ALBERT

Description: A geostatistical framework for quantifying the temporal evolution and predictability of rainfall fields for time lags between 5 min and 3 h is proposed. The method is based on the computation of experimental space–time variogram maps of radar reflectivity fields. Two new metrics for quantifying temporal innovation and predictability based on minimum semivariance values at different time lags are proposed. The method is applied to high-resolution composite radar reflectivity maps over the United States to study the evolution of 25 convective and 25 stratiform events during the warm season of 2014. Results show that the temporal innovation can be modeled as the sum of two exponential functions of time lag, with approximately 50% of the total innovation occurring over the first 60 min. The median predictable scales for convective events are on the order of 1.6 km at 5 min, 5 km at 15 min, and 12.7 km at 1 h. Furthermore, the optimal time lag for predicting future innovation, taking into account measurement uncertainty and natural variability, appears to be between 30 and 60 min.

Description: Precipitation displays a remarkable variability in space and time. An important yet poorly documented aspect of this variability is intermittency. In this paper, a new way of quantifying intermittency based on the burstiness B and memory M of interamount times is proposed. The method is applied to a unique dataset of 325 high-resolution rain gauges in the United States and Europe. Results show that the M–B diagram provides useful insight into local precipitation patterns and can be used to study intermittency over a wide range of temporal scales. It is found that precipitation tends to be more intermittent in warm and dry climates with the largest observed values in the southwest of the United States (i.e., California, Nevada, Arizona, and Texas). Low-to-moderate values are reported for the northeastern United States, the United Kingdom, the Netherlands, and Germany. In the second half of the paper, the new metrics are applied to daily rainfall data for 1954–2013 to investigate regional trends in intermittency due to climate variability and global warming. No evidence is found of a global shift in intermittency but a weak trend toward burstier precipitation patterns and longer dry spells in the south of Europe (i.e., Portugal, Spain, and Italy) and an opposite trend toward steadier and more correlated precipitation patterns in Norway, Sweden, and Finland is observed.

Description: The scaling and distributional properties of precipitation interamount times (IATs) are investigated using 10 years of high-resolution rain gauge observations from the U.S. Climate Reference Network. Results show that IATs above 200 mm tend to be approximately uncorrelated and normally distributed. As one moves toward smaller scales, autocorrelation and skewness increase and distributions progressively evolve into Weibull, Gamma, lognormal, and Pareto. This procession is interpreted as a sign of increasing complexity from large to small scales in a system composed of many interacting components. It shows that, as one approaches finer scales, IATs take over more of the characteristics of power-law distributions and (multi)fractals. Regression analysis on the log moments reveals that IATs generally exhibit better scaling, that is, smaller departures from multifractality, than precipitation amounts over the same range of scales. The improvement is attributed to the fact that IATs, unlike rainfall rates, always remain positive, no matter how small the scale. In particular, the scaling is shown to be more resilient to dry periods within rain events. Nevertheless, most analyzed IAT time series still exhibited a breakpoint at about 20 mm (7 days), corresponding to the average lifetime of a low pressure system at midlatitudes. Additional breakpoints in IATs at smaller and larger time scales are possible, but could not be determined unambiguously. The results highlight the potential of IATs as a new and promising tool for the stochastic modeling, simulation, and downscaling of precipitation.

Description: Spatial downscaling of rainfall fields is a challenging mathematical problem for which many different types of methods have been proposed. One popular solution consists of redistributing rainfall amounts over smaller and smaller scales by means of a discrete multiplicative random cascade (DMRCs). This works well for slowly varying homogeneous rainfall fields but often fails in the presence of intermittency (i.e., large amounts of zero rainfall values). The most common workaround in this case is to use two separate cascade models, namely one for the occurrence and another for the intensity. In this paper, a new and simpler approach based on the notion of equal-volume areas (EVAs) is proposed. Unlike classical cascades where rainfall amounts are redistributed over grid cells of equal size, the EVA cascade splits grid cells into areas of different sizes, with each of them containing exactly half of the original amount of water. The relative areas of the subgrid cells are determined by drawing random values from a logit-normal cascade generator model with scale and intensity-dependent standard deviation (SD). The process ends when the amount of water in each subgrid cell is smaller than a fixed-bucket capacity, at which point the output of the cascade can be resampled over a regular Cartesian mesh. The present paper describes the implementation of the EVA cascade model and gives some first results for 100 selected events in the Netherlands. Performance is assessed by comparing the outputs of the EVA model to bilinear interpolation and to a classical DMRC model based on fixed grid cell sizes. Results show that, on average, the EVA cascade outperforms the classical method, producing fields with more realistic distributions, small-scale extremes and spatial structures. Improvements are mostly credited to the higher robustness of the EVA model in the presence of intermittency and to the lower variance of its generator. However, both approaches have their advantages and weaknesses. For example, while the classical cascade tends to overestimate small-scale variability and extremes, the EVA model tends to produce fields that are slightly too smooth and block shaped compared to the observations. The complementary nature of the two approaches, and the fact that they produce errors of opposite signs, opens up new possibilities for quality control and bias corrections of downscaled fields.

Description: Weather radar has become an invaluable tool for monitoring rainfall and studying its link to hydrological response. However, when it comes to accurately measuring small-scale rainfall extremes responsible for urban flooding, many challenges remain. The most important of them is that radar tends to underestimate rainfall compared to gauges. The hope is that by measuring at higher resolutions and making use of dual-polarization radar, these mismatches can be reduced. Each country has developed its own strategy for addressing this issue. However, since there is no common benchmark, improvements are hard to quantify objectively. This study sheds new light on current performances by conducting a multinational assessment of radar's ability to capture heavy rain events at scales of 5 min up to 2 h. The work is performed within the context of the joint experiment framework of project MUFFIN (Multiscale Urban Flood Forecasting), which aims at better understanding the link between rainfall and urban pluvial flooding across scales. In total, six different radar products in Denmark, the Netherlands, Finland and Sweden were considered. The top 50 events in a 10-year database of radar data were used to quantify the overall agreement between radar and gauges as well as the bias affecting the peaks. Results show that the overall agreement in heavy rain is fair (correlation coefficient 0.7–0.9), with apparent multiplicative biases on the order of 1.2–1.8 (17  %–44  % underestimation). However, after taking into account the different sampling volumes of radar and gauges, actual biases could be as low as 10 %. Differences in sampling volumes between radar and gauges play an important role in explaining the bias but are hard to quantify precisely due to the many post-processing steps applied to radar. Despite being adjusted for bias by gauges, five out of six radar products still exhibited a clear conditional bias, with intensities of about 1 %–2 % per mmh−1. As a result, peak rainfall intensities were severely underestimated (factor 1.8–3.0 or 44 %–67 %). The most likely reason for this is the use of a fixed Z–R relationship when estimating rainfall rates (R) from reflectivity (Z), which fails to account for natural variations in raindrop size distribution with intensity. Based on our findings, the easiest way to mitigate the bias in times of heavy rain is to perform frequent (e.g., hourly) bias adjustments with the help of rain gauges, as demonstrated by the Dutch C-band product. An even more promising strategy that does not require any gauge adjustments is to estimate rainfall rates using a combination of reflectivity (Z) and differential phase shift (Kdp), as done in the Finnish OSAPOL product. Both approaches lead to approximately similar performances, with an average bias (at 10 min resolution) of about 30 % and a peak intensity bias of about 45 %.

Description: The adequacy of the gamma model to describe the variability of raindrop size distributions (DSD) is studied using observations from an optical disdrometer. Model adequacy is checked using a combination of Kolmogorov–Smirnov goodness-of-fit test and Kullback–Leibler divergence and the sensitivity of the results to the sampling resolution is investigated. A new adaptive DSD sampling technique capable of determining the highest possible temporal sampling resolution at which the gamma model provides an adequate representation of sampled DSDs is proposed. The results show that most DSDs at 30 s are not strictly distributed according to a gamma model, while at the same time they are not far away from it either. According to the adaptive DSD sampling algorithm, the gamma model proves to be an adequate choice for the majority (85.81%) of the DSD spectra at resolutions up to 300 s. At the same time, it also reveals a considerable number of DSD spectra (5.55%) that do not follow a gamma distribution at any resolution (up to 1800 s). These are attributed to transitional periods during which the DSD is not stationary and exhibits a bimodal shape that cannot be modeled by a gamma distribution. The proposed resampling procedure is capable of automatically identifying and flagging these periods, providing new valuable quality control mechanisms for DSD retrievals in disdrometers and weather radars.

Description: A particular aspect of the nonstationary nature of intermittent rainfall is investigated. It manifests itself in the fact that the average rain rate varies with the distance to the surrounding dry areas. The authors call this fundamental link between the rainfall intensity and the rainfall occurrence process the “dry drift.” Using high-resolution radar rain-rate maps and disdrometer data, they show how the dry drift affects the structure and the variability of intermittent rainfall fields. They provide a rigorous geostatistical framework to describe it and propose an extension of the concept to more general quantities like the (rain)drop size distribution.

Description: A method for the stochastic simulation of (rain)drop size distributions (DSDs) in space and time using geostatistics is presented. At each pixel, the raindrop size distribution is described by a Gamma distribution with two or three stochastic parameters. The presence or absence of rainfall is modeled using an indicator field. Separable space–time variograms are used to estimate and reproduce the spatial and temporal structures of all these parameters. A simple and user-oriented procedure for the parameterization of the simulator is proposed. The only data required are DSD time series and radar rain-rate (or reflectivity) measurements. The proposed simulation method is illustrated for both frontal and convective precipitation using real data collected in the vicinity of Lausanne, Switzerland. The spatial and temporal structures of the simulated fields are evaluated and validated using DSD measurements from eight independent disdrometers.