Quantification of Model Accuracy

As a part of this review, an attempt was made by the author to quantify the model accuracy by reviewing the comparative studies published in the literature in simulating the event runoff hydrographs of urban catchments. For most of these studies, the plots of simulated and observed hydrographs were given, but no quantification of model errors was done. For these studies, model simulation errors were quantified by measuring the difference between observed and simulated hydrographs. Results of all comparative studies were analysed with three error functions (i.e. Equations 2.23-2.25) relating the differences between observed and simulated hydrograph peak, volume and time to peak. These three attributes are important in design and analysis of urban drainage systems. Peak discharge is required in urban drainage design for sizing pipes, culvert and bridges. Runoff volume is required for design and operation of flood control structures such as retarding basins. Time to peak discharge is required for flood forecasting and operation of control structures during storm events.

Error in runoff volume (VOL),

VOL ={(Vm-Vo) / Vo} x 100 (2.23)

Error in peak discharge (PEAK),

PEAK ={(Pm-Po) / Po} x 100 (2.24)

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TTP = {(TPm-TPo) / TPo} x 100 (2.25)

where Po is the observed peak discharge,

Pm is the modelled peak discharge,

Vo is the observed runoff volume,

Vm is the modelled runoff volume,

TPo is the observed time to peak, and

TPm is the modelled time to peak.

Equations 2.23-2.25 were used to compute the model errors for both calibrated and non- calibrated studies reviewed in Sections 2.5.1 and 2.5.2 respectively. The results are shown in Tables 2.4 and 2.5 respectively. These tables show the catchment characteristics (i.e. area and percent imperviousness), number of events used in calibration and verification, and the error range arising from different events.

Table 2.4: Summary of Percentage Errors for Calibrated Studies

% Error

Volume Time to Peak Model or Method Cat. Area (ha.) Imp. % No. of Eve. Peak Discharge Reference ILSAX 94 24 10 1 to –143 0 to 100 -7 to 100 Dayaratne (1996) 41 37 1 19 1 19 Maheepala (1999) 9 50 1 29 1 36 Maheepala (1999) 14 47 3 26 to 57 0 to 1 4 to 73 Maheepala (1999)

RRL 502 20 5 -53 to -21 N/A -64 to +38 Heeps and Mein (1973a) SWMM 502 20 5 -21 to +64 N/A -53 to +128 Heeps and Mein (1973a)

15 N/A 2 -20 to -16 0 to +5 -25 to -22 Zech et al. (1994) 94 24 10 6 to 99 0 to -50 1 to -108 Dayaratne (1996)

41 37 1 23 2 13 Maheepala (1999) 9 50 1 29 2 15 Maheepala (1999) 14 47 3 26 to 57 0 to 1 3 to 32 Maheepala (1999)

UCUR Model 502 20 5 +45.0 to +134 N/A -48.0 to +66 Heeps and Mein (1973a) ARBM 502 20 78 8 to 26 N/A 0 to -2 Black and Aitken (1977) HSP 502 20 78 4 to 27 N/A 0 to 4 Black and Aitken (1977)

94 24 10 N/A N/A 0 to -120 Dayaratne (1996) DTM 15 N/A 3 -2 to +6 0.0 to +2.0 -2 to +2 Zech et al. (1994) WALLRUS 15 N/A 1 -28 +10 -30 Zech et al. (1994)

Key to Acronyms for Tables 2.4

Cat. Area (ha.) Catchment area in hectares

Imp. Impervious area as a percentage of total catchment area No of Eve. Number of storm events considered in study

N/A Not available or not applicable

The results of the study on level of accuracy of computer models showed a large variability, which does not permit any conclusions to be drawn. However, in general the time to peak has been modelled better than the peak and runoff volume. The routing parameters such as pipe roughness, gutter factors and pit capacity parameters affect the time to peak discharge, which suggests that the routing parameters had been estimated fairly accurately in those studies; these parameters in general have the least variability. The accuracy of time to peak discharge depends on the computational time step used in the analysis. If short time step is used, the accuracy will be more. The results also showed that the runoff peak and volume had larger errors, which suggests that the rainfall excess may

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not have been calculated correctly. The impervious and pervious area parameters such as depression storages, antecedent moisture content and soil curve number, affect the rainfall excess. These parameters in general have the highest variability. Therefore, the study on level accuracy suggests that it is necessary to estimate these impervious and pervious parameters accurately.

Table 2.5: Summary of Percentage Errors for Non-Calibrated Studies

% error Model Method Cat. Area (ha.) Imp. % No. of Eve.

Volume Time to peak Discharge

Peak Discharge

Reference

RRL 32 45 1 +18 +6 +21 Terstriep and Stall (1969) 1 100 10 N/A N/A -17 to +20 Terstriep and Stall (1969) 916 44 28 N/A N/A -27 to +17 Terstriep and Stall (1969) 5 45 2 -27 to -22 +4 to +19 -4 to +24 Papadakis and Preul (1972) 70 36 5 -51 to +103 N/A -9 to +87 Heeps and Mein (1975a) 70 36 16 N/A N/A -97 to +60 Aitken (1975)

5 No. N/A 271 N/A N/A +1 to +6 Aitken (1973) ILSAX 57 55 12 +83 to +414 N/A +33 to +156 Vale et al. (1986)

57 55 12 61 to 320 N/A 17 to 159 Vale et al. (1986) 5 45 1 -14 +25 -11 Papadakis and Preul (1972) 960 55 3 -48 to -22 -40 to +118 -38 to 0 Papadakis and Preul (1972)

70 36 5 +2 to +149 N/A +1 to +107 Heeps and Mein (1973a) Chicago 32 45 1 +36 -6 +21 Terstriep and Stall (1969) Method 5 45 1 +18 -4 +4 Papadakis and Preul (1972) UCUR 5 45 2 -27 to -11 -4 to +31 -7 to +4 Papadakis and Preul (1972) Model 960 55 3 -32 to +1 -18 to +4 -20 to +4 Papadakis and Preul (1972)

70 36 5 +39 to +249 N/A +19 to +203 Heeps and Mein (1973a) RFD 70 36 16 N/A N/A -131 to +56 Aitken (1975)

5 No. N/A 271 N/A N/A -21 to +19 Aitken (1975) Key to Acronyms for Tables 2.5

Cat. No. Catchment number Cat. Area (ha.) Catchment area in hectares

Imp. Impervious area as a percentage of total catchment area No of Eve. Number of storm events considered in study

N/A Not available or not applicable (quantity) no. Number of catchments considered

The inaccuracies in runoff peak and volume are higher for ungauged catchments compared to the gauged. Therefore, the review also highlights the necessity for guidelines or improved methods for the application of urban drainage models for ungauged catchments in simulating of peak discharge and runoff volume. Some studies in this review showed that the model error depends on storm characteristics and the land use conditions of catchments.