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. 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. Outline Study Area and Data Catchment Scale Rainfall
Organization Framework Examination with hydrologic modeling
Conclusions 3
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 Tar River Basin
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 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 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. 8-year Cumulative Rainfall 9 Mostly concentrate over the
southeast of the entire basin
10. Events Selection 10
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
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 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. 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)
17. 17 Rainfall Moments of Sample Event the n-th hour
18. 18 11:00 12:00 13:00 14:00 15:00 16:00
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.
20. Vs of Sample Events 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)
22. Role of Rainfall on Vs 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.
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.
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
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
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)
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)
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)
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)
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)
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)
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
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)
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.
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;
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;
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:
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: