Degree Name

Doctor of Philosophy


Department of Civil and Mining Engineering


Among many consequences of urbanisation, frequent flooding is outstanding as the most common problem resulting from land use change. To discharge surface runoff from cities the Rational method was introduced as one of the first formulas to design drainage pipes/waterways. In the beginning the formula was applied as a deterministic model according to the few available records of rainfall events, however later when recorded data was more commonly available the application changed to a statistical method. After more than a century from the introduction of the Rational method by Mulvaney, this formula still is the centre of attention among practitioners. Despite the simplicity of its application the dilemma of its parameters is still outstanding. The Runoff Coefficient and the Time of Concentration are two ill-defined parameters of the formula which question its accuracy. However, as a design tool in urban stormwater drainage the Rational method is still most commonly used.

In the last two decades the deterministic models received more attention than simple formulas because of the availability of digital computers. Many urban hydrology/hydraulic computer models have been developed and applied on urban catchments to evaluate their drainage network's performance and efficiency. The basic requirement of these models is observed data for calibration of their parameters which has always been an obstacle in their wide application by urban drainage designers. In the early stages the development of deterministic models was intended to obtain a design tool to replace simple methods like the Rational formula. However, the majority of applications of these models has been evaluation and performance of the existing systems since their introduction to the industry.

The present study aims to establish a relation between deterministic and statistical interpretations of the Rational method to achieve more accurate design flood peak regarding land classification of urban catchments. The study follows specifically three broad objectives of flood peak estimation; using the Rational formula, hydrograph simulation using MOUSE model, and design flood estimation using both temporal patterns and design rainfall. The study determines whether the application of a deterministic model such as MOUSE along with design rainfalls and temporal patterns from ARR 87 Vol. 2 can produce similar results to frequency analysis of flood peaks. To achieve more insights into the proportion of rainfall which transforms to runoff, the main theme of the study concentrates on the runoff coefficient, which runs through the thesis from both deterministic and statistical points of view.

Both deterministic and statistical evaluation were carried out on the runoff coefficient the Rational formula. The parameters of the formula: including the time of concentration, Tc, and runoff coefficient were studied using observed rainfall-runoff data for five urban catchments in Sydney.

Values of Tc for the catchments were estimated using three methods including flow velocity, typical minimum time of rise, and lag time. Time of rise in the urban catchments was found to be dependent on rainfall temporal pattern, so it is not a good indicator of Tc. On the other hand, lag times for both impervious and combined events were found to be independent of flood size which shows the stability of Tc in the urban catchments. Regarding these results, the velocity method proposed in Australian Rainfall and Runoff 1987, ARR87, can give reasonable estimates of Tc in ungauged urban catchments.

The rate runoff coefficient was selected as a suitable surrogate for all the effective abstractions from rainfall to produce the flood peak. This coefficient was calculated using recorded values of average rainfall intensities and flood peaks. The average rainfall intensity was calculated during the bursts and also during the Tc of the catchment.

The integration of deterministic values with statistical values was performed by relating the average observed values of runoff coefficient during the catchment's times of concentration and 2-yr return period runoff coefficient from ARR87. It was concluded that ARR 87 estimates for 2-yr return period are correlated very well with the observed values with a coefficient of determination of 0.85. The integration of deterministic values of runoff coefficients with a statistical method can be useful because it incorporates the effects of both soil type and time of concentration of catchments in the statistical method of ARR87.

Besides deterministic evaluation, runoff coefficient was studied from the view point of statistics using partial duration series of flood peaks as well. Log Pearson Type III was fitted to the partial duration series of flood peaks and for return periods of 1.2.5 and 10 years flood peaks were calculated using the distribution. Design rainfalls were scaled off the IFD curves resulting from ARR87 partial duration series of design rainfall for the catchments time of concentration.

For different return periods, it was concluded that statistical runoff coefficient remains constant in the catchments with light soils and has an increasing trend in the catchments with heavy soils.

Generally speaking ARR87 overestimates runoff coefficient. However, for catchments with light soil type the overestimate is higher than that in the catchments with heavy soil type. On average, the magnitude of overestimation is 84 % and 31 % for catchments with light and heavy soil types respectively. Comparison of deterministic runoff coefficient with statistical showed that in catchments with light soils estimation of flood peaks with return period up to 10 years can be performed considering only impervious area of catchments. In catchments with medium soils only 1-yr flow can be assumed to generate from impervious areas and for higher return periods the incorporation of pervious areas is necessary. Both pervious and impervious areas should be considered for flood computation of 1 year return period and higher in catchments with heavy soil type.

Regarding complex models, the MOUSE model from Danish Hydraulics Institute was calibrated for four catchments on impervious area runoff events. Three indices were considered for calibration of the model including: volume, flood peak and time to peak. Volume and flood peak were simulated by adjustment of the Hydrological Reduction Factor, HRF , while for time to peak, the Manning roughness coefficient was adjusted. In this part of the study the coefficients of determination denote that at least 94 % of the runoff volume variations could be explained by the model. The closeness of the simulated and the observed time to peak of hydrographs shows that the magnitude of the Manning's roughness coefficient is reflected correctly by the model.

Combined runoff from both pervious and impervious areas is important in Australian urban catchments and should be considered in network design .and stormwater management. Generally, simulation of combined runoff events in the MOUSE model is performed using Level B Module. In this module excess rainfall is calculated by a water balance equation which incorporates infiltration equation, evaporation and storage data. The excess rainfall is transformed to a hydrograph at each subcatchment outlet by using Kinematic wave equation. The MOUSE model at this level averages the effects of pervious and impervious areas of each subcatchment, however these areas have different responses in producing runoff. Besides the combination of pervious and impervious areas, the process of rainfall excess is very data intensive and the involved parameters have interactions which makes the calibration time consuming and unstable. Because of interactions, the magnitudes of the calibrated parameters have no physical interpretation.

The MOUSE model was modified (MMOUSE) for excess rainfall calculation, and separated storages for impervious and pervious areas. T o convey the separated pervious area runoff to the catchment drainage system a fictitious conduit and a dumm y manhole were added to the catchment drainage system at the outlet of each subcatchment. The beginning of this conduit is the dummy manhole and the ending is the real manhole.

In MMOUSE the excess rainfall of pervious areas is calculated according to the concept of the runoff coefficient for pervious areas and different initial losses for pervious and impervious areas. In this method runoff is calculated from two parallel storages of impervious and pervious areas separately and is added at manholes. The delay between response time of pervious and impervious areas is considered by different times of concentration for them.

Despite using only one parameter to calibrate runoff model, the MMOUSE indicated better results for flood peak and volume compared with the original model (MOUSE). With the proposed method there is a rninimum interaction between parameters and the calibration process is very time efficient. This method gives the practitioners the opportunity to use a complex model like MOUSE and a simple concept like runoff coefficient in urban drainage practice. Using this method the model can be calibrated on a few observed events and be applied in design situation.

The proposed method was tested on two catchments where combined runoff was frequently observed. The results for flood peak simulation were satisfactory. Time to peak and overall hydrograph shape were simulated very well.

Using the runoff volume resulting from simulation of impervious areas of the catchments, and the observed total runoff, runoff from pervious areas of the catchments was calculated. On average the ratio of pervious areas runoff to total runoff in two catchments with clay soil type was calculated equal to 37 % . This fact should be useful in water quality and sediment transport studies in Australian urban areas with heavy soil type.

The pervious area runoff coefficient was investigated in relation to rainfall depth, rainfall intensity and sum of rainfall for five days before the occurrence of the event (P5) which is an index of API. N o significant correlation was found between the pervious area runoff coefficient and rainfall depth or intensity or P5. When sum of the P5 and event rainfall was used as API, the correlation coefficient changed very significantly for one catchment while for the other it did not change at all.

The HRF of the pervious area (HRFPER), calibrated by the MMOUSE, was studied in relation to the pervious area runoff coefficient. They are just slightly different ways of expressing the same concepts. Runoff coefficient was calculated based on the ratio of pervious runoff to total catchment area, but HRFPER was calculated by the ratio of pervious runoff to the pervious area of the catchment.

Deterministic simulation of design flood peaks using both design rainfalls and temporal patterns was accomplished using both MOU E and the MMOUSE in four catchments. Design rainfalls were considered during the time of concentration of catchments and were distributed over the time using temporal patterns from ARR87 Vol. 2. For simulation of design floods in the catchments with light soil type MOUSE Level-A was used while for the heavy soil type catchments MMOUSE which incorporates pervious areas runoff coefficient was used. The median values of Hydrologic Reduction Factor for pervious areas (HRFPER) of the catchments were used for design excess rainfall calculations.

Comparison of the ratios of 10 and 5 years flood to 2 years flood for three methods of ARR87, MMOUSE and frequency analysis showed that the frequency analysis and the MMOUSE results are close together and different from those of ARR87. It is concluded that deterministic simulation of design floods (MMOUSE + Design Rainfall + Temporal Patterns) can produce similar/related values as frequency analysis of flood peaks. However, the results of deterministic simulation were generally overestimated compared with those of frequency analysis. Apart from the different basis of two methods, deterministic for MMOUSE and statistical for frequency analysis, the reasons for overestimation of deterministic simulation can be either high value of HRFPER or inappropriate temporal patterns. Using MMOUSE two other HRFPER values were examined to obtain closer design floods to the frequency analysis. It was concluded that in MMOUSE when HRFPER equals zero the resulting design flood magnitudes approach the frequency analysis results. In other words, assuming both correctness and representativeness of the currently available temporal patterns, in deterministic simulation of design flood ,up to 10 years return period, the incorporation of pervious areas is not required, however, for runoff volume simulation they should be considered.

The results of this study should be useful for both water quantity and quality investigations. Rate runoff coefficient should be used along with the Rational method for stormwater flood peak estimation. Volumetric runoff coefficient should be used for estimation of runoff volume in conjunction with MMOUSE model for impervious and pervious areas of urban catchments.