Maximizing Precipitation and Flood Estimation in the American River Watershed through a Total Storm Approach of Optimizing Historical Atmospheric Rivers

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Anderson, M. Levent Kavvas This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7724680/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 11 You are reading this latest preprint version Abstract Extreme precipitation and flooding pose significant risk to flood control systems and existing infrastructure. Historically, probable maximum precipitation and probable maximum flood estimates have been estimated based on 3-day peaks to assess a reservoir’s ability to contain worst-case scenario flooding. However, this methodology does not account for the risk from long-duration events that contain both intense flow peaks and sustained periods of high inflow. As such, a physically based methodology is presented to produce a maximum flood estimate for six historical atmospheric rivers in the American River Watershed, draining to Folsom Reservoir near Sacramento, California. The results are compared for the maximum precipitation, maximum flood, and historical conditions to assess the underlying mechanisms that contribute to extreme flooding. The importance of the interactions between the atmosphere and land surface are highlighted, particularly the role that temperature and snow processes contribute to amplifying flooding beyond the precipitation totals alone. By using physically based numerical models to estimate extreme flooding, the resulting estimates are not based on extrapolating a probability distribution fit to historical observations and instead directly simulate the hydro-climate interactions that control the hydrologic response to intense precipitation. The time series results can provide further insight into potential extreme flooding that may increase in frequency with climate change. Earth and environmental sciences/Climate sciences Earth and environmental sciences/Hydrology Earth and environmental sciences/Natural hazards Scientific community and society/Water resources Probable Maximum Precipitation Probable Maximum Flood Atmospheric River Optimization Storm Duration Extreme Flooding Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 INTRODUCTION Large scale water resources infrastructure, such as dams or levees, have a high-hazard potential given the consequences that would result to downstream communities should failure occur 1 . By 2025 it is estimated that seven out of ten dams in the U.S. will be 50 years old and originally built and operated based on old standards and flood frequency analysis. Beyond regular maintenance and reassessment to reduce risk to downstream communities, climate change introduces further vulnerability and unknowns. It is possible there will be an increase in the frequency of extreme weather or increase in the probability of the design storm occurring 2 , 3 . Existing risk assessments are based on historical data, leaving aging dams particularly vulnerable to the unknowns that climate change may bring. However, first defining and then determining how extreme flooding will change is difficult due to the complexity of the corresponding hydro-climate system, the nonlinearity and variability in both time and space, and the nonstationarity due to climate change 4 , 5 . Furthermore, the potential of a quick succession precipitation events, building snowpack and antecedent soil moisture, can eventually result in extreme flooding beyond the precipitation totals of a single storm period 6 . Thus, this study will present a physically based, total storm approach to produce a maximum flood estimate for six previously optimized historical atmospheric rivers in the American River Watershed. The American River Watershed (ARW) is in the Sierra Nevada Mountain range of Northern California, draining to Folsom Reservoir upstream of Sacramento (Fig. 1 ). Folsom reservoir has a total storage capacity of approximately 1 million AF, regulating the runoff from an area of approximately 5,000 km 2 . Elevation within the watershed ranges from 120 m near the reservoir to close to 3,000 m in the headwaters of the Sierra Nevada. Flooding will typically occur in the winter wet season, as precipitation and antecedent soil moisture build from the dry summer months, coinciding with precipitation events 7 . Under certain circumstances, such as rain on snow (ROS) events, flooding beyond the magnitude of precipitation is possible when warm precipitation falls on a persistent snowpack. However, historically, almost all major flooding has occurred as a result of persistent or prolonged precipitation events, namely atmospheric rivers (ARs) 8 – 10 . ARs are now classified as a type of extreme storm, emphasizing their importance for regional hydrology and the increased threat they pose should climate change enhance their occurrence and intensity 11 . The significant water vapor transport and extreme winds associated with ARs can produce enhanced orographic precipitation depending on the landfall location and angle of impingement to the local topography 9 , 12 – 16 . The characteristics of the ARs themselves, such as the intensity and duration of the storm system, are important in controlling the hydrologic response to the precipitation totals 11 , 17 , 18 . However, the initial conditions across a watershed also influence if severe precipitation will result in downstream flooding at that watershed. The antecedent soil moisture and whether or not the soil is saturated is critical in determining if precipitation will infiltrate or directly generate runoff 16 , 19 . Additionally, the temperature of the storm system and the existing snow cover across the watershed impact the hydrologic response to precipitation. Flooding can be significantly enhanced should warm rain fall on an already substantial snowpack, leading to extreme snowmelt or ROS events 2 , 20 , 21 . Likewise, should the air temperature lead to snow accumulation, potential flooding can be diminished despite large precipitation totals. The nonlinearity and complexity of the hydro-climate system makes estimating and preparing for exceedingly rare precipitation and flooding events difficult. To design a dam to be able to manage the risk of extreme flooding causing failure, traditionally, a flood frequency analysis (FFA) or a probable maximum flood (PMF) estimate is calculated for a particular watershed 7 , 22 . PMF is commonly a theoretical 3-day flow estimate that poses a flood control threat for a given dam and often times is assumed to be a result of the probable maximum precipitation (PMP) 23 . However, the assumptions within a traditional PMP estimate introduce substantial uncertainty, and recent studies have concluded that the PMF is not always caused by the PMP 2 , 21 , 23 , 24 . Furthermore, it has been suggested that a single deterministic PMF value is not appropriate and should rather be an estimate that includes the uncertainty inherent in the methodology 25 . Similarly, FFA calculates flow magnitudes for certain return periods by statistical methods fit to historical observation data based on the assumption that flows are independent and identically distributed variables that can be represented by a given probability distribution 7 , 26 . This methodology is solely based on historical observation data and does not consider the physical processes that govern runoff generation, and thus, is highly dependent on not only the quality of the observation data but also the quantity 9 , 26 . An extensive historical record is needed to estimate severe floods at a PMF level, with very low annual exceedance probability on the order of 0.001, or else it is necessary to extrapolate beyond the timeframe allowed by the historical record 7 . Furthermore, FFA is based on the assumption of stationarity and supposes that the selected distribution does not change and is appropriate for representing all flood processes and return periods. In 1999 a 3-day flow discharge FFA for ARW was computed for on a Log-Pearson Type III distribution using log-space method of moments. It estimated a maximum 3-day average flow of 485,000 cfs for ARW. However, this estimate does not directly account for long duration precipitation events, antecedent land conditions, or the physical dynamics of the hydrologic system. Furthermore, climate change introduces additional uncertainty as the underlying distribution governing flow may be altered. In terms of precipitation, climate change has been theorized to be intensifying extremes 27 – 29 . However, uncertainty remains on how effects will manifest for precipitation variability and the annual mean totals 30 – 32 . Furthermore, the effect on ARs, which are directly responsible for many historical floods at the subject watershed, is difficult to estimate at a watershed scale 33 . Global circulation patterns may be altered in one way, however, the local dynamics controlling the precipitation generation may change in another. Thus, the complex nature of the atmospheric-land surface interactions must be considered together when estimating future hydrologic extremes. In terms of hydrologic impacts from climate change, extremes are also expected to intensify, as well as the occurrence of whiplash events 2 , 34 . Within the Sierra Nevada, a warmer atmosphere is expected to raise snowlines and produce more rain than snow 8 , 12 , 20 , 21 , 26 . This may lead to changes in peak runoff timing, April 1 snowpack, and the possibility of ROS events occurring 8 , 35 – 38 . The unknowns that remain in the face of a changing climate and the intricacy of the system highlight the need to use physically based models in estimating hydrologic extremes as opposed to relying on purely statistical methodologies. The nonstationarity of the climate system brings further uncertainty to traditional FFA given that future extreme floods may exceed past FFA or that the fit distribution is no longer appropriate for the tails of the probability distribution where observations do not exist 2 , 7 , 9 , 39 , 40 . As such, this study will employ three physically based models to produce a maximum flood (MF) estimate for six previously maximized historical atmospheric rivers. The models include the Weather Research and Forecasting (WRF) Model and snow and hydrologic components of the Watershed Environmental Hydrology Hydro-climate Model (WEHY-HCM). The historical ARs were maximized in terms of storm total precipitation to produce a maximum precipitation (MP) estimate through Atmospheric Boundary Condition Shifting (ABCS) and Relative Humidity Optimization (RHP-IVT) 41 . Instead of limiting the estimate to a 3-day flow magnitude, the cumulative inflow volume over the entire flood duration will be the basis for evaluating the MF estimates. For reservoirs in snow dominated mountainous regions, such as Folsom Reservoir, long duration periods of increased flow and intense peak flows, driven by extreme precipitation potentially augmented by initial conditions across the watershed, can threaten both reservoir capacity and downstream communities and infrastructure. Producing a physically based estimate for potential worst case scenario flooding, independent of historical flow observations and including long duration events, can provide further data necessary to assess existing infrastructure against possible future flooding scenarios. RESULTS The American River being a snow dominated watershed that outflows to a reservoir with a flood control function, in this watershed it is important to consider long duration events in addition to peak flows 42 . The merged reconstruction and individual maximization WRF outputs for all six historical ARs and all ABCS and RHP-IVT combinations were input to the snow and hydrologic components of WEHY-HCM to produce inflow time series. Considering that PMP does not always result in PMF, it is necessary to simulate all maximization combinations when assessing a MF estimate. To then compare floods of different durations, it is necessary to establish a definition that is applied to the hourly flow results. Using the simulated hourly inflow time series to Folsom Reservoir of the reconstruction period (1852–2020) 43 , 95% exceedance probability values were computed for the baseflow and the percentage increase by means of the empirical probability estimates of the Weibull formulas 5 . The 95% exceedance value for the baseflow was computed to be 14,094 cfs . The 95% exceedance value for the percentage increase was computed to be 2.04%. As such, a flood starts when the hourly percentage increase is larger than 2.04% and the hourly flow is larger than 14,094 cfs . Subsequently, the flood ends when the hourly flow decreases beyond the flow value at the start of the flood. This combined definition allows only significant floods to be considered while not being too restrictive to capture both the rising and falling limbs of the hydrographs. To identify the individual ABCS and RHP-IVT combinations, a standard naming convention is used: YYYY ####(n/s)####(e/w) 1.#. YYYY represents the water year, ####(n/s) represents the degrees shifted North or South, ####(e/w) represents the degrees shifted East or West, and 1.# represents the RH multiplier. For example, the original 1997 event is named 1997 0000n0000e 1.0 to specify 0°N, 0°E shifting at an RH multiplier of 1.0. The 5°S, 1°E case at an RH multiplier of 1.5 is named 1997 0500s0100e 1.5. For each of the selected floods, the total flood volume, based on the above flood definition, is compared for all maximization combinations. Furthermore, the time series results for the historical case, the MP case, and MF case are compared for the hourly basin-averaged precipitation, hourly snow water equivalent (SWE) at two stations, and hourly flow, rolling 3-day average flow, and cumulative flow volume for inflow to Folsom Reservoir. The two SWE stations represent one high elevation station (LOS), where snow accumulation is larger and more persistent through the winter, and one mid-elevation station (GKS), where snow accumulation is heavily temperature dependent and more variable over the winter. By comparing the time series results for the precipitation, snow, and flow processes, the underlying mechanisms producing the flood can be recognized and analyzed. Water Year 2017 As with the MP results seen in Snider et al. (2025), the historical 2017 flood event was not significantly changed by the maximization procedure in terms of total inflow volume (Fig. 2 a). The 0000n0000e 1.0 historical case produced a storm total volume of 1,817 TAF while the MF case at 0500s0000e 1.0 produced a storm total volume of 1,997 TAF for an increase of 9.9%. Both ABCS and RHP-IVT minimally changed the storm total volume compared to the historical flood. Additionally, the resulting order of total volume based RHP-IVT multiplier is variable across all shifting degrees. Considering the time series of the precipitation, SWE, and flow for the historical, MP, and MF cases, the importance of the storm and flood definitions applied is apparent (Fig. 3 ). The MF case occurred for the 0500s0000e 1.0 while the maximum average 3-day flow and MP occurred for the 0000n0100e 1.4 case. The time period for the storm, based on a definition using a 10 mm threshold for the rolling 3-day precipitation, is the early January rain bands through the 13th for the historical, MP, and MF maximization cases. However, the resulting maximized floods for each case occurred for the later period in February, where the longer duration of increased flows ultimately resulted in larger cumulative inflow volumes. Though the January floods saw larger 3-day peak flows for the historical and MP case, the MF was significantly diminished. The historical 3-day peak flow was 120,110 cfs and the maximized 3-day peak flow was 157,555 cfs during the January flood. The MF in February had a 3-day peak flow of 100,921 cfs . Despite lower peak flows in the earlier flood period, the MF ultimately had a greater cumulative volume compared to all other shifting combinations during the entire time period. Considering the lower elevation snow cover, the MF case increased SWE through the January storm period, likely due to cooler temperatures as a result of south shifting, whereas the historical and MP cases decreased, corresponding to the largest hourly and 3-day peaks. During the maximized flood period, the MF case begins slightly earlier and has slightly larger hourly peak flows compared to the historical and MP case, resulting in larger cumulative volumes. These results further support previous analysis that the MF does not always result from the MP. Furthermore, it is not a valid assumption that the MF will be a direct result of the largest precipitation volume, depending on other watershed conditions such as the existing snow cover and temperature. Water Year 1997 For the 1997 event, the largest difference from the historical case occurred for a combination of moisture increases and south shifting. The biggest increase in cumulative volume occurred for the 1.2 multiplier but further moisture increases also increased the cumulative volume. The MF was produced by the 0200s0100e 1.6 case though cumulative volume results were similar for 0300s0100e 1.6 and 0400s0000e 1.6 (Fig. 2 b). The historical case at 0000n0000e 1.0 produced a cumulative volume of 1,656 TAF while the maximized case produced a cumulative volume of 2,977 TAF for a 79.7% increase. For the time series comparisons, the earlier and intensified precipitation in the MP and MF cases resulted in a series of early flow peaks prior to the significantly increased peak flow compared to the original flood (Fig. 4 ). The MF and the maximum 3-day rolling average flow were both a result of the 0200s0100e 1.6 case while the MP case was produced by further south shifting at 0490s0000e 1.6. The historical case had a 3-day peak flow of 177,848 cfs while the MF and maximum 3-day peak saw 270,036 cfs. At both elevation stations, the SWE during the historical flood slightly grew or was maintained through the three initial rain bands before melting occurred during the most intense portion of the precipitation event leading to the peak hourly flow. During the MP and MF cases and at both elevation stations, SWE accumulated at similar rates during the first two rain bands. By the third rain band, however, SWE at the GKS station began to exhibit melting while SWE at the LOS station continued to accumulate. The MF SWE at the GKS station melted at a faster rate until it was depleted compared to the MP case which eventually leveled out following the most intense period of precipitation. This is likely due to the further south shifting of the MP case, as cooler temperatures limited mid-elevation melting. At the LOS station, the SWE for the MF case initially began to melt, as precipitation further intensified, before again accumulating as the precipitation decreased. The differences between the MP and MF precipitation and resulting SWE processes resulted in the MF having higher hourly peak flows and 3-day average flows compared to the MP. The MF hourly peak flow coincides with the slight melt at the LOS station and the last remaining GKS snowpack. Compared to the historical case, the MF begins six days earlier and is significantly intensified. The resulting peak hourly flow and cumulative volume are nearly doubled from the historical case to the MF case. Water Year 1986 For the 1986 event, the MF result is primarily due to moisture amplification rather than shifting (Fig. 2 c). The MF was produced by the 0100n000e 1.6 case with a cumulative volume of 2,880 TAF compared to the historical case with a cumulative volume of 2,049 TAF for a 40.5% increase. Considering shifting alone, as was the case with the precipitation maximization, north shifting reduced the cumulative volume compared to the original 0000n0000e 1.0 case. As with the 1997 event, the biggest increase from moisture maximization occurred for the 1.2 multiplier. Larger multipliers resulted in variable increases beyond the 1.2 multiplier depending on the shifting degree. The MF is primarily a result of moisture maximization and as such, time series results are similar compared to the historical case for both atmospheric and land surface processes though significantly amplified (Fig. 5 ). The MF at 0100n0000e 1.6 is significantly different compared to the MP case at 0340s0100w 1.6. The maximum 3-day rolling average flow occurred for the 0000n0100e 1.6 case. Though not shown, the hourly results of the two cases were very similar, particularly for the maximum 3-day peak. Considering the maximum average 3-day peak flow, the historical case peaked at 173,514 cfs , the MF peaked at 250,068 cfs , and the maximum average 3-day flow peaked at 252,400 cfs . The less intense but extended storm period of the MP case is also seen in the resulting flow. The south shifting brought cooler temperatures resulting in additional snow accumulation at the high elevation station and sustained snowpack at the mid-elevation station. The peak flows are dampened below the historical case, but the additional rain band increased the cumulative volume beyond that of the historical case, though below the MF case. The timing of the precipitation associated with the MF follows that of the historical case with an intensified magnitude, as expected due to the additional moisture primarily brought with RHP-IVT. At the LOS station, SWE accumulation between the MF and historical cases are nearly identical. However, at the GKS station, the SWE for the MF case begins to decline with the second rain band whereas the historical case increases slightly before melting to a similar magnitude as prior to the storm. The additional melt, combined with the increased precipitation, contributes to significantly larger hourly flow, hourly peaks, and average 3-day peak flow compared to the historical case. Though the magnitude of the hydrograph is amplified by the maximization procedure, the timing and shape are similar between the MF case and historical case. Water Year 1965 The 1965 event was produced by a combination of shifting and moisture maximization (Fig. 2 d). The historical case at 0000n0000e 1.0 produced a cumulative inflow volume of 2,046 TAF while the MF was produced by the 0300s0100e 1.6 case with a cumulative inflow volume of 2,945 TAF for a 43.9% increase. Considering shifting alone, the resulting cumulative inflow volume greatly depended on the shifting direction. Shifting to the south alone did not considerably increase the total volume. Shifting to the north, however, significantly reduced the total inflow volume, consistent with the precipitation maximization results for the 1965 event 41 . Southward shifting combined with amplified moisture ultimately increased the cumulative inflow volume beyond that of the historical case to produce the MF for the 0300s0100e 1.6 case. The case at 0500s0100w 1.6, which is the MP and 3-day average peak flow case, produced a total inflow volume comparable to the MF, though slightly smaller. The time series results again highlight that slight differences between the maximization cases can impact the conclusions that are ultimately drawn and the importance of the thresholds used to define a flood period. The MF case, at 0300s0100e 1.6, and the MP and maximum 3-day peak flow cases, at 0500s0100w 1.6, have similar cumulative inflow volumes despite their differences in hourly flow and average 3-day flow (Fig. 6 ). The 3-day peak flow for the historical case was 168,403 cfs while the MF case was 290,182 cfs and the MP and maximum 3-day peak cases was 312,810 cfs . Prior to the flood event starting, the MP case had a greater snowpack at both elevations compared to the MF case and historical case. The MP and MF cases exhibit similar precipitation patterns, both amplified compared to the historical case, for the first four days of the storm period. Similarly, the rate of snow accumulation and melting is similar between the two cases through December 23 rd, even if the MP case has a greater depth. Following that, the increased precipitation of the MP case results in larger hourly flow producing the peak hourly flow and peak 3-day flow. The cumulative flow volume is greater for the MP case through the 28th, however, following that the high and mid-elevation snow accumulation slows for the MF case compared to the MP, resulting in larger, sustained hourly flows that eventually increase the cumulative inflow volume of the MF case above that of the MP case. Compared to the historical case, the MF begins about one day earlier and is about six days shorter due to the flood definition that was applied to the time series. Additionally, the definition and variable being maximized impact the resulting MF case. If the hourly peak flow or the maximum 3-day peak flow was the attribute of interest, the 0500s0100w 1.6 case would be considered the maximum flood. However, because the total cumulative volume of the entire flood period is of interest for this study, the 0300s0100e 1.6 case is considered the MF. Depending on flood control systems, the analysis of worst-case scenario flooding should focus on the hazardous condition that threatens the infrastructure, whether that be a peak flow or inflow volume. However, risk analysis considering both a traditional 3-day PMF and a long duration cumulative inflow-based MF can provide a comprehensive picture of how a reservoir may be operated under different conditions. Water Year 1909 The 1909 flood maximization results again follow the precipitation results in terms of shifting alone, though there is added variability depending on the moisture maximization multiplication factor that is applied (Fig. 2 e). The original case at 0000n0000e 1.0 produced a cumulative volume 919 TAF . The MF case at 0300s0100e 1.2 produced a cumulative volume of 3,554 TAF for a percentage increase of 286.7%. The simultaneous application of ABCS and RHP-IVT produced different cumulative volume results depending on the direction of shifting. Shifting to the north alone for the most part reduced the cumulative volume. However, the decreases in volume were made up for as the moisture multiplication factor increased. The largest increase occurred for the 1.2 multiplication factor with further increases in moisture producing diminishing increases. On the other hand, shifting to the south alone increased the cumulative volume. Further moisture increases did produce additional inflow volume, though not to the degree exhibited by shifting to the north. In all shifting cases, there was more variability in cumulative volume across the multiplication factors. Further moisture increases did not necessarily increase total volume, and the MF case was produced by only a 20% increase in moisture. The role of duration in producing significant cumulative volumes is apparent in the time series results of the 1909 event (Fig. 7 ). The precipitation events have numerous rainbands and periods of increased intensity lasting nearly two months and resulting in sustained increased hourly flow throughout the period. Of note, however, is that the peak hourly flow and baseflow of the defined flood is considerably smaller compared to the maximization results of the other years analyzed. The historical case at 0000n0000e 1.0 produced a 3-day peak flow of 36,226 cfs . Though not shown here, the maximum 3-day peak flow case occurred for the 0400n0100e 1.6 case at 103,951 cfs . The hourly flow time series follows that of the original flood, though amplified for the period from January 14 lasting through January 29. The MF at 0300s0100e 1.2 produced a 3-day peak flow of 84,034 cfs while the MP case produced a 3-day peak flow of 86,814 cfs . At both elevations for all three cases, the SWE accumulates for the entire storm period at similar rates despite the different magnitudes. No melting is occurring across the watershed for all three cases, suggesting the resulting flow is primarily a result of the liquid precipitation. The two primary peak hourly flows around January 6 and January 22 are slightly larger for the MP case, however, the increased flow around January 12 for the MF case, combined with the longer duration compared to the MP and historical cases, result in a larger cumulative volume. This case is another example of the flood definition being an important factor in the results. The hourly flow of the historical case maintains an increased period of flow beyond that of the defined flood period. However, because the flow dips below the starting value when the flood begins based on the defined threshold values, it is not considered to be the same flood. The cumulative volume of the MF case and historical cases for the same period of time from December 24 through February 15 are 3,595 TAF and 1,654 TAF , respectively. The resulting percentage increase is thus decreased to 117%. Using a strict threshold to define a flood period allows events of different durations to be compared, however, the sensitivity of the hourly data to the threshold values can be restrictive if the data fluctuates around the beginning flood period value. Water Year 1876 The 1876 volume maximization results again follow that of the precipitation maximization in terms of the increases due to the simultaneous application of ABCS and RHP-IVT methodologies (Fig. 2 f) 41 . The original case at 0000n0000e 1.0 had a cumulative volume of 1,792 TAF . The MF occurred for the 0220n0100e 1.6 case with a cumulative volume of 5,107 TAF for a percentage increase of 184.9%. The moisture amplification through RHP-IVT increased the resulting cumulative volume substantially more than northward shifting alone. As was seen in other years analyzed, the largest increase occurred for the 1.2 multiplier. However, in this case, the 1.4 multiplier also substantially increased the resulting cumulative volume for all northward shifting combinations. The 1.5 and 1.6 multipliers further increase the cumulative volume, though to a lesser extent than the 1.2 and 1.4 multipliers. Of the results across all years analyzed, the 1876 MF case produces the largest cumulative volumes during the flood period. The intensified precipitation due to RHP-IVT is apparent in the flow results as well for the 1876 event (Fig. 8 ). The MF, MP, and maximum 3-day peak flow cases occur for 0210n0100e 1.6, 0230n0100e 1.6, and 0220n0100e 1.6, respectively. The time series for each case is nearly identical given the only difference between the three cases is 0.1°N shifting. The peak 3-day flow was originally 108,108 cfs while the MF peaked at 291,233 cfs and the maximum 3-day flow peak occurred at 293,478 cfs . At the high elevation station, SWE accumulated substantially for both the MF and historical cases. At the mid-elevation station, melting occurred at the start of the defined flood for the MF case. For the historical case, however, SWE initially accumulated or was maintained until the most intense period of precipitation when melting began around December 30, 1875. The hourly inflow time series of the MF case contain multiple peaks following the rainbands and period of intense precipitation. The depletion of the mid-elevation snowpack in the MF case likely saturated the watershed at the start of the storm period leading to more runoff throughout the flood following the precipitation patterns. The historical case, by comparison, does not substantially peak until the mid-elevation melting begins, coinciding with the last rainband. The original flood began after the MF case, likely due to SWE accumulation across the watershed, limiting runoff compared to the melting that occurred for the MF case. The importance of snow processes is again apparent, highlighting the necessity of physically based models to simulate the interactions between the land surface and atmosphere. DISCUSSION Comparison among floods of different durations is not as clear as the standard 3-day PMF estimates. Details for all six flood events maximized are provided in Table 1 for comparison between the historical case, MF case, and maximum 3-day average flow case. If the total flood volume alone is considered, then the 1876 event would be the largest of the analysis presented at 5,107 TAF . However, that characteristic by itself does not give any indication as to the severity of the event if neither the duration nor peak flows are included. Another method of comparison is by a percentage increase from the historical cumulative volume to the MF cumulative volume. By this standard, the 1909 event has the largest percentage increase at 286.7%. However, as we described previously, this result is highly dependent on the flood definition thresholds applied to the time series. If the longer historical flood period was instead compared to the MF, the percentage increase would only be 117% and thus the 1876 event would then be the largest increase from the original flood at 185%. Again, this characteristic alone does not include any indication of the severity of the MF result for the individual events and only describes to what degree the historical flood was increased. Table 1 Comparison of the six maximized flood events (in bold) compared to the historical case and maximum average 3-day flow case Case Volume (TAF) Peak 3-day flow (cfs) Duration (hrs) % Increase Intensity (TAF/hr) 2017 Original 0000n0000e 10 1,817 120,110 520 - 3.5 MF 0500s0000e 10 1,997 100,921 592 9.9 3.4 3day Max 0000n0100e 14 - 157,555 - - - 1997 Original 0000n0000e 10 1,656 177,848 318 - 5.2 MF & 3day Max 0200s0100e 16 2,977 270,036 394 79.7 7.6 1986 Original 0000n0000e 10 2,049 173,514 378 - 5.4 MF 0100n0000e 16 2,880 250,068 384 40.5 7.5 3day Max 0000n0100e 16 - 252,400 - - - 1965 Original 0000n0000e 10 2,046 168,403 439 - 4.7 MF 0300s0100e 16 2,945 290,182 329 43.9 8.9 3day Max 0500s0100w 16 - 312,810 - - - 1909 Original 0000n0000e 10 919 36,226 457 - 2.0 MF 0300s0100e 12 3,554 84,034 1,126 286.7 3.2 3day Max 0400n0100e 16 - 103,951 - - - 1876 Original 0000n0000e 10 1,792 108,108 534 - 3.4 MF 0220n0100e 16 5,107 291,233 589 184.9 8.7 3day Max 0210n0100e 16 - 293,478 - - - An additional method of comparison can be done for the flood intensity. By computing the average inflow volume per hour of the flood period, the duration of the event can be combined with the cumulative volume to provide an indication of the severity of the flooding. For the 2017 event the intensity of the flooding was decreased by the maximization procedure from 3.5 TAF/hr to 3.4 TAF/hr as the duration increased with minimal increases to the cumulative volume. The 1997 event increased from an intensity of 5.2 TAF/hr to 7.6 TAF/hr . Similarly, the 1986 event increased from an original intensity of 5.4 TAF/hr to 7.5 TAF/hr . The 1965 event had the largest maximized intensity of 8.9 TAF/hr compared to the original case at 4.7 TAF/hr . On the other hand, 1909 had the smallest intensity of events analyzed at 3.2 TAF/hr . Over 2,600 TAF were added by the maximization process, however the duration increased by nearly 28 days. This result further emphasizes that duration needs to be explicitly included when comparing floods of different lengths. Finally, the 1876 event increased from an original intensity of 3.4 TAF/hr to 8.7 TAF/hr . Comparing the two largest MF intensities, the 1965 and 1876 events are similar. While the two events have comparable peak 3-day flows, the cumulative volume and percentage increase are much larger for the 1876 event compared to the 1965 event. While these results can provide further insight into potential extreme events, results should be compared to a more traditional FFA to assess a potential exceedance probability. To select a single design flood based on the total storm approach, the variable being maximized influences the resulting conclusions that are drawn. If the peak 3-day average flow was the primary maximization objective, the MF would be a different case for nearly all of the events. Though most are of similar magnitude between the cumulative volume MF and the maximum 3-day peak, 2017 and 1965 would instead correspond to the MP case. While the 3-day peak simplifies comparisons between different events, it alone does not provide any indication of the long-term effects and subsequent consequences from sustained high reservoir releases required to contain long-duration events. Of note, for the cumulative volume MF results, none of the MF cases correspond to the MP case, even if results were similar between the two cases such as with 1876, further supporting previous findings that the MP is not solely responsible for the MF. Beyond selecting a single MF, the physical processes that contribute to enhanced flooding beyond precipitation totals can be assessed. Of the events analyzed here, the consequences of antecedent land conditions, particularly snow cover, and atmospheric temperatures are evident. At the beginning of the storm period, the 2017 event had relatively little snowpack compared to the reconstruction period. However, as the storm systems progressed, snow accumulated at both elevations and across the watershed. While the slight melt of the mid-elevation snowpack likely contributed to the MF peak flow, the accumulated snow would be important for maintaining high spring and summer streamflow 44 . Similarly, in 1909, snow accumulation occurred constantly throughout the storm period at both elevations. The resulting flood was then primarily precipitation driven which is reflected in the lower magnitude hourly flow and lesser peak flows compared to the other events analyzed. Again, for the 1876 event, the fact that the storm occurred early in the water year, before any significant snow had accumulated, means that the flood was primarily driven by direct precipitation runoff. At the mid-elevation station, snow initially accumulated, however, by the second rainband it began melting until depleted. At the high elevation station, snow accumulated throughout the storm period, adding nearly 2 m of SWE. On the other hand, in the MF for 1997, the initial snow accumulation across the watershed eventually led to later melting, driving the peak flow and coinciding with the most intense period of precipitation. The increased precipitation was compounded by the complete melting at the mid-elevation after it had first accumulated to nearly half a meter at the GKS station. Likewise, in 1965, snow accumulated across the watershed at the start of the storm period. The mid-elevation melt, coinciding with the peak precipitation, immediately led to the peak flow, suggesting the watershed was previously saturated. As the storm progressed and snow again accumulated across the watershed, the hydrograph continued to recede despite further rain bands bringing additional precipitation. Finally, in 1986, the steady melt of the mid-elevation snowpack steadily increased the flow corresponding to the precipitation. The depletion of the mid-elevation snowpack with the most intense period of precipitation contributed to the significantly increased peak flow. The complex processes between the atmosphere and land surface must be explicitly modeled to fully understand the hydrologic response to extreme precipitation. By using physically based atmospheric and land surface numerical models, the interactions guiding the snow and hydrologic processes are directly accounted for in the resulting time series data. In conclusion, the physically based optimization of historical ARs to maximize the resulting cumulative inflow volume allows characteristics of the entire storm system to be reflected in the MF estimates that are produced. Furthermore, as these are physically based estimates, independent of historical data, the assumed rarity of these events does not influence the resulting estimate by requiring an extrapolation of a probability distribution fit to historical observations. However, to assess the risk of these long duration, storm total MF estimates, more historical ARs should be maximized to create a larger sample size to assess. As was seen in the results, the MF does not necessarily result from either the MP or the most extreme shifting case. The MF for each event may be primarily a result of moisture maximization, requiring minimal shifting. In terms of climate change, this alone increases the risk of these extreme floods occurring as a warmer atmosphere can hold more water, comparable to only applying RHP-IVT to historical ARs. The possibility of compound flooding resulting from ROS events may also increase if warm winter storms occur when the snowpack has already accumulated, amplifying the flooding beyond the precipitation totals alone. The storm total approach to estimate the worst-case scenario flooding through physically based models allows the entire hydro-climate system to be considered. The time series results for each event analyzed here can be further studied to assess their individual risk to Folsom Reservoir in terms of both amplified 3-day peak flows and sustained periods of high inflow beyond what has been observed historically. METHODS The heterogeneous, mountainous characteristics of ARW require fine scale numerical modeling to resolve the complex atmospheric-land surface interactions that control the snow and hydrological processes that generate runoff within a watershed 20 , 28 , 43 , 45 , 46 . Within ARW precipitation is stored in the snowpack and estimated to contribute between 50–80% of spring and summer flows, and thus flood estimation must directly account for the role of snowmelt in contributing to increased flows 47 – 49 . As such, three physically based models are used to first dynamically downscale global reanalysis data and then simulate the snow and hydrological processes. The models include the Weather Research and Forecasting (WRF) Model and the Watershed Environmental Hydrology Hydro-Climate Model (WEHY-HCM) land surface, snow and hydrologic components. All three models were previously calibrated and validated for ARW specifically, and atmospheric and hydrologic conditions reconstructed from 1852–2020 with results were presented in Snider et al. (2024). The period of reconstruction is the basis for the historical period and is used to assess the maximization results. Previously, six historical AR events were selected and maximized by means of Atmospheric Boundary Condition Shifting (ABCS) and Relative Humidity Optimization (RHP-IVT) through the WRF model to produce a maximum precipitation (MP) estimate 41 . A brief overview of the MP estimate methodology is presented here. However, further details regarding the methodology, results for all maximization cases, and discussion are presented in Snider et al. (2025). Input atmospheric reanalysis data to WRF depends on the year being simulated and includes one of three datasets: the Twentieth Century Global Reanalysis Version 2c (20CRv2c), The European Center for Medium-Range Weather Forecasts twentieth century reanalysis (ERA20C), or the Climate Forecast System Reanalysis (CFSR). WRF maximization simulations were performed for the entire storm period, defined by a rolling 72-hr precipitation threshold of 10mm. ABCS was performed from 5°N to 5°E and 1°W to 1°E at 1° increments. RHP-IVT was simultaneously performed for multipliers of 1.0, 1.2, 1.4, 1.5, and 1.6. Further refinement at 0.1° shifting increments were performed between the top two shifting combinations at the given RHP-IVT multiplier. This process was performed individually for each of the six selected historical ARs in 2017, 1997, 1986, 1965, 1909, and 1876. These selected ARs represent a mix of important historical floods and events that may have had the potential to be intensified by the maximization methodology. To then assess the hydrologic response to each of the maximization combinations of each historical AR, the maximization outputs from WRF were combined into the longer water year reconstruction time series that were computed by Snider et al. (2024) and input to the WEHY-HCM SNOW Module to further refine the atmosphere-land surface interactions. The SNOW Module of WEHY-HCM is a physically-based, energy budget model that uses atmospheric and land data to numerically solve the conservation of mass and energy equations between the snowpack and surrounding environment 47 . The energy budget is solved by computing the solar angle and incoming solar radiation based on digital elevation maps (DEMs) at every node in the grid network. This allows the effects from topography and elevation to be incorporated into the snow process computations at a resolution of 100m. Furthermore, at every node in the grid network, the snowpack is divided into three layers to ultimately simulate the nonuniform vertical temperature profile of the snowpack. In the top, skin layer of the snowpack atmospheric forcings are incorporated to dictate the deeper snowpack temperature profile. Below that is the active layer, where a linear temperature profile is assumed above the evolving freezing depth. Finally, at the deepest portion of the snowpack below the evolving freezing depth, the temperature is assumed to be isothermal at 0°C and disconnected from any atmospheric interactions. Across the domain, those point scale processes are then vertically integrated over the snowpack depth and numerically upscaled, producing a spatially distributed model of snow processes that contain both atmospheric forcings and solar geometry. Ultimately, this module can account for the spatial heterogeneity of snow accumulation and melting processes at a resolution fine enough to resolve the atmospheric mechanisms driving the hydrologic response. The final model used is the hydrologic component of WEHY-HCM 50 – 53 . As a physically-based hydrology model, flow processes are computed for various processes and at different temporal and spatial scales by numerically solving upscaled versions of the conservation of mass, momentum, and energy equations. To account for the atmosphere-land surface interactions, the dynamic exchanges within the boundary layer are coupled through hillslope scale averaged fluxes. The target watershed is delineated into model computation units (MCUs) where land parameters are assumed to be spatially stationary across the individual MCUs. At each MCU the point-scale surface and subsurface processes are computed by using the unsaturated flow to link the overland flow, subsurface flow, and groundwater flow domains. Those point-scale conservation equations are then upscaled to the computational grid scale by ensemble averaging, which are then numerically solved. The unsteady, nonuniform flow discharge at each MCU is then routed through the delineated stream network by means of the channel flow domain to the watershed outlet point. The physical land characteristic inputs are the same between the snow and hydrologic components of WEHY-HCM. DEM data is provided by the USGS National Elevation Dataset. Land use and land cover (LULC) data is provided by the California Department of Forestry and Fire Protection. Geomorphological and soil data are provided by the US Department of Agriculture’s Web Soil Survey. Using DEM data, the basin is delineated for a specific outlet point. In the case of ARW, the outlet of Folsom Reservoir is selected and a total of 54 MCUs and 17 stream reaches are selected for the delineation (Fig. 1 ). Additionally, the LULC, geomorphological, and soil data are delineated to coincide with the DEM delineation. Using these fine resolution physical attributes of the watershed allows the heterogeneity of all grid points in the domain to be accounted for. Following the delineation of the land characteristics, the WRF outputs are input to the SNOW Module. Outputs from the SNOW Module are then input to the hydrologic component of WEHY-HCM to simulate the snow processes and hydrologic response to the atmospheric conditions. Following the simulation of both the atmospheric and land surface processes, the hourly time series results can be analyzed for a variety of characteristics across the hydro-climate system. Declarations ADDITIONAL INFORMATION The authors declare no competing interests. FUNDING DECLARATION This research was funded by the California Department of Water Resources (Agreement Number: 4600013419). Author Contribution All authors contributed to the conceptualization and methodology of the study. E.S. performed the formal analysis, investigation, visualization, and writing of the original manuscript. Y.I. assisted in the investigation. Y.I. and M.L.K. supervised. M.L.K. and M.A. procured and provided resources. All authors reviewed the manuscript. Data Availability Data sets generated during the current study are available from the corresponding author on reasonable request. References Report Card for American’s Infrastructure . infrastructurereportcard.org (2025). Clavet-Gaumont, J. et al. 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J. Hydrol. Eng. 18 , 1262–1271 (2013). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 24 Mar, 2026 Reviews received at journal 14 Mar, 2026 Reviewers agreed at journal 09 Mar, 2026 Reviewers agreed at journal 02 Feb, 2026 Reviews received at journal 21 Jan, 2026 Reviewers agreed at journal 23 Dec, 2025 Reviewers invited by journal 22 Oct, 2025 Editor invited by journal 15 Oct, 2025 Editor assigned by journal 29 Sep, 2025 Submission checks completed at journal 29 Sep, 2025 First submitted to journal 26 Sep, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7724680","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":538385746,"identity":"0cadab60-cbe7-4436-9502-b2b2be6e1aa6","order_by":0,"name":"Emily Snider","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAUlEQVRIiWNgGAWjYFCCBCBig/NsgJix8QCxWhgbGBjSwDRhLQwILYfBLLxa+NnTnz14UGaTzyCR/PzBxz3n7da2HwbaUmMTjUuLZM8bc4OEc2mWDRJpho0znt1O3nYmEajlWFpuAw4tBjdy2CQS2w4bMEgnGDbzHLidbHYAqIWx4TBOLfY30p8BtfwHakn/2PznwLlks/MP8WsxkEgwA2o5ANSSY9jMcOCAndkNArZInHljJpFwLtmATf5N4cyeA8kJZjeAtiTg8Qt/e/ozyR9ldgb8PMc3fPhxwM7e7Hz6wwcfamxwaoEDWAJIBKtMIKQcGdiTongUjIJRMApGBgAAMLtk+5pD/KwAAAAASUVORK5CYII=","orcid":"","institution":"University of California, Davis","correspondingAuthor":true,"prefix":"","firstName":"Emily","middleName":"","lastName":"Snider","suffix":""},{"id":538385749,"identity":"4f138b6d-5e0d-4d56-b95d-ca34391067da","order_by":1,"name":"Yoshihiko Iseri","email":"","orcid":"","institution":"University of California, Davis","correspondingAuthor":false,"prefix":"","firstName":"Yoshihiko","middleName":"","lastName":"Iseri","suffix":""},{"id":538385750,"identity":"ee6481d8-1267-499e-9bae-0a358e83ef5d","order_by":2,"name":"Michael L. 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10:18:18","extension":"jpg","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":228090,"visible":true,"origin":"","legend":"","description":"","filename":"Figure7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/3f7996eeabc72ba64e7093c3.jpg"},{"id":95010611,"identity":"a24e4acd-f416-48ec-be95-701e103569bf","added_by":"auto","created_at":"2025-11-03 10:18:18","extension":"jpg","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":207245,"visible":true,"origin":"","legend":"","description":"","filename":"Figure8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/d01c717631eabd1a0546981a.jpg"},{"id":95010618,"identity":"28cda6a0-2aa2-48f8-a431-2c275fb40d13","added_by":"auto","created_at":"2025-11-03 10:18:18","extension":"png","order_by":19,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":770163,"visible":true,"origin":"","legend":"","description":"","filename":"OnlineFigure1.png","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/673ada234ce9f7e531c23ab4.png"},{"id":95221633,"identity":"9a98d1a9-eb29-43b3-9d7b-6ae9941a8c26","added_by":"auto","created_at":"2025-11-05 16:19:30","extension":"png","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":155903,"visible":true,"origin":"","legend":"","description":"","filename":"OnlineFigure2.png","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/e33f0a4d075114ed29e60051.png"},{"id":95221512,"identity":"e0f67e9c-77d6-4c41-aaa6-ddbd917866ad","added_by":"auto","created_at":"2025-11-05 16:19:13","extension":"png","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":84949,"visible":true,"origin":"","legend":"","description":"","filename":"OnlineFigure3.png","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/7d4f019917c22691751b689a.png"},{"id":95010608,"identity":"61e08d75-0d67-413d-80a5-52ebe1e463a8","added_by":"auto","created_at":"2025-11-03 10:18:18","extension":"png","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":87185,"visible":true,"origin":"","legend":"","description":"","filename":"OnlineFigure4.png","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/af91955f94cbfef8b5125630.png"},{"id":95221106,"identity":"70ac4be5-af42-44c8-94c1-5aedbe58abc4","added_by":"auto","created_at":"2025-11-05 16:18:17","extension":"png","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":89320,"visible":true,"origin":"","legend":"","description":"","filename":"OnlineFigure5.png","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/b68f62dcd35795ce68851594.png"},{"id":95221413,"identity":"283b7b15-b96b-4ec4-9f9e-f2962c87cc25","added_by":"auto","created_at":"2025-11-05 16:18:57","extension":"png","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":88003,"visible":true,"origin":"","legend":"","description":"","filename":"OnlineFigure6.png","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/fcadfb26bdb8834c64f7a479.png"},{"id":95010615,"identity":"2a652dad-093e-43ea-b07d-0f1ac5bfb408","added_by":"auto","created_at":"2025-11-03 10:18:18","extension":"png","order_by":25,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":103816,"visible":true,"origin":"","legend":"","description":"","filename":"OnlineFigure7.png","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/3408f0a6e7f90f1c9c9705a2.png"},{"id":95010621,"identity":"1d38b507-8f29-40b4-b645-eeafa439b8c2","added_by":"auto","created_at":"2025-11-03 10:18:18","extension":"png","order_by":26,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":83087,"visible":true,"origin":"","legend":"","description":"","filename":"OnlineFigure8.png","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/6bb032c53ea2e1b87572c70e.png"},{"id":95010622,"identity":"40eb99aa-b05c-4249-a899-22db362c4ce2","added_by":"auto","created_at":"2025-11-03 10:18:18","extension":"xml","order_by":27,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":137340,"visible":true,"origin":"","legend":"","description":"","filename":"9c3073ccf9bf4565a8d1471bf36cbab01structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/107fbfb7b498bc1c23bbfe11.xml"},{"id":95010620,"identity":"fa21f7bd-d9ed-4e08-8d44-8f34fe618303","added_by":"auto","created_at":"2025-11-03 10:18:18","extension":"html","order_by":28,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":147371,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/10ea94a9ca6e5652d2bf9e01.html"},{"id":95010585,"identity":"2ebfdd37-f65a-4681-ae68-3ef3cfcc6068","added_by":"auto","created_at":"2025-11-03 10:18:17","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":579494,"visible":true,"origin":"","legend":"\u003cp\u003eThe location and elevation of the American River Watershed.\u003c/p\u003e","description":"","filename":"Figure1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/01d6f0611f84ee337b986d76.jpeg"},{"id":95221712,"identity":"05d007d3-ea00-4126-bc8a-83d7fee22833","added_by":"auto","created_at":"2025-11-05 16:19:36","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":393999,"visible":true,"origin":"","legend":"\u003cp\u003eTotal flood volume after ABCS and RHP-IVT for the a) 2017, b) 1997, c) 1986, d) 1965, e) 1909, and f) 1876 events. For each latitudinal shifting case, separate bar plots are presented for each of the meridional shifting cases. For each shifting combination, the bar plot is ordered by total flood volume at each RHP-IVT multiplier.\u003c/p\u003e","description":"","filename":"Figure2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/195344c89e980c3b9e889cbd.jpg"},{"id":95010590,"identity":"cca2e731-abef-4c05-97e8-0bc2321de4bf","added_by":"auto","created_at":"2025-11-03 10:18:18","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":206400,"visible":true,"origin":"","legend":"\u003cp\u003e2017 time series plots for the a) hourly precipitation, b) hourly SWE at two stations, c) hourly flow, and d) rolling 72-hr average flow and cumulative inflow volume. The solid lines represent the defined storm and flood periods. Dashed lines represent the full time series results. Results are also presented for the MP flood (0000n0100e 1.4) and MF flood (0500s0000e 1.0).\u003c/p\u003e","description":"","filename":"Figure3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/20b427681ccd25a895ea564e.jpg"},{"id":95010591,"identity":"ccf9ae2b-ac6a-4576-a87b-b2bbe75e0f5d","added_by":"auto","created_at":"2025-11-03 10:18:18","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":198695,"visible":true,"origin":"","legend":"\u003cp\u003e1997 time series plots for the a) hourly precipitation, b) hourly SWE at two stations, c) hourly flow, and d) rolling 72-hr average flow and cumulative inflow volume. The solid lines represent the defined storm and flood periods. Dashed lines represent the full time series results. Results are also presented for the MP flood (0490s0000e 1.6) and MF flood (0200s0100e 1.6).\u003c/p\u003e","description":"","filename":"Figure4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/185a7f199b52c70e19303248.jpg"},{"id":95010589,"identity":"489e75ee-e483-4e21-be75-750add6864df","added_by":"auto","created_at":"2025-11-03 10:18:18","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":202569,"visible":true,"origin":"","legend":"\u003cp\u003e1986 time series plots for the a) hourly precipitation, b) hourly SWE at two stations, c) hourly flow, and d) rolling 72-hr average flow and cumulative inflow volume. The solid lines represent the defined storm and flood periods. Dashed lines represent the full time series results. Results are also presented for the MP flood (0340s0100w 1.6) and MF flood (0100n0000e 1.6).\u003c/p\u003e","description":"","filename":"Figure5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/14c4d72475739c9dc76012d7.jpg"},{"id":95010598,"identity":"0a573a24-ec4a-450e-bed3-1abc43377f13","added_by":"auto","created_at":"2025-11-03 10:18:18","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":213464,"visible":true,"origin":"","legend":"\u003cp\u003e1965 time series plots for the a) hourly precipitation, b) hourly SWE at two stations, c) hourly flow, and d) rolling 72-hr average flow and cumulative inflow volume. The solid lines represent the defined storm and flood periods. Dashed lines represent the full time series results. Results are also presented for the MP flood (0500s0100w 1.6) and MF flood (0300s0100e 1.6).\u003c/p\u003e","description":"","filename":"Figure6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/50853da01a8f14c960298491.jpg"},{"id":95221048,"identity":"dfef4a0c-6850-4f73-a979-e2673ce70ef6","added_by":"auto","created_at":"2025-11-05 16:18:07","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":228090,"visible":true,"origin":"","legend":"\u003cp\u003e1909 time series plots for the a) hourly precipitation, b) hourly SWE at two stations, c) hourly flow, and d) rolling 72-hr average flow and cumulative inflow volume. The solid lines represent the defined storm and flood periods. Dashed lines represent the full time series results. Results are also presented for the MP flood (0500s0100e 1.6) and MF flood (0300s0100e 1.2).\u003c/p\u003e","description":"","filename":"Figure7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/8c5f7d2caf1e059d62e3f212.jpg"},{"id":95221262,"identity":"049f0ae2-23aa-47fc-a549-0ed48ed228fc","added_by":"auto","created_at":"2025-11-05 16:18:44","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":207245,"visible":true,"origin":"","legend":"\u003cp\u003e1876 time series plots for the a) hourly precipitation, b) hourly SWE at two stations, c) hourly flow, and d) rolling 72-hr average flow and cumulative inflow volume. The solid lines represent the defined storm and flood periods. Dashed lines represent the full time series results. Results are also presented for the MP flood (0230n0100e 1.6) and MF flood (0220n0100e 1.6).\u003c/p\u003e","description":"","filename":"Figure8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/300b54578eeb16c691e7cfec.jpg"},{"id":95312785,"identity":"64983f2a-c893-47b2-b1a4-59c1037c91e7","added_by":"auto","created_at":"2025-11-06 15:50:18","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3087635,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7724680/v1/151fc6cf-86cb-4c41-bbec-d5e663dba7a3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Maximizing Precipitation and Flood Estimation in the American River Watershed through a Total Storm Approach of Optimizing Historical Atmospheric Rivers","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eLarge scale water resources infrastructure, such as dams or levees, have a high-hazard potential given the consequences that would result to downstream communities should failure occur \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. By 2025 it is estimated that seven out of ten dams in the U.S. will be 50 years old and originally built and operated based on old standards and flood frequency analysis. Beyond regular maintenance and reassessment to reduce risk to downstream communities, climate change introduces further vulnerability and unknowns. It is possible there will be an increase in the frequency of extreme weather or increase in the probability of the design storm occurring\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. Existing risk assessments are based on historical data, leaving aging dams particularly vulnerable to the unknowns that climate change may bring. However, first defining and then determining how extreme flooding will change is difficult due to the complexity of the corresponding hydro-climate system, the nonlinearity and variability in both time and space, and the nonstationarity due to climate change\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. Furthermore, the potential of a quick succession precipitation events, building snowpack and antecedent soil moisture, can eventually result in extreme flooding beyond the precipitation totals of a single storm period\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. Thus, this study will present a physically based, total storm approach to produce a maximum flood estimate for six previously optimized historical atmospheric rivers in the American River Watershed.\u003c/p\u003e\u003cp\u003eThe American River Watershed (ARW) is in the Sierra Nevada Mountain range of Northern California, draining to Folsom Reservoir upstream of Sacramento (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Folsom reservoir has a total storage capacity of approximately 1\u0026nbsp;million AF, regulating the runoff from an area of approximately 5,000 km\u003csup\u003e2\u003c/sup\u003e. Elevation within the watershed ranges from 120 m near the reservoir to close to 3,000 m in the headwaters of the Sierra Nevada. Flooding will typically occur in the winter wet season, as precipitation and antecedent soil moisture build from the dry summer months, coinciding with precipitation events\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. Under certain circumstances, such as rain on snow (ROS) events, flooding beyond the magnitude of precipitation is possible when warm precipitation falls on a persistent snowpack. However, historically, almost all major flooding has occurred as a result of persistent or prolonged precipitation events, namely atmospheric rivers (ARs)\u003csup\u003e\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eARs are now classified as a type of extreme storm, emphasizing their importance for regional hydrology and the increased threat they pose should climate change enhance their occurrence and intensity\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. The significant water vapor transport and extreme winds associated with ARs can produce enhanced orographic precipitation depending on the landfall location and angle of impingement to the local topography\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan additionalcitationids=\"CR13 CR14 CR15\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. The characteristics of the ARs themselves, such as the intensity and duration of the storm system, are important in controlling the hydrologic response to the precipitation totals\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. However, the initial conditions across a watershed also influence if severe precipitation will result in downstream flooding at that watershed. The antecedent soil moisture and whether or not the soil is saturated is critical in determining if precipitation will infiltrate or directly generate runoff\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. Additionally, the temperature of the storm system and the existing snow cover across the watershed impact the hydrologic response to precipitation. Flooding can be significantly enhanced should warm rain fall on an already substantial snowpack, leading to extreme snowmelt or ROS events\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Likewise, should the air temperature lead to snow accumulation, potential flooding can be diminished despite large precipitation totals. The nonlinearity and complexity of the hydro-climate system makes estimating and preparing for exceedingly rare precipitation and flooding events difficult.\u003c/p\u003e\u003cp\u003eTo design a dam to be able to manage the risk of extreme flooding causing failure, traditionally, a flood frequency analysis (FFA) or a probable maximum flood (PMF) estimate is calculated for a particular watershed\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. PMF is commonly a theoretical 3-day flow estimate that poses a flood control threat for a given dam and often times is assumed to be a result of the probable maximum precipitation (PMP)\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. However, the assumptions within a traditional PMP estimate introduce substantial uncertainty, and recent studies have concluded that the PMF is not always caused by the PMP\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e,\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. Furthermore, it has been suggested that a single deterministic PMF value is not appropriate and should rather be an estimate that includes the uncertainty inherent in the methodology\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. Similarly, FFA calculates flow magnitudes for certain return periods by statistical methods fit to historical observation data based on the assumption that flows are independent and identically distributed variables that can be represented by a given probability distribution\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. This methodology is solely based on historical observation data and does not consider the physical processes that govern runoff generation, and thus, is highly dependent on not only the quality of the observation data but also the quantity\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. An extensive historical record is needed to estimate severe floods at a PMF level, with very low annual exceedance probability on the order of 0.001, or else it is necessary to extrapolate beyond the timeframe allowed by the historical record\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. Furthermore, FFA is based on the assumption of stationarity and supposes that the selected distribution does not change and is appropriate for representing all flood processes and return periods. In 1999 a 3-day flow discharge FFA for ARW was computed for on a Log-Pearson Type III distribution using log-space method of moments. It estimated a maximum 3-day average flow of 485,000 \u003cem\u003ecfs\u003c/em\u003e for ARW. However, this estimate does not directly account for long duration precipitation events, antecedent land conditions, or the physical dynamics of the hydrologic system. Furthermore, climate change introduces additional uncertainty as the underlying distribution governing flow may be altered.\u003c/p\u003e\u003cp\u003eIn terms of precipitation, climate change has been theorized to be intensifying extremes\u003csup\u003e\u003cspan additionalcitationids=\"CR28\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. However, uncertainty remains on how effects will manifest for precipitation variability and the annual mean totals\u003csup\u003e\u003cspan additionalcitationids=\"CR31\" citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. Furthermore, the effect on ARs, which are directly responsible for many historical floods at the subject watershed, is difficult to estimate at a watershed scale\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. Global circulation patterns may be altered in one way, however, the local dynamics controlling the precipitation generation may change in another. Thus, the complex nature of the atmospheric-land surface interactions must be considered together when estimating future hydrologic extremes. In terms of hydrologic impacts from climate change, extremes are also expected to intensify, as well as the occurrence of whiplash events\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. Within the Sierra Nevada, a warmer atmosphere is expected to raise snowlines and produce more rain than snow\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. This may lead to changes in peak runoff timing, April 1 snowpack, and the possibility of ROS events occurring\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan additionalcitationids=\"CR36 CR37\" citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. The unknowns that remain in the face of a changing climate and the intricacy of the system highlight the need to use physically based models in estimating hydrologic extremes as opposed to relying on purely statistical methodologies. The nonstationarity of the climate system brings further uncertainty to traditional FFA given that future extreme floods may exceed past FFA or that the fit distribution is no longer appropriate for the tails of the probability distribution where observations do not exist\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e,\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. As such, this study will employ three physically based models to produce a maximum flood (MF) estimate for six previously maximized historical atmospheric rivers. The models include the Weather Research and Forecasting (WRF) Model and snow and hydrologic components of the Watershed Environmental Hydrology Hydro-climate Model (WEHY-HCM). The historical ARs were maximized in terms of storm total precipitation to produce a maximum precipitation (MP) estimate through Atmospheric Boundary Condition Shifting (ABCS) and Relative Humidity Optimization (RHP-IVT)\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. Instead of limiting the estimate to a 3-day flow magnitude, the cumulative inflow volume over the entire flood duration will be the basis for evaluating the MF estimates. For reservoirs in snow dominated mountainous regions, such as Folsom Reservoir, long duration periods of increased flow and intense peak flows, driven by extreme precipitation potentially augmented by initial conditions across the watershed, can threaten both reservoir capacity and downstream communities and infrastructure. Producing a physically based estimate for potential worst case scenario flooding, independent of historical flow observations and including long duration events, can provide further data necessary to assess existing infrastructure against possible future flooding scenarios.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003eThe American River being a snow dominated watershed that outflows to a reservoir with a flood control function, in this watershed it is important to consider long duration events in addition to peak flows\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. The merged reconstruction and individual maximization WRF outputs for all six historical ARs and all ABCS and RHP-IVT combinations were input to the snow and hydrologic components of WEHY-HCM to produce inflow time series. Considering that PMP does not always result in PMF, it is necessary to simulate all maximization combinations when assessing a MF estimate. To then compare floods of different durations, it is necessary to establish a definition that is applied to the hourly flow results. Using the simulated hourly inflow time series to Folsom Reservoir of the reconstruction period (1852\u0026ndash;2020)\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e, 95% exceedance probability values were computed for the baseflow and the percentage increase by means of the empirical probability estimates of the Weibull formulas\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. The 95% exceedance value for the baseflow was computed to be 14,094\u003cem\u003ecfs\u003c/em\u003e. The 95% exceedance value for the percentage increase was computed to be 2.04%. As such, a flood starts when the hourly percentage increase is larger than 2.04% and the hourly flow is larger than 14,094\u003cem\u003ecfs\u003c/em\u003e. Subsequently, the flood ends when the hourly flow decreases beyond the flow value at the start of the flood. This combined definition allows only significant floods to be considered while not being too restrictive to capture both the rising and falling limbs of the hydrographs.\u003c/p\u003e\u003cp\u003eTo identify the individual ABCS and RHP-IVT combinations, a standard naming convention is used: YYYY ####(n/s)####(e/w) 1.#. YYYY represents the water year, ####(n/s) represents the degrees shifted North or South, ####(e/w) represents the degrees shifted East or West, and 1.# represents the RH multiplier. For example, the original 1997 event is named 1997 0000n0000e 1.0 to specify 0\u0026deg;N, 0\u0026deg;E shifting at an RH multiplier of 1.0. The 5\u0026deg;S, 1\u0026deg;E case at an RH multiplier of 1.5 is named 1997 0500s0100e 1.5.\u003c/p\u003e\u003cp\u003eFor each of the selected floods, the total flood volume, based on the above flood definition, is compared for all maximization combinations. Furthermore, the time series results for the historical case, the MP case, and MF case are compared for the hourly basin-averaged precipitation, hourly snow water equivalent (SWE) at two stations, and hourly flow, rolling 3-day average flow, and cumulative flow volume for inflow to Folsom Reservoir. The two SWE stations represent one high elevation station (LOS), where snow accumulation is larger and more persistent through the winter, and one mid-elevation station (GKS), where snow accumulation is heavily temperature dependent and more variable over the winter. By comparing the time series results for the precipitation, snow, and flow processes, the underlying mechanisms producing the flood can be recognized and analyzed.\u003c/p\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eWater Year 2017\u003c/h2\u003e\u003cp\u003eAs with the MP results seen in Snider et al. (2025), the historical 2017 flood event was not significantly changed by the maximization procedure in terms of total inflow volume (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea). The 0000n0000e 1.0 historical case produced a storm total volume of 1,817 \u003cem\u003eTAF\u003c/em\u003e while the MF case at 0500s0000e 1.0 produced a storm total volume of 1,997 \u003cem\u003eTAF\u003c/em\u003e for an increase of 9.9%. Both ABCS and RHP-IVT minimally changed the storm total volume compared to the historical flood. Additionally, the resulting order of total volume based RHP-IVT multiplier is variable across all shifting degrees.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eConsidering the time series of the precipitation, SWE, and flow for the historical, MP, and MF cases, the importance of the storm and flood definitions applied is apparent (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The MF case occurred for the 0500s0000e 1.0 while the maximum average 3-day flow and MP occurred for the 0000n0100e 1.4 case. The time period for the storm, based on a definition using a 10\u003cem\u003emm\u003c/em\u003e threshold for the rolling 3-day precipitation, is the early January rain bands through the 13th for the historical, MP, and MF maximization cases. However, the resulting maximized floods for each case occurred for the later period in February, where the longer duration of increased flows ultimately resulted in larger cumulative inflow volumes. Though the January floods saw larger 3-day peak flows for the historical and MP case, the MF was significantly diminished. The historical 3-day peak flow was 120,110 \u003cem\u003ecfs\u003c/em\u003e and the maximized 3-day peak flow was 157,555 \u003cem\u003ecfs\u003c/em\u003e during the January flood. The MF in February had a 3-day peak flow of 100,921 \u003cem\u003ecfs\u003c/em\u003e. Despite lower peak flows in the earlier flood period, the MF ultimately had a greater cumulative volume compared to all other shifting combinations during the entire time period. Considering the lower elevation snow cover, the MF case increased SWE through the January storm period, likely due to cooler temperatures as a result of south shifting, whereas the historical and MP cases decreased, corresponding to the largest hourly and 3-day peaks. During the maximized flood period, the MF case begins slightly earlier and has slightly larger hourly peak flows compared to the historical and MP case, resulting in larger cumulative volumes. These results further support previous analysis that the MF does not always result from the MP. Furthermore, it is not a valid assumption that the MF will be a direct result of the largest precipitation volume, depending on other watershed conditions such as the existing snow cover and temperature.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eWater Year 1997\u003c/h3\u003e\n\u003cp\u003eFor the 1997 event, the largest difference from the historical case occurred for a combination of moisture increases and south shifting. The biggest increase in cumulative volume occurred for the 1.2 multiplier but further moisture increases also increased the cumulative volume. The MF was produced by the 0200s0100e 1.6 case though cumulative volume results were similar for 0300s0100e 1.6 and 0400s0000e 1.6 (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb). The historical case at 0000n0000e 1.0 produced a cumulative volume of 1,656 \u003cem\u003eTAF\u003c/em\u003e while the maximized case produced a cumulative volume of 2,977 \u003cem\u003eTAF\u003c/em\u003e for a 79.7% increase.\u003c/p\u003e\u003cp\u003eFor the time series comparisons, the earlier and intensified precipitation in the MP and MF cases resulted in a series of early flow peaks prior to the significantly increased peak flow compared to the original flood (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). The MF and the maximum 3-day rolling average flow were both a result of the 0200s0100e 1.6 case while the MP case was produced by further south shifting at 0490s0000e 1.6. The historical case had a 3-day peak flow of 177,848 \u003cem\u003ecfs\u003c/em\u003e while the MF and maximum 3-day peak saw 270,036 cfs. At both elevation stations, the SWE during the historical flood slightly grew or was maintained through the three initial rain bands before melting occurred during the most intense portion of the precipitation event leading to the peak hourly flow. During the MP and MF cases and at both elevation stations, SWE accumulated at similar rates during the first two rain bands. By the third rain band, however, SWE at the GKS station began to exhibit melting while SWE at the LOS station continued to accumulate. The MF SWE at the GKS station melted at a faster rate until it was depleted compared to the MP case which eventually leveled out following the most intense period of precipitation. This is likely due to the further south shifting of the MP case, as cooler temperatures limited mid-elevation melting. At the LOS station, the SWE for the MF case initially began to melt, as precipitation further intensified, before again accumulating as the precipitation decreased. The differences between the MP and MF precipitation and resulting SWE processes resulted in the MF having higher hourly peak flows and 3-day average flows compared to the MP. The MF hourly peak flow coincides with the slight melt at the LOS station and the last remaining GKS snowpack. Compared to the historical case, the MF begins six days earlier and is significantly intensified. The resulting peak hourly flow and cumulative volume are nearly doubled from the historical case to the MF case.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\n\u003ch3\u003eWater Year 1986\u003c/h3\u003e\n\u003cp\u003eFor the 1986 event, the MF result is primarily due to moisture amplification rather than shifting (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec). The MF was produced by the 0100n000e 1.6 case with a cumulative volume of 2,880 \u003cem\u003eTAF\u003c/em\u003e compared to the historical case with a cumulative volume of 2,049 \u003cem\u003eTAF\u003c/em\u003e for a 40.5% increase. Considering shifting alone, as was the case with the precipitation maximization, north shifting reduced the cumulative volume compared to the original 0000n0000e 1.0 case. As with the 1997 event, the biggest increase from moisture maximization occurred for the 1.2 multiplier. Larger multipliers resulted in variable increases beyond the 1.2 multiplier depending on the shifting degree.\u003c/p\u003e\u003cp\u003eThe MF is primarily a result of moisture maximization and as such, time series results are similar compared to the historical case for both atmospheric and land surface processes though significantly amplified (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). The MF at 0100n0000e 1.6 is significantly different compared to the MP case at 0340s0100w 1.6. The maximum 3-day rolling average flow occurred for the 0000n0100e 1.6 case. Though not shown, the hourly results of the two cases were very similar, particularly for the maximum 3-day peak. Considering the maximum average 3-day peak flow, the historical case peaked at 173,514 \u003cem\u003ecfs\u003c/em\u003e, the MF peaked at 250,068 \u003cem\u003ecfs\u003c/em\u003e, and the maximum average 3-day flow peaked at 252,400 \u003cem\u003ecfs\u003c/em\u003e. The less intense but extended storm period of the MP case is also seen in the resulting flow. The south shifting brought cooler temperatures resulting in additional snow accumulation at the high elevation station and sustained snowpack at the mid-elevation station. The peak flows are dampened below the historical case, but the additional rain band increased the cumulative volume beyond that of the historical case, though below the MF case. The timing of the precipitation associated with the MF follows that of the historical case with an intensified magnitude, as expected due to the additional moisture primarily brought with RHP-IVT. At the LOS station, SWE accumulation between the MF and historical cases are nearly identical. However, at the GKS station, the SWE for the MF case begins to decline with the second rain band whereas the historical case increases slightly before melting to a similar magnitude as prior to the storm. The additional melt, combined with the increased precipitation, contributes to significantly larger hourly flow, hourly peaks, and average 3-day peak flow compared to the historical case. Though the magnitude of the hydrograph is amplified by the maximization procedure, the timing and shape are similar between the MF case and historical case.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\n\u003ch3\u003eWater Year 1965\u003c/h3\u003e\n\u003cp\u003eThe 1965 event was produced by a combination of shifting and moisture maximization (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed). The historical case at 0000n0000e 1.0 produced a cumulative inflow volume of 2,046 \u003cem\u003eTAF\u003c/em\u003e while the MF was produced by the 0300s0100e 1.6 case with a cumulative inflow volume of 2,945 \u003cem\u003eTAF\u003c/em\u003e for a 43.9% increase. Considering shifting alone, the resulting cumulative inflow volume greatly depended on the shifting direction. Shifting to the south alone did not considerably increase the total volume. Shifting to the north, however, significantly reduced the total inflow volume, consistent with the precipitation maximization results for the 1965 event \u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. Southward shifting combined with amplified moisture ultimately increased the cumulative inflow volume beyond that of the historical case to produce the MF for the 0300s0100e 1.6 case. The case at 0500s0100w 1.6, which is the MP and 3-day average peak flow case, produced a total inflow volume comparable to the MF, though slightly smaller.\u003c/p\u003e\u003cp\u003eThe time series results again highlight that slight differences between the maximization cases can impact the conclusions that are ultimately drawn and the importance of the thresholds used to define a flood period. The MF case, at 0300s0100e 1.6, and the MP and maximum 3-day peak flow cases, at 0500s0100w 1.6, have similar cumulative inflow volumes despite their differences in hourly flow and average 3-day flow (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). The 3-day peak flow for the historical case was 168,403 \u003cem\u003ecfs\u003c/em\u003e while the MF case was 290,182 \u003cem\u003ecfs\u003c/em\u003e and the MP and maximum 3-day peak cases was 312,810 \u003cem\u003ecfs\u003c/em\u003e. Prior to the flood event starting, the MP case had a greater snowpack at both elevations compared to the MF case and historical case. The MP and MF cases exhibit similar precipitation patterns, both amplified compared to the historical case, for the first four days of the storm period. Similarly, the rate of snow accumulation and melting is similar between the two cases through December 23\u003csup\u003erd,\u003c/sup\u003e even if the MP case has a greater depth. Following that, the increased precipitation of the MP case results in larger hourly flow producing the peak hourly flow and peak 3-day flow. The cumulative flow volume is greater for the MP case through the 28th, however, following that the high and mid-elevation snow accumulation slows for the MF case compared to the MP, resulting in larger, sustained hourly flows that eventually increase the cumulative inflow volume of the MF case above that of the MP case. Compared to the historical case, the MF begins about one day earlier and is about six days shorter due to the flood definition that was applied to the time series. Additionally, the definition and variable being maximized impact the resulting MF case. If the hourly peak flow or the maximum 3-day peak flow was the attribute of interest, the 0500s0100w 1.6 case would be considered the maximum flood. However, because the total cumulative volume of the entire flood period is of interest for this study, the 0300s0100e 1.6 case is considered the MF. Depending on flood control systems, the analysis of worst-case scenario flooding should focus on the hazardous condition that threatens the infrastructure, whether that be a peak flow or inflow volume. However, risk analysis considering both a traditional 3-day PMF and a long duration cumulative inflow-based MF can provide a comprehensive picture of how a reservoir may be operated under different conditions.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\n\u003ch3\u003eWater Year 1909\u003c/h3\u003e\n\u003cp\u003eThe 1909 flood maximization results again follow the precipitation results in terms of shifting alone, though there is added variability depending on the moisture maximization multiplication factor that is applied (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee). The original case at 0000n0000e 1.0 produced a cumulative volume 919 \u003cem\u003eTAF\u003c/em\u003e. The MF case at 0300s0100e 1.2 produced a cumulative volume of 3,554 \u003cem\u003eTAF\u003c/em\u003e for a percentage increase of 286.7%. The simultaneous application of ABCS and RHP-IVT produced different cumulative volume results depending on the direction of shifting. Shifting to the north alone for the most part reduced the cumulative volume. However, the decreases in volume were made up for as the moisture multiplication factor increased. The largest increase occurred for the 1.2 multiplication factor with further increases in moisture producing diminishing increases. On the other hand, shifting to the south alone increased the cumulative volume. Further moisture increases did produce additional inflow volume, though not to the degree exhibited by shifting to the north. In all shifting cases, there was more variability in cumulative volume across the multiplication factors. Further moisture increases did not necessarily increase total volume, and the MF case was produced by only a 20% increase in moisture.\u003c/p\u003e\u003cp\u003eThe role of duration in producing significant cumulative volumes is apparent in the time series results of the 1909 event (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e). The precipitation events have numerous rainbands and periods of increased intensity lasting nearly two months and resulting in sustained increased hourly flow throughout the period. Of note, however, is that the peak hourly flow and baseflow of the defined flood is considerably smaller compared to the maximization results of the other years analyzed. The historical case at 0000n0000e 1.0 produced a 3-day peak flow of 36,226 \u003cem\u003ecfs\u003c/em\u003e. Though not shown here, the maximum 3-day peak flow case occurred for the 0400n0100e 1.6 case at 103,951 \u003cem\u003ecfs\u003c/em\u003e. The hourly flow time series follows that of the original flood, though amplified for the period from January 14 lasting through January 29. The MF at 0300s0100e 1.2 produced a 3-day peak flow of 84,034 \u003cem\u003ecfs\u003c/em\u003e while the MP case produced a 3-day peak flow of 86,814 \u003cem\u003ecfs\u003c/em\u003e. At both elevations for all three cases, the SWE accumulates for the entire storm period at similar rates despite the different magnitudes. No melting is occurring across the watershed for all three cases, suggesting the resulting flow is primarily a result of the liquid precipitation. The two primary peak hourly flows around January 6 and January 22 are slightly larger for the MP case, however, the increased flow around January 12 for the MF case, combined with the longer duration compared to the MP and historical cases, result in a larger cumulative volume. This case is another example of the flood definition being an important factor in the results. The hourly flow of the historical case maintains an increased period of flow beyond that of the defined flood period. However, because the flow dips below the starting value when the flood begins based on the defined threshold values, it is not considered to be the same flood. The cumulative volume of the MF case and historical cases for the same period of time from December 24 through February 15 are 3,595 \u003cem\u003eTAF\u003c/em\u003e and 1,654 \u003cem\u003eTAF\u003c/em\u003e, respectively. The resulting percentage increase is thus decreased to 117%. Using a strict threshold to define a flood period allows events of different durations to be compared, however, the sensitivity of the hourly data to the threshold values can be restrictive if the data fluctuates around the beginning flood period value.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003eWater Year 1876\u003c/h2\u003e\u003cp\u003eThe 1876 volume maximization results again follow that of the precipitation maximization in terms of the increases due to the simultaneous application of ABCS and RHP-IVT methodologies (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ef)\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. The original case at 0000n0000e 1.0 had a cumulative volume of 1,792 \u003cem\u003eTAF\u003c/em\u003e. The MF occurred for the 0220n0100e 1.6 case with a cumulative volume of 5,107 \u003cem\u003eTAF\u003c/em\u003e for a percentage increase of 184.9%. The moisture amplification through RHP-IVT increased the resulting cumulative volume substantially more than northward shifting alone. As was seen in other years analyzed, the largest increase occurred for the 1.2 multiplier. However, in this case, the 1.4 multiplier also substantially increased the resulting cumulative volume for all northward shifting combinations. The 1.5 and 1.6 multipliers further increase the cumulative volume, though to a lesser extent than the 1.2 and 1.4 multipliers. Of the results across all years analyzed, the 1876 MF case produces the largest cumulative volumes during the flood period.\u003c/p\u003e\u003cp\u003eThe intensified precipitation due to RHP-IVT is apparent in the flow results as well for the 1876 event (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e). The MF, MP, and maximum 3-day peak flow cases occur for 0210n0100e 1.6, 0230n0100e 1.6, and 0220n0100e 1.6, respectively. The time series for each case is nearly identical given the only difference between the three cases is 0.1\u0026deg;N shifting. The peak 3-day flow was originally 108,108 \u003cem\u003ecfs\u003c/em\u003e while the MF peaked at 291,233 \u003cem\u003ecfs\u003c/em\u003e and the maximum 3-day flow peak occurred at 293,478 \u003cem\u003ecfs\u003c/em\u003e. At the high elevation station, SWE accumulated substantially for both the MF and historical cases. At the mid-elevation station, melting occurred at the start of the defined flood for the MF case. For the historical case, however, SWE initially accumulated or was maintained until the most intense period of precipitation when melting began around December 30, 1875. The hourly inflow time series of the MF case contain multiple peaks following the rainbands and period of intense precipitation. The depletion of the mid-elevation snowpack in the MF case likely saturated the watershed at the start of the storm period leading to more runoff throughout the flood following the precipitation patterns. The historical case, by comparison, does not substantially peak until the mid-elevation melting begins, coinciding with the last rainband. The original flood began after the MF case, likely due to SWE accumulation across the watershed, limiting runoff compared to the melting that occurred for the MF case. The importance of snow processes is again apparent, highlighting the necessity of physically based models to simulate the interactions between the land surface and atmosphere.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eComparison among floods of different durations is not as clear as the standard 3-day PMF estimates. Details for all six flood events maximized are provided in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e for comparison between the historical case, MF case, and maximum 3-day average flow case. If the total flood volume alone is considered, then the 1876 event would be the largest of the analysis presented at 5,107 \u003cem\u003eTAF\u003c/em\u003e. However, that characteristic by itself does not give any indication as to the severity of the event if neither the duration nor peak flows are included. Another method of comparison is by a percentage increase from the historical cumulative volume to the MF cumulative volume. By this standard, the 1909 event has the largest percentage increase at 286.7%. However, as we described previously, this result is highly dependent on the flood definition thresholds applied to the time series. If the longer historical flood period was instead compared to the MF, the percentage increase would only be 117% and thus the 1876 event would then be the largest increase from the original flood at 185%. Again, this characteristic alone does not include any indication of the severity of the MF result for the individual events and only describes to what degree the historical flood was increased.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparison of the six maximized flood events (in bold) compared to the historical case and maximum average 3-day flow case\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e\u003cp\u003eCase\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eVolume\u003c/p\u003e\u003cp\u003e(TAF)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003ePeak 3-day flow\u003c/p\u003e\u003cp\u003e(cfs)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eDuration\u003c/p\u003e\u003cp\u003e(hrs)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003e% Increase\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eIntensity (TAF/hr)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003e2017\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eOriginal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0000n0000e 10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1,817\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e120,110\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e520\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e3.5\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eMF\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e0500s0000e 10\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e1,997\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e100,921\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e592\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e9.9\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e3.4\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3day Max\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0000n0100e 14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e157,555\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003e1997\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eOriginal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0000n0000e 10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1,656\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e177,848\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e318\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e5.2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eMF \u0026amp;\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003e3day Max\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e0200s0100e 16\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e2,977\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e270,036\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e394\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e79.7\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e7.6\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003e1986\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eOriginal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0000n0000e 10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2,049\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e173,514\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e378\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e5.4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eMF\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e0100n0000e 16\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e2,880\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e250,068\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e384\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e40.5\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e7.5\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3day Max\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0000n0100e 16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e252,400\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003e1965\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eOriginal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0000n0000e 10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2,046\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e168,403\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e439\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e4.7\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eMF\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e0300s0100e 16\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e2,945\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e290,182\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e329\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e43.9\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e8.9\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3day Max\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0500s0100w 16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e312,810\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003e1909\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eOriginal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0000n0000e 10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e919\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e36,226\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e457\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2.0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eMF\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e0300s0100e 12\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e3,554\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e84,034\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e1,126\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e286.7\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e3.2\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3day Max\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0400n0100e 16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e103,951\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003e1876\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eOriginal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0000n0000e 10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1,792\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e108,108\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e534\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e3.4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eMF\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cb\u003e0220n0100e 16\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cb\u003e5,107\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u003cb\u003e291,233\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cb\u003e589\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cb\u003e184.9\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e8.7\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e3day Max\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0210n0100e 16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e293,478\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e-\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eAn additional method of comparison can be done for the flood intensity. By computing the average inflow volume per hour of the flood period, the duration of the event can be combined with the cumulative volume to provide an indication of the severity of the flooding. For the 2017 event the intensity of the flooding was decreased by the maximization procedure from 3.5 \u003cem\u003eTAF/hr\u003c/em\u003e to 3.4 \u003cem\u003eTAF/hr\u003c/em\u003e as the duration increased with minimal increases to the cumulative volume. The 1997 event increased from an intensity of 5.2 \u003cem\u003eTAF/hr\u003c/em\u003e to 7.6 \u003cem\u003eTAF/hr\u003c/em\u003e. Similarly, the 1986 event increased from an original intensity of 5.4 \u003cem\u003eTAF/hr\u003c/em\u003e to 7.5 \u003cem\u003eTAF/hr\u003c/em\u003e. The 1965 event had the largest maximized intensity of 8.9 \u003cem\u003eTAF/hr\u003c/em\u003e compared to the original case at 4.7 \u003cem\u003eTAF/hr\u003c/em\u003e. On the other hand, 1909 had the smallest intensity of events analyzed at 3.2 \u003cem\u003eTAF/hr\u003c/em\u003e. Over 2,600 \u003cem\u003eTAF\u003c/em\u003e were added by the maximization process, however the duration increased by nearly 28 days. This result further emphasizes that duration needs to be explicitly included when comparing floods of different lengths. Finally, the 1876 event increased from an original intensity of 3.4 \u003cem\u003eTAF/hr\u003c/em\u003e to 8.7 \u003cem\u003eTAF/hr\u003c/em\u003e. Comparing the two largest MF intensities, the 1965 and 1876 events are similar. While the two events have comparable peak 3-day flows, the cumulative volume and percentage increase are much larger for the 1876 event compared to the 1965 event. While these results can provide further insight into potential extreme events, results should be compared to a more traditional FFA to assess a potential exceedance probability.\u003c/p\u003e\u003cp\u003eTo select a single design flood based on the total storm approach, the variable being maximized influences the resulting conclusions that are drawn. If the peak 3-day average flow was the primary maximization objective, the MF would be a different case for nearly all of the events. Though most are of similar magnitude between the cumulative volume MF and the maximum 3-day peak, 2017 and 1965 would instead correspond to the MP case. While the 3-day peak simplifies comparisons between different events, it alone does not provide any indication of the long-term effects and subsequent consequences from sustained high reservoir releases required to contain long-duration events. Of note, for the cumulative volume MF results, none of the MF cases correspond to the MP case, even if results were similar between the two cases such as with 1876, further supporting previous findings that the MP is not solely responsible for the MF.\u003c/p\u003e\u003cp\u003eBeyond selecting a single MF, the physical processes that contribute to enhanced flooding beyond precipitation totals can be assessed. Of the events analyzed here, the consequences of antecedent land conditions, particularly snow cover, and atmospheric temperatures are evident. At the beginning of the storm period, the 2017 event had relatively little snowpack compared to the reconstruction period. However, as the storm systems progressed, snow accumulated at both elevations and across the watershed. While the slight melt of the mid-elevation snowpack likely contributed to the MF peak flow, the accumulated snow would be important for maintaining high spring and summer streamflow\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. Similarly, in 1909, snow accumulation occurred constantly throughout the storm period at both elevations. The resulting flood was then primarily precipitation driven which is reflected in the lower magnitude hourly flow and lesser peak flows compared to the other events analyzed. Again, for the 1876 event, the fact that the storm occurred early in the water year, before any significant snow had accumulated, means that the flood was primarily driven by direct precipitation runoff. At the mid-elevation station, snow initially accumulated, however, by the second rainband it began melting until depleted. At the high elevation station, snow accumulated throughout the storm period, adding nearly 2\u003cem\u003em\u003c/em\u003e of SWE. On the other hand, in the MF for 1997, the initial snow accumulation across the watershed eventually led to later melting, driving the peak flow and coinciding with the most intense period of precipitation. The increased precipitation was compounded by the complete melting at the mid-elevation after it had first accumulated to nearly half a meter at the GKS station. Likewise, in 1965, snow accumulated across the watershed at the start of the storm period. The mid-elevation melt, coinciding with the peak precipitation, immediately led to the peak flow, suggesting the watershed was previously saturated. As the storm progressed and snow again accumulated across the watershed, the hydrograph continued to recede despite further rain bands bringing additional precipitation. Finally, in 1986, the steady melt of the mid-elevation snowpack steadily increased the flow corresponding to the precipitation. The depletion of the mid-elevation snowpack with the most intense period of precipitation contributed to the significantly increased peak flow. The complex processes between the atmosphere and land surface must be explicitly modeled to fully understand the hydrologic response to extreme precipitation. By using physically based atmospheric and land surface numerical models, the interactions guiding the snow and hydrologic processes are directly accounted for in the resulting time series data.\u003c/p\u003e\u003cp\u003eIn conclusion, the physically based optimization of historical ARs to maximize the resulting cumulative inflow volume allows characteristics of the entire storm system to be reflected in the MF estimates that are produced. Furthermore, as these are physically based estimates, independent of historical data, the assumed rarity of these events does not influence the resulting estimate by requiring an extrapolation of a probability distribution fit to historical observations. However, to assess the risk of these long duration, storm total MF estimates, more historical ARs should be maximized to create a larger sample size to assess. As was seen in the results, the MF does not necessarily result from either the MP or the most extreme shifting case. The MF for each event may be primarily a result of moisture maximization, requiring minimal shifting. In terms of climate change, this alone increases the risk of these extreme floods occurring as a warmer atmosphere can hold more water, comparable to only applying RHP-IVT to historical ARs. The possibility of compound flooding resulting from ROS events may also increase if warm winter storms occur when the snowpack has already accumulated, amplifying the flooding beyond the precipitation totals alone. The storm total approach to estimate the worst-case scenario flooding through physically based models allows the entire hydro-climate system to be considered. The time series results for each event analyzed here can be further studied to assess their individual risk to Folsom Reservoir in terms of both amplified 3-day peak flows and sustained periods of high inflow beyond what has been observed historically.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cp\u003eThe heterogeneous, mountainous characteristics of ARW require fine scale numerical modeling to resolve the complex atmospheric-land surface interactions that control the snow and hydrological processes that generate runoff within a watershed\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e,\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e,\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e. Within ARW precipitation is stored in the snowpack and estimated to contribute between 50\u0026ndash;80% of spring and summer flows, and thus flood estimation must directly account for the role of snowmelt in contributing to increased flows\u003csup\u003e\u003cspan additionalcitationids=\"CR48\" citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e. As such, three physically based models are used to first dynamically downscale global reanalysis data and then simulate the snow and hydrological processes. The models include the Weather Research and Forecasting (WRF) Model and the Watershed Environmental Hydrology Hydro-Climate Model (WEHY-HCM) land surface, snow and hydrologic components. All three models were previously calibrated and validated for ARW specifically, and atmospheric and hydrologic conditions reconstructed from 1852\u0026ndash;2020 with results were presented in Snider et al. (2024). The period of reconstruction is the basis for the historical period and is used to assess the maximization results.\u003c/p\u003e\u003cp\u003ePreviously, six historical AR events were selected and maximized by means of Atmospheric Boundary Condition Shifting (ABCS) and Relative Humidity Optimization (RHP-IVT) through the WRF model to produce a maximum precipitation (MP) estimate\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. A brief overview of the MP estimate methodology is presented here. However, further details regarding the methodology, results for all maximization cases, and discussion are presented in Snider et al. (2025). Input atmospheric reanalysis data to WRF depends on the year being simulated and includes one of three datasets: the Twentieth Century Global Reanalysis Version 2c (20CRv2c), The European Center for Medium-Range Weather Forecasts twentieth century reanalysis (ERA20C), or the Climate Forecast System Reanalysis (CFSR). WRF maximization simulations were performed for the entire storm period, defined by a rolling 72-hr precipitation threshold of 10mm. ABCS was performed from 5\u0026deg;N to 5\u0026deg;E and 1\u0026deg;W to 1\u0026deg;E at 1\u0026deg; increments. RHP-IVT was simultaneously performed for multipliers of 1.0, 1.2, 1.4, 1.5, and 1.6. Further refinement at 0.1\u0026deg; shifting increments were performed between the top two shifting combinations at the given RHP-IVT multiplier. This process was performed individually for each of the six selected historical ARs in 2017, 1997, 1986, 1965, 1909, and 1876. These selected ARs represent a mix of important historical floods and events that may have had the potential to be intensified by the maximization methodology. To then assess the hydrologic response to each of the maximization combinations of each historical AR, the maximization outputs from WRF were combined into the longer water year reconstruction time series that were computed by Snider et al. (2024) and input to the WEHY-HCM SNOW Module to further refine the atmosphere-land surface interactions.\u003c/p\u003e\u003cp\u003eThe SNOW Module of WEHY-HCM is a physically-based, energy budget model that uses atmospheric and land data to numerically solve the conservation of mass and energy equations between the snowpack and surrounding environment\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e. The energy budget is solved by computing the solar angle and incoming solar radiation based on digital elevation maps (DEMs) at every node in the grid network. This allows the effects from topography and elevation to be incorporated into the snow process computations at a resolution of 100m. Furthermore, at every node in the grid network, the snowpack is divided into three layers to ultimately simulate the nonuniform vertical temperature profile of the snowpack. In the top, skin layer of the snowpack atmospheric forcings are incorporated to dictate the deeper snowpack temperature profile. Below that is the active layer, where a linear temperature profile is assumed above the evolving freezing depth. Finally, at the deepest portion of the snowpack below the evolving freezing depth, the temperature is assumed to be isothermal at 0\u0026deg;C and disconnected from any atmospheric interactions. Across the domain, those point scale processes are then vertically integrated over the snowpack depth and numerically upscaled, producing a spatially distributed model of snow processes that contain both atmospheric forcings and solar geometry. Ultimately, this module can account for the spatial heterogeneity of snow accumulation and melting processes at a resolution fine enough to resolve the atmospheric mechanisms driving the hydrologic response.\u003c/p\u003e\u003cp\u003eThe final model used is the hydrologic component of WEHY-HCM\u003csup\u003e\u003cspan additionalcitationids=\"CR51 CR52\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e. As a physically-based hydrology model, flow processes are computed for various processes and at different temporal and spatial scales by numerically solving upscaled versions of the conservation of mass, momentum, and energy equations. To account for the atmosphere-land surface interactions, the dynamic exchanges within the boundary layer are coupled through hillslope scale averaged fluxes. The target watershed is delineated into model computation units (MCUs) where land parameters are assumed to be spatially stationary across the individual MCUs. At each MCU the point-scale surface and subsurface processes are computed by using the unsaturated flow to link the overland flow, subsurface flow, and groundwater flow domains. Those point-scale conservation equations are then upscaled to the computational grid scale by ensemble averaging, which are then numerically solved. The unsteady, nonuniform flow discharge at each MCU is then routed through the delineated stream network by means of the channel flow domain to the watershed outlet point.\u003c/p\u003e\u003cp\u003eThe physical land characteristic inputs are the same between the snow and hydrologic components of WEHY-HCM. DEM data is provided by the USGS National Elevation Dataset. Land use and land cover (LULC) data is provided by the California Department of Forestry and Fire Protection. Geomorphological and soil data are provided by the US Department of Agriculture\u0026rsquo;s Web Soil Survey. Using DEM data, the basin is delineated for a specific outlet point. In the case of ARW, the outlet of Folsom Reservoir is selected and a total of 54 MCUs and 17 stream reaches are selected for the delineation (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Additionally, the LULC, geomorphological, and soil data are delineated to coincide with the DEM delineation. Using these fine resolution physical attributes of the watershed allows the heterogeneity of all grid points in the domain to be accounted for. Following the delineation of the land characteristics, the WRF outputs are input to the SNOW Module. Outputs from the SNOW Module are then input to the hydrologic component of WEHY-HCM to simulate the snow processes and hydrologic response to the atmospheric conditions. Following the simulation of both the atmospheric and land surface processes, the hourly time series results can be analyzed for a variety of characteristics across the hydro-climate system.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eADDITIONAL INFORMATION\u003c/h2\u003e\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eFUNDING\u003c/h2\u003e\u003cp\u003eDECLARATION\u003c/p\u003e\u003cp\u003eThis research was funded by the California Department of Water Resources (Agreement Number: 4600013419).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAll authors contributed to the conceptualization and methodology of the study. E.S. performed the formal analysis, investigation, visualization, and writing of the original manuscript. Y.I. assisted in the investigation. Y.I. and M.L.K. supervised. M.L.K. and M.A. procured and provided resources. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eData sets generated during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003e\u003cem\u003eReport Card for American\u0026rsquo;s Infrastructure\u003c/em\u003e. infrastructurereportcard.org (2025).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eClavet-Gaumont, J. et al. Probable maximum flood in a changing climate: An overview for Canadian basins. \u003cem\u003eJ. Hydrol. Reg. Stud.\u003c/em\u003e \u003cb\u003e13\u003c/b\u003e, 11\u0026ndash;25 (2017).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKuo, C. C. \u0026amp; Gan, T. Y. Risk of Exceeding Extreme Design Storm Events under Possible Impact of Climate Change. \u003cem\u003eJ. Hydrol. 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Eng.\u003c/em\u003e \u003cb\u003e18\u003c/b\u003e, 1262\u0026ndash;1271 (2013).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Probable Maximum Precipitation, Probable Maximum Flood, Atmospheric River Optimization, Storm Duration, Extreme Flooding","lastPublishedDoi":"10.21203/rs.3.rs-7724680/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7724680/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eExtreme precipitation and flooding pose significant risk to flood control systems and existing infrastructure. Historically, probable maximum precipitation and probable maximum flood estimates have been estimated based on 3-day peaks to assess a reservoir\u0026rsquo;s ability to contain worst-case scenario flooding. However, this methodology does not account for the risk from long-duration events that contain both intense flow peaks and sustained periods of high inflow. As such, a physically based methodology is presented to produce a maximum flood estimate for six historical atmospheric rivers in the American River Watershed, draining to Folsom Reservoir near Sacramento, California. The results are compared for the maximum precipitation, maximum flood, and historical conditions to assess the underlying mechanisms that contribute to extreme flooding. The importance of the interactions between the atmosphere and land surface are highlighted, particularly the role that temperature and snow processes contribute to amplifying flooding beyond the precipitation totals alone. By using physically based numerical models to estimate extreme flooding, the resulting estimates are not based on extrapolating a probability distribution fit to historical observations and instead directly simulate the hydro-climate interactions that control the hydrologic response to intense precipitation. The time series results can provide further insight into potential extreme flooding that may increase in frequency with climate change.\u003c/p\u003e","manuscriptTitle":"Maximizing Precipitation and Flood Estimation in the American River Watershed through a Total Storm Approach of Optimizing Historical Atmospheric Rivers","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-03 10:18:13","doi":"10.21203/rs.3.rs-7724680/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-24T04:52:39+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-14T04:28:36+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"299654990438745602006167451247326074273","date":"2026-03-09T21:18:11+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"196320524940334372158308522384930197189","date":"2026-02-03T00:11:01+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-21T11:05:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"144536842719152045960987391465543908245","date":"2025-12-23T17:28:33+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-22T08:51:09+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-10-15T10:16:47+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-29T08:57:43+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-29T04:02:08+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-09-26T20:28:25+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"eb0fe129-bf39-463f-a8fb-dc4fa05234cd","owner":[],"postedDate":"November 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[{"id":57265528,"name":"Earth and environmental sciences/Climate sciences"},{"id":57265529,"name":"Earth and environmental sciences/Hydrology"},{"id":57265530,"name":"Earth and environmental sciences/Natural hazards"},{"id":57265531,"name":"Scientific community and society/Water resources"}],"tags":[],"updatedAt":"2026-03-24T05:08:07+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-03 10:18:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7724680","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7724680","identity":"rs-7724680","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}