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Absolute zero — 0 K on the Kelvin scale — is equivalent to minus 273.15 degrees C (minus 459.67 degrees F). 3. Lande, K.
Typology: Summaries
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flight flight opopsS
he 3-Kelvin-spread rule, an aviation rule of thumb for winter opera- tions, can enhance pilots’ sense of the actual landing risk level by calling attention to the likelihood that aircraft braking performance will not meet pre-landing calculations. The rule takes advantage of information readily available from aviation routine weather reports (METARs), and its potential value has been recognized in the recent report of an investigation of winter operations^1 by the Accident Investigation Board Nor- way (AIBN; ASW, 10/08, p. 14 and 11/10, p. 30). Nevertheless, its ease of adoption comes at the expense of absolute validity. The rule emerged from several years of scientific research and analysis in Nor- way, including my contributions in the report’s Appendix J, which explain the mi- crometeorology of the natural processes involved in water vapor saturation and ice
on runways (see “Can You Stop?” p. 12). The impetus was that about two-thirds of the air transport accidents and serious incidents studied by the AIBN (21 of 30) occurred when a difference between air temperature and dew point (or spread) of 3 kelvin (K)^2 or less was reported by METARs (see Table 1, p. 17, and Table 2, p. 18 for Kelvin-scale conversions). The statistical probability of that proportion occurring by chance is 0.023 (2.3 percent). Such a spread means that air containing water vapor is not very far from being saturated. The appendix discusses many factors involved; this article focuses only on saturated water vapor at freezing temperatures. The rule states, “When the spread (air temperature minus dew point … read at 2-m [6.6-ft] level) is less than 3 K, compacted snow or ice may constitute slippery conditions.” The rule has proved
especially valuable when air temperatures are lower than 3 degrees C (37 degrees F), in cases of recent or current precipitation, when snow contains liquid water and/or when the surface of frozen contaminants is considerably colder than the METAR air temperatures collected 2 m above the runway indicate. The rule’s underlying research was first reported by an AIBN official in
2007.^3 Before then, insufficient friction on the runway during line operations in Norway often had been attributed only to precipitation or to liquid or frozen water deposited on the runway. A spread of 3 K or less means the relative humidity is high — often 80 percent or higher, indicating likely pre- cipitation. Often, such a spread occurs in precipitation, intermittent precipitation and precipitation in the vicinity of fog or in conditions conducive to fog.
By ReinhaRd Mook
Because lower saturation vapor pressure (SVP), the maximum water vapor pressure that can exist at a given air temperature, occurs above ice than above liquid water at a given air temperature, the air temperature–dew point spread exceeds the air temperature–frost point spread under the same physical condi- tions. Therefore, the spread reported to pilots by METARs is larger than the actual air temperature–frost point spread relevant to the physical processes by which ice forms on a runway. Specifically, air temperature–frost point spread can be close to zero while the METAR’s air temperature–dew spread is 1 K or 2 K. An air temperature–frost point spread will be less than the air tempera- ture–dew point spread. Also, the sur- face temperature of the runway more
often than not will deviate from air temperature. But due to lack of routine runway-surface temperature reports from airports, the 2-m level data must suffice for flight operations. AIBN-directed research also found, however, that many exceptional cases of uneventful landings on ice or snow occurred even in conditions where a 3-K-or-less spread existed. Therefore, pilots should not assume that such small spreads always mean “definitely poor run- way conditions” — instead, the METAR information should be interpreted as an early signal of possible threat.
The latest AIBN research essentially recognizes that when the temperature of a solid surface (runway pavement)
decreases below freezing and below the dew point of ambient air — that is, the temperature at which water vapor would be saturated above liquid water — wa- ter vapor pressure is directed from the air to the solid surface. The lower SVP above ice compared with SVP above liquid water means that hoar frost may appear before the spread drops to 0 K. SVP comes into play because the water vapor in an air mass may be saturated at a temperature 3 K colder than reported in the METAR. A frozen runway surface indicates that these SVP conditions exist in the air mass above the ice. As hoar frost is crushed and partial- ly melted by the tires of aircraft landing gear, frequently resulting in slippery conditions, the difference between reported dew point and effective frost
Water Vapor in Air Above a Runway Affects Braking Friction
AIR TEMP/DP SVP-W SVP-I SVP-DIFF SVP-PCT SMR-W SMR-I SMR-DIFF FROST POINT DP/FP-DIFF
–30°C (–22°F/243.2K) 0.509 0.380 0.129 25.3% 0.318 0.238 0.080 –27.2°C (–17.0°F/246.0K) 2.8°C –27°C (–17°F/246.2K) 0.673 0.517 0.156 23.2% 0.421 0.323 0.098 –24.4°C (–11.9°F/248.8K) 2.6°C –24°C (–11°F/249.2K) 0.883 0.699 0.184 20.8% 0.552 0.437 0.115 –21.6°C (–6.9°F/251.6K) 2.4°C –21°C (–6°F/252.2K) 1.150 0.937 0.213 18.5% 0.720 0.586 0.134 –18.8°C (–1.8°F/254.4K) 2.2°C –18°C (0°F/255.2K) 1.488 1.248 0.240 16.1% 0.931 0.781 0.150 –16.2°C (2.8°F/257.0K) 1.8°C –15°C (5°F/258.2K) 1.912 1.652 0.260 13.6% 1.197 1.034 0.163 –13.4°C (7.9°F/259.8K) 1.6°C –12°C (10°F/261.2K) 2.441 2.172 0.269 11.0% 1.529 1.360 0.169 –10.7°C (12.7°F/262.5K) 1.3°C –9°C (16°F/264.2) 3.097 2.837 0.260 8.4% 1.941 1.778 0.163 –8.0°C (17.6°F/265.2K) 1.0°C –6°C (21°F/267.2) 3.906 3.685 0.221 5.7% 2.450 2.310 0.140 –5.3°C (22.5°F/267.9K) 0.7°C –3°C (27°F/270.2K) 4.898 4.757 0.141 2.9% 3.075 2.986 0.089 –2.7°C (27.1°F/270.5K) 0.3°C 0°C (32°F/273.2K) 6.108 6.108 0.000 0.0% 3.839 3.839 0.000 0.0°C (32°F/273.2K) 0.0°C 3°C (37°F/276.2K) 7.575 NA NA NA 4.769 NA NA 3.0°C (37°F/276.2K) NA C = Celsius; F = Fahrenheit; K=Kelvin; hPa = hectopascals; NA = not applicable to ice; AIR TEMP/DP = air temperature (degrees C) for SVP and SMR columns; read as dew point temperature (degrees C) for FROST POINT and DP/FP-DIFF columns; FP = corresponding frost point temperature when air temperature in first column is read as dew point temperature (degrees C); SVP-I = saturation vapor pressure above ice (hPa); SVP-W = saturation vapor pressure above liquid water (hPa); SVP-DIFF = difference (SVP-W minus SVP-I); SVP-PCT = difference as percentage of SVP-W; SMR-I = saturation mixing ratio (grams of water/kilogram of dry air) above ice; SMR-W = SMR above liquid water; SMR-DIFF = difference (SMR-W minus SMR-I); DP/FP-DIFF = absolute difference (dew point minus frost point) Notes : Saturation vapor pressure, the maximum water vapor pressure that can exist in air at a given temperature, increases with a rise in air temperature. Saturation mixing ratio refers to the mass of water vapor relative to the mass of dry air above either liquid water or ice. This table assumes air temperature measured 2.0 m (6.6 ft) above the runway at an SVP of 1,000 hPa (29.53 in of mercury). Source: Reinhard Mook
Table 1
reflect the increasingly strong bonds of liquid water molecules to the ice with falling temperature. An example of how close air can be to saturation is that at an air temperature of 0 degrees C (32 degrees F), the SVP above water is 6.108 hPa; the correspond- ing SVP at minus 3 degrees C (27 degrees F) is 4.898 hPa. That indicates relative humidity of 80 percent for this 3-K spread.^4 At the other extreme of the table — minus 27 degrees C (minus 17 degrees F) and minus 30 degrees C (minus 22 degrees F) — the corresponding SVPs are 0.673 and 0.509 hPa, so this 3-K spread yields a relative humidity of 76 percent, or possibly higher. To quantify the range of the amount of water covered by the 3-K-spread rule, Table 1 also shows the SMR for air at 1,000 hPa above liquid water (SMR- W column) and above ice (SMR-I column). The largest differences (SMR- DIFF column) in gram water vapor (grams per kilogram of dry air) above liquid water and above ice are found between minus 10 degrees and minus 14 degrees C, that is, the interval with the largest differences in SVP. The SMR-W and SMR-I columns show that the respective SMRs at minus 3 degrees C are approximately 10 times larger than those at minus 30 degrees C. For that reason, pilots should not expect that the 3-K-spread rule, or any rule based on a certain fixed spread, can be valid for any temperature. If the SVP of the air above liquid wa- ter — and, logically, the SMR — exceeds the corresponding SVP above ice, the frost point for a certain mass of air will be higher/warmer than the dew point. Read- ing the Table 1 AIR TEMP/DP column values as dew points, the corresponding frost point temperatures are found under the FROST POINT column, and the spreads are found in the DP/FP-DIFF
column. Typically, the dew point vs. frost point differences will be on the order of 0.1 K times the Celsius dew point, a nega- tive number. For example, when a dew point of minus 15 degrees C is reported, the frost point will be about 1.5 degrees K warmer — that is, about minus 13. degrees C (7.7 degrees F). The 3-K-spread rule only refers to dew point because, as noted, MET- ARS report only dew point even at air temperatures below freezing. However, by extrapolating frost point from dew point as above, the spread in that ex- ample can be estimated to be 1.5 K. As dew point moves toward lower/colder values, however, the difference between dew point spread and frost point spread shrinks. With an extrapolated frost point, the rule becomes useful even at temperatures as low as minus 15 degrees C or so, although other effects should be considered. Table 2 shows the maximum amount of water removed from air above the runway when the spread is 3 K or less and the air temperature then decreases by 3 K. If the spread is 3 K and the temperature drops by 3 K, no water will be removed. However, if the spread is 0 K, an amount of water equal to the difference of the SMR in the 3-K temperature interval will be the maxi- mum amount of water removed. For example, at air temperature of minus 3 degrees C with a spread of 0 K, a 3 K drop in air temperature would mean water vapor removal of 0.625 g per kg above liquid water and 0.676 g per kg above ice. The actual amount will differ, depending on whether the spread is 3 K or less. Table 2 also shows that the SMRs above ice decrease more strongly — that is, each change is larger per 3-K drop — than the SMRs above liquid water at temperatures warmer than
minus 13 degrees C (9 degrees F). This is consistent with the relationships among SVPs in Table 1. At temperatures even lower than these, a decrease of SMR above water on a runway will exceed a decrease of SMR above ice on a runway because the air above liquid water is dried less at higher/warmer temperatures than the air above ice. If we compare tem- peratures near the 0-degrees C freezing point with those near minus 30 degrees C, the SMRs decrease by a factor of about 0.1 for each 3K decrease. This underscores the basic principle that small amounts of water vapor exert sig- nificant effects on landing safety at low temperatures, even though the spread may be small. Reinhard Mook, Ph.D., who retired in 2006 as a professor at the University of Tromsø in Norway, is an independent consultant and researcher. He has conducted micrometeorological field work as an independent researcher at Norway’s Svalbard Airport Longyear and analyses of slippery run- way incidents for the AIBN, SAS Scandinavian Airlines and the former Norwegian airline Braathens SAFE.
Notes