Climate (Atms 4600)
Professor Anthony R. Lupo
Department of Soil, Environmental, and Atmospheric Science
University of Missouri
Columbia, MO
ATMS 4600 Climate
• At the University of Missouri, I teach an introductory climates class
(too easy) and a graduate level class (too hard). I wanted to
create something in the middle.
• This class will essentially just go 'upscale' from ATMS 8400 Theory of the General Circulation.
ATMS 4600 Climate
• Some initial questions:
• What is Climate? How does it differ from weather (synoptic, or even the
General Circulation)? How is this different from Climatology?
• Weather  the day to day state of the atmosphere. Includes state
variables (T, p) and descriptive material such as cloud cover and
precipitation amount and type, etc.
ATMS 4600 Climate
• Recall in meteorology, we tend to divide phenomena by scale
based on what processes are important to driving them.
• Table 1
Scale
Time
Planetary
Space
Force
Weather
7 – 14 days 6000+ km
Co, PGF
Jet stream
Synoptic
1 – 7 days
2000 – 6000 km
Co, PGF,
Fric, Bouy
Low pressure
Meso
1 - 24 h
10 – 2000 km
Bouy, PGF,
Fric
Fronts
Micro
< 1 hr
< 10 km
Bouy, Fric,
PGF
Thunderstor
m
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• Time / space Scales / example / forces
• Micro- 1 hour / <10km / tornadoes / Bouyancy, Friction,
Pressure gradient force
• Meso- 1hr-1day / 10-2000km / fronts / Bouyancy / pressure
gradient force
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• Spatial/Temporal Scales
• Synoptic- 1 day-1 week / 2000-7000km / cyclones / Coriolis Force,
Pressure Gradient force
• Planetary- >1 week / >7000km / blocking, jet stream / Coriolis
force, pressure gradient force
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• General Circulation – ‘statistical’ features. We think of planetary
in scale, but time scales are 2 weeks, 1 month, 1 season, 1 year, a
few years.
• Climate  Is the long-term or time mean state of the Earth-Atms.
system and the state variables along with higher order statistics.
Also, we must describe extremes and recurrence frequencies.
ATMS 4600 Climate
• Thus, the general definition of climate is scale independent and a
technical definition would depend on your scale, ie we can
describe micro, meso, and synoptic climates and climatologies.
• Climate as we will discuss it many contexts will be "global" or
large-scale in nature, or "upscale" in time from the General
Circulation.
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FIG. 2.1. Annual global surface temperature departures
from the 1961 to 1990 average. [Sources: NOAA/
NCDC; CRU/UKMO (HadCRUT3); and NASA GISS.]
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• Observations and the Hockey Stick
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• Temperature
Precipitation
ATMS 4600 Climate
• Climatology is the study of climate in a mainly descriptive and a
statistical sense. Climatologists study these issues.
• Dynamic Climatology or Climate dynamics are relatively new concepts
and involve the study of climate in a theoretical and/or numerical sense.
In order to study climate in this sense, we will use models, which will be
derived using basic equations.
• One way to accomplish this is via the scaling of primitive equations, or
using basic 'RT' equations (Energy Models, which use concepts like Stefan
Boltzman's law). We won’t do this in this class, save for ATMS 8600
ATMS 4600 Climate
• Key concepts that will be discussed in this course:
• We'll need to distinguish plainly between weather and climate! (Review
the concept of climatic averaging')
• We'll need to talk about time variations on climate states ('climate'
versus climate change)
• We'll need to examine the components of the climate system
ATMS 4600 Climate
• We'll need to examine the state of the climate, in particular this
means 'internal variables' (internal vs. external).
• We'll need to study climatic 'forcing' (this means 'external
variables (e.g. Solar, Plate tectonics, humans?), (also how they
differ from internal))
• We'll need to examine issues surrounding spatial resolution and
climatic character.
ATMS 4600 Climate
• The earth-atmosphere system, courtesy of Dr. Richard Rood.
(http://aoss.engin.umich.edu/class/aoss605/lectures/)
ATMS 4600 Climate
• The primary components of the Climate system
• 1.
The Atmosphere (typical response time --> minutes to three weeks)
• 2.
The Ocean (typical response time months and years, for upper ocean)
• 3.
The litho-biosphere (we'll treat as one for now)
• 4.
The cryosphere (both land and sea ice, response times on order of
decades to MYs)
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• Aside:
• Typical short-hand notations used now in the study of climate:
• 10,000 Years Before present (10 KY BP) KY = Thousands of years BP
= before present
• MY = Millions of years.
ATMS 4600 Climate
• Another view of the climate system
ATMS 4600 Climate
• Another view
ATMS 4600 Climate
• Each component of the climate system can be described by it's own state
variables, which are considered internal variables.
• External forcing is defined as forcing outside the system or sub-system.
Thus, SST anomalies are internal or state variables for the earth
atmosphere system, or the ocean. But they are considered 'forcing' or
external to the atmospheric component.
• Also, the dynamics of the internals are fairly well know, but heat and
mass exchange processes between sub-sytems not well understood.
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• Atmospheric Composition
• Homosphere: <80 km, good mixture of gas, we focus here
• Heterosphere: above 80 km, gases separate by atomic weight
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• Atmospheric Composition
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•
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Nitrogen 78%,
Oxygen 20.9%,
Argon .9%
CO2 380 ppm,
Water Vapor (big greenhouse gas, 0.2%-4%)
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• Vertical Profile
• Troposphere: Temp Decrease with height (-6C/km) <10km
• Stratosphere: Temp Inversion (+3C/km) 10-50km
• Mesosphere: Temp Decreases (-4C/km) (coldest part of
atmosphere)
• Thermosphere: hottest
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• Ok, now we have to introduce ourselves to the concept of climatic
averaging.
• For any instantaneous climatic variable a;
• a (bar) representing a time mean, and a' the instantaneous
departure from the mean.
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• Recall, that (from mean value theorem):
• where t' will represent a 'dummy' time coordinate, and t is physical time, and
t is the
averaging time usually written as =t . For the above to be valid in a physical sense, then:
•
P(a') <<  << P(a)
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• where P(a) represents a characteristic time period, say a few
seconds for wind gusts (P(a')?), and 3 - 4 days for an extratropical
cyclone (P(a)?)
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• In drawing on the previous slide, I've provided for you a CLEAR
separation between the two periodic fluctuations.
• In the climate system one must look for periods of high and low
variability, to do this we can look at an idealized (not real)
periodogram for the atmosphere.
• Periodogram (real) examines the "power" spectrum within a time
series of say, Temperature. "power" or variance is the square of
the Fourier coefficients:
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•
This spectrum demonstrates 'scale' separations nicely (planetary, synoptic, meso, micro):
•
typical averaging periods: example: 1 sec, 1 hr, 3-12 mo., 30 years, 1 MY
•
Turbulence  way out on right
•
'weather' and gen circ. 12 hr to 1 yr typically.
•
climate (as is commonly thought of) is 1 yr to 27 year peak.
•
climate change scale: 30 yrs to 100 KYs.
•
tectonic change: on left.
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• The State of the Climate System
• In the climate system can be considered a composite system, if as a whole the system is
thermodynamically closed (impermeable to mass, but not energy), (recall from gen circ., we
say mass does not change).
• The individual sub-components are thermodynamically open (transfers of mass and energy
allowed) and cascading (that is the output of mass or energy from one subsystem becomes the
input into another).
• The state of the climate system can be represented in terms of physical variables that
represented additive of extensive properties (e.g., volume or internal energy, or angular
momentum), or in terms of intensive properties ('fields') that are independent of total mass
and that change with time ('temperature', pressure, and wind velocity).
ATMS 8600 Climates
• Equilibration of the Climate System
• If for specific time scales, the internal climate system behaves as if it
has forgotten its past, and responds primarily to external forcing then it
can be considered to be almost in the state of equilibration.
• External forcing can be outside earth atmosphere system, or be forcing
from an internal variable of longer time-response (inertial time scale)
sub-systems forcing on another sub-system (e.g. SST forcing) with a
shorter time response. (e.g., if considering synoptic-scale, then ice
sheets, oceans, and everything is 'external').
ATMS 8600 Climates
• Thus the climate system is a boundary value problem, this is
different from weather forecasting with is primarily an initial
value problem (boundaries there too). These definitions allow us
to define climate in terms of ensemble means and variability of
each sub-system independently.
• If any initial state always leads to the same near equilibrium
climatic state (same equilibrium properties), then the system is
transitive (climate folks) or ergodic (geology folks!).
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• If instead there are two or more different states with different properties that
result from different initial conditions, then the system is intransitive (this
system – stochastic, dynamic laws unknown - pack it up and go home w/r/t
forecasting).
• If there are different subsets of statistical properties, which a transitive system
assumes during its evolution from different initial states, through long but finite
periods of time, the system is almost intransitive.
• In this case, the climate state, beginning from any initial condition will always
converge to the same state eventually, but go through periods w/ distinctly
different climatic regimes. This is best representation of climate system. (Ice
ages?)
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• Climate Modeling
• Definition of a Climate Model:
•
An hypothesis (frequently in the form of mathematical statements) that
describes some process or processes we think are physically important for the
climate and/or climatic change, with the physical consistency of the model
formulation and the agreement w/ observations serving to 'test' the hypothesis
(i.e., the model).
•
"The model (math) should be shortened (approximated) for testing the
hypothesis, and the model should jive with reality".
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• Climate Model
Real Earth-Atmosphere
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• The scientific Method:
•
•
•
•
•
•
•
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1.
2.
3.
4.
5.
6.
7.
8.
Collect Data
Investigate the Issue
Identify the Problem
Form Hypothesis
Test Hypothesis
Accept or Reject hypothesis based on conclusions
If reject, goto 2
If accept, move on to the next problem.
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• Two distinct types of climate models:
• 1)
Diagnostic or equilibrium model (Equilibrium Climate Model - ECM)
with time derivatives either implicitly or explicitly set to zero. The ECM
is most commonly solved for climatic means and variances. (d / dt =
Force + Dissipation)
• 2)
Prognostic models, where time derivatives are crucial and with the
variation with time of particular variables the desired result (i.e., a time
series). Most commonly solved for changes in climatic means and
variances. Weather models (General Circulation Models – GCMs)
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•
Ocean - Atmosphere (one of many subsystems of the climate system)
•
(go back to our diagram)
•
Some basic principles:
•
Conservation of mass precipitation, evaporation: precip = evap over the globe (closed system). Water vapor budget
equation we also use in Atms 8400.
•
Energy: Sun heats land and oceans which, in turn, heats the atmosphere (transparent to shortwave, but opaque to LW).
•
In order to fully understand, we should couple the atmosphere - ocean is more important than considering each separately,
however, we know each separately!
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• 3 Governing Principles for Climate Studies (described by 7
“primitive” eqns)
• Cons of Energy
• Cons of Mass (includes moisture)
• Cons of Momentum
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• Feedback Mechanisms
• Feedback mechanisms complicate things, Nature is highly non-linear. But they are a good way
to get a handle on non-linear coupling mechanisms.
• Feedback mechanisms are all positive (+) or negative (-)
• (+) amplify the linear response to a forcing process. (e.g., ice-albedo) – indicate a “sensitive”
system.
• (-) de-amplify the response to a forcing process. (e.g., clouds – global temperature)
ATMS 8600 Dynamic Climatology
• Examples: Double CO2
• -Positive feedback• Linearly increase CO2 to double the amount has a very small effect on
climate temp. response or forcing.
• It's the other feedbacks that amplify "global warming"
• CO2 is a "potent" greenhouse gas, but a trace gas.
ATMS 8600 Dynamic Climatology
• Water Vapor is more plentiful and 30 times more potent "greenhouse gas" (molecule per molecule, due to
vibrational, rotational absorption bands).
• Increased CO2, (could) mean increased water vapor. This increases the long wave retained by atmosphere,
which heats up atmosphere and oceans. (IPCC)
• Increased water vapor  increased LW heating,  increased evaporation  increased water vapor. (Get
the picture? Positive feedback!). This will go on forever, unless something interrupts.
• Caveat: Increases in air temp, does not necessarily mean corresponding increases in specific humidity and
dew points.
• Formula for + feedback: E happens  A inc  B inc  C inc  A inc.
ATMS 8600 Dynamic Climatology
• -- negative feedback -• Clouds  again same caveat, more vapor not necessarily means more clouds, and consider
cloud characteristics, like droplets, or ice crystals, drop size, optical depth, etc.
• More low clouds, increases Earth's albedo, less SW into the system, LW out exceeds SW in and
cooling.
• May dampen a positive feedback, bring the system back into equilibrium, but not necessarily
at the same state that was the original.
• Formula - feedback: E happens A inc.  B inc.  C inc  A dec.
ATMS 4600 Climates
• Global Energy Balance
• Climate System (Earth-Atmos. System)
• Assumes:
• Earth-Atmos System receives energy from the Sun (99.9%), the
rest come from space (.01%) and geothermal energy (earth’s
core)
ATMS 4600 Climates
Scheme of radiation balance
ATMS 4600 Climates
• Convection-bulk transfer of energy by a fluid (liquid or gas)
• Conduction-energy of contact (hot to cold) (ground heats the
lowest 15 cm of atmosphere)
• Radiation-does not need a medium to be transferred (sun heats
earth’s surface)
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• In summary:
• Energy leaves the atmosphere in the form of infrared energy
• Energy entering the atmosphere heats the earth’s surface
(contact point), and then is transferred into the atmosphere and
other parts of the climate system
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• Energy
• Potential energy- energy of position relative to some baseline in a
field (gravitational PE)
• Internal Energy- energy that exists by virtue of an object that has
a temperature. (IE)
• These add up to be Total Potential Energy (Margules, 1903)
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• Kinetic Energy- energy of motion (for our purposes ignore
molecular level) (KE)
• Latent Heating- energy from phase change of a substance
• 5) Oceanic Heat Transport- cannot ignore even though it is a small
part.
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TPE converted into KE by cyclones (eddies)
• This KE is dissipated by friction
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• Energy Transfer with Climate System
• Incoming solar radiation decreases from equator to pole
• Outgoing radiation is such that outgoing radiation is strongest at
pole and falls off slower than incoming to the pole
• Energy surplus in the tropics, balance around 35o N latitude and
deficit in the polar regions
ATMS 4600 Climates
• The Surplus approx. equals the Deficit.
• Need equilibrium (2nd Law of Thermodynamics)- so we get a
transfer energy from hot (source) equator to cold (sink) pole.
(Cyclones and Anticyclones involved)
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• Radiative Transfer
• Electromagnetic Spectrum
• X-Ray 0.01 microns, Ultraviolet .1, Visible .4 microns
• Near Infrared >1-8 microns, Microwave, Radio, Etc.
• EM Spectrum
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• EM Spectrum
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• EM (NASA)
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• Свет: Длина волны (λ) и частота ( )
• обратно пропорциональна
•
Скорость света:
• C = 3 x108 м/с
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• Solar Energy
• Output of energy by the sun is about 3.9x1026 Watts (J/s)
• Flux density = Energy/Surface area
ATMS 4600 Climates
• Flux density on the sun’s surface:
Sun=3.9x1026/(4*p*(7x108)2)=6.34x107 W/m2
• Earth intercepts only one 2-billionth of this: solar constant ~1370
W/m2 (substitute 1.5x1011m)
• For an average square meter at the suface of earth 342.5 W/m2
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• Solar Activity
• Def’n: Solar luminosity: Flux density of radiant energy from the
sun that falls on a unit area held normal to the direction of the
sun just outside the earth’s atmosphere.
• Varies as the cosine of the Zenith Angle.
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• Hotplate (1000 W over .2 m2= 50000W/m2)
• Compare Nuclear weapon 6 x 10 13 J: over about 3m, and
released in about 0.3 microseconds (~ 6 x 10 11 W / m 2).
• Sun spots can cause a slight energy surplus for the Earth, little ice
age (constant CO2 of 280 ppm, thus solar variations?)
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• Blackbody Radiation
• BB is a coherent mass of material (such as a surface or collection
of molecules) which have the attribute that all radiation incident
is absorbed
• Cor: it can be shown that radiation emitted by a BB is the max
possible by a real body at that temp (stars).
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• Most of the light directed at a star is absorbed. It is therefore
capable of absorbing all wavelengths of electromagnetic
radiation, so is also capable of emitting all wavelengths of
electromagnetic radiation.
• Emissivity=Absortivity=100% for a blackbody (Kirchoff’s Law)
Day 4
• Wien’s Law
• Wavelength (maximum) =2897 / T (T in Kelvin)
• Wavelength (microns) for peak emission for a blackbody at a given
temperature
Day 4
• Wien’s Law
• Important consequence: solar radiation is concentrated more
toward the visible and near infrared spectrum, where radiation
emitted by planets tends to be long Infrared.
• Infrared radiation is lost to space (this is what heats the
atmosphere)
Day 4
• Stefan-Boltzmann’s Law
• Energy emitted by a blackbody is proportional to T4
• E=sT4 (sigma is S-B const) = 5.67x10-8
Day 4
If the surface of the sun emitted as a BB then T=5783 K
• We can set up an exercise to show that the effective BB temp of
earth is 255 K
• This is not the temp if there was no atmosphere more to take into
account besides an albedo assumption
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• Схема
Day 4
• What is the point?
• Sun can be assumed a blackbody
• Earth is not
• Have to take into account absorptance: % of radiation absorbed by
a sfc
Day 4/5
• Emittance-% of energy emitted at a sfc at a particular temp
• Transmittance- % of energy passing through a substance (A+T=1)
• Reflectance (Albedo (a))- % reflected
• For ATMS= Refl.+Abs.+Trans.=1
Day 4/5
• Solar Radiation Budget
• Some in reflection, absorption, transmittance (RAT=100%)
• 30% albedo (reflectance)
• Dark and rough surfaces, absorb more
• Scattering (blue sky - Rayleigh)
• Certain wavelengths of light are scattered more efficiently than others
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• We can use these properties to set up a simple model to represent
the atmosphere:
• (http://biocycle.atmos.colostate.edu/shiny/2layer/
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• Scattering
• Rayleigh scattering and Mie scattering
• Rayleigh scattering- wavelength of light is similar to the size of
the particle doing the scattering…blue light is similar to O2 and N2,
scattered most efficiently when sun is overhead
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• Absence of color at night
• Mie scattering- size of the particles doing the scattering much
larger than visible light water, dust, etc.) (white hint to sky)
(radar applications)
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• Shift gears to pressure, winds, and moisture
• All factor in the density of the air
• Revisit temperature - defn
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• Temp: proportional to KE
• Pressure
• Force per unit area exerted by gravity, molec. motions (1013.25 hPa
(mb))
• Torricelli 1643
• Relationship between two
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• Gas Relationships
• Boyle’s Law
• Pressure*Vol= constant
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• Number of Molecules constant, shrink container
• Charles Law
• Temp=Constant*Vol
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• Combined Gas Law (Avagadro)
• P=r*T*Rd
• r=density, Rd= dry gas constant
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• Pressure Distribution (Surface)
• Low pressure near equator generally
• Tropics, high pressure
• Band of lower pressure around subpolar region
• High pressure at the poles
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• Pressure
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• 500 mb Patterns/PGF
• 500 mb: about half the amount of the atmosphere, can get a
rough idea of jets
• Higher heights in equatorial regions (atmos thicker), poles lower
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• 500 mb heights
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• Drive to equilibrium, mass from equator needs to be spread
toward the poles
• Tight height contours or pressure contours (isobars) represent
greater change (gradient)
• Force needs to be directed toward area of low
pressure====Pressure Gradient Force (PGF)
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• Lows and Highs
• Flow is clockwise around a high in N.H.
• At the surface due to friction the flow is directed outward from H
(divergence)
• Low pressure counterclockwise in N.H.
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• Diagram
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• Courtesy of NASA
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• Friction at the sfc makes flow directed inward to L (convergence)
• Cyclonic is for L in both hemisphere
• Anticyclonic is for H in both hemisphere
• Clockwise and counterclockwise switched
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• Summarize
• 3 basic principles
• 1) Conservation of Energy- 1st Law of Thermo
• 2) Conservation of Mass- Continuity Eqn.
• 3) Conservation of Momentum- Eqn of Motion
• equation of state (ideal gas law), 2nd Law of Thermo (equilibrium)
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• Conservation of Mass-Continuity
• On the climate time scale, the atmos. as a whole is neither
gaining nor losing mass
• Avg. pressure at most station over 100 years there is no real
change unless there was a noticeable regional climate change
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• Over the entire globe there should be no pressure change
• Atmosphere is a continuous fluid (displacement)
• Must be divergence coupled with convergence, we shall see this
later in pressure patterns
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• Diagrams (500 mb) Chpt 8/9 in Intro Books
• Heights on 500 mb decrease toward the pole
• Strength of pressure gradient proportional to wind speed
• Tighter isobars= faster wind
• Winds blow from west to east because of the rotation of the
earth= see conservation of mass
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• Equation of Motion
• Newton’s 2nd Law (no known exceptions) of Motion
• Any body in motion (at rest) stays in motion (at rest) unless
acted upon by an outside force.
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• F=mass* acceleration
• Velocity= change in location with time, vector (has magnitude and
direction) dx/dt
• Acceleration= change in velocity with time dv/dt
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• Equation of motion
• Newton’s law gives rise to this
• A= dv/dt= sum of forces
• dv/dt= PGF+Friction+Coriolis+Gravity
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• This is the equation of motion for the atmosphere (published in
1902 Navier and Stokes)
• PGF- mass moves from source to sink (however wind is influenced
by the other forces as well).
• Equations are valid for the atmosphere until you get to the
mesosphere (parcel theory)
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• Coriolis Force
• A force changing the direction of parcels of air, acts to the right of
motion in the N.H. and to the left in the S.H.
• force based on the earth rotating from a earth-bound frame of
reference
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• If coordinate system based on sun, the coordinate system is stationary
• Simply a conversion factor from sun’s coordinate to the rotational
coordinate system of the earth.
• Acts over large time and space scales (ICBMs qualify)
• Synoptic and Planetary scales must take into account Co
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• Equation of Motion (cont.)
• Infinite solutions, but there are a few that come out more often
than others
• Assume balanced motions for simplicity
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Set of forces exactly balancing with another
• Get rid of the accelerations
• PGF+gravity+coriolis+friction=0
• Look at atmosphere from 1km-50km
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• Hydrostatic balance
• PGF can be broken up into horizontal and vertical components,
the accel. by the vertical ~10 m s-2, horizontal 10-3 m s-2
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• The small horizontal PGF gives rise to the wind
• In the vertical PGF is much greater, but no huge winds in the
vertical….there is a balance
• PGF in vertical balances with Gravity almost perfectly…This is
hydrostatic balance
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• Horizontal Balance
• PGF in the horizontal is approximately equal to the Coriolis from 1
km – 50 km
• This is geostrophic balance (weaker than hydrostatic balance)
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• This is why the winds blow from west to east
• No rotation, motion would go from equator to pole, high to low
pressure, etc. (Venus)
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• Look at Sfc- 1 km layer
• Balance here (planetary boundary layer) is PGF= Co + Friction
• Winds blow across isobars toward lower pressure since friction
slows wind, Coriolis force decreases, pgf forces winds toward low
pressure.
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Geostrophic balance, free atmosphere flow (no friction) causes flow
to be parallel to isobars at the surface cannot ignore friction
• See diagram in texts (on board)
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• From Wikipedia
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• From Physical Geography
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• Atmospheric Moisture
• Water Basics
• Variable from 0-4% by volume in atmosphere
Water mass exists naturally in all 3 phases (solid, liquid, and gas)
ATMS 4600
• Thus the climate system is a boundary value problem, this is
different from weather forecasting with is primarily an initial
value problem (boundaries there too). These definitions allow us
to define climate in terms of ensemble means and variability of
each sub-system independently.
• If any initial state always leads to the same near equilibrium
climatic state (same equilibrium properties), then the system is
transitive (climate folks) or ergodic (geology folks!).