The Divergence of the Water Vapour Flux Over Southern Africa

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					           The Divergence of the Water Vapour
               Flux Over Southern Africa
                                         O. S. McGEE
                      [DEPARTMENT OF GEOGRAPHY, UNIVERSITY OF NATAL,
                                    PIETERMARITZBURG]




Abstract
Data from all available radiosonde ascents during 1967 over            1968) or results which though comparable may be fortuitous
South Africa are used to determine the annual water vapour flux        (Barry, 1972). The theory which now follows relates to the Bel-
divergence. A theoretical approach is given in some detail as well     lamy method and expands the outline given by Palmen and
as certain explanations as to why results appear unrealistic at        Soderman (1966). Standard meteorological symbols are used.
first sight. The need appears for a closer appraisal of topographi-
cal influences and the acceptance of a possible transport of vap-
our through the upper level at which customarily, it is assumed
                                                                       Theory
that there is no such transport.
                                                                       The rate of precipitation per unit mass of air is equal to the
                                                                       decrease of specific humidity* within the mass if it is assumed
Introduction                                                           that no condensed water remains suspended and that no water
                                                                       substance is being added. An Eulerian expansion (Byers, 1959)
Considerable transport of water substance in the vapour phase          of the specific humidity derivative dq dt yields the expression
occurs in the earth's atmosphere. By comparison the transport
in solid and liquid phases is small and little moisture is actually    dq     =      sq      + q   l                                        (1)
stored (the amount being nonetheless comparable to the water                             4
                                                                       dt    St                Sp
content in the rivers of the earth, as estimated by hydrologists)      where successive terms on the right hand side represent the local
(Peixoto, 1970b). Over the years much ingenuity has been exer-         change of q, the horizontal advection of q, (u— + v             ),
cised in attempting to determine as accurately as possible the                                                           8x         Sy
actual amount of water vapour present at any moment, the di-           and the vertical advection of q, respectively; V = the horizon-
rection, intensity and level of its transport and the divergence of    tal wind vector and w = the vertical velocity in pressure
this flux. Because the calculations are based on the far-from-
                                                                       coordinates (w = — ) .
perfect data collected from upper air ascents made by                                   dt
radiosonde equipment it is frustrating that completely satisfac-
tory results are often unobtainable from even the most carefully         If equation (1) is divided by g and integrated directly in the
constructed theories.                                                  xypt-system from the top (p = 0) to the bottom (p = p0) of the
                                                                       atmospheric column, equation (2) is obtained:
   The example given below illustrates this in the case where
certain flux divergence theory is applied to South African upper
air data.

   By way of outline, the reader is first reminded that the net        The integrand of the second term on the right hand side of
convergence or divergence of the water vapour flux for a given         equation (2) may be expanded further:
area and time period may be determined by more than one
method. For large areas of the earth's surface the eastward and
northward components of the flux at the intersections of a
latitude-longitude grid are commonly obtained from isopleths of
the flux field. From such values the net divergence out of each        since from the equation of continuity in the xypt-system,
grid area is calculated. For smaller areas, flux values at particu-
lar stations are assumed to define linear vector fields over triang-   V • V +— = 0 (Hess, 1959).
                                                                              Sp
les with vertices at adjacent stations (Bellamy, 1949). Vertically
integrated values of divergence obtained by the two methods for
a particular area have been shown to produce similar results           •Definitions of specific humidity and precipitable water vapour have been
(Bannon et al, 1961) or results which differ considerably (Barry,      given in WATER SA Vol. 1 no. 1 April 1975 p. 30 footnote. (McGee, 1975)


                                                                                                        Water SA Vol. 2 No. 2 April 1976     73

				
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