Interpolated Climate Data

 

The interpolation program and map generation is based on the interpolation equation given below. 

 

General Definitions:

so  is the station at which we are interpolating a value

do  is the date for which we are interpolating a value

v (s, d) is the value at station s and date  d

e (s) is the elevation at station s

d (si , s2) is the distance between s1 and s2

 

Current Interpolation Method:

Let S be the set of the 10 closest stations s to so for which v (s, do) is not null.

Then v (so, do) can be interpolated as follows:

 

                        ∑  v(s, do) + λe (s)

                     s-S

                                    d (s, so)

 

v(so, do)=                                                          -λ e(so)

                                     1

                       ∑                       

                      s-S      d (s, so)

 

where:  λ is the lapse rate of the sensor being interpolated.

 

 

The previous interpolation method that was used before 2005 (Mott et al. 1994) was:  

Let s1 be the closest station to so such that v(s1, do) is not null and there exist 25 dates δ    for which both v(so, δ ) and v(si , δ) are not null, and let D be the set of the 25 most recent such dates.

 

Let b= ∑   v(si , δ),  c=∑    v(si , δ)2 ,   d=∑    v(so , δ), and e=∑   v(so , δ)  v(si , δ).

          δ- D                  δ- D                  δ- D                          δ- D

 

                                                                    bc-de                       25e-bd

Then v(so , do)=a1 v(si , do) +ao, where ao =                 , and ai =   

                                                                      25c-d2                      25c-d2

 

 

Reference

Mott, Paul. T. W. Sammis and M. Southward. 1994. Climate data estimation using climate information from surrounding climate stations. ASAE Applied Engineering in Agriculture. Vol 10:1 pp414-537.