Subgrid Scale Fluxes (Land surface, surface layer, PBL and SGS turbulence)

1. Subgrid Scale Fluxes(Land surface, surface layer, PBL and SGS turbulence)

2. Radiation

3. Comparison with OK Mesonet Measurements • Plots not available

4. Initial Condition

5. ARPS Components

6. Soil Model Initialization • 1 km soil and vegatation data base • Soil moisture (and T) • Directly from Eta • API • 4DVAR retrieval (under development) • Optionally initialization procedure • To reach a balanced initial state

7. Ways to Initialize ARPS • Idealized, single sounding • Interpolation from GFS, Eta, RUC, etc • ADAS

8. ARPS Data Analysis System (ADAS) • Manages the real time ingest, QC, objective analysis of observations • Doppler radar data (NIDS, base Level II from n systems, VAD) • MDCRS commercial aircraft wind and temperature reports • Wind profilers • RAOBS (conventional, CLASS, dropsondes) • Mobile and fixed mesonets • SAO and METAR observations • GOES satellite visible and IR data for cloud analysis • NCEP gridded model output • Based on Bratseth successive correction method • Handles retrieved radar data (from SDVR et al) • Had its root in FSL LAPS. Data format is about the only one left though.

9. Braseth Analysis Scheme • ADAS use the Bratseth analysis scheme which is a successive correction scheme • The scheme theoretically converges to optimal interpolation (O/I), but without explicit inversion of large matrices • Multi-pass strategy used where more detailed data can be introduced after a few iterations using broad-scale data. • Like OI, the Bratseth method accounts for the relative error between the background and each observation source, and is relatively insensitive to large variations in data density. • Vertical correction in terms of z or q

10. Formulation of Bratseth Scheme

11. Formulation (Continued …)

12. ARPS Data Analysis System (ADAS) • User specifies background error covariances and structure functions. Codes to calculate background error statistics being developed. • Performed on ARPS native (terrain-following) grid • 3-D cloud analysis and diabatic initialization package using GOES, Doppler radar and surface data. • Water vapor, cloud, rain, ice and temperature fields are affected by the cloud analysis • Used to initialize realtime high-res (~kms) forecasts at CAPS since 1996 • Linked closely with ARPS data assimilation system (via, e.g., intermittent assimilation, incremental analysis update method)

13. Incremental Analysis Update Cycles (from Brewster 2003)

15. ADAS analysis – Total u ADAS Background 73x73x43 grid, dx=12km

16. ADAS Analysis– Total q Background ADAS

17. Example of Initial Condition with cloud analysis on a 3km Grid

18. ADAS Cloud Analysis Scheme GOES Visible Image at 1745 UTC on 07 May 1995

19. ADAS Cloud Analysis Scheme Vertical E/W Cross-Section: METAR + GOES IR + WSR-88D

20. ADAS Cloud Analysis Scheme PW and Vertically Integrated Condensate Valid 13 UTC on 12 April 1999 GOES Visible Image Valid 13 UTC on 12 April 1999

21. Application to fine-scale analysis at Kennedy Space Center (Case et al 2002 Wea. Forecasting)

25. ARPS 3DVAR System – Why 3DVAR? Compared to optimal interpolation (OI) or other objective analysis methods, 3DVAR is • Flexible: It can handle data from a variety of sources, including soundings, mesonet, upper air data, satellite, etc., as well as the background; • Powerful. It can perform retrievals (e.g., from satellite radiances and radar reflectivity) at the same time as the analysis by using forward models and their adjoint – i.e., it can make direct use of indirect observations. • For radar data, 3DVAR has the potential to combine the retrievals of single-Doppler velocity and thermodynamic variables, analysis, and initialization into one single step. A good 3DVAR system is an important predecessor to 4D-VAR. • Statistical models, and forward observational operators and their adjoint developed for 3DVAR can be directly used in 4DVAR. • It is less dependent on the prediction model, can therefore be developed before the forward prediction model is completed.

26. ARPS 3DVAR real wind observed component The Radar Problem: Observe radial velocity and reflectivity only, need V, T, P, qx for IC. For thunderstorms, radar is about the only obs platform! • We describe here a preliminary version of an incremental 3DVAR system developed recently at CAPS • Emphasis is given to the storm-scale and the use of radar data

27. The 3DVAR Formulation

28. The ARPS 3DVAR System • The ARPS 3DVAR system will analyze NEXRAD data with or without wind retrievals. • The Jc term, i.e., the dynamic constraints, are currently based on ARPS equations • Incremental formulation

29. ARPS 3DVAR • Background error covariance initially estimated using the “NMC” method. Flow-dependent covariance estimationmethods will be studied, e.g., that based on ensemble Kalman filter. This is more important for intermittent thunderstorms. • Background covariance is modeled using a simple version of recursive filter. More advanced version will be applied in the future (Purser, et al 2002a,b, Wu et al. 2002) • The analysis vector x contains model primitive variables u, v, w, q, p and q’s,ory (streamfunction), c (velocity potential) , w, q, p and q’s • Coupling among variables and balances are achieved via explicit equation constraints contained in Jc. • Analysis is performed on ARPS native terrain-following grid. • ADAS data handling infrastructure is taken advantage of

30. Observation Data  • Single-level surface data, e.g., • SAO • Mesonet • MDCAR • Multiple-level observations, e.g., • Rawinsondes • Wind profilers • Raw Doppler radial velocity or retrieved velocity fields (via SDVR methods) and reflectivity data

31. 3DVAR Versus ADAS – Total u Background 3DVAR ADAS 73x73x43 grid, dx=12km

32. 3DVAR versus ADAS – Total q Background 3DVAR ADAS

33. 4DVAR and EnKF • 3DVAR lays the foundation for 4DVAR • 3DVAR includes the data handling parts and forward operation operators and their adjoint • Adjoint of an old version of ARPS exists and had been used for cloud scale data assimilation • Adjoint of latest version of ARPS being developed with the help of TAF, an automatic adjoint generator (the commercial version of TAMC) • We are also working on ensemble Kalman filter assimilation

34. Boundary Conditions and Nesting

35. Boundary Conditions • Lateral Boundary Conditions • Rigid, zero-gradient, periodic • Open/radiative LBC (only applied to normal velocity) • Externally (can be from the same model) forced • Davies-type relaxation zone, arbitrary width • w not forced • variables (e.g., water) not found in exbc are excluded from relaxation – zero gradient is usually applied • Ensure same terrain at nesting boundaries • Carpenter (1982) – radiation BC with external forcing(?) • Carpenter, K. M., 1982: Note on radiation conditions for the lateral boundaries of limited-area numerical models. Quart. J. Roy. Meteor. Soc., 108, 717-719.

36. Vertical Boundary Condition • Radiation top BC based on cosine Fourier transform (Klemp and Durran 1983) • periodicity requirement at the top relaxed • Still based on linearized equations – difficult to apply to large domain • Upper boundary sponge/absorbing layer • relaxation to coarse grid/external model solution in the layer • or relaxation to the mean state • Rigid, zero-gradient and periodic top-bottom BC • Semi-slip lower BC

37. Two-Way Nesting • Two-way interactive nesting uses the Generalized Adaptive Grid Refinement Interface, a piece of software that I helped Skamarock to develop in the early 1990s • Horizontal nesting only • Allows arbitrary levels and arbitrary number of grids at each level • Allows rotated grids • Allows overlapping grids • Movable via regridding • Quasi-conservative interpolation (quadratic) • Averaged fine grid values replace coarse grid solution • Time interpolation only once every large time step • Used for supercell tornado simulations etc • Terrain issue, MPI

38. Tornado Vortex Simulations using 2-way nestingdx=105m

39. Stratiform Clouds and Precipitation

40. Stratiform Clouds and Precipitation • Microphysics parameterization for grid-scale precipitation • Can be used together with cumulus parameterization schemes • Option to allow condensation at subsatuation (<100% RH) • helps retaining clouds in IC for large grid spacing • improves surface temperature forecast at low-resolution by introducing clouds earlier • Sedimentation term treated implicitly or using time splitting

41. Microphysics Schemes • Kessler warm rain microphysics (qc and qr) • Lin et al (1983) ice microphysics • includes rain, cloud water, cloud ice, snow, graupel/hail, • lookup tables for power and exponential functions • ice-water saturation adjustment procedure of Tao et al (1989) • modifications to hydrometeo fall speeds (Ferrier 1994 and updated coefficients) • Shultz (1995) simplified ice scheme (also include 3 ice categories)

42. ARPS Ice Microphysics Processes ~ 30 processes

43. Accumulated Precipitation from 1977 Del City Supercell Storms with warmrain and ice microphysics

44. Simulation of 1977 Del City Supercell Storms with warmrain and ice microphysics

45. Problems • High precipitation biases at high-resolutions with explicit schemes • resolution problem? • fall speed problem? • process problems? • problem with assumed size distributions • High-precip bias with K-F scheme at high-precip threshold • Still, high-resolution (~3km) precipition forecast with explicit scheme is better than coarser (~9km) grids

46. CAPS Real Time Forecast Domain during IHOP_2002 183×163 273×195 213×131

47. CONUS and 9km ETS in the COMMON 9km domain

48. 9km (SPmeso) and 3km (SPstorm) ETS in the common 3km domain

49. Convective Precipitation

50. Convective Clouds and Precipitation • At high resolutions (=< 3km), use ‘explicit’ microphysics, hopefully the model can resolve the convection well • Cumulus parameterization schemes • Kuo scheme • Old and new Kain-Fritch schemes • Betts-Miller-Janjic scheme • New K-F scheme used most