Hydrology is the scientific study of the movement, distribution, and quality of water on Earth and other planets, including the water cycle, water resources and environmental watershed sustainability. Hydrology subdivides into surface water hydrology, groundwater hydrology (hydrogeology), and marine hydrology.
The estimation of design floods is necessary for the design of hydraulic structures and to quantify the risk of failure of the structures. To date there are only 22 major drainage regions in South Africa which are under 19 water management areas. The water management areas were set-up in October 1999 by the Government notice number 1160, the borders of water management areas lie nearly next to the divides between surface water catchments (Forestry, 2004)
With the recent floods in South Africa, such as those of February 2000 which occurred in the north-eastern part of South Africa, Zimbabwe and Mozambique, flooding in the Western Cape in 2005 and floods in the Free State and Eastern Cape in 2011, highlight the need to re-assess the risks associated with floods. Realistic design flood estimation, where the magnitude of a flood is associated with a level of risk (e.g. return period), is necessary in the planning, design and operation of hydraulic structures (e.g. bridges, culverts, dam spillways, drainage canals etc) for the preservation of human life and property (Rahman et al., 1998; Pegram and Parak, 2004; Reis and Stedinger, 2005).
Standard techniques for design flood estimation have been developed for most countries. These generally include statistical analyses of observed peak discharges and event modelling using rainfall-runoff techniques. Observed streamflow data are often not available at the site of interest and rainfall event-based methods have to be used. Reviews of approaches to design flood estimation are contained in Cordery and Pilgrim (2000) and Smithers and Schulze (2001).
A typical example of a quaternary catchment is catchment station number Q3H005 – Great-Fish River at Rietfontyn lat:32’05’90” Long 25’34’33″W51F. All the analysis, calculations as guided by engineering hyrological principles and calculations for these area will be noted within the report.
With South Africa ranked number 30th in the world in terms of water scarce countries The average annual rainfall is approximately 500mm which is 60% of the world average, and most streams exhibit low flows for most of the year.
1.2 Aim(s) and Objectives of the study
Q3H005 hydrological analysis assementsa and evaluations for surface hydrology in this catchment and estimate the peak design flood for a recurrence period of 1 in 20; 50; 100; 200; 1000 year design storm. The flood area is to be evaluated using the stipulated; Regional Flood Method, Unit Hydrogragh, Probabilistic Method, Muskinggum Flood Routing and PMF.
2.1. Regional Flood Method (RMF)
Most literature shows that flood estimation methods in South Africa are based on three general approaches: empirical, deterministic and probabilistic. The “quick” methods often used as checks are the regional maximum flood (RMF) and the rational formula (RF), which form part of the empirical and deterministic methods respectively. A database of annual flood peaks was used in a probabilistic approach to review these methods and to provide preliminary insight into their estimates of flood peaks. This paper examines the following: the relationship between floods and landscape; the estimation of the return period of the RMF; the use of ratios in scaling RMF flood peak estimates to flow rates of shorter return periods; the applicability of the modified rational formula (MRF); the examination of the relationship between scaling parameters and regional parameters. It turns out that the RMF is the best of all methods examined in this preliminary study (other than statistical) in estimating the 200-year flood peak at an ungauged location.
Note,Kovacs himself estimates the return period to be greater than 200 years (Kovacs, 1988), although he does not explicitly model their probability distribution. Where the representative period (N) of a flood was not known, Kovacs did not allow this to exceed 200 years and a provisional N value was estimated based on the assumption that the ratio of the 200-year peak to RMF, Q200/RMF was 0.65. Below there is a table from TRH 25, 1994 showing a flood estimation beyond 200 to 10000 years return period.
Ratio between T-year flood and 2-year flood (TRH 25, 1994)
T 2 10 20 50 100 200 1000 10000
QT/Q2 1 3.57 5.18 7.80 10.24 13.14 22.00 41.24
Table 1: Return period abstract TRH 25
2.2. Unit Methods
Unit hydrograph is a direct runoff hydrograph resulting from one unit (one mm or one cm) of constant intensity uniform rainfall occurring over the entire watershed. The concept of unit hydrograph is based on linear systems theory and follow the principles of superposition and proportionality. For example, if one mm of excess rainfall produces a direct runoff peak of 100 cfs then two mm of excess rainfall with produce a direct runoff of 2 x 100 = 200 cfs. Similarly if one mm of rainfall is followed by twomm of rainfall, the hydrographs from both rainfall pulses are simply added after accounting for the necessary time lag intensityHaarhoff & Cassa, (2009). The role of unit hydrograph in hydrology is to provide an estimate of direct runoff hydrograph resulting from given excess rainfall hyetograph. In order to use unit hydrograph as a tool for predicting direct runoff hydrograph, we first need to derive a unit hydrograph for a given watershed by Sherman in 1932, Davie (2008). With reference to SANRAL (2013), the Unit hydrograph method is appropriate for averagesized rural catchments ranging around between 15 and 5 000 square kilometres in sizeAccording to Houghton-Carr, 1999 as cited by Smithers, (2012), Unit hydrograph allows a combination of local data, simple to produce for any quaternary catchment and can be easily understood. Han (2010) outlines the Unit Hydrograph Method assumptions as follows:
The effective rainfall is consistently distributed over the whole catchment and the period.
Direct runoff process is linear in superposition and proportionality.
The rainfall runoff does not change with time.
2.3. Muskingum Flood Routing Method
the muskingum equation is frequently used for routing of floods in river channels. The Musking method for roting flood waves in rivers and channels has been widely used in applied hydrology, since it’s first use in connection with a flood control project in the Musking County of Ohio about fifty years ago. Since it’s development around 1934 by McCarty, the Muskingum method has also been a subject of many investigationss (Strupczewski, Napriorkowski & Dooge 2002). Flood routing can be described as a process of calculating outflow rates, reservoirs stages and storage volume from a stream channel once inflow and channel characteristics are known. The principle of routing is used for predicting the temporal and spatial distribution of hydrogragh, during the course of it’s travel through the various sections of a stream (Subramanya 2002)
220.127.116.11Alternative Rational Method
The Alternative Rational Method is an improved version of the standard rational method, SANRAL, (2013). The alternative rational method is applicable to storms of durationup to 6 hours whereby the modified recalibrated Hershfield equation is applied. The Alternative Rational Method is applicable to
18.104.22.168. Standard Design Flood Method
According to SANRAL (2013), the Standard Design Flood Method (SDF) was introduced to provide a uniform approach to flood calculations, the method is simple to use and robust and is applicable to estimation of flood return period of two to 200 years,. The method is based on the historical information that describes the flood frequency correlation; the data required for its application is the size of catchment area, length of the longest watercourse and thegradient of the watercourse and the basin in which the catchment is located(SANRAL, 2013). According to Haarhoff ; Cassa (2009) (Haarhoff ; Cassa, 2009) the longest time for the runoff to flow from a catchment area into a river channel towards the measuring point for the SDF method is measured in days rather than in hours or minutes.
The Standard Design Flood method adopt the calibrated discharge co-efficient for recurrence of 2 and 200 years recurrence in which they are based on the previous data determined for 29 drainage basins in South Africa , SANRAL, (2013).
22.214.171.124. Unit Hydrograph Method
The unit hydrograph is a watershed flow reaction to a unit (1 cm) of effective rainfall happening over a specified period. Aunit hydrograph is described as the graphical representation of surface runoff which is a result of the effective rainfall falling in a unit of a given period of storm such as one hour or a dayas stated by Sherman in 1932, Davie (2008). The unit hydrograph design flood estimation is based on the assumption that, the flood discharge is directly proportional to precipitation intensityHaarhoff ; Cassa, (2009). According to SANRAL (2013), the Unit hydrograph method is appropriate for averagesized rural catchments ranging around between 15 and 5 000 square kilometres in sizeAccording to Houghton-Carr, 1999 as cited by Smithers, (2012), Unit hydrograph allows a combination of local data, simple to produce for any quaternary catchment and can be easily understood. Han (2010) outlines the Unit Hydrograph Method assumptions as follows:
The effective rainfall is consistently distributed over the whole catchment and the period.
Direct runoff process is linear in superposition and proportionality.
The rainfall runoff does not change with time.
, SANRAL, (2013) statesthat statistical methods make use of historical information to establish the flood peak or what for a specified return period. The statical methods are restricted to catchment areas for which suitable flood records are obtainable, or for which historical data from neighbouring catchments aresimilar. These methods are precise and thereforevaluableforestimatingflood peaks for storm of long return periods and accurate historical data covering a long period are availableSANRAL, (2013). These methods lend themselves to extrapolation of data to estimate flood extents for longer recurrence intervals of storm, SANRAL, (2013).
Empirical Methods are applied in order to establish general regional parameters when peak flow rates and catchment characteristics are to be compared. Empirical methods depend on realistic of magnitude of the valuesattained using other methods of determining the flood magnitudes. These methods involve both experience and historical information or the results of the other flood design methods, SANRAL,( 2013).
DESCRIPTION OF STUDY AREA
3.1.1. Quaternary Catchment Selection
The hydrological assessment study is based on quaternary catchment C92B for the purpose of this project.According to WRC2005 and WRC90 studiesquaternary catchment C92B is approximately 1979 square kilometres large in size, without any areas occupied byforests and alien vegetation, within the quaternary catchment, there is 23.22 square kilometres of irrigated areas and 7.81 km2 areas of combined minor dams.
According to the Department of Water Affairs, this quaternary catchment is under primary catchment C and water management area number 10 (Lower Vaal) which is further separated into nine secondary catchments (C1-C9) where C92B is located under secondary catchment C9, also the secondary catchments are divided into twenty three tertiary catchments (C11- C92), of which C92B is positioned on tertiary catchment C92, with two quaternary catchments; C92A and C92C. According to Moodley, et al., (2009)lower Vaal water management area covers 133 354 square kilometres and the largest part of the water management area falls within the catchment of the Molopo River, a tributary of the Orange River.
The river which goes through the quaternary catchment C92B is the Vaal River that is gauged at the outlet of the catchment with stream gauge number C9H024, on the way to the outlet on the way to the outlet a Douglas Weir Dam is found which is one of the registered dams in South Africa as per and its spillway is gauged with gauge number C9R003.The flow in the Vaal River is perennial; this is as a result of great precipitation and large tributaries upstream(DWAF, (2004).Quaternary catchment C92B was selected in order to assess and analyse the hydrology of the catchment, and selected in order to estimate flood peak generated within the catchment, also to determine the flood probability in the catchment for the 50 and 100 year return period over 40 years.
3.1.2.Location of Study Area
The C92B quaternary catchment falls within the South East of the Lower Vaal Water Management Area (primary catchment C)which is situated in the north-western part of the country and boundary of Botswana and form part of the Orange River watercourse, Forestry, (2004). The lower Vaal water management area lies within the three provinces in South Africa which are; Northern Cape, Free State and North West (Moodley, et al., 2009).
The Douglas town is the only closest town that is near the C92B quaternary catchment at about 35km which lies on boundary of quaternary catchment of C92C. The quaternary catchment lies around about 28°57?20.53?East and 23°46?6.15?South according to Global Positioning System of South Africa see Figure 1 belowshowing the location of quaternary catchment C92B indicated with the arrow, and the District municipality which governs the area is called the Z.F Mgcawu District Municipality, Pretorious ; Dennis, (2003).According toMiddleton ; Bailey, (2009)about 50% of the area consists ofendoreic local areas.
Figure 1: Map of South Africa indicating the locality of quaternary C92B
Source: http://www.dwa.gov.za;iwqs; gis_data: 07/12/2015
3.2. Topography and climatic features
According to(Forestry, 2004)approximately 60% of study area is a fairly gentle ground with 40% steeper. Due to the fairly flat terrain of the area this means that surface runoff takes time to reach the stream and low flood peaks are generated in the area. The studyarea hasan average temperature of approximately16?C and the precipitation is strongly seasonal occurring mostly in the summer months,DWA, (2004). The catchment receive approximately 300 to 400 mm of mean annual and generate the mean annual runoff of about 2.5-5 mm and mean annual evaporation of around about 1800-2200 mm, Middleton ; Bailey, (2009).
3.3. Vegetation and Geological Features
The most veld types that can be found in the quaternary catchment is around about 55% of false Karoo, more or less10% of Karoo and Karroid and around about 35% of Tropical bush and Savannah, Middleton ; Bailey, (2009). According WRC90 the area consists of around about 70% shallow sandy flat soil and approximately 30% of shallow sandy loam steep soil;this reveals that a great rainfall falling in. The geological features typically are in a state that around about 45% of the study area is dolomite and limestone, approximately more or less 40% of tillite is also found in the area and around about 15% of assemble tillite and shale is found, Middleton ; Bailey, (2009).
3.4. Land cover, Water usage and Land Use
According to Middleton ; Bailey, (2009), quaternary catchment C92B consistsof cultivated temporary commercial irrigation areas of more or less 25% of the area. The area is mostly dominated byfarming and agricultural activities without urban areas, Moodley, et al., (2009). According to WRC 2005 the aquifer initial storage of the catchment is sitting at 104.57 mm with 16.6 mm aquifer thickness and 8.89 % of groundwater evaporation.
4.1 .Data Collection ; Handling
The topographical map of the study area was compiled taking the following procedure:
Identification of quaternary catchment: The quaternary catchment C92B under water management area number 10 (Lower Vaal) was chosen using the Book of maps, Middleton ; Bailey, (2009)
Naming of maps in which the quaternary catchment covers in order to download the topographical maps referencing withHaarhoff ; Cassa, (2009). These maps were: 2823BC, 2823BD, 2823DA, 2823DB, 2823DC, 2823DD, 2824AC, 2824AD, 2824CA, 2824CB, 2824CC, 2824CD, 2923BA, 2923BB, 2924AA and 2924AB.
The above mentioned topographical maps were downloaded using Mad mappers, (2015) adopting a scale of 1:50 000and then combined into a project using Global mappers, (2015)
Importing primary, secondary, tertiary, quaternary catchments, rainfall stations, stream flowstations and evaporation stations shape files from Department of Water Affairs and Sanitation(2015)using Quantum Geographic Information system software. These shape files are files which wereavailable in the GIS format coverage.
The topographical maps from global mapper’s project were then uploaded to Quantum Geographic Information System software where the quaternary catchment was already delineated and coordinated.
4.1.2 Hydrological data of quaternary catchment C92B
The hydrological analysis undertaken as part of this study is primarily based on the hydrological information obtained from WRC90 and WRC2005 database, while land use areas were checked using the book of maps, Middleton & Bailey, (2009). The period considered for the analysis covered hydro- years 1920-2009.
126.96.36.199 Rainfall Data
In theWRC 90 study the Mean Annual Precipitation obtained by quaternary catchment C92B was sitting at 345mm during 1920-1989 hydro years according to WR90 and due to global warming the Mean Annual Precipitation obtained from WRC2005 was approximately 331mm during 1920-2009 hydro years. According to Department of Water Affairs; the rainfall zone for the area is rainfall zone C9C with 4 rainfall stations and still in operation. The rainfall data obtained from WRC90 was compared with the data obtained from WRC2005 which is to be used for the purpose of this project are tabled below
Table 1: Rainfall Stations data
Gauge No Station
Name Geographic Information
System Co-ordinates WR90
MAP(mm) WR 2005
288528 Tweefontein 28o48′ 23o48′ 336 345
288610 Salmonsfontein 28o40′ 23o51′ 341 365
289102 Schmidtsdrif 28o42′ 24o04′ 332 341
322329 Papkuil 28o29′ 23o41′ 371 331
Adapted from Midgley, et al., (1990)
188.8.131.52 Evaporation Data
The quaternary catchment consists of an American pan, gauge number C9E006, positioned at 29° 03?&, 23°46?S at Douglas station under evaporation zone 9B sitting with approximately 2412 mm Mean Annual Evaporation during 1976-1979 hydro-yearsMidgley, et al., (1990)appendix 3.1.According to WRC2005 it is stated that quaternary catchment C92B consists of the Symons pan which is under evaporation zone 7A with the Mean Annual Evaporation of about 2225 mm.
184.108.40.206 Surface Runoff
The study area(quaternaryC92B)has a perennial river flowing through it, called the Vaal River (Department of Water Affairs).Large volumes of runoff are observed to beprimarily from the Middle Vaal and the lesser runoff volumes originate from quaternary catchment,Moodley, et al., (2009). The Douglas weir dam at the bottom of the catchment is gauged with flow gauge number C9R003 positioned at 29° 02? 37?S and 23° 50? 11? E, covering an area of 193842 km2, full storage of the Douglas weir dam being 16.7 x 106 cubic metres according to 1958-2004 hydro years , Midgley, et al., (2005). The active stream flow gauge in the river is C9H024, Midgley, et al.,( 2005).
Table 2 : Runoff Data
COMPARISON OF WRC2005 MAR AGAINST WRC90
MAR (WR90) MAR (WR2005) Change in MAR
Net Gross Net Gross
x106 m3 x106m3 x106m3 x106m3
5 11.1 4.75 0 5
Adapted from, Midgley, et al., (2005)
4.2.1 Standard Design Flood Method
The Standard Design Flood Method was adopted in order to determine the Flood peak of the area under consideration). This method was preferred becauseit is robust and simple and is applicable to storms with 2-200 years of recurrence, SANRAL, (2013). Haarhoff & Cassa, (2009)&SANRAL, (2013)were used as a guide for the calculations.
Quaternary catchment C92B is located under SDF drainage basin number 8, South African Weather Station number 322 071 Danielskuil site according to figure 3.30, SANRAL, (2013). The topographical map 1:70 000is attached as appendix A with the catchment delineated using Quantum Geographic Information System according to Department of Water Affairs and Sanitation boundary. The catchment area was determined using the triangulation method according to Haarhoff & Cassa, (2009), see attached appendix A. The triangles were formed using the give and take method, using a scale of 1: 70 000. The perpendicular lines were developed for triangles forming right angled triangles. The total area determined using the method was 1979.210 km2. Although the catchment area according to Midgley, et al., (1990) and Midgley, et al., (2005) studies was found to be 1979.0 square kilometres, the determined area, 1979.210 square kilometres determined using triangulation method was adopted for calculations.
The main river in the study area(C92B) is the Vaal River with a total length of 75.7423 km which is the longest water course in the catchment and was determined using the Quantum Geographic Information System software with Google earth program as an alternative. The length was determined by clicking on the layer of rivers and zooming into group as it showed only the longest watercourse and then clicking on the measuring OTF and command measuring line in kilometres. Theelevation at 10% length of the longest watercourse was determined to be equivalent to999 m and at 85% length of the longest watercourse the elevation was found to be1007 m, these were determined on Googlepro earth program using a measuring OTF tool and measuring the path of a river in the catchment. The average slope was determined using the 1085 method as per, SANRAL, (2013) and was determined to be equivalent to0.1408%adopting the 1085 equation as follows:
Sav = H_(0.85 -H_0.10 )/(1000*0.75 L)
The time of concentration in hours was determined by applying the US Soil Conservation Service formula as per (SANRAL, 2013) and it was determined to be equal to 56.436hoursequivalent 3386.188minutes, the equation adapted from SANRAL,(2013) was as follows:
Tc = (0.87* L^2)/(1000 * S_av )^0.385
The time of concentration of 56.436 hours gave a point precipitation of 233.4mmby interpolation, the Hershfield equation was not valid since the time of concentration determined was greater than 24 hours (SANRAL, 2013). The MAP was interpolated between 2 days and 3 days for 1 in 100 year return period, using TR102: Daily precipitation table 5.2 fromHaarhoff & Cassa, (2009). The Areal Reduction Factor was determined to be equal to88. 044%by adopting the equation developed by Alexander as cited by Haarhoff & Cassa, (2009), the equation is as follows:
ARF = (90 000 – 12 800 ln A + 9830 ln t) 0.4
The Point precipitation was then reduced to 205. 495 mm by multiplying the interpolated value with the ARF determined in decimal form: Pit * ARF
Average rainfall Intensity over the catchment was determined to be equivalent to 3.6 mm/h.This was worked out by dividing the reduced point precipitation with the time of concentration: P_it/T_c
The Calibrated runoff co-efficient C2 (2 year return period) were read from table 3B.1,SANRAL(2013) equivalent to 5 and for a 100 year return period equal to 20, return period factor for s 100 year was equal to 2.33 read from table 3.13 (SANRAL, 2013)
Table 3: Return Period Factors
T 2 5 10 20 50 100 200
Yt(-) 0 0.84 1.28 1.64 2.05 2.33 2.58
The runoff coefficient determined for the catchment was equivalent to0.200by adopting the equation from (Haarhoff & Cassa, 2009):
Ct = C_2/100 + Y_T/2.33C_100/100-C_2/100
The Flood Peak was determined for the required return period of 100 years using the standard formula from (SANRAL, 2013): QT = (C*I* A)/3.6 in which the Peak flow was calculated to be equal to 400.35m3/s
4.2.2 Unit Hydrograph Method
In order to perform the calculations of Flood peak for a 1:100 year design storm for the chosen quaternary catchment (C92B) using the unit hydrograph method two books were adopted which were; Haarhoff & Cassa,( 2009) andSANRAL, (2013).
The size of thecatchment area adopted was as determined in the SDF method which was equivalent to 1979.210 km2. The length of the longest watercourse in the catchment (Vaal River) was equal to 75.742 kmas determined in the SDF method, and the average slope was 0.1408284%.
The veld type that quaternary catchment C92B fell under was determined to beveldt type 6as read from Haarhoff & Cassa, (2009)figure 3.6: generalized veld type zones in South Africa. This veld type consists of mostly the false Karoo vegetation according to Haarhoff & Cassa, (2009). The length to catchment centroid was found to be equivalent to 37.300 km; it was determined by isolating the catchment intosemi-full horizontally lines and dividing the horizontal line into half at an angle of 45º according toHaarhoff & Cassa, (2009).
The catchment index was determined in order to calculate the lag time, and it was determined to be equal to 7528.37241 adopting the equation as follows:
Index = (L*L_c)/?S
The lag co-efficient Ctand Kuwere read fromtable 1.6 (Haarhoff & Cassa, 2009)and they were
0.21 And 0.351correspondingly, the table is as shown below:
Table 4: Factors for appropriate veld type
zone Ct Ku
1 0.99 0.261
2 0.62 0.306
3 0.35 0.277
4 0.32 0.386
5 0.21 0.351
5A 0.53 0.488
6 0.19 0.265
7 0.19 0.315
8 0.19 0.367
9 0.13 0.321
Haarhoff & Cassa, (2009)
The Lag time was determined using the basin lag equation fromHaarhoff & Cassa, (2009) where it was found to be equivalent to 17.253 hours, the equation was as follows:
TL = Ct (L*L_c)/?S0.36
A peak discharge equivalent to32.016m3/s was determined adopting the standard peak discharge equation fromHaarhoff & Cassa, (2009).QT = C x I x A
Figure 2: Dimensionless unit hydrograph
Figure 3: Unit hydrograph for veld type 6
The natural hydrograph for veld type 6 was to be developed. The estimation of point intensity was the first step to achieve the results. The study area is described as the inland since it is very far from the ocean and the temperatures for the region are higher; therefore the regional factor formula for inland was adapted from (Haarhoff & Cassa, 2009) and it was determined for each and every hourly storm duration up to twenty four hours of storm, see attached tables for results.
Regional factor (inland) = 217.8/(1+4.164 x t)^0.8832
The MAP factor for each hourly storm was determined using the equation from (Haarhoff & Cassa, 2009)
MAP Factor = (18.79+0.17 x MAP )/100
Frequency factor for the return period was determines as shown in the table below
Table 5: Frequency factor for 100 year return period
RETURN PERIOD FREQUENCY FACTOR
Haarhoff & Cassa, (2009)
These factors were substituted to the point precipitation intensity method as follows, adapting equation fromHaarhoff & Cassa, (2009)
I = regional factor x MAP factor x frequency factor
The point intensity was further distributed over the whole area by multiplying the values with the Areal Reduction Factor. The Areal Reduction Factor values were read off from figure 3.21 of SANRAL, (2013) for medium to large areas.The Areal Intensity were determined up to 24 hours, see attached table.
In order to develop the natural hydrograph for the veld type 6, the storm duration of 24 hours was assumed based on the lag time of approximately 16 hours to determine the design flood peak for over 100 years. The unit hydrograph was manipulated for over 24 hour storm duration in order to obtain flood peak and it occurred at 11th hour storm with the maximum value of 1416.86m3/s.
4.2.3 Probabilistic Hydrological Analysis Method
According to the project briefing, probabilistic technique was to be usedtoanalyses a flood event for over 40 years for a 1 in 50 year return period and 1 in 100 year return period for quaternary catchment C92B. The analysis was carried out with referencing to Haarhoff & Cassa, (2009).A historical data for the stream flow gauge C92H024was exported from (DWA, 2015) for over 21 years due to the lack of data availability and unreliable data from the stream flow gauge.The raw and modified data is attached as an appendindix. In order to determine rank (m) the data points were ranked accordingly and then sorted from maximum to minimum values, see attachedappendix. The total number of data points was equivalent to 21, N.
A return period was determined for each data point using Cunane equation as it is recommended for practical use Haarhoff & Cassa, (2009). The constants of Cunane equation were extracted from table 8.1: a = 1, b = 0.20, c = 1, d = -0.40Haarhoff & Cassa, (2009). The return periods determined for each data points were reduced to log numbers (log T) and the mean annual peak flows were reduced to log numbers in order to plot them on a logarithmic graph paper see attached figure 4 below. The best fit line was developed along the points in order extrapolate the value of the 50 year and 100 year return periods, for 50 year the flood peak was determined to be equivalent to 766.391 cubic metres per second and 943.886 cubic metres per second for a 100 year return period.
Figure 4: Probabilistic of Flood Peak over 21 years
5. RESULTS AND DISCUSSION
The triangulation method adopted in this project for determining the area of the catchment was challenging as its results were not exactly corresponding to the values of the previous studies carried out (WRC 1990, and WRC2005). The level of accuracy for this method is low due to human errors, thereforeforpractical use adopting design software would be recommended.
The results obtained in the design flood estimation methods determined contradict, for this study the Standard Design Flood method results were seemingly the flood peak when comparing with the Unit hydrograph and the Probabilistic analysis. According toSmithers, (2012), it is vital that the design flood estimation for different methods when applied should come-up with similar results alternatively comparable results must be obtained even if same flood estimation method is applied by different hydrologists. In South Africa when estimating for the consistent design flood, the most important constraint is the design storm, stated by Alexander 2009 as cited by Smithers, (2012)
The limitations and assumptions made when these flood estimation methods were developed are the major influence on the results obtained as their assumptions are different. Different authors came up with various ideas about the assumptions made when developing these methods. According to Van Bladeren, (2005) as cited by Smithers, (2012), the SDF method may give unreliable values due to the statistics information used when the SDF method was developed therefore other methods must be applied as to compare the reliability of the SDF method. For this study the Alternative Rational method should have been carried out so as to check the results of the SDF. According to Smithers and Schulze, (2003) as cited by Smithers,(2013), the SDF method assumptions are made to overcome errors made when determining the flood peak
Figure 5: Comparison of calculated flood peak flows
Based on the results generated by the different methods, it is clear that the catchment characteristics and climatic changes have an effect on the surface runoff, therefore affecting the design flood peak. For quaternary catchment C92B, the topographical characteristics had an influence on the design flood peak and as a result the time of concentration was longer and also the lag time was also longer. The unit hydrograph method was not easy to work with for this study and that could result in many errors in determining the values.According to the SDF results quaternary catchment C92B is not under threat of flood, this also goes for the Unit hydrograph method results and the probabilistic method .
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