What s so hard about Stormwater Modelling? A Pugh 1 1 Wallingford Software Pty Ltd, ann.pugh@wallingfordsoftware.com Abstract A common misconception of stormwater modelling is that it is simple. While we seem to intuitively understand that rain water will flow away to the lowest point the physical processes are not always well understood or predictable. This paper will discuss the physical hydrologic and hydraulic processes taking place, and how computer models replicate these processes. As these processes can be very complex, it is also important to carefully consider the different types of computer model available. This paper will provide key points for users to consider when deciding on what level of modelling to undertake to achieve the desired outcomes. Introduction We are all familiar with the part of the water cycle that drainage modelling attempts to predict. When water falls from the sky and there is enough rainfall then puddles will form. If the rainfall continues then surface flow will commence, and in extreme events flooding will occur. Flooding is simply having too much water at one location, but sometimes the cause of flooding may not be obvious. The water may have travelled long distances to cause these floods. Therefore to model drainage systems we need to understand where the water is coming from, determine how much there is, and where it will go. Sounds simple enough, so what s so hard? Before we can successfully model a situation we need to have identified a problem, and decided that a model would be a useful tool to help develop a solution. Often the problem is not clearly defined: in the case of drainage modelling problems are typically identified by localised failures (i.e. flooding) which have occurred as a result of system wide conditions. It will be necessary to develop a solution that considers the technical, financial, environmental, social and political aspects. Ideally this can be achieved but not with one single model. Determining whether a solution was successful will be mean different things for the stakeholders. Fundamental model differences Our first step is to determine which model we are to create. Broadly speaking there are two types of models; process models and data models. Process models are what we as engineers tend to be familiar with. Rain falls on a catchment; the catchment has some characteristics that generate runoff; this flows down a conduit to an outfall. Data models are different. Outputs are generated from inputs without describing the intermediate steps i.e. outflow is a function of rainfall. Both types of models are useful and if used appropriately can deliver an appropriate solution. Figure 1 shows an example of a process model and a data model.
Figure 1: A process model and a data model The simplest approaches to drainage modelling have often involved considering the peak water level of a historical event. These simplistic data sets provide a report on how the catchment has behaved for specific events, and if data is available for a range of events can allow the development of a mathematical prediction model. This type of model will not be satisfactory when the catchment is changing, or it is necessary to know the timing of an event (such as a road being flooded). In these instances we need to develop a processed based model to provide the required flexibility. To create a process model we will need to determine our catchment and conditions. By catchment we need to consider the area on which rain falls; the ground topography, the type of surfaces, and any pipes etc that will convey the water. The conditions include the rainfall both intensity and duration, whether the catchment is wet or dry and if there are flows from elsewhere entering the catchment. In helping to understand the wide range of process models available it is important to consider how drainage modelling has evolved. The significant increases in computing power and available software have allowed models of with increased degrees of freedom to be developed.
The Rational Method The Rational Method is one of the simplest models and was developed to predict a peak flow for an area. The formula is one of the best known hydraulic equations: Q=0.278*CIA where Q is peak flow (m³/s), C is the runoff coefficient, I is the rainfall intensity (mm/hr) and A is the catchment area (km²). While being a simplistic approach with only three variables, this equation has already identified information to be sourced:-catchment size, rainfall intensity and the runoff coefficient. Catchment size is easy to determine, however rainfall intensity and the runoff coefficient are not as simple as may first be thought. The recommended method for determining C is model calibration to a historic event. It is also necessary to note that Australian Rainfall and Runoff (AR&R) observes the value of the runoff coefficient C varies widely from storm to storm on a given catchment. It is therefore important to consider which C factor will be used in the final model. The derivation of a runoff coefficient (or equivalent parameters) applies to all process models, although the methodology for developing a C factor where limited calibration data is available varies. Section 1.3.2 of AR&R contains important advice for anyone using the Rational Method. Rainfall intensities can be developed by following formulae provided in publications such as AR&R, and will depend on the location you are modelling. One limitation of the rational method is that it considers a single rainfall intensity over the whole catchment area. AR&R also highlights the inadequate manner in which the [rational] method considers physical factors such as the effects of temporary storage on the catchment, and temporal and spatial variations of rainfall intensity. If spatial rainfall is a concern it is possible to model several smaller connected catchments with different intensities, although now it will be necessary to consider how the flows are routed through the catchment. The simplest approach is simply to add the peak flows together. This will not consider any attenuation effects in the system and is not appropriate for complex systems. Unit Hydrographs AR&R defines a unit hydrograph as the hydrograph resulting from unit depth of surface runoff produced by a storm of uniform intensity and specified duration. Rather than give a single peak flow, this method allows the consideration of the variation in flow as the event progresses. Development of a unit hydrograph allows some consideration of the physical characteristics of the catchment under investigation such as baseflow and initial loss estimates. Baseflow is comprised of the elements of flow that typically have a longer lag or travel time, such as groundwater infiltration. A Unit Hydrograph study assumes: Catchment linearity; that there is a linear relationship between the input rainfall and the outflow hydrograph (interestingly AR&R observed that for flood events with an ARI greater
than 1.5 years this may be correct, but for smaller events a non linear runoff routing approach should be used); Catchment as a lumped system; that there is one single rainfall hyetograph evenly distributing rain over the catchment as a whole. As before, this limitation can be mitigated by creating smaller catchments and including a routing model. It is important to note that the unit hydrograph approach is usually not suitable for very large catchments, very small catchments, nor to urban catchments. As such it is important that while allowing more complex studies to be undertaken there are important assumptions that should be clearly understood before applying this method Routing models When we talk about routing models there are two main areas that need to be considered. Routing within a catchment can simply be considered using a time of concentration to delay the onset of the rainfall response, but this may not adequately represent a particular catchment. More complex methods such as single linear, single non-linear and double linear routing can be adopted. For example, a single linear method the surface runoff flow flows into an imaginary reservoir, which has a defined routing coefficient depending on the catchment characteristics, such as area, slope, impermeable areas, catchment length. The effect of this reservoir is that the inflow is stored and released at a later timestep, and at a reduced peak flow, and that this relationship is linear in nature. A double linear would have the outflow from the first imaginary reservoir entering a second reservoir before flowing from the catchment. Flow is also routed within the modelled assets, such as pipes and channels. A Energy Grade Line (EGL) analysis should be undertaken to determine the Hydraulic Grade Line (HGL) as shown in Figure 2. An EGL analysis is undertaken by using the energy equation and commences at the downstream end of system. Headlosses due to structures such as culverts and friction head are added to determine the energy line at the upstream end of the pipe and then the velocity head is subtracted to find the HGL, or water level, in the system. Figure 2: Hydraulic Grade Line Output Calibration and Verification Events When building a model of a drainage system it is very important to have historic events (ideally both rainfall and flooding) with which to check the model results. The level of detail available for these events will affect the confidence that can be applied to the model results.
It may be that there is detailed telemetry data available for both rainfall and flows, but this is unusual for drainage systems. It is far more common to have a single daily rainfall figure and top water level. Historical events are critical in creating a validated model that is capable of providing meaningful results. It is important to note that there is a key difference between model results from actual rainfall and model results from a design storm. Results obtained from design storm simulations will have a defined average recurrence interval (ARI), whereas actual rainfall events will only have an approximated ARI. Design Rainfall Events A design flood is a probabilistic or statistical estimate and is generally based on some form of probability analysis of flood or rainfall data. For the design situation, the antecedent conditions are unknown and must be assumed, often implicitly in the design values that are to be adopted. It will come as no surprise that the estimation of design rainfall to be applied on the model is another critical factor in predicting a response in the system. There are currently three different approaches for determining the input rainfall, and it is important to understand the differences in these. Deterministic (Single Event) As has already been mentioned there are well documented equations available for developing design storms with a defined Average Recurrence Interval (ARI) and duration. These equations consider the likelihood of an event and aim to provide an event of known statistical frequency. Thus a solution can be developed that performs satisfactorily for a specific ARI and this level of service can be regulated and applied across different organisations. It is important to not only consider, but also understand, the effects of the choice of initial conditions. As the rainfall is a mathematical construct and not a real event there is no information available as to whether the catchment is wet or dry at the commencement of the storm and whether storages are empty, full or somewhere in between. It is necessary for the modeller to clarify the position of these as this can have a significant effect on the system. Comprehensive (Continuous Simulations) In a continuous simulation a rainfall time series is used and the model s variables change throughout the simulation. Choice of a historic time series or generation of a synthetic series is very important as it is necessary to ensure that the series is representative of the situation to be modelled. For instance choosing a two year time series of rainfall may not be appropriate given we in Australia have a strong four to seven year El Nino cycle. Typically a larger period of time say 30 years is chosen to avoid these smaller climactic effects. Figure 3 shows a 30 year rolling average rainfall for Melbourne and demonstrates how the choice of time series can have a significant effect.
Figure 3: Melbourne Rainfall In the Melbourne scenario a wet 30 year period could have up to 12% more rainfall than a dry period. It is also important to consider whether the period included a few large events or was generally wetter. Also it is worth noting that the period with the highest 30 year average rainfall includes the driest recorded rainfall year. While providing a large set of results for analysis this type of analysis does require good quality data, and a lot of computer power as 30 years of data at 6 minute intervals gives a rainfall record with 2,629,800 entries! Computer models can incorporate parameters that change with time, and if the model is to show a real 30 years it will also be important to consider how the model catchments (runoff changes due to development) and assets (decreased pipe conveyance due to increased roughness or sedimentation) will change over this period. Alternately, time series data can be applied to a snapshot model, to increase confidence in the model s results by providing a larger data set. It is very important to understand the differences in these two approaches. Probabilistic (Monte Carlo Simulations) The probabilistic methods, such as Monte Carlo simulations, use historic information to generate mathematical models that can be used to predict data. These models can be used to generate synthetic rainfall records to apply to process models. As these models are mathematically based it is possible to generate many different probable rainfall scenarios. It is important to note that the new release of AR&R will have an increased focus on Monte Carlo Simulation and its uses. The Monte Carlo approach is often used with continuous simulation and can avoid some of the major assumptions required when using deterministic methods. Genetic Algorithms As with probabilistic simulations the increase in computing power and sophistication has allowed more consideration of more scenarios. Genetic algorithms while commonplace in pressurised water reticulation modelling are currently not widely used in gravity systems.
The main limitation is due to simulation times (gravity models tend to have significantly longer run times than pressure models). Dynamic or Steady State models? Steady state models consider the system at a snapshot and simply work from the upstream end of the system adding flows as the model considers different pipes. Obviously this can lead to errors, particularly when storage is an issue within the system as the model has no way of filling or emptying as there is no true comparison of different timesteps. For the uninitiated however, the replay of results from these steady state models can incorrectly imply that these models are able to consider these system effects. Dynamic models do fully solve the St Venant equations and undertake an iterative approach to solve the backwater equations. These models are able to consider networks with dynamic storage issues (such as detention basins, offline storage, pumped networks and flat systems). Multi dimensional models It can appear that the more dimensions a model considers the better the results will be but this is not always the case. To quickly summarise a very large topic a one dimensional (1D) model will consider flow in one dimension. This is justified and accepted for urban underground systems where flow can only occur in one direction along the pipe. Two dimensional (2D) models provide a framework where momentum is conserved in two dimensions and are suited to applications where flow paths are hard to determine or where point velocities are required. Three dimensional (3D) models conserve momentum in three dimensions. This detailed modelling is very useful in instances such as tidal intrusions where saline content will vary with depth and flows at the top of the river and the bottom may be different. More dimensions in a model will require more data and more equations, hence longer runtimes (or smaller catchment studies) and usually more cost. It is also very important to consider how these models are to be calibrated. It seems that the best solution will be nested models, where smaller pockets of 2D (or 3D) analysis will be included within a larger 1D model.
Other Modelling Considerations So far we have discussed many of the key elements of drainage modelling. There are however many other aspects which should be considered when selecting a method, or tool to use. If your rainfall is actually snow you will need to have a model that considers the accumulation and melting of snow on the catchment. If you have flows from sources other than rainfall, i.e. groundwater infiltration from high water table or tidal influences your mode will need a module that can consider this. Likewise evaporation effects may need to be included. More complicated structures such as culverts (and the different control regimes), bridges, pump stations, detention basins, roadside pits and sustainable urban drainage structures (SUDS) can all be considered within the model, and can have significant effects on estimated and observed flood levels. Conclusions In conclusion drainage modelling is not straightforward. While we all know what happens when it rains there are lots of areas where we are unable to completely describe the physical processes occurring in a form that is suitable for computer calculations. However there are many excellent tools available for anyone wishing to undertake a drainage study. It should be appreciated that these tools are very different and an inappropriate choice can lead to devastating consequences. The use of statistics and sensitivity analysis should not be overlooked as these additional studies can aid understanding and confidence in model results. And finally it Is very important to calibrate and validate any model whether it be process or data driven, dynamic or steady, 1D, 2D or 3D. References and further reading Hill, P and Mein, R and Siriwardena, L. (1998), How much rainfall becomes runoff? CRC for Catchment Hydrology, Report 98/5 Nathan, R. and Wienmann, E (2005), Presentation given at the November 2005 Workshop on the AR&R re-write, Book III Chapter 4 Monte Carlo Simulation. http://www.eng.newcastle.edu.au/~ncwe/ncwearr/nov%202005%20workshop/arr%20 Nov%202005_Book3_Chapter4_%20MonteCarlo.pdf van Waveren, R.H et al (1999), Good Modelling Practice Handbook, Aquest Bureau of Meteorology, Monthly Data for Melbourne Regional Office, Bureau of Meteorology Wallingford Software Ltd, InfoWorks CS version 8 Online Help, Wallingford Software Ltd Institution of Engineers Australia, Australian Rainfall and Runoff Volumes 1 and 2, (2003), Engineers Australia