ESTIMATION OF MISSING RAINFALL DATA
The point observation from a precipitation
gage may have a short break in the record
because of instrument failure or absence of
the observer. Thus, it is often necessary to
estimate the missing record using data from
the neighboring station. The following
methods are most commonly used for
estimating the missing records.
1. Simple Arithmetic Method
2. Normal Ratio Method
3. Modified normal ratio method
4. Inverse distance method
5. Linear programming method
SIMPLE ARITHMETIC METHOD
The missing precipitation Px can be
determined using simple arithmetic average,
if the normal annual precipitation at various
stations are within 10% of the normal
precipitation at station, x, as follows:
๐๐ฅ =1
๐[๐1 + ๐2 + โฏ + ๐๐]
NORMAL RATIO METHOD
If the normal precipitations vary
considerably then Px is estimated by
weighting the precipitation at various
stations by the ratios of normal annual
precipitation. The normal ration method
gives Px as:
๐๐ฅ =๐๐ฅ
๐[๐1
๐1 +๐2
๐2 + โฏ + ๐๐
๐๐]
This method is based selecting m (m is
usually 3) stations that are near and
approximately evenly spaced around the
station with the missing record.
MODIFIED NORMAL RATIO METHOD
Normal ratio method is modified to
incorporate the effect of distance in the
estimation of missing rainfall.
๐
๐ฅ=
โ๐ท๐
1
๐(๐
๐ฅ
๐๐)๐๐
๐
๐=1
โ๐ท๐
1
๐
๐
๐=1
Where ๐๐ is normal rainfall, ๐ท๐ is the distance
between the index station i and the gauge
station with missing data or ungauged
station, n is the number of index stations and
b is the constant by which the distance is
weighted (normally 1.5-2.0) commonly used
๐ท0.5.
INVERSE DISTANCE METHOD
The inverse distance method has been
advocated to be the most accurate method
as compare to other two methods discussed.
Amount of rainfall to be estimated at a
location is a function of:
๏ rainfall measured at the surrounding index
stations
๏ distance to each index station from the
ungauged location
Rainfall ๐
๐ฅ at station x is given by:
๐
๐ฅ=
โ(๐๐
๐ท๐๐)
๐
๐=1
โ(1
๐ท๐๐)
๐
๐=1
๐ = 2 ๐๐ ๐๐๐๐๐๐๐๐ฆ ๐ข๐ ๐๐
