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Parameterization of Runway Visual Range as a Function of Visibility:Implications for Numerical Weather Prediction Models
FAISAL S. BOUDALA, GEORGE A. ISAAC, ROBERT W. CRAWFORD, AND JANTI REID
Cloud Physics and Severe Weather Research Section, Environment Canada, Toronto, Ontario, Canada
(Manuscript received 9 February 2011, in final form 1 September 2011)
ABSTRACT
A parameterization of runway visual range (RVR) has been developed using relevant meteorological pa-
rameters such as visibility (Vk), relative humidity (RH), temperature (T), precipitation intensity (PI), and
precipitation type (PT) measured in years between 2009 and 2011 at Toronto Pearson International Airport
during the Canadian Airport Nowcasting Project. The FD12P probe measured PI, Vk, and PT. The observed Vk
and PT were tested against data reported by hourly surface observations (SAs). The measured Vk has correlated
well with the SA with a correlation coefficient (r) of 0.76 for Vk , 5 km, but the FD12P underestimated visibility
by about 20% with a mean difference (MD) of about 196 m. For Vk , 2 km, the FD12P overestimated visibility
by about 7% with an MD of 60 m. The SA reported slightly more snow events—22% as compared to 17%—but
the FD12P reported many more snow grain cases than the SA. Both the SA and the FD12P reported rain at
similar frequency—4% and 5%, respectively. Using a theoretical approach, a parameterization that can be used
to determine RVR as a function of Vk has been developed. Using the observed T, RH, and dewpoint tem-
perature (Td), a new parameterization for predicting Vk/RVR in fog has been also developed. These param-
eterizations agreed with observations (r ’ 0.8). The parameterizations have been tested using the Canadian
Environmental Multiscale Regional model. The results show that when PI, RH, and T are reasonably predicted
and the fog events are correctly diagnosed, the model can be used to forecast RVR.
1. Introduction
Reduced visibility due to snow, rain, fog, and haze is an
important consideration in the landing and takeoff of air-
craft. Closing a major airport and diverting incoming traffic
because of reduced visibility is a costly operation. Even if
the airport may not be closed, under marginal visibility
conditions the safety of airport operations is diminished.
Takeoff and landing of aircrafts at runway locations in
some major airports are normally managed using a site-
specific visibility measurement called runway visual range
(RVR). In Canada, low-visibility operations are in effect
when the measured RVR is between 600 ft (182.9 m) and
1200 ft (365.8 m). Arrivals and departures are not autho-
rized at all for RVR below 600 ft. RVR is an instrumentally
derived value, based on standard calibrations, that repre-
sents the horizontal distance a pilot will see down the runway
from the approach end. It is based on the sighting of either
high-intensity runway lights (Va) or on the visual contrast of
other targets (e.g., a black object) (Vk)—whichever yields
a greater visual range. RVR is reported in increments of
100 ft (30.5 m) up to 1000 ft (304.8 m), increments of 200 ft
(61.0 m) from 1000 to 3000 ft (914.4 m), and increments of
500 ft (152.4 m) above 3000–6000 ft. RVR is not normally
reported for ranges greater than 6000 ft.
Traditionally, visibility measured using instruments such
as the Vaisala FD12P is represented by Vk, as mentioned
earlier. Currently, some numerical weather prediction
(NWP) models also forecast Vk, but no systematic way of
forecasting RVR has been fully developed. This is partly
due to the fact that RVR prediction not only depends on
atmospheric extinction (b), but also on runway light in-
tensity (I) and background light (BL), which are very dif-
ficult to forecast. This will be discussed in more detail later.
In this paper, new parameterizations that can be used to
forecast RVR under snow, rain, and fog conditions will be
developed and tested using direct observations of RVR
and visibility collected at Toronto Pearson International
Airport (CYYZ) during the Canadian Airport Nowcasting
(CAN-Now) research project (Isaac et al. 2011).
Corresponding author address: Dr. Faisal Boudala, Cloud
Physics and Severe Weather Research Section, Science and
Technology Branch, Environment Canada, 14780 Jane Street, King
City ON L7B-1A3, Canada.
E-mail: [email protected]
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DOI: 10.1175/JTECH-D-11-00021.1
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2. Observations
Runway visual range, visibility, precipitation intensity,
and other standard meteorological observation data were
collected at CYYZ, Ontario, Canada, starting in 2007 as
part of the CAN-Now project. The main CAN-Now in-
strument site is shown in Fig. 1. RVR data are measured
at all runway locations indicated in Fig. 1 and reported
every 5 min in real time on the NAV CANADA avia-
tion weather website (http://atm.navcanada.ca/atm/iwv/
CYYZ). Hourly and subhourly weather observations were
reported by an observer. The data presented in this paper
were collected in the periods from November to December
2009, January to April 2010, and January to May 2011.
a. Instrumentation
The instruments at the CAN-Now site include a
Campbell Scientific CR3000 (CR3k) data acquisition
system equipped with a relative humidity (RH) and
air temperature (T) probe (HMP45C212). The FD12P
measures precipitation, precipitation type, and visibility,
and is also equipped with an LM21 that measures BL
(see Boudala and Isaac 2009 for further description of
the instrument). The accuracy of the RH probe at 208C
is 62% (for RH 5 0%–90%) and 63% (for RH 5 90%–
100%). The accuracy of temperature measurement is
60.1% (for T 5 2508 to 508C).
b. Visibility, relative humidity, and dewpointtemperature
The instruments measuring RH, T, and visibility report
1-min-averaged values, but the dewpoint temperature
(Td) is not directly measured except for ones reported
hourly or in special observations by an observer. Thus,
1-min Td is calculated using the following well-known
approximation, given as
Td 5243:12 ln(RH/100) 1 4283:8T/(243:12 1 T)
17:62 2 ln(RH/100) 2 17:62T/(243:12 1 T),
(1)
where T is in degrees Celsius and RH is in percent.
To compare 1-min-averaged data (CR3k) with those
reported by hourly surface observation (SA), the entire
dataset was interpolated to common time intervals; these
are shown in Fig. 2. Figure 2a shows RH CR3k plotted
against RH SA. Similar plots of the ambient T and Td
measurements are shown in Figs. 2c and 2d, respectively,
and the visibilities are shown in Fig. 2b. There is a signif-
icant bias between the two RH measurements near sat-
uration (100%). The RH CR3k never exceeded 97.5%
even during heavy fog while the observer reported
100%, and hence this is a concern for visibility param-
eterization in fog. While this is within the uncertainty of the
FIG. 1. The Canadian Nowcasting Project: the main instrument deployment site where the
visibility and other meteorological parameters were measured, and runway locations where the
runway visual ranges (RVRs) were measured.
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measurement (3%), visibility compared more favorably
to changes in RH SA over that of RH CR3k when the
relative humidity is near saturation during fog. This will
be discussed more later. Therefore, the 1-min RH CR3k
data have been adjusted accordingly. The comparisons of
T and Td are much better than RH (Figs. 2c,d), but the
1-min Td is determined using Eq. (1). Generally, the
measured visibility using the FD12P corresponds quite
well to that reported by the observer, with a correlation
coefficient near 0.76 for visibility less than 15 km (Fig. 2b).
However, on average, the observer sees higher visibility
by about 20% with a mean difference (MD) of about
700 m, which is quite significant. When compared for
visibilities less than 5 km, although the correlation coef-
ficient remained unchanged, the MD decreased to about
196 m, which is more reasonable. For visibility less than
1 km, the MD becomes smaller near 60 m, and this time
the FD12P overestimates the visibility by about 7%.
Hence, at very low visibilities, on average, the FD12P
appears to overestimate the visibility. However, most of
the discrepancy, particularly the quantization of the data,
is probably related to the poor resolution of the visibil-
ity markers used by the observer and timing and spatial
differences between the observer and the instrument re-
ports. It should be noted that visibility can vary consid-
erably over short time and distance scales.
c. Precipitation and precipitation type
The reduction of visibility/RVR is due to absorption
and scattering (extinction) of light by particles of differing
sizes that are normally associated with fog, haze, snow,
and rain. Since scattering and absorption of light strongly
depend on particle type (i.e., shape, size, and index of
refraction), accurate prediction of extinction/visibility,
and hence RVR, requires accurate prediction of the
shape and size distribution of these particles. Currently,
some of the more sophisticated NWP models are capable
of forecasting snowfall rate and some low clouds and fog,
but the model prediction of these quantities is still a big
challenge. Therefore, before we attempt to develop some
strategy for forecasting RVR, it is necessary to test the
ability of the automated instruments, such as the FD12P,
FIG. 2. (a) RH from the CR3k plotted against observed (SA). (b) Similar plots of visibility (VIS), (c) its mean and
best-fit line, and (d) ambient (T) and dewpoint temperature (Td).
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to identify precipitation phase. Figure 3 shows the ob-
served frequency distribution of precipitation type based
on the FD12P and the observer (Fig. 3a) and precip-
itation intensity (Fig. 3b) based on the FD12P measure-
ments during the period described in section 2. In Fig. 3a,
the FD12P data are interpolated to match the observer’s
observation time. Based on the FD12P, no precipitation
was detected for approximately 68% of the time and the
observer reported a slightly lower no-precipitation fre-
quency of 60%. The frequency of fog occurrence re-
ported by the FD12P, which was close to 2% (Fig. 3a),
could have been underestimated since the observer re-
ported near 6%. The FD12P uses a very simple algorithm
for diagnosing fog; that is, when there is no precipitation
and the 10-min-averaged visibility is less than 1 km,
the probe reports fog, but this may not be strictly cor-
rect. Fog may exist with light precipitation consisting
of many different types of clouds and precipitating
particles as indicated in Fig. 3a, and thus these are not
reported by the FD12P. The observer also reported
more snow events, near 22% compared to 17% that the
FD12P reported. However, the FD12P reported many
more snow grain (SG) cases than the observer (Fig. 3a),
but the observer reported a few cases of snow grain and
fog (SGF) that the FD12P did not see. However, both
the observer and the FD12P reported rain events at
similar frequency (near 4% and 5%, respectively), but
the FD12P reported 12 times more drizzle (L) cases. It
is possible that some of the drizzle cases reported by the
FD12P were mixed with fog. The FD12P also reported
some ice pellets (IP) and freezing drizzle (ZL) cases
that the observer did not report. Based on the 1-min
FD12P data, most precipitation intensities were quite
low, with precipitation rates mainly less than 1 mm h21
(Fig. 3b). These results indicate that automated in-
struments may have difficulty identifying precipitation
type; hence, they should be used with some caution. It
was assumed here that the observation provided by the
human observer is the ground truth, but it should be
recognized that the observer reports have some un-
certainties in identifying precipitation phase and in the
timely reporting of meteorological conditions as well.
FIG. 3. (a) The observed frequency distribution of precipitation type based on the FD12P and
the observer, and (b) the frequency distribution of precipitation intensity based on the data
collected during periods November–December 2009, January–April 2010, and January–May
2011. The symbols are clear (C), snow (S), snow pellet (SP), ice pellet (IP), snow grain (SG), ice
crystal (IC), rain (R), freezing rain (ZR), freezing drizzle (ZL), fog (F), drizzle (L), and un-
known (P). The observer also reports freezing rain and fog (ZRF); snow grain and fog (SGF);
rain, snow, and fog (RSF); rain and fog (RF); drizzle and fog (LF); snow and fog (SF); and
thunder, rain, and fog (TRF).
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3. Theoretical derivation of RVR
a. The Koschmieder method
Visibility based on the Koschmieder (1924) method,
which is based on scattering of light by a black object
that is being observed, is given as
Vk 52ln(«)
b, (2)
where « is the threshold visual contrast, which is usually
taken to be 0.05. Since this threshold is a recommended
value by the World Meteorological Organization (WMO),
many of the visibility-measuring instruments, such as the
FD12P probe, use this value. Since the expression given in
Eq. (2) is derived based on natural daylight, it is sometimes
referred to as ‘‘daytime visibility.’’
b. The Allard method
In the absence of natural daylight, such as during
nighttime, another method is used that is based on un-
directed artificial light, which is normally referred to as
the Allard (1876) method; it is given as (see Boudala and
Isaac 2009)
Vk 5Va ln(«)
ln(V2a ET=I)
, (3)
where ET is the threshold illuminance of the light
source when it is just visible, and I is the luminous in-
tensity of the light source. The luminous intensity I
normally depends on the intensity of the light source.
For typical airport operations, there are six different
light intensity settings used: 0, 15, 120, 500, 2500, and
10 000 candela (cd). The threshold illuminance ET de-
pends on the background light BL and is normally ap-
proximated as
log10(ET) 5 25:7 1 0:64 log10(BL). (4)
The background light BL is directly measured for de-
termination of RVR and this will be discussed in the
next section.
c. Background light observation
Figure 4 shows time series of the observed frequency
distribution of BL during daytime at the Pearson In-
ternational Airport during years between 2009 and 2011
(see section 2 for time periods). The most frequent
(32%) BL value is 1000 cd m22, which is a value that
is commonly associated with a normal day. Very bright
days (BL . 12 000 cd m22) occurred less than 2% of the
time during this period.
Figure 5 shows times series of precipitation type and
visibility (Fig. 5a), and background light and cloud amount
(Fig. 5b) for four consecutive days (14–17 December
2009). During the night, the background light goes
down to a value near 4 cd m22, as indicated in Fig. 5b.
When fog occurs, it is always associated with low visi-
bility, as indicated in Fig. 5a; this has important im-
plications on the intensity light settings that will be
discussed in the next section. As indicated in Fig. 5, the
effect of cloud cover on BL is relatively weak, at least
for this winter case.
FIG. 4. Frequency distribution of the observed background light
in 1000 cd m22 at the Pearson International Airport between years
2009 and 2011.
FIG. 5. Time series of (a) precipitation type and visibility and (b)
background light and cloud amount are plotted against the number
of hours for four consecutive days (14–17 Dec 2009). The local
night and day times are also indicated.
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d. The parameterization of RVR as a function of Vk
Based on the earlier discussions, RVR can be given
as
RVR 5 max(Vk, Va). (5)
Following Boudala and Isaac (2009), Vk can be related
to Va using Eq. (3). Equation (3) is nonlinear, but it can
be numerically solved if proper values for BL and I are
chosen. Runway lights can generally be set at six different
intensity levels. In Canada, RVR reported by the Air
Traffic Service (ATS) is based on the runway lights being
set at intensity level 3 (500 cd) unless the lights are at level
4 (2500 cd) or level 5 (10 000 cd). This means that RVR is
calculated assuming that the lights are at level 3 even if the
lights are off (level zero) or at levels 1 or 2. The level 5 light
setting can be requested by pilots during low-visibility con-
ditions, but it is not typically used. The 10-min Meteoro-
logical Aerodrome Report (METAR) RVR, however, is
based on the lights at level 5 for all conditions; therefore,
only levels 3, 4, and 5 will be considered here.
Figure 6 shows numerical solutions of Eq. (3) for
nighttime (BL 5 6.8 cd m22) (Fig. 6a), normal day (BL 5
1000 cd m22) (Fig. 6b), bright day (BL 5 12 000 cd m22)
(Fig. 6c) using three runway light settings, and for run-
way light level 3 combining night and day times (Fig. 6d).
Also shown in Fig. 6d are the results of Eq. (6) that will be
discussed in more detail later. During the night (Fig. 6a),
the nighttime visibility Va is much larger than the daytime
visibility Vk, particularly at lower visibilities. However,
the effect of the light intensity becomes weaker as the
visibility decreases. The implication of this is that the
choice of light intensity setting does not significantly
affect the relationship between Va and Vk at low visi-
bilities that may be due to heavy fog or snow. During
the day (Figs. 6b,c), Vk is generally larger than Va ex-
cept when the intensity is at level 5 and the visibilities
are less than about 1.5 km. If the light setting is at level
3 (Fig. 6d), the only relevant curve is the nighttime curve
because RVR is taken to be the maximum [Eqs. (4) and
(6)]. Table 1 shows power-law relationships fitted to
the solutions given in Fig. 6. If the light setting is known,
it is possible to use these relationships to predict the RVR
FIG. 6. Numerical solutions of Eq. (3) for (a) nighttime (BL 5 6.8 cd m22), (b) normal day (BL 5 1000 cd m22),
and (c) bright day BL 5 12 000 cd m22) using three light settings, and (d) for runway light level 3 combining night
and day times. The symbols L3, L4, and L5 correspond to the runway light settings 500, 2500, and 10 000 cd, re-
spectively, and the curves based on Eq. (6) are also shown by red and green lines.
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values at the assumed background light levels. How-
ever, in many cases the light intensity setting may not be
known. Based on the earlier discussions and using the
definition of RVR in Eq. (5), for most ATS operations
in Canada, assuming normal day and night conditions
at level 3 light intensity setting in Table 1, RVR may be
approximated as
RVRP 5
"Day max(0:6V0:53
k , Vk)
Night max(1:31V0:71k , Vk)
#. (6)
As indicated in Fig. 6d, during the daytime, the pa-
rameterization will follow the green line, and during
nighttime, it will follow the red line. Note here that for
low-visibility cases (visibility , 500 m), the parameteri-
zation closely follows the normal day line (blue dash), and
otherwise assumes the RVR is the same as the daytime
visibility Vk. During nighttime, the RVR is approxi-
mated by the blue curve—the nighttime visibility. This
assumption will be tested in the following section using
observation data.
4. Verification of the parameterization
a. Two case studies
Figure 7 shows the time series of visibility Vk mea-
sured using the FD12P; measured RVR at the runway
locations 06R, 06L, 33R, 24R, and 24L (locations in-
dicated in Fig. 1); and the parameterized RVR (RVRP)
determined using Eq. (6) (Fig. 7a). The precipitation
type is based on the FD12P and human observer (Fig. 7b),
and precipitation intensity is based on the FD12P (Fig. 7c)
for 25 November 2009 at CYYZ. To switch from night-
time to daytime conditions, the background light BL
measurement was used. The visibility and RVR obser-
vation data had temporal resolutions of 1 and 5 min,
respectively. The human observer typically reported
every hour, but several special reports are also included.
The visibility during the night near 0300 and 0900 UTC
decreased to near 200 m because of a mixture of fog and
drizzle. Note that the FD12P reported snow during this
time period, which seems to be a false alarm based on
the human observer and the observed T. The visibility/
RVR improved during the day after the fog lifted, al-
though there was occasional drizzle and precipitation,
particularly during the day near 1600 UTC. Note that the
observed visibility Vk is significantly lower than the ob-
served RVR during the night, but similar to the observed
RVR during the day. Considering that the parameterized
RVR is based on an approximate solution, the agreement
with the observed RVR at all runway locations is quite
reasonable. Recall also that RVR is reported only when it
is less than 6000 ft (1.83 km), since it is limited by the
length of the runway and runway lights and hence this is
not a typical situation. As a result, it is not possible to test
the RVR parameterization at values higher than this ob-
servational limit.
Another similar example is given in Fig. 8. These
observations were made at CYYZ on 25 October 2010.
Similar to the previous example, the visibility/RVR dur-
ing the night decreased to near 100/500 m because of fog,
which lasted for almost 7 h from 0500 to 1200 UTC. The
earlier reduction of visibility/RVR appeared to be due to
both rain and fog, although the observer missed the rain
event. Both the observed and parameterized RVR values
during the reduced visibility period were significantly
higher than the observed visibility, reaching a factor of 5
when the visibility was approaching 100 m. The param-
eterized RVR in this case also shows an agreement as
compared to the observed RVR reported at all locations.
b. Using the entire dataset
To test the parameterization using the entire dataset,
the measured visibility data were interpolated to the
nearest RVR observation time. In Fig. 9 there are some
examples of scatterplots of RVR measured at the runways
showing the close proximity to each other and pointing in
the same direction (Figs. 9a–c). Also shown is the mea-
sured visibility at the CAN-Now site compared against
RVRs measured at three locations for nighttime and
daytime conditions (Figs. 9d–f). There is a significant vari-
ability in RVR even for runways in close proximity and
pointing in the same direction. On average, during the
daytime the observed RVR is close to the observed visi-
bility, but during the nighttime RVR is in greater agree-
ment with the previous discussions. There is considerable
scatter in the plots that may be attributed to variations
in location, runway intensity light setting, and the RVR
reporting scheme used, as discussed earlier.
Figure 10 shows scatterplots of the measured and pa-
rameterized RVRs at six different runway locations: 06L
(Fig. 10a), 06R (Fig. 10b), 33L (Fig. 10c), 33R (Fig. 10d),
24L (Fig. 10e), and 24R (Fig. 10f). The parameterization
TABLE 1. Power-law relationships fitted to the solutions given
in Fig. 6.
Va
5 aVbk
Intensity
setting
Night
BL 5 6.8
cd m22
Normal day
BL 5 1000
cd m22
Bright day
BL 5 12 000
cd m22
3 a 5 1.31
b 5 0.71
a 5 0.6
b 5 0.53
a 5 0.38
b 5 0.44
4 a 5 1.6
b 5 0.73
a 5 0.9
b 5 0.62
a 5 0.6
b 5 0.54
5 a 5 1.9
b 5 0.76
a 5 1.17
b 5 0.67
a 5 0.84
b 5 0.61
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agreed with observations with a correlation coefficient (r)
near 0.8, which is very encouraging considering the vari-
ability of RVR shown in Fig. 9. The runways that are
farther away from the visibility measurement location (not
shown in this figure) showed relatively lower correlations,
as would be expected. Quantization of the data in the plot
may also be related to the RVR reporting scheme men-
tioned earlier.
Since RVR is parameterized as a function of Vk, ac-
curate estimation of RVR highly depends on the ac-
curacy of Vk, which may be measured or estimated
based on meteorological parameters. For most forecasting/
nowcasting applications, Vk is parameterized using
model-predicted moisture variables, such as RH, dur-
ing a foggy day or precipitation rate during snow or-
rain. Hence, identifying the precipitation type and
understanding its impact on visibility is critical for visi-
bility prediction. These issues will be discussed in fol-
lowing sections.
5. Parameterization of RVR in snow and fog
a. In snow
As discussed earlier, the prediction of RVR using
Eqs. (3) and (4) is not trivial, but the parameterization
of RVR as a function of Vk facilitates using the pre-
dicted Vk to estimate RVR. It has been shown that
visibility in snow or extinction bs can be related to
snowfall rate and T, following Boudala and Isaac
(2009), as
ln(bs) 5 0:71 2 0:0288T 1 0:783 ln(S 1 0:04), (7)
where bs is in kilometers, T in degrees Celsius, and S is
the snowfall intensity in millimeters per hour. Equation
(7) can be converted to Vk in snow using Eq. (2) assuming
« 5 0.05, and this will be referred to as visBI09 from here
on. The application of Eq. (7) in NWP models will be
discussed in section 6.
FIG. 7. Time series of visibility (Vk) measured using the FD12P: RVR measured at various
locations 06R, 06L, 33R, 24R, and 24 (RVR06R, RVR06L, RVR33R, RVR24R, and
RVR24L), and parameterized using (a) Eq. (6), (b) precipitation type [observer (SA) and
FD12P], and (c) precipitation intensity on 25 Nov 2009 at CYYZ.
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b. In fog
Prediction of RVR in fog is difficult since the prediction
of Vk in fog is also difficult. Visibility in warm fog can be
predicted if the microphysical parameters such as liquid
water content (Eldrige1969; Tomasi and Tampieri 1976)
and cloud particle number concentration (Gultepe et al.
2006, 2009) are known. For ice fog, visibility/RVR can be
predicted if the ice water content and mean particle di-
ameter of fog-forming particles are known (e.g., Boudala
and Isaac 2009). However, most of the current operational
NWP models are not capable of resolving the small-scale
fog-forming dynamical and microphysical phenomena.
The cloud parameterization schemes used in these models
usually do not work well near the surface (see section 8
for further discussion). As an alternative, visibility may
be related to RH, Td, and T. To explore this possibility,
the data collected during the time periods mentioned in
section 2 at CYYZ have been analyzed.
Figure 11 shows 1-min-averaged b measured using
the FD12P, measured RH (Fig. 11a), and the dewpoint-
to-ambient temperature ratio (Td/T) (Fig. 11b). The
fog events were determined using the FD12P and the
data from the human observer. There is a positive cor-
relation between b and both RH and Td/T, particularly at
higher values of Td/T and RH. Using the data shown in
Figs. 11a,b, b due to fog can be parameterized as
bf 5
�exp(25:605 1 0:0114RHf), r 5 0:83
exp(214:188 1 0:159RH), r 5 0:75
�, (8a)
where f is defined as
f 5 ln abs1
ln minTd
T, 0:9998
� �� �0B@
1CA
264
375, (8b)
and Td and T are the observed dewpoint and ambient
temperature in kelvins, respectively. The correlation
coefficient (r) is 0.75 only when RH was used. However,
when both RH and f are used, the correlation coefficient
increased to 0.83 [see Eq. (8a)], the F statistical value,
which is a measure of goodness of fit, increased from
11 457 to 15 769, and the estimated error variance de-
creased from 1.3 to 1 km—all indicating improvements.
FIG. 8. Time series similar to Fig. 7, but observations are on 25 Oct 2010.
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The statistical significance testing, or P value, remained
at zero, indicating the statistical significance of both vari-
ables. The ‘‘min’’ expression included in Eq. (8b) is used in
order to avoid infinity at the saturation point. As indicated
in Fig. 11, the extinction b becomes very sensitive to
changes in RH when the RH exceeds 95%; hence, accu-
rate prediction or measurement of RH is very crucial for
such a parameterization. Unfortunately, as discussed
earlier, the accuracy of RH measurements becomes even
smaller for RH . 90%. The application of this param-
eterization and the others discussed in the previous
sections will be discussed in the following section.
6. NWP model application
The NWP model data used in this study were generated
using the Canadian Global Environmental Multiscale
Regional (GEM-Reg) model at 15-km resolution in its
regional configuration (Cote et al. 1998a,b). This version
of the model is described in more detail by Mailhot et al.
(2006). The regional forecast model is run at the Canadian
Meteorological Centre (CMC) 4 times a day (0000, 0600,
1200, and 1800 UTC), out to 48 h. The grid-scale con-
densation scheme is based on Sundqvist (1978). In this
scheme, cloud formation actually begins before the grid-
resolved humidity reaches saturation. The threshold rel-
ative humidity is 80% at the lowest model level, but varies
in the vertical. Precipitation occurs instantaneously at the
ground if the mixing ratio exceeds a certain threshold. In
principle, fog may be related to the liquid water mixing
ratios predicted at lower model levels. However, because
of the coarse vertical and horizontal resolution of the
model, the lower model level moisture field is poorly
predicted and hence fog prediction is not always possible.
Precipitation type in the model is diagnosed based on
the Bourgouin (2000) scheme using the vertical temper-
ature profile. The solar and infrared radiation are based
on Fouquart and Bonnel (1980) and Garand (1983). In
this paper, visibility in the model is determined using
the parameterizations for extinction as follows: for fog
bf see Eq. (8) in this paper, for rain (R) br 5 0:4R0:63 is
based on Marshall and Palmer’s (1948) exponential size
FIG. 9. (a)–(c) Scattered plots of RVR measured near runways pointing at the same directions (see Fig. 1), and
(d)–(f) measured visibility at another location compared against RVRs measured at three locations for night and day
conditions.
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distribution, and for snow (S) bs [Eq. (7)] is based on
Boudala and Isaac (2009).
In the model, fog is diagnosed only if the total pre-
cipitation (P 5 S 1 R) is less than 0.5 mm h21 and T .
08C or P is less than 0.25 mm h21 and T , 08C, provided
that RH . 97%. The relative humidity threshold used in
the model for diagnosing fog has been arbitrarily chosen
for this test. Some models may have a more sophisti-
cated method for diagnosing or predicting fog events
and hence any suitable method can be used. The visi-
bility Vk is then calculated as
Vk 53
b, (9)
assuming that the threshold visual contrast is 0.05 in
Eq. (2). The extinction due to both rain and snow brs is
given as brs 5 br 1 bs, and hence b in the parameteri-
zation is represented as
b 5
264max(brs, bf ) if T $ 0, RH . 98%, P , 0:5 mm h21
max(brs, bf ) if T , 0, RH . 98%, P , 0:25 mm h21
brs, otherwise
375. (10)
FIG. 10. Scattered plots of measured RVRs and parameterized [see Eq. (6)] for six different runway locations (a) 06L, (b) 06R, (c) 33L,
(d) 33R, (e) 24L, and (f) 24R.
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For visibility prediction in fog using Eq. (8), we have
used the average values of the three bottom model levels
of T and Td instead of the surface values.
Figure 12 shows time series of parameterized visibility
visBI09: the visibilities measured (VkFD12P) and based on
human observation (SA) and GEM-Reg (GEM-RegBI09)
(Fig. 12a); precipitation type based on the FD12P and
human observation (Fig. 12b); RVR derived based on the
FD12P (RVRFD12P) and GEM-Reg using Eq. (6); ob-
served RVRs in three locations (24R, 24L, and 33R) (Fig.
12c); and precipitation intensity based on the FD12P and
GEM-Reg (Fig. 12d). The data displayed in the figure
were collected on 5 and 6 February 2011 at CYYZ. In
snow, visibility/RVR is closely linked to the precipita-
tion intensity, as can be seen in Figs. 12a,c,d. Precipi-
tation started at 2000 UTC on 5 February and ended
at 0300 UTC on 6 February. The model captured the
starting and ending times of the precipitation remark-
ably well (Fig. 12b). The observed precipitation type is
mainly snow based on both human observer and FD12P
(Fig. 12b). The observed snowfall intensity reached near
4 mm h21 and the associated minimum visibility and
RVR reached near 400 and 600 m, respectively (Figs. 12c
and a), where the T is close to 248C. Note that the
parameterized visibility, visBI09, correlated well with
observations (Fig. 12a), which implies that the reduction
of the visibility was mainly caused by snow. Although
the model captured the visibility trend, the predicted
minimum visibility only reached about 700 m. This is be-
cause the predicted precipitation only reached a maxi-
mum of 2 mm h21, which is about half the observed
value. If the precipitation intensity was predicted well
(perfect forecast), the visibility forecast would closely
follow the parameterization visBI09. The maximum of the
observed precipitation intensity is also shifted to the left
and this is also reflected in the predicted visibility (see
Figs. 12a,d). The magnitudes of the simulated RVRs are
very close to the observed values (2000–700 m), although
the minimum is shifted to the left in the same manner as
the predicted visibility and precipitation intensity. Con-
sidering the predicted RVR is based on visBI09 derived
using predicted T and S, the agreement with observations
is quite good and encouraging.
Figure 13 shows time series of model-predicted
and -observed RVRs at three locations (24L, 24R, and
33R) (Fig. 13a), observed and simulated relative hu-
midities (Fig. 13b), precipitation type based on both the
FD12P and human observer, simulated and observed
temperatures (Fig. 13c), and precipitation observed
and simulated (Fig. 13d). The data plotted here are
collected on 24 and 25 January 2010 at CYYZ. The
observed temperature remained well between 08 and
78C, although the simulated temperatures were slightly
higher. The low RVR near 37 h (;1400 UTC) on 25
January occurred mainly because of fog based on both
the observer and FD12P (Fig. 13c) but, as indicated by
the human observer in the same panel, the fog was mixed
with rain and drizzle. As discussed earlier, the FD12P is
not able to report fog when it is mixed with precipita-
tion, and hence reported rain or drizzle during this period.
The presence of fog is indicated by relative humidity
reaching near to 100% based on observation and also
model simulation (Fig. 13b). Note that the atmosphere
has warmed during this period, indicating the passage
of a warm front and associated precipitation fog. The
start and end times of the precipitation are well simu-
lated (Fig. 13d), but there are some discrepancies in the
magnitude of the precipitation intensity. Note that the
minimum in RVR (200 m) occurred near 38 h where
the observed precipitation intensities are quite low
(,0.5 mm h21) (Figs. 13a,d), indicating that the RVR
minimum is mainly due to fog, which would mainly be
linked to the parameterization given in Eq. (8). Inciden-
tally, the simulated precipitation intensities are also low,
agreeing with the observed values; as a result, the pre-
dicted RVR reached near 200 m, which also agreed well
with observation during this period, although slightly
FIG. 11. Using the combined dataset, extinction b measured using
the FD12P during CYYZ fog events plotted against (a) measured
RH and (b) dewpoint-to-ambient temperature ratio (T/Td).
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shifted to the left following the maximum in the simulated
RH (Fig. 13b). During the earlier hours between 24 and
30, the parameterization overestimated the RVR. This
is because the model predicted a significant amount of
precipitation, which is not supported by observation.
Thus, based on our algorithm using the model-predicted
variables, the rain droplets would be the main contribu-
tors to the total extinction, which would give a relatively
smaller extinction than that found for fog, and hence the
predicted RVR is larger. Thus, accurate prediction of
relevant meteorological parameters—such as precipita-
tion, relative humidity, and the type of precipitation—has
a critical importance for prediction of RVR using NWP
models. Therefore, the above examples demonstrate that
such parameterizations could be applied to predict the
runway visual range, provided that the relevant param-
eters associated with it are reliably predicted.
7. Summary and conclusions
To develop a parameterization that can be used
for predicting runway visual range (RVR), relevant
meteorological parameters such as visibility (Vk), pre-
cipitation intensity, relative humidity (RH), temperature
(T), and precipitation type measured at the Toronto
Pearson International Airport (CYYZ) during the Ca-
nadian Airport Nowcasting (CAN-Now) project have
been analyzed. The precipitation intensity Vk and pre-
cipitation type were measured using the Vaisala FD12P
probe. The observed Vk and precipitation type were
tested against data reported by a human observer. Gen-
erally, it was found that measured Vk corresponded quite
well to those reported by an observer with a correlation
coefficient r of near 0.76 for Vk , 15 km. However, the
FD12P underestimated Vk by about 20% with a mean
difference (MD) of about 1 km. When the two datasets
were compared for Vk , 5 km, however, the correlation
coefficient was unchanged, but the MD decreased to
more a reasonable value of close to 200 m. For Vk ,
2 km, however, the FD12P overestimated visibility by
about 7% with an MD of 60 m. The observations also
indicated that the human observer reported about 6 times
more fog events than the FD12P, and as would be ex-
pected, the FD12P missed all fog cases that were mixed
FIG. 12. At CYYZ, 5 and 6 Feb 2011 time series of the parameterized visibility, visBI09: (a) the visibilities measured
(VkFD12P) and based on human observer (SA) and GEM-Reg (GEM-RegBI09), (b) precipitation type based on FD12P and
human observer and observed temperature, (c) RVR derived based on the FD12P (RVRFD12P) and GEM-Reg model, and
observed RVRs in three locations (24R, 24L, and 33R); and (d) precipitation intensity based on FD12P and GEM-Reg.
FEBRUARY 2012 B O U D A L A E T A L . 189
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with drizzle, rain, or snow. The observer reported slightly
more snow events—nearly 22% as compared to 17% by
the FD12P; however, the FD12P reported significantly
more snow grain cases than the observer. Both the ob-
server and the FD12P reported rain events at a similar
frequency—near 4% and 5%, respectively—but the FD12P
reported 12 times more drizzle cases. It is possible that the
FD12P reported some of the drizzle cases at the expense
of fog. The FD12P also reported some IP and ZR cases
that the observer did not report.
Using a theoretical approach and aviation air traffic
service operational procedures, a parameterization that
can be used for predicting runway visual range as a func-
tion of visibility has been developed. The parameteriza-
tion was tested using direct measurements of RVR and
Vk during years between 2009 and 2011 at the Toronto
Pearson International Airport during the CAN-Now
project, and the agreement found was quite good, with
a correlation coefficient r near 0.8. Predictions of RVR
using a new parameterization that adapts a suitable pa-
rameterization of Vk as a function of snowfall intensity
and temperature during snow has been discussed and
shown to work quite well. Using measurements of tem-
perature (T), relative humidity (RH), and dewpoint
temperature (Td), a new parameterization that can be
used for forecasting Vk, and hence RVR during fog has
also been also developed; the parameterization agreed
reasonably well with observations, with a correlation
coefficient r of near 0.8. These parameterizations were
tested using Canadian Environmental Multiscale Re-
gional (GEM-Reg) model data. To test the applicability
of these parameterizations in the model, two case studies
using model-simulated data and meteorological observa-
tions under very low-visibility conditions during snow, fog,
drizzle, and rain at CYYZ were presented. The results
show that when the relevant meteorological parameters
FIG. 13. Time series of modeled and observed meteorological parameters for 24 and 25 Jan 2010 at CYYZ:
(a) predicted RVRs using GEM-Reg, RVR predicted using measured FD12P visibility (RVRFD12P), and observed
RVR at three locations (24R, 24L, and 33R); (b) the observed and predicted (GEM-Reg) relative humilities;
(c) precipitation type from the FD12P and a human observer and the observed and model-predicted temperatures;
and (d) observed and predicted precipitation intensities.
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such as precipitation intensity, T, and RH are reasonably
predicted, and fog events are correctly diagnosed, the
model could be used to predict RVR.
Acknowledgments. This work was funded by the Na-
tional Search and Rescue Secretariat, Transport Canada
and NAV CANADA.
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