Midterm Review

Midterm Review
What have we discussed?
Importance of the atmospheric boundary layer
Surface energy balance
Surface water balance
Vertical structure of the ABL
Modeling the ABL
Boundary layer of shallow clouds and deep
• Effects of different surface types and human
• Boundary layer processes in global climate
Importance of the ABL
• The mission of meteorology is to understand and predict weatherrelated disasters (e.g. tornados, hurricanes, winter storms) and
climate-related disasters (e.g. El Nino and global warming).
• The modern climatology (meteorology) was born in the 1940s (a very
young science!), but has been growing very fast! Now we have a
global observational network with many satellites, ships, radars and
surface stations, as well as very comprehensive prediction models
running on the world’s fastest supercomputers.
• The current status of weather and climate predictions: (1) weather
prediction good to 10 days, (2) tropical cyclone prediction good in
track but not in intensity, (3) climate prediction good to two seasons,
(4) climate change projections have a 3-fold difference in magnitude.
• The main reasons of the difficulties: (1) Teleconnection problem, (2)
Feedback problem, and (3) Subgrid-scale problem.
• Importance of the ABL: (1) interface between atmosphere and
ocean/land/ice - flux transfer and feedback, (2) the human beings are
living in the ABL and change the environment, (3) a basic subgridscale process
Surface energy balance
What is energy? 3 methods of energy transfer
The names of the 6 wavelength categories in the electromagnetic
radiation spectrum. The wavelength range of Sun (shortwave) and
Earth (longwave) radition
Earth’s energy balance at the top of the atmosphere.
Incoming shortwave = Reflected Shortwave + Emitted longwave
Earth’s energy balance at the surface.
Incoming shortwave + Incoming longwave = Reflected shortwave
+ Emitted longwave + Latent heat flux + Sensible heat flux
+ Subsurface conduction
What is sensible heat flux? What is latent heat flux?
Bowen ratio B= SH/LH = Cp(Tsurface - Tair) / L(qsurface - qair) provides
a simple way for estimating SH and LH when the net radiative flux
Fr is available LH=Fr/(B+1), SH=Fr B/(B+1)
Factors affecting soil thermal conductivity
Other heat sources: precipitation, biochemical, anthropogenic
Summary: Surface energy balance
Incoming shortwave + Incoming longwave = Reflected shortwave + Emitted longwave
+ Latent heat flux + Sensible heat flux + Subsurface conduction
=SWdn 
=Tair4 =Ts4
LH=CdLV(qsurface- qair)
Fc = -  dT/dz
Methods of
Energy Transfer
• Conduction
– Molecule to molecule transfer
– Heat flow: warm to cold
– e.g. leather seats in a car
• Convection
– transferred by vertical movement
– physical mixing
– e.g. boiling water
• Radiation
– propagated without medium (i.e. vacuum)
– solar radiation provides nearly all energy
– The rest of this chapter deals with radiation
The Electromagnetic Spectrum
The limitations of
the human eye!
Earth’s energy budget (averaged over the whole
globe and over a long time)
heat 7%
Net Longwave 21%
Latent heat
At the top of the atmosphere:
Incoming shortwave = Reflected Shortwave + Emitted longwave
At the surface:
Incoming shortwave + Incoming longwave = Reflected shortwave + Emitted longwave
+ Latent heat flux + Sensible heat flux + Subsurface conduction
Sensible Heat
• Heat energy which is readily detected
• Magnitude is related to an object’s specific heat
– The amount of energy needed to change the
temperature of an object a particular amount in
• Related to mass
– Higher mass requires more energy for heating
• Sensible heat transfer occurs from warmer to cooler
areas (i.e., from ground upward)
Latent Heat
• Energy required to induce changes of state
in a substance
• In atmospheric processes, invariably
involves water
• When water is present, latent heat of
evaporation redirects some energy which
would be used for sensible heat
– Wet environments are cooler relative to
their insolation amounts
• Latent heat of evaporation is stored in
water vapor
– Released as latent heat of
condensation when that change of
state is induced
• Latent heat transfer occurs from regions of
Surface water balance
• Global water cycle
• Surface water balance
• Soil moisture
• Palmer drought severity index
• Desertification
The global water cycle
Components of global water cycle
• Ocean water
• Land soil moisture, rivers, snow cover, ice sheet and
• Sea ice
• Atmosphere water vapor, clouds, precipitation
• Water in biosphere (including human beings)
Surface water balance
The changing rate of soil moisture S
dS/dt = P - E - Rs - Rg + I
(PDSI, desertification)
Soil moisture
• Typically expressed as ‘volumetric soil water content’
S = Vwater / Vsoil
• Increases with depth
• Complicated to measure
Root zone
Palmer drought severity index (PDSI)
• was developed by Wayne Palmer in the 1960s
and uses temperature and rainfall information in
a model to determine dryness of soil moisture.
• is most effective in determining long term
drought (a matter of several months) and is not
as good with short-term forecasts (a matter of
• It uses a 0 as normal, and drought is shown in
terms of minus numbers; for example, minus 2 is
moderate drought, minus 3 is severe drought,
and minus 4 is extreme drought.
Global desertification vulnerability
~1 billion people are under threat
Vertical structure of the ABL
• Vertical structure of the atmosphere and
definition of the boundary layer
• Vertical structure of the boundary layer
• Definition of turbulence and forcings
generating turbulence
• Static stability and vertical profile of virtual
potential temperature: 3 cases
• Boundary layer over ocean
• Boundary layer over land: diurnal variation
Vertical Structure of the Atmosphere
Definition of the boundary layer: "that part of the troposphere that is directly
influenced by the presence of the earth's surface and responds to surface
forcings with a time scale of about an hour or less.”
Scale: variable, typically between 100 m - 3 km deep
Vertical structure of the boundary layer
From bottom up:
• Interfacial layer (0-1 cm): molecular transport, no turbulence
• Surface layer (0-100 m): strong gradient, very vigorous turbulence
• Mixed layer (100 m - 1 km): well-mixed, vigorous turbulence
• Entrainment layer: inversion, intermittent turbulence
Turbulence inside the boundary layer
Definition of Turbulence:
The apparent chaotic
nature of many flows,
which is manifested in
the form of irregular,
almost random
fluctuations in velocity,
temperature and scalar
concentrations around
their mean values in
time and space.
Generation of turbulence in the boundary
layer: Hydrodynamic instability
“Hydrodynamically unstable” means that any small
perturbation would grow rapidly to large perturbation
• Shear instability: caused by change of mean wind in
space (i.e. mechanical forcing)
• Convective instability: caused by change of mean
temperature in the vertical direction (i.e. thermal
Static Stability
• Static stability – refers to atmosphere’s susceptibility to
being displaced
• Stability related to buoyancy  function of temperature
• The rate of cooling of a parcel relative to its surrounds
determines its ‘stability’ of a parcel
• For dry air (with no clouds), an easy way to determine
its stability is to look at the vertical profile of virtual
potential temperature
v =  (1 + 0.61 r )
 = T (P0/P)0.286 is the potential temperature
r is the water vapor mixing ratio
Three cases:
(1) Stable (sub-adiabatic): v increases w/ height
(2) Neutral (adiabatic): v keeps constant w/ height
(3) Unstable (super-adiabatic): v decreases w/ height
Stable or
Neutral or
Unstable or
Diurnal variation of boundary layer
over land
• Daytime convective mixed layer + clouds (sometimes)
• Nocturnal stable boundary layer + residual layer (leftover of
daytime convective mixed layer)
Boundary layer over land:
Comparison between day and night
Strongly stable lapse rate
Kaimal and Finnigan 1994
Weakly stable lapse rate
Strongly stable lapse rate
• Subtle difference between convective mixed layer and residual
layer: Turbulence is more vigorous in the former
Modeling the ABL
• Reynolds averaging: Separation of mean and turbulent
components u = U + u’, < u’ > = 0
• Intensity of turbulence: turbulent kinetic energy (TKE)
TKE = ‹ u’ 2 + v’ 2 + w’ 2 › /2
• Eddy fluxes
Fx = - <u’w’>/z
• The turbulent closure problem: Number of unknowns >
Number of equations
• Surface layer: related to gradient
• Mixed layer:
Local theories (K-theory): < w’a’ >= - Ka dA/dz
Non-local theories: organized eddies filling the entire BL,
could be counter-gradient
Reynolds averaging
(1) Separate mean and turbulent components
Assume you are given a time series of
zonal wind speed u for a period of one
hour, the zonal wind speed can be
decomposed into two components:
u = U + u’
where U = < u > is the time average (< >
means time average, over one hour here)
and is called the time mean component,
while u’ is the fluctuation around U, i.e.
u’ = u - U
and is called the turbulent component.
(2) Do time average
< u’ > = 0
< A u’ > = A < u’ > = 0
Only cross terms <a’b’> are left. They are
also called non-linear terms.
Intensity of turbulence:
Turbulent kinetic energy (TKE)
Mean kinetic energy
MKE = (U2 + V2 + W2)/2
Turbulent kinetic energy TKE = ‹ u’ 2 + v’ 2 + w’ 2 › /2
Time evolution (diurnal)
represents time average
Vertical profile
Eddy fluxes
Away from the regions with horizontal inhomogeneities (e.g. shoreline,
towns, forest edges), the horizontal eddy fluxes are generally much
smaller than the vertical eddy fluxes, and can be neglected:
DU/Dt +u’<u’u’>/x +<v’u’>/y +<w’u’>/z
= - -1 P/x + fV
Then we have:
DU/Dt = - -1 P/x + fV -<w’u’>/z
= Fx (force due to turbulent fluxes)
<u’w’> is called the eddy zonal momentum flux
Derivation is similar for the eddy meridional momentum flux <v’w’>,
eddy heat flux <h’w’>, and eddy moisture flux <q’w’>
The turbulence closure problem
• For large-scale atmospheric circulation, we have six
fundamental equations (conservation of mass, momentum, heat
and water vapor) and six unknowns (p, u, v, w, T, q). So we can
solve the equations to get the unknowns.
• When considering turbulent motions, we have five more
unknowns (eddy fluxes of u, v, w, T, q)
• We have fewer fundamental equations than unknowns when
dealing with turbulent motions. The search for additional laws to
match the number of equations with the number of unknowns is
commonly labeled the turbulence closure problem.
Surface layer
Eddy flux is assumed to be proportional to the vertical
gradience of the mean state variable
• Sensible heat flux
<w’h’> = Qh =  Cd Cp V (Tsurface - Tair)
• Latent heat flux
L <w’q’> = Qe =  Cd L V (qsurface - qair)
Where  is the air density, Cd is flux transfer coefficient,
Cp is specific heat of air, V is surface wind speed,
Tsurface is surface temperature, Tair is air temperature,
qsurface is surface specific humidity, qair is surface air
specific humidity
Mixed layer theory I: Local theories
• K-theory: In eddy-diffusivity (often called K-theory)
models, the turbulent flux of an adiabatically conserved
quantity a (such as θ in the absence of saturation, but
not temperature T, which decreases when an air parcel
is adiabatically lifted) is related to its gradient:
< w’a’ > = - Ka dA/dz
• The local effect is always down-gradient (i.e. from high
value to low value)
• The key question is how to specify Ka in terms of known
Three commonly used approaches:
(1) First-order closure
(2) 1.5-order closure or TKE closure
(3) K-profile
Mixed layer theory II: Non-local theories
Any eddy diffusivity approach will not be entirely accurate if most of the
turbulent fluxes are carried by organized eddies filling the entire boundary
The non-local effect could be counter-gradient.
Consequently, a variety of ‘nonlocal’ schemes which explicitly model the
effects of these boundary layer filling eddies in some way have been
A difficulty with this approach is that the structure of the turbulence
depends on the BL stability, baroclinicity, history, moist processes, etc.,
and no nonlocal parameterization proposed to date has comprehensively
addressed the effects of all these processes on the large-eddy structure.
Nonlocal schemes are most attractive when the vertical structure and
turbulent transports in a specific type of boundary layer (i. e. neutral or
convective) must be known to high accuracy.
Boundary layer of shallow clouds and
deep convection
• Global distribution and vertical structure of shallow clouds
• Global distribution and vertical structure of deep
convection. Four components: convective updraft,
convective downdraft, mesoscale updraft, mesoscale
• Differences between shallow clouds and deep
convection: change of T, q and h in the boundary layer
• Self-suppression processes in deep convection: Overly
stabilized state after deep convection
• Problems in current global climate models: lack of selfsuppression processes
Shallow clouds
• Include stratus, stratocumulus and cumulus clouds
• Cloud top height generally below 4 km
• Sometimes associated with light rain, sometimes not
Global distribution of shallow clouds
Klein and Hartman, 1993
• Do we notice any patterns?
Vertical structure of shallow clouds
• Intense longwave
radiative cooling
at cloud top
drives eddies in
• Eddies pick up
moisture and
maintain cloud
• Eddies also
entrain warm, dry
air from above
the inversion
• Entrainment lifts
the cloud,
lowers it
Bretherton et al. 2004
Deep convection
• Cloud top height above 9 km
• Generally associated with rain
• Sometimes organized into mesoscale convective systems
Global distribution of deep convection
Vertical structure of deep convection:
Four components
Convective updrafts (controlled by
lower troposphere moisture)
Mesoscale updrafts
Convective downdrafts
Zipser (1977), modified by Houze (1993)
Difference in boundary layer between
shallow convection and deep convection
Shallow convection: boundary
layer is well-defined.
Deep convection: boundary layer
is destroyed by penetrating
convective downdrafts, not welldefined
(From Barnes 1982)
Differences in boundary layer between
shallow convection and deep convection
Shallow: T decreases
Deep: T decreases
Shallow: q increases
Deep: q decreases
Shallow: h keeps const
Deep: h decreases
(From Barnes 1982)
Self-suppression processes in deep convection
Missing physics III, IV
High θe
Convective updrafts (controlled by lower
troposphere temperature and moisture)
Mesoscale updrafts
Low θe
Missing physics II
High θe
Convective downdrafts
Missing physics I
Zipser (1977), modified by Houze (1993)
Effects of different surface types and
human activities
• Effects of different surface types: desert, city, grassland,
forest, sea. Deeper heat/water reservoir, decreased
Bowen ratio, thinner BL and enhanced convective
• Effects of vegetation: (1) makes heat/water reservoir
deeper, (2) enhance evaporation, (3) grows and dies in
response to environmental conditions
• Heat island effect. 7 causes
• Dispersion of air pollution. Dependence on stability
(name of 3 types) and inversion (name of 2 types)
• Global carbon cycle and water cycle: linking the world
together. Therefore we need to protect the environment
because it is part of our body
Effects of different surface types
BL depth decreases
Convective instability increases
Deeper heat reservoir (smaller T change)
Deeper water reservoir (Wetter surface)
Bowen ratio decreases (More LH contribution)
Effects of vegetation
• Makes water/heat reservoir deeper (transport deep water
out of soil)
• Enhances evaporation (leafs increase evaporation area)
• Dependent on vegetation type
Vegetation feedback
Vegetation in turn is affected by environmental
conditions (e.g. seasons, droughts, global warming)
Effects of human activities
Human beings are living in the BL and affect the BL in
three different ways:
• Change land cover (deforestation and afforestation)
• Release or cleanse pollutants (aerosols)
• Release or cleanse greenhouse gases
Local effect I: The heat island effect
• Nighttime: City warmer than surrounding rural area
• Daytime: City has same air temperature as rural area
Causes of the heat island effect
• Increased SW absorption caused
by canyon geometry (increased
area and multiple reflection)
• Decreased LW loss caused by
canyon geometry
• Increased greenhouse effect
caused by air pollution
• Anthropogenic heat source
• Increased sensible heat storage
caused by construction materials
• Decreased latent heat flux caused
by change of surface type
• Decrease sensible and latent heat
fluxes caused by canyon geometry
(reduction of wind speed)
“Canyons” between buildings
Local effect II: Dispersion of air pollution
• Dispersion depends on stability of BL
• Dispersion also affected by inversions
Low level inversion
Upper level inversion
Global effect:
Anything released by human beings will be
transported globally by atmospheric circulations
and ocean circulations
Land surface processes in global
climate models
• NCAR CCSM 4 components: Atmosphere, ocean, land, sea ice
• 4 components of CLM: Biogeophysics, hydrological cycle,
biogeochemistry, dynamical vegetation
• 5 sub-grid land cover types: Glacier, wetland, vegetated, lake, urban
• The CLM reproduces many aspects of the long-term mean, annual
cycle, interannual and decadal variations, and trends of streamflow
for many large rivers (e.g., the Orinoco, Changjiang, Mississippi,
etc.), although substantial biases exist.
• Observed soil moisture variations over Illinois and parts of Eurasia
are generally simulated well, with the dominant influence coming
from precipitation.
• The results suggest that the CLM simulations are useful for climate
change analysis.
Framework of National Center for Atmospheric Research
(NCAR) Community Climate System Model (CCSM)
Sea Ice
Configuration of the CLM Subgrid Hierarchy
The land surface is represented by 5 primary sub-grid land cover types
The vegetated portion of a grid cell is further divided into patches of plant functional types,
each with its own leaf and stem area index and canopy height.
Each subgrid land cover type and PFT patch is a separate column for energy and water calculations.
• Please remember to bring your calculator
to the exam!