GIS for Environmental GIS for Environmental ScienceScience

ENSC 3603ENSC 3603

Class 16Class 163/05/093/05/09

Spatial Variability and SamplingSpatial Variability and Sampling

• GIS require data at all points (subject to spatial resolution).

• It is not practical to measure continuous variables at all points.

– Infinite number of points.

– Finite amount of time and other resources.

InterpolationInterpolation

• Problem: Impractical to measure a continuous variable at all points

• Basis: Sample of known points• Objective: Estimate unknown points by similarity and

proximity with known points• Basic Principle: Points close together in space are more

likely to have similar values than points far apart (Tobler’s First Law of Geography)

• Interpolation: the ‘art and science of intelligently estimating unknown values between known attribute values.

Tobler’s First Law of GeographyTobler’s First Law of Geography

• “Everything is related to everything else, but close things are more closely related.” Tobler, W. 1970. “A computer model simulating urban growth in the Detroit region,” Economic Geography 46 (2): 234-240.

Principles of InterpolationPrinciples of Interpolation

• Non-spatial interpolation– Linear– Non-linear

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16 25

14 ?

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10 16

X Y

InterpolationInterpolation

• Sampling – the known points• Sample size – how many?

– Controllable

– Limits: resources, diminishing returns• Sampling pattern – Where?

– Know the study area

– Choice may introduce errors, artifacts, outliers

-- Take enough samples to represent the area

a) 33 ft grid

Fields A3 to A8, Soil Sample Density, pH

c) 99 ft grid

b) 66 ft grid

d) 131 ft grid alternating

< 5.5

< 6.0

< 6.5

< 7.0

> 7.0Red

Orange

Yellow

Green

Blue

Sampling Patterns:Sampling Patterns:• Systematic Sampling

– Spaced uniformly in x and y– Advantages:– Easy to conceive– No subjective judgment– Easy to lay out field sample pattern

– Disadvantages:– Not statistically representative: all areas are represented

the same, but some areas have more variation.– Travel, visiting each site may be difficult or impossible– Aliasing – artifact from coincidence of sample interval with

data patterns. Example, you might sample down an old fence row.

Sampling Patterns:Sampling Patterns:

• Random Sampling– Random X (easting), Y (northing) location

(calculate in spreadsheet…)

• Advantages– Statistically robust – no bias in sampling– Unlikely to match pattern on landscape

– no aliasing.– Easy to conceive and lay out– Not subjective

• Disadvantages– Does not distribute samples in areas of high variation– Travel, visiting each site may be difficult or impossible

Sampling Patterns:Sampling Patterns:

• Cluster Sampling– Group samples around centers– Centers can be located systematically

or randomly (or for convenience, if statistically valid)

– Samples within a cluster can be located randomly, systematically, or otherwise.

• Advantage– Reduced travel time– Take advantage of existing access

• Disadvantages: For cluster center placement, same as for systematic and random point placement

Sampling Patterns:Sampling Patterns:

• Adaptive Sampling – higher sampling density where important variable(s) have greatest variation .– Advantages

– Sampling efficiency optimized

– Logistics can be planned in many cases

-- Disadvantages

– Preliminary sampling may be necessary, e.g. soil chemistry

– Significant prep time

– Subjective

InterpolationInterpolation• All interpolation methods use sampled values and

positions to model points not sampled.

• Deterministic interpolation techniques create surfaces from measured points, based on either the extent of similarity (e.g., Inverse Distance Weighted) or a degree of smoothing (e.g., Trend Surface Analysis).

• Geostatistical interpolation techniques (e.g., Kriging)are based on statistics and are used for more advancedprediction surface modeling, which also includes erroror uncertainty of predictions.

• NOTE: Different methods will (almost always) producedifferent results.

InterpolationInterpolation

• Different methods will produce different results withsame input data.

• No single method is more accurate than others for allsituations.

• Accuracy may be determined by comparison with asecond set of “withheld” samples for accuracy checking.

• The researcher should select the method based onknowledge of the study area, phenomena of interest,and available resources.

InterpolationInterpolation

• Inverse Distance Weighted (IDW) Interpolation:– The Inverse Distance Weighted (IDW) interpolator

assumes that each input point has a local influence that diminishes with distance. It weights the points closer to the processing cell greater than those farther away. A specified number of points, or optionally all points within a specified radius, can be used to determine the output value for each location.

InterpolationInterpolation

Interpolation with GeostatisticsInterpolation with Geostatistics

Spatial Statistics

• Spatial Autocorrelation

– Near things are more alike than far things.

– Spatial dependence

• Variogram (semivariogram)

– Graph of semivariance

• Variography

– Calculation and interpretation of variograms

– One way of examining spatial dependence

Spatial AutocorrelationSpatial Autocorrelation

Autocorrelation locally violates assumption of

randomness, precludes normal distribution of

data values.• Autocorrelated data are not amenable to

standard statistical approaches.• May or may not affect non-spatial statistical

aspects of attribute data.• Variography; the Semivariogram

Interpolation with GeostatisticsInterpolation with Geostatistics

• Kriging

– Developed by D.G. Krige and G. Matheron.

– Statistically-based estimator

– Depends on Variogram analysis

– Weighting to interpolate variable value similar to IDW but weights are based on spatial autocorrelation in the sample, not merely distance.

The SemivariogramThe Semivariogram

• The underlying basis of kriging:

A graph of semivariance:

“The semivariance is

simply half the variance of

the differences between all

possible points spaced a

constant distance apart.”

(Isaaks and Srivastava, 1989)

• Nugget: No distance to consider, so semivariance minimal (but unlikely to equal zero, due to measurement errors)

• Sill: Value of ã(h) where most semivariance becomes equal to variance of the data that doesn’t depend upon h; where the increase with distance levels off

• Range: The lag distance at which autocorrelation is unimportant

• Semivariance: ã(h) = n/2 * Ó(Za – Zb)ã(h) is the estimated semivarianceh is the lag (separation distance) n is

the no. of pairs of points separated by h.

Z is the data value (at a and at b)

The Semivariogram

Interpolation with semvariograms: KrigingInterpolation with semvariograms: Kriging

Selected Models

Advantages of KrigingAdvantages of Kriging

• In theory, no other method of grid generation can produce better estimates (in the sense of being unbiased and having minimum error) of the form of a mapped surface than kriging. In practice, the effectiveness of the technique depends on the correct specification of several parameters that describe the semivariogram…However,because kriging is robust, even with a naive selection of parameters the method will do no worse than conventional grid estimation procedures.(Naser El-Sheimy, Digital Terrain Modeling, The University of Calgary,September 1999)www.geomatics.ucalgary.ca

Types of KrigingTypes of Kriging

• Ordinary – assumes overall area mean; no trend.

• Universal – assumes unknown trend in area mean.

• Simple – assumes known trend.• Block – estimate the average value of a variable

over a small area (“block”), rather than at a point.

• Co-kriging – one or more secondary variables• Know the study area, look carefully at the data.

Arc GISArc GIS

• Geostatistical Analyst, Spatial analyst

Soil SamplingSoil Sampling

•Grid Sampling:

•A technique of dividing a field

•Usually 2-4 acres per grid

•Gathering samples from within the subdivisions

•Sending the samples to a lab for analysis

•What is soil sampling?

•A method for assessing the nutrient levels in a field

Soil Sampling - HistorySoil Sampling - History• Early Mechanized Agriculture

– Theoretical developments in plant/nutrient relations• “Law of the minimum” theory: Justus von Liebig• Very inefficient• Not environmentally friendly

• By the 1930’s and 40’s– Recommendations were developed

• Generally 20 plus acres per sample• Started to recognize the value of random and representative samples

• Post WWII– Fertilizer

• Price decrease• Quantity increased• Law of the minimum began being practiced

• Methods of soil nutrient management– Application of O.M. and amendments

• Enough that the plant would not be limited by nutrients

– Application of nutrients removed by previous crop

• Regardless of soil nutrient status

– Problems with approaches

• Reduced profit margins meant that more efficient application of fertilizer was necessary

– Reduce cost of production to increase profit margin

• Increased environmental concerns

– Social, political, and biological awareness of agriculture and the environment

Soil Sampling - HistorySoil Sampling - History

Traditional Soil Sampling ProcessTraditional Soil Sampling Process

• Divide field into a grid of 10-30 acres in size,• Sample at every point,• Send Sample to lab,• Receive Result,• Identify the lowest point for each analysis (i.e. least

amount of nitrogen phosphorus or potassium available in soil)

• Set application rates so that no part of the area is nutrient limited

• Role of GPS & GIS in Soil Sampling– Introduced to Ag in 1990’s

• Most common technologies were GPS, Yield Monitors, and Variable Rate Technologies

– Capable of managing sub-field units– Ability to reduce over-application (better for the

environment)

• New Uses and Developments– Precision soil sampling and soil maps– Precision Guidance Systems

Precision Soil SamplingPrecision Soil Sampling

Precision Soil Sampling ProcessPrecision Soil Sampling Process• Create a map showing the field boundary• Grid the field (usually 2-4 acres)• Navigate to grid point• Take sample, marking sample location with GPS• Send sample to lab for analysis• Load maps into a GIS package• Attach lab results to sample points on the map• Perform interpolation analysis to develop nutrient bounds

– View in-field variation

Soil SamplingSoil Sampling

• Soil sampling in a Precision Agriculture System– Create a field

boundary map (layer)– Grid the Layer– Navigate to point – Take sample

Review for QuizReview for Quiz

• Environmental Science– Wetlands, Soils, and other applications of GIS

• Precision Agriculture (PA)– Factors influencing yield, PA Components and

Benefits, PA GIS farm layers.

• Spatial Variability and Sampling.– Interpolation, first law of geography, sampling

patterns, types – Soil sampling, History, types,

Example Quiz QuestionsExample Quiz Questions1. All external factors, living and non-living (chemical and

energy), that affect you or any other organism is the ______________.

2. List three environmental applications of GIS.3. List two characteristics of a wetland.4. A simple definition of a wetland.5. What are the benefits of wetland?6. What is STATSGO?7. What is SSURGO?8. List three “Information” precision Ag Components.9. List the important Factors influencing yield in order of

importance.10. List three Precision Ag – Farm GIS Layers.11. Why is it not practical to measure continuous variables at all

points in the landscape.1. 2.

Example Quiz QuestionsExample Quiz Questions

12. Tobler’s First Law of Geography is:13. What are the disadvantages of Systematic Soil Sampling?14. List three sampling patterns15. All interpolation methods use sampled values and positions

to model _________ points16. __________________data are not amenable to standard

statistical approaches.17. Inverse Distance Weighted, Trend Surface Analysis, and

Kriging are examples of___________________ methods used for spatial analysis.

18. From the ESRI Tutorials, name two ways to create point features.

19. How can you create a report that lists the attributes of only some of the features in a layer?

Read and DoRead and Do

• Quiz Next Tuesday

• Turn in Module 8 Next Thursday.

• Read Chapter 4 in Lo.

dracaena cinnabari – Dragons blood Tree , Socotra Yeman. Photo by jan_vandorpe found on Google Earth

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