M

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Spatial Dependence and Multivariate
Stratification for Improving Soil Carbon
Estimates in the Piedmont of Georgia
by Luke Worsham M.S. Candidate
Major Professor Daniel
Markewitz Committee Nate
Nibbelink
Larry T. West
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The Global Carbon Cycle
http//earthobservatory.nasa.gov/Library/CarbonCyc
le/carbon_cycle4.html
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Carbon Cycle

• Soils represent largest terrestrial pool of C
• -1500 PgC (twice the atmospheric pool 300 times
  
• annual atmospheric release)
• 2 PgC unaccounted for ? missing sink (ß-factor)
• 2 PgC annual oceanic uptake
• Current rate of atmospheric increase determined
  by
• relative rate of ocean uptake
• -Uptake rate increasing more slowly than rate of
  emissions

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• Why estimate soil carbon?
• Soil carbon sequestration ameliorates excess
• greenhouse gases from the atmosphere
• Carbon registries
• Chicago Climate Exchange (2002)
• California Climate Action Registry (2001)
• Georgia Carbon Sequestration Registry (2004)
• Climate Registry (2007)
• Regional Greenhouse Gas Initiative (2009)

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What influences soil carbon?

• Input
• - Leaf litter deposition and decomposition
• - Belowground biomass
• Soil attributes
• - Clay content
• - Mineralogy
• Environmental covariates
• - Temperature
• - Moisture
• - Microorganism nutrient cycling

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How do we currently estimate soil carbon content
and change?

• Look-up tables
• USFS developed regional set of look-up tables
• 40 biomes compositions, age, productivity,
  history
• Models
• FORCARB (Century Roth-C) estimates
• Carbon budget land-use change and harvest
  predictions
• Direct Sampling
• Registries require small area estimates often
  heterogeneous landscapes ? direct sampling

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Objectives

• How can we improve the efficiency, accuracy, and
  precision of direct soil sampling?
• Does the spatial dependence and structure of soil
  C content depend on landcover? (Part I)
• Does incorporating ancillary landscape attributes
  affect our ability to estimate soil C content?
  (Part II)

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Part IUsing Spatial Dependence to Estimate
Soil Carbon Contents Under Three Different
Landcover Types in the Piedmont of Georgia
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Does the spatial dependence and structure of soil
C content depend on landcover?
Hypothesis Pasture would demonstrate largest
range and spatial structure.
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What is spatial dependence and structure?
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Toblers Law
1st Law of GeographyEverything is related to
everything else, and near things are more related
than distant things. -W. Tobler (1970)

• Spatial Autocorrelation Quantified by a
  semivariogram

• Separated into bins by lag distances (h)

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Methods

• Samples collected in BF Grant Memorial Forest
  during summer 2006
• 6 Plots Total 2 for landcover, grouped into 2
  blocks
• Hardwood gt 70 years Oak-hickory type
• Managed pine plantation 25 years old
• Grazed pasture gt 70 years

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Methods

• All plots occurred on Davidson loam or clay loam
  ultisols (Kaolinitic Kandiudults)
• with the exception of pine plot in block 2 Vance
  (Typic Hapludult) and Wilkes sandy loam (Typic
  Hapludalf)

(Cecil Series)?
(Wilkes Series)?
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Field Methods

• 64 Sampling Locations per plot in cyclical
  pattern (Burrows et al., 2002) to facilitate
  semivariograms

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Field Methods

• At each location
• 1 bulk density core (7.5 cm depth)
• 3 samples augered (7.5 cm depth), composited
• Leaf litter collected from each of 4 locations,
  composited

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Lab Methods

• Bulk densities dried before weighing corrected
  for roots, rocks
• Soil composites dried, sieved (2mm), ground, and
  dry combusted to determine C N contents
• Same for leaf litter

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Analysis

• C N concentrations () multiplied by bulk
  density (g/cm-3) yield content to 7.5cm
• These data, along with leaf litter, were added to
  GIS attribute table for samples
• Generated semivariograms for each soil property
  at each plot using ArcGIS Geostatistical Analyst
  and SAS (Proc VARIOGRAM)?
• Semivariograms were fit using spherical models to
  express spatial dependence and structure
• Averaged plot data and range/nuggetsill ratio
  were analyzed with One-way ANOVA (n2)

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Distribution of Pairwise Distances
Frequency Count
Midpoint of Intervals
64 Samples ? Number of Pairs 64! / (2!(64
2)!) 2016
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What does a semivariogram tell us?

• Correlation threshold
• - Major range
• Overall variability
• - Sill
• Degree of measurement error or micro-scale
  variation
• - Nugget effect
• Strength, or amount of spatial dependence
• - NuggetSill ratio

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Results
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Bulk Density (g cm-3)

• Landcover (p lt 0.01)
• Block (p lt 0.03)
• Highest for pasture across blocks
• Major range and spatial structure were not
  affected by landcover or block

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C concentration ()

• Landcover (p lt 0.03)
• Block (p lt 0.92)
• Highest for hardwood across blocks lowest for
  pasture
• Major range and spatial structure were not
  affected by landcover or block

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Total C Content (kg ha-1)

• Landcover (p lt 0.28)
• Block (p lt 0.06)
• Highest for hardwood across blocks (p lt 0.04)
• Major range and spatial dependence were not
  affected by landcover or block

asd
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Leaf Litter C Concentration ()

• Landcover (p lt 0.13)
• Block (p lt 0.76)
• Major range and spatial dependence were not
  affected by landcover or block

ffff
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Summary

• Landcover
• only significant for bulk density soil C
  concentration, but not soil C content
• Major range (for soil C content)
• Within the scale of the plots only for pasture
  in both blocks (medium structure)
• Forested plots were inconsistent, 98.8m in block
  2 for C content (maximum lag with weak structure)
• Suggests dependence below or above scale of the
  plot (limited by 10
• 100m point separation)
• Supported by high nugget effect
• Other studies have shown variation in C at scales
  lt 10 m (Schöning et
• al., 2006 Liski, 1995)

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• Overall, inconsistencies of spatial structure and
  dependence between landcovers suggests influence
  of other variables, such as topography (Moore et
  al., 1993 Gessler et al., 2000 Thompson
  Kolka, 2005)

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ApplicationsHow do we incorporate spatial
dependence for C content estimates?

• Kriged surfaces incorporate spatial dependence in
  their estimates and are continuous
• Block kriging sums surface over plot to create
  average estimate

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Applications

• However, quality of kriged estimates are related
  to spatial structure

Block Krige Estimate Block Krige Estimate Block Krige Estimate
Block Landcover Total C Content St. Error St. Error St. Error St. Error
------kgha-1----- ------kgha-1----- ------kgha-1-----
1 Hardwood 29608 6902 6902 6902 6902
Pine 20770 4840 4840 4840 4840
Pasture 22369 3822 3822 3822 3822
2 Hardwood 30252 5564 5564 5564 5564
Pine 19538 5400 5400 5400 5400
Pasture 16785 2885 2885 2885 2885
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Conclusions

• Spatial dependence was not well defined by
  landcover
• - Factors other than landcover (i.e.
  topography) most likely play significant role in
  determining spatial structure of soil C content
• Many soil properties demonstrated ranges
  maximum lag
• - Suggests dependencies gt or lt scale of plot
• Higher standard errors in forested plots for soil
  C concentration and content suggest necessity for
  more intensive sampling due to local
  heterogeneities
• Further information about spatial structure and
  dependence would be necessary in these landcovers
  for kriging estimates to be useful
• Kriging more useful in pasture estimates
• - Stronger spatial structure consistent ranges

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Part IIA Comparison of Four Landscape Sampling
Methods to Estimate Soil Carbon
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Questions
Does the manner in which samples are located
affect our ability to estimate soil C content?
Does incorporating ancillary landscape
attributes affect our ability to estimate soil C
content?
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Introduction
Introduction

• Builds on study by Minasny McBratney (2006)
• Tested relative ability of random, stratified,
  and cLHS sampling to approximate ancillary data
  distributions
• But what if ancillary data are covariates for a
  different variable of interest, such as soil C
  content...
• -Will extra stratification in the presence of
  data afford better estimates?

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Introduction

• A comparison of 4 different landscape sampling
  methods using 5 different sampling sizes
• Sampling Methods Sampling Sizes
• Random Sampling - 10 samples (1)
• Systematic Random Sampling - 40 samples (5)
• Stratified Random Sampling - 100 samples (12)
• Conditioned Latin Hypercube - 300 samples (35)
• Sampling - 500 samples (58)

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Methods

• Samples collected in BF Grant Memorial Forest
  during summer 2007
• Single plot with 903 sampling locations on 10x10
  grid
• Same sampling scheme 1 Bulk Density, 3 Soil
  Composites (1, 2.5, 5m 120)
• Same lab prep dry combustion to
• determine C N
• concentrations
• Combined with
• bulk densities for
• total C content

Sample Space BF Grant
Managed Pine 33 24
Natural Pine 27 28
Hardwood 32 26
Pasture 8 14
Other 0 7
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Methods
21 by 43 plots
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Landscape Variables
Planiform Curvature
Slope ()
Landcover
Soil Series
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Whats a Latin hypercube?
Latin Square
Hypercube gt 3 dimensions

Minasny, B., McBratney, A.B., 2006. A conditioned
Latin hypercube method for sampling in the
presence of ancillary information. Computers
Geosciences 32, 1378-1388.
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Selecting Sampling Locations Simple Random

• No variable consideration

n 10
n 40
n 100
n 300
n 500
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Selecting Sampling Locations Systematic Sampling

• Random Start Consistent Spacing by Row

n 10
n 40
n 100
n 300
n 500
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Selecting Sampling Locations
Stratified Random
cLHS
n 10
n 40
n 10
n 100
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Results

• Random and Systematic overestimate mean at low
  sample size
• Stratified and cLHS underestimate mean at low
  sample size
• No estimate excludes population mean from 95
  confidence interval
• Systematic sampling yielded largest confidence
  intervals
• All methods converge at larger sample sizes

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Results

• Lowest sampling size (n 10) poor approximation
  for any method
• cLHS remains most consistent at small sample size
  (n 40, 100)
• cLHS provides better approximation of
  distribution tails

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Results
Stratified Random
cLHS
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Results

• cLHS, stratified, and random provide close
  estimates of mean at small sample sizes
• Systematic consistently overestimates mean, least
  accurate for mean and std. dev.
• cLHS approximates median well at small sample
  sizes, along with stratified at larger n

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Sample Size Considerations

• Sample sizes n 300 n 500 are
  unrealistically large estimates have
  converged ? utility of stratification techniques
  at much smaller sizes
• Often commercial scale sampling conducted on 1-ha
  grids (Kravchenko, 2003 Mueller et al., 2001),
  but often this scale is regarded as marginal or
  insufficient to estimate soil properties (Mueller
  et al., 2001 Hammond, 1993 Wollenhaupt, 1994)
• Therefore, n 40 and n 100, representing 5
  and 12 sampled area, represent most realistic
  proportions

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Conclusions

• Stratified design showed the narrowest confidence
  interval / best mean approximation when n 40
• cLHS demonstrated the most accurate mean,
  standard deviation, population distribution
  approximation, and narrowest confidence interval
  when n 100
• Might expect a threshold below n 100 at which
  cLHS affords better estimation than stratified
  due to extra variables
• Or, additional continuous variables may offer
  less predictive ability than discrete variables
• Extra effort of systematic sampling appears
  inadequate at all sizes ? even simple random is
  preferable
• At mid-sample sizes (realistic sizes), some
  degree of stratification affords better
  estimates, and is therefore recommended
• Ancillary data can possibly improve efficiency of
  sampling and accuracy of estimates for minimal
  additional effort

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Take-Home Message
Part I Landcover alone does not completely
describe spatial attributes of soil C content
variation also exists outside the scale of our
plots Part II Stratified sampling methods
(stratified random, cLHS) with consideration of
ancillary variables may provide more accurate
estimates of soil C content
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The End
Acknowledgments Daniel Markewitz, Nate
Nibbelink, Larry West, Emily Blizzard, Danny
Figueroa, Erin Moore, Scott Devine, Marco Galang,
Sami Rifai, Patrick Bussell, Budiman Minasny,
Dustin Thompson, Jay Brown, my family, my
friends, and many others...
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Questions?