Attribution of the impacts of the 2008 flooding in Cedar Rapids (Iowa) to anthropogenic forcing

The City of Cedar Rapids was significantly affected by the June 2008 flood. However, little is known about the role anthropogenic warming during this event, not only in terms of hydrologic response but also of impacts. Here we use a continuous distributed hydrologic model forced with precipitation with and without external forcing and show that the impacts of this flood were likely magnified because of increased anthropogenic warming; compared to the baseline scenario with the external forcing removed, this event was ∼1.28-fold larger in flood extent, an approximate 3.4-time larger in the number of affected buildings, and an estimated 5.8- and 7.1-time larger in structural and content damage, respectively. While much of the effort up to this point has focused on the attribution of the physical hazard, our results highlight the cascading increase of the contribution of the external forcing (mainly from anthropogenic forcing) moving from hazard to human impacts.


Introduction
The U.S. Midwest is no stranger to flooding: this is an area of the country that has been plagued by large floods, with their frequency increasing over the recent decades (e.g. Mallakpour andVillarini 2015, Neri et al 2019). Specific flood events can leave long-lasting impacts on the well-being of those affected, especially when these events are experienced multiple times over the years: floods like those that occurred in 1993,2008,2011,2017 and, more recently in 2019, have been responsible for several fatalities and many billion dollars in economic damage.
It has now been over 12 years since the 2008 flooding event (e.g. NWS 2009, Mutel 2010, Zogg 2014, Cedar Rapids 2020, which was characterized by discharge values much larger than those recorded in 1993 across large areas of Iowa . This event remains by far the largest one in the 117-year record. To put it in context, with a peak discharge of 140 000 ft 3 s −1 , it was twice as large as the 1993 peak (71 000 ft 3 s −1 ) and almost twice as large as the second largest value (81 600 ft 3 s −1 ; September 2016). The City of Cedar Rapids was significantly impacted by this event, with over 10 000 (of ∼127 000) residents estimated to have been displaced because of the flood and 14% of the city area impacted by floodwaters, but fortunately not in terms of fatalities. The event replaced the 1993 flood as a reference for 'before' and 'after' in many aspects of life for the residents of Eastern Iowa. Despite a decade of significant progress in flood mitigation preparedness (Krajewski et al 2017), several questions still remain unanswered regarding the potential role external forcing may have played in the rainfall during the 2008 event. Was this event altered by the multi-decadal climate response to these external forcing? This type of attribution question has received substantial attention in the literature, with most of the hydroclimatological focus on rainfall amounts (e.g. Risser and Wehner 2017, Van Oldenborgh et al 2017, Otto et al 2018, Philip et al 2019, with fewer studies assessing the role of external forcing to specific flood events (e.g. Pall et al 2011, Schaller et al 2016. Even less is known about the contribution of global warming to impacts. In this study we seek to quantify the role that anthropogenic warming effects played not only in terms of hazard (i.e. heavy precipitation and flooding), but also regarding impacts, intended here to include flood extent and inundated areas, number of affected buildings, and structural and content damage.

Data and methods
The observed rainfall data are obtained from the Stage IV quantitative precipitation estimates (QPEs) products over the continental United State (CONUS) (Lin and Mitchell 2005) released by the National Centers for Environmental Prediction (NCEP). Stage IV has been shown to have low bias when compared to rain gauge measurements in the state of Iowa (Seo et al 2018). The discharge data are obtained from the United States Geological Survey (USGS).
The six-hour initial and boundary conditions used to simulate the extreme event that occurred during June 6-12 2008 are obtained from the ERA-Interim reanalysis data released by the European Centre for Medium-Range Weather Forecasts (ECMWF), at a spatial resolution of ∼0.7 degree (Dee et al 2011). In addition to ERA-Interim, we performed dynamical downscaling using other reanalysis data including the North American Regional Reanalysis (NARR), the Japanese 55-year Reanalysis (JRA-55), and the NCEP Climate Forecast System Version 2 (CFSv2) 6-hourly products. The ERA-Interim data performed the best in reproducing the observed precipitation with respect to Stage IV.
The Weather Research and Forecasting (WRF) model is used to perform the dynamical downscaling of the extreme precipitation event responsible for the flooding during June 2008. We used the Advanced Research WRF (WRF-ARW) for the simulations, and performed the experiments in two domains with two-way nesting with 12 km and 4 km for the outer and inner domain, respectively (supplementary figure 1 (available online at https://stacks.iop.org/ERL/15/114057/mmedia)). The main parameterization schemes are listed in supplementary table 1. The setting of parameterization schemes for WRF ARW in this study has been used in previous studies (e.g. Talbot et al 2012, Li et al 2013, El-Samra et al 2017, Zhang et al 2018. In particular, the previous WRF tests for this setting can be found in Li et al (2013) and Talbot et al (2012). Although there is still uncertainty in the simulation of WRF experiments due to parameterization schemes, the current setting is expected to be suitable for the simulation of heavy precipitation processes. The WRF simulation is integrated from June 6th 00:00:00 to June 13th 00:00:00, 2008.
We follow the 'pseudo global warming' method used in the literature to examine the role of global warming in shaping weather events (e.g. Schär et al 1996, Rasmussen et al 2011. This approach applies a change associated with global warming to the input variables of the original initial and boundary conditions (e.g. winds, humidity and temperature) based on reanalysis data. The 'global warming' change can be obtained by subtracting the input variables in the historical experiments from future projections. Regional model experiments have indicated that the removal of the historical trend based on the Coupled Model Intercomparison Project Phase 5 (CMIP5) models in the forcing data can cause substantially reduced precipitation during a flood event that affected India during June 2013 (Cho et al 2016).
Here we use a strategy similar to that used in Cho et al (2016), with the forcing variables' trends computed from the large initial condition ensemble experiments performed with the Community Earth System Model developed by National Center for Atmospheric Research (NCAR CESM) (Kay et al 2015). Cho et al (2016) performed Control and No-trend experiments to assess the impacts of global warming (i.e. Control minus No-trend). The Control experiment is forced by the initial and boundary conditions from reanalysis data, and the linear climate trends in all initial and boundary condition variables are removed in the No-trend experiment. More specifically, we run two sets of experiments: the 'Original' and 'Detrend' experiments during the time period of interest and based on the average of 42 members. In the 'Original' experiment, we feed the initial and boundary conditions from ERA-Interim data directly into WRF-ARW. In contrast, the 'Detrend' experiments use the initial and boundary conditions of ERA-Interim but detrend the three-dimensional zonal and meridional wind, geopotential height, and temperature based on the trends computed from the CESM large-ensemble experiments to quantify the impacts of external forcing. The trends are computed using linear regression for the month of June over the base period 1979-2005. We did not remove the trend in relative humidity to avoid the risk of having values larger than 100%. Although removing trend in the temperature field plays a major role in driving changes in precipitation in the study area, we cannot exclude potential impacts of external forcing on other variables (e.g. zonal and meridional winds). Therefore, we also remove the trends in the three-dimensional zonal and meridional wind, and geopotential height.
The three-dimension trends (e.g. degree/year for temperature) of the four variables are vertically and horizontally interpolated into the levels and grids of ERA-Interim before we subtract the trends from the initial and boundary conditions from ERA-Interim. Supplementary figure 2 shows the trends of the bottom-level temperature based on the 42-member large-ensemble CESM experiments and the associated signal-to-noise ratio. The subtraction of the 'Detrend' experiment from the 'Original' one represents the impacts of externally-forced trends on this weather event. The trends based on the large ensemble experiments can quantify the trends due to external forcing because natural variability in different ensembles can cancel each other off (e.g. Cho et al 2016). The trends in the four variables from CESM are subtracted from the four variables from ERA-Interim reanalysis data, which provide initial and boundary conditions for the WRF model. The uncertainties associated with the externally-forced signal are computed using the 95% confidence intervals on the estimated trend coefficients. The 95% confidence intervals on the estimated trend coefficients are defined based on the linear regression model: where Y i is the dependent variable, X i is the independent variable (i.e. time), β 0 is the intercept, β 1 is the slope/trend and ε i is the random error. The 95% CI is calculated based on the equation below: where β 1 is the estimated trend, t α/2, n−2 is the t value for the significance level (here 0.05) with n being the sample size, and S xx andσ 2 are defined as: For the hydrologic simulations, we used the model developed by the Iowa Flood Center (IFC), which produces real-time streamflow predictions for all the communities in the state of Iowa using a continuous distributed hydrologic model known as Hillslope-Link Model (Quintero et al 2016, Krajewski et al 2017. The model is calibration-free i.e. a common configuration of parameters determined a priori applies for all the model inputs, and no adjustments are made for particular basins. The model uses hillslopes and channel links as the primary units for landscape decomposition where the hydrologic processes are modeled. Rainfall conversion to runoff is modeled through accounting for soil moisture changes at the hillslopes. Channel routing is based on a non-linear representation of water velocity that considers the discharge amount as well as the upstream drainage area (Gupta et al 2010, Ghimire et al 2018. Mathematically, the model represents a large system of ordinary differential equations organized following river network topology. The IFC also developed an efficient numerical solver suitable for High Performance Computing architecture (Small et al 2013). The hydrologic simulations obtained with the configuration of the Hillslope-Link Model were extensively validated over a period of seven years and showed good performance when using Stage IV data as rainfall forcing (Quintero et al 2020). We initialized the states of the hydrologic model using the conditions observed for discharge and soil moisture for June 6th 2008. For the estimation of economic losses due to flood we used several sources of data. Inundation maps were developed by the IFC for the city of Cedar Rapids using HEC-RAS to estimate water surface elevations in the river channels and floodplain that results from discharge estimates of different return periods; water surface data were intersected with a 1-m DEM to calculate the flood extents. The inundation maps contain detailed urban flooding analysis that takes into account location and heights of the buildings (

Results
This attribution study involves a combination of observations, and hydrologic, atmospheric and climate modeling. Although flooding and extreme rainfall are not the same thing (e.g. Ivancic and Shaw 2015), heavy rainfall represents the basic ingredient for this flood event; the soil was already saturated because of extensive precipitation earlier in the spring. As discussed in Krajewski and Mantilla (2010), this region experienced one of the snowiest winters; even though the heavy snow was not directly responsible to this event, it left the ground saturated. In late May, a number of storms trailed over Iowa, with rainfall falling on the already saturated ground (e.g. Coleman and Budikova 2010, Krajewski and Mantilla 2010). The conditions were primed for the heavy rainfall across the Cedar River during 6-12 June (figure 1). During 6-8 June, the rainfall was concentrated in the upper part of the basin; as the water flowed downstream and the peak propagated downstream towards the City of Cedar Rapids, the areas with heavy rainfall seemed to follow the crest, with much of the rainfall concentrated in the middle and lower parts of the basin. The amount and timing of the precipitation translated to the observed discharge time series (figure 2), which is well reproduced both in terms of timing and magnitude by the IFC hydrologic model forced with radar-based rainfall estimates, and initialized with soil saturated conditions. For this event the IFC hydrologic model is able to reproduce well the observations. Before quantifying the role of external forcing on this flood event, we examined whether the hydrologic response forced by the dynamically downscaled outputs was similar to the observed one ( figure 1 and  supplementary figure 3). Although not 'perfect' in terms of precipitation, the atmospheric model can reproduce the overall daily rainfall amounts, with good agreement with observed the basin-averaged total rainfall (supplementary figure 3). A notable difference is related to the timing and the detailed regional distribution of the precipitation, with large amounts concentrated in the upper part of the basin. Therefore, from a hydrologic perspective we would expect that the agreement in total rainfall would drive total discharge volumes comparable to observations, while the delay and geographic shift to the upper part of the basin would delay the flood peak by few days. As shown in figure 2, the overall magnitude of the modeled peak is very similar to the observed one (whether when compared against gauge measured discharge or from that estimated by forcing the hydrologic model with radar-rainfall estimates), with the main difference being that the modeled peak is delayed by approximately four days. The focus here is on damages arising from the large flood peak in this event, and not the details in the timing of that peak.
The results in figures 1-2 indicate that the combined reanalysis-hydrologic model system can simulate the rainfall and hydrologic response to this rainfall event in a satisfactory manner, encouraging us to move towards quantifying the associated external component. In our perturbation experiments which focused on the thermal-dynamic effects, we did not find evidence that anthropogenic warming led to a marked change in where and when the higher rainfall occurred (comparing the middle and right panels in figure 1) but had mostly an effect on the magnitude, leading to larger amounts (supplementary figure S3). These impacts are then expected to manifest themselves in a hydrograph that mimics one forced with the raw model outputs, even though the peaks have smaller magnitudes (i.e. the largest peak is lower by 2 m). Mounting evidence has shown that the multi-decadal increase in surface temperature can be mainly attributed to anthropogenic forcing, rather than natural forcing (e.g. volcanic eruption and solar irradiance) and internal variability (Flato et al 2014). The increasing atmospheric temperature plays an important role in driving changes in extreme precipitation events, in part due to increasing atmospheric moisture following the Clausius-Clapeyron (C-C) relation (e.g. Held andSoden 2006, Donat et al 2016). We find that the flood peak at Cedar Rapids was approximately 2 m higher because of anthropogenic warming, an amount that leads to statistically different results at the 5% significance level (figure 2).
Having assessed that anthropogenic warming mainly enhanced the magnitude (or equivalently the Figure 2. Time series of the observed and modeled discharge. The black line represents the observations, with the gaps in the time series due to the stream gage not functioning. The magenta line shows the time series obtained forcing the hydrologic model with radar-based rainfall; the blue and green lines show the modeled discharge when forced with downscaled precipitation before and after removing (together with the 95%-confidence intervals) the effects of the external forcing, respectively. The horizontal lines represent the minor (orange), moderate (red) and major (purple) flood levels established by the National Weather Service. Table 1. Summary of the impacts of external forcing on flood extent, number of affected buildings, and economic losses. The results for 'Original' are based on the initial and boundary conditions from ERA-Interim, which are fed directly into WRF-ARW. In contrast, the results for 'Detrend' are based on the initial and boundary conditions of ERA-Interim but detrended based on the trends computed from the CESM large-ensemble experiments. In both cases, the WRF-ARW outputs are used as inputs for the hydrologic model. The column 'Ratio' shows the ratio between the 'Original' and 'Detrend' scenarios. The results in the square brackets represent the 95%-confidence limits.
Original (9 m probability) of the meteorological hazard, we now seek to propagate this information through to evaluate the major role of this warming from discharge, to flood extent, to economic impacts (table 1). Figure 3 shows the flood extent in Cedar Rapids at 7 and 9 m, and the difference in flooding that can be mainly attributed to anthropogenic warming. Based on our results, the extent of the inundated areas is 1.28 times larger (compare 51.2 km 2 to 39.9 km 2 ; table 1), with large areas of Cedar Rapids that would not have been inundated. Because housing and wealth are not distributed uniformly across the affected area, the impacts are not going to be necessarily of the same order of magnitude. As shown in table 1, the number of affected building increased from an expected ∼1100 to ∼3700, a 3.4-fold increase. Nevertheless, given the type of buildings and their expected content, we can attribute mainly to anthropogenic warming an estimated 5.8-fold and 7.1-fold increase in the structural and content damage, respectively. These non-linear effects are associated with the nonlinear relationships that characterize vulnerability curves, which relate water depth to economic damage (Scawthorn et al 2006).

Conclusions
This study presents a novel framework to quantitatively assess the role of anthropogenic forcing in the context of the socio-economic impacts of the 2008 flooding in Cedar Rapids. We find that the anthropogenic warming-driven changes in water level led to a cascade of increasing impacts when one moves from hydrological to societal and economic impacts. More specifically, a 2-m difference in peak streamflow (1.28-fold increase from 7 m to 9 m) led to an approximately 1.28-fold increase in inundated areas; however, when one considers economic losses, the impact grows to 7 times. These numbers should not be interpreted in an absolute sense, but rather relative to the flood peak and the topography of the affected area: a difference of 2 m resulting in water still being within the banks would have not led to any damage; moreover, the impacts would have been different in areas characterized by higher elevation on the river banks (i.e. compare the flood inundation extent differences close to the urban core of Cedar Rapids and more downstream; figure 3). Studies of this kind will allow us to move away from just the hazard attribution to their impacts, providing basic information that could inform policy changes in light of the economic impacts of climate change.
It is essential to note that this flood event and its impacts are not solely attributable to anthropogenic warming, but rather that this warming modified the amplitude and probability of this event. As shown by the flood inundation map, most of Cedar Rapids would have been flooded even after we removed the radiatively-forced anthropogenic warming. Our findings are based on assumptions related to the way that external drivers (mainly the anthropogenic component) affected the climate system, and the numbers could be slightly different depending on uncertainties in the trend estimation, hence they should be considered as estimates. We also quantified different sources of uncertainties associated with our approach. On the one hand, we found that the uncertainties due to the anthropogenic forcing are relatively small (table 1, figure 2 and supplementary figure 3) compared to its signal (results are significant at the 5% level). On the other hand, the noise associated with internal variability is large (supplementary figure 3). Using the large ensemble runs by the CESM we are able to isolate the externally forced signal, and our study highlights the importance of this type of simulations in making statements about the major role of anthropogenic warming.