Quantitative geomorphic analysis of LiDAR datasets –

application to the San Gabriel Mountains, CA

Roman DiBiaseLiDAR short course, May 1,

2008

Quantitative analysis of topography using LiDAR

• Airborne laser swath mapping (ALSM) consistently provides data good enough to produce 1m digital elevation models (DEMs)

• Ground-based systems can be used for finer scale analysis of millimeter to centimeter scale features

• These datasets are more than just pretty pictures; many important research questions have become testable as a result of this technology

There are many cases where detailed terrain modeling is needed

• Geomorphic mapping– fault scarps, landslides, stream terraces

• Geomorphic process studies– soil production rates, soil transport model

testing– knickpoint form, channel geometry/morphology

• Landscape monitoring– repeat scans using ground-based LiDAR

Alternatives to LiDAR

• Total station surveys– Time consuming!!

• Photogrammetry– Tree cover– Expensive

Field Area: San Gabriel Mountains, CA

modified from Blythe et al., 2000

30 km

NSAF = San Andreas FaultSMF = Sierra Madre FaultCF = Cucamonga FaultSGF = San Gabriel Fault = igneous/metamorphic rocks

10m NED Elevation (sea level – 3000 m)

30 km

Local relief (1km radius)

West-to-east gradient in uplift rate from low to high can be inferred from topography, quaternary slip rates, and low-temperature thermochronometry work

How do we obtain appropriate erosion rates?

• Thermochron cooling ages range from 3-60 Ma

• Even using geologic constraints, the inferred erosion rates are averaged over millions of years

• We need more geomorphically appropriate rates, on the order of landform development…

10Be is produced in quartz grains through the interaction of cosmic rays

with oxygen nuclei

Quartz grains accumulate 10Be proportional to the time they spend within the top meter or so of Earth’s surface.

Quartz grains accumulate 10Be during their path from bedrock to stream sand

By analyzing a bag of sand (~1 kg) in bulk we are in effect averaging over the entire area draining to the sample

Alluvial sand samples average exposure ages of millions of grains

Catchment-averaged sample location map

So far, erosion rates range from ~10 – 1000 m/My

OK, now that we have erosion rates…

• There are a few main questions we can tackle now

– How does hillslope form vary with erosion rate?– What is the erosion rate threshold for hillslope sensitivity?

– How does channel steepness vary with erosion rate?– Do channels have a similar threshold?– Does channel width vary with erosion rate?

– How are conditions different across transition zones (knickpoints)?

– How replicable are basin cosmo rates in bedrock landscapes?

Which processes are acting to lower the landscape?

• Hillslope processes

• Channel incision

• Debris flow scour

• Bedrock landsliding

Which processes are acting to lower the landscape?

• Hillslope processes

• Channel incision

• Debris flow scour

• Bedrock landsliding

Most understood!

What can channels tell us about erosion rates?

Channel long profile analysis

• Well-adjusted channel profiles tend to follow a power-law relationship between slope and drainage area

S = ks A-

– ks = channel steepness index: varies with uplift, climate, lithology

= concavity index: independent of uplift rate

elev

atio

n

distance log A

log

S

Duvall, Kirby, and Burbank, 2004

Cattle Creek

Slope-area plots extracted from 10m DEMs

Debris flow regime?

Fluvial regime S=ksnA-0.45

Cattle Creek

Slope-area plots extracted from 10m DEMs

Channel steepness index, ksn

Slope-area plots extracted from 10m DEMs

Cattle Creek

Spatial variations in erosion rates

red = high uplift zoneblue = low uplift zone

Temporal variations in erosion rates

Bear Creek

Temporal variations in erosion rates

knickpoint

knickpoint

Bear Creek

Temporal variations in erosion rates

knickpoint

knickpoint

ksn = 86ksn = 192

Bear Creek

Map of channel steepness index variation

Green = low channel steepness Red = high channel steepness

Channel steepness vs. cosmogenic erosion rate

NCALM seed project LiDAR coverage

30 km

200m

200m

Tutorial

• Channel network extraction– How do we define a channel?

• Scale issues– What problems do we run into when using

high-resolution elevation data?– Resampling high-resolution data

• Techniques to probe datasets– Extracting elevation profiles, slope profiles

100m

100m

1350

1400

1450

1500

1550

6400 6600 6800 7000 7200 7400 7600 7800

distance (m)

ele

va

tio

n (

m)

2m Lidar

field survey

Channel profile extraction, comparison with field surveys

Channel profile extraction, comparison with field surveys

1350

1400

1450

1500

1550

6400 6600 6800 7000 7200 7400 7600 7800

distance (m)

ele

va

tio

n (

m)

2m Lidar

field survey

1450

1475

1500

1525

1550

7100 7150 7200 7250 7300 7350 7400 7450 7500

distance (m)

ele

va

tio

n (

m) 2m Lidar

field survey

Pretty darn good, though there are some funny offsets

~12m offset

~25m offset

Stream extracted from 2m LiDAR DEM follows a tortuous path around large boulders, etc.

Channel is much wider than 1 pixel!

At high flow,channel is ~15-20m wide

100m

LiDAR contributions to understanding channel processes

• Flow paths are often wrong with high-res data, meaning drainage areas are troublesome to determine

• Local channel slope is underestimated in some cases due to critical jump in scale to less than channel width

• Despite this, lidar data contain valuable information concerning knickpoint form, width variation, and potentially bed roughness

What can hillslopes tell us about erosion rates?

Hypothesis:With increasing erosion rates, slopes

steepen, soil thickness decreases, but once maximum soil production rate is exceeded, threshold, landsliding slopes dominate

Hillslope angle vs. cosmogenic erosion rate

Determining the soil production function

• Use 10Be to measure soil production rate• Exp. relationship between soil thickness and

production

• Does this relationship vary with erosion rate?• Does max soil production rate vary?

maximum soil production rate

log

soil

prod

uctio

n

soil thickness

ssrs qt

e

t

h ~

accumulation

production

transport

Soil continuity equation

Heimsath et al., Nature 388, pp 358-361 (1997)

The Soil Production Function

ssrs qt

e

t

h ~

zqs ~

zt

e

r

s 2

0t

hassume

start with continuity equation

K is constant

soil production topographic curvature

(from LiDAR)

Slope dependent transport processes

tree throw

burrowing

http://wdfw.wa.gov/wlm/living/gophers.htm

rain splash

Soil transport models

• In a simplified view, we can think of the previous processes as acting linearly with slope

• However, slopes reach a threshold near 35-40 degrees, and mass wasting dominates

• How do we deal with this transition?

zqs ~

Non-linear soil transport

• One way to think about this is to have linear transport with a threshold…

• Field data suggest a more gradual transition to threshold slopes

cs S

zzq 1~

(Roering et al. 1999)

zKqs ~cSz 0

Transport model comparison

Roering et al., 1999; WRR 35, p. 853-870

LiDAR contributions to understanding hillslope processes

• High resolution topography is needed to characterize curvature (second derivative!!)

• We can use this to guide fieldwork and the construction of soil production functions calibrated with cosmogenics

• Differences in transport models are subtle, definitely not distinguishable at 10m, but may be resolved at 1m

Dimensionless relief

C

HHT

c

Hsr

c

S

LC

KS

LEE

S

SR

2)/(2*

*

Dimensionless erosion

Even with high resolution topography, nature is still messy!

•How can we best extract information from high-resolution DEMs?

•Monte-carlo methods?

•Hand picking ‘representative’ hillslopes?

following Roering et al. 2007

Ground-based scanning LiDAR

• Up to millimeter scale resolution

• Allows for extremely detailed monitoring studies, using repeat scans

• Potential geomorphic applications include studies of bedrock erosion, sediment transport, and bed roughness modeling

Measuring bedrock erosion in the Henry Mountains, UT

Point cloud data from bedrock erosion monitoring on Colorado

Plateau(photo-derived color)

Images courtesy Steve DeLong

Images courtesy Steve DeLong

8 scans merged together

Images courtesy Steve DeLong

8 scans merged together (photo-derived color)

Images courtesy Steve DeLong