Rainfall-runoff modelling of a humid tropical catchment: the TOPMODEL approach

HYDROLOGICAL PROCESSESHydrol. Process. 16, 231–253 (2002)DOI: 10.1002/hyp.341

Rainfall-runoff modelling of a humid tropical catchment:the TOPMODEL approach

Paul Campling,1* Anne Gobin,1 Keith Beven2 and Jan Feyen1

1 Laboratory for Soil and Water, Faculty of Applied Biological Sciences, Katholieke Universiteit Leuven, Leuven, Belgium B30002 Centre for Research on Environmental Systems and Statistics, Institute for Environmental and Biological Sciences, Lancaster University,

Lancaster, UK

Abstract:

TOPMODEL, a semi-distributed, topographically based hydrological model, was applied to simulate continuously therunoff hydrograph of a medium-sized (379 km2), humid tropical catchment. The objectives were to relate hydrologicalresponses to runoff generation mechanisms operating in the catchment and to estimate the uncertainty associated withrunoff prediction. Field observations indicated that water tables were not parallel to the surface topography, particularlyat the start of the wet season. A reference topographic index �REF was therefore introduced into the TOPMODELstructure to increase the weighting of local storage deficits in upland areas. The model adaptation had the effectof deepening water tables with distance from the river channel. The generalized likelihood uncertainty estimation(GLUE) framework was used to assess the performance of the model with randomly selected parameter sets, and toset simulation confidence limits. The model simulated well the fast subsurface and overland flow events superimposedon the seasonal rise and fall of the baseflow. The top ranked parameter sets achieved modelling efficiencies of 0Ð943 and0Ð849 in 1994 and 1995 respectively. The GLUE analysis showed that the exponential decay parameter m, controllingthe baseflow and the local storage deficit, was the most sensitive parameter. There was increased uncertainty in thesimulations of storm events during the early and late phases of the season, which was due to a combination of: errorsin detecting the rainfall depths for convectional rainfall events; the treatment of rainfall as a catchment areal value;and, the strong seasonality in runoff response in the humid tropics. Copyright 2002 John Wiley & Sons, Ltd.

KEY WORDS rainfall-runoff modelling; TOPMODEL; humid tropical catchment; hydrological response; uncertaintyanalysis

INTRODUCTION

Although there is currently a plethora of rainfall-runoff models developed to predict runoff hydrographs (Singh,1995), there are few published results of model applications in the humid tropics. Most routine measurementsin developing countries are carried out by river basin authorities at a daily or weekly time step in orderto monitor the rainfall-runoff volumes of large regional catchments (>1000 km2). However, daily rainfall-runoff measurements are not sufficiently detailed to capture storm events, during a period of hours. In WestAfrica only a few examples exist of detailed hydrological studies that use sub-daily information on small,experimental catchments (<10 km2) (Dubreuil, 1985, 1986; Chevallier and Planchon, 1993), but there remainsa dearth of detailed rainfall-runoff modelling investigations on medium-sized catchments (10–1000 km2).We endeavoured to redress this shortfall by establishing a hydrological monitoring scheme to understand theprocesses governing runoff generation and to develop a hydrological modelling framework for a medium-sizedcatchment located in a humid tropical environment.

Partial area theory (Betson, 1964) is based upon the division of a catchment into source areas that contributeto runoff production during storm events. Runoff-generating processes in humid tropical regions include

* Correspondence to: P. Campling, Vital Decosterstraat 102, Katholieke Universiteit Leuven, Leuven, Belgium B3000.E-mail: [email protected]

Received 5 June 2000Copyright 2002 John Wiley & Sons, Ltd. Accepted 25 March 2001

232 P. CAMPLING ET AL.

excess infiltration overland flow, excess saturation overland flow, unsaturated subsurface flow and saturatedsubsurface flow (Thomas, 1994). Excess infiltration flow (Horton, 1933) happens when the infiltration capacityof the soil surface is exceeded. ‘Hortonian’ overland flow in the humid tropics is generally associated withsteep slopes, where the natural vegetation has been cut and the shallow soil is exposed. Natural surfaces thathave been compacted, such as along paths and tracks, are also source areas of rapid overland flow (Zieglerand Giamelluca, 1994). Excess saturation overland flow occurs when rainfall or run-on is unable to infiltratedue to near-surface saturation conditions. Near-surface saturation conditions result from high groundwaterlevels (Dunne and Black, 1970) or perched water tables (Bonell et al., 1983). High groundwater levels inlowland areas can be due to hillslope- (Anderson, 1982) or bedrock- (Freer et al., 1997) induced convergenceof subsurface flow, return flow (Hewlett and Hibbert, 1967) or exfiltrating subsurface flow (Hewlett, 1974).Perched water tables in upland areas occur in soil profiles with a relatively impermeable subsoil. The criticaldecline of permeability with soil depth causes a filling up of pore space and saturation near the surface.The general migration of unsaturated water downslope, first recognized by Hewlett (1961), contributes tomaintaining relatively high moisture levels at valley bottoms. The process is often independent of the soilmatrix, and follows preferential flow lines, on account of soil cracks and macropores. Saturated subsurfaceflow (Hursch, 1936) that contributes to storm runoff is generally a result of lateral soilwater flow (Weyman,1973), but could also be due to the displacement of ‘old water’ (Sklash and Farvolden, 1979).

Runoff source areas are known to expand and contract during and between storm events, hence the termvariable source areas (Hewlett and Hibbert, 1967). In West Africa the expansion and contraction of source areashas a marked seasonal dimension on account of the extended dry season, characterized by high temperaturesand Sahara Desert winds. Runoff source areas vary throughout the rainy season as the catchment wets up andgroundwaters rise to the surface. Runoff is not generated until a threshold value of antecedent soil moisturehas been exceeded (Thomas, 1994). Dubreuil (1985, 1986), concludes from observations taken at nearly300 small catchments in West Africa that surface and subsurface runoff generation depends on soil surfaceformations (texture, structure and land cover), geological substrata, weathered material and climate. Severaltypes of runoff-generating process are therefore present in a medium-sized catchment, and the source areasof each type may amount to only a small fraction of the catchment (Dunne, 1983).

TOPMODEL (Beven and Kirkby, 1979) is a topographically based hydrological model that aims toreproduce the hydrological behaviour of catchments in a semi-distributed way, in particular the dynamics ofsurface and subsurface contributing areas. It provides a compromise between the complexity of fully distributedprocess models and the relative simplicity of lumped empirical models (Robson et al., 1993). The functionalrepresentation of the internal catchment hydrological responses ensures that the model is parsimonious, witha limited number of physically interpretable parameters. In addition, the modelling framework also allows thestructure to be modified to meet the hydrologist’s perceptions and field observations. In short, TOPMODELrepresents a set of modelling tools that combines the computational and parameteric efficiency of a lumpedmodelling approach with the link to physical theory (Beven et al., 1995). TOPMODEL has been successfullyused in humid temperate (Beven and Wood, 1983; Hornberger et al., 1985; Beven, 1993; Robson et al.,1993; Lamb et al., 1998; Guntner et al., 1999) and drier Mediterranean regimes (Durand et al., 1992; Pinolet al., 1997). TOPMODEL has only been applied in two small humid tropical catchments: the Booro-Borotoucatchment (1Ð36 km2) in Ivory Coast (Quinn et al., 1991) and a forested headwater catchment (1Ð5 ha) of theRiver Sinnamary in French Guiana (Molicova et al., 1997). In both cases TOPMODEL performed well whenthe catchments were fully wetted up.

Model calibration and the estimation of predictive uncertainty in hydrological modelling have becomeimportant issues in the last decade. Over-parameterization is a serious problem for distributed models, asestimated parameters tend to have large uncertainties associated with them (Jakeman and Hornberger, 1993).The goal of attaining optimum parameter sets, given the recognized nonlinearities and parameter interactionsin many hydrological models, has come into question (Beven, 1993). The generalized likelihood uncertaintyestimation (GLUE) (Beven and Binley, 1992) starts from a premise of equifinality in hydrological modelstructures and parameter sets. Monte Carlo simulation (MCS) is used to make a large number of runs of

Copyright 2002 John Wiley & Sons, Ltd. Hydrol. Process. 16, 231–253 (2002)

RAINFALL-RUNOFF MODELLING 233

a given model, with different sets of parameter values. Likelihood weights are assigned to the parametersets and prediction confidence limits can be set. GLUE allows for the use of additional time series data(Romanowicz et al., 1994) and other sources of data (Lamb et al., 1998) to update or condition the model.GLUE has been used in a number of environmental applications: soil–vegetation–atmosphere transfer (SVAT)modelling (Franks et al., 1999); biogeochemical modelling (Zak et al., 1997; Zak and Beven, 1999); floodfrequency modelling (Cameron et al., 1999); water balance and catchment modelling (Kuczera and Parent,1998); real-time flood prediction (Romanowicz and Beven, 1998); recharge to coastal aquifers (Binley et al.,1997); and, runoff prediction (Ambroise et al., 1996; Freer et al., 1996).

The prospect of adopting a full MCS procedure for fully distributed modelling is still daunting, evenwith increased computing power. O’Connell and Todini (1996) propose a more pragmatic approach to modelcalibration, using prior knowledge and experience of model parameterization to formulate a model validationframework (Ewen and Parkin, 1996; Parkin et al., 1996).

In this paper the semi-distributed and physical aspects, as well as the computational efficacy, of TOPMODELare exploited. The objectives are (1) to relate hydrological responses to runoff generation mechanismsoperating in the catchment; and (2) to estimate the uncertainty associated with runoff hydrograph prediction.TOPMODEL is applied, using multiple parameter sets, to the River Ebonyi headwater catchment (379 km2)in south-eastern Nigeria.

MATERIALS AND METHODS

Study area

The River Ebonyi headwater catchment (379 km2) is located on the western border of the Cross RiverPlains, headed by the Udi-Nsukka Escarpment (Figure 1). It is situated in the transition zone between theGuinea–Congolian wetter-type forest and Guinea savannah eco-climatological zones. The elevation rangesbetween 105 and 565 m above sea level. The mean annual temperature is 23 °C and the mean annualrainfall is 1577 mm. The progress of the rainfall season relates to the advance and retreat of the inter-tropical discontinuity (ITD) (Olaniran, 1988; Adelekan, 1998). Temporal rainfall analysis of historical dailyrainfall from the University of Nigeria Nsukka (UNN) meteorological station (6Ð87 °N, 7Ð43 °E, 442 m) showsthat the peak rainfall period is between mid-August and mid-September (Campling et al., 2000). Full-scalehydrological monitoring of the catchment was operational during 1994 and 1995. Frequency analysis of annualrainfall at Nsukka, between 1949 and 1995 (excluding 1967 to 1970—during the Biafran War), indicates that1995 (1951 mm) was wetter than 1994 (1920 mm), and that both years were relatively wet, having returnperiods of 1 in 15 years (1995) and 1 in 7 years (1994).

Two major landforms are found within the catchment: the sandstone escarpment of the Udi-Nsukka Cuesta;and the shale peneplains of the Cross River Plains. The sandstone escarpment has deeply weathered arenosolswith low water-holding capacity and high hydraulic conductivity. Major ravines are found in association withspring lines and excessive surface runoff caused from tarmac roads (Gobin et al., 1999). The upper interfluveof the shale peneplain, upstream of the River Ebonyi and River Amanyi confluence (Figure 1), has a rolling toundulating topography, intersected by incised streams that flow to narrow valley bottoms. Acrisols at differentstages of denudation are present in the area (Gobin et al., 1998). The presence of ferric properties in the clayhorizon of the lower-lying Ferric Acrisols is pedological evidence of the lateral movement of iron-rich waternear to the surface (Thomas, 1994). The lower interfluve of the shale peneplain, downstream of the RiverEbonyi and River Amanyi confluence, has a flatter topography, with extensive areas of waterlogging in thewet season and a wide valley bottom. The very poorly drained soils in the valley bottoms, are identified asbeing amphi-gleyic (Campling et al., submitted), which is a combination of groundwater (gley) and run-on(pseudo-gley) processes (Brinkman and Blokhuis, 1986).

A continuous river level recorder (hourly river depth) was installed at the catchment outlet (Eha Amufu).A rating curve was established on the basis of successive measurements of discharge and gauge height taken



Figure 1. Location of the River Ebonyi headwater catchment and hydrological monitoring instrumentation

at different stages during the monitoring period (Herschy, 1985). A tipping-bucket rainfall recorder (hourlyrainfall) at the centre of the catchment (Ogbodu Aba) was supported by 36 rain gauges (daily rainfall)across the catchment (Figure 1). Catchment areal rainfall was interpolated between the rain gauges usingthin plate splining (Hutchinson, 1993). Daily evapotranspiration rates were determined from pan evaporationmeasurements located at the UNN meteorological station.

The total rainfall and runoff from the beginning to the end of the wet season were respectively 1Ð657 mand 0Ð922 m during 1994, and 1Ð785 m and 1Ð005 m during 1995 (Table I). Rainfall-runoff coefficients for



Table I. Wet season (1 March to 31 October) water balance components and runoff coefficients for 1994 and 1995

Year RainfallR (m)

Evapotranspiration,Eto (m)

Discharge Q(m)

Change in storageS

(S D R–Eto–Q)

Runoffcoefficient C(C D Q/R)

1994 1Ð657 0Ð878 0Ð992 �0Ð133 0Ð561995 1Ð785 1Ð004 1Ð005 �0Ð224 0Ð56

Table II. Rainfall-runoff coefficients for peak rainfall events from the four phases of the wet season during 1994and 1995

Date Season phase Phase period Rainfall (m) Discharge (m) Runoffcoefficient

23 April 1995 Early season March to May 0Ð046 0Ð0036 0Ð0830 June 1994 Mid season June to mid-August 0Ð067 0Ð0032 0Ð0431 August 1994 Peak season mid-August to

mid-September0Ð054 0Ð014 0Ð25

28 October 1994 End season mid-September tomid-November

0Ð038 0Ð005 0Ð13

the duration of the wet season were 0Ð56 in both years. The catchment storage deficits of 0Ð133 m (1994) and0Ð224 m (1995) at end of the season indicate that, during the early and late periods of the wet season, as wellas during the dry season, the rate of evapotransiration is not at full potential. The extreme seasonality of thehydrological regime of the catchment is further demonstrated by the contrasting 24 h rainfall-runoff coefficientsof peak rainfall events occurring in the start (0Ð08), middle (0Ð04), peak (0Ð25) and end phases (0Ð13) of thewet season (Table II).

Digital terrain analysis

The ANUDEM program (Hutchinson, 1989), was used to create a 50 m resolution digital elevation model(DEM) of the catchment, from digitized contour lines, spot heights, stream lines, and lake polygon coverages.ANUDEM performs an iterative finite difference interpolation technique, based on thin plate splining (Wahba,1990), which uses the shape and spacing of digitized topographic features to produce a hydrologicallycorrect DEM. The single flow direction algorithm for flow accumulation and flow direction grids (Jensonand Domingue, 1988) was used to derive the contributing area and the surface topographic slope gridsrequired to determine the topographic index distribution � [Equation (1)] (Wolock and McCabe, 1995).

TOPMODEL theory

TOPMODEL, fully described by Beven et al. (1995), uses the distribution of the topographic index � asan index of hydrological similarity:

�i D ln(

aitan ˇi

)�1�

where ai (m) is the area draining through a grid square per unit length of contour and tan ˇi is the localsurface slope. Flow is separated into surface runoff generated by rainfall on saturated contributing areas andsubsurface downhill flow. TOPMODEL uses four basic assumptions to relate local downslope flow from apoint to discharge at the catchment outlet:

A1. The dynamics of the saturated zone are approximated by successive steady state representations.A2. The recharge rate r (m h�1) entering the water table is spatially homogeneous.



A3. The effective hydraulic gradient of the saturated zone is approximated by the local surface topographicgradient tan ˇ.A4. The distribution of downslope transmissivity To (m2 h�1) with depth is a function of storage deficit[normally considered exponential, but Ambroise et al. (1996) established linear and parabolic relationships].

Assuming that the recharge rate to the water table is uniform and spatially homogeneous (A1 and A2), thedownslope subsurface flow rate per unit contour length qi (m2 h�1� is:

qi D rai �2�

Assuming that the hydraulic gradient of the saturated zone is equal to the local surface slope and the soiltransmissivity is an exponential function of storage deficit (A3 and A4), then qi is also:

qi D To e�Si/m tan ˇi �3�

where To (m2 h�1� is the lateral downslope transmissivity when the soil is just saturated, Si (m) is a localstorage deficit, and m (m) is a model parameter controlling the rate of decline of transmissivity with increasingstorage deficit.

By combining Equations (2) and (3) it is possible to calculate the local soil moisture deficit Si:

Si D �m ln(

raiTo tanˇi

)�4�

The mean catchment storage deficit S(m) is obtained by integrating Equation (4) over the entire area A (m2)of the catchment:

S D 1

A

∑i

Ai

(�m ln

raiTo tanˇi

)�5�

where Ai is the fractional area of the topographic index class i. Assuming that the water table recharge andthe soil transmissivity are spatially constant then ln r and lnTo are eliminated from Equation (5) and Si isexpressed as:

Si D SC m(�� ln

aitan ˇi

)�6�

where � is the areal average of the topographic index ln�a/ tanˇ�:

� D 1

A

∫ A

0ln(

aitanˇi

)Ai dA �7�

At each topographic index class �i, unsaturated and saturated zone fluxes are simulated. The vertical drainageqv (m h�1� from the unsaturated store at any point i is controlled by the local saturated zone deficit Di (m),which depends on the depth (in metres) of the local water table (Beven and Wood, 1983):

qv D Suz

Ditd�8�

where Suz (m) is the storage in the unsaturated zone, and td (h m�1� is a time delay constant that introduceslonger residence times to cater for deep water table levels. Actual evapotranspiration Ea (m h�1) losses, afterthe gravity drainage zone is exhausted, are controlled by potential evapotranspiration Ep (m h�1� and themaximum root zone storage (or soil water-holding capactiy) Srmax (m):

Ea D Ep

(1 � Srz

Sr max

)�9�

where Srz (m) is the root zone storage.



The catchment flux of water entering the water table, Qv (m h�1� is calculated by summing the qv of eachtopographic index class:

Qv D∑i

qvAi �10�

Output from the saturated store is represented by the baseflow term, Qb (m h�1�, which can be calculatedusing a subsurface storage deficit–discharge function of the form:

Qb D Q0 e�S/m �11�

where Q0 D Ae�� is the discharge when S is zero.The catchment average storage deficit S is updated by subtracting the unsaturated zone recharge and adding

the baseflow from the previous time step:

St D St�1 C [Qbt�1 � Qvt�1] �12�

The initial baseflow Q0 (m h�1) and the initial root zone storage deficit Sr0 (m) are input at the start of thesimulation. Channel routing is based on a network width function and a velocity–discharge relationship thatyields a constant wave velocity parameter for internal catchment routing, RV (m h�1�, and channel routing,CHV (m h�1� (Beven, 1979).

Recession curve analysis

Recession curve analysis of outlet discharge rates shows lumped information on the nature of the catchmentresponse to rainfall. Tallaksen (1995) reviews different procedures characterizing baseflow recession curves.If the effects of evaporation and rainfall are small and there are no significant losses to groundwater orabstractions, it can be assumed that the recession curve represents the drainage of a catchment-wide store(Lamb et al., 1997).

The exponential baseflow store function, Equation (11), was derived by plotting catchment discharge depthQobs (m) against the change in catchment storage deficit S (m). The change in catchment storage deficit wascalculated by summing the instantaneous flow cumulatively with time during the recession period. To obtaina recession curve that represented the whole range of Qobs �S, a master recession curve (MRC) (Nathanand McMahon, 1990) was constructed on the basis of concatenating Qobs values after rainfall events. Therecession function was subsequently determined by curve fitting.

TOPMODEL modification and parameterization

Field surveys of hand-dug, household wells in the study area provided information concerning the depthto the impermeable shale bedrock in relation to position in the landscape. The majority of wells occurredin villages of the upper interfluve areas and were located upstream of the spring sources of incised streams.Transects of well depths in different villages indicated that the impermeable layer increased with distancefrom the valley bottoms. The structure of TOPMODEL was therefore modified to allow for the fact that in theupland sections of the hillslope the water table is not parallel to the surface topography. In the upper sectionsof the Booro-Borotou catchment, where similar conditions were observed, Quinn et al. (1991) assigned areference water table on the basis of hydrological judgement to provide an effective water table gradient forwet conditions. The flow directions and ln�a/tanˇ� distribution were then derived with the reference levelincluded.

We approached this problem differently by identifying a topographic index reference value �REF to increasethe effective depth to the water table in upland areas. The topographic index reference is included into thelocal storage deficit calculation as follows:

Si D SC m(�� ln

aitan ˇi

)C m

(�REF � ln

aitan ˇi

)�13�



Figure 2. A schematic diagram of the representation of the local storage deficit, Si, for increments of the topographic index distribution inthe original TOPMODEL and the modified TOPMODEL

The effect of having the additional term in the local storage deficit function is to increase the weightingof local storage deficits in upland areas, which lowers the effective water table away from valley bottoms.Equation (13) was applied to all � units in the catchment, as all units undergo a degree of wetting up anddrying out cycle in the year and there was no justification for restricting the model to only the sections of thelandscape above �REF. The weighting of increased local storage deficits to upland sections of the landscape,where � values are less than �, means that upland areas have to overcome a relatively greater local storagedeficit Sl than in the original TOPMODEL model structure (Figure 2). Field observations strongly indicateda substantial contribution of spring discharges to runoff towards the peak of the season. Spring position inthe landscape, expressed by �, provided a geomorphologically based procedure for introducing an additionalreference level to �, in order to control the propensity of landscape units to develop saturated conditions.The location of perennial and seasonal springs was derived by means of aerial photograph interpretation andoverlay analysis in a geographical information system (GIS). A representative value of �REF was determined



by taking the mean value of � at: perennial spring points; the lowest grid of first-order streams flowing directlyinto the main channel; and first-order stream stream junctions (Figure 3).

The modified TOPMODEL was parameterized by two physical parameters (� and �REF) and eight processparameters (m, To, td, CHV, RV, Q0, Srmax and Sr0). Both � and �REF were related to the topographic index

Figure 3. Overlay analysis of topographic information and the � grid to select � values to determine �REF



distribution. Recession analysis of discharge depths was used to estimate the decay parameter m. The productof the available water capacity (AWC) and the rooting depth of the soil was used to estimate the effectivemaximum root zone storage Srmax. Field capacity �pF 2 and permanent wilting point �pF 4Ð2 were determinedusing pressure cell desorption techniques on Kopecky ring soil samples, taken from the top three diagnostichorizons of 27 reference profile pits located along toposequences within the catchment. Kopecky ring sampleswere also taken for constant head permeameter tests (Klute and Dirksen, 1986) to derive saturated hydraulicconductivity. Double ring infiltrometer tests (ILRI, 1980) were carried out at selected profile pits to measurethe basic infiltration rate Ibasic, representing an alternative measure of saturated hydraulic conductivity. Thesaturated hydraulic measurements were carried out to provide more field data on runoff mechanisms occurringat different landscapes in the catchment, rather than as input to TOPMODEL. The initial baseflow parameterQ0 was the first measured discharge depth in the time series. The remaining process parameters (To, td, CHV,RV and Sr0) were set ranges that were considered physically reasonable, prior to uniform random sampling.

TOPMODEL requires a sequence of rainfall (metres) and evapotranspiration (metres) data to run, andpredicts the resulting discharge depths (metres). Simulations commenced at the end of the dry season(beginning of March), when the baseflow was at its minimum, and finished after the last rainfall eventsof the season (end of October). The simulation time-step was 3 h, being a compromise between the hourlypoint rainfall, the hourly river outlet discharge and the daily areal catchment rainfall depth measurements.Areal catchment rainfall was timed according to the rainfall recorder data logger located at the centre of thecatchment. Between 16 June and 30 July 1994 the daily areal rainfall was divided into 3 h time steps, as therainfall recorder was not functioning.

GLUE

The purpose of model calibration was to obtain uncertainty prediction estimates for a model to simulate theentire season, rather than individual storm events. The 2 years of time series data were divided into calibrationand validation years.

The GLUE procedure requires a number of choices to be made (Beven and Binley, 1992):

(1) a sampling range for each parameter;(2) a methodology for sampling the parameter space;(3) a likelihood measure(s) of model performance;(4) a criterion for acceptance or rejection of models; and,(5) a methodology for updating likelihood measures.

Choosing a parameter sample range is not normally a problem, as it is possible to set them as wide asconsidered feasible by physical argument or experience (Freer et al., 1996). However, it makes sense to useestimates of parameter values, where at all possible. Random values of parameters m, To, td, CHV, RV, Srmax

and Sr0 were drawn from uniform distributions over specified ranges. 10 000 sets of seven randomly generatedparameters were supplied to TOPMODEL. The likelihood measure to evaluate model performance was themodelling efficiency of Nash and Sutcliffe (1970):

L�ijY� D[

1 � �2i

�2obs

]�14�

where L�ijY� is the likelihood measure for the ith model conditioned on the observations, �2obs is the observed

variance for the period under consideration, and �2i is the associated error variance for the ith model. The

2 years of data were used sequentially, in order to update the likelihood distributions associated with themodel simulations after each year. The 10 000 parameter sets were simulated for the first year calibrationperiod. The criterion for behavioural parameter sets was selected as E > 0Ð5; all other parameter sets wererejected. Scatter plots of E versus Parameter value were made to assess the sensitivity of parameters to



simulation performance. The model was re-run using the top 1500 ranked parameter sets, and in this casethe simulations were saved. From the output data upper and lower 90% confidence limit boundaries weredetermined. The behavioural parameter sets were used for the 1995 time series. We followed the Bayesianprocedure for deriving updated parameter sets:

Lp�Yji� D L�ijY�Lo�i�

C�15�

where Lo�i� is the prior likelihood of parameter set , L�ijY� is the likelihood calculated for the currentevaluation given the set of observations Y, Lp�Yji� is the posterior likelihood for the simulation of Y given, and C is a scaling constant to ensure that the cumulative posterior likelihood is unity. Confidence limitswere then updated according to Lp�Yji�.

RESULTS

The topographic index � indicates the propensity of landscape areas to become wet. The maximum � classwas 28Ð3 and the minimum � class was 4Ð7. The mean topographic index value �, was 8Ð9. High indexvalues were associated with river channel valley bottoms and incised streams (Figure 4). The high index bandwidened from the confluence of the River Ebonyi and River Amanyi down towards the catchment outlet. Thelow � classes were associated with the upland areas, which did not contribute directly to runoff. The mapshowed a trend of increasing � class values from the escarpment to the lower interfluve areas in the east, andindicated that the runoff-contributing areas were largely located in the south-eastern part of the catchment.The topographic index reference �REF was estimated from the mean value of � at 47 grid cells associated

Figure 4. Map of the topographic index and its distribution for the River Ebonyi headwater catchment



with perennial springs across the catchment. The range of � values at grid cells was 13Ð8 to 19Ð5. The �REF

value was associated with landscape positions adjacent to the river channels, valley bottoms and perennialstream heads.

Soil physical measurements of available water capacity (AWC) and saturated hydraulic conductivity Ksat

are grouped by landscape unit and presented as soil profile, top-soil and sub-soil values (Tables III and IV).The basic infiltration rates Ibasic from four reference soil profile pits are given for the top three diagnostichorizons (Table V). The very low values of AWC (AWC D 96Ð1 mm m�1) and very high values of Ksat

(Ksat D 623Ð3 mm h�1, Ibasic 1st-soil horizon D 630 mm h�1� in the valley bottoms were attributed to the sandtransported from the ravines in the escarpment zone and deposited during flooding. The high water tablesfrom run-on and groundwater accumulation from adjacent slopes supported the riparian forest throughoutthe year, and caused a shallow effective rooting zone depth (0–1 m) during the peak of the season. Theaccumulation glacis featured deep acrisols (>2Ð0 m). The increase of clay in the Bt horizon resulted ina decline in AWC (AWC top-soil D 145Ð8 mm m�1, AWC sub-soil D 116Ð1 mm m�1) and Ksat (Ksat top-soil D 277Ð7 mm h�1, Ksatsub-soil D 57Ð5 mm h�1, Ibasic 2nd-soil horizon D 25 mm h�1�. The mixed glaciswith sections of denudated acrisols in skeletic phase, had shallow soils (<0Ð5 m). The ironstone nodulesand clay illuviation caused a decrease in AWC values with depth (AWC top-soil D 134Ð5 mm m�1, AWCsub-soil D 118Ð1 mm m�1). In the top-soil the presence of ironstone nodules resulted in very high Ksat (Ksat

top-soil D 639 mm h�1, Ibasic 3rd-soil horizon D 6 mm h�1), but in the sub-soil there was high compaction,which lowered Ksat (Ksat sub-soil D 232Ð3 mm h�1�. At the base of residual hills the ironstone nodule and clayilluviation effect was further emphasized in terms of AWC and Ksat. The escarpment soils were deep (>3 m),with low AWC (AWC soil profile D 38Ð1 mm m�1) and very high Ksat (Ksat soil profile D 1002Ð4 mm h�1,Ibasic 1st-soil horizon D 465 mm h�1), due to the high sand content from the Ajali Sandstone Formation. Interms of selecting a suitable range of the maximum effective soil rooting zone depth Srmax for the catchment,a range of 0Ð01 to 0Ð25 m was used for uniform random sampling.

The curve fit through the master recession curve was exponential. The m parameter controlling the function’srate of decay was determined as 0Ð046 m (Figure 5). The top section of the curve, at discharge depths greater

Table III. Measured soil available water capacity (AWC) (n: numberof horizons)

Landscape AWC (mm m�1)

Mean SD Max Min n

Soil profileValley bottoms 96Ð1 64Ð7 282Ð2 15Ð2 40Accumulation glacis 126Ð3 44Ð6 230Ð4 29Ð6 105Mixed glacis 125Ð5 33Ð0 192Ð6 71Ð5 31Residual hill 113Ð5 34Ð8 187Ð1 69Ð4 48Escarpment 38Ð1 8Ð4 58Ð5 21Ð3 20

Top-soilValley bottoms 108Ð1 78Ð6 282Ð2 24Ð4 16Accumulation glacis 145Ð8 45Ð6 230Ð4 47Ð9 36Mixed glacis 134Ð5 34Ð2 192Ð6 83Ð6 14Residual hill 148Ð4 38Ð7 187Ð1 83Ð9 6Escarpment 39Ð5 8Ð4 58Ð5 21Ð3 16

Sub-soilValley bottoms 88Ð1 53Ð9 192Ð8 15Ð2 24Accumulation glacis 116Ð1 40Ð8 186Ð3 29Ð6 69Mixed glacis 118Ð1 31Ð1 163Ð5 71Ð5 17Residual hill 98Ð6 19Ð8 121Ð3 69Ð4 14Escarpment 37Ð4 8Ð4 54Ð0 24Ð7 32



Table IV. Measured soil saturated hydraulic conductivity (Ksat) from constant-headpermeameter tests (n: number of horizons)

Landscape Ksat (mm h�1)

Mean SD Max Min n

Soil profileValley bottoms 623Ð3 1020Ð7 4421Ð1 2Ð0 40Accumulation glacis 133Ð0 289Ð0 1379Ð2 0Ð0 105Mixed glacis 415Ð9 941Ð6 3710Ð6 0Ð0 31Residual hill 923Ð6 2369Ð0 8674Ð1 0Ð0 20Escarpment 1002Ð4 982Ð3 4556Ð9 77Ð9 48

Top-soilValley bottoms 390Ð9 385Ð1 1134Ð4 11Ð5 16Accumulation glacis 277Ð7 385Ð1 1325Ð2 0Ð0 36Mixed glacis 638Ð8 1212Ð6 3710Ð6 10Ð2 14Residual hill 1626Ð0 2552Ð9 6335Ð1 60Ð2 6Escarpment 1047Ð3 890Ð1 3460Ð6 77Ð9 16

Sub-soilValley bottoms 778Ð2 1267Ð8 4421Ð1 2Ð0 24Accumulation glacis 57Ð5 185Ð8 1379Ð2 0Ð0 69Mixed glacis 232Ð3 623Ð1 2575Ð9 0Ð0 17Residual hill 622Ð5 2317Ð4 8674Ð1 0Ð0 14Escarpment 980Ð0 1038Ð4 4556Ð9 83Ð5 32

Table V. Basic infiltration rates measured using double-ring infiltrometer tests at fourprofile pits located in different landscapes

Landscape Ibasic (mmÐh�1)

1st soil horizon 2nd soil horizon 3rd soil horizon

Valley bottoms 630 471 361Accumulation glacis 357 25 36Mixed glacis 171 56 6Escarpment 465 533 292

than 0Ð0015 m�1, indicated as m parameter that was smaller. However, as only a few storm events occurredabove 0Ð0015 m h�1, a function differentiating between peak storm and lower flows was not considered.

Table VI. Process parameter values from the top five ranked parameter sets for the 1994 wet season

Rank M (m) To

[log(m2 h�1)]td

(h m�1)CHV

(m h�1)RV

(m h�1)Srmax

(m)SSEa Eb SAEc

1994-Rank 1 0Ð059 4Ð123 0Ð234 1910Ð61 1976Ð71 0Ð027 0Ð0 000 184 0Ð9426 0Ð1 169 91994-Rank 2 0Ð069 6Ð717 0Ð149 2233Ð53 3873Ð65 0Ð025 0Ð0 000 188 0Ð94 134 0Ð1 168 61994-Rank 3 0Ð067 3Ð129 0Ð768 3126Ð38 1765Ð04 0Ð029 0Ð0 000 190 0Ð94 054 0Ð1 169 51994-Rank 4 0Ð054 3Ð288 1Ð416 3593Ð31 2207Ð89 0Ð045 0Ð0 000 193 0Ð93 979 0Ð1 214 11994-Rank 5 0Ð058 2Ð636 2Ð452 3524Ð55 2474Ð87 0Ð031 0Ð0 000 195 0Ð93 893 0Ð1 187 6

a SSE is the sum of squared errors.b E is the Nash and Sutcliffe efficiency.c SAE is the sum of absolute errors.



Figure 5. The river discharge master recession curve at Eha Amufu (m D 0Ð046 m)

Table VII. Process parameter values from the top 5 ranked parameter sets for the 1995 wet season

Rank M (m) To [log(m2.h�1)] td(h.m�1)

CHV

(m.h�1)RV

(m.h�1)Srmax

(m)SSEa Eb SAEc

1995-Rank 1 0Ð067 4Ð374 2Ð371 1996Ð58 1740Ð23 0Ð021 0Ð0 000 553 0Ð84922 0Ð12 7861995-Rank 2 0Ð069 3Ð919 1Ð416 1386Ð36 2297Ð71 0Ð024 0Ð0 000 557 0Ð84795 0Ð12 8481995-Rank 3 0Ð073 5Ð801 1Ð032 1322Ð64 1713Ð77 0Ð015 0Ð0 000 559 0Ð84754 0Ð12 9641995-Rank 4 0Ð066 2Ð792 3Ð239 1565Ð26 2948Ð58 0Ð021 0Ð0 000 560 0Ð84713 0Ð13 1661995-Rank 5 0Ð066 3Ð242 0Ð553 1383Ð53 1181Ð01 0Ð016 0Ð0 000 564 0Ð8462 0Ð13 507

a SSE is the sum of squared errors.b E is the Nash and Sutcliffe efficiency.c SAE is the sum of absolute errors.

The top ranked parameter sets, out of the 10 000 randomly selected parameter sets run through the 1994and 1995 time series, had modelling performance efficiencies of 0Ð943 (Table VI) and 0Ð849 (Table VII)respectively. The m parameters ranged between 0Ð054 and 0Ð069 m, for the 1994 time series (Table VI).The lowest m value (0Ð054 m) corresponded with the highest SRMAX value (0Ð045 m), and the highest mvalue (0Ð069 m) occurred with the lowest SRMAX value (0Ð025 m). This indicated a degree of multi-collinearitybetween parameter sets, whereby a slower recession decay (0Ð069 m) was compensated by a lower maximumstorage zone (0Ð025 m) and a high transmissivity [log�6Ð717 m2 h�1�]. The top ranked parameter sets of 1995had a smaller range of m (0Ð066–0Ð073 m) values than in 1994 (Table VII). This resulted in smaller rangesin the other parameters as well. The low SRMAX values (0Ð016–0Ð024 m) suggested that higher water tablesoccurred during 1995, resulting in smaller effective root storage depths.

The simulated hydrograph using the top ranked parameter set in 1994 compared well with the observedhydrograph (SSE D 0Ð000 018 4, SAE D 0Ð117) (Figure 6a). The timing, shape and magnitude of the simulatedhydrograph during the peak period (between 22 August and 9 September) was very well reproduced by themodel. The model simulated the rise and fall of the seasonal baseflow through the season, with superimposed



Q(Simulated - top94)

Q(observed)

0.0025

0.0020

(a)

0.0015

Dis

char

ge D

epth

(m

)

0.0010

0.0005

0.000005/03 05/04 06/05 07/06 08/07

Date (dd/mm)08/08 08/09 10/10 03/11

0.6

0.5

0.4

0.3

0.2

0.1

0

(b)

Are

al R

ainf

all D

epth

(m

)

05/03 05/04 06/05 07/06 08/07

Date (dd/mm)

08/08 08/09 10/10

Figure 6. (a) Simulated hydrograph using the top ranked parameter set plotted with the observed hydrograph during the 1994 wet season.(b) Daily areal rainfall during the 1994 wet season

overland and fast subsurface flow events. Simulations improved as the rainfall events became more frequentand contributing areas were more established through wetting up. There were, however, four storm events thatproduced discrepancies in the magnitude of simulated and observed runoff. For example, on 28 September



Q(Simulated - top95)

Q(observed)

0.0025

0.0020

(a)

0.0015

Dis

char

ge D

epth

(m

)

0.0010

0.0005

0.000005/03 05/04 06/05 07/06 08/07

Date (dd/mm)08/08 08/09 10/10 03/11

0.6

0.5

0.4

0.3

0.2

0.1

0

(b)

Are

al R

ainf

all D

epth

(m

)

05/03 05/04 06/05 07/06 08/07

Date (dd/mm)

08/08 08/09 10/10

Figure 7. (a) Simulated hydrograph using the top ranked parameter set plotted with the observed hydrograph during the 1995 wet season.(b) Daily areal rainfall during the 1995 wet season

1994 a peak runoff depth of 0Ð001 767 m was observed and the peak simulated runoff depth was only0Ð001 215 m. The runoff underestimation was due to either the model structure or input errors. The arealrainfall depth for that day was 0Ð005 m, which was insufficient rainfall with the model structure and selectedparameter set to reproduce the observed runoff.



0.40.02 0.04

m (m)

0.06 0.08 0.10 0 2 4

Log To (m2.h−1)

6 8 10

0.5

0.6

0.7

0.8

0.9

1.0E

0.40 5

td (h.m−1)

10 15 20 0.00 0.05

Srmax (m)

0.10 0.15 0.20 0.25

1000

RV (m.h−1)

2000 3000 4000 1000

CHV (m.h−1)

2000 3000 4000

0.5

0.6

0.7

0.8

0.9

1.0

E

0.4

0.5

0.6

0.7

0.8

0.9

1.0

E

0.4

0.5

0.6

0.7

0.8

0.9

1.0

E

0.4

0.5

0.6

0.7

0.8

0.9

1.0

E

0.4

0.5

0.6

0.7

0.8

0.9

1.0

E

Figure 8. Scatter plots of behavioural parameter sets run through the 1994 time series

The model did not perform as well with the 1995 time series data (Table VII). The top ranked parameter set(SSE D 0Ð000 055 3, SAE D 0Ð128), reproduced the rise and fall of the seasonal baseflow, but underestimatedsome of the storm events. In one case (29 August 1995) a major runoff event was completely missed. Therainfall network record for that day revealed that the rain gauge at the far south-east of the area (Eha Amufu)recorded a rainfall depth of 0Ð1 m, whereas the catchment areal rainfall depth was only 0Ð003 m (Figure 7b).The sharply peaked shape of the hydrograph supported the conclusion that the major runoff event was due torapid overland and subsurface flow as the result of a localized rainfall event.

The scatter plots of maximum likelihood versus behavioural parameter values for 1994 (Figure 8) showedthat the m parameter was the most sensitive to model performance. The scatter plot had a peaked band of dots,



which meant that the best model performances occurred for parameter sets having m values between 0Ð04and 0Ð07 m. The scatter plot of the logTo parameter indicated a tendency of achieving better results between2 and 4 m2 h�1, but high modelling efficiencies were also obtained from values as high as 10 m2 h�1. Themaximum efficiency occurred at 0Ð1 h m�1 for td. However, td was not a sensitive parameter, as acceptablesimulations were obtained by the maximum td value of 20 h m�1. The scatter plot of the Srmax parameter hada small peak at 0Ð03 m. The runoff routing parameters RV and CHV were completely flat topped across therange of parameter values set. In general, the scatter plots indicated a high degree of equifinality betweenparameter sets, meaning that a wide range of parameter values were included in behavioural parameter sets.

The 90% uncertainty bands for 1994 (Figure 9a) were narrow throughout most of the season. The greatestuncertainty was for storm events, and in some cases the Qobs hydrograph crossed over the upper 90% boundary.The uncertainty also increased for simulations of the recession periods during the early part of the season.During 1995 (Figure 10a) there was more uncertainty than in 1994, especially during the months of June andJuly. In 1995 the conditions were wetter than in 1994 during the early part of the season, so rainfall input

Figure 9. (a) Hydrograph of 1994 time series with 90% confidence limits. (b) Hydrograph of 1994 time series with updated 90% confidencelimits



Figure 10. (a) Hydrograph of 1995 time series with 90% confidence limits. (b) Hydrograph of 1995 time series with updated 90% confidencelimits

errors were more pronounced. The updating of the confidence limits according to Equation (15), therefore didnot narrow the 90% upper and lower boundaries for the 1994 and 1995 seasons (Figures 9b and 10b).

DISCUSSION

The model performed better during the peak phases of the wet season than in early or late season storm events.This was similar to findings from other TOPMODEL applications in tropical catchments (Quinn et al., 1991;Molicova et al., 1997). Subsurface flow was the dominant runoff process, and as the wet season progressedto its peak, fast subsurface and overland storm flows became superimposed on the progressively increasing



baseflow. The theory of partial area hydrology corresponded to the field and hydrological observations of runoffresponses. The soil physical data from reference profile pits within the catchment show how heterogeneousthe soils are within the catchment. The reduction in vertical hydraulic conductivity in the sub-soil of the soilsbelonging to the accumulation glacis and mixed glacis support the observation of Bonell et al. (1983), thatrapid overland flow is an excess saturation rather than an excess infiltration process. Most major runoff eventsoccur when a large event follows soon after a smaller event. The relative decline of the Ksat in the sub-soilcompared with the Ksat in the top-soil allows soil water to temporarily accumulate in the top-soil, so thatwhen the large rainfall event arrives, excess saturation runoff can occur. The deeper unsaturated zones in theupland areas require wetting up before actively contributing to the baseflow and wetting the lower reachesof the landscape. By the peak of the season the valley bottoms are very wet, with high water tables fromrun-on and groundwater due to near-surface and subsurface flow from the adjacent hillslopes, as well as riverflooding. The escarpment area only contributes to the baseflow component of the catchment hydrograph, asthe hydraulic conductivity is very high throughout the soil profile.

The seasonal nature of runoff in the catchment is well illustrated by the contrasting runoff coefficients thatoccur for particular rainfall storm events in different phases of the season. During the early and middle part ofthe wet season the runoff coefficient for two storm events was less than 0Ð1, whereas during the peak periodthe runoff coefficient was as high as 0Ð25. During the end phase of the wet season, a storm event had a runoffcoefficient of 0Ð13.

The reference topographic index was introduced to account conceptually for the water table not beingparallel to the surface as the catchment wetted up and to provide greater weight to subsurface than overlandflow contributing areas. During the middle (June to mid-August) and the end (mid-September onwards) phasesof the season the model was underestimating storm hydrographs owing to insufficient rainfall input. Sincespatial rainfall measurements were interpolated as a single areal catchment value, there was loss for largestorm events that were localized in the south-east part of the catchment. In addition, the density of the raingauge network was not sufficient to monitor some events. The spatial extent of rainfall events at the startand end of the season was smaller than at the peak of the season. Obi and Salako (1995) differentiatedbetween single and multipeak storm events in south-eastern Nigeria. Single storm events were more isolatedin time and spatial extent than multipeak storms, and were associated with the advance and retreat of the ITD.Geostatistical analysis of daily rainfall patterns across the catchment area (Campling et al., 2000) showedthat, although at a daily time step a global climatological variogram with a range of 18 km was suitable forinterpolating areal rainfall, there was clear evidence that major single storm events could have covariancestructures of less than 10 km. The impact of errors in the rainfall input on the hydrograph response was,however, different, because after the peak period of the season the catchment contributing areas were closeto saturation, whereas during the earlier periods of the season the contributing areas were still in the processof wetting up. Thus, model underprediction was greater towards the end of the season than during the middleof the season.

A further explananation for runoff underestimation for some early and late season storm events is that themodel structure is currently not dynamic enough to cater for the strong seasonality in runoff production. Itcould be argued that, as the season wets up, the �REF should also be reduced to allow for the fact that upslopewater tables become more parallel to the surface topography. This could be undertaken by introducing aseasonal parameter to control the value of �REF, which would result in seasonal weightings to subsurface andoverland contributions to runoff.

The runoff underestimations can, therefore, be attributed to a combination of: errors in detecting localized,convectional rainfall events; the treatment of rainfall as a catchment areal value; and the strong seasonalityin runoff response in the tropics.

The GLUE procedure enabled a full exploration of the parameter space. The most sensitive processparameter was clearly the m parameter, which supports the observation that subsurface flow and local storagedeficits are important contributors to the hydrological response of the catchment. The estimated m of 0Ð046 mfrom recession curve analysis was lower than the calibrated m values of the top ranking parameter sets.



From the recession curve analysis a more rapid decline of the recession limb of the runoff hydrographwould have been expected than was in fact realized. The Nash and Sutcliffe objective function is sensitiveto hydrograph peaks. Therefore, in a hydrological system exhibiting strong seasonal characteristics, wherebyrapid runoff is superimposed on the seasonal rise and fall of the baseflow, higher m values, which produceslower recession curves, were important for achieving the highest ranked simulation performances. In thisrespect, a complementary baseflow recession curve could be constructed, which reflects more the rise and fallof the seasonal baseflow than concatenated hydrograph peaks.

The Srmax parameter also showed a degree of sensitivity. Low effective Srmax values confirmed fieldobservations that the sandy valley bottoms with low water-holding capacity and high seasonal water tableslargely contributed to the storm hydrographs. The scatter plots of behavioural parameter sets demonstrated theequifinality of parameter sets, meaning that a wide range of parameter values provided reasonable simulationresults.

The confidence limits provided a measure of uncertainty in the model performance. The uncertainty bandswere wider during the 1995 than the 1994 season, reflecting the decline in model performance. During 1995the catchment received more rainfall at the start of the season (April and May), and model errors incurred atthe beginning persisted throughout the season. Therefore, the updating procedure did not result in narroweruncertainty bands because of the greater dominance of the model structure and input data errors over theerrors associated with the calibration procedure (Figures 9b and 10b).

CONCLUSIONS

TOPMODEL performed well as a continuous hydrograph simulator. The simulations provided an insight intothe response of the catchment at different periods of the season. The spatial distribution of the topographicindex enabled the dynamic contributing areas to be identified. A reference topographic index was introducedinto the calculation of catchment storage deficit to account for deeper water tables in the upland areas.It effectively controlled the expansion of saturated contributing areas and increased the effective storagedeficit for higher topographic index classes. This approach ensured that more weight was given to fast andslow subsurface flow contributions, than to overland flow. The model structure was in keeping with fieldobservations of runoff processes in the catchment. Recession curve analysis provided a means of estimatingthe m parameter, which controls the rate of baseflow decline and the local storage deficit. There was moreuncertainty in modelling storm events during early and late phases of the season, as localized convectionalevents were more prevalent than during the peak phase of the season, which featured more catchment-widefrontal storm events. We have shown that the underestimation of some rainfall events was due to a combinationof: errors in detecting the rainfall depths of localized, convectional rainfall events; the treatment of rainfallas a catchment areal value; and the strong seasonality in runoff response in the humid tropics.

ACKNOWLEDGEMENTS

Funding for this research was provided by the Belgian Agency for Development Cooperation (BADC) throughthe Inter-University Project on ‘Water resources development for domestic use and small scale irrigation inthe rural areas of southeastern Nigeria’. Special appreciation is extended to the project staff and farmers whoassisted in implementing the hydrological monitoring scheme.

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Rainfall-runoff modelling of a humid tropical catchment: the TOPMODEL approach

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