This one is available online for free
An Introduction to Statistical Signal Processing
Robert M. Gray and Lee D. Davisson
When I was working more on fossil fuel depletion modeling several years ago, all I really did was stochastic modeling and applying elements of statistical signal processing. That's really because the models are of large ensembles of events and processes.
In contrast, the big climate models like ENSO and QBO are singular processes likely driven by cyclic forcings. There is actually little that is statistical about this and so regular signal processing and deterministic models are more applicable.
On one of the skeptic sites, I chuckle over the fact that they ascribe it all to noise
> "Without sufficient individual model runs to compare to the single observed realization, I have found that using Singlular Spectrum Analysis allows for non linear trends and decomposition of the temperature series into trend, quasi periodical/cyclical and red/white noise. In these analyses I find no evidence for significant periodic components in either the modeled or observed series and thus I can model the residual noise with ARMA. I have found that confidence intervals determined from those models having multiple runs agrees well with those determined from Monte Carlo simulations using ARMA models."
No significant periodic components? Awfully narrow view imo.