Empirical Heat Exchange Formulae 



The net heat exchange across the sea surface, Q N , is the sum of 

 the direct and diffuse radiation from sun and sky reduced by cloud 

 cover and sea surface albedo, Q 5 , the net long-wave or effective 

 back radiation, Q B , the latent heat flux, Q E , and the sensible heat 

 flux, Q c , as expressed in Equation (1): 



Qs=Qs-Qb-Qe-Qc 



(1) 



Few direct measurements of radiative and turbulent heat fluxes 

 have been made at sea. Observations of short-wave, long-wave, 

 and net long-wave radiation have been analyzed by Tabata (1964), 

 Charnell (1967), Reed and Halpern (1975). Reed (1977), and 

 Simpson and Paulson (1979) for widely separated locations in the 

 eastern and central North Pacific Ocean. Friehe and Schmitt (1976) 

 and Anderson and Smith (1981) have reviewed the few available 

 direct eddy flux measurements of sensible and latent heat. Because 

 direct measurements of air-sea heat transfers are not routinely avail- 

 able overthe ocean, the radiative and turbulent heat fluxes are com- 

 monly parameterized by empirical equations which incorporate 

 empirically determined coefficients and regularly observed atmo- 

 spheric properties at the sea surface and at some standard height 

 above the sea surface. All empirically derived heat exchange com- 

 ponents discussed in this report are expressed in units of watts per 

 square meter. 



Net incoming short-wave radiation from sun and sky, corrected 

 for cloud cover and sea surface albedo, was calculated according to 

 the following equation: 



Gs = a-a)2o(l-0.62C+0.0019/j) 



(2) 



where a. is the fraction of incoming radiation reflected from the sea 

 surface, C is the observed total cloud amount in tenths of sky cov- 

 ered, and h is the noon solar altitude in degrees. The direct and dif- 

 fuse radiation from a cloudless sky, Q , was obtained from an 

 harmonic analysis of the values tabulated in the Smithsonian Mete- 

 orological Tables (List 1949) for an atmospheric transmission coef- 

 ficient of 0.7 (Seckel and Beaudry 1973). Reed (1977) determined 

 that estimates of clear-sky insolation computed from the Seckel and 

 Beaudry formula differed from measurements of short-wave radia- 

 tion under cloudless skies by 4 % or less. 



The reduction of solar insolation due to the presence of clouds 

 has been estimated by various formulae ranging from linear (Kim- 

 ball 1928) to cubic functions (Laevastu 1960) of total cloud 

 amount, regardless of cloud type, or by relationships expressing a 

 dependence on both cloud amount and cloud type (Lumb 1964; 

 Seckel and Beaudry 1973). The linear cloud correction formula 

 suggested by Reed ( 1977) was adopted in this study. The total cloud 

 amount reports in the TDF-1 1 file represent visual estimates of the 

 fraction of the celestial dome obscured by clouds. Such highly sub- 

 jective observations frequently contain significant error and may 

 not warrant using higher order cloud correction formulae. 



The linear cloud correction in Equation (2) is appropriate for 

 cloud cover ranging from 0.3 to 1.0. The reduction in insolation 

 was neglected for cloud amounts < 0.25 (i.e., 2 oktas), a proce- 

 dure recommended by Reed (1977), who also indicated that this 

 formula results in a random error of estimate less than +10% for 

 estimates of monthly mean insolation and ±20% for weekly 

 means. Reed's linear correction is similar to a formula derived by 

 Tabata (1964) which was shown to give excellent agreement with 

 radiation measurements at Ocean Weather Station "PAPA" (OWS- 

 P) at lat. 50°N, where stratus type clouds predominate. Simpson 



and Paulson (1979) compared observations of incident solar radia- 

 tion with predictions based on empirical formulae and demon- 

 strated that Lumb's (1964) formula, which requires very reliable 

 hourly observations of cloud amount and cloud type, was superior 

 to Reed's linear correction formula for predictions averaged over 1 1 

 d. Predictions based on Reed's formula overestimated the 11-d 

 mean incident solar radiation by 6%. The 1 1-d mean was 102.5 W/ 

 m 2 , and the root-mean-square deviation between observations and 

 predictions over the same 1 1 d, amounted to 16.7 W/m 2 . Although 

 cloud type observations are included in surface marine weather 

 reports, we did not consider the additional cloud type information 

 in the TDF-1 1 file to be sufficiently reliable to incorporate Lumb's 

 more accurate formula in calculations of incident solar radiation. 



Net short-wave radiation reaching the sea surface is the differ- 

 ence between incident solar radiation and the radiation reflected 

 from the sea surface. Sea-surface albedo, a, was extracted from 

 tables published by Payne (1972), as a function of atmospheric 

 transmittance and mean daily solar altitude. Transmittance values 

 were calculated by reducing the clear-sky atmospheric transmission 

 coefficient of 0.7 used in this report by the linear cloud correction 

 factor adopted from Reed (1977). In our calculations, albedo 

 ranged from 0.04 in low latitudes during summer under cloudless 

 skies to between 0.20 and 0.30 in higher latitudes during winter. 



Effective back radiation is the difference between the outgoing 

 long-wave radiation from the sea surface, proportional to the fourth 

 power of the absolute sea surface temperature, and the incoming 

 long-wave radiation from the sky, which depends on the water 

 vapor content of the atmosphere and the type, density, and height of 

 clouds. In this report we have adopted the modified Brunt equation 

 (Brunt 1932) with the empirical constants of Budyko (1956) and the 

 linear cloud correction formula of Reed ( 1 976) to compute the net 

 long-wave radiation: 



<2 B = 5.50 xl0- 8 (r s +273.16)(0.39-0.05e/")(l- 0.9Q. (3) 



The atmospheric vapor pressure, e u (mbar), was computed from a 

 formula given by List (1949:366) using the observed surface pres- 

 sure, P, air temperature, T a , and wet-bulb temperature, T w . If any of 

 the required variables were missing, but the dewpoint temperature, 

 T d , was present in the surface weather report, or if the archived wet 

 bulb temperature was derived from a reported dewpoint tempera- 

 ture, as in TDF-1 1 Decks 110, 119, 185, 187, 196, and 281, then 

 atmospheric vapor pressure was computed as the saturation vapor 

 pressure at the dewpoint temperature using an integrated form of 

 the Clausius Clapeyron equation (Murray 1967). In fewer than 

 12% of the reports, atmospheric vapor pressure was computed 

 from the dewpoint temperature. 



In previous studies of the large-scale surface heat flux in the east- 

 ern and central North Pacific Ocean (Roden 1959; Seckel 1970; 

 Clark et al. 1974), effective back radiation was computed from the 

 Berliand (Budyko 1956) formula which includes a nonlinear cloud 

 factor and an additional term based on the air-sea temperature dif- 

 ference. Reed and Halpern (1975) demonstrated that the Berliand 

 formula produces systematically higher values than those com- 

 puted from the Brunt equation. Their estimates of net long-wave 

 radiation predicted by Equation (3) were approximately 10 W/m 2 

 greater than measured daily mean values of 60-65 W/m 2 for two 

 sites off the Oregon coast. Simpson and Paulson (1979) suggested 

 that the formulae of Brunt and Berliand are equally satisfactory and 

 may be used to predict daily values of net long-wave radiation with 

 an absolute accuracy of 20 W/m 2 . 



