27 February 2003

**A note from the author**

This webpage is intended for those pilots who
want to better understand the atmosphere in which they fly, for those
who want to interpret soundings (either observed or model generated)
and their significance for a day's thermalling conditions, and for
recipients of the Thermal Index
Prediction (TIP) emails who wish to better understand the theory
behind the TI method. For these purposes, some understanding of
the convective boundary layer is required. This webpage is
divided into two parts, with Part I
giving basics of the convective boundary layer and Part II describing how plotted soundings can be
analyzed. Those who are primarily interested in how the BL works
can read just Part I. Part II contains some sections that are
slanted towards the Thermal Index method used in my early TIP
forecasts, but it is still generally applicable to all types of
sounding analysis. Note that for simplicity the example soundings use a
basic "temperature vs. height" plot format, not the "skewT" plot
format often used by meteorologists, but the principles involved are
similar for all sounding plot formats.

While writing I find myself drowning in
mental caveats, thinking "BUT ...". Atmospheric processes can be
complex: many variations can occur and seldom will simple descriptions
cover all possibilities. I have tried to include only the
important caveats so as to not overwhelm the reader, so this present
discussion is only an introduction. A different approach to
soundings and the Thermal Index is available at the Forecasting Thermals
Made Easy website. A non-technical description of thermals and
the convective boundary layer is given at the What do thermals look
like? webpage.

The TIP employs virtual temperature for its calculations and the TIP
plots are also of virtual temperature. However, the difference between
virtual temperature and regular temperature is relatively small, usually
less than 4°F. (The virtual temperature will always be larger
than the regular temperature because adding humidity always makes the air
less dense.) Also, the difference between the lapse rates using regular
temperature and virtual temperature is very small. So typically the
difference between virtual temperature and regular temperature can be glossed
over and that is what I will do in these notes. But strictly speaking
every reference to "temperature" herein really means "virtual temperature".

The maximum thermalling height is expected to be somewhat lower than the top of the mixed layer. For this case the TI=0 adiabat based upon the surface temperature coincides, somewhat fortuitously, with the middle of the capping inversion, so the actual mixed-layer top is associated with a TI value just slightly below TI=0. However, with stronger (weaker) mixing the unstable layer near the surface will be deeper (shallower) and the TI=0 adiabat will then lie to the right (left) of the capping inversion, in which case the TI=0 height will overpredict (underpredict) the thermalling height and a lower (higher) TI value is then associated with the thermalling height. In general, on more strongly convective days the thermalling height will be associated with a smaller TI value than on weaker convective days.

(I should note that the features described above are more apparent in observed soundings than in the TIP plots since the latter have coarser vertical resolution. But even observed sounding plots do not depict the exact temperature profile in the mixed layer since not all measured temperatures are plotted, only temperatures at "significant levels". For example, the atmospheric temperature profile in the above figure should be more rounded than the straight-line segments portray.)

*Note: For simplicity the plots below use Temperature as
the horizontal axis and Height as the vertical axis. The same
principles can be utilized in analyzing a "SkewT" diagram in which the
Temperature axis is skewed from the horizontal and Pressure is the
vertical axis - but the SkewT plots will look, er, skewed from those
presented below.*

The numerical Thermal Index at *any* height is the difference
between the AM sounding temperature at that height and the "predicted"
PM temperature at that height (so negative TI values are found below
the TI=0 height). Every height has a TI "__trigger
temperature__": when the surface temperature reaches that trigger
temperature the TI method predicts that mixing will then reach that
height, i.e. then TI=0 at that height.

The Tmax in above example is at an elevation equal to the sounding's release elevation, i.e. the surface is assumed to be flat. The TI method can approximate the mixing over nearby elevated terrain by starting the DALR adiabat at that terrain's elevation with its expected Tmax. This assumes that the valley sounding is also applicable to the elevated terrain, which in many cases is a reasonable approximation.

The TI method can also be used with model PM soundings to estimate
thermalling heights. However, the TI method assumes that the
sounding temperature profile represents an *unmixed* atmosphere,
so *numerical** TI values from PM model soundings are
meaningful, and hence valid, only for heights above the top of the
mixed layer predicted by the model*. (Being a *valid*
prediction is not the same as saying that it is a *correct
*prediction - the latter depends upon whether the TI-assumed Tmax
is accurate!) This also implies that **the TI method is
generally invalid and should not be used if the Tmax utilized for the
TI adiabat is smaller than the model-predicted Tmax**, since in such
a case the adiabat from the TI-assumed Tmax will *not* intersect
the sounding temperature profile below the top of the mixed layer
predicted by the model (and may not intersect the temperature profile
anywhere!).

Analysis of a PM model sounding plot is the best method of
estimating the maximum thermalling height for that soaring day.
Due to the variety of thermal profiles that can occur, using the
brain's pattern recognition capability to visually determine the
predicted top of the mixed layer will provide a better estimate than
any summary number that a computer can calculate. Additionally,
the human eye can judge the degree to which the atmosphere is
predicted to be truly "well mixed": if the predicted lapse rate is
noticeably less than the DALR then the thermalling can be expected to
be degraded. Cloud bases can also be estimated for
overcast or near overcast conditions (scattered clouds are difficult
to predict visually from a sounding, but are more likely
as the difference between the predicted temperature and dew point
temperature decreases). However atmospheric complexity and model
limitations can produce interpretation difficulties. For
example, estimating the top of the mixed layer can be ambiguous
when the lapse rate above the mixed layer is not very different from
the lapse rate in the mixed layer. Still, a computer summary
estimate is always more subject to error than is a knowledgeable
eyeball estimate. One caveat is that PM model soundings used in
the TIP represent conditions at 00Z, after the time of maximum
heating, and thus their surface temperature is below the day's Tmax
and their maximum thermal height tends to be somewhat
underpredicted. Also, of course, they are only model predictions
- the real atmosphere may differ!

Condensation is considered likely when the difference between the
atmospheric temperature and the dew point temperature is about 4°F
(2°C). Remembering that model predictions are for
*area-averages*, "extensive clouds" (overcast or broken clouds)
will be indicated in a sounding when the dew-point temperature is
within 4°F of the atmospheric temperature and the temperature slope
will then be the MALR), i.e. slightly more
"stable" than the DALR. Scattered cloud conditions cannot be
adequately predicted from the TIP sounding plot, since it lacks lines
of constant humidity mixing ratio. [As an aside, if a sounding
is plotted on a SkewT diagram then the absence/existence of BL clouds
can be crudely predicted by noting whether the dew-point temperature
of the maximum humidity mixing ratio within the BL, which typically
occurs at the surface, intersects the atmospheric temperature anywhere
within the BL: if it does not then no clouds are predicted, whereas if
it does then clouds formation is predicted with the degree of sky
coverage increasing as the overlap increases.]. I should note
that moisture (and hence cloud) prediction is a notable weakness of
meteorological models, so cloud predictions should be taken with a
large grain of salt.

When the TI-predicted Tmax is
*warmer* than the model-predicted Tsfc, this generally
means that the expected mixed-layer top, and thus the expected maximum
thermalling height, is just below the TI=0 height. When the
TI-predicted Tmax is *cooler* than the model-predicted Tsfc, then
the model-predicted mixed-layer top must be decreased accordingly to
give the expected mixing height. Remeber that numerical TI values
from PM model soundings are valid only for heights above the top of
the mixed layer predicted by the model, so
the TI method should not be used if the actual surface
temperature is believed to be smaller than the
model-predicted surface temperature.

**Avenal (Lemoore), Jan 30, 2001**

This case is similar to the strongly
convective boundary layer illustrated above. The model lapse rate is
well-mixed, essentially a DALR, up to 3500 ft. The
model-predicted top of the mixed layer is best determined by noting that the
region above the DALR region has an essentially constant lapse rate
that intersects with the DALR region around 4000 ft. The dew
point drops dramatically above 3500 ft, suggesting a mixing height
between 3500-4000 ft. So the best estimate of the
model-predicted maximum thermalling height is between 3500-4000
ft. The dew point is very close to the atmospheric temperature
at 3500 ft, indicating that thin clouds may form at the top of the
mixed layer. The model-predicted Tsfc is slightly lower than
the TI-assumed Tmax (a NWS prediction), by
about 3°F (3 columns). The warmer TI-assumed Tmax predicts a
somewhat higher mixed-layer top of 4750 ft, which is the
TI=0 height - note this is *above* the model-predicted mixed-layer top and is therefore a meaningful TI prediction for the
TI-assumed Tmax . Melding the two predictions together, and
relying on the TI-method's NWS Tmax to be a more accurate surface
temperature prediction, I would estimate the maximum thermalling
height to be around 4250 ft.

**Avenal (Lemoore), Mar 28, 2001**

The model predicts a nearly DALR
(actually very slightly stable) mixed layer extending to a height of
around 3000 ft, above which the stability increases somewhat
before becoming very stable between 4500 and 5000 ft. The latter
marks the capping inversion, so the top of the model's mixed layer is
around 4500 ft. Note that the model's Tsfc is significantly
lower than the TI-assumed Tmax, which predicts a mixed-layer top
(TI=0) of 5250 ft (*meaningful* because it is above the
model-predicted mixed-layer top). Melding the two
predictions together, and placing more weight on the TI-assumed Tmax,
I would estimate a maximum soaring height of around 5000 ft.

**Williams (Marysville), Mar 27, 2001**

The PM model sounding has a nearly
DALR mixed layer up to a height of 4000 ft. The lapse rate
becomes slightly stable up to 4500 ft, then a more strongly stable
region exists between 4500-5000 ft, above which there is a deep layer
of slight stability. Determining the top of the model's
mixed-layer In cases such as this where the lapse rate above the
mixed layer does not differ markedly from the lapse rate in the upper
mixed layer can be difficult, but here the more stable layer seems to
be a capping inversion so I estimate the top of the model-predicted
mixed layer to be 4500 ft. Here the model-predicted Tsfc and
TI-assumed Tmax are very close. There are actually two TI=0
heights, at 900 and 3500 ft (see the TI column since the circles
overplot the asterisk) but neither are meaningful since they are
*below* the model-predicted mixed-layer top, and thus are
*not* meaningful predictions. So the estimated thermalling
height is the model's mixed-layer top, 4500 ft.

**Avenal (Lemoore), Feb 10, 2001**

Just above the surface the
model-predicted lapse rate is nearly DALR up to 4500 ft, above which
it is moderately "stable". However, 5000 ft appears to be a
cloud base since the dew point there nears the atmospheric temperature
and nearly parallels it above that - so thermals likely extend
above 5000 ft and the "stable" lapse rate there is really the

**Hollister (Oakland), Mar 22, 2001**

The model predicts a shallow
mixed layer up to 1000 ft, above which is a strongly stable inversion
layer. The TI-assumed Tmax is much larger than the
model-predicted Tsfc. This forecast is for Hollister so I
greatly favor the NWS Tmax predictions, since the model Tsfc
predictions are for an Oakland location, and would predict the top of
the mixed layer to occur at the TI=0 height between 2000-2500
ft. Note that TI =0 height is above the model-predicted mixed-layer
top and is thus meaningful.

**Avenal (Lemoore), Feb 6, 2001**

The model-predicted well-mixed DALR
layer extends to 2000 ft, above which the sounding is strongly stable,
so the model's mixed-layer top is between 2000-2500 ft. Note
that the TI adiabat never intersects the model-predicted temperature
profile so there is officially *no* TI=0 height - this occurs
because the TI-assumed surface temperature is cooler than the
model-predicted surface temperature in which case use of the TI method
is generally invalid, as occurs here. One's eyeball indicates
that the model-predicted temperature profile is just slightly warmer
than the the TI-predicted adiabat so the model-predicted mixed-layer
temperature is essentially correct and its mixed-layer top is also
essentially correct, though slightly greater than would be predicted
if the model Tmax equalled the NWS predicted Tmax. Weighting the
NWS Tmax more heavily here means that the expected thermalling height
will be slightly below the model-predicted mixed-layer top, and I
would estimate it to be 2000 ft.

**Williams (Marysville), Jan 31, 2001**

Here the model-predicted profile has
no well-mixed layer. The model's lapse rate between 500-1000 ft
is moderately stable, with a very stable region between 1000-1500
ft. The latter may or may not be a capping inversion, but would
indicate a mixed-layer top of 1000 ft. In any event, since
the layer below that is not well-mixed any thermals are predicted to
be weak. The TI-assumed Tmax is significantly larger than the
model-predicted Tsfc and predicts a TI=0 mixed-layer top of 1750
ft. This is a meaningful prediction because this height is above
the model-predicted mixed-layer top, so I would meld the two profiles
together, weighting the TI-assumed Tmax more heavily, to predict a
maximum thermallling height of 1500 ft. But the model's
prediction of very weak thermals indicates the thermalling will be
even worse than the low mixed-layer top would indicate. This is
definitely not a day to expect to do any thermalling!

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