APPLICATION OF A DENSITY CURRENT MODEL TO
AIRCRAFT OBSERVATIONS OF
THE NEW ENGLAND COASTAL FRONT
by
PETER PAUL NEILLEY
B.S.,
McGill University
(1982)
SUBMITTED TO THE DEPARTMENT OF
EARTH, ATMOSPHERIC AND PLANETARY SCIENCES
IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
at the
O~ ~U:;~'
MASSACHUSETTS INSTITUTE OF TECHNOLOGYWITHDRAN
FROM
May 1984
v;
MIT LIBRAfrgn
@
Massachusetts Institute of Technology, 1984
Signature of Author
Department of EarthdAtmospheric a d Planetary Sciences
''
May 1984
Certified by
,-1
..
Richard E. Passarelli
Thesis Supervisor
Accepted by.
Theodore R. Madden
Chairman, Departmental Committee on Graduate Students
-2-
APPLICATION OF A DENSITY CURRENT MODEL TO
AIRCRAFT OBSERVATIONS OF THE NEW ENGLAND COASTAL FRONT
by
PETER PAUL NEILLEY
Submitted to the Department of
Earth, Atmospheric and Planetary Sciences
in partial fulfillment of the requirements for the degree of
Master of Science in Meteorology
ABSTRACT
The vertical structure of the New England coastal front is
determined using aircraft observations. The coastal front is
found to be an extremely narrow transition zone between two
distinct air masses. Horizontal temperature gradients as large
as 12.9 C km- 1 with wind shifts of nearly 180 deg in 200 m
horizontal distance were found across the front. A vertical jet
of about 1.5 m s- 1 characterizes the front and there is evidence
that this updraft directly enhances the observed precipitation
field downstream. The overall structure of the coastal front is
found to be similar to a two-fluid density current.
Thesis supervisor; Dr. Richard Passarelli
Title: Assistant Professor of Meteorology
-3-
INDEX
1.
ABSTRACT................................
2
2.
INDEX...................................
3
3.
LIST OF FIGURES.........................
4
4.
CHAPTER I: INTRODUCTION.................
6
5.
CHAPTER II: STRUCTURE OF THE FRONT......
12
A.
Case of 10 January 1983............
12
B.
Case of 15 January 1984............
31
6.
CHAPTER III: THE DENSITY CURRENT ANALOGY
48
7.
CHAPTER IV: SUMMARY AND DISCUSSION......
55
8.
APPENDIX................................
59
9.
ACKNOWLEDGEMENT.........................
62
10.
LIST OF REFERENCES......................
.63
-4-
LIST OF FIGURES
1.
Surface analysis of the eastern U.S. at 1200 GMT on 10
January 1983....................... .......
2.
Surface
analysis
of
eastern
New
England
January 1983.......................
3.
Raw aircraft data of a)
temperature,
......
.......
.
at
1800
13
GMT
.....................
10
15
b) dew point temperature
c) wind speed and d) wind direction taken during the
15 M
AGL pass through the front on 10 January 1983.............17
4.
Same as 3 a-d except the data are from the 450 m AGL pass
through the front..................... ....................
5.
Cross section of potential temperature (*C) and winds for
the coastal front of 10 January 1983.. ....................
6.
20
The stream function normal to the coastal front of 10
January
7.
18
1983..............................................23
Comparison of vertical gust measured by the aircraft with
that calculated from the stream function..................27
8.
Cross section of the wind speeds parallel to the front
for
the
10
January
1983 case.................................29
...
-5-
9.
Surface analysis of eastern New England at
1500 GMT on 15
January 1983.............................. ...........-----
10.
Raw plots of a)
temperature, b) dew point
32
temperature,
c) wind speed and d) wind direction taken from the 150
AGL pass through the coastal front on 15 January 1983.....34
11.
Same as 10 except that the data are from the 450 m AGL pass
through
12.
the front......................................... 35
Cross section of potential temperature
(0 C) of the 15
January 1983 coastal front.................................37
13.
Stream function corresponding to 12.......................38
14.
Parallel winds corresponding to 12........................39
15.
Mean precipitaion rate (mm/hr) plotted normal to the front
for the 15 Jannuary 1983 case ....................... ......
16.
Calculated snowflake trajectories near the coastal
front of
17.
43
15
January
1983.....................................45
Skematic diagram of a typical
laboratory density
current....................................................50
-6-
CHAPTER I
INTRODUCTION
well
understood
observational
deficiency,
partially
the
New
of
because
the
England
Winter
lack
To
the phenomenon.
study of
has not
eastern New England
in
frontogenesis
Coastal
Storms
a detailed
of
overcome
help
been
Experiment
this
(NEWSEX)
conducted by the Center for Meteorology and Physical Oceanography
at MIT has had as one of its primary objectives the acquistion of
detailed
purpose
of
the
this paper
is
to present
of
results of this effort.
exhibits
New
The
an analysis
of some of
the
It will be shown that the coastal front
in
contrasts
dramatic
front.
coastal
England
observations
just
200
over
m
horizontal
distance of both the thermodynamic and kinematic variables.
coastal
front
will
also
be
shown
to resemble
a classical
The
two-
fluid density current.
The New England coastal front was first documented by Bosart
et
al.
(1972).
a series
They present
of
case
studies
of
a
mesoscale boundary layer frontal zone, often no wider than 10 km,
exhibiting large contrasts
band
normally
extends
in
several
New England coastline and
temperature and wind.
The frontal
hundreds of kilometers along
hence
the
name.
They
the
note however,
-7-
that
the
front
often
forms
as
far
as
50
km
inland
from
the
shoreline, especially in southeastern New England between Boston
and Providence.
Using detailed
found cross-
Bosart et al.
surface analysis,
frontal temperature contrasts between 5 and 10 C, with the cold
air always lying on the inland
from weak
(<
5ms- 1 ) northerly
Cyclonic wind shear
(west) side.
in
the
cold
air to strong
(5-10
easterly or southeasterly in the warm air is found across
ms-1)
the front.
Precipitation sometimes accompanies the front with a
change in form
the
across
front
sometimes
occuring
(e.g.
from
et.
al.
rain to freezing rain or snow).
to
respect
With
the
synoptic
Bosart
conditions,
found that coastal frontogenesis can commence 6 to 12 hours after
the
of
establishment
northern New England.
period
of
front is
12
to
24
a
cold
V-shaped
high
pressure
in
The coastal front typically persists for a
hours
thereafter.
The
dissipation
of
the
triggered by the arrival of a cyclone from the southwest
both
causes the winds to become uniform on
which
ridge
sides of
the
front.
Bosart
(1975) later studied
in greater detail the synoptic
scale conditions that are conducive to the formation of a coastal
front
in New England.
He
found
that coastal
frontogenesis
is
always associated with a high pressure ridge extending into and
receding from New England.
that
a
deep
but
filling
Along with this ridge,
cyclone
in
the
Ohio
he also found
valley
and
a
secondary cyclone forming off the Carolina coast are most often
-8-
associated
with
the
onset
of
coastal
secondary cyclone usually grows
England
and
often
becomes
Most
northeast.
synoptic
other
The
as it moves toward New
rapidly
the dominant weather
the
of
frontogenesis.
feature
in the
conditions
scale
that
Bosart found with coastal frontogenesis are mainly distinquished
by differences in the strength and position of the two cyclones.
The nature of the V-shaped ridge that seems to be essential
He showed
for coastal frontogenesis was studied by Baker (1970).
the result of a pool of dense cold air that has
that the ridge is
become dammed up against the eastern slopes
Mountains
by
a
easterly
large-scale
of the Appalachian
geostrophic
forcing.
surface winds under the ridge are usually northerly as
The
the cold
air drains along the mountains toward lower pressure.
frontogenesis from eight years of data.
of
eight
indicated
New
coastal
England
that this
fronts
form
with
year
each
number is probably too low.
coincident
winter,
coastal
He found that an average
the vast majority of coastal fronts occur in
early
of
climatology
a
compiled
also
(1975)
Bosart
but
He noted
he
that
the late fall and
in
the maximum contrast
land-sea
surface temperatures.
Bosart et al.
surface
friction,
frontogenesis.
when
anticyclone
coastal
Bosart
onshore
converge
configuration,
are
contrast
temperature
occurs
(1972) argued that the effects of differential
and
land-sea
factors
in
coastal
important
(1975)
found
geostrophic
near
orography
the
that coastal
winds
forced
coastline,
frontogenesis
by
probably
the
receding
because
of
-9-
differential
surface
argued,
coastal
there
is
a
set up
by
frontogenesis,
he
the
in
together
collapse
isentropes
as
occur
will
that
presumably
gradient,
contrast,
temperature
land-sea
Provided
temperature
pre-existing surface
the
friction.
convergence zone.
numerical
a
conducted
(1980)
Ballentine
frontogenesis
model.
For real data initializations, he could produce a coastal
the
heat
boundary
geostrophic wind
synoptic scale
layer
took on an
Further, by varying the parameterization of
easterly component.
surface
specialized
on
coastal
front only when
using a highly
experiment
friction, orography
differential
flux,
and
latent
heat release, he concluded that the flux of heat out of the ocean
physical process
is the primary
the
determined
were
factors
other
The
coastline.
leading to frontogenesis along
to
be
secondary.
(1977)
McCarthy
of
vicinity
the
the
studied
coastal
Using
front.
air
upper
the
structure
standard
in
upper
the
air
observations and pertinent surface observations, he constructed
cross
sections
typical
air,
coastal
through
front
the
environment
He
front.
coastal
consists
of
that
found
layers
three
each having a different character and origin.
the
of
The lowest
layer west of the surface frontal position is a cold continential
air
mass
characterized
by
northeasterly winds less than
stability,
high
5 ms-
1,
(except possibly during precipitation).
less than 750 m thick.
and
northerly
low relative
This layer is
or
humidity
generally
Above and east of this layer is a warmer
-10-
This air is, or has recently been
less stable maritime air mass.
in direct interaction with the ocean and therefore has a higher
Winds
content.
moisture
ms- 1 .
10
to
5
southeast
at
inversion
lies above
at a height of 1 km,
typically
this layer,
and
forms the boundary into the third air mass.
has
the highest
relative
usually stronger than 10 ms- 1 .
the
frontal
warm
inversion
cyclone
approaching
and
This top layer
winds
south or southwest
and
humidity
to
frontal
warm
synoptic-scale
A
east
generally
are
layer
this
in
McCarthy noted that the height of
depends
sometimes
upon
the
surface,
the
to
descends
the
of
position
displacing the coastal front.
Along
is
jet
this
precipitation
the
horizontal
enough,
deep
an
winds.
area
in
Provided
enhanced
of
at and west of the surface frontal position should
Indeed,
occur.
strong and
of
jet may occur
a vertical
interface,
convergence
to the
response
that
frontal
the
this
enhancement
degrees by Bosart et al.
has
noted
been
(1972) and Bosart
in
varying
(1975) from surface
observations, by Marks and Austin (1979) using radar, by McCarthy
from
satellite
and
by
Ballentine
using
his
numerical
Bosart et al. (1972) also noted that because of the large
model.
temperature
between
sleet
images
contrast,
frozen
and
snow
the coastal
front often marks the boundary
Freezing
rain,
have all been observed west of a coastal
front
and
non-frozen
precipitation.
while rain was falling to the east.
-11-
Accurate
weather
certainly depends
forecasting
upon careful
of coastal frontogenesis.
are
to
subject
because of the uncertainties
will
and
form,
how
New
eastern
consideration
of
England
the possibility
Still, even the most careful forecasts
errors
large
in
temperature
in
and
precipitaion
in where and when the coastal front
and
persistent
how
it
intense
be.
will
Evidently, significant forecasting improvements will depend upon
the
to which
degree
Many questions
narrow
is
the
is
circulation
circulation
remain
front
is
to be answered
further
be
enhancement?
before this goal can
actual
driven
able
frontal
by
the
zone?
What
front?
to account
for
any
type of
Would
In regard to the mechanics of
Following
where
are
two
the
case
front
will
studies
form
that
vertical
this
vertical
observed precipitation
the front:
does rotation play in the frontogenesis mechanism?
determines
understood.
For instance, in regard to the front's structure:
be achieved.
How
still
coastal
the
and
attempt
how
to
What
role
Finally, what
it
will
answer
these questions and point towards the answers for others.
move?
some
of
-12-
CHAPTER II
STRUCTURE OF THE COASTAL FRONT
The
primary
data
NEWSEX.
In
parameters,
addition
the
in
this
Queen-Air
instrumented
NCAR's
used
study
is
plane
the
equipped
collected
loaned
aircraft
to measuring
were
to
standard
to
with
during
MIT
meteorological
determine
and
cloud
precipitation particle-size distributions with Particle Measuring
by
an
The position of the aircraft is determined
(PMS) probes.
Systems
inertial
sampled
once
navigation
per
second,
system
All
(INS).
yielding
parameters
are
resolution
a horizontal
of
about 70 m at normal cruising speeds.
Two
significant
operational
period
fronts
coastal
of
NEWSEX
in
studied
were
the
winter
during
of
the
1982-1983.
Individual case studies of each are presented here.
1.
eastern
Case of 10 January 1983.
U.S.
during
shown in Fig. 1.
which
Bosart
A
New
morning of
10
These conditions are nearly
(1975)
frontogenesis.
the early
The synoptic conditions in the
northeast
of
extending
southwest
found
most
1040
mb
England
along
on
the
often
1983 are
identical
to those
associated
anticyclone
the
January
previous
Appalachians.
became
with
coastal
established
night
with
a
ridge
A
deep
low
was
moving northeast out of the Midwest and by 1200 GMT (7 am LST) on
the 10th,
a new low had developed off Cape Hatteras.
Radiational
cooling throughout much of the previous night allowed
a strong
-13-
Fig. 1. Surface isobaric analysis in the eastern US at 1200 GMT
on 10 January 1983.
-14-
land-sea
surface
temperature
established along
Fig.
2 presents
1800
GMT.
It
include
eastern New
cloud
reports.
cover
can
northeastward
to
be
at
available observations
The Coast Guard observations do
are
thus plotted with
seen
to
run
just west
England
all
and
of Boston and
front
coastal
(see
an
central
from
"M".
The
Connecticut
then northward along
This
and Maine coastline.
most of the New Hampshire
New
using
eastern New England
of
analysis
the surface
is constructed
front
coastal
the
in
the eastern New England coastline by 1500 GMT.
including Coast Guard
of
to develop
A coastal front began to form by 0900 GMT and was well
England.
not
gradient
is
Bosart
e.g.
typical
et
al.).
The aircraft took off from Bedford MA (BED) at 1630 GMT on
the morning of the 10th.
because
area
observing
Portsmouth NH (PSM)
of
its proximity
relatively sparse air traffic.
to
was selected as the
the
front
the
and
The aircraft arrived on location
by 1700 GMT and proceeded to make six 40 km passes centered on
the
front
at the
350,
and
450 m AGL.
150*-330*
the
which
possible
to
encountered
offshore.
one
altitudes
of
151,
100,
150,
250,
The aircraft maintained a true heading of
at the
The
front.
approximate
data
time was
thought
was
collection
vertical
plane.
about 15 km southeast
to be perpendicular
confined
The
as
coastal
of Portsmouth,
closely
front
or about
to
as
was
7 km
The entire set of observations took about 90 min.
However
1 Over water the flight track was indeed this low.
when the track passed over land the aircraft was forced to fly
was
front
coastal
the
since
However,
higher.
somewhat
encountered over the ocean, it was, in fact, penetrated at about
15 m ASL.
-15-
720
Fig.
71*
70*
Surface analysis in eastern New England at 1800 GMT
2.
Isobars are drawn every 2 mb
(1 pm LST) on 10 January 1983.
Wind barbs are in
and isotherms are drawn every 2.5*C.
knots. Coast guard reports are plotted with a "M".
-16-
time
the
By
had
skies
the
taken,
were
observations
the
to have
become overcast with a stratocumulus deck estimated
a
There were a few breaks in the clouds on both sides
1.2 km base.
of the front but these were more than 20 km away from the surface
frontal position.
There were no other obvious features noted by
the flight observer (the author) in the cloud structure near the
front, and there was no precipitation.
3 a-d are
Figs.
raw plots
wind
dew point,
temperature,
of
speed and wind direction for the lowest pass through the coastal
front.
The coastal front is clearly depicted in these plots as a
sudden
jump
in
is
the large jump
Most of
and
temperature
in
change
represented
direction.
the wind
seconds
three
by just
of
This rapid transition presses the response sensitivity of
data.
the
of
some
instrumentation.
measurement
total
The
the
of
particularly
instruments,
change
dew
in
point
temperature
across the coastal front is 9 C, of which more than half occurs
at
the
jump.
and
front
The wind shift occurs
amounts
to
180
Note that the parameters
deg
over
almost exclusively at the
200
m horizontal
distance.
are generally flat on the warm air side
of the front but have a definite slope in the cold air.
point
shows
trace
a sudden
rise
ahead
of
the
front,
The dew
exactly
coincident with the position of the shoreline.
Figs.
4 a-d are identical to the plots of Fig.
the data are from the the highest
front.
The
transition
in
front
at
this
temperature
height
of
less
3 except that
(~ 450 m AGL) pass through the
is marked
that
only by
1 C, although
a slight
the
dew
1/10/83
15 M AGL
'TEMP vs. DIST
1/10/83 15 M AGL
5
WSPD vs. DIST
5
-I
. .a..
A
-5
- 0~ ..~~~~ pl'
~ - - Ltlia 1
5
10
15
a
0
1/10/83
ISM AGL
- -' - -- - - -- "- -
-to
5
0
stu11
20
a..b
I II
1 A a
25
JL
.
-5
0
5
10
15
20
25
30
35
TD vs. DIST
-'
- -
' ' - '-
I- - -
'-o
10
15
5
20 25
30
DI$TANCE FROM PORTSMOUTH (KM)
Fig.
s
30
35
0
5
10
15
20
25
30
DISTANCE FROM PORTSMOUTH (KM)
3a-d.
Plots of a) temperature, b) dew point temperature
c) wind speed and d) wind direction plotted as a function of
distance from Pease Air Force Base, Portsmoutn NH. The data
were collected during the 15 m AGL pass through the coastal
front.
35
1/10/83
5
450 M AGL TEMP vs. DIST
1/10/83
450 M AGL
WSPD vs. DIST
cn
0
-5
LU
.
.
a
z
-1
-5
0
1/10/83
5
10
15
20
25
30
35
450 M AGL TD vs. DIST
(.O
z
0.
o - i
-5
0
5
10
15
20
25
30
DISTANCE FROM PORTSMOUTH (KM)
Fig.
35
-5
0
5
10
15
20
25
30
DISTANCE FROM PORTSMOUTH (KM)
4a-d.
Plots of a) temperature, b) dew point temperature
c) wind speed and d) wind direction plotted as a function of
distance from Pease Air Force Base, Portsmouth NH. The data
were collected during the 450 m AGL pass through the coastal
front.
35
-19-
Some turbulence-
C over the entire data region.
2*
rises
point
speed at the front.
the wind
like fluctuations are apparent in
The wind direction is nearly constant across the region and is
about the same as that in the warm air at the surface.
Cross sections of the coastal front can be produced provided
in both time and space
the data is transformed
to
perpendicular
systen
the
is
transformation
This
front.
to a coordinate
necessary since the data were not collected synoptically and thus
Further, any along-
any frontal movement must be accounted for.
front structure must also be considered because, despite the best
some of the flight paths strayed from the
efforts of the pilots,
the
plane.
desired vertical
produce
Details
of
used
the procedure
to
the cross sections as well as a discussion of the errors
involved are given in the appendix.
Fig.
with
a cross
5 presents
overlayed
barbs
wind
section
for
head
barb
The
reference.
to the aircraft position.
corresponds
temperature
of potential
Horizontal averaging over
1.5 km has been applied to the data to remove the smallest scale
3 and
4.
This step was omitted, however, in the 3 km region centered
on
fluctuations
the
front
coastal
associated
outside
with
the
evident
are
that
the
in
order
front.
in
to
The
the plots
of
the
preserve
temperature
Figs.
large
and
region shown are relatively flat and
gradients
wind
fields
are therefore
truncated here to allow greater resolution near the front.
Two distinct air masses are
The
cold air
is characterized
evident in
by a high
this cross section.
static stability
(N
POTENTIAL TEMPERATURE (C) AND WIND
500
400
.5
2300
W~
1.
1/10/83
2.0
0.5
100
-
0
-15
-10
Fig.
1..5
0
-5
DISTANCE NORMAL TO FRONT (KM)
5. Cross section normal to the coastal front of potential
temperature and wind.
Isotherms are drawn every 0.50 C and
each wind barb represents a wind speed of 2.5 ms~ 1 .
5
-21-
S-2 )
7-10-4
weak
and
sharp
separates
the
frontal
warm and
The warm air is characterized by a weaker stability
air.
cold
300 m and
up to about
interface exists
A very
winds.
northerly
(N 2 ~7-10- 5
and southeasterly winds.
S-2)
The maximum horizontal
temperature gradient is 12.9 C km-1 and extends over about 210 m
The maximum vertical gradient is about 30 C km-
distance.
180
about
at
occurs
This
position.
m
well
AGL
behind
the
is coincident with
the
surface
1
and
frontal
level of greatest wind
shear.
An interesting aspect of the coastal front occuring over the
water is
the
the fact that its surface position could be observed on
from
surface
ocean
Especially
air.
the
from
the
higher
elevations, the front could be seen on the surface as a dark band
where there seemed to be enhanced interference amoung the surface
waves.
This
horizontal
presented
structure
of
a
unique
the
opportunity
frontal
to
The
interface.
the
observe
flight
observer noted that the band ran along an axis orientated between
5 and
10 degrees
clockwise
from
least to the limits of visibliity.
the
shoreline
and
extended
at
This orientation agrees quite
well with that obtained from the surface analysis of Fig. 2.
It
was also noted that the band axis was generally straight but with
some irregualar oscillations of order 100 m in amplitude and 1 km
in
length
observations
fact
imbedded
are
in
Therefore,
it.
accurate
and
provided
representative
that the aircraft data resolution is
and
that
these
given
the
70 m or so, then the
coastal front may be regarded as essentially two-dimensional.
-22-
The
of
two-dimensionality
simplification
in
the
study of
the
near the
circulation
a
allows
front
coastal
the
front.
If divergence along the coastal front may be neglected and noting
that the depth of the coastal front is much less that the scale
height
allows the
equation
circulation to be
and vertical wind
speeds,
w=a
ax
(2)
(positive into the warm air)
analysis,
less
u is interpolated
in order
resolution
is
to
to evaluate
also
could
than
reliable
condition
not
be
with
but
u and
the
of
those
In
obvious.)
a grid
used,
a
50
m
the integral of Eq.
the
The
(1).
The. computed stream function is
is the
shown
The same smoothing criterion that was applied to the
in Fig. 6.
potential
data
vertical
flow was assumed to be horizontal at z=O so that T(O)=O
lower boundary condition.
is
subject to an appropriate
(1)
(2)
stream function
The
respectivly.
(Eq.
of w are
boundary
appropriate
stream
(1)
by integrating Eq.
condition.
observations
the
u -
where u and w are the front normal
boundary
by
described
such that
function T=T(x,z)
then determined
continuity
incompressible
the
then
atmosphere,
the
of
temperature
plot
is used
here.
convergence
The
of
stream lines at the front again shows the narrow transition zone
between
the
two air
masses.
The
speed
of
the updraft at
front calculated using Eq. (2) is about 1.5 msoscillation
in
the
flow
downstream
discussed later in the text.
of
the
.
the
The apparent
updraft
will
be
STREAM FUNCTION
KM x (M/S)
1/10/83
400
300
200
100
-15
-10
-5
0
DISTANCE NORMAL TO FRONT (KM)
Fig. 6, Stream function
coastal front.
(km.m-s~ 1 ) normal
and relative
5
to the
-24-
and
field
temperature
the potential
Overlaying
the
stream
function shows that the cold air below 180 m flows weakly forward
the
toward
front where
Just above
forced upward.
must
represent
of
a mixture
the warm, maritime air and
180 m the air
the
This
air
has
the
as
two air masses,
the
is
is receding from
incoming maritime air.
than the
is colder
front but
it meets
it
momentum of the warm air but a temperature suggesting origins in
It is also noteworthy that the circulation extends
the cold air.
above
well
450
m
though
even
the
horizontal
gradients
temperature and wind have almost completely disappeared
level.
of
at that
Unfortunately the upper extent of the circulation cannot
be determined from the data.
The exchange of temperature and momentum between the two air
masses can be seen more clearly by following a parcel of air that
Such a parcel will
originates in the cold air near the surface.
closely
follow
circulation
is
the
function
stream
zero
After
steady.
line
the parcel
updraft and begins to recede from the front,
has
it
provided
ascended
the
the
in
the
is warmer than it
was at the surface indicating that a positive flux of heat into
the cold air is occuring.
of
its
rearward
momentum
indicating
accelerate
it
or
momentum into the cold air.
The parcel has also changed the sign
that
that
either
there
a
is
force
a
flux
is
acting
of
to
negative
These changes are acting to weaken
the coastal front and must be balanced by a frontogenetical flux
(or
fluxes)
state.
in
order
that
the
coastal
One possible balancing flux is
front maintain
a steady
the low-level flow of cold
-25-
Certainly this flow carries
air toward the front from the west.
the
If
is
flow
the
between
intersection
the
of
because
then
adiabatic,
momentum.
horizontal
positive
necessary
the
streamlines and isotherms near the surface, it also provides the
necessary
flux
frontogenetical
be
may
One
heat.
of
advection
negative
advection parallel
to
due
possible
other
to
the
front, but this possibility can not be determined here.
for the dissipation
The above analysis suggests a mechanism
If
of the coastal front.
insufficent
is
there
flux of cold air
and positive momentum into the cold air to balance that which is
swept away by the overiding warm air, then the frontal contrasts
will begin to deteriorate.
onset
of
account
parcels in
and
waves
surface
highly turbulent flow.
would
has
instability
This
the
for
along
instabilities
Kelvin-Helmholtz
interface.
breaking
This could be triggered by the sudden
its
characteristics
presence
usually
the
similar
to
indicates
a
Its presence along the frontal
and
temperature
the cold air experience
momentum
frontal
interface
changes
that
as both heat and momentum are
transported down-gradient in the turbulence.
For
a
fluid
with
stratification
instability may commence when
N2,
the Richardson
Ri=
Kelvin-Helmholtz
number Ri,
defined
N2
RioU/az)2
falls below 0.25.
case using Figs.
An analysis of the Richardson numbers for this
5 and
6 interpolated
the region is generally stable.
to grid points shows
that
There are, however, pockets of
-26-
potential
instability above
position
as
as
well
180 m and behind the surface frontal
forward
the
along
of
part
front.
the
Further, many small regions of instability may be overlooked in
mixing
the
of
cause
the
be
may
regions
isolated
these
Together,
smoothing.
horizontal
the
and
data
resolution of the
coarse vertical
of the
this analysis because
inferred.
previously
However, the wind shear needs to be increased by only about 25%
in
This increase
interface.
wind
for
necessary
appears
along
the
frontal
certainly possible as the warm air
the
to
easterly
the
although
Therefore,
is
response
in
increases
speed
instability
global
render
to
order
coastal
cyclone.
approaching
wind
geostrophic
there
frontogenesis,
be
may
a
minimun and a maximum speed that allow it to occur.
As noted earlier, the coastal front was observed first hand
to be a two-dimensional
feature.
This property can be confirmed
quantitatively by comparing the vertical wind speed from
with
that directly measured
stream function was
the
continuity
observed
the
Recall that the
aircraft.
calculated using a two-dimensional form of
equation.
vertical
by
Eq. (2)
Therefore
velocities
are
if
nearly
the
calculated
identical,
and
little
mean divergence must be occuring along the front and therefore it
is two-dimensional.
One problem
in applying this
technique to
the data is that the aircraft automatically removes a 15 minute
mean from the measured vertical wind so as to produce only a gust
component.
since
each
This should not, however, present a large discrepancy
pass
through
the
front
took
about
15
minutes.
-27-
7 (a-b)
in Figs.
Presented
a plot of
is
the vertical
for two representative passes through the front.
is
overall
an
is
there
thus
and
front
the
along
occuring
The high degree
that little divergence
the plots suggests
of correlation of
velocities
two-dimensional structure.
One interesting feature of these plots is
the presence of a
sinusoidal pattern to the vertical velocity, particularly at 250
m.
There
a correlation
is
downstream oscillations
and
analysis shown earlier.
the mean ambient flow.
the
just
determined
buoyancy
the
by
oscillation.
Therefore
the
found
in
the
frequency
N.
that
the
distance
The
mean
wavelength
flow
the
wavelength
waves
observed
is
about 2 km.
of
the
is then
in
travels
may
be
region
one
where
the
supports free modes
of
the observed wavelength.
is
about
oscillations.
vertically
higher
occurs at about 400 m AGL.
This
observed
a
waves
function
jet and travel downstream with
from
gravity
stream
For a parcel oscillating about the 250 m AGL level,
than
less
the
that
suggesting
The frequency for these free oscillations
the wavelength of the free modes
50%
calculated
They appear to be inertial gravity waves
the vertical
that are excited by
is
and
observed
These oscillations are coincident with the
phenomenon is real.
roll
the
oscillations
these
within
velocities
between
propagating
stratification
Such a region
1.5
1.0
S0.5:0.0
z
-0.5
a:
w -1.0-1.5
-
1.5-
150 M AGL
1.0:
, 0.5
z
Q-0P
-
-0.5
w-1.0-1.5
-
-10
- 1.5
Fig.
-5
DISTANCE NORMAL TO FRONT (KM)
0
Comparison of the aircraft measured vertical gust
7a-b.
(thin line) with that calculated from the stream function
(solid line) at the altitudes of a) 250 m AGL and b) 150 m
AGL.
-29-
Fig. 8 presents a cross section of the wind speeds parallel
to the front.
This plot shows
that only
appreciable parallel wind component.
is cyclonic as Bosart et al.
the cold
air has
an
The shear across the front
noted.
There
jet
is an internal
running along the front just behind the surface frontal position
that
lies
just above
the
region having
attempt to achieve geostrophic balance.
thermal
wind
in
the
vicinity of
and
vertical
discrepancy.
jet
is
mixing
However a calculation of
the
front
shows
15% of that expected.
observed response is only about
drag
strongest vertical
This jet may be the result of the front's
temperature gradient.
the
the
certainly
a
have
role
that
the
Surface
in
this
The decrease in the parallel wind speed above
probably a response
to the strong
negative
the
advection of
parallel momentum by the warm air.
Following the completion of the passes through the front the
aircraft made
and
with
45
low-level soundings at three locations between
km into the
the previous
cold air.
cross
Compositing these sounding data
sections shows
maintains a vertical structure above
found 15 km back in the cold air.
the
wind
isotherms
structure
shear
remained
remained
is
near
horizontal.
similar
to
that
35
that
the
coastal
front
the ground similar to that
The height of the maximum in
200
m
This
which
AGl
type
and
of
McCarthy
larger-scale cross-sections through the front.
potential
the
flat
downstream
found
in
his
500
PARR
WINDS
(M/S)
1/10/83
400
(n
;300
0
< 20
100
0-15
-O
-5
DISTANCE
NORMAL
0
TO FRONT (KM)
Fig. 8. Cross section of the wind speed (ms~') parallel to the
coastal front. Negative values are from the northeast.
-31-
The
of
observations
the
of
surface
synoptic maps
this
coastal
front
sequence
time
mature phase of frontogenesis.
made
were
flight as
lost much of
the wind in
southern New
in
its character
did however persist up to 12 hours longer along the
It
England.
the
By 00 GMT of the
the cold air began to veer into the northeast.
the front had
during
that
The front did begin to show signs
of weakening about three hours after the
llth,
indicates
Maine coastline.
2.
Case of 15 January 1983.
The
synoptic
frontogenesis
previous case.
conditions
day
this
on
resulted
that
little
differed
in
the
those
from
coastal
of
the
A high pressure ridge extended along the entire
length of the eastern U.S. seaboard and a deep cyclone was moving
into the upper Great
Lakes at
00 GMT on the 15th.
At the same
time a new low showed signs of developing off the South Carolina
coast.
The pressure falls associated with this new cyclone split
the east coast ridge and formed
This
allowed
the
geostrophic
deck
over
thickening
cloud
radiational
cooling during
the "V"
to
winds
New
ridge in
become
England
the night,
the northeast.
onshore.
prevented
A
strong
so that although coastal
frontogenesis did commence by 0600 GMT of the 15th, there was not
a very large initial land-sea temperature contrast.
-32-
The surface analysis for 1500 GMT 15 January in eastern New
England
is Fig.
is shown
Comparing
9.
this analysis with
the
same analysis for the previous case shows that this coastal front
is not as strong as in the previous case.
Wind shifts appear to
be less than 90 deg everywhere along the front and the isotherms
are not as concentrated.
The aircraft was airborne and en route to Portsmouth by 1500
Portsmouth was again selected not only for the reasons of
GMT.
the previous study, but also because light to moderate snow over
any low-level
much of southern and western New England prevented
The aircraft descended down to Portsmouth from
research flying.
a height of about 3.5 km and then made passes through the front
at 75,
front.
150,
250,
350 and 450 m AGL to 20 km on each side of the
One pass was also made at the minimum possible elevation
Repeat
which varied between 15 m over water and 50 m over land.
passes were made at the
data analysis
250 m levels to facilitate
75 and
Low-level soundings were not made
(see appendix).
after the passes because of
the
constraints
fuel
and deteriorating
weather conditions.
Figs.
speed
and
10 a-d
wind
shows
plots
direction
completely level pass)
for
through
of
dew point,
temperature,
the
the
150
front.
m
pass
The
(the
front
wind
lowest
is again
clearly distinguished by a sudden jump in temperature and a shift
in
wind
direction.
The
contrasts
across
the
front
are
not as
pronounced as in the previous case with only a 2.5 C temperature
jump and a 45 deg wind shift.
The total change recorded across
-33-
4 40 -
-
0
43*
43
-
2
-5
4300
720
Fig.
71*
-
70*
Surface analysis in eastern New England at 1500 GMT
9.'
Isobars are drawn every 2
(10 am LST) on 15 January 1983.
0 C.
Wind barbs are in
2.5
mb and isotherms are drawn every
knots. Coast guard reports are plotted with a "M".
-34-
level
the front at this
is about 4 C and 50 deg of wind shift.
Note that the wind is weaker and more northerly just to the cold
Just a few kilometers further into the cold
side of the front.
as all four plots
to be a pocket of warm air,
air there appears
bulge towards their warm air values.
in
change
is a noticeable
There
the
of
variance
the
point trace across the point coinciding with the shoreline.
vertical wind gust trace
(not shown)
also shows a similar change
occuring over the ocean
This suggests enhanced vertical mixing is
that
in
change
trace
temperature
the
that
indicates
variance
content.
carrying a larger moisture
upward moving parcels
fact
The
The
is highly correlated with the dew point trace.
in variance and
with
dew
not
does
there
is
a
show
similar
a relatively small
vertical gradient of potential temperature.
Fig.
11 a-d
shows
the results
of
highest pass
the
There is still a jump evident in
m) through the coastal front.
the temperature field across the front at this height.
of
this
to
jump
larger than in
weakening
front
and
jump
the
a
at
the
the previous case.
in the wind
2 ms-
1
speed
jump in
(~ 450
just
lower
level
is
The ratio
considerably
The front is also marked by a
to the
the wind
cold
speed
air
at the
side of
the
front.
The
direction of the wind changes by nearly 30 deg over the entire
data
region
with
frontal position.
some
turbulence-like
flucuations
marking
the
The relatively larger temperature jump at this
height as well as the frontal signature
in the winds suggest that
this coastal front extends deeper into the environment than was
150 M AGL
1/15/83
TEMP vs. DIST
Oak
101
- I5
-10
-5
1/15/83
T
W
0
5
150 M AGL TD
W
10
15
20
25
-10
-15
vs. DIST
1/15/83
3601
w
-5
0
5
10
150 M AGL WDIR
20
15
25
vs. DIST
-270'
0
0
LU
a9
180t
-W-
Aj
-101
5
20
15
10
5
0
-5
-10
DISTANCE FROM PORTSMOUTH (KM)
Fig.
901
-
15
11
3
-1 0
'
J
a
l
I
II
A
IA
-5
,A
S
0
5
10
15
20
DISTANCE FROM PORTSMOUTH (KM)
lOa-d. Plots of a) temperature, b) dew point temperature
c) wind speed and d) wind direction plotted as a function of
distance from Pease Air Force Base, Portsmoutn NH. The data
were collected during the 150 m AGL pass through the coastal
front.
AI
--
1/15/83
450 M AGL
TEMP
1/15/83
vs. DIST
450 M AGL WSPD
vs. DIST
K4
.0
0I
W
bi
aU,
a.
- 5
-10
1/15/83
S
-5
0
5
10
15
25
20
450 M AGL TD vs. DIST
.,,,
..
,....
..
,...,,,c
ir,
-15
360
-i0
-5
0
5
20
25
-10
-5
0
5
10
15
20
DISTANCE FROM PORTSMOUTH (KM)
25
1/15/83
450 MAGL WDIR
10
15
vs. DIST
270
01801
.5-
-15
15
20
5
10
0
-5
-10
(KM)
DISTANCE FROM PORTSMOUTH
Fig.
-f5
lla-d. Raw plots of a) temperature,
c) wind speed and d) wind direction
distance from Pease Air Force Base,
were collected during the 450 m AGL
front.
b) dew point temperature
plotted as a function of
Portsmoutn NH. The data
pass through the coastal
-37-
There
previously seen.
is
no apparent change
the dew point trace across
in the variance
of
the coastline at this height although
there is a noticeable change in the variance of the vertical wind
gust
Therefore
(not shown).
there
must
not
be
a
significant
vertical gradient of moisture at this height.
Cross-sections
function
13
and
and parallel
14,
include
of
because there
potential
The
temperature plot
40 km region
is a horizontal
vicinity
temperature,
wind component are presented
respectivly.
the entire
immediate
the
of
the
the
in
stream
Figs.
12,
is expanded
to
over which data were collected
temperature gradient outside
front.
There
are
many
the
general
similarities between these plots and the equivalent ones for the
previous
case.
There
isotherms that marks
a narrow
region
of
tightly
about half
packed
the front from the ground up to about 200
The maximum horizontal gradient of temperature is
m.
or
is
that of the previous case.
The
5.7 C km-1,
stream function
shows that the warm air flows towards the front, rises over the
cold air
in a narrow jet and
cold
has
air
a weak
roll
then oscillates
imbedded
under the
downstream.
The
first wave.
The
parallel winds again show a low level jet just above the cold air
and just above the position of maximum vertical gradient.
The front was not encountered
could
not
be
detected
visually
over
at
the ocean and therefore
the
surface.
However
a
comparison between the observed and computed vertical velocities
is quite good again suggesting a two dimensional structure.
maximum measured updraft is
is 1.1 ms-1.
The
1.3 ms- 1 while the maximum calculated
POTENTIAL TEMPERATURE (C) AND WIND
500
1/15/83
-. 400
..J
C/)
2 300
O
0
4200
~0
100
Ot--20
-10
0
DISTANCE NORMAL TO FRONT
Fig.
12.
Cross section normal to the coastal
temperature
and wind.
10
(KM)
20
front of potential
Isotherms are drawn every 0.50
each wind barb represents a wind speed of 2.5 ms- 1 .
C and
500
STREAM
FUNCTION
KM X (M/S)
1/15/83
400
300
DISTANCE
Fig.
NORMAL TO FRONT
13.
Stream function
coastal front.
(KM)
(km-m-s~ 1 ) normal and relative
to the
PARR WINDS (M/S)
50
1/15/83
w401
(I)
300'0
200
100
0-20
-10
-15
DISTANCE
Fig.
-5
NORMAL 'TO FRONT (KM)
0
Cross section to the wind component parallel to the
14.
coastal front in ms- 1. Positive values are northeastward.
-41-
the
Overlaying
front.
the
horizontal
become
not
do
and
this
front but rather slope upwards away from
immediately behind the
the
between
differences
isotherms
The
case.
previous
notable
some
are
There
that
shows
function
stream
these
isotherms seemingly are being advected by the flow normal to the
front.
However
strong
a
heat
downward
flux
this
in
region
brought about by turbulence could balance the advection and allow
the
isotherms
however,
evident,
as
overall
the
turbulence
Strong
to remain stationary.
stable
is slightly
flow
is not
to
Kelvin-Helmholtz instability.
Another difference in this case is the presence of a small
temperature
horizontal
front.
Recall
temperature
that
gradient
gradient
the
in
in
previous
this
case
indicate considerable mixing is occuring.
in
the region were indeed
air temperatures.
heating,
had
The
region.
due to heating from the ocean surface.
air
warm
the
far
a
only
vertical
from
the
vertical
isotherms
This mixing is likely
Sea surface temperatures
from 1 to 2 C warmer than the surface
In the absence of a heat sink for the ocean
the heated air will be advected toward the coastal front
and presumably cause the front to become stronger.
The computed
1
temperature advection in the warm air, about 1.25* C hr- , gives
a frontogenesis doubling time of just less than 3 h.
However a
time sequence of surface analyses after the flight shows that the
front did not become more pronounced.
Temperatures on both sides
of the front increased and the wind on both sides slowly backed.
The warming of the cold air could be due to diabatic heating.
It
-42-
is, however, more likely due to vertical mixing of warm air since
this
would
Therefore
it
turbulent
heat
in
flux
cold
the
air
the warm air and a
in
that warm advection
appears
that
the process
be
may
direction.
wind
changing
the
for
account
also
allows cross frontal contrasts to remain unchanged.
Another significant difference between the present case and
the previous one is the fact that light snow began to fall in the
Doppler radar at MIT detected
Portsmouth area during the flight.
a
narrow
10
dBZ
surface near Portsmouth.
was
the
was
at
the
reflectivity
radar
5 dBZ
a
coast
the precipitation
Further south where
there
widespread,
more
along
of precipitation
band
enhancement which coincided with the coastal front position.
The
found
observer noted
flight
only
on
the
cold
air
of
side
the
for
a tendency
be
using
investigated
quantitativly
particle measuring probes.
to
that
be
the
This observation
precipitation rate increased during the flight.
can
and
front
the
snow
data
the
from
the
A vertical flux of particle mass can
be obtained from these data using the formula
R=Z{M(D)-C(D)-V(D)}
where
M is
the
mass
of
with
particles
diameter
D,
C is
the
concentration of the particles, and V is the particle fall speed.
This flux may be transformed to a water equivalent precipitaion
rate
by
performed
detect.
the
by
dividing
over the
15
density
of
distribution
water.
cells
The smallest detectable diameter is
limit is 4.5 mm.
The
that
summation
the
PMS
is
probes
.3 mm and the upper
Particles larger than 4.5 mm are counted as 4.5
-43-
mm.
To obtain mass and fall speed from diameter, the relations
(see e.g. Locatelli and Hobbs, 1974)
M=0.2-D 2
and
V=2.0-D
3 1 -W(xz)
for mass M in grams, fall speed V in m-s- 1 and D in cm are used.
The vertical air velocity is denoted by W. The precipitation rate
was calculated as a function of distance from the front for each
pass
passes.
vertically averaged
then
and
front
the
through
over
all
This averaging was necessary because of the relatively
high variance exhibited by each individual pass through the front
and
relatively weak flow in
is justified by the
15.
The result of this analysis is shown in Fig.
a
on
takes
rate
precipitation
the
cold air.
Note that the
horizontal
Gaussian-like
distribution centered about 10.5 km to the cold air side of the
front.
is little or no snow falling in the warm air.
maximum as there
Although
is skewed to the cold air side of the
The distribution
the mean precipitation
is
rate
quite
small,
the
later
passes through the front measured considerable higher values.
The origin of a snowflake arriving at
maximum
the
in
integrating
velocities
precipitation
backwards
of
the
in
time
rate
the
This
snowflake.
can
the position of the
calculated
be
horizontal
is done
by
and
the
calculated
vertical
air
speed
particle fall speed everywhere.
is
subtracted
vertical
assuming
particles have a uniform terminal velocity of 1.1 ms-
1
by
all
from which
to yield
The particles are assumed to
the
.10
.075
E
E
.05
.025-
.00-20
-15
-10
-5
DISTANCE
Fig.
0
NORMAL
5
TO FRONT
10
15
(km)
15.
Precipitaion rate computed with data from a PMS probe
averaged over all passes through the coastal front and
plotted as a function of distance normal to the front.
20
-45-
The integration is carried out
move horizontally with the wind.
up to the highest aircraft pass, above which, the data from the
sounding made prior
height
to
up
the
velocity at 500 m.
updraft
it
should
air motion
vertical
frontal
warm
for the horizontal
used
are
to
decay
inversion
(~2.3
assumed
is
wind
vertical
The
winds.
the passes
to
linearly
with
the
from
km)
While this does not account for a tilt in the
not
cause
error
serious
a
less
much
is generally
the
since
than
mean
the particle
terminal velocity.
A few selected
with
trajectories are shown in
the position of observed clouds, the
vertically after entering
the weak flow in
that
Note
isotherm.
potential
the
the
Fig. 16
updraft and the -2 C
snow generally
cold air.
together
falls
down
This is indicative of
Note also that snow falling
this air mass.
to
the ground at -10.5 km passes over the position of the vertical
jet
at
about
1.5
km
above
The
MSL.
aircraft
a
measured
stratocumulus cloud base at about 1.1 km which is almost exactly
the lifted condensation level of the surface warm air.
of the clouds was at about 1.8 km.
The top
Therefore snow falling at the
point of the observed maximum precipitation rate originated
a position within clouds and above the vertical jet.
MIT radar
observed
Therefore
detected
no
echoes
near Portsmouth
snow must have grown within
it
seems
likely
that
the
above
from
Since the
2 km,
the
the stratocumulus clouds.
coastal
front
is leading
directly to the enhancement of the precipitation at the surface.
2.0
SNOWFLAKE TRAJECTORIES
15 JANUARY 1983
1.5
-
(I)
.
0.5-
-2*
-20
-15
-5
-10
DISTANCE NORMAL TO FRONT (KM)
0
Fig. 16. Computed snowflake trajectories shown schematicaly with
C potential
the position of the observed clouds, the -2*
isotherm and the main updraft.
5
-47-
One aspect of the precipitation
the
coastal front
is that differential evaporative
occur across the front.
temperatures,
point
degree
than
the
enhancement associated with
cooling can
With heavier precipitation and lower dew
the
cold
be
air will
warm air.
Therefore
cooled
to a greater
this evaporative
cooling
could offset any turbulent diffusion of the front, sustaining or
even enhancing the coastal front.
The
coastal
conclusion
of
front persisted
the flight,
lasting
for about
a major role in determining
snow accumulation.
Boston,
hours
after
the
during most of what became
fairly intense storm throughout New England.
played
12
a
The coastal front
the distrubution of the total
for example,
remained
generally
on
the warm side of the coastal front and primarly received a mix of
rain and wet snow.
10
cm.
On
the
The recorded snow accumulation was less than
other
hand,
regions
less
than
30
km
to
the
north-west that remained in the cold air, received up to 60 cm of
snow.
-48-
CHAPTER III
THE DENSITY CURRENT ANALOGY
undercuts another less dense fluid.
in
last section,
the
type of flow.
in
similarly
(1981)
to resemble
seems
front
coastal
simulation
a density
to
From the analysis presented
this
In fact, Ballentine noted that the flows produced
numerical
his
the
fluid
one
results when
flow that
the
is
current
A density
of
Later Passarelli
current.
behaved
front
coastal
the
and
Braham
showed that Great Lake snow squalls were often intimately
related to a density current-like land breeze and speculated that
might
effect
a similar
be
the
for
occurring
coastal
front.
Therefore, a summary of the properties of a density current and a
observed properties
to the
comparison
the
of
coastal
front
is
warranted here.
If
the wall
suddenly
separating
removed,
the
denser
horizontally and undercuts
is
the
because
result
of
of
two
of
the
the lighter
a horizontal
different
of different
fluids
hydrostatic
fluids
fluid.
pressure
in
is
accelerates
The acceleration
gradient
pressures
density
the
that
two
arises
fluids.
The denser fluid continues to accelerate until a dynamic pressure
due
to
the
convergence
pressure gradient.
of mass
at
the
interface
balances
the
The resulting steady flow is called a density
(or sometimes a gravity)
current.
The
current moves under the
-49-
presence
the
In
speed.
phase
constant
a
at
fluid
ambient
Long after
viscosity, this phase speed may be somwhat reduced.
the density current
is
the two
the boundary between
established,
of
fluids becomes flat except near the leading edge of the current.
inviscid
the case of a
In
(1969).
density current was made by Benjamin
the
of
treatment
analytical
extensive
most
The
density current imbedded in an infinitly deep fluid, he concluded
that the speed of the density current through the ambient fluid
is given by
V=k/(gH(P 2 -P 1 )/P
of
invading
the
)
the ambient fluid,
the density of
is
where pi
1
fluid with depth H, and g
P2 is
the density
the gravitational
is
The constant of proportionality k is /2.
acceleration.
Benjamin
further found the structure of the invading fluid to consist of a
that
head wave
depth
rises somewhat higher
He also showed
H.
than
the
downstream mean
that wave breaking must occur on the
head leading to considerable turbulence downstream.
If viscosity, heating or stratification is
included in the
analysis, the density current problem becomes considerably more
difficult and therefore most of what is known about these types
of
density
experiments
currents
similar
to
has
been
those
learned
described
1959), Middleton (1966) and Simpson
type
of
densities
experiment
differing
usually
using
by a few
in
above.
laboratory
Kleugan
tank
(1958,
(1969) all carried out this
segregated
percent.
The
saline
results
water
with
generally
-50-
indicate
those
that within a wide range of Reynolds numbers,
most
often
exhibit behavior
found
in
the
atmosphere,
including
density
currents
similar to that described by Benjamin.
Fig. 17
shows a schematic diagram of a typical laboratory density current
constructed
from
the
work
of
Kleugan,
Middleton
and
Simpson.
Major differences between the theoretical and laboratory currents
include
a slightly
lower
value
of
k and
turbulence on the back side of the head.
varying
degrees
of
The laboratory currents
were also found to have a protruding nose of the denser fluid at
the
leading edge
friction
of
the
retards
to
be
current.
This arises because
advancement
of
the
The maximum height of
lower boundary.
found
the
about
twice
the
downstream
fluid
dense
the
individuality
of
different
apparent in the shape of the head.
and
height
For
high
of
the
Reynolds
head
is
number
density
but
this
Middleton noted
currents
is often
He noted that the elongation
dependent
upon
such
flows,
the
is often
depth,
depends upon the degree of breaking on the head.
that
near
the head wave
fluid
surface
as
the
in
Reynolds
the
nunber.
atmosphere,
density current heads will exhibit a characteristic aspect ratio
(= head height/head length) significantly smaller than is usually
found in saline solution laboratory experiments.
Some
naturally-occuring
density current are saline
(or
mud)
avalanches.
flows
along
a
flows
intrusion
lake
that
similarly
behave
into an estuary,
bottom
and,
to
some
to
a
turbidity
degree,
In the atmosphere where sharp density contrasts are
most often brought about by sharp virtual temperature contrasts,
Fig.
Schematic ,diagram of a typical laboratory density
17.
current produced using two fluids of different salinity.
-52-
flows have been found.
many density-current-like
Simpson
structure.
current
density
in
structure
sea
(1974) and Goldman and Sloss
between
analogies
sucessful
made
(1969)
a
has
front
a similar
found
Both Charba
breezes and haboobs.
cold
a
of
edge
leading
the
that
showed
(1958)
Berson
thunderstorm
analyzed
outflows and a theoretical density current.
A visual comparison between Fig. 17 and either Fig. 6 or 13
aspect
characteristic
ratio
considerable
the
in
similarity
the
in
coastal
downstream depth.
head
wave
both
that rises about
is
model
There is a head
25%
above
the mean
There is a roll in the circulation within the
flows
as
well
condsiderable
as
Absent from the coastal front structure is
mixing.
nose.
on
front
the
of
structure
basic
density current and that of the coastal front.
wave
there
Nonetheless,
work.
Middleton's
from
is
17, as should be
considerably different than that shown in Fig.
expected
head
front
coastal
the
of
The
current.
density
classical
a
with
similarities
structural
many
shares
indeed
front
coastal
the
that
shows
Middleton found,
however,
downstream
a protruding
that the height of the nose may
be as low as .07-H or about 15 m for the coastal front and thus
too low to be detected by aircraft.
air mass
in both coastal
front cases
Further,
because
the cold
is nearly stationary with
respect to the surface, frictional drag of the cold air will be
weak and therefore a nose may not exist.
-53-
be appled
may
equation
speed
phase
Benjamin's
to
directly
replaced
by
which is derived using the equation of state for moist air.
If
density
provided
analysis
front
coastal
the
is
virtual potential temperature, i.e.
1 =0V2 -6vi
P2~P
0v 1
P1
in
applying
front,
the
virtual
average
the
is
ev 2 -evi
to
this
layer up to 500m.
H is
be
to
taken
temperature
500
difference
m, then
the
in
From the potential temperature analysis, this
number evidently accounts for most of the temperature difference
across the front.
air
normal
speed
Since the velocity of the front and the mean
front
the
to
are
independently
known
(see
appendix), the proportionality constant k may be determined.
The
results of this calculation for the two cases presented are shown
in Table 1.
k in
It can be seen that the values of 1.03 and 1.10 for
cases
both
are
than
less
k's found
for other density-current-like
instance,
Charba
found k less
Simpson
seems
that
structure
model.
the
and
k=l.25
than
one
front
coastal
dynamics
found
for
an
They are, however, within the range of
inviscid density current.
found
Benjaman
V2
the
by
a
in
a
typical
For
and
thunderstorm
outflow
breezes.
Therefore
it
both
in
for sea
may
atmospheric flows.
well
be
two-fluid
modeled
density
current
-54-
case
gH-AOv/0vi observed V
Aev
mean wind total obs. V
k
Jan 10
2.92*C
7.25 ms-
1.50 ms- 1
6.0 ms-1
7.5 ms-'
1.03
Jan 15
2.95 0 C
7.28 ms-1
1.35 ms-I
6.7 ms-I
8.05 ms-I
1.11
Table.
1.
Application of Benjamin's
eq.
to the coastal
front.
-55-
CHAPTER IV
SUMMARY AND DISCUSSION
The vertical structure of two New England coastal fronts was
observed by aircraft along the New Hampshire coast.
to consist
of
two
distinct
narrow transition zone.
air masses
are
separated
especially
some features,
to
be
enhancement downstream.
mixing along the
front and seems
characterizes the coastal
for
responsible
directly
There
an
the
A vertical
front has been shown to be basically two-dimensional.
1
a
The flow near the
circulation field, extend to at least 500 m.
jet of about 1.5 ms-
by
Although most of the front's horizontal
lies below about 300 m,
signature
that
It is found
precipitation
observed
is also evidence of considerable
frontal interface although both cases did not,
in general, support Kelvin-Helmholtz instabilities.
The coastal
front is also shown to be similar to a two-fluid density current.
If
the primary
front is
that which
balance
governs
of
forces
for
the
a density current,
steady
coastal
then the favored
positioning of the coastal front that Bosart et al. noted may be
accounted for.
along the
Recall that the coastal front is most often found
coast in New Hampshire
Massachusetts
and
and Maine,
This
southward.
but well
position
is
inland
approximately
equivalent to where the flat coastal plain meets the first
of the Appalachians
Mountains.
If
in
hills
these mountains act as a dam
to any westward movement of the cold air, then because
of mass
the
surface
conservation,
the
depth
of
the
cold
air
and
thus
gradient of hydrostatic pressure, must vary as the inverse of the
-56-
distance between the coastal front and the mountains.
because
of
mountains
this
can
inverse
relation,
support
a
wider
the
region
range
of
Therefore,
close
to
balancing
the
dynamic
pressures (i.e. a wider range of wind speeds normal to the front)
than
a
similar
region
far
from
the
mountains,
and
thus
the
coastal front will be found, more often than not, near the base
of the mountains.
The ability for the mountains
to dam the
cold air depends
upon the ratio of the kenetic energy of the cold air ahead of the
mountains
to the available potential energy
crossing the mountains.
it would have upon
This ratio may be expressed as a Froude
number def ined
NH
U
where
N is
the
buoyancy
frequency,
is
H
the
height
of
the
mountains and U is the cold air wind speed normal to and far from
the mountains.
Damming occurs
1.
Fo
Evaluating
forward because
how
this
has
However,
if
velocity
equal
the
it
for
the
two
if damming has
effected
is
the
assumed
numbers
for Froude
cases
than
studied
is
not
indeed occured,
it
is not clear
stratification
that
greater
the
cold
and
wind
air would
straight
velocity.
have
a wind
to that found east of the coastal front and that
stratification
remains
uneffected
by
the
presence
of
the
coastal front, then the Froude number takes on the values of 2.0
and 1.4 for the two cases presented
damming is indeed occuring.
respectively
indicating
that
(The mean height of the Appalachain
mountains in central New Hampshire is about 600 m.)
-57-
Along
most
of
the
distance between the
Therefore
short.
same
place.
New
shoreline and
England
coastline,
the mountains
the
is relatively
the coastal front may form and stagnate in
However,
coastal plain
northern
may
in
be
50
appear as a land-breeze
southeastern
km wide,
New
England,
the coastal
type density current
where
front may
the
the
first
near the coastline
where a naturally occuring surface temperature gradient exists.
It may
then be forced
inland
by
the mean easterly wind
stagnation point at the base of
the mountains.
to its
Whether or not
the coastal front in this region behaves like a density current
and whether coastal frontogenesis always commences at the coast
is beyond the scope of this study.
The next phase of NEWSEX will
incorporate
mesonet
a
surface
observing
and
thus
be
better
equiped to address this question.
From
this
research,
it
is
apparent
that
further progress
toward understanding coastal frontogenesis lies in understanding
the
nature
of
the
viscous,
stratified density current.
much
more
than
understanding
just
time-dependent
and
continously-
Since this type of flow catagorizes
the
New
England
this problem would have
coastal
front,
an
applications to many other
problems.
Finally from a forecasting viewpoint,
the results presented
here provide an opportunity to forecast the motion of an existing
coastal
both
front.
sides
of
By
the
using
front,
temperature
together
and wind
with
measurements
Benjamin's
equation
on
and
-58-
the proportionality constant found here, it may be possible to
obtain a usable surface velocity of the front.
A practical
application of this procedure is the warning of pilots of
approaching low-level wind shear and possible precipitation type
changes.
Skill in short-range forecasting of precipiation type
and amount may also benefit from this technique.
-59-
APPENDIX
In
data
order to produce
over a period
that are collected
in
a transformation
dimensions,
time
of
and
time and
by
defining
a
new coordinate
D that
in
a mapping
horizontal coordinates onto one is necessary.
from
sections
cross
vertical
synoptic,
all
of
three
the
two
This is done here
the
represents
horizontal
distance that each point in space and time is from some reference
point on the front.
This is
accomplished using the equation
D=(X-Xo)-sin(a)-(Y-Yo)-cos(a)+c(t-to)
where a is the angle that the front makes in the X-Y plane and c
is
the
the
front.
The
reference
point,
which
velocity
represent
the
of
variables
here
is
with
subscripts
chosen
to be
the
position of the front encountered during the lowest pass through
the front.
To determine a, it is assumed that a does not vary in time
or height and that it does not vary over the horizontal distance
in
which
the
frontal
passes
were
made.
Therefore
determined from a carefully plotted surface analysis.
a may
For the
second coastal front case where repeat passes were made at
separate elevations
c was determined
from the distance
be
two
that the
-60-
the time of the repeats.
travelled between
front
analyses,
subsequent
of
the position
the
For this and
for
front
each
pass
is defined as the point where the maximum gradient in temperature
where
wasn't quite so obvious,
it
In cases
In most cases this point was obvious.
was observed.
the point having the greatest
wind shear was used.
For the case of 10 January where only one pass was made at
the possibility of a vertical
each elevation,
tilt
in
had to be accounted for in order to determine c.
this,
a plane was fitted
to the
the front
To accomplish
three lowest points
and c was
calculated as a least squares fit.
The results of this analysis
that a= 4 5 deg
(0 deg is
For
January
the
15
calculations
1.35 ms-
1
yielded
90 deg is
north,
case
a=55
c=1.25 ms-
1
10 January case were
for the
deg
east)
and
and c=l.50 ms- 1 .
the
and c=l.45 ms-
two
1.
The mean of
was used subsequently.
The error to be expected in computing D depends
the
velocity
accuracy
of
the
position
measurements.
largely on
Position
of
the
aircraft is determined using an INS system, the accuracy of which
is known to oscillate in
time with an 84 minute period and an
amplitude
that varies from flight to flight.
amplitude
of
the
error
can
be made
by
An estimate of the
studying
the
indicated
position of the aircraft each time it was known to pass over a
fixed location on the ground.
passes,
the aircraft
Portsmouth.
During each of the coastal front
passed directly over Pease Air Force Base,
This enabled the above
technique to be applied
to
-61-
find the position error.
The results for both cases show that
the magnitude of the horizontal position error was about 300 m.
Therefore
error
if
a is
determined
in D is between
to within 10 deg,
0.5km and
1.5
dependent because of the error in c.
this
error
does
not
represent
the
km.
then the expected
The
error
is time-
It should be stressed that
variance
of
individual
calculations of D because of the systematic nature to the sources
of
the errors.
It
does,
however,
represent
between each of the passes through the front.
the possible
error
-62-
ACKNOWLEDGEMENTS
The author
his
also
ideas,
thanks
thanks his advisor Prof.
support and
Stephen
encouragement
Garner
of
MIT
his
for
research.
He
suggestions
and
this
during
for
Passarelli
Richard
enlightening conversions as well as Spiros Geotis for reviewing
the
Finally
manuscript.
Facility pilots
Bill
he
thanks
Research
Zinser and Pete Orum whose
NEWSEX made this research possible.
grant #8209375-ATM.
NCAR's
Aviation
efforts
during
This work was funded by NSF
-63-
REFERENCES
1970: A study of high pressure ridges to the east of
Baker,D.G.,
the
thesis,
Ph.D.
Mountians.
Appalachian
Meteorology, Massachusetts Institute of Technology,
Ballentine, R.J.,
Benjamin,
T.B.,
127pp.
1980: A numerical investigation of New England
Mon.
frontogenesis.
coastal
of
Dept.
1968:
Gravity
Wea.
108,
Rev.,
currents and
1479-1497.
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