Seasonal stratification and the spring bloom - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 185

Values of F determined from observations can be compared with the controlling

! by regression analysis to determine the constants and

and

^ u 3 M2

h

W 3
h

variables

hence estimates of the efficiencies e and e s . Results from a survey of summer
stratification at 146 stations in the Irish and Celtic Seas (Simpson et al., 1978 ) lead
to efficiency estimates of e

0.023. The higher efficiency of wind
mixing may be explained in terms of the closer proximity of the wind stirring input to
the main density gradient in the thermocline. The inclusion of the wind stirring term
considerably increases the statistical significance of the fit relative to the regression on
tidal stirring alone.

0.004 and e s

6.2 Seasonal cycles in mixed and stratifying regimes

......................................................................................................................
In the previous section we developed a simple, energy-based argument that allows us
to decide whether or not a region of shelf sea will be found to be thermally stratified
or vertically mixed in summer. Our focus was on the summer spatial partitioning of
the shelf sea environment. Now we will look at the temporal evolution of stratifica-
tion over one year. If we neglect the influence of winds, we can revisit Equation (6.18)
and generate the following condition that tells us what surface heat flux is required
for a water column to thermally stratify:

>

3pag
8c p 0 k b e

Q i h
^

1

u 3 M2

ð 6 : 26 Þ

u 3 M2
3pagh

8c p 0 k b e ^

Q i > :

At a particular place within our shelf sea, where we know the depth and the tidal
currents, the collection of parameters on the right of Equation (6.26) is fixed and we
have a condition for the rate of net surface heat flux required to trigger the onset of
stratification. We described in Section 2.2 how the different components that deter-
mine Q i lead to strong seasonality in heat flux, with negative flux (cooling) in winter
switching to positive (warming) sometime in spring. Let us now look at how that
seasonality in the heat flux generates annual cycles of water column structure.

6.2.1 The Two Mixed Layer (TML) model

So far we have represented stratification in terms of the variable F which summarises

the state of water column stratification in a single number. has the virtues of having

a straightforward physical meaning and being easily incorporated into simple models
of stratification like the one we developed in Section 6.1.2. You could take Equation
(6.22) and, with sufficient knowledge of the seasonal heat flux, integrate it forward in
time to track the evolution of the strength of stratification through one year (e.g.
similar to the procedure in Equation 6.24 ).

F