i8 | rainfall riddle Rainfall riddle By Ayman Awadallah, Dar Al-Handasah Developing rainfall Intensity-Duration-Frequency relationships in a data-scarce region in Angola How do you calculate rainfall characteristics when many of the records do not even exist? That was the challenge faced by Dar engineers working in the City of Namibe as they sought to calculate the Intensity-Duration-Frequency, a measure crucial for stormwater and flood protection design. What is an Intensity-Duration-Frequency? The rainfall Intensity-Duration-Frequency (IDF) relationship is one of the most commonly used rainfall characteristics in the design and operation of water resources and flood protection projects. The relationship is between the rainfall intensity i, the duration d and the return period T (or, equivalently, the annual frequency of exceedance, typically referred to as frequency) specific for a certain location. Unfortunately, in many developing countries including Angola, the adequate long historical data sets crucial for developing IDFs are frequently not available. Monthly (and not daily) data were also available from 1998 till 2011. Unfortunately, we could not use the monthly data because severe flooding occurred when intense daily storms prevailed. The first step of the methodology was thus to disaggregate the monthly data and derive the daily annual maxima data using the characteristics of TRMM data. Comparing rainfall data sources and merging old and new data We analyzed the ratio between monthly TRMM data and maximum annual TRMM data, and found that the maximum rainfall amount that fell in one day was nearly equal to 0.6 of the respective monthly data. (The respective monthly data consist of an envelope line for the scatter plot, as shown by Figure 1). For rainfalls greater than 20 mm/day, we used the 0.6 ratio to derive the maximum annual data from the monthly available data. For less intense rainfalls, we considered the monthly maximum to be equal to the daily annual maximum - a conservative assessment. We assumed that the TRMM data were consistent in themselves, and we derived the envelope ratio between monthly and maximum daily TRMM data and applied this ratio on the ground station monthly rainfall data. This approach can only be valid in an arid region with limited rainy days, which is the main limit of applicability of the presented methodology. Next, we assessed whether the daily data derived from monthly data were significantly different from the ground station daily data with respect to the mean and variance of both datasets. For this step, we performed non-parametric tests because our annual maxima series did not follow the known Gaussian bell-shaped distribution. How we reached the IDF Gathering available daily and monthly rainfall data from ground stations and Tropical Rainforest Measuring Mission The data required to develop an IDF is the rainfall depth for various rainfall durations. For the IDFs to be reliable, a dataset of daily rainfall values covering at least 30 years is needed. From the daily rainfall values of each year, one selects the maximum rainfall that fell in one day of that year. For 30 years of data, one ends up with 30 values. These are termed an annual maxima series. The IDF is much harder to develop when there are too few records. It is a bit like trying to predict the weight of the largest person in a city when the only information you have is the weight of a few people randomly sitting in a room. Consequently, the 11 years-worth of available daily data have to be complemented with other rainfall information. We sought Tropical Rainfall Measuring Mission (TRMM) corrected satellite data. TRMM is an American-Japanese satellite mission that monitors tropical and subtropical precipitation. TRMM satellite data are available from 1998 to date. Even so, the TRMM data are not perfect because they were not calibrated for Angola and thus are not representative of what really fell to the ground. 38