Rainfall Indices for MCDM models in ArcGIS: how and Why?

Step I: Data download in tif format

Step II: Cell statistics

Step III: Convert into point

Step IV: Interpolation

The Rainfall intensity is one of the main factors due to its significant impact on the flood magnitude, flash flood, desertification, Bank erosion, Gully Erosion, land degradation, sediment flux, soil erosion etc.

The rainfall intensity map is calculated using the Modified Fournier index methodology

MFI=∑129_(i=1)^12▒ (P_i^2)/P

here, Pi shows the mean monthly precipitation, and P shows the mean annual precipitation.

The rainfall factor, an index unit, is a measure of the erosive force of a specific rainfall. This is determined as a function of the volume, intensity and duration of the rainfall and can be computed from a single storm, or a series of storms to include cumulative erosivity from any time period. Raindrop/splash erosion is the dominant type of erosion in barren soil surfaces. R-factor was developed by Wischmeier and Smith (1978) and modified by Arnoldus (1980).

The Precipitation Concentration Index (PCI) was developed by Oliver (1980) to quantify the periodic variation of rainfall. The Precipitation Concentration Index is calculated by the following procedure for characterizes the temporal concentration of the rainfall.

Rainfall Seasonality Index refers to the degree of variability in monthly rainfall through the year; it assesses seasonal contrasts in rainfall amounts rather than whether months are ‘dry’ or ‘wet’ in an absolute sense. In an attempt to quantify these contrasts, the Seasonality Index (ST) was developed, which is simply the sum of the absolute deviations of mean monthly rainfalls from the overall monthly mean, divided by the mean annual rainfall:

SI=1/R ∑129_(n=1)^12▒ |X_n-R/12|

where Xn represents the total monthly precipitation, and R represents the total annual precipitation.

This index can in theory vary from zero (if all the months have equal rainfall) to 1.83 (if all the rainfall occurs in a single month).

Rainfall Anomaly Index (RAI) developed by van Rooy (1965) is used in depicting periods of dryness and wetness in the area. In this technique, the precipitation values for the period of study will be ranked in descending order of magnitude with the highest precipitation being ranked first and the lowest precipitation being ranked last. The average of the ten highest precipitation values, as well as that of the ten lowest precipitation values for the period of study, is to be calculated. The positive and negative RAI indices are to be computed by using the mean of ten extremes. The formula for calculating positive RAI (for positive anomalies) is given by;

RAI=+3 (P-P ̅)/(M ̅-P ̅ )

Let M ̅ be the mean of the ten highest precipitation records for the period under study, P ̅ the mean precipitation of all the records for the period, and the P precipitation for the specific year

The formula for calculating negative RAI (for negative anomalies) is given by;

RAI=-3 (P-P ̅)/(m ̅┴¯-P ̅ )

Let m ̅ be the mean of the ten lowest precipitation records for the period under study. Then the negative RAI (for negative anomalies) for that year

Rainfall variability Index is the ratio between anomalies over the standard deviation of long period of rainfall data. According to Gocic and Trajkovic (2013), the following equation is to be used to determine RVI

δ_i=(P_i-μ)/σ

where

δi represents RVI,

Pi is annual rainfall for ith year,

µ is the annual mean rainfall

σ standard deviation of rainfall.

The PNPI is one of the most straightforward measures of rainfall deviation from its long-term mean. ‘Normal’ may be and is usually set to a long-term mean precipitation value at a location. The value of ‘normal’ may be calculated for a month, a season or a year and is considered to be 100%. The same PNPI may have different specific impacts at different locations and, therefore, it is a bit of a simplistic measure of precipitation deficit. Also, what is normal may be perceived differently in different regions.

Morid et al. (2006) and Masoudi and Hakimi (2014) used the following equation to monitor drought in the region.

PNPI=∼P_i/P×100

where

Pi is the total precipitation of each year,

P is the average climatology.