the model. Overall pressure variability is large in the upper crust (60 MPa) but reduces significantly by –30 km elevation (20–30 MPa). By –50 km elevation, thick lower-crust generates further disequilibria (25–35 MPa) that are not compensated until –125 km elevation (10–20 MPa). Beneath –125 km elevation higher pressure is observed in the continental domain, extending to the base of the model. This indicates a lithosphere that is to a large degree isostatically compensated near the base of the felsic-intermediate continental crust, and again near the theoretical base of mature oceanic lithosphere.

Description: Nearly 10 y ago, we (1) critiqued the idea of Pleistocene rewilding (2), a misguided attempt to resurrect bygone ecosystems. Much has happened to the Earth’s biodiversity over the decade since the term “Pleistocene rewilding” was coined, most of it bad. More than half a billion people have been added...

Description: In their comment (1) on our review and perspective on trophic rewilding science (2), Rubenstein and Rubenstein launch a critique not so much directed at our study as at trophic rewilding as a conservation approach. They first lament that Pleistocene rewilding has not been scientifically studied since the term was...

Description: By introducing two types of zenith troposphere delay (ZTD) products in precise point positioning (PPP), we developed the ZTD-corrected PPP and the ZTD-constrained PPP, both of them reduced the PPP convergence time. Both enhanced PPP methods are examined by global empirical ZTD models and regional ZTD corrections. For global ZTD models, we verified that ZTD-corrected PPP will deviate the positioning results, while ZTD-constrained PPP could produce unbiased estimations. Therefore, the latter is utilized to study the performance of global ZTD models (ITG, GPT2w, GZTD and UNB3m). After numerous experiments, we found that the performance of ZTD models was positively related to the real ZTD accuracy, and we proposed a universal tropospheric stochastic model 2SQR(9rms) which denotes double the square of nine times ZTD rms, to constrain ZTD in PPP. The proposed model subsequently was validated by real-time static and kinematic ZTD-constrained PPP on the premise that the ZTD rms on every station was known. Compared with traditional PPP, in static PPP, the number of improved stations is increased by 15.5 per cent (ITG), 14.4 per cent (GPT2w), 11.1 per cent (GZTD) and 8.3 per cent (UNB3m). For kinematic PPP, PPP constrained by ITG model still had the best performance, the number of improved stations is increased by 14.4 per cent, after 30 min of initialization time, 13.4 cm east, 13.4 cm north and 11.7 cm up positioning accuracy was obtained, compared with 15.3 cm east, 15.3 cm north and 14.3 cm up accuracy by traditional PPP. In addition, experiments using regional ZTD corrections to enhance real-time PPP showed that both ZTD-corrected PPP and ZTD-constrained PPP can notably reduce the convergence time on the vertical component (within 15 cm).

Description: Tregidgo et al. (1) show that size-selective overfishing has drastically depleted and downsized populations of tambaqui (Colossoma macropomum) along the Purus River, Amazonia. Because fishers have historically targeted the largest individuals, tambaqui ∼1,000 km upriver are twofold larger than those near the Manaus rainforest metropolis (1). Here, we demonstrate that...

Description: Carleton (1) claims that “temperature during India’s main agricultural growing season has a strong positive effect on annual suicide rates.” Using state-scale panel data for 1967–2013, the author suggests that an increase in 1 °C temperature in a single day can cause 70 suicides. The evidence, she argues, is consistent...

Description: Hastings et al. (1) model a fishery with a weak and a strong stock. Using several examples from the US West Coast they conclude that marine protected areas (MPAs) are an effective way to allow harvest of strong stock while allowing for persistence of weak stocks and that MPAs have...

Description: We thank Bridgewater and Babin (1) for their perspective. We are aware of, and appreciate, the consideration of ecosystem services in the management of Biosphere Reserves. However, we see a strong imperative for establishing a protected area (PA) category focused specifically on protecting ecosystem services, for several key reasons articulated...

Description: We appreciate the points made by Hilborn (1) that changing the assumptions we made could lead to different conclusions. In fact, our overall goal in developing the model in ref. 2 was similar to the goal in developing the model in ref. 3 to indicate how a model with clear...

Description: The premise and all error claims by Clack et al. (1) in PNAS, about Jacobson et al.’s (2) report, are demonstrably false. We reaffirm Jacobson et al.’s conclusions. False Premise Clack et al.’s (1) premise that deep decarbonization studies conclude that using nuclear, carbon capture and storage (CCS), and bioenergy...

Description: The words we use matter. The concept of a social norm exists in many social and behavioral science disciplines and research traditions (1). Because the general term “social norm” is a hypernym, an explicit definition is crucial to discussions of its place and usefulness in solving complex social–environmental issues (cf....