Spatial Variability of Soils

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Spatial Variability of Soils

• Agronomy 577
• Soil Physics
• Brian K. Gelder

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Spatial Variability of Soils

• Each soil is unique
• However, to describe them we need to group them
  into similar categories
• Similar texture, hydrology, profiles, etc.
• This means they vary on many scales
• Different is relative to what you are comparing to

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How to Describe Variation

• So, how do we describe this variation?
• Statistics
• Im assuming you know
• Mean, µ
• Standard Deviation, s
• Well cover
• Coefficient of Variance (CV) s/µ
• Necessary sample sizes to estimate mean and SD
• Geostatistics

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How big a sample size do you need

• Since my subject varies, how much do I need to
  sample it to know the mean?
• Exact question How many points are needed to
  estimate with a confidence of 100(1-a) that
  the mean is within a range of µ-d and µd?
• Z0.5a normalized difference from mean (remember
  numbers corresponding to points on the bell
  curve?)

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How big a sample size do you need

• Example Samples to estimate mean clay
• Variance 40.7 (recall variance square of Std.
  Dev.)
• Confidence of 95 Z0.5a 1.96
• Within 5

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How big a sample size do you need

• Guidelines for variability of soil properties

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Correlated Observations

• If you sample one point
• A point one foot away will likely be similar
• A point one mile away will likely be different
• Study of this interdependence of spatial
  observations is called geostatistics

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Correlated Observations

• Values range from 29 to 43
• Mean 35 Std. Dev. 2.8

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Correlated Observations

• How do we numerically describe this variation?
• For h1980 we would compare values from z0 and
  1980 and z20 and 2000 for the part of the above
  equation in brackets
• For h20 we would have 99 comparisons in the
  brackets, i.e. z0 and 20, z20 and 40, etc.

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Correlated Observations

• h20 ?(h)3.88 or about 4 variation at 20 cm
• h500 ?(h)9 or about 9 variation at 500 cm

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Correlated Observations

• Idealized spherical variogram
• ?(h)C0C11.5(h/a)2-0.5(h/1)3 for 0lthlta
• ?(h) C0C1 for hgta
• C0 nugget, C0C1 sill, a range (distance at
  which observations become unrelated)

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Correlated Observations
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Interpolation Methods

• Three different methods
• Nearest Neighbor use the nearest point
• Inverse Distance Weighting
• Estimates by adding m nearest weighted points

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Interpolation Methods

• Kriging Developed by D.G. Krige
• Variogram model used to depict interdependence
• Estimate Z at unsampled point (x0,y0)
• Where ?i is chosen to be unbiased
• and ?i comes from a formula based on distance
  to the predicted point from sampled point

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Interpolation Methods

• Which is best?
• No easy answer
• Root Mean Square Error (RMSE)
• RMSE
• Where Zi measured value and Zi predicted

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Example

• sand values were collected for a soil
• What is the predicted sand content at a point?
• Variogram nugget 2, sill 57, range 450m

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Example
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Example

• Kriging plot more smooth than Inverse Distance
  Weighted plot
• RMSE for interpolated values
• Standard Deviation 7.98
• Inverse Distance Weighting 3.81
• Kriging 3.66

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Questions?