Hydrological and hydrodynamic modelling - Enviro Dynamics Namibia

Report on the Hydrologicaland Hydraulic model17/02/2012

Table of Contents1. INTRODUCTION ................................................................................................................... 11.1 THE ASSIGNMENT ........................................................................................................... 11.2 AIM OF THE STUDY ......................................................................................................... 11.3 STRUCTURE OF THE REPORT ....................................................................................... 12. SOFTWARE USED ............................................................................................................... 22.1 HYDROLOGICAL MODEL ........................................................................................................ 22.2 HYDRODYNAMIC MODEL ....................................................................................................... 23. DATA USED .......................................................................................................................... 43.1 TOPOGRAPHICAL DATA ......................................................................................................... 43.2 RAINFALL DATA .................................................................................................................. 103.3 EVAPORATION ................................................................................................................... 143.4 CALIBRATION DATA ........................................................................................................... 144. EXISTING SITUATION ....................................................................................................... 204.1 HYDROLOGY ...................................................................................................................... 204.1.1 Subcatchment definition ......................................................................................... 204.1.2 Input data ................................................................................................................ 224.1.3 Output data ............................................................................................................. 244.1.4 Estimation of flood return periods ........................................................................... 244.2 HYDRAULICS...................................................................................................................... 294.2.1 Model principles ...................................................................................................... 294.2.2 Boundary conditions ............................................................................................... 354.2.3 Computational details ............................................................................................. 374.2.4 Calibration of the model .......................................................................................... 385. SCENARIO .......................................................................................................................... 405.1 MODEL MODIFICATIONS ...................................................................................................... 405.2 RESULTS ........................................................................................................................... 456. REFERENCES .................................................................................................................... 51AnnexesANNEX A THE PDM HYDROLOGICAL MODEL ................................................... 1A.1 INTRODUCTION .................................................................................................................... 2A.2 PROBABILITY-DISTRIBUTED SOIL MOISTURE STORE ................................................................ 3A.3 REFERENCES ...................................................................................................................... 8ANNEX B MAPS ..................................................................................................... 9I/RA/12077/11.186/TGOversion 1.0 - 17/02/12I

B.1 MODEL SCHEME MAPS ........................................................................................................ 10B.2 CALIBRATION MAP .............................................................................................................. 11B.3 FLOOD FREQUENCY MAPS .................................................................................................. 12B.4 FLOOD MAPS ..................................................................................................................... 13I/RA/12077/11.186/TGOversion 1.0 - 17/02/12II

List of TablesTABLE 3-1: AVAILABLE RAINFALL DATA. ALL DATA ARE DAILY VALUES. CPC IS THE RAINFALLESTIMATION FROM THE CPC/FAMINE EARLY WARNING SYSTEM. .............................................. 10TABLE 4-1: SUBCATCHMENT AREAS. ............................................................................................... 20TABLE 4-2: MODEL PARAMETER VALUES USED. ............................................................................... 24TABLE 4-3: MEAN ANNUAL RAINFALL DEPTH AT NAMIBIAN AND ANGOLAN CLIMATE STATIONS. ............ 25TABLE 4-4: CORRECTION FACTORS FOR THE SUBCATCHMENTS IN THE HYDROLOGICAL MODEL,BASED ON THE CPC/FEWS SATELLITE DATA........................................................................... 26TABLE 4-5: VALUES OF THE PARAMETERS DESCRIBING THE EXTREME VALUE DISTRIBUTION OFTHE CATCHMENT TOTAL FLOW. ................................................................................................ 28TABLE 5-1: BOTTOM WIDTH OF THE OSHANA CONNECTIONS. ............................................................ 40TABLE 5-2: ORIFICE MODEL PARAMETER VALUES. ............................................................................ 41TABLE 5-3: PEAK INTENSITIES, DERIVED FROM THE DRAINAGE MANUAL, FOR A STORM DURATIONOF 6 H. .................................................................................................................................. 45TABLE 5-4: SIMULATED EVENTS AND THEIR ESTIMATED RETURN PERIOD. .......................................... 45TABLE 5-5: SIMULATED PEAK FLOWS DURING THE GIVEN EVENTS, AT THE DIFFERENT OSHANAS,AT THE OSHANA CONNECTIONS INLET. ..................................................................................... 46I/RA/12077/11.186/TGOversion 1.0 - 17/02/12III

List of figuresFIGURE 3-1: DIGITAL TERRAIN MODEL FROM SRTM DATA, WITH A SPATIAL RESOLUTION OF3” X 3”. THE COLOURS RANGE FROM 1000 MAMSL (GREEN) TO 2100 MAMSL (RED). THESCALE BAR REPRESENTS A DISTANCE OF 200 KM. ...................................................................... 5FIGURE 3-2: LOCAL DIGITAL TERRAIN MODEL, WITH A SPATIAL RESOLUTION OF 5 M X 5 M. THECOLOURS RANGE FROM 1086 MAMSL (GREEN) TO 1102 MAMSL (RED). ....................................... 6FIGURE 3-3: DTM OF THE KHOMAS REGION, WITH A SPATIAL RESOLUTION OF 50 M X 50 M. THECOLOURS OF THE REGIONAL DTM RANGE FROM 1086 MAMSL (GREEN) TO 1170 MAMSL(RED), THE COLOURS OF THE LOCAL DTM RANGE FROM 1086 MAMSL (GREEN) TO1102 MAMSL (RED). THE BLACK LINE REPRESENTS THE NAMIBIAN-ANGOLAN BORDER. ................ 7FIGURE 3-4: LONGITUDINAL PROFILE ALONG A TRANSECT CROSSING THE BORDER OF THEREGIONAL AND LOCAL DTM, SHOWING THE DIFFERENCE IN GROUND LEVEL. ................................ 8FIGURE 3-5: MERGED DTM, AT A SPATIAL RESOLUTION OF 5 M X 5 M. ............................................... 9FIGURE 3-6: CUMULATIVE RAINFALL DEPTH, FROM NOVEMBER 2000 TILL NOVEMBER 2011. ............. 11FIGURE 3-7: LOCATION OF THE AVAILABLE METEOROLOGICAL STATIONS. THE SHADED AREA INTHE NORTH OF NAMIBIA AND SOUTH OF ANGOLA REPRESENTS THE CATCHMENTGENERATING RUNOFF TO THE PROJECT AREA. ......................................................................... 12FIGURE 3-8: CPC/FEWS DAILY ESTIMATE OF FEBRUARY 21, 2011. THE DARKER SHADE OFBLUE CORRESPONDS TO A RAINFALL DEPTH OF 25 MM, THE RED SHADE WITH 62.5 MM. THESHADED AREA IN THE NORTH OF NAMIBIA AND SOUTH OF ANGOLA REPRESENTS THECATCHMENT GENERATING RUNOFF TO THE PROJECT AREA. ...................................................... 13FIGURE 3-9: AVERAGE RATES OF EVAPORATION PER YEAR IN NAMIBIA. ............................................ 14FIGURE 3-10: MEASURED WATER LEVELS AT THE GIVEN LOCATIONS, DURING THE EVENT OF 2011(SOURCE: MAWF). ................................................................................................................ 15FIGURE 3-11: MEASURED WATER LEVELS DURING THE EVENTS OF 2010 AND 2011 AT OSHAKATI(SOURCE: MAWF). ................................................................................................................ 16FIGURE 3-12: SPOT5 DATA (PROVIDED BY UNOSAT) ON MARCH 24, 2008. THE PROJECT AREAIS INDICATED AS WELL. ........................................................................................................... 17FIGURE 3-13: TERRASAR-X DATA (PROVIDED BY ZKI) ON MARCH 13, 2009. THE PROJECT AREAIS INDICATED AS WELL. ........................................................................................................... 18FIGURE 3-14: SPOT5 DATA ON APRIL 5, 2011. THE PROJECT AREA IS INDICATED AS WELL. .............. 19FIGURE 4-1: SUBCATCHMENTS IN THE CUVELAI CATCHMENT. THE HORIZONTAL LINE IN THEMIDDLE REPRESENTS THE BORDER BETWEEN NAMIBIA AND ANGOLA (SOURCE:J.M. MENDELSOHN IN LIASON WITH THE HYDROLOGY DIVISION OF THE MINISTRY OFAGRICULTURE, WATER AND FORESTRY.). ............................................................................... 21FIGURE 4-2: OVERVIEW OF THE SUBCATCHMENTS IN THE HYDROLOGICAL MODEL. THETOPOGRAPHICAL SCALE COVERS A RANGE FROM 1050 MAMSL (GREEN) TO 1650 MAMSL(RED). THE GREY SHADED AREA IN THE SOUTH IS THE PROJECT AREA. THE HORIZONTALDOTTED LINE REPRESENTS THE BORDER. ................................................................................ 22FIGURE 4-3: SIMULATED CATCHMENT TOTAL FLOW. THE FLOW IS CALCULATED AS 40% OF THESUM OF THE SUBFLOWS FROM SUBCATCHMENTS CALEMO-CUENDO EAST/WEST, MUI-CUVELAI-CUVELAI DELTA, CENTRAL DRAINAGE AND OSHANA ZONE EAST. THE CIRCLESINDICATE POT (PEAK OVER THRESHOLD) VALUES. ................................................................... 27FIGURE 4-4: CONDITIONAL WEIBULL DISTRIBUTION DESCRIBING THE POT VALUES DISTRIBUTION. ..... 29I/RA/12077/11.186/TGOversion 1.0 - 17/02/12IV

FIGURE 4-5: 'RIVER SECTION' MODEL ELEMENTS (GREEN), CONNECTED WITH ‘LINK’ MODELELEMENTS (BLUE). CROSS SECTION DATA ARE DERIVED FROM DTM DATA. ............................... 30FIGURE 4-6: 'SPILL UNIT' MODEL ELEMENTS (RED), CONNECTING ‘RIVER SECTION’ MODELELEMENTS VIA ‘SPILL LINK’ MODEL ELEMENTS (PINK). CROSS SECTION DATA ARE DERIVEDFROM DTM DATA. .................................................................................................................. 31FIGURE 4-7: 'ORIFICE' MODEL ELEMENT (PURPLE). INVERT LEVEL, SOFFIT LEVEL AND BORE AREAVALUES ARE DERIVED FROM TOPOGRAPHICAL DATA, AVAILABLE PLANS AERIALPHOTOGRAPHS AND TERRAIN VISITS. ....................................................................................... 32FIGURE 4-8: 'STORAGE AREA' MODEL ELEMENT, THE LEVEL-AREA RELATIONSHIP DERIVED FROMDTM DATA. ........................................................................................................................... 33FIGURE 4-9: MODEL LAY-OUT, AS IMPLEMENTED IN INFOWORKS RS. ............................................... 34FIGURE 4-10: UPSTREAM MODEL BOUNDARIES OF THE MAIN OSHANAS. ............................................ 35FIGURE 4-11: INFLOW TIME SERIES AT THE UPSTREAM MODEL BOUNDARIES. ..................................... 36FIGURE 4-12: FLOW-STAGE RELATIONSHIP AT THE DOWNSTREAM BOUNDARY OF THEHYDRODYNAMIC MODEL. ......................................................................................................... 37FIGURE 4-13: DETAIL OF THE CALIBRATION MAP, FOR THE EVENT OF 2011. ...................................... 38FIGURE 4-14: COMPARISON OF MEASURED AND SIMULATED WATER LEVELS. ..................................... 39FIGURE 5-1: EXAMPLE OF THE MODEL IMPLEMENTATION OF A OSHANA CONNECTION. THE BLACKLINE REPRESENTS THE DYKE ALIGNMENT. ................................................................................ 42FIGURE 5-2: MODEL LAY-OUT OF THE CHANNELS AS PROPOSED BY KNIGHT-PIÉSOLD. ....................... 43FIGURE 5-3: EXAMPLE OF A CROSS SECTION REPRESENTING OSHANA CONNECTION 4. ...................... 44FIGURE 5-4: FLOWS AT THE INFLOW OF THE OSHANAS IN THE OSHANA CONNECTIONS. ...................... 46FIGURE 5-5: DETAIL OF THE FLOOD FREQUENCY MAP OF THE CURRENT SITUATION. ........................... 47FIGURE 5-6: LONGITUDINAL PROFILE SHOWING THE WATER LEVEL ALONG THE DIVERSIONCHANNEL, FOR DIFFERENT RETURN PERIODS ........................................................................... 49FIGURE 6-1: THE PDM RAINFALL-RUNOFF MODEL. ............................................................................ 2FIGURE 6-2: DEFINITION DIAGRAMS FOR THE PROBABILITY-DISTRIBUTED INTERACTING STORAGECAPACITY COMPONENT. ............................................................................................................ 5FIGURE 6-3: THE STORAGE CAPACITY DISTRIBUTION FUNCTION USED TO CALCULATE BASINMOISTURE STORAGE, CRITICAL CAPACITY, AND DIRECT RUNOFF ACCORDING TO THEPROBABILITY-DISTRIBUTED INTERACTING STORAGE CAPACITY MODEL. ........................................ 6I/RA/12077/11.186/TGOversion 1.0 - 17/02/12V

1. INTRODUCTIONIn this chapter, an introduction to the project is given, as well as the aim of the hydrologicaland hydrodynamic study.1.1 THE ASSIGNMENTIn recent years, heavy floods occurred in central northern Namibia. In 2008 the floods wereconsidered the highest in living memory, but in 2009 flooding was more severe. In 2010, theregion experienced major flooding as well, although to a lesser extent as the previous years.With the latest flood, in 2011, flows, water levels and inundated areas exceeded by far thoseof 2008 and 2009 (Van Langenhove, 2011).The Town of Oshakati, the capital of the Oshana Region, is affected by these floods as well.Therefore, the Namibian Government, together with the Oshakati Town Council, haveapproved funding for all studies and works necessary to make Oshakati flooding free, and toallow further development of the town as foreseen in the Concept Master Plan. To makeOshakati flooding free, a dyke will be constructed, extending from the north of Okatana to thewest of Oshakati, diverting the main flows conveyed by the oshanas. BAR Namibia has beenselected, after a public tendering procedure, to lead the project. Within the project, IMDC willperform the hydrological and hydrodynamic study.1.2 AIM OF THE STUDYThe purpose of the hydrological and hydrodynamic study is to provide the design of the floodprotection measures with all necessary hydraulic information. For this, a detailedhydrodynamic model is developed, that allows to assess the impact regarding flooding ofconstructing a dyke around Oshakati. To deliver input to this hydrodynamic model, ahydrological model is developed as well. With the model, changes in water levels and flows inand around Oshakati can be calculated. Hence design variables, such as dyke crown height,culvert capacity and bridge width, can be determined.1.3 STRUCTURE OF THE REPORTThis first chapter gives an introduction to the project, and explains the aim of the hydrologicaland hydrodynamic study. Chapter 2 describes the software used to develop the hydrologicaland hydrodynamic model. In Chapter 3, the available data are discussed. In Chapter 4 theexisting situation is described. The governing hydrological conditions are explained, as well asthe model setup and validation. Chapter 5 describes the model setup of the situation with thedike around Oshakati, together with the results of the simulations. A reference list is availablein Chapter 6.I/RA/12077/11.186/TGO 1version 1.0 - 17/02/12

2. SOFTWARE USEDThis chapter describes the software used for modelling the hydrology and hydrodynamics ofthe project area. The general principle is explained, as well as the required input and thegenerated output.2.1 HYDROLOGICAL MODELThe hydrological model converts rainfall time series into a corresponding runoff response ofthe considered catchment. Due to the numerous and complex interactions in a runoffgeneratinghydrological system, the hydrology of a catchment is very often described througha simplification of the main components of the hydrological cycle, i.e. through a conceptualmodel. Different models have been developed over the years, with a different approach inconverting rainfall time series into runoff time series. In this study the Probability DistributedMoisture (PDM) model is used. It is developed and maintained by the UK Centre for Ecologyand Hydrology.The PDM model is a fairly general conceptual rainfall-runoff model which transforms rainfalland potential evaporation data to flow at the catchment outlet. Runoff production at a point inthe catchment is controlled by the absorption capacity of the soil to take up water; this can beconceptualised as a simple store with a given storage capacity. By considering that differentpoints in a catchment have differing storage capacities and that the spatial variation ofcapacity can be described by a probability distribution, it is possible to formulate a simplerunoff production model which integrates the point runoffs to yield the catchment surface runoffinto surface storage. Groundwater recharge from the soil moisture store passes intosubsurface storage. The outflow from surface and subsurface storages, together with anyfixed flow representing, say, compensation releases from reservoirs or constant abstractions,forms the model output (IWRS, 2011). More information on the PDM model can be found in6.Annex A.PDM and similar conceptual hydrological models (like NAM from Danish Hydraulic Institute)have been used all over the world. In particular IMDC used these models with success incountries like Belgium, Ecuador, Italy, Mali, Guinée Conakry and Ghana.2.2 HYDRODYNAMIC MODELThe hydrodynamic model is developed using InfoWorks RS v10.5.12 (Innovyze Ltd, UK),IWRS in short. The program can be used to model open channel flow and overbank flows inany network of channels. Any sensible looped or branched network can be modelled usingInfoWorks, which incorporates a wide range of hydraulic network objects including a variety ofconduit types, hydraulic structures, etc.IWRS computes flow depths and discharges by numerically solving the equations for shallowwater waves in open channels – the de Saint-Venant equations. The program can be used tosolve systems under both steady and unsteady flow conditions, either flows with a pronouncedI/RA/12077/11.186/TGO 2version 1.0 - 17/02/12

1D character or flows with no principal component, i.e. 2D-flow. For this, IWRS uses thegoverning hydraulic equations for each network object. These equations are inevitably acombination of empirical and theoretical equations, many of which are non-linear. The nonlinearequations are first linearised and the solution to the linear version of the problem is thenfound via matrix inversion. An iterative procedure is used to account for the non-linearities.The Preissmann four-point implicit finite difference scheme is employed for the channelequations and the matrix is inverted using a powerful sparse matrix solver (IWRS, 2011).Data regarding dimensions of river cross sections, bridges, culverts etc., as well as informationon the bed and construction material, are necessary to correctly describe the system. A digitalterrain model (DTM), combined with on-site topographical measurements of all relevanthydraulic structures, can provide these data. Next to the geometric boundaries of the entiresystem, the model requires hydraulic boundaries: flow time series in the most upstream part,and water level time series (or a flow-stage relationship) at the downstream ends. The flowtime series are generated by the hydrological model. As measured water levels downstream ofthe model do not exist, a flow-stage relationship will be used.I/RA/12077/11.186/TGO 3version 1.0 - 17/02/12

3. DATA USEDFollowing data will be discussed: topographical data (§3.1) rainfall data (§3.2) evaporation data (§3.3) data that can be used to calibrate the model on (§3.4)3.1 TOPOGRAPHICAL DATAThree digital terrain models (DTM) are available. A first, large scale DTM is available from thedata taken during the Shuttle Radar Topography Mission (in February 2000), an internationalresearch effort spearheaded by the U.S. National Geospatial Intelligence Agency (NGA) andthe U.S. National Aeronautics and Space Administration (NASA). The data were acquiredusing a combination of two radars. The SRTM DTM has a spatial resolution of 3” x 3”(longitude x latitude), which corresponds to a Cartesian resolution of ca. 90 m x 90 m. Figure3-1 shows the SRTM DTM. The subcatchments, relevant to describe the hydrology of theproject area, are indicated as well. More detailed information will be given below (§4.1.1).A second, local DTM with a higher resolution is available as well (Figure 3-2). The DTM has aspatial resolution of 5 m x 5 m, and was acquired using an airborne lidar in a measurementcampaign after the flood of 2009, performed by Southern Mapping Company. The accuracy inelevation is about 10 cm. Some remaining water bodies may not have been filtered out, butthis was not considered problematic during the model building. The same holds for the gaps indata, visible as white are as in Figure 3-2. Whenever necessary, interpolation of the data wasapplied.I/RA/12077/11.186/TGO 4version 1.0 - 17/02/12

Figure 3-1: Digital terrain model from SRTM data, with a spatial resolution of 3” x 3”. Thecolours range from 1000 mamsl (green) to 2100 mamsl (red). The scale bar represents adistance of 200 km.I/RA/12077/11.186/TGO 5version 1.0 - 17/02/12

Figure 3-2: Local digital terrain model, with a spatial resolution of 5 m x 5 m. The colours rangefrom 1086 mamsl (green) to 1102 mamsl (red).I/RA/12077/11.186/TGO 6version 1.0 - 17/02/12

Finally, a third DTM was made available, with a spatial resolution of 50 m x 50 m. This DTMcovers an intermediate scale between the two previous ground models. The DTM basicallycovers the Khomas region, and has been generated from aerial photographs acquired onJanuary 21 to March 2, 2007 from an altitude of 7500 m, performed by Swedesurvey. Figure3-3 shows this DTM, relative to the 5 m x 5 m.Figure 3-3: DTM of the Khomas region, with a spatial resolution of 50 m x 50 m. The colours ofthe regional DTM range from 1086 mamsl (green) to 1170 mamsl (red), the colours of the localDTM range from 1086 mamsl (green) to 1102 mamsl (red). The black line represents theNamibian-Angolan border.Since the original 5 m x 5 m DTM does not cover the entire area of interest for thehydrodynamic model – namely in the western part some data are missing– the local 5 m x 5 mand the regional 50 m x 50 m DTM are merged. An important issue to tackle was a differencein terrain level between the two data sets of 1.20 m, on average, at the border of the localDTM, probably caused by the use of two different reference levels, as can be seen in theprofile in Figure 3-4. The problem was accounted for by adding 1.20 m to the z-values of theregional DTM, as the levels of the local DTM, when comparing them to the additionaltopographic measurements, proved to be correct.The result of the merging operation can be seen in Figure 3-5. During the merging, theregional DTM was resampled on a 5 m x 5 m resolution 1 . Only the area necessary for thehydrodynamic modelling was incorporated in the merging, to limit data processing time.1 It has to be noticed that this operation does not add any accuracy to this part of the DTM. The operationwas necessary for software purposes.I/RA/12077/11.186/TGO 7version 1.0 - 17/02/12

Figure 3-4: Longitudinal profile along a transect crossing the border of the regional and localDTM, showing the difference in ground level.I/RA/12077/11.186/TGO 8version 1.0 - 17/02/12

Figure 3-5: Merged DTM, at a spatial resolution of 5 m x 5 m.I/RA/12077/11.186/TGO 9version 1.0 - 17/02/12

3.2 RAINFALL DATADaily rainfall measurements were delivered by the Namibia Meteorological Services, and thisfor meteorological stations in Windhoek, Ondangua (two time series available), Oshakati,Okatana and Tsumeb. Table 3-1 gives an overview of these stations, together with the timeperiod of available data.Table 3-1: Available rainfall data. All data are daily values. CPC is the rainfall estimation fromthe CPC/Famine Early Warning System.Station ID Name Start Stop- Windhoek 01/01/1913 31/08/20111200866A Ondangua 01/07/1913 31/12/20031200834X Ondangua Met. 20/03/2003 31/05/20111200375A Oshakati 01/03/1967 31/01/199312003759 Okatana 01/01/1999 31/12/200910553743 Tsumeb 01/01/1985 31/12/2009- CPC 30/10/2000 07/12/2011Figure 3-7 shows the location of the stations relative to the project area. It is clear thatespecially the rainfall station at Windhoek is not very representative for the rainfall over theconsidered subcatchments. On the other hand it holds the longest record of daily data, startingon January 1, 1913 2 . Moreover, it is the only station without interruptions. These two aspectsare highly useful when return periods have to be estimated. The other stations are closer tothe subcatchments.Because of the poor coverage of the above mentioned stations, additional rainfall data isimperative. For this, data based on satellite measurements will be used as well. The data aremade freely available by the Climate Prediction Center of the National Oceanic andAtmospheric Administration (CPC/NOAA) of the USA, and are referred to as the ‘CPC/FamineEarly Warning System (FEWS) Daily Estimates’ (CPC, 2011).The data exists from rainfall estimations (RFE), based on four types of input data, i.e. threesatellite sources and ground data: i) daily GTS (Global Telecommunications System) raingauge data for up to 1000 stations ii) AMSU (Advanced Microwave Sounding Unit) satelliteprecipitation estimates up to four times per day iii) SSM/I (Special Sensor Microwave/Imager)satellite rainfall estimates up to four times per day iv) GPI (GOES Precipitation Index) cloud-2 For Tsumeb also rainfall data are available from 1913 but only on the monthly basis.I/RA/12077/11.186/TGO 10version 1.0 - 17/02/12

top IR temperature precipitation estimates on a half-hour basis. The three satellite estimatesare first combined linearly using predetermined weighting coefficients, then they are mergedwith the station data to determine the final rainfall estimation. More information regarding theCPC/FEWS Daily Estimates can be found in CPC (2011).The CPC/FEWS data are available for the entire African continent, in a resolution of 0.1° x 0.1°(longitude x latitude). Using GIS and custom made data processing tools, a catchmentaveraged daily rainfall depth from the covering pixels of each subcatchment is calculated, andthis for the entire available time period, resulting in a rainfall time series for eachsubcatchment. A validation was performed in which the pixel values of the CPC/FEWS data,corresponding to the gauges from Table 3-1, were compared with the gauge data. From thevalidation results (Figure 3-6), the CPC/FEWS data can be found to be suitable for thehydrological modelling.Figure 3-6: Cumulative rainfall depth, from November 2000 till November 2011.Figure 3-8 depicts an example of an CPC/FEWS image containing daily rainfall estimates, onFebruary 21, 2011. As can be seen in the figure, southern Angola experienced heavy rainfallthat day. Developed storm cells are clearly visible.I/RA/12077/11.186/TGO 11version 1.0 - 17/02/12

Figure 3-7: Location of the available meteorological stations. The shaded area in the north ofNamibia and south of Angola represents the catchment generating runoff to the project area.I/RA/12077/11.186/TGO 12version 1.0 - 17/02/12

Figure 3-8: CPC/FEWS Daily estimate of February 21, 2011. The darker shade of bluecorresponds to a rainfall depth of 25 mm, the red shade with 62.5 mm. The shaded area in thenorth of Namibia and south of Angola represents the catchment generating runoff to theproject area.I/RA/12077/11.186/TGO 13version 1.0 - 17/02/12

3.3 EVAPORATIONNo measured time series of evaporation are available for this study. However the evaporationprocess plays an important role in the hydrological cycle, especially in semi-arid and aridclimates, as is the case in Namibia. In Figure 3-9 it can be seen that, on average, the potentialevaporation is 2800-3000 mm per year for Oshakati. Since the average annual rainfall depth inOndangua, near Oshakati, is about 490 mm (Namibia Meteorological Service, 2011), it is clearthat it will be important to take evaporation into account in the hydrological modelling.Figure 3-9: Average rates of evaporation per year in Namibia 3 .3.4 CALIBRATION DATAIn principle, model calibration and validation is performed on an as long as possible timeseries of measured water levels and flows. However, for this study very few time series areavailable.Water levels were measured by the Ministry of Agriculture, Water and Forestry (MAWF).during the floods of 2010 and 2011, at Okatana bridge and in Oshakati as well as upstream ofOkatana (Engela, Shanalumono, …). Figure 3-10 shows measured water levels at Okatana,as well as Engela and Shanalumono, during the flood event of 2011. The last two locations3 Data source: Atlas of Namibia Project, 2002, Directorate of Environmental Affairs, Ministry ofEnvironment and Tourism, http://www.met.gov.na (2003).I/RA/12077/11.186/TGO 14version 1.0 - 17/02/12

are situated about 40 km more upstream, near the Angolan border. Since it will not bepossible to incorporate such large distance into the hydraulic model – due to softwarelimitations –, their measurement data cannot be directly used for validation. However the datado give valuable information regarding the concentration time of the peak, which is one of theparameters of the hydrological model.Figure 3-10: Measured water levels at the given locations, during the event of 2011 (source:MAWF).Figure 3-11 depicts the measured water levels at Oshakati, for the flood events of 2010 and2011. .The data are expressed in relative quantities, i.e. relative to the local ground level.These time series are an average of the water levels at Sky Bridge and Okanjegedi bridge.They will be referenced to mamsl.I/RA/12077/11.186/TGO 15version 1.0 - 17/02/12

Figure 3-11: Measured water levels during the events of 2010 and 2011 at Oshakati (source:MAWF).Next to the time series of measured water levels, satellite data are available as well, for theflood events of 2008, 2009 and 2011. For the event of 2008, these are SPOT5 data taken onMarch 24, 2008. The map is produced by the United Nations Operational Satellite ApplicationsProgram (UNOSAT) of the UN Institute for Training and Research (UNITAR). UNOSATprovides satellite imagery and related geographic information to UN humanitarian anddevelopment agencies and their implementing partners. The data is available at no cost. Thedata can be seen in Figure 3-12.I/RA/12077/11.186/TGO 16version 1.0 - 17/02/12

Figure 3-12: SPOT5 data (provided by UNOSAT) on March 24, 2008. The project area isindicated as well.I/RA/12077/11.186/TGO 17version 1.0 - 17/02/12

For the event of 2009, a map based on TerraSAR-X data, produced by the German Center forSatellite Based Crisis Information (ZKI), is available for March 13, 2009. The ZKI presents aservice of the German Remote Sensing Data Center (DFD) of the German Aerospace Center(DLR). It provides a 24/7 service for the rapid provision, processing and analysis of satelliteimagery during natural and environmental disasters, for humanitarian relief activities and civilsecurity issues worldwide. The resulting satellite based information products are provided torelief organisations and public authorities and are also freely available on the ZKI website. Themap is depicted in Figure 3-13. It covers a much smaller area than the 2008 data.Figure 3-13: TerraSAR-X data (provided by ZKI) on March 13, 2009. The project area isindicated as well.I/RA/12077/11.186/TGO 18version 1.0 - 17/02/12

The flood event of 2011 is captured with the SPOT5 satellite as well, and this for April 5, 2011.Figure 3-14 shows the image.Figure 3-14: SPOT5 data on April 5, 2011. The project area is indicated as well.I/RA/12077/11.186/TGO 19version 1.0 - 17/02/12

4. EXISTING SITUATION4.1 HYDROLOGY4.1.1 Subcatchment definitionThe first step in modelling the hydrology is the delineation of the catchments that generaterunoff flowing to the project area. This delineation is done based on existing hydrologicalstudies (UWP, 2009; Van Langenhove, 2011; Knight, 2011). Figure 4-1 shows a map of thesubcatchments in the Cuvelai catchment, situated in the border region of Namibia and Angola,as compiled by J.M. Mendelsohn, in liason with the Hydrology Division of the Ministry ofAgriculture, Water and Forestry.Flow transported through the project area during floods originates from rainfall runoff, both thedelayed flow coming from the upstream Angolan parts of the catchments and flow from localrainfall. Therefore it is necessary to consider the entire Calemo-Cuendo, Mui, Cuvelai, CuvelaiDelta and Central Drainage subcatchments. Also part of the Oshana Zone should beincorporated into the model, because some streams reach the western border of the projectarea.Using the information depicted in Figure 4-1, as well as topographical data from the DTM andthe digitized lay-out of the main streams in the region, the above mentioned subcatchmentswere delineated using GIS tools. The result is shown in Figure 4-2. The Calemo-Cuendosubcatchment is split into an eastern and a western part, only for mathematical reasons. Alsoonly the part of the Oshana Zone contributing to flows in the project area is modelled; thesubdivision in an eastern and western part is because two different boundaries are defined inthe hydrodynamic model (§4.2). The area values of the modelled subcatchments are given inTable 4-1.Table 4-1: Subcatchment areas.SubcatchmentArea(km 2 )Calemo-Cuendo west 7124Calemo-Cuendo east 7490Mui-Cuvelai-Cuvelai Delta 8456Central Drainage 4563Oshana Zone east 1853Oshana Zone west 375I/RA/12077/11.186/TGO 20version 1.0 - 17/02/12

Figure 4-1: Subcatchments in the Cuvelai catchment. The horizontal line in the middlerepresents the border between Namibia and Angola (source: J.M. Mendelsohn in liason withthe Hydrology Division of the Ministry of Agriculture, Water and Forestry.).I/RA/12077/11.186/TGO 21version 1.0 - 17/02/12

Figure 4-2: Overview of the subcatchments in the hydrological model. The topographical scalecovers a range from 1050 mamsl (green) to 1650 mamsl (red). The grey shaded area in thesouth is the project area. The horizontal dotted line represents the border.4.1.2 Input dataThe PDM model requires two types of input in order to calculate runoff to the project area, i.c.rainfall and potential evaporation time series. The rainfall time series is composed from datafrom different sources, depending on coverage of the subcatchments and data availability(Table 3-1). Only the CPC satellite data cover the subcatchments, and hence these data aregiven highest priority in composing the rainfall time series. For each subcatchment, an areaaveraged daily rainfall estimation is calculated from all the covering pixels above thesubcatchment.I/RA/12077/11.186/TGO 22version 1.0 - 17/02/12

When no CPC satellite data are available, data from ground measurements are used. Whenusing ground data, the order in which the stations are used is: Okatana, Oshakati, OndanguaMet., Ondangua, Tsumeb, Windhoek. This is the so-called composed time series.As already stated in §3.3, no measured (potential) evaporation time series is available. Hencea time series has to be derived, based on the average potential evaporation rate per year (i.e.2800-3000 mm). One possibility is applying a uniform evaporation each day, at a rate of7.67 mm/day. This simple solution however does not take into account that evaporation islower during rainfall events. Therefore, a slightly more complex method is applied. On dayswith a rainfall depth of at least 2 mm, it is assumed that no evaporation occurs. When rainfalldepth is smaller than 2 mm for that day, evaporation is assumed to be 8.5 mm (this numbercorresponds to an average evaporation of 2800 mm/year).Next to the rainfall and evaporation input, the hydrological model requires values for severalparameters, such as soil storage capacity, reservoir time constants and infiltration rate togroundwater. Since the PDM is a lumped conceptual model, representing the hydrologicalprocesses in a simplified way on the scale of the entire subcatchment, these parameterscannot be measured in the field. However ranges of values are available depending on thephysical characteristics of the catchment.Generally, the parameter values are refined using time series of discharge measured at thecatchment outlet, in a trial-and-error procedure. In this calibration process, the model output iscompared with the discharge measurements, and when the output is considered to beadequately similar, the parameter set is accepted. If differences are too large, one or moreparameters are adjusted, and the process is repeated.In this study the hydrological model was calibrated together with the hydraulic model using thedata as mentioned previously (SPOT, water levels) and starting from parameter sets for similarsoils and climates. The calibrated values are shown in Table 4-2. More information on themodel parameters can be found in 6.Annex A.I/RA/12077/11.186/TGO 23version 1.0 - 17/02/12

Table 4-2: Model parameter values used.Model Parameter Unit ValueArea m 2 subcatchment dependentMin. storage capacity mm 100Max. storage capacity mm 1000Ground recharge time constant h/mm 5000Soil tension storage capacity mm 0.0Surface flow linear reservoir time constant 1 h 24Surface flow linear reservoir time constant 2 h subcatchment dependentBaseflow time constant (cubic storage) h/mm 2 5004.1.3 Output dataAfter defining rainfall, evaporation input and model parameters, the PDM model calculatestotal runoff to the catchment outlet, here defined just north of the Town of Oshakati. The totalflow is the sum of direct runoff and baseflow. The calculated flows serve as input to thehydrodynamic model, which simulates the flow entering the oshanas, flowing throughOshakati, further down south.4.1.4 Estimation of flood return periodsAs stated earlier, the Oshakati region has been affected by major flooding in recent years(Van Langenhove, 2011). Water levels, flows and inundated areas during the event of 2011exceeded by far those of 2008 and 2009, which were, in turn, extreme events as well.However, Van Langenhove (2011) also states that “future planning should be based on theprudent assumption that very high floods may appear any individual year, and that even 2011was not the highest possible event in this regard”. Therefore, an extreme value analysisshould be performed, allowing the estimation of the return period of historical events, as wellas the derivation of (synthetic) flows with higher return period.To perform an extreme value analysis a time series spanning a sufficiently long time period isessential. Since no long flow records are available, a time series is calculated using thehydrological model previously described, combined with a rainfall time series which spans atime period from 01/01/1913 till 31/08/2011.This long rainfall time series was constructed as follows:I/RA/12077/11.186/TGO 24version 1.0 - 17/02/12

For the period where CPC data is available (from 2000 on), these data are used.For the period before 2000 Namibian rainfall gauge data is used (a composed timeseries using for each day the data of the nearest station with measurements available,as described earlier) multiplied by a correction factor.An important issue is the fact that in the Angolan region of the catchment, on average, annualrainfall depths are much higher than in Windhoek and Ondangua, as indicated by the numbersin Table 4-3.Table 4-3: Mean annual rainfall depth at Namibian and Angolan climate stations.StationMean annual rainfall depth(mm)Windhoek 362Ondangua Met. 517Vila Pereir 637Cafu 743Mupa 743To cope with this issue, the composed time series is rescaled using a correction factor, basedon the comparison of the cumulative rainfall depth at the Namibian rainfall station and those ofthe catchment averaged CPC/FEWS satellite data, for the available period of the latter, i.c.from 30/10/2000 till 07/12/2011. The correction factor is calculated as the ratio of the slopes ofthe linear regression lines through the origin, of both cumulative rainfall depth time series. Thevalues of this correction factor, for each subcatchment in the hydrological model, are given inTable 4-4.I/RA/12077/11.186/TGO 25version 1.0 - 17/02/12

Table 4-4: Correction factors for the subcatchments in the hydrological model, based on theCPC/FEWS satellite data.SubcatchmentCorrection factor(-)Calemo-Cuendo east 1.42Calemo-Cuendo west 1.52Mui-Cuvelai-Cuvelai Delta 1.43Central Drainage 1.19Oshana zone east 1.09Oshana zone west 1.08Using these correction factors is a conservative approach, since they are based on acomparison of cumulative volumes. In Angola the mean annual rainfall depth is higher, but therainy season lasts longer as well. Hence correcting the Namibian rainfall time series, in whichthe rainy season is generally shorter, with the correction factors, results in more intense eventsthan generally occur in that part of the catchment. As a result the corresponding simulatedrunoff response will show a more peaked course, with higher maxima than could be expectedwhen ‘true’ Angolan rainfall would be used.After adjustment of the rainfall input, the hydrological model is used to simulate the full periodfrom 01/01/1913 till 31/08/2011. Then the flow time series of the subcatchments Calemo-Cuendo east/west, Mui-Cuvelai-Cuvelai Delta, Central Drainage and Oshana zone east aresummed. Oshana zone west is not incorporated, since its runoff does not directly flow towardsthe Town of Oshakati. The resulting runoff flow time series can be seen in Figure 4-3. It mustbe pointed out that, since no ‘true’ Angolan rainfall has been used, these results should not beconsidered as an estimation of historical events – except for the last 11 years – but as a runofftime series that is statistically representative for the considered period.Although the depicted flow time series is simulated using rainfall that is corrected using only11 years of concurrent rainfall between Namibian rainfall gauges and the CPC/FEWS satellitedata – meaning that the quantitative results might be biased –, they strongly suggest that theevent of 2011 was not the most extreme when considering all available data. It do was themost extreme event in the past 30 years, according to the simulated time series.I/RA/12077/11.186/TGO 26version 1.0 - 17/02/12

Figure 4-3: Simulated catchment total flow. The flow is calculated as 40% of the sum of thesubflows from subcatchments Calemo-Cuendo east/west, Mui-Cuvelai-Cuvelai Delta, CentralDrainage and Oshana zone east. The circles indicate POT (peak over threshold) values.In the figure, also peak-over-threshold (POT) values are indicated. POT values arehydrologically independent local maxima of the time series, that are used in fitting an extremevalue distribution. The threshold must be adequately low in order to consider a sufficientamount of POT values. On the other hand the used threshold must be high enough so onlyextreme events are considered. Here, the threshold is set to 160 m 3 /s. Independency of theevents is guaranteed by the use of an inter-event level and a time interval. In this study, theinter-event level is set to 0.37, which means that the lowest of two successive POT values ismultiplied with this factor. The minimum value between two successive POT values has to belower than this inter-event level. The above POT selection parameters result in a set of 30POT values, ranging from about 160 m 3 /s to about 700 m 3 /s.Using the well-proven EVA-tool (Extreme Value Analysis), developed by IMDC, an extremevalue distribution is calculated. The tool calculates a distribution function based on a maximumlikelihood fit on the POT values, and consecutively the RMSE. The procedure is repeatedseveral times using an increasing amount of POT values, resulting in graphs of the RMSE andthe distribution function parameters (including the confidence level) as a function of theamount of POT values used. These graphs aid in selecting an appropriate distributionfunction. More information on the EVA-tool can be found in IMDC (2011), while the reader isreferred to Coles (2001) (among others) for more information on extreme value statistics.The analysis using the EVA-tool results in the selection of the Conditional Weibull distributionas most suitable for the extreme events in the simulated catchment total flow time series. Thecumulative distribution function is described by two parameters, λ and τ:I/RA/12077/11.186/TGO 27version 1.0 - 17/02/12

In Equation (1), x is the catchment total flow, while u is the threshold which has to beexceeded by a POT value, for the distribution to be applicable. The flow X corresponding to agiven return period T can then be calculated using the following equation:(1)(2)with k the number of POT values that exceed the threshold u, and A the number of years inthe available time period. The values of the parameters described above can be found inTable 4-5.Table 4-5: Values of the parameters describing the extreme value distribution of thecatchment total flow.ParameterValueτ 1.0732λ 0.0039937u 161.7172A 98.9316k 28The resulting Conditional Weibull distribution can be seen in Figure 4-4. From the distribution itcan be derived that the (synthetic) event of 1917 has a return period of about 100 years, whilethe event of 2011 only has a return period of about 10 years. Therefore, the design of floodmitigating measures should at least be based on the event of 1917. The events of 2008 and2009 have a return period of approximately 5 years and 7 years respectively.It has to be noticed again that the use of a multiplication factor for the rainfall times seriesbefore 2000 is a conservative assumption. Hence the return period of the flood of 2011 mightbe higher and the flow of a 1 in 100 year event might be lower than calculated. However it isgood engineering practice when designing flood works to use conservative assumptions whendata availability is scarce.I/RA/12077/11.186/TGO 28version 1.0 - 17/02/12

Figure 4-4: Conditional Weibull distribution describing the POT values distribution.4.2 HYDRAULICS4.2.1 Model principlesA hydrodynamic model generally uses two main principles in solving for the water levels anddischarges, present in the modelled area: mass balance and momentum balance. Whendeveloping a hydrodynamic model, it is essential that the model structure comprises allpossible (water) volumes in the project area, since deviations in the volume balance are verydifficult, if not impossible, to compensate by calibrating parameters. This in contrast todeviations in the momentum balance, which can be compensated by calibrating the roughnessparameters. Therefore, the model is built using very wide ‘River Section’ model elementsalong the oshanas, to ensure that all volumes are accounted for, both in the current situationas in scenario analyses, ensuring a representation of flood maps as realistic as possible(Figure 4-5). Cross section data are derived from DTM data (local for most of the area andregional for the western part). River Sections are connected using ‘Link’ model elementsI/RA/12077/11.186/TGO 29version 1.0 - 17/02/12

Figure 4-5: 'River Section' model elements (green), connected with ‘Link’ model elements(blue). Cross section data are derived from DTM data.Friction losses – in the momentum balance – are calculated using the Manning formula:(3)in which S f is the head loss due to friction per unit length (-), A the wetted perimeter of theconsidered cross section (m 2 ), Q the flow through the section (m 3 /s), R the hydraulic radius(m), and n the Manning coefficient (sm -1/3 ). This last parameter is measure for the frictionresistance of the bed material, with high values corresponding to a higher bed roughness.The selection of a suitable Manning coefficient is an important step in the modelling process.Too high values will overestimate friction losses, resulting in too high water levels – at a givenflow. Similarly, a too low value for n will underestimate the occurring water levels. Literatureprovides guidelines and recommends values, depending on relevant parameters, such as bedsurface material, presence of vegetation and flow conditions (e.g. Chow, 1959;Koloseus, 1971). However, due to its empirical nature, n often is considered a calibrationparameter, allowing some alteration in order to obtain a higher degree of correspondencebetween measured and simulated variables.Chow (1959) gives values ranging from 0.025 to 0.033 sm -1/3 for “clean, straight, full stagenatural channels with no rifts or deep pools”, as well as values ranging from 0.025 to 0.035 sm -1/3 for “flood plains with short grass”. According to Koloseus (1971), a Manning coefficient of0.025 sm -1/3 corresponds to “natural channels with some growth and scattered cobbles inI/RA/12077/11.186/TGO 30version 1.0 - 17/02/12

ed”, while this is 0.030 sm -1/3 for “natural channels with extensive growth. For thehydrodynamic simulations, a Manning coefficient n = 0.030 sm -1/3 is used.Because no flow data are available to calibrate the Manning coefficient, a sensitivity analysiswas performed, which showed that there were only differences, on average, of 4 cm, with amaximum of 10 cm, for the event of 2011, when lowering the value from 0.030 sm -1/3 to0.025 sm -1/3 . This is due to the very wide sections of the oshanas, so with anincrease/decrease in n only a small increase/decrease in water level is required to obtain thesame value for S f, with the value for the flow remaining the same.Due to the very flat topography in the region, the interconnected oshanas can exchange flow,of which the direction depends on the governing hydraulic conditions in both oshanas. Theseinterconnections are modelled using ‘Spill Unit’ model elements, that enable lateral flow fromone oshana to the other (Figure 4-6). A Spill Unit model element uses the weir flow equation toestablish a head-discharge relationship. The location of these interconnections are determinedfrom the flood map of April 5, 2011. The connections are defined over a long enough distanceto assure a correct representation when scenarios are simulated.Figure 4-6: 'Spill unit' model elements (red), connecting ‘River Section’ model elements via‘Spill Link’ model elements (pink). Cross section data are derived from DTM data.Not only natural boundaries determine the flow in and around the Town of Oshakati, also manmadestructures, such as bridges crossing the oshanas or culverts underneath roads, have animportant effect on the governing hydraulic conditions. Hence it is imperative to incorporatethese structures into the model. For this, ‘Orifice’ model elements are used; these elementsrepresent the head loss occurring at an hydraulic structure, depending on the bore area, itsinvert and soffit level,. When conveying flow, bridges and culverts generate a backwater effect,causing the upstream water level to rise. If the structure’s capacity is insufficient, this rise canresult in water flowing over the bridge or road surface. To take this effect into account, eachI/RA/12077/11.186/TGO 31version 1.0 - 17/02/12

orifice is accompanied by a spill unit model element, accounting for water flow over thestructure, should this occur.An overview of the bridges and culverts present in the model can be seen on the modelscheme maps in 6.B.1.Figure 4-7: 'Orifice' model element (purple). Invert level, soffit level and bore area values arederived from topographical data, available plans aerial photographs and terrain visits.Finally, some areas are modelled using ‘Storage Area’ model elements. These modelelements are reservoirs with a stage-area relationship assigned to it, derived from DTM data.I/RA/12077/11.186/TGO 32version 1.0 - 17/02/12

Figure 4-8 shows the Storage Areas in the centre of Oshakati.Figure 4-8: 'Storage Area' model element, the level-area relationship derived from DTM data.I/RA/12077/11.186/TGO 33version 1.0 - 17/02/12

Figure 4-9: Model lay-out, as implemented in InfoWorks RS.I/RA/12077/11.186/TGO 34version 1.0 - 17/02/12

4.2.2 Boundary conditionsNext to the ‘geometric’ boundaries, as described above, the hydrodynamic model requireshydraulic boundaries as well. At the upstream end of the model, these boundary conditionsconsist of the catchment runoff, generated by the previously described hydrological model. Intotal there are 6 upstream boundaries defined, each one representing flow from thesubcatchments as defined in Figure 4-2. The flow from each subcatchment is divided over themost upstream River section model elements of each oshana in the project area, the weightsbased on the ratio of the oshana’s discharge to the sum of discharges. The discharges used indetermining the weights were calculated in the assumption of uniform flow and the Manningformula for friction losses. These weights have been refined in the calibration process (§4.2.4).Figure 4-10 shows the upstream model boundaries of the main oshanas, while Figure 4-11shows as an example the inflows of the event of 2011.23 4516Figure 4-10: Upstream model boundaries of the main oshanas.I/RA/12077/11.186/TGO 35version 1.0 - 17/02/12

Figure 4-11: Inflow time series at the upstream model boundaries.The downstream boundary in a hydrodynamic model generally is a time series of water levelsat that location. However such time series is not available in this study, and hence thedownstream boundary is defined using a calculated head-discharge relationship, in theassumption of normal flow. When applied to a location far enough downstream, this is a validassumption. The resulting flow-stage relationship can be seen in Figure 4-12.I/RA/12077/11.186/TGO 36version 1.0 - 17/02/12

Figure 4-12: Flow-stage relationship at the downstream boundary of the hydrodynamic model.4.2.3 Computational detailsThe simulations are run with a timestep Δt of 30 s, 60 s or 120 s, depending on the simulatedperiod. Up to 12 iterations are performed per timestep, to meet the convergence criterion.Depending on the length of the simulated time period, each run takes about 2-3 hours tocomplete.I/RA/12077/11.186/TGO 37version 1.0 - 17/02/12

4.2.4 Calibration of the modelGenerally, the hydrological and hydraulic models are calibrated separately using gauged flowand water level time series respectively. Parameter values are set so as to obtain an optimalcorrespondence between the measurements and the simulation results. Mostly, also theroughness parameters – often expressed using the Manning coefficient, as in this study – areadjusted.In this study however, calibration possibilities are limited, since no gauged flow time series areavailable, and only limited water level time series. Satellite imagery from flood extents do areavailable. Also, as stated already above, the sensitivity of the results towards changes in theManning coefficient is low. Therefore, the hydrological and hydrodynamic were calibratedtogether mainly by adjusting the parameters of PDM and the distribution of flow over theoshanas, and comparing the simulated flood extent of the event of 2011 with the flood extentvisible on the satellite image. The Manning coefficient was kept constant during this calibrationprocess.Figure 4-13 shows a detail of the final result, while Annex6.B.2 contains the full size map. Ingeneral the simulated flood extent corresponds well with the flood extent that can be noticedon the SPOT image.Figure 4-13: Detail of the calibration map, for the event of 2011.Next to the satellite image, the water level measurements at Oshakati are used (Figure3-11) in the calibration process. The available time series is an average of water levels atSky and Kanjengedi bridge. Figure 4-14 shows the final result. It should be noted that thereference level (in mamsl) of the measurements was estimated based on the distances withother reference points. Again, it can be stated that the model performs very well.I/RA/12077/11.186/TGO 38version 1.0 - 17/02/12

Figure 4-14: Comparison of measured and simulated water levels.I/RA/12077/11.186/TGO 39version 1.0 - 17/02/12

5. SCENARIO5.1 MODEL MODIFICATIONSThe hydrological model requires no alterations.The following components are implemented in the hydrodynamic model:DykeInner OshanasOshana ConnectionsNew bridgesDeepening/profiling OC4The oshana connections are implemented as River Sections, with a bottom width as given inTable 5-1. The dyke is situated at their left bank. The model automatically extends the sectiondata vertically, hence accounting for the presence of the dyke. Figure 5-1 shows an example.The southern part of the dyke is not incorporated in the model, to investigate the necessity of adyke in that location.Table 5-1: Bottom width of the oshana connections.Oshana connectionBottom width(m)OC1 200OC2 375OC3 375The channels as proposed by Knight-Piésold are implemented using River Sections as well.The cross sections are based on the design plans, with a bed level from 1091.5 mamsl at theupstream end and 1091 mamsl at the downstream end, resulting in a bed slope of 0.048‰.The bottom width is 60 m in the upstream and downstream branch, as well as in the easternbranch, going to Okanjengedi bridge. The western branch, going to Sky bridge, has a bottomwidth of 40 m. All channels have a side slope of 1:4. The inner island is not explicitly modelled,since the presence of this side branch has little to no hydraulic influence on the water level andflow along the main branches. The channels are connected with Strorage Areas using SpillUnits, all at a level of 1093.5 mamsl.The new and renovated bridges are modelled as orifices, with dimensions according to thedesign. For existing bridges (Sky and Okanjengedi), the current dimensions are keptunchanged, except for the invert level, which is lowered according to the bed level of the innerchannels at that location. The orifice model parameter values are given in Table 5-2.I/RA/12077/11.186/TGO 40version 1.0 - 17/02/12

Finally, OC4 is modelled, however not at its full bottom width initially provided. A bottom widthof 300 m is implemented. The alignment of OC4 is not always concurrent with the dykealignment, since it was attempted to make optimal use of the existing oshana profile.Figure 5-3 shows an example of a cross section along OC4.Table 5-2: Orifice model parameter values.BridgeInvert level(mamsl)Soffit level(mamsl)Bore area(m 2 )BR1 1094.488 1095.688 270BR2 1094.020 1095.220 324BR3 1093.400 1095.200 540BR4 1093.160 109.960 540Sky 1091.224 1096.600 75I/RA/12077/11.186/TGO 41version 1.0 - 17/02/12

BridgeInvert level(mamsl)Soffit level(mamsl)Bore area(m 2 )Okanjengedi 1091.179 1095.000 36Figure 5-1: Example of the model implementation of a oshana connection. The black linerepresents the dyke alignment.I/RA/12077/11.186/TGO 42version 1.0 - 17/02/12

Figure 5-2: Model lay-out of the channels as proposed by Knight-Piésold.I/RA/12077/11.186/TGO 43version 1.0 - 17/02/12

Figure 5-3: Example of a cross section representing oshana connection 4.To take the future increase in impervious area, resulting from the further development of theTown of Oshakati according to the Concept Master Plan, into account, additional hydrologicalboundaries are added inside the dike. These ‘Urban Boundary’ model elements can beregarded as less complex hydrological models, suitable to model urban catchments, whichcorrespond to fast runoff generation.The Urban Boundaries only use a rainfall time series as hydrological input. For thesimulations, the same composed rainfall series have been used, with the addition of a rainfallpeak corresponding to the return period of the simulated event. This peak intensity (andduration) is taken from the Drainage Manual (s.d.), and is given in Table 5-3. Six hourscorresponds to the concentration time of the ‘catchment’. To obtain a conservative approach,the shown intensities are applied to the Urban Boundaries for 6 hours, during the peak of themain flood event.I/RA/12077/11.186/TGO 44version 1.0 - 17/02/12

Table 5-3: Peak intensities, derived from the Drainage Manual, for a storm duration of 6 h.Return period (years)Intensity (mm/h)5 11.5110 14.1725 17.28100 24.285.2 RESULTSBoth the model of the current situation and the scenario are run for several events, which arelisted in Table 5-4, together with their estimated return period according to the extreme valuedistribution described in §4.1.4. From now on the events will be referred to with their returnperiod, since time period and return period cannot be related to each other for the eventsbefore 2000, due to the use of rainfall that is only statistically representative for the Angolancatchment, not historically.Table 5-4: Simulated events and their estimated return period.EventReturn period(years)2008 52011 101921 251917 100Table 5-5 shows the peak flows entering the oshana connections at the different oshanas. Anexplanation of the used codes in that table is given in Figure 5-4.I/RA/12077/11.186/TGO 45version 1.0 - 17/02/12

Table 5-5: Simulated peak flows during the given events, at the different oshanas, at theoshana connections inlet.Peak flow (m 3 /s)Return period(years)Oshana outlet 5 10 25 100Q 1 21 45 64 93Q 2 33 66 93 132Q 3 32 58 89 148Q 4 15 36 48 22Q 5 104 235 325 453Q 3Q 4Q 5Q 2Q 1Figure 5-4: Flows at the inflow of the oshanas in the oshana connections.Flood frequency maps are derived from the results. For this, the flood extent during the peakof an event is calculated using the peak water levels over the entire model, in conjunction withthe DTM data. Figure 5-5 shows a detail of the flood frequency map in the current situation.Annex6.B.3 contains the full size flood frequency maps of the current situation, and thesituation with the dyke around Oshakati.I/RA/12077/11.186/TGO 46version 1.0 - 17/02/12

Figure 5-5: Detail of the flood frequency map of the current situation.I/RA/12077/11.186/TGO 47version 1.0 - 17/02/12

To assess the water level rise along the diversion channel (the oshana connections), thelongitudinal profile in Figure 5-6 can be used.Figure 5-7 show a longitudinal velocity profile along the diversion channels (the oshanaconnections). The depicted values represent the cross sectional average velocity.I/RA/12077/11.186/TGO 48version 1.0 - 17/02/12

Figure 5-6: Longitudinal profile showing the water level along the diversion channel (oshana connections), for different return periodsI/RA/12077/11.186/TGO 49version 1.0 - 17/02/12

Figure 5-7: Longitudinal velocity profile along the diversion channel (oshana connections).I/RA/12077/11.186/TGO 50version 1.0 - 17/02/12

6. REFERENCESChow V.T. (1959). Open channel hydraulics. McGraw Hill Book Company, New York, USA.CPC (2011). CPC/Famine Early Warning System Daily Estimates. RFE2.0 data made freelyavailable by the Climate Prediction Center of the National Oceanic and AtmosphericAdministration of the USA. http://www.cpc.ncep.noaa.gov/products/fews/data.html,December 7, 2011.Coles S. (2001). An introduction to statistical modeling of extreme values. London: Springer-Verlag DC 2011. ISBN: 1852334592.DLR (2009). TerraSAR-X satellite data on the flood extent in the region of the project area, onMarch 13, 2009. http://www.zki.dlr.de.Drainage Manual (s.d.). Government of the Republic of Namibia – Ministry of Works,Transport and Communication – Department of Transport.IMDC (2011). Extreme Value Analysis software tool Manual.IWRS (2011). InfoWorks RS Documentation. Innovyze Ltd.Knight (2011). The rehabilitation and reconstruction of the Ongwediva and Okanjengedibridges both located on MR 92: Between Oshakati and Ongwediva – Volume 3: Book III– Hydrology Report. Study prepared for the Roads Authority of Namibia by KnightPiésold (Pty) Ltd, April 2011.Koloseus H.J. (1971). Rigid boundary hydraulics for steady flow. In Shen H.W. (Ed.), RiverMechanics, Vol. I, Fort Collins, Colorado, USA.Namibia Meteorological Service (2011). Namibia’s long-term climate statistics for specifiedplaces. http://www.meteona.com/index.php/climate/climatological-normals.UNOSAT (2008). SPOT5 satellite data on the flood extent in the region of the project area, onMarch 24, 2008. http://www.unitar.org/unosat.UWP (2009). Investigation of Technical and Financial Feasibility of Flood Mitigation Measuresin the Oshakati-Ongwediva Area. Study prepared for the Ministry of Regional and LocalGovernment, Housing and Rural Development by UWP Consulting (Pty) Ltd,May 29, 2009.Van Langenhove G. (2011). Flooding in Cuvelai. Ministry of Agriculture – Water and Forestry –Department of Water Affairs.Surveyor GeneralCMP (BAR)LIDAR data of Southern Mapping Companyinternet: NOAACPCI/RA/12077/11.186/TGO 51version 1.0 - 17/02/12

Annex AThe PDM hydrological modelI/RA/12077/11.186/TGO 1version 1.0 - 17/02/12

A.1 IntroductionThis Annex provides a concise overview of the main aspects of the PDM. For a moreextensive discussion, the reader is referred to Moore (1985, 1999) and IWRS (2011), amongothers.The Probability Distributed Model or PDM is a fairly general conceptual rainfall-runoff modelwhich transforms rainfall and evaporation data to flow at the catchment outlet (Moore, 1985,1999; Institute of Hydrology, 1992, 1996). Figure 6-1 illustrates the general form of the model.Runoff production at a point in the catchment is controlled by the absorption capacity of thesoil to take up water: this can be conceptualised as a simple store with a given storagecapacity. By considering that different points in a catchment have differing storage capacitiesand that the spatial variation of capacity can be described by a probability distribution, it ispossible to formulate a simple runoff production model which integrates the point runoffs toyield the catchment surface runoff into surface storage. Groundwater recharge from the soilmoisture store passes into subsurface storage. The outflow from surface and subsurfacestorages, together with any fixed flow representing, say, compensation releases fromreservoirs or constant abstractions, forms the model output. The components of the PDMmodel are described in more detail below.Figure 6-1: The PDM rainfall-runoff model.I/RA/12077/11.186/TGO 2version 1.0 - 17/02/12

A.2 Probability-distributed soil moisture storeConsider that runoff production at any point within a river basin may be conceptualised as asingle storage, or tank, of capacity c', representing the absorption capacity of the soil columnat that point. The storage takes up water from rainfall, P, and loses water by evaporation, E,until either the storage fills and spills, generating direct runoff, q, or empties and ceases to losewater by evaporation. Figure 6-2(a) depicts such a storage, whose behaviour may beexpressed mathematically by:where:S 0: initial depth of water in storage [mm]P: rainfall depth [mm]E: evaporation depth [mm]q: resulting direct runoff [mm]over the time interval considered.Now consider that runoff production at every point within a river basin may be similarlydescribed, each point differing from another only with regard to the storage capacity. Thestorage capacity at any point, c, may then be considered as a random variate with probabilitydensity function, f(c), so that the proportion of the river basin with depths in the range (c, c +dc) will be f(c)dc.The water balance for a river basin assumed to have storage capacities distributed in this waymay be constructed as follows. First imagine that stores of all possible different depths arearranged in order of depth and with their open tops arranged at the same height: this results ina wedge-shaped diagram as depicted in Figure 6-2(b). If the basin is initially dry so that allstores are empty and rain falls at a net rate P for a unit duration, then stores will fill to a depth Punless they are of lesser depth than P when they will fill and spill. During the interval theshallowest stores will start generating direct runoff and at the end of the interval stores ofdepth P will just begin to produce runoff, so that the hachured triangular area denotes thedepth produced from stores of different depth over the unit interval. Since, in general, there aremore stores of one depth than another the actual runoff produced over the basin must beobtained by weighting the depth produced by a store of a given depth by its frequency ofoccurrence, as expressed by f(c). Now, at the end of the interval stores of depth less than Pare generating runoff: let this critical capacity below which all stores are full at some time t bedenoted by C* C*(t) (C*=P in the present example). The proportion of the basin containingstores of capacity less than or equal to C* is:The function F(.) is the distribution function of store capacity and is related to the densityfunction , f(c), through the relation f(c) = dF(c)/dc. This proportion is also the proportion of thebasin generating runoff, so that the contributing area at time t for a basin of area A is:(4)(5)(6)I/RA/12077/11.186/TGO 3version 1.0 - 17/02/12

(6)(a) Point representation of runoff production by a single store.(b) Basin representation by storage elements of different depth and their associated probabilitydensity function.(c) Direct runoff production from a population of stores.I/RA/12077/11.186/TGO 4version 1.0 - 17/02/12

Figure 6-2: Definition diagrams for the probability-distributed interacting storage capacitycomponent.The instantaneous direct runoff rate per unit area from the basin is the product of the netrainfall rate, π(t), and the proportion of the basin generating runoff, F(C*(t)); that is:During the ith wet interval, (t, t Δt), suppose rainfall and potential evaporation occur atconstant rates P i and E i, so that net rainfall π i = P i - E i. Then the critical capacity, C*(τ), willincrease over the interval according to:The contributing area will expand according to Equation (6), and the volume of basin runoff perunit area produced over this interval will be:During dry periods potential evaporation will deplete the water content of each storage. It willbe assumed during such depletion periods that water moves between storages of differentdepths so as to equalise the depth of stored water at different points within the basin. Thus atany time all stores will have a water content, C*, irrespective of their capacity, unless this isless than C* when they will be full: the water level profile across stores of different depths willtherefore always be of the simple form shown in Figure 6-2(c). The assumption which allowsredistribution of water between storages of different size during depletion periods is particularlyimportant for real-time applications of the model where the possibility of updating the storecontents is envisaged. Moore (1985) shows how this assumption, when not invoked, leads toa more complex water accounting procedure which is less amenable to real-time empiricalstate adjustment schemes. Particularly important is that a unique relationship exists betweenthe water in storage over the basin as a whole, S(t), and the critical capacity, C*(t), and in turnto the instantaneous rate of basin runoff production, Q(t). Specifically, and referring to Figure6-2(c), it is clear that the total water in storage over the basin is:(7)(8)(9)(10)For a given value of storage, S(t), this can be used to obtain C*(t) which allows the volume ofdirect runoff, V t Δt , to be calculated using Equations (9) together with (8).The dependence of evaporation loss on soil moisture content is introduced by assuming thefollowing simple function between the ratio of actual to potential evaporation, E' i/E i, and soilmoisture deficit, S max - S(t):(11)I/RA/12077/11.186/TGO 5version 1.0 - 17/02/12

either a linear (b e=1 so E' i=(S(t)/S max)E i) or quadratic form (be=2) is usually assumed.Here, S max is the total available storage, and is given by:(12)where c mean is the mean storage capacity over the basin. Further loss as recharge togroundwater may be introduced by assuming that the rate of drainage over the interval, d i,depends linearly on basin soil moisture content at the start of the interval i.e.:where k r is a drainage time constant with units of inverse time, b r an exponent (usually setto 1), and S t the threshold storage below which there is no drainage, water being held undersoil tension. Other recharge formulations are available as well (IWRS, 2011).The above completes the procedure for soil moisture accounting and determining the valueof runoff production according to a probability-distributed storage capacity model. Figure6-3 provides a graphical representation of this procedure for a wet interval (t,t Δt) duringwhich soil moisture storage is added to by an amount ΔS t Δt π iΔt - V t Δt , and avolume of direct runoff, V t Δt , is generated.(13)Figure 6-3: The storage capacity distribution function used to calculate basin moisture storage,critical capacity, and direct runoff according to the probability-distributed interacting storagecapacity model.I/RA/12077/11.186/TGO 6version 1.0 - 17/02/12

I/RA/12077/11.186/TGO 7version 1.0 - 17/02/12

A.3 ReferencesInstitute of Hydrology (1992) PDM: A generalized rainfall-runoff model for real-time use,Developers Training Course, National Rivers Authority River Flow Forecasting System,Version 1.0, March 1992, 26pp.Institute of Hydrology (1996) A guide to the PDM. Version 1.0, January 1996, 45pp.IWRS (2011). InfoWorks RS Documentation. Innovyze Ltd.Moore, R.J. (1985) The probability-distributed principle and runoff production at point andbasin scales. Hydrological Sciences Journal, 30(2), 273-297.Moore, R.J. (1999) Real-time flood forecasting systems: Perspectives and prospects. In: R.Casale and C. Margottini (eds.), Floods and landslides: Integrated Risk Assessment,Chapter 11, 147-189, Springer.I/RA/12077/11.186/TGO 8version 1.0 - 17/02/12

Annex BMapsI/RA/12077/11.186/TGO 9version 1.0 - 17/02/12

B.1 Model scheme mapsI/RA/12077/11.186/TGO 10version 1.0 - 17/02/12

B.2 Calibration mapI/RA/12077/11.186/TGO 11version 1.0 - 17/02/12

B.3 Flood frequency mapsI/RA/12077/11.186/TGO 12version 1.0 - 17/02/12

B.4 Flood mapsI/RA/12077/11.186/TGO 13version 1.0 - 17/02/12