Developing hourly intensity duration frequency curves for urban areas in India using multivariate empirical mode decomposition and scaling theory

Abstract

Development of rainfall intensity–duration–frequency (IDF) curves of short duration such as hourly or sub-daily are quite essential for planning and design of urban storm water drains. However, in developing countries like India, at many places the meteorological observatories do not have long records of hourly rainfall data, at large which may have access to data at daily or higher time scale only. Therefore, the scale invariance property of rainfall and/or the disaggregation process can be a useful mean for obtaining of shorter duration rainfall IDF curves from the daily scale rainfall data. This study proposes an alternative approach for deriving the hourly and sub-daily IDF relationships by using the scale invariance property of rainfall, empirical mode decomposition (EMD) method and extreme value (EV) model formulations. The multivariate EMD method is used for decomposing the rainfall intensity series of different durations simultaneously into a number of orthogonal modes. The logarithmic plot between probability weighted moments of the orthogonal modes and the duration gives the scaling exponent, which is further used for deriving IDF relationships based on EV formulations. To validate the correctness of the proposed method, first the method is applied for rainfall data of Mumbai and Bangalore cities in India, and the results are compared with that obtained by the classical frequency factor method. The results of IDF relationships derived by the two methods displayed good agreement in general, but noticed a larger deviation for the curves of higher return periods. Then the method is applied for the derivation of IDF relationships for hourly durations from the daily rainfall data of eight major cities in Kerala State in India. The results of the study demonstrated the effectiveness of the proposed approach for data-scarce regions in deriving the short duration IDF relationships from the daily rainfall data.