| weightr {transfR} | R Documentation |
Weights of donor catchments
Description
Estimate the weighting applied at each time step and to each gauged catchment (donors) for the calculation of the average net rainfall of an ungauged catchment
Usage
weightr(Rn, distances, ndonors = 5, donors, power = 1, flexible_donor = TRUE)
Arguments
Rn |
net rainfall matrix of donor catchments (rows for time index, and columns for donors index) |
distances |
vector of the distances to each donor catchment (see hdist) |
ndonors |
maximum number of donor catchments to use |
donors |
vector of catchments id from which donors are selected. If empty, the |
power |
exponent applied in the inverse distance weighting function (see details) |
flexible_donor |
boolean indicating if the donor catchments can change during the simulation period according to the availability of discharge observations (see details) |
Details
This function returns a matrix of weights for each time steps (rows) and each gauged catchments
(columns) for the calculation of the average net rainfall of an ungauged catchment (see mixr).
The weights \lambda are estimated by an inverse distance weighting function (de Lavenne et al. 2016):
\lambda_i=\frac{1}{d_i^p}
\Sigma_{i=1}^{ndonors}\lambda_i=1
where d is the distances argument and p is the power argument. The weights are rescaled
so the sum is equal to 1.
Two strategies to handle missing data in the Rn matrix are possible.
If flexible_donor is TRUE, donors catchments are redefined at each time steps, and are chosen among
the ones that are effectively gauged at this given time step. This aims to keep a constant number of donor
catchments throughout the simulation period.
If flexible_donor is FALSE, the donor catchments are chosen once within all the gauged catchments,
regardless of missing data and remain the same throughout the entire simulation period. This stability of
donor catchments might however leads to a reduced number of donors (below ndonors) during periods
of missing data.
Value
A matrix with the same dimensions as Rn.
References
de Lavenne A, Skøien JO, Cudennec C, Curie F, Moatar F (2016). “Transferring measured discharge time series: Large-scale comparison of Top-kriging to geomorphology-based inverse modeling.” Water Resources Research, 52(7), 5555–5576. doi:10.1002/2016WR018716.