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Fit the Horton (1940) infiltration rate model

Source: R/fit_infiltration_horton.R
fit_infiltration_horton.Rd

Fits the Horton (1940) exponential decay model to infiltration rates computed at discrete time intervals: $$f(t) = f_c + (f_0 - f_c) \cdot e^{-k t}$$

Usage

fit_infiltration_horton(data, rate_col, time_col, workers = 1L)

Arguments

data

A data frame or tibble, optionally grouped.

rate_col

Bare column name of infiltration rates (cm/s). Typically .rate from infiltration_rate().

time_col

Bare column name of midpoint times (s). Typically .time_mid from infiltration_rate().

workers

Number of parallel workers (default 1).

Value

A tibble with one row per group containing:

  • Group keys (if grouped)

  • .fc — final/steady-state rate ≈ Ksat (cm/s)

  • .f0 — initial rate (cm/s)

  • .k — decay constant (1/s)

  • .fc_std_error, .f0_std_error, .k_std_error

  • .convergence

Details

where \(f_c\) (cm/s) is the final/steady-state rate (≈ Ksat for ponded ring experiments), \(f_0\) (cm/s) is the initial rate, and \(k\) (1/s) is the decay constant.

Inputs are typically interval rates computed with infiltration_rate(): .rate (y) and .time_mid (x). The first row within each group has NA values and is automatically excluded from fitting.

Starting values are derived automatically from the data range:

  • f0_start = maximum observed rate

  • fc_start = minimum observed rate

  • k_start = 0.01 (1/s)

If data is grouped, the model is fitted independently per group. Parallel fitting is available on Unix via workers > 1.

References

Horton, R. E. (1940). An approach toward a physical interpretation of infiltration capacity. Soil Science Society of America Proceedings, 5, 399–417.

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) |>
  infiltration_rate(time_col = time, infiltration_col = .infiltration)

fit_infiltration_horton(dat, rate_col = .rate, time_col = .time_mid)
#> # A tibble: 1 × 7
#>        .fc     .f0      .k .fc_std_error .f0_std_error .k_std_error .convergence
#>      <dbl>   <dbl>   <dbl>         <dbl>         <dbl>        <dbl> <lgl>       
#> 1 -1.46e-5 6.18e-4 7.14e-4     0.0000187     0.0000156    0.0000611 TRUE