Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 262

This may be important for nontidal lagoons where random wind surge is the leading
forcing factor for marine water influx. In turn, this information may also identify
the physical forcing factors responsible for dominant ventilation of the lagoon by
ocean waters. For lagoons where tides are the major forcing function, spectral
analysis is not so relevant because the tidal harmonic frequencies are well known
and are best resolved using harmonic analysis.

6.3.2.3 Heat Budget

The thermal structure of a lagoon water body and its temporal variations play an
important role in the dynamics, mixing, water quality, and biotic conditions of a lagoon.
In the case of a stratified lagoon, where temperature has a strong influence on water
density, a three-dimensional numerical approach is required. For a nonstratified or a
weakly stratified lagoon, the evolution of temperature in time and space may be
described by a two-dimensional approach. This is expressed by two-dimensional partial
differential equations in Eulerian coordinates (Equation (6.24)) where the left side of
the temperature evolution equation is a total derivative of the temperature in the control
volume and the right side is the net sum of heat fluxes, sources, and sinks:

∂ () VT

t

+⋅ ∂

() VT

x

+⋅ ∂

() VT

x

1

u u =

C AH

( ⋅ + H ), (6.24)

1 2 s Σ s

∂ ∂ ∂ ⋅ ρ

1 2 p

where is the net thermal-energy flux (Wm −2 ), H s is the sum of heat internal
sources and sinks ( W ), V is the control volume (m 3 ), T is the temperature (

H Σ

C), t is
the time (s), u 1 and u 2 are the depth-averaged water velocity components (m s −1 ), A s
is the surface area (m 2 ),

°

ρ is the density of water (e.g., 997 kg m −3 at 25 ° C), and C p

is its specific heat (e.g., 4179 J kg −1 C). The advective transport of the

heat into or out of the control volume is described by nonlinear advective terms on
the left side of the equation and is not included in the net thermal-energy flux.
The net thermal-energy flux is a heat flux through the lagoon surface. A typical
example of the internal or boundary heat source would be the outlet of a power plant
cooling system. The advective heat flows caused by river run-off are usually con-
sidered boundary heat sources or sinks. The marine water influx is usually treated
through the boundary condition for Equation (6.24).
The net thermal energy flux at the lagoon surface includes solar radiation in
short and dispersed waves, back radiation from the water surface, direct heat
exchange with the atmosphere (heat conduction), and latent heat exchange with the
atmosphere in terms of evaporation heat loss or condensation heat gain. A detailed
description of all components of the net thermal energy flux as well as all necessary
formulas for their calculation or estimation can be found, for example, in Martin
and McCutcheon: 4b

° C −1 at 25 °

H Σ

HH H

Σ =

( − ) + ( HH HHH − ) − ± ± (6.25)

SW BSW H BH B L S