FLOOD07101

• County: Statewide
• Basin: Statewide
• Title: A Numerical Modeling Study to Investigate the Assumptions Used in the Calculation of Probable Maximum Precipitation
• Date: 3/1/1999
• Prepared By: Water Resources Research
• Floodplain - Doc Type: Educational/Technical/Reference Information

.I
J
,
i
,I
,

ABBS: INVESTIGATION OF PROBABLE MAXIMUM PRECIPITATION ASSUMPTIONS

menl, the Blue Mountains, and the mesoscale convergence
line, However, the results from EC86_5 show less rainfall pro-
duced in these three regions compared with the rainfall pro-
duced in EC86 _3, although a larger area is affected by precip-
itation. Hence the precipitation is not linearly related to the
precipitable water.
3.2.3. Storm efficiencies. In calculating the PMP for ex-
treme storms it is assumed that the precipitution efficiency of
the existing storms is at a maximum. In this section we calcu-
late the precipitation efficiency (defined below) using output
from the numerical model. Average efficiencies are then cal.
culated for both the heavy and moderate rainfall regions of the
storm.
First, the modeled storm is partitioned into heavy and mod-
erate rainfall regions on the basis of the method of Churchill
olld HOllze [1984] and Too et 0/, [1993]. Model grid points with
a rainfall rate in excess of 25 mm h -I are considered to be
heavy rainfall grid points. Precipitation at all other grid points
is considered 10 be moderate rainfall, These definitions of
heavy and moderate rainfall are used throughout the remain-
der of this report.
The moisture and condensate mixing ratio continuity equa-
tions used in RAMS are given by

ilr" ar" r)r,. ar" (iir")
--, = -II~ - v- - w- + DfF (r ) + -
iH ax ay iJz ,. at con

+ (~")
'"

where rll is the mixing ratio of individual condensate species
(i.e., cloud water, rain, cloud ice, snow, and aggregates). The
first three terms on the right-hand side of (6) are the advection
of each condensate category, the fourth term denotes the dif-
fusion of each condensate category, and the subscripts con and
res denote the tendency from the' convective parameterization
and the resolvable-scale microphysical parameterization.
By summing (6) for each condensate species, neglecting
diffusion. and multiplying through by the density P the total
condensate equation becomes

iir, iir, iir, iir, [ ( iir,) ( iir,) ]
PiJi = -P" iix - P"ay - pw iiz + P iJi + iJi
con rei

Vertical integration of (7) gives

fZ' ,1r fZ' ar fZ' ,1r
p _...!. Az = -pu---..!. Az - 1)V-~-.!. Az - Po
iJt iJx ay
4r: sfc sfc

+ r p[ (~,) '00 + (~:,) J ~z (8)

where Po is the surface precipitation rate. Equation (8) can be
further integrated over the heavy and moderate rainfall regions.
The precipitation efficiency is defined as the ratio of the
rainfall rate to the total condensation rate,

P
PE = 0 (9)

, rp[(~:')=o+(~)J~z

791

...
~
~
~ ..
~
c: ..
.
'ij ...
;:
~
...
~ ..
0
.

(a)

--.--------

~ . . u u ~ >> >> ..

H~,--~--'--JH

~ . . a U D >> U II

Tim. (hra)

...

(b)

~
~
~ ..

..
u
~ . --..----..---------
'ij
;: ...
~
...
~

..

o

.

..

lot 17 . .II II

"

"

.

(6)

I ~ ~-:---~~---n-:nj ~ I

..

.. ..

.. .. ..

"

"

.

Tim. (hra)

..

~
~
~ ..

(e)

~
c:
.
'ij
;:
~
...
~

..

-------

-----.

..

..

o

u . . a u 17 .. U II

(7)

~ - ~-X:-->;--~<---'--- j"
i~r--n:-~-- ~i

. u . . . lot 17 .. SI II

Tim. (hra)

Figure 5. Plots of the precipitation efficiency for the heavy
(snlid curve) and mDderate (dashed curve) portions Df (a) the
control simulation, (b) EC86_3, and (c) EC86_5. The lower
plot in each case shows the number of heavy (solid) and mod-
erate (dashed) rainfall grid points on the finest mesh.

A similar definition of precipitation efficiency has been
adopted in other modeling studies [Fe"ier et al., 1996; Weismall
alld K/emp, 1982].
The temporal variation of PE" for both the heavy and mod-
erate rainfall portions of the system, is shown in Figure 5. In all
cases the system is 60%-70% efficient at generating mod~rate