Statistical methods

Gridpp supports a number of basic statistical methods for gridded forecasts. Many of these methods can be represented by a calibration curve.

The function apply_curve performs this adjustment. The curve itself can be constructed by using various methods.

adjusted_fcst = gridpp.apply_curve(input, curve, policy_below, policy_above)

where input is either a scalar, a 1D vector, or a 2D vector; curve is a calibration curve; and policy_below and policy_above define how to treat inputs that are outside the domain of the calibration curve (see Extrapolation curve below).

Quantile mapping

Quantile mapping uses the relationship between historical forecasts and a reference dataset. A curve is created by sorting the forecast and reference points.

curve = gridpp.quantile_mapping_curve(ref, fcst)

where fcst is a 1D vector of forecast samples, ref is a 1D vector of reference samples, and policy is an extrapolation policcy specifying how values are extrapolated outside the domain of fcst. The following extrapolation policies are supported: gridpp.OneToOne, a one-to-one line is used outside the domain); gridpp.MeanSlope, the slope between the two extreme points on the curve is used to extrapolate; gridpp.NearstSlope, the slope between the two lowest points is used below the curve (similarly for the two highest points); and gridpp.Zero, a slope of 0 outside the curve.

Here is an example:

input = 275
fcst = [250, 270, 290, 310]
ref = [240, 275, 290, 305]
curve gridpp.quantile_mapping_curve(ref, fcst)
adjusted = gridpp.apply_curve(input, curve, gridpp.OneToOne, gridpp.OneToOne)

Extrapolation policy