For generating high resolution (1km, 10 min) precipitation fields correlated both in space and time I use a model based on Fourier Transform (based on the same approach presented in Rebora et. al 2006,- Journal of Hydrometeorology

Volume 7, Issue 4, August 2006, Pages 724-738).

You can obtain similar results by using wavelet models (see e.g. Deidda 2000 - WATER RESOURCES RESEARCH, VOL. 36, NO. 7, PAGES 1779–1794, JULY 2000),.

In the paper by Ferraris et al. 2003 (Water Resources Research, Volume 39, Issue 12, December 2003, Pages SWC121-SWC1216) you can find a review of different models and approaches for generating precipitation fields correlated in space. Similar approaches can be used also for space-time. 

I'm so sorry as I never used the wavelet before I'm going to learn using it to use it in my master's

Dear Nicola,

thanks for the answer! I already had a look at your papers and was happy to see that you also work with Fourier for simulation of spatially correlated noise (similar to the STEPS and SBMcast nowcasting models). I was looking to the wavelet decomposition to see whether we could have a better representation fo the different spatial scales and at the same time a method to generate stochastic noise.

Best Regards

Dear Aparna,

thanks for the feedback.

Some time ago I checked a few papers on non-stationary multiplicative cascades for stochastic simulation. One approach is to handle the non-stationarity within the cascading approach (e.g. discrete multiplicative cascades), which may however lead to unstable cascades. Another approach would be to remove the non-stationarity in a first step and then apply a stationary cascade model.

I do not know the Lipschitz /Sobolev functions within this context and I wonder whether they are applicable to real-time precipitation forecasting, in particular to reproduce important properties of the precipitation fields such as spatial correlations and scaling of the power spectrum.

What is the link between the multiplicative noise models that you mention and the multiplicative cascades of D. Schertzer and S. Lovejoy?

Best Regards

Dear Loris,

I may point you to the following work in the context of spatial verification (scale-decomposition approach):

Casati, B., G. Ross, and D. B. Stephenson. "A new intensity-scale approach for the verification of spatial precipitation forecasts." Meteorological Applications 11.02 (2004): 141-154.

Casati, B. "New developments of the intensity-scale technique within the Spatial Verification Methods Intercomparison Project." Weather and Forecasting 25.1 (2010): 113-143.

Where the precipitation field is decomposed by means of a wavelet-based algorithm.

I'd be interested in generate a spatially correlated stochastic noise field based on wavelet. However, I don't have experience on this topic. Perhaps, one may use similar concepts to those used in spatial verification to constrain an hypothetical  sequence of precipitation fields to respect a predefined and reasonable spatial structure.

Ciao, Cristian