IMPROVING THE REPRESENTATION OF SNOW IN A BULK SCHEME Christopher P. Woods,

1. IMPROVING THE REPRESENTATION OF SNOW IN A BULK SCHEME Christopher P. Woods, Mark T. Stoelinga, John D. Locatelli, and Peter V. Hobbs University of Washington, Seattle, WA

2. Why work with a “classic” single-moment 5-class bulk scheme? [specifically, the Reisner et al. (1998) / Thompson et al. (2004), or “R-T” scheme]: Sophistication of Grid-resolved Microphysics Low High Intentionally simple schemes (oper. NWP) “Classic” SM 5-class bulk schemes More classes/ More moments/ Gamma dist. Spectrally explicit “bin” schemes • As computer power increases, enhanced sophistication in cloud microphysics will always compete with the desire to: • Increase resolution • Enhance other physics schemes (radiation, PBL, LSM) • Add ensemble members • Improved data assimilation

3. from Reisner et al. (1998) • Why focus on snow? • For many important classes of precipitation, most of the precipitation mass reaching the ground initiated as snow: • * cold-season extratropical cyclonic storms • * cold-cloud orographic precipitation • * stratiform precipitation associated with MCSs • Yet snow is the most complicated species to represent in terms of the variety of particle shapes, densities, and size distribution

4. Three aspects of the representation of snow in bulk schemes: • Size distribution • Shape and density assumptions (i.e., mass-diameter relationship) • Velocity-diameter relationship • A case will be made for: • Choosing a reasonable/relevant habit • Enforcing “habit consistency” throughout the scheme • Diagnosing (as in Meyers et al. 1997) or predicting habit variability

5. Size distribution Integrating the third moment over all sizes yields qs is predicted; specify N0s, and solve for λs; or alternatively, specify λs, and solve for N0s.

6. (a) Intercept (N0s) vs. T 109 Best-fit CT only 108 N0 (m-4) 107 Houze et al (1979) Intercept and slope parameters measured by aircraft particle imagers throughout IMPROVE-1 and IMPROVE-2, as a function of temperature 106 (b) Slope (λs) vs. T 101 λ (mm-1) Houze et al (1979) 100

7. Global ice particle spectra, Ryan (1996) 0.1 mm 1 mm Slope (λs) vs. T Intercept (N0s) vs. T IMPROVE IMPROVE R-T scheme

8. Snow particle shape and density • Many bulk schemes (R-T, Tao and Simpson 1993, Ferrier 1994) assume snow particles are spheres of constant density, implying a mass-diameter relationship of: • However, observational and theoretical studies yield more general, habit-dependent power-law relationships of the form • which can also be implemented in bulk schemes (Cox 1988, Meyers et al. 1997).

9. Constants in the m-D power law relationships for various crystal aggregate types (from Locatelli and Hobbs 1974), and for model snow spheres General expression for relationship between qs, N0s, and λs:

10. 108 107 106 105 104 103 102 101 Variation of spectral slope with particle habit (for fixed values of N0s and qs) Needles Dendrites Cold-type N (m-4) Columns Graupel Model spheres Particle diameter (mm)

11. Snow fall speed • Observational and theoretical studies provide habit-dependent power-law relationship between the terminal fall speed of a particle and its diameter (a V-D relationship) of the form • Combining with the exponential size distribution and the appropriate m-D relationship (for the same particle habit) and integrating, one obtains the mass-weighted terminal fall speed for snow particles of that habit:

12. Mass-weighted terminal fallspeed for various particle habits and snow mixing ratios 1.4 - 1 qs=0.2 g kg - 1 1.2 qs=0.4 g kg - 1 qs=0.6 g kg 1 0.8 Fall speed (m s-1) 0.6 0.4 0.2 0 Model spheres (with cold-type V-D reln.) Dendrites Cold-type Columnar Needle Particle Habit

13. Example: Frontal rainband observed off the Washington coast during IMPROVE-1 (1-2 February 2001)

14. E B 1-hr accumulated precipitation (mm), 500 mb temperature (ºC) How does using an empirical mass-diameter relationship for cold-type crystals (not spheres) affect the simulation?

15. Precipitation band Cloud water mixing ratio (g kg-1) Control Cold-type crystals 0 0.05 0.10 0.15 0.20 0.25 0.30 Precipitation band 105 112 111 104 110 103 Distance (km) Distance (km) B E B E Using M-D relationship from Locatelli and Hobbs (1974) results in: - more reasonable levels of RHi for band with modest vert. vel.(e.g., Lin et. al 2002) - reduced CLW above the melting level – eliminated graupel production

16. Precipitation growth and microphysical processes 12km Control Temperature (°C) 12km Cold-type crystals -0.4 -0.2 0 0.2 0.4 Precipitation rate gradient (mm h-1 hPa-1)

17. Precipitation growth and microphysical processes 12km CTL Temperature (°C) 12km MD -0.4 -0.2 0 0.2 0.4 Precipitation rate gradient (mm h-1 hPa-1) Collection of cloud water by snow

18. 14-h MM5 forecast of 1-h precip, 12-km grid, R-T microphysics Control Cold-type crystals Dendrites

19. Contours: qsnow (g kg-1) qrain (g kg-1) T (ºC) Control 0 0 Cold-type crystals Dendrites 0 0 0 0

20. Contours: precip rate (mm h-1) T (ºC) Control 1 1 2 2 3 0 3 0 Cold-type crystals Dendrites 1 1 1 1 2 2 2 3 2 4 0 0 3 5 3 3 0 0

21. Contours: qsnow (g kg-1) qrain (g kg-1) qrain (g kg-1) Control 46.0 ° OREGON WASHINGTON 45.5 ° PACIFIC OCEAN Willamette Valley Cold-type crystals 45.0 ° Cascade Mountains 44.5 ° 124 ° 123 ° 122 ° 121 ° 13-14 Dec 2001 IMPROVE-2 event

22. Recommendations / Future Work: • Constant density spheres are not a good representation of most snow particle types. • Enforce “habit consistency” for the various habit-dependent aspects of the scheme (size distribution, m-D and V-D relationships, capacitance for depositional growth, etc.) • Examine ways to skew the distribution toward smaller particles when ice enhancement is active. Can this be done without going to a double-moment scheme? • Implement particle habit diagnosis (Meyers et al. 1997) • Develop habit prognosis, to test the effectiveness of the simpler habit diagnosis. Snow particle images collected by the UW Convair-580 during IMPROVE-1

24. Temperature = -10 °C Temperature = -7 °C 2D-C particle imagery Particle size distributions 1 10 -10 °C spectrum -7 °C spectrum 0 0 10 10 No (cm-4) -1 -1 10 10 -2 -2 10 10 -3 10 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Size (µm) • distribution intercept (Nos) and slope (λs) as temperature increased • influx of needle-like particles important to distribution shape

25. snow clw graupel rain

26. Precipitation rate (mm h-1)

28. Summary of observations from Convair-580 flight stack: • In regions where model indicated high ice supersaturation: • measured RH was generally near ice saturation • Negligible liquid water was detected • Ice crystal habits were generally found to be sub-water-saturated types, or inconclusive (notably, no dendrites in the dendritic growth zone)

29. One possible problem with the Rutledge and Hobbs (1983) formulation for growth of snow by deposition (PSDEP): • Although the RH83 equation uses capacitance for a 2-D plate, it assumes the population is comprised of spherical particles. • For a given supersaturation, the mass of a growing particle as a function of time behaves as follows: • 3-D growth (e.g., spherical particle): • 2-D growth (e.g., plate, dendrite): • 1-D growth (e.g., needle): • (Young 1993)

30. N0S(qS) N0S obs N0S(qS) N0S(T) 6.0 km (-20 °C) N0S(T), N0S obs Neither formulation for N0S agrees with the “upside-down” behavior of N0S that was observed in Convair-580 flight tracks during the 13-14 Dec 2001 case. (model spectra from 1.3-km MM5 simulation) 4.9 km (-16 °C)