Ben Johnson NCAR: Advanced Study Program / Climate Modeling Section

1. Update on progress with the implementation of a statistical cloud scheme:Prediction of cloud fraction using a PDF-based or “statistical” approach Ben Johnson NCAR: Advanced Study Program / Climate Modeling Section With thanks to: Phil Rasch (NCAR), Adrian Tompkins (ECMWF) & Steve Klein (Lawrence Livermore)

2. Talk outline • Cloud fraction methods • The Tompkins (2002) cloud scheme • Preliminary results from implementation of Tompkins (2002) in NCAR climate model.

3. Why do we need a cloud fraction scheme? • The “All or nothing” approach (if qv> qsat then cloudy, otherwise clear) will not work at GCM resolution! A view of tropical oceanic cloud from space

4. Why is cloud fraction important? SW LW Radiation Latent heating Clear sky Cloud Microphysical processes Cloud fraction

5. Cloud parameterization schemes in GCMs Convection schemes (deep, shallow) Radiation scheme New model State: T,qv,qc,U,V Model State: T,qv,qc,U,V Intermediate model State: T,qv,qc,U,V Cloud fraction scheme Turbulence scheme (boundary layer, free atmosphere) Large-scale condensation & microphysics

6. Current cloud fraction method in CCSM • Diagnose cloud fraction based on empirical • relationships: (Current method in NCAR CAM) a = cloud fraction als asc stratocumulus Large-scale cloud θ700mb-θs RH Rhcrit = 0.9 ac atotal = a(als, asc , ac) Convective cloud • Problems: • No memory • Relationships too simple • a is poorly linked to qc Mass-flux

7. Motivation for developing a new cloud fraction scheme for CAM • Current cloud scheme lacks a solid physical basis and has several deficiencies. • The representation of clouds in climate models is one of the biggest sources of uncertainty in climate change projections.

8. Alternative cloud fraction methods 1. Prognostic cloud fraction (Tiedtke 1993) (ECMWF, GFDL) • Develop evolution equations for cloud fraction: Model State: T,qv,qc,a,U,V Cloud dissipation e.g. mixing with dry air Cloud production e.g. Detrainment - Problems: a is not really a conserved quantity!!

9. Alternative cloud fraction methods 2. PDF-based or “statistical” schemes (Smith 1990, Tompkins 2002) (Met Office, ECHAM) • Construct the PDF of total water (qt) in a grid box Problem: How is the PDF determined? qt = qv + qc Probability qs Clear Cloudy qt

10. qt qt qt How is the PDF determined?1. Choose a PDF model • Aircraft data shows that PDF are usually uni-modal and either gaussian-like, or positively skewed. • Tompkins (2002) uses a beta function with three degrees of freedom: mean, variance & skewness. Symmetric Positively skewed

11. How is the PDF determined?2. Determine the moments • The mean (qt) is given by the model • The variance (qt’2), and skewness (qt’3/qt’2) are unknown. However, lets think about some possible sources and sinks for variance and skewness in the real world...

12. Processes that create variance and skewness Moist air from convection detrains into dry environment DRY Vertical mixing creates and transports horizontal fluctuations Moist

13. Dissipative mixing reduces variance and skewness DRY Over time horizontal mixing dissipates variance Moist

14. Rain-out reduces variance and skewness DRY Moist anomaly loses moisture via precipitation Moist

15. Prognostic equations for the variance budget (Tompkins 2002) (1) (2) (3) (4) • Production by detrainment of condensate convective updraughts • Production by mixing across a gradient • Turbulent transport • Dissipation • (!) or in partially cloudy situations variance can be fitted to qt, ql, and qsat.

16. Prognostic equations for the skewness budget (Tompkins 2002) (1) (2) (3) • Detrainment of condensate from convective updraughts • - K tunable parameter • (2) Conversion of condensate into precipitation (microphysics) • - Δςclosed by assuming no change in lower limit of distribution • (3) Dissipation by turbulent mixing • - parameterized as newtonian relaxation

17. qsat qt An alternative method for deriving the variance 1. In partially cloudy situations only, the variance can be derived by fitting the PDF to the mean qt and cloud condensate (qc) predicted by the model, given a certain skewness. In overcast or clear situations prognostic equations must be used to predict variance. Skewness must be prognosed in all situations. Probability qt

18. Intermediate summary • A PDF-cloud scheme, based on Tompkins (2002) has been implemented in CAM. What next? Single column model tests Global model tests

19. Atmospheric Radiation Measurement (ARM): The Southern Great Plains site (SGP) Single column model tests • Forced using a ARM IOP reanalysis data zhang et al. (MWR, 2001) from July 1997 over the Southern Great Plains site.

20. Single column model test – ARM IOP SGP site July 1997 CAM3: Cloud fraction)

21. Single column model test – ARM IOP SGP site July 1997 CAM3: Cloud fraction with empty clouds removed (where qc is negligible)

22. Single column model test – ARM IOP SGP site July 1997 CAM3: Cloud fraction contribution from large-scale / relative humidity

23. Single column model test – ARM IOP SGP site July 1997 CAM3: Cloud fraction contribution from convective cloud

24. Single column model test – ARM IOP SGP site July 1997 PDF cloud scheme: Cloud fraction

25. Single column model test – ARM IOP SGP site July 1997 CAM3: Cloud fraction with empty clouds removed (where qc is negligible)

26. Single column model test – ARM IOP SGP site July 1997 PDF cloud scheme: Cloud fraction

27. A simplified PDF cloud scheme • A simplified version of the Tompkins (2002) Simplifications made: - PDF skewness = 0 - In clear skies PDF width set consistent with critical relative humidity of 0.9 (cloud initiated as relative humidity exceeds 0.9). - If qc > 0 but qv < qsat then partly cloudy, cloud fraction computed by fitting PDF width to be consistent with qc and qv. - If qv = qsat then overcast, cloud fraction = 1, and PDF width such that PDF minimum = qsat.

28. Single column model test – ARM IOP SGP site July 1997 Simplified PDF cloud scheme: Cloud fraction

29. Single column model test – ARM IOP SGP site July 1997 Full PDF cloud scheme: Cloud fraction

30. Conclusions from single column tests • Empty clouds occur in CAM, especially associated with convective cloud at mid and low levels. • PDF scheme get slightly more high cloud than CAM. • Highly simplified PDF scheme gave very similar result to full PDF scheme.

31. Global model tests • The simplified PDF cloud scheme has been tested offline (diagnostically) in CAM3.2. • Run for 1 year with default climatology for SSTs

32. Annual mean vertically-integrated high cloud fraction

33. Annual mean vertically-integrated mid-level cloud fraction

34. Annual mean vertically-integrated low cloud fraction

35. Annual mean longwave cloud radiative forcing (Wm-2)

36. Annual mean shortwave cloud radiative forcing (Wm-2)

37. Summary chart

38. Conclusions from offline global model tests • Underestimation of low and mid-level cloud fraction, and shortwave cloud radiative forcing. • Slight overestimation of high cloud fraction and longwave cloud radiative forcing.

39. asc ac stratocumulus Convective cloud θ700mb-θs Mass-flux Why such differences / biases? • In CAM cloud fraction is completely independent of qc, therefore could still predict moderate cloud even when qc was very small, or even zero (empty clouds). • In PDF-based scheme cloud fraction was tied to qc, so would give low cloud fraction when qc was small relative to qsat

40. Why such biases? • The non-skewed beta shape used in the simplified PDF scheme is probably a poor approximation. • In upper troposphere one might expect positively skewed PDFs due to cirrus anvils where often we have qc >> qsat • In lower troposphere one might expect negatively skewed PDFs in the lower tropospherre where qc << qsat More appropriate PDF shapes to use in future tests? qsat qsat Upper troposphere Lower troposphere

41. Current & future work • Explore biases in GCM tests, especially underestimation of low cloud (sensitivity to PDF skewness / shape, and PDF closure methods). • Comparison of single column model with ARM and CRM data for specific testcases to develop better understanding of relationships between PDF shape characteristics and atmospheric processes (e.g. Convection, turbulence & microphysics).

42. The end Thanks for your attention!

43. Single column model test – ARM IOP SGP site July 1997 PDF cloud scheme: PDF width / qsat

44. Single column model test – ARM IOP SGP site July 1997 PDF cloud scheme: PDF skewness parameter (PDF is positively skewed when parameter > 2)

45. Prognostic equations for variance budget Moist air detrains into dry envirnoment

46. Prognostic equations for variance budget Vertical mixing across a vertical gradient creates horizontal fluctuations

47. Prognostic equations for variance budget Vertical mixing transports horizontal moisture fluctuations

48. Prognostic equations for variance budget Diffusive horizontal mixing reduces variability in the horizontal turbulence time-scale