Hi all,

I’m using a pretty standard non-linear model in soil physics that relates pressure head (|\psi|) to volumetric water content (\theta):

\theta (\psi) = \theta_r + \frac{\theta_s - \theta_r}{[1 + (\alpha |\psi|) ^ n] ^ {1 - 1/n}}

However, I’d like to extend this model to include some secondary information I have about organic matter (values are continuous, varying from 0 to 1, or 0 to 100%; O_m). That is, I’m curious if it is possible to include O_m in the model, to understand how it might be influencing the model parameters above (i.e., \theta_r, \theta_s, \alpha, n).

This seems conceptually similar to a hierarchical model, except that O_m is continuous, and order matters. On that basis, this kind of extension seems logical, but I’ve not seen anyone apply this kind of model to a non-linear model, using a continuous covariate, so it is unclear to me how to operationalize this kind of modeling framework.

If my question is not well conceived and you think I need some remedial improvements to my understanding, I’d be happy to take any book or article suggestions that you might think are useful for understanding similar issues.

Also, is their a name for the kind of framework I’m trying to operationalize? I was thinking it might be a joint distribution model, since O_m and the other parameters should co-vary, but perhaps my grasp of the nomenclature is not accurate.

Thanks!