PROCEDURE- (An example to estimate annual rainfall)

Statement of missing data problem-

Given the annual precipitation values P1, P2, P3,........,Pm at neighbouring 'm' stations 1, 2, 3,.....,m respectively. It is required to find the missing precipitation Px at a station X not included in the above m stations. Further, the normal annual precipitations N1,N2,....  at each of the above m+1 stations, including station X are known. 

METHOD 1: AVERAGING from all other stations.

If the normal annual rainfall at various stations are within about 10% of the normal annual precipitation at station X then a simple arithmetic average procedure is followed to estimate Px .

Px = [P1 + P2 + P3 + ....+ Pm] / m

METHOD 2: NORMAL RATIO METHOD

If the normal annual precipitations vary considerably, then Px is estimated by weighing the precipitation at various stations by the ratios of normal annual precipitations. This method gives Px as,

Px = (Nx / m)  [ (P1 / N1) + (P2 / N2) + .........+ (Pm / Nm) ]

I hope this help you.

I can imagine finding no close station data, but not finding any suggests you should broaden your search, consult your climate agency or meteorologists for assistance.  There are various ways to restore missing data from other rainfall stations, and also analyze data sets with missing values.  Rainfall = Streamflow + Evaporation + Transpiration + change in soil storage + deep seepage.  If you had or could estimate values for the parts, you could grossly estimate, but you need stream, well, temperature,  etc. to model this water balance.  

I would broaden my search for data, and try to correlate these other sites to your station with missing data.  Othwise I would look into analysis procedures that works with missing data.  I have always found ways to reasonably restore data, but if you had 30 years data, and one year with a bunch of missing values due to station was damaged, I would remove the year from analysis with any remarks pertinent in your reporting to describe this loss.  There could be reasons that doing this might remove extreme values of major storms that you need for your analysis, as these are often associated with lost records.  

Restoring data can be time consuming in obtaining and correlating data from a number of stations, even reviewing old weather reports.  It is thankless work, but necessary if you want the best data set you can provide for analysis.  

Dear Pisinee,

In the estimation of missing data from a raingauge station, performance of a group of neighbouring stations including the one with missing data are considered. A comparison of the recordings of these stations are made by using their NORMAL RAINFALL as standard of comparison. The normal rainfall is the average value of rainfall at a particular date, month or year over a specified 30-year period. The 30-year normal is recomputed every decade. Thus, the term NORMAL MONTHLY PRECIPITATION at a station 'A' means the average precipitation for a particular month at station A based on 30-year of record. Insertion of missing data to a station must be done sparingly. If too many data are estimated, the quality of the total data set may be diluted due to interpolation. Sometimes, if too many gaps exist in a record, it may be worthwhile to neglect that station than to have a station record with too much of interpolated data.  According to a WMO (World Meteological Organisation) guideline, not more than 10% of a record should have interpolated data. Two commonly used methods are Averaged method and normal ration method.

PROCEDURE- (An example to estimate annual rainfall)

Statement of missing data problem-

Given the annual precipitation values P1, P2, P3,........,Pm at neighbouring 'm' stations 1, 2, 3,.....,m respectively. It is required to find the missing precipitation Px at a station X not included in the above m stations. Further, the normal annual precipitations N1,N2,....  at each of the above m+1 stations, including station X are known. 

METHOD 1: AVERAGING from all other stations.

If the normal annual rainfall at various stations are within about 10% of the normal annual precipitation at station X then a simple arithmetic average procedure is followed to estimate Px .

Px = [P1 + P2 + P3 + ....+ Pm] / m

METHOD 2: NORMAL RATIO METHOD

If the normal annual precipitations vary considerably, then Px is estimated by weighing the precipitation at various stations by the ratios of normal annual precipitations. This method gives Px as,

Px = (Nx / m)  [ (P1 / N1) + (P2 / N2) + .........+ (Pm / Nm) ]

I hope this help you.

Apart from the simple methods given above, you can try out the spatial interpolation. It is nowadays highly used.

You may try spatial interpolation or grinding using all the stations and a fixed radius for which station data can be used for a particular grid. You can represent missing data with -999, however, this method assumes that within a certain radius at  least a few stations will have data for that month. You may read Maurer et al. (2002) [Journal of Climate] to better understand the methodology.

NORMAL RATIO METHOD AND simple arithmetic METHOD