1. Robin Hogan Ewan OConnor Anthony Illingworth Department of Meteorology, University of Reading UK PDFs of humidity and cloud water content from Raman lidar and cloud radar

2. Sub-gridscale structure in GCMs Small-scale structure in GCMs can have large scale effects: –Sub-grid humidity distribution used to determine cloud fraction (e.g. in UM) –Sub-grid cloud water distribution affects mean fluxes (crudely represented in ECMWF, not in UM) We use radar and lidar to make high-resolution measurements of water vapour and cloud content: –Raman lidar provides water vapour mixing ratio from ratio of the water vapour and nitrogen Raman returns –Empirical relationships provide ice water content from radar reflectivity Liquid clouds are more tricky! Chilbolton cloud radar Chilbolton Raman lidar

3. Mixing ratio comparison 11 Nov 2001 Raman lidar Unified Model, Mesoscale version Cloud

4. Small-scale humidity structure Correlation between adjacent range gates shows that small-scale structure is not random noise Typical horizontal cell size around 500m ~500m Mixing ratio at 720m ±6m Wind speed ~6 m/s

5. PDF comparison Agreement is mixed between lidar and model: –Good agreement at low levels –Some bimodal PDFs in the vicinity of vertical gradients Further analysis required: –More systematic study –Partially cloudy cases with PDF of liquid+vapour content 12 UTC15 UTC 1.6 km 0.2 km 0.8 km Larkhill sonde Smith (1990) triangular PDF scheme

6. Ice cloud inhomogeneity Most models assume cloud is horizontally uniform Non-uniform clouds have lower emissivity & albedo for same mean due to curvature in the relationships Pomroy and Illingworth (GRL 2000) LONGWAVE: emissivity versus IR optical depth SHORTWAVE: albedo versus visible optical depth Carlin et al. (JClim 2002) We measure fractional variance:

7. Relationship between optical depth and emissivity Ice cloud inhomogeneity Cloud infrared properties depend on emissivity Most models assume cloud is horizontally uniform In analogy to Sc albedo, the emissivity of non-uniform clouds is less than for uniform clouds Pomroy and Illingworth (GRL 2000) Lower emissivityHigher emissivity But for ice clouds the vertical decorrelation is also important

8. Fractional variance We quantify the horizontal inhomogeneity of ice water content (IWC) and ice extinction coefficient () using the fractional variance: Barker et al. (1996) used a gamma distribution to represent the PDF of stratocumulus optical depth: Their width parameter is actually the reciprocal of the fractional variance: for p( ) we have = 1/f.

9. Deriving extinction & IWC from radar Regression in log-log space provides best estimate of log from a measurement of logZ (or dBZ) log Z r log But by definition, the slope of the regression line is r log / log Z (where r is the correlation coefficient), so f is underestimated by a factor of r 2 0.45. Use ice size spectra measured by the Met-Office C-130 aircraft during EUCREX to calculate cloud and radar parameters: =0.00342 Z 0.558 IWC =0.155 Z 0.693

10. For inhomogeneity use the SD line The standard deviation line has slope of log / log Z We calculate SD line for each horizontal aircraft run Mean expression =0.00691 Z 0.841 (note exponent) Spread of slopes indicates error in retrieved f & f IWC log Z log

11. Cirrus fallstreaks and wind shear Low shear High shear Unified Model

12. Vertical decorrelation: effect of shear Low shear region (above 6.9 km) for 50 km boxes: –decorrelation length = 0.69 km –IWC frac. variance f IWC = 0.29 High shear region (below 6.9 km) for 50 km boxes: –decorrelation length = 0.35 km –IWC frac. variance f IWC = 0.10

13. Ice water content distributions PDFs of IWC within a model gridbox can often, but not always, be fitted by a lognormal or gamma distribution Fractional variance tends to be higher near cloud boundaries Near cloud baseCloud interior Near cloud top

14. Variance at each level not enough, need vertical decorrelation/overlap info: Only radar can provide this information: aircraft insufficient Vertical decorrelation Decorrelation length is a function of wind shear: –Around 700m near cloud top –Drops to 350m in fall streaks Lower emissivity and albedo Higher emissivity and albedo

15. Results from 18 months of radar data Variance and decorrelation increase with gridbox size –Shear makes overlap of inhomogeneities more random, thereby reducing the vertical decorrelation length –Shear increases mixing, reducing variance of ice water content –Can derive expressions such as log 10 f IWC = 0.3log 10 d - 0.04s - 0.93 Fractional variance of IWCVertical decorrelation length Increasing shear

16. Distance from cloud boundaries Can refine this further: consider shear <10 ms -1 /km –Variance greatest at cloud boundaries, at its least around a third of the distance up from cloud base –Thicker clouds tend to have lower fractional variance –Can represent this reasonably well analytically

17. Conclusions We have quantified how fractional variances of IWC and extinction, and the vertical decorrelation, depend on model resolution, shear etc. –Full expressions in Hogan and Illingworth (JAS, March 2003) –Expressions work well in the mean (i.e. OK for climate) but the instantaneous differences in variance are around a factor of two Raman lidar shows great potential for evaluating model humidity field Outstanding questions: –Our results are for midlatitudes: what about tropical cirrus? –What other parameters affect inhomogeneity? –What observations could be used to get the high resolution vertical and horizontal structure of liquid water content?