Comparisons of NDVI values

Dean Monroe

Location

Field

Field with N-rich Strip

N-rich Strip

118 120 122 124 126 128

Longitude

0

40

80

120

La

titu

de

N-Rich Strip Compressed Latitude

Distributional Assumptions

0.35 0.40 0.45 0.50 0.55 0.60 0.65

05

01

00

15

0

N-Riched Strip

0.1 0.2 0.3 0.4 0.5 0.6 0.7

01

00

02

00

03

00

04

00

05

00

0

Whole Field

Comparison of NDVI values

Comparing NDVI Values

Iteration

P V

alu

e

0 200 400 600 800 1000

0.0

0.0

20

.04

0.0

6

100 Sample 1000 Iteration T test Assumption:

1. Strip NDVI is Equal to Whole Plot NDVI

Findings:

1. There is a 99.998 % confidence in the falsehood of the assumption of equality

2. This test was performed using standard t and Welch Modified t

Correlation by LongitudeAssumption:

1. Row to row correlation

Findings:

- Correlation is low from row to row

Variogram Interpretation

Distance by 4m lagdist and 2m lag tolerance

Ga

mm

a

0 20 40 60 80

0.0

0.0

01

0.0

02

0.0

03

Omni-directional Semi-Variogram for Macoy

N-rich StripN-rich StripN-rich StripN-rich Strip

Whole Field

Whole field reaches sill in approx. 22 m whereas strip reaches sill in approx. 17 m.

Variogram Assumptions

Data is continuous between sample pointsTobler’s First Law of Geography: “everything is related to everything

else, but closer things are more closely related” (Tobler, W., 1970 Econ Geog 46)

Spatial Statistics (Classical)

Geostatistics Continuous realizations between

samples in continuous space

Lattice Data Continuous realizations in a discrete

vector space

Point Distributions Binomial in continuous vector space

Lattice Data in SpaceAssumption of countable and finite occurrences of realization

Realizations occur in discrete space

Correlation structure depends on the “Neighbor” conceptIs the spatial equivalent of regular time series analysis

Uses a similar class of “auto” models and the Markov Property

A Lattice has the following assumptions Translation Invariance (Location is not a factor) Pairwise-Only Dependence (Simplifying Assumption) Positivity (All possible neighborhood system exist)

Attributes of Lattice Data

Has a multi-variable extensionUtilizes multiple Neighborhood configurations (five in common use)Performs on both regular and irregular lattices as long as:

mjiNtNt

miforNt

tttN

ijji

ii

ikki

,...1, ,

,...1

} ofneighbor a is :{

Reasons for using a Lattice

No assumption of data between pointsBetter suited for separation of large and small scale effects (e.g. Median Polish)

Preferential Clustering The Proportional Effect

Variation Scale Small)(:

effectColumn effect Row Effect Grand)(:

)()(

t

t

ttZ t

Statistics on lattice

Spatial auto-correlation (SAC) Moran’s (I) –Similar to Pearson’s

Moment Geary’s Index (C)

Attribute Pattern Geary's (C) Moran's (I)Clustering of Values 0 < C < 1 I > E(I)Random Assignment C ~ 1 I ~ E(I)Dispersed Attributes 1 < C < 2 I < E(I)

E(I) = (-1)/(n-1) 0 for large nJ. Lee and D. Wong 2001

Example

Subset whole plot into rectangular grid the length of the N-rich and wide as provided by complete rowsPerform SAC on raw and polished gridPerform similar analysis on N-rich stripCompare degree of spatial relatedness

Before Median Polish

621850 621900 621950 622000 622050

long

lat

After Median Polish

621850 621900 621950 622000 622050

long

lat

Results

Geary's (C) Moran's (I)Raw 0.6775 0.3167Polished 0.5339 0.4592E(I)=-1.86 EE-4 - The Polished data yields better correlation values- Both Indices show a moderate degree of clustering

Geary's (C) Moran's (I)Raw 0.7899 9.60E+07Polished NA NA

Whole Plot

Strip

E(I)=-1.0 Approx-Little to no Clustering-Median Polish failed

Interpretation

Results are based on first-order neighbor structure Neighborhood system of one unit lagged

cells. No diagonals

Values in Whole Field experiment are more clustered than those in the StripCaveat: Narrowness of the strip could have contributed to correlation value being low. Ultimately, there is probably a better method for this data.

Extensions for this analysis

Build second-order,hexagonal in, hexagonal out, and diagonal neighborhood systemsExplore assumption of free sampling verses non-free sampling (Assumption of how the data is distributed)Use irregular grid where nearest neighbor systems are defined by distance or nearest (k) neighbors (nonparametric approach) If yield data can be obtained, use NDVI to regress yield with spatial correlation adjustment (similar to regression with auto-correlated error terms