THE NEAR-SURFACE LAYER OF THE OCEAN
The advantage of the regression type parameterizations is that they are
simple and are easy for practical applications, especially when only limited
information on the environmental conditions is available. A fundamental
problem of such parameterizations is that, strictly speaking, they require
adjustment of empirical coefficients to each geographical region, season,
and, perhaps, even to synoptic conditions. Their application for the global
coverage of large diurnal warming events is therefore very limited.
4.5.4 Numerical models
Early numerical models of the diurnal cycle employed the turbulent heat
diffusion equation with constant mixing coefficient. Foster (1971a)
undertook direct numerical simulation of an idealized diurnal cycle in the
upper ocean by solving the equations of motion, heat, and continuity. Wind
mixing was introduced by setting a constant turbulent mixing coefficient; the
solar radiation was treated as a time dependent volume source. The surface
cooling was represented by a constant heat flux from the ocean surface. The
model in general reproduced some qualitative features of the diurnal cycle.
Convection developed during nighttime but was suppressed by solar
radiation during daytime. The initial wind induced turbulence was
unimportant in the vertical transport after development of the nighttime
gravitational convection. Yet for strong initial (wind-induced) mixing, the
convection could not start during nighttime.
The main problem of Foster’s (1971a) model was that the mixing
coefficient did not depend on depth or on time. Thus, it could not be correct
under light winds. Remember that an important feature of turbulent mixing
in the upper ocean under light winds is that it both influences, and is
influenced by, stratification arising due to diurnal heating. This results in a
nonlinear response of the diurnal cycle to external forcing, which could not
be captured by Foster’s (1971a) model.
More realistic models of the diurnal mixed layer include the Kraus and
Turner (1967) integral type model, a second moment turbulence closure
mixed layer model (Wick, 1995), the KPP model (Large et al., 1994;
Soloviev et al. 2001), the Price-Weller-Pinkel (PWP) modelT (Price et al.,
1986)T , and the transilient model (Stull and Kraus, 1987; Soloviev and Lukas,
1997a). No perfect model of the diurnal cycle, however, has been developed:
They all have advantages and disadvantages. Application of the integral
model for the diurnal mixed layer and thermocline modeling is complicated
by some limitations in parameterizing entrainment fluxes at the bottom of
the diurnal mixed layer. The KPP model requires specifying the nonlocal
transport term that has not been well defined. The PWP model does not have
the correct asymptotic convective regime under conditions of very low wind
278
The advantage of the regression type parameterizations is that they are
simple and are easy for practical applications, especially when only limited
information on the environmental conditions is available. A fundamental
problem of such parameterizations is that, strictly speaking, they require
adjustment of empirical coefficients to each geographical region, season,
and, perhaps, even to synoptic conditions. Their application for the global
coverage of large diurnal warming events is therefore very limited.
4.5.4 Numerical models
Early numerical models of the diurnal cycle employed the turbulent heat
diffusion equation with constant mixing coefficient. Foster (1971a)
undertook direct numerical simulation of an idealized diurnal cycle in the
upper ocean by solving the equations of motion, heat, and continuity. Wind
mixing was introduced by setting a constant turbulent mixing coefficient; the
solar radiation was treated as a time dependent volume source. The surface
cooling was represented by a constant heat flux from the ocean surface. The
model in general reproduced some qualitative features of the diurnal cycle.
Convection developed during nighttime but was suppressed by solar
radiation during daytime. The initial wind induced turbulence was
unimportant in the vertical transport after development of the nighttime
gravitational convection. Yet for strong initial (wind-induced) mixing, the
convection could not start during nighttime.
The main problem of Foster’s (1971a) model was that the mixing
coefficient did not depend on depth or on time. Thus, it could not be correct
under light winds. Remember that an important feature of turbulent mixing
in the upper ocean under light winds is that it both influences, and is
influenced by, stratification arising due to diurnal heating. This results in a
nonlinear response of the diurnal cycle to external forcing, which could not
be captured by Foster’s (1971a) model.
More realistic models of the diurnal mixed layer include the Kraus and
Turner (1967) integral type model, a second moment turbulence closure
mixed layer model (Wick, 1995), the KPP model (Large et al., 1994;
Soloviev et al. 2001), the Price-Weller-Pinkel (PWP) modelT (Price et al.,
1986)T , and the transilient model (Stull and Kraus, 1987; Soloviev and Lukas,
1997a). No perfect model of the diurnal cycle, however, has been developed:
They all have advantages and disadvantages. Application of the integral
model for the diurnal mixed layer and thermocline modeling is complicated
by some limitations in parameterizing entrainment fluxes at the bottom of
the diurnal mixed layer. The KPP model requires specifying the nonlocal
transport term that has not been well defined. The PWP model does not have
the correct asymptotic convective regime under conditions of very low wind
278