9. SPATIALLY DISTRIBUTED

HYDROLOGIC MODELS

Single Cell in Landscape

Land Surface

Sub-surface

Atmosphere

PrecipitationEvapo-transpiration

Overlandflow

Sub-surfaceflow

Single Cell in Landscape

Land Surface

Sub-surface

Atmosphere

PrecipitationEvapo-transpiration

Overlandflow

Sub-surfaceflow

But Outflow in Which Direction?

Flow Direction Conventions

Flow Direction from DEM

TIRIBIELEV all elevations in meters Which way out

of cell H9?

Flow Direction from DEM

TIRIBIELEV all elevations in meters Which way out

of cell H9?

Flow Direction from DEM

TIRIBIELEV all elevations in meters Which way out

of cell I9?

Flow Direction from DEM

TIRIBIELEV all elevations in meters Which way out

of cell I9?

Flow Direction from DEM

TIRIBIELEV all elevations in meters Which way out

of cell I10?

Flow Direction from DEM

TIRIBIELEV all elevations in meters Which way out

of cell I10?

Constructing Flow Network

Constructing Flow Network

Constructing Flow Network

Constructing Flow Network

Constructing Flow Network

Constructing Flow Network

Constructing Flow Network

Constructing Flow Network

Constructing Flow Network

Constructing Flow Network

Constructing Flow Network

Constructing Flow Network

Complete Flow Network

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.

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 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.

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)

“ “

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

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

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

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

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

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.

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.

Col 2

5 10 15 20 25 300

5

10

15

20

25

30

Overall flood hydrograph

0 0 0 0 0 0 0 0 0 0 0 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)

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.

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

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”.

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.

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.

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.

Now Assume that Low Areas Receive Most Rain from the Storm and Upper Areas the Least

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

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

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.

• Flood Starts earlier.

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.

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.

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.

Scenario 4: Rainfall falling variably over both time and space.

1. 2. 3. 4.5.

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 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 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

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.

0 0 0 0 0 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

0 0 0 0 0 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

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

1. 2. 3. 4.5.

6.

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

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