Estimating parameters for van-Genuchten soil water retention curve model

Water retaining property of soil is characterized usually by van-Genuchten model in soil physics.
https://en.wikipedia.org/wiki/Water_retention_curve

In this function, I use 'nlinfit' to estimate alpha and n of this model, given some synthetic data (water potential and water content along with residual and saturated water content) . The code is generously commented for easy understanding. First a known soil parameter model is plotted and then synthetic experimental data is generated by erroring and downsampling the model and then we estimate the alpha and n.