Low flow forecasting with a lead time of 14 days for navigation and energy supply in the Rhine River

Low flow forecasting, days or even months in advance, is particularly important to the efficient operation of power plants and freight shipment. This study presents a low flow forecasting model with a lead time of 14 days for the Rhine River. The forecasts inherit uncertainty sources mainly because of model parameterization. Therefore, a systematic uncertainty analysis is applied to indicate the major uncertainty sources in the results. Firstly, the Rhine basin is divided into 7 major sub-basins. Each sub-basin is modeled separately with a data-driven model and the output discharges are routed to Lobith after German-Dutch border with another data-driven model. Five pre-selected low flow indicators (basin averaged precipitation, basin averaged potential evapotranspiration; basin averaged fresh snow depths, basin averaged groundwater levels and major lake levels in the sub-basins) are used as inputs to the models. The basin discretization and the selection of indicators are based on a literature study and seasonality analysis of the discharge time series from 108 sub-basins. The correlations between indicator and low flows with varying temporal resolution and varying lags between indicator and low flows were used to identify appropriate temporal scales of the model inputs.We assume that a suitable model structure for the Rhine basin has been determined; that is, the sub-system boundaries have been specified, the important state variables and input and output fluxes to be included have been identified and selected for each sub-basin. The results in this study show that the data-driven models used for each sub-basin are capable of representing the essential characteristics of the system based on lagged and temporally averaged low flow indicators and are forecasting low flows adequately. In addition to the forecast results, the uncertainties due to specific model parameters in the calibrated data-driven model corresponding to key processes are also given

Uncertainty analysis of a low flow model for the Rhine River

It is widely recognized that hydrological models are subject to parameter uncertainty. However, little attention has been paid so far to the uncertainty in parameters of the data-driven models like weights in neural networks. This study aims at applying a structured uncertainty analysis to a data-driven model for low flow forecasting with a lead time of 14 days in the Rhine River. In the modeling phase, the Rhine basin is divided into seven major sub-basins. Each sub-basin is modeled separately with a data-driven model and the output discharges were routed to Lobith with another data-driven model. Basin averaged precipitation, basin averaged potential evapotranspiration, basin averaged fresh snow depths, basin averaged groundwater levels and major lake levels in the sub-basins are selected as low flow indicators and used as inputs to the models. The basin discretization and the selection of low flow indicators were not arbitrary since the dominant processes were considered by applying seasonality analysis to discharge time series from 108 sub-basins. Moreover, the correlations between indicators and low flows with varying temporal resolution and varying lags were used to identify appropriate temporal scales of the model inputs. The structure of the model can inherit uncertainty too due to many factors, including the lack of a robust hydrological theory at the spatial scale of the seven sub-basins. However, the parameter uncertainty is assumed to be the largest uncertainty source compared to other uncertainty sources. The effects of the input uncertainty were not assessed since averaging over sub-basins significantly reduces the measurement uncertainties. The model parameter sets were estimated using inverse modeling. The uncertainty of each weight is expressed as a probability distribution. Sensitivity analysis was applied for reducing the dimension and size of parameter space before uncertainty analysis. Finally, Monte Carlo Simulation was used to estimate the posterior distributions of the model outputs. The results in this study provide the effects of uncertainties in low flow model parameters on the model outputs. It has also been shown that the explicit assessment of uncertainties in the data-driven model parameters can lead to significant improvements in the information supply for low flow forecasting

Seasonal and long-term prediction of low flows in the Rhine Basin

The aim of this paper is to give information about a new project on the Rhine River. In this project we intent to identify appropriate low flow prediction models for the seasonal and long term by comparing uncertainties in low flows predicted by different pre-selected models

The skill of seasonal ensemble low-flow forecasts in the Moselle River for three different hydrological models

This paper investigates the skill of 90-day low-flow forecasts using two conceptual hydrological models and one data-driven model based on Artificial Neural Networks (ANNs) for the Moselle River. The three models, i.e. HBV, GR4J and ANN-Ensemble (ANN-E), all use forecasted meteorological inputs (precipitation P and potential evapotranspiration PET), whereby we employ ensemble seasonal meteorological forecasts. We compared low-flow forecasts for five different cases of seasonal meteorological forcing: (1) ensemble P and PET forecasts; (2) ensemble P forecasts and observed climate mean PET; (3) observed climate mean P and ensemble PET forecasts; (4) observed climate mean P and PET and (5) zero P and ensemble PET forecasts as input for the models. The ensemble P and PET forecasts, each consisting of 40 members, reveal the forecast ranges due to the model inputs. The five cases are compared for a lead time of 90 days based on model output ranges, whereas the models are compared based on their skill of low-flow forecasts for varying lead times up to 90 days. Before forecasting, the hydrological models are calibrated and validated for a period of 30 and 20 years respectively. The smallest difference between calibration and validation performance is found for HBV, whereas the largest difference is found for ANN-E. From the results, it appears that all models are prone to over-predict runoff during low-flow periods using ensemble seasonal meteorological forcing. The largest range for 90-day low-flow forecasts is found for the GR4J model when using ensemble seasonal meteorological forecasts as input. GR4J, HBV and ANN-E under-predicted 90-day-ahead low flows in the very dry year 2003 without precipitation data. The results of the comparison of forecast skills with varying lead times show that GR4J is less skilful than ANN-E and HBV. Overall, the uncertainty from ensemble P forecasts has a larger effect on seasonal low-flow forecasts than the uncertainty from ensemble PET forecasts and initial model conditions

The skill of seasonal ensemble low flow forecasts for four different hydrological models

This paper investigates the skill of 90 day low flow forecasts using two conceptual hydrological models and two data-driven models based on Artificial Neural Networks (ANNs) for the Moselle River. One data-driven model, ANN-Indicator (ANN-I), requires historical inputs on precipitation (P), potential evapotranspiration (PET), groundwater (G) and observed discharge (Q), whereas the other data-driven model, ANN-Ensemble (ANN-E), and the two conceptual models, HBV and GR4J, use forecasted meteorological inputs (P and PET), whereby we employ ensemble seasonal meteorological forecasts. We compared low flow forecasts without any meteorological forecasts as input (ANN-I) and five different cases of seasonal meteorological forcing: (1) ensemble P and PET forecasts; (2) ensemble P forecasts and observed climate mean PET; (3) observed climate mean P and ensemble PET forecasts; (4) observed climate mean P and PET and (5) zero P and ensemble PET forecasts as input for the other three models (GR4J, HBV and ANN-E). The ensemble P and PET forecasts, each consisting of 40 members, reveal the forecast ranges due to the model inputs. The five cases are compared for a lead time of 90 days based on model output ranges, whereas the four models are compared based on their skill of low flow forecasts for varying lead times up to 90 days. Before forecasting, the hydrological models are calibrated and validated for a period of 30 and 20 years respectively. The smallest difference between calibration and validation performance is found for HBV, whereas the largest difference is found for ANN-E. From the results, it appears that all models are prone to over-predict low flows using ensemble seasonal meteorological forcing. The largest range for 90 day low flow forecasts is found for the GR4J model when using ensemble seasonal meteorological forecasts as input. GR4J, HBV and ANN-E under-predicted 90 day ahead low flows in the very dry year 2003 without precipitation data, whereas ANN-I predicted the magnitude of the low flows better than the other three models. The results of the comparison of forecast skills with varying lead times show that GR4J is less skilful than ANN-E and HBV. Furthermore, the hit rate of ANN-E is higher than the two conceptual models for most lead times. However, ANN-I is not successful in distinguishing between low flow events and non-low flow events. Overall, the uncertainty from ensemble P forecasts has a larger effect on seasonal low flow forecasts than the uncertainty from ensemble PET forecasts and initial model conditions

Impacts of climate change on the seasonality of low flows in 134 catchments in the river Rhine basin using an ensemble of bias-corrected regional climate simulations. Discussion paper

The impacts of climate change on the seasonality of low flows are analysed for 134 sub-catchments covering the River Rhine basin upstream of the Dutch–German border. Three seasonality indices for low flows are estimated, namely seasonality ratio (SR), weighted mean occurrence day (WMOD) and weighted persistence (WP). These indices are related to the discharge regime, timing and variability in timing of low flow events respectively. The three indices are estimated from: (1) observed low flows; (2) simulated low flows by the semi distributed HBV model using observed climate; (3) simulated low flows using simulated inputs from seven climate scenarios for the current climate (1964–2007); (4) simulated low flows using simulated inputs from seven climate scenarios for the future climate (2063–2098) including different emission scenarios. These four cases are compared to assess the effects of the hydrological model, forcing by different climate models and different emission scenarios on the three indices. The seven climate scenarios are based on different combinations of four General Circulation Models (GCMs), four Regional Climate Models (RCMs) and three greenhouse gas emission scenarios.\ud \ud Significant differences are found between cases 1 and 2. For instance, the HBV model is prone to overestimate SR and to underestimate WP and simulates very late WMODs compared to the estimated WMODs using observed discharges. Comparing the results of cases 2 and 3, the smallest difference is found in the SR index, whereas large differences are found in the WMOD and WP indices for the current climate. Finally, comparing the results of cases 3 and 4, we found that SR has decreased substantially by 2063–2098 in all seven subbasins of the River Rhine. The lower values of SR for the future climate indicate a shift from winter low flows (SR > 1) to summer low flows (SR < 1) in the two Alpine subbasins. The WMODs of low flows tend to be earlier than for the current climate in all subbasins except for the Middle Rhine and Lower Rhine subbasins. The WP values are slightly larger, showing that the predictability of low flow events increases as the variability in timing decreases for the future climate. From comparison of the uncertainty sources evaluated in this study, it is obvious that the RCM/GCM uncertainty has the largest influence on the variability in timing of low flows for future climate

Seasonality of low flows and dominant processes in the Rhine River

Low flow forecasting is crucial for sustainable cooling water supply and planning of river navigation in the Rhine River. The first step in reliable low flow forecasting is to understand the characteristics of low flow. In this study, several methods are applied to understand the low flow characteristics of Rhine River basin. In 108 catchments of the Rhine River, winter and summer low flow regions are determined with the seasonality ratio (SR) index. To understand whether different numbers of processes are acting in generating different low flow regimes in seven major sub-basins (namely, East Alpine, West Alpine, Middle Rhine, Neckar, Main, Mosel and Lower Rhine) aggregated from the 108 catchments, the dominant variable concept is adopted from chaos theory. The number of dominant processes within the seven major sub-basins is determined with the correlation dimension analysis. Results of the correlation dimension analysis show that the minimum and maximum required number of variables to represent the low flow dynamics of the seven major sub-basins, except the Middle Rhine and Mosel, is 4 and 9, respectively. For the Mosel and Middle Rhine, the required minimum number of variables is 2 and 6, and the maximum number of variables is 5 and 13, respectively. These results show that the low flow processes of the major sub-basins of the Rhine could be considered as non-stochastic or chaotic processes. To confirm this conclusion, the rescaled range analysis is applied to verify persistency (i.e. non-randomness) in the processes. The estimated rescaled range statistics (i.e. Hurst exponents) are all above 0.5, indicating that persistent long-term memory characteristics exist in the runoff processes. Finally, the mean values of SR indices are compared with the nonlinear analyses results to find significant relationships. The results show that the minimum and maximum numbers of required variables (i.e. processes) to model the dynamic characteristics for five out of the seven major sub-basins are the same, but the observed low flow regimes are different (winter low flow regime and summer low flow regime). These results support the conclusion that a few interrelated nonlinear variables could yield completely different behaviour (i.e. dominant low flow regime)