lecture 9 – modelstoohey/lecture-9-models.pdf · lecture 9 – models atoc/chem 5151 . 2 why talk...
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Lecture 9 – Models
ATOC/CHEM 5151
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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
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Hierarchy of Models
• Simplest form – “box model” – Zero dimensional (0-D) – No transport (or heavily parameterized) – Single point calculation – Only one climate variable (T)
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Elements of a Box Model
From FP&P
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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
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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
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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
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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
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Grids in a 2-D model
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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
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Grid structure of 3-D model
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Elements of 3-D models
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Elements of 3-D models
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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
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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)
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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)
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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
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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
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Photolysis Rate comparisons
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Model Evaluation
• Some done on ad-hoc basis • Formal comparisons/evaluation:
– http://gmi.gsfc.nasa.gov/gmi.html
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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.