Applying Map Analysis Techniques
To Site-Specific Management
Part 2: Mapped Data Analysis
and Spatial Modeling
Joseph K. Berry
Berry & Associates
2000 South College, Suite 300
Fort Collins, CO 80525
Email: jberry@innovativegis.com
Web Site: www.innovativegis.com/basis
Utilizing Remote Sensing for PF
Collecting Remote Sensing Data:
Demo of Video Mapping System
Proximal Sensing:
• Film Cameras
• Video Mapping
Aerial Remote Sensing:
• Film Cameras
• Video Mapping
• Scanners
A video camera is a broadband scanner
Satellite Imaging:
• Scanners
Normalized Density Vegetation Index
(NDVI)… plant vigor
(Berry)
Geo-Registration of Imagery
Geo-registration is facilitated by GPS mapping
ground features visible in the image
• Intersections
• Well pivots
• Building corners
• Grain bins, etc.
Dycam Image
+
GPS Video Survey
“Raw” Aerial Imagery
(Preliminary study, Colorado State University, Soil and Crop Sciences )
Geo-Registered Result
= Georegistered image/data
…”rubber-sheet” corrections
remove image geometric distortions
…in effect, it is like printing the
image on a rubber sheet then
stretching the image to fit the GPS
features
…inside Cessna, M-VMS, Dycam,
35mm, camcorder and battery
Dycam
Belly-Port
Camcorder
and battery
(Preliminary study, Colorado State University, Soil and Crop Sciences )
M-VMS
Related Spatial Technologies (RS)
[3]
[1]
…Electromagnetic Spectrum (Light+)
[4]
…incoming light is
preferentially
absorbed (reflected)
depending on plant
physiology
[2]
Species
Photosynthesis
Water Content
(Berry)
Linking NDVI to Nitrogen Levels
NDVI
Nitrogen Treatment
…there appears to be a strong relationship between NDVI
measurements from remotely sensed data and nitrogen
application levels
(Preliminary study, Wright, Red Hen Systems,)
Delineating Zones
Visible differences in an
aerial image can be used to
delineate portions of a field
that have consistent texture
and color (Management
Zones).
The zones are assumed to
have consistent levels for
each of the field’s driving
variables (uniform
conditions)
(Wright & Berry)
Mgt Zones vs. Map Surfaces …the bottomline
…both approaches “carve” a field into smaller pieces to better represent the unique conditions and patterns
occurring in the field. Zones pre-partitions it into relatively large, irregular areas that are assumed to be
homogenous—discrete polygons. Surfaces, on the other hand, process field samples for an estimate of each
factor at grid cells throughout a uniform analysis grid—continuous gradient.
…relationships among Surfaces
(data layers) are easily
investigated
Air Photo (soil color)
No map analysis is possible with Management Zones
(Berry)
RS Imagery as GIS Data Layers
A RS image is just a “shishkebab
of numbers” like any other
grid map (raster)
Image
52
NIR (R)
46
Red (G)
148
26
(Beyond our sight) Color
Infrared
34
44
Remote sensing
images are composed
of numbers, just like
any other map in a
grid-based GIS…
“Mapematical
Processing”
43
Green (B)
57
P
312
K
257
7.5
7.2
etc.
ph
(Berry)
The Precision Farming Process
As a combine moves through a field 1) it uses GPS to check its location then
2) checks the yield at that location to 3) create a continuous map of the yield
variation every few feet. This map 4) is combined
Steps 1)–3) with soil, terrain and other maps to derive a
5) “Prescription Map” that is used to adjust
fertilization levels every few feet in the field
On-the-Fly
Yield Map
45.00
Step 4)
Farm dB
(Cyber-Farmer, Circa 1990)
Prescription Map
Map Analysis
Step 5)
40.00
35.00
Zone 3
30.00
25.00
Zone 2
20.00
15.00
10.00
Zone 1
5.00
Variable Rate Application
5.00
10.00
15.00
20.00
25.00
30.00
(Berry)
Step 3: Data
Analysis
Map Insights (Univariate-- within a single map)
• Standard Normal Variable (SNV) Maps
• Coefficient of Variation (CoffVar) Maps
• Slope/Aspect (Spatial Derivative) Maps
Relating Maps (Multivariate-- among maps)
• Map Comparison
 Difference
 %Change
 Difference Tests
• Corresponding Areas
Coincidence
Map Similarity
Clustering
• Prescriptive Statistics
Regression
Trend Surfaces
Spatial Data Mining
(Berry)
Linking Data and Map Distributions
A histogram depicts the numerical distribution
A map depicts the geographical distribution
…the data values link the
two views—
Click anywhere on the
map and the histogram
interval is highlighted;
click on a histogram
interval and the map
locations are highlighted
(Berry)
Preprocessing and Map Normalization
Preprocessing involves conversion of raw data into consistent
units that accurately represent field conditions.
Calibration - translates signals into measurements of crop production units, such
as bushels per acre (measure of volume) or tons per hectare (measure of mass).
Adjustments - “tweaking” the values… sort of like a slight turn on that bathroom
scale to alter the reading to what you know is your true weight.
Corrections - dramatically changes the measurement values, such as after the mass
flow correction to GPS coordinates
Normalization involves standardization of a data set, usually for
comparison among different types of data.
Goal - Norm_GOAL = (mapValue / 250 ) * 100
0-100 - Norm_0-100 = ((mapValue – min) * 100) / (max – min)
SNV - Norm_SNV = ((mapValue - mean) / stdev) * 100
(Berry)
Preprocessing and Map Normalization
Applying the MapCalc equation…
Norm_GOAL = (Yield_Vol / 250 ) * 100
…generates a standardized map based on a yield goal of 250 bushels/acre. This map can be used in analysis
with other goal-normalized maps, even from different crops
Since normalization
involves scalar
mathematics (constants),
the pattern of the
numeric distribution
(histogram) and the
spatial distribution (map)
doesn’t change
…same relative distributions
(Berry)
Assessing Localized Variation in Yield
Scan Yield_Volume Coffvar
Within 2
For Yield_Coffvar
Where,
Coffvar= Stdev/mean *100
The “Scan” operation moves a
window around the yield map and
calculates the Coefficient of
Variation with a 2-cell radius of
each location
…higher values indicate areas with more
localized variability
(Berry)
Assessing Rate of Change in Yield
Slope 1997_Yield_Volume Fitted
For Yield_Slope
Where,
Slope= Rise/Run *100
The “Slope” operation moves a
window around the yield map and
calculates the inclination (rate of
change) in yield of neighboring
cells
…higher values indicate areas with rapidly
changing productivity
(Berry)
Analysis“Within” A Surface
Univariate analysis investigates relationships within a single map
• Slope
~ rate of change (spatial derivative) of each surface element (grid cell)
• Aspect
~ orientation (direction) of each surface element
The slope and aspect of an elevation surface (altitude derived from a surveyed points or
rectified orthophotos) identifies terrain steepness and orientation; example uses include
road-building and water runoff modeling
The slope and aspect of a barometric surface (air pressure gradient derived from a set
weather station data) estimates wind speed and direction
The slope and aspect of a thermal gradient in a lake (generated from remote sensing data
of surface temperature) identifies rate and direction of cooling from a thermal input
(nuclear powerplant ponds)
The slope and aspect of a total revenue surface (generated by summing the cash flow
stream for each surface element) identifies a marginal revenue surface which shows the
spatial distribution of relative cash flow
The slope and aspect of a proximity surface determines the speed and direction of the
optimal movement in traversing each surface element
…what would the slope of a slopemap show? …the aspect of a slopemap?
(Berry)
Analysis“Within” A Surface …continued
Univariate analysis investigates relationships within a map surface
• Aggregation
~ sum of the values for all or a portion of the surface elements
(spatial integral); example uses include cut/fill calculations in road building and total
yield estimates in precision farming
• Coefficient of Variation ~ localized variation surrounding each surface
element (surface roughness)
• Mathematical Translations ~ scalar arithmetic, logarithmic, trigonometric
and logical operations; example use of taking the cosine of the zenith angle formed
between the sun’s position and each elevation surface element to calculate insolation (sun
energy at each location)
• Statistical Operations ~ describe and characterize a surface
 Descriptive statistics (min. max, range, median, mode, mean, skewness…)
 Similarity assessment (spatial autocorrelation)
 Predictive statistics (map generalization and interpolation)
 Accuracy assessment (residual analysis of how well a surface fits a data set)
• Other “Stuff” ~ standard Normal Variable Surface; pattern recognition filters
(Berry)
Data Analysis (Visual comparison)
Visual Analysis of 2D Maps
Top-soil Phosphorous
Bottom-soil Phosphorous
…so what do these maps tell you (Data Analysis)?
…what management actions should be taken and where (Spatial Modeling)?
(Berry)
Data Analysis (Map-ematical comparison)
Mapped Data Analysis of Map Surfaces
Top-soil Phosphorous
Phosphorous Difference
Bottom-soil Phosphorous
…Top-Bottom values are subtracted for each location (Map-ematics)?
(Berry)
Data Analysis (Difference map)
Visualizing Difference Map (2D)
…add more Phosphorous just where it is needed (Spatial Modeling)?
(Berry)
Data Analysis (visually comparing maps)
What differences do you see? …where did yield change significantly? …where did it
stay about the same?
(Berry)
Data Analysis (comparing discrete maps)
(Berry)
Data Analysis (discrete maps vs. continuous surfaces)
Discrete maps= intervals Continuous surfaces= values
(Berry)
Comparing Map Surfaces (Difference map)
1997_Yield_Volume
- 1998_Yield_Volume
Yield_Diff
Map Variables… map values within an analysis grid can be
mathematically and statistically analyzed
…green indicates
areas of increased
production
…yellow indicates
minimal change
…red indicates
decreased production
(Berry)
Data Analysis (assessing spatial patterns)
What spatial
relationships do you
see?
…do relatively high levels
of P often occur with
high levels of K and N?
…how often?
…where?
(Berry)
Data Analysis (assessing spatial patterns)
Data Clustering identifies of similar data patterns– Management Zones
…the “data shishkebab” for each grid location is sent to a statistical algorithm that divides the data set
into groups that are 1) as similar within each group and 2) as different between groups as possible
(Berry)
Investigating Surface Correlation (predictive model)
Histogram/Map View
Data Space (magnitude of values)
are linked to
Geographic Space (position of values)
Histogram/Map View
Data Space (joint magnitude of values)
are linked to
Geographic Space (position of values)
(Berry)
Investigating Surface Correlation (error analysis)
…a predicted surface is compared to actual data (% difference map) for an assessment of
overall performance and spatial pattern of errors. In this instance, the model is a good
predictor within the partitioned area but poor along the west and north edges.
(Berry)
Data Analysis (establishing relationships)
On-Farming Testing — Investigating the Effects of Alternatives
(Berry)
Step 4: Spatial Model
Spatial Data Mining —new technology (CART) that is based on large
sample size, repetitive data grouping and data driven to develop more
accurate prediction equations than traditional statistics
Knowledge-Based Relationships — evaluates spatial
relationships given input map data
• Look-Up Table
 If-Then Rules
 Expert Systems
• Evaluating Functions
 Equations
• Optimization Techniques
 Linear Programming
 Induction Modeling
 Genetics Modeling
 Tessellation
(Berry)
Precision Farming’s Big Picture
…a new application of the Spatial
Technologies
…that utilizes spatial relationships
in a field for site-specific
management
(Berry)
So Where Are We in Precision Farming?
(Berry)
Underlying Issues In Precision Farming
...Gaps in Our “Thinking”
• Limited Approach –
Mapping vs.
Data Analysis; Tools vs. Science
• Science Link –
“Scientific Method”
Doctrine, The “Random” Thing,
Appropriate Driving Variables,
Correlation vs. Causation
• Market Confusion – Empirical
Verification, Economic Validation,
Rationalization (Productivity vs.
Stewardship)
The Environmental Trump Card
(Berry)
Micro Terrain Analysis (Slope and Flow)
Characterizing Slope
A digital terrain surface is formed by
assigning an elevation value to each
cell in an analysis grid. The “slant” of
the terrain at any location can be
calculated— inclination of a plane
fitted to the elevation values of the
immediate vicinity
Characterizing Surface Flow
A map of surface flow is simulated by
aggregating the “steepest downhill
paths” from each cell— confluence
Slope and Flow maps draped over vertically exaggerated
terrain surface
(Berry)
Micro Terrain Analysis (Slope and Flow)
Calibrating Slope and Flow Classes:
Areas of Gentle, Moderate, and
Steep slopes are identified; areas of light, moderate and heavy flows are identified
(Berry)
Micro Terrain Analysis (a simple erosion model)
Determining Erosion Potential: The slope and flow classes are
combined into a single map identifying erosion potential
(Berry)
Micro Terrain Analysis (extending the erosion model)
Simple Buffer
Effectively far away, though right near a
stream
…how can that be?
…what about different soils?
…what about roughness?
…or time of year?
(Berry)
Precision Farming… an Oxymoron?
What are your thoughts…
 Are there spatial variations in
agricultural fields?
 Is our technology able to “precisely”
measure the spatial variations?
 Can we derive and validate the spatial
relationships in the patterns?
 Can we develop and implement
spatially-based management actions?
Are you burnt out yet?
(Berry)
More Information on PF Data Analysis
PF Case Study
(uses MapCalc Learner software)
…the MapCalc Learner CD contains a copy of the Precision
Farming Primer and the agriculture data set used in the case
Study
www.redhensystems.com
www.innovativegis.com/basis Online text and Case Study
www.agriculture.com/technology/
Online articles and active discussion forum on
technology
(Berry)
Online PowerPoint Slide Set
www.innovativegis.com/basis
…select Precision Farming Primer then click on Appendix E
…tuned for Internet Explorer 4.0+ and can have problems with some Netscape versions
View in “Medium Text” mode; size window to fit the slides
(Berry)