I want to distribute point temperature data over some Himalayan catchment using Ordinary Kriging. While doing so i also want to use elevation raster as there is high elevation range in my study area? How can this be done this in R software?
i don't know R software but this can be done in Erdas Imagine and ArcGIS
There are at least two methods for incorporating elevation into the interpolation of temperature data (this is analogous to the problem of incorporating elevation into the interpolation of precipitation data). In using any of the different kriging estimators you have to make/use some assumptions. In the case of Ordinary kriging you are assuming that the mean of the random function is an unknown constant but this is not exactly reasonable for either temperature or precipitation. Instead you assume that the unknown mean is a function of elevation and use "kriging with external drift", more specifically the temperature mean is modeled as a polynomial function of elevation. You don't need to know the coefficients in the polynomial.
How to proceed, do a regression on temperature as a function of elevation (actually physics essentially provides an answer to the problem but doesn't take into account any local physical anomalies). Compute the residuals, you use the residuals to estimate and model the variogram. If you use the equations for "kriging with external drift) you use the variogram obtained from the residuals but the original data in the kriging estimator. The kriging variance incorporates the uncertainty in estimating the non constant mean as well as the uncertainty in the interpolation.
An alternative if you do not have software for "kriging with external drift". Again do the regression and compute the residuals. Estimate/model the variogram using the residuals. Use that variogram and the residuals with Ordinary kriging then add the regression values to the kriged values. You will not get a kriging variance for the final results (you can't just add the regression variance since the assumptions for regression are different than for kriging.
Another alternative, treat both temperature and elevation as random functions and use cokriging. The drawback to this is that you not only have to estimate/model two variograms but also the crossvariogram (Using a "Linear Coregionalizaion Model" is one solution to that problem) There are several possible complications (1) you may not have temperature data at the same locations where you have elevations and in fact you will likely have temperatures at a much smaller number of data locations. Theoretically this is not a problem but it does create problems in the software and not all software packages can handle it. (2) Using the Linear coregionalization model is not simple (the gstat package in R can do it)
Finally note that the data locations are really in 3-space and ArcGIS is really designed for 2-space.
Were all the temperatures read at the same time? If not you have a spatial temporal problem.
You should be able to find a number of papers on the precipitation/elevation problem in both the geostatistics and hydrology literature.
Hi Amrit:
You can find an example on how to interpolate both precipitation and temperature using Kriging (within R) on this paper:
https://www.researchgate.net/publication/222171372_Spatio_Temporal_Analysis_of_Daily_Precipitation_and_Temperature_in_the_Basin_of_Mexico
On this other paper I explain how to setup a climatological database and how to use it with R (with one example on interpolation):
https://www.researchgate.net/publication/220274999_The_Basin_of_Mexico_Hydrogeological_Database_BMHDB_Implementation_queries_and_interaction_with_open_source_software
Cheers.
Article Spatio Temporal Analysis of Daily Precipitation and Temperat...
Article The Basin of Mexico Hydrogeological Database (BMHDB): Implem...
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