So you want to calculate flood risk. But how will you choose what flood events to model for this? In this article you’ll learn about choosing several flood events that, together, best characterise flood risk in a region.

To do this, I will first go through why we would model a flood to calculate risk. Then, we will think about what makes different flood events, well, different. From this, we will discover that it is important to simulate many different flood events. Finally, I will develop guiding principles for selecting flood events to model

# Why should we simulate floods for risk assessment?

Imagine that we are in a time before the 1980s. What would you do if asked to assess flood risk?

You may not have a computer available. If you did, it would not handle your case study in 2D using a high-resolution DEM and flood code. Your best approach may be to go back into the historical record. You could ask yourself, *what is the largest flood that has occurred so far*? And, *what would happen if this same flood occurred again*?

**There is a limitation with this approach**. Every flood is different. Future floods are likely to be different from those that have happened before. This becomes more important when you consider how our climate and catchments are changing.

And, as we explored in my previous post, we should be taking a broader look at flood risk. We should consider the range of flood events that *could* happen when assessing risk.

That’s the advantage of modelling. We can simulate many floods that could happen. The floods we simulate should range from very small to very large events. This way, we gain a richer understanding of flood risk in our regions.

**But how do we choose which flood events to model?** Given every flood is different, we could model an unlimited number of flood events. We cannot model them all. We need to find a small set of flood events that best represent *all* the flood events that could occur.

# Understanding the types of flood events that occur

Floods can be large, and they can be small. They can go on for a long time, or they can be very quick. One flood event can be small in one area, and large in another; slow in one part, and fast in another.

Typical flood modelling reports analyse four or so different events in Australia. Typically, something like the 1-in-20, 1-in-50, 1-in-100 events, and something above this, perhaps the 1-in-200 or 500-year event.

**But what do these numbers mean**, and why were these particular events chosen? And even then, who decided what the 1-in-x year event would look like, anyway?

The phrase ‘1-in-x-year event’ indicates how often you might expect a flood that exceeds a certain size. That is the ‘average recurrence interval”. And this is the general principle: Large floods occur infrequently, while small floods occur often. That is why the 1-in-100 year flood is much larger than the 1-in-20 year flood.

When we speak of a 1-in-x year flood, we are not saying that a flood of this sizes occurs at a regular interval. This figure is just the *long-term average* waiting period between two flood events that exceed this level of flooding. We call this the average recurrence interval (ARI).

To give you an example, it is not unexpected to have multiple 1-in-100 year events within a 100 year period. For example, there is a 37% probability of having two 1-in-100 year events within a 100-year period. There is about the same probability of only having one 100-year event in the same period. This is double the probability of having three 1-in-100 year events within the same period.

Unfortunately, many perceive the 1-in-x year language to imply a regular interval between flood events. Thus, contemporary Australian guidelines express the frequency of floods using the annual exceedance probability (AEP). This gives the probability that a flood of a certain size will be exceeded in any given year.

What’s the probability that the largest flood in a location will exceed the 1-in-100-year level this year? Well, it’s 1%. There is a 4.9% chance that the largest flood in a location will exceed the 1-in-20-year event.

Annual exceedance probabilities can be estimated from the ARI, but the 50% AEP does not correspond to the 2-year ARI event. This is because the AEP gives information about the *probability* of the largest flood in any given year, while the ARI gives information about the* average time between* flood events. The time between flood events can contain fractions of a year.

In any given year with a large event, there is likely to be small events, also. This means that the time between smaller events is more frequent than the time between ‘small’ events that also happened to be the largest event that occurred in a year.

So, AEPs are calculated from ARIs by modelling the inter-arrival time of floods exceeding a particular size, using a Poisson process. From this, the probability that a flood with a certain magnitude is exceeded in a given time-frame, t, is given by the relationship:

Where:

Pex is the probability of exceedance within a time period, t; and

ARI is the average recurrence interval statistic for this flood magnitude.

Therefore, the AEP is given by:

## Choosing which flood events to model

As I stated earlier, flooding is typically assessed by simulating events across several different AEPs.

The reason that the 1-in-20, 50, 100 (etc) floods are chosen is twofold. First, design rainfalls are available at these ARIs. Second, they cover a broad range of different flood magnitudes.

However, selecting flood events requires a more sophisticated means. This is because the errors we have in calculating risk are both:

- sensitive to the number of events we model,
- governed by the choice of events we model.

# Calculating flood risk

Risk is often defined as long-term average loss. You can think of it like this:

- Develop a time series of annual flood losses over a very long-time frame. Let’s say 1000 years (though, the longer the time period, the more accurate the calculation)
- Sum these losses across each year; then
- Divide these losses by the 1000 years they were summed across.

this gives you the expectation of annual loss.

## How risk is calculated

We typically calculate risk as the area under the curve relating loss/damage (d) to annual exceedance probability, p(d). An example of this curve is shown in the figure below.

To calculate the area under the curve, we simulate several flood events, and estimate the AEP and losses associated with each of these.

Because we do not model all the events that result in loss, we do not know the exact shape of the p-d curve. We usually only model a few flood events due to the data requirements and computational costs of modelling. So, we only know about five-or-so points on the curve, and usually estimate the area using the trapezoidal rule.

And so, large errors in the computation of risk can result from a poor selection of the events that you model. You can see this in the figure below:

As shown in a 2011 paper by Peter Ward, the final risk value calculated using this method is highly sensitive to the selection of flood events. This is not just the number of events that are modelled, but the specific events that are modelled (i.e. their AEPs). Peter and his coauthors found that over-estimations of risk between 33% and 100% occurred when only three events were modelled, and that assumptions on defense failure or overtopping can have a large effect on risk calculations.

# What to think about when choosing events to model

When choosing what events to model, it is important to consider the characteristics of the p-d curve. In particular:

- the point at which losses begin
- locations on the curve where there are large increases in damage for only small changes in AEP; and
- times where the inclusion of more large-magnitude events results in marginal increases in calculated flood risk.

There usually is a point in the curve where losses start to occur. Floods with sizes below this point are sufficiently small that no flooding occurs. For example, our stormwater systems are designed to cope with a certain magnitude event. Thus, there should be minimal flooding when rainfall is below this design criterion. For many of our creek systems in Adelaide, the indicative level of protection is approximately the 1-in-20-year event.

It is important to include a flood event at the point where flood losses begin to occur. Including events with AEPs higher than this will not improve our risk estimate much. This is because negligible losses occur for flood events with higher AEP.

Now, there will also often be regions of the p-d curve where there are large increases in loss for only a small change in AEP. These can occur when levees fail or are overtopped, or when flood storage levels in a reservoir are exceeded. It is important to include flood events that straddle these regions of the curve. Doing so will ensure that our piece-wise, linear approximation captures the shape of the p-d curve.

Finally, risk estimates usually do not improve with the inclusion of extra-low AEP events. For example, let’s say that your risk analysis includes the 1-in-1000 year flood. There may be little improvement in risk estimates by extending your analysis to include the 1-in-2000 year flood as well. If the additional damage between the 1-in-1000 and 1-in-2000-year flood is relatively small, then the additional area captured by including the 1-in-2000-year event is also small. This is because the difference in AEP between these two events is also very small (0.05%).

In other words, the additional contribution to area under the p-d curve is marginal as ARI becomes large, especially if the damage does not increase at a fast rate as AEP approaches zero. By locating where this occurs on the p-d curve, that point becomes the highest magnitude event modelled for the calculation of risk.

This way, we can strategically select flood events that best characterise flood risk. By doing this, we improve the accuracy of our calculated values of risk.

## Choosing flood events to model requires variation in location, time, and risk mitigation

The p-d curve is not static, but varies with location, changes over time, and is dependent on what mitigation is implemented. So these aspects also need to be considered when selecting events to model.

### Spatial variability

The flood event that causes a specific AEP of damage is not the same everywhere in a catchment. This is not a significant issue for small regions, but can be very significant for studies over large geographic areas.

For example, in parts of catchments with low levels of detention where the catchment responds quickly, more damage occurs in shorter, high-intensity rainfall events. In these cases, the peak of the hydrograph is more important in capturing damage, than is the total amount of flood volume.

However, in other parts, it’s the long duration but less intense rainfall events that cause most flooding. In these cases, the overall volume of flood water is more important in capturing damage.

So, the p-d curve needs to be characterised for each part of the case study region. Thus, the flood events that best capture the shape of the curve need to be chosen separately for each region.

### Temporal nonstationarity

Climate change is changing the nature of floods. Therefore, it is also important to calculate risk not just now, but into the future. We need to calculate time series of risk values into the future (and potentially converted into their present value).

A warming climate is expected to increase the flood magnitude for a particular AEP. This is because a warmer climate intensifies the water cycle, resulting in a general increase in the frequency and severity of rainfall events. However, it should also be noted that climate change affects other hydrological processes beyond precipitation. The combined effect of all these processes on flood risk is complex, and so the effect of climate change should be assessed on a case-by-case basis.

Consequently, changes in climate will affect the shape of the p-d curve. This means that different flood events may need to be used to accurately assess future risk values.

### The impact of mitigation

Mitigation will change the shape of the p-d curve as well. You can see this in the figure below. So, selecting the set of events to use for each combination of mitigation options should also be considered separately.

# How to select events to model

First, we need to think about how accurate our risk assessment needs to be. For example, a higher accuracy in risk calculation may be required when:

- Our mitigation cost-benefit ratios are marginal
- We are comparing alternative mitigation portfolios that have similar risk reduction potential
- We are delineating land use planning zones for development status.

It is extremely difficult to accurately develop the relationship between different flood events and their AEP, especially for case study regions that have no or limited historical flow records. This is because

- Flood hydrology is related to more than just snowmelt and rainfall, but also to other catchment conditions such as soil wetness, the local climate, and land cover;
- The drivers of flooding, such as those identified in (1) above, have complex and interacting seasonal patterns which vary from year-to-year; and
- Multiple rain events can coalesce into one flood event.

To take into account these difficulties, a model-based approach to estimating AEP of floods and/or damages is best. In this approach, the long-term simulation of catchment hydrology is conducted. This uses weather and rainfall-runoff models to capture the highly variable and complex processes that affect the size of a flood. Results from these models are then used to develop flood frequency diagrams.

The problem with the above approach is the computational time needed for long-term simulation. Recent work in our school has found ways of speeding up this calculation by up to 1000 times, using a hybrid causative event framework[1],[2].

Once the relationships between the drivers of flooding are known, simplified, fast-running flood hydraulic models can be used to characterise the nature of the p-d curve across a large number of flood events drawn from the results of the hydrological modelling. One could even explore the possibility of extending the hybrid causative event framework developed in [1],[2] estimate the p-d curve directly by bolting on these fast running hydraulic models, although computational cost may prevent this.

Once the shape of the p-d curve has been estimated, higher accuracy (but slower-running) models can be run for the critical events identified on the p-d curve to calculate risk. The results of these more accurate simulations could even be used to correct the results from the faster running model as well.

# 9 Guiding principles for selecting flood events for risk assessment

- Consider a range of different AEPs, from small, frequently occurring flood magnitudes to large, infrequent flood magnitudes.Messner et al 2007[3] recommend that at least three, and preferably six, flood return periods be used. The Multi-Coloured Handbook recommends at least five floods. While Ward et al[4] demonstrate that even with six optimally chosen flood events, the calculation of risk is overestimated by about 21%.
- Know your catchment well to understand the nature of the p-d curve.
- It is desirable to estimate the point on the p-d curve at which flood-damages begin, and to include a flood event with an AEP at this point.
- Include some higher AEP events for which flood damages occur. For example, as the 1 in ten year flood has an AEP of 0.095, although the loss may be small, the return interval means that if there are losses, they can be a large component of the overall risk due to their higher frequency of occurrence.
- It is helpful to estimate the point on the curve in which additional flood events with lower AEP values do not change the estimated value of risk much. There is little to be gained from modelling events with greater magnitude above this for risk estimates.
- Consider climate change and land cover changes into the future, as these can significantly alterthe nature of risk into the future.
- The flood event that causes a specific AEP of damage is not the same everywhere in a catchment. In other words, the 1-in-100 year flood for one part of the catchment may only be the 1-in-50 year flood in other parts of the catchment. Therefore, choose the set of flood events to model separately for each part of the flood study region (but each event needs to be run separately throughout the entire modelling domain).
- Choose different set of events to characterise how mitigation alters risk, as mitigation will change the shape of the p-d curve.
- Use hydrological models run over the long-term to understand the nature the flow-frequency relationships at the boundary of the study region. Use fast-running, simplified hydraulic models to characterise the shape of the p-d curve based on the outputs of the hydrological models. Based on this, select a set of events that reduce error in calculating risk, and use a more accurate, slower running hydraulic model to calculate damage for each of these points.

## Suggested reference list for further information

**On the hydrological simulation to determine the range of boundary conditions:**

Li, J., Thyer, M., Lambert, M., Kuczera, G., & Metcalfe, A. (2014). An efficient causative event-based approach for deriving the annual flood frequency distribution. Journal of Hydrology, 510, 412–423. http://doi.org/10.1016/j.jhydrol.2013.12.035

Li, J., Thyer, M., Lambert, M., Kuzera, G., & Metcalfe, A. (2016). Incorporating seasonality into event-based joint probability methods for predicting flood frequency: A hybrid causative event approach. Journal of Hydrology. http://doi.org/10.1016/j.jhydrol.2015.11.038

**On the number of events to model:**

Messner, F., Pennning-Rowsell, E. C., Green, C., Meyer, V., Tun- stall, S. M., and Van der Veen, A. (2007). Evaluating flood damages: guidance and recommendations on principles and methods. FLOODsite Report Number T09-06-01, HR Wallingford, Wallingford.

The Multi-Coloured Handbook http://www.mcm-online.co.uk/handbook/

**On the sensitivity of risk calculation to **choice** of food events:**

Ward, P. J., De Moel, H., & Aerts, J. (2011). How are flood risk estimates affected by the choice of return-periods? Natural Hazards and Earth System Sciences, 11, 3181-3195. http://doi.org/10.5194/nhess-11-3181-2011

**On the calculation of risk:**

Meyer, V., Haase, D., & Scheuer, S. (2009). Flood risk assessment in European river basins—concept, methods, and challenges exemplified at the Mulde river. Integrated Environmental Assessment and Management, 5(1), 17–26. http://doi.org/10.1897/IEAM_2008-031.1