Drainage models attempt to predict that part of the water cycle that involves rainfall and its consequences, including potential flooding. Although flooding is, at its simplest, just an excess of water in one location, the causes may not always be obvious.
Water may travel long distances to cause floods, so to adequately model drainage systems it is necessary to understand the origins of the water, to determine the quantities involved and where it will go.
To successfully model any situation, the problem needs to have been identified and a decision made regarding the type of model would be useful in developing a solution. Often problems are not clearly defined; in drainage modeling problems are typically identified by system failures. It is not uncommon for the failure location, that is the flooding, to be some distance from the cause of the failure.
Whether or not a solution is deemed to be successful will depend on the viewpoint of the various stakeholders. Developing a solution will involve considering the technical, financial, environmental, social and political aspects, which cannot be achieved together in one model.
Fundamental model differences
The first step is to determine the type of model to be created. Broadly, there are two types: process models and data models. Process models are familiar to engineers as these models aim to explicity describe the processes occurring. In these models outflow is calculated by mathematically modeling the rainfall, loss, conveyance and routing processes in the catchment.
Data models are different; outputs are generated from inputs without describing the intermediate steps – that is, the outflow is seen as a function of rainfall. Both types of model are valuable and, if used appropriately, can deliver suitable solutions.
The simplest approaches to drainage modeling have often considered the peak water level of a historical event. Such simplistic datasets provide a report on how the catchment has behaved during specific events. If data is available for a series of events, a mathematical prediction model can be developed. This type of model is not sufficient when the catchment is changing or if there is a need to know the timing of an event such as a road being flooded.
In understanding the wide range of process models available, it is helpful to know how they evolved. As computers and software have both become increasingly sophisticated, it has been possible to create more complex models.
The Rational Method
This was one of the simplest models, developed to predict peak flows. The formula is a well-known hydraulic equation with just three variables: peak flow, runoff coefficient and rainfall intensity, with the other factor being the catchment area.
One limitation of the approach is that it uses a single rainfall intensity across the entire catchment area. It is also considered that this method does not adequately deal with physical factors such as the effects of temporary storage on the catchment. The simplest approach for considering flows along a reach or in a catchment, is to add peak flows together which does not consider any attenuation effects in the system, and is not appropriate for complex systems.
Unit hydrographs introduce time as another variable. While allowing more complex studies, there are important assumptions that limit their application.
For instance, a unit hydrograph study assumes a linear relationship between input rainfall and the outflow hydrograph, and that there is an even distribution of rain across the catchment. This can be mitigated by creating smaller catchments and including a routing model.
Routing within a catchment can be simply considered by using a time of concentration to delay the onset of the rainfall response, though this may not adequately represent a particular catchment. More complex methods such as single linear, single non-linear and double linear routing can be used.
In the single linear method the flow is routed using an imaginary reservoir, whose routing coefficient depends on the sub-catchment area, ground slope, impermeable areas, catchment length, storm duration and storm depth. Flow is also routed within the modeled assets such as pipes and channels. A hydraulic grade line analysis of the system should be undertaken as this will include roughness and slope, and head losses due to structures such as culverts.
Calibration and verification events
When building a drainage system model, it is critical to have historical events - ideally both rainfall and flooding - against which the model results can be validated. The level of detail available will affect the confidence that can be applied to the model results. It is unusual to have detailed telemetry data for both rainfall and flows: more often a single daily rainfall figure and top water level will be available.
There is a key difference between model results from actual rainfall and from a design storm: 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, generally based on some form of probability analysis of flood or rainfall data. For the design, the antecedent conditions are unknown and must be assumed, often implicitly, in the design values to be used.
Unsurprisingly, estimating design rainfall to be applied to the model is a critical factor in predicting the system’s response. There are currently three different approaches to determining input rainfall, as described below.
Deterministic (single event)
As mentioned above, there are documented processes for developing design storms with a defined ARI and duration. These consider the likelihood of an event and aim to provide an event of a known statistical frequency, developing a solution that works satisfactorily for a specific ARI.
Considering and understanding the effects of the choice of initial conditions is important. As the rainfall is a mathematical construct, there is no information about pre-existing conditions such as whether the catchment was wet or dry, or whether storage systems were empty, full or in between. The modeler must clarify the situation, as these conditions can have a significant effect on the system.
Comprehensive (continuous simulation)
In a continuous simulation, a rainfall time series is used and the variables change throughout the simulation. Choice of a historic time series or generation of a synthetic series is very important as the series must be representative of the situation to be modeled.
For instance, a two-year time series might not be appropriate in Australia, where there is a strong four to seven-year El Nino cycle. A longer period, such as 30 years, is typically chosen to avoid such smaller climatic effects. But, taking the city of Melbourne in Australia as an example, it is possible for a ‘wet’ 30 year period to have up to 12% more rainfall than a ‘dry’ 30 year period. It is also important to consider whether the period experienced a few large rainfall events or was generally wetter.
While providing a large set of results, this type of analysis needs good quality data and a great deal of computer power – 30 years of data at six-minute intervals equates to 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 is important to consider how catchments and assets change over the period. Alternatively time series data can be applied to a ‘snapshot’ model, to increase confidence in the results by providing a larger data set – it is very important to understand the differences between these two approaches.
Probabilistic (Monte Carlo simulations)
Probabilistic methods like Monte Carlo simulations use historic information to generate mathematical models that can be used to predict data. These models can generate synthetic rainfall records to apply to process models. As they are mathematically based, it is possible to generate many different probable rainfall scenarios.
The Monte Carlo approach is often used with continuous simulation and can eliminate some of the main assumptions required for deterministic methods.
Genetic algorithms, while commonplace in pressurised water reticulation modeling, are currently not widely used in gravity systems. The main limitation is the simulation times – gravity models tend to have significantly longer run times than pressure models. As computers continue to improve this tool will become more accessible to drainage modellers.
Dynamic or steady state models?
Steady state models consider the system as a snapshot and work from its upstream end, adding flows as the model considers different pipes. This can lead to errors, particularly when storage within the system is an issue, as the model has no way of simulating filling or emptying storage as there is no true comparison of different timesteps. Superficially, replaying results from such models can incorrectly imply that they are able to consider these system effects.
Dynamic models fully solve the St Venant equations and take an iterative approach to solving backwater equations. These models can consider networks with dynamic storage issues such as detention basins, offline storage, pumped networks and flat systems. InfoWorks SD contains a fully dynamic solver to accurately model storm water systems.
It can appear that the more dimensions a model considers, the better the results, but this is not always true. A 1D model will consider flow in one dimension, which is justified and accepted for urban underground systems where flow can only occur in one direction.
2D models provide a framework where momentum is conserved in two dimensions. They are suited to applications where flow paths are hard to determine or where point velocities are required.
3D models conserve momentum in three dimensions. This detailed type of modeling is very useful for cases such as tidal intrusions, where saline content will vary with depth and the flows at the top and bottom of a river may be different.
More dimensions equals more data and more equations, and therefore longer runtimes or smaller catchment studies, and usually more cost. It is also important to consider how such models are to be calibrated. The best solution appears to be nested models, where smaller pockets of 2D or 3D analysis are included within a larger 1D model.
Other modeling considerations
Many other aspects need to be considered when selecting a method or tool to use. If snow, rather than rainfall, is to be modeled, it will be necessary to choose a model that considers the accumulation and melting of snow on the catchment. If there are flows from sources other than rainfall – such as groundwater infiltration – there would have to be a model that could consider this.
Complex structures such as culverts and the different control regimes, bridges, pump stations, detention basins and sustainable urban drainage structures (SUDS) can all be considered in the model, and can significantly affect estimated and observed flood levels.
Drainage modeling is not straightforward – while the physical processes involved in rainfall are well-known, there are many areas where they cannot be completely described in a form suitable for computer calculations.
However, there are many excellent tools available for anyone wishing to undertake a drainage study. These are very different, and an inappropriate choice can lead to devastating consequences. The use of statistics and sensitivity analysis should not be overlooked, as such additional studies can aid understanding and confidence in model results.
Finally, it is very important to calibrate and validate any model, whether process or data driven, dynamic or steady, 1D, 2D or 3D.