~R - The prediction of storm rainfall in East by D. Fiddes, J,,A. Forsgate and A. O. Grigg TRANSPORT and ROAD , RESEARCH LABORATORY Department of the Environment TRRL LABORATORY REPORT 623 THE PREDICTION OF STORM RAINFALL IN EAST AFRICA -- x by D. Fiddes, B.SC., M.SC., C.Eng. M. I. C. E., DIC., J. A. Forsgate, B.SC., and A. O. Grigg Any views expressed in this Report are not necessarily those of the Department of the Environment Environment Division Transport Systems Department Transport and Road Research Laboratory Crowthorne, Berkshire 1974 CONTENTS Abstract 1. Introduction 2. Two year, 24 hour point rainfall map for East Africa 3. Twenty-four hour storm rainfall for any return frequency 3.1 Fitting of boundaries between zones 4. Depth – Duration – Frequency Relationships 4.1 Data avaflable 4.2 Model testing 4.2.1 4.2.2 4.3 Further calibration using hourly and daily data 4.4 General depth – duration model for East Africa 4.5 Conclusions 5. Area reduction factors 5.1 Area reduction factors for East African raingauge networks 5.1.1 The Kakira network 5.1.2 The Nairobi network 5.1.3. Sambret network 5.1.4 Atumatak network 5.2 General equation for a~ed reduction factors 5.3 Comparison with published ared reduction factor 6. Conclusions 7. Acknowledgements 8. References 9. Appendix 1: Design curves and worked examples Page 1 1 1 3 5 6 7 7 7 7 9 9 12 13 13 13 15 18 18 20 20 21 22 22 23 @ CROWN COPYRIGHT 1974 Extracts may be quoted except for commercial pu~oses, provided the source is acknowledged THE PREDICTION OF STORM RAINFALL IN EAST AFRICA ABSTRACT A simple method for predicting the characteristics of storms for the design of drainage structures in East Africa is described. The variation of 2 year daily point rainfall, and the 10:2 year ratio for daily rainfall, over East Africa are given in map form. Using these, daily point rainfall for any return frequency can be calculated. To arrive at the design storm the daily point rainfall is adjusted using a generalised depth-duration equation and a graphical representation of the variation of mean rainfall with area. 1. INTRODUCTION Before the hydraulic and structural designs for a road bridge or culvert can be started, an estimate must be made of the peak flo~v that the structure must safely pass. If flow measurements have been made for a number of years on the river, or on a similar but adjacent river, this involves only a statistical analysis of recorded peaks to arrive at a design flood of an a~lpropriate return frequency. In East Africa, particularly on the smaller rivers, such data ~arel)’ exist and use must be made of the much more common rainfall measurements published by the East African M(;teorological Department. From rainfall records a design rainstorm is constructed and routed through a suital)le catchment model to give the design flood. Nthough an impressive amount of rainfall data exists, it has not been published in a form that can be readily used by highway engineers for bridge and culvert design. The purpose of this report is to extract relevant storm data fronl the published records and, combining these with certain unpublished data, to produce a simple method for pre ,?aring design storms for flood estimation. The method involves first estimating the 2 year, 24 hour point rainfall from a storm rainfall map of East Africa. Three adjustments are then made: (a) Using a generalised relationship between rainfall of any return frequency and the two year values the 24 ~our point rainfall for the design return frequency is calculated. (b) A depth-duration rainfall equation is used to calculate the point rainfall for the appropriate time of concentration of the catchment. (c) An areal reduction is read off a graph to convert this to the mean rainfall depth which is the required rair.fall input for the catchment model. 2, TWO YEAR, 24 HOUR POINT RAINFALL MAP FOR EAST AFRICA There are abour 3,000 rainfall stations in East Africa which submit daily records to the Meteorological Department for subsequent publication. The distribution of these is, however, far from uniform and many have been installed ody in recent }ears. The advice often given to engineers requiring a design storm is to select a suitable rainfall station, on, or close to, the carchrnent and to analyse the records for this station. For much of East Africa a station on or close to the catchmellt cannot be found or, if present, it has often been recording for such a short period of years that it can give only unreliable estimates of flood producing rainfall. It was therefore decided to analyse dl available publiiled records and use these to produce maps of storm rainfall from which vrdues for individud catchments could be interpolated. Using records in published form this would have been a mammoth task, but fortunately early in the investigation the East African Meteorological Department transferred all their reliable daily rainfall records for the years 1957-68 and selected stations for 1926-56 to magnetic tape and gave the Laboratory permission to make a copy of the tapes. From the first tape 867 stations which had at least 10 complete data years and from the combined tapes 99 stations with about 40 complete data years were selected. The first set of data was used to map the variation of storm rainfall over East Africa and the second to establish a means of adjusting values read off the map for alternative frequencies. For each station selected for the first set of data the highest 24 hour fall during each calendar year was read off. These were ranked and given ieturn frequencies using the expression: T=— ntl m where T is the return frequency in years n is the number of years of record and m is the ranking order, m = 1 for the largest value, m = n for the smallest. If the rainfall depth is plotted against the assumed return frequency a non-linear relationship becomes apparent. Many methods are available to linearise this relationship which, so long as extrapolation beyond the period of record is not attempted, give very similar results. The most commonly accepted method is the Gumbel method (1) which is of the form Y=a+cloglog Treevident. For example, in the arid areas and the coastal strip, slopes (c) tended to be higher than in Uganda. The gauges were therefore split up into regional groupings. Earlier analysis of data from Kenya and Uganda sugg~sted four regional groups; the coastal strip, the arid area of north and east Kenya, the central Hi~ands and w(;st of the Rift Valley. These regions were therefore used. Unear regressions of Gumbel slope on the 2 year value (y2) were made for each region. In two zones 3 TABLE 1 95 per cent Confidence half band width For Running means of Annual Maximum Daily Rainfall 95 per cent Confidence Half Band Widths (mm) Gauge No. Period @rs) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 913604 2.31 2.03 1.75 1.30 1.10 1.02 1.01 1.14 1.10 1.09 0.96 0.76 0.67 0.58 0.49 0.53 J13606 3.50 3.15 3.12 2.87 2.52 2.20 2.07 2.04 2.06 1.93 1.63 1.43 1.47 1.35 1.22 1.09 913618 4.80 4.55 4.28 4.10 3.82 3.69 3.59 3.57 3.53 3.41 3.38 3.31 3.23 3.15 2.99 2.78 913620 5.72 5.47 5.36 5.13 4.88 4.65 4.32 4.04 3.77 3.41 3.04 2.64 2.24 1.81 1.44 1.31 913624 3.36 3.08 2.93 2.68 2.50 2.25 2.16 2.13 2.12 2.06 2.06 2.00 1.92 1.79 1.68 1.51 913628 3.32 3.11 2.98 2.61 2.30 2.06 2.07 2.20 2.22 2.22 2.16 2.13 2.09 2.00 1.83 1.67 913629 6.15 5.68 5.20 4.64 3.99 3.46 2.99 2.56 2.29 1.96 1.67 1.45 1.42 1.65 1.87 2.14 913630 6.66 2.78 2.67 2.57 2’.49 2.38 2.30 2.30 2.20 2.11 2.02 1.97 1.87 1.76 1.68 1.57 Average 4.48 3.73 3.54 3.24 2.95 2.72 2.56 2.50 2.41 2.27 2.11 1.96 1.86 1.76 1.65 1.57 significant correlations were obtained. In the other two, the coastal and the arid zones, the correlations were not significant but they contained only 8 and 5 gauges respectively and in the case of the coastal zone all the Y2 values were very simdar. The regression equations for the former zones were West of Rift Vatiey Slope = 1.841 t 0.249 y2 Central Highlands Slope = 3.051 t 0.358 y2 For each of the two regression lines there was found to be no significant difference between the slope of the line as calculated and the slope of a line through the origin (o, O) and (Y2, c). It was therefore concluded that the slope of the Gumbel regression line could be replaced by a simple ratio of the values of 2 points on the regression, the 10 year and 2 year ratio (y 10 :y2) being most appropriate. If the Gllmbel equation is yn = a t c x n ylo – y~ = C(2.252 – 0.367) Ylo —— = 1.885C + ~ Y2 Y2 For eack zone the average value for slope (c) and Y2 were calculated and the appropriate Y10:Y2 ratio derived. These are shown below in Table 2. TABLE 2 Zone Average slope Average 2 year storm ylo/y2 - (c) (Y2) West of Rft Valley 17.39e 62.08 1.53 Central ~ighlands 20.77 66.52 1.59 Arid 35.30 ‘65.17 2.01 Coastal :itrip 38.02 94.51 1.76 Because of the scarcity of gauges on the 40 year tape it was necessary to use the records from the 10 year tape to e:,tablish (a) the boundaries between zones (b) th~ best value for the 10:2 year ratio particularly in the coastal and arid zones where records are very scarce, and for most of Tanzania for which no data on the 40 year tape were available. With only 10 :/ears of record the estimates of the 10 year storms, are bound to be inaccurate, but if the scatter is rand jm, and sufficient records are available, sufficiently accurate estimates for the appropriate value for a zone are possible. To check if using the short period of records would introduce any bias a comparison was made of t.le 10:2 year ratio for the 76 stations common to both tapes. The results are shown in Table 3. With thf: possible exception of the arid zone, the results of which are very variable, it can be seen that no bias is likely to be introduced by using the 10 year records and a much larger number of gauges will make defining boun iaries between zones easier. 3.1 Fitting of boundaries between zones The gau ~e numbering adopted by the East African Meteorolo@cal Department is accordingto thedegree square in which the gauge lies. Gauges were therefore easily grouped, and for each degree square the mean and standard deviation for the 10:2 year ratios were calculated. The means for adjacent squares were then compared to see if the differences were significant. In this way the rough boundary to the zones was established. To get a more accurate plot the gauges adjacent to the boundary were located on large scale maps and the boundary 5 TABLE 3 Comparison of 10:2 year ratios from 40 and 10 year tapes No. of stations Mean 10:2 year ratio 95 per cent confidence half band width West zone 40 year 34 1.509 0.042 10 year 34 1.516 0.058 Central Hi@ands 40 year 29 1.597 0.046 10 year 29 1.585 0.057 hid zone 40 year 5 2.006 0.264 10 year 5 1.864 0.317 Coastal strip 40 year 8 1.728 0.098 10 year 8 1.651 0.178 fixed by inspection. Once the line had been fixed it was superimposed on mean annual rainfall and topographical maps to see if there was any physical explanation for zonal differences. The results are shown in Table 4 and Fig. 4. In order to obtain the appropriate storm rainfall value for any given return frequency, read off from Fig. 5 the N:2 year ratio corresponding to the known 10:2 year ratio and multiply by the 2 year daily rainfall, read from Fig. 1. 4. DEPTH – DURATION – FREQUENCY RELATIONSHIPS For most catchments, the rain falling in periods of less than one day are required. These can be estimated using daily values and a suitable depth – duration relationship. Two models were tested (a) I=; where I = intensity in mm/hr T = duration in hours a, b, and n are constants. These are discussed in turn below. 6 TABLE 4 10:2 year ratios for daily rainfall Zone No. of stations 95 per cent confidence hmits for the mean Ratio Remarks Central Hi@and 271 1.60 ~ 0.03 &stern and Southern boundary foflows 1000 m’ countour. Western boundary follows watershed between bke Victoria and RiftValley Drainage Basins. Kenya Arid 29 1.89 t 0.10 Kenya Coast 43 1.68 * 0.06 Bounded by 600 mm isohyet Tanzania south Coilst 11 1.74 t 0.12 Western boundary M defined. Tanzania north Coilst 67 1.64 ~ 0.04 [nland Tanzania ar.d Uganda 419 1.49 t 0.02 Semi Arid Uganda 13 1.64 t 0.10 Western boundary follows 1000 mm isohyet. .Uwanza 16 1.64 t 0.13 No obvious physical explanation. Possibly local bke effect. 4.1 Data available Two sets of c!ata were used. For 23 stations intensities for several durations from 15 minutes upwards were used to select the best model. For a further 18 stations only 1 hour and 24 hour values were available. These were used to assist model calibration. Details are given in Table 5. 4.2 Model testing 4.2.1 I = S Tn This is a mod~l that has been suggested by Mc Callum (3) as being appropriate for East Africa to model intensities from 15 minutes to 24 hours. Mc Callum used data from 6 stations in Kenya and Tanzania. The relationship was fitied to the highest intensity measured at each station. The period of record varied between 8 and 25 years. Beca~lse of the uncertainty about an appropriate return frequency to apply to Mc CaUum’s data direct comparison Iletween his results and those given below is difficult. The Group I data, for which durations of from 15 m – 24 hours were available, were fitted to this model for a 2 year return ]’requency and the results are given in Table 6. 4.2.2 I = ~- (T+b)n This model wdl be seen to be a general equation which reduces to the much quoted I = & if the 7 TABLE 5 Detafisof rainfa~data used Station Range of duration Source of Data ,, GROUP I BUSI,A 15m–24hr ~SESE 15m– 2hr } Supplied by Water Development Dept. WADELAI , 15m– 2hr Uganda “MUGUGA 15m–24hr ATUMATAK 15m–24hr } Extracted from records of East African SAMBRET ~ 15m–24hr Agriculture and Forestry Research SAOSA 15m–24hr Organisation ,, EQUATOR 15m– lhr KABATE 15’rn – 6 hr MSUMU 15m– 6hr MTALE 15m– 3hr ,, MOMBASA 15m– 6hr NANYUW 15m– lhr VOI 15m– lhr DAR ES SALAAM 15m– 6hr DODOMA 15m– 3hr > From Taylor& Lawes (2) UGOMA 15m– 3hr MBEYA 15m– 3hr TABOCA 15m– 6hr ZANZIBAR 15m– 6hr ENTEBBE - 15m– 6hr GULU 15m– 3hr KAMPALA 15m– 3hr GROUP II J ~TALE 7 ., MOLO L~U LODWAR GAWSSA ,. NAKURU ~SUMU ,:~ MOMBASA NANYUH 1 hr and 24 hr Extracted from records of East African > VOI Met. Dept. JINJA MBARAU TORORO KAMPALA GULU ENTEBBE FORT PORTAL J For each duration the largest rainfall value in each calendar year was ranked to form an annual series for the station. Estimates of rainfall depth corresponding to recurrence intervals of 2, 5 and 10 years were then made using the Gumbel method(1). The period of record for the group 1 stations was between 8-35 years, and the group 2 stations were all of 20 years. 8 TABLE 6 ., .. Two year intensity – duration relationships (I = fin model) 1 Station Intensity – Duration Relationship Correlation coefficient BUSIA I = 49.12T ; ‘.83 – 0.994 MUGUCA 1 = 28.09T – 0.69 – 0.994 ~ ATUMATAK I = 32.34T -’86 – 0.994 SM:BR5T I = 37.73T– ‘.83 – 0.997 SAOSA I = 37.96T– ‘.81 – 0.997 ,, index n = 1. Often the simpler form is used with different values for the constants for different ranges of duration. ~e~:e, as‘in East Africa very little data other than dafly totals exist, a relationship containing a. discontinuity is difficult to fit and the general expression, even if slightly more difficult to apply in practice, is . to be preferre[[. .,. The Group I data were “fitted to the model for a number of alternative values of the constant ‘b’ between 0.2 and 1:0 hours. The optimum value varied between stations but as no regional pattern to this variation could be found it was assumed to be due to random errors in the data and an average value of b = 0.33 hrs was selected for further modelling, The results of fitting this model to the 5 stations, for which complete data were available, were very much superior to the previous model. It was therefore adopted and used with d group I stations. The ~erived relationships with b = 0.33 hrs are given in Table 7. 4.3 Further ,calibration.using hourly and daily data Hourly”~ nd daily estimates of rainfall with 2,5 and 10 year recurrence intervals were available for 18 stations covering afl the climatic zones of Kenya and Uganda. These were fitted to the intensity – duration model with thl; constant being equal to 0.33. The results are shown in Table 8. 4.4 General depth – duration model for East Africa Tables 7 and 8 show that a constant value for “n” cannot apply to the whole of East Africa. The area was therefore once again split up into zones. Four zones were considered:– (a) Cc astal strip (b) Arid (c) Central Hi@ands (d) Inland (all other zones on Fig. 4) It wfll b~ seen that for most of the stations in the Inland and Arid zones the value of ‘n’ is approximately 1.0 but that 10wer values are typical for the Coastal and Central Highland areas. For the inland zone, only Entebbe gave a value for ‘n’ well under 1.0. A possible explanation for this is that the perio(l of record included one very large storm which it has been estimated approached the probable maximum pre(:ipitation (4). This would result in an under estimation of the time value of ‘n’. There is therefore no firm evidence for excluding Entebbe from the general inland model. 9 TABLE 7 Values of constants in intensity – duration relationships for Group I Stations Station BUSIA MUGU~A ATUMATAK SAMBRET SAOSA KASESE WADELAI EQUATOR KABETE MSUMU UTALE MOMBASA NANYUW VOI DAR ESSALAAM DODOMA KIGOMA MBEYA TABORA ZANZIBAR ENTEBBE KAMPALA GULU 2 year 5 year 10 year a n a n a n 74.62 1.00 94.88 0.97 105.19 0.96 40.18 0.83 54.86 0.84 63.75 0.85 51.06 1.01 61.33 0.99 68.74 0.97 56.61 1.00 70.34 0.97 77.98 0.96 56.55 0.98 69.35 0.92 81.39 0.90 54.95 1.09 66.65 1.04 73.81 1.01 57.87 0.98 72.24 0.82 81.69 0.75 40.03 0.99 48.53 1.02 54.90 1.03 42.17 0.78 50.24 0.83 59.64 0.84 72.15 1.01 86.39 0.99 96.36 0.98 49.90 0.99 62.90 1.01 70.79 1.01 49.49 0.78 65.88 0.77 74.48 0.83 44.34 0.92 57.81 ‘ 0.81 65.09 0.80 53.39 0.84 79.04 0.57 95.34 0.48 57.83 0.91 68.83 0.86 77.41 0.84 55.35 0.95 71.28 0.91 82.43 0.88 58.51 0.97 74.79 0.88 83.89 0.86 42.20 0.97 55.62 0.97 64.16 0.98 55.20 1.00 70.84 1.02 82.52 1.03 59.83 0.81 76.06 0.72 86.29 0.69’ 63.16 0.88 82.70 0.89 92.85 0.88 58.52 0.97 73.24 0.95 83.36 0.94 70.06 1.01 87.96 0.98 100.83 0.96 2 ,yr correlation coefficient – 0.9998 – 0.9996 – 0.9999 – 0.9996 – 0.9997 2 yr correlation coefficient is shown only for 5 stations for comparison with TABLE 6 10 TABLE 8 Values of constants in intensity – duration relationships”for Group II Stations Model I = a (Tt+)n Station KITALE MOLO LAMU LODWA:l GARISS.I NARKUllU MSUMU MOMBA;SA NANYUlfl VOI JINJA FORT PORTAL MBARAIW TOROR() ENTEBB E KAMPAI,A GULU NAIROB[ 2 year a 51.50 34.38 47.04 47.35 55.33 46.06 70.49 46.14 43.13 53.76 65.43 49.24 51.27 71.97 76.04 60.80 60.84 50.07 n 0.97 0.89 0.77 1.02 1.00 0.97 0.97 0.84 1.00 0.94 1.00 0.98 0.96 1.01 0.96 1.00 0.97 0.86 5 year a 65.41 5“1.11 61.08 58.36 81.42 60.63 84.95 57.85 60.96 83.36 73.28 65.26 69.94 89.00 97.09 76.59 84.12 62.26 n 0.94 0.94 0.70 0.97 0.99 0.99 0.97 0.80 1.05 0.96 0.96 0.99 0.95 0.98 0.88 1.01 1.00 0.88 10year a 74.52 62.38 70.84 65.89 99.19 71.21 95.26 65.02 73.20 103.10 78.80 76.30 81.99 99.80 112.12 87.52 97.75 70.79 n 0.93 0.96 0.67 0.95 0.98 0.99 0.96 0.79 1.07 0.97 0.94 0.99 0.95 0.97 0.86 1.01 1.01 0.87 — The ‘n’ values for the Central Highlands are very variable. The western stations (Equator and Nakuru) give very simflar restdts to Inland stations whereas stations around Nairobi give much lower values. The explanation for”this must be differences in synoptic weather processes. This can be checked by looking at the diurnal variations in rai~fdl occurrence which have been studied by Thompson (5). The conventional “continental” rainfall model gives convective thunderstorms in late afternoon. Much of the inland zone does have a rainfall maximum at ths time as does the northern and western parts of the Central Hi~ands zone, but in the Nairobi area hei~vy rain occurs in the evening, spreading through to the early morning in the “short rains” (November). Thompson claims that a large part of this rain results from the spread of storms from the Hi@ands close by after aljout 5.00 pm. This would explain the longer duration and lower intensity (small h? of Nairobi rainfall. A simil[lr pattern would be expected on all windward slopes of the Kenya – Aberdare range and the Kilimanjaro are;~. The Central Highlands zone has therefore been divided into two halves (by the dotted line in Fig. 4) to show the area simflar to Nairobi and the area similar to the inland stations. Molo is the one station that does not fit this pattern. It is on the eastern facing slope of the Mau plateau and at an altituc!e of 2,500 m, but on the evidence of just one station it is not possible to draw any firm conclusions. 11 Voi does not fit the arid model. Thompson (5) shows that althou~ much of the rain at Voi occurs in the afternoon, there is a significant amount of morning rainfall due possibly to the effect of the adjacent Taita hills. Voi’s position (Fig. 4) on the border between the arid and highland zones is appropriate and Voi is therefore not included in computing average values for’n’below. Atthe coast thunderstorms are not very common and heavy rainfall is more frequently the result of a disturbance or discontinuity in the monsoon (1 3). A different model for the coast is therefore appropriate. Having defined 3 zones, average values for Wwere calculated. TABLE 9 Average values for the index ‘n’ a in the equation I = (Tt~)n I Recurrence Interval I 2 year 5 year 10 year 1. Idand stations 0.98 0.96 0.96 2. Coastal stations I 0.82 I 0.76 I 0.76 I 3. Eastern slopes of Kenya-Aberdare Range 0.82 0.85 0.85 It is proposed that in practice an engineer will estimate the daily rainfall for the appropriate recurrence interval using Figs. 1, 4 and 5. He will then enter this into the relevant intensity – duration model above, to obtain the design rainfall he requires. The form of the above models were therefore adjusted to simplify this operation. ~=a (T t b)n Rainfa~ in time T (~) = (T +a~)n The dady total (RD) = 24a (24 t b)n () 24+b n Eliminating ‘a’ RT = ~ — Ttb % with b = 0.33, a unique set of curves can be developed for converting daily rainfall to rainfall of any given duration. These are shown in Fig. 6. 4.5 Conclusions It was concluded that Fig. 6 is the best means at present available for estimating depth – duration ratios for rainfall in East Africa. Al inland areas other than Eastern and South Eastern facing slopes of the Aberdare – Kenya ranges are satisfactorily modelled using the average irdand curves. It is possible that in very wet mountainous areas elsewhere curves simflar to the Nairobi curve are appropriate but these areas witl 12 be very Iimite(l in extent and with present data impossible to predict. In these areas use of the average inland curve is probal)ly conservative. 5. AREA REDUCTION FACTORS In the previou:; sections a method has been developed for predicting point,rainfall for any duration and recurrence interval. Over :i catchment the point rainfall will vary and it is necessary to be able to predict this variation to estimate the v~)lumetric rainfall input to the catchment. The most convenient way is by means of areal reduction factors (ARF), These are factors by which the appropriate estimates of point rainfa~ are mdtiplied to give the average depth of rainfa~ over the catchment. No factc,rs have been pubhshed for East African data. In this section data from four dense networks of raingauges in Ilast Africa are analysed to derive ared reduction factors and from them a general equation for East Africa is IIeveloped. This is then compared to published equations for other parts of the world. 5.1 Area R ?duction Factors for East African Raingauge Networks 5.1.1 The K:akira Network Sixteen years of record from 29 standard daily read raingauges were available ,’ from a sugar e,;tate on the northern shore of bke Victoria, 12 males east of Jinja, Uganda. The estate is approximately 82 kmz in area and undulating. The gauge network is shown in Fig. 7. The met hod adopted for deriving the ared reduction factors in this and the following network studies was to derive (Iepth-frequency equations for point rainfall for each gauge and to compare these with simdar equations for ihe average rainfall over the catchment. Depth-f] equency equations for each of the 29 gauges were obtained using the Gumbel method(1). Annual series were formed by ranking the maximum 1 day rainfall for each calendar year, for the 16 years. These were plotted on Gumbel extreme value paper to provide a visual check on the assumption of linearity. All gave reasonable stnlight line plots. The Gumbel regression lines were then calculated. Goodness of fit was checked by calculating the correlation coefficients as described by Nash (6) and these are given in Table 10. Over tht network the point data relationships were averaged to give the best estimate of the depth-frequency characteristics of the area. To do this one must assume that the area is homogeneous and that differences between gauges can be reasonably expected to be due to chance. This was checked by using the bngbein homogeneity test (7). The equation for point rainfall for the whole network is also given in Table 10. The net~vork was divided up into six areas labe~ed A – Fin Fig. 7. The mean areal rainfall was calculated for the follow ng combinations of area: (a) Areas A, B, C, D, E and F (approx. 15 km2) (b) Areas A t B t C and D t E t F (approx. 40 km’ ) (c) Total network (approx. 80 km2). The mez.n rainfall for each area was calculated for each day of heavy rainfall using the Thiessen method (14). Annual series were formed for these and Gumbel regression equations computed as before. These are shown in Tabl~ 11. By com])aring these regression equations with the mean equations for point rainfafl, areal reduction factors were c:dculated. These are given in Table 12, and shown also in Figs. 8 to 10. There is no evidence for a change in ared reduction factor with recurrence interval, bearing in mind the width of the confidence band. The regressions are likely to be most accurate at a recurrence interval of just over two years. Thl~ two year values were therefore taken as the best estimate of areal reduction factor for au recurrence int?rvals. 13 ~ TABLE 10 Kakira Network Regression equations for dafly point rainfall Correlation Estimated daily rainfall (mm) Gauge No. Regression equation coefficient for given return frequency (r) 2 yr 5 yr 10yr 20 yr 1 Y = 47.07 t 16.30 X 0.988 53.05 71.52 83.78 95.53 2 Y= 51.35 t 14.53 x 0.962 56.68 73.15 84.07 94.55 3 Y=49.81tll.81X 0.985 54.15 67.54 76.42 84.93 4 Y = 49.93 + 19.26X 0.978 53.70 65.32 73.04 80.43 5 Y = 49.53 t 8.02 X 0.983 52.47 61.56 67.59 73.37 6 Y= 52.81 t 18.81 X 0.963 59.71 81.08 95.17 108.73 7 Y= 50.07+ 13.94x 0.953 55.19 70.98 81.46 91.31 8 Y = 52.43 t 8.63 X 0.989 55.60 65.38 71.86 78.09 9 Y=50.71 t 14.03X 0.949 55.86 71.76 82.31 92.42 10 Y = 53.74+ 12.37X 0.987 58.28 72.30 81.60 90.52 11 Y= 52.54 t 13.54 X 0.966 57.51 72.85 83.03 92.79 12 Y=52.lot 15.05X 0.982 57.62 74.68 85.99 96.84 13 Y= 54.78 t 15.03 X 0.966 60.30 77.33 88.63 99.46 14 Y=55.51t 17.73x 0.971 62.02 82.11 95.44 108.22 15 Y = 53.56 t 12.68 X 0.983 58.21 72.58 82.12 91.26 16 Y=53.81tll.36X 0.993 57.98 70.85 79.39 87.58 17 Y=61.12t 16.16X 0.970 67.05 85.36 97.51 109.16 18 Y = 53.06 t 12.96 X 0.982 57.82 72.50 82.25 91.58 19 Y = 55.69 t’ 18.37 X 0.982 62.43 83.25 97.06 110.30 20 Y= 55.88 t 18.27 X 0.966 62.59 83.29 97.02 110.20 21 Y= 53.75 t 12.27X 0.989 58.25 72.16 81.38 90.23 22 Y = 54.86 t 10.79 X 0.993 58.82 71.05 79.16 86.94 23 Y=52.81t 16.13X 0.965 58.73 77.01 89.13 100.76 24 Y=52.97 +13.14X 0.984 57.79 72.68 72.56 92.04 25 Y=55.09t 15.31 x 0.986 60.71 78.06 89.57 100.61 26 Y = 50.59 t 7.40 x 0.957 53.31 61.69 67.25 72.59 27 Y= 53.33 t 13.28X 0.977 58.20 73.25 83.23 92.81 28 Y=50.91 t 17.44X 0.929 57.31 77.07 90.18 102.76 29 Y = 59.09 t 17.64 X 0.959 ‘ 65.56 85.55 98,82 111.53 Mean equation Y= 53.06 t 13.95 X 0.997 58.19 73.96 84.46 94.51 Notes: Y = Maximum expected dady point rainfa~ in T years (mm) X = – (0.834 + 2.303 log log ~) where T is the return frequency (yrs) 14 TABLE 11 Area A B c D E F At B+(; DtEt]: Mean for 15 l:m2 Mean for 40 l:m2 Total Network Kakira Network Regression equations for mean ared daily rainfa~ Regression equation Y=47.93+11.07X Y =49.85t 6.30X Y=46.50t12.01X Y=47.97t 13.94x Y=45.29t 13.80X Y= 52.36t 13.53X Y= 45.68+8.87X Y =45.90t 13.06X Y=48.31tll.77X Y =45.79t 10.98X Y=42.29tll.llx Correlation coefficient (r) 0.978 0.979 0.982 0.987 0.975 0.990 0.977 0.991 0.995 0.965 0.977 Estimated areal rainfa~ (mm) for given return frequency 2 yr 51.99 52.16 50.91 53.13 50.35 57.33 48.94 50.69 52.63 49.82 46.37 TABLE 12 Kakira Network Areal reduction factors 5 yr 64.54 59.30 64.52 68.88 65.99 72.66 58.99 65.49 65.97 62.26 58.95 10yr 72.86 65.04 73.55 80.36 76.37 82.83 65.66 75.31 74.82 70.52 67.31 20 yr 80.84 68.58 82.21 89.41 86.32 92.58 72.05 84.73 83.30 78.43 75.32 Area Ared Reduction Factor (krn2) 2 yr 5 yr 10yr 15 0.904 0.892 0.886 I 40 I 0.856 I 0.842 I 0.835 I I 80 I 0.797 I 0.797 I 0.797 I I I I I I 5.1.2 The Nairobi Network Close networks of well maintained raingauges set out at a uniform spacing, such as the Kikira network, are rare in East Africa. The bulk of the records that are available are either from” widely spaced. East African Meteorological Department stations or from volunteer observers at schools, railway stations, farms and private houses. The spacing of these over the country is dso very wide except in a few areas, generally rich farming areas where large long established farms exist. The most densely gauged area is around Nairobi, the capital city of Kenya. Here the raingauge density is insufficient to study small area factors but is adequate to c dculate average rainf~ over areas of 100 krnz and larger. Fig. 11 shows the network of gauges and the oudine of the areas over which mean rainfall was calculated. The areas are: A 100km2 BtC 600 kmz B,C 300 km2 D 1200km2 15 Gauge No. 3 4 6 10 13 14 15 18 20 22 24 ‘26 27 28 29 30 35 48 Total Net work TABLE 13 Nairobi Network Regression equations for point daily rainfall Gumbel Regression equation Y= 59.66+ 23.37X Y=54.61 t 15.62X, Y = 59.72+ 18.64X Y = 59.28 t 24.43 X Y= 53.01 t 24.87X Y= 58.47 t 19.00 X Y=61.90t 23.22X Y = 58.57 t 25.63 X Y = 49.56 t 21.89X Y=57.15 t 16.46X Y=51.64t 13.41X Y = 54.03 t 22.53 X Y=62.26t30.12X Y = 58.09 t 22.02 X Y= 56.13 + 22.83X Y=48.21 t 12.07X Y= 53.19t 19.43X Y = 55.30 t 37.69 X Y= 56.20+ 21.77X Correlation coefficient 0.95 0.99 0.98 0.98 0.99 0.98 0.93 0.97 0.96 0.96 0.97 0.98 0.94 0.99 0.97 0.99 0.99 0.95 0.91 Estimated storm rainfall 2,yr (mm) 68.2 60.3 66.6 68.2 62.1 65.4 70.4 68.0 57.6 63.2 56.6 62.3 ; 73.3 66.2 64.5 52.6 60.3 69.1 64.2 Note: Y = dafly storm rainfall (mm) for given recurrence interval. 5 yr (mm) 94.7 78.0 87.7 95.9 90.3 87.0 96.7 97.0 82.4 81.8 71.8 87.8 107.4 L 91.1 90.4 66.3 82.3 111.8 88.9 10yr (mm) 112.3 89.8 101.7 114.3 109.0 101.3 114.2 116.3 98.9 94.2 81.8 104.8 130.1 107.7 107.5 75.4 96.9 140.2 105.2 X = reduced variable as defined in Table 10. 16 The area C was arranged to include the whole of the built up area of the city of Nairobi (shown in Fig. 11 by a full line) !’o that by comparison with area B any effect on areal reduction factors due to the modifications of the climate IOCMYby urbanisation would be shown up. As will be seen below no effect was observed. A major difficulty in calculating rainfafl for such a network is that the number of gauges in operation varies from stc rm to storm. Manual calculation of the Thiessen weighings for over 100 storms is very tedious. A computer plogram was therefore prepared which, given the coordinates and catch for each”gauge in operation for a particular storm, calculates the appropriate Thiessen weighings and average depth of rainfall for any area. (8). A secon(l difficulty is that as continuous records are not available for rdl gauges, point rainfall relationships can ody be calculated for the few gauges for which continuous records are avaflable. For the Nairobi network 18 gauges wer{: avaflable with continuous records for the 20 year study period 1937-56. This period was chosen because prior I01937 relatively few gauges were instrdled and for the years 1957-60 only a selection of gauge records were pubtished. The Gunlbel regression equations for the index gauges are given in Table 13. A bngbein homogeneity test on the data showed that the area could be considered as homogeneous. The data were therefore combined to produce a Clumbel regression equation for the whole area. This is also given in Table. 13. Using ths Thiessen Polygon program the average rainfall for each area was calculated for afl large storms. Annual series were then prepared and Gumbel regression equations for areal rainfall calculated. These are shown in Table 14. TABLE 14 Nairobi Network Regression equations for ared rainfall —— Area A B c Bt(: D Gumbel Regression equation Y=47.02t 19.91 x Y = 46.52 t 14.60 X Y=45.73 + 16.57 X Y = 42.65 t 14.79 X Y=37.19t 12.53x I Area A B c BtC D Correlation coefficient 0.99 0.99 0.99 0.96 0.98 TABLE 15 Nairobi Network Areal reduction factors Area (Sq km) 100 300 300 600 1200 Estimated Storm Rainfti 2 yr (mm) 54.3 51.9 51.8 48.1 41.8 ‘5yr (mm) 76.9 68.4 70.6 64.8 56.0 Areal Reduction Factor 2 yr 0.846 0.808 0.807 0.749 0.651 5 yr 0.865 0.769 0.794 0.729 0.630 10 yr 0.874 0.755 0.790 0.722 0.622 10yr (mm) 91.9 79.4 83.1 76.0 65.4 17 From the results in Tables 13 and 14 area] reduction factors were calculated and are given in Table 15. The regression equations and associated 95 per cent confidence limits are shown in Fig. 12-16. As with the Kakira network the evidence for a variation in areal reduction factor with recurrence interval is inconclusive. The 2 year values are therefore taken as the best estimate for all recurrence intervals. 5.1.3 Sambret Network In this and the next section, 2 raingauge networks on experimental catchments installed by the East African Agriculture and Forestry Research Organisation are studied. The Sambret catchment is 6.9 kmz in area, close to Kericho in Western Kenya. The period of record available was 1960-66 from a network of 17 standard raingauges evenly distributed over the catchment. The analysis using the same methods as described for the Kakira network resulted in the following Gumbel regression equations: Regression equation for point rainfall (using 17 gauges): y = 52.45 + 14.22X r = 0.94 Regression equation for aredrainfdl: y =47.88 + 14.35 X r = 0.93 The ared reduction factors are shown in Table 16. TABLE 16 Areal reduction factors for the Sambret catchments Predicted Rainfall Return period Areal Reduction (yrs) Point Areal Factor (mm) (mm) 2 57.68 53.14 0.921 5 73.79 69.42 0.941 10 84.48 80.19 0.949 5.1.4 Atumatak Network The Atumatak catchments are situated in South Karamoja in Eastern Uganda. The area is semi-arid. The network covers an area of 8.1 km2 and contains 23 evenly spaced raingauges. Records were available for 9 years from 1958-66. Five of the gauges were autographic raingauges from which records of point and mean rainfall for periods less than 24 hours could be extracted. Unfortunately, due to vandalism, several of the autographic gauges were out of action for most of 1962-63. Only 7 years were therefore andysed for periods shorter than 1 day. Gumbel regression equations for point and areal rainfall were calculated as before and are given in Tables 17 and 18. The ared reduction factors from these are given in Table 19. 18 I TABLE 17 Atumatak Network Regression equations for point rainfall [ Estimated Storm Rainfall Period Regression equation Regression (hrs) coefficient r 2 yr (mm) % Y= 19.14+4.61X 0.86 20.83 % Y = 26.69t5.38X 0.86 28.66 1 Y=32.1O+7.O1X’ 0.73 34.67 2 Y = 35.39t 6.47X 0.71 37.76 8 Y =40.22t8.08X 0.80 43.19 24 Y =42.01t 8.63X 0.71 45.18 TABLE 18 Atumatak Network Regression equations for areal rainfall Period Regression equation Regression (hrs) coefficient % Y= 9.95 t 3.62X 0.95 % Y= 16.03 t 5.49X 0.95 1 Y=23.07+6.11 X 0.93 2 Y=27.15 +5.65X 0.93 8 Y = 32.87 t 6.23 X 0.98 24 Y = 35.46 t 8.33 X 0.98 5 yr 10yr (mm) (mm) 26.06 29.51 34.76 38.80 42.62 47.87 45.10 49.95 52.34 58.40 54.96 61.43 Estimated Storm Rainfall 2 yr (mm) 11.28 18.04 25.31 29.22 35.16 38.52 5 yr (mm) 15.38 24.27 32.24 35.63 42.22 47.96 10yr (mm) 18.10 28.38 36.82 39.86 46.89 54.22 19 Period (hrs) 1A 1A 1 2 8 24 TABLE 19 Atumatak Network Areal reduction factors Areal Reduction Factors 2 yr 0.542 0.629 0.730 0.774 0.814 0.853 5 yr 0.590 0.698 0.756 0.790 0.807 0.873 10yr 0.613 0.731 0.769 0.798 0.803 0.883 5.2 General equation for areal reduction factors With data from only four networks it is not possible to arrive at a number of models for areal rainfall and an objective plot of the boundaries of the zones appropriate to each model. All that can be done at this stage is to develop a sin~e model and to apply this in all cases where it is not obviously inappropriate. Further data will become available when analysis is complete on three dense networks of autographic gauges over Nairobi, Kampala and Dar es Salaam and the networks.of the Kenya and Uganda Rural Catchment programme (9). At that time an improved model will be possible. A plot of 24 hour areal reduction factors against area (Fig. 17) shows that the two Uganda networks (Kakira and Atumatak) give smaller values than the two Kenyan networks. This is consistent with the observations of Johnson (15) who divided East Africa up into four zones. a. Hi@and regions of Kenya and Southern Tanzania where rain tends to be widespread. b. Uganda where scattered showers predominate. c. Dry regions of N.E. Kenya and S.W. Tanzania which are intermediate between these two zones. d. The coastal strips. It is therefore concluded that the Sambret and Nairobi results can be combined to form an upper limit curve which will apply to highland areas of Kenya and Tanzania. The same curve will probably not be too conservative for all other areas except Uganda where the results from Kakira and Atumatak should be used as a guide until such time as further data are avaflable. Factors for periods of less than 24 hours are much smaller. This is particularly important for urban catchments which is one of the main reasons for initiating the urban raingauge networks referred to above. For rural areas the lag in runoff means that most storms are shorter than the time of concentration of the catchment so that 24 hour values are appropriate. 5.3 20 Comparison with published areal reduction factor Very few published data are available for tropical Africa and the equations published for other parts of the world are of little use in interpreting African results because the rainfall elsewhere appears to be much more extensive. For example the equation published by the U.S.Weather Bureau (12) as being appropriate to continental U.S.A. is: A~F = , _e-l.lt:A + e(-l.lt;A - O.OIA) where tr = period (hrs) and A = Area (sq. miles) The factors predicted by this equation are much higher than those appropriate to East Africa. (The 1000 km 24 hour value = 0.91). Bruce arid Clark (1O) quote an equation appropriate for India. ARF=I– C4A where A = area in sq. males C = a constant which varies from 0.00275 – 0.00470 This gives values as high or even higher than the U.S. Weather Bureau equation. The onlf published figures for Tropical Africa known to the authors are those by Rodier and Auvray (1 1) for West Africa. These are shown in the Table 20 below. TABLE 20 10 year areal reduction factors for West Africa * Area (kmz ) 10 yr Areal Reduction Factor O-25 1 2650 0.95 51-100 0.90 101-150 0.85 151-200 0.80 These are similar to the East African upper limit curve. It is difficult however to make a direct comparison as they are de~;ignrecommendations and not experimental values and it is possible that some rounding up has been wowed LOsimplify design techniques. 6. CONCLUSIONS It has been sh >wn that daily point rainfall can be predicted for any catchment in East Africa using Figs. 1,4 and 5. Figs. 1 and 4 are in such a form that they can be updated when the East African Meteorological ~partment’s taped daily records have been, extended. It is recommended that the mapping be repeated in about 1978 when the short period tape wfll cover a 20 year period. The depth-duration-frequency equations are adequate for desi~ use for flood prediction in rural areas. They are not iidequate for use with urban flood models but this will be rectified when current research in East Africa using high speed autographic recorders is complete. Improved models for short duration rainfall should therefore be avaflable by early 1975. 21 Further data are required to give a complete picture of the variation of areal reduction factor with location and storm duration. These will be made available by the current rural catchment and urban rain, gauge programme, which it is anticipated will be reported upon early in 1975. 7. ACKNOWLEDGEMENTS The work described in this report was carried out in the Environment Division of the Transport Systems Department of the Transport and Road Research hboratory, and forms part of the programme of research undertaken at the hboratory on behalf of the Overseas Development Administration of the Foreign and Commonwealth Office. The assistance of the Director General of the East African Meteorological Department, the Director of the East African Agriculture and Forestry Research Organisation and the Manager of the Kakira sugar estate in making data available is gratefully acknowledged. 8. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 22 GUMBEL, E. J. Statistical Theory of Extreme Values and some Practical Applications. National Bureau of Standards, Applied Mathematics series 33. U.S. Dept. of Commerce 1954. TAYLOR, C. M. and E. F. LAWES. Rainfall Intensity-Duration-Frequency Data for Stations in East Africa. East African Meteorological Dept. Technical Memorandum No. 17, 1971. McCALLUM, D. The Relationship between Maximum Rainfafl Intensity and Time. East African Meteorological Dept. Memoirs. Vol. III No. 71959. LUMB, F. E. 4th Specialist committee on Applied Meteorology. Nairobi 1968. THOMPSON, B. W. The Diurnal Variation of Precipitation in British East Africa. East Africa Meteorological Dept., Technical Memorandum No. 81957. River Engineering and Water Conservation Works, Ed Thorn R. B. Ch. 6 Applied Flood Hydrology Nash J. E. CHOW, V. T. Handbook of Applied Hydrology McGraw Hill 1964, Section 8 p.36. GWGG; A. O. A program for calculating Thiessen average rainfall. Department of the Environment TRRL Report LR 470, Crowthorne, 1972 (Transport and Road Research Laboratory). FIDDES, D and J. A. FORSGATE. Representative rural catchments in Kenya and Uganda. Ministry of Transport, RRL ReportLR318, Crowthorne, 1970 (Road Research hboratory). BRUCE, J. P. and R. H. CLARK. Introduction to Hydrometeorology. Pergamon Press 1966. RODIER, J. A. and C. AUVRAY. Preliminary general studies of floods on experimental and representative catchment areas in tropical Africa. IASH Symposium of Budapest 1965 Vol 1 pp 22-38. HERSHFIELD, D. M. Rainfall Frequency Atlas for the United States. U.S. Weather Bureau. Technical paper No. 401961. SONSDIN, H. W. The Maximum Possible Rainfall in East Africa, East African Meteorological Dept. Technical Memorandum No. 31953. THIESSEN, A. H. Precipitation averages for large areas, Monthly Weather Review Vol. 39 pp 1082 – 84 1911. JOHNSON, D. H. Rain in East Africa. Ch. 5 Royal Met. Sot. Vol. 88 Jan 1962 pp 1-19. 9. APPENDIX 1 Design curves and worked examples The relevant figures and table are reproduced below. These examples were designed to act as a guide to the design method; developed in the main report and also to show the range of variation in short period rainfall over East Africa. Example I Calculate the c.esign storm required to estimate the flood resulting from 25 year recurrence interval storm rainfall on a 20 kmz catchment, grid reference 32°E 1‘N. hcate the cat:hment on Appendix 1 Fig. 1 (marked with C) The 2 year 24 hr rainfd = 70 mm 70 mm bcate catchment on Appendix 1 Fig. 2 (marked with C) 1.49 10 year: 2 yea: ratio is Group 6 Inland = 1.49 From Appendix 1 Fig. 3 for a 10 year: 2 year ratio of 1.49 and a recurrence intervaf of 25 !/ears the flood factor = 1.74 1.74 The 25 year 2~!.hour point rainfall = 1.74x 70 mm 122 mm = 121.8 (say 122) From Appendix 1 Fig. 4 read off the area reduction factor for a 20 km2 area = 0.9 0.9 The areal rainfall for the catchment is 122x 0.9 llOmm = 109.8 (say 110) From Appendix 1 Table 1 select a suitable ‘n’ value for an inland station (Zone 1) = 0.96 0.96 Using ‘n‘ = 0.!15 in Appendix 1 Fig. 5 select rainfall ratios for 15 reins, 30 reins, 1 hot.r, 2 hours, 4 hours and multiply by 110 mm to obtain R T for each pc riod. These are then plotted as a symmetrical histogram, R ~ being shovn in units of (mm of rain in 15 reins) 15 reins 0.36x 110 RT=39.6 30 reins 0.51 x 110 RT=56.1 1 hour 0.655 X 110 RT = 72.05 2 hour 0.825 x 110 RT ‘90.75 4 hour 0.855 x 110 RT ‘94.05 RT = 39.6 RT = 56.1 – 39.6 = 16.5 RT = 72.1 – 56.1 = 8.0 2 RT = 90.8 – 72.1 = 4.7 4 RT = 94.1 – 90.8 = 0.4 8 These values ale shown plotted on Appendix 1 Fig. 6(a). 23 Example II Assuming a symmetrical shape calculate the 10 year recurrence interval design storms for point rainfall appropriate for (a) Nairobi (b) Kampala (c) Dar es Salaam (a) Nairobi Proceed as in example 1 (point marked ‘N’ on Appendix 1 Fig. 1). From Appendix 1 Figs. 1,2,3 2 year 24 hour rainfall 2 year: 10 year ratio 10 year flood factor 10 year rainfall From Appendix 1 Table 1 ‘Zone 3’ ‘n’ = 70 mm = 1.60 = 1.60 = l12mm = 0.85 Using ‘n’ = 0.85 in Appendix 1 Fig. 5 calculate RT for 15,30 rnins, 1 hr, 2 hr, 4 hr and plot as a symmetrical histogram in units of mm/1 5 reins. 15 reins 0.25 x 112 RT = 28.0 30 reins 0.365 X 112 RT = 40.9 1 hour 0.485 x 112 RT = 54.3 2 hour 0.610x 112 RT = 68.3 4 hour 0.720 x 112 RT = 80.6 These values are shown plotted on Appendix 1 Fig. 6(b) (b) Kampala Proceed as in example 1 (point marked ‘K’ on Appendix 1 Fig. 1) From Appendix 1 Figs. 1,2,3 2 year 24 hour rainfall 2 year: 10 year ratio 10 year flood factor 10 year rainfall RT = 28.0 RT = 40.9 –28.0 = 12.9 RT = 54.3 – 40.9 = 6.7 2 RT = 68.3 – 54.3 = 3.5 4 RT = 80.6 – 68.3 = 1.5 8 = 70 mm = 1.49 = 1.49 = 104mm From Appendix 1 Table 1 Zone 1 ‘n’ = 0.96 4Using ‘n’ = 0.95 in Appendix 1 Fig. 5 calculate RT for 15 rein, 30 rein, 1,2,4 hrs and plot as symmetrical histogram in units of mm/15 reins. 15 reins 0.36 X 104 RT = 37.4 30 reins 0.51 X 104RT = 53.0 1 hour 0.655 x 104 RT = 68.1 2 hour 0.825 x 104 RT = 85.8 4 hour 0.855 x 104 RT = 88.9 These value; are shown plotted on Appendix 1 Fig. 6 (e) (c) Dar e!: Salaam From Appendix 1 Figs. 1,2,3 2 year 24 hour rainfall 2 year: 10 year ratio 10 year flood factor 10 year rainfall From Appendix 1 Table 1 Zone 3 ‘n’ RT = 37.4 RT = 53.0 –37.4 = 15.6 RT = 68.1 –53.0 = 7.5 2 RT = 85.8 – 68.1 = 4.4 4 RT = 88.9 –85.8 = 0.4 8 = 70-80 mm (say 75 mm) = 1.64 = 1.64 = 123 mm = 0.76 Using ‘n’ = 0.75 in Appendix 1 Fig. 5 calculate RT for 15 rein, 30 rein, 1,2,4 hrs. and plot as symmetrical histogram in units of mm/15 reins. 15 reins 0.170 x 123 RT = 20.9 RT = 20.9 30 reins 0.260x 123 RT = 32.0 RT = 32.0 –20.9 = 11.1 1 hour 0.365 X 123 RT = 44.9 RT = 44.9 – 32.0 = 6.5 2 2 hour 0.485 X 123 RT = 59.7 RT = 59.7 –44.9 = 3.7 4 4 hour O.61O X 123 RT = 75.0 RT = 75.0 – 59.7 = 0.5 8 These valu>s are shown plotted in Appendix 1 Fig. 6 (d). 25 APPENDIX 1 TABLE 1 Average values fortheindex’n’ inthe equation I = a (TW.33)n Recurrence Interval Zone 2 year 5 year 10 year 1. Inland Stations 0.98 0.96 0.96 2. Coastal Stations 0.82 0.76 0.76 3. Eastern slopes of Kenya-Aberdare Range 0.82 0.85 0.85 26 I ---- ,,.c “.- Appendix 1. Fig. 1. 2 YEAR 24 HOUR STORM RAINFALL (mm) ,,- - k ---_@- 1 . . W . . 8w; wanz@ 164.. . . - ‘“a . 6. inland 1.49 . . . .W 3WE 3 I I I ... ..- I ..❑ I o“ \ I , Appendix 1. Fig. 2. 10 YEAR :2 YEAR RATIO Q“ c 5 D —~ K 1,1 I 1 I I I 1.0 1.4 1.8 2.2 10:2 year ratio Appentix 1. Fi~ 3 FLOOD FACTORS 0 . ... 0 0’ 0.5 1.0 5.0 10.0 20.0 1.0 0-9 0.8 0.7 .- ; 0.6 — m %.- 2 0.5 0.4 0.3 0.2 01 I I 1 0.1 0.5 1.0 50 10-0 20,0 Time (h) Appendix 1. Fig. 5. EAST AFRICAN RAINFALL RATIOS 1.0 0.9 0.8 0-7 0.6 0.5 0.4 0.3 0.2 01 50r (a) Catchment ‘C’ 30min Ihr 4hr I Time (h) (c) Kampala 15min r 37.4 (b) Nairobi 230 - g = g c.- 2 10 30min 1hr 2hr 4hr, 3.5 , 1.5 I I I I I Time (h) 50r (d) Dar-es-Salaam k =, 15 min 2 .-c 2 10 - 30 min lhr 4hr 2hrl I 3.7 0.5 I I I I I Time (h) Time (h) Appendix 1. Fig. 6. DESIGN STORMS FOR 4 AREAS IN EAST AFRICA .m. ,... , ..= .. . .. . .“ , Fig. 1 2 YEAR 24 HOUR STORM RAINFALL (mm) 140 120 100 80 60 40 20 / ●✏ /“ Y2(10) = Y2(40) / 9 ● / . ● ● ● . . “*** ● * . . 20 40 60 80 100 120 140 Y2 – 10 year(mm) Fig. 2 COMPARISON OF 2 YEAR (mm) ESTIMATES OF STORM RAINFALL USING IO YEAR AND 40 YEAR PERIODS OF RECORD 1 I I I 5 10 15 20 Period of record (years) Fig. 3 95% CONFIDENCE LIMITS FOR RUNNING MEANS OF ANNUAL RAINFALL MAXIMA . . . . . . . . . 6. Inland . 1.49 . 2 1.89 ‘m i i 1 1 .! I . :.” . / . I .{ mm .. .. A. I ..a,“/ I 0. . . . . .1 .“ \ . I m I I I I . L/ .Vuual . M o oro ,.. . J. .,,6:?3 .$ . *... ... ,.:.: . ::::::: ..,:.: . .:::.:.; .:::::::: ,. ..:::2 . . . . . t . . a-. . . . b, I . Fig. 4. 10 YEAR :2 YEAR RATIO 40 3.0 N . . c 2.0 1.0 -. -. -. 5 4 . i 1 I I I I 1.() 1.4 1.8 2.2 10:2 year ratio Fig. 5. FLOOD FACTORS 0.1 05 1.0 5.0 100 20-0 1.0 0.9 , ./ 0:8 0.7 ,’ 0.6 0.-+ mL = 0.5 : c.- : 0.4 0.3 0,2 0.1 I I I I I I I I I I I I I I I I . . . . . 1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 2.1 0.1 0.5 1.0 5.0 10.0 20.0 Time (h) Fig. 6 EAST AFRICAN RAINFALL RATIOS — Fig. 7. KAKIRA RAINGAUGE NEWORK 130 120 110 100 90 80 70 60 50 40 30 Return Frequency (years) 2 5 10 20 I I I I — — — 95% confidence limits 1 I I 1 1 –1.0 0.0 1.0 2.0 3.0 40 Reduced variable Fig. 8 COMPARISON OF AREAL AND POINT DAILY RAINFAL – $ FREQUENCY RELATIONSHIPS FOR AN AREA OF 15 km 130 120 110 100 90 80 70 60 50 40 30 Return frequency 2 5 10 20 I——— 95% confidence limits I . . –1.0 0.0 1.0 2.0 Reduced variable 3.0 { 40 Fig. 9. COMPARISON OF AREAL AND POINT DAILY RAINFALL - FREQUENCY RELATIONSHIPS FOR AN AREA OF 40 km2 130 120 110 100 90 F & > 80 = ~ :C.- ; 70 60 50 40 30 Return frequency 2 5 10 20 —— — 95% confidence limits I 1 / I I 1 I -1.0 0.0 1.0 2.0 Reduced variable 3.0 4.0 Fig. 10 COMPARISON OF AREAL AND POINT DAILY RAINFAL – $ FREQUENCY RELATIONSHIPS FOR AN AREA OF 80 km I ————————— .—.—.—.- .7 -* .—. — .—. — .—. 0 0 —— —.— ——— ——_ ___ Fig. 11 NAIROBI RAINGAUGE NEfiORK & SUBAREAS . ,/ 130 120 110 160 90 80 70 60 50 40 30 Return frequency 2 5 10 20 — — — 95% confidence limits //’! . . . . Point rainfall . . . ‘/: ‘Areal rainfall ‘/ I /, ~, I 1 –1.0 0.0 1.0 2.0 3.0 4.0 Reduced variable .- Fig. 12 COMPARISON OF AREAL AND POINT DAILY RAINFALL - FREQUENCY RELATIONSHIPS FOR AN AREA OF 100 km2 ’130 ,“ 120 I1O 100 90 80 70 60 50 40 30 Return frequency 2 5 10 20 ... . --— 95% confidence limits f . . . . . . I I 1 I I –1.0 0.0 1.0 2.0 3.0 4.0 Reduced variable Fig. 13. COMPARISON OF AREAL AND POINT DAILY RAINFALL – FREQUENCY RELATIONSHIPS FOR AN AREA OF 300 km2 Return frmuencv 130 120 110 100 90 80 70 60 50 40 30 “2 5 10 20 — — — 95% confidence limits I Point rainfall /- 1 /, .——- 1 1 I –1.0 0.0 1.0 2.0 3.0 40 Reduced variable Fig. 14 COMPARISON OF AREAL AND POINT DAILY RAINFALL – FREQUENCY RELATIONSHIPS FOR AN AREA OF 300 km2 130 120 110 100 90 : g > = 80 ~ c.- 2 70 60 50 40 30 Return frequency 2 5 10 20 I I I I ——— 95% confidence limits I Point rainfall Areal rainfall / I /, 1 1 1 –1.0 0.0 1.0 2.0 3.0 40 Reduced variable .. Fig. 15 COMPARISON OF AREAL AND POINT DAILY RAINFALL - FREQUENCY RELATIONSHIPS FOR AN AREA OF 600 km2 Return frequency 2 5 10 20 130 120 110 100 90 z & > = ~ 80 c.- 2 70 60 50 40 30 ——— 95% confidence limits I / I 1 1 –1.0 0.0 ‘ 1.0 2.0 Reduced variable 3.0 4.0 ,. Fig. 16. COMPARISON OF AREAL AND POINT DAILY RAINFALL FREQUENCY RELATIONSHIPS FOR AN AREA OF 1200 km2 o (5S2) Dd635221 1,500 4/74 H~Ltd,So’ton G1915 o 0 m o 0 0 o 0 e o 0 N PRINTED IN ENGLAND ABSTRACT Thepredicting ofstorm rainfali in East Africa: D. FIDDES, B.Se., M.Se., C.Eng., M.I.C.E., DIC., J. A. FORSGATE, B.SC., and A. 0. GRIGG: Department of the Environment, TRRL Laboratory Report 623: Crowthorne, 1974 (Transport and Road Research hboratory). A simple method for predicting the characteristics of storms for the design of drainage structures in East Africa is described. The variation of 2 year daily point rainfti, and the 10:2 year ratio for dafly rainfall, over East Africa are given in map form. Using these, dafly point rainfall for any return frequency can be calculated. TO arrive at the design storm the daily point rainfrdl is adjusted using a generalised depth-duration equation and a graphical representation of the variation of mean rainfa~ with area. ABSTRACT The predicting of storm rainfall in East Africa: D. FIDDES, B.SC., M.SC., C.Eng., M.I.C.E., DIC., J. A. FORSGATE, B.SC., and A. O. GRIGG: Department of the Environment, TRRL Laboratory Report 623: Crowthorne, 1974 (Transport and Road Research Laboratory). A simple method for predicting the characteristics of storms for the design of drainage structures in East Africa is described. The variation of 2 year daily point rainfa~, and the 10:2 year ratio for daily rainfall, over East Africa are given in map form. Using these, daily point rainfall for any return frequency can be calculated. To arrive at the design storm the daily point rainfall is adjusted using a generalised depth-duration equation and a graphical representation of the variation of mean rainfa~ with area.