You should first detrend your data using regression analysis. Afterwards, check the cyclic trends in both your data and climate data, if a common cyclic trend exist in both, then you can do the job. If not, remove cyclic trend from the data and your climate data.

Dear colleague,

Climatic data are also non-stationary and in addition non-linear. So depending on you purposes - you could apply different techniques.

If you simply want to find the best fit between comparable data - use non-linear statistics (e.g. non-linear regression models). However, if you have to repeat the procedure many times (e.g. in points with different coordinates) this is a very much time consuming....

You may apply also simple correlation technique, and correct for non-stationarity. For this purpose I use "Cross-lagged panel correlation" technique described by D.A. Kenny, Correlation and causality (John Wiley & Sons Inc, 1979) - the book is available on-line.

Personally, I don't like linear multiple regression technique - especially if you have to apply it on a longer time scales. As I already mentioned, the variability of climatic parameters is non-linear and non-stationary. So applying linear technique in attempt to find the best fit, you are forced to put more and more independent variables - simply to compensate for the non-linear connectivity between your variables.

And the last advise: if you are looking for a long-term coherence between your variables - use measured values (seasonal, annual, etc.). In case of using daily or monthly values, take care for the seasonal cycle.

If you are interested by the short-term periodicity - use anomalies (i.e. deviations from some mean value). The choose of the mean value is also very important. I use time varying decadal means , but also could be used running averages. I don't recommend to use a stationary mean, especially in case on non-stationary data.

This is not an easy question to answer, since for starters how do you differentiate non-stationarity from random natural variability? This is a problem not only in terms of anthropogenic forcing but also in terms of multiple climate processes in the system, whose effects on the variable of interest may be constant but whose relative amplitudes will not be.

Rather than give a long-winded answer I'll just point to this recent paper:

Solomon, A., and the US CLIVAR Decadal Predictability Working Group, 2011: Distinguishing the roles of natural and anthropogenically forced decadal climate variability: Implications for prediction. Bull. Amer. Meteor. Soc., 92, 141-156, doi: 10.1175/2010BAMS2962.1.

which should help you get an idea about what some other scientists are thinking regarding some of the problems involved.

As formally defined by Yarnal (1993), the field of synoptic climatology is concerned with studying and understanding the relationships between the circulation of the atmosphere and the surface environment for a specific geographic region; however, we are not limited to the atmosphere, and this can be expanded to oceanic factors as well [e.g., sea surface temperature (SST)]. Within the field of synoptic climatology there are two distinct study approaches that Yarnal (1993) classifies as either (a) Circulation to Environment or (b) Environment to Circulation. Under the first approach, the synoptic data might be chosen because they are believed to have an effect on a particular environmental variable, there are no environment-specific criteria set for the data’s inclusion in the classification; furthermore, the classification of the circulation data (e.g., relative humidity, vorticity, SST, etc.) is independent of the environmental response such as with tropical cyclones (TCs). However, under the second approach, the synoptic data are identified as being associated with particular environmental conditions at the surface. In the second circulation to environment approach, synoptic processes are chosen because they are believed to have a distinctive effect on data and measurements and indices as proxies of environmental phenomena such as TCs.

Ysrnal, B., 1993. Synoptic climatology in environmental analysis: A primer, Brent Yarnal, Belhaven Press (London), 1993. No. of pages: xv + 195. ISBN 185293 1175

As Natalya said, the problem is not the non stationarity (any good detrending methodology will solve as Ehsan mentioned), but the non linearity. Use non linear estocastic methods.

Bhim Singh I also came across the same type of problem where to find the cross-correlation between one stationary series and one non-stationary series.

Can I use cross-correlation function (ccf in R) for this analysis?

Or else DCCA is can be used? If yes, what the idea of DCCA value since it gives a single value instead of lags correlations?

You may give me help since you have also done a similar type of study. Can you help me to clarify this doubt?