5.7: Meridional Heat Transport
- Page ID
- 30060
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Overall, Earth gains heat at the top of the tropical atmosphere, and it loses heat at the top of the polar atmosphere. The atmospheric and oceanic circulation together must transport heat from low to high latitudes to balance the gains and losses. This north-south transport is called the meridional heat transport.
The sum of the meridional heat transport in the ocean and atmosphere is calculated from the zonal average of the net heat flux through the top of the atmosphere measured by satellites. In making the calculation, we assume that transports averaged over a few years are steady. Thus any long-term net heat gain or loss through the top of the atmosphere must be balanced by a meridional transport and not by heat storage in the ocean or atmosphere.
Net Heat Flux at the Top of the Atmosphere
Heat flux through the top of the atmosphere is measured very accurately by radiometers on satellites.
- Insolation is calculated from the solar constant and observations of reflected sunlight made by meteorological satellites and by special satellites of the Earth Radiation Budget Experiment.
- Infrared radiation is measured by infrared radiometers on the satellites.
- The difference between insolation and net infrared radiation is the net heat flux across the top of the atmosphere.
Net Meridional Heat Transport
To calculate the meridional heat transport in the atmosphere and the ocean, we first average the net heat flux through the top of the atmosphere in a zonal band. Because the meridional derivative of the transport is the zonal-mean flux, we calculate the transport from the meridional integral of the zonal-mean flux. The integral must be balanced by the heat transported by the atmosphere and the ocean across each latitude band.
Calculations by Trenberth and Caron (2001) show that the total, annual-mean, meridional heat transport by the ocean and atmosphere peaks at 6 PW toward each pole at 35\(^{\circ}\) latitude.
Oceanic Heat Transport
The meridional heat transport in the ocean can be calculated three ways:
- Surface Flux Method calculates the heat flux through the sea surface from measurements of wind, insolation, air, and sea temperature, and cloudiness. The fluxes are integrated to obtain the zonal average of the heat flux (figure \(5.6.2\)). Finally, we calculate the transport from the meridional integral of the zonal-mean flux just as we did at the top of the atmosphere.
- Direct Method calculates the heat transport from values of current velocity and temperature measured from top to bottom along a zonal section spanning an ocean basin. The flux is the product of northward velocity and heat content derived from the temperature measurement.
- Residual Method first calculates the atmospheric heat transport from atmospheric measurements or the output of numerical weather models. This is the direct method applied to the atmosphere. The atmospheric transport is subtracted from the total meridional transport calculated from the top-of-the-atmosphere heat flux to obtain the oceanic contribution as a residual (figure \(\PageIndex{1}\)).
Various calculations of oceanic heat transports, such as those shown in figure \(\PageIndex{1}\), tend to be in agreement, and the error bars shown in the figure are realistic. The total meridional transport of heat by the ocean is small compared with the total meridional heat transport by the atmosphere except in the tropics. At 35\(^{\circ}\), where the total meridional heat transport is greatest, the ocean carries only 22% of the heat in the northern hemisphere, and 8% in the southern (Trenberth and Caron, 2001).