6. Regional flood frequency analysis for Southern Africa
6.2 Data analysis
6.2.1 Available data for the study
Data from a total of 754 gauging stations with average record length of 24 years from eleven countries in Southern Africa were used in this study; full detailsofwhich are shown in Table 6.1. Annual maximum instantaneous discharge series were used for most of the countries but where this information was not available, annual maximum mean daily discharge series were used.
6.2.2 Extension of flood data
In Tanzania only a small proportion of gauging stations are equipped with automatic water level recorders; the manually-read gauges record levels twice or thrice per day.
Fifty-three instantaneous annual maximum (AM) series with an average record length of 15 years were available from self recording stations. The’maximum mean daily discharges extracted from the manual gauging stations were used to extend the instantaneous data by using the following relationship:
130
Southern Africa FRIEND : /HP IV Technical docurnen~s in f(vdrolo~ No ISTable 6. I Summarized information on available flood data for the study
Country Area (k&) No. of sites Record length Con trib. (%) Status of data
Angola 1,246,700 17
Botswana 681,730 14
Lesotho 30,355 23
Malawi 118,484 28
Mozambiq 799,380 16
Namibia 823,145 51
S. Africa 1,221,037 316
Swaziland 17,364 33
Tanzania 945,087 146
Zambia 752,614 24
Zimbabwe 390.580 86
6 2.3 Mmax
16 1.9 Inst.
9 3.1 Inst.
18 3.7 Inst.
25 2.1 Mmax
19 6.8 Inst.
32 41.9 Inst.
14 4.4 Inst.
17 19.4 Ext.
22 3.2 Inst.
21 11.4 Mmax
Total 754
QInst = 1.15 Qmm eq. 6.1
(where Qlns, = Instantaneous discharge, Q,,, = Maximum mean discharge)
This increased the number of stations from 53 to 146, with an average record length of 17 years.
6.2.3 Data screening
The data were checked for inconsistency, dependence and inter-site correlation, as follows:
Discordancy measure
The discordancy measure is a procedure developed by Hosking and Wallis (1993) to identify those sites that are grossly inconsistent with in the group as a whole. The discordancy is measured in terms of the L-moments (Hosking 1986, 1990) of the sites. The L-moments are defined as linear combinations of the Probability Weighted Moments (Greenwood et al., 1979). This measure was used to screen out sites whose at-site sample L-moments were markedly different from other sites.
The discordancy measure for a given site is given by
I -
Di =f(ui-~)TS1(~i-~)
3 eq. 6.2
where u, .= vector of Lcv, L-skew and L-kurtosis for site i, S = covariance matrix of ui and = =mean of vector ui.
A site is declared discordant if the value of D, is greater than 3.
The stations that were discordant were investigated for gross errors or presence of outliers. For countries like Tanzania, where the authors had access to the data record files in .the Ministry of Water, it was found that there were indeed errors
in the data and hence they were corrected. In the case of other countries all discordant stations were dropped from the analysis.
Dependence infloodjlows
Dependence or persistence observed in a time series is a tendency for high values to follow high values and low values to follow low values. The presence of dependence or persistence therefore implies repetition of information given by previous values as opposed to the random process which has no memory of the past. A random process supplies new information each time a new observation is made.
Various studies have been carried out using simulation to investigate the effect of the presence of dependence in annual maximum series on parameter estimation and the standard error of the estimates. The results from such studies indicated that presence of dependence in AM data leads to more biased quantile estimates and larger standard error than when dependence is absent and the correct model form is assumed (Cunnane, 1989).
Linear dependence in a sequence of flow series can be determined by computing the first order serial autocorrelation coefficient (r,). This value can be tested if it is significant within predetermined confidence limits.
Inter-site correlation
Inter-site correlation investigates how the flows for a certain station are correlated with those’of other stations. The correlation in flood flows between stations may result in a situation whereby flood events from neighbouring stations are caused by the same widespread meteorological event (Cunnane, 1987). Stedinger (1983) found that inter-site dependence does not introduce any bias into flood quantile estimates but it does increase their sampling variability.
The presence of a high degree of linear association of flood flows between two stations in a particular region implies that no new information can be obtained by considering both stations in the estimation of regional parameters, therefore only one of the two stations is included in the estimation of regional parameters.
Inter-site correlation analysis determined the degree of linear association of flood flows between stations in the regions studied. Since the record lengths for individual series involved in the study were different, the common recording period between stations was considered in the inter-site correlation analysis. Statistical tests were used to test the level of significance of intersite correlation.
Results.of data screening analysis
The results of dependence tests are shown in Table 6.2. A total of 1.5 stations were found to be discordant (column 3), 69 stations exhibit significant serial correlation (column 4) and 263 exhibit inter-site correlation (coloumn 5). These stations were excluded from further statistical analysis.
The inter-site correlation revealed that many stations were found to be inter-correlated. For a pair of stations which was found to be significantly correlated, judged on the basis of the established confidence limits, one among the two was excluded from tirther analysis. However, attempt was made so that the stations which were retained in the analysis were spatially distributed over the whole region under study.
The number of stations from each country which were excluded from further analysis due to inter-site correlation are shown in Table 6.2 (column 5). Inter-site correlation
analysis carried out from six countries (Lesotho, Namibia, South Africa, Swaziland, Tanzania and Zimbabwe) resulted in the reduction to 263 stations. The examination of the data from these stations indicated considerable inconsistence. All stations featured in columns (3), (4) and (5) were excluded from further analysis. For Angola, Botswana, Malawi, Mozambique and Zambia inter-site correlation analysis was ignored because for these countries the data available for the analysis were limited.
6.2.4 Flood statistics of Southern Africa
Table 6.3 presents flood statistics computed from the remaining stations. It may be observed that the average coefficient of variation (CV) values for Botswana, Mozambique, Namibia, South Africa and Zimbabwe are close to 1 .O. The coefficient of variation provides a useful measure of hydrological variability. It indicates that the distribution of floods in these countries is highly variable.
The cv values determined for Malawi, Lesotho and Swaziland are very similar to each other at about 0.66. The cv values for Angola, Tanzania and Zambia are slightly lower when compared to other countries, i.e. 0.56,0.50 and 0.44 respectively. The different levels of variability in the observed flood samples may be attributed to varying hydrological phenomena responsible for generating the flood events over the different countries.
It may also be observed that average values of skewness (CS) for Malawi, Tanzania and Zambia range between 0.9 to 1.5. The corresponding values for Angola, Lesotho and Swaziland are 1.5 to 2.0. For Botswana, Mozambique, Namibia, South Africa and Zimbabwe the values range
Table 6.2 Number of sites identified as discordant, serially correlated and cross-correlated Country (1)
Angola Botswana Lesotho Malawi Gozambiq Namibia S. Africa Swaziland Tanzania Zambia Zimbabwe
No. of sites (2) Discordant stations (3) Ser.corr. stations (4)
17 0 2
14 0 1
23 1 1
28 0 1
16 0 0
51 0 4
316 13 33
33 1 1
146 0 19
24 0 0
86 0 7
Cross-corr stations (5)
* f 8
44
Total 754 15 69 263
* = Analysis not carried out
132 Southern Af?ica FRlEND : IHP IV Technical docurnent.~ in &drologr No IS
Chapter 6 : Regionalfloodfreyuenc~, ana!vsis for Southern Afkica
Table 6.3 Unbiasedflood statistics for all stations used in the analysis for the I I countries in Sokhern Africa.
Key: (1) Weighted mean value (2) Weighted std. deviation
between 2.0 to 3.0. The range of skewness values observed in Southern Africa indicate that the distribution of flood flows from the region are positively skewed; the values have therefore been corrected for bias by applying the factor (1+8.5/N) suggested by Hazen (1932).
6.3 Regionalization of Southern Africa 6.3.1 Introduction
Regionalization refers to grouping of basins in homogeneous regions. The importance of homogeneity has been demonstrated by Hosking et al. (1985), Wiltshire (1986) and Lettenmaier et al. (1987). Homogeneity implies that regions have similar flood generating mechanisms. A more specific definition of a homogeneous region is that region which consists of sites having the same standardized frequency distributional form and parameters. Such a region is geographically continuous and it forms a basic unit for carrying out regional frequency analysis. There are.no specific guidelines for identifying homogeneous regions because of the complexity in understanding the factors which affect flood generation and hence provide guidelines
to delineate regions with similar catchment characteristics.
Several attempts have been made by different authors to identify hydrologically homogeneous regions in different parts of the world based either on geographical considerations or on flood data characteristics or a combination of both.
6.3.2 Procedure applied to regionalize Southern Africa
Delineation of homogeneous regions
This was based on information on catchment boundaries, a topography map, mean annual rainfall flood statistics and location of gauging stations plus, in the case of South Africa, a map defining maximum flood peak regions (Kovacs, 1988). Identification of homogeneous regions was implemented prior to completion of the thematic databases described in Chapter 3.
The procedure involved digitizing map information and then superimposing upon each other using computer graphics.
The print-out of the map with the combined information was then used as a basis to define the homogeneous regions.
Hydrological background knowledge and experience were important assets in predicting homogeneous flood regimes that were likely to be generated from a combination of different physiographical characteristics and rainfall regimes.
General considerations were that river basins on highlands receiving high annual rainfall were grouped under one region, while those lying on lowlands and receiving low annual rainfalls were grouped within another; basins in semi-arid areas were also grouped into one region. The boundaries of the delineated regions were established using personal judgement.
A preliminary check on whether a proposed region was reasonably homogeneous involved computing a statistic CC, as the coefficient of variation of at site Lcv’s. A homogeneous region was expected to have a low value of CC. The proposed region was further sub-divided and the boundaries of the proposed region redefined if the value of CC was found to be more than 0.3.
Test for regional homogeneity
Two tests were applied to establish if the delineated regions were homogeneous. The first test is the one recommended by Hosking and Wallis (1993) and the second test is a new test proposed in this study. Both the tests are based on the analysis of the variability of the L-moment ratios.
(5, Hosking and Wallis s homogeneity test
Hosking and Wallis (1993) suggested a statistical procedure to test for regional homogeneity. The procedure estimates the degree of heterogeneity in a group of sites and assesses
133 _ --
Mkhandi and and Kachroo
whether the group can be treated as a homogeneous region.
The statistic H is defined as the heterogeneity measure to compare the between-site variation in observed sample L- moments for the group of sites with that which would be expected for a homogeneous region, obtained from simulation. The variance of the at-site Lcv was considered to measure the dispersion in the L-moment ratios. Emphasis
‘was put on Lcv because between site variation in Lcv has a much larger effect than variation in L-skewness or L- kurtosis on the variance of the estimates of flood quantiles.
The heterogeneity measure statistic, H, can be computed from the expression
(V - cc,>
Hz __ eq. 6.3
0”
where V = weighted standard deviation of Lcv, py = mean of simulated Lcv values and CT” = standard deviation of simulated Lcv values.
Hosking and Wallis (1993) established the criteria with regard to assessing the heterogeneity measure such that when:
H<l the region is acceptably homogeneous 1 <H<2 the region is possibly homogeneous H>2 the region is definitely heterogeneous (ii) Graphicalplot test
Each identified region is tested for homogeneity with a graphical test. The test is based on the hypothesis that a region is statistically homogeneous, for a given parent distribution P, if the distribution of the historical at-site data statistics (Lcv, Lcs or Lck) is similar to the distribution of synthetic sequences of the same length as the historical sequence, extracted from the parent distribution P. The test may be elaborated as follows:
(i) Lcv values are calculated from flood data for each site in the region. These are plotted on an EV 1 Probability paper.
(ii) A parent distribution P is assumed. The parameters of this distribution are estimated from L-moments of the grouped average historical data of the region.
(iii) Five hundred synthetic sequences are generated from the assumed parent distribution, P. Each synthetic sequence is equal to the length of the historical data.
(iv) For each synthetic sequence Lcv values equal to the number of historical sites are calculated and stored as order statistics.
(v) From 500 synthetic sequences sampling distributions
of each order Lcv are calculated.
(vi) If the historical Lcv at each order falls within the observed limits of synthetically generated sampling distribution then the region is assumed to be homogeneous for a given parent distribution P. If historical Lcv of any order falls outside the observed limits then the region is deemed to be heterogeneous for distribution P.
6.3.3 Results of regionalization
The homogeneous regions were delineated for Botswana, Malawi, Namibia, Zimbabwe, Tanzania and South Africa including Lesotho and Swaziland. Due to limited availability of flow data from Angola (17 sites), Mozambique (16 sites) and Zambia (24 sites) in relation to their size, the process of regionalization was not carried out for these countries.
Data were therefore combined to form single regions. The situation in Botswana was that only 14 stations were available for flood frequency analysis and as they were concentrated were in the two drainage basins located on the eastern part of the country, these two basins were therefore considered for regionalization.
The delineated homogeneous region for the eight countries of Southern Africa are shown in Figures 6.1 - 6.6. Figure 6.1 shows that the regionalization of Botswana resulted in one homogeneous region for that part of the country where data were available. Fig 6.6 shows that the regionalization process for Lesotho and Swaziland resulted in accepting each of the two countries as a single homogeneous region.
The analysis for the other countries resulted in identifying different homogeneous regions. The description of the physical regions included in the delineated regions are presented in Tables 6.4- 6.9.
The majority of the proposed regions satisfied the homogeneity test applied in the study. Table 6.10 shows that of the 42 proposed regions, 34 regions satisfied the Hosking and Wallis’s homogeneity test, while 41 regions satisfied the graphical plot test described in this study. Of the twelve regions proposed for Tanzania, only live passed the Hosking and Wallis test, while all the twelve passed the graphical plot test.
134
Sourhem A/Co FRIEND : IHP IV Technical docurneni.~ in ~vdrologv No IS- Table 6.4 Description of delineated homogeneous
region of Botswana Region Drainage Basins Physical Regions
Botl Zones 2, 3 and 4 Upper and middle reach tributaries to the Limpopo river system.
Zone 5 MakgadikgadVBoteti drainage basins
Figure 6. I Delineated hydrological homogeneous regions of Botswana
Chapter 6 : Regionol,f[oodfreyuenc~, ana(wis fbr Sourhem A/k!&
Table 6.5 Description of delineated homogeneous regions of Malawi.
Region Drainage Basins Physical Regions
Mall Zone 7 South Rukuru I North Rumphi river basins
Ma12 Zone 16 Nkhata Bay Lakeshore river basin Ma13 Zone 1
Zone 3 Zone 4 Zone 5 Zone 6 Zone 10 Zone 15
Shire (excluding Rue) river basin South West Lakeshore river basin Linthipe river basin
Bua river basin Dwangwa river basin
South East Lakeshore river basin Nkhota - Kota Lakeshore river basin
Ma14 Zone 2 Zone 8 Zone 9 Zone 11 Zone 14 Zone 17
Lake Chilwa river basin North Rukuru river basin Songwe/Lufira river system Lake Chiuta river basin Ruo river basin
Karonga Lakeshore river basin Malawi
Ma12 Zone 16
Ma13 Zone 1
Zone 3 Zone 4 Zone 5 Zone 6 Zone 10 Zone 15
Ma14 Zone 2
Zone 0 Zone 9 Zone 11 Zone 14 Zone 17
Figure 6.2 Delineated hydrological homogeneous regions of Malawi
135
Table 6.6 Description ofdelineated homogeneous regions of Namibia.
Table 6.7 Description of delineated homogeneous regions of Zimbabwe.
Region Drainage Basins Physical Regions Region Drainage Basins Physical Regions
Naml Zone 2900 North coast Atlantic drainage basin.
Nam2 Zone 3000 Zone 400
South and Central Namib Orange River basin
Ziml Zone B
Zim2 Part of Zone A
Limpopo river basin
Makgadikgadi
Zambezi between Lake Kariba and Cuando confluence Nam3 Zone 3100 Auob and Nossob river basins
Nam4 Zones 2300, Zambezi, Kwando and Okavango 2400,250O river basins, respectively
Zone 2600 N.E. drainage to Botswana Zone 2800 Zone 2700 Etosha drainage basin
Zone 2800 Cunene river basin
Zone 2900 North coast Atlantic drainage
Namibia
Figure 6.3 Delineated hydrological homogeneous regions of Namibia
Zim3 Part of Zone A
Zim4 Zone C and of zone D
Zim5 Zone F and part of zone D and E
Zim6 Part of zone E
Tributaries to Lake Kariba
Tributaries between Cabora part Basa and Lake Kariba
Tributaries to Kabora Bassa Tributaries to river Mazowe
Save river basin
Luenha, Pungwe, Buzi and coastal rivers
Runde river basin
Figure 6.4 Delineated hydrological homogeneous regions of Zimbabwe
Table 6.8 Description of delineated homogeneous regions
of
Tanzania.Region Drainage Basins Physical Regions Region Drainage Basins Physical Regions Tan1 2K Bahi depression, Lake Manyara, Lake Natron and Masai steppe internal basins
Kikuletwa and Ruvu sub-catchments upstream nyumba ya Mungu dam Umba and Sigi rivers
Tributaries below the usambara including lower Pangani below gsn.
1DlO.
Pangani basinand associated minor coastal rivers excluding sub- catchments mentioned in R3 Wami river basin
Upper little Ruaha (Upstream station 1 KA2A)
Lower Great Ruaha (tributaries between station 1 ka5 and 1 k3A) Lukosi river
Tributaries upstream Ruvu and Ngerengere confluence Lower Ruvu, Rufiji, Matandu, Mavuji, Mbwemkuru, Lukuledi, Ruvuma and associated minor coastal rivers
Luwegu river, upper Matandu, Mavuji, Mbwemkuru, Lukuledi and Ruvuma rivers
,Kilombero River
Lake Nyasa drainage basin Lake Rukwa drainage basin Lake Tanganyika drainage basin Great Ruaha upstream station 1 KA5
Figure 6.5 Delineated hydrological homogeneous regions of Tanzania
Table 6.9 Description of delineated homogeneous regions of South Africa.
Drakensberg Highlands, South East part of Transvaal Bush Veld of the Drakensberg Highlands Eastern Low Veld
Figure 6.6 Delineated hydrological homogeneous regions of South Africa
137
Table 6.10 Results of the homogeneity test for the proposed regions according IO Hosking and graphical plot procedures.
Country Proposed Hosking Graphical Plot regions and Wallis
Passed Failed Passed Failed
Botswana 1 1 0 1 0
Lesotho 1 1 0 1 0
Swaziland 1 1 0 1 0
Malawi 4 4 0 4 0
Namibia 4 3 1 4 0
Zimbabwe 6 6 0 5 1
Tanzania 12 5 7 12 0
S. Africa 13 13 0 13 0
Total 42 34 8 41 1
6.4 Choosing statistical distributions of flood flows
6.4.1 Introduction
Many flood frequency distributions have been suggested for modelling flood flows, but none has been accepted universally. To achieve some degree of uniformity in the estimation of flood quantiles. some countries have agreed to adopt certain frequency distributions after canying out large scale studies of their flood data. For example, the Log Pearson type 3 distribution was recommended by U.S. Water Resources Council (1967) and Benson (1968) for use in the U.S.A., while the Natural Environmental Research Council (NERC, 1975) recommended the use of the General Extreme value (GEV) distribution in the U.K. and Ireland.
Rossi et a/. (1984) studied Italian flood series and recommended the use of the two component extreme value (TCEV) distribution in Italy. Similarly, the Institution of Engineers in Australia recommended the use of the Log Pearson type 3 in Australia. The Pearson type 3 was recommended for use for flood frequency analysis in China (MWR,1958).
Various studies on how to evaluate the suitability of selecting distributional alternatives for fitting flood flows in a region are reported in the literature. In this study the L- moment ratio diagram was applied as a descriptive ability test to search for a suitable frequency distribution to model
Various studies on how to evaluate the suitability of selecting distributional alternatives for fitting flood flows in a region are reported in the literature. In this study the L- moment ratio diagram was applied as a descriptive ability test to search for a suitable frequency distribution to model