Dear Zohaib,

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) ]

These are the methods for estimating the missing data of rainfall. Apart from these, you can try out the spatial interpolation. It is nowadays highly used.

Restoring data can be time consuming in obtaining and correlating data from a number of stations, even reviewing old weather reports. But its important if you want to have a best dataset for your research. I hope my answers will be helpful to you.

All the best !

 the use of methods of homogenization is unavoidable. These methods allowed us to fill gaps in the collected series, and removal of some stations that have a high heterogeneity in their series.

There are several methods to fill gaps being found in the climate series, among these methods, there is that of Rosenberg (1969), used on the climate data stored in Palestine. This method was adopted by Heusch (1970) in Morocco, these authors used this method to reconstruct the gaps by taking into consideration the distribution of rainfall in space according to climatic, geographic and topographic.

P= (a*H) + (b*D) + (c*L)+ (d*l) e -s

with:

P = Average rainfall (mm);

H = Altitude (m);

D = Distance from the sea (Km);

the Latitude = (m);

L = Longitude (m);

s = slope  (%)

a, b, c, d, e = coefficients of the regression equation

We note that all calculations are based on the method of multiple regression. This method of bringing the best data sets from several variables considered for several stations.