1. Discharge-Area Relations from Selected Drainages
on the Colorado Plateau: a GIS Application
GISWR Term Project By W. Scott Cragun

2. Outline Problem to be addressed Part I Methods Results Conclusions
Part II

3. Problem to be addressed:
A is often substituted for Q in fluvial models
Example: Family of equations knows as Stream Power Laws
Used to:
model aggradation / incision within rivers
model incision rates within rivers
Basic Equations: Z = kQmSn OR Z = kAmSn
k is proportionality constant
Q is discharge
S is slope
m/n are exponents whose values are debated
A is drainage area

4. Commonly held that: Q = bAc ; A is the contributing drainage area
b is a proportionality constant
c is a scaling exponent (1 is most common value)
Most commonly a linear (or nearly linear) relation
Perhaps true for alluvial rivers in humid climatic zones
What about for mixed alluvial-bedrock rivers in semi-arid climatic zones??
From: Mitchell, D.K., 2000

5. Part I - What I’ve Done: Six river basins selected Gunnison River
Upper Colorado River
San Juan River
Paria River
Little Colorado River
Fremont/Dirty Devil River
Encompass the southern/arid basins and the northern/relatively wetter basins

6. Part I - What I’ve Done: The raw DEM’s
DEM’s downloaded from USGS seamless data (
30m DEM projected in UTM and interpolated at 100m cell size
Run TauDEM tools in order to determine flow direction and flow accumulation
Upper Colorado
Fremont
Gunnison
Paria
San Juan
Little Colorado

7. Part I - What I’ve Done:
Obtain USGS gaging station data for each of the 6 drainages (
Mean annual flow
Mean peak flow
35 total gaging stations
Import gage location in GIS
Manually extract contributing area at each
gaging station
compare GIS contributing area to USGS drainage area
plot discharge against contributing drainage area
Little Colorado River

8. Part I - Results: Significantly more scatter in the data from the
Colorado Plateau
Y = 0.08A0.95
R2 = 0.82

9. Part I - Results:
Individual basins show unique downstream discharge patterns

10. Part I - Results:
Hydrographs show peak runoff during - spring (snow melt) : northern drainages
- fall (monsoon) : southern drainages
northern drainages
southern drainages

11. Part I - Results:
However… Individual basins show: 1) grouping of 3 northern basins
2) unique relations in southern 3 basins

12. Part I - Results:
Splitting drainage basins into two groups…

13. Part I - Conclusions: 1) Close Q-A relation in northern drainages
But… scaling exponent (c) is not nearly 1 : value is 0.70
- suggests that streams in humid environments are capable
of generating greater discharges per unit drainage area than in
arid and semi-arid regions
2) Large scatter in Q-A relation in southern drainages (lower r2)
Suggests that - geologic controls influence discharge generation
- climatic influence = greater evaporation
3) Discharge generation per unit area varies between all 6 basins
4) Streams in ARID regions: appropriate Q-A relation should be carefully
chosen even when significant water is available

14. Part II - What I’ve Done:
Obtain precipitation data for western US from PRISM (
clipped out for each drainage
resampled at 1000 m cell size
Can RUNOFF be predicted from PRECIPITATION ??
runoff coefficients estimated for each basin
From:

15. Part II - Results: Initial runoff coefficients too high
Readjusted to better predict runoff
Basin
Initial Estimate K
Refigured K
Fremont
0.21
0.062
Gunnison
0.3
0.22
Little Colorado
0.14
0.0084
Paria
0.24
0.031
San Juan
0.26
0.17
Upper Colorado
0.42
0.30

16. Part II - Results:
First attempt to define precipitation-runoff relation through regression failed
Try, try again…
San Juan shaded relief map
San Juan precipitation map

17. Part II - Conclusions:
Estimated runoff coefficients vary widely between 6 basins
to 0.30
Suggests that - local climate conditions influence discharge
monsoon vs. snow melt
- local geologic characteristics influence discharge
- local soil and vegetation distribution affects discharge
2) Runoff prediction from precipitation is not perfect
oversimplified
3) Need a more robust coverage of drainage characteristics to establish
representative discharge – precipitation relations in each basin