The Random Forest (RF) algorithm, a decision-tree-based technique, has become a promising approach for applications addressing runoff forecasting in remote areas. This machine learning approach can overcome the limitations of scarce spatio-temporal data and physical parameters needed for process-based hydrological models. However, the influence of RF hyperparameters is still uncertain and needs to be explored. Therefore, the aim of this study is to analyze the sensitivity of RF runoff forecasting models of varying lead time to the hyperparameters of the algorithm. For this, models were trained by using (a) default and (b) extensive hyperparameter combinations through a grid-search approach that allow reaching the optimal set. Model performances were assessed based on the R2, %Bias, and RMSE metrics. We found that: (i) The most influencing hyperparameter is the number of trees in the forest, however the combination of the depth of the tree and the number of features hyperparameters produced the highest variability-instability on the models. (ii) Hyperparameter optimization significantly improved model performance for higher lead times (12- and 24-h). For instance, the performance of the 12-h forecasting model under default RF hyperparameters improved to R2 = 0.41 after optimization (gain of 0.17). However, for short lead times (4-h) there was no significant model improvement (0.69 < R2 < 0.70). (iii) There is a range of values for each hyperparameter in which the performance of the model is not significantly affected but remains close to the optimal. Thus, a compromise between hyperparameter interactions (i.e., their values) can produce similar high model performances. Model improvements after optimization can be explained from a hydrological point of view, the generalization ability for lead times larger than the concentration time of the catchment tend to rely more on hyperparameterization than in what they can learn from the input data. This insight can help in the development of operational early warning systems.
New Lump Solutions for Spatio-Temporal Dispersion (1+1)-Dimensional Ito-Equation
