ORIGINAL PAPER Developing hourly intensity duration frequency curves for urban areas in India using multivariate empirical mode decomposition and scaling theory S. Adarsh 1,2 • M. Janga Reddy 1 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2018 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. Keywords IDF  Scaling theory  MEMD  Rainfall  Hydrologic analysis 1 Introduction In recent times, urban flooding is a catastrophe of major concern in many cities worldwide and also in India. Accumulation of high intense rainfall over short duration can be prominent in urban areas of coastal regions, either due to coupled effect of rainfall with tidal actions or due to insufficient/improper drainage facilities, which may even- tually lead to flooding in cities. For planning and design of urban drainage systems, the intensity–duration–frequency (IDF) relationships play a pivotal role in understanding the risks associated with the hydrological extreme events. The frequency of occurrences of a storm of a given intensity and duration can be estimated statistically based on the IDF curves prepared for a specific region. Eventhough, short duration rainfall (hourly or sub-hourly) information is necessary for the planning and design of hydrological projects, the national hydrological services can provide the data mostly at daily time scale. The traditional methods used for the derivation of IDF curves may fail in such circumstances and the scale invariance theory can be used to solve this problem. In the past, the scale invariance theory has received wide attention in hydrology and some of them proposed development of simple and multiscaling models for regional precipitation estimation (Waymire and & M. Janga Reddy mjreddy@civil.iitb.ac.in 1 Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India 2 TKM College of Engineering, Kollam 691005, India 123 Stochastic Environmental Research and Risk Assessment https://doi.org/10.1007/s00477-018-1545-x