Fit the Kostiakov (1932) cumulative infiltration model — fit_infiltration

Fits the Kostiakov power model to cumulative infiltration data: $$I(t) = a \cdot t^b \quad (a > 0,\ 0 < b < 1)$$

Usage

fit_infiltration_kostiakov(data, infiltration_col, time_col, workers = 1L)

Arguments

data: A data frame or tibble, optionally grouped.
infiltration_col: Bare column name of cumulative infiltration depth (cm). Typically .infiltration from infiltration_cumulative().
time_col: Bare column name of elapsed time (s). Use the original time column (not .sqrt_time).
workers: Number of parallel workers (default 1).

Value

A tibble with one row per group containing:

Group keys (if grouped)
.a — Kostiakov coefficient (cm/s^b)
.b — Kostiakov exponent (dimensionless)
.a_std_error, .b_std_error
.convergence

Details

The model is linearised as $\log I = \log a + b \log t$ to derive starting values, then refined with nls() on the original scale.

The instantaneous infiltration rate corresponding to this model is $f(t) = a \cdot b \cdot t^{b-1}$, which decreases monotonically with time when $0 < b < 1$. Note that the Kostiakov model does not approach a finite steady-state value ($f \to 0$ as $t \to \infty$), so it should not be used to estimate Ksat.

The first row within each group typically has t = 0, which would produce a zero or undefined logarithm. Rows with time == 0 or infiltration == 0 are automatically excluded from fitting.

If data is grouped, the model is fitted independently per group.

References

Kostiakov, A. N. (1932). On the dynamics of the coefficient of water-percolation in soils. Transactions of the 6th Commission of the International Society of Soil Science, Part A, 17–21.

Examples

library(tibble)
library(dplyr)

dat <- tibble(
  time   = seq(0, 3600, 360),
  volume = c(500, 440, 390, 355, 328, 308, 292, 280, 271, 265, 260)
) |>
  infiltration_cumulative(time = time, volume = volume, radius = 10)

fit_infiltration_kostiakov(dat,
                           infiltration_col = .infiltration,
                           time_col         = time)
#> # A tibble: 1 × 5
#>       .a    .b .a_std_error .b_std_error .convergence
#>    <dbl> <dbl>        <dbl>        <dbl> <lgl>       
#> 1 0.0142 0.494      0.00457       0.0416 TRUE