Bridging the Gap: A Novel Approach to Flood Risk Assessment for Resilience

Abstract

Flood disasters are growing more common and severe as a result of global warming and climate change. These factors intensify weather extremes, resulting in more unpredictable and disastrous floods around the world. Effective flood risk assessment is critical for reducing the socioeconomic and environmental consequences of catastrophic events. This work proposes a novel technique for flood risk assessment that combines Event Tree Analysis with Dempster–Shafer evidence theory and an optimization approach. The methodology assesses flood scenarios, as well as probabilities and outcomes, to predict risk pathways and uncertainties. Prevention measures, such as flood defenses, early warning systems, and sustainable land use practices, are evaluated for cost-effectiveness and their contribution to flood resilience. The findings emphasize the relevance of multi-layered mitigation techniques for lowering flood risks and increasing community resilience. The model presented in this paper is modular, and since it depends on expert judgement, it can be used in other geographical or regional settings with adjustments from local data and local expert assessments.

1. Introduction

Global warming, climate change, and natural disasters pose substantial and tragically expanding challenges for the development of societies across the globe and to the very sustainability of the planet [1,2].

More and more scientific studies address the issue of natural disasters and begin their investigations with data indicating that the intensity and frequency of disaster occurrences are increasing [3], as are their negative effects on infrastructure, the economy, the environment, and the number of human victims [4,5,6,7,8,9]. Even though scientists do not agree on the causes of the changes in hydrometeorological processes and the direction in which they are occurring, most of them agree that these changes are obvious everywhere in the world, particularly in the atmosphere and hydrosphere [10,11,12,13,14,15].

Floods are known for their sudden occurrence, which may happen due to unpredictable and various reasons, often having devastating consequences, impacting the social and economic stability of the affected area and nation [16,17,18,19,20,21,22], and according to the World Meteorological Organization (WMO) [23], “floods are the deadliest natural hazards, striking numerous regions in the world each year”.

Gaining a comprehensive awareness of both flood causes and consequences is essential for enhancing preparedness, response, and risk mitigation.

In this sense, risk assessment is a crucial step in the flood risk management process. It begins with risk identification and is directly proportional to how thoroughly possible catastrophes are detected [24]. Risk assessment is essential for flood analysis, having several advantages that are multidisciplinary in nature like preparedness and risk mitigation, resource allocation, financial planning, infrastructure planning, environmental protection, climate change adaptation, education and awareness, etc. [25,26,27].

“Flood risk is defined as the probability of loss as a function of three parameters: flood hazard, vulnerability, and exposure” [26,28,29].

An important element of flood risk mitigation is flood resilience, which can be defined as “the ability to prepare and plan for, absorb, recover from, and more successfully adapt to an adverse event” [30] and can be divided into the following three categories: capacity to resist; capacity to absorb and recover; and capacity to transform and adapt [31]. Flood resilience is essential for effective flood risk mitigation as it highlights the capacity of communities, infrastructure, and ecosystems to foresee, prepare for, respond to, and recover from flooding incidents ultimately minimizing flood risks and flood consequences.

“Flood risk management includes risk analysis, assessment, and reduction” [32]. Traditional flood management strategies involve structural and nonstructural measures to mitigate the negative effects of a flood [33]. The growth of flood risk management is a constant adaptive management process that introduces new challenges to uncertainty analysis [34]. Adaptive flood risk management emphasizes balancing increasing flood risks with limited resources, minimizing negative environmental impacts, and dealing with uncertainty [35]. Gradually, the disadvantages of previous management approaches and flood control strategies were progressively transformed into more sustainable ones [32]. This transition from simply avoiding damage to fostering flood resilience shows the importance of a proactive, adaptable flood management system that protects both the people and the infrastructure.

The subject addressed in this paper is Dempster–Shafer evidence theory combined with an Event Tree Analysis and an optimization approach, which help to map out possible outcomes of flooding scenarios and their possibilities, as well as to define possible prevention measures that minimize the risk of intense flooding and improve flood resilience.

2. Materials and Methods

The methodology used in this paper includes the following three phases (Figure 1):

• Defining barriers that could prevent the negative consequences of a flood event, collecting data from experts on the probabilities of the barriers’ success, and aggregating their assessments using Dempster–Shafer theory of evidence.
• Constructing an Event Tree and determining the probabilities of scenarios and their outcomes.
• Defining measures to increase the success of barriers and determining the measures to be taken by applying the optimization approach.

2.1. Dempster–Shafer Evidence Theory

Due to variant modes of failure, design errors, and a poor understanding of failure mechanisms, as well as vagueness or a lack of understanding of systemic phenomena, it is often difficult to predict the probabilities and consequences of certain events [36]. The problems of uncertainty, inaccuracy, and credibility of estimated data arise in all fields that rely on data resulting from measurements, assessments, or predictions. For this reason, many approaches have been developed to overcome this problem, from Gauss’ Theory of Errors from the beginning of the 19th century, through the Theory of Uncertainty at the end of the 19th century, to today’s widely used approaches, such as fuzzy sets, Possibility Theory, Dempster–Shafer evidence theory, etc. [37,38].

Dempster–Shafer evidence theory (DS theory) was first described by Dempster [39], and it was formalized and expanded by Shafer [40]. In the literature, it is often found under the names DS theory and Evidence Theory.

DS theory deals with the epistemic (cognitive) uncertainty of a proposition. In doing so, it relies on the theory of probability, but instead of the concept of event, it uses the concept of proposition [41]. In addition, a significant difference compared to the probability theory is that, in the DS theory, additivity does not apply [38], i.e., it does not apply that the probability of two independent events is equal to the sum of their probabilities.

The risk-oriented approach to DS theory used in this paper is based on a hypothesis related to all possible system states. The frame of discernment, Θ = {H1, H2, …, H_P}, is a limited set of mutually exclusive hypotheses, and the set 2^Θ = {∅, [H1], [H2], …, Θ} is the power set [42]. Each E ∈ 2^Θ represents a proposition that could be included or excluded from the analysis, depending on obtained pieces of evidence. The sources of evidence usually are experts (as is the case with this research as well), measurements, collected information, etc. The amount of evidence (knowledge) about some proposition E is called basic probability assignment (bpa) or mass function and is denoted by m(E). The characteristics of bpa are [41]: m(E) → [0, 1]; m(∅) → 0; ${\displaystyle \sum _{E\in 2^{\Theta }}m(E)}=1$.

DS theory also uses the following two measures: belief measure in a certain proposition, bel(E), and plausibility measure, pl(E), that can be calculated using bpa as follows:

$$bel(E)={\displaystyle \sum _{A\subseteq E}m(A)},pl(E)={\displaystyle \sum _{A\cap E}m(A)}$$

(1)

Each E such that m(E) > 0 is called focal element, and it is included in further uncertainty analyses. The set of all focal elements represents the body of evidence.

If there are several bodies of evidence obtained for some propositions from independent sources, they must be combined into a single bpa. For this purpose, we use Dempster’s rule of combination, as follows:

$$m(E)=\left\{\begin{array}{ll}{\displaystyle \frac{1}{1-K_j}}{\displaystyle \sum _{\cap E_j=E}{\displaystyle \prod _{i\in I}{m}_j(E_j)}}\hfill & E\ne \varnothing \hfill \\ 0\hfill & E=\varnothing \hfill \end{array}\right.$$

(2)

where I represents the set of independent sources, and $K_j={\displaystyle \sum _{\cap E_j=\varnothing }{\displaystyle \prod _{i\in I}{m}_j(E_j)}}$ is inconsistency and conflict among the independent sources.

2.2. Event Tree Analysis

Event Tree Analysis (ETA) is most often used to identify the consequences that may result from the occurrence of a potentially hazardous event. It consists of qualitative and quantitative analyses.

The qualitative analysis includes the construction of the Event Tree, a graphical representation of a logic model that identifies possible scenarios and their outcomes after a given initial event, and depends on the success or failure of the system’s barriers. An edge on the tree structure usually represents success, failure, or partial failure of the barrier, progressing from left to right [43]. The sequence of edges is such that each subsequent one is activated if the previous barrier has failed. Each path leading from the initial event to the outcome represents one scenario. The outcomes of the scenarios can be positive, i.e., the initial event did not cause any damage, acceptable, when there is moderate damage, and they can be negative, i.e., unacceptable. An example of the Event Tree is shown in Figure 2.

If the probabilities of barriers’ success are known or can be estimated, then the quantitative analysis gives the probabilities of outcomes of the scenarios. The probability of outcomes is calculated as the product of the probabilities on the scenario branches leading to that outcome. It is obvious, from Figure 2, that the sum of probabilities of all outcomes is equal to 1. When defining the probabilities of the barriers, it is necessary to consider whether the barriers are independent or dependent, that is, whether the outcome of one barrier influences (positively or negatively) the probability of success of the barriers that are activated after it.

2.3. Optimal Measures Selection

Further analysis proposes prevention measures aimed at increasing the probability of barriers’ success and the selection of those that can most effectively minimize the probability of negative final outcomes.

In order to formulate the mathematical model for optimal measures selection, the following notation is used:

n—number of measures;

m—number of barriers;

p_j—current probability of success of the j-th barrier, j = 1, …, m;

e_ij—increasing the probability of success of the j-th barrier under the influence of the i-th measure, j = 1, …, m, i = 1, …, n;

c_i—cost of i-th measure, i = 1, …, n;

B—available budget.

$$x_i=\left\{\begin{array}{ll}1\hfill & \mathrm{if}i\text{-}\mathrm{th}\mathrm{measure}\mathrm{is}\mathrm{chosen}\hfill \\ 0\hfill & \mathrm{otherwise}\hfill \end{array}\right.,i=1,\dots ,n$$

Depending on the chosen barriers, the probability of success of the first barrier that represents the probability of the first outcome is shown as follows:

$$p_1+{\displaystyle \sum _{i=1}^n{e}_{i1}\cdot x_i}$$

(3)

and the probability of its failure is shown as follows:

$$1-(p_1+{\displaystyle \sum _{i=1}^n{e}_{i1}\cdot x_i})=1-p_1-{\displaystyle \sum _{i=1}^n{e}_{i1}\cdot x_i}$$

(4)

Since the second barrier is activated if the first barrier fails, the probability of success of the first two barriers, which represents the probability of the second outcome, is shown as follows:

$$(p_2+{\displaystyle \sum _{i=1}^n{e}_{i2}\cdot x_i})\cdot (1-p_1-{\displaystyle \sum _{i=1}^n{e}_{i1}\cdot x_i})$$

(5)

and the probability of failure after the first two barriers is shown as follows:

$$(1-p_2-{\displaystyle \sum _{i=1}^n{e}_{i2}\cdot x_i})\cdot (1-p_1-{\displaystyle \sum _{i=1}^n{e}_{i1}\cdot x_i})={\displaystyle \prod _{j=1}^2(1-p_j-{\displaystyle \sum _{i=1}^n{e}_{ij}\cdot x_i})}$$

(6)

Since the third barrier is activated if the first two barriers fail, then the probability of the third outcome is shown as follows:

$$(p_3+{\displaystyle \sum _{i=1}^n{e}_{i3}\cdot x_i})\cdot {\displaystyle \prod _{j=1}^2(1-p_j-{\displaystyle \sum _{i=1}^n{e}_{ij}\cdot x_i})}$$

(7)

Further, since the j-th barrier is activated if all previous j − 1 barriers fail, then the probability of the j-th outcome is shown as follows:

$$(p_j+{\displaystyle \sum _{i=1}^n{e}_{ij}\cdot x_i)\cdot }{\displaystyle \prod _{k=1}^{j-1}(1-p_k-{\displaystyle \sum _{i=1}^n{e}_{ik}\cdot x_i})}$$

(8)

Finally, the probability of the last m-th outcome is shown as follows:

$${\displaystyle \prod _{k=1}^m(1-p_k}-{\displaystyle \sum _{i=1}^n{e}_{ik}\cdot x_i)}$$

(9)

Let the success of the first l barriers lead to the positive and acceptable outcomes. The total probability of positive and acceptable outcomes is shown as follows:

$$(p_1+{\displaystyle \sum _{i=1}^n{e}_{i1}\cdot x_i})+{\displaystyle \sum _{j=2}^l[(p_j+{\displaystyle \sum _{i=1}^n{e}_{ij}\cdot x_i)\cdot }}{\displaystyle \prod _{k=1}^{j-1}(1-p_k-{\displaystyle \sum _{i=1}^n{e}_{ik}\cdot x_i})]}$$

(10)

Recall that the sum of probabilities of all outcomes is equal to 1, as follows:

$$(p_1+{\displaystyle \sum _{i=1}^n{e}_{i1}\cdot x_i})+{\displaystyle \sum _{j=2}^m[(p_j+{\displaystyle \sum _{i=1}^n{e}_{ij}\cdot x_i)\cdot }}{\displaystyle \prod _{k=1}^{j-1}(1-p_k-{\displaystyle \sum _{i=1}^n{e}_{ik}\cdot x_i})]+}{\displaystyle \prod _{k=1}^m(1-p_k-{\displaystyle \sum _{i=1}^n{e}_{ik}\cdot x_i})}=1$$

(11)

The middle term of this formula can be separated into the following two sums:

$$\begin{array}{l}{\displaystyle \sum _{j=2}^m[(p_j+{\displaystyle \sum _{i=1}^n{e}_{ij}\cdot x_i)\cdot }}{\displaystyle \prod _{k=1}^{j-1}(1-p_k-{\displaystyle \sum _{i=1}^n{e}_{ik}\cdot x_i})]=}\\ {\displaystyle \sum _{j=2}^l[(p_j+{\displaystyle \sum _{i=1}^n{e}_{ij}\cdot x_i)\cdot }}{\displaystyle \prod _{k=1}^{j-1}(1-p_k-{\displaystyle \sum _{i=1}^n{e}_{ik}\cdot x_i})]+{\displaystyle \sum _{j=l+1}^m[(p_j+{\displaystyle \sum _{i=1}^n{e}_{ij}\cdot x_i)\cdot }}{\displaystyle \prod _{k=1}^{j-1}(1-p_k-{\displaystyle \sum _{i=1}^n{e}_{ik}\cdot x_i})]}}\end{array}$$

(12)

where the first term represents the sum of success probabilities of barriers 2 to l, and the second term represents the sum of success probabilities of barriers l + 1 to m.

Then, the total probability of the last m − l outcomes, which are negative, can be calculated as follows:

$$\begin{array}{l}1-\{(p_1+{\displaystyle \sum _{i=1}^n{e}_{i1}\cdot x_i})+{\displaystyle \sum _{j=2}^l[(p_j+{\displaystyle \sum _{i=1}^n{e}_{ij}\cdot x_i)\cdot }}{\displaystyle \prod _{k=1}^{j-1}(1-p_k-{\displaystyle \sum _{i=1}^n{e}_{ik}\cdot x_i})]}\}\hfill \\ ={\displaystyle \sum _{j=l+1}^m[(p_j+{\displaystyle \sum _{i=1}^n{e}_{ij}\cdot x_i)\cdot }}{\displaystyle \prod _{k=1}^{j-1}(1-p_k-{\displaystyle \sum _{i=1}^n{e}_{ik}\cdot x_i})]+{\displaystyle \prod _{k=1}^m(1-p_k-{\displaystyle \sum _{i=1}^n{e}_{ik}\cdot x_i})}}\hfill \end{array}$$

(13)

The function (13) can be replaced by the following equivalent formulation:

$${\displaystyle \prod _{k=1}^l(1-p_k-{\displaystyle \sum _{i=1}^n{e}_{ik}\cdot x_i})}$$

(14)

The number of operations required to calculate the probability expressed in (14) is 2ln + 2l − 1, while determining the probability (13) requires (l² + 3l)/2 + 4nl − 2l − 2 operations. The proof is given in Appendix A.

The mathematical model of the problem of optimal measures selection (OMS), can be formulated as follows:

$$\begin{array}{l}\mathrm{OMS}\\ \min f(x)={\displaystyle \prod _{k=1}^l(1-p_k-{\displaystyle \sum _{i=1}^n{e}_{ik}\cdot x_i})}\\ \text{s.t.}\\ {\displaystyle \sum _{i=1}^n{c}_i\cdot x_i}\le B\\ x_i\in \{0,1\},i=1,\dots ,n\end{array}$$

The objective represents the probability of all negative outcomes. The first constraint is related to the available budget, while the second constraint contains the binary restriction on the variables.

For the OMS model to function effectively, the necessary input data consist of the specified barriers from the Event Tree, the chosen prevention measures, the overall available budget, and the individual costs associated with each prevention measure (as seen in the Results section).

Due to a lack of consistent and precise cost data for all flood prevention measures, a reference-based expert judgement approach was used. This was used since the costs of these measures differ from one country to another and depend on various factors. The costs are usually context-dependent, with large variations depending on country, geographic conditions, urban density, labor costs, regulatory standards, and material availability. Additionally, the information that is available to the public about the costs of flood infrastructure is often incomplete or hidden [44]. Even when data are available, they are rarely standardized or sufficiently explained to provide reliable cross-measure comparisons. It should also be noted that many non-structural or nature-based measures, like zoning, community preparedness, or wetland restoration, have costs that are not easy to quantify in cost models. These costs can be things like administration, land value trade-offs, or opportunity costs. Bearing in mind these difficulties, a systematic expert judgement method was used, where experts assessed the comparative costs of each action based on their expertise and information on the cost of building dams and reservoirs (around 20 billion USD [45]). This is consistent with previous studies by Linham et al. [46] (estimation of flood adaptation costs for global cities), Jonkman et al. [47], Aerts et al. [48,49], and Lasage et al. [50] (estimation of flood protection costs and flood-proofing of individual buildings), as well as Bayraktarov et al. [51], Lamond et al. [52], and Narayan et al. [53] (estimation of nature-based measures costs for flood management).

The experts then estimated the costs—if they consider building dams and reservoirs as the highest cost option, then a relative cost can be calculated, and we can express the cost of each prevention measure as a percentage of the cost of building dams and reservoirs. The mean value of experts’ assessments was then calculated for each prevention measure, and they were presented as final relative costs. Appendix C,

Table A3. Experts’ relative cost estimates of flood prevention measures.

	Experts
	E1	E2	E3	E4
Measures	Estimated Cost Ratio	Estimated Cost Ratio	Estimated Cost Ratio	Estimated Cost Ratio	Median Value
m1	1.0	1.0	1.0	1.0	1.0
m2	0.9	0.95	0.9	0.9	0.912
m3	0.85	0.8	0.7	0.85	0.8
m4	0.8	0.85	0.9	0.85	0.85
m5	0.7	0.65	0.7	0.75	0.7
m6	0.65	0.7	0.65	0.6	0.65
m7	0.25	0.3	0.35	0.35	0.3
m8	0.25	0.25	0.3	0.2	0.25
m9	0.2	0.15	0.25	0.20	0.2
m10	0.1	0.2	0.15	0.15	0.15
m11	0.1	0.15	0.1	0.1	0.1
m12	0.25	0.2	0.2	0.2	0.2
m13	0.2	0.1	0.15	0.15	0.15
m14	0.18	0.15	0.18	0.19	0.18
m15	0.1	0.15	0.15	0.2	0.15
m16	0.17	0.15	0.18	0.18	0.17
m17	0.35	0.4	0.3	0.35	0.35
m18	0.2	0.25	0.3	0.25	0.25

, contains the entire set of estimated relative costs that were derived from expert assessments, as well as the final calculated mean values of relative costs.

3. Results

The authors of the research conducted an online survey among four experts in the field of environmental disasters and flooding in Serbia to identify barriers for the Event Tree and their probabilities, as well as to obtain aggregated probabilities of these barriers using DS theory. The experts were from the following groups: Public Water Management Company “Srbijavode” (expert 1—E1); Ministry of public investment—water and flood prevention engineer (expert 2—E2); Water management company DTD Northern Banat (expert 3—E3); and academy professor of Environmental management and Environmental risk management at the University of Belgrade (expert 4—E4). The relatively small number of experts aligns with previously conducted research [54,55,56,57,58,59,60,61,62,63].

The authors chose experts from Serbia because, when assessing complex, geographically specific risks like floods, it is critical to involve regional experts who understand local hydrological behavior, infrastructure resilience, institutional response capacity, and sociocultural factors [64,65]. Serbia itself was chosen having in mind its diverse hydrological landscape, with several major rivers, the most notable ones being the Danube, Sava, and Tisza. Periods of intense precipitation and snowmelt make it particularly vulnerable to flooding, with major flooding happening almost annually, and the most famous and most devastating floods were the May 2014 ones that resulted in severe flooding and significant destruction in extensive areas of Serbia, and Bosnia and Herzegovina [66]. Thus, the geographical setting of this country offers a relevant and complex environment for studying the effectiveness of flood management strategies [67]. While the current model is constructed for river floods in Serbia, the barriers in the Event Tree (B1–B11) can be adapted for urban waterlogging or coastal storm surges by redefining specific barriers (for example, replacing levees with seawalls and early warning systems with surge alerts).

However, the authors recognize that this adaptation would necessitate a recalculation of probabilities and regional experts’ assessment in those specific scenarios [68]. The model is intended for different regional applications, allowing different countries or cities to implement it by utilizing the established framework of barriers or modifying them, along with regional expert assigned probabilities, to align with their unique environmental, geographical, and institutional contexts. This provides the advancement of future research through a scenario-based and modularly structured approach. This also helps in choosing context-specific risk-reducing strategies that fit with the local, national, or regional traits of the flood-prone locations. For example, in coastal settings, barriers must reflect marine protection systems, whereas urban flooding scenarios prioritize drainage networks and impervious surface coverage. Thus, the model does not promise global applicability in its current form but rather provides a transferable framework that may be locally adapted by involving regional experts during implementation in different nations or flood types. The same applies to the selected prevention measures used for the OMS model; some or all can be applied across different geographical contexts, depending on the local flood risk, environmental conditions, and available resources or budget.

3.1. Creating the Event Tree Using DS Theory and Expert Knowledge

Using expert knowledge, the analysis of different possible scenarios for applying the Event Tree Analysis method defined the following 11 barriers that could prevent negative consequences of flooding, with each barrier activating if the previous ones fail:

• B1. Regulated watercourse—the state of the watercourse will prevent flooding.
• B2. Regular flood defense measures are successful.
• B3. Timely detection and activation of warning systems.
• B4. Emergency flood defense measures are successful.
• B5. Water does not threaten agricultural land (non-retention).
• B6. Water does not threaten human settlements.
• B7. Warning measures have been issued to the population.
• B8. The population reacted adequately to flood warning measures.
• B9. The evacuation was carried out successfully.
• B10. A certain part of the population did not evacuate, but people who found themselves in the flood were successfully rescued.
• B11. The successful supply of food to the population affected by the floods is carried out.

The main goal of the conducted survey was for the experts to assign probabilities to the success of barriers based on their perception of the flood situation. The experts were advised to take into account the fact that the barriers are not independent, and that the failure of one barrier may influence the probability of success of the barriers that are activated after it. In other words, the success of each barrier might not be independent; one failure can create a ripple effect, increasing the likelihood of further failures. This is also consistent with a recent study by Zhao et al. [69], which stated that risk factors are not independent of one another and proposed that coupling between risk factors should be addressed when assessing risk.

For each barrier, the experts assigned three plausible probabilities, including most likely, less likely, and least likely probability of success. Then, they assigned a degree of belief in the barriers’ success probability. The total sum of the assigned belief degrees was equal to 1. Appendix B,

Table A1. The answers of the experts.

	Experts
	E1		E2		E3		E4
Barriers	bpa	bel	bpa	bel	bpa	bel	bpa	bel
B1	0.6	0.7	0.8	0.5	0.5	0.6	0.6	0.6
	0.3	0.2	0.1	0.4	0.45	0.3	0.3	0.3
	0.25	0.1	0.1	0.1	0.4	0.1	0.2	0.1
B2	0.45	0.4	0.7	0.7	0.5	0.6	0.6	0.6
	0.4	0.35	0.2	0.2	0.45	0.2	0.4	0.3
	0.5	0.25	0.1	0.1	0.4	0.2	0.3	0.1
B3	0.5	0.6	0.2	0.8	0.5	0.7	0.5	0.7
	0.45	0.3	0.2	0.1	0.45	0.2	0.4	0.2
	0.4	0.1	0.6	0.1	0.4	0.1	0.35	0.1
B4	0.7	0.6	0.9	0.9	0.5	0.6	0.8	0.8
	0.5	0.25	0.1	0.1	0.45	0.3	0.4	0.1
	0.45	0.15	0	0	0.4	0.1	0.4	0.1
B5	0.55	0.65	0.5	0.8	0.4	0.1	0.5	0.7
	0.4	0.3	0.3	0.15	0.45	0.1	0.4	0.2
	0.35	0.05	0.2	0.05	0.5	0.8	0.2	0.1
B6	0.55	0.7	0.5	0.9	0.5	0.5	0.5	0.7
	0.5	0.2	0.25	0.05	0.45	0.3	0.4	0.2
	0.4	0.1	0.25	0.05	0.4	0.2	0.3	0.1
B7	0.6	0.45	0.2	0.8	0.5	0.8	0.5	0.8
	0.45	0.35	0.3	0.1	0.45	0.1	0.4	0.1
	0.4	0.2	0.5	0.1	0.4	0.1	0.35	0.1
B8	0.55	0.7	0.5	0.9	0.5	0.6	0.5	0.8
	0.45	0.2	0.25	0.05	0.45	0.3	0.4	0.1
	0.35	0.1	0.25	0.05	0.4	0.1	0.3	0.1
B9	0.65	0.8	0.7	0.5	0.5	0.7	0.6	0.8
	0.4	0.15	0.2	0.3	0.45	0.2	0.4	0.15
	0.3	0.05	0.1	0.2	0.4	0.1	0.3	0.05
B10	0.35	0.2	0.6	0.4	0.5	0.7	0.5	0.6
	0.4	0.3	0.3	0.4	0.45	0.3	0.4	0.3
	0.6	0.5	0.1	0.2	0.4	0.1	0.5	0.1
B11	0.35	0.05	0.1	0.1	0.5	0.6	0.3	0.05
	0.4	0.2	0.1	0.45	0.45	0.3	0.4	0.25
	0.6	0.75	0.8	0.45	0.4	0.1	0.7	0.7

, provides the experts’ answers.

First, the correlation of the expert responses was examined using Pearsons’ correlation coefficient in the statistical program IBM SPSS ver. 23. The results showed that Expert 4 is most consistent with the other experts, especially with Expert 1 and 2. On the other hand, Expert 3 has the weakest and least significant correlations with the others. The correlation matrix is presented in Appendix B,

Table A2. Pearson’s correlations of the experts’ answers.

Variable		Expert 1	Expert 2	Expert 3	Expert 4
1. Expert 1	Pearson’s r	—
	p-value	—
2. Expert 2	Pearson’s r	0.538	—
	p-value	0.001	—
3. Expert 3	Pearson’s r	0.296	0.320	—
	p-value	0.095	0.070	—
4. Expert 4	Pearson’s r	0.824	0.758	0.399	—
	p-value	<0.001	<0.001	0.022	—

.

After obtaining the answers from the experts, using Dempster–Shafer’s rule of combination, the final probabilities of barriers, i.e., single bpa, were calculated using Equation (2) and are shown in

Table 1. Final probabilities of defined barriers.

Barriers	B1	B2	B3	B4	B5	B6	B7	B8	B9	B10	B11
bpa	0.560	0.421	0.490	0.430	0.511	0.512	0.426	0.512	0.417	0.415	0.418

. The rule applied during the determination of the bpa was that, for each question, only the responses of experts whose assessments had a non-empty intersection with those of the other reviewers were considered. This is consistent with principles of Dempster–Shafer evidence theory and ensures that the bodies of evidence being combined are not in total conflict, which is a fundamental requirement for applying Dempster’s rule of combination. For example, in determining the single bpa for barrier B2, the assessments of Expert 2 were excluded (as shown in Appendix B, Table A1). Other authors overcame these issues by utilizing belief entropy or employing normal distribution to define the domain of acceptable expert opinions [58,60,70].

Using the defined barriers, their final probabilities, and derived probabilities of barrier success based on DS theory, an Event Tree was created (Figure 3). If the barriers fail, the first six barriers relate to the population’s vulnerability, with possible prevention measures to be implemented that could minimize the population’s risk, while barriers 7 through 11 can implement corrective measures activated when the population is already at risk.

In the constructed Event Tree, the first branch B1—“regulated watercourse”—means that the state of the watercourse itself is regulated and managed and will hence prevent any flooding. The probability of this statement being true, as deemed by the experts, is 55.5%. If the watercourse lacks adequate management, then it will trigger flooding. Upon this occurrence, the first line of protection consists of regular flood defense measures (B2), which have a probability of 40% of preventing any further flooding. These are proactive, long-term strategies and infrastructure aimed at preventing or mitigating the effects of flooding over time.

Following this, the next important step is the timely detection and activation of warning systems (B3). Unfortunately, the probability of activating these systems is only 49.2%. If this barrier fails with the probability of 50.8%, then the next defense against major flooding is emergency flood defense measures (B4). Should flooding advance beyond these measures, then it might start to encroach on agricultural land (B5). The probability of agricultural land being threatened is 50.3%.

A critical point in this Event Tree is B6, “human settlements are not threatened”, meaning that water has not reached people’s houses and buildings and is not threatening human health and lives. The probability of B6 holding is a mere 24.3% at this point, meaning that there is a 75.8% chance floodwater will advance into human settlements.

Once the flood has reached human settlements, the next barrier is activated to implement warning measures (B7) for the population, with a success probability of 40%. If the public fails to receive the warnings, the next step involves the population’s response to the warning measures (B8). In the case of the population reacting adequately, the probability of success is 49.8%.

If there is a part of the population that did not react according to the warnings, and the water advances, the evacuation of these populations will be necessary (B9). This barrier has a 60% chance of failure, meaning that a certain part of the population was not successfully evacuated. The next step is the rescue of people (B10), which has a 48.4% chance of success. The final step in this Event Tree is to provide support through the delivery of food and supplies (B11) to the affected population, which has a success probability of 40%.

Given all this, the Event Tree can be divided into three categories based on the severity of flooding, which are low impact, medium impact, and high impact. Low impact flooding would stop at B2 when regular flood defense measures stopped the advancement of flood waters. Medium impact flooding would stop at B6 with human settlements being safe. High impact flooding would advance, devastate the environment (both human and natural), and would end with a humanitarian crisis and the army supplying the people trapped in their houses with food and drinking water via helicopters (B11). When looking at the probabilities of each category, we can observe that a flood has a probability of 74.51% of having a low impact, a probability of 23.72% of having a medium impact, and a small probability of 1.71% having a high impact.

Event Tree Analysis proved to be an effective instrument for calculating flood risk and flood risk mitigation by offering a systematic framework to evaluate prospective scenarios and determine the efficacy of various barriers with the help of experts, as well as determine the respective prevention measures.

3.2. Selecting Prevention Measures and Applying Them to the OMS Model

After generating the Event Tree, the next step was choosing prevention measures that would influence the first six barriers, maximize flood prevention, and minimize the occurrence of devastating flooding. For this, the authors chose 18 different prevention measures divided into the following four categories: structural measures, non-structural measures, natural and ecosystem-based measures, and innovative and technological measures.

Structural measures used are shown as follows [71,72,73,74,75,76,77,78]:

• m1. Dams and reservoirs, relative cost = 1;
• m2. Levees and floodwalls, relative cost = 0.9;
• m3. Diversion channels, relative cost = 0.8;
• m4. Floodgates and sluices, relative cost = 0.85;
• m5. Retention basins and ponds, relative cost = 0.7;
• m6. Detention basins, relative cost = 0.65.

Non-structural measures used are shown as follows [79,80,81,82,83,84,85,86]:

• m7. Flood forecasting and early warning systems, relative cost = 0.3;
• m8. Floodplain zoning and land use planning, relative cost = 0.25;
• m9. Building codes and standards, relative cost = 0.2;
• m10. Emergency response plans, relative cost = 0.15;
• m11. Maintenance of drainage systems, relative cost = 0.1.

Natural and ecosystem-based measures used are shown as follows [87,88,89,90,91,92]:

• m12. Wetland restoration, relative cost = 0.2;
• m13. Riparian buffer zone, relative cost = 0.15;
• m14. Reforestation and afforestation, relative cost = 0.18;
• m15. Sustainable agriculture practices, relative cost = 0.15;
• m16. Coastal wetland protection, relative cost = 0.17.

Innovative and technological measures used are shown as follows [93,94,95]:

• m17. Smart flood management systems, relative cost = 0.35;
• m18. Permeable pavements, relative cost = 0.25.

For each measure and each barrier, the increase of the probability of barriers success was assessed and is given in Appendix C 

Table A4. The assessment of the probability of barriers success.

	Barriers
Measures	B1	B2	B3	B4	B5	B6
m1	0.045	0.045
m2	0.0375	0.040			0.040	0.045
m3	0.033	0.037			0.035	0.040
m4				0.040	0.030	0.035
m5	0.030	0.035		0.035	0.025	0.030
m6				0.030	0.020	0.025
m7		0.030	0.045
m8		0.025				0.020
m9			0.045			0.015
m10			0.030	0.045
m11		0.020				0.010
m12		0.015			0.015
m13	0.018	0.012			0.010	0.005
m14	0.020	0.010			0.005
m15					0.003
m16	0.033	0.008			0.002
m17		0.032	0.048	0.048	0.045	0.048
m18						0.003

.

It is important to note that the model was introduced with constrictions where some flood prevention measures might not be feasible to execute all at the same time, adding more limitations to the OMS model. This method recognizes that redundant or overlapping measures might decrease efficiency and result in logistical conflicts or needless resource utilization. By understanding these constraints, the model is made to allocate resources as efficiently as possible, guaranteeing that every action adds to the overall flood prevention plan without inadvertently overlapping.

A series of optimizations were conducted using the OMS model. The ideal budget level was set at an estimated 3625 monetary units (estimated cost of all prevention measures combined), with the cost of the first measure fixed at 500 (provisional cost for model testing), while the costs of subsequent measures were determined based on a predefined relative cost ratio. Optimizations were carried out for scenarios with available budgets ranging from 10% to 100% of the ideal level, in increments of 10%.

The optimal solutions, or the measures to be taken for each budget scenario, are presented in

Table 2. Optimal selection of measures for varying levels of available budget.

		% of Available Budget
Measure Symbol	Measures	10	20	30	40	50	60	70	80	90	100
m1	Dams and reservoirs	0	0	0	0	0	0	0	0	1	1
m2	Levees and floodwalls	0	0	0	0	0	1	1	1	1	1
m3	Diversion channels	0	1	0	1	1	1	1	1	1	1
m4	Floodgates and sluices	0	0	0	0	0	0	1	1	1	1
m5	Retention basins and ponds	0	0	1	1	1	1	1	1	1	1
m6	Detention basins	0	0	0	0	0	0	0	1	1	1
m7	Flood forecasting and early warning systems	0	0	1	1	1	1	1	1	1	1
m8	Floodplain zoning and land use planning	0	0	0	0	1	0	0	0	0	0
m9	Building codes and standards	1	0	1	0	1	1	1	1	1	1
m10	Emergency response plans	1	1	1	1	1	1	1	1	1	1
m11	Maintenance of drainage systems	0	0	1	1	1	1	1	1	1	1
m12	Wetland restoration	0	0	0	0	1	1	1	1	0	0
m13	Riparian buffer zone	0	1	1	1	1	1	1	1	1	1
m14	Reforestation and afforestation	0	0	0	1	1	1	1	1	1	1
m15	Sustainable agriculture practices	0	0	0	0	0	0	0	0	0	0
m16	Coastal wetland protection	0	0	1	1	1	1	1	1	1	1
m17	Smart flood management systems	1	1	1	1	1	1	1	1	1	1
m18	Permeable pavements	0	0	0	0	0	0	0	0	0	0

.

4. Discussion

The results of the Event Tree Analysis show that all barriers, except B1, displayed a higher chance of failure than success. Managing a watercourse (B1) involves applying proactive strategies to ensure optimal water flow, mitigate flooding risks, safeguard ecosystems, maintain water quality, and guarantee long term resilience. It is the first step in safeguarding any country and its environment against floods. The expansion of urban areas results in the loss of natural flora and extensive soil sealing, thereby enhancing both the amount and speed of surface runoff [96]. This barrier should be improved significantly, so that the odds of the barrier’s success are much higher.

At the same time, B2 exhibits a significantly poor success probability of only 40% in mitigating downstream flood escalation. This causes considerable concerns from both an engineering resilience and decision-support standpoint. The emphasis is on prevention and preparedness instead of instant response. The poor success of B2 indicates significant space for development in preventative infrastructure. Although regular flood defense measures, such as structural prevention measures, are the first line of defense against flooding, they are not without limits. Overreliance on structural interventions can lead to a false sense of security, resulting in under preparedness and increased vulnerability in the case of structural breakdown [97].

The low success rate of B3 may result from human error, lack of communication, outdated technology, or system failure. While early warning systems can dramatically reduce fatalities and economic disruption, their effectiveness is strongly dependent on data integrity, system integration, and public engagement [98]. Delays in sensor-based forecasting, for example, poor communication networks, and ineffective public education efforts frequently result in insufficient warning dissemination.

Emergency response plans, such as those represented by B4, aim to alleviate the immediate effects of a flood and save lives and property. These are responsive measures implemented when a flood risk is imminent or is currently occurring, such as sandbags, temporary barriers, mobile pumps, road closures, and emergency workers and supplies. In the model, B4 has a moderate success rate (43%), indicating both its crucial importance and its vulnerability under pressure. Emergency measures are essentially reactive, and their effectiveness is frequently dependent on early warning (B3), logistical preparedness, inter-agency collaboration, and public awareness [99].

Agricultural flooding (B5—50.3% chance of occurring) has both immediate and lasting socioeconomic and environmental consequences. Floods pose significant hazards to agricultural production and land safety, directly affecting food security, especially in flood-prone rural areas. Crop flooding kills crops, erodes fertile topsoil, and delays planting seasons, resulting in lower yields and long-term land degradation. Flooding also disrupts agricultural supply systems, from input transportation to market access for harvests, exacerbating food poverty in already vulnerable populations after flooding [100].

Barrier B6 is a crucial point in the Event Tree, indicating that human settlements have not yet been affected by advancing floodwaters. This suggests that residential areas, infrastructure, and critical services are secure, and human health and life are not in immediate danger. However, the model determines only a 24.3% chance of success of this barrier, implying that floodwaters will encroach on populated regions with a 75.8% chance. This reveals a major vulnerability in the system and indicates the shift from a manageable flood scenario (B1 to B5) to one with potentially catastrophic repercussions (B6 to B11). The flooding of human settlements has extensive and cascading consequences, including housing damage, public health issues, interruptions to transportation and communication systems, and forced displacement. Furthermore, urban flood resilience is highly associated with land-use planning, early warning systems (B3), and emergency flood defense measures (B4). When these upstream barriers fail, human settlement vulnerability is exposed.

Once human settlements are endangered, warning measures are issued to the population at risk (B7), urging people to prepare for potential floodwaters and evacuate if necessary. The probability of the timely activation of warning measures is 40%. This is a very low number for such an important barrier. Human behavior and the timing of warnings significantly influence the number of casualties during flood evacuation. A delay of 30 min in issuing the warning has the potential to increase the number of casualties by up to six times [101]. If the public fails to receive the warnings due to communication errors, human errors, technical failures, or other factors, then the next step involves the population’s response to the warning measures (B8). In the case of the population reacting adequately with the probability of 49.8%, then no further evacuation of people will be needed. Generally, mass evacuations mean that many people must be evacuated at the same time, especially in vulnerable and populated areas. Vulnerable people (impoverished populations, older generations, ill or immovable patients, etc.) frequently accept the idea of evacuation directly before floodwater approaches their homes, when the chances for successful evacuation are at their lowest [102]. This results in additional evacuation difficulties and more casualties and losses. “Other factors which may also affect the decisions are age, gender, the level of education, house ownership, the number of the floor of the house, the number of members in the household, and also the residency distance from the disaster” [103]. To achieve this purpose, well-designed planning and evacuation management at the early stage of a crisis are critical [104]. If there is a part of the population that did not react according to the warnings, which is usually elderly people who are at risk and are “the most common primary victims” [104,105], or people who have nowhere else to go, or an economically vulnerable population, and the water advances, then the evacuation of these populations will be necessary. “The ability to safely and efficiently evacuate vulnerable people from areas at risk of flooding is one of the most critical disaster risk management strategies” [104,105]. Flaws in communication infrastructure can impede the timely transmission of alerts. Essential flood alerts may not reach the entire population in areas with weak or unreliable communication networks, particularly in rural or isolated areas with limited internet and cellular connectivity. Public education and awareness of flood hazards and response strategies are also required. In the absence of persistent public awareness campaigns and educational programs, the people may be underinformed about how to respond to flood warnings [106]. “Awareness, prevention, mitigation, and readiness” are the essential components of capacity building that are critical for any efficient disaster management program [107]. The lack of readiness frequently results in delayed or inappropriate responses, reducing the overall effectiveness of evacuations.

If the evacuation of the population at risk is successful (B9), then this barrier will hold, and no further adverse effects will take place. Unfortunately, this barrier has a 60% chance of failure, meaning that a certain part of the population was not successfully evacuated during the efforts. Furthermore, the greater likelihood of failure in evacuation and rescue operations could be related to limited resources and competencies within emergency response agencies. If these resources are limited because of budgetary constraints or insufficient logistical assistance, then reaction attempts may be poor or delayed. Additionally, human behavior during floods, such as resistance to leave or poor decision-making under stress, can have a significant impact on the success of evacuation efforts. Understanding these tendencies and incorporating them into evacuation plans may help to reduce hazards [108]. All these variables highlight the importance of a comprehensive approach to improving public response and the effectiveness of emergency services, including investments in infrastructure, public education, and resource allocation.

The next step is the rescue of people (B10) caught in the flood, which, worryingly, only has a 48.4% chance of success. The final step in this Event Tree is providing support through the delivery of food and supplies (B11) to the affected population. This has a success probability of 40%, where adequate provisions reduce suffering, while a 60% probability of failure could lead to a humanitarian crisis, exacerbating the hardship faced by the flood-impacted communities. This is particularly alarming due to the devastating humanitarian consequences that can result when rescue and relief efforts are unsuccessful during flood disasters. In flood-affected regions, the success or failure of relief operations significantly determine mortality rates and long-term psychological trauma [109], and failed humanitarian responses can result in prolonged displacement, increased poverty, as well as a greater susceptibility to future disasters [110].

In addition to the primary analysis, the Event Tree also enables what-if scenario assessments, which allow for the examination of the effects of different sequences of barrier activation during flood events. For example, in the case of barrier B8, two distinct scenarios can be considered. The first scenario assumes that a limited number of individuals were evacuated, that they had access to alternative shelter, and they were able to secure supplies independently. In this case, food and supply distribution would be limited only to those who remained within the flooded area (B11), as modeled in the scenario presented in this study. The second scenario considers a mass evacuation event involving a large number of people who lack alternative accommodation. These individuals would be relocated to temporary shelters, camps, or centers. Under such conditions, following the activation of B8, it would also be necessary to activate B11 to ensure the provision of food and supplies to the evacuees. In this case, in both scenarios, the barriers involved are characterized by success and failure probabilities that do not influence the overall probabilities of medium and high-impact outcomes. These outcome probabilities remain unchanged. Since the total probability across all outcomes must equal one, the aggregate probability of negative outcomes also remains unaffected.

Another what-if scenario is a sensitivity test to show how much flood risk outcomes change when we introduce dependencies between barriers, specifically the failure of Barrier B3 (timely detection and activation) affecting the probability of B9 (successful evacuation) and B10 (successful rescue). In this specific case, adding dependencies where the failure of B3 increased the failure of B9 and B10 by 25% had no significant impact on the outcome probabilities under the current framework. This is because the likelihood of failure for multiple barriers (particularly B6, B7, and B9) is already high; the model shows high-impact outcomes. As a result, slight to moderate changes in B9 and B10 do not significantly alter the outcome distribution because the “damage” has taken place earlier along the event path.

The results of the Event Tree clearly show that prevention is crucial in reducing the chance of severe flooding consequences. Within the OMS framework used in this paper, early stage barriers, particularly those focusing on infrastructure regulation, regular flood defense (B2), and timely warning systems (B3), are identified as the most effective for lowering systemic risk. Unlike reactive or emergency procedures, which activate only after flooding has occurred, preventive actions address risks before disaster circumstances worsen. This not only raises the likelihood of positive results but also minimizes reliance on costly, unpredictable emergency responses. The OMS technique served to identify the best prevention measures by evaluating their impact on overall system reliability and outcomes, allowing for more targeted and cost-effective resource allocation.

The model included constraints, recognizing that certain flood prevention measures may not be implementable at the same time. For example, in certain situations, it may be best to pursue wetland restoration without constructing dams and reservoirs because these strategies have distinct biological and hydrological functions, and combining them might occasionally be ineffective or even detrimental for wetlands. The second restriction was that reforestation/afforestation and riparian buffer zones both involve planting vegetation, but they focus on different parts of flood management and might overlap when used together. Simultaneously, because sustainable agriculture practices, floodplain zoning, and land use planning target overlapping areas but have different focal points, implementing them as concurrent flood prevention measures may lead to conflicts or redundancy; applying both strategies in the same location could impose restrictions on land use, potentially limiting opportunities for sustainable agriculture in floodplain areas. Resources and efforts can be effectively targeted and optimized for efficient flood control by choosing the best course of action depending on regional features, such as prioritizing floodplain zoning in high-risk areas and sustainable agriculture practices in nearby or less vulnerable areas. Furthermore, in some places, constructing ponds and retention basins along with permeable pavements as flood prevention measures may be unnecessary because both strategies aim to control stormwater by letting it seep in and by reducing water flow, but this is conducted in different ways; retention basins might be adequate in a big open space, while permeable pavements work better on paved areas with heavy traffic. Setting location-based priorities for the right measure can increase productivity and cut expenses.

Evaluated prevention measures fell into one of the following four categories: structural measures, non-structural measures, natural and ecosystem-based measures, and innovative and technological measures

Structural measures in flood prevention refer to implementing physical structures and modifications in the environment that are specifically intended to manage and minimize the danger and consequences of floods. These measures are implemented to regulate the water movement, safeguard infrastructure, and prevent further harm to the population and ecosystems. The sole purpose of these structures is to keep floodwaters from accessing and causing harm to a specific area. The drainage systems and good management associated with them can minimize and manage urban floods caused by heavy rainfall. Groundwater-related urban floods are formed when a set of heavy rainfall surpasses the capacity of the underlying infrastructures for drainage, after which water in the streets, buildings, and other urban parts accumulates. Efficient drainage systems and effective management practices are handy for handling these kinds of eventualities. Solutions for such problems can be stormwater drains, combined sewer systems, and regular maintenance and cleaning [86].

Non-structural flood prevention measures refer to methods, policies, and practices that do not include physical structures but play a crucial role in reducing and managing flood hazards. These principles are applicable to the reduction of vulnerability, improvement of readiness, and promotion of successful response and recovery

Natural and ecosystem-based measures make use of the inherent capacity of ecosystems to manage or decrease flood risks and therefore work in partnership with nature to enhance landscapes and communities in their resilience against floods through effective functioning. Their important function includes many obvious benefits, like the preservation of biodiversity, water quality improvement, and the creation of opportunities for recreation.

Innovative and technological measures encompass the use of cutting-edge technology and contemporary engineering solutions to accurately forecast, monitor, and efficiently control flood hazards. These strategies bolster the ability to prevent and address flood occurrences by enhancing data, communication, and infrastructure.

The contribution of prevention measures in the optimal solutions is illustrated graphically in Figure 4, and it can be observed that a measure included in the optimal solution at one budget level may not remain in the optimal solution after an increase in the budget (e.g., measures m3 and m8). The reason for the temporary inclusion of these measures in the optimal solution is that, at lower budget levels, some more efficient measures cannot be included due to their higher costs, which exceed the available budget.

The remaining values related to the optimal solutions are presented in

Table 3. Characteristic values based on optimal solutions.

%Ideal Budget	Available Budget	Probability	No of Measures	Probability Increase
				b1	b2	b3	b4	b5	b6
0.1	362.5	0.9859	3	0.0000	0.0800	0.2498	0.2066	0.0906	0.2598
0.2	725	0.9890	4	0.0901	0.2025	0.1584	0.2066	0.1812	0.3835
0.3	1087.5	0.9934	8	0.1441	0.3425	0.3411	0.2844	0.1651	0.4454
0.4	1450	0.9950	9	0.2387	0.4600	0.2498	0.2844	0.2456	0.5485
0.5	1812.5	0.9964	12	0.2387	0.5600	0.3411	0.2844	0.2758	0.6928
0.6	2175	0.9974	12	0.3063	0.5975	0.3411	0.2844	0.3563	0.7959
0.7	2537.5	0.9980	13	0.3063	0.5975	0.3411	0.3733	0.4167	0.9402
0.8	2900	0.9983	14	0.3063	0.5975	0.3411	0.4399	0.4569	1.0433
0.9	3262.5	0.9987	14	0.3873	0.6725	0.3411	0.4399	0.4267	1.0433
1	3625	0.9987	14	0.3873	0.6725	0.3411	0.4399	0.4267	1.0433

. The first and second columns represent the percentage of the ideal budget and the corresponding amount. The third column shows the probability of positive and acceptable outcomes. The fourth column displays the number of measures that can be implemented with the available budget. The last six columns illustrate the increase in each of the first six barriers.

As expected, with an increase in the available budget, the overall probability of positive and acceptable outcomes also rises. However, not every budget increase leads to a significant improvement in the overall probability. Figure 5 illustrates that the largest probability increase occurs between 10% and 30% of the ideal budget, after which the probability growth slows as the budget continues to increase. In the final case, increasing the budget from 90% to 100% of the ideal budget does not result in a probability increase. For example, if the budget increases from 20% to 30% of the ideal budget, the probability of positive and acceptable outcomes increases by 0.45% (from 0.989 to 0.9934), while the effect of further budget increases is less than 0.16%. The evidence suggests that selecting the right type of measures within the available budget is far more important than simply increasing the budget amount.

From Table 3, it can be observed that the selected (optimal) measures have different impacts on the barriers, which is also illustrated in Figure 6.

As can be seen from Figure 6, none of the barrier probabilities exhibit a constant increase with the rise in available budget. Like the overall probability, the barrier probabilities are not impacted by increasing the budget from 90% to 100% of the ideal budget. Generally, an increase in available budget has the least effect on Barrier B3, timely detection and activation of the warning system. This is because only four out of the 18 selected measures influence this barrier, and they are m7, m9, m10, and m17 (as shown in Appendix C Table A4. Since starting from 50% of the available budget, the optimal solutions (Table 2) include all four of these measures, and the success probability of this barrier could not be increased further from 0.5975, as no further measures address this barrier. Among them, m7 (flood forecasting and early warning systems) and m17 (smart flood management systems) are the most directly tied to technological early warning capabilities, which often have significant initial efficiency but rapidly achieve a state of saturation. On the other hand, m9 (building codes and standards) and m10 (emergency response plans) indirectly enhance early warning outcomes by strengthening institutional readiness and public preparedness. However, these do not exponentially enhance B3’s success once implemented. This signifies a saturation point, at which point further investment produces negligible or no benefit.

The 18 selected flood prevention measures were assessed for both individual efficacy and cost-effectiveness in relation to the most expensive solutions, such as dams and reservoirs [86]. For example, structural interventions, such as those, have large initial costs but provide significant contributions to long-term flood control. Non-structural solutions, such as floodplain zoning and land use planning, offer a cost-effective, long-term benefit by reducing vulnerability in flood-prone areas (with a cost ratio of only 0.25). These non-structural methods contributed significantly to B2 and B3, hinting that combining them could improve flood resilience.

The model shows that optimal flood protection results can be obtained without fully using the budget. Incremental budget allocation increases the possibility of barrier success by 10% to 30% of the optimum budget, emphasizing the need to select the best solutions within the given budget. For example, with a 50% budget, tremendous efficacy can be achieved by implementing measures like emergency response plans and drainage system maintenance, which contribute significantly to various barriers without incurring high costs. Interestingly, budget increases of more than 90% result in modest improvements in success probabilities, demonstrating the lesser benefits above a certain level. This indicates that carefully selecting flood protection methods based on local context and barrier demands can yield positive results without incurring large financial costs.

Despite budget increases having a favorable effect on most flood prevention barriers, B3 is insensitive to additional funding. This constraint creates an opportunity for targeted investment in newer technology to boost early warning capabilities.

The model’s results show that a flood protection strategy would be most effective if it included a suitable combination of structural and non-structural measures, each having a complementary role in reducing flood risks and mitigating potential impacts. Dams, levees, and diversion channels provide the required physical infrastructure to regulate water flow and protect critical areas from flooding. Simultaneously, non-structural measures such as early warning systems, floodplain zoning, and public education highlight risk mitigation and preparedness, allowing communities and authorities to respond more proactively.

Strengthening initial barriers, such as B1 and B2, is critical for minimizing the chance of flooding occurrences progressing to the next phase. If these primary defenses are effective, then they will significantly reduce the need for reactive measures such as emergency evacuations or rescue operations. By preserving the integrity of these first barriers, the country may avoid the costly and resource-intensive procedures required when floodwaters intrude on populated or vulnerable areas. The model demonstrates how early investment in maintenance and upgrading controlled watercourses, along with the deployment of proper flood defense techniques, can provide a “first line of defense” that successfully limits and mitigates possible flood consequences.

The given Event Tree model, which adjusts to river flood scenarios, offers a systematic way of evaluating the effectiveness of various barriers (B1–B11) in reducing the effects of floods. While the current application is geographically specific to fluvial environments, the framework’s structure allows for conceptual application to other forms of floods, such as coastal flooding, flash floods, and urban waterlogging. Each flood type is distinguished by unique hydrodynamic behavior and exposure patterns, necessitating adjustments to both barrier definitions and their corresponding probabilities. For example, in coastal locations, traditional levees (B2) and floodplains (B4) may be replaced with seawalls and surge barriers, while early warning systems (B3) must be adjusted to account for the rapid onset of storm surges [111]. Similarly, in urban contexts, the focus will shift towards stormwater drainage networks, permeable pavements, and smart flood management systems [112]. In flash flood scenarios, where the period between precipitation and flooding is extremely short, essential success factors include timely detection and the activation of warning systems (B3), emergency flood measures (B4), and quick population reaction (B8). These events frequently occur in small catchments with complicated topography and are very sensitive to local land use, indicating the necessity for a localized recalibration of model inputs.

Current cutting edge flood management systems are mostly based on AI, machine learning, geospatial analysis, and different hybrid frameworks [113,114,115,116]. While these methods are data-intensive and require real-time sensors, historical records, and geospatial mapping, the methodology proposed in this paper uses expert-driven probabilities, and has modest computational and data needs. Adaptability to data scarcity and limited access to data is very high since the framework is effective even in low-data environments through structured expert judgment. The model presented in the paper allows for scenario testing, especially where information is limited. While it integrates qualitative expert insight with quantitative probabilistic modeling, offering novel hybrid analysis for flood resilience, as opposed to cutting edge flood management systems, for scalability and generalization, it requires re-calibration with new experts in different regions, scalable with caution. The relatively low cost and lightweight computational complexity provide benefits compared to high infrastructure and data acquisition costs of other flood management systems.

Although the presented study adds to the research field in flood risk assessment for resilience, it has its limitations. Gaps in the availability of data caused the presented OMS model to be based on an estimated cost of prevention measures. Consequently, future research could be improved by the addition of data relating to the real costs of prevention measures. This limitation leads to the conclusion that the development and implementation of a flood management system can be designed with real-time data services and integrated with detailed statistical reporting on the various types of measures that are needed. “In addition, deep learning algorithms can be used for preprocessing tasks of numerical simulation data, correcting and optimizing parameters in numerical analysis models, improving the reliability of models, and enhancing the performance of traditional numerical analysis methods” [117,118,119]. In this way, it is possible to continuously optimize flood management measures so that both they and flood management systems are significantly changed towards more sustainable strategies [32].

Despite these limitations, this paper bridges the gap in the current literature by implementing the joint use of Dempster–Shafer evidence theory, Event Tree Analysis, and an optimization approach in flood risk assessment. This paper investigated and applied a novel model of flood risk assessment in a way that provided scientific information on important issues and added a meaningful perspective on flood risk analysis and flood risk assessment.

5. Conclusions

To this day, disasters are substantial, unresolved issues that challenge the capacity of communities and nations to safeguard populations and infrastructure every year [1,9]. The seemingly random consequences and issues, along with the distinctiveness of catastrophes, necessitate dynamic, efficient, and cost-effective real-time responses, making operational research an effective scientific tool in risk reduction and risk assessment. There is an increasing acknowledgement of the necessity to examine operational research in disaster management, particularly with floods [120,121,122]. Floods are among the most frequent and destructive natural disasters, resulting in substantial death tolls, financial losses, and long-term effects on the environment and human health. Examining the unpredictable nature of floods, their immediate and long-term effects, and the growing danger brought on by socioeconomic and climate change variables [13] helps us understand why exactly they are so terrifying. As weather patterns and the severity of storms are rapidly changing in real time, as evident by the recent Hurricane Milton and Hurricane Helene [123], flood risk management must clearly reflect how flood risk may alter in the future, for example, because of climate change or floodplain development. Furthermore, with a warmer temperature and more noticeable flood seasonality than in the past, the last three decades in Europe have been among the most flood-rich times [124]. Predictions of affected populations and direct damage from flooding show that, with the end of the 20th century, the socioeconomic effect of flooding from rivers in Europe is expected to grow by an average of 220% caused by climate change [125].

This paper introduces a novel hybrid approach to flood risk assessment by integrating Event Tree Analysis with Dempster–Shafer evidence theory and optimization modeling (OMS) to enhance decision-making under uncertainty. The results highlight the significance of early prevention measures, such as controlled watercourses and early flood defense tactics.

The methodology presented allows for the calculation of probabilities for flood barriers under uncertainty and the strategic selection of cost-effective prevention measures that improve flood resilience within budgetary constraints. The model, when applied to Serbia’s hydrologically varied landscape, indicated that the most significant barriers, especially those related to human settlement protection, early warning systems, and emergency responses, exhibited lower probabilities of success, highlighting the pressing need for systemic enhancements in flood preparedness. At the same time, this approach provides applicability by enabling modification to localized context by using local expert assessment, local hazard classifications, and scenario-based probabilities. Its modular design is adaptable for areas susceptible both to riverine, urban, or coastal floods.

Moreover, it addresses concerns recognized by the Intergovernmental Panel on Climate Change, especially the increasing unpredictability of extreme hydroclimatic events [126], which assists in resilient planning in the context of climate change. The implementation of scenarios in modeling offers an optimized framework for flood risk assessment. This approach enables decision-makers to make informed choices and formulate long-term, sustainable strategies aimed at enhancing flood resilience. Additionally, we drew on the knowledge of domain experts to foster a deep understanding of local contexts, which is vital in the complex arena of flood risk assessment [68].

The importance of early, cost-effective non-structural prevention measures, including disaster response planning, drainage maintenance, and land use zoning, was emphasized through the results of the OMS model. The decreasing benefits seen beyond 90% of the optimal budget reinforce the assumption that the selection of prevention measures is more successful than merely raising expenditures, an assessment confirmed by adaptive management frameworks [127].

The significance of incorporating social vulnerability, communication networks, and public behavior (B7, B8, B9) into flood models is widely acknowledged in flood risk research. Inadequate evacuation or delayed warnings of disaster often result in higher human casualties [121,128]. Reducing this risk is a direct recommendation for investment in smart flood warning systems, community education, and informed risk communication [129].

Having all this in mind, enhancing flood resilience demands a layered defense strategy that integrates strong prevention measures with flexible non-structural and nature-based approaches. This paper presented a flexible, evidence-based framework for disaster risk reduction. Further research could broaden this methodology by integrating dynamic hydrological modeling and real-time data from IoT-based sensing devices to augment predictive capability and responsiveness.

In conclusion, resilience must be integrated into the very fabric of our construction, planning, and response in the face of rising floods and changing temperatures. It cannot be reactive but proactive at every step.