Air-Sea Fluxes: Air-Sea Fluxes: A New Approach for A New Approach for

Validation and EstimationValidation and EstimationHuai-Min ZhangHuai-Min ZhangNOAA/NESDIS/NCDC/ScSDNOAA/NESDIS/NCDC/ScSD

John M. Toole and Michael J. CarusoJohn M. Toole and Michael J. CarusoWoods Hole Oceanographic InstitutionWoods Hole Oceanographic Institution

OBJECTIVEOBJECTIVEUse the conservation law of the internal energy (heat) of an Use the conservation law of the internal energy (heat) of an ocean volume to validate and constrain the air-sea flux ocean volume to validate and constrain the air-sea flux estimates based on surface and atmospheric estimates based on surface and atmospheric measurements.measurements.

PROBLEMPROBLEM • Accurate air-sea fluxes are very important for Accurate air-sea fluxes are very important for

weather and climate study predictions.weather and climate study predictions.• There large uncertainties on currently available There large uncertainties on currently available

air-sea fluxes. Validation against measurements air-sea fluxes. Validation against measurements is rare and of limited use. Cross checks of is rare and of limited use. Cross checks of different products (NOAA/NESDIS/NCEP and different products (NOAA/NESDIS/NCEP and NODC/COADS, European ECMWF, British SOC, NODC/COADS, European ECMWF, British SOC, etc.) reveal large differences, but cannot tell etc.) reveal large differences, but cannot tell which one is better.which one is better.

• The correct air-sea fluxes must also be consistent The correct air-sea fluxes must also be consistent with the ocean dynamics and energetics. In this with the ocean dynamics and energetics. In this work we use the conservation of oceanic internal work we use the conservation of oceanic internal energy to validate and constrain the air-sea energy to validate and constrain the air-sea fluxes.fluxes.

METHODMETHOD

• Internal energy (heat) equation:Internal energy (heat) equation: ρρCCpp D DΘΘ/Dt = F/Dt = Fhh (1) (1) where where ρρ=density; C=density; Cpp=heat capacity; =heat capacity; ΘΘ=potential temperature; D/Dt=time =potential temperature; D/Dt=time

differential; Fdifferential; Fhh=divergences of the turbulent and radiative heat fluxes including the =divergences of the turbulent and radiative heat fluxes including the air-sea exchange terms. air-sea exchange terms.

• Integrating the above equation over a volume, V, defined by the instantaneous Integrating the above equation over a volume, V, defined by the instantaneous position of an isotherm (= position of an isotherm (= ΘΘ x), applying Liebnitz's rule on the left and Gauss' x), applying Liebnitz's rule on the left and Gauss' Theorem on the right and shifting terms yieldsTheorem on the right and shifting terms yieldsD/Dt ∫∫∫ D/Dt ∫∫∫ ρρCCpp dV = dV = ρρCCp p ΘΘ x x dV/dt + ∫∫ dV/dt + ∫∫ ρρCCpp(SST- (SST- ΘΘ x x)(P-E)dA + ∫∫ F)(P-E)dA + ∫∫ Fhh dA . (2) dA . (2)∫∫ ∫∫ FFhh dA = ∫∫ F dA = ∫∫ FssdAdAss - ∫∫F - ∫∫FppdAdAbb - ∫∫F - ∫∫FdddAdAbb. (3). (3)FFss=Air-Sea flux; F=Air-Sea flux; Fpp=Shortwave penetration flux; F=Shortwave penetration flux; Fdd= Diffusive flux at bottom.= Diffusive flux at bottom.In words, this equation relates the rate of change in the volumetricIn words, this equation relates the rate of change in the volumetricheat content of a warm pool to the time rate of change in its volume,heat content of a warm pool to the time rate of change in its volume,and the fluxes of heat through the bounding surfaces defining the pool.and the fluxes of heat through the bounding surfaces defining the pool.The second term on the right, arising from fluxes of water byThe second term on the right, arising from fluxes of water byprecipitation and evaporation (P-E) through the free surface (whoseprecipitation and evaporation (P-E) through the free surface (whosetemperature may depart from temperature may depart from ΘΘ x x) is small compared to the other terms and) is small compared to the other terms andis neglected. is neglected.

Diffusivity: K = FDiffusivity: K = Fd/ d/ /T/Tzz; T; Tzz is the temperature gradient. is the temperature gradient.

RESULTSRESULTS

• Climatological Climatological Seasonal Cycle:Seasonal Cycle:

• Data Sets:Data Sets: Ocean Data:Ocean Data: NOAA/NODC NOAA/NODC

WOA98WOA98 Air-Sea Fluxes:Air-Sea Fluxes: NOAA/NODC NOAA/NODC

COADS’94; NOAA/NCEP;COADS’94; NOAA/NCEP; ECMWF; SOC.ECMWF; SOC.• Isotherms:Isotherms: 28 28ooC for the Pacific C for the Pacific and Indian Oceans; and Indian Oceans; 2727ooC for the Atlantic Ocean.C for the Atlantic Ocean.

Climatological SST: Climatological SST: SeptemberSeptember

CONCLUSIONSCONCLUSIONS• Validation Issues:Validation Issues: The un-constrained COADS (which has a large globally averaged heat The un-constrained COADS (which has a large globally averaged heat

imbalance of ~40 W/m2!!) and the SOC fluxes are consistent with ocean imbalance of ~40 W/m2!!) and the SOC fluxes are consistent with ocean dynamics (down-gradient turbulent flux and positive diffusivity), while dynamics (down-gradient turbulent flux and positive diffusivity), while others (constrained COADS with globally balanced heat, NCEP and others (constrained COADS with globally balanced heat, NCEP and ECMWF) are not - with ECMWF) are not - with up-gradient turbulent fluxup-gradient turbulent flux and negative diffusivity and negative diffusivity in the ocean in some time periods, esp. the ECMWF fluxes.in the ocean in some time periods, esp. the ECMWF fluxes.

• Scientific Issues:Scientific Issues:• The warm pool volume and heat content curves tend to parallel each The warm pool volume and heat content curves tend to parallel each

other.other.

• The warm pools expand and contract meridionally with the seasonal The warm pools expand and contract meridionally with the seasonal heating and cooling cycles in the respective hemispheres.heating and cooling cycles in the respective hemispheres.

• Hemispheric assymetries in the western Atlantic and Pacific boundaries Hemispheric assymetries in the western Atlantic and Pacific boundaries and the corresponding continental influence on regional air-sea exchange and the corresponding continental influence on regional air-sea exchange give rise to the annual-period signals in total pool volume and heat give rise to the annual-period signals in total pool volume and heat content that are phased with the northern hemisphere (warmest waters content that are phased with the northern hemisphere (warmest waters in mid-to-late boreal summer). In contrast, the limited geographic extent in mid-to-late boreal summer). In contrast, the limited geographic extent of the North Indian Ocean results in the southern hemisphere driving the of the North Indian Ocean results in the southern hemisphere driving the seasonal cycle.seasonal cycle.

• The first two terms in eq.2 are by far the largest (an order larger) but The first two terms in eq.2 are by far the largest (an order larger) but they have the same sign and appear on opposite sides of the they have the same sign and appear on opposite sides of the equation. Thus it is the residual of the two heat content terms (net equation. Thus it is the residual of the two heat content terms (net heat storage) that relates (in the same order) to the turbulent flux heat storage) that relates (in the same order) to the turbulent flux divergences.divergences.

• Although the net storage is smaller (and changes signs) than Although the net storage is smaller (and changes signs) than other terms of eq.2, in time sequence it is parallel to the air-other terms of eq.2, in time sequence it is parallel to the air-sea flux change. In other words, the net heat storage sea flux change. In other words, the net heat storage captures the time change signals of the air-sea flux; the captures the time change signals of the air-sea flux; the large non-zero time-mean air-sea flux is balanced by the large non-zero time-mean air-sea flux is balanced by the relatively constant diffusive flux through the bottom of the relatively constant diffusive flux through the bottom of the warm pool.warm pool.

• The diffusivity is relatively constant, physically reasonable and The diffusivity is relatively constant, physically reasonable and largely consistent with measurements.largely consistent with measurements.

• Work in Progress:Work in Progress:

Interannual and ENSO variabilityInterannual and ENSO variability