Dennis Meißner

As recent years have shown, inland waterways are prone to hydroclimatic impacts. Dry spells, such as in 2003, 2015 or 2018, significantly affected freight transport as well as passenger shipping along Central Europe’s major inland waterways, such as the River Rhine. At the same time, heavy rainfall and the proceeding sea-level rise increasingly hamper the management of numerous inland waterways, such as the Kiel Canal. As prognostic information enables waterway stakeholders to take preventive measures regarding hydroclimatic impacts, the demand for extended-range hydrological forecasts tailored to the management and use of waterways is significantly increasing. Based on preliminary studies, the Federal Institute of Hydrology started developing preliminary extended-range forecast products for relevant gauges at the German waterways since 2015. Step-by-step operational services supplying these new forecast products have been set-up. For the River Rhine, a ten-day forecast has been publicly available since 2019. In 2022, a six-week forecast for Rhine and Elbe will further extend the waterway-related forecasting services in Germany. This article provides insight into the setting of these extended navigation-related forecasting services, where the communication of forecast uncertainties is still a major challenge.

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 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 (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 timescales for waterway transport and to operationalize the related forecasting service.

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.

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.