Dr Mark Cresswell

A basic modelling primer

69EG6517 – Impacts & Models of Climate Change

Lecture Topics• Introduction (what is a model?)

• Modelling philosophy

• The systems approach to modelling

• Systems analysis

• Climate model basics

• Suggested reading

• Today’s practical – Daisy World

INTRODUCTION

Introduction #1

• A necessarily simplified abstraction of the real-world

• Comprises the known fundamental sources of causality within a natural system

• Disregards factors of little or no importance• Uses assumptions• Uses parameterisations where factors are not

known or hard to calculate

What is a Model?

Introduction #2

• A climate model must attempt to describe the climate system in terms of basic physical, chemical and biological principles (laws)

• The model becomes a series of equations expressing these laws

• Equations must be solved rapidly for individual grid-points and for many time integrations

What is a Model?

Introduction #3

• A process such as weathering (by wind or rain) may be represented mathematically by the inputs (water), outputs (sediment solution) and weathering action involved. An entire system is a collection of processes (like the climate system for example) - each one defined by a set of rules at the simplest level or complex equations and physics at a higher level. The mathematical representation of the dynamics of real world systems is known as simulation modelling.

What is Modelling?

Modelling Philosophy

Modelling Philosophy #1• It has been suggested that the most useful links

between a theory and a model are mediated through imagination (Harvey, 1969)

models

imagination theory

Modelling Philosophy #2

• Natural analogues. The use of actual events or objects occurring in different times or different places to help examine what has, is or will happen to a particular system

• Hardware or physical models. A range of materials (often natural) is used

• Mathematical models. A range of deterministic or stochastic approaches based upon the solution of equations, rules and algorithms.

There are three broad categories of model as outlined by Hardisty, 1995:

Modelling Philosophy #3Example of a very basic model

i npu t

ou tpu t

fu nction state varia ble

Modelling Philosophy #4When modelling a dynamic process (like the climate) we are concerned with the following paradigm:

Future value (or state) = present value + change

We may also consider the following re-arrangement:

Change = future value – present value

Modelling Philosophy #5The MOST important principle of modelling

The Systems Approach

The Systems Approach #1• Complex systems (such as the climate or

ecosystem) may be disassembled into smaller sub-systems, each of which has individual inputs and outputs

• By breaking down a large system in this way, we can study and model individual components more easily. This strategy is known as the systems approach

• Many natural systems blur into other systems making the demarcation of a system (and hence the limits of the model boundary) a difficult issue

The Systems Approach #2• Since the 1970s there has been a shift (in the

environmental sciences) to a dynamical systems approach after the realisation that models can evolve in time as the processes and sub-systems they represent change and evolve.

• The study of the functioning and composition of systems is known as systems analysis (Hardisty et al., 1995). Systems analysis is very closely allied to modelling as system construction is an early phase in modelling itself

Systems Analysis

Systems Analysis #1• There are four phases

• Phase 1: The lexical phase. This requires the (a) definition of the system boundaries; (b) selection of system components (more correctly referred to as state variables); and (c) estimation of the value (state) of the state variables. Huggett (1980) calls these stages system closure, entitation and quantitation respectively

Systems Analysis #2• Phase 2: The parsing phase. This involves

defining the relationships of the state variables of the system in a mathematical way. Relationships may be deterministic (a single value) or stochastic (a more probabilistic or random value).

• Deterministic model solutions provide a single outcome - with no estimate of error or probability

• Stochastic models provide both probabilities and estimates of skill and reliability

Systems Analysis #3• Phase 3: The modelling phase. The first step is

model construction which requires that changes in controlling and state variables are well understood. The second step is running the model.

• In advanced global climate model simulations the ocean model is coupled to the atmospheric model

• Less advanced (and hence less computationally intensive) climate models run atmospheric models with oceanic persistence or climatology

Systems Analysis #4• Phase 4: The analysis phase. This is where the

model is validated – when we compare the model output against actual observations. Once we are happy the model performs well, we can begin to trust its outputs

• Observational data used for validation of climate models is often referred to as reanalysis

• ECMWF produces ERA-15 (1979-1993)

• ERA-15 however is flawed and hence climate models have been affected as a result

Climate model basics

Climate model basics #1• Radiation: input, output and absorption of solar

radiation and the emission of infrared radiation• Dynamics: movement of energy around the

globe by oceans and winds - both horizontal and vertical

• Surface processes: effects of sea- and land-ice, snow, vegetation, albedo, emissivity and surface-atmosphere energy exchanges

• Chemistry: chemical composition of the atmosphere

• Resolution: both in time and space

Climate model basics #2

• Conservation of energy (first law of thermodynamics):– Input energy = increase in internal energy + work done

• Conservation of momentum (Newton’s second law of motion): – Force = Mass x Acceleration

• Conservation of mass (the continuity equation)• Ideal gas law

Fundamental equations solved in GCMs

Climate model basics #3

Dv

Dt 2v 1p g F

DDt

v C E

1. Conservation of momentum

2. Conservation of mass

3. Conservation of energy

DI

Dt p

d -1

dt Q

4. Ideal gas law

p RT

Suggested reading

Text BooksHardisty J, Taylor DM and Metcalfe SE (1995). Computerised environmental modelling: A practical introduction using Excel. Published by John Wiley & Sons, England.

Berry J and Houston K. (1995). Mathematical modelling. Published by Edward Arnold, London

Giordano F, Weir M and Fox W. (1997). A first course in mathematical modeling. Published byBrooks and Cole, California.

Deaton M and Winebrake J. (1999). Dynamic modelling of environmental systems. Published bySpringer Verlag, New York

Today’s Practical

James Lovelock