1006: Ideas in Geography
Environmental Modelling: I
Dr. Mathias (Mat) Disney
UCL Geography
Office: 113 Pearson Building
Tel: 7670 0592
Email: [email protected]
www.geog.ucl.ac.uk/~mdisney/currentteaching.html
Models in Geography?
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“Believe nothing just because a so-called wise person said it. Believe
nothing just because a belief is generally held. Believe nothing just
because it is said in ancient books. Believe nothing just because it is said
to be of divine origin. Believe nothing just because someone else believes
it. Believe only what you yourself test and judge to be true”.
Siddartha Gautama (Buddha) c. 500BC
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“A hypothesis or theory [model] is clear, decisive, and
positive, but it is believed by no one but the man who
created it. Experimental findings [observations], on the
other hand, are messy, inexact things, which are
believed by everyone except the man who did that
work.”
Harlow Shapley (1885-1972), eminent American astronomer, from his
autobiography “Through Rugged Ways to the Stars” (1969)
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Models in Geography?
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“[The] advantage of a mathematical statement is that it is so definite that it
might be definitely wrong…..Some verbal statements have not this merit;
they are so vague that they could hardly be wrong, and are
correspondingly useless."
Lewis Fry Richardson (1881-1953), Mathematician, Quaker, pacifist – first to apply mathematical
methods to numerical weather prediction
Key: modellers need to know strengths AND weaknesses of their models
“All models are wrong but some are useful” – George Box
“The purpose of models is not to fit the data but to sharpen the
questions” – Samuel Karlin
“No one trusts a model except the person who wrote it. Everyone
trusts an observation except the person who made it.” – Anon.
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Models in Geography: How and why?
•  Empirical
–  Based purely on observation e.g. rainfall v latitude, popn. density v
energy consumption….
•  Physical
–  Simplified representation of physical processes e.g. climate, hydrology,
remote sensing, geomorphology etc. etc.
•  Semi-empirical (semi-physical?)
–  Based partly on observations, partly on physical principles e.g.
population dynamics, biodiversity etc. etc.
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Models in Geography: How and why?
•  Black/”grey” box / process models
–  Stocks (how much stuff?) and fluxes (how does stuff move?) e.g.
simple hydrological and glacier mass balance…..
–  No “physics” in boxes – based on conservation of mass, energy
momentum etc. i.e. stuff in = stuff out
–  Describe key processes only e.g. terrestrial and/or oceanic carbon
cycle
•  Conceptual?
–  Use broad concepts to explain systems e.g. evolution, plate
tectonics…. Daisy World?
–  Ideally lead to more powerful models
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Cover today…
•  Examples:
–  Conceptual: Gaia hypothesis - Daisy World
–  Empirical: Latitude v. T or Energy v. pop. density
–  Physical 1: Hydrological
–  Physical 2: Remote Sensing models
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Daisy World and “Gaia Hypothesis”
•  Gaia - Greek goddess who drew the living world forth
from Chaos
•  Dr. James Lovelock
–  British atmospheric chemist - invented detector for measuring
trace elements in atmosphere - measure impact of CFCs
•  Late 1970s, revolutionary idea - Gaia Hypothesis:
–  The biosphere (plants and animals) can regulate climate and
hence conditions for growth
–  i.e. Earth as a self-regulating system (Gaia)
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Daisy World
•  V. simple hypothetical (conceptual) model
–  Earth-like planet, orbiting Sun which has grown progressively brighter through
time, radiating more and more heat (like ours)
–  YET surface T ~ constant because biosphere consists only of dark (black) and
light (white) coloured daisies
–  Daisies act to moderate temperature through their albedo or reflectivity
•  dark daisies absorb most of the Sun's heat
•  light daisies reflect much of it back to space.
•  Can we use idea to understand/predict homeostasis?
–  ability of an organism or cell to maintain internal equilibrium by adjusting its
physiological processes
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Daisy World
White daisies
Black daisies
Available fertile
land
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Assumptions?
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Rate of population change depends on the death rate and potential birth rate
and amount of fertile land available for growth
Birth rate for both species of daisy depends on temperature, Tlocal
Tlocal depends on αplanet - αlocal and on Tglobal
Tglobal depends on luminosity of Sun and αplanet
αplanet is sum of local albedo components i.e.
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αplanet = areablack*αblack + areawhite*αwhite + (areaplanet - areablack - areawhite)*αbare soil
Available fertile land depends on the total amount of fertile land (fixed) and the
current coverage of the two species of daisy
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Daisy World: results
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What happens to planet if sun goes on getting hotter?
–  More white daisies grow at expense of black (reducing αplanet)
–  Eeventually gets too hot even for white daisies (+4 Gyr) and Tplanet ↑
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Allows us to ask “real-world” questions re planetary albedo and climate feedbacks:
–  Deforestation → reduced albedo → increase T?
–  Increase T → reduce snow cover → reduce albedo → increase T? +ve feedback??
–  Increase CO2 → increase vegetation → increase low clouds → reduce T? -ve feedback??
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So what?
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Simple approach can lead to improved understanding and asking new
questions e.g.
CLAW hypothesis:
–  Charlson, Lovelock, Andreae and Warren (1987) Oceanic phytoplankton,
atmospheric sulphur, cloud albedo and climate. Nature, 326, 655-661.
–  Increasing temperature (e.g. global warming) causes phytoplankton to emit
more dimethyl sulphide (DMS), causing increased cloudiness and hence
reducing solar radiation
–  Regulate temperature via negative feedback!
•  Has biosystem evolved to regulate climate for own benefit??
http://www.atmosphere.mpg.de/enid/1w1.html
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Empirical: latitude v temperature
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Observations may indicate
a relationship
E.g. simple “best-fit” line
Allows us to interpolate
(between observations)
BUT extrapolation
dangerous
NEVER infer causality!
To find a reason we need
some physical description
(physical model?)
T = 2.5L - 20
From: http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/essentials/stats.html#Figure%20EG.22
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Empirical 2: pop. density v per capita energy use
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Not simple linear
relationship?
Negative exponential?
Function of e-pop
Implies sparse urban areas
use more energy
–  Travel further to work?
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BUT no causal relationship
Maybe use other
observations??
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City lights from remote sensing
• Bright Lights, Big City: http://earthobservatory.nasa.gov/Study/Lights/
• Develop some empirical relationship between light intensity, popn. density
and energy usage
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Hydrological (catchment) models
•  How much water comes out of catchment in a given time
–  Response to rainfall event? How much water left in soil?
–  Flood prediction, resource management etc.
•  Simplest models not dependent on space i.e. 1D “lumped model”
–  Catchment as simple “bucket”
–  “Stuff” out = “stuff in”
•  Time-area hydrograph: some consideration of area
–  predicts discharge, Q (m3s-1), based on rainfall intensity, i (mm hr-1), and
catchment area, A (m2)
–  i.e. Q = ciA (c is (empirical) runoff coefficient i.e. fraction of rainfall which
becomes runoff, %)
–  more than one area? Divide drainage basins into isochrones (lines of
equal travel time along channel), and add up….
–  Qt = c1A1i(t-1) + c2A2i(t-2) + ….. + cnAni(t-n)
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Process-type catchment models
•  River catchment/basins
–  Function of precipitation, evapotranspiration, infiltration
–  soil moisture conditions (saturation, interflow, groundwater flow,
throughflow, overland flow, runoff etc.)
•  From conservation of “stuff” - water balance equation
–  dS/dt = R - E - Q
–  i.e. rate of change of storage of moisture in the catchment
system, S, with time t, is equal to inflow (rainfall, R), minus
outflow (runoff, Q plus evapotranspiration, E)
–  E.g. STORFLO model (in Kirkby et al.)
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More complex?
•  Consider basin morphometry (shape) on runoff
–  Slope, area, shape, density of drainage networks
–  Consider 2D/3D elements, soil types and hydraulic properties
•  How to divide catchment area?
–  Lumped models
•  Consider all flow at once... Over whole area
–  Semi-distributed
•  isochrone division, sub-basin division
–  Distributed models
•  finite difference grid mesh, finite element (regular, irregular)
–  Use GIS to represent - vector overlay of network?
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Time / space issues?
•  How accurate is space/time representation required, mm,
m, km etc.?
–  More accurate spatial/temporal representation means bigger
memory/processing requirement
–  Limits of temporal representation:
•  discrete time “jumps” (e.g. month by month - may miss/cause
discontinuities)
–  Limitations of (spatial) grid-based methods:
•  problem of flows between grid units
•  size/shape of grid units
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Very complex: MIKE-SHE
• Mike-SHE
(System
Hydrological
European)
• Combination of
physical, empirical
and black-box…
• Can “simulate all
major processes in
land phase of
hydrological
cycle” !!
From: http://www.dhisoftware.com/mikeshe/Key_features/
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MIKE-SHE: catchment soil water content
From: http://www.geog.ucl.ac.uk/~jthompso/shyloc_modelling.stm
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Physical models for remote sensing
• Highly detailed 3D
models
• Simulate canopy
reflectance behaviour
• Compare with remote
sensing observations
• Allow us to
understand what we see
from space
• Make predictions e.g.
about carbon cycle
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Physical models for remote sensing
Change detection
Rondonia 1975
Rondonia 1986
Rondonia 1992
Can we derive
relationship between
reflectance (colour)
and forest cover?
http://earth.jsc.nasa.gov/lores.cgi?PHOTO=STS046-078-026
http://www.yale.edu/ceo/DataArchive/brazil.html
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Remember!
• Empirical (black box) models are simple
• BUT only valid for observations/system they are based on
• Model not valid for different locations OR extrapolation
• So useful for explaining but NOT predicting (limited power)
• Physical models much more complex (difficult to
derive/test)
• BUT have physically meaningful parameters
• Can be inverted against measured data for estimating parameter values
• Can be more general – use for predictions (most powerful)
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Reading
Basic texts
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Barnsley, M. J., 2007, Environmental Modelling: A Practical Introduction,
(Routledge). Excellent, practical introduction with many examples, and code using
freely-available software.
Kirkby, M.J., Naden, P.S., Burt, T.P. and Butcher, D.P. 1993 Computer Simulation in
Physical Geography, (Chichester: John Wiley and Sons). Good introduction with
simple computer programs of environmental models.
Computerised Environmental Modelling: A practical introduction using Excel, J.
Hardisty et al., 1993, John Wiley and Sons.
Casti, John L., 1997 Would-be Worlds (New York: Wiley and Sons). A nice easy-toread introduction to the concepts of modelling the natural world. Excellent examples,
and well-written. A good investment.
Advanced texts
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Gershenfeld, N. , 2002, The Nature of Mathematical Modelling,, CUP.
Boeker, E. and van Grondelle, R., Environmental Science, Physical Principles and
Applications, Wiley.
Monteith, J. L. and Unsworth, M. H., Principles of Environmental Physics, Edward
Arnold.
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