parameter estimation for urban runoff modelling

Parameter estimation for urban runoff modelling

Kyung-sook Choi, James E. Ball *

Water Research Laboratory, School of Civil and Environmental Engineering, The University of New South Wales, Kiny Street, Manly Vale,

NSW 2093, Australia

Received 13 July 2000; received in revised form 26 February 2001; accepted 16 November 2001

Abstract

Accurate estimation of the control parameters for spatially distributed physically based catchment modelling systems requires

considerable work to establish credibility. Presented in this paper is a methodology for estimation of control parameter values based

on the application of a decision support system within a hydroinformatic system. The proposed methodology uses information

contained within a GIS database together with optimisation techniques to infer spatially variable control parameters for utilisation

with a catchment modelling system such as the Stormwater Management Model (SWMM). A case study application of the proposed

methodology was undertaken using the Musgrave Avenue Stormwater System in Centennial Park, Sydney. Results from this ap-

plication suggest that the proposed approach is capable of providing accurate spatially distributed control parameters for imple-

mentation with physically based catchment modelling systems. � 2002 Published by Elsevier Science Ltd.

Keywords: Calibration; Catchment; GIS; Modelling; SWMM; Urban

1. Introduction

Management of the quantity and quality of storm-water runoff from urban areas is a complex task whichhas become an increasingly important environmentalissue for urban communities. Together with economicand social issues, this increased awareness of the impactsof urban drainage systems has resulted in a need forsystem managers to obtain information regarding thedrainage system response to varying climatic conditions.Two standard approaches for obtaining the desired in-formation are:• monitoring of the system for both water quantity and

quality, or• implementation of catchment modelling systems

which simulate the important processes influencingthe quantity and quality of stormwater runoff theurban environment.

Where changes to the management of a stormwatersystem are proposed and it is desired that the impacts ofthese changes be assessed then it is necessary to adoptthe second approach as the first approach can only

provide historical information; consequently, monitor-ing of the stormwater system can provide the desiredinformation only after implementation of the proposedchanges. Implementation of a catchment modellingsystem simulating flows in a stormwater system, how-ever, requires monitored information to ascertain thereliability and robustness of the predicted flow condi-tions. Where this monitored information is not avail-able, the necessary information for reliable and robustpredictions must be obtained from other available in-formation sources. In both cases, the necessary infor-mation is that required to calibrate and validate thecatchment modelling system.

In an ideal situation, stormwater systems would bedesigned and analysed with catchment modelling sys-tems which fully replicated the important processes in-volved with the generation and transmission ofstormwater and its entrained contaminants. This idealsituation, however, requires catchment modelling sys-tems, generally mathematical in form, to be developedthat include all potential and feasible processes whichinfluence the response of the system to the various cli-matic conditions. In practice this does not occur because• generation and transmission of surface runoff and the

entrained contaminants are complicated and involvemany processes resulting in a full mathematical de-scription being impossibly complex;

Urban Water 4 (2002) 31–41

www.elsevier.com/locate/urbwat

*Corresponding author. Tel.: +61-2-9949-4488; fax: +61-2-9949-

4188.

E-mail address: [email protected] (J.E. Ball).

1462-0758/02/$ - see front matter � 2002 Published by Elsevier Science Ltd.

PII: S1462-0758 (01 )00072-3

• even when a catchment process can be described con-cisely and completely, the volume of calculations in-volved may be prohibitive; and

• the data that is available to assist in definition of con-trol variables for the models are limited in both spa-tial and temporal dimensions.As a result of these limitations, simplifying assump-

tions are made and the real situation is idealised to en-able the economical and efficient use of catchmentmodelling systems. The fundamental philosophy ofcatchment modelling systems is a reductionist approachwhereby the total response of the system may be ascer-tained through simulation of the response of individualcomponents of the system. Since the dominant processesin each component of the system will be different, sim-ulation of the one system is likely to require differingmodels for alternative components in the system. Whenconsidering the different components of the system, it ispossible to arbitrarily divide the components into anumber of conceptual modules. One subdivision intofour conceptual modules was proposed by Ball (1992)who suggested the following four modules:• Generation – that module in the system concerned

with modelling the spatial and temporal variationof rainfall, the availability of pollutant constituents,and any models associated with control parameterestimation.

• Collection – the module in the system primarily con-cerned with the accurate prediction of the temporalvariation of the stormwater quantity and quality fluxat the entry points to the transport module of the sys-tem. This module generally is considered to be thehydrologic component of the system.

• Transport – the module in the system where the quan-tity and quality of the stormwater runoff is routedthrough the physical links in the drainage system.This module generally is considered to be the hydrau-lic component of the system.

• Disposal – that module of the system concerned withthe manner by which the stormwater quantity andquality is discharged into the receiving waters.A schematic arrangement of these modules is shown

as Fig. 1. Also shown in Fig. 1 is the direction of in-formation flow. It is important to note that the flow isunidirectional; a consequence of this unidirectional flowis that a successful reproduction of the dischargehydrograph does not imply all processes that influencethe outflow hydrograph are simulated correctly or thatthe selected model control parameter values are accu-rate. In essence, this problem arises from the number ofparameters used in the models for description of theprocesses which influence runoff characteristics duringany stage in the runoff cycle and the nonlinear mappingof these parameters. Furthermore, the values of manyparameters are linked; for example, for a knowncatchment average depth of rainfall excess, the differ-

ences between alternative average depths of rainfallobtained from different spatial rainfall models can becompensated by differences in the parameters used in theloss model. As a result, there are an infinite number ofalternative parameter sets which will result in the totalsystem replicating the catchment response. The problemof the catchment modeller is to select the set of pa-rameter values that is appropriate for the processes thatare being simulated in an individual component of thesystem while also being appropriate for the total systemreplication of the catchment response.

Presented herein is an approach based on applicationof a hydroinformatics system and, in particular, a de-cision support system for selecting values of the catch-ment modelling system control parameters.

A hydroinformatics system can be defined as theapplication and manipulation of information about theaquatic environment in a computerised format. As dis-cussed by Ball (1994), there is an obvious need for hy-droinformatic systems to deal with significant volumesof multidimensional catchment information to obtaininteractive management methodologies in water re-sources. The general components of the hydroinformaticsystems that would be expected for a system concernedwith the management of a catchment are:• information database for storage, retrieval and dis-

play of spatial and temporal data;• catchment modelling system for simulating the catch-

ment response to hydrologic events, and• decision support system for enhanced modelling and

data analysis capabilities.In this study, a Decision Support System (DSS) was

developed to support decisions regarding appropriate

Fig. 1. Conceptual components of a catchment modelling system.

32 K.-s. Choi, J.E. Ball / Urban Water 4 (2002) 31–41

values for the catchment modelling system controlparameters. The Stormwater Management Model(SWMM) (Huber & Dickinson, 1988) was used to sim-ulate the response of an urban catchment to stormevents, while ARC/INFO was employed to handle spa-tial and non-spatial attribute information.

2. Control parameter evaluation

2.1. Types of catchment modelling system control param-eters

Calibration of a catchment modelling system requiresthat the control parameters (input data) for each ofthese conceptual components be determined so that theresultant system of process models and input informa-tion mimics the real response of the catchment. Sincesurface runoff varies with the catchment characteristics,calibration of a catchment modelling system usuallyrequires adjustment of the model control parameters tominimise prediction errors.

For operation of a catchment modelling system, it ispossible to categorise the control parameters as• Measured parameters. These are parameters that are

physically measured such as pipe diameters, catch-ment areas, rainfall depth or rainfall intensity, etc.;and

• Inferred parameters. These are parameters that arenot measured and are determined from the applica-tion of a model. Examples of inferred parametersare Manning’s roughness for catchment surfaces orchannels, depression storage, catchment or subcatch-ment imperviousness.While the interface between these categories may

appear as an absolute division, in reality, the interfacebetween these categories is vague with parametersoscillating between the categories depending on theviewpoint of the user. For example, rainfall depth inthe above discussion is defined as a measured pa-rameter, but this measurement is only at the rainfallgauge itself with rainfall at other locations within thecatchment (assuming the rain gauge is within thecatchment) being inferred by the application of aspatial rainfall model. Ball and Luk (1998) discuss thepotential errors introduced through different inferencemodels for the spatial distribution of rainfall over acatchment. Consideration of other control parameterssuch as the catchment, or subcatchment, area alsoreveals a variability in measured parameters dependingon, for example, the scale of the map from whichthe area was measured. In general, the values of in-ferred parameters are considered those that need to beadjusted during calibration, while measured parame-ters are assumed error free during the calibrationprocess.

2.2. The calibration process

Control parameter values for a catchment modellingsystem typically are determined by one of two alterna-tive methods; these alternative methods are:• modification of control parameter values until the

simulated and monitored hydrographs, or othercatchment response measure, are similar; and

• selection of control parameter values based on somehydrological, hydraulic or other characteristic of thecatchment.The first of these alternatives can be described as a

‘‘trial and error’’ method whereby the values of thecontrol parameters are modified in a systematic mannerto achieve correlation between the monitored parame-ters and the predicted parameters describing thecatchment response. A number of studies have focussedon improving this alternative through application ofsophistical mathematical search algorithms; examplesof these studies are those by Kuczera (1983a,b), Guptaand Sorooshian (1985), Duan, Sorooshian, and Gupta(1992), Ibrahim and Liong (1992, 1993), Liong andIbrahim (1994), and Gupta, Sorooshian, and Yapo(1998) who all used optimisation algorithms to searchfor the control parameter values. Alternative mathe-matical approaches, although still based on a searchalgorithm for the control parameter values, have beenstudied by Baffaut and Delleur (1990) and Liong,Chan, and Lum (1991) who used knowledge-basedsystems, and Wang (1991), Liong, Chan, and ShreeRam (1995) and Balascio, Palmeri, and Gao (1998)who used genetic algorithms to search for the controlparameter values that resulted in the best reproductionof the monitored information. Both of these ap-proaches were capable of evaluating the control pa-rameters. The disadvantage of all of these approaches,however, is that evaluation of the control parametersrequires monitored information to assess the suitabilityof the values being tested.

Many catchments are not monitored and conse-quently information necessary for implementation of the‘‘trial and error’’ approaches used in the above studies isnot available. A similar situation occurs when thecatchment modelling system is intended to assess theimplications of a changed management strategy prior toits implementation. An alternative approach for evalu-ation of the control parameters is therefore necessary. Inthese circumstances, the second of the two genericcontrol parameter evaluation methods can be used.

As previously discussed, a ‘‘trial and error’’ approachis used when calibrating a catchment modelling systemwith monitored information. This approach is shown inFig. 2. When this approach is being applied for deter-mination of spatially variable control parameters, theuser is faced with the problem of distinguishing betweena significant number of variables and, in many cases,

K.-s. Choi, J.E. Ball / Urban Water 4 (2002) 31–41 33

inadequate information to ascertain values of individualvariables.

An alternative approach is to adopt the concept im-plicitly implemented with the use of inferred controlparameters; this concept is based on the application ofan inference model to determine the value of the controlparameter. Inclusion of these inference models in thecalibration process (1) results in the approach shown inFig. 3. The approach shown in Fig. 3 is the basis of thestudy reported herein. It is worthwhile noting that when

monitored information is not available, the inferencemodels may be used to obtain spatially distributed val-ues of the control parameters based on the catchmentcharacteristics.

2.3. Calibration of SWMM

Presented in Table 1 are some of the major controlparameters in the RUNOFF Block of SWMM. Thesecontrol parameters are influenced by many factors re-lated to the characteristics of the subcatchments withsuggested influencing factors for these control parame-ters shown in Table 2. These influencing factors werestored in a GIS (Arc/Info) database.

Transformation of the information stored within thespatial database requires inference models which are themodels used to infer the control parameter values. Anexample of an inference model is that presented byZaman and Ball (1994) for estimation of the imperviousfraction of a subcatchment. This model is based on de-fining the impervious fraction of individual land useswithin the subcatchment and then weighting these im-pervious fractions by the proportion of the subcatch-ment that is covered by an individual land use.Algebraically, this model can be expressed as

Aimp ¼P

LUiAi

A; ð1Þ

where Aimp is the fraction of the subcatchment that isimpervious, LUi is the impervious fraction of land use i,Ai is the area associated with land use i, and A is thesubcatchment area. Presented in Table 3 are the im-pervious fraction of land uses suggested by Zaman andBall (1994). It was shown by Zaman and Ball (1994) thatthe use of these impervious fractions resulted in reliableestimation of the total catchment impervious fractionfor the Salt Pan Creek catchment where their study wasundertaken. The concept of estimating the impervious-ness of catchments from the component land uses wasextended in this study to the estimation of individualsubcatchment imperviousness fractions and for the es-timation of other control parameter values for individ-ual subcatchments.

Calibration of the catchment modelling system whenthese inference models are used to evaluate the controlparameters consists of adjusting the parameters in theinference model until satisfactory agreement betweenthe predicted and the monitored hydrograph charac-teristics is achieved. For the inference model used toevaluate the impervious fraction of a subcatchment (Eq.(1)), the parameters in the inference model adjusted arethe impervious fractions (LUi) of the individual landuses. Other inference model parameters calibrated dur-ing this study were the subcatchment overland flowlength, overland flow Manning’s roughness, and thedepression storage for an individual land use.Fig. 3. Proposed calibration procedure.

Fig. 2. Traditional calibration procedure.


Implementation of these inference models requiredthe extraction of relevant information from the GISwith the resultant control parameter values placeddirectly into the files necessary for operation of theSWMM. Optimisation of the inference model param-eters was achieved through use of the SequentialQuadratic Programming (SQP) method as imple-

mented in MATLAB (Mathworks, 1997). This opti-misation technique is a nonlinear constrainedoptimisation technique that consists of three stageswhich are:• updating of the Hessian matrix of the Lagrangian

function (using BFGS method);• Quadratic Programming (QP) problem solution; and• line search and merit function calculation.

At each major iteration an approximation is made ofthe Hessian of the Lagrangian function calculated usinga quasi-Newton updating method (the BFGS formula).This then generates a QP subproblem whose solution isused to form a search direction for a line search proce-dure. The resultant new estimates of the inference modelparameters were used then to determine new controlparameters with a new hydrograph prediction obtainedfrom operation of SWMM with the new control pa-rameter values.

Table 2

Factors influencing control parameter value

Control parameters Influential factor

Subcatchment width Subcatchment area,

topographic characteristics, over land flow length

Subcatchment impervious fraction Land use, imperviousness, Amc

Depression storage Pervious area Soil type

Surface vegetation

Antecedent conditions

Interception

Infiltration

Impervious area Interception

Antecedent conditions

Manning’s roughness coefficient Impervious area Roof material type

Road material type

Other impervious surface types

Pervious area Vegetation

Soil type

Ground cover type

Drainage system Channel/pipe type

Infiltration (Horton’s equation)a Fc: Soil typeFo: Soil type, initial moisture content

K: initial moisture content (Surface wetness)

Slope Elevation difference, overland flow length, slope model

a (fo) maximum initial infiltration rate; (fc) min. infiltration rate; (k) infiltration decay rate.

Table 3

Imperviousness of land use (after Zaman & Ball, 1994)

Land use Impervious fraction

Low density residential 37

Medium density residential 45

High density residential 55

Commercial 55

Open space 0

Industrial 55

Special use 50

Table 1

SWMM runoff block control parameters (quantity)

Measured parameters Inferred parameters

Subcatchment area Impervious area factor

Length of channel/pipe Subcatchment length/width ratio

Shape and bed slope of channel/pipe Subcatchment slope

Characteristic dimension of conduit Maximum and minimum infiltration

Manhole type Impervious area manning’s roughness coefficient

Catchment soil type Pervious area manning’s roughness coefficient

Catchment land-use type Impervious area detention storage

Rainfall depth within last record period Pervious area detention storage

Percentage of imperviousness of subcatchment

Conduit roughness coefficient

Decay rate of infiltration curve


3. Case study

3.1. Catchment details

The catchment used for this study was the CentennialPark Catchment located in the eastern suburbs ofSydney in Australia. The catchment of 132.7 ha areaupstream of the gauging station located at the outlet ofMusgrave Avenue Stormwater Channel was modelled(see Fig. 4). Land use within the catchment (see Fig. 5)consists mainly of residential area (40.0% of area).Presented in Table 4 are the land uses within the Cen-

tennial Park Catchment as an area and as a percentageof the total catchment. The catchment is served anddrained by a separated sewer system with the storm-water system consisting of a series of pipes, boxes,culverts and open channels (see Fig. 6). The catchmentarea was subdivided into 42 subcatchments with thelength of stormwater channel in each subcatchmentbeing between 24.1 and 258.2 m.

The average subcatchment slope is about 5.3%, andthe geological composition of the catchment is Botanysands containing mainly two sand soil types, namely,Hammondvill Soil (85%) and Moore Soil (15%).

Fig. 4. Centennial Park Catchment area.


The School of Civil and Environmental Engineeringat the University of New South Wales installed in1993 two 0.2 mm tipping bucket pluviometers atWaverley Public School and at Musgrave AvenueStormwater Channel. The rainfall data were down-loaded fortnightly into HYDSYS which is a softwareused to store, process, analyse and report hydrometrictime series data. At the gauging station installed onMusgrave Avenue Stormwater Channel, flow quanti-ties were monitored continuously by an ultrasonicprobe which monitored the flow depth. This recordedflow depth was converted to a flow discharge using a

Fig. 5. Land use within the Centennial Park Catchment.

Table 4

Land use within the Centennial Part Catchment

Land use types Area (ha) Percentage (%)

Special building 16.5 12.4

Road and street 30.8 23.2

Low residential 21.6 16.2

Medium residential 20.8 15.7

High residential 10.8 8.1

Open space and park 28.7 21.6

Commercial/business 3.5 2.7

Total 132.7 100


rating curve determined from a physical model of thestormwater channel and gauged flows (Abustan,1997). Further details of the gauging station instru-mentation and operational protocol are provided byAbustan (1997).

Rainfall information from Waverley Public Schooland flow data from the gauging station installed on theMusgrave Avenue Stormwater Channel was availablefrom HYDSYS at user defined time steps. For purposesof catchment modelling system calibration and valida-tion, data was extracted at 5 min intervals.

3.2. Catchment simulation

For simulation of the rainfall-runoff process, theRUNOFF and TRANSPORT blocks of SWMM wereused. In the project reported herein, nine parameters ofthe RUNOFF Block were calibrated for each sub-catchment through the inference models; this resulted inthe calibration of 378 control parameters. These pa-rameters were the subcatchment width, the imperviousfraction, the depression storage of the impervious andpervious areas within a subcatchment, the Manning’sroughness for flow over the impervious and pervious

areas within the subcatchment, and the parameters forHorton’s infiltration equation. While these parameterswere calibrated for each subcatchment, the calibrationprocess consisted of modification of the control pa-rameters for the inference models; this reduced thenumber of control parameters to be calibrated from 378to 61 which considerably enhances the tractability of theproblem. Additional details of the calibration process,such as the bounds applied to the control parametervalues, are presented by Choi (2001).

The objective of the application of a catchment modelsystem is generally to determine runoff depth, peak flowrate, and hydrograph shape and timing. To compare theproposed calibration process with a more traditionalcalibration process, the evaluation criteria used were therelative error in peak flow and runoff depth and thehydrograph root mean square error. Algebraically, thesecriteria were:• Relative error (RE) for an arbitrary variable x

RE ¼ xo � xsxo

; ð2Þ

where xo is observed value of a hydrograph charac-teristic and xs is the simulated value of the samecharacteristic.

Fig. 6. Stormwater drainage system in Centennial Park Catchment.


• Root mean square error (RMSE) for discharge

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1½QoðiÞ � QsðiÞ�2

n

s; ð3Þ

where QsðiÞ and QoðiÞ are the simulated and observeddischarges, respectively, and, n is number of obser-vations in the time series.As shown in Table 5, three storm events were used for

the catchment modelling system calibration and vali-dation, respectively. Since low rainfall generates runoffprimarily from the impervious portion of the catchment,this study considered only small events. For comparisonwith the traditional calibration method, the storm eventsfor validation were the same events used by Abustan(1997). The antecedent wetness of the catchment wasbased on the total amount of rainfall within the previous24 h; shown in Table 6 are the categories adopted forthis control parameter.

Listed in Table 7 are the measured and simulatedvalues of peak flow and runoff depth. In this study, thevalues of runoff depth resulting from the calibration

produced generally lower differences between the mea-sured and simulated results compared to the values inpeak flow. A similar trend was observed by Abustan(1997). Consideration of this suggests that it is moredifficult to reduce prediction error of peak flow thanprediction error of runoff depth. The average relativeerror (RE) in peak flow was )1.45%, while, for therunoff depth, the average RE was 0.24%. In addition,the averages of root mean square errors (RMSE) in peakflow and runoff depth were 0:03 m3=s and 0.01 mm,respectively. The values of RE and RMSE for the vali-dation events are similar to those obtained for the cali-bration events. The validation events had an average REof 4.75 peak flow and an average RE of )1.24% inrunoff depth; consideration of these errors suggests thatadequate reproduction of the catchment response by thecatchment modelling system has been achieved. TheRMSE for peak flow and runoff depth were 0:02 m3=sand 0.02 mm, respectively. From the RMSE results, theprediction errors were well balanced in terms of peakflow and runoff depth objectives. The comparison ofsimulated and measured hydrographs for a calibratedand a validated event are plotted in Figs. 7 and 8.

Evaluation criteria developed using the proposed andtraditional calibration methods are shown in Table 8. Asshown in Table 8, the proposed calibration approachresulted in better predictions for both peak flow andrunoff depth. In other words, the proposed method re-sulted in the accurate estimation of spatially variablecontrol parameters.

4. Conclusion

A hydroinformatic system for estimating catchmentmodelling system control parameters has been devel-oped to improve the traditional calibration process,which requires a time intensive and tedious search foraccurate values of a large number of model parameters.Catchment information was constructed in an ARC/INFO database and transformations developed usingthis information to generate the input information nec-essary for operation of a SWMM-based catchmentmodelling system to simulate surface runoff processes in

Table 5

Characteristics of calibration and validation events

Event date Rainfall

(mm)

Duration

(min)

Catchment

wetness

Calibration

Jan. 28, 1995 7.2 270 Dry

Mar.19, 1995 5.6 45 Dry

Feb. 4, 1996 9.6 210 Dry

Validation

Nov. 29, 1994 3.0 60 Dry

Dec. 08, 1994 4.0 240 Dry

Dec. 22, 1994 4.2 90 Dry

Table 6

Antecedent conditions (after Abustan, 1997)

Catchment wetness Amount of rainfall within 24 h

(mm)

Dry 0–2.5

Rather dry 2.5–5.0

Wet >5:0

Table 7

Monitored and simulated hydrograph characteristics

Event date Monitored Simulated

Peak flow ðm3=sÞ Runoff depth (mm) Peak flow ðm3=sÞ Runoff depth (mm)

Jan. 28, 1995 0.84 1.85 0.85 1.87

Mar. 19, 1995 3.68 1.63 3.65 1.63

Feb. 4, 1996 1.51 2.86 1.57 2.85

Nov. 29, 1994 0.33 0.75 0.32 0.76

Dec. 8, 1994 0.32 0.95 0.28 0.98

Dec. 22, 1994 1.57 1.30 1.59 1.29


the Centennial Park Catchment. The optimisation al-gorithm in MATLAB was employed to search for theoptimum values of factors influencing the transforma-tion of catchment information into catchment modellingsystem control parameters. Resulting from this ap-proach, it was found that high accuracy control pa-rameter estimation was obtained. Furthermore, thisapproach allowed the development of spatially variablecontrol parameters without the problem of optimisingover a large number of control parameters. From thecomparison of the new and traditional calibration ap-proaches, it was found that hydroinformatic systems canbe used effectively to evaluate catchment modellingsystem control parameters, and to improve the accuracyand efficiency of the catchment modelling system cali-bration process.

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Table 8

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Peak flow Runoff depth Peak flow Runoff depth

RE

(%)

RMSE

ðm3=sÞRE

(%)

RMSE

(mm)

RE

(%)

RMSE

ðm3=sÞRE

(%)

RMSE

(mm)

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Dec. 8, 1994 12.5 0.04 )3.16 0.03 15 0.06 8.7 0.09

Dec. 22, 1994 �1.27 0.02 0.76 0.01 )21 0.27 )5.7 0.07

Average 4.75 0.02 )1.24 0.02 )5.33 0.12 )0.4 0.06

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parameter estimation for urban runoff modelling

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