@Alexandre,

In the following discussion rooms you can find what you need.

https://www.researchgate.net/post/How_to_interpolate_spatial_climate_data_according_to_DEM

https://www.researchgate.net/post/Do_we_need_to_take_into_account_of_elevation_while_interpolating_temperature_data_spatially

https://www.researchgate.net/post/How_do_you_interpolate_precipitation_data

https://www.researchgate.net/post/Is_it_possible_to_interpolate_temperature_data_by_using_temperature_data_from_4_nearby_meteorological_stations

https://www.researchgate.net/post/How_can_I_find_the_best_spatial_resolution_for_a_point_data_interpolation

https://www.researchgate.net/post/Is_there_a_relevant_and_convenient_method_to_generate_climatic_rasters_from_stationary_data

You own the data, the most difficult part, what you need now is a software that espacialize and make the necessary geostatistics. I used the IDRISI, but there are others as ERDAS, ArcGIS, or an open source option, the QGIS / Quantum GIS.

The Idrisi is very easy and didactic.

Basic solution may be to create a background relief map from DEM and overlay temperature contours on them as polylines with colours. You may also consider to add some elevation contours (with gray colour) on relief map additionally but your emphasis should be on temperature.

I recommend you take a look at the Peruvian maps at http://www.senamhi.gob.pe/

In Peru we have even more topography than El Salvador.

Since you want to generate the temperatures map according to the Digital elevation model(DEM) you have , then its easy. You can easily use the regression equation.

Example , if your data looks like 

Elevation(m)     Temp(C)

2000               20

1500               23

1700               18

2500               15

Then prepare a regression equation, where Y=temperature, X=Elevation

Equation will be  y = -108.8x + 3992

Then on raster calculator in any GIS software, add this equation, on x add  your dem

Temperature map= -108.8(DEM)+3992

There you are!

every GIS software will do that properly

For the open-source approach for interpolation I recommend SAGA GIS. QGIS is fine for working with vector data and especially for final print outputs but SAGA has more and in my opinion better tools to process raster data.

PS: QGIS now supports native SAGA grid files so no problem to work with both programs together :-)

Hi Alexandre,

There are numerous studies argue the mathematical model e.g. Thiessen, Inverse Distance and or Linier correlation model are not well performed to spatially average rainfall in a mountainous region. You'd be better to use geostatistical approach to obtain better prediction and more robust calculation. Since you have quite plenty of climate stations and would like to consider two variables i.e. elevation and temperature, I suggest you to use co-kriging method. You can automatically perform this method within the Geostatistical Analyst tools in ArcGIS.

Good luck!

For a quick preview I suggest trying Multilevel B-spline interpolation (SAGA can provide it) which is quick, easy and provides similar output to kriging - not as sophisticated method, but the results are really good.

Yes you can.

But have u came across any relation between DEM and temp data variation with proper high resolution temp data..

regards

No yet, I will carry out a regression, I have daily records (2010-2015) from 16 stations. However El Salvador is 21000 km2. May be there is no a high density of weather stations however this is the only data.

Dear colleagues, thank you very much for your suggestions! Specially to Raoof Mostafazadeh for the complete research gate review about the topic!

Read the following pages to get more information for your project. I think the data is already available for USA but not for central or south America. Good luck

https://books.google.com/books?id=QJbOIPVpdGsC&pg=PA29&lpg=PA29&dq=DEM+data+combined+with+temperature+data&source=bl&ots=YwgqA5rCgA&sig=_LUhR7SRdi_Qt4YR4e66FjfPFfo&hl=en&sa=X&ei=sXlUVbW_JcvGogTy1oGoDQ&ved=0CDQQ6AEwAzge#v=onepage&q=DEM%20data%20combined%20with%20temperature%20data&f=false

Why not see if you can obtain data from a broader area (adjoining countries) to increase sample size, then develop the regression model and interpolate residuals? n=16 is pretty limiting.

Alternatively, search the literature for existing models and use data from your 16 stations as validation of other models.

Dear Alexandre:

First, you need to plot the temperature values of each station against their elevation values. This plot may suggest some sort of relationship between the temperature and the elevation.  Second, you may need to compute the correlation coefficient between the temperature and the elevation at the 16 points. The correlation coefficient is dimensionless number and its value is between 1 & -1.  I looked to your country in Google Earth and I found that there is a big variation in the elevation values along a longitudinal and cross-sectional profiles, which may suggest that you many need to partition your 16 points into small zones or tiles and do local regression for each zone, then stitch the results for the whole country. If you send your data (temp,elevation) I will write a MATLAB script to do a quick test.

Regards,

Gamal

In addition to what  Catherina said, I think you can interpolate the temperature data of your 16 sites and compare with the world climate data. 

Dear Alexandre,

I have dealt with similar issues while modeling orographic precipitation and temperature gradients for Peru.  The suggestions above are very helpful, so I will only add a few comments of my own. 

I have been able to produce solid results using co-kriging, using both instrumental data on ppt/T and DEM.  I've used ArcGIS for this, which provides great flexibility in the semivariogram modeling to produce results with lower residuals.  More details on co-kriging are mentioned in the threads Raoof Mostafazadeh referred you to. 

WorldClim will provide a dataset similar to what you are interested in, but it interpolates climatic dynamics based on several global models.  You likely have a better chance of capturing local variation using your instrumental data.

If you are interested in capturing temperature (is this temperature at the ground?), you could look into using the MODIS TERRA.  MODIS land surface temperature and emissivity products (MOD11) are available at 1000 m and 5600 m resolution, for daily observations, and 8-, 16- day averaged products.  MODIS products offer the benefit of directly observed surface temperatures, where as any interpolation with rely on geostatistical models.  More information on the specific products is at: https://lpdaac.usgs.gov/products/modis_products_table and information on usage policies is at: https://lpdaac.usgs.gov/products/modis_policies.

In your data condition, one of the good method will be using co-kriging, which is used when the number of primary variable data (temp data in your case) is smaller than the secondary variable (elevation from DEM). But as you most probably have the DEM data in raster form, you should first create point cloud from them. Then you can run the co-kriging, which creates an estimation surface for the temperature by taking into account the relationship between two parameters.