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  1. 1. Yiwen Mei, Emmanouil N. Anagnostou, Dimitrios Stampoulis, Efthymios I. Nikolopoulos, Marco Borga, Humberto J. Vegara Rainfall Organization Control on the Flood Response of mild-slope Basins 1
  2. 2. Objectives This study evaluates the catchment response to rainfall for a large number of storm events with the aim of quantifying the role of spatiotemporal rainfall organization relative to the basin geomorphology on hydrologic modeling. 2
  3. 3. Outline Study Area and Data Catchment Scale Rainfall Organization Framework Examination with hydrologic modeling Conclusions 3
  4. 4. Study Area and Data Tar-River Basin, NC Data Digital Elevation Model (DEM) Radar Rainfall (US NWS MPE product ) Streamgauge Flow Events 4
  5. 5. 5 Tar River Basin
  6. 6. 6 Geomorphology Basin ID B1 B2 B3 B4 Basin Area (km2) 110 6 201 2 239 6 565 4 Elevation (m) 128 106 99 76 Flow- length Statistics (km) mea n 56 110 111 142 std 26 49 56 66 max 108 199 214 287 Slope Statistics () mea n 3.2 2.9 2.7 2.3 std 2.2 2.1 2.0 1.9 max 32 32 32 32
  7. 7. 7 Data Type Dimensio n Coverage Resolutio n Rainfa ll Space Entire Tar River Basin 4km4km Time 2002~2009 Hourly Flow- length * Space Entire Tar River Basin 29m29m Runoff Time 2002~2009 Hourly *Flowlength is derived based on the DEM data with the same resolution. It is the length of flow path measured from a giving point within the basin to the basin outlet.
  8. 8. 8 Data Gaug e Code s Mean Annual Precipitatio n (mm/year) Mean Annual Runoff (mm/year) Annua l Runoff Ratio Mean Maximum Annual Flow (m3/s) B1 1015 298 0.29 166.6 B2 1027 300 0.29 174.1 B3 1038 311 0.30 206.2 B4 1074 310 0.29 347.0
  9. 9. 8-year Cumulative Rainfall 9 Mostly concentrate over the southeast of the entire basin
  10. 10. Events Selection 10
  11. 11. 11 Basin ID B1 B2 B3 B4 Num. of event 44 42 40 38 Rainfall Volume (mm) rang e [12.8, 124.5] [13.4, 123.8] [16.5, 128.7] [18.8, 221.7] mea n 42.1 49.6 54.5 61.0 Ts (h) rang e [12, 124] [11, 219] [12, 219] [28, 377] mea n 41 71 81 132 Direct flow (mm) rang e [3.7, 65.9] [4.4, 66.6] [3.9, 58.1] [3.8, 87.0] mea n 16.2 14.7 17.1 18.8 Tf (h) rang e [81, 558] [123, 551] [140, 573] [202, 1030] mea n 225 270 280 390
  12. 12. Catchment Scale Rainfall Organization Spatial Moments of Catchment Rainfall (1 & 2) Catchment Scale Storm Velocity (Vs) 12
  13. 13. 13 Spatial Moments of Catchment Rainfall n-th spatial moment of rainfall, pn(t): n-th spatial moment of flowlength, gn: Dimensionless 1st order moment of rainfall, 1(t): Dimensionless 2nd order moment of rainfall, 2(t): = 1 , , , = 1 , 1 = 1 0 1 2 = 1 2 1 2 2 0 1 0 2 (1) (2) (3) (4)
  14. 14. 14 Spatial Moments of Catchment Rainfall n-th spatial moment of rainfall over a time period Ts, Pn: Dimensionless 1st order moment of rainfall over a time period Ts, 1: Dimensionless 2nd order moment of = 1 1 = 1 0 1 2 = 1 2 1 2 2 0 1 0 2 (5) (6) (7)
  15. 15. Meaning of the Moments 15 >1 =1 0 Vs = 0 Vs < 0 Upbasin Moveme nt Stationary (Lumped Rain) Downbas in Moveme nt = 1 , 1 1 , 1 = 0 0 (8) (9)
  16. 17. 17 Rainfall Moments of Sample Event the n-th hour
  17. 18. 18 11:00 12:00 13:00 14:00 15:00 16:00
  18. 19. 19 Rainfall Moments of Sample Event Similar temporal patterns, especially for B2 and B3; 1 and 2 exhibit relatively large variability The storm centroid was located towards the headwater most of the time; Down basin movement (negative 1) at around the 2nd peak; 2 smaller than 1 most of the hours (one-core storm); 2 generally reflect the trend of 1.
  19. 20. Vs of Sample Events 20
  20. 21. 21 Vs of Sample Events Magnitude of catchment scale storm velocity for the main event was relatively low (within 0.5 m/s); Vs reveals the time evolution of 1 ,particularly during periods with a minor rate of change of w(t); = 1 , 1 (10)
  21. 22. Role of Rainfall on Vs 22
  22. 23. 23 Role of Rainfall on Vs Extreme values of Vs(t) are likely to occur at the time that rainfall rate reaches its maxima or minima. The 2nd linear regression term offsets the 1st term when rainfall rate is changing rapidly; Vs(t) represents the change of 1(t) when the change of basin areal rainfall rain is null or negligibly small; Vs(t) reflect the temporal variability of p0(t) when p0(t) is significantly fluctuated over time.
  23. 24. 24 Scale dependency of Vs Event-based Vs(t) from larger basins are larger and have higher degree of variability; The inter-event variability of Vs(t) is also scale dependent.
  24. 25. Framework Examination with hydrologic modeling 25 Hydrologic Model Evaluation of HL-RMS performance Role of the Framework in Hydrologic Modeling Control on Timing of the Hydrograph Control on the Shape of Hydrograph
  25. 26. 26 Hydrology laboratory research modeling system (HL-RMS) Water Balance Model: Sacramento Soil Moisture Accounting Model (SAC-SMA) Kinematic Hillslope and Channel Routing Models Hydrologic Model
  26. 27. 27 Absolute Error of Event Runoff Volume (V): Absolute Error of Event Peak Flow Rate (p): Root Mean Square Error (RMS): Evaluation of HL-RMS Performance = 100% = 100% = =1 2 =1 (11) (12) (13)
  27. 28. 28 Bi Bii Biii Biv p (%) mean 27.13 31.86 31.64 28.16 STD 6.59 22.61 20.43 15.89 V (%) mean 25.96 28.56 27.55 28.01 STD 5.01 13.12 13.74 9.83 RMS mean 0.67 0.62 0.56 0.48 STD 0.28 0.44 0.31 0.25 mean 0.82 0.81 0.86 0.75 STD 0.09 0.1 0.05 0.06 Evaluation of HL-RMS Performance Correlation coefficient of the event hydrograph, : = =1 =1 =1 =1 =1 2 =1 =1 2 (14)
  28. 29. Role of the Framework in Hydrologic Modeling 29 Non-stationary rainfall; Two-stage catchment flood response: 1) rainfall excess stage and 2) runoff routing stage; Spatial constant runoff routing velocity; Constant runoff coefficient within an event. Assumptions: = + Tq: Catchment flood response time (h); Tr: Rainfall excess time (h); Tc : Runoff transport (h). (15)
  29. 30. Role of the Framework in Hydrologic Modeling 30 The expectation and variance of Tq are given as: E(Tq) and var(Tq) are given as: = + = + + 2 , = = 2 (16) (17) (18) (19)
  30. 31. Role of the Framework in Hydrologic Modeling 31 E(Tc), var(Tc) and cov(Tr, Tc) are given as: = 1 1 = 2 2 1 2 2 , = (21) (20) (22)
  31. 32. Control on Timing of Hydrograph 32 Difference in timing dE is: Substitute in E(Tq,d) and E(Tq,l), yield: = , , = 1 1 1 (24) (23)
  32. 33. Control on Timing of the Hydrograph 33 Basin ID B1 B2 B3 B4 Intercept -31 -57 -61 -99 Slope 31 57 61 97 r2 0.5 8 0.8 4 0.8 2 0.6 5
  33. 34. Control on the Shape of Hydrograph 34 Difference in degree of dispersion dvar: Substitute in var(Tq,d) and var(Tq,l), yield: Given that var(T) is uniformly distributed on Ts, we have: = , , = 2 1 2 2 2 + 2 2 1 2 2 = 2 1 2 2 2 + 1 6 2 2 1 2 2 (26) (25) (27)
  34. 35. 35 Control on the Shape of Hydrograph Basin ID B1 B2 B3 B4 Intercept - 164 - 640 - 316 - 1971 Slope1 202 638 326 1865 Slope2 0.0 9 0.0 2 0.0 3 0.02 r2 0.1 6 0.1 6 0.1 9 0.16 [MY1]Marco, the two paragraphs have been merged as one since v removed the first possible cause.
  35. 36. Control on the Shape of Hydrograph 36 The regression intercept and the first slope coefficient are close to each other; The second slope coefficient is close to zero; Eq.(27) is unable to capture the tendency of the bulk 2, VsTs 2 and dvar; The residuals are distributed within a considerable range with non-negligible displacement from zero of their medians;
  36. 37. Control on the Shape of Hydrograph 37 The framework lumps hillslope and channel routings together and assumes spatiotemporal constant runoff routing velocity since it is designate for small scale basins and flood events with bank-full condition (e.g. flash floods); The HL-RMS differentiates hillslope from channel routing and assigns spatiotemporal variable as the channel routing velocity; The square operator of v in amplify the disagreement between the framework and hydrologic model;
  37. 38. Conclusions 38 2 generally reflect the trend of 1 (2 close to zero when 1 is far from one; 2 around one when 1 is close to unity); Vs is closed to zero; Hourly Vs(t) was found to be rainfall intensity dependent Mean and variability of the event-based Vs(t) were basin-scale dependent; On the Framework:
  38. 39. Conclusions 39 Catchment response is relatively sensitive to the spatial heterogeneity of rainfall quantified on the basis of 1, 2, and Vs; Strong linear dependency was exhibited between dE and 1; The correlation was weak in terms of difference in peakedness of the hydrograph (dvar and 2, Vs ); Different processes in routing kinematics disrupt the On the Sensitivity Test:
  39. 40. 40