Download Analysis and prediction of visibility at sea. Schramm, William George 1966-05

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Thesis and Dissertation Collection
1966-05
Analysis and prediction of visibility at sea.
Schramm, William George
Monterey, California. Naval Postgraduate School
http://hdl.handle.net/10945/24612
ANALYSIS AND PREDICTION OF
VISIBILITY AT SEA
M GEORGE SCHRAMM
LIBRARY
NAVAL POSTGRADUATE SCHOOL
MONTEREY, CALIF. 93940
5
6- 7-
ANALYSIS
AND PREDICTION
OF VISIBILITY AT SEA
by
William George Schramm
Lieutenant, United States Navy
B.S.
United States Naval Academy, 1958
,
Submitted in partial fulfillment
for the degree of
MASTER OF SCIENCE
from the
UNITED STATES NAVAL POSTGRADUATE SCHOOL
ABSTRACT
Visibility over the sea is one of the prime environmental
parameters affecting naval operations and current forecasting
methods
for visibility are inadequate.
Low
visibilities at sea
are related to moisture in the air and saturation of the air.
Fleet Numerical
Weather Facility
at
Monterey produces a
of the difference in vapor pressures of the sea
this field
may be used as
a humidity index.
and the
field
air
An attempt
The
is
and
made
to use this field plus other environmental parameters, such as
air temperature, to
produce a regression equation for visibility.
Humidity, air temperature and wind speed are determined to be
the most important variables, however, the equation is inaccurate
when
the visibility is low.
Graphical techniques were applied to these variables and
a scattergram of visibility as a function of air temperature and
vapor pressure difference revealed a significant relationship
that
was used
to forecast fog probability and visibility.
TABLE OF CONTENTS
Page
Section
1.
Introduction
11
2.
Background
14
3.
FNWF
17
4.
Objectives
19
5
Data Compilation
20
6.
Data Analysis
23
7.
Conclusions
32
8.
Bibliography
45
.
Vapor Pressure Program
TABLE OF SYMBOLS
constant (.18)
c
e
e
AND ABBREVIATIONS
Q
w
vapor pressure of the air
vapor pressure of the sea
k
constant
r
distance
t
time
Ta
dry bulb temperature of the air
T^p
dew
Tw
temperature of the sea
V
surface wind speed
(.
15)
point temperature of the air
LIST
OF TABLES
Page
Table
I
II
III
IV
V
FNWF
verification of
Date time groups
of
a'
w -e_)
field
34
analyzed data
35
(e
Visibility code for ship reports
36
Statistical results of problem eight
37
Statistical results of problem five
38
LIST
OF ILLUSTRATIONS
Page
Figure
1
.
39
Chart of Air-Sea vapor pressure
difference field
40
2.
Grid overlay over
3.
Ship weather report
4.
Graph of dew point spread vs
5.
Graph of visibility as a function
air temperature and (e -e )
(e
w -e Q
Smoothed plot
field
41
w
6.
)
(e
w ~e a
)
of
and
(e
43
q
of visibility as a function
of air temperature
42
-e
)
44
1
.
Introduction
Modern technology has provided recent and rapid advances
in the fields of
meteorology and oceanography including numerical
computer techniques, however, the ultimate value of any new
technology lies in
its
application to consumer products.
If
the
U. S. Naval Weather Service is considered as a producer of
services and the Naval
involved
is that
Commander
is the
consumer then the product
information concerning the environment that the
Commander needs
to
make rapid and accurate decisions. This
information includes, but is not limited to, such parameters as
precipitation, cloud distribution, sea state, wind and visibility.
The analysis and forecasting of some of these parameters has been
improved by the application of the digital computer, however, this
technique has not been applied to the prediction and analysis of
visibility.
Visibility at sea has
always been a problem to the Naval
Meteorologist, as well as others concerned with transport over the
sea.
Commercial shipping interests are faced with the danger
collision at sea in areas of low visibility.
Naval Commanders have
additional factors to consider besides collision.
may
restrict air operation
increase transit times
if
of
and training exercises.
speeds must be reduced.
Low
It
In
visibility
also
may
many naval
operations the effective threat of electronic countermeasures has
precluded the use of radar and resulted in visual search becoming
11
all important.
Therefore, while the
Commander may want
areas of low visibility or hide in them,
it
is
to avoid
important that the
U. S. Naval Weather Service have an accurate and prompt
technique for the prediction of visibility at sea.
At the present time, forecast visibilities are based on reports
from ships in the general area, knowledge of air mass and frontal
movements and climatology.
of reported data
This method
may
suffer from the lack
and during war the number of reports would be
even smaller.
This lack of reported data also prevents direct analysis by
the computer and the fact that low visibility areas are not generally
advected complicates the problem of forecasting.
However,
visibility is dependent on the interaction of other parameters that
lend themselves to analysis and prediction by objective methods.
One
of the
of the air.
most important of these parameters
is the
humidity
The U.S. Naval Fleet Numerical Weather Facility,
located at the Naval Postgraduate School, Monterey, California,
produces a humidity field for the Northern Hemisphere.
at the request of the Fleet Numerical
It
was
Weather Facility that the
research connected with this paper was conducted.
The author wishes to express his appreciation for the
assistance and encouragement given by Doctor T. Laevastu of
the Fleet Numerical Weather Facility and Professor G. Haltiner
of the U. S.
Naval Postgraduate School.
12
Thanks are also given
to the Fleet Numerical
Weather Facility
data.
13
for providing
the necessary-
2
.
Background
Atmospheric obscurations or restrictions to visibility are
caused by the presence
of a large
held in suspension in the air.
number
of
minute particles
|_lj
These may be solid particles of smoke, sand or dust or
hydrometeors such as water droplets and ice particles.
The solid particles in the air are usually a problem only over
land or in ocean areas adjacent to large cities or deserts.
Occasional dust storms will blow far out to sea, however, these
phenomena will not be considered
in this paper.
The hydrometeors or moisture particles may be further divided
into precipitation and
suspended moisture.
Precipitation is
primarily a restriction to visibility in storms and fronts and these
areas
may be
forecast by standard techniques for analysis and
forecasting of fronts and pressure systems.
The suspended moisture
in the air
becomes more and more
a restriction to visibility as the particles grow in size.
always water vapor
in the air but this only
of
There is
becomes visible when
condenses on hydroscopic condensation nuclei.
If
these suspended
moisture particles become a definite restriction, they are referred
to as fog or haze.
Fog
is
defined by the Admiralty Weather Manual
\l\
as a
condition producing a horizontal visibility of less than 1/2 mile,
while haze results in visibility between 1/2 mile and one mile.
14
it
For the purposes of this paper the definition suggested by Byers
will be used.
[_4j
He states
that fog is a stratus cloud cover
that forms at the ground or close to
it
as to affect the surface
visibility.
Condensation on the nuclei only takes place after the
has become saturated.
|5j
air
This saturation of the air is caused
by either cooling of the air to saturation temperature or evaporation
Fog
of moisture into the air.
is classified
by type according to
the processes causing either the evaporation or the cooling.
Fl
2J
Frontal fog is associated with the passage of frontal weather
bands and the forecasting
forecasting.
of this
type of fog is related to frontal
Radiation fog takes place over land during the night.
The ground radiates and cools and in turn cools the
saturation temperature.
and cools but convection
air to
The ocean also radiates during the night
in the
water replaces the surface heat
and keeps the cooling to a minimum and thus prevents the formation
Sometimes radiation fog will
of radiation fog.
drift
the water, but this only takes place near the shore.
fog or sea fog as
open ocean.
Moist air
it
is
from land over
Advection
called is the type that appears over the
\4~\
is
advected over colder water and
is
cooled to the
saturation point by latent and sensible heat exchange between the
air
and water.
15
There has been very
its
little
study on the subject of sea fog and
prediction or the conditions that form
it.
G.
I.
Taylor studied
fog in the vicinity of the Grand Banks prior to 1917 and decided
that
wind speed and the difference between
temperatures were the dominant factors,
air
and sea
[llj
Laevastu has postulated that sea temperature
factor because of the rapid rate with
characteristics of the sea
it
which the
air
is
the primary
assumes the
passes over.
Because fog formation and low visibility are dependent on
saturation
it
is
apparent that humidity of the air is an important
variable to be considered.
The Fleet Numerical Weather Facility produces a hemispheric
chart of vapor pressure difference between the air and the sea and
data on other important parameters such as air temperature are
available from ship weather reports.
16
1
3.
FNWF
Vapor Pressure Program
The Fleet Numerical Weather Facility
at
Monterey produces
a comprehensive program of oceanographic charts by numerical
methods using the
CDC
1604 digital computer.
Part of this
oceanographic program consists of the forecasting and analysis
of sea surface temperatures
These products depend,
and mixed layer depths.
in great part,
1
10
7,
on a detailed knowledge of
heat exchange between the air and the atmosphere.
This heat
exchange includes both sensible (Q^) and latent (Q e heat
)
Sensible heat depends on the difference between the
exchanges.
air
and sea temperatures, while latent heat depends on the
difference between the vapor pressures of the air and the sea.
Laevastu has developed the following equations for the
If (e T „
w
term.
- e a ) is positive;
Qe
If (e
Qe
= (0.26+0. 077V)
-e a )
Qe
is
(e
w -e a )Lh
negative;
= 0.077V(e w -e )L h
a
The vapor pressure of the air
is
computed from reported
values of dew point temperature from ship reports and the following
relationship:
log 10 e a = 9.405-2353/T dp
The vapor pressure of the sea water
is
computed using the
water temperature in place of the dew point temperature
including a factor of
.
98
.
17
,
but
j
log
1Q
e
w
= .98(9.405-2353/T )
w
Because of the lack
of data at sea,
any analysis
of the vapor
pressure difference field over the sea should be based both on
initial
values from reports and on computation of the responses
of the air properties to the sea as the air is
water.
FNWF
advected over the
has solved this problem by using the following
equation by Amot for the computation;
An equivalent equation,
that is more suitable for numerical
computations, has recently been introduced at FNWF* 17, 10
The
(e
w -e
)
field
has been verified by
of this verification is listed in Table I.
18
FNWF
and a sample
.
4.
Objectives
Investigate the effects of available meteorological and
a.
oceanographic parameters on visibility at sea and fog formation.
This includes not only humidity but the other parameters included
in ship
b.
weather reports
Relate the Fleet Numerical Weather Facility chart of vapor
pressure difference, as an index of humidity, to visibility.
c.
Determine which of the investigated parameters have the
most effect on visibility by both numerical and graphical techniques
d.
Attempt to obtain a linear regression equation for visibility
as a function of the most important parameters.
e.
Determine
if it is
feasible to use Fleet Numerical Weather
Facility vapor pressure charts plus other parameters available to
FNWF
along with numerical computer techniques to produce large
scale analysis and forecast charts of visibility at sea.
19
.
5
.
Data Compilation
Raw data was provided by the Fleet Numerical Weather
Facility
and consisted of hemispheric charts of vapor pressure difference
(e
w -e
)
and world-wide ship weather reports
The data was from selected days
during both 1965 and 1966.
in the
for the
same times.
months of April and May,
This time of year is a period of high
fog incidence over the northern oceans.
The particular dates and
times of the charts used are listed in Table
was
Selection of data points
II.
restricted to the North Atlantic
ocean because of the density of the reports
in this area
and the
importance of the area to commercial shipping and naval operations
Only points north of 20 degrees north latitude and south of 70
degrees north were used due to the boundary limitations of the
computer.
The area was further restricted to points
at least
one
grid width from land to eliminate land effects such as radiation
fog and also because the vapor pressure program produces the
best results
away from
One
land.
grid width is about 150
NM.
The ship reports to be used were selected from the area
described above.
Only complete reports with the same date time
group as the chart of
were used.
(e
w ~e a
)
with which they were to be compared
All reports with precipitation indicated in the present
weather column were not used because the visibility reported
in
such cases would be related more to the precipitation than to any
moisture particles suspended in the air.
20
The actual extraction
FNWF
of the
Figure
of the data
began with the analysis
vapor pressure charts.
1
is
an example of such an analysis which
is printed
on a 1:30,000,000 polar stereographic projection and analyzed
at
one millibar intervals.
To relate particular ship reports to the
(e
w -e a
)
charts
necessary to use a plastic grid overlay over the chart.
shows the
I
and
J
grid overlay in position over the
Figure 2
analyzed chart.
ship weather report
,
coordinates and thus
The ships' positions, as reported on the
are
it
changed by
was possible
FNWF
for
to
I
and
J
grid
to find the position of the
ship on the chart and extract the value of
(e
w ~e a
) .
This
was
each of the data points and the values recorded with the
appropriate ship weather report.
Figure 3 is a sample of a ship weather report as
recorded by
FNWF. From each
.
Air temperature (T a )
2.
Dew
point temperature (T^
3.
Dew
point spread (Tg-T^p)
4
Air-sea temperature difference
.
5.
Wind speed
6.
Three hour pressure change
(V)
21
it
is
selected report the following
variables were extracted:
1
The
coordinates of the grid are printed on the overlay and are
visible in the Figure.
done
was
it
)
(T
-T
)
7
.
Time
8
.
Visibility
9.
of report
Vapor pressure difference ( e
the
FNWF
w ~© a
)
which had come from
charts.
Because visibility was to be the dependent variable
it
was
recorded in three forms to allow different possibilities of
correlation.
These forms were:
1)
visibility
code as
it
is
recorded on the
ship weather report and which is non-linear with respect to actual
distance,
2)
visibility in nautical miles
(NM) and
All these forms of the visibility parameter
with the other parameters.
3)
fog or no fog.
were recorded along
Eleven hundred data points were thus
treated and used for the analysis.
22
6.
Data Analysis
After selection of the parameters to be analyzed and
extraction of the data from the charts and ship reports the next
step
was analysis. The purpose
was
of the analysis
each of the independent variables
to
check
for correlation with visibility
and the effect each had on visibility.
Two techniques were used:
variables using the
techniques and
2)
CDC
1)
numerical analysis of the
1604 digital computer and regression
graphical analysis using scattergram techniques
These two methods will be discussed separately.
Numerical Analysis
The computer center at the U.
S.
Naval Postgraduate School
maintains a library of subroutines for use with the
computer.
CDC
1604
This library includes several numerical correlation
programs, but on the basis of their limitations and restrictions
the list
was narrowed down
to three.
All three of these
programs
were tried at least once with the same sample of data to observe
which would best
programs are:
1)
suit the objectives of the paper.
These three
BMD
13.
BIMED
09,
2)
comparing the respective results
would be used
BIMED
for the
it
03R, and
3)
was decided
BMDX
that
After
BIMED 09
numerical analysis.
09 is a linear regression program for use with one
dependent variable and n independent variables.
23
It
performs a
.
multiple stepwise regression that adds independent variables one
at a time
and prints the results
for
each step.
At each step the
variable added is the one that gives the best goodness of
fit.
Transformations of variables and transgeneration of new variables
are both possible and weighting factors
may be applied
to the
data.
were used with the exception
All these features
of the
weighting factors.
Results programmed for printing include
sums
raw sums of squares, average values
of variables,
of
variables, residual sums of squares, and simple correlation
coefficients.
For each step in the regression, the variable used, F level,
standard error, regression constant, and regression coefficient
are also printed.
A comparison
of actual
the dependent variable and the deviation
The variables were tried
in different
and predicted values of
may also be
printed.
combinations and each
one of these combinations was referred to as a problem.
eight "problems" were analyzed with the computer.
these problems used
(e
w -e a
)
Twenty
Half of
as the humidity parameter and half
used the dew point spread, this being the only difference between
the two groups.
This
was done
to insure that the vapor pressure
difference would indeed act as a valid humidity index.
of the
dew
problems
w -e)
a
(e t
In
each
produced the same general results as
point spread
24
The fourteen problems where the vapor pressure difference
was used were
further divided into
two groups
of
seven based
on values for the constant term in the regression equation.
first
the data
to zero.
was processed and
the constant term
was
At
restricted
The dependent variable was then tried in seven different
forms:
code from ship reports
(1)
visibility
(2)
square root of visibility code
(3) log-.Q
code
of the visibility
(4)
fog or no fog
(5)
visibility in nautical miles
(6)
square root of visibility in
(7)
log jo °f the visibility in
NM
NM
The square root and log^Q values were computed using the
transformation feature of the
BIMED
09 program and the fog - no
fog values were a result of transgeneration by directing that all
visibilities less than one mile be considered fog
than one mile be no fog.
changed to visibility
and
all greater
The values of visibility code were
in nautical
miles by use of Table
III.
The same seven variations of the dependent variables were
then used allowing the computer to produce a value for the
constant term in the regression equation.
The statistical results of each problem were compared to
results of the other problems.
25
The relative success of each problem was based on the
prediction of the fog cases by use of the related regression
equation.
Print-outs of actual vs predicted visibilities were
Two percentages were computed:
obtained and evaluated.
percent of actual fog cases that were predicted, and
percent of predicted fog cases that verified.
2)
1)
the
the
Standard error of
estimates were also compared.
Those problems
in
which the constant term was not restricted
to zero produced the smallest standard errors, however, they did
a poor job of fog prediction.
In
each
of the
problems in this
group the independent variables were selected by the computer
in the following order:
1)
Humidity
2)
Air temperature T a
3)
Wind speed
(e
w -e &
)
Problem number eight
group.
is
an example of a problem
in this
Vapor pressure difference was used for the humidity
parameter and the visibility code was used for the dependent
variable.
The constant term
in the regression
equation had a
value of 6.34656 and the standard error of estimate was 1.02,
which was one
of the lowest obtained.
fog cases predicted by this equation
of predicted
The percentage
of actual
was 25%, while the percent
cases that were really fog was 100%.
The
regression equation is a linear function and the large constant
26
term, while improving the standard error for the curve as a whole,
caused larger errors
end of the curve where low visibilities
(See Table IV)
occur.
In
at the
each problem where the constant term was restricted to
zero the standard error was larger, but the fog prediction was
In these cases the line of the regression equation
better.
being forced through the origin bringing
of visibility.
Problem number five
it
closer to the low values
fell in this
produced the best results for fog prediction of
problems.
and 19%
category and
all the
numerical
The percent of actual fog cases predicted was 75%,
of the predicted
was 2.14.
was
cases were fog.
The standard error
This problem also used the vapor pressure difference
as the humidity parameter and visibility code for the dependent
variable.
(See Table V)
In all the
problems where the constant
term was zero, the computer selected the significant variables
in a different order:
1)
Air temperature
2)
Wind speed
3)
Humidity
When
the constant term
was used,
all the deviations
between
actual and predicted values for fog cases were large negative
values caused by the large constant term.
Because
of this a
value of 3.17 was used for the constant while retaining the
regression coefficients from problem number eight.
27
This improved
the results to
75%
of the fog
cases being predicted and 40% of
the predicted cases being fog.
The difference between sea and air temperatures and the
time of report were significant variables in only three problems
and then were only considered after
air temperature,
wind speed,
and humidity.
In problem
number
five they
decreased the standard error
from the 2.21 with the first three variables to 2.14 with all five.
The other independent variables, dew point temperature and three
hour pressure change, were insignificant in all the problems.
Graphical Analysis
Based on the results of the numerical analysis
wind speed, and vapor pressure difference
for
air temperature,
independent
variables, and the visibility code figures for the dependent
variable
were considered
These
for the graphical analysis.
variables were plotted in different combinations on scattergrams.
Sea temperature and the difference between sea temperature and
air temperature
were also tried as variables because
importance placed on them by Laevastu
In addition, graphs
(8)
of the
and Taylor
(11).
were plotted of vapor pressure difference
vs dew point spread and wind speed vs visibility.
The plot of vapor pressure difference vs dew point spread
was
quite scattered, however,
when values
of plus or
minus one
degree are considered for the dew point spread the plotted points
fit
a linear function.
(See Figure 4)
28
Wind speed vs
All visibilities
Of
all the
visibility
were present
showed no meaningful relationship.
at all
wind speeds up to 48 knots.
combinations of the variables suggested by the
numerical analysis the one that gave the most meaningful results
was
that of visibility code as a function of air temperature and
Air temperatures were plotted on the
vapor pressure difference.
vertical axis and
(e
w -e
)
on the horizontal axis
were plotted with the values
If
W -e aa'
the zero value for
of the fog
in other
cases are
of visibility code.
(e tA
is
)
and the points
(See Figure 5)
considered as saturation, then 76%
in the saturation area left of the zero point;
words, where the vapor pressure of the air would be
Only 39%
higher than that of the water.
of all the points left of
the zero point were fog cases and this is nearly the same results
as obtained from the best numerical problem.
of the data points in the saturated zone
showed a direct relation-
ship between fog cases and air temperature.
were
in the saturated
A best
Data points that
zone with respect to vapor pressure difference,
but had high air temperature
visibilities.
Further analysis
fit
,
were not likely to have low
curve, which is depicted on Figure 5,
was
then smoothed on the graph in an attempt to divide the areas of
fog and no fog.
The resulting curve had the equation:
X=A+BY 3
The area to the
left of this
curve was then considered as
the modified saturation zone, and in this area
29
72%
of the actual
.
fog cases were present while the percentage of predicted cases
that
Half of the remaining 40%
were fog rose sharply to 60%.
were cases with visibilities less than two miles.
While the majority
of the fog
cases had wind speeds of less
than 20 kts, any attempt to restrict fog prediction to that range
resulted in the exclusion of a significant number of actual fog
reports.
Visibility as a function of the difference in air and sea
temperatures and the difference in vapor pressures was plotted,
but the fog cases were scattered across the graph and no
conclusions could be made.
The majority of the values
for the
difference in temperatures for the 1100 data points were less
than two degrees.
The temperature
of the
water was computed for each point
and visibility was plotted as a function of this and vapor pressure
difference
The resulting scattergram showed a strong resemblence to
Figure
5
,
because
of the interaction
results in the small differences
was more
between the sea and
in sea-air temperatures.
air that
There
scattering of low visibility cases, however, and the
fog prediction percentages were not as high.
Applications
The scattergram
of visibility
as a function of air temperature
and vapor pressure difference gave the best results
30
in fog
prediction, and applications for a forecasting method were based
Two
on this graph.
was
a
forecasting methods were sought.
method to forecast fog probability
from zero to one hundred.
in terms of
The
first
percentages
The other was a method to forecast
visibility in miles or in terms of the visibility code.
Fog probability lines were constructed directly on the scattergram.
cases
(See Figure
6)
The percentages were based on the fog
1100 data points.
in the
Visibility prediction directly from the scattergram
attempted but
visibility
it
was
difficult to fit curves in the area
was greater than one mile.
Smoothing
then undertaken by use of a Laplacian technique.
of visibility
intersections on the graph were
was thus considered
of the four intersections around
smoothing and
visibility.
visibility
to miles.
where the
of the data
was
Average values
were computed at each intersection on the graph by
averaging all the values in an area 10
data point
was
it
5
mb by
mb and
in the
it.
was then possible
2
it
degrees.
The
degrees apart so each
average value for each
This provided the necessary
to construct isolines of
The values of these lines were
code and
4
in
terms of the ships
would be a simple matter to convert them
Figure 7 shows the smoothed values and the visibility
lines.
31
7.
Conclusions
1)
The vapor pressure difference field that
is
computed by
the Fleet Numerical Weather Facility is a valid humidity index.
2)
wind speed and humidity are the primary
Air temperature,
parameters effecting visibility over the sea.
reaches 100% and the air
is
When
becomes quite low.
When
the humidity
saturated fog forms and visibility
the vapor pressure difference is used
as the humidity parameter air temperature must be considered
Air temperature and sea temperature are
before predicting fog.
closely related and the difference between them becomes smaller
as time passes.
3)
Ordinary regression equations are not applicable to fog
prediction because the relationships between visibility and the
other parameters are apparently non-linear.
4)
Fog
is
caused when saturation
of the air occurs
and a
completely accurate field of relative humidity could be transposed
into a visibility field
formation.
field,
This is not true for the vapor pressure difference
because there
sea and air.
where saturation would correspond to fog
If
is
a difference in the temperatures of the
the air is warmer than the sea, then the air itself
is not truly saturated
when
to that of the water.
If
the vapor pressure of the air is equal
the temperatures were equal and the
vapor pressures equal then saturation would be present.
same reasoning,
if
By the
the air is colder than the water, the air will
32
.
.
be saturated when e a is
still
less than e w
.
These anomalies
occur because the saturation vapor pressure of the air
is a
function of the temperature of the air and not of sea temperature
5)
There is greater probability of the air temperature being
warmer than the sea temperature
and cooler than the sea
saturation curve in Figure
6)
low
for
for high values of air temperature,
The modified
air temperatures.
follows this concept.
5
For fog prediction the best results are obtained by plotting
visibility as a function of air temperature
difference.
72%
of the fog
and vapor pressure
cases were predicted and 60% of the
predicted cases were fog.
7)
A smoothed version
of the
above graph
is
adaptable to
the prediction of visibility in miles.
8)
Using the above described methods, wind spread cannot
be considered because wind mixing depends on thethickness of
the inversion layer.
However, wind speed
is a
term in the
equation for the difference in vapor pressures and a large wind
speed will result in a large difference and decrease the chance
of low visibilities being forecast.
9)
The primary limitation in this investigation was in the
use of reported ship visibilities as the dependent variable.
Observations of visibility at sea are not accurate
10) It is feasible to
program fog probability and visibility
charts for the open ocean areas using the vapor pressure difference
field
and air temperature
field.
33
Table
Interval
in
mbs
I
Ship
Land
reports
reports
more
12
139
to 6.99
3
43
3to4.99
26
127
to 2.99
60
295
241
867
-3 to -1.01
41
235
-5 to -3.01
10
68
-7 to -5.01
2
34
under -7
2
18
7 or
5
1
-1 to .99
FNWF
verification of one chart of (e -e ) based on
comparisons of actual and prediction values.
34
Table
II
1966
1965
OOZ
2
May
00Z
1
April
12Z
2
May
12Z
1
April
12Z 4
May
OOZ
2 April
12Z
5
May
12Z
2 April
OOZ
6
May
OOZ
3 April
12Z
6
May
12Z
3 April
OOZ
7
May
OOZ 4 April
OOZ
8
May
12Z 4 April
12Z 8
May
OOZ
5 April
OOZ
May
12Z
5
9
OOZ 10
May
12Z 10
May
OOZ 11
May
12Z 11
May
OOZ 12
May
12Z 12
May
OOZ 13
May
OOZ 14
May
12Z 14
May
OOZ 15
May
12Z 15
May
OOZ 16
May
Dates and times
of charts
and reports used
35
April
in study
Table
Second digit
code figure
III
of
Visibility
less than 50 yd
1
50 yd
2
200 yd
3
1/4
NM
4
1/2
NM
5
1
NM
6
2
NM
7
5
NM
8
10
NM
9
25
NM
Visibility code for ship weather reports
36
p
Tabe IV
Stepwise Regression
Problem No.
8
Variable
1
- T.
2 "
T
3
- T -T
w
a
4 -
wind speed
5
- time
6
*"
dP
e
w—ea
Simple Correlation Coefficients
X(l) vs
X(3) vs
X(5) vs
Y=
Y=
Y=
.398
X(2) vs
-.176
X(4) vs
Y=
Y=
.009
X(6) vs
Y=.519
Standard error of
Y
.276
-.202
= 1.305
Regression steps
Variable entering - 6
Step no. 1
183.86
F level
Standard error of estimate - 1. 1169
Constant - 6.59765
Variable entering Step no. 2
F level - 46.52
Standard error of estimate - 1.0691
Constant - 5.95 737
1
Step no. 3
Variable entering - 4
F level - 16.55
Standard error of estimate - 1.0528
Constant - 6.34652
Regression coefficients
Coefficient
Variable
1
.00494
4
-.01976
6
.02978
Statistical Results of Numerical Problem Eight
37
Table V
Stepwise Regression
Problem No.
5
Variables
1
- T.
2 -
T dp
3
- T -T
a
w
4 -
Wind speed
5 -
6 - e
time
w -e a
Simple Correlation Coefficients
X(l) vs
X(3) vs
X(5) vs
Y=
Y=
Y=
.928
Y
vs Y
vs Y
X(2) vs
-.155
X(4)
.680
X(6)
882
826
834
Regression steps
Variable entering -
Step No.
1
F level |
3135.69
1
Standard error of estimate - 2.8144
Constant Step no. 2
Variable entering - 4
F level
187.75
Standard error of estimate - 2.4001
Constant Step no. 3
Variable entering F level - 85 78
Standard error of estimate - 2.2183
6
.
Constant Step no. 4
F level - 31.65
Variable entering -
5
Standard error of estimate - 2.1528
Constant Variable entering Step no. 5
F level
6.54
Standard error of estimate - 2. 1408
3
Constant Regression coefficients
Variabl e
Coefficient
1
.03631
3
-.01136
4
5
.09250
1.05074
6
.04901
Statistical Results of Numerical Problem Five
38
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Figure
2
- Grid Overlay Over Analyzed Field of
40
(e
-e
)
.
GVCT
- ship call sign
- time of report
550
-
2623
-
6
- ship course
6
- ship speed
+ 137
- pressure diff
+220
- dry bulb temp.
-15
-T..-T
a
+165
-
-20
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2
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wave period
2
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wave height
2
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wave direction
4
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4
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33
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2
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8
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6
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1
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6
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3
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I
column
J
row
dew
w
pt.
temp.
amount low cloud
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- type high cloud
5
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3
- present weather
98
- visibility
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BIBLIOGRAPHY
1
.
2.
Admiralty Weather Manual.
Department, 1941.
Admiralty Hydrographic
Amot, Audvin. On the Temperature Difference Between the
Air and the Sea Surface and Its Applicability in the Practical
Weather Analysis. Meteorologiske Annaler BD. 1, NR. 19,
1944: 490 - 527.
.
3.
Boyum, Gunnvald. A Study of Evaporation and Heat Exchange
Between the Sea Surface and the Atmosphere
Geofysiske
Publikasjoner Geophysica Norveqica. V. 22, NO. 7,
January 1962.
.
4.
Byers, H. B.
Hill, 1937.
5.
Haltiner, G.
6.
Synoptic and Aeronautical Meteorology
J.
.
Hewson,
W. and
E.
.
McGraw
Martin. Dynamical and Physical
McGraw-Hill, 1957.
and F.
Meteorology
and Applied
.
R.
L.
W.
Longley.
Meteorology Theoretical
Wiley & Sons, 1944.
7.
Laevastu, T. and L. P. Carstensen. Numerical Analysis and
Forecasting of Surface Air Temperature and Water Vapor
Pressure. U. S. Naval Fleet Numerical Weather Facility.
Technical Note No. 17, April 1966.
8.
Sea-Air Temperature Relations.
Hawaii Institute of Geophysics, University of Hawaii. Report
to National Science Foundation. HIG - 64 - 3.
9.
Petterssen, S. Some Aspects of Formation and Dissipation
of Fog. Geofysiske Publikasjoner Geophysica Norvegica
V. 12, NO. 10, 1939.
Laevastu, T. and K. Inouye.
.
10.
Synoptic Numerical Oceanographic Analysis and Forecasting
Program s
U.S. Naval Fleet Numerical Weather Facility
Technical Memo NO. 5, January 1965.
.
.
11.
Taylor, G.
Toumal
12.
I.
The Formation of Fog and Mist.
of the Royal Meteorological Society.
Willett, H. C. Fog and Haze.
V. 56, 1928: 435 - 467.
45
Quarterly
V. 43, 1917:
Monthly Weather Review
.
INITIAL DISTRIBUTION LIST
No. Copies
1.
Defense Documentation Center
20
Cameron Station
Alexandria, Virginia
2
.
22314
Library
U.
S.
2
Naval Postgraduate School
3.
Dept. of Meteorology & Oceanography
U. S. Naval Postgraduate School
Monterey, California 93940
1
4.
Office of the U. S. Naval Weather Service
1
Washington Navy Yard
Washington, D. C. 20390
5.
Professor G. Haltiner
Dept. of Meteorology & Oceanography
U. S. Naval Postgraduate School
Monterey, California 93940
6.
LT
W.
G. Schramm
1
3
38 Revere
Monterey, California
7
.
Officer in Charge
1
Naval Weather Research Facility
U. S. Naval Air Station, Bldg. R-48
Norfolk, Virginia 23511
8.
Commanding Officer
1
FWC/JTWC
COMNAVMAR
FPO San Francisco 96630
9
.
10.
Commanding Officer
U. S. Fleet Weather Central
FPO San Francisco 96610
1
Commanding
1
Officer
U. S. Fleet Weather Central
Navy Department
Washington, D. C. 20390
46
11.
Commanding
U.
S.
Officer
Fleet Weather Central
Naval Air Station
Alameda, California
12.
94501
Officer in Charge
U. S. Fleet Weather Facility
FPO New York 09597
13.
Officer in Charge
U. S. Fleet Weather Facility
FPO New
14
.
York
09510
Officer in Charge
U. S. Fleet Weather Facility
FPO New York 09571
15.
Officer in Charge
U. S. Fleet Weather Facility
FPO San Francisco 96662
16.
Officer in Charge
U. S. Fleet Weather Facility
FPO San Francisco 96652
1
7
.
Officer in Charge
Fleet Numerical Weather Facility
U. S. Naval Postgraduate School
Monterey, California
18.
93940
Commander
Air Force
Attn:
Cambridge Research Center
CROOTR
Bedford, Massachusetts
19.
Geophysics Research Directorate
Cambridge Research Center
Cambridge, Massachusetts
Air Force
20.
Program Director for Meteorology
National Science Foundation
Washington, D. C.
21. American Meteorological Society
45 Beacon Street
Boston, Massachusetts
47
22.
Commander,
23.
Office of Naval Research
Department of the Navy-
Air Weather Service
Military Airlift Command
U. S. Air Force
Scott Mr Force Base, Illinois 62226
Washington, D. C.
24.
20360
U. S. Naval Oceanographic Office
Division of OceanographyWashington, D. C. 20390
Attn:
25
.
26.
Superintendent
United States Naval Academy
Annapolis, Maryland 21402
Director
Coast and Geodetic Survey
U. S. Department of Commerce
Attn: Office of Oceanography
Washington, D. C.
27.
Office of Naval Research
Undersea Warfare (Code 466)
Department of the Navy
Washington, D. C. 20360
Attn:
28.
Office of Naval Research
Geophysics Branch (Code 416)
Department of the Navy
Washington, D. C. 20360
Attn:
29.
30.
Program Director for Oceanography
National Science Foundation
Washington, D. C.
Director
Woods Hole Oceanographic Institution
Woods Hole, Massachusetts 02543
31.
Chairman
Department of Meteorology & Oceanography
New
York University
University Heights, Bronx
New York, New York
48
32.
Director
Scripps Institution of Oceanography
University of California, San Diego
La Jolla, California
33.
Chairman
Department
of
Meteorology & Oceanography
University of Hawaii
Honolulu, Hawaii
34.
Chairman, Department of Oceanography
Oregon State University
Corvallis, Oregon 97331
35.
Chairman, Department of Oceanography
Texas A & M University
College Station, Texas 77843
36.
Executive Officer
Department of Oceanography
University of Washington
Seattle, Washington 98105
37.
Director, Biological Laboratory
Bureau of Commercial Fisheries
U. S. Fish & Wildlife Service
450-B Jordan Hall
Stanford, California
38.
National Research Council
2101 Constitution Avenue
Washington, D. C.
Attn:
Committee on Undersea Warfare
39.
Department of Meteorology and Climatology
University of Washington
Seattle, Washington 98105
40.
Department of Meteorology
Massachusetts Institute of Technology
Cambridge, Mass. 02139
41.
Hawaii Institute of Geophysics
University of Hawaii
Honolulu, Hawaii
49
42.
Meteorology International, Inc.
Box 1364
Monterey, California 93940
P. O.
43. The Travelers Research Center, Inc.
650 Main Street
Hartford, Connecticut
44
.
Department of Meteorology
University of Melbourne
Grattan Street
Parkville, Victoria
Australia
45.
Bureau of Meteorology
Department of Interior
Victoria and Drummond Streets
Carlton, Victoria
Australia
46. International Antarctic Analysis Centre
468 Lonsdale Street
Melbourne Victoria
Australia
,
47.
C. S. I. R. O.
Division of Meteorological Physics
Station Street
Victoria
Australia
Aspendale
48. Institut
f
.
,
Meteor, u.
Geophysik Universitat Innsbruck
Schopfstrassee 41, Insbruck
Austria
49.
Department of Meteorology
McGill University
Montreal, Canada
50.
Central Analysis Office
Meteorological Branch
Regional Adm Building
.
Inter. Airport
Dorval, Quebec, Canada
50
51.
Meteorological Office
315 Bloor Street West
Toronto 5 Ontario, Canada
,
52.
Department of MeteorologyUniversity of Copenhagen
Copenhagen, Denmark
53.
Institute of Meteorology
University of Helsinki
Helsinki - Porthania, Finland
54
.
Geophysical Institute
Tokyo University
Bunkyo-ku
Tokyo, Japan
55. Institute of Geophysics
University of Bergen
Bergen, Norway
56.
Meteorological Office
London Rd.
Bracknell
Berkshire, United Kingdom
57.
Commonwealth
Scientific and Industrial
Research Organization
314 Albert Street
East Melbourne, C. 2, Victoria
Australia
58.
Director
Pacific Oceanographic Group
Nanaimo, British Columbia
Canada
59.
Fisheries Research Board of Canada
Atlantic Oceanographic Group
Bedford Institute of Oceanography
P. O. Box 1006
Dartmouth, Nova Scotia
Canada
51
60.
National Institute of Oceanography
Wormley, Godalming
Surray, England
Great Britain
61.
Ocean Research
Institute
University of Tokyo
Tokyo, Japan
62.
U. 5. Department of Commerce
Weather Bureau
Washington, D. C.
52
UNCLASSIFIED
Security Classification
DOCUMENT CONTROL DATA
(Security classification ot
ORIGINATING ACTIVITY
1.
title,
•
R&D
body ot abstract and indexing annotation must be entered when the overall report
2a.
(Corporate author)
le
classified)
REPORT SECURITY CLASSIFICATION
UNCLASSIFIED
NAVAL POSTGRADUATE SCHOOL
MONTEREY, CALIFORNIA
U. S.
26 CROUP
REPORT TITLE
3.
ANALYSIS
AND PREDICTION OF
DESCRIPTIVE NOTES (Type
4.
VISIBILITY AT SEA
ot report and Inclusive dates)
Master of Science Thesis (Meteorology)
5.
AUTHORfSJ (Last name,
first
SCHRAMM,
name,
Initial)
William G.
REPORT DATE
6.
May
9
8a.
6.
LT,
USN
7a-
TOTAL
9a.
ORIGINATOR'S REPORT NUMBERfS)
NO.
NO.
OF PASES
7
b.
NO.
OF REFS
49
1966
CONTRACT OR GRANT
PROJECT
,
NO.
9
b.
OTHER REPORT
no(S) (A ny other numbers that may be assigned
this report)
10.
AVAILABILITY/LIMITATION NOTICES
MTT
11.
SUPPLEMENTARY NOTES
12
SPONSORING MILITARY ACTIVITY
Chief of Naval Operations
OP-09B7
Washington, D. C.
13.
20350
ABSTRACT
This paper is concerned with the problem of visibility at sea and
fog over the sea. Restrictions to visibility in general are discussed
and suspended moisture is related to low visibilities at sea. Fleet
Numerical Weather Facility at Monterey produces a field, of the
difference between the vapor pressures of the sea and air. This field
is used as a humidity index to determine the moisture in the air and
is related to visibility.
1100 data points from the North Atlantic were
analyzed and an attempt made to produce a linear regression equation.
The regression equation proved to be most inaccurate in the area of
low visibilities. A scattergram of visibility as a function of air
temperature and the vapor pressure difference revealed a significant
relationship. Using this relationship it is possible to forecast
visibility and fog probability.
(U)
\J \J
1
JAN
64
1473
53
UNCLASSIFIED
Security Classification
UNCLASSIFIED
Security Classification
LINK A
14-
KEY WORDS
LINK B
ROLE
ROLE
WT
LINKC
ROLE
WT
FOG PROBABILITY
VISIBILITY AT SEA
VAPOR PRESSURE DIFFERENCE
NUMERICAL REGRESSION
HYDROMETEORS
ADVECTION FOG
SEA FOG
INSTRUCTIONS
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JAN
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1473 (BACK)
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54
UNCLASSIFIED
Security Classification
:
I
?3Thesis
c.
Schramm
Analysis and
prediction of
visibility at sea.
S344
c.l
OCT 68
2 AU&7I
ty
OIHDERY
17 70H
19• 65/
c
2
AUG74
6 AUG 63
Thesis
S344
Schramm
c »*
Analysis and
prediction of
visibility at sea.
•
7
65
2807 6
26609
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