Phase Space Reconstruction and Predictability of Spectral Solar Irradiance From SOLSTICE


Authors:        Guoyong Wen (1,2) and Robert F. Cahalan (1)

Affiliations:     1) NASA/Goddard Space Flight Center (NASA/GSFC)

                     2) Goddard Earth Sciences and Technology Center, University of Maryland Baltimore County (GEST/UMBC)


Observations of TSI and SSI have been now made for a relatively long time, allowing us to perform statistical analysis. This work focuses on the predictability of spectral solar irradiance by analyzing SOLSTICE data. In the analysis, a time delay T is used to create a vector in d dimensions,



where  is observed spectral irradiance at wavelength  and time step n. The time delay T is determined such that the average mutual information between a time series and a delayed time series reaches minimum. The dimension d may be determined by the false nearest neighbor analysis, or simply allowing  to span 8~10 27-day rotation cycles.  is a data point in d dimensions vector space at time step n. A simple way to predict the future of the time series after time step L is look at its past () to find the vector  that is nearest to the latest  in the d-dimensional space.  Values after i’th () are the predictions after time step L (.).  We found the spectral irradiance in some wavelengths can be reasonably predicted, while other spectral irradiances are less predictable using this method. We further examined the average mutual information of a spectral irradiance time series and its delayed time series. The predictable time series using this simple “phase space match” method demonstrates a strong peak at a time delay of 360 days distinct feature in the average mutual information with the delay time series. A quasi-annual cycle appears to be associated with those predictable spectral irradiances.