Real-Time Hydrologic Modelling and Floodplain Modelling in the Kafue River Basin, Zambia

Research Collection

Doctoral Thesis

Real-time hydrologic modelling and floodplain modelling in the Kafue river basin, Zambia

Author(s): Meier, Philipp

Publication Date: 2012

Permanent Link: https://doi.org/10.3929/ethz-a-007578064

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ETH Library DISS. ETH NO. 20421

REAL-TIME HYDROLOGIC MODELLING AND FLOODPLAIN MODELLING IN THE KAFUE RIVER BASIN, ZAMBIA

A dissertation submitted to

ETH ZÜRICH

for the degree of Doctor of Sciences

presented by

PHILIPP MEIER Dipl. Ing. ETH Zürich

born 22. September 1979 citizen of Zürich

accepted on the recommendation of

Prof. Dr. Wolfgang Kinzelbach Prof. Dr. Dr.-Ing. András Bárdossy

2012

Abstract

Hydropower dams make an important contribution to the economic development of many countries. However, in too many cases the negative impacts outweigh the positive ones. A river where the negative impacts of dams are visible is the Zambezi river basin in Southern Africa. A fundamental prerequisite for a holistic management is a good knowledge of the physical system. Long term forecasts on the inflow of a dam and a model predicting the downstream effects of a dam can help improving the operation of a dam, thus minimising the negative impacts. A set of tools for dam management is presented in this thesis using the example of the Kafue river system, the largest tributary of the Zambezi. Since a dam divides the physical system of the river basin into two parts, an upstream and a downstream part, they have to be modelled separately. The upstream part consists of a forecasting framework for river discharges at a specific location. A simple conceptual model, which is solely based on remote sensing data providing soil moisture and rainfall estimates, builds the core of the framework. Sequential data assimilation using the Ensemble Kalman Filter provides a tool that is both efficient and robust for real-time modelling. The soil moisture product used is based on the back-scattering intensity of a radar signal measured by a radar scatterometer. These soil moisture data correlate well with the measured discharge of the corresponding watershed if the data are shifted by a time lag. This time lag is the basis for the applicability of the soil moisture data for hydrological forecasts. The applied conceptual model features two storage compartments. Its processes modelled involve evaporation losses, infiltration and percolation. The application of this model in a real-time modelling framework yields good results. The lead time of the forecast is dependent on the size and the retention capacity of the watershed. For the largest watershed a forecast over 40 days can be provided. The quality of the forecast increases significantly with decreasing prediction time. In a watershed with a small retention storage and a quick response to rainfall events, the performance is relatively poor and the lead time is as short as 10 days only. The downstream part aims at predicting the flooding patterns in the Kafue Flats in Zambia correctly. The progression of flooding is assessed using data retrieved from remote sensing satellites. Two methods for the recognition of flooding patterns are used, one based on data from a passive satellite system operating in the optical range, the second on an active microwave system. The classification applied for the optical data involves a simple numerical indicator for the presence of liquid water. The classification of the active microwave data is more complex. A stepwise approach based on the backscattering intensity, inundation probability maps and the spatial arrangement of the single pixels is applied. Despite their drawbacks both methods are suited to retrieve information about the flooding patterns, though not comparable. To model the flooding extent, strategies can range from simple conceptual black-box models to one-dimensional hydraulic models and fully distributed hydrological models. The most promising modelling approach was found to be a distributed model based on MODFLOW. It consists of two layers: a subsurface layer, representing the saturated flow in the groundwater, and a surface water layer representing the flow on the flooded surface. In between these two layers the unsaturated zone is modelled. A module was developed to handle the coupling of the two layers. The flow in the main river channel of the Kafue is simulated explicitly. The model cells have a size of 1 × 1 km2. This model is calibrated using the flooding patterns derived from active microwave data. After calibration the model is found to be able to reproduce the seasonal progression of the flooding in the Kafue Flats. Some shortcomings of the model unveiled after calibration can be addressed by improving the structure of the model, as well as by using a better digital elevation model.

ii Zusammenfassung

In zahlreichen Ländern ist die Stromproduktion aus Wasserkraft ein wichtiger ökonomis- cher Faktor, dessen durchwegs positiven Effekte in vielen Fällen durch negative Folgen der Wasserkraftnutzung aufgewogen werden, so zum Beispiel im Einzugsgebiet des Sambesi im südlichen Afrika. Eine alle Faktoren umfassende Bewirtschaftung eines solch komplexen Flusssystems muss sich auf eine fundierte Kenntnis des hydrologischen Systems abstützen. So bieten längerfristige Prognosen der Zuflüsse eines Stausees, sowie die detail- lierte Vorhersage der hydrologischen Prozesse unterhalb des Wasserspeichers eine wertvolle Hilfe zur Verminderung negativer Auswirkungen. Im Rahmen dieser Arbeit werden solche Werkzeuge am Beispiel des Kafue River entwickelt. Der physikalischen Trennung des hydrologischen Systems oberhalb und unterhalb eines Staudammes, wird durch eine geson- derte Betrachtung Rechnung getragen. Zur Vorhersage des Zuflusses eines Staudammes, wird ein Prognosesystem basierend auf einem einfachen hydrologischen Modell und der Datenassimilierung mittels Ensemble Kalman Filter erstellt. Als Eingangsdaten dienen ausschliesslich aus Fernerkundungsdaten abgeleitete Grössen, wie Bodenfeuchte und Niederschlag. Die Bodefeuchte wird bestimmt, indem die Streuung eines Radarsignals an der Erdoberfläche gemessen wird. Der so er- mittelte Wassergehalt des Bodens weist eine gute Korrelation mit gemessenen Abfüssen auf, wenn die Zeitreihen um einen bestimmten Betrag zueinander verschoben werden. Diese zeitliche Verschiebung bildet die Grundlage einer Prognose. Das verwendete hy- drologische Modell besteht aus zwei Linearspeichern und bildet die wichtigsten Prozesse, wie Verdunstung, Infiltration und Zwischenabfluss, ab. Die so erhaltene Prognose ist all- gemein von guter Qualität. Es können, abhängig von der Grösse eines Einzugsgebietes, Prognosehorizonte von bis zu 40 Tagen erreicht werden, jedoch ist die Prognose für näher- liegende Ereignisse wesentlich genauer. Problematisch ist die Anwendung des Systems auf Einzugsgebiete mit geringer Bodenmächtigkeit und folglich schnellem Abfliessen nach Re- genereignissen. Die Einflüsse des durch Staudämme veränderten Abflussregimes macht sich im Kafue- Einzugsgebiet vor allem im grössten Feuchtgebiet, den Kafue Flats, bemerkbar. Um die Dynamik der jährlichen Überflutung in Raum und Zeit abzuschätzen, werden zwei Metho- den vorgestellt, welche die überfluteten Flächen anhand optischer und radar-gestützter Fernerkundungsdaten bestimmen können. Aus den optischen Satellitendaten wird die Überflutung anhand eines einfachen Index berechnet. Die Klassifikation der Radar-Daten ist um einiges aufwändiger und berücksichtigt neben der Intensität des zurückgestreuten Radar-Signals auch deren räumliche Verteilung und Informationen zur erwarteten Über- flutungshäufigkeit. Obwohl beide Methoden nicht direkt vergleichbar sind, können beide erfolgreich zur Bestimmung der Überschwemmungsdynamik eingesetzt werden. Um die überfluteten Flächen zu modellieren, bieten sich verschiedene Konzepte an, die von einer einfachen Bilanzbetrachtung, über eindimensionale, hydraulische Modelle bis zu komplexen, räumlich aufgelösten, physikalischen Modellen reichen. Ein räumlich verteiltes Modell basierend auf MODFLOW erlaubt eine zuverlässige Simulation der über- fluteten Flächen. Es besteht einer Grund- und einer Oberflächenwasserschicht, und der ungesättigte Zone dazwischen. Für die Kopplung der hydrologischen Prozesse in beiden Schichten wird MODFLOW um ein Modul erweitert. Dieses Modell erlaubt die explizite Simulation der Abflüsse im Hauptfluss und der Überflutung im angrenzenden Feuchtge- biet mit einer Auflösung von 1 × 1 km2. Kalibriert wird es anhand der Flächen, die aus den Radar-Satellitendaten extrahiert wurden. Auch wenn nach der Kalibrierung einige Schwächen dieses Modellansatzes hervortreten, kann die komplexe saisonale Dynamik der Überschwemmungen in den Kafue Flats nachgebildet werden. Eine Verbesserung der Re- sultate könnte durch eine optimierte Modellstruktur erreicht werden, vor allem aber durch die Verwendung eines genaueren topographischen Datensatzes.

iv Contents

1 Introduction1 1.1 Water for life – water for the environment...... 1 1.2 Outline...... 3 1.3 The Zambezi river system...... 4 1.3.1 Geomorphology and geology...... 4 1.3.2 Climate...... 6 1.4 The Kafue river basin...... 6 1.4.1 Headwaters...... 6 1.4.2 Kafue Flats...... 7 1.4.3 Reservoirs...... 9

2 Real-time Prediction of River Discharge 11 2.1 Real-time hydrological modelling based on soil moisture data. 11 2.2 Study area...... 12 2.3 Data...... 13 2.3.1 Soil moisture...... 13 2.3.2 Rainfall...... 15 2.3.3 Discharge...... 15 2.4 Calculating discharge from soil moisture...... 15 2.4.1 Soil water column content...... 15 2.4.2 Soil moisture – runoﬀ model...... 16 2.4.3 Reference method...... 21 2.5 Real-time modelling and data assimilation...... 21 2.5.1 Sequential data assimilation...... 21 2.5.2 The Ensemble Kalman Filter...... 23 2.5.3 Application of the real-time model...... 24 2.5.4 Generating input data ensembles...... 24 2.6 Results and discussion...... 28 2.6.1 Deterministic model...... 28 2.6.2 The inﬂuence of the parameter T for SWI...... 31 2.6.3 Real-time model...... 32 2.7 Other modelling approaches...... 35 2.7.1 The Pitman model...... 35

v 3 Flooding patterns 37 3.1 Flooded area from MODIS...... 37 3.1.1 Detection of flooded areas from the NDWI...... 38 3.1.2 Results...... 38 3.2 Flooded area from ENVISAT ASAR...... 39 3.2.1 Classification of flooded areas...... 41 3.2.2 Comparison with Landsat data...... 43 3.2.3 Results of the classification...... 44

4 Floodplain Modelling 49 4.1 Water resources of the Kafue Flats...... 49 4.2 Available data...... 50 4.2.1 Rainfall data...... 50 4.2.2 Estimates of monthly evapotranspiration...... 54 4.2.3 Evapotranspiration from remote sensing data...... 55 4.2.4 Digital elevation model...... 60 4.2.5 River cross sections...... 60 4.3 Floodplain models...... 61 4.3.1 Black box model based on the digital elevation model. 61 4.3.2 Correlation between storage change and flooded area.. 61 4.3.3 KAFRIBA...... 63 4.4 One-dimensional hydraulic model...... 64 4.4.1 Model geometry...... 64 4.4.2 Hydraulic roughness...... 66 4.4.3 Hydrological data...... 66 4.4.4 Simulation results...... 67 4.4.5 Overall evaluation...... 72 4.5 Distributed floodplain model...... 72 4.5.1 Data...... 73 4.5.2 Estimation of lateral inflows...... 73 4.5.3 Model geometry...... 74 4.5.4 Correction of the digital elevation model...... 75 4.5.5 Implementation of the model...... 75 4.5.6 Coupling the overland flow to the groundwater..... 76 4.6 Model alternatives - MIKE SHE...... 77 4.6.1 Properties of MIKE SHE...... 77 4.6.2 Implementation of the Kafue Flats model...... 79 4.6.3 Parameter sensitivity...... 80 4.6.4 Results...... 81 4.7 River - floodplain interaction...... 83

vi 5 Calibration of the distributed floodplain model 87 5.1 Calibration data...... 88 5.1.1 Comparing ASAR data to the model – a resolution problem 88 5.1.2 The influence of the DEM on the fraction of flooding.. 88 5.1.3 Generation of flood maps at model resolution...... 90 5.2 Manual sensitivity analysis...... 92 5.3 Model stability...... 94 5.4 Zones...... 95 5.5 Sensitivity analysis...... 96 5.6 Calibration process...... 100 5.7 Calibration results...... 101 5.7.1 Uniform parameters...... 101 5.7.2 Parameters by zone...... 106

6 Conclusions and recommendations 111 6.1 Real-time forecast...... 112 6.2 Detection of flooding patterns...... 114 6.3 Floodplain modelling...... 116 6.4 Calibration of the distributed floodplain model...... 117 6.5 Improvements of the distributed floodplain model...... 119

Acknowledgements 121

Bibliography 123

Appendix 135

A Documentation of the MATLAB MODFLOW tools 135 A.1 General remarks...... 135 A.2 Import and preparation of input data...... 136 A.3 Main function...... 141 A.4 Write input ﬁles...... 142 A.5 Import MODFLOW output...... 148

B Using Parallel-PEST 151 B.1 About Parallel-PEST...... 151 B.2 Implementation on the Amazon Elastic Compute Cloud (EC2) 152 B.2.1 About EC2...... 152 B.2.2 Implementation...... 152 B.3 Running PEST on a computer cluster...... 154

vii

List of Figures

1.1 Overview of the Zambezi River Basin and the Kafue watershed.5 1.2 Schematic of the Zambezi River Basin with the existing reservoirs and lakes and the large wetlands...... 7 1.3 Map of the Kafue Flats based on a Landsat 5 TM+ satellite image.8 1.4 Spillgates of the Itezhi-Tezhi reservoir...... 10

2.1 Overview of the Zambezi River Basin and the three watersheds where the real-time model is applied...... 12 2.2 The setup of the ERS radar scatterometer instrument. The multiple antennas allow to observe the backascattering properties of the surface dependent from different incidence angles...... 14 2.3 The probability of a rainfall event given a Soil Water Index class and the average rainfall amount for the same classes for the three watersheds Upper Zambezi, Kafue River and Luangwa River.. 17 2.4 Correlation between Basin Water Index and discharge shifted by the time lag which resulted in the best correlation...... 18 2.5 The influence of the Lukanga Swamps wetland on the measured soil water index...... 18 2.6 Structure of the conceptual hydrological model...... 19 2.7 Conventional modelling compared to real-time modelling.... 22 2.8 Comparing the assimilated discharges obtained by the model using rainfall errors following a Gaussian distribution and a gamma distribution...... 25 2.9 Effect of the uncertainty of the BWI on the RMSE of the predicted discharge and of the model error at the time of data assimilation...... 27 2.10 Effect of the uncertainty of the BWI on the Nash-Sutcliffe efficiency of the predicted discharge and of the model error at the time of data assimilation...... 27 2.11 The discharge simulated in the hindcast mode including the 95% confidence interval compared to the measured discharge and the results of the reference method...... 30 2.12 Absolute and relative forecast error for all three watersheds for the different forecast periods and the assimilation step...... 34

ix 3.1 Time series of the total flooded area in the Kafue Flats derived from MODIS satellite data using the NDWI...... 38 3.2 The NDWI in the Kafue Flats during the dry season and the wet season...... 40 3.3 ASAR image of the lower Kafue Flats from the flooding season. 41 3.4 Deriving the MNDWI threshold value for extracting water pixels. 44 3.5 Comparison of the inundation patterns derived from Landsat and from ASAR satellite images...... 45 3.6 The effect of single pixels containing both, open water surface and flooded vegetation, as observed on an ASAR satellite image. 46 3.7 Total flooded area derived from ASAR images...... 47

4.1 Mean annual rainfall and discharge compared to the long term mean...... 51 4.2 Correlation analysis between the different sources of rainfall data. 53 4.3 The surface temperature as a function of the surface albedo... 56 4.4 Time series of the potential evapotranspiration measured at the evaporation pan at ITT compared to the timeseries obtained from MODIS data...... 58 4.5 Measured evaporation from an evaporation pan at ITT vs. evapotranspiration obtained from MODIS data...... 59 4.6 Flooded area and stored water volume of the Kafue Flats for uniform flooding at different water levels...... 62 4.7 Correlation between daily water storage and flooded area.... 63 4.8 The cross sections as defined in the HEC-RAS model, the area of the main channel, the floodplain area and the main river channel. 65 4.9 Elevation profile of the Kafue river including the Kafue Gorge reservoir...... 65 4.10 Comparison of the measured discharge at Kafue Gorge dam and the modelled discharge (using HEC-RAS)...... 68 4.11 Simulation results of the HEC-RAS model...... 69 4.12 The water levels along the river as simulated by the HEC-RAS model for the high flow season (April) and the low flow season (November)...... 70 4.13 The cross sections of the lower Kafue Flats before the constriction, at the constriction and in the upper part of the Kafue Gorge reservoir...... 71 4.14 Model boundary and aquifer thickness of the MODFLOW model. 74 4.15 Comparison of the modelled and the measured outflow of the Kafue Gorge reservoir...... 82 4.16 Total flooded area as simulated with the MIKE SHE model for the actual case with dams and a presumably natural state (without dams)...... 83

x 4.17 Simulation results of the simple river – ﬂoodplain oxygen model. 86

5.1 Upscaling of the measured flooded area to the model resolution for different flooding thresholds from 10% to 90%...... 89 5.2 Correlation between the maximum flooded fraction and the standard deviation and between the maximum elevation difference within one model cell...... 89 5.3 Map of the maximum flooded fraction in each model cell.... 90 5.4 The flooded area measured directly from the ASAR data and measured from the generated flood maps compared to the flooded area derived with the static threshold method...... 91 5.5 The time series of the total flooded area in the floodplain which results from the different test simulations...... 93 5.6 Sensitivities of the river roughness parameters dependent on the calculation time step chosen...... 95 5.7 For calibration the model domain is divided into 5 zones.... 96 5.8 The relative sensitivities of each parameter on selected statistical parameters of the flooding in the different zones...... 99 5.9 The sensitivities of the different parameters...... 100 5.10 Comparison between the modelled total flooded area and the area determined from the ASAR images after model calibration using uniform parameters...... 102 5.11 Comparison between the modelled and the measured flooded area at the time where the best fit is achieved (May 10, 2004). 103 5.12 Comparison between the modelled and the measured flooded area at the time where the highest residual is found (February 2, 2004)...... 104 5.13 Comparison between the modelled total flooded area and the area determined from the ASAR images after model calibration using a different value for each zone...... 109

A.1 The graphical interface of the IBOUNDeditor...... 137

B.1 Schematic of the virtual computer cluster on Amazon EC2 used for model calibration...... 153

List of Tables

2.1 Estimated parameters for the three sub-basins and the 95% confidence interval for each parameter...... 28 2.2 RMSE of the different forecast lead times up to the maximum possible lead time...... 31 2.3 Nash-Sutcliffe efficiency of the different forecast lead times up to the maximum possible lead time...... 32 2.4 Influence of the parameter T on the model parameters ki in the Kafue river basin and the Luangwa watershed...... 33

3.1 Constraints for the classiﬁcation of the ASAR back-scattering data in three classes...... 45

4.1 Summary of the average annual water balance of the Kafue Flats. 52 4.2 Properties of the NOAA-CPC and the TRMM data...... 52 4.3 Corrected crop coefficient values for the estimation of the evapotranspiration in the Kafue Flats...... 55 4.4 Manning’s n values for the different zones of the HEC-RAS model. 66 4.5 LAI and root depth for the three major vegetation zones in the Kafue Flats as defined for the MIKE SHE model...... 80

5.1 Parameter configurations used for test cases compared to the reference simulation...... 92 5.2 The parameters assessed in the automatic sensitivity analysis.. 98 5.3 Calibrated parameters and their associated uncertainties.... 105 5.4 Parameter covariance and correlation matrix...... 106 5.5 Calibrated parameters using different parameter values for five zones of the model domain...... 107

xiii

List of Abbreviations

ASAR Advanced Synthetic Aperture Radar. An active radar instrument on-board the Envisat satellite. ASCAT Advanced Scatterometer. A satellite based instrument to retrieve soil moisture. BWI Basin Water Index CHD Time dependent specific head module of MODFLOW DN Digital number EnKF Ensemble Kalman Filter ERS European Remote Sensing Satellite ET Evapotranspiration FEWS NET Famine Early Warning Systems Network GIS Geographical information system GWP Global Water Partnership HEC-RAS Hydrologic Engineering Center - River Analysis System ITT Itezhi-Tezhi reservoir IWRM Integrated water resources management KG Kafue Gorge reservoir LAI Leaf area index LST Land surface temperature MIKE SHE Finite difference hydrological model developed by DHI Wa- ter & Environment, based on the Système Hydrologique Eu- ropéen MNDWI Modified Normal Difference Water Index MOD09 MODIS Surface-Reflectance Product MOD11 MODIS Land Surface Temperature and Emissivity product MODFLOW U.S. Geological Survey MODular finite-difference groundwater FLOW model MODIS Moderate Resolution Imaging Spectroradiometer NDVI Normalised Difference Vegetation Index

xv NDWI Normalized Difference Water Index NIR Near infrared NOAA-CPC National Oceanic and Atmospheric Administration – Climate Prediction Center RMSE Root mean square error S-SEBI Simplified Surface Energy Balance Index SAR Synthetic Aperture Radar SDD Stress degree days SFR Streamflow module of MODFLOW SMAP Soil Moisture Active-Passive instrument SMOS Soil Moisture and Ocean Salinity Mission SRTM Shuttle radar topography mission SSM Surface soil moisture SWI Soil Water Index SWIR Short wave infrared TRMM Tropic Rainfall Measuring Mission UTM Universal Transverse Mercator coordinate system UZF Unsaturated zone flow module of MODFLOW WCD World Commission on Dams ZESCO Zambia Electricity Supply Company, the state owned power supplier of Zambia.

xvi List of Symbols

A Area a,b,c Parameters of the simple hydrological model used to estimate the tributary inﬂows to the Kafue Flats.

χQ Hydrometric scaling factor d Observation matrix Ensemble of perturbations of the observation d E(X) Expected value of the random variable X εa Emissivity of the air

εs Emissivity of the surface E Nash-Sutcliﬀe eﬃciency e0 Water vapor pressure in the atmosphere ET Evapotranspiration

ET0 Potential evapotranspiration

ETact Actual evapotranspiration F Measure of fit between a simulated flooding pattern and the corresponding measured flooding pattern f(.) Model function used to propagate states in time

G0 Soil heat ﬂux H Measurement operator, relating the model state to the observations H Sensible heat ﬂux

IGW Direct infiltration of rainfall to the subsurface storage K Kalman gain matrix k Shape parameter of the gamma distribution ki Model parameters of the soil moisture – runoff model kC Crop coefficient λE Latent heat flux Λ Evaporative fraction

Lv,water Latent evaporation heat of water Pf Error covariance of the forecast f Pe Estimated error covariance of the forecast ψa Analysed, updated model state

xvii ψf Predicted model state

ψt Model state at time t ˜~ P t Rainfall ensemble at time t ˜i Pt ith member of the rainfall ensemble at time t P Rainfall Q Total discharge

Q0 Baseﬂow parameter

QGW Subsurface runoﬀ

QS Surface runoﬀ R Error covariance of the observation

Re Estimated error covariance of the observation

ρi Surface reﬂectance in the spectral band i

ρw Density of water r0 Surface albedo

RL Longwave radiation

Rn Net radiation

RS Shortwave radiation rX,Y Correlation coeﬃcient between two random variables X and Y σ Stefan-Boltzmann constant

σX Standard deviation of the random variable X S Storage

SGW Groundwater storage of the soil moisture – runoﬀ model

SS Surface storage of the soil moisture – runoff model ∆τ Time lag parameter of the soil moisture – runoff model θ Scale parameter of the gamma distribution T Parameter of the exponential filter used to generate the SWI t Time

T0 Earth surface temperature

Ta Air temperature

TH Surface temperature of a completely dry area

TλE Surface temperature of a completely wet area ut Forcing data at time t w Modiﬁcation factor for the crop coeﬃcient kC

xviii Chapter 1 Introduction

1.1 Water for life – water for the environment

Dams for hydropower production make an essential contribution to economic development in many countries. The benefits brought by these dams are considerable. They not only provide electricity to growing economies, in many cases they also secure the availability of safe drinking water and sufficient quantities of irrigation water. During the 20th century a huge number of dams was built to satisfy the needs of water resources management. It is estimated that around 30% to 40% of the irrigated land worldwide is dependent on dams. About 19% of the worlds electricity production is generated by hydropower. Thus, more than 60% of the rivers are affected by dams (WCD, 2000). Water storage dams are by design changing the natural distribution and timing of the discharge of rivers. Impacts of such changes can be observed in many cases. They are generally very diverse and range from direct physical and chemical impacts to indirect impacts on downstream ecosystems. Physical changes involve the consequences of blocking the river and thus altering the natural discharge pattern, the sediment balance and the water quality due to different chemical processes taking place in large reservoirs. Indirect impacts are the consequence of the direct impacts. Changed conditions for the riverine ecosystems influence the plant life in downstream habitats. Alterations of the fauna are often found due to blocking of migration paths for fish or changed water quality, such as oxygen concentration, which influences the food availability for many aquatic animals. The World Commission on Dams (WCD, 2000) states that large dams have a strong impact on river systems, in many cases more negative than positive. The changed flow regimes not only affect downstream riverine ecosystems, but also compromises the livelihood of people living with the river. The mitigation of these ecological and social tradeoffs is a complex process. In many cases the negative effects were not anticipated before the dam was constructed. Defi- cient knowledge of the natural river system and its influence on the livelihoods of the riparian population leads to huge uncertainties when such impacts are predicted. Many impacts remain therefore unidentified prior to the construc-

1 2 1.1 Water for life – water for the environment tion of a dam. The implementation of measures for the reduction of negative impacts needs to be an ongoing process also after building a dam throughout its operation. However, ecological rehabilitation measures have to be implemented while the economical services of the system, such as hydropower production or flood protection, are still available reliably. Hence, ecosystem management involves multiple purposes, multiple objectives and multiple stakeholders (Loucks, 2006). Based on these considerations the principle of integrated water resources management (IWRM) is developed and formulated at the Dublin Conference on Water and Environment in 1992 (GWP, 2000). The concept of IWRM inte- grates different water users in a watershed, such as hydropower, water supply, sanitation, irrigation, drainage and the environment, into a holistic approach of basin management. It makes sure that economic, social, technical and environmental dimensions are included into management considerations. For managing a reservoir in this context of multiple objectives, usually optimisation models are applied. Although they are mostly based on simplified system configurations, these are especially successful for the evaluation and planning of operation policies (Oliveira and Loucks, 1997). Traditional optimisation approaches however, maximize a single monetary valued objective function. A water resources system is inherently multi-objective. Also many of its objectives, mainly social and environmental, cannot be expressed in monetary units. Additionally the principles of IWRM ask for a participatory approach, which involves users and policy makers at all levels (GWP, 2000). Such an approach can only be implemented if tools are developed which not only provide a single optimal value but a set of Pareto-optimal solutions. These solutions can be a starting point for a decision taken with the participation of relevant stakeholders. A river where the struggle for a holistic approach for managing water is ongoing for some time now is the Zambezi river. The water resources in the Zambezi river basin are more and more developed. Feasibility studies for several new hydro-power plants are being carried out and new irrigation schemes are developed all over the river basin. While pressure on the resources is growing, long term forecasts of the discharge with a few weeks lead time can help to optimise the operation of smaller reservoirs and water abstraction schemes for irrigation without neglecting the river-dependent ecosystems as an important water user. Such a forecast of the inflows of the reservoir can be useful, especially if the management of a reservoir is targeted at the release of ecological flows. For these releases the timing is of great significance (Galat and Lipkin, 2000; Acreman and Ferguson, 2010). Operating a dam according to a strict rule curve without any information on future inflows leads to a very late flood pulse since the flood is attenuated until a prescribed water level is reached in the reservoir. Chapter 1 Introduction 3

With some information on the expected inflow ecological releases can mimic a more natural flow. But not only the knowledge about future inflows to a dam are necessary for an effective management. Also some information on what effects a management decision will have is very important. This is even more important when a valuable ecosystem, such as a floodplain, is affected by a dam and the management is targeted at mitigating the negative impacts of a dam. Floodplain ecosystems not only depend on a certain quantity of water each year. The natural hydrological cycle to which an ecosystem has adapted over centuries has to be preserved to a certain degree. In a floodplain the driving hydrological variable is mainly the flooding. If through management of a dam the natural flooding patterns can be mimicked to some extent, a floodplain ecosystem can be preserved at least partly. A fundamental prerequisite for starting an optimisation exercise is a good knowledge of the physical behaviour of the system. Since through a dam the hydrological system of a river basin is decoupled into an upstream and a downstream part, these two systems have to be modelled differently. Also the requirements for modelling the two parts are not the same. Whereas for the upstream system information on the discharge is normally sufficient, the downstream system needs to be modelled physically correct and in a distributed manner. In this thesis a set of models for dam management is developed and applied to the Kafue River basin in Zambia, which is a tributary of the Zambezi river. The two main parts are (1) a forecasting framework for the river basin upstream of the dam which is able to predict the inflow and (2) a physically based distributed model to simulate the flooding patterns downstream of the dam.

1.2 Outline

This thesis is organised in six chapters. In the first chapter, the introduction, the research objectives and the characteristics of the study area are described. In Chapter2 a real-time prediction framework for discharges is presented. The prediction is based on remote sensing data, such as soil moisture and rainfall, only. The application of sequential data assimilation allows to provide an updated prediction when newly measured discharge becomes available. Ad- ditionally alternative models suitable for use with a real-time framework are discussed. In Chapter3 and4 tools for the purpose of floodplain modelling are presented. As study area the Kafue Flats floodplain is chosen. First, in Chap- ter3, two methods to retrieve flooding patterns from remote sensing data are introduced. These flooding patterns can be retrieved from data from passive 4 1.3 The Zambezi river system satellite based senors, operating in the optical range or from active microwave systems. While active microwave systems are only marginally influenced by the presence of clouds, the optical systems provide a much higher temporal resolution. In Chapter4 tools for the hydrological simulation of a floodplain system are presented. These models range from a simple water balance to complex physically based distributed models. Special attention is paid to the calibration of a distributed model. The whole calibration process is described in Chapter5. Finally, conclusions are drawn in Chapter6 and recommendations for future developments are made.

1.3 The Zambezi river system

1.3.1 Geomorphology and geology

The Zambezi river basin is one of the most valuable natural resources in Africa. However, it is also one of Africa’s most heavily dammed river systems. Dam-induced ecological changes have already had consequences on wildlife and ecosystem-based livelihood of downstream residents. The Zambezi is the fourth largest river in Africa, flowing eastwards for more than 2 800 km from the Ka- lene Hills in northern Zambia to its mouth at the Indian Ocean in central Mozambique. Its watershed covers an area of 1 351 365 km2 and is shared by 8 countries: Angola (18.3%), Botswana (2.8%), Malawi (7.7%), Mozambique (11.4%), Namibia (1.2%), Tanzania (2.0%), Zambia (40.7%) and Zimbabwe (15.9%). The largest part of the basin lies on Zambian territory (Figure 1.1). The Zambezi river basin can be divided into three major sections with distinct geomorphic properties. The Upper Zambezi basin, the Middle Zambezi and the Lower Zambezi area (Vörösmarty and Moore, 1991). A schematic of the Zambezi river system is shown in Figure 1.2. The Upper Zambezi ranging from the source to the Victoria Falls is met in its first section by more than a dozen tributaries before the topography becomes very uniform and the river is characterised by numerous floodplains. The Upper Zambezi watershed covers a total area of around 500 000 km2. At Victoria Falls the Zambezi has a mean discharge of 1 200 m3 s−1. The largest wetland in the Upper Zambezi is the Barotse Plains. They stretch along the river for around 200 km from the city of Lukulu upstream to Senanga. The maximum width is around 50 km and the wetland covers an area of 7 500 km2. The underlying formation consists mainly of Kalahari sands (Moore and Larkin, 2001). These sands form an enormous ground water reservoir (Winsemius et al., 2006). The Middle Zambezi is notable for the two man-made lakes Kariba and Ca- hora Bassa. Between the two lakes the Kafue River drains into the Zambezi constituting its largest tributary. This part of the river is mainly characterised by a major rift zone with alternating gorges and basins where the river chan- Chapter 1 Introduction 5 Delta

Zambezi Shire °

35 Lake Malawi Lake Tanzania Mozambique Malawi Cahora Bassa

Zimbabwe Luangwa Zambia ° 30 Lusaka • •

• Kafue

Kitwe Lake Kariba Lake Lukanga Swamps Longitude Chingola Kafue Flats • Victoria Falls Congo ° 25

Senanga Lukulu

Plains •

• Zambezi Barotse- Botswana

Cuando Angola Overview of the Zambezi River Basin (light blue) and the Kafue watershed (blue). ° 20 Namibia Figure 1.1: ° ° °

-10 -15 -20 Latitude 6 1.4 The Kafue river basin nel widens (Vörösmarty and Moore, 1991). At the Kariba reservoir the mean annual runoff is around 1 300 m3 s−1. The operation of the Kariba reservoir, mainly for hydropower production, has altered the natural seasonal flow patterns significantly. Consequently a decreased annual flooding in the downstream floodplains is observed (Beilfuss and dos Santos, 2001). Just upstream of the Cahora Bassa reservoir the Luangwa river joins the Zambezi contributing a mean annual runoff of 550 m3 s−1. The Lower Zambezi extends from the dam of Cahora Bassa to the Indian Ocean coast descending from the Central African Plateau into a broad floodplain with many parallel channels and shifting sandbanks, the Zambezi Delta.

1.3.2 Climate The most crucial climatic element in the Zambezi Basin is rainfall whose year to year variability is very high. Its abundance or deﬁciency strongly impacts the welfare of the people by aﬀecting the agricultural production. Rainfall is strongly seasonal and occurs almost exclusively between October and April. The total amount of rainfall is on average around 1 000 mm yr−1, the potential evapotranspiration around 2 000 mm yr−1. The Zambezi basin features a humid subtropical climate with three distinct seasons. The cold dry season with temperatures from 15℃ to 27℃ lasts from May to September. This season is followed by a dry hot season from October to November where temperatures reach up to 32℃. The hot rainy season from December to April is characterised by high temperature and high humidity. Tropical thunderstorms yield local rainfall amounts of up to 1 200 mm.

1.4 The Kafue river basin

The Kafue Basin is one of the major subcatchments of the Zambezi river. It lies entirely within Zambia covering around 20% of its territory. Almost half of the Zambian population lives in the Kafue Basin (Schelle and Pittock, 2005). The Kafue river basin roughly divides into two major sections: the headwaters upstream of the Itezhi-Tezhi reservoir and the lower Kafue basin downstream of the Itezhi-Tezhi. While in the headwaters the ﬂow is still mostly unregulated, in the lower basin the hydrology is strongly inﬂuenced by the two dams Itezhi- Tezhi and Kafue Gorge.

1.4.1 Headwaters The Kafue river headwaters originate from the plateau of the South Equatorial Divide in the Copperbelt Province of Zambia near the border to the Demo- cratic Republic of Congo. From its source, the Kafue river ﬂows in southeast- Chapter 1 Introduction 7

Zambezi Kafue Luangwa Lake Malawi

Lukanga Swamp

Itezhi-tezhi Dam Kafue Flats

Barotse Shire Plains Kafue Gorge Dam Zambezi Delta

KaribaDam CahoraBassaDam

Figure 1.2: Schematic of the Zambezi River Basin with the existing reservoirs and lakes (blue triangles) and the large wetlands (green a triangles). ern direction through the cities of Chingola and Kitwe. This region is mainly characterised by mining industry, where huge deposits of copper ore and other minerals exist. After Kitwe, loaded with heavy metal rich sediments, the Kafue river flows southwest towards one of its major wetlands, the Lukanga Swamps. The Lukanga Swamps play an important role in the hydrology of the Kafue river. They are a huge floodplain which is not directly connected to the river. Only during high flows the Kafue spills into the swamps which are flooded completely once a year. Not only the flood peaks are attenuated by this process, also the transported sediments of the river are deposited in the Lukanga Swamps, thus improving the water quality remarkably since the heavy metals transported by the river are mainly attached to particles. Downstream of the Lukanga Swamps the Kafue river flows westwards first and then towards south before it spills into the Itezhi-Tezhi reservoir. Up to here the Kafue river has drained a watershed of more than 100 000 km2 with a total river length of around 1 000 km.

1.4.2 Kafue Flats The Kafue Flats are an extensive, 250 km long and up to 90 km wide wetland, which extends from downstream of the Itezhi-Tezhi reservoir (ITT) down to the Kafue Gorge reservoir (KG) covering an area of 6 500 km2 (Figure 1.3). The Kafue river meanders through this extremely ﬂat area with an average slope of 3 cm km−1, hence the travel time of the water through the Flats is up to two months. Local measurements show ﬂow velocities of 0.2 to 1.0 m s−1 (Wamu- lume et al., 2012). 8 1.4 The Kafue river basin iue1.3: Figure a fteKfeFasbsdo ada M aelt mg aqie nFbur 2002). February in (acquired image satellite TM+ 5 Landsat a on based Flats Kafue the of Map

Itezhi-Tezhi dam Itezhi-Tezhi • Namwala • Busangu • Nyimba • Mazabuka • Kafue Lusaka • au og dam Gorge Kafue Chapter 1 Introduction 9

The flooding extent in the Kafue Flats is driven by strongly seasonal discharge. Generally a high discharge leads to a wide spread inundation. However the spatial distribution of flooding, which is an important parameter for the ecosystem, cannot be derived from a discharge measurement alone. If discharge in the main channel exceeds 170 m3 s−1 to 250 m3 s−1 the floodplain starts to be inundated (Mumba and Thompson, 2005; Chabwela and Mumba, 1996). The strong seasonal discharge is mainly caused by heavy rainfalls occurring from November to March in the headwaters of the Kafue River where the mean annual rainfall is around 1 400 mm yr-1 (Mumba and Thompson, 2005). The seasonal rainfall in the floodplain itself of around 800 mm yr-1 only causes local flooding during the rainy season. The main flood that causes flooding over large areas arrives at Itezhi-Tezhi between March and April. The Flats, which are considered to be a major wetland in ecological terms, are protected under the Ramsar convention since the year 1991 (Ramsar, 2011). They provide the habitat of endemic species such as the Kafue Lechwe and the Wattled Crane (Schelle and Pittock, 2005). The wetland is also important in economic terms. It sustains the local farming by providing grounds for cattle grazing, flood recession agriculture and fisheries.

1.4.3 Reservoirs

The Kafue hydroelectric scheme consists of a system of two dams, the Ka- fue Gorge dam for hydropower production and the Itezhi-Tezhi reservoir as a seasonal storage to supply a steady inﬂow to the Kafue Gorge.

Kafue Gorge

The Kafue Gorge reservoir, built in 1972 right downstream of the Kafue Flats, is an earth-rockﬁll dam with a total height of 50 m. The six turbines installed have a generation capacity of 900 MW and will be extended to 990 MW within the next few years. At the full operation level of 976.6 m a. s. l. the backwater of the reservoir reaches far west into the Kafue Flats up to Nyimba (Beilfuss and dos Santos, 2001). Such high water levels lead to a very large surface area of the reservoir and therefore to very high evaporation losses. To avoid this situation the Itezhi-Tezhi reservoir was built as an extended storage upstream of the Kafue Flats.

Itezhi-Tezhi

The Itezhi-Tezhi (ITT) reservoir was completed in 1978 and is mainly built as an extended storage for the Kafue Gorge (Figure 1.4). At ITT originally no turbines for electricity production were installed. Though plans to do so were implemented in 2010. ITT is an earth-rockﬁll dam with a length of 1 800 m 10 1.4 The Kafue river basin

Figure 1.4: Spillgates of the Itezhi-Tezhi reservoir. and a height of 65 m. It is especially designed to allow managed flood releases to maintain a certain flooding in the floodplain downstream. However, the operation rules of the dam are very strict and usually the benefit of increased power production was chosen over a distinct flood release for the floodplain. Chapter 2 Real-time Prediction of River Discharge

2.1 Real-time hydrological modelling based on soil moisture data

As soil moisture is a key parameter in land surface hydrology, the availability of area representative measurements offers a unique opportunity to improve hydrological modelling. The first satellite-derived global dataset on soil moisture was presented by Wagner et al.(1999a). It was shown that runoff predictions were greatly improved when measured soil moisture, both from ground measurements and from remote sensing, were incorporated (Aubert et al., 2003; Crow and Ryu, 2009). Recent studies have shown the usefulness of radar scatterometer derived soil moisture data for hydrological applications. Despite the generally coarse resolution, these data can be applied successfully for hydrological modelling since small scale spatial variability of the soil water content is averaged within the scatterometer footprint (Ceballos et al., 2005; Scipal et al., 2005). The application of remotely sensed soil moisture data becomes more and more feasible. Several satellite missions have been launched, or will be launched in the near future, equipped with instruments to retrieve soil moisture information using microwave frequencies. These missions include the MetOp Advanced Scatterometer (ASCAT), the Soil Moisture and Ocean Salinity Mission (SMOS) and NASA’s Soil Moisture Active-Passive instrument (SMAP) (Kerr et al., 2001; Naeimi et al., 2009; Piles et al., 2009). Wagner et al.(2007) showed the usefulness of high resolution soil moisture data from the Envisat Advanced Synthetic Aperture Radar (ASAR) instrument in hydrological modelling. A prediction framework for river discharge based solely on remotely sensed data of soil moisture and rainfall, a simple conceptual model and data assimilation techniques is presented here. The performance of the prediction is evaluated in three different sub-basins of the Zambezi river basin (Figure 2.1). The availability of the input data in real-time allows the model to be operated in real-time, providing a prediction for discharge each time new input data are

11 12 2.2 Study area

−5°

Tanzania Congo

−10° Angola Mozam− (3) bique (1) (2) −15° Latitude Zambia

Zimbabwe −20° Namibia Botswana

−25° 15° 20° 25° 30° 35° 40° Longitude

Figure 2.1: Overview of the Zambezi River Basin (light blue) and the three watersheds where the real-time model is applied. (1) Upper Zambezi; (2) Kafue

River; (3) Luangwa River. The outlets of the watersheds are marked ( ). retrieved. When observation data are available the model state is updated using sequential data assimilation techniques. The update step allows the model to be relatively simple.

2.2 Study area

This modelling approach is evaluated in three diﬀerent sub-basins within the Zambezi River Basin (Figure 2.1). The three watersheds are (1) the Upper Zambezi upstream of the gauging station Senanga with an area of 281 000 km2, (2) the Kafue River where the discharge is measured at the Kafue Hook Bridge with an area of 95 300 km2 and (3) the Luangwa River which is gauged a few kilometres upstream of the conﬂuence with the Zambezi River (142 070 km2). Chapter 2 Real-time Prediction of River Discharge 13

These watersheds cover together more than one third of the whole Zambezi watershed and contribute more than half of the total runoff at the mouth of the Zambezi, where the Upper Zambezi catchment contributes the largest amount (850 m3 s−1 mean annual discharge), the Kafue River discharges 300 m3 s−1 and the Luangwa River 700 m3 s−1. The Upper Zambezi watershed is mainly characterised by gentle slopes and large flood-plains along the course of the river. The largest flood-plain, the Barotse Plains, spreads along the river for around 200 km, a maximal width of 50 km and an area of around 7500 km2. Similarly, the Kafue river basin features a flood-plain, the Luangwa Swamps with an area of around 2500 km2. The main effect of the flood-plains is the attenuation of the flow and the loss of water through increased evaporation (Vörösmarty and Moore, 1991). The Luangwa river valley is an extension of the East African rift valley characterised by steep slopes mainly in the upstream. The tributaries of the Luangwa drain the steep escarpment of the rift valley and therefore have a quick response to rainfall (Winsemius et al., 2009).

2.3 Data

2.3.1 Soil moisture

The vadose zone is one of the most important components of the global water cycle. Through the coupling of water and energy fluxes, soil moisture determines the local and global climate. However, the variability of soil moisture is very high in both space and time. Traditional measurement methods, such as Time Domain Reflectometry, are reasonably accurate, but they provide information on a very local scale. Monitoring large areas is nearly impossible. Typically, a correlation between such measurements can be observed if they are not more than a few tens of meters to a few hundred meters apart (Western et al., 2004). On larger scales the temporal variation seems to be very stable since it is mainly influenced by climatic conditions (Brocca et al., 2010). Therefore, remotely sensed soil moisture data provide a valuable dataset for hydrological monitoring on a larger scale. There is a wide variety of techniques for measuring the soil water content through remote sensing. However, the data can only be retrieved by indirect measurements. Both, active and passive methods rely on the measurement of radiation intensities in a certain range of wavelengths. For passive systems operating in the thermal infrared wavelength band, the measurement target is the soil surface temperature (Verstraeten et al., 2006). The radiation intensity measured by systems operating in the microwave band is controlled by the dielectric constant of the top soil layer. Especially soil moisture products based on radar satellite imagery provide an attractive source for data since 14 2.3 Data

57° Antenna ERS-1

25° Orbit

18° Position 45.5° of 45° satellite 45° 25°

Ground track

57°

Figure 2.2: The setup of the ERS radar scatterometer instrument. The multiple antennas allow to observe the backascattering properties of the surface dependent from different incidence angles (changed after Wagner(1998)). the influence of cloud cover and changing atmospheric conditions is minimal. Although they are governed by the same physical principles, generally three types of microwave techniques are distinguished: Passive radiometry and the two active methods using synthetic aperture radar (SAR) and radar scatterometer (Wagner et al., 2007). SAR systems, providing data with a high spatial resolution, show a good performance over bare soils. Despite the significantly lower spatial resolution, the multiple antenna configuration of scatterometers can facilitate the data processing to reduce the influence of vegetation on the signal (Baghdadi et al., 2008). In this study the dataset of soil moisture derived from the radar scatterometer on board the two European remote-sensing satellites (ERS) is used (Wagner et al., 1999b). The ERS radar scatterometers are operating in the C-band at a frequency of 5.3 GHz using three sideways-looking antennas arranged at an angle of 45 degrees (Figure 2.2). The measured back-scattering intensity is dependent on different properties of the surface, mostly on the surface roughness, the vegetation and the soil moisture. Generally, wet soil results in higher back-scattering intensity than Chapter 2 Real-time Prediction of River Discharge 15 dry soil. Since the arrangement of the antennas allows for the ruling out of the effects of vegetation, and the surface roughness can be considered to be constant over time, the dry and the wet state of each pixel can be determined using a change detection algorithm (Wagner et al., 1999a).

2.3.2 Rainfall Besides the soil moisture data, rainfall data are used as forcing data. The rainfall dataset is provided by the NOAA Climate Prediction Centre (NOAA- CPC) for the Famine Early Warning Systems Network (FEWS NET) and can be downloaded free of charge from the Internet. A detailed description and an assessment of the quality of this data can be found in Section 4.2.1. The data are available at a 10 day interval starting from July 1995. FEWS NET rainfall data incorporate various satellite-based rainfall estimates and data measured at gauging stations (Herman et al., 1997). Since the soil moisture data used are available only up to January 2002, the period where soil moisture data and rainfall data overlap is only little more than six years.

2.3.3 Discharge Measured discharge data are used for updating the model in real-time. Daily discharge data are available at the outlets of the three sub-basins. For the Kafue and the Luangwa sub-basin the data available cover the whole period where rainfall and soil moisture data are available simultaneously. The discharge of the Upper Zambezi sub-basin is measured from October 1996 only.

2.4 Calculating discharge from soil moisture 2.4.1 Soil water column content While the surface soil moisture can be derived directly from the scatterometer data, the soil column water content has to be estimated. This is due to the fact that the electromagnetic waves in the microwave bandwidth only penetrate the top few centimetres of the soil. Wagner et al.(1999b) proposed a method to calculate a so-called Soil Water Index (SWI) based on a simple two-layer moisture balance model. It computes a weighted average of the past measurements −t using an exponential filter of the form exp( T ) and therefore acts as a low- pass filter. A value of 20 days was assigned to the parameter T globally. The dataset used in this study provides SWI data at a 10-daily time step. Scipal et al.(2005) concluded that even this low resolution soil moisture data can be applied in hydrological modelling. The scatterometer based soil moisture data are strongly correlated to the occurrence of rainfall events but less correlated to the magnitude of these rainfall 16 2.4 Calculating discharge from soil moisture events (Figure 2.3). In all three catchments the probability that a rainfall event has taken place grows for higher soil moisture in the same period, whereas the amount of rainfall is mainly correlated to soil moisture when the soil has not yet reached a certain degree of saturation (around values of 0.8). A similar effect can be observed if the correlation between the Basin Water Index (BWI) and the measured discharge is analysed (Figure 2.4). The BWI is calculated by averaging the SWI over the whole river basin (Scipal et al., 2005). The variation of the discharge is relatively small for low soil moisture values. If the values exceed 0.5 to 0.6 the variation suddenly increases. This indicates that the discharge is to some extent decoupled from the soil moisture as the soil approaches complete saturation. This decoupling is mainly caused by rainfall. Therefore modelling efforts which include rainfall data seem to be more realistic. It also shows, that to obtain the best correlation the discharge has to be shifted by very different time lags. Not surprisingly, the largest watershed shows a long time lag of two months. For the second largest watershed (Luangwa River) the time lag has to be set to zero to obtain an optimal fit, indicating that the response time is significantly less than 10 days. The optimal time lag for the Kafue River up to Kafue Hook Bridge is one month. These differences can be explained by the geological and geomorphic settings of the watersheds. The more gentle slopes of the Upper Zambezi and the Kafue River and the large wetlands retard the flow of the water. The water storage in wetlands cannot be tracked by the soil moisture product used. These wetlands are usually small compared to the area of the whole watershed. They therefore cause an additional retardation of the discharge formed outside the wetlands. The influence of the wetlands on the soil moisture data can be seen in Fig- ure 2.5. The Lukanga Swamps in the Kafue River basin create a distinct signal in the soil moisture measured. Due to the flooded area during the wet season, which results in a low backscattering intensity, the soil moisture inside the wetland is classified as being low. In the dry season one can clearly see that the soil moisture in the wetland itself is significantly higher than in the surrounding areas. Thus the influence of the wetlands on the discharge is not only limited to the retardation. In strongly seasonal climates they can also contribute to the low flows in the dry season. In the wet season they are less significant, since rainfall is dominating the river discharge.

2.4.2 Soil moisture – runoﬀ model In hydrological forecasting, fully distributed, physically based models provide the ability to account both for the heterogeneity of a watershed and physical changes of the system (e.g. the construction of irrigation schemes or land use changes). On the other hand, simple conceptual models can provide a satisfactory performance for forecasts. This can be an advantage, especially in regions with limited facilities for the measurement of relevant hydrological data. Chapter 2 Real-time Prediction of River Discharge 17

(a) 100 1 Average rainfall Probability of rainfall 80 0.8

60 0.6

40 0.4 Rainfall (mm) 20 0.2 0 0 0.2 0.4 (b) 0.6 0.8 1 100 1

80 0.8

60 0.6

40 0.4 Rainfall (mm) 20 0.2 0 0 0.2 0.4 (c) 0.6 0.8 1 100 1

80 0.8

60 0.6

40 0.4 Rainfall (mm) 20 0.2

0 0 0.2 0.4 0.6 0.8 1 SWI (m3 m−3)

Figure 2.3: The probability of a rainfall event given a Soil Water Index (SWI) class and the average rainfall amount for the same classes for the three watersheds Upper Zambezi (a), Kafue River (b) and Luangwa River (c). For both, the SWI and the rainfall, 10-daily values are used. 18 2.4 Calculating discharge from soil moisture

) 3000 1500 5000 −1

s 4000 3 1000 2000 3000

2000 1000 500 1000

Discharge (m 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 BWI (−) BWI (−) BWI (−) (a) (b) (c)

Figure 2.4: Correlation between Basin Water Index (BWI) and discharge shifted by the time lag (∆τ) which resulted in the best correlation. (a) Upper Zambezi: ∆τ = 60 d; (b) Kafue River: ∆τ = 30 d; (c) Luangwa River: ∆τ = 0 d.

100 100 −12° −12° 80 80

−13° 60 −13° 60

40 40 SWI (%) SWI (%) −14° −14° 20 20

0 0 26° 27° 28° 26° 27° 28°

(a) Wet season; January 30, 1993 (b) Dry season; September 30, 1993

Figure 2.5: The inﬂuence of the Lukanga Swamps wetland (arrow) on the measured soil water index (SWI). Chapter 2 Real-time Prediction of River Discharge 19

Rainfall (R) Soil moisture (BWI) time lag k1BWI R × BWI dSS ∆τS ∝ dt k2SS

∆τGW k1(1 BWI) R k4SGW − × dSGW dt

Figure 2.6: Structure of the conceptual hydrological model.

The ﬁnding that the BWI correlates well with the observed discharge only for low values of BWI leads to the conclusion that additional data are needed to model the discharge. This is the reason why rainfall data are included in the model. To model the discharge at the outlet of a basin a simple conceptual model was developed. The model consists of two compartments: a surface water storage and a subsurface water storage (Figure 2.6). All input data of the model, the soil moisture and the rainfall, are averaged over the whole river basin. Hence, the spatial variability is not considered. The basin-averaged soil moisture is equivalent to the Basin Water Index (BWI) introduced by Scipal et al.(2005). The model we developed in this study is based on the following balance equations: IGW = k1AP (t) (1 − BWI(t)) (2.1)

∆SS(t) = k1AP (t) − IGW − k2SS(t − 1) (2.2) ∆t

∆SGW(t) = max (IGW + k3 (BWI(t) − BWI(t − 1)) ; 0) (2.3) ∆t −k4SGW(t − 1) where SS and SGW are the surface storage volume and the subsurface storage 3 volume in m , respectively, IGW is the direct inﬁltration of rainfall to the subsurface storage in m3/10 d, P is the average rainfall in the river basin in 2 mm/10 d, A is the total area of the watershed in km and ki are the model parameters. The BWI is dimensionless and can take values between 0 and 1. 20 2.4 Calculating discharge from soil moisture

The storage compartments are considered to be single linear storages. De- pending on the value of the BWI, a part of the rainfall is routed to the surface water storage whereas the remaining water volume is routed to the subsurface storage. If BWI is 0 all water is routed to the subsurface. If BWI is 1 all water is routed to the surface storage. The storage change in the subsurface is modelled through the measured change in soil moisture (BWI(t)−BWI(t−1)). The sum of the rainfall routed to the subsurface and the measured change in soil moisture represent the recharge to the subsurface compartment which is not allowed to be negative in this model. For the surface runoff (QS) and the subsurface runoff (QGW) two different time lags ∆τS and ∆τGW are applied to calculate the total discharge according to Equation (2.4).

Q(t) = QS(t − ∆τS) + QGW(t − ∆τGW) (2.4) with QS(t) = k2SS(t − 1) and QGW(t) = k4SGW(t − 1).

According to Equation (2.1–2.4) the parameter k1 is dimensionless, the pa- −1 3 −1 rameters k2 and k4 have the unit s and k3 has the unit m s . A physical interpretation of the parameters assigns the parameter k1 to the losses through evaporation and interception of rainfall before it enters a storage. Besides being dependent on the infiltration properties of the soil it also depends on the average retention time in the catchment and is therefore correlated to the size of the watershed. For larger watersheds a lower value of k1 is expected. The parameter k3 relates the BWI to the total volume of water stored in the subsurface zone. The two parameters k2 and k4 are the rates at which the linear storage compartments are depleted. These model parameters are calibrated by running the model in deterministic mode using the Levenberg-Marquardt algorithm (Marquardt, 1963). In a strict sense, parameter T which governs the estimation of the soil column water content (see Section 2.4.1) is a model parameter for itself. It drives the infiltration rate at which the measured water content at the surface flows downwards. A sensitivity analysis revealed that parameter T has only a marginal influence on the goodness of the fit between the observed and the modelled discharge. The time lags (∆τS and ∆τGW) are mostly dependent on the size of the watershed. In this model the time lags are considered to be an integral multiple of the length of a single time step (∆τ = n∆t, n = 1, 2, 3,...). Due to the discrete nature of the time lag, the parameter identification is done in two steps. For different pairs of ∆τS and ∆τGW the model parameters ki are calibrated. The set of time lags with the minimal root mean square error (RMSE) between the observed and the computed flow together with the corresponding ki are then chosen as the optimal parameter set. Since the input data used are available every ten days the time step ∆t of the model was set to ten days. Chapter 2 Real-time Prediction of River Discharge 21

A long time lag entails a long potential forecast period. Therefore, models using only soil moisture and rainfall as input have a longer lead time in larger watersheds.

2.4.3 Reference method The regression model developed by Scipal et al.(2005) was used for comparison. This model applies a logarithmic regression between soil moisture and discharge (Equation 2.5). It uses three parameters representing a baseﬂow (Q0), a hydrometric scaling factor χQ and a time lag ∆τ. BWImax Q(t) = Q0 + χQ ln (2.5) BWImax − BWI(t − ∆τ)

To assess the overall quality of the model presented above it is run in deterministic mode, without the data assimilation step. The simulated discharges are compared to the measured ones by calculating the root mean squared error (RMSE) and the Nash-Sutcliffe efficiency (Nash and Sutcliffe, 1970). Further- more, they are compared to the discharges simulated with the reference model (Equation 2.5).

2.5 Real-time modelling and data assimilation 2.5.1 Sequential data assimilation Kitanidis and Bras(1980a) stated that effective water management in a river basin system needs a reliable real-time forecast. This involves a continuous correction of the forecasts based on the prediction errors of earlier forecasts. The application of a model is accompanied by several sources of errors, such as model input and parameter uncertainty. This leads to a deficient knowledge of the system states. Hence it is appropriate to use observations to update the states of the system (Kitanidis and Bras, 1980a,b). This so-called data assimilation problem can be solved in different ways. In real-time applications a new assimilation problem is formulated at every time step. To solve this problem efficiently sequential assimilation techniques are considered superior (McLaughlin, 2002). Sequential assimilation algorithms, also known as filtering algorithms, are divided into two steps: first a propagation step, where the system states are propagated through time using a model and forcing data; second an update step, where the modelled states of the system are updated based on the difference between the model output and the real-world observation. A comparison between conventional modelling and a real-time modelling framework including data assimilation can be found in Figure 2.7. 22 2.5 Real-time modelling and data assimilation

System state (t) System state (t) Input data Input data Observations Observations Model C Model DA

System state (t + 1) System state (t + 1)

(a) Conventional modelling. Estimation of (b) Real-time modelling. Input data, model parameters using a calibration pro- model parameters and observation data cedure (C) and historical observation data. are incorporated as statistically distributed variables. Model parameters are updated using a data assimilation procedure (DA).

Figure 2.7: Conventional modelling compared to real-time modelling. The thick arrows in the real-time modelling scheme illustrate the fact, that not a single value is used, but a number of values (ensemble) reﬂecting the statistical properties of the parameter. Chapter 2 Real-time Prediction of River Discharge 23

2.5.2 The Ensemble Kalman Filter The Ensemble Kalman Filter (EnKF) provides a state of the art method of sequential data assimilation (McLaughlin, 2002). The EnKF was first introduced by Evensen(1994) and its application was clarified by Burgers et al. (1998). To solve nonlinear filtering problems it has proven to be both efficient and robust. Its popularity in a wide field of applications is mainly based on the ease of implementation and its simple conceptual formulation (Evensen, 2003). EnKF has, along with standard batch calibration, the advantage of being able to incorporate a wide range of uncertainties. The uncertainties of forcing data, model parameters and model output are considered separately but can be incorporated in the same mathematical scheme (Thiemann et al., 2001). As discussed above, data assimilation is usually divided into two steps: the propagation step and the update step. In the propagation step, the state ψt of a model f is propagated forward in time, based on forcing data ut

f ψt+1 = f(ψt, ut), (2.6)

f providing the predicted model state, or forecast ψt+1 at time t + 1. In Monte- Carlo based methods, such as EnKF, the model state ψ is represented by a matrix with dimensions N × s, where N is the ensemble size and s is the number of state variables. Also, model forcing ut consists of an ensemble, generated by adding perturbations to a measured value (see Section 2.5.4). As all sequential filter methods, the update step of the EnKF is applied to reinitialise the states of a model whenever observation data are available. The predicted model state ψf is updated by the weighted difference between the predicted observation Hψf and the observation d to obtain the analysed state ψa: ψa = ψf + K(d − Hψf ) (2.7) with the Kalman gain matrix K defined as

K = Pf HT (HPf HT + R)−1, (2.8) where H is the measurement operator matrix, which relates the model state ψ to an observation. Hψ can also be regarded as the “predicted observation”. The error covariances of the predicted states and the measurement are denoted as Pf and R. Pf is deﬁned by the following expected value expression, dependent on the true state of the system ψt:

f f t f t T P = E (ψ − ψ )(ψ − ψ ) (2.9)

However, since neither the true states nor their error covariance are usually known, they are estimated from the ensemble of states. The mean of the states 24 2.5 Real-time modelling and data assimilation

f ψ is assumed to be the best estimate for the true value. Thus, we can calculate the error covariance of the ensemble f h f f f f T i Pe = E (ψ − ψ )(ψ − ψ ) . (2.10) To carry out the assimilation it is essential to treat the observations as a random variable (Evensen, 2003). Therefore, we define the ensemble of observations dj as dj = d + j, with j = 1,...,N (2.11) where ε is the matrix of perturbations. This matrix is used to represent the estimated error covariance of the observations T Re = (2.12) With this definition the update step of the EnKF can be written as a f f T f −1 f ψ = ψ + Pe H (HPe H + Re) (d − Hψ ) (2.13) f Since in this formulation the error covariance of the states Pe is estimated, we have to make sure that the ensemble represents the real uncertainty involved. Generally, too small ensemble sizes lead to underestimated error variances (van Leeuwen, 1999). This is partly due to the fact that the gain K used to update the ensemble is calculated from the same ensemble. Also a small ensemble cannot represent the uncertainty of the states adequately, because its variance is poorly represented by the sample (ensemble). van Leeuwen(1999) recommends to use an ensemble size of at least 100 members. Since the conceptual model used here is not very demanding in terms of computation time, we can afford to use a large ensemble, without compromising performance. Therefore, an ensemble size of 1 000 is chosen.

2.5.3 Application of the real-time model The state variables which are updated in this study are the storage volumes SS and SGW. As observation data the measured discharge is used. Observed discharge data are available on a daily basis. Since the temporal resolution of the model is 10 days, data assimilation is carried out in every time step. To assess the possible accuracy of the forecast, the model is run in hindcast mode which includes the data assimilation step for the historic time series from 1995 to 2002.

2.5.4 Generating input data ensembles Rainfall For the real-time modelling framework an ensemble of randomly perturbed input and observation data are generated. This step has to be carried out very Chapter 2 Real-time Prediction of River Discharge 25

1500 Measured discharge Assimilated discharge (Gaussian distribution) Assimilated discharge (gamma distribution) )

−1 1000 s 3

500 Discharge (m

0 1996 1997 1998 1999 2000

Figure 2.8: Comparing the assimilated discharges obtained by the model using rainfall errors following a Gaussian distribution (red dotted line) and a gamma distribution (blue dashed line). carefully since the statistical distribution the errors follow, is a very crucial component. It is usually safe to assume that the errors of some input and observation data are following a Gaussian distribution. For some data however, this assumption can lead to an unexpected behaviour of the model. For the model presented here it was found that the errors of the rainfall data have to be introduced carefully. In Figure 2.8 the effect of the chosen distribution is shown. When for the errors of the rainfall a Gaussian distribution is used, the simulated discharge is overestimated to an extent that the data assimilation procedure is not able to correct the model states sufficiently. The main reason for this are the negative values which can occur when the noise is added to the initial data. These negative values have to be filtered, which is usually done by either setting them to zero or by omitting these values. Thus, the ensemble mean increases significantly if the percentage of negative values is high. This is also the reason why the strongly overestimated discharges mainly occur from December to April during the rainy season (Figure 2.8). Since assuming a Gaussian distribution of the errors of the rainfall data leads to unsatisfying model results, the ensemble is generated using the gamma distribution on the NOAA-CPC rainfall data. The gamma distribution only needs two parameters (Γ(k, θ)). The expected value of a gamma distributed random√ variable X is defined as E(X) = kθ and the standard deviation as σX = kθ. The standard deviation is set to a fixed value (σP = 50 mm) which 26 2.5 Real-time modelling and data assimilation reflects the uncertainty of the rainfall data product (Herman et al., 1997). Using the measured rainfall amount as expected value of the perturbed rainfall for each time step, the two parameters k and θ can be calculated. Based on ~˜ these parameters the rainfall ensemble Pt at time t is generated according to Equation (2.14).

 ˜1  Pt P 2 σ2 ˜~  .  ˜i t P P t = . , with Pt ∼ Γ(k; θ) = Γ 2 ; , (2.14)  .  σ Pt ˜i P Pt where Pt is the measured rainfall at time t.

BWI

For the uncertainty of the BWI a Gaussian distribution is assumed and the standard deviation is set to 0.025. This is according to the standard error found by Ceballos et al.(2005) for the SWI. Whether this uncertainty can be translated directly to the BWI is unclear. The uncertainty of the BWI is a quantity which is hard to estimate. Mathe- matically it is the arithmetic average of a number of SWI values. Therefore the uncertainty of the BWI should be smaller than the uncertainty of the single SWI values. However, only studies assessing the uncertainty of the SWI are carried out up to now. Wagner et al.(2003) estimated the upper limit of the SWI measurement error to be 0.03 m3 m−3 to 0.07 m3 m−3. A more detailed analysis by Ceballos et al.(2005) found an error between ground measurements and the SWI around 0.025 m3 m−3. Whether these uncertainties can be translated directly to the BWI needs to be further investigated. They provide more like a worst case error. The uncertainty of the input data is a crucial parameter for the Ensemble Kalman Filter. However, the uncertainties of the rainfall data are always much bigger than those of the BWI. With a mean rainfall in one time step of around 30 mm the uncertainty of the rainfall product is around 50 mm (RMSE). This implies that the influence of the BWI uncertainty is limited. The sensitivity analysis reveals that the uncertainty of the BWI has almost no effect on the accuracy of the forecast within an uncertainty range between 0.0 m3 m−3 and 0.07 m3 m−3 (Figure 2.9 and 2.10). There is some influence on the uncertainty of the forecast. If one increases the uncertainty by 0.01 m3 m−3 the width of the error band is increased by around 10%. However, the dominant sources of uncertainty in the real-time modelling framework are the rainfall data. Chapter 2 Real-time Prediction of River Discharge 27

100

80 ) −1 s 3 60

40 RMSE (m 20 assimilated 10 d 20 d 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Uncertainty of BWI (m3 m−3)

Figure 2.9: Eﬀect of the uncertainty of the BWI on the RMSE of the predicted discharge (10 d and 20 d) and of the model error at the time of data assimilation.

0.8

0.6

0.4

0.2 assimilated 10 d Nash−Sutcliffe efficiency (−) 20 d 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Uncertainty of BWI (m3 m−3)

Figure 2.10: Effect of the uncertainty of the BWI on the Nash-Sutcliffe efficiency of the predicted discharge (10 d and 20 d) and of the model error at the time of data assimilation. 28 2.6 Results and discussion

Table 2.1: Estimated parameters for the three sub-basins and the 95% conﬁ- dence interval for each parameter.

Upper Kafue Luangwa Zambezi River River

∆τS 40 d 20 d 10 d ∆τGW 100 d 70 d 50 d −5 k1 (×10 ) 4.22 ± 1.13 5.00 ± 0.99 10.44 ± 3.68 −1 k2 (s ) 0.22 ± 0.09 0.29 ± 0.09 0.68 ± 0.46 3 3 −1 k3 (×10 m s ) 32.23 ± 6.41 5.61 ± 1.32 18.06 ± 5.58 −1 k4 (s ) 0.15 ± 0.03 0.13 ± 0.03 0.35 ± 0.09

Discharge For the observed discharge data the variance of the added noise is proportional to their magnitude with a standard deviation of 0.05 times the measured value, as the absolute measurement error of discharge measurements is generally considered to be dependent on the discharge itself. As for the BWI, the discharge perturbations are considered to follow a Gaussian distribution.

2.6 Results and discussion

The parameters for the developed model are calibrated for all three watersheds. To analyse the performance of the model, it was assessed both in a deterministic modelling mode and in hindcast modelling mode.

2.6.1 Deterministic model The model parameters obtained by calibration in the deterministic mode are shown in Table 2.1. For the time lags one can see a similar dependency on the size and geomorphology of the diﬀerent watersheds as it was already observed for the correlation analysis (Figure 2.4). The Upper Zambezi catchment has by far the longest response time whereas the Luangwa river basin shows a relatively quick response. The only model parameter that shows a distinct dependency on the area of a watershed is the parameter (k3) that correlates the BWI to the total volume of water stored inside the subsurface storage. One can assume that the wetlands present in the Upper Zambezi and the Kafue watersheds have a huge impact on the water storage capacity. The parameter k1 mainly reﬂects the water losses in the watershed. The Upper Zambezi basin, being the largest watershed, shows the lowest value for Chapter 2 Real-time Prediction of River Discharge 29

k1. The Kafue River basin shows a very similar value of k1 which suggests that the soil properties in the two basins are similar. However, due to the absence of detailed information on the soil properties in the area this statement cannot be verified. The influence of the size of the watershed on the parameter k1 is marginal. While the area of the Luangwa basin is only one half of the size of the Upper Zambezi watershed the parameter value of k1 is twice as big. This supports the conclusion that the water drains quickly from the surface to the river and therefore losses are low. While the parameters k2 and k4 show similar values for the Upper Zambezi basin and the Kafue river, they are much higher for the Luangwa river. This correlates well with the generally steeper slopes in the Luangwa basin where water flows faster. The performance of the model running in the deterministic mode is illus- trated in Figure 2.11 and compared to the reference method. The modelled discharge agrees in general quite well with the measured flows. For all the applied models the root mean squared error (RMSE) and the Nash-Sutcliffe efficiency are calculated (Table 2.2 and 2.3). The model developed gives better results than the reference method for the Upper Zambezi and the Kafue River basin where both the Nash-Sutcliffe efficiency and the RMSE are slightly higher or lower, respectively. It is clearly visible that the flood maxima are reproduced much better than in the reference method. Obviously the inclusion of rainfall information is most beneficial for the maxima as the correlation between BWI and rainfall deteriorates for large precipitation events. However, for the Luangwa river the model performance was not satisfactory when running in the deterministic mode. It even showed a slightly poorer performance than the reference method which also does not allow for adequate modelling of the situation. Due to the parameter uncertainty the error band becomes large, especially in the wet season. This uncertainty is mostly attached to the model parameter k1 since with a high rainfall amount a slight change in the parameter can greatly affect the amount of water which is routed to the system. A drawback for the testing of the method is the short time period over which data are available. The model relies on soil moisture data, on rainfall data and on measured discharge. The overlap of these three datasets dictates the longest continuous time span that can be modelled. Eventually, it is only possible to test the model on a period of a bit more than six years, for the Upper Zambezi catchment even less. For this reason a validation of the model was not possible. The available data were used to obtain a stable calibration. The application of the model provides a seamless integration of remote sensing products. With only four parameters and a simple conceptual formulation this model is applicable to a class of watersheds which comply with certain characteristics. All data used are developed to an operational standard. Therefore 30 2.6 Results and discussion

(1) Measured discharge ) 3000 Modelled discharge

−1 Reference method s 3 2000

1000 Discharge (m

0 1997 1998 1999 2000 (2)

) 1000 −1 s 3

500 Discharge (m

0 1997 1998 1999 2000 (3) 5000

) 4000 −1 s 3 3000

2000

Discharge (m 1000

0 1997 1998 1999 2000 Year

Figure 2.11: The discharge simulated in the hindcast mode (red line) including the 95% conﬁdence interval compared to the measured discharge (blue line) and the results of the reference method (black line) for the three watersheds Upper Zambezi (1), Kafue River (2) and Luangwa River (3). Chapter 2 Real-time Prediction of River Discharge 31

Table 2.2: RMSE of the diﬀerent forecast lead times up to the maximum possible lead time (∆τS). For comparison the RMSE of the deterministic model run and the reference method are indicated. All values are given in m3 s−1.

Upper Zambezi Kafue River Luangwa River Lead time: Lag 4 (40 d) 281.5 Lag 3 (30 d) 265.1 Lag 2 (20 d) 238.8 70.5 Lag 1 (10 d) 199.1 59.8 483.6 assimilated 131.4 46.5 412.6 Deterministic 269.3 99.5 513.7 Reference 285.0 103.8 502.6 the user does not have to undertake extensive data processing. This model is especially suited for use in a real-time modelling framework.

2.6.2 The influence of the parameter T for SWI The use of the soil water index (SWI) to calculate the discharge implies that the filter parameter T which is used to generate the SWI from the surface soil moisture is a model parameter in a very strict sense. This parameter therefore should be calibrated together with the model parameters ki. However, including it in the calibration is only useful if the parameter is sensitive and not or only weakly correlated with the other model parameters. In addition we think that a conceptual model should have as little parameters as possible. For the application of surface soil moisture (SSM) data as model input it has to be averaged in time over 10 days (the time step of the model is 10 days due to the availability of rainfall data) and in space to calculate the BWI. This averaging already leads to BWI values which are very similar to the BWI calculated from the soil water index (SWI). The BWI obtained by using the SSM data directly is therefore already a filtered time series. T can be considered as a parameter which drives the infiltration velocity. A low value of T corresponds to a quick response of the total soil moisture (SWI) to the SSM, a high value of T corresponds to a slow response of the SWI to the SSM. The influence of the parameter T on the model parameters ki is shown in Table 2.4(a) and 2.4(b). While T correlates well with the two parameters k2 and k3, its influence on the other parameters is generally low. k2 governs the surface runoff, which is slower with quicker infiltration rate. k3, which relates the BWI to the total amount of water stored in the subsurface, is higher for slower infiltration. The influence on the quality of the fit is marginal, even with 32 2.6 Results and discussion

Table 2.3: Nash-Sutcliffe efficiency of the different forecast lead times up to the maximum possible lead time (∆τS). For comparison the Nash-Sutcliffe efficiency of the deterministic model run and the reference method are indicated.

Upper Zambezi Kafue River Luangwa River Lead time: Lag 4 (40 d) 0.85 Lag 3 (30 d) 0.87 Lag 2 (20 d) 0.90 0.84 Lag 1 (10 d) 0.93 0.88 0.68 assimilated 0.98 0.96 0.80 Deterministic 0.90 0.82 0.74 Reference 0.88 0.80 0.75 the simple 10 days average good calibration results can be obtained. However, even for the Luangwa catchment the application of the SWI with T = 20 d seems to be better than just using the averaged SSM. The concern that the use of SWI instead of SSM suppresses peaks in discharge was found to be not justified. The Nash-Sutcliffe efficiency which is sensitive to the predictive accuracy of peaks is slightly higher if the SWI (T = 20 d) is used.

2.6.3 Real-time model The successful application of a real-time prediction model does not necessarily depend on the mechanistic correctness of the model, but it needs to reflect the correct tendency. When operating in the data assimilation mode the quality of the forecast is of interest. The length of the forecast period is defined by the shortest time lag (∆τ) in the model. The ensemble of the forecast can be represented by the ensemble mean and the confidence interval. As time approaches the time of prediction for a certain time step the error generally gets smaller (Figure 2.12). This statement is supported by the analysis of the RMSE and the Nash-Sutcliffe efficiency (Table 2.2 and 2.3). While the prediction for the maximum forecast time shows the highest RMSE and lowest coefficient of efficiency, the model prediction gets significantly more accurate for shorter forecast periods. Again the absolute error of the prediction is much higher in the wet season, whereas the relative error is especially high during ascending and receding flows (Figure 2.12). These results show that the model presented is capable of providing useful discharge forecasts in semi-arid river basins. Yet this model can not be applied to every river since its model structure is not designed to reproduce the Chapter 2 Real-time Prediction of River Discharge 33

Table 2.4: Influence of the parameter T on the model parameters ki in (a) the Kafue river basin and (b) the Luangwa watershed. To give an estimate on the goodness of the fit the RMSE and the Nash-Sutcliffe efficiency (E) are calculated. For the 10 days average the arithmetic mean was calculated from the SSM measurements available within the time step.

(a) Kafue river

−5 3 k1 (×10 ) k2 k3 (×10 ) k4 RMSE E 10 days average 6.66 0.19 3.01 0.12 111.0 0.78 T = 5 d 6.33 0.21 3.55 0.12 108.0 0.79 T = 10 d 5.80 0.22 4.47 0.12 104.8 0.80 T = 20 d 5.00 0.29 5.61 0.13 99.2 0.82 T = 30 d 4.82 0.34 6.03 0.14 97.8 0.83

(b) Luangwa river

−5 3 k1 (×10 ) k2 k3 (×10 ) k4 RMSE E 10 days average 17.6 0.34 7.36 0.28 550.9 0.71 T = 5 d 16.3 0.39 8.67 0.30 561.5 0.69 T = 10 d 12.1 0.47 15.2 0.29 526.6 0.73 T = 20 d 10.4 0.68 18.1 0.35 513.7 0.74 T = 30 d 13.6 0.73 13.5 0.43 523.8 0.73 34 2.6 Results and discussion siiainstep. assimilation 2.12: Figure

−1000 3 −1 −1000 3 −1 −1000 3 −1 −1000 3 −1 −1000 3 −1 1000 1000 1000 1000 1000 (m−500 s ) (m−500 s ) (m−500 s ) (m−500 s ) (m−500 s ) 500 500 500 500 500 0 0 0 0 0 1997 a pe abz basin Zambezi Upper (a) assimilated 10 d 20 d 30 d 40 d boueadrltv oeaterrfraltrewtrhd o h ieetfrcs eid n the and periods forecast diﬀerent the for watersheds three all for error forecast relative and Absolute 1998 1999 2000 −100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100

(%) (%) (%) (%) (%) 3 −1 3 −1 3 −1

−500 (m−250 s ) −500 (m−250 s ) −500 (m−250 s ) 250 500 250 500 250 500 0 0 0 1997 assimilated 10 d 20 d relative absolute b au river Kafue (b) 1998 1999 2000 −100 −50 0 50 100 −100 −50 0 50 100 −100 −50 0 50 100

(%) (%) (%)

(%) (%) Chapter 2 Real-time Prediction of River Discharge 35 processes in watersheds with a relatively low storage volume and a quick response to rainfall events. This is the case in the Luangwa river basin where uncertainties become very large. The SWI which was used to calculate the BWI assumes a uniform soil thickness everywhere. The actual thickness of the soil in a river basin does not have a big impact on the model results. The spatial variability of the soil thickness, however, has a huge inﬂuence on the results because certain areas with a relatively thin soil layer can suddenly dominate the behaviour of the system.

2.7 Other modelling approaches

2.7.1 The Pitman model

The Pitman model was developed to address the needs of hydrological modelling in Southern Africa. For most of the basins discharge data are available for a short period only. For some rivers even no data are available at all. This situation fosters the need of including as many physical information as possible into the model (Pitman, 1973). Since there are still many ungauged basins in Southern Africa, the Pitman model remains to be quite popular (Hughes and Metzler, 1998; Hughes et al., 2006, 2010). The Pitman model uses precipitation data and the potential evapotranspiration as input. The model is designed to deliver simulated discharges on a monthly time step. The model design features two active storages, the interception storage and the soil moisture. Evapotranspiration is only considered to be active from these two storages. Many hydrological processes are simulated explicitly. These processes include interception, direct runoff on impervious areas and resulting from exceeding the infiltration capacity, infiltration to the soil moisture and runoff from soil moisture. Additionally the runoff are attenuated by a certain time lag. All the processes are formulated as empirical relation- ships between the physical quantities. The spatial variability of soil infiltration properties within the catchment is included in the model by describing these parameters using frequency distributions. Flow routing is implemented using the Muskingum equation (Ponce, 1994). In gauged catchments the model parameters can be obtained through calibration. In ungauged catchments the parameters can also be estimated through including soft information, such as soil maps. The Pitman model was successfully applied to a wide variety of river basins in South Africa. Its structure allows the application to all catchments where precipitation is not falling as snow. Such a model could be useful if one wishes to incorporate remote sensing data, such as soil moisture and rainfall, into a more physically based forecast framework. 36 2.7 Other modelling approaches

Within the KAFRIBA modelling toolbox for the upper Kafue Basin, the Pitman model is used to provide a forecast of the discharges based on actual rainfall measurements and a seasonal forecast (Schelle and Pittock, 2005; DHV, 2006). Details about KAFRIBA are found in Section 4.3.3. Chapter 3

Flooding patterns

3.1 Flooded area from MODIS

Flooding patterns derived from satellite data can provide valuable information for the calibration of hydrological models (Milzow et al., 2009a). However, datasets suitable for the detection of inundated areas have to be chosen carefully. For hydrological applications in general, long time series covering the whole year are needed. For wetland applications a number of methods has been developed. McCarthy et al.(2003) developed a method for automatic classification of the flooded area in the Okavango Delta using the NOAA Ad- vanced Very High Resolution Radiometer (AVHRR). While only providing a resolution of 1 km the AVHRR dataset covers a period of more than 30 years. The seasonal and the inter-annual variation can be observed. The low resolution in combination with the applied clustering algorithm however, leads to an overestimation of the flooded area (Milzow et al., 2009b). In addition, for optical wavelengths only cloud free scenes can be used which reduces the number of usable scenes and thus the temporal resolution. Data available from higher resolution sensors have often a limited spatial or temporal coverage, which makes data acquisition and data processing more difficult. To obtain both a long temporal coverage and a high temporal resolution the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument on- board the Terra and Aqua satellites operated by NOAA provides an ideal data source. The MODIS sensor acquires data in 36 spectral bands including infrared and the visible range (wavelengths of 14 000 nm to 400 nm). Since these fractions of light are heavily influenced by atmospheric conditions (e.g. water vapor content) some atmospheric correction has to be carried out. The data product used (MOD09) includes 7 bands which are already corrected. The spatial resolution is 500 × 500 m2. These data are used to calculate the flooded area. The data are available on a daily basis with some data gaps due to maintenance data loss.

37 38 3.1 Flooded area from MODIS

8000 7000 )

2 6000 5000 4000 3000

Flooded area (km 2000 1000 0 2002 2004 2006 2008 2010 Time

Figure 3.1: Time series of the total ﬂooded area in the Kafue Flats derived from MODIS satellite data using the NDWI.

3.1.1 Detection of flooded areas from the NDWI A very simple method to calculate the flooded area is to use the so called Normalized Difference Water Index (NDWI). It uses the reflectance in the near infrared spectrum (band 2, 841 nm - 876 nm) and in the short wave infrared spectrum (band 5, 1230 nm - 1250 nm). The NDWI is sensitive to the presence of liquid water on the earths surface (Gao, 1996).

NIR − SWIR ρ2 − ρ5 NDWI = = , (3.1) NIR + SWIR ρ2 + ρ5 where ρi is the surface reflectance for each band. Open water surfaces are usually represented by positive values of the NDWI. Like all passive satellite systems operating in the infrared and visible range of the light, MODIS data are heavily influenced by clouds. If these clouds are not detected before information is derived from the satellite images, erroneous results are likely. The data product used already includes the information whether a pixel is covered by clouds or influenced by the shadow of a cloud. This cloud mask is applied before the NDWI is calculated.

3.1.2 Results In Figure 3.1 the time series of the flooded area as calculated from the MOD09 dataset is shown. The seasonality of the flooding is captured very well. How- Chapter 3 Flooding patterns 39 ever, during the wet season when the area is prevalently covered by clouds the fluctuation of the measured flooded area is very high. Only after the rainy season, during the period of receding floods the flooded area shows a smaller day to day fluctuation. Other than the flood recession the period of rising floods is captured poorly. This is due to the timing of the rainy season and the high flows; the rainy season starts before the inflow to the floodplain increases. In Figure 3.2 one can see that the difference of the NDWI between the dry season (October) and the wet season (February) is considerable. In the dry season the lagoons (Chunga Lagoon and Blue Lagoon) as well as the main river channel and its surroundings are captured very well by the NDWI method. All dry areas show distinct negative values. In the wet season the situation presents itself differently. Almost the whole area of the image shows positive values, also in areas which are normally not flooded. This might lead to a significant overestimation of the flooded area. The NDWI is mostly sensitive to presence of liquid water and therefore yields generally high values in the rainy season when liquid water is abundant. This problem of overestimation adds to the difficulties in tracking the dynamics of the flooding due to cloud cover. The application of passive satellite systems will always suffer from these shortcomings. Due to the atmospheric conditions changing from day to day either the data has to be corrected on a daily basis, which depends on accurate data from the ground, or simple approaches, such as the NDWI, have to be applied. The only alternative to this situation is the use of active satellite systems such as radar devices.

3.2 Flooded area from ENVISAT ASAR

In this study Wide Swath Level 1 data from the ASAR instrument operating in C-band (5.6 cm wavelength) on board the ENVISAT satellite were used. The data have a pixel spacing of 75 m and the transmitter-receiver polarization HH (horizontal/horizontal) was used. Each data point consists of the intensity of the back-scattered signal only. These data are acquired by the satellite approximately once a month. Radar remote sensing techniques have been proven to be an important data source for monitoring hydrological processes. The sensitivity to open water surfaces and to soil moisture in the top soil layer oﬀer a large potential for mapping changes in earth surface properties related to water while being nearly independent of weather conditions and completely independent of daytime (Rosenqvist and Birkett, 2002; Bartsch et al., 2008, 2009). The interaction of the radar signal with the earth surface is controlled by the surface roughness and the dielectric constant of the top soil layer. A high dielectric constant leads to high reﬂectivity whereas high surface roughness leads to high scattering. Due to the high dielectric constant and the generally 40 3.2 Flooded area from ENVISAT ASAR

8 300 0.4 0.2 0 8 250

−0.2 NDWI (−) Northing (km) −0.4 400 450 500 550 600 Easting (km) (a) 28. October 2003

8 300 0.4 0.2 0 8 250

−0.2 NDWI (−) Northing (km) −0.4 400 450 500 550 600 Easting (km) (b) 6. February 2004

Figure 3.2: The NDWI in the Kafue Flats during the dry season (October 2005) and the wet season (February 2004). UTM coordinates, zone 35, south. Chapter 3 Flooding patterns 41

8 280 Northing (km)

8 250

540 570 600 Easting (km)

Figure 3.3: ASAR image of the lower Kafue Flats from the flooding season (May 2009). The flooded areas can clearly be identified as the very dark areas mainly along the fringes of the floodplain and as very bright areas in the western part of the image (UTM coordinates, zone 35, south). smooth surface, open water surfaces are characterised by a low back-scattering intensity on radar images. At wavelengths of 23.5 cm (L-band) or longer, radar signals can penetrate vegetation canopy, which allows to see inundation in presence of plants covering the surface. In forested areas microwave signals interact within the vertical forest profile with branches and trunks. However, the intensity of the back- scattered signal strongly depends on ground properties. Dry ground causes a diffuse and attenuated back-scattered signal whereas the smooth surface of flooded ground leads to a significantly higher signal due to dihedral reflection between the water and trunks (Rosenqvist et al., 2002, 2007). The effect of dihedral reflection can be observed in wetlands using C-band radar. The radar signal does not penetrate dense vegetation cover but sparse vegetation and blades of grass surrounded by water are characterised by a high back-scattered signal (Figure 3.3).

3.2.1 Classification of flooded areas After basic preprocessing of the data, the first step in the classification of flooded areas is the identification of zones likely to be flooded. Zones with 42 3.2 Flooded area from ENVISAT ASAR seasonal flooding can be identified under the assumption that they are under- going a relatively high change in surface properties over one year. Therefore the temporal variance of the back-scattering intensity should be high in sea- sonally flooded areas. Due to the spotted nature of the radar image and to the limited availability of images the temporal variance is strongly non-uniform in space. On a small scale, where one would expect the same probability of being flooded for all pixels, the values of the temporal variance differ significantly. To smooth the inhomogeneous appearance of the temporal variance a 5×5 median filter was applied. With the availability of a larger number of images this non- uniformity might be reduced and there would be no need to perform filtering. By normalising the variance and by applying histogram equalisation a probability map was derived where the values correspond more or less directly to the probability of seasonal flooding. To further minimise the number of pixels to be processed, a refined mask was derived in which all pixels with a probability value of less or equal to 0.05 are given a value of zero.

Although the back-scattered intensity of a pixel follows some regularities it is still influenced by a wide variety of factors. Therefore a simple classification, using threshold values, leads to unsatisfactory results. On the other hand, classification criteria should be simple enough to be easily implemented in an automatic image classification framework.

For the classification of open water surfaces and flooded vegetation a stepwise approach is chosen. The intensity value of a pixel, its temporal variance and the properties of surrounding pixels were taken as basis for classification. (1) A first class of inundated pixels showing unambiguously low or high intensities respectively are classified without applying additional criteria. Pixels with low values represent open water surfaces while pixels with high values represent flooded vegetation. (2) A second class is formed by those pixels having an intensity value within a close range to the values of the first class. As an additional constraint, the inundation probability of that particular pixel has to be greater or equal to 0.5. (3) The third class finally is composed of pixels in the medium-low and medium-high intensity ranges. For this class a stronger criterion for values on the probability map is applied. As second constraint pixels of this class must belong to a continuous cluster of pixels of which at least one is classified in the first or second class. The continuous clusters are selected from the image using a region growing algorithm.

Using the classiﬁcation algorithm described above a series of 16 ASAR images is processed to derive a time series of the ﬂooded area. Chapter 3 Flooding patterns 43

3.2.2 Comparison with Landsat data1

Since the method to extract flooding patterns from the ASAR images is based on thresholds, some ground referencing has to be carried out. Two Landsat 5 L1T TM scenes (Path/Row: 172/71) from the lower part of the Kafue Flats were selected and the water surfaces were extracted – one scene in the low-flow season of September 2008 and one of the high-flow season in May 2009. Both Landsat images coincide in time with an ASAR scene. The spatial resolution of the Landsat data is in the same order of magnitude as the one of the ASAR data (30 × 30 m2 vs. 75 × 75 m2). To derive the flooded area from each Landsat image the digital number of each band was converted to radiance and then, except for the thermal band, to reflectance (Chander et al., 2009). The reflectances of bands 2 and 5 were used to calculate the Modified Normalised Difference Water Index, MNDWI (Xu, 2006), as shown below:

GREEN − MIR ρ2 − ρ5 MNDWI = = (3.2) GREEN + MIR ρ2 + ρ5 where ρ is the calculated reflectance from the respective bands. Water pixels normally show positive MNDWI values. With the appropriate threshold value MNDWI can be used to extract open water pixels with high efficiency. Sensor brightness temperature (TB) can be calculated from band 6 radiance. With a mono-window algorithm (Qin et al., 2001) or single-channel method (Cristobal et al., 2009; Jimenez-Munoz and Sobrino, 2003; Sobrino et al., 2004) TB can be converted to land surface temperature. In this study the mono-window method of Qin et al.(2001) was used because it is simple and does not require much more input data. The difference between the land surface and air temperature, with the latter being calculated from meteorological station data, leads to the stress degree days (SDD). The relationship between MNDWI and SDD is then used to determine the threshold value of MNDWI, based on the principle that pixels with extremely high SDD values should not be chosen as water pixels as shown in Figure 3.4. The pixels with MNDWI above this threshold are water pixels. This method can extract open water surface accurately. Flooded vegetation with high water content is extracted well by this method, but it has been shown to underestimate flooded areas in the presence of dense vegetation. Based on the flooded areas derived from the Landsat images as truth, the threshold parameters of the ASAR classification are determined by minimising the number of not correctly classified pixels using a genetic algorithm (Conn et al., 1997).

1The method described in this section is developed by Haijing Wang, who also wrote the major part of it. It is found here for the sake of completeness. 44 3.2 Flooded area from ENVISAT ASAR

0.8

0.6 Water pixels 0.4 0.2 0 −0.2 MNDWI (−) −0.4 −0.6 −0.8 −5 0 5 10 15 20 25 30 35 SDD (°C)

Figure 3.4: Deriving the MNDWI threshold value for extracting water pixels.

3.2.3 Results of the classiﬁcation

The threshold parameters obtained for the ASAR classification through comparison to the Landsat images are shown in Table 3.1. Figure 3.5(a) and 3.5(b) show the flooding patterns obtained by the different methods for the dry season and the wet season, respectively. There are some significant differences especially in areas with predominantly flooded vegetation. Since the method used to classify the Landsat data is known to underestimate flooded vegetation no quantitative analysis of the error is possible. However, the fit obtained by the genetic algorithm is relatively accurate. The area of pixels not classified equally in the two approaches is 0.3% of the total area shown in Figure 3.5 during the dry season and 2.1% in the wet season. These mismatches correspond to approximately 10% of the flooded area in the dry season and 15% in the wet season. As neither of the two classification methods is able to reflect the true inundation state in the Kafue Flats this fit is considered acceptable. At the transition between open water surfaces and flooded vegetation a seam of unclassified pixels can be observed (Figure 3.6, right part). Within this area the back-scattering characteristics of the water surface and the vegetation are superimposed, therefore leading to an intermediate back-scattering intensity. In the lower left corner of Figure 3.6 the structure of a river reach can be seen clearly. The river reach itself, being too narrow to be detected at the given resolution of 75 m, was not classified on the image. Due to the limited extension of these areas the error caused by this effect is neglected. Even after the radiometric calibration of the ASAR scenes there are some differences in the overall brightness of the images caused by different incidence Chapter 3 Flooding patterns 45

Landsat Landsat

8 280 8 280

Northing (km) 8 250 8 250

ASAR ASAR

8 280 8 280

Northing (km) 8 250 8 250

540 570 600 540 570 600 Easting (km) Easting (km) (a) September 5, 2008 (b) May 8, 2009

Figure 3.5: Comparison of the inundation patterns derived from Landsat and from ASAR satellite images (UTM coordinates, zone 35, south). The classiﬁ- cation algorithm for the ASAR images is able to separate open water surfaces (black) from ﬂooded vegetation (gray area).

Table 3.1: Constraints for the classification of the ASAR back-scattering data in three classes. The upper values are used for the classification of open water surfaces and the lower values for the classification of flooded vegetation.

Class 1 Class 2 Class 3 DN≤3 3DN≥176 176>DN≥171 Probability p > 0.5 p > 0.75 Adjacencies Class 1 & 2 46 3.2 Flooded area from ENVISAT ASAR

8 270 Northing (km)

8 260

590 600 610 Easting (km)

Figure 3.6: The effect of single pixels containing both, open water surface (black) and flooded vegetation (gray), as observed on an ASAR satellite image (UTM coordinates, zone 35, south). angles or changing soil moisture conditions. Especially in areas with dense vegetation the back-scattering coefficient is strongly dependent on the incidence angle (Wagner et al., 1999a). Dry soil generally leads to a lower back-scattering signal. Smooth and dry surfaces, such as the clay in dried ponds, might erro- neously be classified as open water surface. The time series of the total flooding shows that the classification of the ASAR data is capable of catching the seasonal characteristics of the flooding (Figure 3.7). The highest flooding occurs from April to May and the lowest from October to December. Chapter 3 Flooding patterns 47

2000 ) 2 1800 1600 1400 1200 1000 800 600 400

Measured flooded area (km 200 0 2003 2004 2005

Figure 3.7: Total ﬂooded area derived from ASAR images.

Chapter 4 Floodplain Modelling

The influence of dams on riverine ecosystems can be immense. However, often these effects are very diverse and their mitigation is a complex task. A good hydrological model of the river system downstream of the dam can help assessing management options. In the Kafue Flats the hydrological system is not only determined by the upstream dam (ITT) but also by the backwaters of the Ka- fue Gorge dam downstream of the wetland. This rather complex hydrological setup has to be considered while a modelling strategy is chosen. Also, the poor availability of ground data determines the choice of a suitable model. The analysis of the existing data shows that the inter-annual variation between wet and dry years is very high. Limited data availability – especially the non-existence of long time series – limits the validity of model results in both, dry and wet years. Therefore, for every modelling effort the trade-off between simplicity and physical correctness has to be found. A simple (i.e. conceptual) model takes into account the limited spatial coverage of the available data. A physically based model is suited better if the temporal coverage of the data is small. In this chapter different modelling strategies are presented and assessed. The models presented incorporate simple black-box models to complex two- dimensional surface water - groundwater models.

4.1 Water resources of the Kafue Flats

An estimate of the water balance in the Kafue Flats is established to explore the dimensions of water storage and flow. To calculate the balance the system boundary was chosen to be at the two dams, Itezhi-Tezhi (ITT) and Kafue Gorge (KG), and at the fringes of the floodplain. The data which have to be used are therefore the releases of the two reservoirs (QITT and QKG), the inflows of tributary rivers and creeks (Qlat), rainfall inside the floodplain (P ) dS and evapotranspiration (ET ). The total storage change ( dt ) is calculated according to Equation 4.1. dS = QITT(t) − QKG(t) + Qlat(t) + P (t) − ET (t) (4.1) dt

49 50 4.2 Available data

While for the discharge of the reservoirs reliable data are available, the lateral inflows are mostly based on estimates. Such estimates are provided by the KAFRIBA model (Section 4.3.3). However, the data are only available for a bit more than 2 years from October 2002 to December 2004. The total water balance was therefore only calculated for those two years. The analysis of the rainfall measured at ITT reveals that the mean annual rainfall of the rainy seasons 2002 through 2004 is close to the long-term mean rainfall (Figure 4.1(a)). However, the analysis of the discharge shows that all three years in question show a mean annual discharge which is 20% to 30% below the long term average (Figure 4.1(b)). Therefore the period chosen for the water balance calculation represents relatively dry conditions. The summary of the water balance (Table 4.1) reveals that in an average year around half of the inflow to the Kafue Flats originates from the release of the Itezhi-Tezhi dam. The other half is contributed by lateral inflows (32%) and by rainfall in the floodplain itself (17%). The outflows are also divided in equal shares between the outflow at the Kafue Gorge dam and the evapotranspiration. While the release at ITT and at Kafue Gorge are measured on a daily basis and provide a reliable data source, the other data is prone to errors. For the lateral inflows for most tributaries no reliable discharge data are available. The rainfall data used is derived from remote sensing data and has a relatively high uncertainty (Section 4.2.1). Since the evapotranspiration is estimated in order to fulfill the condition that the total storage change approaches zero, the uncertainties of the other data add to the one of the evapotranspiration (Sec- tion 4.2.2). The absolute numbers of the different contributors to the water balance might differ depending on the year one chooses to calculate the balance for, especially since the current water balance was assessed in relatively dry years (Figure 4.1). Despite these drawbacks a simple water balance can provide some insights in the hydrological system. How much the floodplain in the Kafue Flats is affected by the construction of the two dams heavily relies on the contribution of the flow from the Itezhi-Tezhi dam compared to the total flow. The information about the water balance can also be used to check more complicated modelling approaches for their validity.

4.2 Available data

4.2.1 Rainfall data

To account for the rainfall inside the ﬂoodplain diﬀerent data sources can be used. At the Itezhi-Tezhi dam and at Lusaka International Airport a long time series of rainfall measurements is available. To obtain distributed information of rainfall in the area two products based on remote sensing techniques are avail- Chapter 4 Floodplain Modelling 51

160 100 Rainfall 140 Rainfall anomaly 120 50 100 80 0 60 Rainfall (mm) 40 −50 Rainfall anomaly (%) 20 0 −100 1990 1992 1994 1996 1998 2000 2002 2004 2006 Time (a) Rainfall time series as measured at the Itezhi-Tezhi dam and the deviation of the annual mean rainfall from the long-term mean.

100 1600 Discharge Discharge anomaly 1400

) 50

−1 1200 s 3 1000 800 0 600

Discharge (m 400 −50 Discharge anomaly (%) 200 0 −100 1990 1992 1994 1996 1998 2000 2002 2004 2006 Time (b) Discharge time series and the deviation of the annual mean discharge from the long term average as measured at Kafue Hook bridge.

Figure 4.1: Mean annual rainfall and discharge of the Kafue basin compared to the long term mean. For both data the long term mean is calculated by averaging over the years 1979 to 2006. 52 4.2 Available data

Table 4.1: Summary of the average annual water balance of the Kafue Flats.

3 −1 from ITT QITT 174 m s 51 % Mean annual inﬂow 3 −1 lateral Qlat 109 m s 32 % Mean annual rainfall P 60 m3 s−1 17 % 3 −1 Mean annual outﬂow QKG -166 m s -48 % Mean annual ET ET -187 m3 s−1 -55 % Total ∆S -10 m3 s−1 -3 %

Table 4.2: Properties of the NOAA-CPC and the TRMM data.

NOAA-CPC TRMM Algorithm RFE 2.0 3B-42 Spatial coverage Africa, Central America, Between 50° South and Middle East, South Cen- 50° North tral Asia, South Asia Temporal coverage July 1995 - today: every January 1998 - today: ev- 10 days, January 2001 - ery 3 hours. today: daily. Resolution 8 × 8 km2 0.25° × 0.25°, this corresponds to approximately 25 ×25 km2 in the Kafue region able. (1) The Climate Prediction Centre of the National Oceanographic and Atmospheric Administration (NOAA-CPC) provides a rainfall estimate (RFE 2.0) which is distributed through the Famine Early Warning Systems Network (FEWS NET). It provides rainfall data for Africa (and other regions) on a ten days basis since 1995 and on a daily basis since 2001 (Xie and Arkin, 1996; Herman et al., 1997). (2) The Tropical Rainfall Measuring Mission (TRMM) provides 3-hourly data since January 1998 (Huffman et al., 1995, 1997; Adler et al., 2003; Huffman et al., 2007). Both data products incorporate rain gauge data. The properties of each dataset can be found in Table 4.2. The quality of both datasets is assessed in previous studies. Dinku et al. (2008) compared several satellite based rainfall products with gauged data in Ethiopia and Zimbabwe. They concluded that both satellite products, NOAA- CPC and TRMM, are good at detecting the occurrence of rainfall. However, the estimation of the amount of rainfall is considered to be problematic. The analysis of the different data sources reveals that between the two gauging stations at Itezhi-Tezhi (ITT) and at Lusaka International Airport the cor- Chapter 4 Floodplain Modelling 53

50 rX,Y=0.21 40

10 Gauge ITT (mm) 0 50 rX,Y=0.16 rX,Y=0.06 40

10 Gauge Lusaka (mm) 0 50 rX,Y=0.72 rX,Y=0.22 rX,Y=0.18 40

TRMM (mm) 10

0 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 NOAA−CPC (mm) Gauge ITT (mm) Gauge Lusaka (mm)

Figure 4.2: Correlation analysis between the diﬀerent sources of rainfall data. The rainfall data for this comparison was obtained by averaging the rainfall over an area of 10 × 10 km2 around Itezhi-Tezhi (ITT). The data measured at Lusaka International airport are provided by the NOAA National Climatic Data Center (NCDC), the data at ITT are provided by ZESCO. 54 4.2 Available data

relation is very poor (rX,Y = 0.06). Therefore the quality of the data obtained from satellite measurements have to be compared to ground data at a local scale rather than comparing the average values over the whole Kafue Flats. It also allows to draw the conclusion that a rainfall product which provides distributed information on rainfall is essential. The two rainfall data products which are derived from satellite data are compared locally in an area of 10 × 10 km2 around the Itezhi-Tezhi rainfall gauge (Figure 4.2). The correlation between the TRMM data and NOAA-CPC data is relatively high (rX,Y = 0.72). Both products seem to deliver comparable results. The measurements at the gauging station at Lusaka International Air- port is only weakly correlated with the data of the two remote sensing products. Since the correlation of the data of the two gauging stations is even weaker, this is not relevant for the evaluation of the rainfall data. However, the correlation between the satellite based rainfall measurements and the data retrieved from the gauging station at ITT is not very strong either. This is presumably due to the fact that in the rainy season rainfall mainly occurs in storm cells at a very local scale. TRMM derived rainfall data with a spatial resolution of 25 ×25 km2 and the NOAA-CPC data with a resolution of 8 × 8 km2 are not able to resolve very local rain showers. The averaging leads to a smaller diurnal variation of rainfall, thus to relatively weak correlations. For hydrological applications not targeted at short-term flash-flood forecasting satellite derived rainfall products retain their validity if the amount of rainfall over a longer period matches the ground data. Where the yearly gauged rainfall amount is around 700 mm yr−1 the yearly amount observed by the TRMM is as low as 550 mm yr−1. The rainfall data provided from NOAA- CPC yield an average of 670 mm yr−1. This significant difference between the two products can also be observed if only single rainy seasons are considered. For this reason only NOAA-CPC data is used for all modelling approaches presented later.

4.2.2 Estimates of monthly evapotranspiration

Another parameter which is not measured directly in the floodplain area is the evapotranspiration (ET). It therefore has to be estimated. For the calculation of the water balance monthly estimates of the potential ET (ET0) provided by FAO are used (FAO, 2000). To obtain the actual evapotranspiration based on this data the concept of crop coefficients (kC) is used. According to Allen et al. (1998) for wetlands a crop coefficient of kC = 1.2 can be assumed during the main vegetation period. Before and after the values of kC should be between 0.7 and 1. For the very dynamic system of the Kafue Flats floodplain however, this simple concept is not adequate. The strong seasonality of the flooded area limits the availability of water for evaporation. Therefore the crop coefficient Chapter 4 Floodplain Modelling 55

Table 4.3: Corrected crop coeﬃcient values for the estimation of the evapotranspiration in the Kafue Flats.

Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec w · kC 0.9 1.0 1.0 0.625 0.4 0.3 0.2 0.1 0.1 0.1 0.3 0.6 is modiﬁed by a factor w to account for the dry season (Equation 4.2).

ETact = w · kC · ET0 (4.2)

The values of w are following the fraction of ﬂooding in the ﬂoodplain and are chosen in a way that the total change in storage over one year is approximately zero. The values applied for w·kC can be found in Table 4.3. The highest values are assigned towards the end of the rainy season, in February and March, since the availability of water reaches its maximum in these two months.

4.2.3 Evapotranspiration from remote sensing data Calculating the spatial distribution of the evapotranspiration from satellite data is very data intensive. Besides data which allow to calculate the surface radiation balance in the short and long wave spectra, ground data on air temperature and water vapor content have to be used. For the short wave surface energy balance the same data which were used to determine the flooded areas in Section 3.1 were used (MOD09GA). For the long wave radiation balance the MODIS land surface temperature product was used ((MOD11A1). The air temperature and the water vapor pressure are measured daily at Lusaka International Airport. This data are considered to be representative for the whole Kafue Flats. The spatial pattern of the evapotranspiration is calculated using the Sim- plified Surface Energy Balance Index (S-SEBI) as presented by Roerink et al. (2000). The spatial resolution of MODIS data is 1 × 1 km2 and an image is retrieved every day. However, only cloud free images are suitable to calculate the surface energy balance. To identify the areas covered by clouds the cloud mask which is included in the MOD11A1 surface temperature product is used. The S-SEBI algorithm is based on the assumption that the latent heat flux at the earths surface can be estimated by calculating the radiation balance. The net radiation Rn at the surface can be calculated as follows:

Rn = G0 + H + λE, (4.3) where G0 is the soil heat flux, H is the sensible heat flux and λE is the latent heat flux (Roerink et al., 2000). The latter two heat fluxes are not calculated 56 4.2 Available data

325

320 TH · Radiation controlled 315

310 T0 · 305

300 TλE · 295 Evaporation controlled Land surface temperature (K) 290 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Surface albedo (−)

Figure 4.3: The surface temperature as a function of the surface albedo. In the whole satellite image the radiation controlled and the evaporation controlled pixels are extracted. The evaporative fraction is then calculated using Equation 4.4. explicitly, but as the evaporative fraction Λ which is deﬁned as

λE λE TH − T0 Λ = = = . (4.4) λE + H Rn − G0 TH − TλE

The evaporative fraction Λ can therefore be calculated from the earths surface temperature T0 (Figure 4.3). The two extreme temperatures TH and TλE can be determined from the satellite image directly as long as the atmospheric conditions can be considered constant over the whole image. While TH is the temperature over a completely dry pixel (radiation controlled), TλE is the temperature over a completely wet pixel (evaporation controlled). The surface temperature T0 and the emissivity is taken from the MODIS land surface temperature (LST) daily product (MOD11A1). The data has a resolution of 1×1 km2 and provides a day temperature and a night temperature. The satellite normally overpasses the area at around 10:00 am and at 10:00 pm local time. From these two temperatures the average is calculated. ↓ ↑ The net radiation Rn is composed of the net shortwave radiation RS − RS ↓ ↑ and the net longwave radiation RL − RL. The net shortwave radiation can also be expressed using the surface albedo. The incoming longwave radiation is a function of the air temperature Ta and the emissivity of the air εa, which again is dependent on the water vapor Chapter 4 Floodplain Modelling 57

pressure in the atmosphere e0 (Bisht et al., 2005):

1 !! 2 ↓ 4 46.5e0 46.5e0 RL = σεaTa , with εa = 1 − 1 + exp − 1.2 + 3 Ta Ta (4.5) σ = 5.67 × 10−8 W m−2 K−4 is the Stefan-Boltzmann constant. The emissivity εa is not a very sensitive parameter. Given the maximum range of the water vapor pressure e0 and the air temperature Ta measured at Lusaka International Airport its minimum is εa = 0.9977 and the maximum εa = 0.9996. Therefore the inﬂuence of the air humidity on the net longwave radiation can be neglected. It is only governed by the air temperature and ranges for the meteorological station at Lusaka International Airport between 350 W m−2 and 500 W m−2. ↑ The outgoing longwave radiation RL is a function of the emissivity of the surface εs and the surface temperature T0. Both parameters are available on a daily basis from the MOD11A1 dataset. The emissivity of the surface in bands 31 and 32 are provided by the same dataset. From the evaporative fraction Λ the daily evapotranspiration is calculated −3 according to Equation 4.6 with the density of water ρw = 1000 kg m . The latent evaporation heat Lv,water was calculated using an empirical formula by Rogers and Yau(1989).

λE −1 ETdaily = 86400 × m d (4.6) Lv,waterρw where

3 2 Lv,water = −0.0614342 × (T0 − 273.15) + 1.58927 × (T0 − 273.15) (4.7) −1 −2 364.18 × (T0 − 273.15) + 2 500 790 J kg

The surface albedo r0 is calculated according to Liang(2001). The net radiation Rn is calculated as the sum of the net shortwave radiation and the net longwave radiation. From MODIS satellite images only the instantaneous net radiation Rn can be derived. To calculate the daily average net radiation Rn,daily a sinusoidal model as described in Equation 4.8 is used (Bisht et al., 2005).

2Rn Rn,daily = (4.8) π sin π toverpass−trise tsettrise

The soil heat ﬂux (G0)is calculated as described in Roerink et al.(2000). It is dependent on the net radiation, the earth surface temperature and the Normalised Diﬀerence Vegetation Index (NDVI). The NDVI is a measure for the density of the vegetation cover. 58 4.2 Available data

) 14 Pan evaporation at ITT

−1 Mean ET from MODIS 12

2 Evapotranspiration (mm d 0 2002 2003 2004 2005 2006 Time

Figure 4.4: Time series of the potential evapotranspiration measured at the evaporation pan at ITT compared to the timeseries obtained from MODIS data. The thick lines shows the data ﬁltered using a 14 days running average, the faded lines show the daily values.

T0 − 273.15 2 2 G0 = ΓRn, where Γ = 0.32r0 + 0.62r0 1 − 0.978 × NDVI r0 (4.9) With this equation all the components of the surface energy balance are complete. Due to heavy cloud cover during the rainy season the data have to be interpolated to fill the data gaps. Each pixel is interpolated linearly in time but not in space. This method preserves the pattern of the evapotranspiration. The ET obtained from MODIS data is compared with measured data from an evaporation pan at ITT (Figure 4.4). The values of the evaporation pan are multiplied with a factor of 0.7 to correct for the overestimation of evaporation due to effects of the pan geometry and material. The values of evapotranspiration obtained from both methods agree generally quite well. While they are in approximately the same range the seasonality is different. This difference in seasonality can be expected since the pan evaporation device measures the potential evapotranspiration which is mainly driven by meteorological parameters. The evapotranspiration obtained from MODIS data measures the actual evapotranspiration which is mainly driven by the availability of water. Thus, the flooding season in the Kafue Flats can easily be identified from the time series of actual evapotranspiration. In the time of Chapter 4 Floodplain Modelling 59

20 20 ) ) −1 −1 15 15

10 10

5 5 ET from MODIS (mm d ET from MODIS (mm d 0 0 0 5 10 15 20 0 5 10 15 20 Pan evaporation at ITT (mm d−1) Pan evaporation at ITT (mm d−1) (a) Pan evaporation vs. evapotranspiration (b) Pan evaporation vs. the maximum evapo- averaged over the whole model domain. ration measured in the ﬂoodplain. The maximum should be equivalent to the potential evapotranspiration.

Figure 4.5: Measured evaporation from an evaporation pan at ITT vs. evapotranspiration obtained from MODIS data.

maximal flooding between April and June the evapotranspiration is high. One can also identify the relatively dry years 2002 and 2005, where the evaporation is lower in the flooding season. These two years are characterised by generally low discharge (Figure 4.1(b)). The correlation between the two measurements however, is fairly weak (Fig- ure 4.5). This is mostly caused by the different seasonality of the potential and the actual evapotranspiration. If the evaporation derived from MODIS data is averaged over the whole area of the floodplain the two datasets show very similar values and a similar variation (Figure 4.5(a)). If one assumes that the maximum of the measured evapotranspiration from MODIS is equivalent to the potential evapotranspiration the correlation looks very different (Figure 4.5(b)). Although the effect of the different seasonality vanishes to a certain degree, there is a very strong bias. The values of the ET derived from satellite data are more than twice the ones measured from the evaporation pan. In a floodplain the actual evapotranspiration can be higher than the potential ET (Allen et al., 1998). However, the processes in the floodplain can not explain the large difference alone. Because of the many assumptions which have to be made to compute the actual evapotranspiration from satellite data 60 4.2 Available data one does not expect the measurements to be very accurate. Still they provide valuable information especially on the spatial distribution of evaporation.

4.2.4 Digital elevation model

One of the freely distributed digital elevation models (DEM) available for the Kafue Flats is the Shuttle Radar Topography Mission (SRTM) data (Farr et al., 2007). The digital elevation model is a crucial input to spatially distributed hydrological models. Obviously the flow of water is governed by the terrain. Usually hydrodynamic flood models cannot reach the spatial resolution of the available DEM. Either the DEM is not accurate enough or the computational time of the model run is limiting. In the first case the model resolution can be increased if a better DEM is available. In the latter case the model results can still profit from a more accurate DEM. The micro-topography within one model cell contains a wide variety of valuable information at sub-grid scale (Milzow et al., 2009b). The SRTM Mission was conducted in February 2000 during 11 days. A specialised radar interferometry system was mounted on the space shuttle “En- deavour” to obtain the most complete global terrain model. The Kafue Flats were not completely dry during this time, especially the lower part shows some flooding. This has some implications if the dataset is used for hydraulic modelling. The level of the river bed can therefore not be derived directly from the data. The accuracy of the SRTM DEM is most critical for flat areas such as floodplains. These errors are mainly due to the not perfect stability of the spacecraft and due to surface inhomogeneities. These errors are estimated for each continent. For Africa the absolute error was estimated to be 5.6 m and the relative error 9.8 m. A detailed spatial analysis of the error shows that the absolute error over the Southern African subcontinent is generally between 3 and 5 meters (Rodriguez et al., 2005).

4.2.5 River cross sections

Within the framework of the Kafue Flats hydrological studies carried out in 1980 by DHV Consulting Engineers river cross sections of the Kafue river between ITT and Kasaka were measured (DHV, 2006). The cross sections were retrieved using an echo sounding device every 2 km along the main river channel. All the data measured are available in a printed report and therefore the data have to be digitised ﬁrst. This is done using a MATLAB script which allows to digitise a whole cross section by specifying the reference level and one point along the plotted cross section. The data are then read automatically. Chapter 4 Floodplain Modelling 61

4.3 Floodplain models

4.3.1 Black box model based on the digital elevation model

A very simple method to correlate the storage with the flooded area is to use the digital elevation model. The flooding is considered to be distributed in a way that the water surface is at the same level everywhere. This very static approach does not take into account the dynamic effects of the flooding such as a flood wave travelling through the floodplain. The DEM used is derived from the SRTM dataset (Section 4.2.4). For different water levels the flooded area and the stored volume can be calculated. This way one can obtain a relation between the stored volume and the flooded area. This relation can then be used for a very simple black box model, which uses the inflows and the outflows (including evapotranspiration) as input data. The relation established using the DEM is shown in Figure 4.6. The flooding is analysed starting from a water level of 968 m a. s. l. up to a level of 997 m a. s. l. The shape of the curves shown in Figure 4.6 allows to draw some conclusions about the shape of the floodplain itself. Up to a water level of 977 m almost no flooding is observed. At higher levels the flooded area shows a sudden increase and with a water level raise of only 10 m (up to 987 m a. s. l.) almost the whole area of the floodplain is flooded. This indicates that in a first stage the river channel itself is filled and in a second stage, with a water level higher than 977 m a. s. l., the very flat floodplain is filled with water. At a certain water level the flooding hits the fringes of the floodplain and the flooded area does not increase any further. The water volume of the flooding also shows a sudden increase as soon as the water level has reached 980 m. This corresponds to the water level where already more than 2 000 km2 are flooded. This supports the conclusion that the flooding which occurs at levels between 977 m and 980 m is very shallow. At higher water levels the volume increases in an approximately linear manner. The correlation between the stored volume and the flooded area makes these findings even clearer. At first the flooded area grows without a large increase in stored water. Later, after the flooding has reached an area of 4 000 km2, the stored volume starts to increase at a higher rate.

4.3.2 Correlation between storage change and ﬂooded area

The change in storage of water in the Kafue Flats as presented in Section 4.1 can be used for a very simple black box model. If the main goal is the simulation of the total flooded area a simple correlation between the stored volume and the flooded area can be established (Figure 4.7). This correlation is assessed using the water balance and the flooded areas measured from MODIS data (Section 3.1). However due to the high variability of the measured flooded area 62 4.3 Floodplain models

10000 10000 ) )

2 8000 2 8000

6000 6000

4000 4000

Flooded area (km 2000 Flooded area (km 2000

0 0 965 970 975 980 985 990 995 1000 0 20 40 60 80 100 120 Water level (m.a.s.l.) Stored volume (km3)

1000 995 990 985 980 975

Water level (m.a.s.l.) 970 965 0 20 40 60 80 100 120 Stored volume (km3)

Figure 4.6: Flooded area and stored water volume of the Kafue Flats for uniform ﬂooding at diﬀerent water levels. Chapter 4 Floodplain Modelling 63 ) 2 5000

4000

3000

2000

1000

0 Flooded area from MODIS (km 0 20 40 60 80 100 Daily water storage (106 m3)

Figure 4.7: Correlation between daily water storage and flooded area. the correlation is rather weak. When the daily water storage approaches its minimum, the total flooded area is also small. If the daily storage increases only slightly, in some cases a very large total flooded area is measured. Therefore not only the uncertainty of the measured flooded area contributes to the weak correlation. Also the dynamics of the flooding plays an important role. This leads to the conclusion that the Kafue Flats system can not be considered to be a simple reservoir where the flooded area is related directly to the storage. Modelling attempts should involve the dynamical flooding processes.

4.3.3 KAFRIBA

The KAFRIBA model is a hydrodynamic model of the Kafue Flats which was originally developed in 1980 by DHV Consulting Engineers (DHV, 2006). In 2006 it was extended by a graphical user interface. The model is based on a finite elements approach and uses a total of 124 model nodes. It allows to simulate the water levels in the river and the floodplain. Additionally it is able to provide a 12 weeks forecast of the discharge into the Itezhi-Tezhi reservoir. This forecast is based on the Pitman model. The Pitman model is a hydrological model that is designed to simulate the most important processes in Southern African river basins (Pitman, 1973). It is running at a monthly time step. The forecast is based on the classification of actually measured rainfall into wet (i.e. above average), dry (below average) and normal (average). Details on the hydrological model can be found in Section 2.7.1. The KAFRIBA model provides a simulation of natural conditions serving as a reference situation for a designed flood release. The modelling framework 64 4.4 One-dimensional hydraulic model should allow to operate the two reservoirs at the Kafue in a more flexible way (DHV, 2006). However, the KAFRIBA model has never been validated.

4.4 One-dimensional hydraulic model

Due to the size of the Kafue Flats the box type model (Section 4.3.1) does not cover the dynamics of the flooding. From the satellite images one can clearly see the progression of the flood. When discharge starts to increase first the western part of the floodplain is inundated. The flood wave then moves towards the Kafue Gorge. At the end of the flooding season only the eastern (lower) parts are flooded. This is partly because of the movement of the flood wave and because backwaters of Kafue Gorge. The progression of the flood is modelled using a one-dimensional hydraulic model. The software used is HEC-RAS1 provided by the US Army Corps of Engineers. HEC-RAS allows to model steady and unsteady flow and sediment transport along a river channel. It features a graphical user interface and a module which allows to derive the river cross sections directly from a digital elevation model in the GIS software ArcView. The model is based on the one- dimensional Saint Venant equations (Hydrologic Engineering Center, 2010).

4.4.1 Model geometry

The area of the Kafue Flats was delineated using the SRTM DEM (Section 4.2.4). A seeded region growing algorithm was used to group the area which is flat and therefore belonging to the floodplain. A number of seed points belonging to the floodplain are specified. The algorithm classifies the flat in a way that the statistics of the seed points is maintained. The area which is cut out in that way is used as model boundary. The SRTM DEM was also used to derive the cross sections. The main river channel was manually extracted from a Landsat satellite image. Along the river channel with a length of 450 km the whole floodplain was divided into 56 cross sections (Figure 4.8). HEC-RAS provides a tool to extract the elevation information along the selected cross section. Due to the errors in the SRTM dataset and its acquisition time the river transects have to be corrected. In order to run the model correctly the deepest elevation of each transect has to lie within the river channel. Therefore many of the automatically extracted cross sections have to be corrected by hand. Additionally one can assume that the elevation of the river bed is decreasing continuously. To fulfill this criterion the river bed elevation has to be interpolated in some places. The elevation profile along the river is shown in Figure 4.9.

1Hydrologic Engineering Center - River Analysis System Chapter 4 Floodplain Modelling 65

8300

8250 Latitude (km)

Cross sections Main channel River banks 8200 400 450 500 550 600 650 Longitude (km)

Figure 4.8: The cross sections as deﬁned in the HEC-RAS model, the area of the main channel, the ﬂoodplain area and the main river channel.

1000 990 980 970 960 950

Elevation (m a.s.l.) 940 930 Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 920 400 350 300 250 200 150 100 50 0 Length (km)

Figure 4.9: Elevation proﬁle of the Kafue river including the Kafue Gorge reservoir. Zone 1: Upper Kafue Flats; Zone 2: Naminwe Plains; Zone 3: Lagoons area; Zone 4: Backwater area; Zone 5: Kafue Gorge. 66 4.4 One-dimensional hydraulic model

Table 4.4: Manning’s n values for the diﬀerent zones of the HEC-RAS model (Figure 4.9). The location of the transects is measured in meters from the Kafue Gorge dam.

Transect Manning’s n Zone Location location (m) River channel Floodplain 1 Upper Kafue Flats 448 239 - 322 586 0.05 0.08 2 Naminwe Plains 322 586 - 237 856 0.07 0.08 3 Lagoons 237 856 - 55 210 0.09 0.1 4 Backwater zone 55 210 - 29 785 0.077 0.13 5 Kafue Gorge 29 785 - 0 0.042 0.15

The Kafue Gorge reservoir is also included in the hydraulic model. Since the exact water levels and the discharge are known at the dam it provides an ideal lower boundary condition for the model. In addition the backwater effects of the different storage levels are of interest. While the geometry of the dam itself is known, no information on the bathymetry was available. The reservoir was approximated with a V-shape transverse profile with a uniformly increasing depth reaching its largest depth at the dam.

4.4.2 Hydraulic roughness

For the hydraulic roughness of the surface two different values (Manning’s n) can be specified: one for the main channel and one for the floodplain (Fig- ure 4.8). These parameters have to be estimated based on the properties of the underlying sediment, the variation of the cross section area, the influence of the vegetation and the size of the meanders. The Kafue Flats area is divided into five different sectors with similar hydraulic properties each. The most upstream zone (Zone 1) is characterised by the highest slopes and a meandering river channel. The second zone (Zone 2) forms the transitional zone between the steeper meandering part and the very wide and flat part which is mainly characterised by lagoons and less constrained river channel (Zone 3). The next zone (Zone 4) is mainly influenced by the backwater of Kafue Gorge. It consists of large parts which are permanently flooded. The last zone (Zone 5) is the Kafue Gorge reservoir itself. The values for Manning’s n are estimated for each sector separately (Table 4.4).

4.4.3 Hydrological data

The upper boundary condition is defined as the release of the Itezhi-Tezhi reservoir. The lower boundary condition is defined by the measured water Chapter 4 Floodplain Modelling 67 level at the Kafue Gorge dam. These data are available on a daily basis. To estimate the lateral inflows the data available within the KAFRIBA model (Section 4.3.3) and rainfall data from the NOAA-CPC are used (Section 4.2.1). The evaporation was estimated using the FAO data and the concept of crop coefficients (Section 4.2.2). Rainfall and evapotranspiration are considered to be evenly distributed over the whole floodplain. For each cross section i the contributing area Ai is calculated. The total rainfall P (t) and the total daily evapotranspiration ET (t) are applied to each cross section according to its contributing area:

Ai Qin,i(t) = (P (t) − ET (t)) + Qlat,i (4.10) Atot where Qin,i is the total lateral inflow to each transect. This value is allowed to be negative (net loss). Qlat,i is the lateral inflow of the tributary which discharges into the transect i. Atot is the total area of the model domain which is 8 450 km2. This area includes partial areas which are not flooded regularly and is therefore higher than the estimated area of the floodplain (6 500 km2).

4.4.4 Simulation results

Generally the model simulations reveal that using this type of model the flooded area is over-estimated significantly. While the measurements from satellite images show a flooding extent between 200 km2 and 2 500 km2, the flooding extent is estimated to be between 2 000 km2 and over 6 000 km2 by the HEC- RAS model. An important information on the quality of the simulation is the check whether the water balance fits to reality. A good proxy quantity for the water balance is the discharge at the Kafue Gorge dam where the water level is known (Figure 4.10). While the large peak discharge in spring 2001 is captured quite well, the simulated discharge shows a seasonality which is not found in reality. The annual mean discharge fits quite well. This seasonality could be explained by an active storage which is not captured by the model. This can be the case if a physical storage is underestimated in the model. It is possible that the volume of the Kafue Gorge reservoir is underestimated. Especially its backwater to the Kafue Flats is an important part of the storage. Due to the acquisition time of the SRTM DEM in February, when the water levels were high, this part of the storage is not or only partly included in the model. Another possibility of an underestimated storage is a process which acts as a storage but is not included in the simulation. Such processes could be the runoff formation after rainfall in the Kafue Flats, the travel time of the lateral inflows before they reach the main channel or an attenuated flow in the floodplain where flooding is shallow and reeds are dense. Additionally small channels and ponds are also 68 4.4 One-dimensional hydraulic model

1200 Measured discharge

) 1000 Modeled discharge −1 s

3 800

600

400

Discharge (m 200

0 01/2000 07/2000 01/2001 07/2001 01/2002 07/2002 01/2003 07/2003 01/2004 07/2004 01/2005 07/2005 01/2006

Figure 4.10: Comparison of the measured discharge at Kafue Gorge dam and the modelled discharge (using HEC-RAS). active in transporting water. These cannot be simulated in a one-dimensional model. The most important storage, however, is the groundwater. It is not included in this model and therefore an important part of the hydrological cycle is neglected. To assess the influence of the dams on the natural cycle of flooding in the Kafue Flats different scenarios were assessed. The influence of each dam was considered separately. First, the influence of the Itezhi-Tezhi dam was assessed by replacing its discharge by a presumably natural discharge. The measured discharge of the Kafue river to the reservoir was considered to provide an accurate estimate of the natural flow conditions. Second, the influence of the Kafue Gorge dam was assessed by simulating both, the situation without a dam and with an increased maximum water level in the reservoir. To simulate the flow conditions without dam uniform flow was set as a boundary condition. The simulation of natural inflow conditions showed mainly an increased fluctuation of the total flooded area (Figure 4.11(a)), while in wet years (2000 and 2001) the maximum flooding is reached by the high releases from the reservoir. During the normal to dry years the amplitude of the total flooded area is around 2 000 km2 with the current release from the reservoir and around twice as big under natural conditions. The influence of the Kafue Gorge reservoir can not be identified that clearly. If the simulation is run without the dam the total flooded area does not change at all (Figure 4.11(b)). This is due to a constriction in the channel which is located between around 30 km and 50 km upstream of the Kafue Gorge dam. Chapter 4 Floodplain Modelling 69

8000 7000 ) 2 6000 5000 4000 3000 2000 Flooded area (km Actual inflow 1000 Natural inflow 0 01/2000 07/2000 01/2001 07/2001 01/2002 07/2002 01/2003 07/2003 01/2004 07/2004 01/2005 07/2005 01/2006 (a) The influence of the Itezhi-Tezhi reservoir on the total flooded area in the Kafue Flats. The inflow to the reservoir was considered to provide a good estimate of the natural discharge at the location of the dam.

10000 Current situation

) Without KG 2 8000 KG +2 m KG +3 m 6000

4000

Flooded area (km 2000

0 01/2000 07/2000 01/2001 07/2001 01/2002 07/2002 01/2003 07/2003 01/2004 07/2004 01/2005 07/2005 01/2006 (b) The influence of the Kafue Gorge dam (KG) on the total flooded area in the Kafue Flats. To simulate the system without the Kafue Gorge dam a uniform flow boundary condition was set at the location of the dam.

Figure 4.11: Simulation results of the HEC-RAS model. 70 4.4 One-dimensional hydraulic model

1000 Water level in April 2000 990 Water level in November 2000 980 970 960 950

Elevation (m a.s.l.) 940 930 Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 920 400 350 300 250 200 150 100 50 0 Length (km)

Figure 4.12: The water levels along the river as simulated by the HEC-RAS model for the high ﬂow season (April) and the low ﬂow season (November).

The water level during the high flow season in April shows a relatively steep gradient in this zone (Figure 4.12). Upstream and downstream of this zone the water level gradients are very low. In the low flow season (November) the same effect is less pronounced, but it can still be observed. This water level drop at the constriction is also shown in Figure 4.13. One can clearly see that while the water level stays nearly the same the area gets significantly smaller. After the drop the water spills into the Kafue Gorge reservoir where the slope of the water level is nearly zero as the flow velocities are close to zero. However, this decoupling of the Kafue Gorge reservoir and the Kafue Flats does not reflect reality (Mumba and Thompson, 2005). Backwater effects of the downstream reservoir can be observed up to the gauging station at Nyimba (Figure 1.3). Therefore the constriction which is acting as a flow barrier does not reflect reality. A possible reason for this is the overestimation of the elevation in the lower Kafue Flats due to the acquisition of the digital elevation model during the wet season (Section 4.2.4). If one assumes a higher mean water level at Kafue Gorge the backwater effects can be evaluated at least qualitatively. For this purpose the water level time series of the Kafue Gorge reservoir is shifted by 2 meters and by 3 meters, respectively. In Figure 4.11(b) one can see that in a wet year the maximum flooding is not changed significantly. Also if the level is increased by 2 meters the maximum flooding extent is almost not affected. The minimum flooding extent in contrary is influenced more strongly. Since the backwater of Kafue Chapter 4 Floodplain Modelling 71

1020 (a) 1010 1000

990 980 Water level: 979.42 m 970

1020 (b) 1010 1000 990 980 Water level: 979.22 m 970 Elevation (m a.s.l.)

1020 (c) 1010 1000

990 980 Water level: 976.34 m 970 −10 −5 0 5 10 Distance (km)

Figure 4.13: The cross sections of the lower Kafue Flats before the constriction (a), at the constriction (b) and in the upper part of the Kafue Gorge reservoir (c). 72 4.5 Distributed ﬂoodplain model

Gorge floods only the lower part of the floodplain, its influence on the total flooding must be higher in the dry season. In the wet season large parts of the floodplain are flooded anyway.

4.4.5 Overall evaluation

Generally, one can observe that the model presented is suitable to simulate the seasonality of flooding in a plausible manner. Even with the strongly overestimated flooding extent the tendency of the influence of the two dams can be evaluated. The Itezhi-Tezhi dam mainly influences the upper part of the Kafue Flats. The Kafue Gorge reservoir causes permanent flooding in the lower part of the floodplain, if the water levels are high. Besides the inaccuracies of the digital elevation model the simple construction of the model is a disadvantage. Important processes such as the very complex river - floodplain interaction are not modelled correctly. The lack of a groundwater storage which seems to play an important role in the water balance probably leads to an overestimation of the flooded area. Also the total water balance is influenced by the presence or absence of an underlying aquifer. The second major simplification which influences the model results significantly is the static handling of evapotranspiration. It is only implemented as a fixed abstraction of water in each model cell and the same monthly values are used for the whole simulation period. This leads to an overestimation or an underestimation of evaporation in dry years or in wet years, respectively. In dry years where the total flooded area is much smaller and the availability of water is limited in general evapotranspiration is expected to be smaller. In wet years the increased flooding is expected to lead to higher evaporation.

4.5 Distributed ﬂoodplain model

To be able to model the relevant hydrological processes, such as groundwater storage and evapotranspiration, more accurately a distributed, physically based hydrological model is developed. The ecological system depends on several processes at diﬀerent spatial and temporal scales (Bauer et al., 2006). An approach originally developed for the distributed inundation modelling of the Okavango Delta was transferred to and adapted for the Kafue Flats. The model of the Okavango Delta is based on the widely used groundwater modelling software MODFLOW 2000 (Bauer et al., 2006; Milzow et al., 2009b). For the Kafue Flats the newer version MODFLOW 2005 is used (Harbaugh, 2005). Among other features, MODFLOW 2005 allows to model processes in the unsaturated zone directly using a one-dimensional approximation of the Richards’ equation. Chapter 4 Floodplain Modelling 73

4.5.1 Data Since this model is physically based and has a relatively high spatial resolution one has to take care that the used input data can reproduce the spatial differences. Therefore, where available spatially distributed data are used. Mainly the rainfall data from the NOAA-CPC (Section 4.2.1) and the evapotranspiration data obtained from MODIS satellite data (Section 4.2.3) are valuable data sources. The inflow from the Itezhi-Tezhi reservoir is available on a daily basis, as are the water levels at Kafue Gorge dam. These two boundaries determine to a large degree the hydrology of the floodplain. Since for the lateral inflows no long time series are available, they have to be estimated (Section 4.5.2). The estimation of the parameters determining the flow of water in the groundwater and the overland flow can not rely on such datasets. In the Kafue Flats itself only limited data on the hydraulic properties of the soil are available. A few measurements are made near Mazabuka but not for the vast area of the Kafue Flats itself. Therefore for the flow in the unsaturated zone and in the saturated zone parameters are taken from literature. It was assumed that the whole Kafue Flats aquifer system consists of fine sand. The values used are determined from Stankovich and Lockington(1995) and can be found in Table 5.2.

4.5.2 Estimation of lateral inflows Along the fringes of the Kafue Flats several small rivers and creeks drain the surrounding watershed. However, only few of these tributaries are equipped with a gauging station. The only systematic estimates of the lateral inflows was done for the development of the KAFRIBA model (DHV, 2006). These data only includes time series starting from October 2002 to September 2004. For the floodplain model a longer time series is necessary. Therefore some estimate based on the measured data has to be established. This estimate was done using a simple rainfall – runoff model. The model uses three parameters and features a groundwater storage (Fiering, 1967; Vogel and Sankarasubramanian, 2003):

Q(t) = aP (t) + cSGW(t − 1), (4.11) with

SGW(t) = SGW(t − 1) + (1 − a)(1 − b)P (t) − cSGW(t − 1) (4.12)

For each tributary the corresponding watershed was determined based on the digital elevation model SRTM (Section 4.2.4). The rainfall inside these watersheds was calculated based on the NOAA-CPC data. All the input data 74 4.5 Distributed ﬂoodplain model

200 8 300 150

100 8 250 50 Thickness (m) Northing (km) 0 400 450 500 550 600 Easting (km)

Figure 4.14: Model boundary and aquifer thickness of the MODFLOW model. are averaged to monthly values. The model however is running on a daily time step. For each watershed the three parameters are calibrated using a least square ﬁt. The discharge of the single tributaries is then calculated for the whole simulation period using the calibrated models. To add the tributary inﬂow to the model it is simply added to the rainfall in the cell where the tributary joins the model domain.

4.5.3 Model geometry

The model consists of two layers, a groundwater layer and an overland flow layer. The two layers are divided by the ground surface. The layer geometry is defined by a digital elevation model. The topography is derived from the SRTM DEM (Section 4.2.4). First the data gaps were filled with a value of 970. Then for each model cell of 1000 × 1000 m2 the average elevation was calculated. After this step the Chunga Lagoon is introduced. The Chunga Lagoon was implemented as an implicit lake by setting the elevation of all pixels inside the lagoon 5 meters deeper. The top of the whole system is set to a constant value of 1 100 m a. s. l. The thickness of the overland flow layer is the distance between this elevation and the ground elevation. The thickness of the groundwater layer is defined to be 200 m in general. To avoid steep fringes of the groundwater layer and to make sure that the groundwater is less thick when the floodplain is narrow, the boundaries were smoothed (Figure 4.14). The model domain itself is the same as it was used for the one-dimensional model (Section 4.4). The course of the main channel was traced from a Landsat mosaic of the Kafue Flats. The elevation and the slope of the river channel is determined from the full resolution digital elevation model for every model cell. Since the course of the main river channel is not very well captured by Chapter 4 Floodplain Modelling 75 the DEM, the rivers elevations are corrected to make the river flow downwards. The same method was also applied in the one dimensional model (Section 4.4).

4.5.4 Correction of the digital elevation model A detailed analysis of the terrain model shows, that there is a number of ground depressions in the area of the floodplain which can not drain to the main river channel. These depressions can cause problems if the flooding has to be predicted correctly. Such depressions cause the model to predict areas as flooded which usually are dry. Also, at the point where the Kafue river spills into the Kafue Gorge reservoir, the elevations provided by the DEM are too high. This implicates that the lower part of the Kafue Flats are a closed basin which can only be drained by a river. Based on a model run the depressions which cause unnatural flooding are identified. They are filled using an algorithm which increments the elevation of each basin until there is a direct drainage to the main river channel or to the lagoon. In total eight large depressions are identified with a total area of almost 700 km2, where the largest one has an area of around 235 km2. With the algorithm used to fill the depressions they are replaced by a per- fectly flat area. The drainage of these areas, however, was not improved significantly by the removal of the hollows. Therefore within all the filled areas the natural slope was approximated by interpolating the elevations linearly. Al- though in some places again small depressions are introduced in the surface of the floodplain, the drainage of the areas in question is greatly improved. How- ever, the algorithm presented here can not be used to correct for the missing drainage of the lower part of the floodplain. This can only be done by adding a river, which has to be properly introduced into the model (Section 4.5.3).

4.5.5 Implementation of the model The model is divided into 242 × 82 regular cells with a size of 1 km by 1 km, each divided into two layers. The lower layer represents the groundwater whereas the upper layer represents the overland flow in the swamp. The two layers are coupled through the unsaturated zone flow module (UZF) where evaporation from the groundwater and recharge are modelled using a one dimensional kinematic wave approximation of the Richards’ equation (Niswonger et al., 2006). The main channel of the Kafue river is implemented using the streamflow package (SFR2) where the discharge in the river is computed using Manning’s equation for the river channel (Niswonger and Prudic, 2009). The channel geometry was derived from a study carried out by DHV engineers in 1980 (Section 4.2.5). To be used in the model these river cross sections have to be approximated with 8 points. This process was done automatically using an optimisation algorithm. 76 4.5 Distributed floodplain model

With the model approach chosen mainly the model cells of the overland flow layer are changing their status from wet to dry very often. In MODFLOW this could lead to an increased computational effort to solve the flow equations. For this reason the decision whether a cell is wet or dry is done in the very first iteration of each time step. For small time steps this is a reasonable approximation (Bauer, 2004). The inflow at ITT is directly added to the main river channel. The lower boundary condition is implemented using the time dependent specific head package of MODFLOW (CHD). The water level at Kafue Gorge is used directly. Backwater effects within the reservoir are not considered. Since most of the data are available on a daily basis the length of the stress periods (period with constant driving forces) is chosen to be one day. The time step at which the models equations are solved is a very crucial parameter. If it is chosen too short the simulation times increase significantly. If it is chosen to be too long it is more likely that the iterative solver of the model does not find a solution of the equations. This is usually the case when gradients are high. In this model the gradients are high mainly at the beginning of the simulation when the initial condition has to be compensated. For this reason the time step was set to 15 minutes for the first 10 stress periods and to half an hour for the following 10 (stress period 11 to 20). For the rest of the model run the time step is chosen to be one hour. For the evaluation of the model a period of four years, from the beginning of 2002 to the end of 2005 was used. This results in a total of 1461 stress periods. The simulation time on one Intel Core 2 Processor with a clock rate of 2.4 GHz is around three to four hours.

4.5.6 Coupling the overland flow to the groundwater To allow the coupling between the surface water layer and the unsaturated zone flow MODFLOW has to be modified. The water content in each cell of the overland flow layer has to be connected to the unsaturated zone flow module (UZF). The UZF module can route the exfiltrating water only to a river or a lake. The overland flow layer as it is implemented in the model acts similar to an additional groundwater layer. Therefore the correct routing of the exfiltrating water and the water stored in the surface water layer has to be added to MODFLOW. The coupling is done between two stress periods of the model and therefore is divided into two steps. First the water exfiltrating from the groundwater layer or the water volume which exceeds the infiltration capacity of the unsaturated zone is added to the surface water layer. In the next stress period rainfall is added to the water volume of the overland flow layer. This total volume is then added to the UZF package as rainfall which makes it available for infiltration. Again the water which exceeds the infiltration capacity is added to the overland flow layer. Chapter 4 Floodplain Modelling 77

To allow seamless integration of this coupling a module was added to MOD- FLOW. The module is built according to the standards of the software and is written in FORTRAN. For the correct coupling with the unsaturated zone the UZF module code has to be changed slightly. A new array storing the excess infiltration has to be introduced. Additionally the module has to be added to the main iteration loop of MODFLOW. For the module developed a matrix has to be specified which determines for each model cell whether the exfiltrating water is added to the overland layer or whether the water should be routed according to the specifications in the UZF input file (e.g. routed to a river or lake).

4.6 Model alternatives - MIKE SHE2

4.6.1 Properties of MIKE SHE

Another model which is capable of simulating the coupled surface - groundwater system is MIKE SHE (Graham and Butts, 2006). MIKE SHE was already successfully applied in modelling the flooding extent in the Okavango Delta (Ja- cobsen et al., 2005). The model was also targeted at predicting the correct flooding patterns. However, due to the very long calculation time needed for running a relatively short simulation period it was calibrated only manually. Nevertheless, applying MIKE SHE to develop a floodplain model seems to be an attractive option. MIKE SHE is initially based on the fully distributed physical model SHE (Système Hydrologique Européen) which was developed by a European con- sortium (Abbott et al., 1986b,a). It was later improved and extended by DHI Water & Environment. It is a very complete and versatile model which is capable of simulating, besides the movement of water, the transport of solutes, geochemical processes and nitrogen processes in the root zone associated to the growth of crops. The module for the simulation of the movement of water is divided into four major parts: (1) saturated groundwater flow, (2) overland flow, (3) unsaturated zone, (4) evapotranspiration and the hydraulic simulation of rivers and lakes. It also includes their interactions. To simulate the transport of water the model domain is, according to a standard finite difference scheme, divided horizontally into grid cells and vertically into layers. The user can determine the level of complexity at which the calculations are carried out by defining the components included in the simulation and by defining the method for the solution of the physical equations.

2The model described in this section is developed by Maria Niedermeier as part of her diploma thesis. 78 4.6 Model alternatives - MIKE SHE

The saturated zone component uses a three-dimensional flow formulation according to Darcy’s law. It allows to specify the hydraulic conductivity in each direction, thus it is suited to simulate anisotropic behavior of a porous media. The overland flow of water can be simulated using a diffusive wave approximation of the St. Venant equations. The equations are solved based on a finite difference grid which is used for the whole model. Overland flow is formed by exfiltrating groundwater or by rainfall amounts which exceed the infiltration capacity. As soon as the water level at the surface reaches a certain value water starts to flow. The flow path and the flow velocity is determined by the topography, the hydraulic roughness of the surface and the water losses from the surface through evaporation or infiltration into the groundwater. While the unsaturated zone does not store a significant amount of water it attenuates the influence of the processes at the surface, such as rainfall and evaporation, on the groundwater table. The water flow through the unsaturated zone is assumed to be one-dimensional in vertical direction. This is a valid assumption if the model cells are large compared to the thickness of the unsaturated zone. To calculate the water fluxes the one-dimensional Richards’ equation is used. The soil water retention curve and the unsaturated hydraulic conductivity are parameterised using the Van Genuchten formulation. This flow equation is solved using an implicit finite difference scheme. The evapotranspiration is calculated according to the method presented by Kristensen and Jensen(1975). This method uses empirically derived equations to determine the actual evapotranspiration based on land use and land cover characteristics and the potential evapotranspiration calculated from meteorological data. The processes of interception, plant transpiration and soil evaporation are modelled separately. This allows a more physical approach in calculating the actual evapotranspiration. It is, however, much more data intensive. To calculate the interception and the plant transpiration vegetation is characterised by the leaf area index (LAI) and the distribution of active roots in the soil. The soil evaporation is dependent on the soil type and the vegetation cover above ground (equivalent to the LAI). Rivers and lakes are simulated separately from the grid in a hydraulic model representing the geometry of the rivers and lakes in more detail. The tool used for modelling the flow in the rivers is called MIKE 11. It is a one dimensional model where the channel geometry is specified at each model node, similar to the HEC-RAS model (Section 4.4). It therefore allows the user to define the river channel in as many details as information on the river is available. The one-dimensional St. Venant equations can be solved using the full dynamic approach or the diffusive or kinematic wave approximation. For coupling MIKE 11 to MIKE SHE the course of the river channel is interpolated to the model grid in a way that the river always lies at the boundary between two grid cells. If the most complex coupling is applied the river banks act as a weir Chapter 4 Floodplain Modelling 79 in both directions, from the floodplain towards the river and from the river to the floodplain. The exchange rate depends on the head difference between the river and the overland flow in the surrounding model cells. Additionally the river can be coupled to the groundwater. This coupling is implemented using the concept of a leakage coefficient.

4.6.2 Implementation of the Kafue Flats model Based on the same model geometry and the same input data as used for the MODFLOW model a model of the Kafue Flats was constructed using MIKE SHE. To make the model comparable to the model constructed in MOD- FLOW the same grid cell size is chosen (1 × 1 km2). However, due to the different model structure and the input data which is not always available in perfect quality, some data has to be adapted. The ground water component are comparable and the same geometry and hydraulic properties can be implemented in both models. The more physical implementation of the overland flow induces data requirements. The hydraulic roughness of the surface has to be estimated and a water level threshold for the detention storage on the surface has to be specified. Since not much data is available uniform values have to be estimated. For the hydraulic roughness of the surface a value of 0.1 (Manning’s n) is assumed and the threshold for the detention storage is set globally to 5 mm. For the unsaturated zone the parameterisation of the flow properties is different from the MODFLOW model. While the MODFLOW model uses the Brooks-Corey formulation to calculate the unsaturated hydraulic conductivity, MIKE SHE uses the Van Genuchten formulation. Therefore different parameters have to be chosen. For this model standard parameters for clay soils are used. The evapotranspiration is also implemented in a more complex manner. The estimates from remote sensing (Section 4.2.3) were not available at the time of the model construction. Therefore the potential evaporation measured at an evaporation pan at ITT is used. Normally, measurements from evaporation pans overestimate the evaporation. To correct for this error a factor of 0.75 is applied. The distinction between plant and soil evaporation, which is made in the calculations of MIKE SHE, requires information about the vegetation properties (Kristensen and Jensen, 1975). The Kafue Flats mainly consists of three major vegetation zones, the floodplain, the termitaria and the woodlands. Since these vegetation zones are mainly dependent on the flooding in the wetland they are also found at certain elevation zones. Generally the floodplain vegetation is found at elevations below 980 m a. s. l. The termitaria zone is found at the transition zone between the woodlands and the floodplain at elevations between 980 m and 981 m a. s. l. At higher elevations woodland vegetation is dominant. Since the topography of the Kafue Flats shows a distinct 80 4.6 Model alternatives - MIKE SHE

Table 4.5: LAI and root depth for the three major vegetation zones in the Kafue Flats as deﬁned for the MIKE SHE model.

Vegetation type LAI root depth Floodplain 4 0.3 m Termitaria 2 0.3 m Woodlands 5 5 m gradient from West to East, this gradient of 0.05‰ is considered when determining the vegetation zones. Due to the permanent availability of water in the soil of the floodplain vegetation these areas are covered grass all over the year. A higher value is therefore assigned to the LAI (Table 4.5). Also the woodland is considered to have a high leaf density. Due to the lack of information on the root depth of the plants, the same value was assigned to the termitaria and the floodplain vegetation zones. The hydraulic simulation of the main river channel also allows to include available information. The stream flow package of MODFLOW only allows to simulate a diffusive wave approximation of the flow and measured cross sections have to be approximated with eight points only. The measured cross sections are available in more detail (Section 4.2.5). However, including all the details available is only possible at the cost of longer computational time. Also some numerical instabilities can be introduced into the model if the geometry of the river model is too complex. Therefore, the cross section geometry is smoothed and only every fourth cross section is added as a model node to fulfill the Courant-Friedrichs-Levy criterion. Additionally the model surface elevations have to be modified in order to align the bank elevation of the river and the elevation of the model cells connected to the river. If this correction is not done the geometry governing the exchange between river and floodplain is not correctly represented.

4.6.3 Parameter sensitivity

A sensitivity analysis reveals that similar to the MODFLOW model (Sec- tion 5.5) the parameters driving the water transport in the river and the water flow in the unsaturated zone are very sensitive parameters. The transport in the river is dominated by the cross sections, which are considered to be constant over time, and the hydraulic roughness (Manning’s n). The parameters driving the flow in the unsaturated zone which are found to be sensitive are the van Genuchten parameter, the residual and the saturated soil moisture content and wilting point. Also the hydraulic conductivity of the groundwater is found to be very sensitive with respect to the total flooded area. Chapter 4 Floodplain Modelling 81

Another group of parameters which shows a large inﬂuence on the total ﬂooded area is the parameters which govern the evaporation and the transpiration. These are the root depth and the leaf area index (LAI). The LAI is a parameter which can also be determined from vegetation maps or from satellite images. This parameter does not necessarily need to be calibrated. Though it is very important to use a good algorithm to estimate the LAI. The spatial distribution of the root depth can also be derived from vegetation maps.

4.6.4 Results This model, being rather a study of the applicability of MIKE SHE than the development of an operational model, remains uncalibrated to date. Since for all the parameters used for the simulation reasonable values were assumed, and since the simulation itself is governed by physical principles, the results should still be meaningful. These results are presented hereafter as they can be used to check whether such a model can simulate the hydrological processes in the floodplain reliably. To assess the hydrological changes in the Kafue Flats caused by the construction of the two dams a scenario of the current state with dams and a natural state without dams are simulated. For the natural scenario the releases of ITT where replaced by the discharges measured at Kafue Hook bridge. This discharge measurement is a good proxy for a natural discharge since its natural watershed remains unchanged to date. Also there are only minor tributaries joining the river before it spills into the ITT reservoir. One important indicator to see whether the simulation is able to reproduce reality is the water balance. Mainly the fit of the modelled and the observed outflow at Kafue Gorge is a good measure for the reliability of the model. The simulated discharge from Kafue Gorge shows a relatively strong seasonal signal but much less day to day variation compared to the measured outflows (Figure 4.15). This higher variation can be expected since the reservoir itself is not part of the model, but the water level at the dam was considered to define the lower boundary condition of the model. The accumulated discharge volume however, should be the same over a longer time period. This was found to be true. The mean accumulated discharge volume showed only a difference of around 200×108 m3 per year which is around 4% of the mean annual discharge. The comparison of the flow velocities in the river with measured data shows whether the physical system is reproduced accurately. However, no distributed data of the flow velocities exist. Only measurements in the lower part of the Ka- fue flats are available which show that the flow velocities are between 0.2 m s−1 and 1 m s−1. Since the gradient in the Kafue Flats is generally low it is safe to assume that the flow velocities do not deviate too far from these measured values. Although the hydraulic model of the river channel was built using measured transects, the simulation of the hydraulics shows some severe instabilities. 82 4.6 Model alternatives - MIKE SHE

350 modelled outflow from KG 300 measured outflow from KG )

−1 250 s 3 200

150

100 Discharge (m 50

0 2002 2003 2004 2005 2006

Figure 4.15: Comparison of the modelled and the measured outﬂow of the Kafue Gorge reservoir.

They mainly occur in places where the river bank elevation is low and therefore the exchange between the river and the floodplain is strong. The reason for these instabilities remains unclear. It could be caused by the concept of how the exchange between the river and the floodplain is implemented. Despite these instabilities both the average flow velocities and the average water level are simulated well. Therefore the flood maps should show at least the right tendency, since they are mainly linked to processes which happen at a longer time scale than those at which the instabilities occur. The simulated flooded area is shown in Figure 4.16 for the actual situation in the Kafue Flats with the dams and for a natural scenario where there are no dams present. The short spikes of the total flooded area are mainly caused by heavy rainfalls in the floodplain itself where the amount of rain exceeds the infiltration capacity of the soil locally. While this situation could theoretically happen in reality they are considered to be model artefacts. The seasonality of the total flooding is reproduced quite well. The peak flood occurs in April and the low flood from October to November. This can also be found in reality. However, the amplitude of the flooding seems to be underestimated. The analysis of the satellite images suggests that the total flooded area should fluctuate between a few hundred and a few thousand square kilometers. The simulated natural situation shows some significant differences to the current state. Mainly the flood peaks are much higher (up to 1 000 km2). In the low flood season the difference is smaller, therefore the fluctuation in flooded areas is larger under natural conditions. Chapter 4 Floodplain Modelling 83

8000 7000 With dams )

2 Without dams 6000 5000 4000 3000 2000 Flooded area (km 1000 0 01/2002 04/2002 07/2002 10/2002 01/2003 04/2003 07/2003 10/2003 01/2004 04/2004 07/2004 10/2004

Figure 4.16: Total ﬂooded area as simulated with the MIKE SHE model for the actual case with dams and a presumably natural state (without dams).

Although these findings seem to reflect the general idea about the influence of the dams, the interpretation is not as simple. The model has never been calibrated and even obtaining a stable model run seems to be a difficult task. Considering that the model parameters are mainly estimated to reflect reasonable values, the model is able to reproduce reality within certain limits. A calibration based on satellite and ground measurement data would help to apply this model as a powerful tool for simulating not only the hydrological processes but also bio-geochemical processes which are linked to the flowpath of the water.

4.7 River - ﬂoodplain interaction

Bio-geochemical measurements revealed that the oxygen concentration in the main channel of the Kafue Flats drops to extremely low values in areas where the water is mainly flowing through the floodplain (Wamulume et al., 2012). The hypothesis is that the oxygen is used in the flooded areas when organic matter which accumulates at the top of the soil is decomposed. One possible application of the models discussed above (MODFLOW and MIKE SHE) would be a simulation of the chemical processes which are heavily influenced by the flowpath of the water. To see whether it is possible to explain the measurements with oxygen uptake at the bottom of the floodplain and with exchange of water between the main river channel and the floodplain, a simple one-dimensional model was built. 84 4.7 River - floodplain interaction

The model implements some basic principles of transport modelling in a river – floodplain system. The hydraulic system consists of a rectangular main channel and a rectangular floodplain on both sides of the river. The dimensions of the channel and floodplain geometry can be specified. For the test simulation presented here a channel width of 75 m and depth of 8 m was chosen. The floodplain has a width of 1 km on each side. The slope of the river was chosen to be similar to the mean slope in the Kafue Flats (0.03‰). Only steady state discharge is considered and therefore the flow velocities v and the total discharge Q were calculated using the Gauckler-Manning-Strickler formula (Equation 4.13).

1 2 1 v = R 3 I 2 (4.13) n hy R

− 1 − 1 The hydraulic roughness (n) is set to 0.033 s m 3 and 0.066 s m 3 for the main river channel and the ﬂoodplain, respectively. The water temperature which drives the oxygen exchange with the atmosphere is set to 20℃. The transport in the river is modelled using the standard one-dimensional transport equation for steady state ﬂow:

∂c ∂c ∂ ∂c + v − D = qin (cin − c) (4.14) ∂t ∂x ∂x ∂x

The equation is integrated using an explicit difference scheme with upwind differences. However this method leads to numerical dispersion which adds to the modelled dispersion. Therefore the discretisation in space needs to be as fine as possible. To fulfill both, the Friedrichs-Courant-Levy stability criterion and the Neumann criterion, the time step needs to be very small. The spatial resolution of the model is set to 30 m and the time step is chosen to be one second. So far only processes of the oxygen cycle are considered. The rate of uptake of oxygen (ruptake) in the sediment is modelled using an approach according to the Michaelis-Menten kinetics:

cO2 U ruptake = kuptake,max , (4.15) cO2 + KO2 A

where kuptake,max, the maximum uptake rate, and KO2 , the concentration at which the rate r = 0.5kmax, are empirical constants which have to be measured −3 or taken from literature. In this simulation they are set to KO2 =0.1 g m −1 and kuptake,max=0.0005 g s . U and A are the wetted perimeter and the cross section area, respectively. The reaeration was implemented using the empirical equation of O’Connor and Dobbins(1958) with the temperature correction as recommended by the Chapter 4 Floodplain Modelling 85

ASCE(1991): r 1 v T −20 rreaeration = Dw 1.0241 · (cO ,sat − cO ) , (4.16) h 0.4h 2 2 where h is the water depth, Dw is the molecular diffusion coefficient, v is the mean flow velocity and T is the water temperature in ℃. cO2,sat is the saturation concentration of oxygen at a given temperature in ℃. 468 cO ,sat = . (4.17) 2 31.6 + T Another source of dissolved oxygen could be the oxygen produced from pho- tosynthesis. This process is not yet implemented in this model. The exchange of water between the river and the floodplain is simulated using a constant flow rate per unit length of the river. It is set to 0.05 m3 m−2 s−1. It is assumed that the water mixes completely in every time step. The volume of water in the river channel and in the floodplain remains constant. The results show that on a river stretch of 20 km the oxygen concentrations can easily drop to nearly zero if the floodplain and the oxygen uptake at the bottom of the floodplain is large enough (Figure 4.17). Oxygen is used in the floodplain very quickly and at a rate that reaeration can not compensate for the oxygen loss. While the ratio of water coming from the floodplain starts to dominate the water in the main channel, the oxygen concentrations in the main channel can be very low. 86 4.7 River - floodplain interaction

10 1 Proportion of floodplain water O2 conc. in the floodplain O conc. in the main channel ) 8 2 0.8 −3

6 0.6

4 0.4 conectration (g m 2

O 2 0.2 Proportion of floodplain water (−) 0 0 0 5 10 15 20 River length (km)

Figure 4.17: Simulation results of the simple river – ﬂoodplain oxygen model. Chapter 5 Calibration of the distributed ﬂoodplain model

If changes in the hydrological system are to be modelled in a distributed manner, the model must be able to reproduce the flooding patterns correctly. Thus validation or calibration efforts have to be based on distributed information on the inundation state (Milzow et al., 2009b). The large extent and the limited accessibility however, constrain the direct acquisition of spatial information on the ground. The application of remote sensing techniques therefore is very attractive (Jensen et al., 1995; Munyati, 2000; Bartsch et al., 2007). Seasonal flooding patterns derived from satellite imagery can provide valuable information. Yet, the applicability of remote sensing data has to be reviewed for each dataset. The exposure of the vegetation to seasonal variation and the small scale topography result in complex patterns of land cover in the wetlands. Therefore the data suited for the purpose need to have a relatively high spatial and spectral resolution (Neuenschwander et al., 2005). The distributed floodplain model presented in Section 4.5 is calibrated using flooding patterns from satellite images. For the comparison of the flood maps derived from ASAR data (Section 3.2) and the model predicted flooding a measure of fit F is used according to Equation 5.1(Horritt et al., 2007).

AC − AFP F = − 1, (5.1) AC + AFP + AFN where AC is the size of the area which is correctly predicted as being flooded by the model, AFP is the area predicted as wet but observed to be dry (false- positive) and AFN is the observed wet area which is predicted to be dry by the model (false-negative). In case of a perfect fit the value of F is zero. The calibration itself is carried out using the PEST1 parameter estimation suite version 12.0 (Doherty, 2005). PEST is a highly flexible calibration tool which estimates the model parameters based on a modified Levenberg- Marquardt algorithm (Marquardt, 1963). It features the calibration of model

1Model-Independent Parameter Estimation and Uncertainty Analysis

87 88 5.1 Calibration data parameters for any model accepting text ﬁles as model input. The applied algorithm also allows PEST to determine the parameter uncertainties.

5.1 Calibration data

As discussed in Section 3.1 the major drawback of optical remote sensing systems is their dependency on an external radiation source and the presence of clouds compromising the data. Active microwave systems such as SAR systems provide an alternative to retrieve surface data without being dependent on so- lar radiation and with almost no inﬂuence of clouds. Therefore the ﬂooding patterns derived from Envisat ASAR satellite images presented in Section 3.2 are used for calibration.

5.1.1 Comparing ASAR data to the model – a resolution problem

The different resolution of the calibration data and the model output raises the question of how they should be compared. The ASAR data have a much higher resolution than the model output, 75 × 75 m2 compared to 1 × 1 km2. Thus if one compares the modelled area to the measured area, discrepancies can be expected. Due to the averaging of the elevation in the model, a model cell is either completely flooded or completely dry. The measured flooding in the same model cell can resolve much finer detail. To overcome this discrepancy the measured data have to be scaled. One way of doing this is to define a flooding threshold. If the partial flooding of a particular cell exceeds the threshold the whole cell is considered as being flooded. In Figure 5.1 this upscaling is analysed for different thresholds. Clearly a very low threshold for partial flooding of 10% yields larger flooded areas. However, this static upscaling is a rather inflexible approach of handling partial flooding. The maximum extent to which a model cell can be flooded is mainly determined by the topography. Therefore if possible, information on the topography should be included in the process of determining such thresholds for every single model cell.

5.1.2 The inﬂuence of the DEM on the fraction of ﬂooding

If the modelled output is at a scale where a single cell contains a large number of elevation measurements, statistical information can be derived for each cell. This information can be correlated to the maximum flooded fraction of the cell. For the Kafue Flats this is done using linear regression correlating the maximum altitude difference and the standard deviation of the elevation within one model cell to the fraction of flooding derived from ASAR satellite images. Chapter 5 Calibration of the distributed floodplain model 89

3000 10% ) 2 30% 50% 70% 2000 90%

1000 Total flooded area (km

0 2003 2004 2005

Figure 5.1: Upscaling of the measured flooded area to the model resolution for different flooding thresholds from 10% to 90%.

5 25 Linear fit Linear fit 4 20

3 15 h h σ ∆ 2 10

1 5

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Flooded fraction Flooded fraction (a) (b)

Figure 5.2: Correlation between the maximum ﬂooded fraction and (a) the standard deviation σh, (b) the maximum elevation diﬀerence ∆h within one model cell. 90 5.1 Calibration data

1 8 300 0.8 0.6 0.4 8 250

Northing (km) 0.2 0 400 450 500 550 600 Easting (km)

Figure 5.3: Map of the maximum ﬂooded fraction in each model cell.

The correlation between the maximum elevation difference within one model cell and the maximum flooded fraction shows a weak negative correlation (Fig- ure 5.2(b)). The same is true for the correlation between the standard deviation in one single model cell and the flooding fraction (Figure 5.2(a)). However, for both measures the variation is too high to provide a stable measure for the scaling of the model output. Statistical tests show that the slope of the regression lines are not significantly different from zero. The reason for this is the quality of the DEM. The SRTM-DEM was found to have an absolute error of around 5 meters on the African continent. For the southern part of Zambia these errors are even a bit smaller (Rodriguez et al., 2005; Farr et al., 2007). In a very flat area such as the Kafue Flats where the variability of the relief within one model cell is much less than the absolute error of the DEM data, information on the micro-topography of the single model cells can not be exploited.

5.1.3 Generation of ﬂood maps at model resolution

Nevertheless, some information about the small scale topography is implicitly included in the flooding patterns obtained from the ENVISAT ASAR data. If the time series is long enough for each model cell the maximum flooding fraction can be determined (Figure 5.3). This flooding fraction is mainly governed by the small-scale topography within the cell. One assumes that the flood extent within one single model cell can not exceed the maximum flooding observed from the data. Flood maps at the resolution of the model are generated from each ASAR satellite image. For every cell the amount of flooding relative to the maximum flooding is calculated. This way the maps not only contain the information whether a model cell is flooded or not but also to what extent it is flooded. This improves the flexibility in the calibration of the model since model cells Chapter 5 Calibration of the distributed floodplain model 91

3000 ASAR (1) ASAR (2) ) 2

2000

1000 Flooded area (km

0 2003 2004 2005

Figure 5.4: The flooded area (1) measured directly from the ASAR data and (2) measured from the generated flood maps compared to the flooded area derived with the static threshold method. The blue shaded areas are the total flooding extent if a fixed threshold (10%, 30%, 50%, 70% and 90%) for partial flooding is applied (Figure 5.1).

which are only partly flooded do not have a large impact on the goodness of fit in case of wrong classification. Therefore, if the model result in a cell is compared to the measurements, the flooded extent measured translates directly to the probability that the model result is correct or wrong, respectively. If, for example, the flooding extent in a cell is measured to be 0.7 and the model classifies the very same cell as flooded, the probability that the model result is correct is 0.7. Thus, the probability that the model result is wrong is 0.3.

Figure 5.4 shows the influence of including this information of the maximum possible flooding extent on the total flooding extent retrieved from the radar satellite images. Compared to the values retrieved by applying a static threshold some differences can be observed. During low flood periods the relative difference between the total flooded area and the adjusted flooded area is very small. During the flooding season the relative difference becomes much bigger. This might be caused by the structure of the topography in the floodplain. During the dry season only the flat areas of the wetland are flooded, while in the wet season areas with a higher variation in topography are flooded. There- fore the generation of flood maps based on the maximum fractional flooding of each model cell is very important to catch the flood peaks correctly. 92 5.2 Manual sensitivity analysis

Table 5.1: Parameter conﬁgurations used for test cases compared to the reference simulation. The parameters changed for each case are highlighted.

Parameter Reference Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 VKS 7×10−5 3.5×10−5 7×10−5 7×10−5 7×10−5 7×10−5 3.5×10−5 SHC 1×10−3 1×10−3 5×10−4 1×10−3 1×10−3 2×10−3 1×10−3 ROUGHC 0.02 0.02 0.02 0.02 0.01 0.02 0.01 ROUGHB 0.02 0.02 0.02 0.02 0.01 0.02 0.01 SF2 0.05 0.05 0.05 0.12 0.05 0.05 0.05

5.2 Manual sensitivity analysis

In order to understand the influence of some selected model parameters on the progression of the total flooded area, simulations using different parameter configurations were carried out. For every test simulation only one or two parameters are altered. A selection of the different parameter sets used are found in Table 5.1. The corresponding results are shown in Figure 5.5. The results of these simulations show the influence of each parameter on the total flooding in the Kafue Flats. One can observe that the two parameters VKS and ROUGHC and ROUGHB (i.e. the saturated hydraulic conductivity of the unsaturated zone and the hydraulic roughness of the river channel) have the largest influence on the total flooding extent. While a larger value of VKS leads to a general shift of the total flooded area and to smaller peaks from rainfall events, a decreased roughness (ROUGHC and ROUGHB) lead to a stronger fluctuation and to larger peaks from rainfall events (Figure 5.5(a) and 5.5(d)). If the permeability of the unsaturated zone is higher, water can infiltrate much faster and the flooding caused from rainfall events is therefore smaller. This causes a smoother curve of flooding since single rainfall events are less important for the total amount of flooding. If the roughness of the main channel is reduced the fluctuation of the total flooded area is increased. A smoother river channel leads to higher flow velocities. Thus the water is transported out of the system much quicker which leads to lower flooding in the dry season. The influence of the streambed conductivity and the drainable porosity of the groundwater (or specific yield) is smaller but still obvious (Figure 5.5(b) and 5.5(c)). The porosity of the aquifer determines how much water can be stored per unit volume. If this amount is increased the recharge to or discharge from the groundwater leads to a smaller water level change. At least parts of the floodplain are inundated through groundwater which exfiltrates to the ground surface. A higher porosity is therefore leading to a smaller total flooded area. However, the observed change of the area is relatively small. Chapter 5 Calibration of the distributed floodplain model 93

8000 8000 Reference Reference

) 7000 Case 1 ) 7000 Case 2 2 2 6000 ASAR (upscaled) 6000 ASAR (upscaled) 5000 5000 4000 4000 3000 3000 2000 2000

Flooded area (km 1000 Flooded area (km 1000 0 0 2003 2004 2005 2006 2003 2004 2005 2006

(a) Case 1: VKSnew = 5 VKS (b) Case 2: SHCnew = 0.5 SHC · old · old 8000 8000 Reference Reference

) 7000 Case 3 ) 7000 Case 4 2 2 6000 ASAR (upscaled) 6000 ASAR (upscaled) 5000 5000 4000 4000 3000 3000 2000 2000

Flooded area (km 1000 Flooded area (km 1000 0 0 2003 2004 2005 2006 2003 2004 2005 2006

8000 8000 Reference Reference

) 7000 Case 5 ) 7000 Case 6 2 2 6000 ASAR (upscaled) 6000 ASAR (upscaled) 5000 5000 4000 4000 3000 3000 2000 2000

Flooded area (km 1000 Flooded area (km 1000 0 0 2003 2004 2005 2006 2003 2004 2005 2006

(e) Case 5: SHCnew = 2 SHC (f) Case 6: SHCnew = 2 SHC and · old · old SF2new = 2.4 SF2 · old

Figure 5.5: The time series of the total flooded area in the floodplain which results from the different test simulations with the parameters shown in Ta- ble 5.1. The most significant parameter change is highlighted for each case. The parameter names are described in Table 5.2. 94 5.3 Model stability

A lower conductivity of the streambed in the main channel leads to a smaller flooded area, especially during the dry season. If the exchange between the river channel and the ground water happens at a lower rate, the influence of the river on the groundwater table is reduced. While during the rainy season flooding is mainly determined by the rainfall and the tributary inflows, being less dependent on the flows in the main channel, the flooding in the dry season seems to be mainly driven by the river itself. Also the flow of river water to the groundwater or to the floodplain seems to dominate over the drainage from the floodplain to the river. This finding is also supported by the model results shown in Figure 5.5(e), where a more permeable streambed leads to a higher flooding. If drainage was more dominant the opposite effects should be observed.

5.3 Model stability

During some model runs for the manual sensitivity analysis (Section 5.2) problems with model stability were observed. For some parameter sets the iterative solver which solves the model equations does not converge to a unique solution. Unfortunately it was not possible to find a general rule which parameter constellation causes the model to abort. There are some indications that the stability issues are attached to the simulation of the main river channel. Mainly at long calculation time steps and when certain parameter constel- lations occur the model iteration is not able to find a solution. An indication that the calculation time step plays an important role is found by the analysis of the parameter sensitivities of the hydraulic properties of the river. The parameter which determines the flow in the main river channel and on the attached floodplain is the hydraulic roughness (Manning’s n). In the floodplain model these parameters are named ROUGHC and ROUGHB (Table 5.2). A significant change of the sensitivities of the parameter ROUGHC can be observed if the calculation time step is varied between 3 hours and 30 minutes (Figure 5.6). This dependency of the sensitivity on the time step can only be explained if the time step is too large for achieving a stable simulation of the river channel itself. At the same time the sensitivity of the hydraulic roughness of the floodplain stays more or less stable. One can see that if the calculation time step is shorter than one hour the sensitivity of the river roughness does not change anymore. One can therefore assume, that the river channel model is stable at time steps smaller than or equal to one hour. The calculation time step length of the river model can only be controlled by changing the time step of the entire model. However, even with a rather small time step it was not possible to have stable model runs with all the different parameter sets. Mainly when the flow velocities in the river became high (i.e. through low hydraulic roughness) the Chapter 5 Calibration of the distributed floodplain model 95

20 Main channel Floodplain 15

10 Sensitivity 5

0 30 min 1 h 1.5 h 2 h 3 h Calculation time step

Figure 5.6: Sensitivities of the river roughness parameters (Manning’s n) dependent on the calculation time step chosen. solver of the model was not able to find a stable solution anymore. Therefore for the following calculations and for the model calibration the streamflow part of the model was simplified. Instead of using the measured cross-sections the river was divided into five segments according to the five zones identified in Section 5.4. The flow in these segments is calculated using the approximation of the Manning’s equation which is valid for wide rectangular river channels (h >> b). The width of the river channel is introduced as additional model parameter (Table 5.2). In return, the hydraulic roughness of the river banks (ROUGHB) is not needed anymore. Also a small time step for the calculations is not necessary anymore if the simplified river channel is used. For the following model runs a time step of three hours is sufficient to achieve convergence in all cases.

5.4 Zones

Prior to calibration the model domain is divided into five zones according to different hydrological properties (Figure 5.7). The most upstream zone (1) is located in between the Itezhi-Tezhi dam and Namwala (Map in Figure 1.3). This part is characterised by a meandering river flowing in a well constrained river bed and is mainly influenced by the daily regime of releases from the reservoir. The second zone (2) reaches from Namwala to Busangu. The Kafue river meanders in a confined river bed and its hydrological regime is mainly influenced by the release of Itezhi-Tezhi. The third zone (3) covers the very flat area of the permanent lagoons, the Blue Lagoon and the Chunga Lagoon. Apart from the two water bodies the river flow is not constrained to the river bed but 96 5.5 Sensitivity analysis

8 300

(4) (2) (3) (5) (1) 8 250 Northing (km)

400 450 500 550 600 Easting (km)

Figure 5.7: For calibration the model domain is divided into 5 zones. For each zone a set of parameters is calibrated. it extends to vast flooded areas during high flow. The next downstream zone (4) spans from the outlet of the Chunga Lagoon down to the Mazabuka area. In this part of the floodplain the river channel itself disappears for long distances. Water is flowing mainly within the dense vegetation dominated by reed. The flooding in this zone can also be strongly influenced by the backwater of the Kafue Gorge reservoir. The lowest zone (5) finally extends from downstream of the Mazabuka area to the Kafue Gorge reservoir. The flooding in this zone is mainly influenced by the back water of the Kafue Gorge dam and mostly consists of permanent water bodies.

5.5 Sensitivity analysis

To choose which parameters have to be calibrated a sensitivity analysis was carried out using the PEST software suite (Doherty, 2005). PEST offers two different tools to calculate the sensitivity of model parameters. The SENSAN utility allows to define the parameter variations explicitly. It allows to assess the sensitivity of a parameter with respect to any arbitrary criteria. During the calibration process PEST itself calculates the Jacobian matrix for the initial and all subsequent parameter sets. The sensitivities of each parameter with respect to the measure of fit used for calibration can be calculated directly from the Jacobian matrix. The SENSAN utility is used to assess the sensitivity of each parameter in a range around the initial value. The initial value of each parameter was multiplied by 0.5 and by 2. Then the corresponding sensitivities with respect to the maximum, the minimum and the average extent of flooding as well as the Chapter 5 Calibration of the distributed floodplain model 97

flooding frequency and the standard deviation of the flooding extent are calculated. While the different parameter values are chosen to be uniform over the whole model domain, their sensitivity was calculated for all of the 5 different zones. This results in a total of 15 parameters which are assessed (Table 5.2). Because of problems with model stability (Section 5.3) this sensitivity analysis was carried out using the simplified model. Instead of using the measured river cross-section data the main river channel was modelled using the approximation of the Manning’s equation for wide rectangular channels (h >> b). The analysis shows that the parameter governing the exchange between the river and the groundwater, the streambed hydraulic conductivity (SHC), and the hydraulic roughness of the river channel (ROUGHC) are very sensitive parameters with respect to the dynamics of the total flooding (Figure 5.8). The streambed hydraulic conductivity mainly determines how much water is flowing from the river to the floodplain and vice versa. The hydraulic roughness of the river is important because it influences the flow velocity in the river and therefore has a significant influence on the water levels and on the residence time of the water in the floodplain. Also the vertical hydraulic conductivity of the unsaturated zone (VKS) shows a high sensitivity. It mainly influences the rate at which water infiltrates from the surface layer to the groundwater, thus governing the duration of flooding of a model cell as long as the groundwater table does not reach the surface. Other parameters with a relatively high sensitivity are the thickness of the streambed (TCK) and the vertical leakance between the two model layers (VCONT). The sensitivity of the streambed thickness however, is strongly linked to the one of the streambed hydraulic conductivity. This result was expected since they both influence the infiltration rate of the river in the same manner. The vertical leakance between the surface layer and the groundwater layer shows only a high sensitivity in the zones where flooding is important and lasting for several months (i.e. zone 4 and 5). The leakance becomes only important when the unsaturated zone in between vanishes due to long-lasting flooding. In general most of the parameters show their highest sensitivity in zones 3 and 4. Since these zones are both, the ones with the lowest gradient and the largest area, they are most influential on the total flooding in the Kafue Flats. The second possibility of carrying out a sensitivity analysis is to assess the influence of every single parameter on the measure of fit used for calibration (Equation 5.1). This is done using the PEST calibration software directly, since the first step of every calibration is to calculate the Jacobian matrix from which the sensitivities can be calculated. For this analysis also the simplified version of the model is used (Section 5.3). Other than in the previous analysis all parameters are assessed for each of the five zones. Since all parameters (Table 5.2) are divided according to the zones, this results in a total of 75 parameters. 98 5.5 Sensitivity analysis

Table 5.2: The parameters assessed in the automatic sensitivity analysis. They are part of the Block-Centered Flow package (BCF), the Unsaturated Zone Flow package (UZF) and the Stream Flow Package (SFR).

Parameter Description Package Initial value Dimension SF1 Specific yield of layer 1 BCF 0.5 m3 m−3 HY1 Hydraulic conductivity BCF 40 m s−1 of layer 1 VCONT Vertical leakance BCF 3×10−7 s−1 SC2 Confined storage coeffi- BCF 1×10−7 m3 m−3 cient of layer 2 HY2 Hydraulic conductivity BCF 1×10−4 m s−1 of layer 2 SF2 Specific yield of layer 2 BCF 0.1 m3 m−3 VKS Saturated vertical hy- UZF 7×10−5 m s−1 draulic conductivity of the unsaturated zone EPS Brooks-Corey epsilon of UZF 2.34 - the unsaturated zone THTS Saturated water con- UZF 0.37 m3 m−3 tent of the unsaturated zone EXTDP ET extinction depth UZF 5.0 m EXTWC ET extinction water UZF 5×10−2 m3 m−3 content TCK Thickness of the SFR 1.0 m streambed SHC Hydraulic conductivity SFR 1×10−3 m s−1 of the streambed −2 − 1 ROUGHC Manning’s roughness SFR 2×10 s m 3 coefficient for the main river channel WIDTH Channel width of the SFR 100 m main river channel Chapter 5 Calibration of the distributed floodplain model 99 TCK SHC ROUGHC WIDTH SF1 HY1 VCONT SC2 HY2 SF2 VKS EPS THTS EDP EWC mean 100000 max min std Zone 1 freq 10000 mean max min std 1000 Zone 2 freq mean max min 100 std Zone 3

freq Sensitivity mean max 10 min std Zone 4 freq mean 1 max min std Zone 5 freq 0.1 0.5 2.0 0.5 2.0 0.5 2.0 0.5 2.0 0.5 2.0 0.5 2.0 0.5 2.0 0.5 2.0 0.5 2.0 0.5 2.0 0.5 2.0 0.5 2.0 0.5 2.0 0.5 2.0 0.5 2.0

Figure 5.8: The relative sensitivities of each parameter on selected statistical parameters of the flooding in the different zones. For each zone the sensitivity of the parameters with respect to the mean value (mean), the maximum and the minimum flooding (max and min), the standard deviation (std) and the mean flooding frequency is shown. The sensitivities are calculated for two values of each parameter: the initial parameter is multiplied by 0.5 and by 2.0. 100 5.6 Calibration process

102

101

100

10−1 −2 Sensitivity 10

10−3 −4 10 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 SF2 SF1 SC2 EPS HY2 HY1 SHC VKS TCK THTS EXTDP WIDTH VCONT EXTWC ROUGHC

Figure 5.9: The sensitivities of the different parameters. For each parameter the sensitivities were calculated for all five zones. The parameter names are defined in Table 5.2.

The sensitivities with respect to the measure of fit (Equation 5.1 are very similar to those of the first analysis (Figure 5.9). The streambed hydraulic conductivity (SHC), the hydraulic roughness of the river (ROUGHC) and the vertical hydraulic conductivity of the unsaturated zone (VKS) are again the most sensitive parameters. The sensitivity analysis with respect to statistical parameters of the flooding (Figure 5.8) shows some patterns of increased sensitivities in the zones most prone to flooding. These patterns can not be observed when the sensitivities are assessed with respect to the measure of fit. One has to consider that the parameter changes for this analysis are rather small compared to the ones made for the previous analysis. The parameter set chosen uses the initial parameters of the model (Table 5.2), therefore the sensitivities might change for the calibrated model.

5.6 Calibration process

As a result of the sensitivity analysis (Section 5.5) the subset of model parameters which are calibrated is chosen. The parameters which are most sensitive mainly drive the flow in the river and the river – floodplain interaction as well as the unsaturated zone and the groundwater flow. In order to minimise the number of necessary model runs, only the most sensitive parameters are selected. These parameters include the vertical hydraulic conductivity of the Chapter 5 Calibration of the distributed floodplain model 101 unsaturated zone (VKS), the hydraulic roughness of the main river channel (ROUGHC), and the streambed hydraulic conductivity (SHC). For the calibration of these parameters a two step approach is chosen. In a first step the three parameters described above are assumed to be uniform over the whole model domain. Thus, in the first step only three parameters have to be calibrated which can be done at relatively small computational costs. In a second step the same parameters are calibrated for all the zones. This results in a total of 15 parameters. To make the optimisation process more stable, regularisation is introduced. For all three physical parameters (SHC, ROUGHC and VKS) a so called smoothing constraint is added. This constraint requests the difference between the model parameters of one group (i.e. the same physical parameters in all zones) to be zero. If this condition is violated it contributes to the value of the objective function which is minimised. Such smoothing reduces the discontinuities of the parameter values introduced at the boundaries between the calibration zones. In PEST this is implemented by introducing so called regularisation observations. They are defined by assigning an observed value of zero to the difference between the corresponding parameters in the different zones.

5.7 Calibration results

5.7.1 Uniform parameters

The first calibration step was carried out by calibrating three parameters which are considered to be uniform over the whole model domain (Section 5.6). A comparison between the total flooded area of the calibrated model and from the satellite images is shown in Figure 5.10. The optimised parameters calculated with automatic calibration are found in Table 5.3. The total flooded areas can provide some information on the quality of the fit (Figure 5.10). While the areas generally are in the same order of magnitude one can also observe that the modelled flooded areas in general have a higher value. Such a systematic error can either be caused by the quality of the satellite images or by a structural error in the model. The analysis of the residuals shows that they all have a value between -1 and -2. The largest residual has a value of -1.80, the smallest is -1.19 and the mean is -1.56. A perfect fit would have a value of zero. The lowest residuals are found when the total area of the model and the measurements are approximately the same. This situation is found during the flood peak and in the low flow season. When the flooding is generally high the fit gets better since the ratio of correctly predicted flooding is high. The highest residuals are found during the beginning of the flooding between December and February. The measured flooded areas indicate that the flood levels are raising later than the model predicts. In Figure 5.11 the 102 5.7 Calibration results

3000 ASAR 2500 Model ) 2 2000

1500

1000 Flooded area (km

500

0 −1 Residuals

−1.5 Residual (−) −2 2003 2004 2005 2006

Figure 5.10: Comparison between the modelled total flooded area and the area determined from the ASAR images after model calibration using uniform parameters. In the lower plot the corresponding residuals of the measure of fit are shown. Chapter 5 Calibration of the distributed floodplain model 103

1 8 300 0.8 0.6 0.4 8 250

Northing (km) 0.2 0 400 450 500 550 600 Easting (km) (a) Satellite image

8 300

8 250 Northing (km)

400 450 500 550 600 Easting (km) (b) Model

Figure 5.11: Comparison between the modelled and the measured flooded area at the time where the best fit is achieved (May 10, 2004). simulated flooded area on May 10, 2004 is shown, where the best fit is achieved. The worst fit between the satellite image and the model is found on February 2, 2004 (Figure 5.12). On this image one can clearly see that two large areas along the northern fringe of the floodplain and one area along the south-eastern border are simulated as flooded. The same areas are classified as dry on the satellite image. The main reason for this are errors in the model geometry as well as structural shortcomings of the model. The DEM used, being corrected for the most obvious deficiency, still contains depressions which do not drain due to the slope. Also the model structure facilitates an over-estimation of flooding. This is due to the lateral inflows along the fringes which, in the model, are added to the rainfall. These tributaries contribute a large amount of water to the surface in a locally limited area, where the infiltration capacity of the soil is exceeded quickly. According to Equation 5.1 values below -1 occur when there are more pixels which are modelled as flooded and classified as dry on the satellite images (false 104 5.7 Calibration results

1 8 300 0.8 0.6 0.4 8 250

Northing (km) 0.2 0 400 450 500 550 600 Easting (km) (a) Satellite image

8 300

8 250 Northing (km)

400 450 500 550 600 Easting (km) (b) Model

Figure 5.12: Comparison between the modelled and the measured ﬂooded area at the time where the highest residual is found (February 2, 2004). Chapter 5 Calibration of the distributed ﬂoodplain model 105

Table 5.3: Calibrated parameters and their associated uncertainties (95 % con- ﬁdence interval). The dimensions of the parameters are found in Table 5.2.

Initial Calibrated Confidence Parameter name value value interval (95 %) SHC: Streambed hydraulic × −7 1.0×10−3 3.65×10−5 6.93 10 conductivity 1.92×10−3 ROUGHC: Manning’s n for the × −5 0.02 0.005 8.08 10 main channel 3.09×10−1 VKS: Saturated vertical hy- −4 −4 −2 6.45×10 draulic conductivity of the un- 7.0×10 1.00×10 1.55×10−1 saturated zone positive) than pixels which match. This also supports the conclusion that the model structure might lead to an overestimation of the flooded area in certain regions. More information can be provided by a detailed analysis of the output of the calibration tool (PEST). The optimised model parameters show that the fit achieved has a rather high uncertainty (Table 5.3). The 95% confidence interval of the single parameters spans over at least two orders of magnitude. However, the confidence interval indicated by PEST has some limitations. It is calculated under the assumption of linearity throughout the parameter range, which might not be valid in such a complex model. The covariance matrix (Table 5.4(a)), where the diagonal elements are the variances of the respective parameters, also shows that the parameter uncertainty is rather high. Usually this is the case when too few parameters are used for calibration. However, the matrix of the correlation coefficients shows that the parameters calibrated are not completely uncorre- lated (Table 5.4(b)). The parameters show a weak to medium correlation. The strongest correlation is found between the parameters SHC and ROUGHC. Being negative, it can be interpreted along with the physical meaning of the parameters. If the hydraulic roughness of the river channel (ROUGHC) is low the streambed hydraulic conductivity (SHC) needs to reach a higher value to maintain the exchange rate between the river and the ground water. This correlation contributes also to the high parameter uncertainties. Another factor that contributes to a high parameter uncertainty are the two parameters ROUGHC and VKS which reach the boundary defined for calibration. As stated above the parameter ROUGHC is not a completely independent parameter. A different parameter set of SHC and ROUGHC might therefore also calibrate the model equally well. The calibration process can have a tendency to push a correlated parameter towards the boundary depending on the initial parameter set. In contrast, the parameter VKS, which determines 106 5.7 Calibration results

Table 5.4: Parameter covariance and correlation matrix.

(a) Parameter covariance matrix. SHC ROUGHC VKS SHC 5.135 0.278 0.697 ROUGHC 0.278 5.886 1.408 VKS 0.697 1.408 2.187

(b) Parameter correlation coeﬃcient matrix. SHC ROUGHC VKS SHC 1.0 -0.752 -0.320 ROUGHC -0.752 1.0 0.291 VKS -0.320 0.291 1.0

the infiltration rate through the unsaturated zone, is a rather independent parameter. A very high calibrated value of VKS might be caused by areas where either the model topography or the lateral inflow which are added to the surface layer lead to an overestimation of flooding. Areas where this happens can be identified in Figure 5.12. In order to minimise the effect of the lateral inflow on the flooding, a high hydraulic conductivity of the unsaturated zone is necessary. Such an unrealistic value of VKS can be successful if defined locally to dampen the effects of structural shortcomings of a model. However, if these local effects outweigh the physical properties of the whole model domain, uniform model parameters turn out to be inappropriate.

5.7.2 Parameters by zone

The need for non-uniform parameters is shown in the section above. Instead of calibrating only three parameters, now for each zone (Figure 5.7) a different parameter set is used. The parameters obtained by this calibration procedure (Table 5.5) are generally in the same order of magnitude as the uniform parameters (Table 5.3). However, especially in the most downstream zone (zone 5) the parameter set found by calibration is rather different. The reason for this is, that all the water which leaves the system spills to the Kafue Gorge dam right at the outflow of this zone. In addition, in the model, the outflow is only allowed to flow within the main river channel. Therefore, mainly the two parameters pertaining to the river hydraulics (ROUGHC) and the exchange between the river and the floodplain (SHC) show a different value. The roughness of the river channel, determining the flow velocity, is very low in zone five. This implicates that the carrying capacity of the river, which is Chapter 5 Calibration of the distributed floodplain model 107

Table 5.5: Calibrated parameters using diﬀerent parameter values for ﬁve zones of the model domain. The dimensions of the parameters can be found in Table 5.2.

Initial Calibrated Parameter name value value SHC: Streambed hydraulic conductivity Zone 1 1.0×10−3 2.513×10−5 Zone 2 1.0×10−3 3.870×10−5 Zone 3 1.0×10−3 1.831×10−5 Zone 4 1.0×10−3 2.394×10−5 Zone 5 1.0×10−3 1.058×10−4 ROUGHC: Manning’s n for the main Zone 1 0.02 1.128×10−2 channel Zone 2 0.02 1.083×10−2 Zone 3 0.02 5.966×10−3 Zone 4 0.02 7.293×10−3 Zone 5 0.02 5.000×10−3 VKS: Saturated vertical hydraulic con- Zone 1 7.0×10−4 6.527×10−3 ductivity of the unsaturated zone Zone 2 7.0×10−4 9.317×10−3 Zone 3 7.0×10−4 5.952×10−3 Zone 4 7.0×10−4 8.332×10−3 Zone 5 7.0×10−4 7.049×10−3 108 5.7 Calibration results determined by the geometry and the roughness, needs to be very high. Since the geometry is constant (rectangular channel with a width of 100 m), the channel needs to be very smooth. This shows that the river geometry bears the potential of improvement. The hydraulic conductivity of the stream bed (SHC) in the most downstream zone is prominent for its high value. In this zone the hills which confine the floodplain converge towards Kafue Gorge. Water which is flowing overland in the floodplain is therefore forced to drain in the main river channel. A more pervious streambed accounts for the drainage in zone five. The values of the conductivity of the unsaturated zone (VKS) are more uniform. Slightly higher values can be observed in zone 2 and 4, where the corrections made to the DEM were most severe (Section 4.5.4). In these two zones the infiltration rate needs to be higher in oder to compensate for the areas which can not drain superficially. Also the tributary inflows along the fringes spill to the floodplain mostly in these areas. As described above these lateral inflows are added to the surface layer of the model and thus directly cause local flooding. An analysis of the parameter correlation and the covariances is not possible in PEST if regularisation is used. One can assume that the slight correlation between the river roughness and the permeability of the river bed can also be found, when non-uniform parameters are used. The analysis of the total flooded areas (Figure 5.13) shows, that the difficulty of the model to simulate the seasonal progression of the total flooding persists. The flooding in the model apparently reacts quicker to rainfall than it does in reality. A reason for this could be the lateral inflows which are simulated using a simple rainfall-runoff model. They usually react quickly to rainfall events even if they use only monthly averages as input data. The confinement of the drainage in the lower part of the floodplain has also a large effect on the progression of the total flooding. It might be the main reason for the significant mismatch between the measured and the modelled flooding at the beginning of the rainy season. Since the drainage is probably too slow in the model, the flooded area increases earlier than in reality and it also decreases later. This finding is also reflected in the seasonal progression of the residuals (Figure 5.13). The largest residuals are always found during the rainy season between December and March. While the residuals are generally lower than obtained by the calibration with uniform parameters, they are still in the same value range (mean -1.52; largest -1.85; smallest -1.13). Thus, the areas simulated as being flooded and measured to be dry still outweigh the correctly classified areas. The regularisation (or smoothing constraint) of the parameters of the different zones had only a marginal influence on the calibration process. The differences between the parameter values in each zone are very small compared to the residuals of the flooded area. Chapter 5 Calibration of the distributed floodplain model 109

3500 ASAR 3000 Model )

2 2500

2000

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Flooded area (km 1000

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0 −1 Residuals

−1.5 Residual (−) −2 2003 2004 2005 2006

Figure 5.13: Comparison between the modelled total flooded area and the area determined from the ASAR images after model calibration using a different value for each zone. In the lower plot the corresponding residuals of the measure of fit are shown.

Chapter 6 Conclusions and recommendations

In developing countries the management of water resources is often a very chal- lenging endeavour. Climatic conditions, the lack of an appropriate institutional setup and the lack of resources to finance projects lead amongst other reasons to a lack of knowledge about the hydrological systems. A growing population and changes of the climate might increase challenges of water management, such as the equitable supply of sufficient water to its users, in the future. As stated before, a good physical knowledge of the hydrological system is very important. In these areas where large parts of the river basins remain ungauged, the application of remote sensing techniques for hydrological modelling is very attractive. The wide variety of remote sensing data which are available today offer a unique opportunity for hydrologists. However, these data also have their disad- vantages. Hydrological parameters can only be measured indirectly. Generally, one can measure differences or changes in physical properties which change the response of the surface to electromagnetic radiation. This means that either the reflectance of sunlight of the earth surface or changes of the backscattering of microwave radiation are measured. Measurements from remote sensing therefore record hydrological parameters very different from the way it is done in ground based gauging stations. However, all the hydrological models and concepts applied today are developed in order to be used with ground measurements. While for some datasets, such as rainfall, integration into a hydrological model is quite straight forward, for other datasets this might not be the case. The measurement of soil moisture on the ground for example is very different from measurement of soil moisture using a radar scatterometer. The microwave signal emitted by the radar instrument is scattered at the surface depending on its dielectric constant. While the presence of water has a huge influence on the dielectric constant, it is not the only one. Also the back-scattered intensity is only sensitive to the water content in the top few centimetres. Ground based methods of measuring soil moisture determine the water content in a certain volume. The most striking

111 112 6.1 Real-time forecast difference between the satellite based and the ground based method is the scale at which they are effective. While the satellite system covers an area of at least 1 × 1 km2 for one measurement, the ground based measurement covers a volume of less than 10 cm3. Therefore, the data can not be compared directly as they do not reproduce exactly the same quantity. In other cases when ground measurement data are missing, classical measurements have to be replaced by other measurements. For example, if no discharge gauges are available the flooded area can be used as a proxy to determine either the discharge or the storage of water in a certain area. The flooded area however can only be used as a proxy if a good hydraulic model is available which in turn needs other input data. Generally speaking, if one wishes to use data from remote sensing for hydrological modelling either the data have to be processed to fit the model or the models have to be adapted to incorporate the data. The models presented in this thesis are two examples for this. The real-time discharge prediction framework uses a model which is especially designed to use the satellite based soil moisture data. The model used for floodplain modelling is a standard model which is, as far as possible, fed by data derived from remote sensing data. Still the application of remote sensing data is not very common among hydrologists. The ratio of publications on hydrology and remote sensing among all the publications about hydrology did not grow since the mid 1990’s. There might be several reasons for this. First of all the integration of remote sensing data into a model is still a complicated and time consuming process. The most crucial drawback of satellite data however, is the nonexistence of long time series. The longest time series of satellite data available is for a bit more than 30 years. Usually satellite instruments are operational for around 10 to 20 years. Although in some cases continuity missions are planned and put into operation, the interoperability of the different systems is not guaranteed. Therefore there is some risk that the time series stay rather short. Hydrological modelling under conditions of data scarcity remains therefore a big challenge. Recent developments offer promising opportunities to advance in this field. On one hand, real-time modelling techniques allow the assimilation of data in a model, updating the modelled system state every time observation data are available. On the other hand, techniques for extracting information on the hydrological cycle from remote sensing data have advanced in the past few years.

6.1 Real-time forecast

While some years ago satellite systems were designed to gather as many types of data as possible in order to provide the scientific community with data that could be exploited in several ways, nowadays satellite missions are designed for Chapter 6 Conclusions and recommendations 113 a specific purpose. Several satellite missions have been deployed recently, or will be launched in the near future, especially for the retrieval of soil moisture. Radar scatterometer data were found especially promising for use in hydrological modelling where the soil moisture is one of the most important parameters. Since the radar signal penetrates only the top few centimetres of the soil, hence only giving information on the surface soil moisture, the water content in the soil column has to be modelled. The simple two-layer model used to generate the SWI produces data which are appropriate to be used as input data for a conceptual model. Since rainfall is one important driver of soil moisture a conceptual model should also utilise rainfall data. The prediction framework presented exploits the available data sets on rainfall and soil moisture. The relatively simple conceptual model consisting of two reservoirs, for the surface water and the subsurface water, and an infiltration process based on the soil moisture, shows a fairly good performance. The forecast framework for discharges as it is presented in this thesis is only applicable to very specific applications, such as the implementation of environmental flow releases. This is mainly due to very high uncertainties. These uncertainties are composed of different contributions: (1) the used input data are all derived from satellite data therefore only represent an indirect measurement; (2) the simple conceptual model involves a structural error since by far not every process taking place is included. Additionally such conceptual models are site-specific. Their ability to be transfered to other watersheds is rather limited. Especially in watersheds where the storage of water in the soil is of high importance the model predictions are accurate. In the Luangwa river basin, which is dominated by steep slopes and quick runoff formation, the model’s performance is not satisfactory. The first source of uncertainties, the one associated with the input data, has the potential to decrease with new satellite systems put into operation and new methods of deriving hydrological data from it. Hydrological parameters derived from satellite data, such as soil moisture, will always provide an indirect measurement. However, due to a higher spatial resolution and a better temporal coverage they offer a huge potential. Data with higher spatial resolution allow for the application of more physical models. Thus, the models are less site- specific and usually involve a smaller structural error. Running the model in real-time with a data assimilation procedure provides long term forecasts which can be used for a wide variety of applications. To manage a river basin system such a forecast is beneficial since the discharge expected for the next few weeks can be quantified. Releases for power production, irrigation water demands or ecological flood releases can be planned based on this information. If water management options for a period exceeding the forecast lead time have to be assessed the conceptual model is not suitable because it is not physically based. Due to the relatively long time step flood forecasting is also 114 6.2 Detection of flooding patterns not possible. If the quality of the input data is greatly improved flash flood forecasting could eventually be an option. More and more data from newer satellite systems will be available in real-time. A higher temporal and/or a higher spatial resolution can greatly improve modelling efforts. A higher spatial resolution of the data (e.g. as provided by Envisat ASAR) would allow a higher spatial resolution of the model. Since the BWI and the rainfall are averaged over the whole area, the runoff processes are also averaged. The spatial variability of the different runoff processes is completely neglected. If heavy convective rainfall is occurring in an area with high soil moisture a peak in the runoff should be observed. Therefore if the soil moisture data allow the model to divide the watershed into sub-basins a better prediction of peak discharges could be feasible. A higher temporal resolution of soil moisture data can allow models to account for the usually high temporal variability of the soil water content. Considering this, further research should focus on the improvement of the quality of the data and the development of more sophisticated hydrological models tailored to use remotely sensed soil moisture data. An interesting option could be to assimilate the measured soil moisture to one of the physically based models, therefore making its calibration not only dependent on the discharge at a single gauging station. This would allow to exploit the spatial information provided by the soil moisture data. The quantification of the relevant uncertainties demands attention as well. If the generally high uncertainties of the prediction presented in this study can be minimised such a forecast can be used for applications where low uncertainties are essential.

6.2 Detection of ﬂooding patterns

For successful application hydrological models of floodplains have to be able to predict the flooding patterns correctly. The large extent and a limited accessibility often make remote sensing products the only data source which can be exploited. The requirements such data have to fulfill are high for hydrological applications. Essential properties are the availability of long time series and a good seasonal coverage. While the MODIS data used in this study have a very high temporal resolution, the ASAR data have a better seasonal coverage. The calculation of the NDWI from MODIS data provides a very simple method to detect the presence of liquid water on the earth surface. The cloud cover in the rainy season makes the estimation of flooded areas from optical satellite data during this hydrologically important time almost impossible. The ASAR data used in this study, being almost independent of weather conditions, provide a better seasonal coverage and are therefore a valuable data source for the extraction of flooding patterns. The reflection of the radar signal on smooth surfaces and the dihedral reflection of the signal if reeds are Chapter 6 Conclusions and recommendations 115 standing in the water are the basic principles of a classification algorithm using only back-scattering intensity images. Since the flooding processes and their effect on the scattering of the radar signal are relatively complex a simple threshold method is not efficient. The approach chosen involves grouping of pixels into three classes, each for open water surfaces and flooded vegetation. This allows to classify pixels based on constraints dependent on the probability of flooding and their spatial configuration. Such a threshold based method, however, necessarily has to be compared to some reference data. The values of the thresholds are successfully obtained by using flooding patterns derived from Landsat data as reference. A time series of flooded areas is derived from both data sets, the MODIS and the ASAR data. The total flooded area matches generally well to the expected seasonal behaviour of the system as well as to the seasonal progression of the area derived by the hydrological model. The classification of the MODIS data yields much higher flooded areas in the wet season. This might be caused by the generally wet conditions. Inaccurate classification of ASAR images is observed in a few images where either the effect of a different incidence angle of the radar signal or the influence of the soil moisture on the back-scattering intensity is a probable cause. Both methods have their drawbacks which are intrinsic features of the classification method applied. The NDWI, being sensitive to the presence of liquid water, overestimates the flooded areas under generally wet conditions. For the classification of the ASAR data the inability of the algorithm to detect flooding in pixels, where different back-scattering properties are detected might lead to an underestimation of the total flooding. Although the methods for the detection of flooding presented generally pro- duce good results, some attention has to be paid to the uncertainties and the inaccuracies. One of the main issues with the correct classification is the occurrence of mixed pixels. They can generally be divided into two main classes: (1) pixels where the area of different classes meet within the boundary of the pixel itself; and (2) pixels where the characteristics of two or more classes are superimposed on a small scale. The first type of mixed pixels can be observed on the boundary between an open water surface and the floodplain vegetation. The area covered by these pixels can be reduced easily if higher resolution images are used. The second type of mixed pixels are found in a floodplain if either the vegetation gets flooded but not totally covered by the water, or if in a flooded area the vegetation starts to grow over the water surface. The detection of such pixels can not be improved with the application of data with higher spatial resolution. A possible solution to this problem would be the detection of flooded areas using a combined approach, incorporating data from different sensors (e.g. radar data and thermal infrared data) acquired at the same time. This however, is a complex task since the data has to be measured on the same day. Many 116 6.3 Floodplain modelling satellite sensors (those using the visible range of light) can not acquire data of the earth surface when the sky is covered by clouds. Thus, the continuous application of a combined dataset is nearly impossible. A more feasible approach would be to combine different datasets asynchro- nously. This approach is partly implemented in the Kafue Flats. Data with a good seasonal coverage (ASAR data) are acquired for as many days as possible, whereas the data with higher spatial resolution and lower temporal coverage (Landsat data) are used to calibrate the method for extracting the flooding patterns. However, to make the detection of flooding more robust the combination of Landsat and ASAR data needs to be extended to a longer time period. If only two different images are used the uncertainties remain quite large.

6.3 Floodplain modelling

Choosing a modelling strategy for floodplain modelling is a rather complex task. Therefore, different modelling strategies are applied and assessed in the Kafue Flats wetland. The water balance of the Kafue Flats shows that the inflow at ITT contributes at least half of the total inflow to the wetland, while the other half is supplied by rain falling directly into the floodplain and by small streams flowing in the system along its fringes. Considering the strong seasonal variations of discharge and the large storage volume of the reservoir, it is obvious that the flooding in the flats is mostly dependent on the water release at ITT. Additionally, the backwaters of the Kafue Gorge reservoir determine a large portion of the flooding. The interaction between the upper and the lower dam causes a rather complex hydrology. For this reason the simple black-box model was not able to capture the dynamics of the flooding. A relation between the flooded area and the total water storage could not be established. The advantage of such a model is that it only uses few measured data, such as discharge, rainfall from remote sensing and an estimate of the evapotranspiration. However, only more complex models have the potential to simulate the seasonal flooding well. The one-dimensional hydraulic model of the Kafue Flats uses slightly more data than a simple box model. Most importantly, information about the geometry has to be available. The topography and the course of the river have to be known in the floodplain. While this model simulates the hydraulics of the surface flow in the floodplain, hydrological processes are implemented in a very simple way. This way the model does not need lots of data but it has also limited capabilities. The simulation results show that important processes and storages are missing from the model. Mainly the backwaters of the Kafue Gorge dam are not captured well. The main reason for this is the quality of the elevation model which causes a hydraulic disconnection between the reservoir Chapter 6 Conclusions and recommendations 117 and the floodplain. Also the missing groundwater storage causes the flooded area to be significantly overestimated by the model. Even if the amount of data which has to be gathered for a more complex, physically based model is significantly larger, it has the potential to compensate for the shortcomings of simpler models. The high data demand however, needs to be satisfied with information from various data sources. In regions where the supply of data is generally poor, they need to be chosen based on their availability. The quality of the data does not have equal priority. Many data sources used, mainly those derived from remote sensing products, are prone to errors. The magnitude of these uncertainties is hard to estimate, also because a comparison to data from other sources is not possible. The spatially distributed model presented in this thesis is tailored to satisfy the needs for an accurate simulation of the flooding patterns in the Kafue Flats, while accommodating the restrictions of the data availability. The main advantage of the model based on MODFLOW 2005 is its flexibility. The concept can be applied to almost any floodplain system. Where necessary, simplifications can be implemented easily, or a process can also be modelled in greater detail. The model MIKE SHE is very similar to the one based on MODFLOW. It is a very complete and powerful model, yet it does only partly allow to be applied on different levels of complexity. Therefore, in areas where few data area available, many assumptions and estimates have to be made.

6.4 Calibration of the distributed ﬂoodplain model

Both, when choosing the data used to calibrate the model, and when choosing the parameters calibrated, one needs to be very careful. The data used for calibration often needs some further processing before it can be used for calibrating a model. The choice, which model parameters are going to be calibrated, significantly determines whether the calibration process is successful or not. The satellite data used for calibrating the distributed floodplain model needs to be upscaled to the model resolution. It is shown that a successful upscaling needs to be based on physical properties of the model domain. Even if these properties are poorly known, a more realistic upscaling can be achieved when the available information is exploited. By extracting the maximum flooded area from each model cell, implicit information on the micro-topography is extracted directly from the calibration dataset. A drawback of this approach is that it needs relatively long time series of flooding patterns. The more data are available in the flooding season, the higher is the probability that the maximum flooding for each cell is captured. 118 6.4 Calibration of the distributed floodplain model

An important advantage of such upscaling is the introduction of partial flooding of a model cell in the calibration data. The hydrological model itself allows only two states of flooding: wet or dry. In contrast, the measurements feature partial flooding. This way, for the comparison of measured and simulated flooding, a measure for the probability of the match is introduced. If, for example, a model cell is measured to be flooded by an extent of 20% and it is simulated to be dry, the probability that the simulation is wrong is 20%. The probability that the model prediction is correct is therefore 80%. During the calibration process this compensates for the low spatial resolution of the model. For predictive model runs however, such information is not available. A downscaling of model results is therefore more difficult. The complexity of physically based models is mainly reflected in the number of parameters which can be adjusted. If one decides to split the model domain into different zones, this leads to even more parameters. However, especially if the model runtime is long, the calibrated parameters have to be chosen carefully. This is usually done based on a sensitivity analysis. Not only the sensitivity analysis, but also the way how the model domain is divided into zones is very important. In the model presented in this thesis, the zones were established based on morphological properties of the floodplain. These do not necessarily reflect the (unknown) hydrological properties. Two of the three parameters calibrated only affect the river channel. Thus, the river is divided into five reaches with different parameters. This usually is an acceptable choice. However, the calibrated values show that the most downstream reach is dominated by the drainage of the whole system. This affects both parameters which are adjusted, the hydraulic conductivity of the streambed and the hydraulic roughness of the river channel. While the streambed conductivity takes a high value within a reasonable range, the value of the hydraulic roughness is very low, which is equivalent to a very smooth riverbed. The main reason for this is found in the structure of the model. Drainage is only allowed through the river itself. In such a setup it might be justified to set a parameter to an unphysical value locally. If a major part of the river is affected, this can lead to unwanted effects on the model results. The only value calibrated, which affects the whole area of the floodplain is the vertical hydraulic conductivity of the unsaturated zone. This parameter shows much smaller differences. Although it has the tendency to be very low, to compensate for the flaws in the DEM, it is relatively uniform over the whole area. A more adapted calibration strategy could therefore divide the river itself in smaller parts, especially in the lower part of the Kafue Flats (zones 3 to 5). The five zones for vertical hydraulic conductivity can be maintained as defined in this thesis. In general, the calibrated model is found to be able to reproduce the seasonal progression of flooding. The best fit between measured and simulated flooding Chapter 6 Conclusions and recommendations 119 is achieved in the dry season and at peak flooding. An insufficient agreement is present mainly during the period of rising flood levels and during flood recession. These shortcomings can be explained by the model structure, which needs to be revised to some extent.

6.5 Improvements of the distributed ﬂoodplain model

The improvements presented in this section mainly address the deficiencies of the model which are apparent after calibration. They mainly concern the model geometry and the model structure. The basis of the model geometry is set by the digital elevation model. It defines not only the ground level but also the elevation and the slope of the river segments. As it was shown, the DEM currently used is not free from defects. Even if it was possible to fill the major depressions, there are still areas where the DEM is known to be inaccurate but can not be corrected in a straightforward way. Recently, more accurate data sources for a digital terrain model are developed. Most notably the TanDEM-X mission developed by the German Aerospace Center (Krieger et al., 2007). The system is designed to achieve a vertical accuracy of less than two meters with a resolution of 12 × 12 m2. Such a high quality dataset has the potential to improve the model geometry significantly. The very high resolution of this dataset compared to the models resolution can also provide valuable information of the micro-topography within a model cell. An adapted technique to determine the representative elevation of a model cell still needs to be developed. Another cause of serious overestimation of the flooded area, the discharge of lateral inflows to the surface layer of the model, can not be solved by using a more accurate DEM. A strategy to avoid this excess flooding would be the implementation of a more complex river network. If the course of the major tributary rivers is added explicitly to the model, the drainage of very flat areas can be enhanced. As noted above, the connection between the floodplain and the Kafue Gorge reservoir needs to be revised. To compensate for the overestimation of elevation in the downstream part of the floodplain, the drainage is confined to the river. To account for this, either the groundwater layer can be made more pervious locally, or the river width could be enlarged. Another important aspect is the quality and the availability of satellite data used for calibration. Up to now the available flood maps cover only a period of three years. All these years are characterised by discharge values below average at the Kafue river. Also the rainfall amounts in the same period are mostly lower than average. With longer time series of measured discharge available, 120 6.5 Improvements of the distributed floodplain model the model period can be extended. Also, this allows to obtain a greater number of flood maps. After model calibration a proper validation can be carried out. Acknowledgements

Without the support of many people, a Ph.D. thesis would never succeed. First of all I would like to thank my supervisor, Wolfgang Kinzelbach, who gave me the opportunity to work on this project in Zambia, a very interesting environment, not only from a scientific perspective. I greatly appreciate his support, by sharing his immense knowledge and experience, as well as his amicable nature. The conferences and courses, I was encouraged to participate, were a unique occasion to meet fellow scientists from throughout the world. I would also like to thank András Bárdossy for his willingness to be the co-referee of this thesis. Working in an interdisciplinary project, is a unique experience. Even more, it allows to share ideas with people across various areas of expertise. I would like to thank the whole ADAPT team, under the direction of Bernhard Wehrli. During their work for the ADAPT project in Zurich David Senn and Amaury Tilmant were taking the time to have fruitful discussions. I would like to express my gratitude to them. Seeing the progress of the other PhD students in the project, Lucas Beck, Manuel Kunz, Roland Zurbrügg and Wilma Blaser, was a constant source of motivation for me. I will never forget the exhausting but cheerful days in the Kafue Flats with Wilma Blaser, Griffin Shanungu and Florian Köck. During many trips to Zambia Collins Nzovu was not only helping me in getting hydrological data from ZESCO, but I also appreciated his always good humour. I would also like to thank Romas Kamanga, the former head of the hydrology department at ZESCO. Also Imasiku Nyambe from the School of Mines at UNZA deserves my appreciation. Many thanks go to the students who have made an important contribution to this thesis. I greatly appreciate the excellent work of Andreas Frömelt and Maria Niedermaier, who chose to work on a topic in the Kafue area for their masters and diploma thesis. Also a number of students chose the Kafue area as a topic for their bachelor thesis: Anna Hostettler, Martina Kauzlaric, Johannes Manser and Manuel Pauli. I would like to thank all my colleagues at IfU who all contributed to the motivating and positive work environment. Special thanks go to Christian Milzow, who helped me finding my way into research. Sincere thanks are given to Haijing Wang, who was always willing to share her knowledge about satellite remote sensing. Special thanks go to Peter Bauer-Gottwein, from whom I had the opportunity to learn about river basin modelling and optimisation techniques. I am also grateful that Florian Köck will carry on the project,

121 122 Acknowledgements ensuring that the work I have started ﬁnds a continuation. I wish him good success! Finally I would like to express my gratitude to my family. I always felt great support. Above all I would like to thank Christine, not only for the many hours she spent proof-reading my thesis, but also for her encouragement, her sense of reality, and for making my life delightful. Bibliography

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133

Appendix A Documentation of the MATLAB MODFLOW tools

A.1 General remarks

For the MODFLOW version used to run the floodplain model, no graphical user interface (GUI), such as PMWIN or similar, is available. Therefore the model input files have to be generated manually, or a tool which generates the input files has to be developed. Because a complete model of a floodplain uses a huge bunch of data which has to be imported and converted from very different files and data formats, a flexible preprocessing tool for the input data is necessary. Such a tool is developed using MATLAB. The programming capabilities which MATLAB provides are suited for the import and manipulation of large data sets. Particularly the mapping toolbox facilitates the handling of geographical data. Many tasks usually processed using a GIS, can therefore be implemented in MATLAB. This is important if the same task has to be repeated over and over (e.g. the calculation of daily ET values). The tools presented in the following section provide a fully functional preprocessing / post-processing suite for MODFLOW 2005. It is optimised to satisfy the needs of floodplain modelling. It therefore might not be the tool of choice to establish a MODFLOW based groundwater model for other purposes. How- ever, since the source code of tools is available it can be extended and adapted to individual needs. The whole collection of scripts consists of more than 18 000 lines. Many details on the algorithms used can therefore not be described in this chapter. However, whenever possible there are comments in the scripts itself which might be helpful. In the following sections the most important tools for the setup of a MOD- FLOW model and the output data extraction are presented. They are all written in MATLAB and tested against version R2009b. Each function is presented in a consistent manner. A short description of what it does is followed by a description of the input and output variables. All function names are typed in bold face (exampleFunction), the outputs are printed in slanted font

135 136 A.2 Import and preparation of input data

(exampleOutput) and the input variables are printed normal. Optional inputs or outputs are denoted with square brackets (mandatoryInput[,optionalInput]).

A.2 Import and preparation of input data

The tools presented here do not provide the capabilities to establish a new model from scratch. The NAME file (*.nam) has to be written by hand before the MATLAB tools can be used successfully. Also the model geometry has to be defined first. For this purpose some tools are provided which support this task. There is a graphical editor for the boundary conditions (IBOUNDeditor, see below) and functions which facilitate the export of gridded data into a file format suitable for MODFLOW. Many input data used have to undergo a more or less complex preprocessing, before they can be used as model input data. For this purpose a set of tools is developed, which facilitate the seamless integration of such data into the model. If, for example, the evapotranspiration data is generated from MODIS satellite data, as described in Section 4.2.3, a tool to import the data directly to a suitable format is available.

A.2.1 IBOUNDeditor.m The IBOUNDeditor calls a self-explanatory graphical user interface which allows the user to define the boundary condition of the MODFLOW model (Figure A.1). The user can load data which is generated using a GIS software and edit the details, such as adding a fixed head or an impermeable boundary. The data can be exported as a plain-text *.dat file which can directly be used for MODFLOW. Instead of importing a matrix from and exporting it to a file, the user can also pass a matrix as input argument in the command line and pass the modified matrix to a variable in MATLAB.

Usage:

[modifiedMatrix] = IBOUNDeditor ( [initialMatrix] ) modifiedMatrix Optional output. The final version of the boundary condition after editing. initialMatrix Optional argument. Initial version of the boundary condition. One can also use this input to define the dimensions

A.2.2 writeMFdata.m This function writes arbitrary gridded data (a matrix) to a ﬁle which is directly read by the MODFLOW model. Appendix A Documentation of the MATLAB MODFLOW tools 137

Figure A.1: The graphical interface of the IBOUNDeditor. 138 A.2 Import and preparation of input data

Usage: success = writeMFdata ( data,filename[,format] ) success returns 0 in case of successful execution data Matrix with values filename Full path to the file to be written. format Optional argument. Format of the numbers to be printed in the file (see help page of the fprintf(...) function (default: %4.2f)

A.2.3 readNCDCdata.m

This function reads data as it is provided by the National Climatic Data Center (NCDC). The imported data is in a form, which allows the direct use by other functions, such as SsebiMODIS().

Usage: metData = readNCDCdata ( filename ) metData Data structure containing the meteorological data, as provided in the used input file. filename Full path to the file which should be imported.

A.2.4 SsebiMODIS.m

This function calculates the S-SEBI (Simpliﬁed Surface Energy Balance Index) from MODIS satellite data using the algorithm described in Section 4.2.3.

Usage:

ET[,ETdate[,pET]] = SsebiMODIS ( StartDate,nper,modX,modY,MOD09path, MOD11path,TempPath,UTMzone,AOI, metData ) ET Actual evapotranspiration as calculated by the S-SEBI algorithm, projected to an arbitrary coordinate system, which is defined by the function input. The output is stored in a cell array with a separate matrix for each day. ETdate Date (in MATLAB format) for each day where data are available Appendix A Documentation of the MATLAB MODFLOW tools 139 pET Proxy for the potential evapotranspiration over the area (equivalent to the maximum measured ET in the defined area). StartDate Start date (first day) of the ET calculations nper Number of days to read modX,modY Coordinate system to which the ET data is projected MOD09path Full path to where the MOD09GA data resides on the file system MOD11path Full path to where the MOD11A1 data resides on the file system TempPath Folder where temporary files are stored in oder to continue the calculations in case of an unexpected interruption. utmZone Zone number if the data is to be projected to UTM. AOI Area of interest. metData Meteorological data as provided by the readNCDCdata() function.

A.2.5 interpolateGridTS.m This function interpolates a time series of grid data in a way that every single NaN grid cell is filled with a value obtained by linear interpolation in time. No spatial interpolation is done. However, for some cases filtering in space might be necessary. If you specify a date vector series or an index vector and one day or one index is missing, an additional grid is inserted with the missing index. Empty matrices in the original data are filled with matrices consisting of NaN’s with the same dimensions as the original data.

Usage: newGridTS = interpolateGridTS ( GridTS,GridDate ) newGridTS Grid time series with all data gaps ﬁlled by interpolation in time. GridTS The grid time series to be interpolated. GridDate The date vector or an index vector where each time series member is given a unique index or a date. Missing indices or days are ﬁlled with interpolated data.

A.2.6 readFEWSdaily.m Import daily rainfall estimates distributed by the Famine Early Warnings System Network (FEWSNet) and project it to UTM coordinates. The data can be down- 140 A.2 Import and preparation of input data loaded at http:earlywarning.cr.usgs.govaddsdatatheme.php.

Usage: rainfall[,rX,rY] = readFEWSdaily ( file[minlat,maxlat,minlon,maxlon[,mstruct]] ) rainfall Daily rainfall data stored in a matrix, covering the whole area of interest. rX,rY Coordinate matrices of the exported data. file Full path to the file to be imported. minlat, maxlat Minimum and maximum latitude of the area of interest. minlon, maxlon Minimum and maximum longitude of the area of interest.

A.2.7 generateTributaryInflows.m

Generate time series for the tributary inﬂows using a very simple model and the discharge data provided by the KAFRIBA model. The daily discharge data is stored in a matrix of the same size as the model, where the model cells receiving discharge have non-zero values. It can then be added to the rainfall data.

Usage:

TributaryInflows[,WSinfo] = generateTributaryInflows ( tributaryDataPath, rainfallPath,pETfile, RFfile,tributaryWSfile, tributaryOutlets,ibound, modX,modY, SimulationStartDate, petStartDate,nper, mstruct,tmpfolder ) TributaryInflows Data structure with the generated discharges for each tributary. WSinfo (optional) Information on the watersheds used, such as outlet coordinates or the model parameters of the simple model. tributaryDataPath Folder where the original discharge data resides on the file system. rainfallPath Folder where the rainfall data is stored. Internally the data are read using the readFEWSdaily() function. pETfile Path to a CSV-file where potential ET is saved for the time period used. Appendix A Documentation of the MATLAB MODFLOW tools 141

RFfile CSV file, which might be needed to correct the pET datam, if it is measured from an evaporation pan and it contains negative values. tributaryWSfile ArcGIS Shapefile of the watersheds for each tributary. tributaryOutlets ArcGIS Shapefile containing the outlets of each watershed. ibound IBOUND variable of the MODFLOW model. modX, modY Coordinates for each model cell of the MODFLOW model. SimulationStartDate Start date of the simulation. petStartDate Start date of the pET time series. nper Number of periods (days) used in the model. mstruct Map projection of the models coordinate system. tmpfolder Folder where temporary files are stored.

A.3 Main function

A.3.1 runSimulation.m

The main part of the script collection which brings all the single functions together is the runSimulation() function. It defines most of the very basic parameters of the model, such as the modelled period, the model dimensions or general options on the structure of the model. Additionally it defines the functions used for data import and preparation. It also calls the single functions which prepare the different input files of the model. The parameters which are intended to be changed by the user can be found within the first approximately 180 lines of the function. Changes below this line should only be done if the user intends to expand the functionality of the tool. An essential prerequisite for the successful execution of the main function is an existing NAME-file for the MODFLOW model. This file defines, which modules are used and thus, which input files are written by runSimulation.m.

Usage: success = runSimulation ( modelPath[,MODFLOWPath[,execModel]] ) success Should be zero in case of normal termination. modelPath Directory on which the model files are stored. MODFLOWPath Optional argument. The full path to the MODFLOW exe- cutable. execModel Optional argument. Flag which defines whether the simulation should be run from within MATLAB or not. 142 A.4 Write input files

A.3.2 readMFnam.m This is an important helper function for the main script. It extracts the information on modules used by MODFLOW from the NAME file and provides the filenames of the used input files.

Usage:

ﬁlename[,UnitNumber] = readMFnam ( FileType,ModelPath[,ModelName] )

filename Filename of the input file associated with the requested module. UnitNumber Unit number of the input file, which is internally used by MODFLOW. FileType Data type of the input file, which is extracted from the NAME file. Valid expressions are either the name of a MODFLOW module (’BCF6’, ’WEL’, or similar) or a MOD- FLOW specific data format (’Data’ and ’DATA(BINARY)’) ModelPath Path to the model files. ModelName Optional argument. Name of the models NAME file (.nam). This parameter only needs to be specified if there is more than one NAME file in the directory specified in ModelPath.

A.4 Write input ﬁles

A.4.1 writeMFbas6.m This function writes the basic package (BAS6) input ﬁle for MODFLOW2005.

Usage: success = writeMFbas6 ( BAS6file,IBOUNDunit,HNOFLO,[initHead|’External’, extUnit] ) success Zero in case of normal termination. BAS6file Filename of the MODFLOW BAS6 input file. IBOUNDunit File unit number(s) of the IBOUND data file(s) for each layer. HNOFLO The value of head to be assigned to all inactive (no flow) cells. initHead Initial head assigned to each layer. Either a matrix with a value assigned to each cell or a constant value. The initial Appendix A Documentation of the MATLAB MODFLOW tools 143

value is assigned to each layer separately, thus initHead has to be a cell array containing the initial head for each layer. If an external data file should be imported use the alternative funcion call (using the keyword ’External’ and the unit number of the external file as specified in the NAME file) and specify the unit numbers for the files for each layer. Do not forget to list the external files in the NAME file.

A.4.2 writeMFdis.m

The function is used to write the discretisation ﬁle for MODFLOW.

Usage: success = writeMFdis ( nlay,ncol,nrow,nper,nstep,perlen,itmuni,lenuni,delc,delr,top, topoFile,bottomFile,trans,DISfile ) success Zero in case of normal termination. nlay Number of layers of the model. ncol, nrow Number of columns and rows. nper Number of stress periods. nstep Number of time steps per period. Often the first few iterations of a model need a shorter time step if the initial condition is not very natural. In these cases a dynamic time step can be chosen which assinges a value of 48 to the first ten stress periods, 24 to the next ten, then 12, 8, 6, 4, 3, 2, 1 until it reaches the default value. In this case nstep has to be specified as follows: nstep={’dyn’,}, (e.g. nstep={’dyn’,8};). perlen Duration of one stress period (units: see itmuni). itmuni Time unit, 0: undef; 1: sec; 2: min; 3: hours; 4: days; 5: years. lenuni Length unit, 0: undef; 1: feet; 2: meters; 3: cm. delc, delr Resolution of the model in x- and y- direction. top Top of system. topoFile Topography file to be used by the model (generated with writeMFgriddata). bottomFile Aquifer bottom file to be used by the model (generated with writeMFgriddata). trans ’TR’ if simulation is transient, ’SS’ for steady state simulations. DISfile Filename of the MODFLOW DIS input file. 144 A.4 Write input files

A.4.3 writeMFoc.m

This function writes an output control ﬁle for MODFLOW 2005.

Usage: success = writeMFoc ( nper,nstep,IWRITEtimes,nlayer,OCfile ) success Zero in case of normal termination. CHDfile Filename of the CHD input file. headdata Time series of the time dependent head for the cell(s) specified. For each model cell where a time-variant head is used headdata contains one column. ROW, COL, LAT Row, column and layer of the cell(s) with a varying head. nper Number of stress periods of the model.

A.4.4 writeMFwel.m

This function is used to write well package ﬁle for MODFLOW 2005. At the moment this function is only suited to include non-parameter wells.

Usage: success = writeMFwel ( nper,lay,col,row,Q,WELfile ) success Zero in case of normal termination. nper Number of stress periods of the model. lay, col, row Layer, column and row of the cell where a well is located. Q Vector of recharge (Q(i)>0) or pumping (Q(i)<0). The first nper timesteps are used. WELfile Full path to MODFLOW-2005 well package input file.

A.4.5 writeMFevt.m

This function writes the MODFLOW-2005 evaporation package input ﬁle.

Usage: success = writeMFevt ( EVTfile,topography,extinctionDepth,pET,nper[,OutUnit] ) success Zero in case of normal termination. Appendix A Documentation of the MATLAB MODFLOW tools 145 topography Surface elevation of each cell. If topography is a string, data will be read from the specified file, otherwise topography has to be specified explicitly as array. extinctionDepth Extinction depth of each cell. If extinctionDepth is a string, data will be read from the specified file, if extinctionDepth is specified using an array its size needs to fit the size of IBOUND, if extinctionDepth is a scalar the extinction depth will be set constant all over the area. pET Potential evapotranspiration at each cell. There are different ways to define pET: 1. Define one single value: pET will be constant over all cells and stress periods. 2. Define an array which fits the size of IBOUND: pET will be constant over all stress periods. 3. Define pET as a one dimensional array of (MATLAB-) cells each containing 3a. a scalar value: pET will be constant over all cells, 3b. an array which fits the size of IBOUND: pET will be defined for each single cell at each stress period. In case 2 and 3 the time series will be repeated from the beginning if it is shorter than the simulation period. nper Number of stress periods. OutUnit (optional) File unit of the output file as indicated in the NAME file.

A.4.6 writeMFsfr2.m This function writes streamflow routing package (SFR2) input file for MODFLOW 2005. The algorithm used checks for each cell, whether it contains a stream reach or not. To calculate the physical parameters for each reach, the coordinates where the river crosses the border between two model cells are calculated first. The river length and the slope (based on the DEM) is then calculated using these points.

Usage: success[,runbnd] = writeMFsfr2 ( riverShape,IBOUND,X,Y,dem,demX,demY, SFRfile,layer,cellSize,nper,Inflow[,elevation, UZFoutput,useZones,zones] ) success Zero in case of normal termination. runbnd A matrix of the size of IBOUND, which serves as IRUNBND variable needed by the UZF package (see MODFLOW documentation for details). 146 A.4 Write input files riverShape ArcGIS Shapefile where the rivers are stored (as line). IBOUND MODFLOW IBOUND variable. X,Y Coordinate matrices of IBOUND. dem Matrix of the digital elevation model. demX, demY Coordinate matrices of dem. SRFfile Filename of the MODFLOW SFR2 input file. layer Layer to which the streams are added. cellSize Cell size of IBOUND. nper Number of stress periods. Inflow Inflow/diversion for each stream segment. One column per stream segment, one value per stress period. elevation (optional) Elevation of each stream reach. UZFoutput (optional) Flag whether output should be prepared for the UZF package. If set to true, a runbnd matrix is created. useZones A sting indicating whether we use zones or not (’zones’). zones A matrix of the size of IBOUND with a unique number for each zone.

A.4.7 writeMFsfr2CS.m This function provides exactly the same functionality as writeMFsfr2.m, described above. The only difference is that it also supports the definition of the river cross- sections using an eight point approximation (as described in the documentation of the SFR2 package. Also all the inputs and outputs are introduced in exactly the same manner, except the input parameters described below. The measured cross-sections are introduced in the model at the location where they are measured and left constant following the river downstream, until the next cross-section measurement is available. If no measured cross-section is available at the very beginning of the river segment, the most upstream one is used. The eight point approximation needs to be calculated separately using an appropriate script. The data needs to be saved from MATLAB for each location using a filename of the form fitcs.mat, where is the number assigned to each location in the shapefile providing the locations of the cross-sections.

Usage: success[,runbnd] = writeMFsfr2CS ( riverShape,CSshape,CSpath,IBOUND,X,Y, dem,demX,demY,SFRfile,layer,cellSize,nper, Inflow[,elevation,UZFoutput,useZones, zones] ) CSshape An ArcGIS shapefile containing the locations of measured cross-sections. The shapefile must also contain a unique Appendix A Documentation of the MATLAB MODFLOW tools 147

ID, corresponding to the ID of the ﬁle where the data is stored. CSpath Directory where all the cross-section data are stored.

A.4.8 writeMFuzf.m

This function writes the unsaturated zone ﬂow package (UZF1) input ﬁle for MOD- FLOW2005.

Usage: success = writeMFuzf ( UZFfile,IUZFBND,IRUNBND,nper,VKS,BCEPS, THTS,THTI,FINF,PET,EXTDP,EXTWC[,IUZFCB1] ) success Zero in case of normal termination. UZFfile Filename of the MODFLOW UZF input file. IUZFBND Variable which defines to which layer the UZF modelling is applied. * IRUNBND Variable defining to where the surface runoff is routed. * nper Number of stress periods. VKS Vertical hydraulic conductivity of the layer. * BCEPS Brooks-Corey epsilon of the unsaturated zone. * THTS Saturated volumetric water content of the unsaturated zone. * THTI Initial volumetric water content. * FINF Infiltration rate (L T−1) at the land surface. ** PET Potential evapotranspiration. ** EXTDP Extinction depth of the evpotranspiration. * EXTWC Extinction water content for evapotranspiration. * IUZFCB1 (optional) An integer value used as a flag for writing groundwater recharge, ET, and ground-water discharge to land surface rates to a separate unformatted file. The number corresponds to the unit number specified in the NAME file. * Either the whole array of the variable or the unit number of the external file assigned in the NAME file has to be specified. ** This variable can either be a cell array, containing an infiltration rate for each model cell, or a constant value over the whole model area. If it is not a cell array, the number provided is assumed to be the unit number of an external data file as assigned in the NAME file. 148 A.5 Import MODFLOW output

A.4.9 writeMFwetc.m This function writes the wetland coupling input file for the modified version of MODFLOW 2005. Usage: success = writeMFwetc ( WETCfile,WETCactive,IWETCIT,OUTUNIT,IEXFBND ) success Zero in case of normal termination. WETCfile Filename of MODFLOW input file. WETCactive 1 if WETC should e set to active, 0 if it should be inactive. IWETCIT 1 if coupling should take place in all iterations, 0 if coupling should take place only in the first iteration. OUTUNIT Unit of the output file as indicated in the NAME file. IEXFBND Array of integers indicating for each cell the layer number, to which the exfiltrating water should be added. Set to 0 if water should be routed to nowhere or to a stream or lake (according to the UZF input file).

A.5 Import MODFLOW output

There are two functions which can be used to import the simulation output of MODFLOW into MATLAB. One is designed to import all groundwater-related data (readMFresults.m), and the other one is used to import data related to streamﬂow (readMFstreamflow.m).

A.5.1 readMFresults.m This function extracts the results of a MODFLOW 2005 simulation. Usage: data = readMFresults ( ModelPath[,ModelName][,PARAM,VALUE] ) data Results of the MODFLOW simulation, organised as MATALB data structure. Its contents are dependent on the data, which the user desires to read from the model results. data contains all, or a subset of the following ﬁelds: head Head data for each time step, each cell and layer. ddown Drawdown data. storage Storage data. Appendix A Documentation of the MATLAB MODFLOW tools 149

constH Constant head flow data. flowWE Cell-by-cell flow from West to East. flowNS Cell-by-cell flow from North to South. flowTB Cell-by-cell flow from top to bottom. gwET Evapotranspiration from groundwater. UZFinfilt Infiltration into the unsaturated zone. UZFrech Recharge from the unsaturated zone to the groundwater. UZFleak Surface leakage from the unsaturated zone. ModelPath Directory where the model files are located. ModelName (optional) Name of the model; the name of the output file is read from the .nam file. This parameter only needs to be specified if there are more than one *.nam file. PARAM,VALUE (optional) The only parameter this function accepts at the moment is ’Data’ (not case-sensitive). This parameter is used to specify what data is read from the MODFLOW output files. All values other than ’Data’ are ignored. The content of VALUE is a character or an array of characters (string) which specifies the kind of data to be read. ’B’ for reading all data from the budget file (constH, flowWE, flowNS and flowTB), ’D’ for reading drawdown data, ’H’ for reading heads and ’E’ for reading the exfiltration and evapotranspiration from groundwater, if the UZF module is active (gwET, UZFinfilt, UZFrech and UZFleak). These characters can be combined (e.g. ’HB’, ’BE’ or ’BDH’). The default is to read all of them.

A.5.2 readMFstreamflow.m

This function reads the output of the MODFLOW SFR2 package.

Usage: rchdata[,geom] = readMFstreamflow ( ModelPath[,ModelName] ) rchdata MATLAB structure of reach data containing the time series of inflow, infiltration, discharge and overland flow for each stream reach of the model. 150 A.5 Import MODFLOW output geom (optional) n by 6 array with the geometry data of all the reaches. The columns are [segment reach length elevation slope width]. ModelPath Directory where the model files are stored. ModelName (optional) Name of the model; the name of the output file is read from the .nam file. This parameter only needs to be specified if there are more than one *.nam file. Appendix B

Using Parallel-PEST

B.1 About Parallel-PEST

During the parameter optimisation process of PEST the model has to be run many times. Especially during the step where the Jacobian matrix is calculated the model has to be run at least once for each parameter optimised. Usually the run time of PEST is almost solely determined by the run time of the model. Therefore, running the models in parallel with different parameters will usually result in a much higher performance. PEST implements this parallel model execution in a relatively simple way. The only prerequisites are (1) that each model run uses and produces unique input and output files and (2) that the PEST software and the model have read and write access to the models working directory. Parallel PEST is organised using a master/slave concept. The master controls the whole calibration process (i.e. distributing the necessary input files to the slaves and collecting and processing the model results) and the slave takes care to run the model as requested by the master. The master and the slave usually communicate through signal files.. The most efficient way of running the model on as many processors as possible is to use different machines. Therefore the best way of implementing a parallel model calibration is to distribute the necessary model files in different directories on the different machines so that the model runs locally on each computer. The communication between the models is achieved by making the local model directories accessible to the computer the PEST master program is running on using a network file system (i.e. shared folders, NFS or SMB). For the calibration of the floodplain model described in Chapter4 a PEST version for GNU/Linux was used. It provides the exactly same features as the Microsoft Windows version available for download at www.pesthomepage.org.

151 152 B.2 Implementation on the Amazon Elastic Compute Cloud (EC2)

B.2 Implementation on the Amazon Elastic Compute Cloud (EC2)

B.2.1 About EC2

The Amazon Elastic Compute Cloud (EC2) is a web service that oﬀers computing capacity in the “cloud”. Cloud computing refers to the provision of computing capacity over a network, usually the Internet. The user can submit a computing task to a service provider. Therefore computing tasks do not have to be carried out locally on the computer. The EC2 provides not single application (such as word processing) but it provides a whole operating system (OS) based on a virtual machine. Therefore the user can choose to obtain computing capacity for any OS in any number (for private users the number of machines is limited to 20). The user is able to connect to single virtual machines over the network. The virtual machines are able to communicate with each other over the TCP/IP protocol (using a local IP-address). EC2 provides a web interface to manage and conﬁgure the computing capacity (e.g. start and terminate instances).

B.2.2 Implementation

The preparation of a virtual computer cluster on EC2 is quite straight forward. Since the floodplain model itself and the PEST software suite are available for GNU/Linux, the virtual machines on the EC2 are also using the Linux operating system. To provide an environment where the software necessary for the calibration is running, an image of the OS has to be created based on a minimal Linux installation. There is a need for two types of images one for the master machine which is run only once, and one for the slave machines which is run many times in parallel. The master has to manage the whole calibration process and take care of the communication between the slaves and between the user and the master machine. The slave therefore only needs a very basic configuration, whereas the master has to offer more functionality. The detailed specification of the master and the slave operating system are described below. Since the Parallel PEST master communicates with its slaves through the file system it is sufficient to mount all the working directories of the slaves to the master machine using a network file system protocol. To control the slaves interactively they are also connected to the slave through a secure shell connection. This communication only takes place inside the EC2 computing cloud and usually does not need any user interaction. The user however, has to interact with the master computer. It is therefore convenient to install a graphical user interface and a remote desktop server. This allows the user to keep track of the calibration process and to interfere if necessary. Appendix B Using Parallel-PEST 153

Local user

Remote desktop

Amazon EC2 Master

running ppest

SSH NFS NFS SSH SSH NFS

Slave 1 Slave 2 ... Slave n running pslave running pslave running pslave

Figure B.1: Schematic of the virtual computer cluster on Amazon EC2 used for model calibration. From the master machine the slave processes are invoked on the slaves interactively via secure shell (SSH). The Paralell PEST program (ppest) and the PEST slave program (pslave) communicate through a network ﬁle system (NFS).

The number of slaves used should be dependent on the number of parameters which are to be calibrated. If for example 22 parameters are calibrated PEST runs the model at the most 44 times to determine the Jacobian matrix. It is therefore appropriate to use 44 slaves. If this is not possible one optimally uses a fraction of the maximum number such as 22 or 11. With 44 slaves the calculation of Jacobian matrix takes as much time as one model run, with 22 slaves twice as long. Since in the Amazon EC2 the maximum number of virtual machines is 20 only 11 slaves are used. A schematic of the setup is shown in Fig. B.1.

Speciﬁcation of the slave machine

• Basic Linux operating system

• Secure shell server (OpenSSH)

• Network File System server (NFS) To simplify the firewall configuration (which is mandatory when using EC2) the NFS server has to re-configured in order to use static TCP port numbers. 154 B.3 Running PEST on a computer cluster

• The binary executables of the model and the PEST software suite

• The data used to run the model

Speciﬁcation of the master machine • Basic Linux operating system

• Secure shell server and client (OpenSSH)

• Network ﬁle system client (NFS)

• The binary executables of the PEST software suite

• A graphical user interface (X Window System and GNOME)

• A remote desktop server (NoMachine NX)

B.3 Running PEST on a computer cluster

The implementation of a parallel PEST run on a computer cluster is very similar to the approach described in the previous section. A computer cluster designed for high performance computing is usually composed of inexpensive hardware (such as personal computers) tied together with a high bandwidth network. The cluster interacts with its users as if it was only one computer. Therefore the communication between the different processes is much simpler, since all the processes have access to exactly the same file system. Thus, the network component of the process management is not necessary anymore. The calibration process is easily scalable and the setup can be done using a relatively simple shell script (Listing B.1). For each node a directory with all the necessary input files is created. The user has the full flexibility of choosing the number of nodes, as long as the input files for the model and the necessary files to control the calibration are prepared correctly. Also the monitoring of the calibration process becomes easy since information on the each node resides in a separate directory and can be collected in a standardised way.

Listing B.1: Shell script to set up the calibration process on a computer cluster automatically.

1 #!/bin/bash

2 # Run the model calibration using ParallelPEST on the ETH

3 # Beowulf cluster BRUTUS

4 #

5 # This script is written by Philipp Meier in May 2011

7 echo "Bash␣version␣${BASH_VERSION}..." Appendix B Using Parallel-PEST 155

9 # g e n e r a l v a r i a b l e s NUMNODES=20 DIRPREFIX="/home/phm"

10 TPLDIR="$DIRPREFIX/calib0"

11 CALIBCASE="modflow"

12 NODEWD="$DIRPREFIX/calib"

13 WDIR=$ (pwd)

15 BINDIR=/home/phm/ bin

17 RUNTIME=25000

19 # Create the run management file

20 rm $TPLDIR/$CALIBCASE . rmf

21 touch $TPLDIR/$CALIBCASE . rmf

23 echo "prf" >> $TPLDIR/$CALIBCASE . rmf

24 echo "$NUMNODES␣0␣1.0␣1" >> $TPLDIR/$CALIBCASE . rmf

26 # Create node directories

27 for ( ( i = 1 ; i <= $NUMNODES ; i++ ) )

28 do

29 echo "Copy␣files␣for␣node␣$i␣..."

30 eval "rsync␣-a␣$TPLDIR/␣$NODEWD$i"

31 cd $NODEWD$i

32 # start the slaves

33 p s l a v e < command. txt > "$NODEWD$i/pslave.log" &

34 # update run management file

35 echo "node$i␣␣$NODEWD$i" >> $TPLDIR/$CALIBCASE . rmf

36 done

38 RUNSTR=""

39 # add the runtimes to the run management file

40 for ( ( i = 1 ; i <= $NUMNODES ; i++ ) )

41 do

42 RUNSTR="$RUNSTR␣$RUNTIME"

43 done

45 echo "$RUNSTR" >> $TPLDIR/$CALIBCASE . rmf

47 # change to the master directory

48 cd $TPLDIR

50 # run the model

51 ppest $CALIBCASE