Hydrologic ensemble forecasts driven by atmospheric ensemble prediction systems need statistical postprocessing in order to account for systematic errors in terms of both location and spread. Runoff is an inherently multivariate process with typical events lasting from hours in case of floods to weeks or even months in case of droughts. This calls for multivariate postprocessing techniques that yield wellcalibrated forecasts in univariate terms and ensure a realistic temporal dependence structure at the same time. To this end, the univariate ensemble model output statistics (EMOS) postprocessing method is combined with two different copula approaches that ensure multivariate calibration throughout the entire forecast horizon. The domain of this study covers three subcatchments of the river Rhine that represent different sizes and hydrological regimes: the Upper Rhine up to the gauge Maxau, the river Moselle up to the gauge Trier, and the river Lahn up to the gauge Kalkofen. In this study, the two approaches to model the temporal dependence structure are ensemble copula coupling (ECC), which preserves the dependence structure of the raw ensemble, and a Gaussian copula approach (GCA), which estimates the temporal correlations from training observations. The results indicate that both methods are suitable for modeling the temporal dependencies of probabilistic hydrologic forecasts.

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Abstract. Traditionally, navigation-related forecasts in central Europe cover short-to medium-range lead times linked to the travel times of vessels to pass the main waterway bottlenecks leaving the loading ports. Without doubt, this aspect is still essential for navigational users, but in light of the growing political intention to use the free capacity of the inland waterway transport in Europe, additional lead time supporting strategic decisions is more and more in demand. However, no such predictions offering extended lead times of several weeks up to several months currently exist for considerable parts of the European waterway network. This paper describes the set-up of a monthly to seasonal forecasting system for the German stretches of the international waterways of the Rhine, Danube and Elbe rivers. Two competitive forecast approaches have been implemented: the dynamical set-up forces a hydrological model with postprocessed outputs from ECMWF general circulation model System 4, whereas the statistical approach is based on the empirical relationship ("teleconnection") of global oceanic, climate and regional hydro-meteorological data with river flows. The performance of both forecast methods is evaluated in relation to the climatological forecast (ensemble of historical streamflow) and the well-known ensemble streamflow prediction approach (ESP, ensemble based on historical meteorology) using common performance indicators (correlation coefficient; mean absolute error, skill score; mean squared error, skill score; and continuous ranked probability, skill score) and an impact-based evaluation quantifying the potential economic gain.The following four key findings result from this study: (1) as former studies for other regions of central Europe indicate, the accuracy and/or skill of the meteorological forcing used has a larger effect than the quality of initial hydrological conditions for relevant stations along the German waterways.(2) Despite the predictive limitations on longer lead times in central Europe, this study reveals the existence of a valuable predictability of streamflow on monthly up to seasonal timescales along the Rhine, upper Danube and Elbe waterways, and the Elbe achieves the highest skill and economic value. (3) The more physically based and the statistical approach are able to improve the predictive skills and economic value compared to climatology and the ESP approach. The specific forecast skill highly depends on the forecast location, the lead time and the season. (4) Currently, the statistical approach seems to be most skilful for the three waterways investigated. The lagged relationship between the monthly and/or seasonal streamflow and the climatic and/or oceanic variables vary between 1 month (e.g. local precipitation, temperature and soil moisture) up to 6 months (e.g. sea surface temperature).Besides focusing on improving the forecast methodology, especially by combining the individual approaches, the focus is on developing useful forecast products on monthly to seasonal timesc...

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Predictive uncertainty (PU) is defined as the probability of occurrence of an observed variable of interest, conditional on all available information. In this context, hydrological model predictions and forecasts are considered to be accessible but yet uncertain information. To estimate the PU of hydrological multi-model ensembles, we apply a method based on the use of copulas which enables modelling the dependency structures between variates independently of their marginal distributions. Given that the option to employ copula functions imposes certain limitations in the multivariate case, we model the multivariate distribution as a cascade of bivariate copulas by using the pair-copula construction. We apply a mixture of probability distributions to estimate the marginal densities and distributions of daily flow rates for various meteorological and hydrological situations. The proposed method is applied to a multi-model ensemble involving two hydrological and one statistical flow models at two gauge stations in the Moselle river basin. Verification and inter-comparison with other PU assessment methods show that copulas are well-suited for this scope and constitute a valid approach for predictive uncertainty estimation of hydrological multi-model predictions.

Abstract. Traditionally, navigation-related forecasts in Central Europe cover short- to medium-range lead-times linked to the travel times of vessels to pass the main waterway bottlenecks leaving the loading ports. Without doubt, this aspect is still essential for navigational users, but in light of the growing political intention to use the free capacity of the inland waterway transport in Europe, additional lead-time supporting strategic decisions is more and more in demand. However, no such predictions offering extended lead-times of several weeks up to several months ahead currently exist for considerable parts of the European waterway network. This paper describes the set-up of a monthly to seasonal forecasting system for the German stretches of the international waterways of Rhine, Danube and Elbe rivers. Two competitive forecast approaches have been implemented: the dynamical set-up forces a hydrological model with post-processed outputs from ECMWF general circulation model System 4, whereas the statistical approach is based on the empirical relationship (teleconnection) of global oceanic, climate and regional hydro-meteorological data with river flows. The performance of both forecast methods is evaluated in relation to the climatological forecast (ensemble of historical streamflow) and the well-known Ensemble Streamflow Prediction approach (ESP, ensemble based on historical meteorology) using common performance indicators as well as an impact-based evaluation quantifying the potential economic gain. The following four key findings result from this study: (1) As former studies for other regions of Central Europe indicate, also for relevant stations along the German waterways meteorological forcings dominate initial hydrological conditions in most cases already after the first forecast month. (2) Despite the predictive limitations on longer lead-times over Central Europe, this study reveals the existence of a valuable predictability of streamflow at monthly up to seasonal time-scales along Rhine, Upper Danube and Elbe, while the Elbe achieves the highest skill and value. (3) The more physically-based as well as the statistical approach are able to improve the predictive skills compared to climatology and the ESP-approach. The specific forecast skill highly depends on the forecast location, the lead-time and the season. (4) Currently, the statistical approach seems to be most skilful for the three waterways investigated. The lagged relationship between the monthly/seasonal streamflow and the climatic/oceanic variables vary between one month (e.g. local precipitation and temperature, soil moisture) up to six months (e.g. sea surface temperature). Besides improving the forecast methodology, especially by combining the individuals approaches, the focus is on developing useful forecast products on monthly to seasonal time-scale for waterway transport and to operationalize the related forecasting service.

Inland waterway transport benefits from probabilistic forecasts of water levels as they allow to optimize the ship load and, hence, to minimize the transport costs. Probabilistic state‐of‐the‐art hydrologic ensemble forecasts inherit biases and dispersion errors from the atmospheric ensemble forecasts they are driven with. The use of statistical postprocessing techniques like ensemble model output statistics (EMOS) allows for a reduction of these systematic errors by fitting a statistical model based on training data. In this study, training periods for EMOS are selected based on forecast analogs, i.e., historical forecasts that are similar to the forecast to be verified. Due to the strong autocorrelation of water levels, forecast analogs have to be selected based on entire forecast hydrographs in order to guarantee similar hydrograph shapes. Custom‐tailored measures of similarity for forecast hydrographs comprise hydrological series distance (SD), the hydrological matching algorithm (HMA), and dynamic time warping (DTW). Verification against observations reveals that EMOS forecasts for water level at three gauges along the river Rhine with training periods selected based on SD, HMA, and DTW compare favorably with reference EMOS forecasts, which are based on either seasonal training periods or on training periods obtained by dividing the hydrological forecast trajectories into runoff regimes.

Abstract. As a result of the severe floods in Europe at the turn of the millennium, the ongoing shift from safety oriented flood control towards flood risk management was accelerated. With regard to technical flood control measures it became evident that the effectiveness of flood control measures depends on many different factors, which cannot be considered with single events used as design floods for planning. The multivariate characteristics of the hydrological loads have to be considered to evaluate complex flood control measures. The effectiveness of spatially distributed flood control systems differs for varying flood events. Event-based characteristics such as the spatial distribution of precipitation, the shape and volume of the resulting flood waves or the interactions of flood waves with the technical elements, e.g. reservoirs and flood polders, result in varying efficiency of these systems. Considering these aspects a flood control system should be evaluated with a broad range of hydrological loads to get a realistic assessment of its performance under different conditions. The consideration of this variety in flood control planning design was one particular aim of this study. Hydrological loads were described by multiple criteria. A statistical characterization of these criteria is difficult, since the data base is often not sufficient to analyze the variety of possible events. Hydrological simulations were used to solve this problem. Here a deterministic-stochastic flood generator was developed and applied to produce a large quantity of flood events which can be used as scenarios of possible hydrological loads. However, these simulations imply many uncertainties. The results will be biased by the basic assumptions of the modeling tools. In flood control planning probabilities are applied to characterize uncertain-ties. The probabilities of the simulated flood scenarios differ from probabilities which would be derived from long time series. With regard to these known unknowns the bias of the simulations was considered by imprecise probabilities. Probabilities, derived from measured flood data were combined with probabilities which were estimated from long simulated series. To consider imprecise probabilities, fuzzy sets were used to distinguish the results between more or less possible design floods. The need for such a differentiated view on the performance of flood protection systems is demonstrated by a case study.