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<br />ABBS: INVESTIGATION OF PROBABLE MAXIMUM PRECIPITATION ASSUMPTIONS
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<br />model of the atmosphere and (2) that the model can simulate
<br />realistically the amount and distribution of precipitation on the
<br />catchment scale, We will address the validity of these assump-
<br />tions in sections 3 and 4.
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<br />2.1. Step 1: Model Validalion
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<br />The first step is to show that the numerical model being used
<br />is capable of simulating observed extreme storms and then to
<br />compare the simulated DDA curves with observations. The
<br />model simulations need to be classified according to synoptic
<br />systems. In developing this methodology the current Bureau of
<br />Meteorology generalized storm categories of (I) short dura-
<br />tion thunderstorms. (2) southeastern Australian storms, and
<br />(3) tropical storms are the appropriate classifications, Short
<br />duratiDn thunderstorms that lead to flash flooding need to be
<br />validated against observed extreme thunderstorms. By con-
<br />trast, in those areas of northern Australia where the flooding is
<br />generatedby synoptic depressions or tropical cyclones, a dif-
<br />ferent family of simulations will be required and the modeling
<br />constraints might well be different. For example, thunder-
<br />storms are relatively short-lived (<12 hours) and occur over a
<br />small area, thus requiring a very high resolution grid, typically
<br />with a grid spacing of <I km, to be modcled successfully. In
<br />contrast, a tropical cyclone may last for a number of days and
<br />affect a large area. Systems such as these need to be modeled
<br />for a much longer period but at a much lower resolution (5-10
<br />km) than an individual thunderstorm.
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<br />2.2. Step 2: Comparison With the Simple Two-Parameter
<br />Moisture Maximization Model
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<br />The fundamental assumption in the two-parameter physical
<br />model is that both parameters (the moisture inflow and the
<br />low.level convergence) are independent. A major aim of our
<br />study is to use the numerical simulation to test the validity of
<br />this assumption. It is assumed that in an extreme storm the
<br />low-level convergence ill maxhnJ%c:d but the moisture is not, so
<br />the maximized storm can be derived by maximizing the mois-
<br />ture inflow. The modeling studies are able to test directly this
<br />hypothesis by repeating the simulation after maximizing the
<br />moisture inflow to the storm. In addition, the increased model
<br />rainfall can be compared with the maximized precipitation
<br />calculated from the generalized technique (see (5)). In this
<br />study the moisture values have been increased by uniformly
<br />increasing the temperatures of the atmosphere everywhere
<br />while maintaining the relative humidities. In this way the sys-
<br />tem remains in dynamic balance, but the specific humidity, and
<br />hence prec:ipitohlo wuler, hu. bdon Incrotllfcu. The Inuxlmbu-
<br />tiun factor is defined as the ratio of the precipitable water for
<br />the increased moisture simulation to the precipitable water for
<br />the control simulation. Since it is common practice to calculate
<br />the maximization factor using the actual precipitable water in'
<br />a saturated column [Wiesner, 1970] the model-derived maximi-
<br />zation factor is determined from those portions of the storm
<br />for which the atmosphere is saturated. This method is compa-
<br />rable tD the technique used to maximize storms in the current
<br />generalized approach.
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<br />203. Step 3: Sensitivity to Increases in the Moisture
<br />Avullablllty llnd 1.upugrnphy
<br />An advantage of using numerical models is that the model is
<br />able to simulate cDmplex, nonlinear processes that cannot be
<br />represented realistically otherwise. Such processes include, for
<br />example, changes in the convective processes as the moisture
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<br />available to the storm increases and the effect of terrain on the.:
<br />wind field and hence on the location and timing of the rainfall.
<br />By performing an ensemble of simulations in which the mois-
<br />ture availability to the storm is changed it is possible to deter-
<br />mine some of these effects. Similarly, it is possible to perform
<br />simulations in which the effects of terrain are removed to
<br />investigate the development of the modeled storm under these
<br />hypothelical conditions.
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<br />2.4. Colorado State U niversily Regional Atmospheric
<br />Modeling System
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<br />In sections 2.1-2.3 it was implicitly assumed that extreme
<br />precipitatiun events could be modeled with the current gener-
<br />ation of numerical mesoscale atmospheric models. Numerical
<br />models of the atmosphere solve the three-dimensional equa-
<br />tions of motion, the thermodynamic equation, and the mois-
<br />ture equation. This is achieved by converting these equations
<br />to finite difference form and solving them on a regular ,three-
<br />dimensional grid that covers the geographic region of interest.
<br />As the grid spacing used in the solution of these equations is
<br />decreased, the corresponding time step must be decreased to
<br />maintain computational stability.
<br />The numerical model used in this study is the Colorado State
<br />University Regional Atmospheric Modeling System (CSU
<br />RAMS) described in detail by Tripoli alld COIIOIl [1982] and
<br />COIIOIl et 01. [1982, 1986]. This is a quasi-Boussinesq mudel
<br />[Dillion alld Fiehll, 1969] with predictive equations fur the
<br />three velocity components, the Exner function, the ice-liquid
<br />water potential temperature [see Tripoli alld COIIOIl, 1981], Ihe
<br />total water mixing ratio, and the mixing ratios of rain droplets,
<br />pristine ice crystals, snow, graupel, and aggregate particles.
<br />The funedunction 1T is defined by 1T = Cp(P!PmiJR1C" where
<br />C p is the specific heat capacity for dry air at constant pressure,
<br />P is the total ambient air pressure, P 00 is 1000 hPa, and R is
<br />the gas constant for dry air. Diagnosed quantities are potential
<br />temperllture, temperature, prcuure, and the mixing ratios of
<br />water vapor and cloud droplets. The equations are solved on
<br />the staggered grid described by Tripoli alld COllon [I982J, A
<br />terrain-following sigma-z coordinate [Gal-Chell and Somer-
<br />ville, 1975a, b] is employed for the vertical direction.
<br />In our study the non hydrostatic, compressible version of the
<br />modeling system is used. This uses a time-splitting scheme in
<br />which the acoustic terms are integrated on a short time step
<br />using the Crank-Nicholson scheme. All other terms are inte-
<br />grated on a long time step using the leap frog procedure.
<br />Long and short wave radiation effccts are paramctcrizcd
<br />uaing lho achom~ dc~rlhQd by Chen and Cotton (19833, b J. The.:
<br />surface fluxes of heat, water vapor, and momentum Wefe cul-
<br />culated using the scheme of Louis {1979], and mixing is pa.
<br />rameterized using a modified form of the eddy viscosity typt::
<br />scheme. The soil model of McCumber and Pielke (1981] was
<br />coupled to the atmosphere using the surface energy balanct::
<br />model of Tremback and Kessler [1985 J. Cloud microphysics art::
<br />parameterized using the scheme described by Flalau el ai,
<br />[1989] in which ice crystals are initiated whenever the cloud
<br />becomes water saturated and the temperature is below We.
<br />Activated crystals have an initial diameter of 12.9 p.m, corre-
<br />sponding to an initial mass of 10-9 g. It was necessary to cDuple
<br />RAMS to a convective parameterization ~chcmu thul wmt .\lilQ
<br />able for use at resolutions of the order of 10 Ian. The convec.
<br />tive parameterization scheme ChDsen was that Df Frallk alld
<br />Cohen (1985, 1987] and Chen alld Frank [1993].
<br />The model has been used to simulate the passage of a cold
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