modwt.vt.val {WASP}

Variance Transformation Operation for Validation

Description

Variance Transformation Operation for Validation

Usage

modwt.vt.val(data, J, dwt, detrend = FALSE, backward = FALSE, verbose = TRUE)

Arguments

data

A list of response x and dependent variables dp.

J

Specifies the depth of the decomposition. This must be a number less than or equal to log(length(x),2).

dwt

A class of "modwt" data. Output from modwt.vt().

detrend

Detrend the input time series or just center, default (F).

backward

Detrend the input time series or just center, default (F).

verbose

A logical indicating if some “progress report” should be given.

Value

A list of 8 elements: wf, J, boundary, x (data), dp (data), dp.n (variance transformed dp), and S (covariance matrix).

References

Jiang, Z., Sharma, A., & Johnson, F. (2020). Refining Predictor Spectral Representation Using Wavelet Theory for Improved Natural System Modeling. Water Resources Research, 56(3), e2019WR026962. doi:10.1029/2019wr026962

Examples

data(rain.mon)
data(obs.mon)

## response SPI - calibration
SPI.cal <- SPI.calc(window(rain.mon, start=c(1949,1), end=c(1979,12)),sc=12)
#SPI.cal <- SPEI::spi(window(rain.mon, start = c(1949, 1), end = c(1979, 12)), scale = 12)$fitted

## create paired response and predictors dataset for each station
data.list <- list()
for (id in 1:ncol(SPI.cal)) {
  x <- window(SPI.cal[, id], start = c(1950, 1), end = c(1979, 12))
  dp <- window(obs.mon, start = c(1950, 1), end = c(1979, 12))
  data.list[[id]] <- list(x = as.numeric(x), dp = matrix(dp, nrow = nrow(dp)))
}

## variance transformation - calibration
dwt.list <- lapply(data.list, function(x) {
  modwt.vt(x, wf = "d4", J = 7, boundary = "periodic", cov.opt = "auto")
})

## response SPI - validation
SPI.val <- SPI.calc(window(rain.mon, start=c(1979,1), end=c(2009,12)),sc=12)
#SPI.val <- SPEI::spi(window(rain.mon, start = c(1979, 1), end = c(2009, 12)), scale = 12)$fitted

## create paired response and predictors dataset for each station
data.list <- list()
for (id in 1:ncol(SPI.val)) {
  x <- window(SPI.val[, id], start = c(1980, 1), end = c(2009, 12))
  dp <- window(obs.mon, start = c(1980, 1), end = c(2009, 12))
  data.list[[id]] <- list(x = as.numeric(x), dp = matrix(dp, nrow = nrow(dp)))
}

# variance transformation - validation
dwt.list.val <- lapply(
  seq_along(data.list),
  function(i) modwt.vt.val(data.list[[i]], J = 7, dwt.list[[i]])
)

## plot original and reconstrcuted predictors for each station
for (i in seq_along(dwt.list.val)) {
  # extract data
  dwt <- dwt.list.val[[i]]
  x <- dwt$x # response
  dp <- dwt$dp # original predictors
  dp.n <- dwt$dp.n # variance transformed predictors

  plot.ts(cbind(x, dp))
  plot.ts(cbind(x, dp.n))
}