9. SPATIALLY DISTRIBUTED
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Transcript of 9. SPATIALLY DISTRIBUTED
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9. SPATIALLY DISTRIBUTED
HYDROLOGIC MODELS
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Single Cell in Landscape
Land Surface
Sub-surface
Atmosphere
PrecipitationEvapo-transpiration
Overlandflow
Sub-surfaceflow
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Single Cell in Landscape
Land Surface
Sub-surface
Atmosphere
PrecipitationEvapo-transpiration
Overlandflow
Sub-surfaceflow
But Outflow in Which Direction?
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Flow Direction Conventions
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Flow Direction from DEM
TIRIBIELEV all elevations in meters Which way out
of cell H9?
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Flow Direction from DEM
TIRIBIELEV all elevations in meters Which way out
of cell H9?
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Flow Direction from DEM
TIRIBIELEV all elevations in meters Which way out
of cell I9?
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Flow Direction from DEM
TIRIBIELEV all elevations in meters Which way out
of cell I9?
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Flow Direction from DEM
TIRIBIELEV all elevations in meters Which way out
of cell I10?
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Flow Direction from DEM
TIRIBIELEV all elevations in meters Which way out
of cell I10?
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Constructing Flow Network
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Constructing Flow Network
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Constructing Flow Network
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Constructing Flow Network
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Constructing Flow Network
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Constructing Flow Network
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Constructing Flow Network
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Constructing Flow Network
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Constructing Flow Network
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Constructing Flow Network
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Constructing Flow Network
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Constructing Flow Network
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Complete Flow Network
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Computation of Travel Time
How Fast? ~ ManningV = f(D, S, n)Slope: From DEMManning’s n: From channel characteristicsDepth: Field estimates
Travel time? ~ Distance/V
Distance: From flow net to river outlet (Electriona)
Each cell can be assigned a travel time for water to reach the outlet.
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 29 30 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23 24 25 26 27 28 29 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 22 23 24 25 26 27 28 29 0 0 0 0
0 0 0 1 2 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 20 21 22 23 25 25 26 27 28 0 0 0 0 0
0 0 0 0 2 3 4 5 6 7 9 10 11 12 13 14 14 15 17 17 18 19 20 21 23 24 24 25 26 27 0 0 0 0 0 0
0 0 0 0 0 4 4 5 6 7 8 9 11 11 12 13 14 15 16 17 18 19 20 21 22 23 25 25 26 0 0 0 0 0 0 0
0 0 0 0 0 6 5 5 6 8 8 9 10 11 12 13 14 15 16 18 18 19 20 21 22 23 24 25 0 0 0 0 0 0 0 0
0 0 0 0 0 7 6 6 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 0 0 0 0 0 0 0 0
0 0 0 0 0 8 7 7 7 7 8 10 11 12 13 13 15 15 16 17 18 19 20 21 22 23 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 8 8 8 8 8 8 9 10 13 13 14 16 16 17 18 19 19 20 21 22 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 14 13 9 9 9 9 9 10 11 14 14 17 17 18 18 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 15 15 13 12 11 10 10 10 10 11 12 14 15 18 19 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 16 14 13 12 12 11 11 11 11 11 12 14 15 19 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 16 15 14 14 13 12 12 12 12 12 12 13 14 15 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 15 15 14 13 13 13 13 13 13 13 14 14 15 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 16 15 14 14 14 14 14 14 14 14 15 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 15 15 15 15 15 16 15 15 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ISOCHRONES: Surface and subsurface flow characteristics.
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Unit HydrographTiribi at Electriona
Travel time (hrs)
5 10 15 20 25 30
Bas
in A
rea
(km
2 )
0
5
10
15
20
25
30
35
1.4
2.8
4.2
5.6
6.9
8.3
9.7
Dis
char
ge (m
3 s-1)
“ “
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Scenario 1: Rainfall falling uniformly spatially (but not temporally)
Time (hours)
1 2 3
Rainfall (inches)
0.0
0.5
1.0
1.5
2.0
2.5
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1mm1hr Unit HydrographTiribi at Electriona
Travel time (hrs)
5 10 15 20 25 300
2
4
6
8
10
12
14
16
18D
isch
arge
(m3 s-1
)
1 inch per Hour
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2mm1hr Unit HydrographTiribi at Electriona
Travel time (hrs)
5 10 15 20 25 30
Dis
char
ge (m
3 s-1)
0
2
4
6
8
10
12
14
16
18
2 inches per Hour
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0.5mm1hr Unit HydrographTiribi at Electriona
Travel time (hrs)
5 10 15 20 25 300
2
4
6
8
10
12
14
16
18
0.5 inches per Hour
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5 10 15 20 25 300
5
10
15
20
25
30
5 10 15 20 25 300
5
10
15
20
25
30
0.5 “ in first hour
Contribution to flood hydrograph
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5 10 15 20 25 300
5
10
15
20
25
30
5 10 15 20 25 300
5
10
15
20
25
30
2” in second hour
Combined contributions to flood hydrograph.
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5 10 15 20 25 300
5
10
15
20
25
30
5 10 15 20 25 300
5
10
15
20
25
30
1 “ in third hour
Combined contributions to flood hydrograph.
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Col 2
5 10 15 20 25 300
5
10
15
20
25
30
Overall flood hydrograph
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 29 30 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23 24 25 26 27 28 29 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 22 23 24 25 26 27 28 29 0 0 0 00 0 0 1 2 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 20 21 22 23 25 25 26 27 28 0 0 0 0 00 0 0 0 2 3 4 5 6 7 9 10 11 12 13 14 14 15 17 17 18 19 20 21 23 24 24 25 26 27 0 0 0 0 0 00 0 0 0 0 4 4 5 6 7 8 9 11 11 12 13 14 15 16 17 18 19 20 21 22 23 25 25 26 0 0 0 0 0 0 00 0 0 0 0 6 5 5 6 8 8 9 10 11 12 13 14 15 16 18 18 19 20 21 22 23 24 25 0 0 0 0 0 0 0 00 0 0 0 0 7 6 6 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 0 0 0 0 0 0 0 00 0 0 0 0 8 7 7 7 7 8 10 11 12 13 13 15 15 16 17 18 19 20 21 22 23 0 0 0 0 0 0 0 0 0 00 0 0 0 0 8 8 8 8 8 8 9 10 13 13 14 16 16 17 18 19 19 20 21 22 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 14 13 9 9 9 9 9 10 11 14 14 17 17 18 18 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 15 15 13 12 11 10 10 10 10 11 12 14 15 18 19 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 16 14 13 12 12 11 11 11 11 11 12 14 15 19 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 16 15 14 14 13 12 12 12 12 12 12 13 14 15 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 15 15 14 13 13 13 13 13 13 13 14 14 15 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 16 15 14 14 14 14 14 14 14 14 15 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 15 15 15 15 15 16 15 15 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1
2
3 Precipitation not only varies temporally, but also spatially. Can use simple technique like Thiessen polygons to alter inputs to various parts of basin.
Scenario 2: Rainfall falling variably over space, but uniformly over time)
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CellsStation Station Station
1 2 31 1 2 2 3 2 4 4 5 4 6 7 7 8 8 12 9 9 1
10 8 2 11 8 6 12 7 9 13 8 12 14 10 16 15 8 17 16 6 5 217 8 018 6 419 3 820 821 822 723 824 625 826 527 428 329 330 1
Each polygonal area corresponds to a differing set of travel times or isochrones.
Rain falling at same time in yellow area will reach outlet later than that in orange area.
Rain falling in green area will all arrive at outlet within a 7 hour period, while the rain falling on the orange area will be distributed over a 19 hour period.
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Time of Arrival of Cell/Polygon Contributions at Electriona.
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 9 3 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 2 4 2 5 2 6 2 7 2 8 2 9 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 0 0 0 0
0 0 0 1 2 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 9 2 0 2 1 2 2 2 3 2 5 2 5 2 6 2 7 2 8 0 0 0 0 0
0 0 0 0 2 3 4 5 6 7 9 1 0 1 1 1 2 1 3 1 4 1 4 1 5 1 7 1 7 1 8 1 9 2 0 2 1 2 3 2 4 2 4 2 5 2 6 2 7 0 0 0 0 0 00 0 0 0 0 4 4 5 6 7 8 9 1 1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 5 2 5 2 6 0 0 0 0 0 0 0
0 0 0 0 0 6 5 5 6 8 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 8 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 0 0 0 0 0 0 0 0
0 0 0 0 0 7 6 6 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 0 0 0 0 0 0 0 0 0
0 0 0 0 0 8 7 7 7 7 8 1 0 1 1 1 2 1 3 1 3 1 5 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 8 8 8 8 8 8 9 1 0 1 3 1 3 1 4 1 6 1 6 1 7 1 8 1 9 1 9 2 0 2 1 2 2 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 4 1 3 9 9 9 9 9 1 0 1 1 1 4 1 4 1 7 1 7 1 8 1 8 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 5 1 5 1 3 1 2 1 1 1 0 1 0 1 0 1 0 1 1 1 2 1 4 1 5 1 8 1 9 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 1 6 1 4 1 3 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 4 1 5 1 9 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 6 1 5 1 4 1 4 1 3 1 2 1 2 1 2 1 2 1 2 1 2 1 3 1 4 1 5 1 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 5 1 5 1 4 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 4 1 4 1 5 1 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 6 1 5 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 5 1 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 5 1 5 1 5 1 5 1 5 1 6 1 5 1 5 1 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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SPATIAL VARIABILITY OF INPUTS
• Assume that a storm occupies the entire Tiribí basin, but that the quantity of rain it delivers increases towards the headwaters.
• As the air is forced to rise it produces greater precipitation at higher elevations.
• The low lying orange area receives Excess precipitation of 0.5”.
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0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
Response of low lying area to excess precipitation of 0.5 “ in the first hour.
Time distributed contribution of lowland areas’ excess precipitation at Electriona.
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0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
Response at Electriona to higher areas of the Jorco and Cañas receiving excess precipitation of 1.0” falling during the hour of the storm.
Combined effects at Electriona of both the lower (faster, temporally dispersed response, but less excess precipitation), and upper (slower, less dispersed response, to large excess precipitation) parts of the basin.
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0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
Response at Electriona to highest areas of the Chiquito and Tres Ríos receiving excess precipitation of 2.0 mm falling during the hour of the storm, but requiring longer travel times to reach the outlet.
Combined effects at Electriona of spatially varying excess precipitation inputs falling on cells with varying travel times to outlet. Basically becoming “wetter” as one proceeds away from the outlet.
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Now Assume that Low Areas Receive Most Rain from the Storm and Upper Areas the Least
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0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
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6
8
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12
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0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
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12
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0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
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8
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12
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0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
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0 5 10 15 20 25 30
Dis
char
ge
0
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Storm Max in Highlands
Storm Max in Lowlands
Arbitrarily set a discharge of 4 as a critical flood level
• Flood Starts later.
• Flood Starts earlier.
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0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
Storm Max in Highlands
Storm Max in Lowlands
Arbitrarily set a discharge of 4 as a critical flood level
• Flood Starts later.• Peaks at same time.
• Flood Starts earlier.• Peaks at same time.
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0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
Storm Max in Highlands
Storm Max in Lowlands
Arbitrarily set a discharge of 4 as a critical flood level
• Flood Starts later.• Peaks at same time.• Lower peak above
threshold.
• Flood Starts earlier.• Peaks at same time.• Higher peak above
threshold.
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0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
0 5 10 15 20 25 30
Dis
char
ge
0
2
4
6
8
10
12
Storm Max in Highlands
Storm Max in Lowlands
Arbitrarily set a discharge of 4 as a critical flood level
• Flood Starts later.• Peaks at same time.• Lower peak above
threshold.• Fewer hours of
inundation.
• Flood Starts earlier.• Peaks at same time.• Higher peak above
threshold.• More hours of
inundation.
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Scenario 4: Rainfall falling variably over both time and space.
1. 2. 3. 4.5.
6.
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2375 1832
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1244 1297 1412 1886 1996 2125 1781 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1075 1078 1278 1327 1433 1905 1970 2024 2234 0
751 540 827 895 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1069 961 953 1123 1189 1365 1339 1806 1872 1922 0 0
0 844 809 847 854 873 938 979 995 1015 1087 1043 1054 1085 869 957 899 917 1063 865 1004 1185 1148 1150 1250 1831 1891 0 0 0
0 0 621 844 917 860 878 906 925 1017 950 973 982 748 806 831 866 1270 1209 949 1200 1002 1045 1189 1282 1338 0 0 0 0
0 0 658 854 857 881 942 900 917 924 936 950 709 725 774 891 925 948 888 915 813 885 952 1004 1121 0 0 0 0 0
0 0 800 914 918 865 897 902 909 914 923 950 744 720 735 873 813 818 838 975 869 937 1001 1018 0 0 0 0 0 0
0 0 902 698 709 912 742 750 808 979 990 751 802 696 760 770 792 682 900 922 1050 972 1032 0 0 0 0 0 0 0
0 0 1053 995 987 805 774 758 768 993 1036 794 843 835 732 743 764 872 893 818 845 960 0 0 0 0 0 0 0 0
0 0 994 960 1057 1095 827 692 792 848 888 925 990 970 962 784 760 914 0 0 0 0 0 0 0 0 0 0 0 0
0 1252 1015 1064 937 853 762 748 722 814 870 967 999 799 762 773 929 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1175 1222 1094 973 894 791 796 772 875 670 949 749 1034 1040 1053 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1083 1255 1090 1097 1015 889 849 882 840 799 672 688 733 1011 1021 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1271 1313 1316 1004 970 900 764 857 844 847 771 903 980 1011 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1298 1313 953 925 854 924 894 926 1150 810 863 1010 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 960 953 1027 894 924 1149 1128 1150 887 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Southwest toNortheast StormTrack
CenterHour 1
CenterHour 2
CenterHour 3
CenterHour 4
CenterHour 5
CenterHour 6
CenterHour 7
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0.2
0.2 0.4 0.2
0.2 0.4 0.6 0.4 0.2
0.2 0.4 0.6 0.8 0.6 0.4 0.2
0.2 0.4 0.6 0.8 1.0 0.8 0.6 0.4 0.2
0.2 0.4 0.6 0.8 0.6 0.4 0.2
0.2 0.4 0.6 0.4 0.2
0.2 0.4 0.2
0.2
Hypothetical Spatial Distribution of Rainfall Relative to Center of Storm.
All figures expressed as proportions of the maximum rainfall at the center.
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 29 300 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23 24 25 26 27 28 29 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 22 23 24 25 26 27 28 29 01 2 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 20 21 22 23 25 25 26 27 28 0 00 2 3 4 5 6 7 9 10 11 12 13 14 14 15 17 17 18 19 20 21 23 24 24 25 26 27 0 0 00 0 4 4 5 6 7 8 9 11 11 12 13 14 15 16 17 18 19 20 21 22 23 25 25 26 0 0 0 00 0 6 5 5 6 8 8 9 10 11 12 13 14 15 16 18 18 19 20 21 22 23 24 25 0 0 0 0 00 0 7 6 6 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 0 0 0 0 00 0 8 7 7 7 7 8 10 11 12 13 13 15 15 16 17 18 19 20 21 22 23 0 0 0 0 0 0 00 0 8 8 8 8 8 8 9 10 13 13 14 16 16 17 18 19 19 20 21 22 0 0 0 0 0 0 0 00 0 14 13 9 9 9 9 9 10 11 14 14 17 17 18 18 19 0 0 0 0 0 0 0 0 0 0 0 00 15 15 13 12 11 10 10 10 10 11 12 14 15 18 19 19 0 0 0 0 0 0 0 0 0 0 0 0 00 16 14 13 12 12 11 11 11 11 11 12 14 15 19 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 15 14 14 13 12 12 12 12 12 12 13 14 15 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 15 15 14 13 13 13 13 13 13 13 14 14 15 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 16 15 14 14 14 14 14 14 14 14 15 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 15 15 15 15 15 16 15 15 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ### ###0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ### ### ### ### ### ### ### 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ### ### ### ### ### ### ### ### ### 0
751 540 827 895 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ### 961 953 ### ### ### ### ### ### ### 0 00 844 809 847 854 873 938 979 995 ### ### ### ### ### 869 957 899 917 ### 865 ### ### ### ### ### ### ### 0 0 00 0 621 844 917 860 878 906 925 ### 950 973 982 748 806 831 866 ### ### 949 ### ### ### ### ### ### 0 0 0 00 0 658 854 857 881 942 900 917 924 936 950 709 725 774 891 925 948 888 915 813 885 952 ### ### 0 0 0 0 00 0 800 914 918 865 897 902 909 914 923 950 744 720 735 873 813 818 838 975 869 937 ### ### 0 0 0 0 0 00 0 902 698 709 912 742 750 808 979 990 751 802 696 760 770 792 682 900 922 ### 972 ### 0 0 0 0 0 0 00 0 ### 995 987 805 774 758 768 993 ### 794 843 835 732 743 764 872 893 818 845 960 0 0 0 0 0 0 0 00 0 994 960 ### ### 827 692 792 848 888 925 990 970 962 784 760 914 0 0 0 0 0 0 0 0 0 0 0 00 ### ### ### 937 853 762 748 722 814 870 967 999 799 762 773 929 0 0 0 0 0 0 0 0 0 0 0 0 00 ### ### ### 973 894 791 796 772 875 670 949 749 ### ### ### 0 0 0 0 0 0 0 0 0 0 0 0 0 0
### ### ### ### ### 889 849 882 840 799 672 688 733 ### ### 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 ### ### ### ### 970 900 764 857 844 847 771 903 980 ### 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 ### ### 953 925 854 924 894 926 ### 810 863 ### 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 960 953 ### 894 924 ### ### ### 887 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 29 300 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23 24 25 26 27 28 29 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 22 23 24 25 26 27 28 29 01 2 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 20 21 22 23 25 25 26 27 28 0 00 2 3 4 5 6 7 9 10 11 12 13 14 14 15 17 17 18 19 20 21 23 24 24 25 26 27 0 0 00 0 4 4 5 6 7 8 9 11 11 12 13 14 15 16 17 18 19 20 21 22 23 25 25 26 0 0 0 00 0 6 5 5 6 8 8 9 10 11 12 13 14 15 16 18 18 19 20 21 22 23 24 25 0 0 0 0 00 0 7 6 6 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 0 0 0 0 00 0 8 7 7 7 7 8 10 11 12 13 13 15 15 16 17 18 19 20 21 22 23 0 0 0 0 0 0 00 0 8 8 8 8 8 8 9 10 13 13 14 16 16 17 18 19 19 20 21 22 0 0 0 0 0 0 0 00 0 14 13 9 9 9 9 9 10 11 14 14 17 17 18 18 19 0 0 0 0 0 0 0 0 0 0 0 00 15 15 13 12 11 10 10 10 10 11 12 14 15 18 19 19 0 0 0 0 0 0 0 0 0 0 0 0 00 16 14 13 12 12 11 11 11 11 11 12 14 15 19 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0
16 15 14 14 13 12 12 12 12 12 12 13 14 15 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 15 15 14 13 13 13 13 13 13 13 14 14 15 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 16 15 14 14 14 14 14 14 14 14 15 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 15 15 15 15 15 16 15 15 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2375 18320 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1244 1297 1412 1886 1996 2125 1781 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1075 1078 1278 1327 1433 1905 1970 2024 2234 0
751 540 827 895 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1069 961 953 1123 1189 1365 1339 1806 1872 1922 0 00 844 809 847 854 873 938 979 995 1015 1087 1043 1054 1085 869 957 899 917 1063 865 1004 1185 1148 1150 1250 1831 1891 0 0 00 0 621 844 917 860 878 906 925 1017 950 973 982 748 806 831 866 1270 1209 949 1200 1002 1045 1189 1282 1338 0 0 0 00 0 658 854 857 881 942 900 917 924 936 950 709 725 774 891 925 948 888 915 813 885 952 1004 1121 0 0 0 0 00 0 800 914 918 865 897 902 909 914 923 950 744 720 735 873 813 818 838 975 869 937 1001 1018 0 0 0 0 0 00 0 902 698 709 912 742 750 808 979 990 751 802 696 760 770 792 682 900 922 1050 972 1032 0 0 0 0 0 0 00 0 1053 995 987 805 774 758 768 993 1036 794 843 835 732 743 764 872 893 818 845 960 0 0 0 0 0 0 0 00 0 994 960 1057 1095 827 692 792 848 888 925 990 970 962 784 760 914 0 0 0 0 0 0 0 0 0 0 0 00 1252 1015 1064 937 853 762 748 722 814 870 967 999 799 762 773 929 0 0 0 0 0 0 0 0 0 0 0 0 00 1175 1222 1094 973 894 791 796 772 875 670 949 749 1034 1040 1053 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1083 1255 1090 1097 1015 889 849 882 840 799 672 688 733 1011 1021 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 1271 1313 1316 1004 970 900 764 857 844 847 771 903 980 1011 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 1298 1313 953 925 854 924 894 926 1150 810 863 1010 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 960 953 1027 894 924 1149 1128 1150 887 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
TRAVEL TIMES
STORM PRECIPITATION
SHORTER
LONGER
DRIER
WETTER
SLOWER
FASTER
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0 5 10 15 20 25 30 35
Num
ber o
f Cel
ls fr
om E
ach
Sto
rm P
ositi
on R
each
ing
Out
let
0
5
10
15
20
25
C. 1C. 2C. 3C. 4C. 5C. 6C. 7
Time (hours)
0 5 10 15 20 25 30 350
5
10
15
20
25
Southwest to Northeast
Northeast to Southwest
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1. 2. 3. 4.5.
6.
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SW - NE Storm Track
Time (hours)
0 5 10 15 20 25 30 35
Dis
char
ge (m
3 s-1
)
0
2
4
6
8
10
12
14
16
18
Hour1Hour2Hour3 Hour4 Hour5Hour6Hour7
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NE - SW Storm Track
Time (hours)
5 10 15 20 25 30 35
Dis
char
ge (m
3 s-1
)
0
2
4
6
8
10
12
14
16
18
Hour7 Hour6 Hour5 Hour4 Hour3 Hour2 Hour1
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