As regards the first question, you can use the Co-Kriging in ArcGIS (Geostatistical Analyst). However, I would recomend you other methods like Multiple Regression, Regression Kriging, etc. Really, each method adjusts better others...depending on the situation.

Secondly, the accuracy of Worlclim is not stationary around the world. Pay atention about the distribution of weather stations (see the map attachment). I may recommend some predictors based on my short experience. However, the relative importance of predictors is very different depending on where, mainly when we want to mapping the precipitations.

References: 

Hijmans, R. J., Cameron, S. E., Parra, J. L., Jones, P. G., & Jarvis, A. (2005). Very high resolution interpolated climate surfaces for global land areas. International Journal of Climatology, 25(15), 1965–1978.

Li, J., & Heap, A. D. (2014). Spatial interpolation methods applied in the environmental sciences: A review. Environmental Modelling & Software, 53, 173–189.

Ninyerola, M., Pons, X., & Roure, J. M. (2000). A methodological approach of climatological modelling of air temperature and precipitation through GIS techniques. International Journal of Climatology, 20, 1823–1841.

Peña-Angulo, D., Brunetti, M., Cortesi, N., & Gonzalez-Hidalgo, J. C. (2016). A new climatology of maximum and minimum temperature (1951–2010) in the Spanish mainland: a comparison between three different interpolation methods. International Journal of Geographical Information Science, (August), 1–24. 

More accurate than .....? What data set was the benchmark for your statement on accuracy?

WorldClim values are interpolations of meteorological point data by lat, long and elevation. The locations of meteorological stations is mostly biased. The relevance of WorldClim interpolations versus your own interpolations likely depends on the densities and the magnitude the location bias of the points underlying each  interpolation.

ArcGIS does not contain an algorithm/operation for your purpose as I understand the latter from the short Intro. I suggest you try a range of SDM algorithms with your data set of point (bio-)climate parameters as dependent variable and projected coordinates plus elevation as three independent variables (co-variates).  Next you may test other co-variates (vegetation; Incoming solar radiation). 

Have fun

Article Where the bears roam in Majella National Park, Italy

As regards the first question, you can use the Co-Kriging in ArcGIS (Geostatistical Analyst). However, I would recomend you other methods like Multiple Regression, Regression Kriging, etc. Really, each method adjusts better others...depending on the situation.

Secondly, the accuracy of Worlclim is not stationary around the world. Pay atention about the distribution of weather stations (see the map attachment). I may recommend some predictors based on my short experience. However, the relative importance of predictors is very different depending on where, mainly when we want to mapping the precipitations.

References: 

Hijmans, R. J., Cameron, S. E., Parra, J. L., Jones, P. G., & Jarvis, A. (2005). Very high resolution interpolated climate surfaces for global land areas. International Journal of Climatology, 25(15), 1965–1978.

Li, J., & Heap, A. D. (2014). Spatial interpolation methods applied in the environmental sciences: A review. Environmental Modelling & Software, 53, 173–189.

Ninyerola, M., Pons, X., & Roure, J. M. (2000). A methodological approach of climatological modelling of air temperature and precipitation through GIS techniques. International Journal of Climatology, 20, 1823–1841.

Peña-Angulo, D., Brunetti, M., Cortesi, N., & Gonzalez-Hidalgo, J. C. (2016). A new climatology of maximum and minimum temperature (1951–2010) in the Spanish mainland: a comparison between three different interpolation methods. International Journal of Geographical Information Science, (August), 1–24. 

Hi Joseph,

As others have mentioned, the quality of the WorldClim surfaces vary depending upon your area of interest. There is also likely to be bias induced by record length and years of operation at many stations. If you have your own point data and sufficient point density, I would suggest taking a look at trivariate thin plate smoothing splines (and potentially partial spline models). This can be done using R or by using ANUSPLIN. 

Best regards,

Steve

Stewart, S. B. and Nitschke, C. R. (2016), Improving temperature interpolation using MODIS LST and local topography: a comparison of methods in south east Australia. Int. J. Climatol.. doi:10.1002/joc.4902

thanks

Hi there.

I would like to suggest Least Square Collocation (LSC) with Gaussian Distribution-based of Model Covariance Function (from empirical data).

This method is popular for interpolation geoscience data such as ionosphere, gravity, and and seismology. Krigging method more or less to cope with small region (local area) whereby the changes of geophysical signals is considerably linear in spatial sense. But it is non-linear.

However, cross validation is needed to see the efficiency of the LSC. More in-situ data, better empirical distribution and covariance function will be generated.

Regards

Wan Anom Wan Aris

Sometimes good results give just kriging method - if the situation and relief are clear and not very complicated, but co-kriging  is one of the best, because of applying few variables at the same time. Good regards!

Apart from the cokriging (built in ArcGIS) for considering elevation as a secondary variable in kriging, you can even implement another additional type of kriging named "regression kriging" using a free toolbox available and you can do it in ArcGIS10 environment.

Please refer to the following video. It is so simple.

https://www.youtube.com/watch?v=uDWBT1wn8Ps

https://www.esri.com/news/arcuser/0704/files/interpolating.pdf