Hasil untuk "River protective works. Regulation. Flood control"

Min Li, Xiaoye Han, Yonggao Yao et al.

Haijing Gao, Qian Wang, Zheng Zhou et al.

The effective management of river networks in coastal plains is crucial to flood control, water quality improvement, and sustainable flow distribution. This study aims to optimize the hydrodynamic performance of a plain river network in eastern China through water diversion and circulation scheduling, addressing challenges such as channel narrowing and sedimentation. This research study utilized a partitioned water allocation approach modeled in MIKE11 to simulate the effects of various diversion projects, including locks and connecting rivers, on the primary conveyance channel and supporting rivers. The simulation results indicated that flow velocities exceeded 0.1 m/s in most rivers, with significant improvements in flood discharge and water quality in the main conveyance channel and one supporting river. However, some sections of the network showed poor hydrodynamic performance due to narrow channels, encroachment, and sedimentation, and smaller rivers exhibited inadequate flow capacity. The findings provide critical insights for optimizing hydrodynamic regulation in coastal plain river systems, emphasizing the need to address specific issues to enhance overall network performance and flood resilience.

P. Vallés, I. Echeverribar, P. García-Navarro

Flood-control reservoirs are crucial for mitigating flood risks. When linked to flood-prone river reaches, 2D numerical models that capture river-reservoir dynamics are essential. However, 2D reservoir discretization requires many cells, being areas with near-zero velocity. This study introduces a 2D-0D coupled model, combining a 0D reservoir representation with a 2D shallow water model for the river and incorporating a PID control for reservoir level regulation based on dam height. The aim is to improve computational efficiency without sacrificing the accuracy of fully 2D models, water level control in the reservoir. Test cases reveal similar accuracy between the two models, with the 2D-0D approach offering substantial computational benefits. Realistic scenarios confirm these findings, yielding an effective, accurate tool for such applications.

I. García-Ledesma, J. Madrigal, C. Domínguez-Sánchez et al.

ABSTRACT Flood risk is essential today as extreme events increase and generate significant economic and social losses. However, traditional flood control infrastructures such as dams generate a sizeable initial investment cost. This article applies a methodology that contemplates a cost-benefit analysis to make appropriate selection when proposing new infrastructure to protect the population from the impact of floods based on economic risk and social and cost-benefit evaluation. The study area is in the Morelia city, located in Michoacan, Mexico. The constant growth of the city, together with its orographic conditions and limited natural flood zones, have caused catastrophes, such as floods, to occur annually in the area without extraordinary rain events. In this study, we analyzed an urban drainage system composed of small protective works. We observed that this system represents a small-scale socioeconomic benefit, as opposed to the large structures used to mitigate floods.

Febrian Kusmajaya, L. Limantara, E. Yuliani et al.

This research aims to optimize the management of Limboto Lake as a flood control measure in Gorontalo Province. Limboto Lake serves as a flood retention basin, receiving inflows from 23 rivers and discharging through a single outlet, the Tapodu Canal, which flows into the Bolango River and ultimately drains into the Bone River (Tomini Bay). Flooding in Gorontalo Province and Gorontalo City often occurs due to the absence of a regulated operation pattern for Limboto Lake. The study employs optimization techniques by simulating various scenarios of Tapodu gate operation under different design flood return periods, considering the canal's capacity of 199.00 m³/s. Given that the lake's storage capacity at an elevation of +7.00 m is 172.465 million m³, the embankment remains structurally safe for floods with a return period of up to 1,000 years. However, in the event of a Probable Maximum Flood (PMF), the embankment is expected to experience overtopping by 0.28 cm. Optimization results indicate that, without gate regulation, the outflow and maximum lake elevation reach 369.74 m³/s at +6.09 m for a 1,000-year flood and 408.80 m³/s at +6.84 m for a PMF event. In contrast, with gate regulation, these values are significantly reduced to 110.50 m³/s at +6.58 m for a 1,000-year flood and 142.00 m³/s at +7.28 m for a PMF event. Given that the Tapodu Canal's capacity is 199.00 m³/s and the lake's elevation is +7.00 m, uncontrolled outflows could lead to an overflow of the Tapodu Canal by 0.28 cm. Doi: 10.28991/HEF-2025-06-01-010 Full Text: PDF

Dong Li, Min Zhao, Hailong Zhang et al.

The inland water portion of the carbon cycle is an essential component of the global carbon cycle and is a promising direction to seek missing carbon sinks. Inland waters fix inorganic carbon to form autochthonous organic carbon (Auto-OC) and accept laterally transferred terrestrial OC. Calculating the carbon sink flux of inland water requires a quantitative estimation of the proportion of the aforementioned processes. In the current study, n-alkanes are used as biomarkers and the dual carbon isotope method (Bayesian mixing model) is applied to estimate the proportions of Auto-OC in the sediment of a simulation site comprising five shallow submerged macrophyte-dominated subsystems. The study results showed that a high proportion of Auto-OC was present in all sediment, regardless of the season or subsystem. However, the proportions were higher in the warm-humid season than in the cold-dry season. Results from a correlation analysis showed that temperature-controlled seasonal variations in the photosynthetic strength of aquatic organisms are the most likely cause of this difference. The average deposition rates of total organic carbon and Auto-OC were high (66.7 and 58.2 g C/m2/yr, respectively). Throughout the year, the weighted average percentage of Auto-OC ranged from 76% to 90%, with a mean value of 86% in the five aquatic subsystems. Establishing and maintaining submerged macrophyte-dominated systems have a potential of decreasing carbon dioxide (CO2) evasion and sequestrating more carbon (C) in headwaters. Working for clear submerged macrophyte-dominated lakes is beneficial for increasing carbon sinks.

Dwinata Aprialdi, Reza Mohammadpour, Afri Fajar et al.

Abstract We study a tropical river in South‐East Sumatra, where land drainage in the coastal zone has resulted in subsidence and increased flooding risks, exacerbated by sea tides. The novelty of this research is in determining the effect of tide on the lowland drainage system for forestry in a coastal tropical region and the impact of river cleaning on flood management. Five monitoring stations were set up along the Lebong Hitam river and its primary channels to observe flow characteristics, water level, and bathymetry. The results show how the tide effects water level in the river and the adjacent drainage area with Eucalyptus plantations. Cleaning of the river had a significant effect on each station and increased the discharge and velocity by more than five times and reduced the water depth by more than 40%. In light of this research, it can be concluded that the cleaning up process improves flood risk management by decreasing the water level and increasing the discharge and velocity at each of the upstream stations. The cleaning did not have a significant effect on downstream sections of the river where sea levels control the water level in the river to a large extent. The work provides an analysis of tidal river and provides recommendations for current and future drainage and water management.

Ali Nasiri Khiavi, Mehdi Vafakhah, Dongkun Kim et al.

ABSTRACT This study develops a comprehensive framework for mapping flood susceptibility and vulnerability in the Cheshmeh‐Kileh forest watershed in northern Iran by integrating remote sensing (RS), local knowledge, and machine learning (ML) algorithms. This was accomplished through the application of various MLs, such as K‐nearest neighbor (KNN), random forest (RF), support vector regression (SVR), and Naive Bayes. In this study, flood susceptibility refers to the physical propensity of an area to experience flooding, influenced by geo‐environmental factors, while flood vulnerability captures the socio‐economic and institutional dimensions that determine a community's ability to cope with and recover from flood events. This research first identified critical geo‐environmental factors influencing flood susceptibility and utilized remote sensing to locate areas prone to runoff generation. Flood risk zoning was then implemented using machine learning techniques in Python. To assess flood vulnerability, data were collected from local residents via questionnaires, focusing on economic, infrastructural‐physical, institutional‐policy, and social‐cultural aspects. The flood vulnerability map was created by integrating these survey results with population density data to identify areas where high social exposure coincides with high physical susceptibility. Findings indicated that the combined remote sensing‐SVR model was the most effective for sensitivity classification, identifying sub‐watersheds 2 and 8 in the Sehezar River (a major basin within the study area) as the areas with the highest and lowest flooding susceptibility, respectively, with sub‐watershed 10 in the Dohezar River (another major basin) being the most vulnerable. The estimated values for Mean Absolute Error (0.041), Mean Square Error (0.042), Root Mean Square Error (0.205), and Area Under the Curve (0.980) demonstrated high model accuracy. The Friedman statistical test showed that the average scores for the different dimensions of vulnerability decreased in the order of: economic (0.48), social‐cultural (0.44), infrastructural‐physical (0.34), and institutional‐policy (0.28). Consequently, the economic dimension was prioritized for its highest score. Flood vulnerability mapping revealed that sub‐watersheds 5, 11, 14, and 15, which had higher population densities, were naturally more vulnerable to floods. This finding reflects a direct relationship between population density and flood vulnerability. Overall, this study underscores the urgent need for effective planning and preventive strategies to mitigate flood risks and enhance resilience in the region.

Dawid Aleksander Szatten, Oleksandr Obodovskyi, Marta Brzezińska

The stability of river channels results from the impact of spatially diversified natural characteristics of the catchment, which are additionally intensified by the pressure of human activities. The aim of the current study was the overall assessment of the riverbed stability in the Brda River catchment (Poland) in the two periods 1980–1989 and 1991–2018. The study area is characterized by a high discharge regularity, resulting from the river-lake system in the upper part of the catchment, and strong human pressure caused by the presence of hydrotechnical structures in the middle and lower parts of the catchment. The hydrological, sedimentological, and land cover archival data were used in the current study. Also, in the field campaign, the characteristics of the river channel were delimited. Finally, the erosive stability channel factor is proposed, reflecting the level of pressure on the fluvial system from the catchment. The results show that in the first period, there was a tendency to accumulate sediment on the riverbed, resulting in its instability. However, in the second period, the river channel was stable, and erosion and sedimentation processes did not occur. The links between the stability of the bed of the Brda River, and the temporal and area-related pressures made it possible to identify long-term trends in the degradation of the fluvial environment as a result of human activities and to indicate the directions for sustainable sediment management in the catchment.

Jonathan D. Paul, Aneena Ajmi, Doris Bolaji‐Dada et al.

ABSTRACT Groundwater behavior in superficial gravel aquifers is globally poorly understood, especially across urban regions where drinking water is sourced from elsewhere. This study focuses on one such region around Staines, SE UK, where local River Terrace Gravels form a thin (< 10 m) superficial aquifer. The objective was to explain the unusually broad and long‐lived distribution of flooding by investigating local groundwater level fluctuations and flow. Over a period in January 2024, a targeted citizen science program was instigated to leverage local knowledge of floodwater, which was determined to match groundwater chemistry. Geophysical surveys (ground‐penetrating radar and seismic refraction) were designed to produce high‐resolution water table maps, validated against well measurements. Flow rates and hydraulic conductivity, K, of the gravels were determined both in the field (via pumping and tracer tests) and laboratory, to obviate any scale effects. K depended nonlinearly on hydraulic gradient, with Darcyan behavior breaking down at low (< 0.03) gradients, in conditions approaching turbulent flow. Large and localized fluctuations in groundwater level, combined with the existence of several fast‐flow pathways, are explained by the strong heterogeneity of the gravels, as well as their sensitivity to the imposition of subsurface obstacles such as clay‐lined backfilled gravel pits, or deep basements. These manifestations of urbanization drive observed patterns of groundwater emergence, together with aquifer thickness, rather than changes in river stage or surface elevation alone. Our experience motivates us to suggest that groundwater flooding be considered as significant as fluvial flooding in the production of risk maps by environmental regulatory bodies.

Hongqi Wang, Zixia Liu, Jingyun Feng et al.

ABSTRACT Amidst intensifying climate change, flash floods are becoming more recurrent, posing significant threats to safety and assets, especially in mountainous areas. Given the non‐negligible influence of bridges on flash floods, this research capitalized on fluid dynamics simulations to examine the mechanisms by which six bridges within the investigation zone affect the evolution of flash floods. Moreover, bridge blockage from debris accumulation was methodically investigated under multiple return periods. Results indicated that during the two historical floods, the bridges altered the distribution pattern of flash floods from various flood elements, including the backwater effect, flow velocity, and inundation. It is noteworthy that the spillway bridge (M1) notably raised water levels and slowed flows, whereas the influence of other bridges on flood dynamics was more muted. The presence of six bridges resulted in expanded flooded areas, particularly near the upstream bridges, raising risks for Qishi Village. Furthermore, the increasing blockage ratios at bridge B2 during multiple return periods exacerbated the impacts on flood elements, consequently amplifying the disaster of flash floods. This research strongly emphasizes the importance of incorporating bridges and their blockages into flood risk management. It further provides technical insights to bolster the basin's resilience against extreme hydrological events.

Diego Panici, Prakash Kripakaran, Richard E. Brazier

ABSTRACT Bridge owners and regulatory agencies have a duty to assess risks derived from hydraulic actions including scour, uplift, drag, debris impact, deck displacement, and other consequences that can lead to a loss in the load carrying capacity of a bridge. In the UK, the CS469 (Management of scour and other hydraulic actions at highway structures) is the standard for the assessment of hydraulic actions to highway bridges. The methodology in CS469 for the calculation of the hydraulic characteristics of the flow at critical cross‐sections within the channel and the bridge crossing, although simplistic by design to minimize computational effort, is intrinsically inaccurate since it makes use of unrealistic (i.e., non‐physically based) approximations. This results in estimations of risk and vulnerability levels that could include high levels of uncertainty. In this paper, we propose to bypass these approximated hydraulic calculations by harnessing the computational power of 2D hydraulic models, which would not require any additional field data collection than needed for the original CS469 method. We recommend a fully 2D HEC‐RAS model with the inclusion of bridges as 1D elements within the flow areas and only requiring publicly available data or data obtained from existing assessments in order to future‐proof the approaches and adhere to an open‐source/open‐access philosophy, but also imposing only a marginal increase in cost for bridge management teams. Results from the two models—2D HEC‐RAS and the existing approach in CS469, are compared for a number of real‐world bridges. The comparisons show that the estimations by HEC‐RAS are substantially higher for water depth (up to 138%) and lower for flow velocity (down by 58%). When these values are applied to the estimation of hydraulic vulnerability and scour risk, the differences are significant. Scour depths with the use of HEC‐RAS models are typically much lower (up to 3.9 m, and on average 1.7 m) than with simplified hydraulic equations, and this translates into lower (yet, more appropriate) scour risk levels. Hydraulic vulnerability to submergence of the assessed bridges is also assessed very differently, typically higher by the 2D model method. Overall, the results show that 2D numerical hydraulic simulations present a much more accurate estimation than existing methods, better balancing risks deriving from scour and hydrodynamic actions and with comparable effort and data requirements. The model displays consistency across an exhaustive set of simulations for a range of variables and bridges, showing limited variability and proneness to errors, whilst values estimated by CS469 are in most cases significantly different. Future versions of CS469 and similar documents should prioritize this methodology to provide a more accurate and realistic risk estimation.

Wayne Carpenter, Bradley Goodwiller, Daniel Wren

The National Center for Physical Acoustics (NCPA) at The University of Mississippi has developed a single-frequency acoustic attenuation system (SFAAS) to monitor the concentration of suspended fine sediments in rivers and streams. The system was operated in the Goodwin Creek Watershed in Panola County, Mississippi, USA, from November 2019 to February 2023. The system collected data when the stream stage was above 0.3 m, and physical pump samples were collected concomitantly to provide calibration data. A subset of the data, comprising 14 storm events recorded over the multiyear deployment, will be presented here to demonstrate the operation of the SFAAS and its potential to aid in hydrologic research. SFAAS was able to provide high-resolution fine sediment concentration data with a stable calibration relationship for a given hardware configuration. The data were used to investigate the behavior of fine sediment concentrations in the watershed, including hysteresis in the relationship between flow rates and sediment concentrations during streamflow hydrographs and sediment rating curves that relate stream depth to transport rates.

Joe Forbis, Cuong Ly

Abstract The US Army Corps of Engineers (USACE) prescribes flood control operations for reservoirs it regulates in watershed‐specific water control manuals (WCMs), which can be decades‐old and may not capture changed conditions in the watersheds or include the benefit of state‐of‐the‐science weather and streamflow prediction. Considering the specific characteristics of a reservoir, forecast‐informed reservoir operations (FIRO) may be used to enhance flood risk reduction, improve water availability, and achieve other benefits. The first FIRO pilot project at Lake Mendocino in California focused on determining if water supply reliability could be improved using FIRO without increasing flood risk. The final report concluded that FIRO concepts could indeed improve water supply reliability while enhancing flood risk reduction. Subsequently, USACE chose additional reservoir systems in California with different characteristics as additional pilot study locations to further investigate FIRO concepts. These successful FIRO efforts have provided justification to continue its expansion beyond the initial pilot sites. The lessons learned from the FIRO pilot projects are being used to inform the development of the FIRO Screening Process, a screening level framework intended to scale up the implementation of FIRO. The lessons learned could support FIRO implementation at suitable USACE reservoirs by updating WCMs.

Asid Ur Rehman, Vassilis Glenis, Elizabeth Lewis et al.

Flood risk managers seek to optimise Blue-Green Infrastructure (BGI) designs to maximise return on investment. Current systems often use optimisation algorithms and detailed flood models to maximise benefit-cost ratios for single rainstorm return periods. However, these schemes may lack robustness in mitigating flood risks across different storm magnitudes. For example, a BGI scheme optimised for a 100-year return period may differ from one optimised for a 10-year return period. This study introduces a novel methodology incorporating five return periods (T = 10, 20, 30, 50, and 100 years) into a multi-objective BGI optimisation framework. The framework combines a Non-dominated Sorting Genetic Algorithm II (NSGA-II) with a fully distributed hydrodynamic model to optimise the spatial placement and combined size of BGI features. For the first time, direct damage cost (DDC) and expected annual damage (EAD), calculated for various building types, are used as risk objective functions, transforming a many-objective problem into a multi-objective one. Performance metrics such as Median Risk Difference (MedRD), Maximum Risk Difference (MaxRD), and Area Under Pareto Front (AUPF) reveal that a 100-year optimised BGI design performs poorly when evaluated for other return periods, particularly shorter ones. In contrast, a BGI design optimised using composite return periods enhances performance metrics across all return periods, with the greatest improvements observed in MedRD (22%) and AUPF (73%) for the 20-year return period, and MaxRD (23%) for the 50-year return period. Furthermore, climate uplift stress testing confirms the robustness of the proposed design to future rainfall extremes. This study advocates a paradigm shift in flood risk management, moving from single maximum to multiple rainstorm return period-based designs to enhance resilience and adaptability to future climate extremes.

Lorenzo Zino, Mattia Boggio, Deborah Volpe et al.

We deal with controlling the spread of an epidemic disease on a network by isolating one or multiple locations by banning people from leaving them. To this aim, we build on the susceptible-infected-susceptible and the susceptible-infected-removed discrete-time network models, encapsulating a control action that captures mobility bans via removing links from the network. Then, we formulate the problem of optimally devising a control policy based on mobility bans that trades-off the burden on the healthcare system and the social and economic costs associated with interventions. The binary nature of mobility bans hampers the possibility to solve the control problem with standard optimization methods, yielding a NP-hard problem. Here, this is tackled by deriving a Quadratic Unconstrained Binary Optimization (QUBO) formulation of the control problem, and leveraging the growing potentialities of quantum computing to efficiently solve it.

Haijing Gao, Jingyuan Cui, Qing Wu et al.

To enhance regional flood control capacity, this study focused on the DX River section in Zhejiang Province. Unmanned vessel bathymetry was employed to obtain precise river cross-section data. A hydrodynamic model was established to simulate flood propagation processes and conduct flood routing analyses. Flood scenarios under 5-year, 10-year, and 20-year return periods were simulated to assess water level variations and overflow risks. The results indicate that under a 5-year flood, 19.5% of the right bank fails to meet flood control standards. This risk intensifies significantly with increasing return periods. Building on these findings, a flood optimal operation model was developed. The resulting coordinated strategy, which lowers the peak water level by 1.2 m during a 20-year flood, is sufficient to prevent overflow at the critical section and enhances regional flood control capacity. This is followed by dynamic gate regulation to match the outflow to the inflow. Dynamic regulation of spillway gates should then be implemented to achieve outflow rates commensurate with the incoming flood magnitude. This study demonstrates a robust workflow from high-resolution data acquisition to actionable operational rules, providing a transferable framework for mitigating flood risks in complex, regulated river systems.

Xin Huang, Juqin Shen, Shuqin Li et al.

Climate change has exacerbated the frequency and magnitude of extreme rainfall, which has led to the perpetuation of flooding as a hazard to humans and society. China has begun to consider introducing Flood drainage rights (FDR), a sustainable flood control measure, into non-engineering measures as a complement to engineering measures for flood control. FDR represent the right of regions to discharge regional floodwaters caused by extreme rainfall into the river, and are the primary means of controlling the amount of floodwaters from regions when regional flood capacity is exceeded. However, existing studies on quantitative FDR allocation still have limitations, and some previous methods have resulted in allocation schemes that are not entirely reasonable and fair because they do not comprehensively consider the influencing factors of FDR or the allocation method is unreasonable. This paper explores the impact of flooding on rural and agricultural areas. We incorporate the factors of agricultural economy and security and construct a system of the allocation indicators of FDR composed of five principles: Natural Environmental Endowment, General Economic and Social Development, Agricultural Economy and Security, Macro policy regulation, and Respect for Historical Background. Second, considering the influence of expert judgment and data of different time nodes on the allocation of FDR, we introduce the concepts of expert weight and time weight into the allocation model of FDR, and construct a new set of framework for the allocation of FDR, i.e., "[(expert weight + subjective weight)+(time weight + objective weight)]+decision making model ". To reduce the loss of information during the transformation of subjective judgments, we also introduced triangular fuzzy numbers for the transformation between expert judgments and numbers. Finally, we take the five provinces in the middle and lower reaches of the Yellow River as an example. Using the data from 2010 to 2021, we obtain the final allocation scheme (proportion) of FDR as Henan (33.26%) > Shaanxi (23.08%) > Inner Mongolia (21.31%) > Shanxi (14.44%) > Shandong (7.91%). On this basis, this paper utilizes sensitivity analysis and comparative validation to demonstrate the rationality and effectiveness of the method, and identifies several indicators that have a greater impact on the results of the allocation of FDR. FDR can form part of a set of integrated flood management system together with flood control projects, which greatly alleviates the drainage conflicts arising from flooding caused by extreme precipitation. Under extreme rainfall conditions, FDR improves drainage efficiency and minimizes the overall damage caused by flooding in the watershed. This study can contribute to the sustainable development of the watershed and provide a reference for the promotion and utilization of sustainable flood control measures.

Jhoselyn Milagros Aramburú-Paucar, F. Martínez‐Capel, Carlos Puig-Mengual et al.

Flow regulation in gravel-bed rivers impacts the hydrology, sediments and morphology, riparian vegetation, and vertical connectivity with the hyporheic zone. In this context, previous works have suggested that flood events may have riverine morphological and ecological benefits. In a Mediterranean-climate river system, we analyzed the impact of a 18-year return period flood on river morphology, riparian vegetation, fish aquatic habitat quality, and hyporheic exchange in a dam-regulated gravel-bed river, Serpis River (Spain). We collected pre- and post- flood riparian vegetation distributions and bathymetries, which were used to develop two-dimensional surface and three-dimensional subsurface numerical models to map surface and hyporheic hydraulics. Results show that the large flood removed the invasive giant reed from large areas, reshaped the in-channel morphology, by forming new bars and pools and enhancing the complexity of the flow field by scouring around large boulders. The habitat availability for the endemic Eastern Iberian chub (Squalius valentinus) and invasive bleak (Alburnus alburnus) increased. Hyporheic exchange showed limited change under losing conditions, but noticeable under neutral ambient groundwater condition. This study corroborates the beneficial effects that flood events or high flow releases may have on regulated streams and the potential use of high flow pulse as a restoration tool.

Hongjun Joo, Wonyoung Choi, Chansoo Jeon

Abstract Floods are the most frequent types of natural disasters. From the perspective of disaster management, indicators associated with floods are important for accurate flood risk assessment. However, the application of all indicators related to flood risk assessment decreases the evaluation efficiency, because the definitions of the indicators may overlap. Moreover, the volume of data required for collection and evaluation is significantly large, making the evaluation practically impossible. Thus, a scientific and objective method to select indicators for flood risk assessment based on the entropy theory was developed herein. First, the existing 28 assessment indicators were analyzed and probability‐based data were constructed for each indicator considering 28 districts in a midwestern region of Korea. The information quantity for each indicator was then obtained using marginal entropy and mutual information generated in the entropy theory. Next, the total information quantity based on the numbers of combination of indicators was derived by considering the information quantity for each indicator and the overlapping mutual information between the indicators. The maximum amount of information (161.55) was obtained by combining 18 out of the 28 flood risk indicators. The selected 18 indicators reflected regional characteristics better than those used in the existing method, demonstrating that the flood risk of the target area could be adequately assessed.