Evaluation of spline and bezier interpolation functions in reference evapotranspiration modeling using satellite image data

Introduction

Reference evapotranspiration is one of the important processes in the water cycle that has a great impact on water resources and agriculture. Climate change can affect this process and requires accurate spatial-temporal analysis. The standard method for calculating reference evapotranspiration is the FAO-56 Penman-Monteith method that requires meteorological data. But in some areas, there is not enough data and therefore other methods such as machine learning and remote sensing are used. These methods can estimate reference evapotranspiration with high accuracy using different variables such as vegetation indices, temperature, humidity, and wind speed. Some of these methods are random forest, support vector regression, generalized regression neural network, and gene expression programming. These methods can also help in assessing the importance of predictor variables and their uncertainties.

Materials and Methods

The aim of this article is to model daily reference evapotranspiration (ET0) using data collected from meteorological and satellite sources and implementing random forest (RF) algorithm. The standard FAO-Penman-Monteith method, which is based on the Penman-Monteith equation that integrates radiometric and aerodynamic parameters, was adopted as the base method for calculating ET0 of a reference crop. However, this method demands a large amount of meteorological data such as solar radiation, relative humidity, wind speed, and maximum/minimum temperature, which can be challenging to obtain. To overcome this limitation, satellite images from Google Earth Engine system for the years 2001 to 2021 were processed using Landsat and MODIS sensors to extract parameters such as land surface temperature (LST), enhanced vegetation index (EVI), leaf area index (LAI), and normalized difference vegetation index (NDVI). These parameters can be used to estimate effective evapotranspiration continuously in the short term by applying models and interpolations. One of the problems of planning and management based on satellite image data is the lack of daily images of the study area. One of the ways of time microscaling of this valuable information is interpolation. In other words, interpolation is a mathematical process that estimates unknown data at other points using data available at specific points. This process is used to fill in gaps, increase resolution, or create continuous maps from satellite data. The importance of satellite data interpolation is that it can help improve the quality and accuracy of data and use them to study and predict various meteorological, agricultural, geological, etc. phenomena. In this research, LST (8 days) and vegetation cover data (16 days) were converted into daily data using spline and cubic spline interpolation functions. This work has been done using spline and Bezier interpolation functions and for days without data with equal intervals by coding in Mathematica programming environment.

Results and Discussion

This research used satellite and meteorological data and the random forest machine learning method to estimate the ET0 at Tabriz and Ardabil stations. The results showed that the saturation vapor pressure and the land surface temperature at night and day had the highest correlation and coefficient of determination with the ET0. The highest accuracy of ET0 estimation at Tabriz was in scenario 10 with error of 0.364 and at Ardabil in scenario 12 with error of 0.430. The best model was the combination of meteorological and satellite parameters. The spline interpolation method provided a better modeling than the bezier method. Additionally, increasing the parameters involved in machine learning and the LAI parameter reduced the accuracy.

Douna et al. (2021) investigated the ability of the RF method to predict daily ET0 in three regions in Australia from 2010 to 2014, using satellite data of LAI and LST and regional meteorological parameters. They stated that the LAI is the most important variable, and they also obtained satisfactory performance in three regions, with RMSE errors of about 1 mm per day. At the same time, for Tabriz and Ardabil stations, the LST values were more important than the LAI and more correlated with ET0. Therefore, by combining meteorological and satellite data, the amount of RMSE errors was reduced to 0.364 and 0.430 mm in Spline and Bezier intyerpolation functions.

Conclusion

The results of the research showed that 1) at Tabriz station, among all meteorological parameters, saturation vapor pressure and among satellite parameters, land surface temperature at night had the highest correlation with daily ET0. 2) At Ardabil station, in the same time period, saturation vapor pressure also had the highest correlation of 0.887, but among satellite parameters, land surface temperature at day had the highest correlation of 0.737 with daily ET0. 3) The highest accuracy of daily ET0 estimation at Tabriz was in spline and random forest methods in scenario 10 with error of 0.364 and in bezier methods in scenarios 14 and 16 with error of 0.380. 4) At Ardabil station, both spline and bezier methods had the highest accuracy in scenario 12 with errors of 0.430 and 0.453, respectively. 5) In both spline and bezier interpolation methods, the most accurate model was the combination of meteorological and satellite parameters. 6) In general, spline interpolation method provided a better modeling than bezier. Increasing the parameters involved in machine learning, which were calculated using the available data, had no positive effect on the accuracy of the model. 7) Adding the LAI parameter, which was calculated using the EVI data, to the machine learning model, reduced the accuracy in spline method.