Rainfall-runoff modelling using genetic programming

Abstract

The problem of accurately determining river flows from rainfall, evaporation and other factors, occupies an important place in hydrology. The rainfall-runoff process is believed to be highly non-linear, time varying, spatially distributed and not easily described by simple models. Practitioners in water resources have embraced data-driven modelling approaches enthusiastically, as they are perceived to overcome some of the difficulties associated with physics-based approaches. Such approaches have proved to be an effective and efficient way to model the rainfall-runoff process in situations where enough data on physical characteristics of catchment is not available or when it is essential to predict the flow in the shortest possible time to enable sufficient time for notification and evacuation procedures. In the recent past, an evolutionary based data-driven modelling approach, genetic programming (GP) has been used for rainfall-runoff modelling. In this study, GP has been applied for predicting the runoff from three catchments - a small steep-sloped catchment in Hong Kong (Hok Tau catchment) and two relatively bigger catchments located in the southern part of China (Shanqiao and Shuntian catchments). For the runoff predictions in Hok Tau catchment, the performance of the data-driven technique was not very satisfactory. This catchment, being a very steep-sloped catchment, has high peak discharge magnitudes with steep rising and recession limbs, which the GP models are unable to capture. This catchment being a small one with an area of about 5 km2 has a time of concentration of about 30-45 minutes, but the time interval of the available data is one day, which seems to be another reason for GP's inability to capture the complex rainfall to runoff transformation on this catchment. Using a dataset of smaller time interval, the data-driven model should perform better. A key advantage of GP as compared to traditional modelling approaches is that it does not assume any a priori functional form of the solution. For instance, in a typical regression method, the model structure is specified in advance (which is in general difficult to do) and the model coefficients are determined. For neural networks, the time consuming task of initially defining the network structure has to be undertaken and then the coefficients (weights) are found by the learning algorithm. On the other hand, in GP, the building blocks (the input and target variables and the function set) are defined initially, and the learning method subsequently finds both the optimal structure of the model and its coefficients. Moreover, since GP evolves an equation or formula relating the input and output variables, a major advantage of the GP approach is its automatic ability to select input variables that contribute beneficially to the model and disregard those that do not. GP can thus reduce substantially the dimensionality of the input variables. In GP, as in any data-driven prediction model, the selection of appropriate model inputs is extremely important. This is especially so when lagged input variables are also used. Inclusion of irrelevant inputs leads to poor model accuracy and creation of complex models, which are more difficult to interpret as compared to simpler ones. Thus, for the remaining two catchments, an attempt is made to use the evolutionary search capabilities of GP for selecting the significant input variables. These variables, indicated as significant by GP are then used as inputs for the actual predictions. In contrast to the not so satisfactory performance by the GP models for predicting the runoff from Hok Tau catchment, their performance for the other two catchments is quite satisfactory, as the GP models are able to capture the peaks quite well and the goodness-of-fit measures are also acceptable. These results indicate that GP can be used as a viable alternative for rainfall-runoff modelling, and the analytical form of the evolved equations facilitate easy interpretation. In this study, the GP evolved models are used for selection of significant variables influencing the rainfall to runoff transformation.