david schneider memorial university, st. john’s, canada scale, scope, and power laws in...
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Scope of Phenomena, Impacts, and Action Examples –Coral Reefs –H1N1 –meHg in fishTRANSCRIPT
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David Schneider Memorial University,St. John’s, Canada
Scale, Scope, and Power Laws in Environmental Science. Part II.
Environmental Science 600017 September 2009
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• Scale –Dependence: examples and definitionapplication (student examples)
• Space-Time Diagramsexamplesgroup projects in class
• Calculation across scalesexamples with backgroundexamples (worked in groups)
• Summary
Scale, Scope, and Power Laws in Environmental Science
1.0 10 100 1000
10
1.0
100
1000
10
1.0
100
1000
Kilometers
F
P
Z
= t1.17
Day
sD
ays
Fladenexperiment
Single ship dataP
Z
Fish stock surveys
F
(a)
(b)
H k V 2 3/
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Scope of Phenomena, Impacts, and Action
• Examples– Coral Reefs– H1N1– meHg in fish
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Quantitative Definition of Scope – The Scope of Phenomena
Lake depths
L akeSuperiorL akeH em ing
148 m3 m
4 9
LLo
El Niño return times
M axim um T im eM in im um T im e
year
73 5
2 year.
TTo
B lue W hale ggM ycoplasm a
1 01 0
8
1 32110
Body MassMM o
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Surveyor’s chain
E xten t m eterm illiR eso lu tion 5 m eter
1 53 310
E xten t m eterR eso lu tion m illim eter
11
10 3Meter Stick
Satellite Image
E xten t M egam eterR eso lu tion 4 m eter
10 2 5 6. 10
Definition of Scope –The Scope of Instruments
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Multiscale Analysis is Accomplished by Systematically Changing the Scope
spatial
temporal
mass
Method of changing scope Applications
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Graphical Expression of Scope:Space – Time Diagrams
Scope (a ratio) is the vertical or horizontal distance in space-time diagrams
cm m km1000 km
minute
hour
dayweek
monthyear
decade
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1.0 10 100 1000
10
1.0
100
1000
10
1.0
100
1000
Kilometers
F
P
Z
= t1.17
Day
sD
ays
Fladenexperiment
Single ship dataP
Z
Fish stock surveys
F
(a)
(b)
The first space-time diagrams in ecology
come from Steele (1978)
Conceptual
Instrumental
Displaying Scope:Space-Time Diagrams
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Displaying Change in Scope:Space-Time Diagrams
Diagrams showing spatial and temporal scope have become increasingly common.
1900 1920 1940 1960 1980 2000
13.3 % / year
Tem
pora
l
scal
e
Spatial scale
Num
ber o
f gra
phs
per y
ear
64
16
4
1
0
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Space-Time Diagrams:The Problem of Scale
Environmental scientists collect data from limited areas, at small spatial scales.
cm m km
hourday
weekmonth
year
The questions they address extend over large areas, at the scale of populations and ecosystems.
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Scope Diagrams:Statistical Scale-up
S=900 Haul Survey
H H=Haul
S
Stock
16,000 / 5 = 3000 : 1
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-more insightful literature reviews
-workshop setting (what are you talking about?)
-operationally defined science
-derive one power law from another
-test predictions
Utility of the Concept of Scope
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Case Study – Manukau monitoring
Utility of the Concept of Scopein a Workshop Setting
chroniccontaminants
tidalmixing
pointrelease
data
Spatial Scale (mm 2)10 6 10 14 10 1810 1010 2
century
min
hour
dayweek
month
yeardecade
century
min
hour
dayweek
month
yeardecade
m2
sample flat harbor
Manukaucontaminants
km2
Conceptual Diagram
Instrumental Diagram
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Utility of the Concept of Scopein a Workshop Setting
data
harboursample
month
hour
minute
decade
year
week
day
model
a. Data vs. modelflatsiteplot
b. Embedded experiment
minute
Spatial Scale
day
week
year
decade
hour
month
X
X
cm 10 km 1000 km100 mm
Increase extent of experiment ?Increase resolution of model ?Develop embedded model ?Develop power law ?
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Summary - Scope Diagrams
• Characterization of:– Scale of phenomena– Scale of natural processes– Scale of human impact– Scale of current information– Scale of feasible research activity
• Comparison• Research planning
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Scale, Scope, and Power Laws in Environmental Biology
Group project: Working in groups of 4 (or 3 is possible), construct a conceptual scope diagram. Then construct an instrumental scope diagram.