Reduction of water levels during river floods is key in preventing damage and loss of life. Computer models are used to design ways to achieve this and assist in the decision-making process. However, the predictions of computer models are inherently uncertain, and it is currently unknown to what extent that uncertainty affects predictions of the effect of flood mitigation strategies. In this study, we quantify the uncertainty of flood mitigation interventions on the Dutch River Waal, based on 39 different sources of uncertainty and 12 intervention designs. The aim of each intervention is to reduce flood water levels. Our objective is to investigate the uncertainty of model predictions of intervention effect and to explore relationships that may aid in decision-making. We identified the relative uncertainty, defined as the ratio between the confidence interval and the expected effect, as a useful metric to compare uncertainty between different interventions. Using this metric, we show that intervention effect uncertainty behaves like a traditional backwater curve with an approximately constant relative uncertainty value. In general, we observe that uncertainty scales with effect: high flood level decreases have high uncertainty, and, conversely, small effects are accompanied by small uncertainties. However, different interventions with the same expected effect do not necessarily have the same uncertainty. For example, our results show that the large-scale but relatively ineffective intervention of floodplain smoothing by removing vegetation has much higher uncertainty compared to alternative options. Finally, we show how a level of acceptable uncertainty can be defined and how this can affect the design of interventions. In general, we conclude that the uncertainty of model predictions is not large enough to invalidate model-based intervention design, nor small enough to neglect altogether. Instead, uncertainty information is valuable in the selection of alternative interventions.

The number of people living in areas exposed to river flooding is projected to exceed 1 billion in 2050

Proper understanding and communication of uncertainty are important both for scientists and decision makers

Uncertainty quantification of impact analysis for real-world solutions suffers from two compounding issues specific to intervention design studies.
First, there is a practical need for sufficiently detailed models given the increasingly complicated design of interventions, which moves from traditional flood prevention (building dikes or levees) to more holistic designs.
This is in part motivated by the paradoxical “levee effect” that states that flood control measures do not decrease but increase flood risk

In the present paper we address the lack of studies into the model uncertainty of model predictions used in impact design.
Our objective is twofold.
The first objective is to quantify the effect of parameter uncertainty on the predicted effect of flood mitigation measures, by implementing 12 different interventions of varying type and intensity in a section of the Dutch River Waal, using a detailed hydraulic model.
To limit the computational burden we use

Our analysis proceeds in three steps.
First, we set up the numerical model for the Dutch River Waal and select the uncertainty sources in Sect.

The River Waal, situated entirely in the Netherlands. The study area is a stretch of about 15 km between km 913 and 928. The hatched area shows the total extent of the model domain, which overlaps with the river and its floodplains bounded by the dikes.

The River Waal is selected as the case study for its extensive history of human intervention and good data availability.
The Waal is a distributary of the River Rhine and, by discharge, the largest river in the Rhine–Meuse–Scheldt delta, located in western Europe.
The present-day river has a main channel about 8 m deep at bank-full discharge, a bank-full width of about 250 m and relatively narrow floodplains.
Before the construction of the dikes from 1000 CE onward, it was a meandering river with regular overbank deposition

Our study domain covers the entire Waal River (Fig.

The intervention area is characterised by a relatively straight river stretch with narrow floodplains and the strongly curved St. Andries river bend, which provides a known bottleneck during high discharges. Nine towns border directly on the dikes along this 17.5 km stretch. Interventions in this area to increase flood safety, considering the narrow floodplains and the populated surrounding land, present both a technical and a societal problem.

To simulate the hydrodynamic response of the flow to various interventions we use the Delft3D Flexible Mesh modelling system

All interventions are modelled as changes to a reference state of the system.
This reference state is the Waal River after all interventions from the Room for the River programme, which approximately corresponds to the 2016 situation.
We consider 12 additional system states, each one corresponding with a particular human intervention (Fig.

A schematic overview of a typical cross section of the River Waal and the flood mitigation measures studied in this paper. Figure is based on

Groynes (also known as wing dikes or spur dikes) are (stone) structures perpendicular to the flow. During normal conditions, groynes restrict the effective channel width to promote navigable depths. However, during high flows groynes obstruct flow. Prior to 2016, many groynes in the Waal were already lowered as part of the Room for the River programme. The intervention as implemented in this study further reduces the groynes' crest heights. Groynes were lowered to the crest height corresponding to the water levels with exceedance frequency of 150 d (low intensity) and 363 d (high intensity) per year.

The River Waal floodplains are compartmentalised by minor embankments, of which original purpose is to prevent flooding of the floodplains during minor (summer) floods. This intervention lowers the crests of these embankments to reduce their obstruction during high flow. Low and high intensity lowered the crests to a water level with exceedance frequency of 50 d (low intensity) and 150 d (high intensity) per year.

Lowering or excavation of the floodplains increases the maximum water volume within the existing bounds of the river corridor, thereby increasing conveyance.
In this study, we lower the level of the floodplain without changing existing vegetation or other floodplain configuration to isolate the effect of lowering.
Floodplains were lowered to the corresponding water level with an exceedance frequency of 20 d yr

Vegetation in the floodplain greatly contributes to resistance during high flows.
Replacing existing high-friction vegetation by low-friction vegetation mitigates this problem.
Here, the existing vegetation was replaced by production meadow (roughness code 1201 in Table

In the River Waal, dikes are the primary defence against flooding. However, they also contribute to flood risk by restricting the river corridor. Dike relocation increases the floodplains and allocates more space to the river. While this is perhaps the best example of combatting problematic constriction of the river corridor, it is also the most invasive – considering human settlement near and on the dikes. At low intensity, concave dike sections of less than 700 m are replaced by straight dikes, whereas at high intensity concave sections of 7000 m are straightened, while creating small polders around existing built-up areas.

Finally, the construction of secondary (side) channels within the existing corridor both increases the available volume and decreases vegetation friction.
All new channels are assigned “side channel” roughness (code 105 in Table

Modelling real-world rivers on the scale of nearly 100 km necessarily involves various simplifications, discretisations and parameterisations.
Sources of uncertainty for this river were identified by

A summarised overview of the stochastic variables. A full overview is given in Table

The hydraulic roughness of the main channel is chiefly determined by the material of the bed (“grain roughness”) and the bed forms (“form roughness”).
Various models have been proposed that calculate the friction factor based on the characteristics of the bed

In the following we will use the joint cumulative density function of the five roughness models to sample representative roughness height

The combined probability function of the main bed roughness is based on Weibull extrapolation of Nikuradse roughness height

The Baseline database divides the floodplain into vegetation classes, riverbanks and water bodies. Each class is given a specific roughness code called a trachytope, which is then coupled to an appropriate roughness formula and parameters specific to that formula. Spatially, the vegetation in the floodplains is discretised by polygons, which are designated by either one or a combination of distinct vegetation classes.

For vegetation, the generation of roughness by vegetation is complex, resulting from obstruction by stems and leafs and turbulent flow through the vegetation and over the canopy.
The relationship between vegetation and roughness is extensively studied, leading to various models to compute hydraulic friction from vegetation traits

Six trachytopes are associated with water bodies or riverbanks, accounting for about 27 % of the total areal.
We model the friction for these six classes with the Manning formula:

Available vegetation maps are likely to contain “impurities”

Schematic overview of the efficient uncertainty estimation method

In this study we focus on prediction of the maximum flood levels (see Fig.

However, MCS is not always practically feasible or desirable. Although MCS has been applied for estimation of flood level uncertainty before

The main advantage of this approach is a significant decrease of required computational resources by reducing the number of model evaluations.
The total number of hydrodynamic model evaluations was 1240, divided over 13 model states (the reference plus 12 interventions).
This is a decrease of computational effort of more than 90 % compared to direct MCS with all states, which would have totalled 13 000 model evaluations.
It is important to state that the consequence of having a probabilistic correlation model is that the intervention state estimator

To maintain correlation between the

As a data reduction step, we summarise the results using the following metrics based on the water level reduction effect

Confidence intervals measure the distance between two percentiles (e.g. the 10 % and 90%) of a cumulative density function (cdf).
We refer to the confidence intervals of the stochastic variables

It is important to note that

To compare the uncertainty of interventions we calculate the relative uncertainty, i.e. the uncertainty relative to the expected effect.
For this, we use an adapted version of the coefficient of variation, defined as

Figure

The expected lowering of flood levels for side channel construction (

The primary objective of the flood mitigation measures is to lower flood levels during a given design discharge.
In deterministic approaches, this effect is typically communicated with an along-channel diagram showing the difference (i.e. before and after the intervention) in flood levels (see, for example, Fig. 3 in

The novelty of Fig.

Next, we compute the relative uncertainty (

It is interesting to note that in theory, the adaptation length (i.e. the length scale of the backwater curve) is affected by the equilibrium water level and can therefore result in converging or diverging confidence intervals.
Since

A comparison of all interventions (Table

The expected values for the relative uncertainty (

Summarised results for each measure.

Probability densities of the relative uncertainty (

A straightforward way to compare differences between the effect of two or more interventions is to look at the backwater figures.
In Fig.

To systematically compare interventions we compute the relative uncertainty

The expected effect (

By linearly interpolating between the expected values of the low and high intensities, we obtain a first approximation of the uncertainty for a given expected effect for each intervention (Fig.

Instead of looking at the expected effect, the confidence intervals can be marginalised by designing for a given exceedance probability of the effect.
The desired effect is related to the expected effect through the exceedance probability.
To illustrate how the exceedance probability can be used to guide intervention design, we linearly interpolated between the low-intensity and high-intensity variants as a function of the expected effect (Fig.

The high-intensity variant of

This approach can be applied to the earlier example of a planned mitigation measure with a 25 cm flood level decrease objective.
In Fig.

Our results show that some interventions are inherently more uncertain than other interventions.
Given the complexity of high-detailed modelling of floodplains, it is not straightforward to explain these differences.
The statistical causes of uncertainty are discussed in detail by

A lack of computational resources is often named as the main obstacle that motivates the use of deterministic approaches over probabilistic approaches.
The analysis performed in this study is nonetheless feasible due to the

Our study focused on providing uncertainty estimations for many different interventions, not on providing an optimal intervention for the given case study.
Following this approach we made several simplifications that must be resolved if an optimal intervention design is pursued.
The linear interpolation between low-intensity and high-intensity interventions in Figs.

Our approach is a form of forward uncertainty analysis: the quantification of model output uncertainty based on uncertainty in model assumptions without taking historical evidence of the goal variable (i.e. water level measurements) into account.
We justify choosing this approach based on the assumption that no historical information can be used to infer or narrow the distributions of the uncertain parameters because (a) such information does not exist for our study case, and (b) measurements after the intervention will never be available ex ante.
The results of our analysis are therefore conditional on our assumptions about the validity of the model, the selection of uncertainty sources and the probability distributions of these sources.
We have taken care to select the stochastic variables, and their distributions, based on previous research specific to our study case.
Forward uncertainty analysis is contrasted

Models can play a role in decision support under (deep) uncertainty, and the uncertainty quantification is an important step to model the future

In general, our study shows that explicitly quantifying the uncertainty of predicted flood mitigation measures provides decision makers and modellers with valuable information. On the one hand, results show how taking uncertainty into account can lead to different design choices. On the other hand, even small effects on flood levels can be quantified because small effects are accompanied by small uncertainties. This shows that model uncertainty does not invalidate model-supported decision-making in river management, but it enriches it.

Our first objective was to quantify the effect of parameter uncertainty on the predicted effectiveness of flood mitigation measures. Based on previous studies, we quantified the parameter uncertainty for 39 variables and estimated the uncertainty of model output. Results show that the absolute uncertainty of the predicted effect of flood level decrease is highly dependent on the type of intervention and location along the river. However, we found that the confidence bounds of flood level decrease along the river can be adequately described by a single relative uncertainty metric, defined as the ratio between the 90 % confidence interval and the expected effect. This ratio remains relatively constant along the river and between intensities of intervention types and enables us to make some general observations. First, all uncertainty is “generated” when the intervention has modified the river system. Upstream from there, the uncertainty gradually diminishes upstream with a constant rate following typical backwater curves. Second, a higher expected flood level decrease led to a higher uncertainty, and a small flood level decrease was accompanied by a small uncertainty. The ranges of the expected relative uncertainty varied between 15 % and 40 % for most interventions, which means that the size of the 90 % confidence bounds of those interventions is less than half of the expected flood level decrease.

The second objective was to explore the relationship between the expected effect and its uncertainty, to aid in the decision-making process. We observe that interventions of different types may reach the same expected flood level decrease but have different uncertainty. Specifically, a large-scale but relatively ineffective intervention such as floodplain smoothing (by removing high-friction vegetation) has a high relative uncertainty compared to alternative interventions. The intensity of an intervention (e.g. total area of vegetation smoothed) may be increased to reach a higher effect. Our results show that higher intensity also leads to a higher uncertainty, while the relative uncertainty remains approximately constant. This relationship was then used to show how explicit uncertainty quantification and differences in relative uncertainty between various interventions may affect design choices, depending on the level of acceptable uncertainty. For a fixed level of acceptable uncertainty (i.e. by a given exceedance probability), we graphically demonstrated that interventions need to be designed for a larger expected flood level decrease than the given objective.

In this article we used the following code and software. For the hydraulic modelling we used Delft3D Flexible Mesh (FM) version 1.1.261.52670. Delft3D FM is available from

Parameters of the floodplain roughness class distributions. Codes marked with an asterisk

The supplement related to this article is available online at:

Author contributions are reported following the CASRAI CRediT system (

The authors declare that they have no conflict of interest.

This article is part of the special issue “Flood risk assessment and management”. It is a result of the EGU General Assembly 2018, Vienna, Austria, 8–13 April 2018.

This study is part of the research programme RiverCare, supported by the domain Applied and Engineering Sciences (AES), which is part of the Netherlands Organisation for Scientific Research (NWO). This study benefited from cooperation within the Netherlands Centre for River Studies (NCR). We thank Jan Kwakkel, Jonathan Remo and Joseph Guillaume for their critical contributions to the review, which have improved the quality and framing of this work significantly.

This research has been supported by the Netherlands Organisation for Scientific Research (grant no. P12-4).

This paper was edited by Cristina Prieto and reviewed by Joseph Guillaume, Jan Kwakkel, and Jonathan Remo.