Nonparametric method for estimating the effects of climatic and catchment characteristics on mean annual evapotranspiration

Abstract

It is now well known that forested catchments have higher evapotranspiration than grassed catchments. Models for mean annual evapotranspiration have been developed to quantify catchment scale differences in mean annual evapotranspiration. Zhang et al. (2001) developed a simple, one parameter, model for the relationships between evapotranspiration and vegetation cover by evaluating the differences of model parameter values for different vegetation covers. However, other factors such as climate and catchment topography may also affect evapotranspiration and therefore the model parameter. Simple models acknowledging only categorical vegetation cover (forested, mixed, and grassed) may introduce some uncertainty, and more seriously, lead to inconsistent conclusions regarding relationships between vegetation cover and evapotranspiration. Zhang et al. (2004) investigated possible inclusion of climatic factors and catchment characteristics to improve the estimation of mean annual evapotranspiration by modeling the residuals of the model parameter via a stepwise linear regression. In this paper we propose the use of a multivariate adaptive regression spline (MARS) model for estimating the model parameter. In contrast to a simple stepwise regression, the MARS model provides not only insight into the interactions between explanatory factors but also a potential for prediction for ungauged basins as long as the values of explanatory factors are within the domain of calibration catchments. The MARS model is able to determine statistically significant factors and therefore is a powerful tool to identify important factors and their interactions. Using 241 Australian catchments where climate factors and catchment characteristics are available, we found the following significant terms affecting the mean annual evapotranspiration. (1) The functional relationship with the number of months that peak precipitation follows peak potential evapotranspiration (PfE) states that closer phase between precipitation and potential evapotranspiration results in less streamflow. (2) The interactions between coefficient of variation of precipitation and average storm depth shows that the value of the model parameter is smaller when the coefficient of variance of precipitation is larger than 2.24 and the average storm depth is less than 8.70 mm d−1. (3) The interaction between relief ratio and average storm depth term shows that both larger average storm depth in flat catchments and smaller average storm depth in hilly catchments result in more streamflow. (4) The interaction between relief ratio and forest coverage reveals that for flat catchments with reasonable forest cover, increasing forest cover generally results in more mean annual evapotranspiration and less mean annual streamflow. The performance of the MARS model was assessed by a calibration‐testing procedure to support its usage for prediction for ungauged basins.