Disentangling the Sources of Uncertainties in the Projection of Flood Risk Across the Central United States (Iowa)

We explore the projected changes in flood impacts across Iowa (central United States) and the associated uncertainties by forcing a hydrologic model with downscaled global climate model outputs and four Shared Socioeconomic Pathways. Our results point to projected increasing magnitude and variability in flooding across the state, especially for high‐emission scenarios. Next, we partition the flood impacts' projections into: (a) the response of the global climate models to anthropogenic forcing, (b) scenario uncertainty due to emissions, and (c) internal climate variability. We find scenario uncertainty plays a small role, while climate model uncertainty and internal climate variability dominate the flood impacts' projections, with the contribution of model uncertainty increasing toward the end of this century. Insights from our work can be utilized by stakeholders to understand the current limitations of flood impact projections and provide suggestions about where modelers should focus efforts to reduce uncertainty.

model uncertainty but flood projections are dominated by internal variability, then an improvement in climate models would only lead to a minor reduction in the total uncertainty for flood projections.Therefore, developing this information can provide basic information toward focusing future modeling efforts.
Iowa is of particular interest when trying to understand flood projections and uncertainty as the state has been prone to large flood damages in recent decades (e.g., J. A. Smith et al., 2013;Tate et al., 2016;Villarini et al., 2020).Analysis of observed flood peaks across Iowa by Mallakpour and Villarini (2015) indicates increasing trends in the frequency of events, while trends in magnitude are not detected as strongly.Projections of flood peaks in Iowa based on the previous Coupled Model Intercomparison Project (CMIP5) found increasing trends in magnitudes for eastern Iowa by the end of the century (Michalek, Quintero, et al., 2023).Furthermore, midcentury projections (2050) for Iowa have been completed with inputs from the CMIP6 High Resolution Intercomparison Project, not showing significant changes in magnitude but significant changes in the interannual variability (Michalek, Villarini et al., 2023).However, neither of these studies have examined the uncertainty in the projections and related flood impacts.
Here we address these knowledge gaps by quantifying the projected trends, changes in mean, and changes in variance of annual flood peaks for river communities across the State of Iowa (central United States).Flood peaks projections are generated by forcing the Iowa Flood Centers' (IFC) Hillslope Link Model (HLM) with statistically downscaled climate models outputs from the CMIP6 suite.Additionally, we quantify the contribution of different sources of uncertainty in flood projections with the methodology developed by Hawkins and Sutton (2009).Finally, we translate flood peaks to flood-relevant impacts such as the number of affected buildings, content damage, and structural damage based on provided inundation maps developed by the IFC.Our objective is to provide information to guide future flood modeling efforts, highlight uncertainties that stakeholders should be aware of when utilizing flood projections (e.g., infrastructure design, risk assessment, water resource management), and provide recommendations for the modeling community toward uncertainty reduction.

Study Site
We focus on the State of Iowa and all basins draining into the Missouri and Mississippi Rivers.Specifically, we focus on 1,000 communities as well as 10 cities with flood risk information (Figure S1 in Supporting Information S1).The study area is agriculturally dominated with low relief and can be divided into seven distinct landforms.The landscape has a high drainage density in the Southern Iowa Drift Plains, Loess Hills, Iowan Surface, Northwest Iowa Plains, and Paleozoic Plateau, each of which consist of a loess cover (Prior, 1991).The Des Moines Lobe has the poorest surface drainage.Iowa has a seasonally variable climate, with the largest amounts of rainfall occurring in summer and snow in winter.

Hydrologic Modeling
For hydrologic modeling, we utilize the TETIS version of the HLM (e.g., Mantilla et al., 2022;Quintero & Velasquez, 2022).It is a fully distributed hydrologic model that decomposes the landscape into hillslopes and channels.Runoff generation at the hillslope occurs through the simulation of multiple physically based processes.Total hillslope runoff is aggregated in the river channel from the contribution of overland flow, interflow, and base flow.A nonlinear hydrologic routing model transports flow in the channels and considers the scaling of the geomorphologic characteristics of the river network.A full model description can be found in Quintero and Velasquez (2022).The HLM requires inputs of precipitation, temperature, and evapotranspiration, and is set up to provide streamflow simulations for every channel in the state.We use 18 global climate models (GCMs, Table S1 in Supporting Information S1) from the Coupled Model Intercomparison Project 6 (CMIP6, Eyring et al., 2016) with four shared socioeconomic pathways (SSPs).We select climate models that have precipitation, temperature, and evapotranspiration for the historical, SSP126, SSP245, SSP370, and SSP585 scenarios (Figure 1, step 1).We utilize daily precipitation and temperature, with monthly evapotranspiration.Temperature and evapotranspiration are taken as the spatial average across Iowa for a given day and month, respectively.We use these variables in the described way as the memory and computational time requirements to incorporate these as spatially variable in the HLM is too large to make the simulations feasible.
Precipitation is the most spatially variable parameter for strong model performance.For this reason, we apply equal quantile mapping (eqm) bias-correction and statistical downscaling to create climate model precipitation at a 4-km spatial grid (see Michalek, Villarini, et al. (2023)), more suitable for hydrologic modeling at the community level (Quintero et al., 2022).The reference precipitation data set we utilize to perform the eqm is the Parameter-elevation Regression on Independent Slopes Model (PRISM) precipitation (Daly et al., 2002) from 1981 to 2014.We also bias-correct the temperature and evapotranspiration, with temperature and evapotranspiration derived from the PRISM data set (Figure 1, step 2).The hydrologic simulations are conducted from 1981 to 2100 (Figure 1, steps 3 and 4) across Iowa for all climate models and scenarios (i.e., 720 simulation sets in total).The model set up was the same one utilized and validated with respect to observations as seen in Michalek, Villarini, et al. (2023).We validate how well the model performs by comparing annual maximum discharges from 1981 to 2014 from a reference PRISM-derived simulation (Michalek, Villarini, et al., 2023) with HLM simulations forced with outputs from each climate model using the Kolmogorov-Smirnov (KS) test (Massey, 1951) at the 1,000 river communities in Iowa.Flood projections for each climate model are only kept if they are not statistically different for at least 90% of the communities based on the KS test.Once this is completed, we perform step 5 in Figure 1 to determine which analysis is to be performed based on whether flood hazard data are available for a community.

Flood Impact Data
For the 10 cities previously mentioned (Figure 1, step 5), we gather the publicly available flood impact data (Figure 1, step 7a) consisting of inundation, affected buildings, content damage, and structural damage from the Iowa Flood Information System (IFIS; Krajewski et al., 2017).For these communities, IFIS provides flood impact data based on a discrete number of discharge values.With the provided flood impact data for each location of interest, we fit logistic curves (Figure 1, step 7b) between each flood impact variable (i.e., affected buildings, content damage, structural damage) and discharge to develop estimates for all hydrologic simulations.We utilize a logistic curve as it best fits the relationship for flood impacts for all sites.The logistic curves for the 10 communities of interest are provided in Figures S2-S11 in Supporting Information S1.For this analysis, we did not account for future changes in the number of buildings and the cost of their contents due to a lack of available information for Iowa.With the logistic curves completed, we generate hazard projections (Figure 1, step 7c) based on the hydrologic model outputs (Figure 1, step 5).

Historical and Future Discharge Comparison
For the communities without hazard information (Figure 1, step 5), we perform a trend analysis by applying the non-parametric Mann-Kendall trend test (Kendall, 1975) for annual maximum discharges from 2015 to 2100 at each community to determine if there is a statistically significant increasing or decreasing monotonic trend (Figure 1, step 6a).The test is conducted per emission scenario (SSP) as well as for each climate model.For the two statistical tests described above, we apply the generalized false discovery rate approach to control for type I errors in our multiple hypothesis testing (Benjamini & Yekutieli, 2001;Ventura et al., 2004).All statistical tests are conducted at a 5% significance level.
For our primary analysis, we compare projected changes in variance and mean utilizing the ratios for three future periods (Figure 1, step 6a).The historical period ranges from 1987 to 2014, with the three future periods of 2016-2043, 2044-2071, and 2072-2099.We define the ratio of the variance (VR) as: where   2 Historical and   2 Future are the historical and future variances for 28 years of annual maximum discharge simulations for a given river community, climate model, and emission scenario.Next, we define the ratio of the means (MR) as: where μ Historical and μ Future are the historical and future means for 28 years of annual maximum discharge simulations for a given river community, climate model, and emission scenario.A value greater (less) than 1 indicates an increase (decrease) in the future mean/variance compared to the historical simulations.

Uncertainty Partitioning
For the uncertainty partitioning of the flood impacts, we applied the methodology described in Hawkins and Sutton (2009) to separate the contribution from the different sources of uncertainties: model uncertainty, scenario uncertainty, and internal variability.Model uncertainty defines the uncertainty based on the climate models' response to radiative forcings.Scenario uncertainty is the uncertainty that originates among emission scenarios (i.e., SSP).Finally, internal variability is the natural variability of the climate system.We utilized a modified version of the methodology by Hawkins and Sutton (2009) as follows: 1. We applied a 10-year (decadal) moving average window on the input predictions (e.g., discharge or hazards projections).2. The smoothed predictions (1) are transformed into anomalies by subtracting the mean from 1985 to 2014 for a given climate model and SSP. 3.Each individual prediction from (2) was fitted with a loess function from 1985 to 2095, which is different from the fourth-order polynomial proposed in Hawkins and Sutton (2009).4. The models are assumed to be independent and equal weights are calculated (Hawkins & Sutton, 2011). 5. Internal variability is determined by taking the variance of the residuals from (2) for each climate model and summing up the variances multiplied by the weights in (4).6. Model uncertainty is calculated by taking the variance of values from (4) for a given year and averaging across SSPs.7. Finally, scenario uncertainty is calculated as the variance of the weighted average of the values (4) per year across climate models.8. Steps 1-7 are repeated for each community of interest.
This methodology is applied first to flood peak projections across the 1,000 communities in Iowa (Figure 1, step 6a) and for the flood hazards (discharge, affected buildings, content damage, and structural damage) for the 10 cities (Figure 1, step 7d).

Changes in Annual Maximum Flood Peaks
There is a tendency toward increasing trends in projected annual maximum flood peaks across 1,000 river communities in Iowa (i.e., 2015-2100; Figure S12 in Supporting Information S1) under the higher emission scenarios of SSP370 (568 sites) and SSP585 (955 sites) at the 5% level.For the lower emission scenarios (SSP126 and SSP245), none of the communities show a statistically significant increasing trend at the 10% or 5% level.Furthermore, there are no communities with a statistically significant decreasing trend.The detection of trends during the 21st century, when present, could be driven by increases in the magnitude of flood peaks and/or decreases in the interannual variability (i.e., noise).For the trend results in Figure S12 in Supporting Information S1, we reduce the inter-model variability and noise by focusing on the median of the annual maximum daily discharge from the 18 GCMs; however, a trend signal was much harder to detect when we computed it based on each model separately.This is more apparent when we compare the change in variance to the change in mean between historical and future simulations for flood peaks stratified by climate model as shown in Figure 2.For all scenarios and periods, our results indicate the variance and mean are expected to increase, on average, for nearly all climate models.Furthermore, the results in Figure 2 highlight that climate models producing larger increases in variance typically produce larger changes in the mean of flood peaks.This tendency becomes more apparent as we move toward the end of the 21st century.Moreover, there is a dependence on the strength of these changes on scenarios.For SSP126, the average ratio of change in variance and mean follows a linear pattern and tends to stay constant across all three periods (Figure 2, top row), with the variance ratio that ranges from 1 to 3.75, while the mean ratio ranges from 1 to 1.6.For the other three SSPs, the pattern between variance and mean ratios changes over time.Under SSP245 (Figure 1, 2nd row), the 2016-2043 and 2044-2071 periods show a similar pattern, with ratios of variances and means ranging from 1 to 3.75 and 1 to 1.5, respectively.However, for the 2072-2099 period, the largest variance ratios (above 3.75) do not align with the largest mean ratios (above 1.5).This relationship can also be seen under SSP370 and SSP585 for the same period (2072-2099), where some models have large variance ratios (above 5) that do not align with large mean ratios (above 1.75).Our results highlight disagreement in both the signal (mean) and noise (variance) of projected flood peaks across models and a dependence on scenarios and study period.
Based on the results in Figure 2, there is variability in the projected changes in annual maximum flood peaks depending on scenarios and models' response to the forcings.What sources of uncertainty dominate the projected changes in flooding across Iowa?To this end, we examine the partitioning of flood peak uncertainty as described in Section 2.5.The uncertainty in annual flood peaks for the 1,000 river communities across Iowa is dominated by internal variability at the beginning of the century (Figure 3, top row); by 2030, internal variability accounts for at least 50% of all uncertainty across the state, followed by model uncertainty (∼30%-40%).However, as we move toward the end of the century, model uncertainty becomes the dominant factor across communities in Iowa (Figure 3, bottom row).Furthermore, by the end of the study period, the scenario uncertainty for eastern Iowa increases to 10+% and becomes closer in fraction to the internal variability.These results are similar to those in Figure 2, as the change in mean and variance for the end of the century is much more dispersed among climate models.
An important point to take away from Figure 3 is the spatial heterogeneity of the uncertainty sources across the region.The examination of the internal variability and model uncertainty fractions in Figure 3 suggests that the flood projections for communities in the eastern and western portions of Iowa are dominated by internal variability compared to communities in the northern and southern regions, for which uncertainties are more evenly split between the internal variability and model uncertainty for the 2030 period.Spatial heterogeneity in uncertainty sources is accentuated as we move forward in the projection period.For the 2070 period, we can observe a split along a southwest to northeast line, where internal variability and model uncertainty control uncertainty.In the northwestern portion of the state, flood projections are expected to be dominated by internal variability as the main source of uncertainty, whereas for southeastern communities are dominated by model uncertainty (Figure 3).

Changes in Flood Impacts
Up to this point, we have focused on the flood hazard and quantified what the dominant sources of uncertainties are.However, what can we say about projected changes in impacts (i.e., structural and content damage, number 10.1029/2023GL105852 6 of 12 of affected buildings) and their dominant sources of uncertainty?These are important considerations if current information can be improved upon so that is the best available for stakeholders who can develop better plans to mitigate projected socioeconomic impacts of flooding.We subset our analyses of the 10 communities in Iowa that have flood impact data (Figure S1 in Supporting Information S1) to examine the projected changes in these Comparison of the ratio between future and historical variances and means of annual maximum daily discharge.Each point represents the average variance and mean ratio for 1,000 communities for a given climate model.The rows represent the emission scenarios, and the columns represent the future 28-year period of comparison with respect to the historical period .The black lines represent ratios of 1, where the future and historical mean and variances are the same, where a value larger (smaller) than 1 indicates the future variance or mean is greater (smaller) than the historical value.
quantities.Given the monotonic relationship between discharge and the flood hazard (e.g., buildings affected, content damage, structural damage), our analysis indicates that the projected changes follow a similar pattern to that of the annual flood peaks under the assumption that buildings and their content values remain similar to observed for rest of the century.
For a more detailed discussion of our flood impact uncertainty analysis, we present the results for all 10 communities in Figure 4, with the total uncertainty provided in Figure S13 in Supporting Information S1.For all 10 cities, the internal variability and model uncertainty are shown to be the dominant source of uncertainty across all four flood risk categories of interest.Early in the 21st century, content damage and structural damage show a small fraction of uncertainty due to scenario uncertainty.Furthermore, the flood hazards have a smaller amount  of uncertainty due to the scenario uncertainty from 2050 to 2099.However, the patterns in uncertainty differ from community to community (Figure 4).For some communities (e.g., Fort Dodge; Des Moines River), the fraction of variance among sources remains relatively constant throughout the middle of the century, whereas places such as Iowa City (Iowa River) have a continuous increase in the model uncertainty fraction.Interestingly, for Waverly (Cedar River), the scenario fraction from 2060 to 2090 increases from approximately 0 to 0.2 (Figure 4, bottom row).However, this is not reflected in the flood impacts, where the scenario uncertainty does not visibly change.A similar pattern occurs for Monticello (Maquoketa River), where the end-of-century scenario fraction of variance is approximately 0.1 for the flood peaks but 0.2 for the flood impacts.While there are differences in the fractions of variance between the 10 communities, our analysis indicates that uncertainty in flood peaks due to emission scenario can be muted through the translation to flood impacts.This limited strength is caused by the upper bound of flood impacts model by a logistic function which means they cannot grow indefinitely and the rate of increase in impacts slows down for the large discharge values.

Concluding Discussion
Overall, our examination of the projections in annual flood peaks reveals increasing monotonic trends under SSP370 and SSP585 across Iowa when utilizing an ensemble average.However, trends are not detected when examining simulations from individual climate models.The lack of trend detection is caused by the variability within the flood projections among climate models, emission scenario, and time period.For users of these models, our results point to the importance of utilizing multiple climate models when studying flood impacts as the signal and noise vary greatly among climate models.A comparison of the change in variances and means by climate models in future flood peaks indicates a positive dependence between these two quantities.For climate model simulations with large projected increases in variance, the projected increases in mean are also large.However, changes in interannual variability are much larger compared to the mean.These large variabilities could be influencing when the climate change signal in flooding can be detected in the projections.For this reason, we encourage researchers to explore this impact for floods based on the signal-to-noise and time of emergence analysis similar to Deng et al. (2022).Furthermore, it should be noted that our framework focuses on the daily annual maxima and may not be suitable for applications that require higher temporal resolution.
These statements about changes in noise and signal are supported by our partitioning of the uncertainty in flood peak projections.We show internal variability and model uncertainty dominate depending on the projection period.As we move toward the end of the century, model uncertainty tends to dominate for most of Iowa, which is also shown in the projected changes of the variance and mean.We speculate that, if simulations were extended through the next century, scenario uncertainty may become an important factor.Our results are similar to those of the projections of tropical storms (Villarini & Vecchi, 2012) and precipitation extremes (Blanusa et al., 2023), pointing to future needs of extreme event modeling.Additionally, we find that these uncertainties in flood magnitude cascade to flood impacts at the community level and accentuate the variability within projections.The switch from internal variability to model uncertainty as the dominant source of uncertainty highlights paths forward for improvement for both short-and long-term flood prediction and projections.For the short term where internal variability dominates, we recommend the modeling community to examine if the chaotic nature of the climate system is realistically captured by current models and translated appropriately to flood projections utilizing frameworks such as the one by Deser et al. (2020) that incorporate large ensemble experiments to better understand internal variability.Finally, to prepare our communities for future flood impacts at the end of the century, we need modeling efforts to focus on improving agreement among climate models' forcings important for hydrologic modeling (i.e., precipitation, temperature, evapotranspiration).
Regarding the limitations of this study, we did not incorporate the uncertainties due to bias correction and downscaling of climate model outputs.We implicitly corrected the bias in the forcings for each model individually assuming stationarity in the bias corrections.For precipitation, this was accomplished using a quantile mapping approach to improve the resolution for hydrologic application and is commonly utilized to improve climate models (e.g., Cannon et al., 2015;Gutjahr & Heinemann, 2013;Leander & Buishand, 2007;Piani et al., 2009).However, climate models tend to not capture the convective processes driving precipitation, and applications of dynamical downscaling methods should be explored to understand these potential limitations (Blanusa et al., 2023).Furthermore, as we only examined results from a single hydrologic model (i.e., HLM), we were not able to quantify the uncertainty due hydrologic model selection and suggest future works examine its role in flood projections.

Figure 1 .
Figure 1.Workflow of the analyses performed in the study.Rectangular boxes represent statistical analysis or modeling performed.Parallelogram boxes represent outputs from models.The arrows indicate the direction of data flow.The steps are provided and referenced throughout Section 2.

Figure 2 .
Figure 2.Comparison of the ratio between future and historical variances and means of annual maximum daily discharge.Each point represents the average variance and mean ratio for 1,000 communities for a given climate model.The rows represent the emission scenarios, and the columns represent the future 28-year period of comparison with respect to the historical period.The black lines represent ratios of 1, where the future and historical mean and variances are the same, where a value larger (smaller) than 1 indicates the future variance or mean is greater (smaller) than the historical value.

Figure 3 .
Figure 3. Fraction of variance for decadal projections based on uncertainty partitioning for the 1,000 Iowa river communities across time period (rows) and uncertainty type (columns).The summation of a location across each row sums to 1.

Figure 4 .
Figure 4. Fractional contribution to uncertainties in CMIP6 projections of modeled flood risks for 10 cities in Iowa with flood inundation data.Each row represents the respective flood risk derived for projected annual flood peak.