Here is a plot of ARMA (1,1) coefficients for the CRU data set plotted up against a world map. I ‘ve not seen anything like this plotted up before. I think that the patterns are really quite pretty.
I’ve mentioned a couple of other studies that have examined relationships between temperature and ARMA processes, but these have been (to my knowledge) at a global level. I’ve not seen gridcell detail as shown in the graphics here. I also don’t think that there has been as specific a focus on ARMA(1,1) processes; the tendency has been to use AR(k) models, but some nice clean information is obviously coming out of the ARMA(1,1) models at gridcell detail. The tropical oceans show very clearly in extremely AR1 coefficients. Continental AR1 coefficients are markedly lower (shown even more clearly in the square root coloring scheme in the figure at the bottom of the page, which accentuates this.) MA1 coefficients in the oceanic Southern Hemisphere are consistently stronger than in the more continental NH. Some nice detail features can be observed: e.g. the El Nino tongue has lower MA1 coefficients. DETAIL
Figure 1. ARMA(1,1) Coefficients for Gridcell CRU Data. Top – AR1 Coefficient; Bottom – MA1 – Coefficient
Coefficients are calculated here if there is a count of at least 100 measurements using the na.pass option. This means that coefficients are calculated for a lot of series with very sparse measurements. I suspect that the cacophony of colors in the Southern Ocean results from calculations on sparse information, rather than actual discontinuities in ARMA coefficient behavior. I get the impression that CRU has grabbed measurements in sparse areas and homogeneity is a hope rather than something that has been demonstrated – the evidence of these coefficients certainly suggests a great deal of non-homogeneity in the data in this area. If you squint, you can see some suspicious entries elsewhere: e.g. northeast Brazil has a gridcell with a highly positive MA1 coefficient; the far northeast Siberian AR1 coefficients look suspicious.
Figure 2. ARMA(1,1) Coefficients for Gridcell CRU Data. Top – AR1 Coefficient; Bottom – MA1 – Coefficient. Both on sqaure root scale.