___________________________________________________________________________________
ANALYSIS OF STATISTICAL STRATEGIES FOR ADVANCING MONITORING AND
ASSESSMENT OF TERRESTRIAL ECOSYSTEMS IN THE MEXICAN STATE OF JALISCO:
PILOT STUDY SYNTHESIS
Robin M. Reich
Colorado State University
This was a complete project description covering the planning stage, definition of conditions
to be mapped, obtaining the available data sets (landsat TM Bands, elevation, slope, aspect
and vegetation type), design of ground sampling, methods of statistical analysis, and mapping
for conditions. Field sampling and data collection processes were based on a two stage stratified random sampling design and a systematic design with random starts. Several counties
around the City of Guadalajara were part of the study. The total area was approximately
425,000 hectares. Because of the assessment questions that need to be addressed the project
centered on providing geospatial and temporal information to local decision-makers. The
modeling task was split into two parts large-scale trend surface model and small-scale binary
regression tree model. The final product was a 10-m resolution map and relevant summary
statistics.
A description of this project was submitted to the USDA Forest Service, Rocky Mountain
Research Station, “Analysis of Statistical Strategies for Advancing Monitoring and Assessment
of Terrestrial Ecosystems in the Mexican State of Jalisco: Pilot Study Synthesis,” by Robin M.
Reich, Celedonio Aguirre-Bravo, and Vanessa A. Bravo.
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Robin M. Reich _______________________________________________________________________________
SPATIAL STATISTICAL
ESTIMATION AND MODELING
APPLICATIONS
“ MEXICO INVENTORY AND
MONITORING PILOT
PROJECT”
Robin M. Reich, Professor, Forest Biometrics/Spatial Statistics
Department of Forest, Rangeland and Watershed Stewardship
Colorado State University
Fort Collins, Colorado, USA
286
PROJECT SPONSORS
• State Government of Jalisco
– Foundation for Forestry and Natural
Resources Development (FIPRODEFO)
– Secretary of Rural Development,
Department of Forestry, Natural
Resources, and Sustainability
– CAMESA, Consortium for Advancing
the Monitoring of Ecosystem
Sustainability in the Americas
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__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
PROJECT SPONSORS
• USDA Forest Service
– Rocky Mountain Research Station
– Forest Inventory and Analysis Program
(FIA)
• Colorado State University
• University of Colima
287
PROJECT SPONSORS
• Cooperators and Collaborators
– U.S. EPA
– Canada Natural Resources
– CONAFOR
– INIFAP, CONABIO, INEGI
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
PILOT PROJECT
GOAL
TO DEVELOP NEW APPROACHES FOR MONITORING
AND ASSESSES THE CONDITION AND CHANGES OF
ECOSYSTEM RESOURCES, SO THAT THE VARIETY
OF “NEEDS AND WANTS” OF STAKEHOLDERS CAN
BE MET, AT MULTIPLE SCALES AND RESOLUTION
LEVELS, FOR MULTIPLE STRATEGIC AND TACTICAL
APPLICATIONS.
288
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__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
States of Jalisco and
Colima, Mexico
289
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Robin M. Reich _______________________________________________________________________________
JALISCO AND COLIMA
HAVE A VERY
DIVERSE LANDSCAPE
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SPATIAL STATISTICAL
ESTIMATION AND
MODELING
Examples from the U.S.
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__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
Black Hills National Forest
South Dakota
297
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Robin M. Reich _______________________________________________________________________________
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DEPENDENT VARIABLES
•
•
•
•
•
•
•
Depth of Duff (in)
Depth of Litter (in)
Fuel Height (in)
0” – 0.25” Fuels (tons/acre)
0.25” – 1” Fuels (tons/acre)
1” – 3” Fuels (tons/acre)
> 3” Fuels (tons/acre)
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__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
INDEPENDENT VARIABLES
• Landsat TM Bands 1, 2, 3, 4, 5, 6L,
6H, 7, 8
• Elevation (m)
• Slope (%)
• Aspect
• Vegetation type
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Modeling Approach
• Data = Large-scale Variability +
Small-scale variability
– Large-scale – trend surface model
– Small-scale – Binary regression tree
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__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
MODELING RESULTS
301
Table 1. Description of the multiple regression models for describing the course-scale
variability in forest fuels on the Black Hills National Forest. Circles indicate the inclusion
of a variable as a main effect, while shaded cells indicate an interaction between forest
classes and topographic and Landsat TM bands. Forest classes were treated as dummy
variables with pine being the default forest type.
Model
Topography
E
Duff (cm)
Litter (cm)
Fuel Ht. (cm)
0-0.6 cm (tonnes/ha)
0.6-2.5 cm (tonnes/ha)
2.5-7.6 cm (tonnes/ha)
< 7.6 cm (tonnes/ha)
> 7.6 cm (tonnes/ha)
S
•
Landsat TM Bands
A
B1
•
•
B2
B3
B4
B5
B6L
B6H
Vegetation Class
B7
•
•
•
•
•
•
•
•
B8 P
R
•
•
•
•
•
•
•
SP
AS
M
•
•
1
E – elevation, S - slope, A – aspect
B1 – band 1 B2 – band2, B3 - band4, B5 – band5, B6L – band 6 low, B6H – band 6 high, B7 – band 7,
B8 - band 8
3 P – pine, R – riparian, SP – spruce, AS – aspen/deciduous, M – meadows/openings.
2
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__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
Table 5. Continued.
Statistic 1
0.6-2.5 cm
(tonnes/ha)
2.5-7.6 cm
(tonnes/ha)
151
< 7.6 cm
(tonnes/ha)
> 7.6 cm
(tonnEs/ha)
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IQR
4.77
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18.25
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36.36
28.56
17.64
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1.21
1.40
0.81
0.87
0.95
confidence
coverage
rate
0.95
0.90
0.95
0.93
1 IQR = interquartile range, MAE = mean absolute error, RMSE = root
mean square error, SMSE = standardized mean square error.
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Canopy Surface Roughness
Influences Bird Diversity in the
Black Hills National Forest, South
Dakota, USA
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Kaibab National Forest
Arizona
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Cover
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MORE ON THE
MEXICO PILOT PROJECT
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The first phase of the pilot
project was to develop a
vegetation map of the States of
Jalisco and Colima, Mexico
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To help improve the
accuracy and precision of
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other modeling components
climate models are being
developed
333
Climate Models of Jalisco and
Colima, Mexico
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Location of Weather Stations
Used in the Analysis
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Temperature
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December
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Temperature Zones
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Precipitation
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Evaporation
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July
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
August
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September
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
October
354
November
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
December
355
Precipitation - Evaporation
Zones
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
356
Climate Zones
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
357
Applications
• Modeling land cover types and
components of forest structure
• Identifying areas suitable to plant
certain species
• Identifying areas where rare and
endangered species may be growing
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
Revised Land Cover Map Based
on Climate Zones
358
Accuracy = 87%
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
SAMPLING METHODOLGY
359
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Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
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Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
PILOT TEST AREA
361
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Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
362
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
Stratification Design for the Pilot
Test Area
363
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
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Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
Some Results from the Pilot Test
Area
365
Forest Stand Structure
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
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Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
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Forest Fuel Loadings
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
368
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
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Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
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Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
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Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
Presence – Absence Data
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Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
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Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
374
SPATIAL INTEGRATION
In addition to being able to
assess the level of uncertainty
associated with our models, it
is also important that the models
are capable of providing
unbiased estimates at any
spatial scale or level of support.
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
SPATIAL INTEGRATION
Assume a sample of n 30-m x
30-m cluster plots consisting
of m = 9 10-m x 10-m sub-plots
are randomly selected from one
of the modeled surfaces.
375
SPATIAL INTEGRATION
The modeled surfaces are used
to provide an estimate of the
mean on each of the nm subplots, along with the model
prediction variance.
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
SPATIAL INTEGRATION
Estimate of the Mean Value
per Sub-Plot
n m
n
ˆz sp = 1 ∑∑ zˆ ij = 1 ∑ zˆ i
nm i =1 j =1
n i =1
376
SPATIAL INTEGRATION
Within Cluster Mean Square
2
n m
1
SSW
MSW =
=
∑∑ (zij − zi )
n (m − 1) n(m − 1) i =1 j =1
1 n m 2
≈
σˆ
2 ∑∑ ij
nm i =1 j =1
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
SPATIAL INTEGRATION
Between Cluster Mean Square
SSB
m n
(zi − z sp )2 ≈ 1
=
MSB =
∑
n − 1 n − 1 i =1
n
n
m
∑∑ σˆ
2
ij
i =1 j =1
377
SPATIAL INTEGRATION
Variance of the Mean
( )
MSB
Vˆ zˆ sp =
nm
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
SPATIAL INTEGRATION
Using these relationships it
is possible to obtain estimates
of any of the modeled variables
at any spatial scale along with
its corresponding estimate of
the variance.
378
Modeling at a 10 m Resolution
• Data is spatially independent between
clusters
• Data is spatially correlated within clusters
• GLS is used to account for spatial
dependencies in the trend surface model
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
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Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
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Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
__________________ Analysis of Statistical Strategies in the Mexican State of Jalisco: Pilot Study Synthesis
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FOR MORE INFORMATION
CONTACT
Dr. Celedonio Aguirre-Bravo
CAMESA, General Coordinator
USDA Forest Service,
Rocky Mountain Research Station
Fort Collins, Colorado
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data
Robin M. Reich _______________________________________________________________________________
THANK YOU
382
Workshop Proceedings: Quantitative Techniques for Deriving National Scale Data