This paper presents a study on the optimal setup for discharge assimilation within a spatially distributed hydrological model. The Ensemble Kalman filter (EnKF) is employed to update the grid-based distributed states of such an hourly spatially distributed version of the HBV-96 model. By using a physically based model for the routing, the time delay and attenuation are modelled more realistically. The discharge and states at a given time step are assumed to be dependent on the previous time step only (Markov property). Synthetic and real world experiments are carried out for the Upper Ourthe (1600 km2), a relatively quickly responding catchment in the Belgian Ardennes. We assess the impact on the forecasted discharge of (1) various sets of the spatially distributed discharge gauges and (2) the filtering frequency. The results show that the hydrological forecast at the catchment outlet is improved by assimilating interior gauges. This augmentation of the observation vector improves the forecast more than increasing the updating frequency. In terms of the model states, the EnKF procedure is found to mainly change the pdfs of the two routing model storages, even when the uncertainty in the discharge simulations is smaller than the defined observation uncertainty.@en

Sound spatially distributed rainfall fields including a proper spatial and temporal error structure are of key interest for hydrologists to force hydrological models and to identify uncertainties in the simulated and forecasted catchment response. The current paper presents a temporally coherent error identification method based on time-dependent multivariate spatial conditional simulations, which are conditioned on preceding simulations. A sensitivity analysis and real-world experiment are carried out within the hilly region of the Belgian Ardennes. Precipitation fields are simulated for pixels of 10 km × 10 km resolution. Uncertainty analyses in the simulated fields focus on (1) the number of previous simulation hours on which the new simulation is conditioned, (2) the advection speed of the rainfall event, (3) the size of the catchment considered, and (4) the rain gauge density within the catchment. The results for a sensitivity analysis show for typical advection speeds >20 km hĝ̂'1, no uncertainty is added in terms of across ensemble spread when conditioned on more than one or two previous hourly simulations. However, for the real-world experiment, additional uncertainty can still be added when conditioning on a larger number of previous simulations. This is because for actual precipitation fields, the dynamics exhibit a larger spatial and temporal variability. Moreover, by thinning the observation network with 50%, the added uncertainty increases only slightly and the cross-validation shows that the simulations at the unobserved locations are unbiased. Finally, the first-order autocorrelation coefficients show clear temporal coherence in the time series of the areal precipitation using the time-dependent multivariate conditional simulations, which was not the case using the time-independent univariate conditional simulations. The presented work can be easily implemented within a hydrological calibration and data assimilation framework and can be used as an improvement over currently used simplistic approaches to perturb the interpolated point or spatially distributed precipitation estimates.@en

In radar hydrology the relationship between the reflectivity factor (Z) and the rainfall intensity (R) is generally assumed to follow a power law of which the parameters change both in space and time and depend on the drop size distribution (DSD). Based on disdrometer data, this study tries to improve our understanding of the temporal variability of the power-law relationship between Z and R using a scaling-law formalism for the raindrop size distribution proposed in previous contributions. In particular, this study focuses on the inter-event variability of Z-R coefficients and associated DSD-parameters and their relationship to the type of precipitation. This is crucial for developing improved quantitative precipitation estimation algorithms for extreme, flash flood triggering rainfall.Within the DSD scaling-law framework a new normalized parameter estimation method is presented, which calculates significantly faster than the original method and leads to bulk event estimates of the DSD-parameters and associated Z-R coefficients. Based on a 2.5-year disdrometer dataset collected in the Cévennes-Vivarais region in the south of France, comprising a total of 70 events, it is shown that the quality of the resulting Z-R relationships obtained by the new method compares well to two standard least-squares fitting techniques. A major benefit of the new implementation, as compared to such purely statistical methods, is that it also provides information concerning the properties of the DSD.For each of the 70 events this study also estimates the convective activity based on a threshold technique. Results show that convective events generally tend to have smaller Z-R exponents, which is assumed to result from an increased amount of drop interaction. For stratiform events, a much larger range in exponents is obtained, which is thought to depend on differences in meteorological origin (snow vs. ice). For the types of precipitation events observed in the Cévennes region, for a given value of the exponent, the prefactor of the Z-R relation tends to be larger for the more convective type of events. This emphasizes the different meteorological origin of the heavy rainfall observed in the south of France as compared to other regions of the world.@en

This study offers an approach to estimate the rainfall kinetic energy (KE) by rain intensity (I) and radar reflectivity factor (Z) separately, or jointly, based on the one- or two-moment scaled raindrop size distribution (DSD) formulation, which contains (a) I and/or Z observations, (b) dimensionless probability density function (pdf) and (c) some intrinsic parameters. The key point of this formulation is to explain all variability of the DSD by the evolution of observations, hence the paland intrinsic parameters are considered as constants. A robust method is proposed to estimate the climatic values for these parameters, and our 28-month DSD data are used to test this estimation process. The results show that three relationships (KE-I, KE-Z and KE-IZ) which link the observations (I and/or Z) to rainfall kinetic energy (KE) are well established based on the climatic scaled DSD formulation. In particular, the combination of Iand Z yields a significant improvement of estimation of KE.@en

This paper presents a novel approach to estimate the vertical profile of reflectivity (VPR) from volumetric weather radar data using both a traditional Eulerian as well as a newly proposed Lagrangian implementation. For this latter implementation, the recently developed Rotational Carpenter Square Cluster Algorithm (RoCaSCA) is used to delineate precipitation regions at different reflectivity levels. A piecewise linear VPR is estimated for either stratiform or neither stratiform/convective precipitation. As a second aspect of this paper, a novel approach is presented which is able to account for the impact of VPR uncertainty on the estimated radar rainfall variability. Results show that implementation of the VPR identification and correction procedure has a positive impact on quantitative precipitation estimates from radar. Unfortunately, visibility problems severely limit the impact of the Lagrangian implementation beyond distances of 100 km. However, by combining this procedure with the global Eulerian VPR estimation procedure for a given rainfall type (stratiform and neither stratiform/convective), the quality of the quantitative precipitation estimates increases up to a distance of 150 km. Analyses of the impact of VPR uncertainty shows that this aspect accounts for a large fraction of the differences between weather radar rainfall estimates and rain gauge measurements. Key Points A new Lagrangian based VPR identification methodRadar rainfall uncertainty estimation from spatial precipitation variabilityImproved weather radar based surface rainfall estimation@en

Between 25 and 27 August 2010 a long-duration mesoscale convective system was observed above the Netherlands, locally giving rise to rainfall accumulations exceeding 150. mm. Correctly measuring the amount of precipitation during such an extreme event is important, both from a hydrological and meteorological perspective. Unfortunately, the operational weather radar measurements were affected by multiple sources of error and only 30% of the precipitation observed by rain gauges was estimated. Such an underestimation of heavy rainfall, albeit generally less strong than in this extreme case, is typical for operational weather radar in The Netherlands. In general weather radar measurement errors can be subdivided into two groups: (1) errors affecting the volumetric reflectivity measurements (e.g. ground clutter, radar calibration, vertical profile of reflectivity) and (2) errors resulting from variations in the raindrop size distribution that in turn result in incorrect rainfall intensity and attenuation estimates from observed reflectivity measurements. A stepwise procedure to correct for the first group of errors leads to large improvements in the quality of the estimated precipitation, increasing the radar rainfall accumulations to about 65% of those observed by gauges. To correct for the second group of errors, a coherent method is presented linking the parameters of the radar reflectivity-rain rate (Z- R) and radar reflectivity-specific attenuation (Z- k) relationships to the normalized drop size distribution (DSD). Two different procedures were applied. First, normalized DSD parameters for the whole event and for each precipitation type separately (convective, stratiform and undefined) were obtained using local disdrometer observations. Second, 10,000 randomly generated plausible normalized drop size distributions were used for rainfall estimation, to evaluate whether this Monte Carlo method would improve the quality of weather radar rainfall products.Using the disdrometer information, the best results were obtained in case no differentiation between precipitation type (convective, stratiform and undefined) was made, increasing the event accumulations to more than 80% of those observed by gauges. For the randomly optimized procedure, radar precipitation estimates further improve and closely resemble observations in case one differentiates between precipitation type. However, the optimal parameter sets are very different from those derived from disdrometer observations. It is therefore questionable if single disdrometer observations are suitable for large-scale quantitative precipitation estimation, especially if the disdrometer is located relatively far away from the main rain event, which was the case in this study. In conclusion, this study shows the benefit of applying detailed error correction methods to improve the quality of the weather radar product, but also confirms the need to be cautious using locally obtained disdrometer measurements.@en

Distributed hydrological modelling moves into the realm of hyper-resolution modelling. This results in a plethora of scaling-related challenges that remain unsolved. To the user, in light of model result interpretation, finer-resolution output might imply an increase in understanding of the complex interplay of heterogeneity within the hydrological system. Here we investigate spatial scaling in the form of varying spatial resolution by evaluating the streamflow estimates of the distributed wflow_sbm hydrological model based on 454 basins from the large-sample CAMELS data set. Model instances are derived at three spatial resolutions, namely 3 km, 1 km, and 200 m. The results show that a finer spatial resolution does not necessarily lead to better streamflow estimates at the basin outlet. Statistical testing of the objective function distributions (Kling–Gupta efficiency (KGE) score) of the three model instances resulted in only a statistical difference between the 3 km and 200 m streamflow estimates. However, an assessment of sampling uncertainty shows high uncertainties surrounding the KGE score throughout the domain. This makes the conclusion based on the statistical testing inconclusive. The results do indicate strong locality in the differences between model instances expressed by differences in KGE scores of on average 0.22 with values larger than 0.5. The results of this study open up research paths that can investigate the changes in flux and state partitioning due to spatial scaling. This will help to further understand the challenges that need to be resolved for hyper-resolution hydrological modelling.@en

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 models.@en

On 26 August 2010 the eastern part of The Netherlands and the bordering part of Germany were struck by a series of rainfall events lasting for more than a day. Over an area of 740 km2 more than 120 mm of rainfall were observed in 24 h. This extreme event resulted in local flooding of city centres, highways and agricultural fields, and considerable financial loss. In this paper we report on the unprecedented flash flood triggered by this exceptionally heavy rainfall event in the 6.5 km2 Hupsel Brook catchment, which has been the experimental watershed employed by Wageningen University since the 1960s. This study aims to improve our understanding of the dynamics of such lowland flash floods. We present a detailed hydrometeorological analysis of this extreme event, focusing on its synoptic meteorological characteristics, its space-time rainfall dynamics as observed with rain gauges, weather radar and a microwave link, as well as the measured soil moisture, groundwater and discharge response of the catchment. At the Hupsel Brook catchment 160 mm of rainfall was observed in 24 h, corresponding to an estimated return period of well over 1000 years. As a result, discharge at the catchment outlet increased from 4.4 × 10-3 to nearly 5 m3 s-1. Within 7 h discharge rose from 5 × 10-2 to 4.5 m3 s -1. The catchment response can be divided into four phases: (1) soil moisture reservoir filling, (2) groundwater response, (3) surface depression filling and surface runoff and (4) backwater feedback. The first 3 5 mm of rainfall were stored in the soil without a significant increase in discharge. Relatively dry initial conditions (in comparison to those for past discharge extremes) prevented an even faster and more extreme hydrological response.@en

The identification of hydrological drought at global scale has received considerable attention during the last decade. However, climate-induced variation in runoff across the world makes such analyses rather complicated. This especially holds for the drier regions of the world (both cold and warm), where, for a considerable period of time, zero runoff can be observed. In the current paper, we present a method that enables to identify drought at global scale across climate regimes in a consistent manner. The method combines the characteristics of the classical variable threshold level method that is best applicable in regions with non-zero runoff most of the time, and the consecutive dry days (period) method that is better suited for areas where zero runoff occurs. The newly presented method allows a drought in periods with runoff to continue in the following period without runoff. The method is demonstrated by identifying droughts from discharge observations of four rivers situated within different climate regimes, as well as from simulated runoff data at global scale obtained from an ensemble of five different land surface models. The identified drought events obtained by the new approach are compared to those resulting from application of the variable threshold level method or the consecutive dry period method separately. Results show that, in general, for drier regions, the threshold level method overestimates drought duration, because zero runoff periods are included in a drought, according to the definition used within this method. The consecutive dry period method underestimates drought occurrence, since it cannot identify droughts for periods with runoff. The developed method especially shows its relevance in transitional areas, because, in wetter regions, results are identical to the classical threshold level method. By combining both methods, the new method is able to identify single drought events that occur during positive and zero runoff periods, leading to a more realistic global drought characterization, especially within drier environments.@en

During the past decades large-scale models have been developed to simulate global and continental terrestrial water cycles. It is an open question whether thesemodels are suitable to capture hydrological drought, in terms of runoff, on a global scale. Amultimodel ensemble analysis was carried out to evaluate if 10 such large-scalemodels agree on major drought events during the second half of the twentieth century. Time series of monthly precipitation, monthly total runofffrom 10 global hydrologicalmodels, and their ensemblemedian have been used to identify drought. Temporal development of area in drought for various regions across the globe was investigated. Model spread was largest in regions with low runoffand smallest in regions with high runoff. In vast regions, correlation between runoffdrought derived from the models and meteorological drought was found to be low. This indicated that models add information to the signal derived from precipitation and that runoffdrought cannot directly be determined from precipitation data alone in global drought analyses with a constant aggregation period. However, duration and spatial extent of major drought events differed between models. Some models showed a fast runoffresponse to rainfall, which led to deviations from reported drought events in slowly responding hydrological systems. By using an ensemble of models, this fast runoffresponse was partly overcome and delay in drought propagating from meteorological drought to drought in runoffwas included. Finally, an ensemble of models also allows for consideration of uncertainty associated with individual model structures.@en

Quantitative precipitation estimation (QPE) using ground-based weather radar is affected by many sources of error. The most important of these are (1) radar calibration, (2) ground clutter, (3) wet-radome attenuation, (4) raininduced attenuation, (5) vertical variability in rain drop size distribution (DSD), (6) non-uniform beam filling and (7) variations in DSD. This study presents an attempt to separate and quantify these sources of error in flat terrain very close to the radar (1-2 km), where (4), (5) and (6) only play a minor role. Other important errors exist, like beam blockage, WLAN interferences and hail contamination and are briefly mentioned, but not considered in the analysis. A 3-day rainfall event (25-27 August 2010) that produced more than 50mm of precipitation in De Bilt, the Netherlands, is analyzed using radar, rain gauge and disdrometer data. Without any correction, it is found that the radar severely underestimates the total rain amount (by more than 50 %). The calibration of the radar receiver is operationally monitored by analyzing the received power from the sun. This turns out to cause a 1 dB underestimation. The operational clutter filter applied by KNMI is found to incorrectly identify precipitation as clutter, especially at near-zero Doppler velocities. An alternative simple clutter removal scheme using a clear sky clutter map improves the rainfall estimation slightly. To investigate the effect of wet-radome attenuation, stable returns from buildings close to the radar are analyzed. It is shown that this may have caused an underestimation of up to 4 dB. Finally, a disdrometer is used to derive event and intra-event specific Z-R relations due to variations in the observed DSDs. Such variations may result in errors when applying the operational Marshall-Palmer Z-R relation. Correcting for all of these effects has a large positive impact on the radar-derived precipitation estimates and yields a good match between radar QPE and gauge measurements, with a difference of 5-8 %. This shows the potential of radar as a tool for rainfall estimation, especially at close ranges, but also underlines the importance of applying radar correction methods as individual errors can have a large detrimental impact on the QPE performance of the radar.@en

Radars are known for their ability to obtain a wealth of information about spatial storm field characteristics. Unfortunately, rainfall estimates obtained by this instrument are known to be affected by multiple sources of error. Especially for stratiform precipitation systems, the quality of radar rainfall estimates starts to decrease at relatively close ranges. In the current study, the hydrological potential of weather radar is analyzed during a winter half-year for the hilly region of the Belgian Ardennes. A correction algorithm is proposed which corrects the radar data for errors related to attenuation, ground clutter, anomalous propagation, the vertical profile of reflectivity (VPR), and advection. No final bias correction with respect to rain gauge data was implemented because such an adjustment would not add to a better understanding of the quality of the radar data. The impact of the different corrections is assessed using rainfall information sampled by 42 hourly rain gauges. The largest improvement in the quality of the radar data is obtained by correcting for ground clutter. The impact of VPR correction and advection depends on the spatial variability and velocity of the precipitation system. Overall during the winter period, the radar underestimates the amount of precipitation as compared to the rain gauges. Remaining differences between both instruments can be attributed to spatial and temporal variability in the type of precipitation, which has not been taken into account.@en

This study offers a unified formulation of single- and multimoment normalizations of the raindrop size distribution (DSD), which have been proposed in the framework of scaling analyses in the literature. The key point is to consider a well-defined "general distribution" g(x) as the probability density function (pdf) of the raindrop diameter scaled by a characteristic diameter Dc. The two-parameter gamma pdf is used to model the g(x) function. This theory is illustrated with a 3-yr DSD time series collected in the Cévennes region, France. It is shown that threeDSD moments (M2,M3, and M4) make it possible to satisfactorily model the DSDs, both for individual spectra and for time series of spectra. The formulation is then extended to the one- and twomoment normalization by introducing single and dual power-law models. As compared with previous scaling formulations, this approach explicitly accounts for the prefactors of the power-law models to yield a unique and dimensionless g(x), whatever the scaling moment(s) considered. A parameter estimation procedure, based on the analysis of power-law regressions and the self-consistency relationships, is proposed for those normalizations. The implementation of this method with different scaling DSD moments (rain rate and/or radar reflectivity) yields g(x) functions similar to the one obtained with the three-moment normalization. For a particular rain event, highly consistent g(x) functions can be obtained during homogeneous rain phases, whatever the scaling moments used. However, the g(x) functions may present contrasting shapes from one phase to another. This supports the idea that the g(x) function is process dependent and not "unique" as hypothesized in the scaling theory.@en