MODULE 4.2G
SHORT RANGE FORECASTING OF
CLOUD, PRECIPITATION AND VISIBILITY
Sample Nomograms
Table of Contents
1. INTRODUCTION ...................................................................................................................................................1
2. A NOMOGRAM FOR FORECASTING THE TIME OF FORMATION OF CEILINGS DUE TO
STRATUS.....................................................................................................................................................................1
INTRODUCTION ....................................................................................................................................................1
DESCRIPTIONS OF THE NOMOGRAM...............................................................................................................2
PROCEDURES ........................................................................................................................................................3
REMARKS ON THE USE OF THE NOMOGRAM ................................................................................................4
REFERENCES ..............................................................................................................................................................5
3. JACOBS’ METHOD FOR TIMING THE ONSET OF RADIATION FOG.....................................................7
4. KAGAWA TECHNIOUE FOR TIMING THE CLEARANCE OF RADIATION FOG ...............................12
5. OSBORNE’S METHODS FOR FORECASTING SEA FOG...........................................................................16
SEA FOG IN WESTERLY GEOSTROPHIC FLOWS ...........................................................................................................16
SEA FOG IN SOUTH TO SOUTHWEST GEOSTROPHIC FLOWS ........................................................................................17
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1. INTRODUCTION
The use of nomograms to forecast boundary layer clouds and weather goes back many years in
the history of meteorology. You will not see nomograms used very often today in operational
meteorology. One reason is that nomograms are usually site specific, and often one cannot use a
nomogram in a different location from where it was developed. Also, nomogram use has
become too time consuming in the busy schedules of many of today’s meteorologists, and more
frequently, forecasters rely on their knowledge and experience of local effects for forecasting
boundary layer effects.
The nomograms provided in this document are samples of how the method can be applied. It is
not required that you be able to use each of these nomograms, it is more important that you
become familiar with the important parameters and thought processes that go into forecasting
boundary layer weather.
2. A NOMOGRAM FOR FORECASTING THE TIME OF FORMATION OF
CEILINGS DUE TO STRATUS
INTRODUCTION
The use of the techniques developed by Goldman (1951) for forecasting the time of formation of
ceilings due to stratus cloud has been described by Lee (1955). The Goldman technique can be
used to forecast the time of formation of ceiling due to:
a) airmass or marine stratus, and
b) stratus formed in precipitation.
The method uses the wet-bulb depression at either 1000 Local Standard Time or 2000 LST with
empirical and theoretical relationships, which were developed by Goldman, for the rate of
decrease of wet-bulb depression at the level of interest. The nature of these relationships is
indicated below.
a) The rate of decrease of wet-bulb depression is a function of height and increases with height.
b) The factors contributing to the decrease of wet-bulb depression can be grouped into two broad
categories:
i) those not due to evaporation of precipitation (radiation, moist advection, diabatic
processes and vertical mixing), and
ii) those due to evaporation of precipitation (cooling and the increase of moisture by
evaporation).
c) The rate of decrease of wet-bulb depression, during periods when evaporation of precipitation
is not a factor, is dependent on whether the trajectory is;
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i) moist (over water or from close to the centre of a rain area), or
ii) dry (over land and not from close to the centre of a rain area).
d) The rate of decrease of wet-bulb depression at any level, due to all factors other than the
evaporation of precipitation, can be treated as a linear function of time for that particular level
and trajectory. The decrease due to these factors will continue after precipitation begins.
e) The rate of decrease of wet-bulb depression due to evaporation of precipitation can be treated
as a negative exponential function of time.
f) After continuous precipitation begins, both sets of factors listed (in b) operate and their results
are cumulative.
Some important assumptions on which the method is based are discussed below.
a) In developing the method, it was reasoned that when the surface wet-bulb depression was at
its mean value for the day, it would be representative of the wet-bulb depression in the lower
1000 feet of the atmosphere. Study of the Washington records indicated that the wet-bulb
depression tended to be at its mean value for the day at about 1000 and 2000 LST. Various
relations were then developed to relate the surface wet-bulb depression, which is taken as the
wet-bulb depression at the level of interest, to the time of formation of stratus at that level.
b) The method assumes that the wet-bulb depression will decrease steadily from its 1000 (2000)
LST value until the air becomes saturated at which time a stratus ceiling forms. Accordingly, the
method should only be used in those situations in which such a decrease would be a logical
assumption. As the wet-bulb depression would normally increase during the daylight hours prior
to maximum temperature time, use of the method immediately following 1000 LST would only
be valid in those situations where advective or other factors are such as to reverse the normal
wet-bulb depression trend.
c) In using the method it is assumed that the empirical relationships which were developed from
data from Portland, Maine, are applicable to the station for which the forecast is being prepared,
and that they are applicable in the particular meteorological situation which exists.
The extent to which these assumptions are true will affect the validity of the resulting forecast.
DESCRIPTIONS OF THE NOMOGRAM
The nomogram is shown in Figure 1. It consists of three sections which are described below.
In the upper left section (OABC) the sloping lines represent the rate of decrease of wet-bulb
depression for selected levels during periods when continuous rain is not occurring. The solid
lines show the rate of decrease when the trajectory is moist, and the broken lines when it is dry.
At 300 feet the rate of decrease is the same for either type of trajectory. This section of the
nomogram is used to determine either:
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a) the elapsed time from 1000 (2000) LST to formation of stratus, when continuous rain is not
expected or when the stratus will form before continuous rain begins, or
b) the decrease in wet-bulb depression during the period before rain is forecast to begin.
The upper right section (OCDE) is used to subtract the decrease in wet-bulb depression before
continuous rain begins at 1000 (2000) LST. The vertical lines labelled along CD represent the
1000 (2000) wet-bulb depression values. The sloping lines are the guide lines for the subtraction
process.
In the lower right section (OEFG) the curved lines represent the rate of decrease of wet-bulb
depression during periods of continuous rain. They are a combination of the rate of decrease of
wet-bulb depression due to the evaporation of precipitation and due to factors other than
evaporation of precipitation at the selected levels during such periods. Solid lines are for use
when the trajectory is from over water or from near the centre of the rain area. The broken lines
are for use when the trajectory is from over land and not from near the centre of the rain area. At
300 feet the rate of decrease is the same for either type of trajectory.
PROCEDURES
The nomogram is designed for use in predicting the time for formation of stratus in two
situations; namely when continuous rain is expected and when continuous rain is not expected.
In either case, the arrows on the nomogram indicate the direction of the path to be followed.
Case 1. Continuous rain is expected.
a) Enter AO with the forecast elapsed time from 1000 (2000) LST to the beginning of rain.
b) Travel up to the sloping line representing the level and trajectory of interest.
c) Proceed right into section OCDE, to the vertical line representing the wet-bulb depression
value at 1000 (2000) LST.
d) Proceed diagonally down parallel to the sloping lines to intersection with OC or OE.
i) If intersection is made with OC, stratus will form before rain begins and time of
formation should be determined as in Case II.
ii) If intersection is made at 0, stratus will form at time. of beginning of continuous rain.
iii) If intersection is made with OE, travel down into section OEFG, to the curved line for
the level and trajectory of interest. Then, proceed left to OG and read off the time from
beginning of rain to formation of stratus. Add this time to the time of beginning of rain
to obtain the time of formation of the stratus ceiling.
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Case II. Continuous rain is not expected or stratus will form before rain begins.
a) Enter AB with the surface wet-bulb depression at 1000 (2000) LST. (To double the range of
values over which the nomogram can be used, bracketed values twice the unbracketed values are
given along AB and BC. If the bracketed values are used on AB they should also be used on
BC).
b) Travel right to the sloping line representing the level and trajectory of interest.
c) Proceed vertically to BC and read off the elapsed time from 1000 (2000) LST to time of
formation of stratus.
d) Add this elapsed time to 1000 (2000) LST to obtain the time of the stratus ceiling formation at
the level of interest.
REMARKS ON THE USE OF THE NOMOGRAM
Lee (1955) indicated that a brief test of the Goldman method has been carried out. The
magnitude of forecast errors at various locations in Canada was such that the method could be
considered to have general application, particularly as an objective check on more empirical
methods. In addition, as stratus tended to form later than forecast, the method might be used
operationally to forecast ceilings not lower than a specified period of time.
The use of the nomogram simplifies the method so that it can be readily built into the forecast
office objective routines. It is suggested that it be used mechanically to obtain a preliminary
estimate of the time of stratus formation. This preliminary estimate would require further
consideration on the part of the forecaster. Some considerations affecting the forecast are
indicated below.
a) The extent to which the actual conditions in the particular situation and location correspond
with the assumptions on which the method is based.
b) The extent to which it can be established that the trajectory is moist or dry.
c) The variation in low level winds during the forecast period.
i) With light winds fog may result instead of stratus.
ii) With strong winds, stratus will form sooner than forecast at higher levels and later
than forecast at lower levels.
d) The duration of continuous rain. Stratus may not form if the duration of rain is not sufficient.
e) Variations in the intensity of type of precipitation.
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i) Short periods of very light or showery precipitation prior to the beginning of
continuous rain may not affect the situation significantly and can generally be
disregarded.
ii) Moderate or heavy rain will result in more rapid saturation of the air and will result in
the formation of stratus earlier than forecast.
f) The approach of a front or marked trough. This may result in the formation of stratus earlier
than forecast.
g) Frontal passages.
i) The passage of a cold front will generally result in the advection of drier air over the
region and the cessation of the stratus forming conditions.
ii) With the passage of a warm front, the departure of middle cloud may result in the
stratus deck breaking up because of heating during the daylight period.
References
1. Goldman, L., 1951: On Forecasting Ceiling Lowering during Continuous Rain. United States
Department of Commerce, Weather Bureau, Mon. Wea. Rev. 79, 133-142.
2. Lee, R., 1955: Forecasting the Lowering of Ceiling in Continuous Rain. Canada, Department
of Transport, Meteorological Branch, Technical Circular Series. CIR-2622, TEC-212.
3. Lee, R., 1955: Stratus Forecasting. Canada, Department of Transport, Meteorological Branch,
Technical Circular Series. CIR-2677, TEC-219.
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Note: The wet bulb depressions on this table are in °F. To convert to °C, use the table below.
°F
°C
°F
°C
2
1
7
4
4
2
9
5
5
3
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3. JACOBS’ METHOD FOR TIMING THE ONSET OF RADIATION FOG
A number of techniques have been developed to determine when (and if) radiation fog will form,
using surface observations. The one presented here was developed based on a technique for
forecasting minimum temperatures by Jacobs. This technique is quite straight forward to use,
and is easy to automate. A number of weather offices employ this method through a short
computer program which allows them to input the critical numbers and receive a quick estimate
of timing for radiation fog.
Observations have shown that a liquid water content of .05 g/kg corresponds to a fairly dense
fog. Air must be cooled below its dew-point to condense this much liquid water, the amount of
extra cooling being inversely related to the dew point. Table 1 shows the required amount of
cooling for a given initial dew point to produce the dense fog described above.
Table 1 Cooling Below Dew-Point Required for Fog Formation
-2 to 2
3 to 6
7 to 9
10 to 14
Dew-Point Range (°C)
4
3
2.5
2
Extra Cooling (°C)
15 to 21
1
One must determine the total amount of cooling required to form fog based on the sunset values
of dry bulb temperature and dew-point, and the correlation found in Table 1.
Thus for a sunset situation with T = 15 and Td = 5 the amount of cooling required would be 13
degrees (15 - 5 + 3).
A minimum temperature forecasting diagram based on Brunt's radiational cooling formula is
shown in Figure 1. The results are strictly applicable to El Centro, California, and corrections
must be made for other locations. In the diagram:
ΔT1 = change (decrease) in temperature after sunset in °C and is plotted along the ordinate.
t = number of hours after sunset and is plotted along the abscissa.
The decrease in temperature after sunset ΔT1 as a function of time after sunset t is shown for
various sunset dew point temperatures. In order to construct this graph, Jacob assumed the mean
radiative temperature to be 280 degrees K.
The required corrections for other locations are for two factors, namely:
a) the mean radiative temperature T, which was assumed 280 K for El Centro.
b) the soil constant S, which was taken to be 0.082 for El Centro.
E
Correction for Mean Radiative Temperature
In general, the mean radiative temperature T will differ from 280 K so that correction must be
applied. The correction factor was defined as:
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E = 2σT4
= 1.0105
where T = mean radiative temperature
σ = Stefan's constant
and 1.0105 = the value of 2σ(280)4.
Value of E may be found from the insert in Figure 1 if the mean radiative temperature T is
known. For all practical purposes, T may be taken as the mean temperature for the night (i.e.
between sunset and sunrise). The mean temperature for the night is usually estimated by taking
the mean of the sunset temperature and the minimum temperature.
D
Correction for Soil Constant
In general, the soil constant S will differ from the value of 0.082 used for El Centro, since it
depends upon the density, specific heat and conductivity coefficient of the soil. The correction
factor, denoted D, is given by:
D=
0.082
S
Ideally, the soil constant and the correction factor for the soil constant are required for the
particular night one wishes to consider. In practice, it has been found that the soil constant can
be found empirically from past hourly observations of temperature and dew point during a
previously clear, calm night. From this empirically determined value of S, D can be computed
from the above equation.
To calculate the correction factor, D, for a given station, tabulate the forecast and actual
temperature drop at the station for a recent clear calm night. The method of calculation is as
follows.
Procedure for Determining the Soil Constant, S, and correction Factor D, from Observed
Temperature Data
STEP 1
Select a clear calm night for the station of interest.
STEP 2
Tabulate hourly temperature, to the nearest tenth of a degree Celsius, from sunset
using Table 2. Terminate the tabulation when the temperature levels off or rises,
i.e., when non-radiative effects become important. Calculate ΔT2 the actual
temperature change after sunset.
STEP 3
Find the dew point at sunset. From Figure 1, find and tabulate values ΔT1 for
each hour, corresponding to the sunset dew points.
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STEP 4
Compute the ratio of ΔT1/ΔT2 hourly. Find an average value of this ratio,
omitting the first hour after sunset if it differs significantly from the others.
STEP 5
Determine E using the insert in Figure 1. The arithmetic mean of observed dry
bulb temperatures is sufficiently accurate.
STEP 6
Find the soil constant S =
STEP 7
Finally, D = 0.082/S
Local Time (HRs)
ΔT1
E
ΔT2
Table for use in calculating S
Temp
ΔT1
ΔT2
ΔT1/ΔT2
SUNSET
SUNSET + 1
SUNSET + 2
SUNSET + 3
SUNSET + 4
SUNSET + 5
SUNSET + 6
SUNSET + 7
SUNSET + 8
SUNSET + 9
SUNSET + 10
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CHECKLIST FOR RADIATION FOG FORMATION (JACOBS)
STATION:
DATE:
SUNSET TIME (LST):
SUNRISE TIME (LST):
SUNSET TEMPERATURE:
SUNSET DEW POINT:
ΔT2 = (T - Td)SUNSET + ADDITIONAL COOLING (Table 1)
SOIL CONSTANT, D =
MEAN RADIATIVE TEMPERATURE = (TSUNSET + TMIN) / 2 =
RADIATIVE CORRECTION, E (INSERT, FIGURE 1) =
ΔT1 = ΔT2 / (DE) =
NUMBER OF HOURS TO PRODUCE COOLING OF ΔT1 =
(FIGURE 1)
FOG WILL FORM AT
HOURS
LST
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Figure 1. Minimum temperature forecasting diagrams (after Jacobs).
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4. KAGAWA TECHNIOUE FOR TIMING THE CLEARANCE OF
RADIATION FOG
A number of straightforward techniques are available to aid the forecaster in determining when
visibility in radiation fog will improve significantly. A technique presented by Kagawa will be
given here.
Figure 2 shows how the vertical profiles of temperature and dew point in and just above a
radiation fog at sunrise might appear. Also shown in a possible profile after the fog has
dissipated. This is the basic model used by Kagawa.
Figure 2. Model of ascent curve of typical conditions during radiation fog.
For evaporation of the fog to take place, the temperature of the air must increase from T1 to T2.
The energy H required to warm dry air from T1 to T2 is proportional to the area under AT1T2 (on
a tephigram). In order to determine H, a graph has been constructed which gives H as a function
of fog depth D and (T2 - T1) - see Figure 3.
In order to warm moist air from T1 to T2 requires additional energy which can be determined by
multiplying H by a factor F. This can be found by using the graph shown in Figure 4. The
energy (HxF) represents the total energy which must be supplied by insolation to cause the fog to
evaporate.
If it is known at what time this amount of energy is available from solar radiation, it would be
possible to predict the time of fog clearance. Figure 5 shows, in graphical form, the amount of
energy available for fog evaporation in different seasons as a function of the local standard time.
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It should be noted that this graph is valid for 50 degrees North latitude. However, it has been
found applicable at locations between 45 and 55 degrees North.
Figure 3. Diagram to determine H, the heat required to warm dry air from sunrise
temperature T1 to fog clearance temperature T2 (after Kagawa).
The diagrams were developed by Kennington and modified by Bartham before being applied to
Canadian sites by Kagawa. In using Figure 3 it was found that one could reasonably estimate the
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fog depth by noting its time of formation. The depth can be assumed to be 10 mb, unless the fog
formed prior to 0200 LST, in which case the depth as taken is 15 mb.
To determine T2, the temperature at the time of fog clearance, add the value from Table 1
(section 3, Jacob’s Method), to the corresponding fog formation temperature. Also, T2 - T1 is
never assigned a value less than 3°C.
Figure 4. Diagram to determine HxF, the total heat required for fog clearance (after
Kagawa).
The method has been applied with reasonable results at a number of Canadian locations,
providing that only radiation fogs are considered. The method suffers, however, for a couple of
reasons:
1. The assumption that all radiation fogs conform to a model vertical temperature profile
(Figure 2).
2. The assumption that the fog clearance temperature T2 could be found via an indirect
method, as above.
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Figure 5. Diagram to determine time of fog clearance (after Kagawa).
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Improvements that can be made to the above technique are:
• use of radiosonde data to directly estimate fog depth (when such data are available), and
• empirical knowledge of values of T2 gained from any available local forecast studies. By
saving data related to radiation fog situations a better feeling for the clearance time at various
stations may be gained by the forecaster.
5. OSBORNE’S METHODS FOR FORECASTING SEA FOG
Sea fog in westerly geostrophic flows
Figure 6.
In a summertime westerly flow such as shown in Figure 6, often associated with a cold front
over Quebec and Ontario, for on occasion forms to affect Yarmouth and the cold coastal band;
for relatively strong flows Sable Island can also be affected. The table below summarizes the
requirements for fog produced in a westerly flow. The last column indicates how much the
surface wind should be adjusted from geostrophic for a given flow strength.
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Vg (kt)
10
20
30
Trajectory (nmi)
90
90
180
Td - Ts (°C)
1-2
3-5
5
VSFC vs Vg
Unchanged
Backed 40°
Backed 25°
Trajectories are calculated using 60% of the geostrophic speeds.
necessary requirements for westerly flow fog events.
Figure 7 also illustrates
Figure 7. Diagram to determine distance required to form fog in geostrophic flows from
225° to 290° for various mean dew point - sea temperature differences.
Sea fog in south to southwest geostrophic flows
An empirical method that was computed by Osborne is to take 60% of the geostrophic flow and
back the flow 25 degrees. Recommended steps are:
a) Select a point “P” upwind of the area for which you are preparing the forecast.
b) Measure the geostrophic flow at point “P” and apply the empirical rule to determine the
advecting wind
c) Extend a streamline from the area upwind for a nine hour motion
d) Using the surface chart, repeat the steps to extend the streamline upwind for another nine
hours.
e) Should the streamline reach dew points of 16°C, forecast fog over the colder water if the flow
is 30 knots or less. Forecast fog elsewhere if the dew point exceeds the sea temperature by 3
degrees and the geostrophic flow is 18 knots or less. As the coastal band warms in August,
apply the 3 degrees and 18 knot rule.
Under conditions of light winds one can practically draw the sea water isotherms by following
the edge of the fog bank. With stronger flows, the distance required to produce saturation, and
fog, increases. With tropical storms over the Maritime Provinces, the air is very warm with high
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dew points but fog seldom forms - the air being so mixed that it is not cooled to temperatures
below its dew point at the surface.
For stronger flows the following rules may be applied:
Vg (kt)
30 - 45
Forecast ceiling (100 ft)
3-8
45 - 60
8 - 12
Forecast visibility (nmi)
1 - 3 (coastal)
4 - 8 (elsewhere)
4 - 8 (all regions)
Forecast the dissipation of fog or lifting of stratus above 1000 feet within 50-100 miles behind a
cold frontal passage, when the dew point drops below the local sea temperature.
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Figure 8. Distance required to produce fog with south to southwest geostrophic flows.
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