The global climatology of an interannually varying air–sea flux data set

Abstract

The air–sea fluxes of momentum, heat, freshwater and their components have been computed globally from 1948 at frequencies ranging from 6-hourly to monthly. All fluxes are computed over the 23 years from 1984 to 2006, but radiation prior to 1984 and precipitation before 1979 are given only as climatological mean annual cycles. The input data are based on NCEP reanalysis only for the near surface vector wind, temperature, specific humidity and density, and on a variety of satellite based radiation, sea surface temperature, sea-ice concentration and precipitation products. Some of these data are adjusted to agree in the mean with a variety of more reliable satellite and in situ measurements, that themselves are either too short a duration, or too regional in coverage. The major adjustments are a general increase in wind speed, decrease in humidity and reduction in tropical solar radiation. The climatological global mean air–sea heat and freshwater fluxes (1984–2006) then become 2 W/m² and −0.1 mg/m² per second, respectively, down from 30 W/m² and 3.4 mg/m² per second for the unaltered data. However, decadal means vary from 7.3 W/m² (1977–1986) to −0.3 W/m² (1997–2006). The spatial distributions of climatological fluxes display all the expected features. A comparison of zonally averaged wind stress components across ocean sub-basins reveals large differences between available products due both to winds and to the stress calculation. Regional comparisons of the heat and freshwater fluxes reveal an alarming range among alternatives; typically 40 W/m² and 10 mg/m² per second, respectively. The implied ocean heat transports are within the uncertainty of estimates from ocean observations in both the Atlantic and Indo-Pacific basins. They show about 2.4 PW of tropical heating, of which 80% is transported to the north, mostly in the Atlantic. There is similar good agreement in freshwater transport at many latitudes in both basins, but neither in the South Atlantic, nor at 35°N.

Appendix: Bulk transfer coefficients

The bulk transfer coefficients as defined by Eq. 3 depend on height above the surface, atmospheric stability and surface roughness lengths for momentum, z _o, evaporation, z _q , and heat, z _θ. In an ideal world of plentiful, reliable flux measurements, coefficient estimates would be binned according to height and stability, so that further roughness dependencies, for example on the wind speed and sea state (Bourassa et al. 1999), could be determined for each bin. Unfortunately, direct flux estimates are too difficult, expensive and rare. Therefore, most coefficient determinations are shifted to a standard reference height of Z _r  = 10 m and neutral stability, where the three coefficients become;

$$ C_{{\rm DN}} = {\frac{\kappa^{2}}{[{\rm ln}({\frac{Z_r}{z_{\rm o}}})]^{2}}}; \quad C_{{\rm HN}} = {\frac{\kappa \sqrt{C_{{\rm DN}}}}{{\rm ln}({\frac{Z_r}{z_{\theta}}})}} ; \quad C_{{\rm EN}} = {\frac{\kappa \sqrt{C_{{\rm DN}}}}{{\rm ln}({\frac{Z_r}{z_q}})}} $$

(9)

and κ = 0.4 is the von Karman constant. The wind speed is usually shifted to an equivalent 10 m, neutral value, U _N, before searching for roughness dependencies on wind speed. The iterative procedure used to find U _N from $\Updelta \vec{U}$ and for converting the above coefficients to those in (3) is detailed both in LY04 and Large (2006).

The roughness length dependencies of these coefficients have been explored using many data sets, but rarely with combined data. This search has not been conducted in a single standard way, so the procedure, rather than the data, can be responsible for differences in results. The approach adopted here follows Vera (personal communication, 1983), who combined multiple data sets to span a range of wind speeds from less than 1 m/s (Schacher et al. 1981) to more than 25 m/s Large and Pond (1981). A multivariate analysis of $|\vec{\tau}| / \rho = u^{*2}$ on integer powers of U _N, gave the coefficients of the polynomial

$$ u^{*2} = a_0 + a_1 U_{\rm N} + a_2 U_{\rm N}^2 + a_3 U_{\rm N}^3 + \cdots +a_n U_{\rm N}^n . $$

(10)

Consistent with the principle of zero wind speed yields no net stress, this exercise gave a ₀ = 0; with a ₁ = 0.00270 m/s, a ₂ = 0.000142 and a ₃ = 0.0000764 (m/s)⁻¹ the only statistically significant nonzero coefficients.

However, there have been a number of more recent investigations of the behavior of C _DN at higher winds. In particular, Donelan et al. (2004) compile wind tunnel measurements and conclude that there is saturation for U _N between 33 and 50 m/s. In this range C _DN is approximately constant between 0.0022 and 0.0025. At lower speeds, the over ocean values of Large and Pond (1981), tend to be higher than the wind tunnel results, but the few data points at U _N ≥ 25 m/s are consistent with a leveling off. It is possible to make a smooth transition to the wind tunnel results for U _N between 30 and 33 m/s. by retaining a negative coefficient a ₈ = −3.14807 × 10⁻¹³ (m/s)⁻⁶ in polynomial (10).

Division of (10) by U ²_N then yields

$$ C_{{\rm DN}} = a_1 /U_{\rm N} + a_2 + a_3 U_{\rm N} + a_8 U_{\rm N}^{6},\quad U_{\rm N} < 33\,{\rm m/s} $$

(11a)

$$ = 0.00234,\quad U_{\rm N} \ge 33\,{\rm m/s} $$

(11b)

This formulation of C _DN(U _N) is plotted if Fig. 15. The first derivative of (11a) is zero at U _N = 33 m/s, where C _DN equals 0.00234, compared to 0.00272 for a ₈ = 0.0 (thin dashed line).

Fig. 15

The neutral, 10 m transfer coefficients as a function of 10-m neutral wind speed, U _N. The drag coefficient, C _D, formulation follows the thick solid line, not the thin dashed extrapolation of LY04. Only C _H is different in stable, C _Hs, than unstable, C _Hu atmospheric stratification

Recent aircraft measurements (French et al. 2007) and radiosonde profiles (Powell et al. 2003) in hurricane conditions also indicate a leveling off, or even a decrease in C _DN at very high wind speeds. The latter show C _DN decreasing from 0.0022 at U _N = 30 m/s to about 0.0017 at 50 m/s. The former are very scattered and C _DN is only about 0.017 for U _N greater than 22 m/s, but in better agreement with Fig. 15 at lower wind speeds. Thus, these two hurricane results are inconsistent and both differ significantly from Donelan et al. (2004). Reasons for this situation may include the difficulty of measuring near surface processes in hurricanes, and different wind-wave conditions under a hurricane than under other storms or in a wind tunnel.

Over the most important wind speed range (5 m/s < U _N < 15 m/s) the drag coefficient formulation of Fig. 15 tends to be larger than windtunnels (Donelan et al. 2004), about the same as the COARE 2.0 algorithm (Fairall et al. 1996) and smaller than COARE 3.0 (Fairall et al. 2003). The unbounded rise at very low winds is more rapid than given by Smith (1988).

Historically, formulations of heat and evaporation coefficients have more closely followed (10), which is rarely used to formulate the drag coefficient. Specifically, measured heat and evaporation fluxes have been regressed on U _N times a 10 m, neutral air–sea temperature, or humidity difference, respectively. In the case of evaporation, the offset is not significantly non-zero, so the slope gives C _EN directly from (3b). However, in the heat flux case there is a significant positive offset, and furthermore, the slope is found to be steeper in unstable atmospheric conditions, than in stable. Thus, it is necessary to treat stable and unstable heat fluxes separately. The positive offset is consistent with an unbounded transfer coefficient (slope) as wind speed approaches zero, but the flux, as in the case of stress (10), should diminish. This behavior can also be achieved by using fluxes to compute the roughness lengths in the form used in (9):

$$ {\frac{\kappa}{{\rm ln}(10m/z_{\theta})}} = 0.0327 ; \quad {\rm unstable}$$

(12a)

$$ = 0.0180;\quad {\rm stable} $$

(12b)

$$ {\frac{\kappa}{{\rm ln}(10m/z_q)}}= 0.0346. $$

(13)

There is relatively little scatter in these values (Large and Pond 1982) because much of the observed variability in measured C _HN and C _EN is accounted for in the drag coefficient on the right hand sides of (9). Once determined, these numbers directly give the formations of C _HNu (unstable), C _HNs (stable) and C _EN shown in Fig. 15.