1

Lecture 9 – Models

ATOC/CHEM 5151

2

Why talk about models? • Atmospheric chemistry is data-rich; hard to

interpret without some analysis framework • Models are useful for testing our

understanding of fundamental processes • Many journal articles include model results • Models have flaws – useful to know what

those might be

3

Hierarchy of Models

• Simplest form – “box model” – Zero dimensional (0-D) – No transport (or heavily parameterized) – Single point calculation – Only one climate variable (T)

4

Elements of a Box Model

From FP&P

5

Elements of a Box Model

Sources: Flux in, Emission, Chemical production Sinks: Flux out, Deposition, Chemical loss Inventory: amount of X in box (also reservoir)

From Jacob text

6

7

Eulerian formulation

• Referenced to a fixed spatial grid point ∂N/∂t + u(∂N/∂x) = 0

• Traditional model scheme

– Fixed grids are easy to use; winds are prescribed or calculated

– Limitation is stability (diffusion and/or dispersion)

– Time step and spatial resolution tightly related

8

Hierarchy of Models

• One-dimensional models (1-D) – Generally limited to vertical transport, which is

parameterized by eddy diffusion (Kzz) – Appropriate for a global-average look at

something – Column calculations of photochemistry,

radiation – “Radiative-convective” models – useful

method for calculating effects of atmospheric instability

9

Hierarchy of Models

• Two-dimensional models (2-D) – Latitudinal and seaonal behavior – “Zonal averages” – Used to be the premier tool for chemistry

assessment studies (when computing power was more limited)

– Have a “closure” problem – tend to get mass accumulation or loss over time

10

Grids in a 2-D model

11

Hierarchy of Models

• Three-dimensional models (3-D) – Full 3-D (+ time) behavior – Come in several “flavors”

• Mechanistic – prescribe certain behaviors, to focus on others

• Off-line – active transport, chemistry done separately

• Assimilation – use observed winds, T, tracers • GCMs – self-consistent calculations • CTMs – GCM + chemistry

12

Grid structure of 3-D model

13

Elements of 3-D models

14

Elements of 3-D models

15

Lagrangian Models

• Basically follow a parcel of air as it is moved by winds – Air assumed to be homogeneous – Usually a simple scheme with no numerical

diffusion – Utility limited to short periods of time, due to

accumulating errors in parcel location

16

17

Semi-lagrangian scheme

• Mixture of Lagrangian and Eulerian types – Solution at grid points is derived based on a

Lagrangian calculation – Common in CTMs, but non-conservative because of

interpolation to grid-points

<v>

(x, t)

(x0, t – Δt)

18

Cautions - Altitude

• This would seem to be an invariant quantity, but…. – Many models are formulated on pressure surfaces, or

use terrain-following coordinates (called σ-layers)

19

Cautions - Temperature

• Some models calculate T interactively, but many (most?) use climatological T – This can matter a lot for chemistry, especially

for things that have thresholds or are very T-sensitive

• E.g., cloud formation • NO + O3, k=2.0 x 10-12 exp(-1400/T) • NO2 + O3, k=1.2 x 10-13 exp(-2450/T)

– A 5 K temperature difference change rate 20 and 36 %, respectively

20

Cautions – Photolysis Rates

• Can vary tremendously from model to model – Solar flux is pretty standardized, so not much

error there – Ozone column – use climatologies, but daily

variations can be important – Presence or absence of aerosol scattering – Plane-parallel vs. fully spherical calculations

• Especially for SZA > 75

21

Photolysis Rate comparisons

22

Model Evaluation

• Some done on ad-hoc basis • Formal comparisons/evaluation:

– http://gmi.gsfc.nasa.gov/gmi.html

23

Box model practice

Water is supplied to the atmosphere by evaporation from the surface and is removed by precipitation. The total mass of water in the atmosphere is 1.3x1016 kg, and the global mean rate of precipitation to the Earth’s surface is 0.2 cm day-1. Calculate the residence time of water in the atmosphere.