I have about 10 weather stations situated in an area. They are not evenly spaced, and are at different elevations. I would like to give an area average in terms of monthly temperatures (min, max and avg). How do I go about this?
Air temperatures are expected to be fairly even in a smaller area on the same elevation. Are you interested in acquiring representative values for a location between the stations, or for the entire area as a whole? The temperature will vary in elevation, therefore gaining representative values for the entire area will depend on the average elevation, or the proportion of land surface at low and high elevation. If you have a weather station at low elevation in the middle of the area, and the total area is 90% low elevation, then the data from this station is expected to be representative.
One option is to calculate distance from each weather station to a representative 'middle point' of the area, and then factor in that stations further away from this middle point will be weighed less than stations closer to it. The same could apply for elevation as with distance. It will really depend on the spatial extent of this area and how large the environmental heterogeneity is.
Several potential complications are as follows:
1.Whether the land faces in the same direction throughout the area of study. If so, Carl's answer is fine. If not, then deal with each section of land facing in a given direction separately.
2.Is the area covered by the same vegetation. If not, separate the stations by vegetation cover.
3.Check that the sites have similar drainage conditions both for cold air drainage and for moisture status of the ground.
4.Is part of the land shaded for part of the day? If so, take this into consideration when interpreting the results.
Stuart.