On the relative importance of water temperature versus radiation for ANN-based pan evaporation modelling

Evaporation from the water surface is among the main water losses from natural and artificial lakes and ponds. Air temperature (T_a), wind speed (v_a), relative humidity (RH), atmospheric pressure (p_a), surface water temperature (T_w) and radiation (R) are among the physical controls of this process. In recent years, water temperature data have increasingly become available so that the question arises, if the measurement of radiation (which, in turn, affects water temperature) may still be required.

The method employed in this study is modelling of daily evaporation by means of artificial neural networks (ANNs) of the multilayer perceptron type (backpropagation, one hidden layer), using varying sets of input variables. Evaporation data from a white Class A pan (Qiu et al., 2022) served as target (50 patterns of daily averages). A logistic activation function was used. Data records were divided 2:1 into training and testing sets, resp.

Data were scaled to the interval between 0.1 and 0.9, and for each run (10⁵ epochs) the root mean square error (RMSE) of the scaled output was computed.

Learning rate (η), momentum (α) and number of hidden nodes were subject to optimization for three different sets of input variables. ANN runs of series S1 comprised T_a, v_a, RH, p_a, T_w and incoming solar radiation (R) as inputs (6 in total). Series S2 and S3 were subsets of S1, with S2 using T_a, v_a, RH, p_a and T_w as inputs. For the input data of Series S3, water temperature T_w  was replaced by radiation R.

The neural networks achieved a fair representation of the evaporation data. Optimization yielded a minimum RMSE for Series S1 of 0.0514 and 0.0669 for training and testing, resp. (6 hidden nodes, η=0.009 and α=0.0). 

Using the same input variables with the exception of the incoming radiation (in total, therefore, 5 inputs) S2 reached a minimum training RMSE of 0.0557 and a minimum testing RMSE of 0.0887 (5 hidden nodes, η=0.012 and α=0.0).

Series S3 with the 5 inputs T_a, v_a, RH, p_a and R (with water temperature left out), finally achieved an RMSE of 0.0545 for training and 0.0775 for testing, resp. (6 hidden nodes, η=0.006 and α=0.2).

Comparison of Series S2 and S3 shows that, in the case of the data set studied here, the ANNs including incoming radiation among their input variables (but excluding water temperature) outperformed those explicitly accounting for water temperature in lieu of radiation. Using both radiation and water temperature as inputs (S1) resulted in a notable improvement of the ANN output as compared to the runs with either of these variables not accounted for explicitly.

References

Qiu, G. Y., Gao, H., Yan, C., Wang, B., Luo, J., & Chen, Z. (2022): An improved approach for estimating pan evaporation using a new aerodynamic mechanism model. Water Resources Research, 58, e2020WR027870. https://doi.org/10.1029/2020WR027870.