A comprehensive data driven modeling experiment is presented in a two-part paper. In this first part, an extensive data-driven modeling experiment is proposed. The most important concerns regarding the way data driven modeling (DDM) techniques and data were handled, compared, and evaluated, and the basis on which findings and conclusions were drawn are discussed. A concise review of key articles that presented comparisons among various DDM techniques is presented. Six DDM techniques, namely, neural networks, genetic programming, evolutionary polynomial regression, support vector machines, M5 model trees, and K-nearest neighbors are proposed and explained. Multiple linear regression and naïve models are also suggested as baseline for comparison with the various techniques. Five datasets from Canada and Europe representing evapotranspiration, upper and lower layer soil moisture content, and rainfall-runoff process are described and proposed, in the second paper, for the modeling experiment. Twelve different realizations (groups) from each dataset are created by a procedure involving random sampling. Each group contains three subsets; training, cross-validation, and testing. Each modeling technique is proposed to be applied to each of the 12 groups of each dataset. This way, both prediction accuracy and uncertainty of the modeling techniques can be evaluated. The description of the datasets, the implementation of the modeling techniques, results and analysis, and the findings of the modeling experiment are deferred to the second part of this paper.

In this second part of the two-part paper, the data driven modeling (DDM) experiment, presented and explained in the first part, is implemented. Inputs for the five case studies (half-hourly actual evapotranspiration, daily peat soil moisture, daily till soil moisture, and two daily rainfall-runoff datasets) are identified, either based on previous studies or using the mutual information content. Twelve groups (realizations) were randomly generated from each dataset by randomly sampling without replacement from the original dataset. Neural networks (ANNs), genetic programming (GP), evolutionary polynomial regression (EPR), Support vector machines (SVM), M5 model trees (M5), K-nearest neighbors (K-nn), and multiple linear regression (MLR) techniques are implemented and applied to each of the 12 realizations of each case study. The predictive accuracy and uncertainties of the various techniques are assessed using multiple average overall error measures, scatter plots, frequency distribution of model residuals, and the deterioration rate of prediction performance during the testing phase. Gamma test is used as a guide to assist in selecting the appropriate modeling technique. Unlike two nonlinear soil moisture case studies, the results of the experiment conducted in this research study show that ANNs were a sub-optimal choice for the actual evapotranspiration and the two rainfall-runoff case studies. GP is the most successful technique due to its ability to adapt the model complexity to the modeled data. EPR performance could be close to GP with datasets that are more linear than nonlinear. SVM is sensitive to the kernel choice and if appropriately selected, the performance of SVM can improve. M5 performs very well with linear and semi linear data, which cover wide range of hydrological situations. In highly nonlinear case studies, ANNs, K-nn, and GP could be more successful than other modeling techniques. K-nn is also successful in linear situations, and it should not be ignored as a potential modeling technique for hydrological applications.

This paper explores the use of flow length and travel time as a pre-processing step for incorporating spatial precipitation information into Artificial Neural Network (ANN) models used for river flow forecasting. Spatially distributed precipitation is commonly required when modelling large basins, and it is usually incorporated in distributed physically-based hydrological modelling approaches. However, these modelling approaches are recognised to be quite complex and expensive, especially due to the data collection of multiple inputs and parameters, which vary in space and time. On the other hand, ANN models for flow forecasting are frequently developed only with precipitation and discharge as inputs, usually without taking into consideration the spatial variability of precipitation. Full inclusion of spatially distributed inputs into ANN models still leads to a complex computational process that may not give acceptable results. Therefore, here we present an analysis of the flow length and travel time as a basis for pre-processing remotely sensed (satellite) rainfall data. This pre-processed rainfall is used together with local stream flow measurements of previous days as input to ANN models. The case study for this modelling approach is the Ganges river basin. A comparative analysis of multiple ANN models with different hydrological pre-processing is presented. The ANN showed its ability to forecast discharges 3-days ahead with an acceptable accuracy. Within this forecast horizon, the influence of the pre-processed rainfall is marginal, because of dominant influence of strongly auto-correlated discharge inputs. For forecast horizons of 7 to 10 days, the influence of the pre-processed rainfall is noticeable, although the overall model performance deteriorates. The incorporation of remote sensing data of spatially distributed precipitation information as pre-processing step showed to be a promising alternative for the setting-up of ANN models for river flow forecasting.

This study proposes a new hybrid model for monthly streamflow predictions by coupling a physically based distributed hydrological model with a deep learning (DL) model. Specifically, a simplified hydrological model is first developed by optimally selecting grid cells from a distributed hydrological model according to their soil moisture characteristics. It is then driven by bias corrected general circulation model (GCM) predictions to generate soil moistures for the forecasting months. Finally, model‐simulated soil moisture along with other predictors from multiple sources are used as inputs of the DL model to predict future monthly streamflows. The proposed hybrid model, using the simplified Variable Infiltration Capacity (VIC) as the hydrological model and the combination of Convolutional Neural Network and Gated Recurrent Unit (CNN‐GRU) as the DL model, is applied to predict 1‐, 3‐, and 6‐month ahead reservoir inflows for the Danjiangkou Reservoir in China. The results show that the hybrid model consistently performs better than VIC and CNN‐GRU models with great improvement in Kling‐Gupta efficiency (KGE) values for lead times up to 6 months. Additional tests indicate that hybrid models based on CNN‐GRU outperform those based on LASSO, XGBoost, CNN, and GRU models. Moreover, compared with the distributed hydrological model, the hybrid model greatly reduces the computation burden of rolling prediction. It also saves decision‐makers the time and effort of trying different combinations of predictors, which is indispensable when building DL models. Overall, the new hybrid model demonstrates great potential for monthly streamflow prediction where training data are limited.

The recent concerns for world-wide extreme events related to climate change have motivated the development of large scale models that simulate the global water cycle. In this context, analysis of hydrological extremes is important and requires the adaptation of identification methods used for river basin models. This paper presents two methodologies that extend the tools to analyze spatio-temporal drought development and characteristics using large scale gridded time series of hydrometeorological data. The methodologies are classified as non-contiguous and contiguous drought area analyses (i.e. NCDA and CDA). The NCDA presents time series of percentages of areas in drought at the global scale and for pre-defined regions of known hydroclimatology. The CDA is introduced as a complementary method that generates information on the spatial coherence of drought events at the global scale. Spatial drought events are found through CDA by clustering patterns (contiguous areas). In this study the global hydrological model WaterGAP was used to illustrate the methodology development. Global gridded time series of subsurface runoff (resolution 0.5°) simulated with the WaterGAP model from land points were used. The NCDA and CDA were developed to identify drought events in runoff. The percentages of area in drought calculated with both methods show complementary information on the spatial and temporal events for the last decades of the 20th century. The NCDA provides relevant information on the average number of droughts, duration and severity (deficit volume) for pre-defined regions (globe, 2 selected hydroclimatic regions). Additionally, the CDA provides information on the number of spatially linked areas in drought, maximum spatial event and their geographic location on the globe. Some results capture the overall spatio-temporal drought extremes over the last decades of the 20th century. Events like the El Niño Southern Oscillation (ENSO) in South America and the pan-European drought in 1976 appeared clearly in both analyses. The methodologies introduced provide an important basis for the global characterization of droughts, model inter-comparison of drought identified from global hydrological models and spatial event analyses.

In hydrological sciences there is an increasing tendency to explore and improve artificial neural network (ANN) and other data-driven forecasting models. Attempts to improve such models relate, to a large extent, to the recognized problems of their physical interpretation. The present paper deals with the problem of incorporating hydrological knowledge into the modelling process through the use of a modular architecture that takes into account the existence of various flow regimes. Three different partitioning schemes were employed: automatic classification based on clustering, temporal segmentation of the hydrograph based on an adapted baseflow separation technique, and an optimized baseflow separation filter. Three different model performance measures were analysed. Three case studies were considered. The modular models incorporating hydrological knowledge were shown to be more accurate than the traditional ANN-based models. Résumé En sciences hydrologiques il y a une tendance croissante à explorer et améliorer les réseaux de neurones artificiels (RNA) et d'autres modèles de prévision conditionnés par les données. Les tentatives d'amélioration de tels modèles sont largement reliées aux problèmes reconnus de leur interprétation physique. Cet article traite du problème de l'incorporation de connaissance hydrologique dans le processus de modélisation grâce à l'utilisation d'une architecture modulaire qui tient compte de l'existence de divers régimes d'écoulement. Trois différents schémas de partition ont été employés: une classification automatique basée sur le regroupement, une segmentation temporelle de l'hydrogramme basée sur une technique adaptée de séparation de l'écoulement de base, et un filtre optimisé de séparation l'écoulement de base. Trois différentes mesures de performance de modélisation ont été analysées. Trois études de cas ont été considérées. Les modèles modulaires incorporant de la connaissance hydrologique se...