Robert Hahn & Cliff Mass
University of Washington

• Until recently, several notable mesoscale models did not conserve moisture because of overlooked numerical challenges in advection schemes.
• Advection schemes can introduce both positive and negative errors, particularly when there are sharp gradients.
• This becomes significant when dealing with microphysical quantities because some moisture values can have sharp edges where the quantity goes to zero.
• When negative mass values are generated, models often reset or ‘clip’ these values to zero and moisture is added to the model, artificially.
• Positive Definite Advection (PDA) schemes eliminate non-physical generation of negative values, while conserving mass (see figure).
*graphics from a presentation by Morris Weisman

• Theory indicates that PDA should have it’s greatest effect where large gradients in moisture species are present.
• Both convection and orography induce such large gradients in many microphysical fields.
• Orography also provides temporal stability of the flow pattern and associated microphysical fields, making it ideal for examining the generation of spurious sources of mass in a real-time simulation.

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• Passage of a strong baroclinic zone.
• Cross-barrier flow with winds in excess of 40 m s -1 at crest level.
• Heavy precipitation with deep reflectivity and orographic enhancement.
• Wealth of observational assets providing and in-depth view of dynamic and microphysical characteristics of the storm.
• Vigorous synoptic and orographic forcing combine to make this case ideal for the study of PDA.

• WRF ARW Version 2.2
• Thompson Microphysics
• MRF PBL scheme
• CAM radiation
• Runge-Kutta (RK3) time integration scheme with splitting for stabilization of higher-frequency acoustic modes (Skamarock et al., 2008).
• 5 th order horiz. advective transport
• 3 rd order vert. advective transport

a b
NOPDA PDA-NOPDA
PDA b d
% Difference

• Areas with orography tend to be affected more at coarser grid resolution.
• Grid spacing increases % Difference.
• Even at the lowest resolutions, the effects are significant.

DIFF HORIZ-AVERAGED MIXING RATIO (g kg -1 ) PCT DIFF HORIZ-AVERAGED MIXING RATIO (g kg -1 )

• Small contributions accumulate in time.
• The cloud field in the COAMPS model broaden without the PDA Limiter.
COAMPS-LES results provided courtesy of Dr. Chris Golaz and Jerome Schmidt

Qcloud Advection
Mag. Of Gradient Edge Gradient

• Definition: Positive mixing ratios that touch zero values of like mixing ratios within the plane of the
E-W cross-section shown in previous slide.
• The range of each histogram distribution corresponds to the magnitude of spurious production of moisture in non-PDA schemes.

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• Thompson Scheme (Thompson et al., 2008)
– Assumed snow size distribution depends upon ice water content and temperature.
– Non-spherical snow crystal shape and correspondingly varying bulk density.
– Variable collection efficiency for rain, snow, and graupel collecting cloud droplets.
• Morrison Scheme (Morrison & Grabowski, 2007a,b)
– Builds from the existing double-moment warm rain scheme
• RimedMassFraction

Qrimed
Qrimed

VaporDep
– 3 rd prognostic var: Number concentration of ice.


BIAS

100 *
Model
Obs


BIAS

100 *
Model
Obs

• Undercatchment is expected at most observation sites.
• Garvert et al. (2005) had noted particularly high bias scores over the windward valleys and in the immediate lee of the crest
(simulations performed using MM5, Reisner-2 micro).
• Morrison bias scores are quite large in the immediate lee of the
Cascade Crest for the Morrison, but reasonable in the Thompson.
• Both schemes studied overpredict on the windward slopes. Is there a dependence upon model elevation?
THOMPSON BIAS SCORE MORRISON BIAS SCORE

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=

• Morrison tends to have fewer precipitation hydrometeors than Thompson overall, but slightly more at the lowest altitude.
• Thompson has more cloud.
• The next few panels further illustrate these points.

Morrison Background
Contours = Morrison - Thompson

Morrison Background
Contours = Morrison - Thompson
Signature of excess snow aloft in Thompson

Morrison Background
Contours = Morrison - Thompson

• PDA scheme eliminates a large spurious source of moisture noted at all grid scales.
• PDA was applied uniquely to individual hydrometeor variables.
• Large horizontal gradients in moisture fields induced by orographically generated mountain waves helped generate sharp gradients and strong advections at cloud edges, resulting in strong negative tendencies on upwind side of clouds.
• New Microphysics in WRF Version 3 appears promising.
• Verifications illustrate similar biases to those found by
Garvert et al (2005), but are somewhat improved in the latest Thompson Scheme and did not appear to be model elevation dependent for either Thompson or
Morrison.

• Braun, S.A., 2004: High-Resolution Simulation of Hurricane Bonnie (1998). Part II: Water Budget. J. of Atm.
S., 63, 43-64.
• Garvert, M. F., B. A. Colle, and C. F. Mass, 2005: The 13–14 December 2001 IMPROVE-2 event. Part I:
Synoptic and mesoscale evolution and comparison with a mesoscale model simulation. J. Atmos. Sci., 62,
3474–3492.
• Garvert M. F., B. Smull, and C. Mass, 2007: Multiscale mountain waves influencing a major orographic precipitation event. J. Atmos. Sci., 64, 711–737.
• Lin, Y. and B. A. Colle, 2008: The 4-5 2001 IMPROVE-2 Event: Observed Microphysics and Comparisons
With the Weather Research and Forecasting (WRF) Model. Submitted to Mon. Wea. Rev.
• Medina, S., Sukovich, E., and Houze, R.A., 2007: Vertical Structures in Cyclones Crossing the Oregon
Cascades. Mon. Wea. Rev., 135, 3365–3586.
• Morrison H., and W. W. Grabowski, 2007: Comparison of bulk and bin warm-rain microphysics models using a kinematic framework. J. Atmos. Sci., 64, 2839–2861.
• Morrison H., and W. W. Grabowski, 2008: A Novel Approach for Representing Ice Microphysics in Models:
Description and Tests Using a Kinematic Framework. J. Atmos. Sci., 65, 1528-1548.
• Schmidt, J. M. (personal communication).
• Skamarock, W.C., 2005: Positive-Definite and Monotonic Limiters for Unrestricted-Time-Step Transport
Schemes. Mon. Wea. Rev, 134, 2241-2250.
• Skamarock, W.C. and Weisman, M.L., 2008: The Impact of Positive-Definite Moisture Transport on NWP
Precipitation Forecasts. Submitted: Mon. Wea. Rev. In press.
• Thompson, G., P. F. Field, R. M. Rasumussen, and W. D. Hall: Explicit Forecasts of Winter Precipitation Using an Improved Bulk Microphysics Scheme. Part II: Implementation of a New Snow Parameterization.
Submitted: Mon. Wea. Rev. In press.
• Cotton, W. C. (personal communication).