Assessment of extreme rainfall events over Kerala using EVA and NCUM-G model forecasts

Abstract

Assessment of extreme rainfall events (ERE) is crucial for disaster management. Numerical weather prediction (NWP) model-based predictions often fail to predict the extremes. This could be due to several reasons, including insufficient model resolution to capture the sub-grid scale processes, inadequate high-quality observational data for assimilation, uncertainty in initial conditions and approximations in model physics. Estimation of rainfall for different return periods (RP) using extreme value analysis (EVA) can aid in better decision-making. RP of an event indicates its probability and rarity over the region. The current study shows how EVA can be used to supplement model predictions. This study uses the high-resolution (0.25×0.25) gridded observed rainfall data from India Meteorological Department (IMD), which has been available for 117 years (1901–2017). The generalised extreme value (GEV) distribution is applied with suitable goodness-of-fit tests. Rainfall amounts corresponding to 100-year RP are estimated using EVA over the entire data period (1901–2017) and three epochs (1901–1940, 1941–1980, and 1981–2017). The results indicate increasing rainfall amounts corresponding to 100-year RP. Similarly, rainfall amounts for 25, 50, 100, and 200-year RP over Kerala are computed to compare with the extremely heavy rainfall (≤21 cm/day) amounts reported during JJAS 2018 and 2019. Further, this approach supplements the operational forecasts of NCUM-G model forecasts.

Appendices

Appendix 1

See table A1.

Table A1 The goodness-of-fit test statistic and P value.

Appendix 2

2.1 Anderson–Darling test

The Anderson–Darling test (Stephens 2017) is used to test if a sample of data came from a population with a specific distribution. The Anderson–Darling test is an alternative to the chi-square and Kolmogorov–Smirnov goodness-of-fit tests.

The Anderson–Darling test is defined as: H₀: The data follow a specified distribution. H_a: The data do not follow the specified distribution.

Test statistic: The Anderson–Darling test statistic is defined as:

$$A^{2} = - N - S$$

where

$$S = \sum\limits_{{i = {1}}}^{N} {{{\left(\frac {{{2}i - {1}}} {N}\right)}}\left[ {{\text{ln}}\,F\left( {Y_i} \right) + {\text{ln}}\left( {{1} - F\left( {Y_{N + {1} - i}} \right)} \right)} \right]}$$

F is the cumulative distribution function of the specified distribution. Y_i is the ordered data.

2.2 Kolmogorov–Smirnov test

The maximum vertical distance between the EDF F_data(X) and the theoretical function F₀(X) is measured by the K–S test statistic (Kolmogorov as cited in Stephens 1992)

$$D = {\text{ Maximum }}\left| {F_0\left( X \right) - F_r(X)} \right|$$

where

• F₀(X) = Observed cumulative frequency distribution of a random sample of n observations.

• F₀(X) = k/n = (no. of observations ≤ X)/(total no. of observations).

• F_r(X) = The theoretical frequency distribution.