MODELLING RIVERFLOW IN THE VOLTA BASIN OF WEST AFRICA: A DATA-DRIVEN FRAMEWORK Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus, prof. dr. ir. J.T. Fokkema, voorzitter van het College voor Promoties in het openbaar te verdedigen op woensdag 18 januari 2006 om 10.30 uur door Barnabas Akurigo AMISIGO Master of Science, University of Guelph geboren te Bolgatanga, Ghana Dit proefschrift is goedgekeurd door de promotor: Prof.dr.ir. N.C. van de Giesen Technische Universiteit Delft, The Netherlands Samenstelling promotiecommissie: Rector Magnificus Technische Universiteit Delft, voorzitter Prof. dr. ir. N.C. van de Giesen Technische Universiteit Delft, promotor Prof. dr. J.J. Bogardi United Nations University Prof. dr. ir. A.W. Heemink Technische Universiteit Delft Prof. dr. A.E. Mynett Technische Universiteit Delft / UNESCO IHE Prof. dr. ir. H.H.G. Savenije Technische Universiteit Delft / UNESCO IHE Prof. dr. ir. G.S. Stelling Technische Universiteit Delft Dissertation prepared at the Center for Development Research, University of Bonn, in the context of the GLOWA Volta Project "Sustainable water use under changing land use, rainfall reliability and water demands in the Volta Basin" financed by the Ministry of Science and Education (BMBF) of the Federal Republic of Germany. To my parents for their foresight, and to my wife Hawa and daughter Mmalebna ABSTRACT The 400,000 km2 Volta Basin is an international basin covering almost 28% of the West Coast. Basin of Africa. It extends from longitude 5o 30 W to 2o 00E and from latitude 5 30o N to 14o 30 N and is shared by the six West African countries Benin, Togo, Ghana, La Cote d’Ivoire, Burkina Faso and Mali. The water resources of this basin are under severe stress due to both human and natural causes. High population growth rate coupled with widespread and indiscriminate water mobilisation and use in the basin on the one hand, and high spatial and temporal variability of rainfall and high potential evapotranspiration on the other, are putting enormous pressure on the basin’s water resources. As a result, there are serious water resources management problems such as flooding, water shortage, water pollution and loss of aquatic biodiversity. It is, therefore, recognised that integrated transboundary water resources management is necessary and urgent to ensure environmental integrity and sustainable water use in the basin. Streamflow modelling and prediction are essential components of any water resources management framework developed for the water-allocation and -use managers in the basin. In this thesis, a riverflow modelling framework developed for monthly riverflow prediction in the Volta Basin is presented. By analysing available catchment rainfall, runoff and potential evapotranspiration series in the basin using methods such as correlation plots, autoregressive (AR) and autoregressive with exogenous input (ARX) modelling, it is shown that the monthly catchment rainfall-runoff process is better characterised by non-linear models. First, a spatio-temporal linear dynamic model employing the Kalman smoother and the Expectation-Maximisation (EM) algorithm was developed and applied to filling in short gaps in daily riverflow series in the basin. This model was found to be a very good and powerful tool for filling in such data gaps. Then, two non-linear modelling frameworks - a non-linear autoregressive and moving average with exogenous input (NARMAX) polynomial and a data-based mechanistic (DBM) modelling framework - were developed and applied to the monthly rainfall-runoff series in the basin for river catchment runoff prediction. The NARMAX model was able to capture much of the nonlinearity in the runoff generation process and provided good predictions of riverflow. However, it is a purely black-box formulation providing no physical interpretation of the runoff process in the basin. The DBM framework was very successful in representing the runoff mechanism in the basin, adequately predicting monthly river runoffs. Unlike the NARMAX models, the DBM framework is a grey-box that provided physically interpretable results at the catchment scale. Results from this modelling framework show that monthly runoff in the basin can be interpreted to occur in two pathways: a fast flow pathway and a slow, mainly delayed flow, pathway. Catchment effective rainfall in the basin was found to have a power law relationship with catchment runoff. In addition, the Identification of unit Hydrographs And Component flows from Rainfall, Evaporation and Streamflow (IHACRES) type effective rainfall-catchment wetness non-linear relationship in which the basin drying time constant is exponentially related to basin potential evapotranspiration, was found to be suitable for characterising the runoff processes in the basin. Therefore, it is recommended that data-driven approaches be considered as the most appropriate for riverflow modelling in the Volta Basin. This is due, in part, to the fact that the approaches provide very good results that are, to some extent, physically interpretable and also because the quality, quantity and diversity of hydrological data used for riverflow modelling in the basin are too poor to enable effective use of the more elaborate distributed hydrological models. TABLE OF CONTENTS 1 INTRODUCTION .................................................................................................. 1 1.1 Structure of the thesis .................................................................................. 3 1.2 Systems approach in hydrology and the river catchment as a system......... 5 1.2.1 System identification................................................................................ 7 1.2.2 Digital filters and the differential and difference equations description of dynamic systems................................................................................. 11 1.2.3 External model description ..................................................................... 12 1.2.4 State- space representation of the general models of dynamic systems . 13 1.2.5 Transfer function (TF) models of dynamic stochastic systems .............. 16 1.3 Background to the study............................................................................ 17 1.4 Research question and objectives.............................................................. 21 2 THE STUDY AREA............................................................................................. 22 2.1 Introduction ............................................................................................... 22 2.2 Climate....................................................................................................... 24 2.2.1 Rainfall ..................................................................................................24 2.2.2 Potential evapotranspiration....................................................................24 2.3 Land cover and use.................................................................................... 26 2.4 Hydrology.................................................................................................. 27 2.4.1 Drainage.................................................................................................. 27 2.4.2 Stream flow distribution ......................................................................... 29 2.5 Hydrogeology ............................................................................................ 29 2.5.1 Geology ..................................................................................................29 2.5.2 Groundwater occurrence and flow.......................................................... 30 2.5.3 Borehole yields....................................................................................... 31 2.6 Water use in the basin................................................................................ 32 2.7 Water resources management problems in the basin................................. 33 3 EXPLORATORY DATA ANALYSIS................................................................ 36 3.1 Introduction ............................................................................................... 36 3.2 Rainfall-runoff characteristics of the monthly riverflow data................... 43 3.2.1 Persistence in river runoff....................................................................... 55 3.2.2 Autoregressive and moving average modelling of monthly runoff........ 58 3.2.3 Non-linearity in monthly rainfall-runoff relationship............................. 69 3.3 Conclusions ............................................................................................... 73 4 SPATIO-TEMPORAL MODEL FOR FILLING GAPS IN DAILY STREAM FLOW SERIES.................................................................................... 74 4.1 Introduction ............................................................................................... 74 4.2 The discrete spatio-temporal dynamic modelling framework................... 76 4.3 Missing observations................................................................................. 84 4.4 System matrices parameterisation ............................................................. 84 4.5 Application of the modelling framework .................................................. 85 4.6 Results and discussion............................................................................... 87 4.7