Statistics and Spatial Interpolation

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28-0-0 @ 150 lbs/A Hydra-Hume @ 1gal/A +CoRoN 25-0-0 @ 2 gal/A

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$22.05/Aprofit increase

Improving Wheat Profits

2005- Eakly, OK Irrigated, Behind Cotton

r correlation coefficient◦ P and K, slope and texture, N and OM◦ Are they correlated at that site

r2 correlation of determination ◦ N and yield, irrigation and yield, lime and soil pH◦ Independent (controlled) and dependent (result)

R2 Regression how well does a model explain the data. Linear, quadratic, Linear plateau

The 3 R’s

Regression R2

Interpolation:In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.

Methods◦ Proximal / Inverse Distance◦ Moving Average/distance weighted.◦ Triangulation ◦ Spline◦ Kriging provides a confidence in estimates

produced.

Spatial Interpolation

Inverse Distance Weighting (IDW) is a type of deterministic method for multivariate interpolation with a known scattered set of points. The assigned values to unknown points are calculated with a weighted average of the values available at the known points.

The name given to this type of methods was

motivated by the weighted average applied since it resorts to the inverse of the distance to each known point ("amount of proximity") when assigning weights.

Inverse Distance Weighting

Known value, distance between and a Power

How much could distance influence value of unknown. identify the power that produces the minimum RMSPE root mean square prediction error

IDW

Shepard's interpolation in 1 dimension, from 4 scattered points and using p=2.

Kriging is a group of geostatistical techniques to interpolate the value of a random field (e.g., the elevation, z, of the landscape as a function of the geographic location) at an unobserved location from observations of its value at nearby locations.

Kriging belongs to the family of linear least squares estimation algorithms

Use of variograms.

Kriging

Kriging

Example of one-dimensional data interpolation by kriging, with confidence intervals. Squares indicate the location of the data. The kriging interpolation is in red. The confidence intervals are in green.

In IDW, the weight, ?i, depends solely on the distance to the prediction location. However, in Kriging, the weights are based not only on the distance between the measured points and the prediction location but also on the overall spatial arrangement among the measured points.

To use the spatial arrangement in the weights, the spatial autocorrelation must be quantified.

Thus, in Ordinary Kriging, the weight, ?i , depends on a fitted model to the measured points, the distance to the prediction location, and the spatial relationships among the measured values around the prediction location.

Impact of Resolution of samples