Decision makers in fluvial flood risk management increasingly acknowledge that they have to prepare for extreme events. Flood risk is the most common basis on which to compare flood risk-reducing strategies. To take uncertainties into account the criteria of robustness and flexibility are advocated as well. This paper discusses the added value of robustness as an additional decision criterion compared to single-value flood risk only. We do so by quantifying flood risk and system robustness for alternative system configurations of the IJssel River valley in the Netherlands. We found that robustness analysis has added value in three respects: (1) it does not require assumptions on current and future flood probabilities, since flood consequences are shown as a function of discharge; (2) it shows the sensitivity of the system to varying discharges; and (3) it supports a discussion on the acceptability of flood damage. We conclude that robustness analysis is a valuable addition to flood risk analysis in support of long-term decision-making on flood risk management.

Flood disasters continue to show that flood protection cannot provide a 100 % safety. The Japan tsunami flood levels, following the 8.9 magnitude earthquake in March 2011, far exceeded the design heights of the flood walls. Other examples include the flooding of Queensland, Australia in January 2011, and the flooding of Bangkok, Thailand in October 2011. These disasters emphasize the inherent variability of hazards, and the often devastating impact of beyond-design events. The question is how decision-makers and planners should deal with this natural variability in the management of their system.

The traditional way to deal with climate variability is risk-based decision-making. Also in flood risk management, flood risk is the key criterion for decision-making, which is often balanced with the investment cost of the strategy. However, there are two reasons why flood risk may not suffice.

The first reason is that flood risk does not shed light on the acceptability of flood consequences. Flood risk is usually expressed as a single number, for example as the expected annual damage, which does not distinguish between high-probability/low-consequence and low-probability/high-consequence risks (Merz et al., 2009). This implies that potential consequences may grow unlimitedly, as long as the flood probability is reduced. Whether the consequences of low-probability events are acceptable is seldom questioned. Already 30 years ago, Kaplan and Garrick (1981) stated that a single number is not enough to communicate the idea of risk. Instead, they suggested using the full risk curve, which shows flood consequences as a function of the probability of exceedance, thereby putting emphasis on the tail of the distribution.

A different way to emphasize the low-probability/high-consequence part of flood risk is to add a risk aversion factor. Risk aversion refers to the fact that an accident with hundred fatalities is judged worse than a hundred accidents with one fatality each (Slovic et al., 1977). Different ways have been proposed to include risk aversion in risk analysis (see Jonkman et al., 2003), all resulting in higher single-value risk values. Although including this factor may increase the benefit of consequence-reducing measures, it does not provide a basis for discussing damage acceptability.

The second reason why risk may not suffice as decision-criterion is that it is uncertain how it will change over time following socio-economic developments and climate change. This paper is limited to the effects of climate change. The difficulty is in deciding upon the most cost-effective strategy, for which future flood risk needs to be quantified, while it is unknown how the climate will develop and how this affects river discharge variability. A range of equally plausible climate scenarios can be used to explore the future (Bouwer, 2013; De Bruijn et al., 2008), but applying only one scenario may imply either spending too much if the future climate change is slower, or spending too little if the climate change is faster than the scenario suggests. Attempts to solve this issue are numerous, for example robust decision making (Lempert et al., 2003), tipping points analysis (Kwadijk et al., 2010) and adaptation pathways (Haasnoot et al., 2012). Although these methods can support decisions about when to implement a strategy in time, they do not solve the issue of how well a system can deal with extreme events.

An alternative way to a broader analysis of flood risk is to consider a system's robustness to a full range of river discharges. The idea is that a system that can deal better with natural variability is also better prepared for climate change. As Brown et al. (2012) note, often climate-related risks are dominated by the present climate variability, and much can be done to reduce the vulnerability for extreme weather events. We have already proposed robustness analysis as a way to incorporate uncertainty about system disturbances (Mens et al., 2011). System robustness refers to how well a system can cope with disturbances such as high river discharges, given uncertainty about the occurrence of these discharges. A robust system may have the same flood risk as its less-robust counterpart, but unexpected events are less likely to unfold in an unmanageable situation. For example, in a robust system the failure of one of the flood defences will cause minor flooding instead of major flooding that will take years to recover from.

Robustness analysis involves presenting the consequences of flooding as a function of discharge by means of a response curve. The response curve can be considered a risk curve, where probabilities are replaced by the discharge at the boundary of the system. The response curve forms the basis to quantify four robustness criteria: resistance threshold, response severity, response proportionality, and point of no recovery. The resistance threshold refers to the smallest discharge that will cause flood damage. Severity is the impact of the flood, for example economic damage. Proportionality is the relative change in damage when the disturbance magnitude increases. The fourth criterion, point of no recovery, indicates the event from which recovery will be virtually impossible and/or the system will change significantly.

Case study area: IJssel River valley with delineation of dike-ring areas.

The aim of this paper is to discuss the added value of system robustness analysis, by applying it on several alternative flood risk system configurations, and compare the results with an analysis of flood risk. For this we performed a case study of the IJssel River valley in the Netherlands. The IJssel River is a branch of the Rhine River.

The flood risk system under study is the IJssel River valley in the
Netherlands, a natural river valley with embankments on both sides of the
river. The flood-prone area is divided into 6 dike-ring areas, which are
areas surrounded by a closed ring of flood defences and higher grounds
(Fig. 1). The defences are designed to withstand river flood levels that
occur on average once in 1250 years. As a consequence of climate
change, the future Rhine design discharge may be raised from
16 000 to 18 000 m

Note that population growth for the Netherlands is insignificant compared to economic growth in terms of its impact on flood risk.

This was recently investigated for the Netherlands in Klijn et al. (2012). The Delta Programme (Deltaprogramme, 2011) currently explores how to deal with the increased future flood risk.Overview of alternative system configurations.

In this paper, we quantify flood risk and robustness of different system configurations. We define a system configuration as a combination of physical and socio-economic characteristics of the flood risk system, including assumptions about the stage-discharge function near the breach locations, embankment height and strength (quantified by a fragility curve), and land use. Each system configuration is a potential “reality”, in which measures such as raising embankments are implemented compared to the current (reference) situation. For each alternative configuration we calculated flood risk and robustness. The system configurations are explained in Table 1.

Steps in the flood risk analysis.

We calculated the flood risk of the entire IJssel flood risk system based on
flood simulations of eight different breach locations with corresponding
probabilities and consequences. We simulated flooding using the
two-dimensional hydrodynamic model Delft-FLS (WL

We modelled embankment breaches with a breach growth function at a predefined location. This function relates the breach width and water level difference with the inflowing discharge. The breach width increases to 220 m in 72 h. For flood waves that exceed the local embankment, breaches start as soon as the water level exceeds the crest level. For smaller flood waves, the breach starts at the peak of the flood wave. These breaches are assumed to be initiated by structural failure of the embankment, for example by the piping mechanism.

To estimate the flood risk for the entire IJssel system, we followed four
steps (Fig. 2):

calculate water level probability distribution per breach location;

define fragility curve at each breach location;

calculate potential damage for each breach location and combinations of breaches;

calculate flood probability and risk for the entire system.

In this step we derived the IJssel discharge frequency curve from the Rhine
discharge frequency curve, and then converted it to a water level exceedance
curve at each breach location. The IJssel frequency curve was derived from
Eq. (1) (Van Velzen et al., 2007). Because it is uncertain how much water
diverts into the IJssel River, we used three diversion fractions: 0.15, 0.16
and 0.18. A fraction of 0.15 means that 15 % of the Rhine River discharge
diverts into the IJssel River. In all studies for the Dutch government, it is
presently assumed that 15.4 % of the Rhine discharge diverts to the
IJssel. The parameters

To obtain a water level frequency curve, the discharge in the above equation
was replaced by the corresponding water level at each breach location, based
on the stage–discharge relation. Next, the water level return period at
location

Fragility curve for dike-ring 48.

The embankment fragility curve gives the relation between the river water
level and the probability of embankment failure given that water level.
Although different curves should be constructed for each failure mechanism
(Van der Meer et al., 2008), we assumed one encompassing fragility curve
representing all mechanisms. We approached the curve with a standard normal
distribution function with

In the alternative system configurations we adapted the fragility curves to
represent embankment reinforcements, by increasing the

Potential flood damage was calculated for the eight breach locations, using the maximum flood depth maps as input for the damage model. Although the damage will increase with increasing discharge, we only used the damage figures corresponding to a flood with design discharge in the risk calculation. This will slightly underestimate the risk. However, higher damages also have a lower probability, thus contributing less to the risk.

The flood risk calculation of the IJssel valley combines flood probabilities
and consequences of eight breach locations. Because these potential flood events
are correlated, we applied a Monte Carlo approach. To this end, we sampled
10 000 events from the local independent flood probabilities at each breach
location. We defined the flood probability at each location with a so called
limit-state function

The

The

The reliability index is chosen such that

To calculate the flood risk, the set of failure scenarios is first combined
with the potential damage of the location that fails. If more than one
location fails, the damages are added up. This approach thus does not take
into account positive hydraulic system behaviour (Van Mierlo et al., 2007):
the effect that downstream water levels will drop when breaches occur
upstream. The result is a set of 10 000 scenarios of flood damage, from
which a risk curve or loss-exceedance curve can be constructed. Flood risk is
defined as the area under this curve:

For “unbreachable” embankments we used a slightly different approach. Since we assumed that such embankments are strong enough to withstand extreme water levels, even those that exceed the crest level, fragility curves do not apply in the calculation of risk. Whether and where the embankments are overtopped is completely determined by the flood simulation itself (i.e. we did not define overtopping locations beforehand). In practice, this means that upstream embankments will overtop first, if all flood defences have the same design standard. For the alternative systems with “unbreachable” embankments, additional flood simulations were carried out to obtain damage figures for a range of discharge waves. The risk curve is now obtained by combining the IJssel discharge frequency curve with the response curve (damage as a function of discharge). The flood risk then equals the area under this curve.

The estimated flood probability and flood risk are given in Figs. 4 and 5. The uncertainty band reflects the different possible discharge diversion fractions. For comparison, the diamond shows the flood risk for this area according to a recent policy study (“WV21”; Kind, 2014).

The reference system has the largest flood risk. From the alternative systems, “unbreachable” embankments reduce the risk most. The system with raised embankments (CE) has a lower risk than the reference system, because the flood probability is reduced. The room for the river alternative (RR) also has a lower flood probability, but in this case because the measures affect the stage–discharge relationships and, as a consequence, the water level frequency. Therefore, higher discharges are required to cause critical water levels. Additionally, CE increases the flood damage, because critical water levels are higher, causing a higher volume of flood water flowing through the breach. This is not the case for RR. The “unbreachable” embankment alternatives (UE1 and UE2) reduce the flood risk, because the probability of breaching is reduced to practically zero, and once the water overtops the defences, less water flows into the area compared to when the embankments would breach.

Flood probability of reference system and alternative configurations with uncertainty bounds reflecting the different diversion fractions.

Robustness analysis involves presenting the consequences of flooding as a function of discharge by means of a response curve, and using this curve to obtain scores on four robustness criteria: resistance threshold, response severity, response proportionality and recovery threshold (Mens et al., 2011). In this paper, we suggest combining response severity and recovery threshold into one measure of manageability: to what degree will the consequences of flooding still be manageable? Response severity refers to the absolute consequences of flooding, and can be indicated for instance by the economic damage. The recovery threshold refers to the maximum consequences (economic damage, affected persons or casualties) from which a society can still recover. We suggest that response severity becomes a more meaningful criterion when it is compared to a recovery threshold. When presented as an absolute value, the response severity (or the flood damage) is not an adequate indicator for whether the system can remain functioning, since the degree of disruption depends on how this damage is spread over the area and over the functions, and how it relates to what the area can deal with. Instead, manageability better reflects whether the flood damage, if it occurs, exceeds the recovery threshold.

For the analysis of robustness we used the same models and data as for the
risk analysis, but we performed additional flood simulations for discharge
waves that are below and above the design discharge for the following
reasons. Firstly, the fraction of the discharge that diverts from the Rhine
River to its IJssel branch is uncertain and may be higher than expected;
a fraction of 18 % would cause a design discharge of
2880 m

Flood risk of reference system and alternative configurations with uncertainty bounds reflecting the different diversion fractions. The diamond “WV21” refers to the outcome of a recent policy study (Kind, 2014).

By applying the Monte Carlo approach, as explained in Sect. 3, we obtained a probability distribution of damage for each discharge wave. The median of this distribution is used for the response curve. Whereas we used one damage estimate per breach location for the calculation of risk, we used the full relation between discharge and damage for the robustness analysis.

The resistance threshold (i.e. the discharge where damage is first to be
expected) was quantified in two ways. The first one is based on the design
discharge. The reference system has a design discharge of
2560 m

For UE1 and UE2, the resistance threshold only depends on the height of the embankments, because it was assumed that the embankments cannot breach. The effect is that both indicators coincide.

We measure the proportionality by the maximum slope of the response curve.
The resulting value represents the additional damage that is caused by
increasing the discharge peak by a standard volume increase
(1 m

Determination of the resistance threshold for the reference situation, based on the fragility curves of eight breach locations (0.1, 0.5 and 0.9 values). Vertical dashed line indicates the system resistance threshold as the lowest 10 % value of all locations. The diamond indicates the resistance threshold when it would be assumed equal to the design discharge.

Economic damage in USD for some major flood events as
percentage of region's GDP

As a measure of manageability, we distinguish three zones of recovery: easy recovery, difficult recovery and no recovery/regime shift. Two thresholds indicate the transition from one zone to the other, expressed in terms of flood damage. Defining the thresholds requires a discussion on when a flood event is considered an unmanageable situation or disaster.

As noted by Barredo (2007), it is difficult to find a quantified threshold
for classifying an event as major natural disaster or catastrophe. The IPCC (2012)
considers a flood “devastating” if the number of fatalities exceeds 500
and/or the overall loss exceeds USD 650 million (in 2010 values).
Reinsurance company Munich RE uses a relative threshold to classify a flood
event's impact as “great catastrophe” (for developed countries): overall
losses

Based on the above, we assume that when flood damage exceeds 5 % of the
regional GDP, this region is unable to recover without financial aid from
other regions (national scale for small countries). Likewise, if the damage
exceeds 5 % of the national GDP, international aid is needed. The first
recovery threshold equals the regional 5 % level, and the second recovery
threshold the national 5 % level. Figure 7 shows the economic damage of
some recent flood events as a percentage of the regional and national GDP,
where the regional GDP is calculated as per capita GDP

Applying these thresholds to the IJssel case, with reference year 2000, results in the following two thresholds: EUR 3.4 billion (5 % of GDP of the provinces of Gelderland and Overijssel) and EUR 21 billion (5 % of Netherlands GDP) (Statline, 2013).

Response curves for reference system and alternative configurations.

Figure 8 shows the response curves of the reference situation and the
alternative system configurations. These curves already reveal that all
alternatives increase the ability to remain functioning, compared to the
reference situation. The alternative with “unbreachable” embankments
(version 2) increases the robustness most, because it takes a discharge of
3200 m

The reference system has the lowest resistance threshold: a discharge of
2500 m

The proportionality decreases when embankments are being raised, because the maximum change in damage is increased. Making room for the river does not change the proportionality, whereas “unbreachable” embankments significantly reduce it. Because in the second version of “unbreachable” embankments the crest levels are varied, the increase in damage is smaller than in the first version.

The manageability scores best in the second version of
“unbreachable” embankments, and second best in the first version of
“unbreachable” embankments. In UE2 the zone of difficult recovery is
reached at a discharge of about 3200 m

Overview of scores on the robustness criteria. REF

The main purpose of this paper was to explore the added value of robustness criteria compared to single-value flood risk, when evaluating alternative flood risk system configurations. We consider it added value when different insights are obtained with a robustness analysis in comparison to those obtained from a flood risk analysis. Added value could also be assessed by comparing the ranking of alternative strategies based on a cost-benefit analysis with a ranking based on system robustness. Such a comparison was done by Klijn et al. (2014), who show that robustness analysis may indeed lead to a changed priority setting of alternative flood risk management strategies. Here, we limit ourselves to a comparison of risk with robustness of the reference and alternative configurations. In general, we found that flood risk is reduced in all configurations, but robustness is only enhanced in the configurations with “unbreachable” embankments. This means that if the risk reduction would have been equal in all configurations, a strategy with “unbreachable” embankments would have been preferred from a robustness perspective. This, however, does not take into account the costs of implementing unbreachable embankments. Each robustness criterion is discussed next and compared with flood probability or flood risk.

Obviously, the higher the flood defence the higher the resistance threshold and the lower the flood probability. However, the resistance threshold is expressed in terms of discharge, a physical parameter, whereas the flood probability is “likelihood”. The flood probability needs assumptions on discharge variability and discharge diversion and will thus change when new information becomes available and when the climate changes. In contrast, the resistance threshold remains unchanged when assumptions about the natural discharge variability are adapted. Only when embankments are raised or strengthened, or when knowledge about the failure mechanisms increases, are both resistance threshold and flood probability affected. Thus, the resistance threshold depends less on assumptions about discharge variability and climate change. This is considered of additional value to flood risk.

The second robustness criterion, response proportionality, is another additional element compared to flood risk. It values a low sensitivity of damage to a change in discharge. A proportional response curve means that a slightly higher or lower discharge than expected would not result in substantially different damage. Thus, in systems with “unbreachable” embankments (like UE1 and UE2), which score high on proportionality, an accurate prediction of the discharge is less critical; if the discharge is slightly higher than anticipated, the effect on flood damage will be minimal.

The third robustness criterion, manageability, has additional value to flood risk by introducing a reflection on the flood consequences compared to what is considered acceptable. In contrast, the risk approach implies that as long as the probability is small enough, the absolute damage is irrelevant. In this paper, we proposed three recovery zones as indication of manageability. In practice, these thresholds would be the result of a societal discussion among decision makers and other stakeholders.

This paper discussed the added value of robustness analysis for flood risk management by comparing five alternative configurations of the IJssel flood risk system. The system with “unbreachable” embankments that differ in height has the lowest flood risk. If the implementation cost would be known, the most cost-effective measure could be chosen. However, the flood risk and thus the cost-effectiveness depend on uncertain flood probabilities and discharge diversion fractions. Because of these uncertainties it is considered important to obtain insight into how well the system can deal with extremely high discharges. The robustness criteria show that the systems with “unbreachable” embankments are best able to cope with extreme events. This is because the damage increases proportionally with an increase in discharge. When “unbreachable” embankments are built with different heights, the ability to cope with extreme events increases even more, because the absolute damage is smaller.

To summarize, the robustness analysis gave us the following insights:

Whereas the flood probability reduction differs between all system configurations, the resistance threshold hardly distinguishes between the systems. This means that although the flood probability is reduced, the resistance threshold (i.e. the discharge where a flood event has a likelihood of at least 10 %) is similar in all configurations. Because quantifying the resistance threshold does not require assumptions about current and future discharge return periods, the score does not change with climate change.

The proportionality criterion is a valuable addition to flood risk, because it shows how flood consequences vary with the river discharge. This indicates how sensitive the system is for uncertainties about, or changes in, the design discharge.

Scoring on manageability adds to flood risk, because it allows an explicit discussion of damage acceptability. In contrast, the risk approach implies that as long as the probability is small enough, the absolute damage is irrelevant.

It makes explicit how a measure influences different constituents of flood risk. Some measures reduce the flood-probability by changing the stage–discharge relationship and others by affecting the fragility curve of the defence. Some also reduce the inflow volume or the maximum flood depths and hence the flood consequences. The response curve shows these differences.

It supports a discussion on flood damage acceptability, by triggering questions like: “what if the design standard is exceeded?” The risk may be considered acceptable, but the potential flood damage may not.

It moves the discussion away from uncertain design standards and uncertain flood probabilities, towards how the system functions and what can be done to manage the entire flood risk system under a range of plausible discharges. It poses the question: which discharge range do we want to be prepared for and how?

This research was carried out for the Netherlands Knowledge for Climate programme. This research programme is co-financed by the Ministry of Infrastructure and the Environment. We greatly acknowledge their financial support. We also thank Ralph Schielen of the Netherlands Delta Programme Large Rivers for his valuable feedback during this project. Edited by: T. Glade Reviewed by: four anonymous referees