by Luke Worsham M.S. Candidate

1. 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

2. The Global Carbon Cycle http://earthobservatory.nasa.gov/Library/CarbonCycle/carbon_cycle4.html

3. 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 (β-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

4. 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)

5. What influences soil carbon? • Input - Leaf litter deposition and decomposition - Belowground biomass • Soil attributes - Clay content - Mineralogy • Environmental covariates - Temperature - Moisture - Microorganism nutrient cycling

6. 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

7. 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)

8. Part I:Using Spatial Dependence to Estimate Soil Carbon Contents Under Three Different Landcover Types in the Piedmont of Georgia

9. Does the spatial dependence and structure of soil C content depend on landcover? Hypothesis: Pasture would demonstrate largest range and spatial structure.

10. What is spatial dependence and structure?

11. Tobler’s Law 1st Law of Geography:Everything 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)

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

14. 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)‏

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

16. 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

17. 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

18. 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/nugget:sill ratio were analyzed with One-way ANOVA (n=2)

19. Distribution of Pairwise Distances Frequency Count Midpoint of Intervals 64 Samples  Number of Pairs = 64! / (2!(64 – 2)!) = 2016

20. 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 - Nugget:Sill ratio

21. Results

22. Bulk Density (g cm-3) Block Landcover Mean St. Error Range Sill Nugget Nugget:Sill g·cm-3 m 1 Hardwood 1.09 0.02 39.4 0.0179 0.0144 0.81 Pine 1.19 0.02 28.8 0.0176 0.0111 0.63 Pasture 1.52* 0.01 79.5 0.0083 0.0058 0.70 2 Hardwood 0.98 0.02 98.8 0.0160 0.0136 0.85 Pine 1.11 0.02 98.8 0.0180 0.0089 0.49 Pasture 1.37* 0.02 77.9 0.0191 0.0106 0.56 • Landcover* (p < 0.01) • Block* (p < 0.03) • Highest for pasture across blocks • Major range and spatial structure were not affected by landcover or block

23. C concentration (%) Block Landcover Mean St. Error Range Sill Nugget Nugget:Sill -------%------- m 1 Hardwood 3.67 0.09 98.8 0.552 0.332 0.60 Pine 2.34 0.08 98.8 0.422 0.354 0.84 Pasture 1.95 0.04 42.9 0.119 0.066 0.56 2 Hardwood 4.10 0.09 98.8 0.600 0.204 0.34 Pine 2.31 0.10 98.8 1.215 0.251 0.29 Pasture 1.62 0.04 98.8 0.257 0.042 0.28 • Landcover* (p < 0.03) • Block (p < 0.92) • Highest for hardwood across blocks; lowest for pasture • Major range and spatial structure were not affected by landcover or block

24. Total C Content (kg ha-1) Block Landcover Mean St. Error Range Sill Nugget Nugget:Sill kg ha-1 m 1 Hardwood 29884 896 64.0 5.41·107 3.95 ·107 0.73 Pine 20694 609 28.8 2.28·107 2.18 ·107 0.96 Pasture 22216 611 79.5 1.73·107 9.62 ·106 0.56 2 Hardwood 29865 774 98.8 4.19·107 2.53 ·107 0.60 Pine 18932 839 98.8 4.61·107 2.86 ·107 0.62 Pasture 16558 428 77.9 1.32·107 6.27 ·106 0.47 • Landcover (p < 0.28) • Block* (p < 0.06) • Highest for hardwood across blocks (p < 0.04) • Major range and spatial dependence were not affected by landcover or block asd

25. Leaf Litter C Concentration (%) Block Landcover Mean St. Error Range Sill Nugget Nugget:Sill kg ha-1 m 1 Hardwood 29.91 0.72 94.6 33.3 33.3 1.00 Pine 33.96 1.19 80.4 65.6 59.8 0.91 Pasture - - - - - - 2 Hardwood 30.33 0.95 98.8 75.1 22.2 0.30 Pine 33.00 1.15 39.7 0.0307 0.0259 0.84 Pasture - - - - - - • Landcover (p < 0.13) • Block (p < 0.76) • Major range and spatial dependence were not affected by landcover or block ffff

26. 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 < 10 m (Schöning et al., 2006; Liski, 1995)

27. 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)

28. Applications—How 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

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

30. 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 > or < 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

31. Part II:A Comparison of Four Landscape Sampling Methods to Estimate Soil Carbon

32. 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?

33. 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?

34. Introduction A comparison of 4 different landscape sampling methods using 5 different sampling sizes: Sampling MethodsSampling 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%)

35. 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

36. Methods 21 by 43 plots

37. Landscape Variables Planiform Curvature Slope (%) Landcover Soil Series

38. What’s a Latin hypercube? Latin Square Hypercube > 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.

39. Selecting Sampling Locations: Simple Random • No variable consideration n = 10 n = 40 n = 100 n = 300 n = 500

40. Selecting Sampling Locations: Systematic Sampling • Random Start; Consistent Spacing by Row n = 10 n = 40 n = 100 n = 300 n = 500

41. Selecting Sampling Locations Stratified Random cLHS n = 10 n = 40 n = 10 n = 100

42. 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

43. 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

44. Results Stratified Random cLHS

45. Results Total C Content Random Systematic Stratified cLHS Population N = 10 Mean 25064 42191 21619 22719 23997 St. Dev. 5176 34892 6445 5349 10346 Median 25296 26356 21658 22148 22759 N = 40 Mean 24756 25987 23587 25070 23997 St. Dev. 9697 16411 6487 8912 10346 Median 23777 21728 23222 23204 22759 N = 100 Mean 24649 24220 24414 23545 23997 St. Dev. 12145 12107 11335 9133 10346 Median 22927 22876 22700 22344 22759 • 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

46. 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

47. 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

48. 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

49. 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...

50. Questions?