|
<br />. 786
<br />
<br />ABBS: INVESTIGATION OF PROBABLE MAXIMUM PRECIPITATION ASSUMPTIONS
<br />
<br />situ maximization" method. When storms that occur in adjoin-
<br />ing and geographically similar regions to the catchment area
<br />are also considered. Ihe method is called the "transposition
<br />and maximization method."
<br />Hm1 (1982) ~huwll the phYlicnl bn"ilil for storm mAximization
<br />is bas~d on a simple two-parameter model of the storm derived
<br />as follows. A storm is considered to consist of a convergent
<br />mass flow at low levels that rises and diverges in an upper
<br />outfl(IW layer. The water vapor budget equation associated
<br />with the storm can be written as
<br />
<br />(" [aq ] dp
<br />E - P =)0 at + V . (qV) -Ii
<br />
<br />wher~: E is evaporation. P is precipitation, q is specific humid-
<br />Ity. V Is the horlzontnl wiUd vactor, g j" the A,;,cch:rntion due tn
<br />gravity, Po is the surface pressure, and the vertical integration
<br />is carried out over the dcpth of the atmosphere. For major
<br />storms it is assumed that the evaporation term E, the rate of
<br />water vapor slorage term (aq/at). and the moisture gradient
<br />in the, vicinity of the storm are negligible, With these assump-
<br />tions, (1) can be rewritten as
<br />
<br />(PO ap
<br />p= -)0 qV'Vg
<br />
<br />that Is. the r"lntult Is upproXhUtttdly dLtllll1 Il' lht!' wfticully
<br />integrated product of the mass convergence and the spccific
<br />humi:.lity. If the model is further simplified to comprise an
<br />inflow layer 6.p 1 and an outflow layer 6.P2 with uniform diver-
<br />gencf:s DI and D2 and specific humidities q, and q2' the
<br />precipitation P reduces to
<br />
<br />p = _( ql"p,D, ~ q,t.P,D~)
<br />
<br />From considerations of mass continuity, 6.p t D I = ~.p2D z and
<br />ql ~> qz. and hence the precipitation is approximated by
<br />
<br />q,t.p,D,
<br />p~-
<br />9
<br />
<br />To calculate the maximi~ed precipitation, :he product of the
<br />moisture inflow and mass convergence needs to be maximized.
<br />The term q I lip 1 is the effective precipitable water We for a
<br />storm, and this can be maximized by using 24-hour persisting
<br />dew points to calculate a maximum effective precipitable watcr
<br />w.. . The maximizcd prccipitation is then calculated by ad-
<br />jusii:,g the observed rainfall by a moisture adjustment factor
<br />w,,",)"',.. However, as pointed out by J.VieSI1,?r [lQ70]. it is com~
<br />mon practice to calculate the moisture adjustment factor from
<br />the actual precipitable water in a saturated atmospheric col-
<br />umn and the maximized precipitable water W n"'~ as given hy
<br />the maximum 24-hour persisting dew points, The dew point
<br />uniquely defines the mixing ratio at cloud hase and therefore
<br />the precipit<lble water in the saturated column. This indirect
<br />technique arises because there is usually no way of character-
<br />izing the extreme mass convergence, so the observed rainfall is
<br />taken as an implicit measure of this quantity. It is assumed that
<br />extreme precipilation storms have the highest efficiency, The
<br />maximized precipitation is thus calculated from the precipita-
<br />hie water w derived from the observed dew point, the ma:'{i~
<br />mized precipitable water W ma,,' and the observed rainfall P
<br />
<br />(normally in the form of depth-duration-area (DDA) curves)
<br />as
<br />
<br />(Wm,,)
<br />p ~ -- XP
<br />ma~ w
<br />
<br />m
<br />
<br />(1)
<br />
<br />More recently, a technique known as the "generalized
<br />method" has been developed to calculate the PMP. Such meth-
<br />ods use rainfalls recorded over a large region and from a large
<br />datahase of storms. The storm datahase is generalized hy sep-
<br />arating out that portion of the rainfall attributable to regional
<br />meteorological conditions from that which may be considered
<br />to be due to site-specific (e.g.. topography) characteristics.
<br />Hansen [1987] discusses the concepts and some of the consid-
<br />erations necessary for the estimate of PMP, particularly as they
<br />pertain to the United States. Similar techniques to thC/iC hflVQ
<br />hocn u~otJ hy tho AUllttullull Bureau of Meteorology to help
<br />overcome the problems associated with the shortness of Aus-
<br />tralia's rainfall record and to provide regionally consistent
<br />[Pearce and Kennedy, 19941 estimates of the PMP, The Aus-
<br />tralian Bureau of Meteorology has developed three general-
<br />ized methods that are applicable to the country: the general-
<br />ized short duration method (GSDM). the generalized tropical
<br />storm method (GTSM). and the generali~ed southeastern Aus-
<br />tralia method (GSAM). The GSDM is applicable for small
<br />areas up to 1000 km2 and for time periods up to 6 hours, The
<br />GTSM and the GSAM are used for larger areas of the order of
<br />1{)4 km2,
<br />1'henim of the overall study has been to develop a tech.
<br />niquc. using numerical mesoscale atmospheric mouels, to eval-
<br />uate independently the assumptions used in the simple two-
<br />parameter conceptual model that is used for PMP calculations.
<br />These assumptions arc (1) the precipitation is linearly related
<br />to the precipitable water (i,e" P, = (w2/w) X P); (2) the
<br />precipitation efficiency of the storm does not change as the
<br />moisture available to the storm increases; and (3) terrain mod.
<br />ulates the distribution of the precipitation but does not affect
<br />the synoptic~scale dynamics of the storm.
<br />The relalionship between the precipitable water and the
<br />precipitation (assumption 1) is particularl)' important since it is
<br />this relationship that underlies the foundations for both the
<br />moisture maximization and the storm transposition techniques
<br />currently employed in the GSAM, The report of the National
<br />Research Cot/ncil [1994] also concludes that the scientific foun-
<br />dations of the traditional PMP procedures, such as moisture
<br />maximization and storm transposition. require detailed study.
<br />That report points to numerical models as key 10Dls for en-
<br />hancing PMP procedures.
<br />The following steps are used to used to evaluate the assump.
<br />tions detailed ahove, (1) Use a numerical model of the almo-
<br />sphere to simulate recent large storms. (2) Compare the model
<br />results with the observed rainfall ami storm development. (3)
<br />Carry out sensitivity analyses to determine the maximum pre~
<br />cipitation efficiency of the storms, (4) Develop a hypothetical
<br />"worst ease storm" that would allow a comparison between the
<br />model.generated DDA curves amI the DDA curves calculated
<br />using the maximization relationship of the current generalized
<br />technique.
<br />
<br />I
<br />I
<br />I
<br />t
<br />
<br />(2)
<br />
<br />(3)
<br />
<br />(4)
<br />
<br />2. Methodology
<br />
<br />In this section it will be assumed (1) that it is possible to
<br />model accurately extreme storms using a mesoscale numerical
<br />
<br />I
<br />
|