Combining FAO Model and Vegetation Indices to Estimate Crop Coefficient Using Principle Component Analysis

The globally growing demand for water has shown the need for its efficient and judicial utilization, and particularly in agriculture being single largest consumer of water. Crop evapotranspiration represents crop water demand and governed by weather and crop conditions and most of the current water demand models are non-spatial models, they use point data. Global scale satellite images can solve these problems. According to the high performance of satellite indices, it is necessary to estimate crop coefficient using combination of reflectance and thermal bands. The aim of this research was to estimate the effective crop coefficient of potato using vegetation indices and principle component analysis.
Principle component analysis (PCA) was used for effective crop coefficient estimation. Modeling of associations between vegetation indices and crop coefficient were conducted using artificial neural network. In the present study, NDVI, RI, EVI, SAVI, MSAVI, NVSWI, TVX, TVI, mNDVI and mTVI were the used as vegetation indices. PCA is designed to transform the original variables into new and uncorrelated variables (axes), namely the principal components, which are linear combinations of the original variables. The new axes lie along the directions of maximum variance. PCA provides an objective procedure of finding indices and information on the most meaningful parameters, which describes a whole data set affording data reduction with minimum loss of original information. Artificial neural networks are a computational model which is based on a large collection of simple neural units, loosely analogous to the observed behavior of a biological brain's axons. RMSE, MAE and MARE were the statistics used for investigating the performance of crop coefficient of vegetation indices with FAO crop coefficient.
Eleven MODIS vegetation indices are derived in the period of 2013 to 2016 for potato over the limited area between Tabriz and Bostanabad. The last year was considered as the validation period. According to the FAO-56 paper, the lengths of initial stage, crop development stage, mid-season stage, late season stage were considered to be 25, 30, 45, 30 days, respectively. The vegetation indices were derived using MODIS sensor with 2×2 pixels. The PCA showed that with increasing the number of components, the eigenvalues decreased. The analysis indicated that the three first components accounted for the 85.45 % of the total variance of data and the eigenvalues of them were greater than 1, the three first components were thus selected. NDVI, RI, TVI, MSAVI and NVSWI in the first component, mNDVI in the second component and LST in the third component had the highest coefficients. NDVI in the first component with high coefficient indicted the importance of index in the crop coefficient determination. The coefficients of SAVI and MSAVI were higher than NDVI. From the three investigations on the kind of principle component, the first investigation led to a 55.75 % decrease in RMSE relative to the second and third investigations. The first and second components together had less error rather than third component. The average of MAE for first, second and third investigations was, respectively, 0.17, 0.22 and 0.2. Therefore, component with exact values of particular vectors resulted in a reduced error. The sensitivity of artificial neural network led to an increase in the simulation accuracy (for example the RMSE decreased from epoch 100 to 50 was 48.27%). Crop coefficient estimation using vegetation indices of principle component analysis was underestimated about 1% in the validation period. Overestimation and underestimation were found in the initial and crop development stages, respectively.
The quantities of statistics showed the improvement of artificial neural network performance with combination of vegetation indices using principle component analysis. The vegetation indices with reflectance bands performed well. The combination of thermal and reflectance bands enhanced the vegetation indices efficiency. In addition to NDVI index for crop coefficient estimation, improvement of indices according to the study area condition increased the indices performance. The kind of mathematical equations of indices can increase the indices performance which using the same bands with different equations have different results. The selected component of principle component analysis has important role in increasing the simulation accuracy. The error reduction of simulated crop coefficients can increase the precision of irrigation consumption and agricultural planning which the principle component analysis has more important role.