Fits the ODE $$\frac{dy}{dz} = -\lambda_0 e^{-\mu z} (y - y_\infty)$$ to one soil pedon by minimising the sum of squared errors between the ODE-predicted and the observed values, with an L2 regulariser on the (re-parametrised) parameters. Physics is encoded in the forward model itself — the fit can never produce a profile that violates the prescribed exponential-asymptote dynamics.
Usage
piml_profile_fit(
depths,
values,
y_surface = NULL,
start = NULL,
reg = 0.001,
control = list(maxit = 2000)
)Arguments
- depths
Numeric vector of horizon mid-depths (same units, e.g. centimetres below surface).
- values
Numeric vector of observed property values, same length as
depths.- y_surface
Optional numeric; if supplied, the surface value
y(0) = y_surfaceis fixed and not optimised. Use this when you have a reliable 0 cm observation (or a laboratory A-horizon value).- start
Optional named numeric vector of starting parameters (
log_lambda0,mu,y_inf, and optionallyy0). IfNULL, a data-driven guess is built from the observed range and depths.- reg
Numeric L2 regularisation strength on the parameter vector.
- control
List passed to
stats::optim'scontrolargument (default islist(maxit = 2000)).
Value
A edaphos_piml_profile object with components:
- params
Named list with the fitted
lambda0,mu,y_inf,y0.- theta
The unconstrained parameter vector the optimiser found.
- objective
Final regularised SSE loss.
- converged
Logical, whether
optimreported convergence.- depths, values, y_surface
Inputs echoed back.
- rmse
Unregularised RMSE on the training data.
Examples
depths <- c(5, 15, 30, 60, 100)
values <- c(25, 18, 12, 8, 6.5) # e.g. SOC (g/kg) decreasing with depth
fit <- piml_profile_fit(depths, values)
fit
#> <edaphos_piml_profile>
#> dy/dz = -lambda0 * exp(-mu*z) * (y - y_inf)
#> lambda0 = 0.04846 mu = 0.003277
#> y_inf = 6.162 y0 = 30.08
#> n obs = 5 rmse = 0.09798
#> converged = TRUE
piml_profile_predict(fit$params, c(10, 50))
#> [1] 21.009577 8.720935