Fitting the parameters of the RIA parameterization of the soil water retention curve

RIAfitter is a  Fortran95 code that fits the five parameters of the RIA parameterization of de Rooij et al. (2021) and de Rooij (2022) of the soil water retention curves on observed values of the volumetric water content for an arbitrary number of matric potentials.

Version 1.2.2.1, May 2023

Changes with respect to version 1.0:
- Small error in the partitioning of the liquid water content for plotting data fixed.
- Clarity of the comments improved, references to equations in de Rooij (2022) added.
- Calls to WCRIA with dummy variables now use multiple dummies instead of using a single dummy multiple times because not all compilers can handle repeated invocations of the same dummy in a single subroutine call.
- FUNCTION hjRIA now slightly decreases the calculated value of hj so that it is not quite at its theoretical limit.

Changes with respect to version 1.1:
- Estimates of the saturated hydraulic conductivity calculated according to Eqs. (1) and (15) of Timlin et al. (Soil Sci. Soc. Am. J. 1999).
- During every iteration, c and hd are iteratively determined from the value of alpha, n, and the target value of hd to ensure that (1 + c)*hd closely approximates the target hd. Therefore, c and the corrected value of hd are no longer computed after the fitting process is completed but are instead updated during the parameter optimization process by subroutine WCRIA. See the User Manual for details.

Changes with respect to version 1.2 and 1.2.1:
- Bug removed in subroutine BiSectionForC
- Reduced the value of the upper limit for the first iteration of the Bisection algorithm and moved it from subroutine BiSectionForC to MODULE SCEBisParameters.
- Akaike's information criterion calculated and written to output.

Change with repect to version 1.2.2: a bug in the calculation of Akaike's Infomration Criterion was fixed.

The version of the equation that is fitted is that of de Rooij (2022), in which the matric potential at oven-dryness (hd) and alpha are among the fitting parameters, and the matric potential at the junction point (hj) is a derived parameter.

Each data point needs to have an estimate of the standard deviation of the error of the matric potential, and of the water content. These are used to calculate the weight assigned to each data point.

The code minimizes the root mean square error (RMSE) of the fitted vs. the observed values using shuffled complex evolution. It also  generates a regular grid of map points with the associated RMSE that covers the parameter space. The code evaluates ten convergence criteria for each fitting parameter. Five of these apply to all parameters simultaneously. See Subroutine ConvergenceCheck for details.

To guard against local minima, three runs are performed. If so desired, two of these runs have starting points based on the map of the parameter space. Based on the RMSE, the best fit is determined. If at least two runs return the same RMSE, the run with the largest total number of times a parameter met a convergence criterion is selected. If at least two runs score the the same on both criteria, the run with the smallest rank number is picked (Run 1 over run 2, run 2 over run 3).

The correlation matrix of the fitting parameters is calculated based on a random sample of a prescribed number of fits prior to and including the final fit.

A table with points on the soil water retention curve (and its components) is written to output.

Together with the code, a document that desribes the code and its use is made available.

N.B. The theory underlying version 1.2.2 and 1.2.2.1 is given in:

de Rooij, G.H. 2022. Technical note: A sigmoidal soil water retention curve without asymptote that is robust when dry–range data are unreliable. Hydrology and Earth System Sciences, 26, 5849-5858, doi 10.5194/hess-26-5849-2022.