Transcript Slide 1

Large Eddy Simulations of Entrainment and Inversion Structure
Alison Fowler (MRes Physics of Earth and Atmosphere) Supervisor: Ian Brooks
☼ The Entrainment Zone (EZ) is found in the
uppermost part of the planetary boundary layer (PBL). It
is characterised by a layer of intermittent turbulence and
overshooting thermals which have risen up from the
ground and as they fall back down, free atmospheric air
is mixed down into the top of the PBL.
☼ The depth of the EZ is controlled by the
strength of the capping temperature inversion, and
the strength of the surface heat flux which drives the
turbulent thermals.
☼ The EZ is important as it is responsible for the
growth of the PBL during the day, determining: the
dilution of pollutants from the surface, and the
distribution of stratocumulus affecting the global
radiation budget.
Statistics of the Entrainment
Zone
Figure 2. Comparison of the four different normalised EZ depths
plotted against a convective Richardson number. The flux defied EZ
depth has the weakest relationship with Ri* as it is a measure of
instantaneous entrainment whilst the others measure the cumulative
affect of entrainment on q.
h
zi

1
Ri *
Where Δh is the EZ depth and zi
is the height of the PBL.
Entrainment Zone Definitions
The entrainment zone has been defined in various ways which do
not necessarily produce the same results or represent the same
physical mechanisms; currently there is no universally
applicable definition of the EZ.
Figures 1 and 2 compare estimations of the EZ depth made by
four different methods.
The wavelet method (Brooks,2003) was found to have the
most robust relationship with the convective Richardson
number, Ri* :
Ri * 

where θ* is the mixed layer
*
temperature scale, and Δθ is the
jump in potential temperature across the inversion which defines
the inversion strength. The Richardson number is used as a
measure of the dynamic stability.
~200m
~200m
~650m
Figure 1. A cross section of q at the height of the inversion, with the
estimation of the EZ zone by different methods marked; 5-95%
probability distribution (dash-dot blue), area of negative flux (solid red),
significant gradient (dash green) and individual estimates of EZ top
(white upward pointing arrows) and EZ bottom (white arrows pointing
down) from wavelet analysis. It is clear that area averaged methods can
not include all of the detail of the EZ which is important for studying
entrainment mechanisms.
Area of negative buoyancy flux:
☺ Most physically meaningful, as measures the
area where energy is consumed by entrainment
• Applied to an area averaged profile, however,
entrainment is a local process. Area averaged
profiles may also be affected by gravity waves.
• Impossible to measure in in-situ observations
Area of Significant Gradient in a conserved scalar
quantity, q:
☺ Can be applied to profile of aerosol backscatter
using lidar.
• Applied to an area averaged profile
• Sensitive to large background gradients
• Arbitrary choice of ‘significant’ gradient
Limits of Probability distribution of the Maximum
Gradient in a conserved scalar quantity, q:
• Not truly a measure of EZ thickness but the
variability of the PBL top. (Davis et al. 1997)
☺ Can be applied to profile of aerosol backscatter
using lidar.
☺ Uses local individual estimates of ML top (max
grad) to define EZ.
Wavelet Analysis:
☺ Automated, can process large amounts of data
☺ Less sensitive to gradients in background signal
than other gradient methods
☺ Produces individual estimates of EZ top and
bottom- which tell you a lot about the turbulent
structure of the BL.
Figure 4. Standard deviation of the
percentage of high ML tops or ‘upwellings’
as a function of the mean convective
Richardson number. This shows that
although the variability of the ML top
Figure 3. Variability of the
becomes much greater as the PBL gets
PBL top, assumed to be the
more turbulent the ratio of ‘upwellings’ to
altitude of the maximum
gradient in q, for a varying ‘downwellings’ is less variable and is always
close
to 0.5. This is explained partly by the
Richardson number; (left)
change in time scales of entrainment for
low, (middle) medium and
less
turbulent
PBLs, and also the spatial
(right) high.
scale which entrainment occurs.
The statistics of the ML top and its relationship with the
Richardson number have been investigated in previous studies
(Sullivan et al. 1998) but until the wavelet technique it has not
been possible to study the statistics of the EZ top and bottom.
The skewness and the standard deviation of the EZ top and
bottom are strongly dependent upon the Richardson number.
Figures 7 and 8 show that the difference in the statistics
between the top and bottom of the EZ are also consistent as
the Richardson number decreases.
Figure 5. Cross sections of water vapour mixing ratio, q. The thick white
line shows the variability of EZ bottom and the thick red line shows
variability of EZ top, both estimated by the wavelet technique. These are
compared across a range of Ri*; a) low Richardson number b) medium
Richardson number c) high Richardson number.
Figure 7. The difference between the skewness of the EZ top and EZ
bottom plotted as a function of Ri*.
Figure 8. The difference between the standard deviation of the EZ top
and bottom, normalised by the mean ML depth, plotted as a function
of Ri*. The strong relationship seen, means it may be possible to
estimate Ri* from lidar profiles of backscatter from aerosols
σ bοο  σ tοο
zi
1
 Ri *
Figure 9. Comparison of entrainment rate normalised by the
convective velocity scale, or updraft speed, w*, vs. Ri*-1. The
relationship appears to be dependent upon some function of the
strength of the inversion, Aσ. An estimation of the entrainment rate is
important for understanding the growth of the PBL and cannot be
measured directly.
we
w*

A
Ri *

we
w*
 A
 bot   top
zi
References:
Figure 6. Probability distribution of EZ top and EZ bottom for a range of
Richardson number. Both the variability and the shape of the distribution
appear to change with the Richardson number. The EZ bottom appears
to be more variable than the EZ top due to thermals which cause
entrainment rising up from below, and these have the most energy before
they enter and are slowed by the temperature inversion.
Brooks, I. M., 2003: Finding Boundary Layer Top: Application of
a Wavelet Covariance Transform to Lidar Backscatter Profiles. J.
Atmos. Ocean. Tech., 20, 1092-1105.
Davis, K. J., D. H. Lenschow, S. P. Oncley, C. Kiemle, G. Ehret,
A. Giez, J. Mann, 1997: Role of entrainment in surfaceatmosphere interactions over the boreal forest. J. Geophys. Res.,
120, 219-230.
Sullivan,P. P., C.-H. Moeng, B. Stevens, D. H. Lenshow and S.
D. Mayor, 1998: Structure of the Entrainment Zone capping the
Convective Boundary Layer. J. Atmos. Sci., 55, 3042-3064.