Diagnostics of the Theoretical Underpinning of the Socio-hydrological Model in "Water Effciency in Sustainable Cotton-based Production Systems" Project in Maharashtra, India: Evaluation of model performance and the quantication of errors using Monte Carlo sampling, GLUE, linear regressions, linear PCA, and kernel PCA
This research is part of the project "Water Efficiency in Sustainable Cotton-based Production Systems” between Solidaridad Asia and TU Delft. The project aims to increase the livelihood of smallholder farmers in the Maharashtra, India through. A socio-hydrological (SH) model is used extensively in this research as an evaluation tool. However, the baseline research indicates that the lack of stress mechanics in the SH model used in the intervention might cause inaccuracies in yield estimation. Furthermore, it has never been validated at a farmer level before. This research aims to implement the stress mechanics in the SH model, evaluate the overall performance of the model in terms of predicting crop yield, identify potential sources of errors, and give recommendations for future studies. The research uses iterative top-down approach due to the large study area and the varied nature of the 308 farmers surveyed. The research implements the water and temperature stress mechanics based on Food and Agriculture Organization's (FAO) AquaCrop framework. For the performance evaluation process, this research uses four model scores namely Nash-Sutcliffe (NS), log of NS, Mean Absolute Error (MAE), and the coefficient of determination. Furthermore, the sources of uncertainties are divided into two categories namely lack of knowledge (i.e. generated by parameter, input, observation, and structural errors) and variability (i.e. generated by climate variations). The lack of knowledge uncertainty is investigated using Monte Carlo Sampling calibration and the Generalized Likelihood Uncertainty Estimation (GLUE) concept is used to obtain the uncertainty intervals of the model. Going further, the errors are divided into residual and structural error. The latter is explained and quantified through a structural error model using a combination of qualitative analysis, Principal Component Analysis, multiple linear regressions, and projection of the data into kernel space. Then residuals between the model yield + structural error vs. the observed yield is thought to be explained by the residual errors. Lastly, the effects of climate variations to the stability of the model are evaluated.
After the initial calibration, the model scores are NS: -0.343 to -0.996, log of NS: -0.655 to -1.91, MAE: 447.1 to 553.2 kg/ha, and r-squared: 0.003 to 0.008. Because of the poor performance of the model, the uncertainty intervals from GLUE are not enough to capture the total errors of the model. However, after adjustment using the structural error model, the model scores become NS: 0.83, log of NS: 0.56, MAE: 149 kg/ha, and r-squared: 0.859. The adjusted yield calculation has a residual error as Gaussian distribution with standard deviation of 150 kg/ha. The qualitative analysis identified several factors that contribute to the errors viz. farmers' capital, irrigation behavior, and crop production process such as canopy cover growth. Lastly, there is no major instability found through the bootstrap analysis. The physical model is not performing well, especially when it is calculating yield for individual farmers over a large study area. However, the structural error model can adjust the yield prediction so that it is close to the observed yields. This indicates the poor performance is likely to be caused by the prevalence of structural errors in the model instead of the uncertainties regarding parameters, input, or observation values. Therefore, it is recommended for future research to address this first. This can be done by further study and incorporation of more crop production processes, soil water simulation, and exploratory interviews to identify patterns and more factors that can influence the errors.