An Index Used to Evaluate the Applicability of Mid-to-Long-Term Runoff Prediction in a Basin Based on Mutual Information

Abstract

Accurate and reliable mid-to-long-term runoff prediction (MLTRP) is of great importance in water resource management. However, the MLTRP is not suitable in each basin, and how to evaluate the applicability of MLTRP is still a question. Therefore, the total mutual information (TMI) index is developed in this study based on the predictor selection method using mutual information (MI) and partial MI (PMI). The relationship between the TMI and the predictive performance of five AI models is analyzed by applying five models to 222 forecasting scenarios in Australia. This results in over 222 forecasting scenarios which demonstrate that, compared with the MI, the developed TMI index can better represent the available information in the predictors and has a more significant negative correlation with the RRMSE, with a correlation coefficient between −0.62 and −0.85. This means that the model’s predictive performance will become better along with the increase in TMI, and therefore, the developed TMI index can be used to evaluate the applicability of MLTRP. When the TMI is more than 0.1, the available information in the predictors can support the construction of MLTRP models. In addition, the TMI can be used to partly explain the differences in predictive performance among five models. In general, the complex models, which can better utilize the contained information, are more sensitive to the TMI and have more significant improvement in terms of predictive performance along with the increase in TMI.