Analysis of Missing Precipitation Data
Methods for Estimation of Missing Rainfall Data
There are two methods for estimation of missing data.
According to the arithmetic mean method the missing precipitation 'Px' is given as:
Where 'n' is the number of nearby stations, 'Pi' is precipitation at ith station and 'Px' is missing precipitation.
In case of three stations 1, 2 and 3,
Px = (P1 + P2 + P3)/3
Naming stations as A, B and C instead of 1, 2 and 3
Px = (Pa + Pb + Pc)/3
Where Pa , Pb and Pc are defined above.
According to the normal ratio method the missing precipitation is given as:
Where Px is the missing precipitation for any storm at the interpolation station 'x', Pi is the precipitation for the same period for the same storm at the "ith" station of a group of index stations, Nx the normal annual precipitation value for the 'x' station and Ni the normal annual precipitation value for 'ith' station.
For example, for the symbols defined above for three index stations in a catchment area.
If the normal annual precipitation of the index stations lies within ±10% of normal annual precipitation of interpolation station then we apply arithmetic mean method to determine the missing precipitation record otherwise the normal ratio method is used for this purpose.
Consider that record is missing from a station 'X'.
N = Normal annual precipitation. (Mean of 30 years of annual precipitation data)
P = Storm Precipitation.
Let Px be the missing precipitation for station 'X' and Nx , the normal annual precipitation of this station, Na, Nb and Nc are normal annual precipitations of nearby three stations, A, B and C respectively while Pa, Pb and Pc are the storm precipitation of that period for these stations.
Now we have to compare Nx with Na , Nb and Nc separately. If difference of Nx - Na, Nx - Nb, Nx - Nc is within 10% of Nx then we use simple arithmetic mean method otherwise the normal ratio method is used.
Find out the missing storm precipitation of station 'C' given in the following table:
In this example the storm precipitation and normal annual precipitations at stations A, B, D and E are given and missing precipitation at station 'C' is to be calculated whose normal annual precipitation is known. We will determine first that whether arithmetic mean or normal ratio method is to be applied.
10% of Nc = 93.5 x 10/100 = 9.35
After the addition of 10% of Nc in Nc, we get 93.5 + 9.35 = 102.85
And by subtracting 10% we get a value of 84.15
So Na, Nb, Nd or Ne values are to be checked for the range 102.85 to 84.15.
If any value of Na, Nb, Nd or Ne lies beyond this range, then normal ratio method would be used. It is clear from data in table above that Nb, Nd and Ne values are out of this range so the normal ratio method is applicable here, according to which
Pc = (1/4)(93.5 x 9.7/100.3 + 93.5 x 8.3/109.5 + 93.5 x 11.7/125.7 + 93.5 x 8.0/117.5) = 7.8 cm
Precipitation station "X" was inoperative for part of a month during which a storm occurred. The storm totals at three surrounding stations A, B and C were respectively 10.7, 8.9 and 12.2 cm. The normal annual precipitation amounts at stations X, A, B and C are respectively 97.8, 112, 93.5 and 119.9 cm. Estimate the storm precipitation for station 'X'.
Pa = 10.7 cm Na = 112 cm
Pb = 8.90 cm Nb = 93.5 cm
Pc = 12.2 cm Nc = 119.9 cm
Px = ? Nx = 97.8 cm
10% of Nx = 97.8 x 10/100 = 9.78 cm.
Nx - Na = 97.8 - 112 = -14.2 cm Þ More than + 10% of Nx (no need of calculating Nx - Nb and Nx - Nc
Px = (1/3)( 97.8x 10.7/112+ 97.8x 8.90 /93.5 + 97.8x 12.2 /119.9)
Px = 9.5 cm
Estimation of Missing Precipitation Data
This situation will arise if data for rain gauges are missing (e.g. due to instrument failure). Data from surrounding gauges are used to estimate the missing data. Three approaches are used:
Use when normal annual precipitation is within 10% of the gauge for which data are being reconstructed
Normal ratio method (NRM) is used when the normal annual precipitation at any of the index station differs from that of the interpolation station by more than 10%. In this method, the precipitation amounts at the index stations are weighted by the ratios of their normal annual precipitation data in a relationship of the form:
Pm = precipitation at the missing location
Reciprocal Inverse Weighting Factor Approach
A double-mass curve is used to check the consistency of a rain gauge record:
Areal Precipitation Estimation
Potentially most accurate approach, but subjective
All soils are classified into four hydrologic soil groups of distinct runoff-producing properties. These groups are labeled A, B, C and D. Following is the brief of their runoff and infiltration properties:
A Lowest runoff potential (Greater than0.03 in/hr)
Land use and Treatment
Ground surface (Hydrologic) condition
Hydrologic condition is based on combination of factors that affect infiltration and runoff, including:
Poor: Factors impair infiltration and tend to increase runoff