Heat Transfer

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Heat Transfer
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Energy Balance
Rnet G H LE
H
Rsd
Rlu
Rsu
LE
G
Energy balance can be used to estimate LE LE
Rnet G - H
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Radiation
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(Campbell and Norman, 1998)
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(Dingman, 2002)
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(Dingman, 2002)
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S Solar Constant irradiance of a surface held
perpendicular to the solar beam at the mean
distance of the earth from the sun (1.50x108 m)
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Convective Fluxes Sensible and Latent Heat
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Convective Fluxes

• Convective fluxes require
• Vertical gradient of temperature / water AND
• Turbulence (mixing)
• Vertical gradient, but no turbulence
• only very slow diffusion of heat / water
• No vertical gradient, but turbulence
• ? mixing, but no net transport of heat / water

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Sensible Heat Flux
Day Night
Eddy turbulent whirl
Eddy moves warm humid air up and dry air down.
Both motions contribute to a positive (upward)
flux of latent heat (water flux).
z
LE
humidity
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Sensible Heat Flux
Day
Eddy moves warm air up and cold air down. Both
motions contribute to a positive (upward) flux of
sensible heat (temperature flux).
z
H
T
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Sensible Heat Flux
Night
Eddy moves cold air up and warm air down. Both
motions contribute to a negative (downward) flux
of sensible heat (temperature flux).
z
H
T
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Convective Fluxes
Sunrise/Sunset
Moist air / Fog
z
z
?
?
H
LE
Air saturated with water vapor
T
humidity
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Evapotranspiration Evaporation Transpiration
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EVAPOTRANSPIRATION PROCESS Evaporation liquid
water is converted to water vapor and removed
from evaporating surface (lake, river,
pavement, soils, and wet vegetation).
Transpiration vaporization of liquid water
contained in plant tissue and the vapor
removal to the atmosphere through the
stomata. Evapotranspiration evaporation and
transpiration occur simultaneously and there
is no easy way of distinguishing between the
two processes.
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FACTORS AFFECTING EVAPOTRANSPIRATION
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Transpiration
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is difference in two rates
Evaporation
1) number of molecules leaving water
surface depends on temperature 2) number of
molecules captured by surface depends on
concentration of vapor molecules in overlying air
E (humidity dependent capture)-(temperature
dependent boil off)
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How much water vapor can air hold?
(Monteith Unsworth, 1990)
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Atmospheric observations of temperature profiles
(Rosenberg, 1974)
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Mean hourly temperature profiles above alfalfa at
Mead, Nebraska
Time of day
(Rosenberg, 1969)
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Atmospheric Turbulence
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The Atmospheric Boundary Layer
Stull, 1988
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Atmospheric Boundary Layer
Diurnal cycle from Lidar measurements
clean
polluted
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Surface Layer and Mixed Layer
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Why is the lower atmosphere turbulent?

• Shear production of turbulence
• Measured by shear stress or friction velocity
• Buoyant production / destruction of turbulence
• Measured by sensible heat flux
• Obukhov length describes relative effect

L gt 0 stable conditions L lt 0 unstable
conditions L inf neutral conditions
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Non-neutral boundary layers

• Unstable
• Large eddies
• Deep atmospheric surface layer and atmospheric
  boundary layer
• Stable
• Small eddies
• Shallow surface layer

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Neutral (wind tunnel) Boundary Layer
(Monteith Unsworth, 1990)
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Neutral (wind tunnel) Boundary Layer
Most simple and most investigated Log layer
(constant flux layer) dq/dz E/(u z rho
k) EC measurements make sense only above
roughness sublayer and in the constant flux layer!
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Stability correction functions for mean velocity
profile

• Stability effects in the surface layer
  parameterized by Obukhov length L

Hogstrom, 1988, Bound.-Layer Meteor.
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Eddy Correlation
3-d sonic anemometeru, v, w, Tv at 20 Hz
Latent heat flux Sensible heat flux
Krypton Hygrometer q at 20 Hz
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sonic anemometer
Cup anemometer
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Correlation and Fluxes
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Reynolds decomposition
All atmospheric entities show short term
fluctuations about their longer term mean.
This is result of turbulence which causes
eddies to continuously move and carry with them
heat, vapor, momentum and other gases from
elsewhere.
s is value of an entity (T, vertical wind
speed, vapor conc) s-bar is time-averaged
entity s is instantaneous deviation from mean
s-bar
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Over a longer time period the value of the
vertical wind speed w-bar equals zero since
mass continuity requires that as much air moves
up as down during a certain period (eg 10-20
minutes). The properties contained and
transported by an eddy are its mass ? (when
considering a unit volume), its vertical velocity
w, and the volumetric content of any entity it
possesses (heat, vapor, CO2). Each of those
components can be broken into a mean and a
fluctuating part. Therefore, the mean vertical
flux S of the entity s
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All terms involving a single primed quantity are
eliminated since the average of all their
fluctuations equals zero by definition. For
uniform terrain without areas of preferred
vertical motion (i.e. no hotspots) the mean
vertical velocity (w-bar) equals zero.
The averages of w and s are zero over a long
enough time period. However, the average ws
which is the covariance of w and s will only
rarely be negligible. Transport of all entities
depends on the vertical wind speed
fluctuations. covariance(w,s) correlation
coefficient (w,s) vertical flux of s
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Basic Statistics

• Signal mean fluctuationse.g.
• ? Variances
• Fluxes covariance wT
• Correlation coefficient covar. / variance

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(Oke, 1987)
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Consider the following entities s momentum

temperature
vapor concentration Sensible
heat flux H and latent heat flux E are measured as
?a density of air kg m-3 cp specific heat of
air J kg-1 K-1 Lv Latent heat of vaporization
J kg-1 ?v water vapor density kg H2O / m3
air q specific humidity kg H2O / kg air If
measurements can be made at least ten times per
second, eddy covariance is an attractive method
for direct measurements of transport into the
atmosphere.
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Typical Installation

• Energy Budget 3d Sonic Anemometer (CSAT3),
  Infrared Gas Analyzer (IRGA), Soil Heat Flux
  Plates, Net Radiometer
• Mass flux CSAT3, IRGA
• Location selection homogeneous surface, upwind
  fetch, orientation (leveled), averaging period

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Eddy Correlation Energy Balance
Turbulent heat fluxes
Net radiation
Soil heat flux
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Data Processing and QC

• Calibrate sensors before and after experiment
• Calculate derived variables (e.g. fluxes, q)
• Apply flux corrections ? EDAC
• Plot same variables from different instruments in
  same plot (e.g. soil temperature, air temp.)
• Plot related variables in related (sub)plots
  (e.g. H, LE, G, Rnet)
• Find bad data outliers. Assign NaN with care.
• Check, check, check

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Data quality control

• Diurnal cycle of energy budget components (Rnet,
  H, LE, G), temperature, and relative humidity
• Vertical velocity average 0?
• Energy Balance 0?

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Fetch and Footprint
Monteith Unsworth
Growth of inner boundary layer
Source http//cloudbase.phy.umist.ac.uk/people/do
rsey/Edco.htm on March 1, 2005
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Determining the area to which flux measurements
applyFlux footprint models
f footprint function
Schmid AFM 2004/5?
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Footprint of Energy Balance Measurements

• H, LE upwind
• G, Rnet at Tower

• Homogeneity of tower location and upwind area
  desirable
• Field of view of net radiometer should be
  representative of flux footprint
• Soil near soil heat flux plates should be
  relatively undisturbed

Install soil heat flux plates and net radiometer
further away from flux tower
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Example of footprint issues
Campo experimental UTalca
100
30 m
70
gt 17 leaves
10 leaves
5 leaves
wind
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Irrigation quantity

• Heterogeneous terrain
• Influence of wind direction on footprint
  characteristics
• evaporation measurements of vineyards which are
  only partially irrigated or plants with leaves
  cut off

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Datalogger Programming
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What is a datalogger?

• A datalogger is like a versatile, low-power
  tough-book without screen. It consists of
• CPU
• Flash EEProm Hard drive
• ports for wires and for connecting laptops
• Its features are
• Operation in rugged environments possible (but
  handle with care and protect from moisture)
• Low power operation ( 100 mW)
• 2 MB memory storage

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Datalogger Setup

• Power 12V Battery, solar panel, charge
  controller
• Wiring
• connect sensor wires to appropriate logger ports
• Datalogger program
• interpretation of incoming voltages by logger
• Data access
• locally through laptop serial cable
• remotely through cellular modem / wireless network

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Datalogger Program

• Input
• Where (which port?), when (1Hz, 10Hz?), and how
  (Pulse, Excitation, Differential single ended
  voltage) to measure
• Processing
• How to convert voltages to physical variables
• Output
• Frequency (10 30 min) and order of output

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Tools for datalogger programming

• Program Editors
• CRBasic, Edlog
• Program Generators
• ShortCut
• Instrument manuals
• www.campbellsci.com
• Contact manufacturer / Campbell Scientific

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Remote Sensing SEBAL
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SEBAL ET from Landsat
SEBAL Surface Energy Balance Algorithm for Land
April 07 2000
June 16 2002
September 14 2000
Rio Grande basin, NM
ET
Hong, Kleissl et al. WRR 2006
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Improving ET from remote sensing

• Calibrate sensible heat flux using ground
  measurements
• Improve parameter estimation using LES
• Roughness length zo
• Advection effects