Is DWT helpful in reducing bias for further downscaling?
Many bias correction techniques such as standardisation and quantile mapping have been employed under the assumption of stationarity. Can discrete wavelet transforms denoise the data considering the non-stationarity of a GCM dataset (wind, temperature)? If yes, then in what way can it be effective in noise removal? Can it help further improvement of results if DWT is carried out in addition to bias correction?
Bias correction is not for noise removal, but for systematic error removal... Bias means systematic error which is different from noise...
DWT (or its alternate form DSWT) is very useful for decomposition, manipulation of individual components and reconstruction, just like in the way of a transmultiplexer filter bank; it won't remove biasing. But yes, DWT is very useful for non-stationary data. Using a Daubechies wavelet of order 5 or higher with no more than 7 or 8 level decomposition, could lead to good results. I've used them that way for denoising wind, temperature, moisture, even water currents from ADCP recordings. If your're not quite comfortable programing them ad-hoc, the WAVEMENU toolbox in Matlab could be of great help for you.
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