Raindrop size distribution and radar reflectivity-rain rate relationships for radar hydrology

The conversion of the radar reflectivity factor Z (mm6m-3) to rain rate R (mm h-1) is a crucial step in the hydrological application of weather radar measurements. It has been common practice for over 50 years now to take for this conversion a simple power law relationship between Z and R. It is the purpose of this paper to explain that the fundamental reason for the existence of such power law relationships is the fact that Z and R are related to each other via the raindrop size distribution. To this end, the concept of the raindrop size distribution is first explained. Then, it is demonstrated that there exist two fundamentally different forms of the raindrop size distribution, one corresponding to raindrops present in a volume of air and another corresponding to those arriving at a surface. It is explained how Z and R are defined in terms of both these forms. Using the classical exponential raindrop size distribution as an example, it is demonstrated (1) that the definitions of Z and R naturally lead to power law Z-R relationships, and (2) how the coefficients of such relationships are related to the parameters of the raindrop size distribution. Numerous empirical Z-R relationships are analysed to demonstrate that there exist systematic differences in the coefficients of these relationships and the corresponding parameters of the (exponential) raindrop size distribution between different types of rainfall. Finally, six consistent Z-R relationships are derived, based upon different assumptions regarding the rain rate dependence of the parameters of the (exponential) raindrop size distribution. An appendix shows that these relationships are in fact special cases of a general Z-R relationship that follows from a recently proposed scaling framework for describing raindrop size distributions and their properties

Geostatistical simulation of two-dimensional fields of raindrop size distributions at the meso-¿ scale

The large variability of the raindrop size distribution (DSD) in space and time must be taken into account to improve remote sensing of precipitation. The ability to simulate a large number of 2-D fields of DSDs sharing the same statistical properties provides a very useful simulation framework that nicely complements experimental approaches based on DSD ground measurements. These simulations can be used to investigate radar beam propagation through rain and to evaluate different radar retrieval techniques. The proposed approach uses geostatistical methods to provide structural analysis and stochastic simulation of DSD fields. First, the DSD is assumed to follow a Gamma distribution with three parameters. As a consequence, 2-D fields of DSDs can be described as a multivariate random function. The parameters are normalized using a Gaussian anamorphosis and simulated by taking advantage of fast Gaussian simulation algorithms. Variograms are used to characterize the spatial structure of the DSD fields. The generated fields have identical spatial structure and are consistent with the observations. Because intermittency cannot be simulated using this technique, the size of the simulation domain is limited to the meso-¿ scale (2-20 km). To assess the proposed approach, the method is applied to data collected during intense Mediterranean rainfall. Taylor's hypothesis is invoked to convert time series into 1-D range profiles. The anisotropy of the fields is derived from radar measurements. Simulated and measured reflectivity fields are in good agreement with respect to the mean, the standard deviation, and the spatial structure, demonstrating the promising potential of the proposed stochastic model of DSD field

Errors and uncertainties in microwave link rainfall estimation explored using drop size measurements and high-resolution radar data

Microwave links can be used for the estimation of path-averaged rainfall by using either the path-integrated attenuation or the difference in attenuation of two signals with different frequencies and/or polarizations. Link signals have been simulated using measured time series of raindrop size distributions (DSDs) over a period of nearly 2 yr, in combination with wind velocity data and Taylor’s hypothesis. For this purpose, Taylor’s hypothesis has been tested using more than 1.5 yr of high-resolution radar data. In terms of correlation between spatial and temporal profiles of rainfall intensities, the validity of Taylor’s hypothesis quickly decreases with distance. However, in terms of error statistics, the hypothesis is seen to hold up to distances of at least 10 km. Errors and uncertainties (mean bias error and root-mean-square error, respectively) in microwave link rainfall estimates due to spatial DSD variation are at a minimum at frequencies (and frequency combinations) where the power-law relation for the conversion to rainfall intensity is close to linear. Errors generally increase with link length, whereas uncertainties decrease because of the decrease of scatter about the retrieval relations because of averaging of spatially variable DSDs for longer links. The exponent of power-law rainfall retrieval relations can explain a large part of the variation in both bias and uncertainty, which means that the order of magnitude of these error statistics can be predicted from the value of this exponent, regardless of the link length

Linking meteorology and hydrology: measuring water balance terms in Cabauw, the Netherlands

Climate models need information about energy and water fluxes at the soil surface. In Cabauw (Netherlands) these fluxes and the belonging balances are measured. Water balances have been set up for a summer and a winter period to check the correctness of these fluxes. In winter precipitation is the largest input term and outflowing discharge the highest output term. In summer inflowing discharge is the largest input term and evapotranspiration the highest output term

The effect of reported high-velocity small raindrops on inferred drop size distributions and derived power laws

It has recently been shown that at high rainfall intensities, small raindrops may fall with much larger velocities than would be expected from their diameters. These were argued to be fragments of recently broken-up larger drops. In this paper we quantify the effect of this phenomenon on raindrop size distribution measurements from a Joss-Waldvogel disdrometer, a 2-D Video Distrometer, and a vertically-pointing Doppler radar. Probability distributions of fall velocities have been parameterized, where the parameters are functions of both rainfall intensity and drop size. These parameterizations have been used to correct Joss-Waldvogel disdrometer measurements for this phenomenon. The effect of these corrections on fitted scaled drop size distributions are apparent but not major. Fitted gamma distributions for three different types of rainfall have been used to simulate drop size measurements. The effect of the high-velocity small drops is shown to be minor. Especially for the purpose of remote sensing of rainfall using radar, microwave links, or optical links, the errors caused by using the slightly different retrieval relations will be masked completely by other error sources

The hydrological response of the Ourthe catchment to climate change as modelled by the HBV model

The Meuse is an important river in Western Europe, which is almost exclusively rain-fed. Projected changes in precipitation characteristics due to climate change, therefore, are expected to have a considerable effect on the hydrological regime of the river Meuse. We focus on an important tributary of the Meuse, the Ourthe, measuring about 1600 km2. The well-known hydrological model HBV is forced with three high-resolution (0.088°) regional climate scenarios, each based on one of three different IPCC CO2 emission scenarios: A1B, A2 and B1. To represent the current climate, a reference model run at the same resolution is used. Prior to running the hydrological model, the biases in the climate model output are investigated and corrected for. Different approaches to correct the distributed climate model output using single-site observations are compared. Correcting the spatially averaged temperature and precipitation is found to give the best results, but still large differences exist between observations and simulations. The bias corrected data are then used to force HBV. Results indicate a small increase in overall discharge, especially for the B1 scenario during the beginning of the 21st century. Towards the end of the century, all scenarios show a decrease in summer discharge, partially because of the diminished buffering effect by the snow pack, and an increased discharge in winter. It should be stressed, however, that we used results from only one GCM (the only one available at such a high resolution). It would be interesting to repeat the analysis with multiple model

Climatology of daily rainfall semi-variance in The Netherlands

Rain gauges can offer high quality rainfall measurements at their locations. Networks of rain gauges can offer better insight into the space-time variability of rainfall, but they tend to be too widely spaced for accurate estimates between points. While remote sensing systems, such as radars and networks of microwave links, can offer good insight in the spatial variability of rainfall they tend to have more problems in identifying the correct rain amounts at the ground. A way to estimate the variability of rainfall between gauge points is to interpolate between them using fitted variograms. If a dense rain gauge network is lacking it is difficult to estimate variograms accurately. In this paper a 30-year dataset of daily rain accumulations gathered at 29 automatic weather stations operated by KNMI (Royal Netherlands Meteorological Institute) and a one-year dataset of 10 gauges in a network with a radius of 5 km around CESAR (Cabauw Experimental Site for Atmospheric Research) are employed to estimate variograms. Fitted variogram parameters are shown to vary according to season, following simple cosine functions. Semi-variances at short ranges during winter and spring tend to be underestimated, but semi-variances during summer and autumn are well predicted

Parameter Sensitivity in LSMs: An Analysis Using Stochastic Soil Moisture Models and ELDAS Soil Parameters

Integration of simulated and observed states through data assimilation as well as model evaluation requires a realistic representation of soil moisture in land surface models (LSMs). However, soil moisture in LSMs is sensitive to a range of uncertain input parameters, and intermodel differences in parameter values are often large. Here, the effect of soil parameters on soil moisture and evapotranspiration are investigated by using parameters from three different LSMs participating in the European Land Data Assimilation System (ELDAS) project. To prevent compensating effects from other than soil parameters, the effects are evaluated within a common framework of parsimonious stochastic soil moisture models. First, soil parameters are shown to affect soil moisture more strongly than the average evapotranspiration. In arid climates, the effect of soil parameters is on the variance rather than the mean, and the intermodel flux differences are smallest. Soil parameters from the ELDAS LSMs differ strongly, most notably in the available moisture content between the wilting point and the critical moisture content, which differ by a factor of 3. The ELDAS parameters can lead to differences in mean volumetric soil moisture as high as 0.10 and an average evapotranspiration of 10%–20% for the investigated parameter range. The parsimonious framework presented here can be used to investigate first-order parameter sensitivities under a range of climate conditions without using full LSM simulations. The results are consistent with many other studies using different LSMs under a more limited range of possible forcing condition