David Schneider Memorial University,St. John’s, Canada

Scale, Scope, and Power Laws in Environmental Science. Part II.

Environmental Science 600017 September 2009

• 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/

Scope of Phenomena, Impacts, and Action

• Examples– Coral Reefs– H1N1– meHg in fish

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

                                

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

Multiscale Analysis is Accomplished by Systematically Changing the Scope

spatial

temporal

mass

Method of changing scope Applications

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

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

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

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.

Scope Diagrams:Statistical Scale-up

S=900 Haul Survey

H H=Haul

S

Stock

16,000 / 5 = 3000 : 1

-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

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

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 ?

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

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.