1. Air-Sea Fluxes: A New Approach for Validation and Estimation Huai-Min Zhang NOAA/NESDIS/NCDC/ScSD John M. Toole and Michael J. Caruso Woods Hole Oceanographic Institution OBJECTIVE Use the conservation law of the internal energy (heat) of an ocean volume to validate and constrain the air-sea flux estimates based on surface and atmospheric measurements.

2. PROBLEM PROBLEM Accurate air-sea fluxes are very important for weather and climate study predictions. Accurate air-sea fluxes are very important for weather and climate study predictions. There large uncertainties on currently available air-sea fluxes. Validation against measurements is rare and of limited use. Cross checks of different products (NOAA/NESDIS/NCEP and NODC/COADS, European ECMWF, British SOC, etc.) reveal large differences, but cannot tell which one is better. There large uncertainties on currently available air-sea fluxes. Validation against measurements is rare and of limited use. Cross checks of different products (NOAA/NESDIS/NCEP and NODC/COADS, European ECMWF, British SOC, etc.) reveal large differences, but cannot tell which one is better. The correct air-sea fluxes must also be consistent with the ocean dynamics and energetics. In this work we use the conservation of oceanic internal energy to validate and constrain the air-sea fluxes. The correct air-sea fluxes must also be consistent with the ocean dynamics and energetics. In this work we use the conservation of oceanic internal energy to validate and constrain the air-sea fluxes.

3. METHOD Internal energy (heat) equation: Internal energy (heat) equation: ρC p DΘ/Dt = F h (1) ρC p DΘ/Dt = F h (1) where ρ=density; C p =heat capacity; Θ=potential temperature; D/Dt=time differential; F h =divergences of the turbulent and radiative heat fluxes including the air-sea exchange terms. where ρ=density; C p =heat capacity; Θ=potential temperature; D/Dt=time differential; F h =divergences of the turbulent and radiative heat fluxes including the air-sea exchange terms. Integrating the above equation over a volume, V, defined by the instantaneous position of an isotherm (= Θ x), applying Liebnitz's rule on the left and Gauss' Theorem on the right and shifting terms yields Integrating the above equation over a volume, V, defined by the instantaneous position of an isotherm (= Θ x), applying Liebnitz's rule on the left and Gauss' Theorem on the right and shifting terms yields D/Dt ∫∫∫ ρC p dV = ρC p Θ x dV/dt + ∫∫ ρC p (SST- Θ x )(P-E)dA + ∫∫ F h dA. (2) ∫∫ F h dA = ∫∫ F s dA s - ∫∫F p dA b - ∫∫F d dA b. (3) F s =Air-Sea flux; F p =Shortwave penetration flux; F d = Diffusive flux at bottom. In words, this equation relates the rate of change in the volumetric 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. The second term on the right, arising from fluxes of water by precipitation and evaporation (P-E) through the free surface (whose temperature may depart from Θ x ) is small compared to the other terms and is neglected. Diffusivity: K = F d/ /T z ; T z is the temperature gradient. Diffusivity: K = F d/ /T z ; T z is the temperature gradient.

4. RESULTS Climatological Seasonal Cycle: Climatological Seasonal Cycle: Data Sets: Data Sets: Ocean Data: NOAA/NODC WOA98 Ocean Data: NOAA/NODC WOA98 Air-Sea Fluxes: NOAA/NODC Air-Sea Fluxes: NOAA/NODC COADS’94; NOAA/NCEP; COADS’94; NOAA/NCEP; ECMWF; SOC. ECMWF; SOC. Isotherms: 28 o C for the Pacific Isotherms: 28 o C for the Pacific and Indian Oceans; and Indian Oceans; 27 o C for the Atlantic Ocean. 27 o C for the Atlantic Ocean. Climatological SST: September

8. CONCLUSIONS Validation Issues: Validation Issues: The un-constrained COADS (which has a large globally averaged heat imbalance of ~40 W/m2!!) and the SOC fluxes are consistent with ocean dynamics (down-gradient turbulent flux and positive diffusivity), while others (constrained COADS with globally balanced heat, NCEP and ECMWF) are not - with up-gradient turbulent flux and negative diffusivity in the ocean in some time periods, esp. the ECMWF fluxes. The un-constrained COADS (which has a large globally averaged heat imbalance of ~40 W/m2!!) and the SOC fluxes are consistent with ocean dynamics (down-gradient turbulent flux and positive diffusivity), while others (constrained COADS with globally balanced heat, NCEP and ECMWF) are not - with up-gradient turbulent flux and negative diffusivity 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 other. The warm pool volume and heat content curves tend to parallel each other. The warm pools expand and contract meridionally with the seasonal heating and cooling cycles in the respective hemispheres. The warm pools expand and contract meridionally with the seasonal heating and cooling cycles in the respective hemispheres. Hemispheric assymetries in the western Atlantic and Pacific boundaries and the corresponding continental influence on regional air-sea exchange give rise to the annual-period signals in total pool volume and heat content that are phased with the northern hemisphere (warmest waters in mid-to-late boreal summer). In contrast, the limited geographic extent of the North Indian Ocean results in the southern hemisphere driving the seasonal cycle. Hemispheric assymetries in the western Atlantic and Pacific boundaries and the corresponding continental influence on regional air-sea exchange give rise to the annual-period signals in total pool volume and heat content that are phased with the northern hemisphere (warmest waters in mid-to-late boreal summer). In contrast, the limited geographic extent of the North Indian Ocean results in the southern hemisphere driving the seasonal cycle.

9. 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 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 divergences. 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 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 divergences. Although the net storage is smaller (and changes signs) than other terms of eq.2, in time sequence it is parallel to the air-sea flux change. In other words, the net heat storage captures the time change signals of the air-sea flux; the large non-zero time-mean air-sea flux is balanced by the relatively constant diffusive flux through the bottom of the warm pool. Although the net storage is smaller (and changes signs) than other terms of eq.2, in time sequence it is parallel to the air-sea flux change. In other words, the net heat storage captures the time change signals of the air-sea flux; the large non-zero time-mean air-sea flux is balanced by the relatively constant diffusive flux through the bottom of the warm pool. The diffusivity is relatively constant, physically reasonable and largely consistent with measurements. The diffusivity is relatively constant, physically reasonable and largely consistent with measurements. Work in Progress: Work in Progress: Interannual and ENSO variability Interannual and ENSO variability