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<br />SEPTEMBER 1981
<br />
<br />DAVID A. MATTHEWS
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<br />975
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<br />TABLE 3. Model versus aircraft observations of cloud-base height and cloud-top height, Miles City, summer 1977.
<br />
<br /> Morning sounding cases-sample size 13 Afternoon sounding cases-sample size 13
<br /> Mean values Mean values
<br /> Correlation Correlation
<br /> Air- Bias rms coefficient Air. Bias rIDS coefficient
<br /> Model craft ~ error Model craft ~ error
<br />Cloud-base beight (km) Cloud-base height (km)
<br />Maximum observed 3,13 3,21 -0,08 0.48 0,78 Maximum observed 3.46 3,21 0,25 0,67 0,79
<br />Minimum observed 3,13 2,77 0,36 0,86 0,54 Minimum observed 3.46 2,78 0,68 1.03 0,68
<br />Cloud-top height (km) Cloud-top height (km)
<br />Model radius (km) Model radius (km)
<br />0,5 6.41 8,65 -2,24 3.48 0,14 0,5 5,45 8.65 -3.20 3,62 0,53
<br />1.0 8.03 8,65 -0,62 2,89 0.20 1.0 6.48 8,65 -2,17 2,70 0,66
<br />1.5 8,80 8,65 0,15 2,86 0,22 1.5 7.05 8,65 -1.60 2.29 0,71
<br />2,0 9,44 8,65 0,79 2,86 0,25 2.0 8.00 8,65 -0,65 1.68 0,84
<br />3,0 10,62 8,65 1.97 3.42 0,24 3.0 8.88 8,65 0,23 1.82 0,86
<br />10,0 12,24 8,65 3,59 4,43 0,26 10.0 10.13 8,65 1.48 2.93 0,73
<br />Best top fit of model for all radii, morning soundings, n = 13, ~ = 0,89, rr ~ 1.27. SE ~ 0,35,
<br />Best top fil of model for all afternoon radii, n = 13, ~ ~ 0,78, rr = 1.05, SE = 0,29 km,
<br />(~) ~ mean error (bias); (rr) = standard deviation; (SE) = standard error of the mean,
<br />
<br />overpredict cloud occurrence by 10-20%; how-
<br />ever, statistical summaries of model results were
<br />limited to those cases where convective clouds were
<br />observed. It should be noted that comparison
<br />between results using the MESOCU model (which
<br />incorporated mesoscale lifting as a triggering mech-
<br />anism when mesoscale lines and clusters were
<br />observed in satellite imagery) and GPCM results
<br />in the same cases showed that GPCM predicted
<br />clouds in more cases than MESOCU and MESOCU
<br />required lifting to initiate convection. Surface
<br />heating alone in many cases was not sufficient to
<br />trigger convective clouds in MESOCU (Matthews
<br />and Silverman, 1980).
<br />
<br />d. Cloud-base height and cloud-top ver(fication
<br />
<br />Model sensitivity to errors in cloud~base height as
<br />small as 500 m has been noted by Sax (1972). A dif-
<br />ference between observed cloud-base height and
<br />model-determined height as small as 500 m may
<br />produce large errors in model-diagnosed cloud de-
<br />velopment. The effect of the cloud-base height
<br />error on diagnosed cloud development depends on
<br />the size of this error and the nature of the sounding.
<br />To minimize this error in cases having large vertical
<br />gradients of moisture near the ground, the mixing
<br />depth used to determine the CCL was set at 5 kPa or
<br />~500 m, throughout this modeling experiment.
<br />Soundings with large mixing ratios in the surface
<br />layer (surface to 2 kPa AGL) and much dryer con-
<br />ditions at 4 to 5 kPa AGL would produce cloud-base
<br />heights lower than that observed when the surface
<br />mixing ratio was used to compute the CCL. There-
<br />fore, mixing ratios from the surface to 5 kPa above
<br />the surface were averaged to provide a more
<br />representative mean planetary boundary layer
<br />(PBL) mixing ratio. This mixed CCL would better
<br />
<br />represent a convective air mass environment during
<br />the summer.
<br />The model determination ofCCL assumes that the
<br />surface convective temperature will be reached,
<br />thus producing sufficient heating to form a cloud at
<br />that level. In order to minimize errors in cloud
<br />diagnosis, checks were added so cases that required
<br />heating in excess of the climatological extreme were
<br />rejected. Excessive heating was required in nearly
<br />10% of all cases.
<br />A sample of days when cloud physics aircraft
<br />observations at cloud base and cloud top were
<br />available was used to determine the model's
<br />ability to correctly diagnose observed cloud de-
<br />velopment. The sample consisted of 26 morning
<br />and afternoon rawinsondes observed on 13 days
<br />during May, June and July of 1977 at Miles City,
<br />Montana. The model was initialized with six cloud
<br />updraft radii (0.5, 1.0, 1.5, 2.0, 3.0 and 10.0 km).
<br />The comparison between model and observed
<br />cloud properties is presented in Table 3 for 13 cases
<br />having simultaneous cloud-base and cloud-top
<br />aircraft observations. In general, for all rawinsonde
<br />data, the model was able to diagnose the observed
<br />convective cloud development reasonably well
<br />considering problems of sounding representative-
<br />ness and the limitations of a one-dimensional
<br />steady-state model. The correlation coefficients for
<br />cloudcbase height (0.78), cloud-top height (0.86 for a
<br />cloud model updraft radius of 3.0 km) with a
<br />relatively small rms error and bias for the after-
<br />noon soundings indicate that the model is able to
<br />diagnose important cloud properties reasonably
<br />well when the sounding is taken close to the time
<br />of cloud development. The average observed cloud
<br />radius in these cases was ~2.7 km. Examination of
<br />the 1200 GMT early morning sounding (Table 3)
<br />showe:d that the correlations were poorer and errors
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