Introduction

Design storm hyetographs are important inputs in hydrological models. Even with the availability of Intensity-Duration-Frequency (IDF) curves, the assumed temporal distribution of the design storm remains crucial in hydrological models, especially those relying on Unit Hydrograph methods. According to Veneziano and Villani (1999), most methods used in developing design storms can be classified into four classes: (1) assuming a certain geometrical shape anchored to a single point of the IDF curve, (2) using the entire IDF information via the Alternating Block Method (ABM) (Chow et al. 1988), (3) obtaining standardized profiles directly from rainfall records, and (4) undertaking simulations based on stochastic models (Cunderlik and Simonovic 2004).

Among the methods classified under the third above-mentioned class are the well-acknowledged procedures of Huff (1967), the Soil Conservation Service (SCS, now the Natural Resources Conservation Service (NRCS)) derivations of their four types of storm profiles (Kent 1973) and the procedure initiated in the Flood Studies Report (NERC 1975) to derive the UK 50% (UK50) storm profiles.

Huff (1967) analyzed two hundred sixty-one rainfall storms collected from 49 rainfall gauges that covered the state of Illinois, USA, dividing the storms into four quartiles—based on the time of occurrence of the peak rainfall intensity—and provided the 25th, 50th, 75th, and 90th percentiles dimensionless hyetograph curves.

The Soil Conservation Service (SCS) (Kent 1973) developed four types (termed I, II, III, and IA) of dimensionless hyetograph curves covering many regions of the USA. Kent (1973) stated that the cumulative curve, which is the basis for type II distribution for example, was “established by (1) plotting a ratio of rainfall amount for any duration to the 24-hour amount against duration for a number of locations and (2) selecting a curve of best fit.” Average intensity-duration values were used to develop the above-mentioned curves and were arranged so that the greatest 30-min depth occurs near the middle of the 24-h period, the second largest in the next 30 min, and the third largest in the preceding 30 min. The procedure used to derive these symmetrical nested storm profiles is generally termed the Alternating Block Method (ABM) (Chow et al. 1988). Using these nested profiles, in stormwater networks design for example, avoids multiple runs to determine critical storm duration (as all durations are nested within one single profile) but tends to overestimate intensities, particularly for frequent events (Frederick et al. 1977). Yet, methods based on alternating rainfall blocks are common in codes of practice and are included, for example, in most drainage manuals of the USA (such as that of Texas (TxDOT 2016) to give an example of an arid state), in the HEC-HMS Technical Reference Manual of the Hydrologic Engineering Center (HEC) (Feldman 2000), in relatively recent handbooks and textbooks such as Chin et al. (2013), Wurbs and James (2002) and McCuen (2005).

As for the UK50 storm profiles, a family of standard, symmetrical profiles was produced by Wallingford Institute of Hydrology, in the framework of the Flood Studies Report (NERC, 1975), with maximum rainfall intensity at the center of the storm and variable in amplitude. The FSR procedure was later updated by the Flood Estimation Handbook (CEH 1999); however, the UK50 storm profiles were maintained. The UK50 storm profiles were derived for different storm durations using the same number of time increments within the storm duration instead of fixing the same time step across durations. A “peakedness” factor of the profiles is defined as the ratio of maximum to mean intensity and the percentile peakedness is the percentage of storms that are equally or less peaked. The profile shape was not found to vary significantly with storm duration, return period, or geographical region. However, on average, summer storms were found to be more peaked than winter ones, with a peakedness factor for the UK50 summer storm profile of 3.92 (Butler and Davies 2004).

Design storm profile research is still on vogue, despite the number of decades that passed since the above-mentioned pioneering studies (Al-Saadi 2002; Thompson et al. 2002; Asquith 2003; Reilly and Piechota 2005; Ogunlela et al. 2012; to name a few). Fewer studies focused on the Arab Gulf regions: Awadallah and Younan (2012) derived the design storms from IDF curves. Al-Rawas and Valeo (2009) used the actual storm recordings; however, they confused the processed form of data with that of the original storms and thus obtained unrealistic and also unsafe design storm profiles.

The objective of this research is thus to develop dimensionless design storm hyetographs from actual storms, for hyper arid and arid regions, based on measured data from seventeen rainfall stations distributed over Oman. The obtained results are compared with the SCS type II and the UK50 summer profile. The SCS type II storm profile is in fact stipulated to be used in Egypt (MWRI 2011) and Saudi Arabia (Riyadh Municipality 2012; MOC 1989) codes of practice, while the UK50 summer storm profile is used in Qatar (PWA 2005), Kuwait (Hyder Consulting 2002), and Dubai (MWH 2014) codes of practice, with their corresponding American-or British-derived values without comparing them to values derived from the actual rainfall records in the above-mentioned countries. The only code of practice proposing a different storm profile is the Omani Highway Design Manual (Ministry of Transport and Communications of Oman 2010) which stipulates the use of Wheater and Bell (1983) storm profile.

Available rainfall data

Two hundred thirty-six rainfall storms were collected from seventeen rainfall gauges in Sultanate of Oman. The rainfall records begin in different years (i.e., from 1952 to 2007) and end in 2007. The available data of storm profiles only begin in 1993. The number of storms for each rainfall station ranged from one storm recorded in Amrat and Wadi Al Khawd1 stations to sixty-four storms recorded in Tahwah 3 station. Fig. 1 shows a map of the locations of the rainfall gauges over the study area, while Table 1 shows the metadata collected for each station including the station name, station ID, years of records, coordinates, and data available for the study with respect to number of recorded storms and years with continuous storm profile recordings.

Fig. 1
figure 1

Rainfall gauges locations over the study area

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Table 1 Metadata of the used rainfall gauges
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Methodology and results

As described in the literature review, possible ways to derive design storm profiles are based either on the individual storms or on the resulting IDF values. To derive the design storm profiles based on individual storms, one has to identify prevailing storm patterns. This could be achieved by classifying the storms based on their storm durations and checking if each group shows specific characteristics (i.e., randomness or, on the contrary, peak of storms occurring in a certain quartile, specific ratios of peak intensities to average intensities, etc.). If no such patterns are depicted, design storm profiles could be developed based on design considerations rather than meteorological ones; i.e., storm profiles could be developed in such a way to produce the highest peak discharges, taking into consideration the method used for rainfall-runoff transformation.

The two hundred thirty-six storms were thus classified into four categories according to their durations. Categories 1, 2, 3, and 4 include storms that have total durations ranging from 5 min to 1 h, 1 to 6 h, 6 to 12 h, and 12 to 24 h, respectively. The dimensionless cumulative hyetograph is a plot between the dimensionless cumulative duration (i.e., percentage of the cumulative duration to the total storm duration), on the x-axis, and the dimensionless cumulative rainfall depth (i.e., percentage of the cumulative rainfall depth to the total rainfall depth), on the y-axis. Fig. 2a–d shows the cumulative dimensionless hyetographs for the four categories. From the figure, it is clear that storms, in all four groups, have no definitive pattern with peak intensities occurring in the beginning, middle, and end of the storm. This variation is the main reason behind searching for a design (critical) storm that could produce higher runoff discharges, such as symmetrical, nested, peak-centered profiles, derived using ABM.

Fig. 2
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Cumulative dimensionless hyetographs for each storm category. a Storm durations from 5 min to 1 h. b Storm durations from 1 to 6 h. c Storm durations from 6 to 12 h. d Storm durations from 12 to 24 h

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The ABM consists of calculating the rainfall depth for different storm durations, with a user-defined analysis time step (usually in the range of 5 to 10 min) and arranging the incremental rainfall depth blocks alternatively at each side of the center of the storm hyetograph. This type of ABM derived from actual storms is hereafter termed ABM_Storms. Rainfall depths for different time increments are obtained from the individual storms. To allow averaging storms with different durations and depths, dimensionless hyetographs are first derived by dividing each depth by the total storm depth and each duration by the total storm duration. The averages of the dimensionless profiles are computed at each time increment to obtain the design storm hyetographs. Fig. 3 presents the obtained average hyetograph for each storm duration category. It is clear from this figure and from Table 2 that the ratio of the peak rainfall depth at 5-min duration to the rainfall depth corresponding to the total storm duration decreases with the storm duration (e.g., from a ratio of 0.368 for storms with durations ranging from 5 min to 1 h to a ratio of 0.077 for storms with durations ranging from 12 to 24 h).

Fig. 3
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Dimensionless design hyetographs developed by ABM from the individual storms and ABM from the IDF

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Table 2 Ratios of peak central depth to total storm depth of the dimensionless design hyetographs developed by ABM from the individual storms and ABM from the IDF
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Another method to derive design storm profiles is to apply the ABM on the IDF values. This method is hereafter termed ABM_IDF. First, to derive the intensity-duration, the maximum values of the 5-min incremental rainfall depths are obtained for each storm. For all rainfall gauges, the maximum value of the 5-min depths for each year is calculated. The previous procedure is repeated for the 10, 15, 30, 60, 120, 180, 360, 720, and 1440 min rainfall durations. Frequency analyses are undertaken on these series of annual maxima using the Method-of-Moments (Pearson 1936) for parameter estimation. Four common statistical distributions are tested to fit the rainfall data: Lognormal, Gumbel, Pearson Type III, and 2-parameter Gamma statistical distributions. The distribution that best fits the data is selected based on the ordinary moment diagram, the log-log plots and the mean excess function (El Adlouni et al., 2008) and the Akaike Information Criterion (Akaike 1974) and Bayesian Information Criterion (Schwarz 1978) using HYFRAN (HYdrological FRequency ANalyses) (INRS-ETE 2008) software. Two-parameter Gamma distribution was found to give the best fit on all durations based on the previously mentioned selection criteria. The 5-, 10-, 25-, 50-, and 100-year rainfall depths are calculated using the 2-parameter Gamma for each duration, applying the Method-of-Moments for the estimation of fitting distribution parameters. To derive the design storm profiles, the same ABM is used but this time, on the IDF results, using time increments of multiples of 5 min. The storm profile derived using ABM_IDF procedure for the 100-year return period is also shown in Fig. 3. From the zoomed graph of this figure, the ABM_IDF 24-h storm profile is in between the 12- and 24-h ABM_Storms storm profiles.

Table 2 shows also the ratios of peak rainfall depth to total depth of the storm profiles based on ABM_IDF. The numerical values of these ratios either decrease (as for the first category) or increase (as for the last three categories) regularly as the return period decreases. In fact, the mean of the annual maxima of rainfall depths increases, as expected, with increased storm duration; however, the coefficient of variation (CoV) (ratio of the standard deviation to the mean of the annual maxima) tends to decrease with the increase of storm duration. The values of CoV range from 0.7 to 0.75 for 5 min to 1 h duration, while they fluctuate around 1.1 for durations of 6 to 24 h. The shape parameters of the parent (Gamma) distributions fitted for the annual maxima of different durations are thus not duration-invariant which affects the ratios for all four categories reported in Table 2. This situation may appear in practice, due to the fact that the sample estimator of the shape parameter of the parent distribution—thus the IDF relationship—is sensitive to the sampling errors, which increases as the sample size decreases. The available sample sizes of annual maxima used in deriving the Gamma-based IDF curves for each station are equivalent to the number of complete years with continuous storm recordings available for each station (Table 1). Moreover, and since our approach relies on selecting the annual maxima across all stations, the sample size on which the frequency analyses are undertaken is 17, equal to the number of complete years with continuous storm recordings available for of the GK308083AF station which has the maximum number of years available. Still, 17 years is subject to high uncertainties.

The procedures for deriving ABM_Storms and ABM_IDF are very different in essence, at least because the ABM_IDF procedure is linked to return periods, while as ABM_Storms procedure relies on averaging across reshuffled storm profiles. In many practical cases, only IDF relationships are available in codes of practice and the practitioner could use an ABM procedure, on the IDF values, to derive storm profiles. The question that arises is whether the generated ABM_IDF profiles are safe to use when compared to other storm profiles derived from actual (or even reshuffled) storm patterns? Table 2 aims to answer this question. The resulting ratios of peak rainfall depth to total depth of the storm profiles, comparing ABM_IDF to ABM_Storms, were found to be quite similar from a practical design point of view (in the sense that they produce similar peak discharges). The only exception is for the 5 min–1 h storm profile, where the ABM_Storms profile produces slightly higher peak discharges. Fig. 4d shows a comparison of the entire ABM_IDF and ABM_Storms profiles. It shows in general that the central slope (peak) of the ABM_IDF is larger (steeper rise in the cumulative profile) but the profile tends to have a milder transition through time increments towards the central time. On the contrary, the ABM_Storms profile shows a smaller central peak but the transition is less smooth. However, as previously noted, both storm profiles are quasi-equivalent, as far as the generated peak discharges are concerned and the ABM_IDF storm profile is considered safe to use in stormwater networks design without the need to undertake individual storm analyses.

Fig. 4
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Comparison between storm profiles for all storm durations

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Comparison with standard storm profiles used in Arabian Gulf countries codes of practice

The developed dimensionless rainfall profiles using ABM_Storms or ABM_IDF are compared to the standard SCS type II and the UK50 summer storm profiles (Fig. 4a–d). For all storm durations, the developed profiles are more critical (steeper rises) than both the SCS type II and the UK50 summer storm profiles, indicating the inadequacy of the use of these storm profiles in arid regions. On the contrary, when compared to the Wheater and Bell (1983) storm profile (Fig. 4d), the developed storm profiles were found less critical.

Moreover, to further compare with the UK50 summer storm profile, the ratios between the peak intensity and the average intensity for all storms were obtained and averaged for each of the previously mentioned four storm duration categories. The average ratios are not constant across storm durations and the four obtained ratios are more than double the value 3.92 of the UK50 storm profile, indicating the large discrepancy between the characteristics of the UK50 storm profile (derived for the UK) and those of the studied Oman storms.

Conclusions and recommendations

Analyses of the temporal storm profiles for Oman region are carried out. Two hundred thirty-six rainfall storms are collected and classified into four categories according to their total durations. Design storm hyetographs are derived from raw rainfall records for all four categories using the Alternating Block Method (ABM) and were also computed by ABM applied on the calculated IDF values.

The recommendations from the current research are summarized in the following points:

  • No storm patterns are noticeable from the analysis of storm profiles. These profiles vary in their durations, shapes, and times of peak occurrences, confirming the storm random nature. Consequently, design storm profiles should be developed based on design considerations rather than meteorological ones, aiming to produce safe-generated peak discharges, taking into consideration the method used for rainfall-runoff transformation.

  • If only IDF relationships are available, the current research recommends that the suitable procedure to derive design storm profiles is via the ABM. In fact, the storm profiles obtained via ABM_IDF procedure are similar to those obtained via ABM_Storms procedure. In stormwater network design for example, the advantage of using ABM_IDF procedure, which produces a nested design profile, is that it avoids multiple runs to determine the critical storm duration for each element of the stormwater network, as all durations are nested within one single-storm profile.

  • The four storm profiles derived via the ABM_Storms method are more representative of the actual storms. However, in any drainage design, all four storm profiles have to be tested on the proposed drainage elements, as it is not known a priori which one will be critical for a certain element, especially if the proposed design is a combination of storage and conveyance elements.

  • ABM_Storms and ABM_IDF design storm profiles are compared and it is found that the ABM_IDF storm profiles are equivalent to the four ABM_Storms profiles. Thus, on the contrary to results from previous publications, which when studying humid climates showed that ABM_IDF storm profiles tend to overestimate intensities, the ABM_IDF design storms in Oman (as an example of an arid region) are not in general significantly more conservative than ABM_Storms profiles.

  • The developed ABM_Storms profiles are more conservative (i.e., resulting in higher peak discharges) when compared to the SCS type II and the UK50 summer profiles, despite the wide utilization of these two profiles in many codes of practice in arid and hyper arid regions. Thus, the use of the SCS type II and the UK50 summer profiles is unsafe and may lead to underestimated designed stormwater network elements, especially in catch basins spacing and beginning of networks and similar drainage elements which are designed considering the peaked portion of the storm profile.

  • Finally, it is recommended to extend the study using data from other arid and hyper arid countries to generalize the obtained results.