Error propagation approach for estimating root mean square error of the reference evapotranspiration when estimated with alternative data

Estimation of reference evapotranspiration (ET₀) with the Food and Agricultural Organisation (FAO) Penman-Monteith model requires temperature, relative humidity, solar radiation, and wind speed data. The lack of availability of the complete data set at some meteorological stations is a severe restriction for the application of this model. To overcome this problem, ET₀ can be calculated using alternative data, which can be obtained via procedures proposed in FAO paper No.56. To confirm the validity of reference evapotranspiration calculated using alternative data (ET_0(Alt)), the root mean square error (RMSE) needs to be estimated; lower values of RMSE indicate better validity. However, RMSE does not explain the mechanism of error formation in a model equation; explaining the mechanism of error formation is useful for future model improvement. Furthermore, for calculating RMSE, ET₀ calculations based on both complete and alternative data are necessary. An error propagation approach was introduced in this study both for estimating RMSE and for explaining the mechanism of error formation by using data from a 30-year period from 48 different locations in Japan. From the results, RMSE was confirmed to be proportional to the value produced by the error propagation approach (ΔET₀). Therefore, the error propagation approach is applicable to estimating the RMSE of ET_0(Alt) in the range of 12%. Furthermore, the error of ET_0(Alt) is not only related to the variables’ uncertainty but also to the combination of the variables in the equation.