Covariance Inflation Specification for IES

Builds a control object that tells pesto_ies_callback() and pesto_ies_filter() how to counteract ensemble under-dispersion — the progressive collapse of posterior spread that an iterative ensemble smoother suffers with a finite ensemble. Inflation re-expands the post-update parameter spread each iteration; the default method = "none" leaves the update byte-identical to the un-inflated smoother.

Usage

pesto_inflation(
  method = c("none", "rtps", "adaptive", "multiplicative"),
  alpha = 0.5,
  factor = 1,
  retention_floor = 0.5,
  max_factor = 5
)

Arguments

method: Character. One of "none" (default), "rtps", "adaptive", "multiplicative".
alpha: Numeric in [0, 1]. RTPS relaxation coefficient (default 0.5); used only when method = "rtps".
factor: Numeric \(\ge\) 1. Fixed inflation factor for method = "multiplicative" (default 1, i.e. no inflation).
retention_floor: Numeric in (0, 1]. Target floor on the mean spread-retention ratio for method = "adaptive" (default 0.5).
max_factor: Numeric \(\ge\) 1. Upper bound on any single-iteration inflation factor for "rtps" and "adaptive" (default 5).

Value

An object of class "pesto_inflation".

Details

Four methods are offered. "rtps" is relaxation-to-prior-spread (Whitaker & Hamill 2012): each parameter's posterior anomalies are rescaled by \(\alpha(\sigma^{b} - \sigma^{a})/\sigma^{a} + 1\), where \(\sigma^{b}\) and \(\sigma^{a}\) are the background (pre-update) and analysis (post-update) standard deviations. Being per-parameter, it re-inflates the directions that collapsed hardest, so it is the spectrally-aware workhorse. "adaptive" is a global, magnitude-targeting scheme: it measures the mean spread-retention ratio \(q = \mathrm{mean}_j(\sigma^{a}_j/\sigma^{b}_j)\) and, when q falls below retention_floor, applies a single multiplicative factor \(\min(\texttt{max\_factor}, \texttt{retention\_floor}/q)\) to restore the lost variance magnitude. "multiplicative" applies a fixed factor every iteration. "none" disables inflation.

The companion diagnostic is the spectral spread-ESS (ensemble_spread_ess()), recorded each iteration regardless of method: it reports the effective number of variance-carrying directions and is what detects directional collapse. Because that participation ratio is invariant to a global rescaling, a global ("multiplicative" / "adaptive") inflation restores variance magnitude but not the spectral shape; "rtps" is the method that reshapes the spectrum. The two compose well.

References

Whitaker, J.S. & Hamill, T.M. (2012). Evaluating methods to account for system errors in ensemble data assimilation. Monthly Weather Review, 140(9), 3078–3089.

Examples

inf <- pesto_inflation("rtps", alpha = 0.5)
inf
#> $method
#> [1] "rtps"
#> 
#> $alpha
#> [1] 0.5
#> 
#> $factor
#> [1] 1
#> 
#> $retention_floor
#> [1] 0.5
#> 
#> $max_factor
#> [1] 5
#> 
#> attr(,"class")
#> [1] "pesto_inflation"