- Open Access
Intensity-Duration-Frequency (IDF) rainfall curves, for data series and climate projection in African cities
© De Paola et al.; licensee Springer. 2014
- Received: 2 November 2013
- Accepted: 25 February 2014
- Published: 9 March 2014
Changes in the hydrologic cycle due to increase in greenhouse gases cause variations in intensity, duration, and frequency of precipitation events. Quantifying the potential effects of climate change and adapting to them is one way to reduce urban vulnerability. Since rainfall characteristics are often used to design water structures, reviewing and updating rainfall characteristics (i.e., Intensity–Duration–Frequency (IDF) curves) for future climate scenarios is necessary (Reg Environ Change 13(1 Supplement):25-33, 2013).
The present study regards the evaluation of the IDF curves for three case studies: Addis Ababa (Ethiopia), Dar Es Salaam (Tanzania) and Douala (Cameroon). Starting from daily rainfall observed data, to define the IDF curves and the extreme values in a smaller time window (10′, 30′, 1 h, 3 h, 6 h, 12 h), disaggregation techniques of the collected data have been used, in order to generate a synthetic sequence of rainfall, with statistical properties similar to the recorded data. Then, the rainfall pattern of the three test cities was analyzed and IDF curves were evaluated.
In order to estimate the contingent influence of climate change on the IDF curves, the described procedure was applied to the climate (rainfall) simulations over the time period 2010–2050, provided by CMCC (Centro Euro-Mediterraneo sui Cambiamenti Climatici). The evaluation of the IDF curves allowed to frame the rainfall evolution of the three case studies, considering initially only historical data, then taking into account the climate projections, in order to verify the changes in rainfall patterns. The same set of data and projections was also used for evaluating the Probable Maximum Precipitation (PMP).
- Frequency curves
- Disaggregation analysis
- Climate change
Degradation of water quality, property damage and potential loss of life due to flooding is caused by extreme rainfall events. Historic rainfall event statistics (in terms of intensity, duration, and return period) are used to design flood protection structures, and many other civil engineering structures involving hydrologic flows (McCuen 1998; Prodanovic and Simonovic 2007).
Any change in climate produces modifications in extreme weather events, such as heavy rainfall, heat and cold waves, in addition to prolonged drought occurrences (Almazroui et al. 2012).
Since rainfall characteristics are often used to design water structures, reviewing and updating rainfall characteristics (i.e., Intensity–Duration–Frequency (IDF) curves) for future climate scenarios is necessary (Mirhosseini et al. 2013).
A lot of studies, especially recently, have been developed to analyze the factors for assessment, adaptation and mitigation of climate change, and to enhance and sharpen the disaster management for the many and various stakeholders.
El-Hadji and Singh (2002), using long-term data (from 1951 to 1990) of rainfall and annual runoff, have developed an investigation of spatial and temporal variability of rainfall and runoff in the Casamance River basin, located in southern Senegal, West Africa.
Chowdhury and Beecham (2010,2012) have analyzed the effects of changing rainfall patterns in Australia, in order to define the design parameters of Water Sensitive Urban Design (WSUD) technologies, as bioretention basins and permeable pavements, describing how these systems behave under varying rainfall conditions.
Kuhn et al. (2011) have analyzed the effect of climate change and continuing land use change in the Gallocanta Basin (Spain), one of only a few bird sanctuaries. Therefore, in order to obtain an appropriate management of the bird sanctuary, it was important to understand the impact of climate change on basin hydrology in terms not only of total amount of rainfall, but also considering the individual extreme events, that affect the basin level.
Sherif et al. (2011,2013) have analyzed spatial and temporal characteristics of rainfall in the United Arab Emirates (UAE). The rainfall patterns, rainfall probability of occurrence, rainfall intensity-duration-frequency (IDF) relationship, probable maximum precipitation (PMP) and drought scenarios were investigated, using standard statistical techniques, as Gumbel, log Pearson, GEV, log normal, Wakeby and Weibull probability distributions.
The IDF curves were also estimated for 13 stations in Cote D’Ivoire in the Sora et al. study, using rainfall data series of durations ranging from 15 minutes to 4 hours.
Furthermore, in the three cities considered, available rainfall records are limited to daily time steps. Since rainfall data at shorter time steps are essential for the evaluation of IDF curves, a daily rainfall disaggregation model was adopted.
The climate projections used, provided by CMCC, were performed following the IPCC (Intergovernmental Panel on Climate Change) 20C3M protocol for the 20th Century, and the RCP4.5 and RCP8.5 radiative forcing scenarios for the 21st century: they are characterized by horizontal resolutions of about 8 km and 1 km.
In addition, for the three case studies, was also estimated, both for data series and projections, Probable Maximum Precipitation (PMP), for duration rating from 10′ to 24 h. Extreme rainfall features and estimates of PMP for different return periods, evaluated in this study, will be useful to planning and designing flood protection structures.
Probability distribution for IDF
The intensity-duration-frequency curves are used in hydrology to express in a synthetic way, fixed a return period T and a duration d of a rainfall event, and for a given location, the information on the maximum rainfall height h and the maximum rainfall intensity i. Known these parameters, it is possible to build synthetic rain graphs that are useful to the elaboration of flood hydrographs.
in which a(T) and n are the parameters that have to be estimated through a probabilistic approach.
in which k is the considered duration, in this work equal to 7 (10′, 30′ minutes, 1, 3, 6, 12, and 24 hours).
Disaggregation of daily rainfall data
Characteristics of the meteorological stations of the three test cities
Available data range
Dar Es Salaam
In order to define the extreme values in a smaller time window (10′, 30′, 1 h, 3 h, 6 h, 12 h), a synthetic sequence of rainfall was generated, with statistical properties equal to those of the observed rainfall. In greater detail, the daily rainfalls have been successively disaggregated using two models:
cascade-based disaggregation model
short-time intensity disaggregation method
Assuming that daily rainfalls derive from a marked Poisson process, i.e. rainfall lag and heights are drawn from exponential probability density functions (whose parameters are calculated from observed rainfall series), it is possible to use a simple stochastic model of daily rainfall, that describes the occurrence of rainfall as a compound Poisson process with frequency of events λ. The distribution of times τ between precipitation events is an exponential with mean 1/λ, and exponentially distributed rainfall amounts h with mean γ. This model fits the observed daily data for individual seasons quite well.
Cascade level refers to the time series at a certain resolution. The transition from one cascade level to the higher one, corresponding to a doubling of resolution, is called modulation. A time interval at an arbitrary cascade level (i.e. time scale) is termed a box, which is characterized by an associated precipitation amount (0 if dry, >0 if wet). The break-up of a wet box into two equally sized sub-boxes is denoted branching. In one branching, the total amount is redistributed according to two multiplicative weights, 0 ≤ W1 ≤ 1 and 0 ≤ W2 ≤ 1 (W1 + W2 = 1). The model is a multiplicative random cascade of branching number 2 with exact conservation of mass (microcanonical property as opposed to canonical cascades where the volume is only approximately conserved). The model divides daily precipitation into non overlapping time intervals. If the precipitation in a day is Pd, P1 = PdW1 is the precipitation amount assigned to the first half of the day, and P2 = PdW2 the amount assigned to the second half. Similarly, each half is then branched to a doubled resolution, and so on. The implementation of cascade – based model allows the conversion of daily amount into 12-hourly (1 steps), 6-hourly (2 steps), and 3-hourly (3 steps) values.
where U is a uniform random number in the range 0–1.
To apply this model with reference to the case studies, the software CRA.clima.rain was used (Agricoltural Research Council - CLIMA version 0.3 2009).
With these estimated point (10′-30′-1 h, 3 h, 6 h, 12 h and 24 h) using the procedure described for the Gumbel distribution, it was possible to define the rainfall probability curves for the case studies.
Estimation of the probable maximum precipitation: statistical approach
Probable Maximum Precipitation (PMP) is defined as the greatest depth of precipitation for a given duration meteorologically possible for a design watershed or a given storm area at a particular location at a particular time of year, with no allowance made for long-term climatic trends (World Meteorological Organization 1986).
where: XM, and σn are the highest, mean and standard deviation for a series of n annual maximum rainfall values of a given duration; and σn−1 are the mean and standard deviation, respectively, for this series excluding the highest value from the series; and km is a frequency factor.
To evaluate this factor, initially Hershfield (1961) analysed 2645 stations (90% in the USA) and found an observed maximum value of 15 for km, and so he recommended this value to estimate the PMP by equation (20). Later, Hershfield (1965) found that the value 15 was too high for rainy areas and too low for arid areas. Furthermore, it was too high for rain durations shorter than 24 h, so he constructed an empirical nomograph (World Meteorological Organization 1986) with km varying between 5 and 20 depending on the rainfall duration and the mean . Koutsoyiannis (1999) fitted a generalized extreme value (GEV) distribution to the frequency factors obtained from the 2645 stations used by Hershfield and found that the highest value 15 corresponds to a 60000-year return period, at the low end of the range considered by the NRC (National Research Council 1994). Casas et al. (2010) for the city of Barcelona assigned a frequency factor of 9.4 to this mean value: higher than any of the observed frequency factors, which vary from 2.1 to 6.6. In the present work, the value of km, for different durations, was evaluated using the equation (21) and then also using the WMO nonmograph, as shown in the following paragraph.
Climate change projection
The climate simulation has been performed following the IPCC (Intergovernmental Panel on Climate Change) 20C3M protocol for the 20th Century. The initial conditions were obtained from an equilibrium state reached by integrating the model for 200 years with constant greenhouse gases (GHGs) concentrations corresponding to 1950s conditions. Once the climate of the model was in equilibrium with the prescribed constant radiative forcing (GHG and aerosol concentrations), the simulations have been developed by increasing the GHG and aerosol concentrations in line with observed data.
The projections were performed using the RCP4.5 and the RCP8.5 emission scenarios, developed in the framework of the 5th Coupled Model Intercomparison project (CMIP5, http://cmippcmdi.llnl.gov/cmip5/).
CMCC has performed a set of climate simulations with the coupled global model CMCC-MED (resolution 80 km), over the time period 1950–2050. These simulations have been downscaled to a spatial resolution of about 8 km, performing regional simulations on three limited domains, including the cities of interest, with the regional model COSMO-CLM,
The CLM is the climate version of the COSMO model, which is the operational non-hydrostatic mesoscale weather forecast model developed by the German Weather Service. Successively, the model has been updated by the CLM-Community, in order to develop also climatic applications.
The output of climate models are affected by a systematic error, so the rainfalls projection outputs cannot be used in hydrological models or in decision making without performing some form of bias correction (Sharma et al. 2007; Hansen et al. 2006; Feddersen and Andersen 2005). A realistic presentation of future precipitation from climate models is extremely important for vulnerability and impact assessment (Wood et al. 2004; Schneider et al. 2007). Therefore, modelers use bias correction techniques to obtain more realistic outputs.
The bias correction technique adopted in this work is the “quantile mapping” one: mean and variability of the simulated values are corrected using the anomaly of the modeled cumulative frequency distribution compared to the observed cumulative frequency distribution. The algorithm systematically removes the median differences to zero and adopts the model output variance characteristics equal to the observed one.
A simulated value is the input to the process and is associated with a particular quantile in the simulated distribution. This same percentile is extracted from observed distribution and this quantile in the observed distribution becomes the bias corrected value.
Moreover, rainfall prediction on scales of order of a few kilometers in space and less than a hour in time is a necessary ingredient to issue reliable flood alerts in small area.
Downscaling techniques aim at generating an ensemble of stochastic realizations of the small-scale precipitation fields that have statistical properties similar to those measured for rainfall in a given area and/or synoptic situation. Since a downscaled precipitation field is the product of a stochastic process, it cannot be taken as a faithful deterministic prediction of small scale precipitation, but rather as one realization of a process with the appropriate statistical properties (Rebora et al. 2005).
The method introduced for stochastic rainfall downscaling is the Rainfall Filtered Autoregressive Model (RainFARM) and is based on the nonlinear transformation of a Gaussian random field: it conserves the information present in the rainfall fields at larger scales. By using this method it was possible to obtain, starting from the output of the regional model COSMO-CLM, climate projection at spatial resolution of about 1 km for the three case studies.
Overview of the three case studies
Addis Ababa– Ethiopia
The city is situated in the high plateau of central Ethiopia in the North–south oriented mountain systems neighboring the Rift-Valley.
The city is overlooked by mount Yarer to the east having approximately the same height as mount Entoto and mount Wochecha to the west, which is approximately 3361 m above sea level. The meteorological station, located in the relatively low altitude parts of the city, around Bole International airport, is at 2408 masl, while the elevation in Entoto mountain, north of the city, is more than 2444 masl.
Addis Ababa has a pronounced rainfall peak during the boreal summer (July to September) and exhibits a rainfall minimum during the boreal winter (November to February). The city has a temperate climate due to its high-altitude location in the subtropics. Mean annual precipitation vary between 730 mm, considering historical data, and 980 mm, considering climate projections (Giugni et al. 2012).
Mean value μ, standard deviation σ and coefficient of variation c v for the monthly maximum rainfall, evaluated in the different months, for the city of Addis Ababa
AddIs Ababa - 1964-2050
Dar Es Salaam– Tanzania
Dar Es Salaam is the largest city in Tanzania with an estimated population of 3.4 million inhabitants.
The present day climate of Dar Es Salaam is characterized by a strong seasonal rainfall cycle, with the “long rains” from March to May, and the “short rains” from November to January, and a dry period from June to August. The mean annual rainfall is around 1000 mm.
Mean value μ, standard deviation σ and coefficient of variation c v for the monthly maximum rainfall, evaluated in the different months, for the city of Dar Es Salam
Dar Es Salaam - 1958-2050
Douala experiences a wet, tropical monsoonal climate, with the average total annual rainfall exceeding 3000 mm.
Mean value μ, standard deviation σ and coefficient of variation c v for the monthly maximum rainfall, evaluated in the different months, for the city of Douala
Douala - 1958-2050
Finally, it can be summarized that the three test cities are very differently located in position and altitude and are characterized by different rainfall patterns.
The city of Addis Ababa, with about 800 mm of mean annual rainfall, has a dry season during the months of November and December, while the highest rainfall values were recorded in the month of August. Dar Es Salaam, characterized by values of annual rainfall of about 1000 mm, shows maximum values in April.
At the end, Douala, with an average annual rainfall exceeding 3000 mm, has obviously the highest values of maximum rainfall with a peak in August.
IDF curves, PMP and climate change
The procedure applied for the evaluation of the IDF curves was shown in the previous paragraphs. More in details, for each case study, the available daily rainfall data, for all years of observations, were disaggregated in 7 durations. In particular, using the cascade - based model, the values for the 3, 6 and 12 hours were obtained. In order to evaluate also durations less than three hours (10, 30 minutes and 1 hour), the short time intensity disaggregation model was used.
Once obtained the maximum values for the seven durations considered (10′, 30′ 1, 3, 6, 12 and 24 hours), these values were fitted by the Gumbel distribution and the IDF curves were evaluated, expressed in the form μ(d) = a μ d n .
The KT values for different return periods were evaluated, in particular for 5, 10, 30, 100 and 300 years.
The illustrated procedure was at a later stage applied to the climate simulations over the time period 2010–2050 provided by CMCC. More in details, the IDF curves for each test city were evaluated considering a rainfall series that consist of historical data and climate projections. In particular, the two emission scenarios RCP4.5 and RCP8.5 and the two different spatial resolutions, 8 km and 1 km, were considered, taking into account therefore four different options.
IDF parameters for the three test cities
Historical data (1964–2010)
CMCC 8.5 8 km
CMCC 8.5 1 km
CMCC 4.5 8 km
KT = 5
KT = 10
KT = 30
KT = 50
KT = 100
KT = 300
Dar Es Salaam
Historical data (1958–2010)
CMCC 8.5 8 km
CMCC 8.5 1 km
CMCC 4.5 8 km
KT = 5
KT = 10
KT = 30
KT = 50
KT = 100
KT = 300
Historical data (1976–2010)
CMCC 8.5 8 km
CMCC 8.5 1 km
CMCC 4.5 8 km
KT = 5
KT = 10
KT = 30
KT = 50
KT = 100
KT = 300
The IDF curves show that the two different scenarios, considering the same spatial resolution, don’t display substantial deviations. Instead, a meaningful deviation depends on the different downscaling: in fact, as shown, the 1 km downscaling provided projections that afford to capture extreme events.
In terms of frequency, as shown by the curves of growing factor variation KT, it’s possible to note how the effect of climate change, in the three test cities, involves a rise of frequency of extreme events. In fact, as shown in Figures 12, 13 and 14(b), keeping constant KT, the corresponding return period value is reduced taking in account the climate projections.
Finally, in terms of intensity, the effects of climate change are different for the three cities considered.
For the cities of Dar Es Salaam and Douala, there is a decrease in terms of intensity, in fact the IDF curves that take in account the climate projection are lower than those evaluated with the only historical data series, considering both the downscaling, 8 km and 1 km. Instead, in the case of Addis Ababa, the curve evaluated for the scenario 8.5 referring to a 1 km spatial resolution is very similar to the one evaluated from the historical data.
In order to give useful information and a complete picture of the rainfall pattern of the three test cities, the Probable Maximum Precipitation (PMP) for the three cities was analyzed.
Evaluation of k m and PMP for Addis Ababa
Evaluation of k m and PMP for Dar Es Salaam
Evaluation of k m and PMP for Douala
Evaluation of return period for the PMP values for the duration of 24 hours
Historical data + projections
1.E + 05
2.E + 05
Dar Es Salaam
1.E + 05
1.E + 06
4.E + 04
2.E + 04
This result is very interesting and should be pointed out that the stations used to create the WMO nomograph are located mostly in USA, so in an area characterized by rainfall patterns very different from the african one.
So, it is more advisable to use the Hershfield’s procedure to evaluate the PMP that can be used for the design of hydraulic structures in African cities.
Finally, in order to verify the goodness of the applied procedure, a comparison was made with the IDF curve obtained for the station of Bouake (Côte d’Ivoire) in the work of Soro et al. (2010). Indeed, in this work, the curve was evaluated based on rainfall series of durations ranging from 15 minutes to 4 hours.
IDF parameters for Bouake (Côte d’Ivoire)
Bouake - 1959-2001
KT = 2
KT = 5
KT = 10
KT = 20
KT = 50
KT = 100
The present work shows a methodology for the evaluation of the IDF curves from daily rainfall data. In particular, to obtain durations shorter than 24 hours, two different models of disaggregation were applied to the historical data available for the three cities considered, Addis Ababa, Dar Es Salaam and Douala. The IDF curves were obtained later using the probability distribution of Gumbel.
In order to estimate the contingent influence of climate change on the IDF curves, the illustrated procedure was applied to the rainfall projections over the time period 2010–2050 provided by CMCC, for two different emission scenarios and different spatial resolutions (8 km and 1 km).
The analysis of the IDF curves showed moderate deviations between the two scenarios, RCP 4.5 and RCP 8.5, while substantial variations depend on the different downscaling and, in particular, the 1 km downscaling provided projections that afford to capture extreme events.
Analyzing the growing factor KT, it is possible to note that the effect of climate change in the three test cities involves a rise of frequency of extreme events. The effects of climate change in terms of intensity are different. In fact, while Dar Es Salaam and Douala, there is a decrease in terms of intensity, considering both the downscaling, 8 km and 1 km, for Addis Ababa, the IDF curve evaluated for the scenario 8.5 referring to 1 km spatial resolution, is very similar to the one calculated by the historical data.
In conclusion, the results of the climate model projections suggest that future rainfall intensity could be subjected to decreases or increases depending on the different area considered, but with an increase in terms of frequency.
Moreover, two different approaches were applied satisfactorily to obtain the PMP in the three test cities for several durations ranging from 10 min to 24 h, using not only historical data but also climate projections (scenario RCP 8.5), In particular, has been pointed out that the PMPs evaluated using the WMO nomograph returns values of return period too high, so the Hershfield’s procedure is the more advisable in order to evaluate the PMP that can be used for design of hydraulic structures in African cities.
This work was supported by the European Commission’s seventh framework program Climate Change and Urban Vulnerability in Africa (CLUVA), FP7-ENV-2010, Grant No. 265137. This support is gratefully acknowledged.
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