soilphysics: Soil Physical Analysis

Documented in iwc

iwc <- 
function(theta_R, theta_S, alpha, n, a, b, hos = 0, 
      graph = TRUE, 
	xlab = "Matric head (cm)", 
	ylab = expression(cm^-1), 
	xlim1 = NULL,
	xlim2 = NULL, 
	xlim3 = NULL,
	ylim1 = NULL, 
	ylim2 = NULL, 
	ylim3 = NULL,
	col12 = c("black", "blue", "red"),
	col3 = c("orange", "black"),
	lty12 = c(1, 3, 2), 
	lty3 = c(2, 1), ...)
{
    stopifnot(hos >= 0)

    # Ch (van Genuchten's first derivative)
    x <- NULL
    der. <- function(x, theta_R, theta_S, alpha, n) 
    {
        out <- abs((theta_S - theta_R) * 
           (1 + (alpha * x)^n)^(1/n - 1) * 
           (1/n - 1) * (alpha * x)^n * 
           (n/(x * (1 + (alpha * x)^n))))
        return(out)
    }

    # weight limiting function for salinity
    ws <- function(x, theta_R, theta_S, alpha, n)
    {
        theta <- soilwater(x, theta_R, theta_S, alpha, n)
        out <- ( 1 + hos * theta_S * theta^-2 *
           der.(x, theta_R, theta_S, alpha, n) )^-1
        return(out)
    }

    # Es
    der <- function(x, theta_R, theta_S, alpha, n)
    {
        out <- ws(x, theta_R, theta_S, alpha, n) *
           der.(x, theta_R, theta_S, alpha, n)
        return(out)
    }

    # Hydraulic conductivity limiting function
    Kr <- function(x, theta_R, theta_S, alpha, n) 
    {
       out <- (1 - (alpha*x)^(n-1) * 
          (1 + (alpha*x)^n)^(1/n - 1) )^2 *
          (1 + (alpha*x)^n)^( (1 - n) / 2*n)
       return(out)
    }

    # Kr weight function
    wK <- function(x, theta_R, theta_S, alpha, n) 
    {
        out <- ( Kr(x = 330, theta_R, theta_S, alpha, n) / 
           Kr(x, theta_R, theta_S, alpha, n) )^0.08
        return(out)
    }

    EK <- function(x, theta_R, theta_S, alpha, n) 
    {
        out <- wK(x, theta_R, theta_S, alpha, n) * 
           der(x, theta_R, theta_S, alpha, n)
        return(out)
    }

    # inverted van Genuchten's function for potential determination
    potential <- function(theta, theta_R, theta_S, alpha, n)
    {
        m <- 1 - 1/n
        out <- (( (theta_S - theta_R) / 
           (theta - theta_R) )^(1/m) - 1 )^(1/n) * 1/alpha
        return(out)
    }
    h10 <- potential(theta_S - 0.10, theta_R, theta_S, alpha, n)
    h15 <- potential(theta_S - 0.15, theta_R, theta_S, alpha, n)

    # weight function for air porosity limiting function
    wa <- function(x) 
    {
        A <- 1 / ( log10( h15 / h10 ) )
        out <- A * log10(x / h10 )
        for(i in 1:length(x)) {
        if (out[i] < 0) out[i] <- 0
        if (out[i] > 1) out[i] <- 1
        }
        return(out)
    }

    EKa <- function(x, theta_R, theta_S, alpha, n) 
    {
        out <- wK(x, theta_R, theta_S, alpha, n) * 
           wa(x) * 
           der(x, theta_R, theta_S, alpha, n)
        return(out)
    }

    # weight function for PR limiting function
    wR <- function(x, a, b)
    {
        out <- 2.5 - a * x ^ b
        return(out)
    }

    ER <- function(x, a, b, theta_R, theta_S, alpha, n) 
    {
        out <- wR(x, a, b) *
           der(x, theta_R, theta_S, alpha, n)
        return(out)
    }

    # integration interval for PR = 1.5 and PR = 2.5 MPa
    h1.5 <- (1.5 / a) ^ (1/b)
    h2.5 <- (2.5 / a) ^ (1/b)

    # dry hydraulic conductivity
    Kdry <- Kr(x = seq(12000, 15000, by = 50), 
        theta_R, theta_S, alpha, n)
    fit2 <- fitsoilwater4(theta = Kdry, 
        psi = seq(12000, 15000, by = 50), 
        model = "Ross")

    # weight limiting function for Kdry
    wKdry <- function(x, d)
    {
        out <- (12000 / x) ^ (-d)
        return(out)
    }

    ERKdry <- function(x, a, b, d, theta_R, theta_S, alpha, n) 
    {
        out <- wR(x, a, b) * wKdry(x, d) *
           der(x, theta_R, theta_S, alpha, n)
        return(out)
    }

    # ----------------------------------------------
    # IWC integrations
    # EKa
    ave1 <- trapez(x = seq(h10, h15, length = 1000), 
        y = EKa(x = seq(h10, h15, length = 1000), 
           theta_R, theta_S, alpha, n))

    # EK
    ave2 <- trapez(x = seq(h15, 330, length = 1000), 
        y = EK(x = seq(h15, 330, length = 1000), 
           theta_R, theta_S, alpha, n))

    # Ch
    ave3 <- trapez(x = seq(330, h1.5, length = 1000), 
        y = der(x = seq(330, h1.5, length = 1000), 
           theta_R, theta_S, alpha, n))

    # ER
    if (h2.5 > 15000) h2.5. <- 15000 else h2.5. <- h2.5
    ave4 <- trapez(x = seq(h1.5, h2.5., length = 1000), 
        y = ER(x = seq(h1.5, h2.5., length = 1000), 
            a, b, theta_R, theta_S, alpha, n))

    # ERKdry
    ave5 <- trapez(x = seq(12000, 15000, length = 1000), 
        y = ERKdry(x = seq(12000, 15000, length = 1000), 
            a, b,	d = coef(fit2)[2], theta_R, theta_S, alpha, n))

    # ------------------------------------------------
    # integral energy calculation
    # hEKa
    hEKa <- function(x, theta_R, theta_S, alpha, n) 
    {
        out <- x * EKa(x, theta_R, theta_S, alpha, n)
        return(out)
    }
    ave1h <- trapez(x = seq(h10, h15, length = 1000), 
        y = hEKa(x = seq(h10, h15, length = 1000), 
           theta_R, theta_S, alpha, n))

    # hEK
    hEK <- function(x, theta_R, theta_S, alpha, n) 
    {
        out <- x * EK(x, theta_R, theta_S, alpha, n)
        return(out)
    }
    ave2h <- trapez(x = seq(h15, 330, length = 1000), 
        y = hEK(x = seq(h15, 330, length = 1000), 
           theta_R, theta_S, alpha, n))

    # hCh
    hder <- function(x, theta_R, theta_S, alpha, n)
    {
        out <- x * der(x, theta_R, theta_S, alpha, n)
        return(out)
    }
    ave3h <- trapez(x = seq(330, h1.5, length = 1000), 
        y = hder(x = seq(330, h1.5, length = 1000), 
           theta_R, theta_S, alpha, n))

    # hER
    hER <- function(x, a, b, theta_R, theta_S, alpha, n) 
    {
        out <- x * ER(x, a, b, theta_R, theta_S, alpha, n)
        return(out)
    }
    ave4h <- trapez(x = seq(h1.5, h2.5., length = 1000), 
        y = hER(x = seq(h1.5, h2.5., length = 1000), 
            a, b, theta_R, theta_S, alpha, n))

    # hERKdry
    hERKdry <- function(x, a, b, d, theta_R, theta_S, alpha, n) 
    {
        out <- x * ERKdry(x, a, b,	
            d, theta_R, theta_S, alpha, n)
        return(out)
    }
    ave5h <- trapez(x = seq(12000, 15000, length = 1000), 
        y = hERKdry(x = seq(12000, 15000, length = 1000), 
            a, b,	d = coef(fit2)[2], theta_R, theta_S, alpha, n))

    # -------------------------------------------------
    # graphic
    if (graph) {
        layout(matrix(c(1, 3, 2, 3), 2))
        curve.(der(x, theta_R, theta_S, alpha, n), 
            from = 1, to = 350,
            xlim = xlim1,
            ylim = ylim1, 
            xlab = xlab, ylab = ylab, 
            main = "Wet range",
            col = col12[1],
            lty = lty12[1], 
            shade = col12[1], ...)
        curve.(EK(x, theta_R, theta_S, alpha, n), 
            add = TRUE, 
            col = col12[2],
            lty = lty12[2], 
            shade = col12[2])
        curve.(EKa(x, theta_R, theta_S, alpha, n), 
            add = TRUE,
            col = col12[3],
            lty = lty12[3], 
            shade = col12[3])
        legend("topright",  c(expression(C(h, h[os])), 
             expression(EK[R](h, h[os])), 
             expression(EKa[RKdry](h, h[os]))), 
             lty = lty12, col = col12, 
             bg = "lightyellow")
    
        #dev.new(width = 5, height = 5)
        curve.(der(x, theta_R, theta_S, alpha, n), 
            from = h1.5, to = 15000,
            xlim = xlim2,
            ylim = ylim2, 
            xlab = xlab, ylab = ylab, 
            main = "Dry range",
            col = col12[1],
            lty = lty12[1], 
            shade = col12[1], ...)
        curve.(ER(x, a, b, theta_R, theta_S, alpha, n), 
            add = TRUE, from = h1.5, to = h2.5., 
            col = col12[2],
            lty = lty12[2], 
            shade = col12[2])
        curve.(ERKdry(x, a, b, d = coef(fit2)[2], 
            theta_R, theta_S, alpha, n), 
            add = TRUE, from = 12000, to = 15000, 
            col = col12[3],
            lty = lty12[3], 
            shade = col12[3])
        legend("topright",  c(expression(C(h, h[os])), 
             expression(E[R](h, h[os])), 
             expression(E[RKdry](h, h[os]))), 
             lty = lty12, col = col12, 
             bg = "lightyellow")

        #if (hos != 0) {
        #   dev.new(width = 5, height = 5)
           curve.(der.(x, theta_R, theta_S, alpha, n), 
              from = 1, to = 15000, log = "x",
              xlim = xlim3,
              ylim = ylim3,
              xlab = xlab, ylab = ylab, 
              main = "Salinity effect",
              col = col3[1],
              lty = lty3[1], 
              shade = col3[1], ...)
           curve.(der(x, theta_R, theta_S, alpha, n), 
               add = TRUE, from = 1, to = 15000, 
               log = "x",
               col = col3[2],
               lty = lty3[2], 
               shade = col3[2])
           legend("topright", c(expression(C(h, h[os]==0)), 
               expression(C(h, h[os]))), 
               lty = lty3, col = col3,
               bg = "lightyellow")
        #}        
    }

    # ----------------------------------------
    # output
    IWC <- c(ave1, ave2, ave3, ave4, ave5, 0)
    EI <- c(ave1h, ave2h, ave3h, ave4h, ave5h, 0) / (10 * sum(IWC))
    li <- round(c(h10, h15, 330, h1.5, 12000, 0), 2)
    ls <- round(c(h15, 330, h1.5, h2.5., 15000, 15000), 2)
    h.Range <- paste(li, "-", ls)
    mout <- data.frame(IWC = round(IWC, 4), 
       EI = round(EI, 2), h.Range)
    mout[6, 1:2] <- c(sum(IWC), sum(EI))
    rownames(mout) <- c("EKa(h, hos)", "EK(h, hos)", "C(h, hos)", 
       "ER(h, hos)", "ERKdry(h, hos)", "Sum")
    return(mout)
}


# --------------------------------------------
# numerical integration: trapezoidal rule
trapez <- 
function(x, y)
{
   if (length(x) != length(y))
      stop("incompatible dimensions!")
   xy <- sortedXyData(x, y)
   x <- xy[["x"]]
   y <- xy[["y"]]
   n <- nrow(xy)
   out <- 0.5 * sum((x[2:n] - x[2:n - 1]) * 
      (y[2:n] + y[2:n - 1]))
   return(out)
}

# --------------------------------------------
# shaded curve()
curve. <- 
function (expr, from = NULL, to = NULL, n = 101, add = FALSE, 
    type = "l", xname = "x", xlab = xname, ylab = NULL, log = NULL, 
    xlim = NULL, shade = "black", ...) 
{
    sexpr <- substitute(expr)
    if (is.name(sexpr)) {
        expr <- call(as.character(sexpr), as.name(xname))
    }
    else {
        if (!((is.call(sexpr) || is.expression(sexpr)) && xname %in% 
            all.vars(sexpr))) 
            stop(gettextf("'expr' must be a function, or a call or an expression containing '%s'", 
                xname), domain = NA)
        expr <- sexpr
    }
    if (dev.cur() == 1L && !identical(add, FALSE)) {
        warning("'add' will be ignored as there is no existing plot")
        add <- FALSE
    }
    addF <- identical(add, FALSE)
    if (is.null(ylab)) 
        ylab <- deparse(expr)
    if (is.null(from) || is.null(to)) {
        xl <- if (!is.null(xlim)) 
            xlim
        else if (!addF) {
            pu <- par("usr")[1L:2L]
            if (par("xaxs") == "r") 
                pu <- extendrange(pu, f = -1/27)
            if (par("xlog")) 
                10^pu
            else pu
        }
        else c(0, 1)
        if (is.null(from)) 
            from <- xl[1L]
        if (is.null(to)) 
            to <- xl[2L]
    }
    lg <- if (length(log)) 
        log
    else if (!addF && par("xlog")) 
        "x"
    else ""
    if (length(lg) == 0) 
        lg <- ""
    if (grepl("x", lg, fixed = TRUE)) {
        if (from <= 0 || to <= 0) 
            stop("'from' and 'to' must be > 0 with log=\"x\"")
        x <- exp(seq.int(log(from), log(to), length.out = n))
    }
    else x <- seq.int(from, to, length.out = n)
    ll <- list(x = x)
    names(ll) <- xname
    y <- eval(expr, envir = ll, enclos = parent.frame())
    if (length(y) != length(x)) 
        stop("'expr' did not evaluate to an object of length 'n'")
    if (isTRUE(add)) 
        lines(x = x, y = y, type = type, ...)
    else plot(x = x, y = y, type = type, xlab = xlab, ylab = ylab, 
        xlim = xlim, log = lg, ...)
    x. <- c(min(x), x, max(x))
    y. <- c(0, y, 0)
    polygon(x = x., y = y., 
       border = NA,
       col = adjustcolor(shade, alpha.f = 0.1))
    invisible(list(x = x, y = y))
}