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Fit a within-month daily shape at gauges

Source: R/wet_shape_fit.R
wet_shape_fit.Rd

The water balance's daily shape within the month (#70): where a month's water falls among its days, carried from gauges to ungauged watersheds. A gauge's within-month weights w are its day-of-year flow divided by its month's total (wet_station_doy(), then the internal wet_shape_within()), so each month's weights sum to 1. Two methods:

Usage

wet_shape_fit(
  d,
  w,
  method = c("donor", "basis"),
  static = c("elev", "e_km", "n_km"),
  k = 5,
  n_comp = 6,
  shares = NULL
)

Arguments

d

data.frame of the gauges, with the static columns.

w

Matrix of within-month weights, one row per row of d and 365 columns (a common year).

method

"donor" or "basis".

static

Names of the predictor columns in d.

k

Donors per watershed ("donor"), capped at the number of gauges.

n_comp

Principal components kept ("basis"), capped at the rank.

shares

Optional matrix of the gauges' 12 monthly shares ("basis" only); a fit made with them needs them at prediction too.

Value

An object of class wet_shape_fit.

Details

  • "donor": a new watershed takes the inverse-distance mean of the weights of its k nearest gauges in the space of the static predictors, each divided by the gauges' standard deviation. Distance weights are 1 / (d + 1e-6 * median(d)); a gauge at distance 0 takes the whole weight.

  • "basis": principal components of the gauges' centred ratio to flat (w * days), the first n_comp, whose scores are regressed by ordinary least squares on the static predictors and, when given, the 12 monthly shares. A prediction is reconstructed, floored at 0 and renormalised per month; a month whose reconstruction is all 0 or less falls back to flat.

Both apply through wet_shape_predict(), and wet_shape_daily() turns monthly means and weights into daily flows that keep every monthly mean.

Examples

set.seed(1)
m <- wet:::wet_doy_month()
# eight gauges: a freshet whose timing within May moves with elevation
d <- data.frame(elev = seq(300, 2000, length.out = 8), e_km = 1:8, n_km = 8:1)
q <- t(sapply(d$elev, function(e) dnorm(1:365, 120 + e / 50, 30) + 1e-3))
w <- wet:::wet_shape_within(q)
fit <- wet_shape_fit(d, w, "donor", static = c("elev", "e_km", "n_km"), k = 3)
w_new <- wet_shape_predict(fit, data.frame(elev = 1000, e_km = 4.5, n_km = 4.5))
tapply(w_new[1, ], m, sum)  # each month sums to 1
#>  1  2  3  4  5  6  7  8  9 10 11 12 
#>  1  1  1  1  1  1  1  1  1  1  1  1