# Sindex: The S Index In soilphysics: Soil Physical Analysis

## Description

Function to calculate the S index (Dexter, 2004) for evaluating the soil physical quality based on the Water Retention Curve (van Genuchten, 1980).

S = - n * (θ_S - θ_R) * (1 + 1/m)^{-(1 + m)}

## Usage

 ```1 2``` ```Sindex(theta_R, theta_S, alpha, n, m = 1 - 1/n, vcov = NULL, nsim = 999, conf.level = 0.95, graph = TRUE, ...) ```

## Arguments

 `theta_R` the residual water content. `theta_S` the water content at saturation. `alpha` a scale parameter of the van Genuchten's formula. `n` a shape parameter in van Genuchten's formula. `m` a shape parameter in van Genuchten's Formula. Default is 1-1/n (Mualem, 1976). `vcov` optional (default is `NULL`); a variance-covariance matrix of the estimates which is used to perform Monte Carlo simulations of the parameters `theta_R`, `theta_S`, `alpha` and `n` for building a simulated confidence interval of the S index (in modulus). `nsim` the number of Monte Carlo simulations; default is 999. It is used only if `vcov` is specified. `conf.level` the confidence level; default is 0.95. It is used only if `vcov` is specified. `graph` logical; if TRUE (defaul), the soil water retention curve is plotted. `...` further graphical arguments.

## Value

A list of

 `h_i ` the modulus of the water potential at the inflection point. `theta_i ` the water content at the inflection point. `S.index ` the modulus of the S index. `PhysicalQuality ` A character indicating the soil physical quality, as proposed by Dexter (2004). `simCI ` the simulated confidence interval. It is stored only if `vcov` is specified. `conf.level ` the confidence level for the simulated confidence interval. It is stored only if `vcov` is specified.

## Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

## References

Dexter, A. R. (2004). Soil physical quality Part I. Theory, effects of soil texture, density, and organic matter, and effects on root growth. Geoderma, 120:201-214.

Genuchten, M. T. van. (1980). A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44:892-898.

Mualem, Y. (1976). A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resource Research, 12:513-522.

`soilwater`, `fitsoilwater`
 ```1 2 3 4 5 6 7``` ```# Dexter (2004, Table 1) Sindex(0, 0.395, 0.0217, 1.103, xlim = c(0, 1000)) Sindex(0, 0.335, 0.0616, 1.139, xlim = c(0, 1000)) # ... Sindex(0, 0.226, 0.0671, 1.581, xlim = c(0, 1000)) # End (not run) ```