1. Probability Density Functions of Liquid Water Path and Total Water Content of Marine Boundary Layer Clouds Hideaki Kawai Japan Meteorological Agency Joao Teixeira Jet Propulsion Laboratory, Caltech

2. 1. Data 2. Relationships between PDFs of LWP and PDFs of total water content 3. Impact of inhomogeneity on precipitation and radiation processes 4. PDFs for various types of marine boundary layer Today’s Talk

3. 1. Data Data: GOES visible channel data (0.55-0.75µm) * spatial resolution : 1km mesh * temporal resolution : less than 30 minutes Location : GPCI line, 20S line, 88W line (Each line consists of 8 locations) Area size : 200km x 200km Period: 1999-2001 (Jan, Apr, Jul, Oct) Number of used snapshots : ~ 100,000 (3 (lines) x 8 (locations) x 3 (years) x 4 (months) x 30 (days/month) x 10-20 (times/day))

4. GPCI line 20S line 88W line EPIC Buoy

5. Homogeneity: Skewness: S Kurtosis: K Wood and Hartmann (2006)

6. 2. PDFs of LWP and PDFs of total water content

7. Relationship among PDFs of total water content, liquid water content and liquid water path Assumptions (1) Average of Total Water Content is constant in the mixed layer. (2) PDF of total water content is the same through the mixed layer. (3) Saturation specific humidity decreases linearly upward. (4) Spatial fluctuation of total water content is vertically coherent. (Structure of overlap of PDF is correlated completely.

8. Liquid Water Path Under the assumptions, what should the relationship between PDFs of Liquid Water Path and PDFs of total water content be? PDF of : depth of cloud, : just below the cloud top using the substitution (1) As a result, this equation is mathematically equivalent to the equation of PDFs of cloud depth and PDFs of LWP by Considine et al (1997).

9. PDF of total water content GaussianUniformTriangular PDF of liquid water content (at the cloud top) corresponding PDF of liquid water path Examples of PDFs of and corresponding PDFs of ( X and Y axes are normalized so that the integral of the PDF =1 and σ of the PDF=1. )

10. Points : Observation data ● : median ○ : 25th & 75th percentile values All the original data (~100,000 snapshots ) are used for this statistics. Lines : Theoretical Curves Two lines correspond to two mimicked detection limits (10% or 20% of average liquid water path). Relationship between cloud amount and skewness of LWP PDFs Cloud Amount Skewness

11. 3. Impact of inhomogeneity on precipitation process and radiation process

12. Correction ratio for autoconversion rate Often used equation of autoconversion rate Calculation used usually in GCMs Correction ratio for autoconversion rate More appropriate calculation : LWC Want to know this ratio!

13. PDF of total water content is assumed to be Gaussian. Correction ratio for Autoconversion rate Cloud Amount [%] Correction Ratio

14. Effective Thickness Approach (ETA) To get the factor Effective LWP Want to know this factor! Reduction factor for LWP used in radiation process : a function to convert reflectance to LWP

15. Reduction factor used in radiation processes Cloud Amount [%] Reduction Factor PDF of total water content is assumed to be Gaussian and corresponding PDF of LWP is derived analytically.

16. 4. PDFs for various types of marine boundary layer

17. Relationship between cloud amount and skewness of LWP PDFs Skewness Cloud Amount [%] Four ABL types categorized using h* 850 -h 1000

18. Summary 0. Subgrid-scale variability of marine boundary layer cloud LWPs is investigated using GOES visible channel data. 1. Generally speaking, Gaussian function seems to represent PDFs of total water content well under the set of our assumptions. 2. Effect of inhomogeneity of cloud water on autoconversion rate and shortwave reflectance are deduced as a function of cloud amount. 3. When the ABL is strongly or moderately stable, PDFs of total water content is triangular or Gaussian. On the other hand, when the ABL is unstable, the shape of the PDFs is almost unique with low homogeneity and high skewness & kurtosis.

19. The End Thank you!

20. Supplemental Slides

21. Processing Elimination of Middle & High Clouds Using infrared channel (IR1, 10.2-11.2µm) * Criterion : T bb M.-CL or H.-CL * More than 1% -> The snapshot is not used. Cloud Threshold * threshold albedo = 0.13 (LWP=5[g/m 2 ]) Count Data -> Radiance post launch calibration, solar zenith angle calibration Radiance -> Reflectance Reflectance -> Liquid water path Using the relationship by Han et al. (1998) (r e : MODIS)

22. Comparison between LWP from GOES and EPIC LWP 6 days data is used

23. Comparison between Homogeneity/Skewness from GOES and MODIS Homogeneity Skewness Homo. (MODIS) Skew. (MODIS) Skew. (GOES) Homo. (GOES)

24. GPCI line Each dot : median of 30 (days/month) x 3 (years) daily-averaged data Bars : 90% confidence intervals from bootstrap method Larger γ, smaller S and K toward sea coast. Largest γ, smallest S and K are in NH summer. Spatial variation is larger than seasonal variation. Along SH line, results are similar.

25. 20S line Largest γ, smallest S and K are in SH winter and spring.

26. 88W line Largest γ, smallest S and K are in SH winter and spring. Seasonal variation is larger than spatial variation.

27. sensible heat flux, latent heat flux, P sea, U 10m, V 10m, 10m wind speed, temperature advection near surface, T 2m, lifting condensation level, ω 700, ω 850, U 850, V 850, Wind shear (850-1000), RH 850, RH 925, RH 1000, θ 700 −θ 1000, θ v 700 −θ v 1000, h* 700 −h 1000, EIS (Wood & Bretherton 2006), θ 775 −θ 1000, θ v 775 −θ v 1000, h* 775 −h 1000, θ 850 −θ 1000, θ v 850 −θ v 1000, h* 850 −h 1000, (h 850 −h 1000 ) − k·L· (q 850 −q 1000 ) (k=0.70, 0.53, 0.23), h 850 −h 1000, Buoyancy of plume: T plume(850<-1000) −T 850, T v plume(850<-1000) −T v850 Used meteorological data : ERA40 Parameters examined Used Metric Spearman’s rank correlation, Kendall’s rank correlation, Pearson’s correlation Above Metrics are calculated for monthly-based data, daily data, daily anomaly data to each month data. Δθ e − k·(L/C p )· Δq t

28. As an example, if CGLMSE (k=0.70) is plotted in X axis… Each color consists of 8 locations x 4 seasons. Location closest to the land

30. These conventional functions seem not to be able to represent PDFs of Liquid Water Path... (The case that PDFs of LWP themselves are conventional functions)

31. Points : Observation data ● : median ○ : 25th & 75th percentile values All the original data (~100,000 snapshots ) are used for this statistics. Lines : Theoretical Curves Two lines correspond to two mimicked detection limits (10% or 20% of average liquid water path). Relationship between cloud amount and homogeneity of LWP PDFs Cloud Amount Homogeneity

32. Relationship between cloud amount and skewness/kurtosis of LWP PDFs When PDFs of total water content are assumed to be Gaussian, the corresponded functions derived using the conceptual model are able to represent the observed relationship between cloud amount and statistical properties of PDFs of Liquid Water Path relatively well. Cloud Amount Kurtosis Skewness

33. When ABL is strongly stable, the PDFs of total water content tend to be similar to Triangular distribution. When ABL is unstable, the PDFs have a unique shape with low homogeneity, high skewness and high kurtosis regardless of the cloud amount. Relationship between cloud amount and skewness/kurtosis of LWP PDFs Cloud Amount [%] Kurtosis Skewness

34. Production of Precipitation Effect of inhomogeneity on conversion of cloud water to precipitation

35. Shortwave Reflectance Effect of inhomogeneity on shortwave reflectance : Optical Thickness

36. Four ABL types categorized using h* 850 -h 1000 US : Unstable, WS : Weakly Stable MS : Moderately Stable, SS : Strongly Stable SSMSWSUS SSMSWSUS