# Presentation: 130923

## 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.

##  PROBLEM 

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.

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.

- 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.
- 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.

## METHOD

Internal energy (heat) equation:

                      ρCp DΘ/Dt =   Fh                     (1)

     where  ρ=density; Cp=heat capacity; Θ=potential temperature; D/Dt=time differential; Fh=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

	D/Dt ∫∫∫ ρCp dV = ρCp Θ x dV/dt + ∫∫ ρCp(SST- Θ x)(P-E)dA + ∫∫ Fh dA .    (2)

	∫∫ Fh dA = ∫∫ FsdAs - ∫∫FpdAb - ∫∫FddAb.                        (3)

	Fs=Air-Sea flux; Fp=Shortwave penetration flux; Fd= 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 =  Fd/ /Tz; Tz is the temperature gradient. 

- Internal energy (heat) equation:
-                       ρCp DΘ/Dt =   Fh                     (1)
-      where  ρ=density; Cp=heat capacity; Θ=potential temperature; D/Dt=time differential; Fh=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
- 	D/Dt ∫∫∫ ρCp dV = ρCp Θ x dV/dt + ∫∫ ρCp(SST- Θ x)(P-E)dA + ∫∫ Fh dA .    (2)
- 	∫∫ Fh dA = ∫∫ FsdAs - ∫∫FpdAb - ∫∫FddAb.                        (3)
- 	Fs=Air-Sea flux; Fp=Shortwave penetration flux; Fd= 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 =  Fd/ /Tz; Tz is the temperature gradient.

## RESULTS

_**Climatological Seasonal Cycle:**_
**Data Sets:**
-          **Ocean Data:** NOAA/NODC WOA98
-          **Air-Sea Fluxes:** NOAA/NODC
-              COADS’94; NOAA/NCEP;
-              ECMWF; SOC.
**Isotherms:** 28oC for the Pacific
-              and Indian Oceans;
-              27oC for the Atlantic Ocean.

**Climatological SST: September**

## Slide 5

## Slide 6

## Slide 7

## CONCLUSIONS

**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.
**Scientific Issues:**
- 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.
- 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.

## 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.

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

Work in Progress: 

    Interannual and ENSO variability

***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.
- Work in Progress:
-     Interannual and ENSO variability