parameterization of runway visual range as a function of

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]

FEBRUARY 2012 B O U D A L A E T A L . 177

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).



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).



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.



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.



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



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.



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.



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.



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.



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).



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.



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.



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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