1006: Ideas in Geography Environmental Modelling: I

Dr. Mathias (Mat) Disney UCL Geography Office: 113 Pearson Building Tel: 7670 0592 Email: mdisney@ucl.geog.ac.uk www.geog.ucl.ac.uk/~mdisney/currentteaching.html

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Models in Geography?

•  “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?

•  “[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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•  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

Daisy World

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Daisy World

White daisies

Black daisies

Available fertile land

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Assumptions?

•  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.

–  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

•  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 ↑

•  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?

•  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

•  Observations may indicate a relationship

•  E.g. simple “best-fit” line •  Allows us to interpolate

(between observations)

From: http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/essentials/stats.html#Figure%20EG.22

T = 2.5L - 20 •  BUT extrapolation dangerous

•  NEVER infer causality! •  To find a reason we need

some physical description (physical model?)

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Empirical 2: pop. density v per capita energy use

•  Not simple linear relationship?

•  Negative exponential? •  Function of e-pop •  Implies sparse urban areas

use more energy –  Travel further to work?

•  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

From: http://www.dhisoftware.com/mikeshe/Key_features/

• Mike-SHE (System Hydrological European)

• Combination of physical, empirical and black-box…

• Can “simulate all major processes in land phase of hydrological cycle” !!

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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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Rondonia 1975

Physical models for remote sensing

Change detection

http://earth.jsc.nasa.gov/lores.cgi?PHOTO=STS046-078-026

http://www.yale.edu/ceo/DataArchive/brazil.html

Rondonia 1986 Rondonia 1992

Can we derive relationship between reflectance (colour) and forest cover?

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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 •  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-to-read introduction to the concepts of modelling the natural world. Excellent examples, and well-written. A good investment.

Advanced texts •  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.