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Marc Schleiss

Abstract

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.

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Marc Schleiss and Alexis Berne

Abstract

A stochastic method to disaggregate rain rate fields into drop size distribution (DSD) fields is proposed. It is based on a previously presented DSD simulator that has been modified to take into account prescribed block-averaged rain rate values at a coarser scale. The integral quantity used to drive the disaggregation process can be the rain rate, the radar reflectivity, or any variable directly related to the DSD. The proposed method is illustrated and qualitatively evaluated using radar rain rate data provided by MeteoSwiss for two rain events of very contrasted type (stratiform versus convective). The evaluation shows that both types of rainfall are correctly disaggregated, although the general agreement in terms of rain rate distributions, intermittency, and space–time structures is much better for the stratiform case. Possible extensions and generalizations of the technique (e.g., using radar reflectivities at two different frequencies or polarizations to drive the disaggregation process) are discussed at the end of the paper.

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Marc Schleiss and James Smith

Abstract

A geostatistical method to quantify the small-scale 3D–time structure of the drop size distribution (DSD) from the ground level up to the melting layer using radar and disdrometer data is presented. First, 3D–time radar reflectivity fields are used to estimate the large-scale properties of a rain event, such as the apparent motion, spatial anisotropy, and temporal innovation. The retrieved quantities are then combined with independent disdrometer time series to estimate the 3D–time variogram of each DSD parameter. A key point in the procedure is the use of a new metric for measuring distances in moving anisotropic rainfall fields. This metric has the property of being invariant with respect to the specific rainfall parameter being considered, that is, it is identical for the radar reflectivity, rain rate, mean drop diameter, drop concentration, or any other weighted moment of the DSD. Evidence is shown of this fact and some illustrations for a stratiform event in southern France and a convective case in the midwestern United States are provided. The proposed framework offers a series of new and interesting applications, including the possibility to compare the space–time structure of different rain events, to interpolate radar reflectivity fields in space–time and to simulate 3D–time DSD fields at high spatial and temporal resolutions.

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Marc Schleiss

Abstract

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.

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Marc Schleiss and James A. Smith

Abstract

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 MB 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.

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Marc Schleiss, Joel Jaffrain, and Alexis Berne

Abstract

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.

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Ricardo Reinoso-Rondinel and Marc Schleiss

Abstract

Conventionally, Micro Rain Radars (MRRs) have been used as a tool to calibrate reflectivity from weather radars, estimate the relation between rainfall rate and reflectivity, and study microphysical processes in precipitation. However, limited attention has been given to the reliability of the retrieved drop size distributions (DSDs) from MRRs. This study sheds more light on this aspect by examining the sensitivity of retrieved DSDs to the assumptions made to map Doppler spectra into size distributions, and investigates the capability of an MRR to assess polarimetric observations from operational weather radars. For that, an MRR was installed near the Cabauw observatory in the Netherlands, between the International Research Center for Telecommunications and Radar (IRCTR) Drizzle Radar (IDRA) X-band radar and the Herwijnen operational C-band radar. The measurements of the MRR from November 2018 to February 2019 were used to retrieve DSDs and simulate horizontal reflectivity Z e, differential reflectivity Z DR, and specific differential phase K DP in rain. Attention is given to the impact of aliased spectra and right-hand-side truncation on the simulation of polarimetric variables. From a quantitative assessment, the correlations of Z e and Z DR between the MRR and Herwijnen radar were 0.93 and 0.70, respectively, while those between the MRR and IDRA were 0.91 and 0.69. However, Z e and Z DR from the Herwijnen radar showed slight biases of 1.07 and 0.25 dB. For IDRA, the corresponding biases were 2.67 and −0.93 dB. Our results show that MRR measurements are advantageous to inspect the calibration of scanning radars and validate polarimetric estimates in rain, provided that the DSDs are correctly retrieved and controlled for quality assurance.

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Marc Schleiss, Sabine Chamoun, and Alexis Berne

Abstract

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.

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Christos Gatidis, Marc Schleiss, Christine Unal, and Herman Russchenberg

Abstract

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.

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