I am trying to fit a nonlinear regression to infiltration data in order to
determine saturated hydraulic conductivity and matric pressure. The
original equation can be found in Bagarello et al. 2004 SSSAJ (green-ampt
equation for falling head including gravity). I am also VERY new to R and
to nonlinear regressions. I have searched the posts, but am still unable to
determine why my data come up with the "singular gradient" error.
Here are the data:
time <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19)
#time in minutes
cumul <-c(2, 5, 7, 9.5, 11, 13, 14, 15, 16, 18.5, 21, 23, 24.5, 26.5, 28,
29.5, 31, 31.5, 32.5) #cumulative infiltration in cm per min
df <- data.frame(time, cumul)
df$cumul.m <- df$cumul/100/60 #convert to meters per second
df$time.s <- df$time*60 #convert to seconds
b2 <- 1-(0.196/(0.06/0.01131)) #relationship between soil moisture and the
size of the ring infiltrometer (6 cm radius by 113.1 cm2 cross sectional
area)
theta <- 0.196 #difference in residual soil water and field capacity
Here is the formula:
#Where a = K_fs and b=psi_f
nlsfit <-
nls(time.s~(theta/a*b2)*((cumul.m/theta)-(((0.16-b)/b2)*log(1+((cumul.m*b2)/(theta*(0.16-b)))))),
data = df, start=list (a=1, b=0.5), trace=TRUE)
-----
I am likely "over parameterizing", but I must admit, that I am not entirely
sure what that means. Any help offered would be greatly appreciated. I am
sorry if I sound naive, but I am an ecologist, not a hydrologist.
Kate
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