Vamsi

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 wasnt randomly allocated.
• We expect perhaps some spatial autocorrelation
  among the sample sites.

4
Simple calculations

• Author calculated simple pooled t-test
• p .809.
• p gt a
• Thus no relation
• Doesnt account for spatial autocorrelation among
  the 195 chisel-plow and 200 non-till strips.
• Doesnt 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.

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What does this mean? I know youre 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 its 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, wed have to include spatiality instead
  of linear model
• TC(si) ß0 ß1TN(si) e(si)
• Errors are spatially correlated.
• We need to model it though

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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,
  ß0 intercept and ß1 TN.

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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. Wowestimates of the expected
  value of TC and Predictions of TC are almost the
  same. Amazing! pg 684