Impact of Soil Moisture Dynamics and Precipitation Pattern on UK Urban Pluvial Flood Hazards Under Climate Change

The diversity of flood‐generating mechanisms superimposed on catchment physiographic features with non‐stationary meteorological drivers makes future flood hazard assessment a grand challenge. To date, many studies have examined patterns in rainfall and streamflow, but far fewer have investigated trends in the other drivers of flooding. The complex transfer function between precipitation and flooding makes it potentially misleading to simply look at the change in rainfall to express the hazard. Furthermore, there are very few studies that have directly used output from km‐scale climate models in flood modeling. Coarse resolution climate data sets may not credibly resolve local climate and weather extremes. Changes in rainfall distribution and antecedent moisture over extended time periods due to climate change have so far been ignored when assessing urban pluvial flood risk. In this paper, an urban flood hazard assessment framework using the latest 2.2 km resolution UK Climate Projections Local is proposed. Global warming induced changes in pluvial flood risks under RCP8.5 are projected, focusing on the impact of changing precipitation patterns and soil moisture dynamics on flood generation. Results indicate a strong increase in the frequency of occurrence of extreme floods, and the resultant future (2060–2080) annual flood volume is expected to increase up to 52.6% relative to 1980–2000 over a major UK urban region, and these patterns are likely to hold more generally elsewhere in the UK. Shifts to a later occurrence of extreme flooding is identified under global warming. Previous studies that have neglected soil moisture dynamics are unlikely to give accurate flood estimates.


Introduction
There is a widespread consensus that the frequency and intensity of extreme precipitation events are expected to increase under global warming (Wasko et al., 2015;Wasko, Nathan, et al., 2021;Westra et al., 2014).Correspondingly, there is speculation that future urban flood risks will worsen, and an increasing fraction of impervious areas in urban catchments due to development may further aggravate flood disasters (Fadhel et al., 2018;Hettiarachchi et al., 2018).However, evidence from observed decreases in streamflow indicates that flood magnitude may not necessarily be correlated with precipitation only (Berghuijs et al., 2016;Bloschl et al., 2019;Ivancic & Shaw, 2015;Wasko, Parinussa, & Sharma, 2016;Wasko, Nathan, et al., 2021), while antecedent moisture status modulates some of the increase in flood risk even in urban catchments (Bennett et al., 2018;Hettiarachchi et al., 2018Hettiarachchi et al., , 2019;;Wasko & Nathan, 2019).Global-scale flood risk assessments have also projected both decreases and increases in future floods using multiple hydrological and climate models, ensemble scenarios, bias-correction, and flood indicators (Bloschl et al., 2019;Gudmundsson et al., 2019;Tabari, 2020).All of this hinders developing a common perspective on future flood changes.On top of this, though evaluation of global flood risk trends in climate model products has suggested that there will be a "wet-gets-wetter" response in areas that are already wet (Chou et al., 2013;Woldemeskel & Sharma, 2016), recent research has questioned the accuracy and reliability of coarse (50-100 km) grid resolution CMIP-class climate models in simulating the water cycle, particularly for climate extremes at local scales (Slingo et al., 2022).A comprehensive investigation of regional and seasonal flood impacts in a global warming world is therefore still lacking, particularly for urban catchments where there may be large impacts from flooding in terms of economic losses.Currently, most urban flood risk assessment under global warming focuses on single storm events of a particular return period, either estimated with an intensity-duration-frequency (IDF) curve representing the precipitation field or using a real-world flooding event (Chen et al., 2022;Hettiarachchi et al., 2018;Lin et al., 2020).Changes in rainfall spatial distributions and antecedent moisture status over extended periods of time due to climate change have so far been ignored when assessing urban pluvial flood risk (e.g., Hettiarachchi et al., 2019;Luo et al., 2022).We argue that the distributed precipitation pattern and soil moisture dynamics should be included in urban flood modeling.To help address this need we here develop a scenario-based future urban flood risk assessment framework using the latest UK Climate Projections (UKCP Local) at the hourly and kilometer scale.Multi-information sources regarding changes in the flood-generating mechanisms, including the precipitation patterns and soil moisture response, are incorporated to assess future flood hazard under climate change.Taking the UK city of Bristol (∼746 km 2 ) as a typical example, the direct surface water flooding hazard is evaluated using rainfall events extracted from three UKCP Local periods: the past , the present or near future  and the (far) future .Impacts of soil moisture dynamics and the meteorological drivers on the formulation of urban surface water flooding hazard is evaluated.

Background
The complexity of flood-generation processes, along with catchment physiographic features (e.g., impervious area, size and channelization) and dynamically evolving meteorological mechanisms (e.g., atmospheric circulations, and convection), make it extremely challenging to accurately forecast flood hazards (Fowler et al., 2021).It remains difficult to explore the relationship between heavy rainfall and flood changes in a warmer world, and it is also unclear whether the links between heavy precipitation changes and moisture conditions can be generalized to flood changes (Berghuijs et al., 2019;Tabari, 2020).The complex transfer function between precipitation and flooding suggests that it is not possible to characterize flood hazard with changes in rainfall alone, while more emphasis should be paid to understanding how changes in other meteorological parameters might contribute to flood danger.Whilst the spatial distribution, time evolution and rarity of precipitation are the direct causes responsible for urban flood hazards (Zischg et al., 2018), antecedent wetness conditions preceding a rainfall event also have a tremendous impact on the hydrological response of a catchment.Wasko and Nathan (2019) found that regions with decreasing soil moisture are visibly and statistically related to falling peak flow magnitude in Australia.Berghuijs et al. (2016) revealed that the principal flood-generating processes in the United States are soil-moisture-dependent precipitation excesses.Though infiltration rates in the urban environment tend to be much lower than that of a natural environment due to prevalence of impervious land cover, an assessment of flooding trends in both natural/urban catchments based on historically recorded climate data confirmed that changes in soil moisture can lead to decreasing flood magnitude though rainfall extremes are increasing (Hettiarachchi et al., 2019;Wasko & Nathan, 2019).Moreover, although many studies examine patterns in rainfall and streamflow (Gebremicael et al., 2017;Milly et al., 2005;Strauch et al., 2015), few studies investigate trends in the other drivers of flooding (Villarini & Wasko, 2021;Wasko & Nathan, 2019).As high uncertainty is associated with future climate scenarios, historical records may not be enough for evaluating the combined impacts of soil moisture and precipitation change on flood magnitude, especially when the objective is to assess future urban flood risk.Furthermore, climate change may fundamentally alter flood-generating mechanisms, changing the probability of flood hazards and their climatological drivers relative to the past, and possibly shifting future flood risk outside the envelope of historical variability (Arnell & Gosling, 2014;Fowler et al., 2021;Wasko, Westra, et al., 2021).Therefore, quantifying the antecedent moisture impact on flood magnitude using recorded gauge streamflow and precipitation data lacks the ability to reveal the flood generation mechanism in a nonstationary climate, and limited experience can be acquired from historical flood hazards to direct future flood mitigation efforts.
The newly-released UKCP Local is a very high resolution (2.2 km) Regional Climate Model over the UK that suggests hotter, drier summers and milder, wetter winters featuring increases in the frequency and intensity of extreme rainfall events in the future (Kendon et al., 2019(Kendon et al., , 2023)).Less uniform rainfall distributions with more localized intense rainfall during storm events are captured on hourly and kilometer scales as evidence shows a greater increase in peak rainfalls than storm volumes due to a shift to more frequent higher intensity but shorter duration convective storms.In addition, there is evidence that short-duration extremes, associated with convective storms under warming, increase more than total storm volume (Kendon et al., 2023;Miao et al., 2019;Wasko, Sharma, & Westra, 2016).Extreme precipitation at multiple timescales (from sub-hourly through to multi-day) is projected to increase with short-duration rainfall more likely to exhibit a greater increase.A shift to shorter more intense rainfall bursts may lead to flash flooding or moderate rainfall over several days which can overflow rivers or dams, and the long dry periods between events may evaporate more water.A large buffer is available to dampen precipitation increases causing lower runoff (Tabari, 2020).A high-resolution precipitation data set is required, while coarse resolution climate data sets may not be credible and reliable to resolve the small-scale local climate patterns, such as those important for large convective storms in summer (Navarro-Racines et al., 2020).However, there are very few studies to date that have directly used output from km-scale climate models in flood modeling.Here, the convection permitting UKCP Local data set which provides projections of future changes in weather extremes at local scales is applied to drive flood inundation modeling (Fung et al., 2018;Kendon, Prein, et al., 2021).UKCP Local captures not only changes in mean rainfall, but also changes in the intensity, frequency, temporal clustering, and spatial structure of hourly precipitation events, which is critical for understanding future changes in flooding across the UK.UKCP Local also gives a much better representation of the number and intensity of hourly rainfall extremes.It is worthy to note that there are bias associated with the data set, for example, heavy rainfall tents to be too intense due to local convective process not being fully resolved; nevertheless, UKCP Local gives a much better representation of the number and intensity of hourly rainfall extremes (Kendon et al., 2023).Importantly, here we quantify the influence of changes in both soil moisture conditions and precipitation on future flood risk, which may have advantages over more standard approaches.
Incorporating multi-source information on changes to flood-generating mechanisms into specific flood estimation methodologies remains a major challenge, and no consensus has been achieved regarding the best flood hazard estimation method under climate change (Delgado et al., 2014;Fowler et al., 2021;Hirabayashi et al., 2013).A review of the literature shows that most research now aims to project rainfall IDF curves, either through explicit consideration of non-stationarity using time-based statistical covariates or by downscaling climate model projections of rainfall to the point scale (Madsen et al., 2014;Salas et al., 2018;Wasko, Westra, et al., 2021).The IDF curve provides a flexible method for flood risk assessment with different return periods, but for urban pluvial flooding many compound factors are responsible for the formation of the flooding.A representative design storm event using IDF curves may not be able to reveal the surface water flood-generating mechanism, especially in the context of climate change.This is because when IDF curves are extended from point scales to areas they necessarily only represent spatially uniform rainfall and not the full spatial signatures of an ensemble of rainfall events.To address both these issues, here a physics-based flood inundation model (LISFLOOD-FP) which explicitly incorporates the multiple spatial information sources of changes in flood-driving factors is further developed (Bates et al., 2010;Neal et al., 2012;Rong et al., 2023;Sampson et al., 2015), to account for changing soil moisture and antecedent conditions.Together with 12 ensemble members of UKCP Local climate data at the hourly and kilometer scale, a scenario-based framework for future flood hazard assessment is proposed.Taking Bristol, a major UK urban area, as a typical example, a fully distributed flood hazard projection driven by timeseries precipitation data is implemented with a separately configured water balance model continuously tracking soil moisture dynamics.Implications of changes in extreme rainfall and soil moisture on flood magnitude, and how this influence varies with antecedent moisture condition, rainfall event temporal clustering, spatial distribution and rarity are revealed in this paper.

Study Area
Here, the City of Bristol and its surrounding area are considered for future flood hazards assessment.The study area, covering ∼746 km 2 , is located in the southwest of England near the Severn Estuary and Bristol Channel.Due to the finite capacity of the surface water sewers to accommodate rainfall volume in the study area, intense rainfall events larger than the design standard can overwhelm drainage systems and lead to flooding.As a result, Bristol is recognized as one of the UK's top 10 areas that are susceptible to surface water flooding according to the city Earth's Future 10.1029/2023EF004073 government's flood risk management strategy (Bristol City Council, 2018).Larger or more frequent heavy precipitation events would be expected to increase the overall magnitude and/or frequency of flood events under climate change.Figure 1 shows the location of the main river channels and urbanized zones within the study area, and the whole area is included for the surface water flood modeling.Potential pluvial flood hazards occur in lowlying zones, local topographic minima and around river confluences, especially where the River Frome joins the River Avon in central Bristol.

Methods
Evaluating flood hazard under climate change over urban catchments is a challenging task due to the complex interactions between multiple flood-driving factors (e.g., precipitation patterns and soil moisture response).To our knowledge, few models are able to handle these interactions at a spatial resolution of ∼30 m or less over such a large domain, and a specially designed model structure is demanded to couple all these processes (precipitation, infiltration, drainage loss, and inundation) together.Therefore, a UK future flood hazard assessment framework under global warming is proposed.A physics-based flood inundation model LISFLOOD-FP (Bates et al., 2010;Neal et al., 2012;Rong et al., 2023) which explicitly incorporates the flood-driving factors is further developed, with a separately configured water balance model and an integrated Green-Ampt infiltration model accounting for changing soil moisture and antecedent conditions.Characteristics of flood-producing rainfall events and their corresponding consequences in a warmer world are analyzed.The following methodology section outlines the steps associated with assessing how direct surface water flooding varies under global warming using the hourly and kilometer scale precipitation data from UKCP Local.It is expected that robust decisions regarding the designation of at-risk areas and investment in long-lived infrastructure can be made, though uncertainty about the exact trajectory of future change coupled with the complexity of hydrological processes presents significant challenges.

UK Future Flood Hazard Assessment Framework Under Global Warming
Currently, both the continuous models (simulating runoff dynamically over time) and event-based models (simulating a single flood event in isolation) can be applied for flood hazard assessment.Considering that each UKCP Local ensemble member covers a time span of 60 years (in three epochs: 1980-2000, 2020-2040, 2060-2080) at the hourly and kilometer scale, it is unfeasible to conduct continuous hydrodynamic modeling over nontrivial and policy relevant domain scales due to the high computational burden, especially when the grid resolution of flood modeling is ∼30 m or less.Therefore, within the proposed UK future flood hazard assessment framework, a rainfall event identification approach is included to separate the rainfall events from the continuous precipitation data (Section 4.2).The flood hazard assessment is therefore conducted based on all the identified rainfall events.A separately configured water balance model which continuously tracks moisture conditions is also integrated, and the distributed soil moisture status before every rainfall event is extracted and taken as the antecedent moisture status for flood modeling (Section 4.4).A Green-Ampt infiltration model (Green & Ampt, 1911) is newly implemented in LISFLOOD-FP to update the infiltration loss rate on each individual ∼30 m grid based on the local rainfall/flow status during the inundation process (Section 4.5).As is shown in Figure 2, four components (antecedent moisture status, precipitation, rainfall drainage loss, infiltration) are linked together with the flood inundation model, LISFLOOD-FP.Driven by hourly and kilometer scale precipitation data and the antecedent moisture status, the subgrid channel (SGC) solver in LISFLOOD-FP can capture the surface water flow movement and simulate the water depth distribution using a "rain-on-grid" approach for each individual ∼30 m Digital Elevation Model (DEM) grid cell.River channel conveyance capacity and water exchange at the river-floodplain interface is estimated using an approach which in natural channels takes the 1 in 2 year simulated water depth as the channel depth (Section 4.6) following the methods in Neal et al. (2021).Preceding the flood inundation process, a direct reduction to the rainfall intensity in the urban area is applied to simulate the drainage loss by the sewer system (Sayers et al., 2020;Smith et al., 2015;Xing et al., 2022), and the value is determined by rainfall event frequency analysis (Section 4.3).The reason why a simplified drainage loss estimation method is favored as opposed to a flow hydraulics calculation in the sewer network is due to the lack of sewer system data, which can be a typical situation in urban inundation modeling.Although some uncertainty is inevitable with this simplified treatment, we hope to cover the envelope of flood hazard variability using four drainage loss rates under different return periods (Figure 2).Additionally, a drainage loss rate of 0 is applied to simulate the flood hazard status in the absence of a sewer system.

Rainfall Events Extraction Using UKCP Local Hourly Precipitation Data
The UKCP Local Regional Climate Model projections, released in July 2021, consist of an ensemble of 12 simulations at 2.2 km grid-spacing over the UK run for three epochs 1980-2000 (past), 2020-2040 (present) and 2060-2080 (future) under the RCP8.5 high emission pathway (Kendon et al., 2019).Each 2.2 km prediction provides a set of plausible projections of climate change for the UK on hourly and kilometer scales for use in risk assessments, with ensemble members differing owing to natural climatic variability and uncertainty in global model physics.The explicitly modeled convection at 2.2 km grid spacing instead of the parameterized scheme results in a much better representation of the number and intensity of hourly precipitation extremes, as well as the local surface influences including topography, soil moisture and urban effects (Kendon et al., 2023).Critical atmosphere behavior dominating the formulation of most extreme weather events, the convection process, is permitted using the 2.2 km grid spacing though smaller showers and convective plumes are not explicitly resolved (Kendon, Prein, et al., 2021).As a result, the simulated annual maximum hourly precipitation in the convectionpermitting UKCP Local model agrees well with hourly gridded observations (Kendon et al., 2023).Specially, when compared with the historical observed precipitation data (Lewis et al., 2022), the bias is not significant over the relatively small Bristol study area.Therefore, no bias correction is implemented for UKCP Local in this paper.However, it is worth noting that there are bias associated with the UKCP Local rainfall data set.A diligent examination of rainfall bias against historical data for each specific local flood modeling remains imperative.Bias corrections can play a crucial role in flood modeling, particularly for some coarse-resolution parameterized convection climate models where significant bias in projected rainfall exists against observations (Lane et al., 2022).Additionally, when undertaking large-scale flood modeling using UKCP Local, considering and addressing these biases may become paramount for ensuring the model accuracy and reliability.Nevertheless, the enhanced spatial detail and information on changes in precipitation at local and hourly timescales allow us to examine the risk of extreme weather events in local areas for the coming decades, and therefore help to understand how short-duration intense rainfall events and flash floods might change in the future.Precipitation data falling within the study area are used to extract the rainfall events.
Rainfall events were chosen based on a peaks-over-threshold algorithm where individual events were identified as peak rainfall intensity over the domain exceeding a predefined threshold, and being separated by a continuous 6 hr of rainfall intensity less than 1 mm/hr (Bezak et al., 2014;Wasko & Nathan, 2019).After some trial and error, a threshold of 6 mm/hr was selected to extract the rainfall events.This resulted in the selection of 30,098 events from the 720 years of climate data.In particular, the event set includes 10,381 rainfall events in summer.Figure 3a compares the monthly average rainfall depth from the selected rainfall events with different peak thresholds.The lower the threshold, the greater the number of precipitation events identified.A further analysis of the characteristics of all the rainfall events shows that a greater number of less-severe rainfall events (small peaks, small accumulated rainfall volume and rainfall depth) are additionally extracted with a smaller threshold (2 and 4 mm/ hr), while a threshold of 6 mm/hr can better identify the potential hazardous rainfall events.As we can see, more monthly average rainfall volume is filtered out in the colder but wetter winter compared with the drier but hotter summer, and therefore a large difference exists between the line plot and bar in the winter seasons.Figure 3b shows the annual average rainfall depth for 12 UKCP Local projections under RCP8.5, with the ensemble members differing from Ens01 to Ens12.Differences between these 12 members are largely due to them sampling different realizations of natural variability (but note they do not comprehensively sample the full envelope of uncertainty, Kendon, Prein, et al., 2021).Overall, the rainfall depth is expected to increase to varying degrees under global warming.A sharp increase in the total rainfall is anticipated from scenario Ens02, where the future (2060-2080) annual average rainfall depth increases by 49.3% compared with the past epoch .Though the exact trajectory of future change is unclear, it is expected that the 12 ensemble members cover key aspects of the envelope of future pluvial risk across a plausible range of changes in intensity and seasonality.

Soil Texture Classification and Drainage Loss Estimation
Soil texture determines the physical properties of soil (maximum moisture deficit, suction head at the wetting front, and saturated hydraulic conductivity), which are key parameters in both the Green-Ampt infiltration model and the water balance model.Specifically, these parameters determine how much rainfall can be translated into infiltration loss.Here, soil texture is classified according to the USDA criteria, and a total of 12 soil textures containing clay, sandy clay, silt and loamy sand etc. are classified based on the relative weight of three soil components (sand, clay and silt).A global digital soil mapping database, SoilGrids (Batjes et al., 2019), is used to acquire the fraction of each soil component (clay, silt, loam) at six standard depth intervals with a spatial resolution of 250 m.Local soil classification data sets would be preferred where these exist, however the SoilGrids data can be an alternative for regions without publicly available soil data sets.Soil texture classification results indicate that Bristol and its neighboring area is clay loam dominated, with this soil type having a share of 52% by area.Clay and silty clay loam have similar coverage, each taking up ∼21% of the domain.
A uniform drainage loss rate by the surface sewer system is estimated based on a rainfall intensity-frequency analysis (Sayers et al., 2020;Smith et al., 2015;Xing et al., 2022), and the drainage loss rate is then used to directly reduce the rainfall intensity in urbanized areas (Marston et al., 2022).During flood modeling, a uniform value from these estimated drainage loss rates across various rainfall intensities (0, 10, 18, 21, 31 mm/hr) is applied to calculate the net rainfall over the identified delineated urban regions (gray area in Figure 1).Only rainfall intensities surpassing this specified value are considered to reach the ground at each timestep, while less intense rainfall is disregarded.It is important to note that this approach represents a simplified treatment, assuming that the drainage loss rate to be equal to the rainfall intensity under different return periods.This simplification only partially accounts for the complexities of the drainage system and the hydraulics process in drainage system but is implemented within this framework for the sake of computational simplicity.To estimate these drainage rates under different return periods, peak rainfall intensity in each identified rainfall event is ranked, as well as their corresponding recurrence interval.Four drainage loss rates under different return periods (1 in 2 year, 1 in 5 year, 1 in 10 year, and 1 in 20 year) are estimated using the rainfall intensity frequency curve (Figure 2).For Bristol, the estimated drainage loss rate with a return period of 2 years is 10 mm/hr, and it can reach to 31 mm/hr for a return period of 20 years.A loss rate of 0 is additionally applied to simulate flood situations in the absence of drainage system.
The model structure used here does not explicitly include the drainage network hydraulics, however at peak drains were most likely overwhelmed and so the modeled inundation is believed to be a fairly accurate representation in the urbanized areas (Schumann et al., 2011).Also, it is currently not possible to collect data on the sewer networks at such a large scale and this is a typical situation in urban inundation modeling.Adoption of more complex representations of these drainage systems to enable a sewer hydraulics calculation is impracticable.Despite these limitations, this assumption that the rainfall intensity can be directly reduced by the drainage system is accepted by the scientific community and adopted in a number of recent works (Sayers et al., 2020;Smith et al., 2015;Xing et al., 2022).

Retrieval of Initial Soil Moisture Status With Continuous Water Balance Model
A simplified water balance model in which evapotranspiration and runoff ratios are expressed as simple functions of soil moisture is applied to continuously track the soil moisture status over 20 years in each UKCP Local projection.This is a similar model structure and process representations to the MGB-IPH and HBV models (Aghakouchak & Habib, 2010;Hundecha & Bárdossy, 2004).Continuous modeling to account for the full changes in the spatial and temporal characteristics of rainfall as provided by the UKCP Local climate simulations is achieved in this way.By taking an individual ∼30 m DEM pixel as a grid cell (Collischonn et al., 2007;Kay et al., 2022) and ignoring the horizontal fluxes between two surrounding grid cells, hydrologic process (i.e., precipitation, evapotranspiration and runoff, etc.) are continuously simulated driven by the UKCP Local daily average rainfall data, and the volumetric water content is calculated using the ratio of current soil water storage to maximum moisture content.Here, the 2.2 km daily average precipitation and temperature data calculated from UKCP Local is processed to drive the water balance model.The water balance model adopts a daily time step instead of hourly for tracking soil moisture dynamics in order to produce a robust update of the moisture dynamics.
High uncertainties in the separately configured water balance model emphasize the importance of calibrating hydrological model parameters.Maximum water storage (W m ) measures the water holding capacity in the upper layer of soil, which is estimated in a similar way to the Green-Ampt infiltration model.Depending on the soil texture, the topsoil layer thickness and the effective porosity can be estimated empirically, and W m is equal to the product of these two outputs.Parameter b represents the statistical distribution of the water storage capacity of the soil.With a larger value of b, the grids in the domain will have a soil storage capacity lower than W m and generate more runoff.K bas is a parameter which gives the percolation rate to groundwater in the case of saturated soil, similar to the saturated hydraulic conductivity K s .cc is an empirical value modulating the effect of temperature change on PET, especially when the mean daily temperature deviates considerably from its long-term average.The parameter cc ranges from 0.01 to 0.07 and can be estimated based on observations via model calibration.A large cc value can induce more PET, implying a strong impact of warmer temperatures on the PET rate.A complete description of these parameters can be found in Collischonn et al. (2007).To validate the water balance model, one solution used here is to compare the simulated soil moisture with the COSMOS-UK field survey data.The COSMOS-UK data is acquired from a long-term network of soil monitoring sites that uses the cosmic-rays to sense soil moisture over an area of about 12 ha (Zreda et al., 2012).The soil moisture data has been validated with the field calibration using the oven-drying method, and used for a range of applications, including improving weather forecasting, flood prediction (Andreasen et al., 2016;Cooper et al., 2021).At first, long-term volumetric water content data from 2017 to 2023 at the Tadham Moor station (close to the study area) was collected from COSMOS-UK site (https://cosmos.ceh.ac.uk/), and monthly average soil moisture was processed (Cooper et al., 2021;Stanley et al., 2023).With the objective of minimizing the difference between the field survey monthly average soil moisture and the simulated results, parameters (b, cc, and K bas ) were selected from a range of possible values, as shown in Table 1.
With the water balance model continuously tracking the soil moisture dynamics over 20 years in each UKCP Local epoch, the soil water content evolves dynamically to reflect the spatial and temporal patterns of precipitation.Compound impacts from multiple successive rainfall events on the flood generation can be addressed this way: a higher antecedent moisture status can be expected with multiple successive rainfall events, and the wetter moisture would result in more flood volume for the coming rainfall events.The moisture status therefore shows the impacts of previous rainfall events on current flood generation, though ponding water depth from previous rainfall events is neglected.In this way the approach also takes into account changes in the sequencing of rainfall events in current and future climates.Considering that rainfall events are separated by a continuous 6 hr of rainfall intensity less than 1 mm/hr, in most cases the ponding of water can be released through the river channel or any other infrastructure within this period, and therefore limited impact can be expected due to the ponding of water from previous events.

Green-Ampt Infiltration Model Integration in LISFLOOD-FP
A Green-Ampt infiltration model is, for the first time, explicitly integrated into the flood inundation model, LISFLOOD-FP, to simulate the impacts of rainfall intensity and duration on vertical infiltration processes in each individual ∼30 m DEM grid.By resampling these processed soil texture classification and antecedent moisture data according to the DEM resolution, the surface water flood model can dynamically retrieve the rainfall intensity and calculate the ponding water depth and flux exchange between adjacent grid cells.Within each wetted grid cell, vertical water velocity in the soil is given by Darcy's Law as a function of the saturated hydraulic conductivity K s , the capillary suction head along the wetting front Ψ s , the depth of ponded water at the surface d, and the depth of the saturated layer below the surface L s .As the infiltrated water moves vertically downward in a saturated layer, beginning at the surface, the wetted zone moisture content is reaching its saturation status while moisture content in the unwetted zone is still at the initial moisture status.A wetting front is conceptually present in the soil profile which separates the soil column into these two regions.As the wetting front moves vertically downward, the depth of the saturated layer below the surface grows, and the infiltration capacity decreases gradually.With the classified soil texture map, soil properties used to estimate the infiltration rate in Green-Ampt infiltration model can be found in Rawls et al. (1983).The recommended parameter values which result in a better performance on average are adopted, although a large range of parameters can be selected.
Though the lateral movement of soil water is neglected, horizontal surface flow movement is activated in the form of momentum exchange which can accelerate the infiltration speed.Expressed in the same form as the rainfall intensity i, the ponding water depth d and momentum exchange Q between four surrounding grid cells are included in Equation 1, to show their impact on the infiltration generation (Rossman, 2010;Rossman & Huber, 2016).This ensures that the dominant vertical water fluxes impacting the infiltration process are included.
Before a saturated layer develops at the ground surface, the infiltration capacity f p is equal to the rainfall intensity i a .After the soil gets saturated, the infiltration capacity f p can be calculated as in Equations 2 and 3.
Where F is cumulative infiltration.θ d is the soil moisture deficit, which is the difference between the saturated moisture content and the moisture content in the un-wetted zone.Equation 2 is an integrated form of the Green-Ampt equation, to avoid numerical errors over long time steps.With a known cumulative infiltration at the start of the time step F 1 , the cumulative infiltration at the end of the time step F 2 can be solved numerically according to Equation 3. The average infiltration capacity f p over the time step ∆t can then be computed as (F 2 F 1 )/∆t (Rossman & Huber, 2016).
Synchronization of the timestep from the hydrodynamics model and the infiltration process is another problem deserving much more attention.For the distributed hydrological infiltration process, a larger time step (∼300 s) would not induce numerical oscillations, while during dry periods an even looser constraint on the time step can be applied, considering that the rainfall data has a temporal resolution of 1 hr.However, the time step in the (explicit) hydrodynamic model is necessarily controlled by the Courant-Fredrich-Levy (CFL) condition, which is generally less than 1 s depending on the flow status for the grid scales typically used in urban inundation modeling (∼30 m or less).Computational burden can be increased abruptly without improving the simulation accuracy by using the same small time step for both the hydrology and hydrodynamics model, while a larger time step can Earth's Future 10.1029/2023EF004073 RONG ET AL. make the numerical scheme in the hydrodynamic model divergent.Therefore, an asynchronous time step update mechanism is applied to conform to the time step in these two processes.At the initial stage, the flood model updates the flow status with a predefined time step, and then the infiltration rate in each DEM grid is acquired, and the infiltration model updates at a larger time step (300 s).While the flood model is evolving at a smaller time step controlled by the CFL conditions, the infiltration rate is fixed until flood simulation time exceeds the hydrology model and the infiltration rate is updated.

River Channel Bathymetry Estimation and LISFLOOD-FP Model Setup
For the purpose of estimating the river channel bathymetry, an empirical method is adopted which uses the 1 in 2 year simulated water depth as the depth of the approximated rectangular river channel, and the channel width is approximated using hydraulic geometry theory given by the 1 in 2 year discharge.Details of the river channel bathymetry estimation process can be found in Neal et al. (2021).With the estimated river channel depth and width profile, 100 rainfall events either with a large rainfall intensity or a large total rainfall volume are simulated.By comparing the maximum flood inundation extent with the Bristol Flood Risk Management results (Bristol City Council, 2023) and some government reports (Bristol City Council, 2013), the river channel bathymetry estimation results were adjusted and validated.
Figure 4 shows how all mentioned components (water balance model, rainfall event identification, Green-Ampt infiltration model, and sewer networks simplification) are linked with LISFLOOD-FP.Processes 2-5 detail the rainfall event generation procedures, and processes 6-8 describe the soil moisture tracking routine with the separately configured water balance model and the integrated Green-Ampt infiltration model.All these routines work together to either provide data for flood modeling or assist the calculation of vertical flow movements in each individual DEM grid cell during the flood inundation process.With the provided data sets (precipitation, initial soil moisture, DEM, river bathymetry, soil texture etc.), LISFLOOD-FP is able to handle the interactions between precipitation generation, river flow calculation, inundation and infiltration processes.The surface water flooding model is specifically designed to elucidate the spatial-temporal distribution of rainfall across an uneven surface, as represented by the DEM.This intricate process entails the calculation of volume exchange between neighboring grid cells, subsequently influencing updates to the water depth within each grid.These adjustments are determined by the water surface gradients, in accordance with the principles of the shallow water equations, thereby effectively simulating the dynamic inundation patterns associated with rainfall-driven floods.It is important to note that the model does not represent lateral water movement in the subsurface.We hypothesize that this is an acceptable simplification for short-duration rainfall driven flooding, particularly in urban areas with a high proportion of impervious surfaces and small catchment areas.For events with durations of just a few hours we assume subsurface contributions to the stream network must be relatively unimportant and this allows us to significantly streamline the model structure.As accumulated surface water converges and reaches the river channel, it undergoes downstream transfer within the channel.Here, the dynamics of the river channel and the adjoining floodplain are captured through a hybrid 1D-2D representation.It is noteworthy that the grid is established as the basic computational unit throughout this integrated process.Controlled by both the ponding water depth, the rainfall intensity and discharge exchange with neighboring elements, the infiltration rate is estimated and the infiltration loss within each grid at every time step is updated.A mass balance check is performed to ensure the preservation of mass conservation property.Manning's friction for floodplain flow movement is set at 0.06 m 1/3 s, while for the river channel a uniform Manning friction of 0.04 m 1/3 s is applied.Free boundary conditions are set for the boundaries with a predefined slope of 0.5‰, allowing water to flow out of the domain under the control of the local inertial form shallow water equations.The sea level is defined as the baseline at 0 m, allowing for unimpeded discharge of surface water into the sea since the surface water flooding is the main focus in this paper.For each rainfall event, the maximum water depth in each individual grid during the computation is acquired, which is used to assess the flood hazard.A detailed description of the hybrid 1D-2D surface water flood model can be found in Bates et al. (2010), Neal et al. (2012), and Rong et al. (2023).

Validation of the Proposed Surface Water Flood Modeling Framework
The performance validation of flood hazard maps (e.g., Figure 5) poses a unique challenge as these do not represent individual observable events.Instead, these maps highlight areas at risk from plausible UKCP Local rainfall events under the highest emissions baseline scenario (RCP8.5).It is important to note that the simulated rainfall events may not necessarily align with observed rainfall events in terms of spatial and temporal distribution.This misalignment complicates the use of historical surveyed flood inundation extents for model validation.Nevertheless, insights into plausible flood inundation patterns can be gleaned from numerous instances of simulated rainfall events.The yellow-shadowed region in Figure 5 illustrates historical recorded flood outlines sourced from the Environment Agency (https://www.data.gov.uk),encompassing floods induced by tidal, fluvial, and pluvial drivers since 1946.A notable observation is that the majority of the estimated floods align closely with the hazard map produced for this paper.We do not expect a perfect match because this additionally reflects tidal and large river flooding which are not represented in our mode, and the surveyed data may fall short in adequately capturing instances of widespread small surface water flooding.Figure 5 underscores the capacity of surface water flooding to manifest in areas beyond traditional river channels, especially in the future RCP8.5 scenario under climate change.
Moreover, hydrodynamic models, in contrast to hydrological models that commonly rely on streamflow/ discharge data at downstream gauges for validation, primarily generate flood depth distributions and extents.
Obtaining detailed field surveys of flood depth distributions is inherently challenging.This is especially true for urban rainfall driven flood events where the events usually have a short duration and are highly localized.Satellite data, while valuable for monitoring floods, faces limitations in accurately detecting inundation in urban areas (Rahman & Di, 2016).The scarcity of available flood event data further exacerbates these challenges: since 2000, only the flood events of 2012 and 2018 have been attributed to surface water flooding (Bristol City Council, 2023).A pragmatic approach to validating flood modeling results therefore involves comparing the simulated maximum inundation extent from historical rainfall events with surveyed and detailed local inundation extent data.We reproduced the flood inundation extent of a real flood event using historical observed rainfall data, specifically the CEH-GEAR observed hourly 1 km rainfall data (Lewis et al., 2022).Illustrated in Figure S1 in Earth's Future 10.1029/2023EF004073 Supporting Information S1, we present the simulation of the November 2012 flood in the Brentry and Southmead areas of Bristol using our proposed framework.Our model demonstrates a robust correlation with the flood extent identified in a government report on the flooding (Bristol City Council, 2023), accurately capturing nearly all of the inundation zones as identified by the local authority.It is important to acknowledge that our simulated inundation extent records all pixels that were once covered with a water depth higher than 0.1 m during the 4-day validation period.Consequently, some overestimation of the flood extent is apparent, primarily attributed to the consideration of shallow water depths and the ∼30 m grid resolution, which is coarser than the very highresolution flood map used in the government report.Due to limited availability of historical flood information, our validation efforts were concentrated on comparing flood extents within this constrained region.
Finally, the surface water flood model, LISFLOOD-FP, has recently undergone validation against UK national flood maps with a 1 in 100 year return period, as provided by the Environment Agency (2018).Bates et al. (2023) reported a critical success index value of 0.65 for England by applying LISFLOOD-FP to replicate the 1 in 100 year flood hazard map, indicating a satisfactory level of model performance.It is important to note that we cannot directly compare our results to the national official maps as they did not align in terms of return periods and treatment of flood hazards (only surface water flooding layer in official maps without river floods).This mismatch in data and methodology prevented a like-for-like comparison to serve as a benchmark.Notably, the structure of our proposed connected model framework closely aligns with that employed by Bates et al. (2023), enhancing confidence in the reliability of our simulated results.

Results
The proposed framework is applied to assess the future flood hazard over Bristol using the latest UKCP Local data set.The 12 ensemble UKCP Local projections which provide a plausible range of changes in precipitation intensity and seasonality under global warming are utilized, and future flood hazards are predicted accounting for changes in the precipitation patterns and soil moisture dynamics.Future surface water flooding hazards are assessed for the 2080s under a high emission pathway.

Overall Flood Risk in Bristol
Flood occurrence maps over 20-year epochs were generated using LISFLOOD-FP for the past , present (2020-2040), and future (2060-2080) periods using the 12 UKCP Local ensemble members, with the specific value indicating how frequently the area is submerged with a water depth over 0.10 m per year.The changes in flooded area over the region are shown in Figures 5a and 5c for the extreme (future epoch in Ens02) and median (median over all 12 future epochs) estimate of flood hazards, with additional consideration of the soil moisture status and the drainage system (assumed 10 mm/hr in the urban area), while Figures 5b and 5d ignore both the infiltration process and the sewer system.Here Ens02 is displayed because it has the highest total rainfall volume (Figure 3b) as well as the highest number of identified rainfall events (1,052) in the future epoch, and correspondingly the study area is most likely to be submerged, with more than 12% of inundated area being hit more than 10 times over 20 years (most are river-surrounding area).Assuming the present-day population and development levels, the results highlight concentrations of infrastructure risk in many urbanized regions (e.g., Bristol city center nearby the confluence of the Rivers Frome and Avon) in the future.Coastal areas near the Severn Estuary also face a significant increase in surface water flooding hazards.These results are likely to be underestimated as no effort is made to explicitly consider the compound impact of sea-level increase, storm surges, and intense precipitation.
The projected flood frequency at or nearby tributary confluence elevates the future overall flood risk in these parts of the study area.Once the River Chew discharge joins the River Avon, the conveyance capacity of the River Avon is not enough to route the combined discharge downstream efficiently.As a result, flooding with a water depth over 0.10 m occurs nearly once a year at this location in the future scenario of Ens02.The same situation applies to the Bristol central area nearby the confluence of River Frome and River Avon.It is anticipated that the central area would be hit by a severe rainfall event once every 10 years, and the resultant water depth can be higher than 0.10 m, though the median estimate of the future rainfall is lower.In most cases above the median estimate scenario (Ens03, Ens06, Ens9, Ens12) the central area may encounter a flood hazard (with a water depth higher than 0.10 m) once every 20 years in the future epoch .
We want to address the vital importance of incorporating the sewer system and the infiltration process during the flood inundation process.A large extent of industrialized area along the three streams would be submerged in (b) and (d), while only a small proportion of this area is submerged with the additional consideration of the drainage system and the infiltration process.A comprehensive comparison of the present flood hazard status from observed (Bristol City Council, 2023) and the simulated results indicates that the inclusion of the infiltration process and the drainage system enables a much closer approximation of the flood inundation extent.

Annual Flood Risk Pattern
Figure 6 shows the annual average rainfall volume from the 12 UKCP Local ensemble members, and the corresponding projected accumulated maximum flood volume and volumetric moisture content over the study area.Average status is shown in the line plot, with the shaded region indicating the variability from 12 different ensemble members.Impacts of drainage rate on flood generation are illustrated with two different lines, showing the correlations between the drainage system and the generated flood volume.The average trend of these ensemble members was evaluated through a Theil-Sen robust regression method, while the statistical significance was tested using the Mann-Kendall statistics for monotonic trends (Panda & Sahu, 2019).Projections for the study area indicate virtually certain (∼100% confidence) increase of total annual precipitation and flood magnitude, with the Sen's slope of 1.07 × 10 6 m 3 /year (annual total rainfall volume).Compared with the past epoch, Bristol is projected to have roughly a quarter greater annual average rainfall volume and a 50% increase in flood volume in the future epoch, while only a slight increase (4.4%) of soil moisture is shown in Figure 6.This suggests that the rise in dry days and longer dry spells under global warming has the potential to alter overall soil wetness, despite intense rainfall temporarily wetting the soil.The non-linear relationship between rainfall and flood volume, in which a 25.9% increase in rainfall volume ((future average rainfall volume past average rainfall volume)/past average rainfall volume) causes a 52.6% rise in flood volume, highlights the severity of flood hazards in the coming decades.
The complex transfer function between the precipitation and flood volume that exists is substantially influenced by the soil moisture dynamics and the drainage system.Overall, approximately two-thirds of the rainfall volume undergoes direct transfer to infiltration loss and drainage loss, of which three quarters of the loss is caused by infiltration and nearly one quarter is lost directly to the drainage system.This substantial rainfall loss is primarily attributed to numerous less severe rainfall events that were easily absorbed by the soil moisture store or drainage system.In contrast, extreme rainfall events result in a larger proportion of rainfall transforming into surface runoff after surpassing the infiltration capacity and conveyance capacity of the sewer system.The flood volume curves under two different drainage rates (10 and 31 mm/hr) show a similar trend, with a ∼20% greater reduction of the flood volume using a large drainage rate.For the minimum rainfall intensity every year from 12 UKCP Local ensemble members, quite a large proportion of rainfall events have a peak rainfall intensity less than 10 mm/hr.As a result, lower bounds of the spread are shared by these two scenarios, while a distinctive increase in the upper bounds of the spread is achieved with a smaller drainage rate.
There is an obvious distinction between the rainfall and flood volume compared with the smaller difference in flood volume caused by the two different drainage conditions (10 and 31 mm/hr), which underlines the principal role of flow infiltration process.For an urban catchment with a large proportion of built-up areas, the annual total infiltration volume is greater than the total drainage volume (even with a drainage rate of 31 mm/hr).It is worthy to note that the conclusion stems from the analysis of annual total flood statistics across a wide area.The significant infiltration volume can primarily be attributed to the rural areas and these less intense rainfall events.Additionally, the spatial distribution of rainfall where the southwest rural regions are much more wet are also responsible for the large infiltration over time.
The substantial difference between the rainfall and the flood volume in Figure 6 suggests it is unfeasible to simply look at the change in rainfall to express urban flood hazards.As the flood-generating process changes, it is more important than ever to incorporate moisture dynamics into urban flood modeling as even here some of the increase in flood risk is modulated by antecedent moisture status.Therefore, an approach which incorporates both the soil wetness and precipitation pattern in urban flood modeling is required.

Impact of Antecedent Moisture Status on Flood Hazard
Figure 7a displays the impact of the initial moisture and rainfall volume on flood generation during each rainfall event, with circle size proportional to flood volume across three epochs.In the case of events with low rainfall volumes (<3.0 × 10 7 m 3 ), we observed a pronounced impact of soil moisture on regulating flood generation.Specifically, when the soil moisture is initially dry, a significant portion of the rainfall can infiltrate into the soil.On the contrary, flood generation is more likely when soil moisture is initially saturated.This relationship diminishes with increased rainfall volume due to limited soil porosity, leading to easier soil saturation and direct surface runoff for the remaining rainfall.Figure 7b shows the monthly distribution of the soil moisture availability, and the size of these circles also demonstrates the flood volume magnitude.A clear connection between the flood volume and extreme precipitation changes with seasonal soil wetness is shown, pointing to a larger increase for the regions and seasons with higher moisture availability.Limited antecedent moisture in dry environments may offset precipitation increases, while in water-abundant seasons amplified moisture convergence can intensify the effects of extreme precipitation.This suggests that attention should be paid not only to how much water the atmosphere can hold, but on how much soil moisture is available.The seasonal distribution of the soil moisture from Figure 7b confirms that in the future drier summers would become even drier (Kendon, Prein, et al., 2021;Kendon, McCarthy, et al., 2021;Kendon et al., 2023).However, the limited modulating impact of soil wetness cannot shift the intensification of the flood volume due to the overall increasing rainfall intensity and frequency in the future.Therefore, we can still observe several large magnitude floods (denoted by blue circles in Figure 7b) in future summer periods.
To determine the primary driver of the flood hazard, a Pearson relationship analysis has been conducted in which relevant interactions between the maximum flood volume and the total rainfall volume, soil wetness, peak rainfall intensity over the domain, and event duration are analyzed.As shown in Table 2, the rainfall volume is always the primary driver of the flood volume, with a relationship coefficient of up to 0.85 when accounting for all rainfall events.A coefficient of 0.33 is observed for the antecedent moisture status.When excluding the top 10% largest rainfall events, the coefficient for soil wetness rises to 0.38, while the relationship with rainfall volume is still 0.73.These results emphasize the secondary (but non-negligible) impact of antecedent moisture status on flood hazard.The more severe the rainfall event, the less of a modulating effect antecedent soil moisture has on the resultant flood volume.
Influence of peak rainfall intensity, event duration and antecedent moisture status on flood generation shows seasonality in Table 2. From June to September, a correlation coefficient of 0.17 is discerned for antecedent moisture status, while both peak rainfall intensity and event duration equally influence flood volume, each having a correlation of 0.37.Notably, in this period, peak rainfall intensity exhibits the strongest correlation with flood volume amongst the different seasons, while event duration shows the weakest correlation.The effect of peak rainfall intensity outweighs soil wetness as short and intense rainfall events are prominent in this summer period for Bristol.Dry soils have a limited modulating effect on flood generation as the rainfall rate easily exceeds the infiltration capacity.From October to January, the event duration dominates the flood generation compared to antecedent moisture and intensity.Rainfall in mild and wetter seasons has a more homogeneous distribution and therefore the event duration is to some extent related with the rainfall volume.Abundant moisture availability also exerts limited influence on flood generation due to fewer fluctuations in soil moisture deficit.The soil wetness plays a key role in modulating flood generation from February to May, while the correlation between peak rainfall intensity and flood volume diminishes.During this period, the event duration carries a similar weight to moisture conditions in influencing flood generation.These seasonal variations highlight the nuanced interplay of meteorological and soil factors in shaping flood dynamics throughout the year.

Monthly Distribution of Rainfall Volume, Soil Wetness, and Flood Volume
Monthly average rainfall volume, soil wetness and flood volume in the three epochs are shown in Figure 8 separately, with the boxplot showing the statistical distribution of these 12 ensemble members in each month.Figure 8 indicates again that summers in Bristol would become drier and hotter under global warming, while more floods are expected in the wetter winters in future.Median rainfall volumes are lowest in August and peak in December in the future.Compared with past epoch, a 39.2% increase in the rainfall volume from October to March in the future makes the soil wetter, which in turn causes a 58.3% increase in flood volume.Conversely, a 21.6% decrease in the summer rainfall leads to a significant reduction (50.9%) in soil moisture availability from June to August.Our results suggest a situation in Bristol where smaller floods, which supply water during the Special attention should be drawn to the seasonal distribution of the soil moisture status.An obvious decreasing trend of soil wetness from May to September is illustrated in Figure 8, with a more than 50% reduction in overall wetness in the future compared with the past.The winter period witnesses an elevated overall soil wetness.Under the compound effect of the rainfall pattern and the antecedent moisture status, the seasonal pattern of flood volume suggests changes in summer and winter are anticipated to emerge and are expected to intensify in the future.Specially, the contrast between a steep reduction in rainfall volume during the dry summer and a dramatic rise in rainfall amount in the winter highlights the intensification of the forthcoming dry summer periods and winter flood hazards.

Pattern of Extreme Flood Hazard
The intensification of hazardous rainfall events under global warming poses a significant challenge to the flood system of Bristol. Figure 9 shows the seasonal distribution of extreme rainfall events and the corresponding flood hazards in the past and future epochs.Days of occurrence of these rainfall/flood activities are represented using degrees in these two circular plots, with the radius of these circular plots showing the magnitude of the rainfall/ flood.Points within the red circles are sampled at a twentieth of their total number, but all data outside the circles are retained.Shadows in the plots indicate the relative number of extreme rainfall and flooding events with a volume magnitude exceeding 5 × 10 6 m 3 .The days of occurrence for these events are categorized into three groups: the first 10 days, the middle 10 days, and the last 10 days, and are counted separately for each month.In the past epoch, a total of 1,410 flood events were extracted from all 12 ensemble members, whereas in the future scenario, 2,207 events were identified (Figure 9b).Correspondingly, the number of selected rainfall events in these periods was 5,187 and 6,001, respectively, shown in Figure 9a.This observation suggests that a significantly greater number of rare rainfall events have the potential to evolve into severe flooding episodes in the coming decades.
Figure 9 illustrates the pronounced intensification, both in terms of frequency and intensity, of extreme rainfall events and corresponding rare flood hazards.Notably, concentrated rare flood hazards experience severe intensification in November and December under climate change.Anticipated changes in summer weather patterns reveal an even drier future, with a ∼47.1% decrease in the number of extreme rainfall events from June to September.It is worthy to note whilst analysis of UKCP Local (Kendon et al., 2023) shows a significant increase in the number and intensity of hourly precipitation extremes under global warming, overall summers are projected to become drier.This discrepancy is attributed to the fact that, in summer, rainfall is less frequent, albeit heavier when it occurs.The corresponding number of flood event, however, decreases by ∼23.3%.This may be attributed to the intensification of rainfall events in a warmer world, leading to more frequent infiltration-excess runoff (where rainfall intensity exceeds the infiltration capacity) rather than saturation-excess runoff (when the soil becomes saturated and there is no longer any space for water to infiltrate).The difference between the distribution of rainfall events and floodings highlights the critical role of flood modeling, and inferring the flood hazard status solely from the rainfall pattern may lead to false alarms.
A late seasonal occurrence of the rare flood hazards (with a volume magnitude larger than 5 × 10 6 m 3 ) is found under global warming, in which the majority of historical extreme floods occurred in the November (18.1%, orange shadow in Figure 9b), whereas the majority of future high flood hazards occur in the December (21.1%, light blue shadow).Meanwhile, the magnitude of individual flood events is expected to increase dramatically, as The past events are colored using yellow outlines, while the blue points show the events in the future.Light blue shadow outlines the intensification of future extreme rainfall/flood hazards (whose magnitude is large than 5 × 10 6 m 3 ) using the number of flood events every month, as well as the shift to a delayed occurrence of rare flooding activities in a warmer world, compared with past flood events represented with orange shadow.A total of 5,187 rare rainfall events in the 12 past ensemble members is extracted, with 6,001 rainfall events from the future epoch.The number of floodings in the past and future epochs are 1,410 and 2,207 respectively.
Earth's Future global warming shifts future flood hazard outside the envelope of historical variability.Bristol will be more vulnerable to flood hazards in the future.

Discussion
A novel surface water flood modeling framework which simultaneously integrates soil moisture dynamics and precipitation pattern is proposed to explore the impacts of the climate change on the future flood risk at an urban scale.Based on a peaks-over-threshold algorithm, a total of 30,098 rainfall events from an equivalent 720 years of climate data are identified and used for flood modeling with an assumption that the compound effect from concentrated rainfall events can be represented in the form of antecedent moisture status.The utilization of a hydrodynamic flood modeling approach with a resolution of ∼30 m over extended time periods presents a notable challenge when attempting to implement this framework on a national scale.Nonetheless, the proposed framework is well-suited for direct application in other regions to facilitate local-scale flood hazard assessments.While the conclusions about future flood scenarios are drawn from observations within Bristol area, it is reasonable to anticipate the generalizability of these findings to other regions.This expectation is rooted in the evolving precipitation trends across the UK, which contribute to the broader applicability of these conclusions (Cotterill et al., 2021;Kendon, McCarthy, et al., 2021;Kendon et al., 2023).

Uncertainty in the Proposed Future Flood Hazard Assessment Framework
Uncertainty in UKCP Local precipitation projections under a high emission pathway derives from discrepancies in the climate change patterns predicted by different global model ensemble members, generated by perturbing uncertain parameters in the model physics.Projected changes and associated uncertainties in precipitation represents the possible uncertainty in the future climate system, and they are conditional on the knowledge, data, methods and subjective choices used to construct them (Fung et al., 2018).While the combined evidence of UKCP Local covers a range of potential future climate pathways for the UK, it does not comprehensively sample all uncertainties and it remains possible that observed future changes could lie outside the envelope of these (Fung et al., 2018;Kendon, Prein, et al., 2021;Kendon, McCarthy, et al., 2021).
In addition to the uncertainty in precipitation, the proposed future flood hazard assessment is impacted by additional sources of uncertainty associated with many components and data sets employed in the modeling chain to predict flood hazard.Uncertainty in the soil moisture dynamics either in the water balance model or the infiltration process is prominent, as well as in the soil texture classification data sets.Though the water balance model is validated at a point scale by comparison with an in-site COSMOS-UK data set, there is less confidence that the actual soil wetness can be well-represented by the estimated soil moisture considering the large coverage of the study area.Controlled by the soil texture classification, the infiltration rates and the recovery of infiltration capacity are estimated empirically, as well as the maximum water storage in the upper soils.A wide range of these parameters is available, and parameter selection can to some extent impact the final water depth results.The compound impact of uncertainties from the modeling chain may alter the future flood projections to varying degrees.However, the majority of those procedures have been evaluated against observable or higher resolution data (Rossman & Huber, 2016;Tügel et al., 2021).Therefore, though the water depth distribution may be altered slightly with different parameters, the conclusions regarding the future flood risk trend are likely to hold with the recommended parameters in the future flood risk assessment framework.
Simplified treatments of the drainage system in urban area are also associated with uncertainties.The spatially uniform drainage loss rate estimated from rainfall events frequency analysis is applied to directly reduce the rainfall intensity.Without the response of the sewer networks, the rainfall accumulation and conveyance using the drainage system is not dynamically updated and therefore could cause the flood risk to be over-or underestimated.Despite these limitations, this assumption is commonly accepted by the scientific community and adopted in a number of recent works (Sayers et al., 2020;Smith et al., 2015;Xing et al., 2022).Also, it is currently not possible to collect data on the sewer networks at such a large scale and this is a typical situation in urban inundation modeling.Hence, adoption of more complex representations of these drainage systems to enable a sewer hydraulics calculation is impracticable.

Compound Impacts of Successive Rainfall Events
The interactions of multiple rainfall events and their compound impacts on flood generation is a complex issue that should be treated seriously.Assuming that the impact of the previous rainfall event can be transferred into the distributed soil moisture and evolves with time, the present study aims to assess the flood risk caused by each individual rainfall event.Therefore, with the water balance model continuously tracking the soil moisture dynamics over 20 years, we expect that the soil water content can to some extent reflect the spatial and temporal patterns of precipitation.However, one constraint with this assumption is that the remaining water depth from a previous extreme rainfall event cannot be transferred to the next storm, and only a saturated soil state is kept for the following events.Flood generation processes can be altered with the initial water depth distribution over the domain compared with saturated moisture status, especially when the river conveyance capacity is overwhelmed by previous rainfall event.Considering that rainfall events are separated by a continuous 6 hr of rainfall intensity less than 1 mm/hr, in most cases the accumulated rainfall depth can be released by the drainage system and the river channel within this time period given the size of the model domain.Therefore, each individual rainfall event is used for the flood risk assessment, and implications of previous rainfall events are indirectly applied in the form of antecedent moisture status.

Compound Impacts From Fluvial and Pluvial Flooding and Sea Level Rise
One limitation of this research is that it solely considers the city response to direct surface flooding, leaving out downstream tidal flooding.The tidal water body from the Severn Estuary has the second highest tidal range in the world, and historical experience indicates that tidal flood risk from the River Avon represents the most significant flood risk facing the city center (Bristol City Council, 2023), and these rivers have historically been known to cause significant flooding to the surrounding communities.None of these flood-producing mechanisms are changing in isolation, and the manner in which they combine is also changing (Zscheischler et al., 2018), especially under the climate change impact.Ignoring these compound impacts on the flood generation systems will inevitably modulate the flood hazard.It is worth noting that, in most UKCP Local projections under RCP8.5, Bristol central area is exposed to severe flood hazards with large consequences in terms of economical loss, assuming the present-day population and development levels.Compound impacts from the fluvial flood, storm surge and tidal may further aggravate the flood hazard status in these areas, and a flood hazard assessment framework which includes all these drivers will be investigated in subsequent work.

Conclusions
A total of 30,098 rainfall events with a peak rainfall intensity exceeding 6 mm/hr were extracted from an equivalent 720 years of climate data contained within the 12-member UKCP Local 2.2 km resolution ensemble.Maximum water depth and corresponding flood volume were derived for each individual rainfall event using a new hydrodynamic model that accounts for antecedent soil moisture and its evolution over the event.The results are then aggregated over different temporal and spatial scales to provide flood statistics for the past, present and future climate.Using this scheme, we were able to analyze in detail the impact of the antecedent moisture status on flood generation and the response of the flood system to the evolution of the future precipitation under global warming.Whilst the framework was applied to a single city region in the UK, the findings are likely to be generally true elsewhere even if the precise expression may be somewhat different.The significance of this framework rests in its comprehensive evaluation of both soil moisture dynamics and precipitation patterns in shaping future flood modeling outcomes.Moreover, its adaptability for application in diverse locations underscores its utility for conducting localized flood hazard assessments at local scale.

Impacts of Antecedent Moisture Status on the Flood Generation
From the results presented it is evident that rainfall volume is the primary driver of flood generation, while the soil moisture dynamics can modulate some of the increase in flood risk due to shift to drier soils in the future.The more severe the rainfall event, the less of a modulating effect soil moisture has on the resultant flood volume.A Pearson relationship analysis indicated that the influence of soil wetness on flood generation shows obvious seasonality.From June to September when convective rainfall is prominent, intense rainfall rates can easily exceed the infiltration capacity, and flood generation starts without thoroughly saturated soils.As a result, a limited modulating impact of soil wetness on the flood volume exists.From October to January, greater Earth's Future 10.1029/2023EF004073 atmospheric moisture availability can cause large total rainfall accumulations with little infiltration loss into already saturated soils, and therefore soil wetness exerts a weaker constraint on flood generation.The remaining months have a relatively lower rainfall rates and greater moisture deficits, and rainfall typically only starts to accumulate on the surface after the soils get saturated, therefore there is a much greater impact of soil wetness on the flood-producing mechanism.
Though a secondary impact of antecedent moisture status on flood risk has been identified, the following moisture dynamics process should be treated seriously.In our model approximately half of the rainfall volume from our events is transferred into the soil via infiltration losses, depending on the soil texture and precipitation pattern.Therefore, a reasonable approximation of the soil texture over the study area and a well-presented infiltration loss calculation should be incorporated to enable a more realistic flood inundation simulation.Ignorance of the infiltration system would seriously affect the credibility of the results.

Nonlinear Relationships Between the Increase of Rainfall and Abrupt Growth of Flood Volume
Our analysis indicates that rising temperatures lead to an intensification of the hydrological cycle, which in turn causes more intense rainfall accumulation in the study area.One quarter more rainfall volume is anticipated every year in the future based on all identified rainfall events.Larger or more frequent heavy precipitation events would be expected to increase the overall magnitude and/or frequency of flood events, and the resultant flood volume is expected to increase up to 52.6%.The nonlinear relationship between the growth of rainfall and flood volume in which a mild increase in annual total rainfall volume (25.9%) causes a sharp rise in flood volume highlights the severity of flood hazards in the coming decades.Changes in rainfall characteristics such as intensity, spatial extent and temporal clustering, with the heaviest events being primarily responsible for flooding and increasing at a faster rate, are important and may amplify the increase in flood volume compared to rainfall volume.Compared with the standard uplift approach that assumes a direct relationship between rainfall and flood volumes without considering the complexities associated with changing rainfall characteristics and catchment responses, the framework proposed here can account for the complex interactions between rainfall, runoff, infiltration, and river routing to provide more accurate predictions of flood volumes.Neglecting these factors can result in inaccurate predictions and may not adequately represent the real-world flood dynamics, particularly in the context of climate change where changes in rainfall patterns, intensities, and clustering are significantly altered.As a result, a statistically significant increase in flood hazard was found due to the combination of the future flood situations and information on infrastructures exposure.

A Shift to a Later Seasonal Occurrence of Rare Flood Activities Under Global Warming
The circular plot of Figure 9 clearly reveals a later seasonal occurrence of extreme precipitation for the coming decades.It is evident that global warming has a controlling influence, not only on the frequency and intensity of rainfall events, but on the seasonality of flooding.The results clearly reveal a strong footprint of climate change on extreme precipitation in different seasons over the Bristol area, and this is likely to hold true for many other UK cities too.In other words, summer and earlier autumn extreme precipitation is sharply reduced in terms of total volume under global warming, and instead an abrupt increase in the frequency and intensity of extreme precipitation from November to December exists, resulting in shifts in the timing of extreme flooding.Whilst there is a significant increase in the number and intensity of hourly precipitation extremes under global warming, overall summers are projected to become drier due to a decrease in the frequency of rainfall in this season.From the perspective of rainfall/flood volume, winter will experience more extreme floods in the future.

Figure 1 .
Figure 1.Main river channels and urbanized areas in Bristol and its surrounding region.The entire area is included in the proposed grid-based surface water flood modeling framework, to evaluate the pluvial flooding hazard status under climate change.

Figure 2 .
Figure 2. Framework for assessing UK future flood hazard under climate change.Four components (water balance model, precipitation generation, drainage loss rate estimation, and infiltration process) are linked together with the hydrodynamic model LISFLOOD-FP, to estimate the future flood hazard status under global warming.

Figure 3 .
Figure 3. (a) Monthly average rainfall depth across the 12 UKCP Local ensemble members, and (b) annual average total rainfall depth for 12 ensemble members under RCP8.5.The line plots show the monthly average rainfall depth from the rainfall events identified with two different thresholds (2 and 4 mm/hr), and the bar plot in (a) are based on rainfall events extracted with a threshold of 6 mm/hr.

Figure 4 .
Figure 4. Approach to assessing the future flood hazard using UKCP Local precipitation data.These processes detail the procedures used to link all components with the flood modeling and describe the workflows of the future flood risk assessment framework.

Figure 5 .
Figure 5. Flood occurrence map where frequency of maximum water depth higher than 0.1 m per year is depicted.Panels (a) and (b) are extreme estimates of the future hazards (Ens02) where annual accumulated rainfall depth doubled to ∼800 mm over 20 years, while (c) and (d) are median estimates of the future hazard (median over all 12 future ensemble members) in which the total rainfall depth only amounts to ∼75% of the extreme estimates.Panels (a) and (c) are calculated with both the infiltration process and the activated drainage system (assumed 10 mm/hr), while no rainfall loss is considered in both (b) and (d).

Figure 6 .
Figure 6.Multi-model ensemble projections depict annual average rainfall volume alongside corresponding accumulated flood volume and volumetric moisture content at three epochs: the past (1980-2000), present (2020-2040), and future (2060-2080).The shaded region represents the spread across all 12 UKCP Local ensemble members, with the central lines denoting the average status.Statistical information on each panel includes Sen's slope (b) and the p-value indicating the significance of the Mann-Kendall test for trend.For each rainfall event, flood volume, and soil moisture are computed as the summation of the maximum water depth and volumetric soil moisture, respectively, across all grid cells during the event.

Figure 7 .
Figure 7. Impact of the antecedent moisture on flood volume and the seasonal distribution of soil wetness based on a random sampling procedure from all 30,098 rainfall events with a sample size of 20%.Average initial moisture varies from 0% to 100%, with 100% indicating that the maximum water storage in the upper layer of soil has been achieved.Circles with different colors show the rainfall events in three different epochs, and the size of the circles represents the flood magnitude.

Figure 8 .
Figure8.Seasonality of flood drivers included in analysis are the rainfall volume, antecedent moisture status and flood volume.Boxplots per month from the three epochs(1980-2000, 2020-2040, and 2060-2080)  of monthly total (a) rainfall volume, (b) soil moisture, and (c) flood volume.The lines insides the boxes represent the median value, and the box edges correspond to the 25th and 75th percentiles while the whiskers correspond to the 5th and 95th percentiles of the data and outliers outside the boxes are also shown.

Figure 9 .
Figure9.Seasonality of a sample of extreme large rainfall events and corresponding flooding hazards in 12 UK Climate Projections Local scenarios.Degrees in the circular plots presents the day of the occurrence of the rainfall/flood, with the radius (R) indicating the magnitudes of rainfall/flood volume.Points within the red circles are sampled at a twentieth of the scale and all data outside the circles are retained.The past events are colored using yellow outlines, while the blue points show the events in the future.Light blue shadow outlines the intensification of future extreme rainfall/flood hazards (whose magnitude is large than 5 × 10 6 m 3 ) using the number of flood events every month, as well as the shift to a delayed occurrence of rare flooding activities in a warmer world, compared with past flood events represented with orange shadow.A total of 5,187 rare rainfall events in the 12 past ensemble members is extracted, with 6,001 rainfall events from the future epoch.The number of floodings in the past and future epochs are 1,410 and 2,207 respectively.

Table 1
Parameters Used in the Water Balance Model

Table 2
Relevance of Rainfall Characteristics With Flood Volume in Pearson Relationship Analysis RONG ET AL. drier summer, are declining but larger floods, which endanger lives and damage infrastructure, are growing in winter.