Chapter 5
The Ocean Heat Budget
Physical oceanography
Instructor: Dr. Cheng-Chien Liu
Department of Earth Sciences
National Cheng Kung University
Last updated: 16 October 2003
Introduction
 The sunlight reaching Earth
• 1/2  oceans and land
• 1/5  atmosphere
 The heat stored by the ocean
• Evaporation and infrared radiation 
atmosphere
• Transported by current  ameliorate Earth’s
climate  development of ice age
The oceanic heat budget
 Heat budget
• The sum of the changes in heat fluxes into or out of a
volume of water
• QT = QSW + QLW + QS + QL + QV
The resultant heat gain or loss QT [wm-2]
Insolation QSW, the flux of sunlight into the sea
Net Infrared Radiation QLW, net flux of infrared radiation from the sea
Sensible Heat Flux QS, the flux of heat out of the sea due to conduction
Latent Heat Flux QL, the flux of heat carried by evaporated water
Advection QV, heat carried away by currents
 Change in energy
• DE = CpmDT
Cp  4.0  103 J kg-1 0C-1
The oceanic heat budget (cont.)
 Importance of the ocean
• During an annual cycle
Cp(Rock)  800 J kg-1 0C-1  0.2Cp(water)
• Exchange heat depth
Water: 100m
Land: 1m
• Exchange heat mass
Water: 1001000 = 100,000 kg
Land: 13000 = 3,000 kg
• Typical change in temperature
Water: 100C
Land: 200C
• Ratio of seasonal heat storage: DEoceans / DEland  100
Heat budget terms
 QSW
• Factors influencing QSW
qs = fn(latitude, season, time of day)
Length of day = fn(latitude, season)
The cross-sectional area
 The surface absorbing sunlight = fn(qs)
Attenuation
 k = fn(clouds, path length, gas molecules, aerosol, dust)
Reflectivity
 fn(qs, surface roughness)
• Fig 5.2: surface solar insolation
• Average annual range (Fig 5.3)
30 < QSW < 260 Wm-2
Heat budget terms (cont.)
 QLW
• Fig 5.4: Atmospheric transmittance
Greenhouse effect
Greenhouse gasses
• Factors influencing QLW
The clarity of the atmospheric window
 fn(clouds thickness, cloud height, atmospheric water-vapor content)
 Changes in water vapor and clouds are more important than changes in Tsurface
Water Temperature
Ice and snow cover
• Average annual range
-60 < QLW < -30 Wm-2
Heat budget terms (cont.)
 QL
• Factors influencing QL
Vwind
Relative humidity
• Average annual range
-130 < QL < -10 Wm-2
 QS
• Factors influencing QS
Vwind
Air-sea temperature difference
• Average annual range
-42 < QS < -2 Wm-2
Direct calculation of fluxes
 Gust-Probe Measurements of Turbulent
Fluxes  the only method
• Characteristics
On low-flying aircraft or offshore platforms
 Usually at 30m height
 Need fast-response instruments
 Measure u, v, humidity, T
Expensive
Measurements  large space or longer time
Only for calibration
• Calculation (Table 5.1: Notation Describing Fluxes)
T = <ru'w'> = r<u'w'>  ru*2
QS = Cp<rw't'> = rCp<w't'>
QL = LE <w'q'>
Indirect calculation of fluxes: Bulk
formulas
 Bulk formulas
• The observed correlations between fluxes and
variables
T = rCDU102
QS = rCpCSU10 (ts - ta)
QL = rLECLU10 (qs - qa)
 ta  thermometers on ships
 ts  thermometers on ships or AVHRR
 qa  relative humidity made from ships
 qs  ts (assuming saturated air on surface)
 CD, CS, CL  correlating gust-probe measurements with the variables in the
bulk formulas (Table 5.1: suggested values)
Indirect calculation of fluxes: Bulk
formulas (cont.)
 Calculations of each variable
• Wind stress and speed
See chapter 4
Sources of error
 Sampling error (insufficient measurements in time and space)
 CD
• Insolation
 QSW = S(1-A) – C
 S = 1365 W m-2
 A: albedo
 C: constant including absorption by ozone, other gasses and cloud droplets
Sources of error
 Angular distribution of sunlight reflected from clouds and surface
 Daily variability of QSW
Indirect calculation of fluxes: Bulk
formulas (cont.)
 Calculations of each variable (cont.)
• Rainfall (water flux)
Difficulties of ship measurements
 Rain falls horizontally and its path is distorted by the ship’s superstructure
 Most rain at sea is drizzle  difficult to detect or measure
TRMM (Tropical rain measurement mission 1997 –) (Fig 5.5)
 Infrared observations  height of cloud tops
 Microwave radiometer
Re-analyses of the output from numerical weather forecast models
Ship observations
Combinations
Sources of error
 Rain rate  cumulative rain fall (Sampling error)
 Miss storm
Indirect calculation of fluxes: Bulk
formulas (cont.)
 Calculations of each variable (cont.)
• Net long-wave radiation
F = <e> (Fd –ST4)
 <e> : average emissivity of the surface
 Fd : downward flux (from satellite, microwave radiometer data or numerical models)
 S : Stefan-Boltzmann constant
F tends to be constant over space and time  not necessary to improve
• Latent heat flux
 QL = rLECLU10 (qs - qa)
Difficult to measure from satellite (not sensitive to qs)
 Two indirect ways to use satellite measurements
 Monthly averages of surface humidity  water vapor in the air column
 SST from AVHRR + water vapor and wind from SSM/I
Indirect calculation of fluxes: Bulk
formulas (cont.)
 Calculations of each variable (cont.)
• Sensible heat flux
Ship observations of air-sea temperature difference and
wind speed
Numerical models output
Almost small everywhere
Global data sets for fluxes
 COADS  NOAA
• Two releases
The first COADS release: 70 million reports (1854 – 1979)
The second COADS release (1980 – 1986)
• 28 elements
Weather, position, …
• Summaries
14 statistics for each of eight observed variables
 Ta, Ts, Vwind, Psurface, q, cloudiness
11 derived variables
• Three principal resolutions
Individual reports
Year-month summaries in 20 by 20 boxes
Decade-month summaries
Global data sets for fluxes (cont.)
 Satellite data (Table 5.3: levels)
• Operational meteorological satellites
NOAA series of polar-orbiting, meteorological satellites
SSM / I
Geostationary meteorological satellites
 NOAA (GOES), Japan (GMS) and ESA (METEOSTATS)
• Experimental satellites
Nimbus-7, Earth Radiation Budget Instruments
Earth Radiation Budget Satellite, Earth Radiation Budget Experiment
The European Space Agency's ERS-1 & 2
The Japanese Advanced Earth Observing System (ADEOS)
Quicksat
The Earth-Observing System satellites Terra, Aqua, and Envisat
Topex/Poseidon and its replacement Jason-1.
Global data sets for fluxes (cont.)
 International Satellite Cloud
Climatology Project
• Collect observations of clouds
by dozens of meteorological satellites (1985 – 1995)
Using visible-light instruments on polar-orbiting and
geostationary satellites
• Goals
Calibrate the the satellite data
Calculate cloud cover using carefully verified techniques
Calculate surface insolation
Global data sets for fluxes (cont.)
 Global Precipitation Climatology Project
• Three sources of data  rain rate
Infrared observations (GOES)  the height of cumulus clouds
 The basic idea: the more rain produced by cumulus clouds, the higher the cloud top, and
the colder the top appears in the infrared. Thus rain rate at the base of the clouds is related
to infrared temperature
Measurements by rain gauges on islands and land.
Radio-frequency emissions (SSM/I) from atmospheric water droplets
• Accuracy: 1 mm/day
• Data available:
2.50  2.50 grid from July 1987 to December 1995 (NASA GSFC)
• Xie and Arkin (1997)
A 17-year data set based on seven types of satellite and rain-gauge data
combined with the output from the NCEP/NCAR reanalyzed data from
numerical weather models
Global data sets for fluxes (cont.)
 Reanalyzed Data From Numerical Weather
Models
• Calculated from weather data using numerical
weather models by various reanalysis projects
• Recent suggestions on the data
Biased fluxes, The time-mean model outputs  ship observations
More accurate in the northern hemisphere
Zonal means differences > 40 Wm-2 between model and COADS data
ECMWF data set averaged over 15 years gives a net flux of 3.7 Wm-2
into the ocean
• Summary
Reanalyzed fluxes  forcing ocean, GCM
COADS data  calculating time-mean fluxes
Geographic distribution of terms in
the heat budget
 Figure 5.6
• The mean annual radiation and heat balance
Top of the atmosphere: Insolation = infrared radiation
 342 = 107 + 235
At the surface, latent heat flux + net infrared radiation =
insolation
 168 + 324 = 390 + 24 + 78
Sensible heat flux is small
The sunlight reaching Earth
 1/2 (168 / 342)  oceans and land
 1/5 (67 / 342)  atmosphere
Driving of the atmospheric circulation
 Thunderstorms are large heat engines converting the energy of latent heat into
kinetic energy of winds
Geographic distribution of terms in
the heat budget (cont.)
 Fig 5.7
• The zonal average of the oceanic heat-budget terms
Zonal average: an average along lines of constant latitude
QSW = max at EQ
QS is small
The areal-weighted integral  0
 errors in the various terms in the heat budget
 Can be reduced by using additional information (constraint)
 Heat and fresh water transport
 Fig 5.8: annual-mean QSW and QLW
 Fig 5.9: annual-mean QL
 Fig 5.10: annual-mean QS
Meridional heat transport
 Meridional transport
• North-south transport
 Meridional heat transport
•  the divergence of the zonal average of the
heat budget measured at the top of the
atmosphere
•  satellite
• Assumption: steady state
Meridional heat transport (cont.)
 Heat Budget at the top of the Atmosphere
• Measurement
Insolation  meteorological satellites and by special satellites (e.g. the
Earth Radiation Budget Experiment Satellite)
Back radiation  infrared radiometers
The net heat flux across the top of the atmosphere = insolation - net
infrared radiation
• Calculation
Average the satellite observations zonally  zonal average
Calculate their meridional derivative  the north-south flux divergence
Divergence = the heat transport by the atmosphere and the ocean
• Errors
Calibration of instruments
Inaccurate angular distribution of reflected and emitted radiation
Meridional heat transport (cont.)
 Oceanic Heat Transport
• Three methods
Surface Flux Method




Measurements: wind, insolation, air, and sea temperature, and cloudiness
Bulk formulas  the heat flux through the sea surface
Integration  the zonal average of the heat flux (Figure 5.7)
the meridional derivative  the flux divergence = heat transport in the ocean
Direct Method
 Measurements: current velocity and temperature from top to bottom along a zonal section
spanning an ocean basin  the heat transport
 The flux = northward velocity  heat content
Residual Method
 Measurements: atmospheric measurements or the output of numerical weather models 
the atmospheric heat transport
 The oceanic contribution = the top-of-the-atmosphere heat flux (satellite) - the
atmospheric transport (Figure 5.11)
Meridional fresh water transport
 The Earth's water budget
• Dominated by evaporation (86%) and
precipitation (78%) over the ocean
• A map of the net evaporation (Fig 5.12)
• Meridional transport of fresh water by the
Atlantic (Fig 5.13)
Same calculation as the heat transport
• Significance
Understanding the global hydrological cycle, ocean
dynamics, and global climate
Variation in solar constant
 Solar constant  constant
• Sunspots and faculae (bright spots)
 the output varied by ± 0.2% over centuries
 the changes in global mean temperature of Earth's
surface of ± 0.4°C (Fig 5.14)
• A small 12yr, 22yr, and longer-period
variations of SST
measured by bathythermographs and ship-board
thermometers over the past century
• Solar variability  climate change ?
Important concepts
• Sunlight is absorbed primarily in the tropical ocean.
The amount of sun-light changes with season, latitude,
time of day, and cloud cover.
• Most of the heat absorbed by the oceans in the tropics
is released as water vapor which heats the atmosphere
when water is condenses as rain. Most of the rain falls
in the tropical convergence zones, lesser amounts fall
in mid-latitudes near the polar front.
• Heat released by rain and absorbed infrared
radiation from the ocean are the primary drivers for
the atmospheric circulation.
Important concepts (cont.)
• The net heat flux from the oceans is largest in midlatitudes and offshore of Japan and New England.
• Heat fluxes can be measured directly using fast
response instruments on low-flying aircraft, but this is
not useful for measuring heat fluxes over oceanic
areas.
• Heat fluxes through large regions of the sea surface
can be calculated from bulk formula. Seasonal,
regional, and global maps of fluxes are available
based on ship and satellite observations.
Important concepts (cont.)
• The most widely used data sets for studying heat
fluxes are the Comprehensive Ocean-Atmosphere
Data Set and the reanalysis of meteorological data by
numerical weather prediction models.
• The oceans transport about one-half of the heat
needed to warm higher latitudes, the atmosphere
transports the other half.
• Solar output is not constant, and the observed small
variations in output of heat and light from the sun
seem to produce the changes in global temperature
observed over the past 400 years.