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Fit the Philip two-term infiltration model

Source: R/fit_infiltration.R
fit_infiltration.Rd

Fits the Philip (1957) two-term polynomial to cumulative infiltration data to extract the hydraulic conductivity proxy C₁ and sorptivity proxy C₂: $$I = C_2 \sqrt{t} + C_1 t$$

Usage

fit_infiltration(data, infiltration_col, sqrt_time_col, workers = 1L)

Arguments

data

A data frame or tibble, optionally grouped with dplyr::group_by().

infiltration_col

Bare column name of cumulative infiltration depth (cm). Typically .infiltration from infiltration_cumulative() or beerkan_cumulative().

sqrt_time_col

Bare column name of the square root of elapsed time (s^0.5). Typically .sqrt_time.

workers

Number of parallel workers. Defaults to 1 (sequential). Values > 1 use parallel::mclapply() on Unix; silently reduced to 1 on Windows.

Value

A tibble with one row per group (or one row for ungrouped data) containing:

  • Group keys (if input was grouped)

  • .C1 — quadratic coefficient (cm/s), the time-proportional term

  • .C2 — linear coefficient (cm/s^0.5), the sorptivity term

  • .C1_std_error, .C2_std_error — standard errors

  • .convergence — TRUE if lm() succeeded

Details

The fit uses ordinary least squares on the linearised form I ~ sqrt_time + I(sqrt_time^2) (with intercept), matching published methodology (infiltrodiscR, Zhang 1997 tables).

Interpretation by mode:

  • Minidisk: C₁ feeds into hydraulic_conductivity_minidisk() via K(h) = C₁ / A.

  • Ring (ponded): C₁ ≈ Ksat at steady state.

  • BeerKan: C₁ provides a quick Philip estimate before running the full fit_best() algorithm.

If data is grouped with dplyr::group_by(), the model is fitted independently for each group, returning one row per group in the result. Parallel fitting across groups is available on Unix-like systems via workers > 1.

References

Philip, J. R. (1957). The theory of infiltration: 4. Sorptivity and algebraic infiltration equations. Soil Science, 84(3), 257–264.

Zhang, R. (1997). Determination of soil sorptivity and hydraulic conductivity from the disk infiltrometer. Soil Science Society of America Journal, 61(4), 1024–1030. https://doi.org/10.2136/sssaj1997.03615995006100060008x

Examples

library(tibble)
library(dplyr)

dat <- tibble(
  time   = seq(0, 300, 30),
  volume = c(95, 89, 86, 83, 80, 77, 74, 73, 71, 69, 67)
) |>
  infiltration_cumulative(time = time, volume = volume)

fit_infiltration(dat,
                 infiltration_col = .infiltration,
                 sqrt_time_col    = .sqrt_time)
#> # A tibble: 1 × 5
#>      .C2     .C1 .C2_std_error .C1_std_error .convergence
#>    <dbl>   <dbl>         <dbl>         <dbl> <lgl>       
#> 1 0.0600 0.00252       0.00753      0.000396 TRUE        

# Grouped: one row per sample
multi <- tibble(
  sample = rep(c("A", "B"), each = 11),
  time   = rep(seq(0, 300, 30), 2),
  volume = c(95, 89, 86, 83, 80, 77, 74, 73, 71, 69, 67,
             83, 77, 64, 61, 58, 45, 42, 35, 29, 17, 15)
) |>
  group_by(sample) |>
  infiltration_cumulative(time = time, volume = volume)

fit_infiltration(multi,
                 infiltration_col = .infiltration,
                 sqrt_time_col    = .sqrt_time)
#> # A tibble: 2 × 6
#>   sample    .C2     .C1 .C2_std_error .C1_std_error .convergence
#>   <chr>   <dbl>   <dbl>         <dbl>         <dbl> <lgl>       
#> 1 A      0.0600 0.00252       0.00753      0.000396 TRUE        
#> 2 B      0.0160 0.0135        0.0363       0.00191  TRUE