Predict in-lake water quality concentrations

ok_inlake() applies nutrient retention coefficients from ok_retention() to predict in-lake total phosphorus (TP) and total nitrogen (TN) concentrations via the mass balance $$C_{lake} = C_{in} \times (1 - R)$$ then uses empirical log-log regression to predict chlorophyll-a from in-lake TP and Secchi depth from chlorophyll-a.

Note on retention identity: when coefficients = "walker" (Walker BATHTUB Model 1), the retention coefficient stored by ok_retention() is back-calculated from Walker's quadratic mass balance solution so that C_lake = C_in * (1 - R) exactly reproduces the Model 1 result.

Usage

ok_inlake(x, predict_chla = TRUE, predict_secchi = TRUE)

Arguments

x: An okBATHTUB object produced by ok_retention().
predict_chla: Logical. Whether to predict chlorophyll-a from in-lake TP. Default TRUE.
predict_secchi: Logical. Whether to predict Secchi depth from chlorophyll-a. Requires predict_chla = TRUE. Default TRUE.

Value

An okBATHTUB object at pipeline step "inlake".

Chlorophyll-a from TP

Log-log linear regression: $$\log_{10}(\text{Chl-a}) = a + b \times \log_{10}(\text{TP}_{lake})$$ Default coefficients are Walker's nationally-derived values ($a = -1.136$, $b = 1.449$); Oklahoma ecoregion-specific values are applied when coefficients = "oklahoma".

Secchi depth from chlorophyll-a

$$\log_{10}(\text{Secchi}) = a + b \times \log_{10}(\text{Chl-a})$$ Default Walker national: $a = 0.616$, $b = -0.473$.

In high-turbidity Oklahoma reservoirs, Secchi depth is often controlled more by inorganic suspended sediment than by algal biomass. This is partly captured by the Oklahoma ecoregion-specific Secchi regressions, but for reservoirs with very high non-algal turbidity (e.g. central and western Oklahoma), Secchi predictions should be interpreted with caution.

Examples

result <- ok_load(
  inflow_m3yr   = 45e6,
  tp_inflow_ugl = 120,
  tn_inflow_ugl = 1800
) |>
  ok_hydraulics(surface_area_ha = 890, mean_depth_m = 4.2) |>
  ok_retention() |>
  ok_inlake()
print(result)
#> -- okBATHTUB Result --
#>   Pipeline step : inlake
#>   Segment       : main
#>   Coefficients  : walker
#> 
#>   inflow_m3yr                 : 4.5e+07
#>   tp_inflow_ugl               : 120
#>   tp_load_kgyr                : 5400
#>   tn_inflow_ugl               : 1800
#>   tn_load_kgyr                : 8.1e+04
#>   surface_area_ha             : 890
#>   surface_area_m2             : 8.9e+06
#>   mean_depth_m                : 4.2
#>   volume_m3                   : 3.738e+07
#>   outflow_m3yr                : 4.5e+07
#>   hydraulic_residence_time_yr : 0.8307
#>   areal_water_load_myr        : 5.056
#>   tp_retention_coeff          : 0.632
#>   tn_retention_coeff          : 0.5535
#>   tp_retention_form           : walker_model1
#>   tn_retention_form           : walker_model1
#>   tp_inlake_ugl               : 44.16
#>   tn_inlake_ugl               : 803.8
#>   chla_ugl                    : 17.68
#>   chla_coeff_source           : walker_1985_national
#>   secchi_m                    : 1.061
#>   secchi_coeff_source         : walker_1985_national
#>   ecoregion_applied           : NA