Numerical Experiment of Stratification Induced by Diurnal Solar Heating Over the Louisiana Shelf

Abstract

The effect of diurnal solar heating on the stratification of waters over the Louisiana shelf was examined using the 3-dimensional Finite Volume Community Ocean Model (FVCOM). The simulation was for June 2009 to examine the effects of solar heating on summertime stratification. The input components of solar radiation to the FVCOM model were calculated using available relationships for shortwave, longwave, latent heat, and sensible heat radiation and using Metocean field data obtained from WAVCIS stations. Simulation results showed a continuous increase in water temperature and stratification during June 2009 with daily fluctuations of sea surface temperature as large as 0.9 °C. The corresponding stratification strengthening was quantified by an increase in the gradient Richardson number and buoyancy frequency. Development of shelf-wide stratification coincided with a significant decline in bottom water oxygen concentration. Our results demonstrate how, under certain conditions, solar heating can significantly contribute to vertical stratification and may also create conditions conducive to the formation and persistence of hypoxia.

Appendix A: Formulation of Different Surface Heat Components

(All parameters are described in Table 1.1)

Table 1.1 Parameters used for the formulation of surface heat components

Shortwave Radiation: Relationships presented by Guttman and Matthews (1979), Ivanoff (1977), and Cotton (1979) were used to calculate shortwave radiation flux:

$$ Q_{\text{o}} = \frac{{Scos^{2} Z}}{{\left( {\cos Z + 2.7} \right)e \times 10^{ - 5} + 1.085\cos Z + 0.10}} $$

(1.9)

The cosine of the zenith angle is computed using the formula:

$$ \cos Z = \sin \phi \,\sin \delta + \cos \phi \,\cos \delta \,\cos HA $$

(1.10)

The declination is $\delta = 23.44^{^\circ } \times {\text{cos }}\left[ {\left( {172 - day\, of\,year} \right) \times 2\pi /365} \right]$, and the hour angle is $HA = \left( {12\,h - solar\,time} \right) \times \pi /12.$ The correction for cloudiness is given by

$$ SW \downarrow = Q_{\text{o}} (1 - 0.6c^{3} ) $$

(1.11)

The cloud correction is optional since some sources of radiation contain it already.

Longwave Radiation: The clear sky formula for incoming longwave radiation is given by Wyrtki (1965):

$$ F \downarrow = \sigma T_{a}^{4} \left\{ {1 - 0.261\exp \left[ { - 7.77 \times 10^{ - 4} \left( {273 - T_{a} } \right)^{2} } \right]} \right\} $$

(1.12)

while the cloud correction is given by:

$$ LW \downarrow = \left( {1 + 0.275c} \right) F \downarrow $$

(1.13)

Sensible Heat: The sensible heat is given by the standard aerodynamic formula (Imberger and Patterson 1981):

$$ H \downarrow = \rho_{a} c_{p} C_{H} V_{wg} \left( {T_{a - } T_{sfc} } \right) $$

(1.14)

Latent Heat: The latent heat depends on the vapor pressure, and the saturation vapor pressure given by Imberger and Patterson (1981):

$$ e = 611 \times 10^{{a(T_{d} - 273.16)/(T_{d} - b)}} $$

(1.15)

$$ e_{s} = 611 \times 10^{{a(T_{\varepsilon fc} - 273.16)/(T_{\varepsilon fc} - b)}} $$

(1.16)

The vapor pressures are used to compute specific humidity according to:

$$ q_{10m} = \frac{ \in e}{{p - \left( {1 - \in } \right)e}} $$

(1.17)

$$ q_{s} = \frac{{ \in e_{s} }}{{p - (1 - \in )e_{s} }} $$

(1.18)

The latent heat is also given by a standard aerodynamic formula:

$$ LE \downarrow = \rho_{a} LC_{E} V_{wg} (q_{10m} - q_{s} ) $$

(1.19)