SOES6002: Modelling in Environmental and Earth

System Science

Geophysical modellingTim Henstock

School of Ocean & Earth Science

University of Southampton

Geophysics Modelling

Data analysis => structure and physical properties

Effective medium modelling Geodynamic modelling Most powerful when all three are

recursively combined with experimental observations

Mid-ocean ridges

Ocean crust/lithosphere formed here within past ~200Ma

Important for heat budget of Earth Important for chemical balance of oceans Many types of process operate, probably

strong time-dependence Most important for shallow features

mediated by magma-hydrothermal interaction

Use as example of geodynamic modelling

Large scale:

Model lithosphere formation and long-term heat flow by advection-diffusion equation:

Isostatic balance and heatflow over ~150Ma determines required parameters

Initial conditions on scale ~10km irrelevant beyond ~1Ma

TTvt

T 2.

Large scale:

Successes:» Match observed depth-age relationship» Match observed heat flow decay

Failures:» Measured conductive heat flow near

axis much lower than prediction» Does not let us constrain any details at

axis

Detailed scale:

Try to use observations to constrain model setup:

Seabed

Melt sill

Detailed scale:

Upper crust

Lower crust

Mantle

Sill +- axial intrusion zone

Problems:

Fundamental physics, advection-diffusion eqn (even steady state) actually:

» We can no longer make many of the normal approximations

» Several important factors are difficult to model “properly”

0).().( TkTvC p

Latent heat:

Energy is released as melt solidifies Latent heat

» Heat budget and temperatures OK, instantaneous release of energy at point

Excess temperature» Heat budget OK, temperatures invalid

(possible effects on conduction)

Increase heat capacity during solidification» Ideal, but extra terms in adv-diff equation

Hydrothermal:

Hydrothermal circulation enhances heat transport

Nusselt number/enhanced conductivity» Heat fluxes OK, temperatures wrong

(isothermal convective system with 2 boundary layers?)

Explicit model of fluid flow» May be correct, but strong dependence on

permeability structure and water properties

Hydrothermal:

Disagreements over depth variation!

Time dependence:

All processes likely to vary in time Melt transport/emplacement

» Dyking events ~hours/days repeat at interval ?years

» EPR ?steady state, MAR melt present at <10% of locations studied (probably)

Hydrothermal systems unstable» At MAR large hydrothermal systems only

present few% of time» Pattern of convection time dependent, driven

by melt emplacement…..

Mechanics:

Decide on approximations, then fix correct equation, eg (time-averaged)

Next sort out boundary conditions» Fix T, dT/dz, d2T/dz2

Finally solve (probably numerically)

0... 2TkTkvdTCTvC

dT

dCT pp

p

Testing:

Must get model predictions into testable form, ie compare with experiments» Seismic velocity» Temperature structure/history» Heat flow

But……» Usually only work at top of system» Must worry about quality of observations as

well as the physics of the model

Testing:

Eg seismic velocity» Lab expts convert

T to dv

Testing:

Consider what we are trying to achieve:» “Most realistic” – complicated model,

matches or not» “Hypothesis testing” – is a particular

factor significant/required» Alternative explanations

Hypothesis testing:

But beware:

Just because a particular class of model predicts a particular feature of the observations this does not mean» The model is correct» The class of model is the only one

which will predict that feature!

Example:

Geophysics Modelling

Data analysis => structure and physical properties

Effective medium modelling Geodynamic modelling Most powerful when all three are

recursively combined with experimental observations

Electromagnetic fields in the Earth

Beware …..

Garbage in, garbage out…. Use of an appropriate model

algorithm Parameterization Careful checking

Data analysis

Forward modelling Hypothesis testing – classes of

models Inverse modelling

Successive iterations

Inversion

Seek minimum misfit ….. Or seek minimum structure Combine both in Occam and similar

methods ‘Objective Function’ Requires robust estimates of errors

(random and systematic) in your data

Conclusions

Modelling is an indispensable and extremely powerful tool

But must be applied with care and using a self-critical approach

A priori data from other sources is always valuable

Having a physically and mathematically sound modelling algorithm is necessary but not sufficient……..