FEBRUARY 2004 BENJAMIN ET AL. 473
Mesoscale Weather Prediction with the RUC Hybrid Isentropic±Terrain-Following Coordinate Model
STANLEY G. BENJAMIN,GEORG A. GRELL,* JOHN M. BROWN, AND TATIANA G. SMIRNOVA* NOAA/Forecast Systems Laboratory, Boulder, Colorado
RAINER BLECK Los Alamos National Laboratory, Los Alamos, New Mexico
(Manuscript received 17 April 2003, in ®nal form 5 August 2003)
ABSTRACT A mesoscale atmospheric forecast model con®gured in a hybrid isentropic±sigma vertical coordinate and used in the NOAA Rapid Update Cycle (RUC) for operational numerical guidance is presented. The RUC model is the only quasi-isentropic forecast model running operationally in the world and is distinguished from other hybrid isentropic models by its application at fairly high horizontal resolution (10±20 km) and a generalized vertical coordinate formulation that allows model levels to remain continuous and yet be purely isentropic well into the middle and even lower troposphere. The RUC model is fully described in its 2003 operational version, including numerics and physical param- eterizations. The use of these parameterizations, including mixed-phase cloud microphysics and an ensemble- closure-based cumulus parameterization, is fully consistent with the RUC vertical coordinate without any loss of generality. A series of experiments con®rm that the RUC hybrid ± coordinate reduces cross-coordinate transport over a quasi-horizontal coordinate. This reduction in cross-coordinate vertical transport results in less numerical vertical diffusion and thereby improves numerical accuracy for moist reversible processes. Finally, a forecast is presented of a strong cyclogenesis case over the eastern United States in which the RUC model produced an accurate 36-h prediction, especially in a 10-km nested version. Horizontal and vertical plots from these forecasts give evidence of detailed yet coherent structures of potential vorticity, moisture, and vertical motion.
1. Introduction part, by a vision to translate the simplicity of the is- entropic perspective of three-dimensional (3D) baro- Numerical atmospheric prediction using an isentropic clinic structures as shown by Rossby et al. (1937), Na- vertical coordinate was ®rst introduced in 1968 (Elias- mias (1939), and others (see review by Gall and Shapiro sen and Raustein), and for the last 35 years, isentropic 2000) into atmospheric modeling. Although most ap- modeling has received a modest yet steady stream of plications of isentropic models up to this time have been research attention. Much of this work has centered on in research, an exception is the Rapid Update Cycle recasting atmospheric representation to better handle the (RUC), a regional mesoscale high-frequency data as- lower boundary condition, resulting in the development similation (Benjamin et al. 2004) and short-range nu- of a variety of hybrid isentropic±terrain-following co- merical prediction system running operationally at the ordinate models (e.g., Bleck 1978; Deaven 1976; Gall National Centers for Environmental Prediction (NCEP). 1972; Uccellini et al. 1979; Johnson et al. 1993; Bleck The RUC model is also distinctive in its application at and Benjamin 1993, hereafter BB93; Konor and Ar- akawa 1997). These efforts were all driven, at least in a much ®ner horizontal resolution (currently 10±20 km) than previous isentropic models. Isentropic-coordinate models are potentially advan- * Additional af®liation: Cooperative Institute for Research in tageous in that they reduce vertical transport through the Environmental Sciences, University of Colorado, Boulder, coordinate surfaces. In these models, lateral mixing is Colorado. carried out on isentropic surfaces rather than across them, meaning that no unwanted cross-isentropic mix- Corresponding author address: Stan Benjamin, NOAA/FSL, 325 ing occurs. Spurious growth of entropy in non- models, Broadway, R/E/FS1, Boulder, CO 80305. resulting in a cold bias in climate applications (Johnson E-mail: [email protected] 1997) or lack of ensemble spread (Egger 1999), is avoid-
Unauthenticated | Downloaded 09/29/21 03:20 PM UTC 474 MONTHLY WEATHER REVIEW VOLUME 132 ed. Atmospheric variables frequently display strong with terrain-following coordinates (Phillips 1957) grad- contrast in statically stable layers, including wind (e.g., ually turning into isobaric coordinates above some in- Shapiro 1978), water vapor (e.g., Johnson et al. 1993), termediate constant pressure level, we limit our discus- hydrometeors, and trace constituents (e.g., Zapotocny sion here speci®cally to isentropic±sigma (±) hybrid et al. 1997b; Reames and Zapotocny 1999). Weaver et coordinate de®nitions. al. (2000) showed that laminar structures of ozone in Bleck (1978) describes four different types of hybrid polar regions are better represented with a 3D of¯ine ± models. All of these designs de®ne a speci®c co- chemistry and transport model con®gured in isentropic ordinate surface where representation near the ground coordinates than with a similar model using a sigma- makes a transition to representation aloft. One of these pressure coordinate with more vertical levels. Diabatic options (B), with the transition level at a ®xed pressure effects from radiative ¯ux divergence, always present distance above the surface, is found in the University in the atmosphere, and intermittent latent heating/cool- of Wisconsin (UW) hybrid ± model (Johnson et al. ing cause departures of material ¯ow from isentropic 1993). This model has been the basis for a number of surfaces. However, to a ®rst-order approximation, is- studies that have demonstrated various numerical ad- entropic surfaces are material surfaces in the free at- vantages of the hybrid coordinate representation over mosphere. Moreover, the moisture and potential vortic- the pure representation (e.g., Johnson et al. 1993, ity environment for areas of precipitation may be fore- 2000; Zapotocny et al. 1994). Only one of the hybrid cast with better coherence using an isentropic model design options (option D) described by Bleck (1978) (Johnson et al. 1993; BB93). Isentropic coordinates also avoids coordinate intersections at the interface between have an advantage in that they provide adaptive vertical and domains. In option D, an above-ground isen- resolution, greater in layers of higher static stability trope is speci®ed as the lower boundary of the domain, where strong vertical gradients of other variables are with the atmosphere below that interface resolved by likely to occur. The concentration of isentropes in frontal coordinates. An example of an option D hybrid model zones of high thermal contrast means that these zones is the global circulation model described by Zhu et al. appear as larger-scale features in both alongfront and (1992) that used a lowest pure isentropic level of 352 cross-front dimensions when viewed from an isentropic K, a value necessitated by the fact that observed surface perspective (e.g., Dutton 1976; Benjamin 1989; Gall and potential temperatures over the Himalayas in summer Shapiro 2000). All of these advantages of isentropic reach as high as 335 K. Johnson and Yuan (1998) have modeling in the atmosphere have counterparts in iso- developed an option D variant of the UW hybrid global pycnal modeling in the ocean (e.g., Bleck and Boudra model (called a ± model) with a lowest pure isentro- 1981; Bleck 2002; Drijfhout 1992). This has led over pic level of 336 K. the years to a two-way technology transfer that has ben- Two other hybrid ± designs have emerged since e®tted both ®elds. the Bleck (1978) hybrid design classi®cation, neither of The RUC numerical forecast model is an advanced which uses ®xed transition levels. The ®rst (which we version of the hydrostatic primitive equation model de- label as option E) is the two-condition (isentropic; su- scribed by BB93. Its vertical coordinate is also used in perseded by minimum layer thickness constraint) de®- the RUC assimilation system described in Benjamin et nition described by BB93, which provides isentropic al. (2004). The use of a generalized vertical coordinate representation far closer to the ground than previous in a numerical weather prediction model introduced in hybrid coordinate de®nitions. As described in BB93, BB93 is demonstrated again in this paper, but now in this de®nition marked a signi®cant departure from pre- an application with much higher horizontal resolution vious de®nitions, avoided any interface level, and, in (10±20 km compared to 100±160 km in BB93) and fact, used an equation set written for a fully generalized increased emphasis on modeling of diabatic processes. vertical coordinate. The BB93 design, used in the 20- Here we emphasize issues in the design of hybrid and 10-km versions of the RUC model, is derived from isentropic models and describe experiments with the a hybrid isopycnic approach in the ocean model of Bleck RUC model to investigate the particular issue of cross- and Boudra (1981), of which the Hybrid Community coordinate vertical transport. Ocean Model (HYCOM) ocean circulation model (Bleck 2002) is a modern descendant. The details of this design are described in greater detail in section 4. 2. Design of hybrid isentropic±sigma models Perhaps the best way to characterize the present hybrid Various hybrid isentropic model schemes have been scheme is to call it arbitrary Lagrangian±Eulerian developed with the goal of retaining the advantages of (ALE), a term originally coined by Hirt et al. (1974). isentropic representation while eliminating the main Note however, that our scheme goes far beyond ALE shortcoming of a pure isentropic scheme, which lies in in that it adds the element of ``coordinate maintenance,'' the treatment of the planetary boundary layer or other that is, the migration of coordinate surfaces toward a layers where entropy is constant or even may decrease set of prede®ned target surfaces, in this case isentropes, with height. While other types of hybrid coordinate wherever minimum thickness conditions allow. models exist, especially hybrid sigma±pressure models A second, more recent hybrid ± design (which we
Unauthenticated | Downloaded 09/29/21 03:20 PM UTC FEBRUARY 2004 BENJAMIN ET AL. 475 label option F) de®nes the vertical coordinate as a linear The reduction in vertical advection found in quasi- combination of (terrain following) and , as described isentropic models can be illustrated in the context of an by Konor and Arakawa (1997). The Konor±Arakawa inviscid version of the hydrostatic continuity equation, design, like option E (BB93), has no coordinate inter- which is written in generalized vertical coordinates as sections. Zhu and Schneider (1997) adopted a hybrid p⌬ץ p ⌬p⌬ץ coordinate similar to that of Konor and Arakawa into a (V ϩ sÇ ϭ 0, (1 ´ ١ ϩ s ⌬s ץt⌬s s ⌬s ץ general circulation model and showed improvements over a p version of the same model. Purser et al. (2002) have described developmental work on a hybrid isen- where ⌬p/⌬s is the pressure thickness between two gen- tropic coordinate that is similar to option F but uses a eralized vertical coordinate (s) levels, and s is the vertical constant pressure at the top, similar to the Zhu et al. level index. In quasi-horizontal models, the ®rst term of (1992) option D model. this equation is ϳ0, meaning that any nonzero horizontal With the hybrid coordinate de®nition used in the RUC mass ¯ux divergence (term 2) will cause mass to be model (option E), coordinate surfaces more than 100± transferred between layers (term 3) to maintain speci®ed 300 hPa above the surface tend to be purely isentropic. pressures at each level. In a -coordinate model without This characteristic is similar to the UW hybrid ± mod- diabatic effects, the last term (vertical advection) is zero, el (option B) but not the Konor±Arakawa hybrid model implying that layers expand and contract depending on (option F) nor the UW ± model (option D). Thus, the mass ¯ux divergence. In other words, isentropic models RUC coordinate combines the advantages of the UW achieve a reduction of vertical advection by replacing the ± model (isentropic coverage down to midtropo- balance between terms 2 and 3 in Eq. (1), which is typical spheric levels) with those of the Zhu et al. and Konor± of sigma- or pressure-coordinate models, with a balance Arakawa models (no intersecting surfaces). By resolv- between terms 1 and 2. ing much of the troposphere with isentropic levels, this coordinate is desirable for the weather forecasting ap- 4. Numerics plication of the RUC model. Initial efforts to use a quasi-isentropic coordinate in In this section, we discuss the numerical techniques a nonhydrostatic framework have been introduced more used in the RUC model and the speci®c con®guration recently by Skamarock (1998) and He (2002). These used for the 20-km version of the RUC (RUC20) im- models also use generalized vertical coordinate frame- plemented operationally at NCEP in April 2002. works in which the target coordinate, based on a smoothed isentropic±sigma structure, can change with a. Vertical grid structure time. The de®nition of the RUC model vertical structure follows that described by BB93, (their section 2e). The 3. Reduction of vertical transport in hybrid RUC hybrid coordinate has terrain-following layers near isentropic-sigma models the surface, with isentropic layers above, as shown in Among the advantages (listed in section 1) of using Fig. 1, a vertical cross section of RUC coordinate levels a largely isentropic coordinate in an atmospheric model, from an actual case. The 20-km RUC uses 50 vertical one of the most signi®cant is the reduction in arti®cial levels, with each one assigned a reference or ``target'' numerical dispersion resulting from vertical motion virtual potential temperature () value (Table 1). The across coordinate surfaces, especially oscillatory motion algorithm used to de®ne vertical levels by BB93 is ap- associated with internal gravity waves. This reduction plied separately in each grid column and at every model occurs because, under adiabatic conditions, vertical ad- dynamical time step and consists of only about 10 lines vection is identically zero in gridpoint space in an is- of code. Operating on one coordinate level at a time, entropic model since 3D atmospheric motion is captured the algorithm uses two criteria: 1) move the coordinate in two dimensions on quasi-material surfaces. In sit- surface to the pressure where the target value is found uations with latent heating associated with ascending (Table 1; the isentropic de®nition) and 2) maintain a saturated air, an isentropic model will have some cross- minimum pressure spacing between coordinate surfaces coordinate vertical advection, but this advection will be starting upward from the surface (the sigma de®nition). of nonoscillatory nature and will generally be smaller If the pressure yielded by the isentropic criterion (1) is than in a quasi-horizontal model. The reduction of ver- less than that from the sigma criterion (2), the gridpoint tical dispersion in isentropic models leads to improved pressure is de®ned as isentropic, otherwise as terrain- transport of moisture and other scalar quantities, as dem- following (sigma). A ``cushion'' function (BB93) mod- onstrated in global models with horizontal resolution of i®es the minimum spacing in the transition zone between well over 100 km (Johnson et al. 1993, 2000, 2002). In and de®nitions to avoid discontinuities in slope this paper, we investigate cross-coordinate vertical between the and portions of a given coordinate transport in a hybrid ± model applied at a horizontal surface. From this two-part criterion, a new pressure, resolution of 20 km. pnew, is de®ned at each grid point in the column.
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FIG. 1. Vertical cross section showing RUC native coordinate (is- entropic±sigma hybrid) levels for 20-km RUC with 50 levels. Data are taken from an RUC 12-h forecast valid at 1200 UTC 2 Apr 2002. FIG. 2. Vertical cross section of RUC hybrid isentropic±sigma co- Cross sections are oriented from south (Mississippi) on left-hand side ordinate levels for 1800 UTC 14 Jan 2002. Orientation of the cross- to north (western Ontario) on right-hand side. section is approximately west±east through California (left), Colorado (center), and the Appalachian Mountains (right). s), canץ/pץ)The coordinate-relative vertical velocity, sÇ now be calculated as equate resolution of the planetary boundary layer and mixing near the surface. These minimum pressure thick- (p (p Ϫ pÃץ sÇ ϭ new , (2) nesses are reduced over higher terrain to avoid ``bulges'' -s ⌬t of layers protruding upward in these regions (illusץ where ⌬t is the model dynamical time step, and pà is trated in Fig. 2). the pressure at the outset of the vertical regridding pro- The hybrid ± algorithm used to de®ne the 3D pres- cedure described in the previous paragraph. The value sure ®eld in the RUC model can be replaced by a sigma± pressure (p) algorithm, resulting in a p version of the s) will be zero on all levels where at theץ/pץ)of sÇ beginning of the regridding step matches the target val- RUC generalized coordinate model. Table 2 contrasts the parameters that must be prede®ned for a ± versus ue. If it is not zero, a new value of is also determined, as explained in BB93, in a manner that avoids geopo- a coordinate and the variables used in the adaptive tential perturbations in the grid column above. de®nition of gridpoint placement in each vertical col- The minimum pressure spacing in the RUC is applied umn. only between the ground and 600 hPa and is set as 2.5, The maximum value in the RUC20 is 500 K; this 5, 7.5, and 10 hPa in the lowest four layers near the surface is typically found at 45±60 hPa for the opera- surface and 15 hPa at layers above that, providing ad- tional RUC domain, with a latitude range of ϳ15Њ± 60ЊN. A characteristic of the RUC hybrid coordinate is that more levels ``pile up'' near the surface in warmer TABLE 1. Target values (K) for the RUC20 (50 levels). areas, while more of the vertical domain is de®ned using Level 12345678910 isentropic surfaces in colder areas. This behavior, which is bene®cial, as it tends to provide high near-surface 224 232 240 245 250 255 260 265 270 273 level 11 12 13 14 15 16 17 18 19 20 TABLE 2. De®nition of 3D pressure ®eld contrasted in ±pressure 276 279 282 285 288 291 294 296 298 300 vs ± generalized vertical coordinates. Variables for which prede- level 21 22 23 24 25 26 27 28 29 30 ®ned values (as a function of vertical level K) must be set are shown for each coordinate system, as well as the variables used in the adap-
302 304 306 308 310 312 314 316 318 320 tive de®nition of the 3D pressure ®eld. level 31 32 33 34 35 36 37 38 39 40 pressure ± generalized 322 325 328 331 334 337 340 343 346 349 Prede®ned p(k) ⌬pmin p level 41 42 43 44 45 46 47 48 49 50 top - ref(k) Adaptively based on psfc psfc
352 355 359 365 372 385 400 422 450 500
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FIG. 3. Vertical cross sections of RUC native coordinate levels, with vertical axis as coordinate
level (1±50), for same winter case shown in Fig. 2: (a) p (contour interval is 25 hPa) and (b) (contour interval is 4 K).
vertical resolution for convective boundary layer mod- United States, with a lowered tropopause and frontal eling during the warm season and year-round at low zones extending to the surface on both sides. latitudes, is apparent in Fig. 1. The case shown here is Alternative perspectives of this same cross section from 2 April 2002, with the cross section extending from are shown in Fig. 3, with pressure (Fig. 3a) and virtual Mississippi (on the left-hand side) northward through potential temperature (Fig. 3b) both as functions of gen- Wisconsin (center point), across Lake Superior (slightly eralized coordinate level (k). These perspectives may be higher terrain on each side), and ending in western On- compared with the more familiar presentation in Fig. 2 tario, Canada. A frontal zone is present in the middle to obtain some insights into the RUC hybrid coordinate. of the cross section, where the RUC levels (mostly is- For instance, the versus k cross section (Fig. 3b) entropic) between 700 and 300 hPa are strongly sloped. shows that well over half of the generalized grid points
In the RUC20, the isentropic levels from 270 to 355 K in this depiction are resolved as isentropic levels [ are resolved with no more than 3-K spacing (Table 1). ϭ Ϫref(k)] for this winter case. The layer (where The adaptive variability of the generalized hybrid ± generalized vertical levels have been resolved as lev- coordinate used in the RUC is further explored in Fig. els) is deepest (in k space) at this time over the Rocky 2 (a west±east vertical cross section of RUC hybrid Mountains because of the combination of a relatively levels for a winter case) and Fig. 3. The cross section warm air mass and the lower surface pressure together in Fig. 2, also shown in the companion paper on the with the minimum pressure thickness constraint. The RUC assimilation system (Benjamin et al. 2004), is daytime boundary layer is represented in k space as west±east across the United States, passing south of San nearly vertical isotherms of isopleths near the surface Francisco, California, through the eastern slopes of the (Fig. 3b). Rocky Mountains in Colorado (where a mountain wave The pressure versus k cross section (Fig. 3a) depicts is evident between 300 and 600 hPa), and through south- pressure thickness between k levels (⌬p/⌬s, where s is ern Virginia on the East Coast. Again, as in Fig. 1, the the generalized vertical coordinate using the level k), typical higher resolution using the RUC coordinate near larger where isobars are closely packed. In the ``isen- fronts and the tropopause is apparent, as is the piling tropic levels'' where spacing is constant, the closeness -. Closely packed isoץ/pץ up of terrain-following levels in warmer regions (over of isobars is proportional to the Paci®c Ocean at the left-hand side of the ®gure, in bars in these isentropic levels represent lower thermal this case). A classic cold dome is evident over the central stability, common in the upper troposphere, whereas
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FIG. 4. Same as Fig. 3, except for a summer case (1200 UTC 23 May 2000) instead of a winter case. Horizontal location is same as in Figs. 2 and 3, west±east across the RUC domain, through California, Colorado, and Virginia.
Vץ pץ V V 2ץ -more loosely spaced isobars represent ``thin'' RUC lay ١s ϩ ( ϩ f )k ϫ V ϩ sÇ ers with higher static stability. These stable layers are ϩ pץ sץt 2 ץ found in the stratosphere and are found also at lower k 2 (V) ϩ F. (3 ٌ ´ ١)´ ١ ϩ levels where the tropopause is lower in the main upper- ϭϪ١sssssM ϩ⌸١ level trough associated with the cold dome located to y)s is the relativeץ/uץ) x)s Ϫץ/ץ) the east (right) of the center of the cross section. In this equation, ϭ vorticity, M ϭ ϩ⌸ is the Montgomery potential, To provide a seasonal contrast in the behavior of the R/Cp ϭ gz is the geopotential, and ⌸ϭCp(p/p 0)is# RUC hybrid coordinate, pressure versus k and versus k cross sections are presented in Fig. 4 for a summer the Exner function. The horizontal diffusion coef®cient case (25 July 2001) for the same west±east line as in is based on horizontal deformation in the wind ®eld Fig. 3. In this summer case, a much higher percentage (Smagorinsky 1963) and is enhanced within ®ve rows of the RUC hybrid levels are resolved as terrain-fol- of lateral boundaries and in the top three layers as an lowing levels, about 30 out of the 50 levels (Fig. 4b). upper-level sponge. Otherwise, if there is no deforma- The boundary layer depth in k space is shallow, except tion, no momentum diffusion is performed. The variable over oceans, and in this case valid at 1200 UTC (early F represents the effects of vertical turbulent mixing (sec- morning) . tion 5e). The continuity equation, pץ pץץ pץ pץץ b. Basic governing equations (4) , ١ ´ ١ ١sss´ V ϩ sÇ ϭ ϩ s ץs ץs ץs ץs ץtץ For completeness, the governing equations presented by BB93 are repeated here with some modi®cations can also be thought of as a tendency equation for mass consistent with the current RUC con®guration. All of thickness between levels. Diffusion is applied only in these equations are written for the generalized vertical the top three layers as part of the sponge near the top coordinate s and are solved on all horizontal surfaces, boundary. whether they are purely , purely , or some combi- The thermodynamic equation nation. All horizontal and temporal derivatives are eval- ץ pץ ץ (2 ) ϩ ˙ (5ٌ ´ ١)´ ١ ϩ sÇ ϭ ١ ´ uated on s surfaces. ϩ V p sssץ sץ t s ץ The horizontal momentum equation is written
Unauthenticated | Downloaded 09/29/21 03:20 PM UTC FEBRUARY 2004 BENJAMIN ET AL. 479 is solved at all points, whether or not they happen to TABLE 3. Frequency of calls to physical parameterizations in RUC20. lie on target surfaces. If there are no diabatic effects and the generalized coordinate surface is fully isentro- Physical parameterization RUC20 frequency (min) pic, this equation collapses to Cloud microphysics 2 Convection 2ץ ϭ 0. Turbulence 2 t Land surface 2ץ Shortwave radiation 30 The source/sink term ˙ refers to diabatic processes de- Longwave radiation 60 scribed in section 5. The moisture conservation equation q based on the outcome of the regridding process (sectionץ pץqaaץ (2q ) ϩ qÇ (6ٌ ´ ١)´ ١ q ϩ sÇ ϭ ١ ´ ϩ V p s s s a a 4a). Next, the thermodynamic equation (5) exceptingץ sץt saץ vertical advection is solved forward in time. The ad- represents advection and horizontal diffusion processes vective form of the Smolarkiewicz (1983) positive def- applied to several moisture variables represented ge- inite advection scheme (appendix B of BB93) is used nerically by qa. The symbol qa represents mixing ratios for the horizontal advection of and all moisture var- of water vapor (q), cloud water (qc), cloud ice (qi), iables. The conservation equation for moisture variables rainwater (qr), snow (qs), and graupel (qg). The cloud (6) is then solved, also forward in time and without microphysics interactions between these variables and vertical advection. Fourth-order diffusion is applied to their source and sink terms are explained in more detail and water vapor mixing ratio. in section 5a. The full source/sink term q for all mois- a At this point, new provisional values (de®ned with ) ture variables has potential contributions from many of are available for pressure thickness (and pressure, pà the physical parameterizations in section 5, including from vertical summation of the pressure thicknesses), resolved and subgrid-scale cloud processes and turbu- ˆ , and all moisture variables, qà a, based on the solutions lent mixing. to (4)±(6). These new values are then used as input to As explained in BB93, Eqs. (3)±(5) form a closed set the physical parameterizations (mixed-phase stable of equations, if there is no diabatic forcing, with the cloud microphysics, convective clouds, turbulent mix- addition of a hydrostatic equation and a de®nition of ing, radiation and land surface processes) described in the vertical coordinate s. The pressure gradient term in section 5, depending on the time splitting described in the momentum equation (3) is written in terms of M, section 5f. Tendency terms from physical parameteri- ⌸, and .Inthe domain near the surface where zations are applied at this point in each time step, up- is not constant horizontally, this pressure gradient term dating ˆ and qà a, but the tendencies themselves are up- is de®ned with two terms with the attendant potential dated only at the frequency shown in Table 3 in section for cancellation errors. However, in the isentropic do- 5f. The updated ˆ and qà a are used as input to the land main above the surface where is constant horizontally, surface model, which determines energy and moisture the pressure gradient in the RUC model has only one budgets at the surface to couple the atmospheric and -١sM. Thus, it is convenient to de®ne the hydro ,term soil domains. Updated values of pà and ˆ are then used static equation with the Montgomery potential as for a reintegration of the hydrostatic equation (7) to .M update Mץ ϭ⌸. (7) The momentum equation (3) is now solved using aץ second-order Adams±Bashforth scheme for the hori- zontal advection term. The Coriolis terms for the u (and ) components are calculated using the new values of c. Time integration (or u) at alternating time steps to assure that these The time integration of RUC model equations over terms are centered in time. a single time step may be viewed as consisting of two At this point, completing part 1 of the time integra- parts; ®rst, the model equations are solved as if the tion, all of the equations have been solved in a gener- model were a material coordinate model, and, second, alized vertical coordinate, with no accounting for its the vertical regridding described in section 4a is carried speci®c structure. Now (Table 2), the algorithm is ap- out. The ®rst part begins with a forward-in-time solution plied to vertically regrid all variables to the hybrid ± of the continuity equation (4) using the ¯ux-corrected coordinate, restoring to the minimum pressure spacing transport algorithm of Zalesak (1979), a positive de®nite and target values described in section 4a (part 2). scheme that prevents zero or negative pressure thick- Finally, values of all variables (except hydrometeors) nesses. In other words, the layers expand or contract are nudged at and near lateral boundaries toward values based on the horizontal mass ¯ux convergence in the from some external model (the NCEP Eta Model is typ- second term of (4) in a manner reminiscent of material ically used) using the Davies and Turner (1977) ap- coordinates, but layer thicknesses are later readjusted proach.
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The horizontal grid in the RUC model is de®ned as gation of snow crystals at temperatures near freezing, the Arakawa C grid (Arakawa and Lamb 1977), in which and the formation of supercooled liquid water, are all u and grid points are each offset from mass points to included. This explicit mixed-phase prediction is dif- improve numerical accuracy. There is no vertical stag- ferent from the diagnostic mixed-phase prediction used gering, meaning that all prognostic variables are de®ned in the Eta-12 (Ferrier et al. 2002). In the RUC model, on the s-coordinate full levels, rather than at half levels. all six cloud/hydrometeor variables are carried as dis- A full vertical velocity is diagnosed in the RUC model tinct predicted variables and so are advected horizon- as tally (on the hybrid coordinate surfaces) and vertically (section 4c). Fallout of rain, snow, and ice particles is pץ pץ ١s p, (8) considered separately from vertical advection through ´ ϭ sÇ ϩϩV .tΗs coordinate surfacesץ sץ A primary motivation for introducing such a complex where the ®rst term is the vertical motion through co- scheme into an operational model is to provide better ordinate surfaces, the second term is the vertical motion guidance, via explicit prediction of supercooled liquid of the coordinate surfaces, and the third term is the water, for forecasts of regions where aircraft icing is vertical motion along coordinate surfaces. The di- likely. The present version of the scheme is a direct agnostic is not a part of the RUC prognostic equation outgrowth of long-term (and continuing) active collab- set. oration with scientists at NCAR under partial sponsor- ship of the Federal Aviation Administration. With the 5. Physical parameterizations paucity of comprehensive observational datasets, a cru- cial aspect of this work has been the use of results from The RUC model includes a set of parameterizations a very detailed and computationally intensive bin mi- of physical processes that are generally equivalent in crophysical scheme implemented in a 2D version of sophistication to those used in other operational regional MM5 (Rasmussen et al. 2002) as a sort of ground truth models, including NCEP's Eta Model (Rogers et al. for evaluating the performance of prototype revisions 2001) and the Canadian Meteorological Centre (CMC) of the present bulk scheme. Global Environmental Multiscale (GEM) Model (CoÃte The details of the latest version of the scheme are et al. 1998). These parameterizations are all applied col- described in Thompson et al. (2004). These represent a umnwise without any special treatment needed for the considerable revision from the original scheme as de- RUC vertical coordinate, and the frequency of their ap- scribed in RRB and originally implemented in the RUC plication is discussed at the end of this section. in April 1998. This earlier version produced unrealistic amounts of graupel and insuf®cient supercooled liquid a. Mixed-phase bulk cloud microphysics water. The new version of the scheme, now operational in the RUC20, exhibits much improved predictions of The RUC model uses an updated version of the ex- supercooled liquid water as well as precipitation type plicit mixed-phase bulk cloud microphysics originally at the ground. Continued enhancements to the RUC mi- described as the ``level 4'' scheme of Reisner et al. 1998 crophysics scheme are expected, with a focus on ice (hereafter RRB), originally applied in the ®fth-genera- nucleation and explicit prediction of freezing drizzle in tion Pennsylvania State University±National Center for weakly forced synoptic situations. Atmospheric Research (PSU±NCAR) Mesoscale Model (MM5; Grell et al. 1994). This microphysics routine explicitly predicts the mixing ratios of cloud water (qc; b. Convective parameterization very small droplets that travel with the air), rainwater
(qr; larger water drops that fall relative to the air), cloud A new convective parameterization (Grell and De- ice (qi; pristine or slightly rimed ice particles that are venyi 2002) is used in the RUC20. This parameteriza- small and fall slowly), snow (qs; larger ice crystals or tion is based on a very simple convective scheme de- aggregates of larger crystals, possibly rimed) and grau- veloped by Grell (1993) and discussed in more detail pel [qg; heavily rimed ice particles (snow pellets) or by Grell et al. (1994). For the RUC20 implementation, frozen raindrops (ice pellets) that are denser than snow the original scheme was ®rst expanded to include lateral and may fall more rapidly], as well as the number con- entrainment and detrainment, including detrainment of centration of cloud ice particles (Ni). Sources, sinks, cloud water and ice to the microphysics scheme dis- and conversion processes between these categories in- cussed in the previous section. In addition, the scheme clude representations for all the major recognized mi- draws on uncertainties in convective parameterizations crophysical processes (Fig. 5). For example, ice nucle- by allowing an ensemble of various closure and feed- ation and cloud condensation, deposition and riming on back assumptions (relating to how the explicitly pre- frozen hydrometeors, sublimation and evaporation, ice dicted ¯ow modi®es the parameterized convection, multiplication when ice particles collide with raindrops which in turn modi®es the environment) to be used ev- at temperatures just below freezing, enhanced aggre- ery time the parameterization is called. The four main
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FIG. 5. Schematic of the mixed-phase bulk microphysics scheme in the operational RUC20. Sedimentation of ice is allowed, but ice generally sublimates, or melts to become cloud water that evaporates, before reaching the ground. (Courtesy of the COMET Program.) groups of closures that are used in the RUC20 appli- The application of the Grell±Devenyi (2002) con- cation are based on removal of convective available vective scheme in the RUC model also includes a re- potential energy (CAPE) (Kain and Fritsch 1992; Fritsch moval of the negative buoyancy capping constraint at and Chappell 1980), destabilization effects (Arakawa the initial time of each model forecast in areas where and Schubert 1974; Grell et al. 1994), moisture con- the Geostationary Operational Environmental Satellite vergence (Krishnamurti et al. 1983), and low-level ver- (GOES) sounder effective cloud amount (Schreiner et tical velocity (Frank and Cohen 1987). al. 2001) indicates that convection may be present. This These four groups are then perturbed by 27 variations technique can aid modeled convection in starting at grid of sensitive parameters related to feedback as well as points where observed if there is positive CAPE, al- strength of convection, giving a total of 108 ensemble though it cannot create positive CAPE. In addition, an members that contribute to the convective scheme. Out- upstream dependence is introduced through relaxation put from the parameterization includes the ensemble of stability (convective inhibition) constraints at adja- mean, the most probable value, and a probability density cent downstream points based on 0±5 km above ground function, as well as other statistical values (see also level mean wind and through allowing the downdraft Grell and Devenyi 2002). Currently, only the ensemble mass ¯ux at the previous convective time step to force mean is fed back to the dynamic model. convection at the downstream location.
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FIG. 6. Schematic presentation of the surface processes in the RUC land surface model. (Courtesy of the COMET Program.) c. Land surface physics provided by the mixed-phase cloud microphysics rou- tine (see section 5a). In the RUC20, the convective pa- Forecasts of near-surface conditions and boundary rameterization (section 5b) also contributes to the snow layer processes in the RUC model are dependent on accumulation if the surface air temperature is at or below accurate estimates of surface ¯uxes, and in turn, on reasonably accurate soil moisture and temperature es- 0ЊC. With or without snow cover, surface runoff occurs timates provided by the RUC land surface model (LSM; if the rate at which liquid phase becomes available for Smirnova et al. 1997, 2000b). The RUC LSM contains in®ltration at the ground surface exceeds the maximum a multilevel soil model, treatment of vegetation, and a in®ltration rate. The solid phase in the form of snow or two-layer snow model, all operating on the same hor- graupel (treated identically by the LSM) is accumulated izontal grid as the atmospheric model. It solves heat and on the ground/snow surface to subsequently affect soil moisture transfer equations at six levels for each soil hydrology and thermodynamics of the low atmosphere. column, together with the energy and moisture budget The most recent version of the LSM implemented in equations for the ground surface, and uses an implicit the RUC20 has a number of improvements in the treat- scheme for the computation of the surface ¯uxes. The ment of snow cover over those described in Smirnova energy and moisture budgets are applied to a thin layer et al. (2000b). It allows evolution of snow density as a spanning the ground surface and including both the soil function of snow age and depth, the potential for re- and the atmosphere with corresponding heat capacities freezing of melted water inside the snowpack, and sim- and densities (Fig. 6). (The budget formulation over a ple representation of patchy snow through reduction of layer rather than at the skin level is one of the primary the albedo when the snow depth is small. If the snow differences between the RUC LSM and LSMs in other layer is thinner than a 2-cm threshold, it is combined operational models.) The RUC frozen soil parameteri- with the top soil layer to permit a more accurate solution zation considers latent heat of phase changes in soil by of the energy budget. This strategy gives improved pre- applying an apparent heat capacity, augmented to ac- diction of nighttime surface temperatures under clear count for phase changes inside the soil, to the heat trans- conditions and melting of shallow snow cover. fer equation in frozen soil in place of the volumetric In applications of the RUC LSM in current and pre- heat capacity for unfrozen soil. The effect of ice in soil vious versions of the RUC, volumetric soil moisture and on water transport is also considered in formulating the soil temperature at the six soil model levels, as well as hydraulic and diffusional conductivities. canopy water, snow depth, and snow temperature are Accumulation of precipitation at the surface, as well cycled. In the RUC20, cycling of the temperature of the as its partitioning between liquid and solid phases, is second snow layer (where needed) is also performed.
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The RUC continues to be unique among NCEP oper- trace constituent. Johnson et al. (2000) extended this ational models in its speci®cation of snow cover and study to examine the treatment of moist reversible pro- snow water content through cycling (Smirnova et al. cesses and conservation of equvalent potential temper-
2000a). The two-layer snow model in the RUC20 im- ature (e) with the same two models. In all of these proves the evolution of these ®elds, especially in spring- studies, the key issue is the degree of cross-coordinate time, more accurately depicting the snow melting season vertical transport causing aphysical diffusion. As shown and spring spike in total runoff. by Johnson et al. (2000), the UW ± model conserves
e with greater ®delity overall at higher levels where the grid is purely isentropic than near the surface, where d. Atmospheric radiation the solution is dominated by terrain-following numerics. The RUC model uses a variation of the atmospheric Johnson et al. (2002) performed additional diagnostics radiation package developed by Dudhia (1989) and used on these experiments to stratify components of the errors with MM5, with additions for attenuation and scattering in the UW and CCM models. by all hydrometeor types, including graupel. This The RUC model is applied operationally at much scheme is a broadband scheme with separate compo- smaller grid lengths than the UW ± global model; nents for longwave and shortwave radiation. hence, extrema of diabatic processes are much more pronounced than on a coarse scale. Moreover, its pur- pose is operational prediction of signi®cant weather e. Turbulent mixing events often characterized by strong diabatic effects. The RUC prescribes turbulent mixing at all levels, Therefore, it is of interest to examine the behavior of including the boundary layer, via the level 3.0 turbu- cross-coordinate vertical transport and ability to con- lence scheme of Burk and Thompson (1989), with ex- serve e for moist reversible processes in the RUC mod- plicit forecast of turbulent kinetic energy and three other el with its mesoscale application. turbulence variables. The surface layer mixing continues A set of experiments was carried out with the RUC to be prescribed by Monin±Obukhov similarity theory, model to investigate these issues. Alternative versions speci®cally the three-layer scheme described in Pan et of the model were developed, one with the hybrid ± al. (1994). coordinate de®nition and one using a ``®xed'' -coor- dinate de®nition. The -coordinate version of the RUC model was de®ned by setting an initial 3D sigma ®eld f. Time splitting for physical parameterizations [(i, j, k)] and then forcing this ®eld to remain ®xed As with other mesoscale models, the RUC model during the model integration. All other numerical tech- gains ef®ciency by use of a time-splitting scheme in niques and physical parameterizations described in sec- which physical parameterizations use time steps longer tions 4 and 5 were used in both versions of the model. than the dynamical time step. The time step used in the The version of the RUC model is designed not to be 20-km RUC model for each physical parameterization a competitive forecast model but only to provide a con- is shown in Table 3. Tendencies to the predictive var- trolled comparison with the ± version for the exper- iables calculated in these parameterizations are applied iments described in this section. To eliminate any issues at each dynamical time step, avoiding the shock that from coordinate differences associated with lateral would result from applying them only when the param- boundary conditions, all experiments were performed eterizations are evaluated. with constant boundary conditions. Two cases with 24- h forecasts were run, a warm-season case initialized at 1200 UTC 23 May 2000 and a cold-season case at 1200 6. Experiments on cross-coordinate vertical UTC 8 February 2001. transport and moist reversibility using RUC The results from these experiments, shown in the fol- with different vertical coordinate lowing sections, are in¯uenced by the degree to which representations grid points in the 3D domain are resolved as isentropic Johnson (1997) documents that the aphysical sources or sigma levels. Figure 7 shows the fraction of the do- of entropy in numerical integration include dispersion main resolved on isentropic levels by number of grid from vertical advection. As noted by Johnson, some points and by mass for the summer and winter cases numerical dispersion is inevitable in Eulerian calcula- shown. This fraction can change over time, but it tions. Zapotocny et al. (1996, 1997a,b) and Johnson et changed by less than 1% over 24 h in these cases, so al. (2000, 2002) document resulting nonreversibility of the values at the 12-h forecast time are shown. Consis- transport processes with diagnostic conservation tests tent with the structures shown in Figs. 3 and 4 and in two different global models, the UW ± hybrid explained in section 4a, the RUC hybrid coordinate is model and the NCAR Community Climate Model expected to resolve more levels as isentropic in colder (CCM), a -coordinate model. Zapotocny et al. (1996, areas and colder seasons. Assuming an average surface 1997a,b) examined the ability of these models to con- pressure of 1000 hPa over the RUC domain, this implies serve potential vorticity and extrema of a hypothetical that the average depth of the sigma domain is about 220
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FIG. 8. Mean absolute cross-coordinate vertical transport s)) | ] for May 2000 expts 1 and 3. Units are 0.01 hPa (timeץ/pץ)FIG. 7. Fraction of 3D domain resolved as isentropic levels in RUC [|(sÇ hybrid coordinate experiment for warm- and cold-season cases as a step)Ϫ1. Averaged over vertical levels (not mass averaged). function of (i, j, k) grid points and as a function of mass (accounting for variable layer thicknesses). boundary layer depth averaged over the North American RUC domain. hPa in the cold-season case and 320 hPa in the warm- Next, the cross-coordinate transport from expt 1 (con- season case. trol) is broken down into a mean value in the domain versus that in the domain. As shown in Fig. 9, the mean absolute cross-coordinate transport is about 6±9 a. Cross-coordinate vertical transport times larger in the domain than in the domain. It The primary diagnostic quantity examined in this ®rst may also be noted from Fig. 9 that the late-afternoon set of experiments was the mean (domainwide) absolute peak in cross-coordinate transport is found only in the value of the cross-coordinate vertical transport, domain but not in the domain, showing that this s)] | (calculated every 10 min). Three experi- diurnal variation is located in the lower troposphereץ/pץ)sÇ]| ments were run for both the warm-season (23 May 2000) rather than the middle and upper troposphere, which are and cold-season (8 February 2001) cases: predominantly represented isentropically. A possible explanation for the difference in cross- 1) hybrid isentropic sigma with full moist and boundary coordinate transport between expts 1 (hybrid) and 3 layer physics (control), 2) hybrid isentropic sigma with no moist or boundary layer physics, 3) ®xed sigma with full moist and boundary layer phys- ics. Results are ®rst presented for the May 2000 case, which was characterized by strong convection and some severe weather (wind gusts, hail, tornadoes) stretching from New England southwestward to Oklahoma. Averaged over the vertical levels of the model, the cross-coordinate vertical transport is clearly smaller (Fig. 8) with the quasi-isentropic coordinate (expt 1), about 60%±70% of that from the ®xed coordinate run (expt 3). Since the layers between adjacent levels in this warm-season case are somewhat thinner, on aver- age, than those between adjacent levels, this ratio would be somewhat smaller still if the transport from both experiments were mass averaged. Figure 8 also shows a peak in cross-coordinate transport in the late FIG. 9. Mean absolute cross-coordinate vertical transport for May afternoon (about 2300 UTC), corresponding approxi- 2000 expt 1 (controlÐhybrid vertical coordinate) strati®ed into vs mately to the time of maximum surface temperature and parts of the domain and averaged over vertical levels.
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FIG. 10. The 3-h precipitation for 0900±1200 UTC 24 May 2000 for forecasts initialized at 1200 UTC 23 May for (left) expt 1 (hybrid) and (right) expt 3 (®xed). Contour interval is 0.5 cm (3 h)Ϫ1.
(®xed) could have been a major difference in precipi- main tracks fairly closely in the two experiments. The tation behavior. Figure 10 shows 3-h precipitation be- total (resolved plus subgrid-scale) precipitation has one tween 9 and 12 h from the initial time for both expts 1 maximum near 2000 UTC, 8 h into the forecast, and and 3, and the domain-averaged precipitation rate from another at the end of the forecast period at 1200 UTC. both experiments as a function of time over the 24-h These maxima do not correspond closely to the peak forecast period is depicted in Fig. 11. The 3-h precip- cross-coordinate transport shown in Fig. 8. Overall, this itation (Fig. 10) shows local differences but similar pat- suggests that the cross-coordinate transport peak in Fig. terns from the two experiments, with slightly more pre- 8 is associated with increased vertical motion in the cipitation from the hybrid model (expt 1) in a band from boundary layer but not from increased precipitation at James Bay through southern New England. The domain- that time. averaged precipitation (Fig. 11) over the full RUC do- The contrast between cross-coordinate transport in the and domains is most pronounced, as might be ex- pected, in expt 2, from which moist and boundary layer physics were excluded (Fig. 12). In this no-physics run in which the only diabatic process is diffusion, the cross- coordinate transport is about 50±60 times smaller in the domain than in the domain. The absence of the 2300 UTC peak in cross-coordinate transport in expt 2, com- bined with the precipitation results shown in Figs. 10 and 11, again points to heating-induced boundary layer vertical motion as the cause of the peak in expt 1. The same set of experiments was also run for the cold-season case of 8 February 2001, with an initial time of 1200 UTC. Here, the mean absolute cross-co- ordinate transport in the hybrid ±, averaged by levels rather than mass, was reduced by 50% over the ®xed model (Fig. 13). The cross-coordinate transport again showed a very large reduction at the levels compared to levels, down by a factor of about 7 with full diabatic physics. When no moist or boundary layer physics were FIG. 11. Averaged precipitation (resolved and subgrid-scale) over domain for May 2000 expts 1 (control) and 3 (®xed sigma). Units allowed in the hybrid model run (expt 2), the cross- are 0.001 mm (10 min)Ϫ1. Horizontal axis is time over 24-h period. coordinate vertical transport was reduced again by a
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FIG. 12. Mean absolute cross-coordinate vertical transport for expt 1 (controlÐhybrid including full moist and boundary layer physics) FIG. 13. Same as Fig. 8, but for winter case (8 Feb 2001). and expt 2 (hybrid with no moist or boundary layer physics). Values are plotted for both and parts of the domain and averaged over vertical levels. cloud microphysics was modi®ed to include only water saturation and latent heating from condensation. These factor of 50±60 (Fig. 14), this time for a cold-season modi®cations to the RUC model to better approximate case. moist reversibility were applied both to the ± and
versions. Empirical frequency distributions of (e±te) b. Moist reversibility experiments were calculated for 24-h forecasts over all grid points in the model domain, and speci®cally at levels 10 (lower A problem in atmospheric prediction at all time troposphere) and 40 (near tropopause) of 50 levels. The scales, from short-range weather prediction to climate results comparing ± and versions of the RUC model prediction, is accurate simulation of reversible process- proved to be very similar to those from Johnson et al. es. Zapotocny et al. (1996, 1997a,b) studied the ability (2000, 2002) comparing the UW ± model and CCM. of different global models, including the UW ± mod- For the warm-season case, the frequency distributions el, to conserve equivalent potential temperature, poten- of (e±te) are shown in Fig. 15 for all levels combined, tial vorticity versus a proxy ozone tracer variable, and level 10 only, and level 40 only. With 0.1-K class in- extrema of this tracer variable. Johnson et al. (2000, tervals, the probability density function (PDF) for all 2002) extended this work to study the ability of these levels combined (Fig. 15a) reaches a mode value of global models to conserve moist entropy, as follows. A about 0.5 for the ± model but only about 0.1 for the proxy ®eld of equivalent potential temperature (desig- model. There is very little difference in the frequency nated as te) was set to initially match the actual e ®eld. Equations in the model were simpli®ed to corre- spond to moist reversible isentropic processes. The proxy te variable was advected as a tracer and then compared to e calculated from model ®elds of , water vapor, and pressure at forecast durations of up to 10 days. The experiments of Johnson et al. (2000, 2002) have been repeated here for 24-h forecasts using the limited- area RUC model, comparing the moist reversibility of the ± and versions. Speci®cally, the degree of con- servation of e is compared. Experiments were carried out for the same warm-season and cold-season cases used for the experiments described in section 7a. As done by Johnson et al., initial values of te were cal- culated using the formulation of Bolton (1980). The proxy te was advected using the horizontal and vertical advection schemes described in section 4. Parameteri- zations for radiative, turbulent mixing, land surface, and convective processes were turned off. The mixed-phase FIG. 14. Same as Fig. 12, but for winter expt.
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FIG. 15. Empirical relative frequency distributions, PDF
of simulated differences of e, and proxy e from RUC ± (solid) and (dashed) versions for 24-h forecasts from warm-season case initialized at 1200 UTC 23 May 2000. Bin width is 0.1 K, vertical axis is PDF, and horizontal axis is temperature difference in K. (a) All levels com- bined, (b) level 10 only, and (c) level 40 only. Note dif- ferent vertical scales for (a)±(c).
distribution at level 10 (Fig. 15b), which is well within tion of grid points are resolved as isentropic levels (Fig. the range over almost all of the horizontal domain for 7). The improved accuracy of moist reversible processes this warm-season case. At level 40 (Fig. 15c), which is in the RUC ± model compared to the RUC model resolved entirely as an isentropic level in the ± model, is even more pronounced in this case. The peak fre- the frequency distribution is most different, reaching quencies near zero are considerably higher for the ± over 1.0 for the hybrid model but only about 0.12 for model in this case, reaching 2.0 for level 40, and even the sigma model. These results show that the simulation 0.25 at level 10 (compared to 0.1 for the model). In of moist reversible processes is much more accurate in contrast, the peak frequencies for the model are about the RUC ± model than in the RUC model, which 0.1 regardless of level and regardless of season. Overall, does not bene®t from any isentropic representation and the use of isentropic coordinates in the RUC hybrid ± therefore has larger cross-coordinate vertical transport model results in much higher accuracy for moist re- (section 6a). versible processes in both warm-season and cold-season The same frequency distributions were calculated for simulations at 20-km resolution. The poorer conserva- the cold-season case (Fig. 16), where a greater propor- tion by the RUC model may be due, in part, to use
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FIG. 16. Same as Fig. 15, but for cold-season case, 24-h forecast initialized at 1200 UTC 8 Feb 2001.
of low-order vertical advection numerics. However, the model for a cyclogenesis case (1200 UTC 4 February± experiments nevertheless con®rm the much lower sus- 0000 UTC 6 February 2001) along the east coast of the ceptibility to truncation errors in the ± model from United States. Initial conditions for this case are pro- decreased cross-coordinate vertical transport. Moreover, vided by the RUC analysis (Benjamin et al. 2004). the differences in accuracy reported in these mesoscale Lateral boundary conditions are prescribed from the op- tests with the RUC model are very similar to those erational Eta Model initialized at 1200 UTC 4 February. shown by Johnson et al. (2000, 2002) between the UW We will concentrate on a quasi-isentropic perspective ± and the CCM global models. for this case, using maps of the pressure of the dynamic tropopause [de®ned as the ®rst pressure, starting from the top of each column of the native hybrid ± grid, 7. Case study at which potential vorticity (PV) drops below 2.0 PVU] In this section, a brief case study of 36-h forecasts is as an indicator of the overall upper-level dynamics. At presented using 20- and 10-km versions of the RUC the 12-h forecast (valid 0000 UTC 5 February), the
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FIG. 17. Pressure (hPa) of the dynamic tropopause from 20-km RUC forecast initialized at 1200 UTC 4 Feb 2001: (a) 12-, (b) 24-, and (c) 36-h forecast. Line through eastern part of domain is the location of vertical cross sections shown in Fig. 20.
tropopause pressure (Fig. 17a) shows a major wave with evolution shows a weak surface low near Chicago, Il- a slight positive tilt over the eastern United States, with linois, (not shown) at the initial time. A surface front a base near the Arkansas±Louisiana border and embed- present at this time over the Florida peninsula and ex- ded waves over Illinois and Michigan. These three fea- tending northeastward into the Atlantic also played a tures are traceable to the 24-h forecast of tropopause role in the later development. By the 12-h forecast time pressure (Fig. 17b), at which time the base of the wave (Fig. 17a), the Midwest low had drifted over Michigan is located over southern Alabama and the embedded without intensi®cation. Of more signi®cance was a waves are merging over the southern Appalachians. By 1016-hPa low off the Georgia coast, likely formed in 0000 UTC 6 February (36-h forecast; Fig. 17c), the response to latent heat release in the model forecast. tropopause pressure shows a pronounced negative tilt, By the 24-h forecast time, this surface low, now near with a classic hook of lowered tropopause now rotating Cape Hatteras, North Carolina, had become the dom- north-northeastward over southern New England, with inant feature and had deepened to 1007 hPa. This low a trailing wave off the North Carolina coast. The con- subsequently tracked northeastward in the forecast to tinuity of ®ne ®lamental features in the tropopause and southern Connecticut, deepening to 992 hPa (Figs. 17c, PV in these forecasts is typical for the RUC model. 18a). This position and strength was fairly close to the The corresponding sea level pressure (SLP) ®eld verifying RUC SLP analysis for 0000 UTC 6 February
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FIG. 18. SLP (hPa) valid at 0000 UTC 6 Feb 2001 for (a) 36-h forecast from 20-km RUC, (b) analysis from 20-km RUC, and (c) 36-h forecast from 10-km RUC.
(Fig. 18b), which showed a 992-hPa low south of Nan- UTC 5 February and 0000 UTC 6 February from the tucket Island, Massachusetts. The RUC forecast had 20- and 10-km versions of the RUC both showed sig- tracked the low center too far to the west and had a ni®cant precipitation over New England in association larger envelope of cyclonic circulation than was ob- with the coastal low (Figs. 19a,b). These forecasts may served. The 10-km RUC, one-way nested inside the be compared with the stage IV gauge and radar precip- full 20-km RUC, produced a more realistic 36-h fore- itation estimate from the same 3-h period (Fig. 19c), cast (Fig. 18c) of the cyclonic circulation over New showing that the 20-km RUC forecast too-heavy pre- England and a very accurate estimate of the position cipitation over central New England and back into the of the low, within 50 km. upper Hudson valley over this period. Even the 10-km The 36-h forecasts for the 3-h period between 2100 RUC appeared to overestimate precipitation in south-
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FIG. 19. Estimates of 3-h precipitation (mm) for 2100 UTC 5 Feb±0000 UTC 6 Feb 2001 from (a) 36-h forecast from 20-km RUC, (b) 36-h forecast from 10-km RUC, and (c) stage IV precip- itation estimate from gauge and radar data.
eastern New Hampshire and southern Maine but was latent heat release, is evident along the surface-based still a better forecast. front. Areas of slight negative PV are shown over the Vertical cross sections were taken along a north±south ocean in the marine boundary layer where sensible heat- (with respect to the grid) line through central Connect- ing is occurring, and over Quebec where the absolute icut from the 20-km RUC 36-h forecast of , potential vorticity is slightly negative. The main wave near south- vorticity, relative humidity, and vertical velocity (Fig. ern New England is also associated with dry air sub- 20) to give an additional 3D perspective on the lower- siding to its south to nearly 900 hPa (the dry slot) and and upper-level trough at this time. The three lowered nearly saturated air along the front in a plume up to tropopause undulations apparent in Fig. 20a may be almost 400 hPa (Fig. 20b). This moist air is associated matched to areas of low tropopause pressure evident in with upward vertical motion up to Ϫ80 bsϪ1 in the Fig. 17c, with the central extrusion associated with the 36-h RUC forecast (Fig. 20c). Again, this case is pre- surface cyclone. A center of high PV, associated with sented as a demonstration of interacting dynamical and
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FIG. 20. Vertical cross sections from 36-h forecasts from 20-km RUC model along north±south line shown in Fig. 17c for potential temperature (solid lines; every 4 K): (a) potential vorticity (PVU), (b) relative humidity (%), and (c) vertical velocity (ϫ10 bsϪ1; Ϫ7 ϭϪ70 bsϪ1).
precipitation processes in the RUC model for a case Here the model is applied in various tests at 20- and with strong development. 10-km resolutions (as in real-time real-data applica- tions), much higher resolutions than other hybrid is- entropic models. Furthermore, the RUC model is the 8. Summary only hybrid ± model used for operational prediction The Rapid Update Cycle (RUC) model is a hybrid at this time. isentropic±terrain-following model suitable for meso- One of the primary advantages of modeling in is- scale weather prediction, fully compatible with param- entropic coordinates, reduced cross-coordinate vertical eterizations of diabatic and/or subgrid-scale processes transport, is clearly demonstrated in real-data experi- typically used in operational models of this resolution. ments shown in this paper with full diabatic physics.
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This vertical transport is reduced by 30%±35% for a Two ®gures (5 and 6) are from the Cooperative Program summer case and 50% for a winter case, averaged over for Operational Meteorology, Education, and Training levels. For both cases, cross-coordinate vertical trans- (COMET) Web site at http://www.comet.ucar/edu of the port is lower by factor of 6±9 (reduced by 84%±88%) University Corporation for Atmospheric Research at levels compared to levels. In experiments with (UCAR), funded by the National Weather Service. A no diabatic effects allowed, cross-coordinate vertical Web site on the RUC is available at http:// transport was found to be smaller by a factor of 50±60 ruc.fsl.noaa.gov. (reduced by 98%) at levels compared to levels for both summer and winter cases. The RUC coordinate is able to resolve levels as fully isentropic down into the REFERENCES midtroposphere in summer and lower troposphere in Arakawa, A., and W. H. 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