1. Revisting Melton: Analyzing the correlation structure of geomorphological and climatological parameters
Richard A. Carothers1
, Harish Sangireddy1
, Paola Passalacqua1
1-Center for Research in Water Resources, Environmental and Water Resources Engineering,
Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin
( richardcarothersut@gmail.com,hsangireddy@utexas.edu, paola@austin.utexas.edu)
EP53C-0841
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Abstract
Melton, M. A. (1957). An analysis of the relations among elements of climate, surface properties, and geomorphology
(No. CU-TR-11). COLUMBIA UNIV NEW YORK
Passalacqua, P., Do Trung, T., Foufoula-Georgiou, E., Sapiro, G., & Dietrich, W. E. (2010). A geometric framework for channel
network extraction from lidar: Nonlinear diffusion and geodesic paths. Journal of Geophysical Research:
Earth Surface (2003–2012), 115(F1).
PRISM Climate Group, Oregon State University, http://prism.oregonstate.edu, created 4 Feb 2004
Soil Survey Staff, Natural Resources Conservation Service, United States Department of Agriculture. U.S. General
Soil Map (STATSGO2). Available online at http://soildatamart.nrcs.usda.gov
USGS National Map Viewer, United States Geological Survey. Web. 10 June 2013. http://viewer.nationalmap.gov/viewer/
Western U.S. Historical Climate Summaries, Western Regional Climate Group, 2013. Web. 10 June 2013.
http://www.wrcc.dri.edu/Climsum.html
References
Acknowledgements
Expanding the climatic range and
grouping by soil order
Drainage Density: State of art
Mark Melton’s analysis in 1957
Problem of resolution
Revisting Melton: creating a correlated geo database
Results: Comparing drainage density estimates
Comparing drainage density estimates from GeoNet
Runoff increases
while vegetation
changes little
Vegetation increases
while suppressing
changes in runoff
Runoff increases
while vegetation
changes little
Drainagedensity
Mean annual precipitation
Melton (1957)
Abrahams(1972)
Daniel (1981)
Gregory(1976)
Abrahams and
Ponczynski(1984)
Moglen et al. (1998)
Colins and Bras 2010, WRR
Drainage density is perceived as a morphological
expression of the landscape.
It has been recognized that drainage density varies
with climate, vegetation type, soil and topography.
Drainage density =
Total length of channels
Total basin area
(L)
(L2
)
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Utah
Arizona
Colorado
New Mexico
Melton analyzed around 80
basins in Arizona, New Mexico,
Colorado and Utah to study
the correlation of landscape
morphometry with climatic
factors. He analyzed all the
landscape morphomteric
variables from 1:24,000
topographic maps
(a) (b) (c)
Drainagedensity(miles/squaremiles)
P-E Index Runoff intensity (q) Percent bare (b)
(a) Drainage density shows a negative
correlation with P-E index
(precipitation -evaporation index)
(b) Drainage density shows a positive
correlation with runoff intensity (q)
(c) Drainage density shows a positive
correlation with percentage of
vegetation cover in the landscape.
Drainagedensityfrom
bluelines
Drainagedensityfrom
contourmethods
Drainage density from field measurements
Measurements of streams as indicated in the topographic
maps differ from actual field measurements. [ Morisawa, 1957,
1961; Schneider 1961]. The comparison of the esitmates of
drainage density from blue lines and contour crenulation
method with field measurements show a poor agreement .
With the advent of high resolution lidar datasets, the problem
of resolution can be now resolved.
Bland Quadrangle, New Mexico
Paso del Norte Basin (Fourth Order)
[Melton 1957]
Correlation of drainage density
with causative factors of climate
Methodology
- Create a correlated geographic database for all
the Melton datasets.
- All the 80 basins are identified manually by
cross referencing the maps available in the
Melton 1957 report.
- The Elevation, hydrography and land cover data
is obtained from the National Elevation Dataset
(10 m resolution). http://ned.usgs.gov/
- Mean annual precipitation is obtained from
the PRISM Climate dataset (800 m resolution).
http://www.prism.oregonstate.edu/
- Runoff intensity for 5 year return period storms
of 1hr durations is obtained from NOAA
Precipitation frequency dataset.
http://hdsc.nws.noaa.gov/hdsc/pfds/index.html
- GeoNet2.0 is used to extract the slope,
curvature and drainage density from the
elevation data
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Harshaw - Sycamore Canyon
Harshaw - Finley and Adams Canyon
! MeltonLocations
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Bland - Paso del Norte Basin
! MeltonLocations
Harshaw Quadrangle (AZ) Bland Quadrangle (NM)
Hillshade generated by using elevation data at 10m resolution
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Hillshade generated by using elevation at 1m resolution
−200 −150 −100 −50 0 50
0
5
10
15
20
25
30
35
40
Histogram of residuals
Residuals (D g
− D m
)
Frequency
Mean = −6.4543
Median = 3.2511
A total of 76 out of 105 catchments
are estimated by GeoNet to have a
higher drainage density than that
measured by Melton in 1957.
0 5 10 15 20 25 30 35
0
5
10
15
20
25
30
35
Draiange density measured by Melton 1957 (D m
)
DrainagedensitymeasuredbyGeoNet(D
g
)
Drainage density (miles/sqmiles) comparison
0 100 200
0
10
20
30
40 Complete data
300 400 500 600 700 800 900
0
5
10
15
20
25
30
35
Mean Annual Precipitation estimates from PRISM climate dataset (mm)
Drainagedensity(Dm
)[miles/sqmiles]byMelton1957
Drainage density vs Mean annual Precipiatation
data
Theil−Sen linear trend line
+95% confidence interval
−95% confidence interval
10 m resolution elevation
datasets are used for the
analysis reported here.
The drainage density is
estimated as the number
of channelized pixels in a
basin given by the skeleton
of likely channlized pixels
in GeoNet 2.0
Mann-Kendall coefficient adjusted for ties: -0.31736
Mann-Kendall coefficient not adjusted for ties: -0.31306
p value: 1.1022e-05
sen’s slope: -0.020402
0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
0
5
10
15
20
25
30
35
Runoff intensity from NOAA PFD server (mm/hr)
Drainagedensity(D
m
)[miles/sqmiles]byMelton1957
Drainage density vs Runoff intensity
data
Theil−Sen linear trend line
+95% confidence interval
−95% confidence interval
Mann-Kendall coefficient adjusted for ties: 0.26587
Mann-Kendall coefficient not adjusted for ties: 0.26227
p value: 0.00023114
sens slope: 646.0309
0 10 20 30 40 50 60 70
0
5
10
15
20
25
30
35
Percent bare of landscape(b)(%)
Drainagedensity(D
m
)[miles/sqmiles]byMelton1957
Drainage density vs Percent bare of landscape
data
Theil−Sen linear trend line
+95% confidence interval
−95% confidence interval
Mann-Kendall coefficient adjusted for ties: 0.36011
Mann-Kendall coefficient not adjusted for ties: 0.35135
p value: 0.0022266
sens slope: 0.21467
0 20 40 60 80 100
5
10
15
20
25
30
35
Percent bare of landscape(b)(%)
Drainagedensity(Dm
)[miles/sqmiles]byGeoNet
Drainage density vs Percent bare of landscape
data
Theil−Sen linear trend line
+95% confidence interval
−95% confidence interval
Mann-Kendall coefficient adjusted for ties: 0.34767
Mann-Kendall coefficient not adjusted for ties: 0.33647
p value: 0.00047632
sens slope: 0.10433
0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
5
10
15
20
25
30
35
Runoff Intensity from NOAA PFD server(mm/hr)
Drainagedensity(D
m
)[miles/sqmiles]byGeoNet
Drainage density vs Runoff Intensity
data
Theil−Sen linear trend line
+95% confidence interval
−95% confidence interval
Mann-Kendall coefficient adjusted for ties: 0.1523
Mann-Kendall coefficient not adjusted for ties: 0.15
p value: 0.023361
sens slope: 344.7298
Mann-Kendall coefficient adjusted for ties: -0.24649
Mann-Kendall coefficient not adjusted for ties: -0.24267
p value: 0.00024225
sens slope: -0.013957
100 200 300 400 500 600 700 800 900
5
10
15
20
25
30
35
Mean Annual Precipitation from PRISM climate dataset (mm)
Drainagedensity(Dm
)[miles/sqmiles]byGeoNet
Drainage density vs Mean annual precipitation
data
Theil−Sen linear trend line
+95% confidence interval
−95% confidence interval
y = -0.0313x + 134.61
R² = 0.2131
y = -0.0127x + 25.287
R² = 0.1393
1
10
100
1000
0 500 1000 1500 2000 2500
Andisols
Entisols
Inceptisols
Mollisols
Spodosols
Ultisols
Null
Melton 1957 Data
0
5
10
15
20
25
30
35
0 100 200 300 400 500 600 700 800 900 1000
Alfisols
Ardisols
Entisols
Inceptisols
Mollisols
Melton 1957 datasets grouped by soil order
Mean annual precipitation from PRISM climate data (mm)
DrainagedensitybyGeoNet(miles/squaremiles)
Mean annual precipitation from PRISM climate data (mm)
DrainagedensitybyGeoNet(miles/squaremiles)
Conclusion
The general trends of drainage density with climatic parameters such as precipitation and runoff intensity remains the same.
Mann Kendall tests show that the trends are significant.
The drainage density seems to be controlled by the dominant soil order under similar climatic patterns.
(1) Patterns of channelization carry strong, codependent signatures in the form of statistical correlations
of rainfall variability, soil type, and vegetation patterns.
(2) Channelization patterns reflect the erosion processes on sub-catchment scale and the subsequent
processes of vegetation recovery and gullying