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Spatial Random Field Models – Comparing C/N Ratio among Tillage Treatments

Spatial Random Field Models – Comparing C/N Ratio among Tillage Treatments. Vamsi Sundus Shawnalee. Purpose. “Data collected under different conditions (i.e. treatments)  whether the conditions are different from each other and […] how the differences manifest themselves.”

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Spatial Random Field Models – Comparing C/N Ratio among Tillage Treatments

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  1. Spatial Random Field Models – Comparing C/N Ratio among Tillage Treatments Vamsi Sundus Shawnalee

  2. Purpose • “Data collected under different conditions (i.e. treatments)  whether the conditions are different from each other and […] how the differences manifest themselves.” • This data concerns soil.

  3. The Setup • Soils are first chisel-plowed in the spring • Samples from 0-2 inches were collected. • Measured N percentage (TN) • Measured C percentage (CN) • Calculated C/N, ratio between the two treatments. • Looking at the sample setup on 674, we see that it wasn’t randomly allocated. • We expect perhaps some spatial autocorrelation among the sample sites.

  4. Simple calculations • Author: calculated simple pooled t-test: • p = .809. • p > α • Thus no relation… • Doesn’t account for spatial autocorrelation among the 195 chisel-plow and 200 non-till strips. • Doesn’t convey the differences in the spatial structure of the treatments.

  5. Analysis • They used SAS to obtain least squares + restricted maximum likelihood  common nugget effect was fit. • Considerable variability of C/N ratios due to nugget effect. • Using “proc mixed” we get predictions of the C/N ratio.

  6. Analysis (cont.) • With proc mixed we assume that the C/N ratios are assumed to depend on the tillage treatments. • The SAS program is included in the section. Omitted since this is a class in R. • But, in the programming • Semivariogram – ensure both have same nugget effect.

  7. Looking at the SAS Generated Output • Pg 677-678 (SAS Output) • Looking at the curvy wavy thingy (surface plots) • We see one looks smoother and more predictable (no-tillage). This means greater spatial continuity (larger range). I.e. positive autocorrelations = stronger over same distance.

  8. What does this mean? I know you’re lost. • At this point in the analysis: • There is no difference in the average C/N values in the study. [when sampling two months after installment of treatment.] [pooled t-test] • There are differences in the spatial structure of the treatments [3D plot]. • If we do a SSR (sum of squares reduction) we see that it’s extremely significant that a single spherical semivariogram cannot be used for bother semivariograms (Ha). • Using ordinary least squares we also find significance, but less so. • .0001 versus .00009 • .-3-1 versus .-4-9.

  9. Next section

  10. Spatial Regression of Soil Carbon on Soil N • What if only one variable was important (i.e. either C or N) but not the combination of the two (i.e. C/N or N/C ratio)? • Here: Consider: predicting soil carbon as a function of soil nitrogen. • From the scatterplot (TC v TN) we see an extremely strong correlation of sorts. [pg. 679]

  11. Good model • If we wanted to have a more accurate model though, we’d have to include spatiality: instead of linear model: • TC(si) = β0 + β1*TN(si) + e(si) • Errors are spatially correlated. • We need to model it though

  12. e(si) • Need to model the semivariogram. Two steps • Model fit by normal least squares and the “empirical semivariogram of the OLS residuals is computed to suggest a theoretical semivariogram model.” • We need the theoretical model to get initial semivariogram parameters. • Need mean and autocorrelation structure  restricted maximum likelihood. • Here: we use proc mixed to estimate both the mean function and the autocorrelation structure (and predictions at unobserved locations).

  13. Output Analysis • (1-Residual sum of squares)/corrected total sum of squares = .92 = estimate of R2 • Doing the proc mixed procedure, we generate a lot of output: 9.17 (pg 682 – 683) • From the output generated we look at the “solutions for fixed effects” for estimates of the parameters were interested in. Specifically, β0 = intercept and β1 = TN.

  14. What does this mean? • For every additional percent of N, we increase C by 11.11 percentage points. • After playing a short game of “find the difference” on 9.50, I see that they are nearly the same patterns. Wow…estimates of the expected value of TC and Predictions of TC are almost the same. Amazing! [pg 684]

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