Prediction of evapotranspiration using a nonlinear local approximation approach

Evapotranspiration is a key process in the water cycle. Evapotranspiration is influenced by several hydro-meteorological variables in complex and nonlinear ways and, therefore, its estimation is often very challenging. This study employs a chaotic time series approach to predict evapotranspiration. Measured monthly evapotranspiration data over a period of 40 years (1976–2015) from the Rietholzbach monitoring station in Switzerland are analysed. The nonlinear local approximation prediction method, which uses nearest neighbours, is employed. The method involves the following steps: (1) Phase-space reconstruction of a single-variable time series in a multi-dimensional phase space using delay embedding; (2) Identification of the nearest reconstructed vectors using Euclidean distance; and (3) Prediction of the future value based on the evolution of the nearest neighbours in the phase-space. The phase-space reconstruction is done with embedding dimension (m) from 1 to 10, and nearest neighbours (k) varying from 1 to 300 are used for prediction. Out of the 480 monthly evapotranspiration values available, the first 320 values are used for phase-space reconstruction and prediction, and the remaining 160 values are used for checking the prediction accuracy. The performance of the prediction method is evaluated using correlation coefficient and root mean square error. The results generally indicate very good predictions. The prediction accuracy generally increases with an increase in the embedding dimension up to a certain point and then somewhat saturates beyond that point. The best predictions are achieved when the embedding dimension is five and the number of neighbours is 10, with a correlation coefficient value of 0.86 and root mean square error value of 14.64 mm. The low embedding dimension and small number of neighbours yielding the best predictions suggest that the dynamics of monthly evapotranspiration in the Rietholzbach station exhibit chaotic behaviour dominated by five governing variables. The optimal embedding dimension value obtained from the prediction method also matches with the optimal embedding dimension estimated using the False Nearest Neighbour (FNN) algorithm, which is a dimensionality-based approach. The results from this study have important implications for modelling and prediction of evapotranspiration.

Keywords:

Evapotranspiration, Chaos, Local approximation prediction, Phase space reconstruction, False nearest neighbour algorithm