at.vt {WASP}

Variance Transformation Operation - AT(a trous)

Description

Variance Transformation Operation - AT(a trous)

Usage

at.vt(
  data,
  wf,
  J,
  boundary,
  cov.opt = "auto",
  flag = "biased",
  detrend = FALSE
)

Arguments

data

A list of response x and dependent variables dp.

wf

Name of the wavelet filter to use in the decomposition.

J

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

boundary

Character string specifying the boundary condition. If boundary=="periodic" the default, then the vector you decompose is assumed to be periodic on its defined interval, if boundary=="reflection", the vector beyond its boundaries is assumed to be a symmetric reflection of itself.

cov.opt

Options of Covariance matrix sign. Use "pos", "neg", or "auto".

flag

Biased or Unbiased variance transformation, c("biased","unbiased").

detrend

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

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.

Jiang, Z., Sharma, A., & Johnson, F. (2021). Variable transformations in the spectral domain – Implications for hydrologic forecasting. Journal of Hydrology, 126816.

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 seq_len(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
dwt.list <- lapply(
  data.list,
  function(x) at.vt(x, wf = "d4", J = 7, boundary = "periodic", cov.opt = "auto")
)

## plot original and reconstrcuted predictors for each station
for (i in seq_len(length(dwt.list))) {
  # extract data
  dwt <- dwt.list[[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))
}