R-Instat is a front end to the R program language. Visit https://r-instat.org/ for more information on this statistical program. Otherwise, if you have access to Excel, you can run a statistical T-test for the two series.

Staying with R, I would suggest to use the Openair program, but that needs some additional training.......

Good luck!

Thank you Marcel Severijnen and Özgür Zeydan for the suggestion. I think it might help.

Hello Surajit,

First thing is to start with the basics: do the time-series have the same time-interval between data values? Are the measurements taken at the same (or different) times of day? How far apart (i.e., in km) are the 2 stations? Are they at the same or different elevations? What are the means and standard deviations of each? Are your experimental "air temperature" measurements taken with the same precautions for shade, isolation, etc. as the meteorological station data?

You can probably learn a lot just by plotting the timeseries together. That will show any consistent offset (or bias), and time-lags, and give you a good idea of their correlation (which you can calculate systematically in any case). Otherwise, plot each coincident measurement (exp. value, met-station value) as the (x,y) coordinates of a scatter plot and see how closely they line up along the (45-degree) diagonal. All of that should give you some idea of how well (or badly) a missing data-point in one series could be replaced by the corresponding point from the other.

More formally, you can use a t-test to check if the means of both time-series are different, given the null hypothesis that they are the same. But first you should probably subtract the annual cycle from each series, since both timeseries are only normally distributed about that underlying cycle. The variances should also be the same for the t-test to formally apply.

It's also easy to calculate the basic correlation between the 2 series (you can even lag/lead one or the other). You can measure the significance ("p-value") of that correlation coefficient based on its value and number of time-points by first calculating the t-test value, and looking up the p-value from the t-table. (See e.g., https://towardsdatascience.com/eveything-you-need-to-know-about-interpreting-correlations-2c485841c0b8 and google t-table to find the t-table...).

From the information you provide, most likely your 2 timeseries are highly significantly correlated. What might be interesting would be to subtract the physical "signal" from each (e.g., the annual or diurnal cycles, but also synoptic events like frontal passages..), until you are left with just random noise, which should not be significantly correlated. Then you can say here's the physical signal, and here's the random noise, which might really be saying a lot!