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We investigate the depth-duration relationship of maximum rainfall over the whole of Germany based on 16 yrs of radar derived Quantitative Precipitation Estimates (namely, RADKLIM-YW, German Meteorological Service) with a space-time resolution of 1 km and 5 min. Contrary to the long-term historic records that identified a smooth power law scaling behavior between the maximum rainfall depth and duration, our analysis revealed three distinct scaling regimes of which boundaries are approximately 1.5 h and 1 d. Few extraordinary events dominate a wide range of durations and deviate to the usual power law. Furthermore, the shape of the depth-duration relationship varies with the sample size of randomly selected radar pixels. A smooth scaling behavior were identified when the sample size is small (e.g. 10 to 100), but the original three distinct scaling regimes became more apparent as the sample size increases (e.g. 1000 to 10 000). Lastly, a pixel wise classification of the depth-duration relationship of the maximum rainfall at all individual pixels in Germany revealed three distinguishable types of scaling behavior, clearly determined by the temporal structure of the extreme rainfall events at a pixel. Thus, the relationship might change with longer time series and can be improved once available. [ABSTRACT FROM AUTHOR]

Compound hydro-meteorological extreme events represent a simultaneous occurrence of extremes or one extreme triggering another. These events do not necessarily require extremes in any of the components, but their combination could lead to an extreme. This study brings insights on compound extremes from the watershed scale perspective by applying a multivariate distribution approach to estimate return periods of compound precipitation-discharge extremes. Main research question concerned the degree of the agreement between extremes in terms of joint return periods (JRP). Additionally, impacts of spatial generalization for copula functions (best-per-area) and outstanding extreme events were investigated and finally an attempt to correlate JRP with catchment characteristics was performed. The study was elaborated using data of small catchments from 5 to 675km² (with median value of 103km²) in Saxony (Germany) interpolated on a 1×1km grid. A specially designed block-maxima subset was defined to account for cases when the annual daily discharge and the annual daily precipitation maxima do not occur on the same day. 20 copulas were tested to find the one, which fits best-per-grid. Afterwards, the most frequent copula (best-per-area) was chosen to estimate JRP for compound extreme events. Additionally, a pool of the most frequent copulas for the study area was used to create an ensemble and calculate various quantiles of JRP. All chosen copulas have undergone two goodness-of-fit tests to account for the legitimacy of the approach, which result in very low percentage of rejection for both statistics. Overall, the approach shows a good agreement between precipitation-discharge extremes and a high potential for a probabilistic instead of a deterministic analysis of JRP. For the investigated catchments, compound precipitation-discharge extremes are highly correlated. Large uncertainty in the estimation of the JRP was revealed by comparing different copulas. This uncertainty increases with larger non-exceedance probability of the compound event. Few spatial patterns with either very low or high anomalies of JRP were identified. A best-per-area distribution can be detected based on a frequency analysis of the best-per-grid distributions. Nevertheless, in case of time-series shortage it could be more compelling and reliable to create an ensemble of the most frequent copulas since it allows already a probabilistic instead of a deterministic estimation of JRP. It is concluded that outstanding extreme events, which occurred in 2002 and 2013 have a significant effect on the compound extreme statistics. Finally, the catchment response seems to be largely independent of size and mean elevation of the catchment, as no clear correlations between those and the corresponding JRP were found. [ABSTRACT FROM AUTHOR]

Often detailed point information from future climate projections is needed for hydrological and other impact models. Therefore, two problems must be solved, first the bias correction is needed for the unbiased application of projected data and second the general scale gap between gridded model data and pointwise observation data has to be taken into account. The latter is often ignored, but contributes systematically to the model bias as model output is often referring to mean values or budget closing on grid level, while measurements are typically point measurements by nature. We present an approach, which solves the aforementioned problems by applying a parametric quantile mapping (QM) with a special focus on extremes in precipitation. We selected 16 model combinations of the multi-model ensemble matrix of the projects Euro-Cordex (Coordinated Downscaling Experiment – European Domain) and ReKliEs-De (Regional climate projections ensemble for Germany) as climate projections. Since the study area is the Free State of Saxony in Germany, 17 observation stations from the reference dataset by ReKIS (Referenzdatensatz V1.0 (10/2017), Regional climate information system – www.rekis.org) are used as the observation dataset. We fitted two parametric distribution functions with the maximum likelihood method to datasets of various situations (i.e. seasons, stations and model combinations). First, the often used Gamma distribution is fitted to the datasets. Second, a dynamical mixed Gamma and generalized Pareto distribution is fitted, to be able to describe the extremes more in detail. The different correction functions are generated to correct the bias between gridded model data and pointwise observation data. A cross-validation is carried out to evaluate the performance of the different fitted distributions. Therefore, 10 years from 1971-2015 are picked randomly as validation period and the remaining years are used for the calibration of the fitting process. This procedure is repeated 30 times for each single situation. Subsequently, the Akaike information criterion (AIC) and the Cramér-von Mises criterion (CvM) are calculated as skill scores to select the most appropriate distribution for each situation. However, the analysis of the skill scores shows different pattern of the chosen distributions, the AIC and CvM often suggest different distributions. Hence, to analyse which skill score delivers the better bias corrected model data, both skill score decisions are used to correct the model dataset for each situation to generate two corrected model datasets for the period 1971-2015. The final evaluation is performed by a comparison of quantile-quantile plots of the two corrected model datasets with respect to the observation data. The analysis shows that both distributions have their entitlement and that more reliable results can be generated, if not only one distribution is prescribed for each situation. [ABSTRACT FROM AUTHOR]

Precipitation usually exhibits scale-invariant behaviour on a large range of temporal and spatial scales which has been explained physically as well as empirically in many studies. Here, we investigate intensity-duration relationships from radar data for Germany from 2001 to 2016. A newly released radar composite product from the German Meteorological Service (Radolan-YW, DWD 2018) with a resolution of 5 minutes and 1x1 km² was used for the analysis. After a conversion of the whole raster data set into time series, the maximum intensities per duration were derived with 1) moving window, 2) fixed window, and 3) interpolated fixed window aggregation. Out of the data set, the maximum and percentiles of maximums were plotted against their duration and compared with existing theoretical as well as empirical relationships from point observations. The results show unexpected scale breaks after around 1 hour, which suggests a non-consistent scaling behaviour of the radar data. This implies a careful usage of the data set in context of extreme value statistics as well as its application. [ABSTRACT FROM AUTHOR]

Brook90 is a widely used lumped hydrological model for evaporation, soil water, and streamflow. Its development lasts back to the 70s by Federer. Since that time, the model found a vast extent of applications, mainly in the field of forestry. The simple reason for its popularity is the profound process description, especially its detailed description of evaporation processes. The original model was written in FORTRAN and translated into Visual Basic. Both languages are highly capable and recommended to run the model. However, user preferences and demands are changing over time and current demands, like model applications in web technologies hardly can be performed with the original model versions. Therefor we present a well-documented R-implementation of Brook90 (https://github.com/rkronen/Brook90%5fR).The implementation shows marginal numerical differences at single iteration steps due to different variable precisions. These small differences in the balance only can be observed between single time steps and disappear at daily and larger time steps. The current R version of the model takes twice as long to calculate as the original Visual Basic version.However, the R implementation enables the user to run Brook90 simply in batch mode, to run it in parallel for different catchments and even to run it spatially distributed as the water fluxes of different catchments can easily be connected. This R version of the Brook90 allows for comprehensive investigation of all model parameters and variables at every time step, which is another great advantage. The R version of Brook90 has a detailed documentation and might therefore find also application in academic teaching. [ABSTRACT FROM AUTHOR]