Geoscience Reference
In-Depth Information
the derivation of prognostic equations of escalating complexity for the case of
velocity components.
Because the process of deriving successive 'orders' of prognostic equations
always results in more new unknowns than new equations, it is not possible to use
this approach to derive a suite of physically based equations that by themselves are
an independent basis for describing turbulent transport in the ABL. To allow such
a description it is always necessary to provide additional equations that relate the
unknown variables to each order. The process of providing these additional
equations to complement the prognostic equations derived at any specific order of
complexity is known as making 'turbulent closure.
To obtain turbulent closure at a particular order it is necessary to 'parameterize'
higher order moments in terms of lower order moments through new equations.
In practice, these additional equations are often observation-stimulated, and are
usually approximate descriptions that are applicable in restricted regions of the
ABL and/or in particular stability conditions. The range of turbulent closure
schemes that can be proposed is limited only by human ingenuity, but a closure
scheme is only credible if its use can be shown to result in a description that is
confirmed by observations. Proposed turbulent closure schemes can be
local
if the
values of unknown quantities at a specific point are assumed related to each other.
Or they can be
nonlocal
if some unknown quantities are related to other quantities
at many points. In this text the closure scheme described is that most commonly
used in the surface layer of the ABL, i.e., local closure at first order. However the
next section first discuses closure at lower order than this.
Low order closure schemes
The lowest order closure possible is
zero order closure
. This is the trivial case in
which the spatial and temporal distributions of mean atmospheric variables are
specified simply as numerical or algebraic functions, i.e., as global, regional, or
local space-time maps.
Sometimes a form of closure is used in the ABL in which the variation in space
and time of mean meteorological variables is described, but without explicit
representation of turbulent transport mechanisms. This approach is sometimes
called a
Slab Model
and is used to describe the daytime evolution of the ABL over
homogeneous, flat surfaces. In such a model the temperature and humidity profiles
are assumed to have a fixed (but plausible) height dependency, but the mean value
of these profiles changes with time in response to the input of sensible heat and
water vapor.
A slab model is illustrated in Fig. 19.2. The surface fluxes and rate of entrainment
into the ABL are described by subsidiary equations, and the divergence of fluxes is
assumed negative and constant with height. This is consistent with assuming the
two profiles have time-independent height dependence. The rates of change of
temperature and humidity content in the 'slab' are then calculated from
