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Quantify uncertainty and invert for parameters (GLUE)

Source: R/flood_uncertainty.R
flood_uncertainty.Rd

Applies Generalized Likelihood Uncertainty Estimation (GLUE) to the routing stage. Uncertain parameters (Manning's roughness and channel width) are sampled from priors, the flood depth is predicted for each sample, and each sample is weighted by an informal likelihood measuring its agreement with an observed depth. This yields a predictive uncertainty band on flood depth and, as the inverse problem, weighted parameter estimates conditioned on the observation.

Usage

flood_uncertainty(
  x,
  observed_depth_m,
  n_sim = 5000,
  n_range = c(0.02, 0.08),
  width_range = c(10, 40),
  obs_error = 0.1,
  behavioural_fraction = 0.1,
  seed = NULL
)

Arguments

x

A flood_project whose route slot has been populated, or a flood_route object directly. The routing settings (slope, area, peak discharge) are taken from it.

observed_depth_m

Observed peak flood depth in metres to condition on, for example from a surveyed high-water mark or satellite estimate.

n_sim

Number of Monte-Carlo samples. Default 5000.

n_range

Length-2 numeric range for the Manning's \(n\) prior. Default c(0.02, 0.08).

width_range

Length-2 numeric range for the channel width prior (m). Default c(10, 40).

obs_error

Relative observation error (standard deviation as a fraction of the observed depth) used in the Gaussian likelihood. Default 0.1.

behavioural_fraction

Fraction of samples, ranked by likelihood, kept as behavioural. Default 0.1.

seed

Optional integer seed for reproducibility.

Value

If x is a flood_project, the same object with its uncertainty slot populated. Otherwise a list of class flood_uncertainty with elements observed_depth_m, n_behavioural (count kept), depth_band (named vector: lower, median, upper of the weighted predictive band), obs_in_band (logical), estimates (weighted-mean and range for each parameter), equifinality (the n-width correlation among behavioural sets), and behavioural (a data frame of kept samples and weights).

Details

GLUE is the workhorse uncertainty method in hydrology. A key feature it reveals is equifinality: many different parameter combinations can reproduce the same observation, so individual parameters may stay uncertain even when the prediction is well constrained. The function reports the parameter spread honestly rather than collapsing it to a single point.

References

Beven, K. and Binley, A. (1992) The future of distributed models: model calibration and uncertainty prediction. Hydrological Processes 6, 279–298. doi:10.1002/hyp.3360060305

See also

flood_route for the model being conditioned.

Examples

disc <- data.frame(
  date = seq(as.Date("2020-06-01"), by = "day", length.out = 12),
  Q_mm = c(0, 1, 3, 8, 18, 30, 22, 14, 8, 4, 2, 1)
)
r <- flood_route(disc, method = "muskingum-cunge", area_km2 = 300)
u <- flood_uncertainty(r, observed_depth_m = r$peak_depth_m,
                       n_sim = 2000, seed = 1)
u$depth_band
#>  lower median  upper 
#>  2.739  2.853  2.966 
u$obs_in_band
#> [1] TRUE