Dam System and Reservoir Operational Safety: A Meta-Research

Abstract

Dams are critical infrastructure necessary for water security, agriculture, flood risk management, river navigation, and clean energy generation. However, these multiple, and often conflicting, objectives introduce complexity in managing dam operations. In addition, dam infrastructure has been evolving as complex systems-of-systems with multiple interacting components and subsystems, all susceptible to a wide range of uncertainties. Such complexities and uncertainties have triggered extensive research initiatives focused on dam systems and reservoir operational safety. Focusing on the latter, this paper meta-researches (conducts research-on-research) previously published studies to identify the critical research gaps and propose future research directions. In this respect, this paper first performs a quantitative analysis of the pertinent literature, using text mining and subsequent topic modeling, to identify and classify major and uncover latent topics in the field. Subsequently, qualitative analysis is conducted to critically review the identified topics, exploring the concepts, definitions, modeling tools, and major research trends. Specifically, the study identified seven topics: optimization models; climate change; flood risk; inflow forecasting; hydropower generation; water supply management; and risk-based assessment and management. The study also presents three main research gaps associated with the limitations in modeling concepts, modeling tools capabilities, and the lack of resilience-guided management of dam operational safety. Overall, this study presents a road map of the currently available dam and reservoir operational safety research and associated knowledge gaps, as well as potential future research directions to ensure the resilience of such critically important infrastructure, especially in the age of climate change.

1. Introduction

Since the fourth millennium BC, dams have been critical structures constructed to regulate water discharge required for irrigation and to protect people from flood consequences [1]. Attributed to the expansive socio-economic development over the last century, the global demand for water and energy, and, thus, safely operable dams, has been significantly and rapidly increasing [2,3,4,5,6]. In addition, climate change has recently highlighted the role of dams as climate risk mitigation infrastructure [7,8] whereby dams can alleviate the impact of climatological hazards such as droughts and floods. Moreover, several countries increased their reliance on dams for hydropower generation, considered the most efficient clean energy source to reduce greenhouse gas emissions [9]. As a result, hydropower dam construction significantly increased in the past decade to reach nearly 50,000 dams worldwide, with the expectation of continued growth in the future [10].

In parallel to their critical importance, dams are highly complex system-of-systems consisting of several intra-dependencies, including physical (e.g., gates and turbines) and non-physical (e.g., human decisions and maintenance time) components. Dams also have several inter-dependencies with other dams along the same river system (i.e., cascading dams) and other critical infrastructure systems within the communications, energy, food and agriculture, transportation, and water sectors [11]. Such intersectionality of dam operation objectives creates decision-making complexity considering the multi-purpose dam operational rules. For example, flood control operations require a low reservoir water level, while a high reservoir water level is essential for efficient hydropower generation. In addition, on the one hand, dams are considered key for climate risk mitigation [7,12]. On the other hand, climate change is likely to affect dam operational safety, as it introduces uncertainties in the meteorological and hydrological variables that directly impact the temporal and spatial water availability for dam operations [13]. These dynamic, complex, non-linear, and uncertain behaviors introduce serious challenges to dam and reservoir operations, leading to challenges in understanding and predicting dam system operational failures [14]. Given the destructive consequences of such operational failures, extensive research has been established to investigate the safety of dam systems and reservoir operations under multiple stressors.

Several research studies [15,16,17,18,19] reviewed pertinent extensive previous work to identify the critical research gaps in the existing field. However, these traditional reviews were usually subjective in terms of selecting only a subset of documents pertaining to the specific selected sub-topic (e.g., optimization models) within the field. This is prevalent in literature even though the literature showed that topics addressing dam systems and operational safety are very broad due to dam interdependencies and their use’s multi-objectivity. Accordingly, the current study adopts a meta-research (conducting research-on-published research) approach to first identify and classify the main research topics using text analytics (i.e., a machine learning tool that extracts meaningful information from textual data) and subsequently uncover the latent topics and the key research gaps (i.e., ill-covered areas) within the dam system and operational safety. Topic modeling is employed to identify latent topics in different fields such as transportation [20], operational research [21], city resilience [22], and structural engineering [23]. More specifically, this study adopted two stages to represent the meta-research on dam systems and reservoir operational safety. Stage 1 includes quantitative analysis, using topic modeling to identify major topics and uncover the literature’s latent topics (i.e., the topics that do not frequently appear within the literature). Subsequently, Stage 2 includes a qualitative review, examining the definitions, concepts, and recent research trends related to the identified topics. Using quantitative and qualitative analyses, this paper can determine the key research gaps that are not well covered in the literature and can significantly impact dam systems and reservoir operational safety.

2. Quantitative Analysis

2.1. Data Collection

Initially, this study considered more than 1000 journal articles relevant to dam systems and operational safety to be analyzed using text analytics (i.e., topic modeling) to identify the major topics in the field. The data collection process started by searching the titles of the journal articles through the Web of Science (https://www.webofknowledge.com, Last accessed: 1 August 2023) and Engineering Village database (https://www.engineeringvillage.com, Last accessed: 1 August 2023) from 1984 to 2023 using the common keywords related to the field. The considered keywords in the search process are [(Dams OR Reservoirs) AND (Operations OR System) AND (Safety OR Risk OR Resilience OR Uncertainties OR Reliability OR Failure OR Vulnerabilities OR Hazard OR Stochastic)]. The selected articles were subsequently filtered by exploring each article’s abstract and evaluating its relevance to the field. After this abstract-based screening process, the selected articles were further filtered, which yielded 871 journal articles considered for further analysis. The analysis process considers the articles’ abstracts. The abstract is usually adopted by different topic modeling studies [24,25,26] to represent the entire article. Abstracts typically summarize the overall study objective, research questions, methodology, significant findings from the study results, and recommendations through short and precise sentences.

2.2. Pre-Processing

The raw abstracts of the selected articles usually contain various sources of linguistic noise that negatively affect the statistical analysis performed within the topic modeling [27]. This linguistic noise is mainly produced as a result of case type variation (e.g., DAM and dam), special characters (e.g., punctuation), word forms (e.g., operation and operational), and the presence of the English common words (e.g., the, and, of). As such, pre-processing is essential before topic identification to eliminate such linguistic noise. Pre-processing is typically performed through four steps [28]: (1) the transformation step is adopted to change the format of all words to be in lower case; (2) the tokenization step is adopted to convert the unstructured text into words to be analyzed; (3) the treatment step is adopted to act as a filter with ‘stop’ word list to remove the common words out of the text data; (4) the stemming step is adopted to remove all the affixes and return them to the word stem.

Figure 1 shows the word clouds before and after the pre-processing of the raw abstracts data set, showing the words with a minimum of 70 times of occurrence (frequency) within the analyzed text. The size of each word represents its importance, where it reflects the word’s probability of occurrence in the analyzed text. As such, the words with large sizes represent the most frequent (i.e., key) words in the analyzed text. Based on this fact, the comparison between the word clouds in Figure 1 can show that Figure 1a includes highly frequent nontechnical common words (e.g., the, for, and), while Figure 1b eliminates such noise and only represents the technical words related to dam systems and reservoir operational safety (e.g., risk, optim, inflow). This comparison illustrates the critical role of the pre-processing step in text analytics in eliminating the non-essential words that significantly increase the computational cost and affect topic identification.

2.3. Latent Dirichlet Allocation (LDA)

Latent Dirichlet Allocation (LDA) is a generative probabilistic model developed by Blei et al., 2003, [29] based on the probabilistic latent semantic analysis (pLSA) model [30]. The LDA model is used in topic modeling to identify the latent topics of a group of textual documents (more details about how this model works within scientific documents can be found in [31,32]. The main advantage of LDA over other topic models (e.g., Correlated topic models) is the reasonable computational time. LDA significantly reduces the number of dimensions (i.e., words) within the analyzed documents while maintaining the critical relationships between this document’s dimensions and their major topics [29]. Therefore, several studies adopted the LDA model in different fields [33], such as genetic data, music, and structural engineering [23].

The concept of the LDA model is to represent each document (d) (composed of a collection of words (w_d)) as a distribution of topics K (θ_d) (e.g., Two-topic model: document 1 is 70% of topic A and 30% of topic B). Each topic (k) (k $\in$ K) is characterized by a distribution of words (ψ_k) (e.g., Topic A consists of 10% of word 1, 20% of word 2, 30% of word 3, etc.). The LDA model aims to estimate the θ_d and ψ_k, so the user can infer the major topics represented within the analyzed documents using the frequent words related to each topic. The two distributions, ψ_k and θ_d, are evaluated using two Dirichlet distributions Beta (β) (i.e., per-topic-per-word probabilities) and Gamma (α) (i.e., per-document-per-topic probabilities), respectively (for more details about Dirichlet distributions formulation, see [34]). The LDA algorithms procedure can be summarized as shown in Figure 2:

(1)

The model user determines the analyzed documents (D);

(2)

Define the number of topics (K);

(3)

The algorithm randomly assigns a particular topic k_di to each word w_di based on:

• The word distribution for each topic k (ψ_k), evaluated by initial Dirichlet (β);
• The topic distribution for each document d (θ_d), evaluated by initial Dirichlet (α)

• where w_di is the word (i) in the word collection (w_d) per document (d), d $\in$ [1, D], i $\in$ [1, N_d (number of words in w_d)], and k_di is the topic assigned to the word i (w_di) in the document (d), k_di $\in$ [1, K];

(4)

Using Gibbs sampling [35] with iteration j (j = 1000 in this study), the algorithm improves the topic assignment in terms of enhancing the values of β and α, where the algorithm can calculate the probability that word (w_di) is generated from the topic (k_di);

(5)

The algorithm re-assigns each word (w_di) with the new topic (k_di) based on the previous step calculations.

2.4. Perplexity

One of the most challenging steps in the LDA algorithm is evaluating the optimum number of topics (K) within the analyzed documents (D). This paper adopted perplexity metrics to determine the optimum number of topics. Perplexity is a statistical measurement used as a guide to select the optimum number of topics in topic modeling [29]. Perplexity metrics evaluate the ability of the probability models to predict a sample by calculating the relative degree of uncertainty among such models, where the best model should have the least perplexity value. Figure 3 shows the sensitivity of the perplexity evaluation values to the number of topics. A threshold of 30 topics was chosen as the maximum number of topics to be considered, which is a relatively large number compared to the number of articles under consideration. In this study, we consider 7 as the optimum number of topics, considering the slope of the perplexity curve (dash line) firstly changes at 7, and the differences in the perplexity value between 7 and 30 are relatively small, as shown in Figure 3.

2.5. Topic Identification

Figure 4 and Figure 5 show the identified seven topics, where the word cloud for each topic is represented in Figure 4, while the β value for the top ten words per topic is shown in Figure 5. In Figure 5, β can be interpreted as the probability that each word is generated from one of the identified topics. For example, the β value for “water” in Figure 5e is 0.12, meaning that “water” represents 12% of Topic 5, which consists of a collection of words. The β value can also refer to the level of this word frequency in the topic. The words of high β values in Figure 5, shown large in size for the word clouds in Figure 4, refer to the most frequent words in each topic that can be used to infer the main focus of the topic.

Topic 1 shows high frequency of word stems such as “optim”, “model”, and “algorithm”, which can refer to the (Optimization models) that are used in dam operations. Using the same approach, the high-frequency word for Topic 2, such as “climat”, “change”, “river”, and “flow”, can refer to the variation of the hydrological and meteorological variables caused by (Climate Change) that directly affect dam operational safety. Moreover, the high-frequency word for Topic 3, such as “flood”, “risk”, and “control”, can refer to (Flood Risk) that significantly threaten the safety of dam operations. In addition, the high-frequency word for Topic 4, such as “inflow”, “forecast”, and “uncertainti”, can refer to the effect of (Inflow forecasting) uncertainties for dam operational safety. Furthermore, the high-frequency word stems for Topic 5, such as “hydropower”, “generate”, and “schedule”, can refer to the safety of the (Hydropower generation) operation under various operational conditions. In addition, the high-frequency word stems for Topic 6, such as “water”, “rule”, “hedg”, “drought”, and “suppli”, can refer to the risk of water shortage in (Water Supply Management) due to the increasing water demands and the increasing rate of drought events. Finally, the high-frequency word for Topic 7, such as “risk”, “analysi”, “evalu”, and “assess”, can refer to (Risk-based Assessment and Management) approach that is adopted in dam safety assessment studies.

3. Qualitative Analysis

This section aims to comprehensively review the identified topics in the previous section, citing 376 recent studies related to dam and reservoir operational safety. This section cites such a massive number of the most recent research papers; however, it is worth mentioning that due to space limitations, this section is restricted to concisely stating the definitions, concepts, modeling tools, and major research trends adopted in each of the identified seven topics. For more in-depth details about mathematical formulations and modeling tools application, the paper refers to the recent review papers and textbooks conducted to review each topic specifically. It should also be noted that “reservoir” and “dam” are used interchangeably throughout the literature and this review, referring to the same dam and its reservoir system.

3.1. Topic 1: Optimization Models

Optimization is defined as a mathematical formulation in which algorithms are used to compute the values for a set of decision variables (e.g., outflow, gate positions) that maximize or minimize the objective functions (e.g., flood control, hydropower generation), considering problem constraints (e.g., release constraints, storage constraints). For more details about dam operations optimization model variables, constraints, and objective formulations, see [36]. In the context of dam operations, two approaches are generally adopted to determine the optimal operational rules. One approach is to pre-define the operational rule form (e.g., rule tables, rule curves) and subsequently use the optimization algorithms to optimize the parameters of such defined rules [37]. However, this approach is inflexible as it restrains its results to the pre-defined form. Also, it requires extensive computational time in multi-objective problems. As such, a more flexible approach is adopted, where the optimization models are used first to generate optimal input–output solutions, and then data mining methods are applied to extract the optimal operational rules [38,39]. Accordingly, various complex modeling tools are adopted to conduct such two approaches in optimal dam operations problems. These complex modeling tools, including optimization programming techniques, solution algorithms, and inference models, can be classified into five main categories as shown in Figure 6: (1) implicit stochastic optimization (ISO) models, (2) explicit stochastic optimization (ESO) models, (3) computational intelligence (CI) models, (4) multi-objective optimization (MLO) models, and (5) simulation-optimization (S-O) models.

ISO is an optimization modeling technique that implicitly includes stochastic features of reservoir random variables (e.g., spatial and temporal variations of inflow discharges) using deterministic optimization programming techniques such as linear programming (LP) [40,41,42,43,44] and its extensions (binary LP (BLP), integer LP (ILP), mixed-integer LP (MILP), non-linear programming (NLP) [45,46,47,48,49] including the successive LP (SLP), sequential quadratic programming (SQP), generalized reduced gradient (GRG), deterministic dynamic programming (DDP) [50,51,52,53,54] and its modified models to solve its curse of dimensionality (dynamic programming successive approximation (DPSA), incremental DP (IDP), discrete differential DP (DDDP), and discrete-time optimal control theory (DOCT)) [55,56]. The deterministic optimization models can generate the optimal policies for several historical or synthetically time-series data for reservoir random variables (e.g., inflow). Subsequently, statistical inference methods (e.g., multiple regression analysis) are used to infer the operating rule curves from such generated optimal operating policies, considering current reservoir conditions (e.g., current storage level). However, this approach, ISO modeling, usually has various limitations. For example, such inferred operating rule curves are unique to the input (historical or synthetical) time-series data. Moreover, poor correlations resulting from regression analysis may invalidate the inferred operating rules. Also, using advanced inference methods (e.g., ANNs, FRB) to infer such operating rules (rather than the regression analysis) requires extensive computational cost due to the multiple trials and errors to reach an efficient result.

Unlike ISO, ESO modeling explicitly provides the probabilistic description for the stochastic features of reservoir random variables using stochastic programming techniques such as stochastic linear programming (SLP) [57,58,59], stochastic dynamic programming (SDP) [60,61,62,63], chance-constrained programming (CCP) [64,65], and stochastic optimal control theory (SOCT) [66]. In this respect, the proper probability distribution (parametric or nonparametric) can be fitted for the random reservoir variables based on the statistical frequency analysis. Thus, the inferred advantages of ESO over the ISO are: (1) the optimization process directly considers variables’ uncertainty; (2) The optimal operation rule can be directly determined without using any interference tools. However, ESO programming is more computationally demanding than ISO, particularly in complex multi-objective problems.

Alternatively, CI models solve complex cases that cannot be solved using conventional methods. As such, CI models have a wide range of applications in optimal dam operation complex problems, especially during the development of the current computational capabilities. CI refers to a set of nature-instigated computational models that generally includes three main methods: (1) Evolutionary computation (EC), (2) Artificial neural network (ANN), and (3) Fuzzy logic systems (FLS).

EC models, known as heuristic searching tools, include metaheuristic algorithms such as Genetic algorithms (GA) [67,68,69,70,71], Ant colony optimization (ACO) [72], Particle swarm optimization (PSO) [73,74], Simulated annealing (SA) [75,76], and Honey bees mating optimization (HBMO) [77]. Unlike other algorithms, meta-heuristic algorithms are known for their efficiency in searching for near-optimal (i.e., Pareto optimal) solutions. They can also compute optimal global solutions to problems in which the conventional algorithms fail to converge or become stuck in local optima [51]. As such, EC-based algorithms, using their unique natural structure, can address the complexities of reservoir operation problems such as discontinuity, uncertainty, nonlinearity, multi-objectives, and discreteness. For more information about using metaheuristic algorithms in dam operation, see reviews [78,79,80].

Although ANNs cannot be classified as an optimization model per se, ANN is one of the most powerful data mining methods used to infer the optimal operating rules from optimization model results (e.g., ISO) [51]. ANNs also have a wide range of applications within reservoir operations, such as inflow forecasting (see, Topic 4). ANN is a paralleled-distributed information processing system. It aims to simulate the brain’s information process for thinking and reasoning by resembling the brain’s biological neural networks [81]. In this respect, ANNs typically consist of a large number of nodes (i.e., neurons) arranged in specific patterns (i.e., layers). Within such layers, the information (i.e., data) is typically transmitted between the nodes from the input to the output layers through multiple hidden layers using directional links (i.e., assigned by weights). Each node (other than input layer nodes) is defined by an activation function that evaluates the activation status of each node based on the weighted inputs and added bias. Accordingly, ANNs have multiple architecture types according to the number of layers (e.g., single (Hopfield network), by-linear (adaptive resonance networks), multilayer (backpropagation networks)), and the direction of the information flow (e.g., unidirectional in feed-forward ANN, radial flow in radial basis). More details about ANNs configurations can be found in [82]. It should be noted that most of the recent ANNs studies are cited in Topic 4. More details about ANNs application in dam operation can be found in [19,83].

Similar to ANNs, FLS is considered an advanced inference tool used as an alternative solution to regression analysis to infer operating rules from historical operations or ISO model results [84]. Fuzzy logic, developed by Zadeh in 1965 [85], is a logical-mathematical procedure based on the “If/Then” procedure that simulates the human way of thinking computationally. Unlike complex mathematical models, fuzzy logic models use linguistic descriptions to define the relationships between input data and output decisions. As such, it enables FLS to deal with uncertain decision-making problems. The fuzzy system typically consists of four main components: (a) Fuzzification is a process of transforming the numeric data (i.e., crisp) to fuzzy input; (b) Knowledge base is a collection of fuzzy conditional rules that link the input to the output variables; (c) Inference engine is a process to combine fuzzy rules output; (d) Defuzzification is a process to transform the fuzzy output back into the numeric data. Besides being an inference tool for dam operational rules, Bellman and Zadeh, 1970 [86] introduce the integration of fuzzy sets in the optimization algorithms (i.e., fuzzy optimization models) to represent the imprecision and vagueness in the constraints and objective functions. These fuzzy constraints and objectives are characterized by their membership functions, where the decision is selected based on the intersections of the fuzzy constraints and objectives. This concept is then adopted to develop different fuzzy optimization models (e.g., fuzzy DP [63,87], grey fuzzy SDP [88]) to solve such uncertainty in reservoir operation optimization problems. For more details, see [89].

As most of the recent dam-operation problems are multi-objectives, two approaches: the epsilon-constraint method and the weighting method, are commonly adopted by the optimization models (stated above) to solve the multi-objective operation problem [19]. Regarding the epsilon-constraint method, the multi-objective problem is converted to a single objective by considering the least important operation objectives as the problem constraints. However, for the recent multi-objective dam operations, optimizing all objectives simultaneously using a single solution value is impossible. Instead, a set of efficient non-inferior optimal solutions (i.e., Pareto optimal solutions) is determined to define a boundary beyond which none of the objectives can be improved without sacrificing at least one of the other objectives. Unlike the epsilon-constraint method, the weighting method combines the operation objectives by assigning comparative values (i.e., weights) to each objective, where the Pareto optimal solutions are computed by varying the weights for each objective and solving the problem sequentially. Subsequently, the Pareto front (PF) can be defined as the set of all non-dominated Pareto optimal solutions for the objectives vector. For other details of multi-objective programming, see [90,91,92]. After quantifying the PF, multicriteria decision-making (MCDM) methods are usually employed to rank these Pareto optimal solutions and determine the most preferred solution that needs to be implemented (For more details about MCDM methods and ranking process, see [93,94,95].

Despite the advancement of optimization models, simulation models are still one strategic tool to estimate the dam and reservoir system’s behavior under various conditions. However, simulation models are very time-consuming in complex operation cases with a large number of operational policies. Thus, several studies of large-scale systems use optimization models to preliminary screen such operation policies to significantly improve simulation model efficiency [96,97,98,99]. In this respect, the simulation and the optimization models are preferred to work in a loop sequentially, where the optimization models use the simulation model outputs to find the optimal solution that can then be considered a better-simplified input to the simulation model. Accordingly, several simulation-optimization (S-O) models, such as simulation-GA–GA models [100,101], are adopted in the various dam and reservoir operational problems. More details about S-O modeling techniques application in reservoir operation can be found in [36]. For more details about comparing the recent optimization models adopted in reservoir operations, see the reviews conducted by [102,103,104,105,106].

3.2. Topic 2: Climate Change

Despite the role of dams and reservoirs as a climate-change risk mitigation infrastructure, climate change, in turn, directly affects the safety of dam operational objectives (e.g., flood control, hydropower generation, and water supply management) [7,107,108,109,110,111,112,113]. Climate change intensifies weather extremes that subsequently induce a series of devastating natural hazard events (e.g., floods, droughts). Moreover, the frequent changes in climate conditions increase the uncertainties in the meteorological and hydrological variables, which subsequently introduce risk in dam operational decisions. For example, the rise in water surface temperature reduces snow storage (i.e., snow-pack) and increases the water losses due to evaporation, leading to reduced and earlier spring runoff. Accordingly, dam operators should refill the reservoirs early to ensure adequate summer water supply storage. However, the early refill reduces the flood storage capacity and increases flood risk. In addition to the variation of runoff temporal characteristics, climate change can also affect river runoff discharge due to the rapid variation in precipitation patterns, which introduces uncertainty of floods’ magnitude and frequency. Climate change may also introduce uncertainty in dam components’ operational function (i.e., performance). For instance, intensive rainfalls may excite the soil particles, where the fine sediment particles in water may increase the possibility of gate abrasion and erosion processes, while the oversized particles (e.g., debris, tree branches) can lead to gate blockage. Furthermore, the change in atmospheric temperature can expose gates to additional stresses and deformations, which affect the gates’ maneuvering mechanism. For more information about the impact of climate change on dam operational safety, see [2,107,114,115].

In addition to the significant climate change impact on dam operational safety, most of the existing dams have inefficient construction and operation schemes that neglect the ever-changing climatological conditions [116,117,118]. Accordingly, several models have been developed to provide adaptive operational rules to consider such induced climate change operational risk. In this respect, the integration of climate, hydrology, and optimization models are used to provide adaptive dam operation rules for various climate change scenarios [119,120,121,122,123,124,125].

General circulation models (GCMs) are numerical models that represent atmospheric processes through complex mathematical equations. GCMs are commonly used to generate various climate scenarios [126]. However, GCM outputs have a too-coarse temporal and spatial resolution, which cannot be directly used by the hydrological simulation models. Thus, downscaling techniques are usually adopted to transform the coarse resolution of the GCMs into more acceptable (finer) resolution results. The main idea of downscaling is to convert the large-scale changes in the atmospheric variables (i.e., predictors) generated by GCMs, to local climate variables (i.e., predictands). These downscaling techniques can be classified into dynamic and statistical downscaling models, with some approaches combining the two techniques for higher-resolution results (see [127,128,129]).

Dynamic downscaling usually refers to regional climate models (RCMs) or limited-area models (LAMs), which provide high-resolution regional simulations. RCMs are driven by GCM outputs, as model boundary conditions, to dynamically extrapolate the effect of the large-scale climate pattern to the regional scale. However, the limitation of the dynamic downscaling techniques refers to the computational cost that restricts the downscaling results to a specific resolution level, typically 20–50 km. Subsequently, the model results usually require further downscaling and bias correction for its outputs (see the review in [130]). In contrast, statistical downscaling models require minimal computational time and are easier to implement and interpret. Statistical downscaling models use several statistical-based models (e.g., multiple regression analysis, analog method, LARS-WG) to develop the statistical relationship between the GCM outputs and observed local climate responses, assuming that this relationship does not change in the future under changing climate conditions (i.e., stationarity predictor-predictand relationships) (see [131]). However, statistical downscaling techniques have some limitations due to the lack of observed data with high quality. Therefore, selecting the downscaling technique is a challenging step that depends on the financial and time constraints and the desired temporal and spatial resolutions of the generated climate scenarios (for more details about the comparison between the dynamic and the statical downscaling models, see [132]).

These climatic scenarios, generated by the downscaling techniques, are used as hydrological simulation model inputs. These hydrologic simulation models, such as Variable Infiltration Capacity (VIC) [133,134] and SWAT model [135,136], are employed to simulate the river runoff corresponding to the given climate scenarios. Reservoir response (e.g., storage status) can then be developed for each climate scenario based on the simulated river runoff and the reservoir releases using the operating rule curves generated by the optimization models (stated in Topic 1). The reservoir conditions are then evaluated based on the specified safety and operation criterion, and thus, the best optimal operating rule curve can be selected. This top-down integration approach is one of the widely adopted decision-scaling frameworks in developing dam safety assessment plans, where the reservoir response to the expected future climate scenario drives stakeholder decision-making [137]. Meanwhile, a bottom-up approach [138] is also applied to investigate reservoir system vulnerabilities and the probability of system operational failure. Within the bottom-up approach, the operational failure limits are first defined using the historical records and dam stakeholders’ safety standards. GCMs can then be employed to generate future climate scenarios and subsequently identify the system’s possibility of being pushed into a vulnerable state beyond those limits (see [139]). For more details about the interaction between climate change and dam operations, see the reviews conducted by [2,7,140,141,142].

3.3. Topic 3: Flood Risk

Floods are one of the most destructive natural disasters with severe consequences of human fatalities and economic losses [143]. In the last ten years, floods have caused more than 50,000 deaths and more than USD 400 billion in property damage (Flood Disaster Database, available at https://ourworldindata.org/, Last accessed: 1 December 2022 and https://www.emdat.be/, Last accessed: 1 December 2022). Thus, reservoir flood control operation (RFCO) is a crucial objective in reservoir operations to reduce flood peaks and mitigate flood damage to the downstream and the dam structure itself. RFCO objectives can be specified based on the number of reservoirs, Single or Multi-reservoir systems. For single reservoirs, RFCO aims to minimize the maximum reservoir water level (MRWL) during flood peak discharge, considering the downstream safety against dam releases [144,145,146]. However, a single reservoir may not provide adequate storage capacity for downstream safety. Therefore, multi-reservoir systems are operated together to protect such areas from flood consequences. However, RFCO objectives change for multi-reservoir systems according to the configuration of the reservoirs within the system, cascading (series), parallel, or mixed reservoir system. Cascading reservoirs have hydraulic inter-relationship and storage compensation rules. As such, the downstream reservoir’s safety is affected by the RFCO objectives of the upstream reservoir. In this respect, RFCO aims not only to minimize MRWL to ensure dam safety but also to ensure the safety of different critical flood sections downstream, considering the safety of the downstream area and the following dam structure. On the contrary, parallel reservoirs do not have any hydraulic inter-relationship, where the safety of the downstream area is affected by the coordination in RFCO of the parallel reservoirs. Regarding the mixed reservoir systems, RFCO is more complicated, where the complexity of hydraulic connection for the cascading reservoirs and the coordination of asynchronous peak flows for the parallel reservoirs should be considered simultaneously (see [147,148,149,150,151,152]).

Within each reservoir among these reservoir systems, RFCO objectives can be specified based on the operational stage, which is typically carried out through three main stages [153]: (1) Prior flood event, the operator aims to increase the reservoir storage capacity by pre-releasing reservoir water discharge; (2) During flood event but prior flood peak flow, the operator releases as possible from flood discharge ensuring the safety of reservoir water storage levels; (3) After flood peak flow, the operator aims to balance between maintaining MRWL within the allowed reservoir limits, increasing the reservoir storage to be used in hydropower generation and decreasing dam releases to ensure the safety of the downstream area.

RFCO objectives are typically performed through fixed operating rules that mainly rely on historical or synthetic statistical flood analysis [152,154]. These operating rules can consequently define the RFCO targets (e.g., target reservoir water level) for each operational stage, considering the designed reservoir operational parameters (e.g., designed flood storage). However, these operating rules usually depend on subjective experts’ judgment that cannot provide optimal flood control operations, especially for multi-purpose reservoirs. Therefore, advanced optimization and simulation methods (reviewed in topic 1) were adopted to provide optimal real-time RFCO operating rules under various operational conditions. These studies consider different aspects of the RFCO, including single and multiple reservoirs [147,155,156,157], short-term and long-term scheduling [148,158,159], single and multi-objective approaches [144,160,161,162,163,164], and multi-criteria decision-making models [93,94,165,166]).

However, the obstacles to the safety of RFCO problems are not only related to the complexity of extracting the optimal rules for RFCO operational stages but also the associated uncertainties of RFCO variables (e.g., flood peak flow) and, subsequently, the RFCO targets. Therefore, several studies considered the uncertainties in RFCO and estimated their corresponding risks to support the decision-makers in developing effective dam operational plans under various conditions [161,167,168,169,170,171,172,173,174,175,176,177]. These uncertainties are introduced from four main sources [178,179,180]: (1) hydrological (e.g., inflow) and meteorological variables (e.g., precipitation) uncertainties that introduce randomness in flood frequency and its magnitude; (2) flood forecasting and river flood routing errors, as a result of models structure uncertainty, parameter estimation errors, imperfection of initial and boundary conditions, and simplification of the physical processes; (3) hydraulic uncertainties, such as errors in reservoir outflows (e.g., due to debris accumulations), and errors in reservoir discharge curve (i.e., the difference between actual and designed spillway capacity resulted from flow coefficients and measurement errors of the spillways); and (4) other uncertainties (i.e., deep uncertainties), such as operation time delay, human decision errors, information unavailability, poor communication. These uncertainties were introduced to quantify the corresponding risk in RFCO using risk-based models as reviewed in Topic 7.

3.4. Topic 4: Inflow Forecasting

Inflow is one of the most critical variables for dam and reservoir operations [181]. Accurate inflow forecasting can provide preceding inflow information that can significantly reduce the risk of floods and droughts, improve water allocation schemes for water supply management, and enhance hydropower scheduling plans [182]. Hence, several techniques have been developed to forecast reservoir inflow. Such techniques can be classified as statistical, physical, and intelligent methods. Physical and statistical methods have been widely used in the past decades to predict inflow characteristics. Statistical models, such as Autoregressive, Autoregressive Moving Average (ARMA), and Seasonal ARIMA (see [183] for a comparison between the three models), are used to estimate the temporal inflow variation, assuming that the behavior of the historical data is valid for the future (e.g., seasonal variation) [184]. Although the statistical methods are relatively simple and mature, they suffer from low accuracy in considering the dynamic, non-stationary, and non-linear inflow behavior [183]. Alternatively, the physical models (e.g., soil and water assessment tools), including semi-and fully physically distributed models, use physical-based equations (e.g., mass, momentum, or energy conservation equations) to represent the hydrological characterizations of the inflow data (e.g., [185]). Although physical-based models are more accurate than conceptual hydrological models, they usually require complex mathematical procedures, a large number of parameter calibrations, and complex initial/boundary condition determination. For more details about comparing the physical and conceptual hydrological models, see [186,187]. Alternatively, advanced intelligent methods were adopted to overcome the limitations of the physical and hydrological predictive models, such as artificial neural networks [188], support vector machine [189], decision tree models [190], Bayesian Networks [191], fuzzy inference system [192], grey model [193], wavelet transforms [194], and clustered k-nearest model [195]. The main advantage of such data-driven models is their ability to provide real-time forecasting and include external factors (e.g., weather conditions) that can improve forecasting accuracy (see [196]). Moreover, data-driven models only depend on the historical hydro-meteorological data without directly considering underlying physical processes and thus require much less input and parameter data. For the comparison between the data-driven and physical models, see [197]. However, the forecasting accuracy of the data-driven models can be affected by data representation (i.e., data quality) that affects the extraction and learning features of the historical data [198]. Moreover, using only one data-driven may not be sufficient, as each model has its features that may not be suitable for all rivers’ hydrological characteristics [199]. Therefore, hybrid models have been recently developed [199,200,201,202,203,204,205,206,207,208] to consider the advantages of each forecasting model. Thus, hybrid forecasting models can improve forecasting accuracy and subsequently develop efficient reservoir operation rules. For more details about the application of hybrid models in inflow forecasting, see the comparative study performed by [209] and the review conducted by [210].

Despite the advances in inflow forecasting techniques, their application in reservoir operation is constrained by a limited forecasting horizon (FH) [211,212]. Reservoir operations require a long enough forecasting leading time to provide sufficient information for the decision process horizon. However, a meaningful forecast horizon is usually shorter than the required operation horizon—the shorter the FH, the lower the possibilities of error and uncertainties. Thus, several studies were conducted to determine the effective FH for inflow forecasting models that can provide efficient forecasting leading time for reliable operational decisions (see, [181,213]). Within these studies, posterior evaluation values of forecasts with different lengths of leading time are obtained based on comparing the actual decisions (performed based on the observed inflow) and the numerical decisions generated using the forecast models. These studies concluded that effective FH could be specified based on reservoir operation objectives. The short FH is efficient for reservoirs with small capacities operated for short-term objectives such as flood protection. However, the long FH is essential to large and medium-capacity reservoirs used for long-operating objectives such as water supply and hydropower generation.

The uncertainty of Inflow forecast models not only varies by the forecasting horizon time; but is also affected by the modeling errors, including errors in the initial and boundary conditions, errors in model parameters, poor model resolution, simplifying the physical process, and the imperfect representation of the actual topography [214]. Therefore, nowadays, probabilistic forecasts are preferred over deterministic ones [215,216]. Probabilistic forecasts provide decision-makers with a better trade-off for risks and benefits than the single-value forecast that ignores uncertainties [217,218]. Moreover, probabilistic forecasts can provide reservoir operations with a relatively longer leading time than deterministic forecasts [219,220]. In this respect, the probabilistic distributions are typically generated using ensemble forecasts to randomly sample the uncertainty range in inflow forecasts. However, ensembles are often under-dispersive and, therefore, are typically unreliable in inflow forecast applications [221]. As such, simple uncertainty models, such as the binned probability ensemble and Gaussian uncertainty model, are used to fit the probability distribution functions to the ensembles using the statistical properties of the generated ensemble. Unlike such simple uncertainty models, other complex uncertainty models, such as the generalized likelihood uncertainty estimation and Bayesian recursive estimation, are used to produce probabilistic forecasts by sampling the uncertainty of the hydrology model parameters [222,223,224]. However, due to the assumptions made by the uncertainty models, the resulting probability forecasts should be statistically calibrated for risk-based decision-making. These calibration approaches can be classified into two main groups: (1) ensemble calibration, such as Bayesian model averaging [225], which adjusts the forecasted ensembles to enhance the inflow forecast result; and (2) probability calibration, such as the weighted ranks method [226,227], which directly adjusts the generated probabilities (i.e., uncertainty model results). For more details about calibration techniques and uncertainty models, see [216].

3.5. Topic 5: Hydropower Generation

Power generation is the primary contributor to global warming, producing more than 30% of greenhouse gas emissions (GHG) [228]. Therefore, several countries have increased their reliance on dams as hydropower generation facilities to reach GHG reduction targets. Hydropower is considered one of the largest sources of renewable energy based on the United Nations reports [9,12] and the World Energy Generation database available at https://ourworldindata.org, Last accessed: 1 December 2022. These rates are expected to increase, considering the rapid global energy demand due to the global growth of the population and economy. As such, dam construction has globally boomed in the past decade, with expectations of a continuous increase in construction rates in the future [10]. However, it is more economical to develop advanced dam operational rules to ensure the safety of the existing hydropower power dams and improve their efficiency under various conditions [229,230].

The existing hydropower dams can be classified into Run-of-River (RoR) and reservoir-based hydropower dams. RoR is considered lower in risk than reservoir-based dams. RoR has no or little water storage; instead, it uses the instantaneous flowing discharge of water to generate electricity [231]. However, it is considered a small hydro project that generates limited and unsustainable energy rates. As such, reservoir-based hydropower dams are widely used in hydropower generations that use the reservoir’s storage and the differences in reservoir water elevations to operate the turbines and generate electricity [232]. Although various operation modes are adopted in reservoir-based dams (e.g., peaking, storage–release, pump storage), the main objective of such operations is to maximize hydro generation rates and minimize the production cost under multiple conditions. For more details about the types of hydropower operations, see [233].

Pumped-storage hydropower (PSH) is considered one of the most widely adopted systems for large-scale energy storage. The advantages of such a technique include the high-potential energy stored in the hydro reservoirs, the low production cost per power unit, the efficiency of the energy conversion of the whole cycle, and its flexibility in short-term hydropower operations. The basic idea of the PSH technique is having two water reservoirs at different elevations that can provide a long energy storage period by pumping the water from the lower reservoir to the higher one, converting kinetic energy to stored potential energy. Typically, the water is pumped to the higher reservoir in the low-demand periods (off-peak hours), and it is then released during the high-demand periods (the peak hours). As such, PSH usually takes advantage of electricity price variations (higher prices in peak hours) and ensures the continuity of the energy supply during different seasonal events.

Based on a such basic idea, several studies have been conducted to improve various aspects of PSH operations to maximize the economic benefits and power production efficiency.

Table 1. Summary of the recent studies conducted on PSH systems (2023–2020).

Ref.	Main Goal	Case Study
[239]	Investigate the economic and energy efficiency of the coordinated operations between a hybrid PSH, integrating a pumping station between cascading conventional hydropower stations, with wind and photovoltaic systems at different time scales.	Wujiang River, China
[240]	Investigate the peak shaving of cascade hydropower with mixed PSH to decrease the variation of the residual load of the external power grid, considering the hydraulic coupling of multiple reservoirs and water delay time in the hydropower model.	Southwest China
[241]	Review and assess the research conducted on the operation, cost, and desired locations of PSH resources in the Railbelt transmission system.	Alaska, USA
[242]	Develop a new mixed-integer linear optimization model for allocating the PSH unit on the next day of the unit commitment program, using the Autoregressive integral Moving Average (ARIMA) and Stationary Autoregressive integral Moving Average (SARIMA) to predict the market prices of the next day, considering the electricity market uncertainties.	Ontario, Canada
[243]	Develop a comprehensive power and energy model for PSH integrated with conventional hydropower (CH), aiming to maximize the energy production of the CH, improve PSH operations to consider the discharge variation, achieve a monthly balance between PSH and CH operations, determine the optimum value for PSH and CH based on the range of the charge and discharge ratio, compare capacity optimization of PSH and CH with and without water stream.	Balakot hydropower plant, Pakistan
[244]	Review the recent advanced pumped storage hydropower technologies, including conventional pumped storage hydropower, adjustable speed pumped storage hydropower, and ternary pumped storage hydropower.	N.A.
[245]	Investigate the short-term operation of a hybrid wind farm-PSH system transmitting power to multiple cross-regional power grids through ultra-high-voltage transmission lines.	Eastern China
[246]	Propose an optimal unit model for a coordinated wind-PSH generation system, considering wind uncertainties using a chance-constrained optimization model.	Northwest, China
[247]	Develop a Quaternary PSH combining the Conventional-PSH and Adjustable speed-PSH technologies, aiming to provide fast power support and efficiently consider the uncertainties of power generation.	N.A.
[248]	Develop a GIS-based model to transfer a conventional hydropower dam to PSH, determining the most suitable second reservoir location, and calculating its hydroelectricity energy potential.	Porsuk Dam, Turkey
[249]	Develop a new mixed integer linear programming model for PSH, allowing a greater number of breakpoints, leading to more realistic solutions, and reducing computational efforts.	Argentine Republic
[250]	Proposed a generic method to model and optimize small-scale PSH that can be applied to different PSH technologies, including adjustable-speed and hydraulic short circuits and PSH configurations such as ternary, reversible, and separate turbines and pumps.	Shell Energy North America (SENA) modular PSH concept
[251]	Review the existing types of PSH, highlighting the advantages and disadvantages of each PSH system.	N.A.

summarizes the recent studies and trends performed on PSH systems between 2020 and 2023. However, for the previous studies, please see the reviews [234,235,236,237,238].

Despite the previous research conducted on pumped-storage hydropower systems, more proper dam safety assessment plans are required to improve the efficiency of this system in energy storage.

Moreover, various studies have been established to employ the advanced optimization models (stated in topic 1) in hydropower generation scheduling through short-term, medium-term, and long-term time intervals. These studies can be summarized in

Table 2. Summary of the recent hydropower scheduling studies (2023–2018).

Ref.	Main Goal	Case Study
Short-Term Hydropower Scheduling (STHS)
[257]	Propose a dynamic capacity short-term scheduling model based on one-dimensional unsteady flow for Three Gorges in China.	Three Gorges, China
[258]	Propose a two-step technique based on mixed-integer linear programming (MILP) to solve the STHS by exploring the symmetry related to the identical generating units in San Antonio and obtaining the optimal load distribution.	San Antonio, Brazil
[259]	Develop a linear mixed-integer optimization model to maximize total hydropower generation among all periods of the operation year, considering the production rate at the maximum storage for all possible operational scenarios of the turbine and the most efficient point of water discharge.	Saguenay-Lac-St-Jean, Quebec, Canada.
[260]	Develop a rolling horizon robust online scheduling scheme that employs stochastic optimization within a feedback model to consider the uncertainties in hydropower operation, including electricity prices, power demand, inflow, and model parameters.	Ontario, Canada
[261]	Compare five mixed-integer linear programming formulations for efficient STHS.	Hypothetical three hydropower plant system
[38]	Identify a quick decision approach for STHS for cascaded hydropower plants using data mining algorithms.	Tianshengqiao, Guangdong, China.
[262]	Propose a dynamic determination process for the breakpoints of the piecewise linear approximation method for solving STHS, considering the intake loss, efficiency of the head-dependent turbine, penstock loss, the varying time head effect, and tailrace loss.	Northern Norway
[263]	Develop mixed-linear programming for hourly hydropower scheduling applied to a cascading hydropower system with hydraulic coupling and multiple prohibited zones for head-dependent operation.	Tianshengqiao, Hongshui River, southwest China
[264]	Develop a multi-objective mixed-integer non-linear programming for the peak shaving operations to enhance power efficiency and control the peak loads.	Beipanjiang, China
[265]	Propose a stochastic multicriteria decision-making framework for STHS under multiple uncertainties.	Qingjiang, Hubei, China
[266]	Determine the efficiency of genetic algorithms with different selection operators for optimizing the STHS problem.	Gezhouba, China
[267]	Develop a rolling optimal operation model for hourly (ultra) STHS in real-time for cascading hydropower dam system.	Yunnan, China
[268]	Develop a short-term peak-shaving method using fuzzy clustering analysis and linear mixed-integer programming for cascading hydropower systems with sensitive heads, considering water spillage adjustments.	Hongshui, China
[269]	Develop an improved cloud adaptive quantum-inspired binary social spider optimization model to optimize short-term scheduling sub-problems, economic load dispatch, and unit commitment.	Three Gorges hydropower station, Yangtze, China.
[270]	Develop an advanced optimization model to improve the hydropower economic profit of a large chain of reservoirs, considering ecological restrictions, European regulations, and operation uncertainties.	Guadalquivir, southern Spain.
[271]	Develop a successive approximation approach to consider the STHS non-linear characteristics.	Ten Reservoir System, China
[272]	Used linear and dynamic programming to determine the number of operating units and the power in each quarter-hour and for each hydro plant.	Yunnan, China
Mid-Term Hydropower Scheduling (MTHS)
[273]	Develop a successive quadratic programming model with linearization updated by the non-linear constraints of the hydropower facility composed of cascading reservoirs.	Jinsha River, China
[274]	Develop a bi-level stochastic model based on information gap decision-making theory for MTHS of cascading hydropower systems, considering the economic and hydrologic uncertainties in hydropower market participation.	Southwest China
[275]	Develop a two-stage decomposition approach for the MTHS problem, where every state is represented as a multi-period stochastic model.	Brazil
[276]	Develop an MTHS approach acting as a price-maker in the automatic frequency restoration reserve market.	Northwest Spain
[277]	Develop a stochastic optimization model for mid-term scheduling using Latin hypercube sampling and Cholesky decomposition coupled with sensitivity analysis, considering the uncertainty of natural inflows.	China
[278]	Apply stochastic dual dynamic integer programming (SDDIP) to a non-convex MTHS problem.	Norwegian hydropower
Long-Term Hydropower Scheduling (LTHS)
[279]	Improves the traditional weekly hydropower scheduling by integrating the hourly power and capacity balances (HPCB), which are formulated in the form of mixed-integer linear constraints involving the spare, reserve, maintenance, disabled, and working capacities, besides optimizing the levels and orders of hydro plants in peak-shaving the hourly power load curve.	Lancang River, China
[280]	Develop improved dynamic programming with successive approximation at each stage and relaxation strategy to solve the joint optimal operation problem of the large-scale hydropower plan groups.	Yangtze River, China
[281]	Illustrate the advantages of coupling the periodic autoregressive and the moving average (PARMA) over using only the periodic autoregressive (PAR) model to represent inflow uncertainties within the SDDP optimization model of LTHS.	Quebec, Canada
[46]	Develop a hybrid linear and nonlinear hydropower reservoir optimization model to provide an efficient and faster solution for the LTHS problem.	California, USA
[282]	Develop the LHTS approach to consider inflow forecasting uncertainty based on the adaptive nearest neighbor Gaussian temporal disaggregation method.	Xiluodu-Xiangjiaba, China
[283]	Develop an improved optimal method to control water levels, considering the two-stage analysis of LTHS and adjustable policy for the target outflow.	Xiluodu and Three Gorges, China
[284]	Develop a hybrid decomposition-coordination and discrete differential dynamic programming model (IDC–DDDP) for solving the LTHS for large-scale hydropower systems.	Southwestern China
[285]	Develop a multi-objective quantum-behaved particle swarm optimization model based on improved Tchebycheff decomposition with a modified generator of direction vectors to maximize the total production rate and firm the hydropower output.	Three Gorges and Gezhouba, China
[286]	Develop a linear mixed-integer optimization model to consider peak shaving demands, aiming to maximize the power generation profit within the LTHS of an interprovincial hydropower plant.	Xiluodu, China
[287]	Develop a chaotic adaptive multi-objective bat algorithm for cascade hydropower dams.	Qingjiang, southern China
[288]	Develop an adaptive multi-objective particle swarm optimization model based on the dominance and decomposition of a multi-objective long-term generation.	Three Gorges, China
[289]	Develop an improved differential evolution algorithm based on the LSHADE evolutionary algorithm, using new mutation strategies to provide a wider search range and accelerate convergence.	Jinsha River, western China.
[290]	Develop a series division method based on particle swarm optimization and firefly algorithm for the LTHS problem.	Himreen lake, Diyala/Iraq
[291]	Develop a novel optimization model based on copula theory to consider the uncertainty of electricity prices and the correlation between multiple markets.	Wu river, southwestern
[292]	Develop a novel piecewise linearization method for LTHS that converts the non-linear problem to a linear programming problem without using integer variables.	Lancang River, southwest of China.

, stating the main goal and case study for each research work. It should be noted that only the recent studies (from 2023 to 2018) are considered due to the paper space limitations, while for more information about the earlier studies, see reviews conducted by [80,252,253,254,255,256].

3.6. Topic 6: Water Supply Management

Water scarcity is a rapidly increasing problem for many countries that inevitably affects various social and economic sectors [293,294,295]. As a result of environmental degradation, water resources become depleted and subsequently cannot meet the ever-increasing water demands driven by socioeconomic development [296,297]. Moreover, due to global warming, dry and heat weather waves cause severe imbalances in water cycles, causing extreme drought events [298,299,300]. Hence, efficient water supply management in dam operation is critical for regulating the fluctuating water discharge and reducing the imbalances between water supply and water demands. However, the continuous depletion of water resources, dam multi-objective operations, the uncertainty in water demand and hydrological variables, and the possibility of drought events introduce a complexity of water supply operation rules to achieve the optimum water allocation for multiple sectors.

Dams employed several water supply rules such as Pack Rule, Space Rule, New York City Rule, Linear Decision Rule and Standard Operation Policy (SOP), and Hedging Rules (HR) to determine reservoir releases and the starting and ending conditions of supplying water (see, [301]). Among these rules, SOP is widely used in dam operations to satisfy the requirements for water supply management [302]. However, SOP fully releases water demands if the available water is sufficient, saving only the surplus water for future delivery. Consequently, SOP may not be efficient in reserving water discharge for dry seasons and subsequently causes severe water shortages during drought events [303,304,305,306,307]. Accordingly, HR is developed based on optimizing SOP operation rules to reduce the severity of drought events. HRs accept reducing water supply discharge in normal situations and reserve a portion of such water discharge to decrease the expected water shortage during droughts. Thus, effective HRs lead to a balanced water supply operation, which enhances dam performance to mitigate drought risks (see [37,308,309,310,311]).

Two points commonly define HRs: the starting water availability and the ending water availability. Between such two points, the water supply operation follows HRs, and beyond these points, the SOP is followed [312,313]. Thus, several HRs have been developed, such as the Two-point linear hedging rule [314], One-point linear hedging rule [315], Reserve-storage two-point linear hedging rule [316], Three-point linear hedging rule [317], Discrete phased hedging rules [318], to identify the HR parameters within the starting and ending hedging points, aiming to answer two main questions: (1) When to hedge? and (2) How much to hedge? For more information about comparing such types of HRs in dam operation, see [319,320,321,322]. The answer to the two questions is determined according to the parameters of HR trigger and rationing factors, respectively. The trigger can be defined as the initial and terminate threshold at which the HR is to start (i.e., “When to hedge?”), while the rationing factor is the ratio of the reduced water supply from the original target delivery (i.e., How much to hedge). These hedging rule parameters are typically obtained using simulation models, optimization models, or simulation-optimization (S-O) models (for more details, see [323,324,325,326,327,328]) that are summarized in topic 1. For more details about HR parameters quantifications, see [329].

3.7. Topic 7: Risk-Based Assessment and Management

Generally, absolute dam and reservoir operational safety is not possible to be attained due to the multiple associated uncertainties, including aleatory uncertainties (e.g., the randomness of nature), epistemic uncertainties (e.g., errors in model parameters), and deep uncertainties (e.g., failure scenario uncertainty) (see [330]). Such uncertainties introduce risk in dam and reservoir system operation decisions. Risk is defined as the potential losses that may occur corresponding to hazardous events [328,331,332,333]. For each hazard event, the risk is responsible for answering three main questions: what can happen (i.e., system failure response), how likely this can happen (i.e., probability of failure), and what are the consequences of this failure (i.e., failure consequence analysis generally). Absolute dam and reservoir operational safety is not possible to be attained due to the multiple associated uncertainties, including aleatory uncertainties (e.g., the randomness of nature), epistemic uncertainties (e.g., errors in model parameters) and deep uncertainties (e.g., failure scenario uncertainty) (see [330]). Such uncertainties introduce risk in dam and reservoir system operation decisions. Risk is defined as the potential losses that may occur corresponding to a hazardous event realization [328,331,332,333]. For each hazard event, the risk is responsible for answering three main questions: what can happen (i.e., system failure response), how likely this can happen (i.e., probability of failure), and what are the consequences of this failure (i.e., failure consequence analysis).

As such, risk has been the main focus of the International Commission on Large Dams (ICOLD) for several years, concluding that risk-based management is key to effective dam safety assessment plans that consider the associated hazard and uncertainty [334]. Risk-based management has recently evolved into “Risk-informed management”, as described by FERC, 2016 [335]. The latter is a process that provides comprehensive safety guidance to dam decision-makers typically established through four main steps [336,337]: (1) Risk analysis aims to estimate and describe the risk posed to the system through a systematic procedure including, the definition of system components and their inter-relations, the identification of potential system hazards and the corresponding system failure mode, the estimation of dam failure risk and the corresponding failure consequences, and the identification of vulnerabilities in system components to be included in risk assessment plans. (2) Risk evaluation provides the understanding and judgment of risk significance to the system. It defines the tolerable level of risk considering the safety standards of dam owners and regulators and the acceptable safety limits to the public, including the economy and human society. This step is considered essential decision guidance for how the estimated risk can be assessed. (3) Risk assessment is the core of the risk management process, which integrates the results for risk analysis (i.e., estimated system risk) and risk evaluation (i.e., tolerable system risk) to assess dam safety level. Accordingly, this step is responsible for assessing the alternatives of risk mitigation plans essential for risk control. (4) Risk control improves the existing risk mitigation and emergency plans according to dam risk assessment and develops the surveillance procedures to monitor the efficiency of the process to avoid or/and control the risk.

Various risk quantification approaches are proposed for dam operation risk with two commonly-adopted approaches [338,339]: (1) Risk is, conceptually, the product of hazard (i.e., probability of hazard occurrence), vulnerabilities (i.e., the possibility of system failure during this hazard event), and exposure (i.e., the possibility of the system to be exposed by this event); or (2) Risk is, conceptually, the product of hazard and its consequences (i.e., severity). Several risk analysis techniques are employed to quantify dam operational failure risk, which can be classified into six main categories. (1) The return period method, introduced by Fuller in 1914 [340], had been widely adopted for decades due to its simplicity in determining dam operation risk in terms of predicting the frequency of hazard events, especially in floods [341,342,343]. In this respect, the return period value is inversely related to the probability of a specific variable (e.g., flood flow) exceeding a particular value (e.g., 100-year flood means the probability that the magnitude of this flood to be exceeded at any year flood is equal 1%). However, it has some limitations in representing the integrated risk of flood control operations (for more details about the return period method, see [344]). (2) The stochastic differential equation method estimates system risk through integral or differential calculations based on the probability density function (PDF) of the uncertain variables [345,346]. (3) Reliability-based methods, such as the first order second moment (FOSM) method and its advanced methods (AFOSM) [347,348,349], calculate system failure risk based on reliability index, β, a relative measure of confidence in the system’s ability to perform its function efficiently. Their advantage over stochastic differential methods is their ability to deal with uncertain variables without a distribution function [350]. However, these methods neglect the higher-order moments so they may underestimate the risk. (4) Stochastic simulation, known as the Monte Carlo (MC) method [351,352], is a widely used statistical sampling technique that generates the PDF of a set of random variables. Using MC simulations, the probability of failure of the system can be calculated based on the joint PDF of its uncertain components (i.e., random variables). MC simulations are considered more accurate than reliability-based methods as they compute the probability of failure of the whole system using more precise PDFs of all uncertain variables. However, the MC results’ accuracy significantly depends on the number of samples generated. The large number of samples is critical for reliable model results, leading to extensive computational costs in complex cases. Thus, several sampling methods, such as latent hypercube sampling and importance sampling, have been developed to decrease the required sampling number and, consequently, decrease the results’ variance (for more details about MC sampling methods, see [353,354]). (5) Tree logical diagrams, such as Event tree analysis (ETA), Fault tree analysis (FTA), and Bow-Tie analysis, are methods of failure risk analysis where the consequences of a single system component failure are identified and tracked through the whole system [355]. Once the dam system is broken down into individual components, the logic diagram can be determined based on asking questions such as “What happens if a component fails?” in ETA (down-top approach), “What are the causes of component failure” in FTA (top-down approach). By answering these questions, tree diagrams can link the failure to its controllers and identify the subsequent probability of system failure using joint probability distributions (For more details about logical tree diagrams, see [336]). (6) The Bayesian belief network (BBN), proposed by Pearl in 1988 [356], is a probabilistic reasoning network that uses the Bayes theorem and graph representation to determine the propagation of system uncertainties through its components [357]. Generally, a BN consists of nodes (vertices) connected by directional links (arcs) that represent the dependencies between the connected nodes. By defining the probability distribution of the basic nodes (i.e., independent variables), the network can represent the propagation of the uncertainties of such basic nodes through the represented system using the Bayes theorem. The advantage of the BBN over the basic tree diagrams is the ability to incorporate updated information and easily be linked to other simulation models to represent dam system behavior (for more details about the advantages of the BBN over the conventional logical tree diagrams, see [358,359,360,361]). However, recent studies adopted hybrid BBN models in dam risk analysis (e.g., Monte Carlo-BBN models [362]; Markov Chain-BBN models [363]) to overcome the drawbacks of the traditional BBN (e.g., static and acyclic representation). For more details about BBN and dynamic BBN, see [360,363].

4. Research Gaps

This section aims to first present the contribution of the identified seven topics to the literature (i.e., the distribution of the seven topics in the analyzed documents). Subsequently, using the qualitative and quantitative analyses stated in the previous sections, this section aims to discover the research gaps that are not well explored (i.e., blue oceans [23]) pertaining to dam and reservoir operational safety. Figure 7 shows the summation of the gamma values for each topic (the probability of each document per topic), representing each topic’s contribution to the analyzed articles. Figure 7 shows that Topic 1 (Optimization Modeling), Topic 3 (Flood Risk), and Topic 7 (Risk-based Assessment and Management) are the highest topics with gamma values, respectively. As such, these topics can be considered the top three topics adopted in the literature related to the remaining five Topics 2, 5, 6, and 4, which have relatively lower gamma values, respectively.

To give a more in-depth understanding, the study identified the following three research gaps as opportunities for future studies. These research gaps are identified by reviewing such massive literature that had been cited in Section 3, including the published research articles, review papers, and textbooks, whereas the results of the quantitative analysis for the most available publications in the field are also used to demonstrate the authors’ perspective about the relatively less-covered areas in the literature. Moreover, within the identified three research gaps, the study presents deeper discussions for such studies that consider the identified relatively less-covered research area, aiming to determine the gaps within such studies by reviewing them qualitatively.

The first research gap is related to the limitation of the modeling concepts adopted in dam operational safety assessment studies. Most adopted models lack multi-hazard interactions, where a primary hazard can trigger one or more secondary hazards within a spatiotemporal scale (for more information about multi-hazard interaction, see [364]). However, they relate dam operational failures to a single external extreme event, where the excepted hazard events are independent. This conclusion can be supported using the quantitative analysis results, where “Multi” or “Multihazard” words do not appear in any of the topic’s word clouds. On the other hand, “Flood” (i.e., single extreme event) is the second higher topic considered by the literature (i.e., Topic 3 (see Figure 7)). Even though, there are several studies (e.g., [365,366,367]) that showed that dam operational failure usually occurs due to a combination of internal (e.g., lack of maintenance, delay in dam access) or external (e.g., windstorm) disturbance events that may also be individually considered within the design envelope.

The second research gap pertains to the capability limitation of the modeling tools adopted in the available dam operational safety assessment studies. The quantitative analysis shows the relatively higher adoption of optimization models (Topic 2 is the highest contributor topic to the literature, see Figure 7) and the risk analysis models (Topic 7 is the third contributor topic to the literature, see Figure 7) compared to employing dynamic dam system simulations in dam operational safety literature. Regarding the risk analysis tools, most of the adopted traditional risk analysis tools (stated in Section 3.7 (e.g., FTA, ETA, B.N.)) are usually static and do not consider the dynamic behavior of dam operation factors (e.g., hydrologic variables, gates operation) [363,368]. This can also be proved from the quantitative analysis results, where the “dynamic” word stem was not one of the most frequent words that appeared in Topic 7-word cloud). Some recent studies tried to represent the dynamic characteristics to predict dam operation failure risk using, for example, the coupling between Monte Carlo simulations and risk analysis techniques (e.g., [362]), dynamic B.N. (e.g., [172]); however, such studies still suffer from significant limitations in terms of the computational cost. In addition, the developed dynamic risk analysis models still need a more general representation approach to fit the different inter-relationships between complex dam systems components (e.g., cyclic or/and acyclic relations), which is a typical feature in dam systems. Moreover, considering the recommendations (e.g., [96,100]) for the essential coupling between the optimization models and dynamic simulation models to capture the dynamic characteristics, in real-time, of dam systems (as discussed in Section 3.1); thus, various researchers (e.g., [365,367,369]) pointed to the importance of system approach in simulating dam system operations.

However, most of the developed dam system dynamic models usually decompose complex dam systems into more manageable systems to be simply analyzed, ignoring system component interactions [14,366]. Thus, the general description of the dam complex system simulation approach has been introduced by King et al., 2017 [365] (using the system dynamics tool) in the context of dam operational safety assessment. The complex system simulation can provide a holistic representation of dam physical and non-physical dam system components/modules and their interrelationships and, thus, can provide a more realistic and more in-depth dynamic system response to various operational scenarios. Complex dam system simulations are then evolved in dam system operation safety (e.g., [370,371]). Nonetheless, the proposed models still suffer from two main shortcomings. (1) The deterministic definition of system components and ignoring the stochastic representation of uncertainties within the system operation modeling. In addition, the limited number of studies that represent the probabilistic definition of dam system components only consider the aleatory uncertainties (e.g., inflow randomness) and the epistemic uncertainty (e.g., model parameters errors) with the lack of representation of deep uncertainties (e.g., human behavior, uncertain failure scenario) that may significantly impact dam operational safety. This can be inferred from the quantitative analysis, where the word “uncertanti” appeared only in Inflow Forecasting and Flood Risk topics, see Figure 4. For more details about aleatory, epistemic, and deep uncertainties, see [330]. (2) The models still need more development to consider the effect of future climate change on the designed dam operational rules. The coupling between the climate models and the complex dam system simulation model can estimate dam system response (in real-time) to multiple climate scenarios. Subsequently, the coupling approach can facilitate the development of more realistic adaptive dam operational rules to mitigate climate change risk.

The third research gap refers to the limitation of adopting the Risk-based Assessment and Management concept in dam operational safety assessment studies. Risk-based management is the third contributor topic to the literature, see Figure 7, whereas the “resilience” word stem does not appear as any of the frequent words within the analyzed documents. The drawbacks of risk-based management can be concluded: (1) Risk definition relies mainly on probabilities estimation of hazard, which is affected by the lack of information and subjective assigning of probabilities; (2) Risk typically combines the probability and severity of hazard events into a single value, which results in similar risk levels for different hazard severity classes (e.g., Low possible event with high severity and high possible event with low severity have the same risk overall value); (3) Risk-based management focused on the immediate response of the system under a specific hazard event; however, the resilience-based management focuses more on the dynamic system functionality (gain or reduction), system recovery and deterioration time (after hazard occurrence), resource allocations pre- and post-hazard realization, and restoration costs [372]; and (4) Bachear et al. (2016) [330] also highlighted the advantages of the resilient-guided dam system in dealing with deep uncertainty that is barely considered in dam safety assessment studies, where the resilience-based assessment ensures that the system can bounce back to its standard level after any hazard event.

As such, the focus of several infrastructure systems (e.g., power, transportation) design standards have been shifted to resilience-based management [373,374]. However, the word “resilience” does not appear in any of the word clouds presented in Figure 1 and Figure 4. Moreover, the limited number of studies introducing resilience-based assessment in dam systems and operational safety (e.g., [371,375]) has some limitations on dam resilience quantification. The developed approaches depend only on simplified dynamic models. However, each system component usually has a different response to the applied hazard, which significantly affects the system’s overall response (including system functionality deterioration and recovery rates) and subsequently affects the quantified system resilience. As a result, the more sophisticated the model is, the more realistic the quantified resilience value for such a system. In addition, the previous studies did not investigate the resilience of dam systems under multiple hazards (consecutive and/or intersected). To overcome such limitations, Badr et al., 2023 [376] introduced the development of a comprehensive resilience-centric system dynamics model for the quantification of dam systems’ dynamic resilience under multi-hazard environments. However, the proposed model was also deterministic and did not explicitly consider the various operational uncertainties and the probabilistic hazard behavior associated with dam system operation under normal and hazardous disruptive conditions. Taking into consideration that the probabilistic resilience quantification is more efficient and realistic for infrastructure systems safety assessment than the deterministic quantification approach [372]. As such, more studies are still required to develop more reliable approaches to provide more efficient resilience-based assessment plans for dam systems’ operational safety.

5. Conclusions

The complexity of dam systems-of-systems, the multi-objective nature of their operations, and their uncertain vulnerability to climatic change pose serious challenges to dam operational management. Notwithstanding the criticality of dam infrastructure to society, such challenges triggered extensive research studies to investigate dam operational safety from various perspectives. Unlike other studies that subjectively considered only specific topics and related documents, this paper meta-researches (quantitively and qualitatively) the entire published literature on dam and reservoir operational safety from 1984 to 2023. This meta-research aims to identify and classify the major topics and subsequently uncover the latent topics in dams and reservoir operational safety. Subsequently, by examining such latent topics qualitatively, the key research gaps are identified as opportunities for future studies. More specifically, using the textual topic modeling, seven key topics are identified from analyzing 871 identified relevant journal articles. Such topics are optimization models; climate change; flood risk; inflow forecasting; hydropower generation; water supply management; and risk-based assessment and management. The contribution of such topics in the pertaining literature is subsequently presented, highlighting that: optimization models, flood risk, and risk-based assessment and management are more relatively considered in the literature than the remaining five topics. The importance of the quantitative analysis (text analytics) is not only limited to identifying the seven topics presented in Section 2, and providing the contribution of each of the seven topics to the literature, as shown in Figure 7; however, the text analytics key value shows up in Section 4, where the authors used the quantitative analysis results to support the authors’ perspectives for the potential research gaps. In addition, the qualitative review of these topics cited 376 research to identify the definitions, concepts, modeling tools, and recent research trends. Using quantitative and qualitative analyses, the study identified three major research gaps in dam safety assessment studies related to the limitations in both modeling concepts and modeling tools, as well as the lack of developing and adopting resilience-guided management strategies. Overall, this study presents a road map of dam and reservoir operational safety literature and associated knowledge gaps. The study also recommended future research directions on dam systems and reservoir operational safety to ensure the resilience of such important infrastructure and water resources in our changing climate.