I am doing my master thesis research on spatial data in some specific domain, and I simulated the random fields with Gaussian process in univariate case(gstat package in R, data space 50*50). In first step, I would like to check estimating equation of variogram is monotonic or not corresponding to the parameter of interest(range).

I derived the estimating equation with generalised least square for different variograms and found that, except spherical variogram, estimating equation is not monotonic in certain space corresponding to the parameter range(specifically, Gaussian variogram and exponential variogram).

I checked several text books and couldnt find why in certain region, range is not monotonic and how to define the range parameter space in simulated variogram, image for exponential and Gaussion estimating equation plots are below.

PS: range = 10 and lags = 20 in the routine.

I would like to know why and how range parameter space changes, and how can I define the certain space of range parameter which makes estimating equation monotonic. Thank you