Supplemental Material Understanding Flood Seasonality and Its Temporal Shifts within the Contiguous United States

Supplemental Material: Understanding Flood Seasonality and Its Temporal Shifts within the Contiguous United States Sheng Ye1, Hong-Yi Li2,3, L Ruby Leung2, Jiali Guo4,5, Qihua Ran1, Yonas Demissie6, and Murugesu Sivapalan7,8 Institute of Hydrology and Water Resources, School of Civil Engineering, Zhejiang University, Hangzhou 310058, China Pacific Northwest National Laboratory, Richland, WA 99352, USA Now at Department of Land Resources and Environmental Sciences, Montana State University, Bozeman, MT 59715, USA College of Civil and Hydropower Engineering, China Three Gorges University, Yichang 443002, China State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China Department of Civil and Environmental Engineering, Washington State University, Richland, WA 99352, USA Department of Geography and Geographic Information Science, University of Illinois at Urbana-Champaign, Urbana, IL, USA Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA Contents of this file Text S1 Snowmelt-adjusted rainfall estimation Text S2: Seasonality statistics Text S3: The derivation of the cutoff at |ρP, EP| = 0.6 Figures S1-7 Introduction This supplementary material includes (1) a description of the method used to estimate snowmelt-adjusted rainfall, (2) a description of the method used to calculate seasonal statistics, (3) a description of the estimation of the distance between the seasonality of AMR and AMF, and (4) seven supplementary figures Text S1: Snowmelt-adjusted rainfall estimation A conceptual model based on the degree-day factor is used to partition daily precipitation between snowfall and rainfall, and thus to estimate the snowmeltadjusted rainfall by including the daily snowmelt [Eder et al., 2003]:  P = P,T > T r crit   Ps = P,T < Tcrit (S1) dSn = Ps − Qn dt (S2) Qn = min{H posddf, Sn}, H pos = max{T − Tcrit, 0} (S3) where Pr is rainfall, Ps is snowfall, Tcrit is the snow-rain transition temperature, which is assumed to be 0ºC, Sn is snowpack storage, Qn is snowmelt, Hpos is the temperature excess over the critical temperature (Tcrit) and ddf is the degree-day factor setting prescribed at 1.5mm day-1 K-1 The snowmelt-adjusted rainfall is defined as the sum of the rainfall (Pr) and snowmelt (Qn), which is the total liquid water applied to the ground surface (i.e., effective rainfall) for the abstraction process Text S2: Seasonality statistics The seasonality index (SI) and mean date (MD) of annual maximum rainfall and flood events are estimated as following: (S4) , (S5) (S6) , where (S7) is the date of the maximum event in the ith year presented as an angle in a circle, YRLEN is the total number of days in a calendar year, i.e., 366 for a leap year and 365 otherwise Text S3: The derivation of the cutoff at |ρ P, EP| = 0.6 The threshold 0.6 is observed from the scatter plot of the difference between the seasonality of AMR and AMF versus the absolute value of coefficient of correlation between P and EP (Figure S3) The difference (or the distance) between the seasonality of AMR and AMF (D) is calculated as follows: 2 D = SI AMR + SI AMF − 2SI AMRSI AMF cos(MDAMR − MDAMF ) (S8) Figure S1: Illustration of 50-year mean monthly precipitation, discharge and soil water storage at nine catchments across the contiguous US Catchments are ordered by their geographic location Figure S2: Spatial distribution of the Nash-Sutcliffe efficiency (NSE) for the monthly runoff simulation using the abcd model Figure S3: Scatter plot of the difference between the seasonality of AMR and AMF (D) versus the absolute value of coefficient of correlation between P and EP The dots are colored by the mean date of AMF Figure S4: Spatial distribution of the seven geographic regions presented in Figure Note that this grouping is qualitative, purely based on the location There is no statistically clustering for the grouping presented here Thus this is just for illustration Figure S5: Spatial distribution of the 13 selected catchments from the Newman dataset for comparison with the abcd-snow model used in this study Figure S6: Mean monthly soil water storage (thick black line) and the confidence interval (blue lines) for the 13 selected catchment calculated from the Newman’s dataset Figure S7: the normalized standard deviation (standard deviation of daily soil water storage within each month normalized by the mean storage) for the 13 selected catchment calculated from the Newman’s dataset, based on the daymet climate input The title denotes USGS ID, the state catchment located, the average of normalized standard deviation, and the average soil water storage for each catchment  ... S2: Seasonality statistics The seasonality index (SI) and mean date (MD) of annual maximum rainfall and flood events are estimated as following: (S4) , (S5) (S6) , where (S7) is the date of the. .. EP| = 0.6 The threshold 0.6 is observed from the scatter plot of the difference between the seasonality of AMR and AMF versus the absolute value of coefficient of correlation between P and EP (Figure... rainfall, (2) a description of the method used to calculate seasonal statistics, (3) a description of the estimation of the distance between the seasonality of AMR and AMF, and (4) seven supplementary