Comparing M5 Model Trees and Neural Networks for River Level Forecasting

Artificial neural networks (ANNs) have been the subject of much research activity in hydrological modelling over the last decade yet this represents only one data-driven modelling approach from among a very rich set. M5 model trees are an example of a technique that has had little application in the hydrological domain yet the results are promising (Solomatine and Xue, 2004). They are a machine learning approach that combines regression trees and classification. The input space is partitioned into subsets based on entropy measures, and regression equations are then fit to these subsets. The advantages over ANNs are (a) their ability to provide knowledge in the form of a decision tree and (b) much faster training times. This has important implications for operational use as they are not black box models. In this study ANNs, M5 model trees and time series analysis have been used to develop models to predict river levels at a gauging station in the River Ouse catchment in Northern England. Two lead times have been used: t+6 and t+24 hours. The input data consisted of historical levels at the gauging stations, upstream level data and rainfall from five rain gauges across the catchment, determined by correlation with the output. The results of the study showed that the ANNs outperformed both the M5 model trees and time series approaches when considering global goodness-of-fit measures such as root mean squared error and coefficient of efficiency. However, the difference in performance between the ANNs and M5 model trees was not large, e.g. 1 percent difference in coefficient of efficiency for t+6 hours. When considering the longer lead time of t+24 hours, the performance of the ANNs and M5 model trees almost converged. The M5 model tree, however, also provides the rules of operation. The first partition for both the t+6 and t+24 hour models was determined by the value of the river level at one of the upstream stations. The individual regression equations associated with each partition clearly indicate the importance of different inputs; for example, one of the rain gauges is never used, despite selection through correlation analysis. The importance of different upstream stations as level increases is also clearly identified. This type of knowledge coupled with a good performing model has shown that M5 model trees have great operational potential. Solomatine, D.P. and Xue, Y.P. 2004. M5 model trees and neural networks: Application to flood forecasting in the upper reach of the Huai River in China, J. of Hydrol. Eng., 9: 491-501.