Characteristics of Ice Super Saturated Regions in Washington, D.C. Airspace (2019–2023)

Abstract

Contrails are estimated to contribute 2% of the Earth’s anthropogenic global warming. Contrails are ice crystal clouds formed by the emission of soot and water vapor from jet engines in atmospheric conditions known as Ice Super Saturated (ISS) regions. The formation of contrails can be avoided by flying over or under the ISS regions. Aircraft operators/dispatchers and air traffic control need to know the location of ISS regions in a given airspace to flightplan to avoid contrails. This paper describes the statistics for the presence of ISS regions in the airspace over metropolitan Washington, D.C. These statistics can be used to better understand the operational implications for contrail avoidance. Based on the measurements taken from the twice-daily launch of an aerosonde from Sterling, Virginia (adjacent to Washington, D.C.), analysis of five years of data (2019–2023) indicated that this airspace experiences ISS regions 40% of the days. ISS regions were equally likely during daylight hours (26%) than nighttime (27%). The vertical depth of the ISS region averaged 3000 feet but with a median of 2000 feet. The ISS region floor and ceiling varied by season, with an annual average floor of FL330 and ceiling of FL360. The implications of these results on the operations to avoid contrails, limitations, and future work are discussed.

1. Introduction

Contrails contribute an estimated 2% to the Earth’s total anthropogenic global warming [1]. At night, contrails trap outgoing thermal infrared radiation emitted by the Earth resulting in a warming effect. During the day, contrails absorb the outgoing thermal radiation (warming effect) and can, under specific Sun azimuth conditions, reduce the entry of solar radiation (cooling effect). The net effect during daylight is warming.

Contrails form when water vapor and soot, emitted by jet engines in specific atmospheric regions, form ice crystals [2]. When the ambient atmosphere is Ice Super Saturated (ISS), the ice crystals form and grow into the contrail clouds which can last up to 10 h [3].

Ice Super Saturated conditions exist in the atmosphere when the temperature is less than –42 degrees Fahrenheit and the relative humidity is greater than 100% [2]. In the troposphere, temperature exhibits a predictable pattern, decreasing at a lapse rate as altitude increases. Relative humidity, however, does not exhibit any pattern. Humidity at any altitude is determined by the dynamics of airmasses and the associated frontal systems. As a consequence, the geographic location and depth of ISS regions varies with the weather patterns. They occur in thin layers [3] and are notoriously challenging to forecast [4].

Researchers have proposed several strategies to prevent contrail formation [5]. The least-cost, most-effective strategy is “navigational avoidance”. In navigational avoidance, flights avoid flying through ISS regions in the airspace by either flying below or above the ISS region. This requires precise information on the geographic and vertical location of the ISS region in an airspace. In the event airline pilots, airline dispatchers, and air traffic controllers are required to perform navigational avoidance, they would like an understanding of the following:

• the probability of the presence of ISS regions in an airspace;
• the vertical depth of the ISS region;
• the floor and ceiling of the ISS region.

This paper analyzes the atmospheric conditions with regard to ISS regions in the Washington, D.C. airspace using five years (2019–2023) of aerosonde/weather balloon data for the Sterling, Virginia launch site (located close to Washington Dulles International Airport). This airspace averages over 2000 flights per day on flight tracks routed on north-east/south-west jet airways. The aerosondes are released at midnight and midday and ascend and drift according to prevailing atmospheric conditions.

These ISS statistics have practical implications for airline and air traffic control flight operations. First, they provide information on the frequency of operational adjustments that would need to occur to avoid ISS regions. Second, they provide information on the characteristics and the likelihood of success of the different types of avoidance maneuvers.

This paper is organized as follows: Section 2 provides an overview of contrails and Ice Super Saturated regions; Section 3 describes the data source and the method of analysis; Section 4 describes the results of the analysis; Section 5 provides a discussion of the results; and Section 6 examines the implications of these results, limitations of the study, and future work.

2. Contrails and Ice Super Saturated (ISS) Regions

Contrails, also known as Aircraft-Induced Clouds (AICs), are high-altitude ice-crystal clouds. These anthropogenic clouds form when particulates (e.g., soot) and water vapor are emitted from aircraft jet engines. The soot serves as nuclei for the crystallization of the water vapor. The formation of ice crystals occurs according to a thermodynamic theory developed by Schmidt [6] and Appleman [7], and later revised by Schumann [8] in very specific atmospheric conditions.

According to the Schmidt–Appleman Criterion (SAC) [8], the formation of contrails depends on ambient pressure, humidity, and the ratio of water and heat released into the exhaust plume. When an aircraft flies through atmospheric conditions that satisfy the SAC, saturation with respect to liquid water occurs, resulting in contrail formation. The air temperature should be below −40 °F (233.15 K), and the relative humidity to ice should be in excess of 100% [8,9].

The relationship between temperature and relative humidity is illustrated in the Schmidt–Appleman Diagram (Figure 1). There are three regions: always contrails, possible contrails, and never contrails. If the ambient temperature exceeds the line of relative humidity with respect to water (RHw) at 100%, contrails are not expected to form [10,11]. In conditions where the relative humidity is greater than 100% and the ambient temperature is less than 40 degrees F, contrails will form. Between these two lines, the formation of contrails depends on the relative humidity and pressure.

Under specific atmospheric conditions, the linear contrails can morph into cirrus-like clouds and persist for up to 10 h [7]. The mean duration of contrails is 3 h [6]. During this period, thermal radiation emitted by the Earth is trapped in the atmosphere resulting in global warming.

2.1. Contrail Mitigation

Researchers have proposed several strategies to prevent contrail formation [5]. The least-cost, most-effective strategy is to avoid the Ice Super Saturated (ISS) regions by flying below or above the ISS regions. This is known as “navigational avoidance”.

Several contrail navigation avoidance flight trials have been conducted [4,12,13]. These trials used the Weather Research and Forecasting (WRF) weather data to forecast the locations of the ISS regions. The WRF model is considered to be a state-of-art mesoscale numerical weather prediction system that was designed for both atmospheric research and operational forecasting applications.

In an operational study in the Maastricht airspace, Sausen et al. [12] found that for at least 24% of the flights, ISS regions were misidentified. This study concluded that forecasting persistent contrails is “a difficult task with current numerical weather prediction models”. In another operational study with a U.S. airline, Elkins et al. [13] also identified the challenges of accurately identifying the exact location of ISS regions using the WRF weather data.

Gierens et al. [4] identified the problem with predicting contrail persistence using climate simulations was due to inaccuracies in the prediction of relative humidity in general and for ice supersaturation in particular. The WRF atmospheric forecasts use physics-based models to interpolate between data from a small number of aerosonde weather balloons released twice daily.

To perform contrail avoidance navigation in the presence of the thin, variable layers of ISS regions, airline pilots, airline dispatchers, and air traffic controllers would like to know what is the likelihood of the presence of an ISS region in airspace, the vertical depth of the ISS region, and the flight levels most likely to align with the ISS region.

2.2. Ice Super Saturated Regions

Ice Super Saturated (ISS) conditions exist in the atmosphere when the temperature is less than −42 degrees Fahrenheit and the relative humidity is greater than 100% [2]. In the troposphere, temperature decreases at a lapse rate as altitude increases (Figure 2). Relative humidity, however, does not correlate with altitude as it is a consequence of airmass composition and frontal systems from weather patterns. As a result, ISS regions occur in thin layers [3]. An example of a temperature and relative humidity-to-ice profile is illustrated in Figure 2.

The ISS region is in the vertical location when both temperature and relative humidity conditions are met. The ISS region is defined by a floor and ceiling, and the difference between the floor and ceiling is the vertical depth.

3. Data and Methods

This section describes the data source and the analysis process, algorithms, and equations used.

3.1. Data Sources

The data examined for this analysis are from the Integrated Global Radiosonde Archive (IGRA), a collection of radiosonde and pilot balloon observations collected and consolidated by the National Oceanic and Atmosphere Administration (NOAA) [14].

This paper considers measurements from the Sterling station for 5 calendar years, 2–019–2023. Each time a weather balloon is launched, a metadata record is documented, providing information such as the date and time of the sounding, and the number of data records recorded.

Each of these metadata records has an associated set of records taken as the measurement apparatus rises. The fields examined in this analysis are pressure, temperature, and relative humidity.

3.2. Process, Equations, Metrics

The seven-step process for generating the metrics for the characteristics of the airspace is summarized in Figure 3.

Data pre-processing includes identifying null data and other erroneously formatted data in the IGRA dataset. The analysis required several unit conversions and data transformations:

• Step 1: Calculate Pressure Altitude

Pressure readings (mb) were converted to altitude (feet). The calculation for pressure altitude is defined in Equation (1) (NOAA, n.d.).

$$h_{alt} = \left(1-{\left({\displaystyle \frac{P}{1013.25}}\right)}^{0.190284}\right)·\mathrm{145,366.45}$$

(1)

where P is pressure (mb).

• Step 2: Calculate Temperature in Fahrenheit

Temperatures in Kelvin were converted to Fahrenheit (Equation (2)).

$$°\mathrm{F}\mathrm{}=\mathrm{}(\mathrm{K}\mathrm{}-\mathrm{}273.15)\mathrm{}\times \mathrm{}1.8\mathrm{}+\mathrm{}32$$

(2)

where F is the temperature in Fahrenheit and K is the temperature in Kelvin.

• Step 3: Calculate Relative Humidity to Ice

The aerosonde relative humidity to water was converted to relative humidity to ice as defined by Equations (3)–(5). These equations are the Goff and Gratch equations [15], as applied by Roosenbrand et al. [16].

$$R{H}_w={\displaystyle \frac{e}{e_w}} R{H}_i={\displaystyle \frac{e}{e_i}}$$

(3)

$$\begin{gathered} \log e_w=-7.90298\left({\displaystyle \frac{T_{st}}{T}}-1\right)+5.02808\log \left({\displaystyle \frac{T_{st}}{T}}\right)-1.3816\mathrm{}·{10}^{-7}\left({10}^{11.344\left(1-{\displaystyle \frac{T}{T_{st}}}\right)}-1\right) \\ +8.1328·{10}^{-3}\left({10}^{-3.49149\left(1-{\displaystyle \frac{T_{st}}{T}}\right)}-1\right)+\log \left(e_{st}\right) \end{gathered}$$

(4)

where e_w is the saturation water vapor pressure (hPa), T_st is the steam point temperature (373.15 K), T is the temperature (K), and e_st is the steam point pressure (1013.25 hPa).

$$\log e_i = -9.09718\left({\displaystyle \frac{T_0}{T}}-1\right)-3.56654\log \left({\displaystyle \frac{T_0}{T}}\right)+0.876793\left(1-{\displaystyle \frac{T}{T_0}}\right)+\log e_{i0}$$

(5)

where e_i is the saturation water vapor pressure over ice (hPa), T₀ is the ice point temperature (273.16 K), T is the temperature (K), and e_i0 is the ice point pressure (6.1173 hPa).

• Step 4: Calculate ISS Region

For each pressure altitude up to FL430, determine if the SAC are met (i.e., Temp < −40 deg F and RH_Ice > 100%).

• Step 5: Calculate Floor and Ceiling of ISS Region

Starting from FL300 and moving to FL430, tag the lowest FL with SAC conditions as the floor. Tag the highest FL with SAC as the ceiling. Tag FLs between floor and ceiling as intermediate. Note: to avoid extraneous readings, the floor and ceiling are defined by two consecutive FLs that meet SAC.

• Step 6: Calculate Max Position Drift

Position drift of the aerosonde as it ascended was calculated using the time between measurements, wind speed, and bearing. The Haversine formula was used to calculate the drift distance in nautical miles (nm) [17,18]. See Equations (6)–(11).

$$d = time · velocity$$

(6)

$$la{t}_t = {\sin }^{-1}\left(\sin \left({\displaystyle \frac{\pi }{180}}·la{t}_1\right)·\cos \left({\displaystyle \frac{d}{R}}\right)+\cos \left({\displaystyle \frac{\pi }{180}}·la{t}_1\right)·\sin \left({\displaystyle \frac{d}{R}}\right)·\cos \left({\displaystyle \frac{\pi }{180}}·b\right)\right)$$

(7)

$$la\mathrm{t}2 = {\displaystyle \frac{\pi }{180}}·lo{n}_1$$

(8)

$$\begin{gathered} lo{n}_t = {\displaystyle \frac{\pi }{180}}·lo{n}_1 + {\tan }^{-1}\left(\sin \left({\displaystyle \frac{\pi }{180}}·b\right)·\sin \left({\displaystyle \frac{d}{R}}\right)·\cos \left({\displaystyle \frac{\pi }{180}}·la{t}_1\right), \cos \left({\displaystyle \frac{d}{R}}\right)- \\ \sin \left({\displaystyle \frac{\pi }{180}}·la{t}_1\right)·\sin \left(la{t}_t\right) \right) \end{gathered}$$

(9)

$$lo{n}_2 = {\displaystyle \frac{\left(180·lo{n}_t\right)}{\pi }}$$

(10)

$$hav\left(\theta \right)={\displaystyle \frac{1-\cos \left(\theta \right)}{2}}$$

(11)

$$drift = 2R·{\sin }^{-1}\left(\sqrt{hav\left(la{t}_2-la{t}_1\right)+\left(1-hav\left(la{t}_1-la{t}_2\right)-hav\left(la{t}_1+la{t}_2\right)\right)·hav\left(lo{n}_2-lo{n}_2\right)}\right)$$

(12)

where d is distance (m), time is the time change between measurements (s), velocity is the wind speed (m/s), R is the radius of the Earth (637,1000 m), lat1 is the initial latitude, lat2 is final latitude, lon1 is the initial longitude, lon2 is the final longitude, and b is the bearing in degree.

• Step 7 Calculate Statistics for each Metric

Statistics for the following metrics are calculated:

• Number of days with measurements;
• Percentage of days with ISS regions;
• Percentage of measurements with ISS regions by hour;
• Vertical depth of ISS regions (ft—pressure altitude);
• ISS region floor (ft—pressure altitude);
• ISS region ceiling (ft—pressure altitude);
• Geographic position drift from launch locations (nm).

4. Results

Five years (2019–2023) of aerosonde/weather balloon data for the Sterling, Virginia region from the Integrated Global Radiosonde Archive (IGRA) curated by the National Oceanic and Atmosphere Administration (NOAA) were evaluated. Aerosonde readings are taken at midday and at midnight.

Missing or invalid readings were less than 2.6% for 2019 (2.6%), 2020 (2.2%), 2022 (2.4%), and 2023 (0.1%). The year 2021 had 15% of missing or null data. Results are reported only for the readings when data were available and valid.

The results of the analysis are summarized in

Table 1. Summary of ISS region statistics for the Washington, D.C. airspace in 2023.

Characteristics	Statistics
Number of Days with Measurements	1757
Percentage of Days with ISS Regions	40%
Percentage of Measurements with ISS Regions by Midday/Midnight	26% Midnight; 27% Midday
Vertical Depth of ISS Regions (ft—pressure altitude)	Min = 1000′ Median = 1936′ Mean = 3072′ Max = 12,482′ Standard Deviation = 3120′
ISS Region Floor (ft—pressure altitude)	Min = 30,019′ Median = 33,136′ Mean = 33,609′ Max = 43,943′ Standard Deviation = 3104′
ISS Region Ceiling (ft—pressure altitude)	Min = 30,120′ Median = 36,545′ Mean = 36,681′ Max = 43,976′ Standard Deviation = 3648′
Maximum Geographic Position Drift from Launch Locations (nm)	Min = 0 nm Median = 49 nm Mean = 157 nm Max = 3107 nm

.

4.1. Annual Frequency of ISS Regions in the Washington, D.C. Airspace

Analyzing 1757 days in 2019–2023, the Sterling aerosonde data identified 40% of the days with temperature (<−42 degrees) and relative humidity to ice (>100%) satisfying the conditions for an ISS region (Table 1).

The midday aerosonde met the ISS conditions 26% of the days, while the midnight aerosonde met the conditions 27% of the days. Note that on the same days the ISS conditions were present at midday but not at midnight, or midnight but not at midday, this resulted in a combined midday/midnight percentage at 40%.

4.2. Monthly Frequency of ISS Regions in the Washington, D.C. Airspace

In the period 2019–2023, the average percentage of days per month with ISS regions is 40%. This is equivalent to 12 days per month for a 30-day month. The median was 38%, with a minimum of −36% and a maximum of 50%.

The distribution of the monthly % of days with ISS regions skews to the right (Figure 4). Eight months have the average % of days with an ISS region below the mean of 40%. Four months were at or above one standard deviation: August, November, December, and February.

October consistently experienced the lowest number of days with an ISS region. The majority of days in October had temperatures under −42 °F; however, the criteria for relative humidity to ice values above 100% was not met.

4.3. Vertical Depth of ISS Regions in the Washington Airspace

The vertical depth of an ISS region represents the difference between the pressure altitude of the floor and ceiling of the ISS regions (see definition in Figure 2). The average vertical depth was 3000′, the median was 2000′, and the maximum was 12,000′ (Table 1).

Fifteen percent of the midday/midnight readings had an ISS region with a vertical depth of 1000′ or less (Figure 5). Twenty-three percent of ISS regions had a vertical depth less than 2000′. Thirty percent of ISS regions had a vertical depth of more than 5000′.

Across the 5-year period, the vertical depth was the same at midnight as midday.

Patterns in the vertical depth of the ISS regions are not apparent (Figure 6). Seasonal patterns are consistent with the ceiling/floor analysis discussed in the next section.

The probability of one vertical depth transitioning to another vertical depth is shown in

Table 2. The probability of one vertical depth (rows) transitioning to another vertical depth (columns) does not exhibit any dominant patterns.

Current Vertical Depth	Next Vertical Depth
	No ISS Region	2000′	4000′	6000′	8000′	10,000′	12,000′
No ISS Region	59.7%	8.8%	2.0%	1.8%	1.5%	1.3%	1.3%
2000′	3.7%	1.5%	0.3%	0.4%	0.4%	0.4%	0.4%
4000′	2.0%	0.7%	0.3%	0.3%	0.3%	0.2%	0.1%
6000′	1.8%	0.6%	0.1%	0.1%	0.1%	0.1%	0.1%
8000′	1.8%	0.6%	0.1%	0.2%	0.1%	0.1%	0.2%
10,000′	1.6%	0.5%	0.2%	0.1%	0.1%	0.1%	0.1%
12,000′	1.5%	0.4%	0.3%	0.1%	0.1%	0.1%	0.1%

. Sixty percent (59.7%) of the time when there was no ISS region, the next aerosonde reading also had no ISS region.

When there was no ISS region, the likelihood of the next reading having an ISS region of any vertical depth was 17%. Likewise, when there was an ISS region of any vertical depth, the likelihood of the next aerosonde reading having no ISS region was 12%.

When there was an ISS region of any depth, the likelihood of transitioning to another vertical depth was 10%.

4.4. ISS Region Floor/Ceiling in the Washington, D.C. Airspace

Over the course of the year, the floor of the ISS regions ranged from 30,000′ to 44,000′ (Figure 7). The mean (33,384′) was close to the median (32,963′), indicative of symmetrical distribution (Table 1). The standard deviation of 3000′ results in 66% of the floor being between 30,000′ and 36,000′.

The floor and ceiling were higher by approximately 3000′ in the summer months of June, July, August, and September.

4.5. ISS Region Flight Level in the Washington, D.C. Airspace

FL340 exhibited the greatest number of days with ISS conditions for both midday (6%) and midnight (6%) (Figure 8). FL330–FL350 exhibited ISS conditions for 17% for the readings at midday and for 16% of the readings at midnight. FL320–FL360 exhibited ISS conditions for 27% for the readings at midday and for 25% of the readings at midnight.

4.6. Geographic Shift in Aerosonde during Ascent

When the aerosonde is released, the lateral position is subject to prevailing atmospheric conditions (i.e., horizontal winds). The maximum distance from launch location up to FL430 ranged from a minimum of 0 nm to a maximum of 3106 nm (Figure 9). The median position drift was 56 nm with a mean of 177 nm (Table 1). It should be noted that at higher altitudes the atmosphere is relatively homogeneous, so even large drift distance can still represent the atmospheric characteristics of the region in the Washington, D.C. airspace.

5. Discussion

The results reported above for the Washington, D.C. airspace are consistent with the results described in Roosenbrand et al. [16] and experienced by Sausen et al. [12] and Elkins [13]. The ISS regions form at the flight levels most commonly used by airliners for cruise flights between FL320 and FL360. The ISS regions exhibit a thin vertical depth with a median of 2000′ and mean of 3000′ which enables a 2000′ deviation described by Sausen et.al. [12] and Elkins [13] as feasible. Further, the formation and dissipation of the contrails is difficult to forecast [6,12,13].

This section discusses the implications on operations for navigation avoidance [5] of ISS regions in the Washington, D.C. airspace. In navigational avoidance, flights avoid flying through ISS regions in the airspace by either flying below or above the ISS region. This information is useful for airline pilots, airline dispatchers, and air traffic controllers.

5.1. Avoiding/Encountering ISS Regions in the Washington, D.C. Airspace

The results above show that aircraft operating in the Washington, D.C. airspace should expect to experience an ISS region 40% of the time. The probability of experiencing an ISS region during the day is the same as at night. It should be noted that the global warming impact of contrails at night is greater than during the day.

The probability of encountering an ISS region is greater during the winter months of November, December, and February. Another month that would have a higher likelihood of encountering an ISS region is August.

Avoiding cruise flight levels between FL320 and FL360 would further reduce the probability of encountering an ISS region by 48%.

5.2. Taking Actions to Avoid ISS Regions

In the event an aircraft encountered an ISS region, and assuming the aircraft was operating in the middle of the ISS region, adjusting the cruise flight level for 2000′ would result in avoiding an ISS region 50% of the time. This is compatible with air traffic control procedures that operate with 2000′ vertical separation for traffic flying in the same direction.

Twenty-three percent (23%) of the readings had a vertical depth of 6000′ or more. When the ISS region has this vertical depth, it is probably prohibitive to use navigational avoidance to fly over or under the ISS region.

5.3. Predicting ISS Regions for the Next 12 Hours

When there is no ISS region in the airspace, there is a 78% chance that there will be no ISS region in the next 12 h period (

Table 3. Sequential transition probabilities of ISS regions.

Current Time	Next 12 Hours
	No ISS Region	ISS Region
No ISS Region	78.1%	21.9%
ISS Region	55.3%	44.7%

). When there is no ISS region, there is a 22% chance of an ISS region in the next 12 h period.

When there is an ISS region, there is a 55% chance of no ISS region being present in the next 12 h. When there is an ISS region present, the chance of there being an ISS region in the next 12 h is 45%.

These probabilities can be combined with the probabilities above (i.e., vertical depth and cruise flight level) to improve the odds of avoiding contrails.

6. Conclusions

IGRA aerosonde data for the airspace over the Washington, D.C. region was analyzed for the 5-year period 2019−2023. The analysis provides insights into the likelihood of occurrence of ISS regions by day of year and time of day (midnight or midday). The analysis also showed statistics for the vertical depth, floor/ceiling of ISS regions, and the likelihood of ISS conditions at each flight level between FL330 and FL440.

These statistics have practical implications for airline and air traffic control flight operations. First, they provide information on the frequency of operational adjustments that would need to occur to avoid ISS regions. Second, the characteristics and the likelihood of success of the different types of avoidance maneuvers have been characterized.

Given the challenges in accurately collecting humidity data and accurately predicting ISS regions, it may be the best for the industry to conceive of contrail avoidance in “probabilistic” terms. These statistics provide the reference benchmark for the reduction.

Limitations and Future Work

The geographic drift of several hundred nautical miles as the aerosonde ascends raises questions related to how much these readings apply to the airspace in the Washington, D.C. region on the days the aerosonde exhibited significant drift. Further work is required to evaluate the magnitude and direction of the wind.

This analysis analyzed data only greater than FL300. It may be prudent to include data below FL300 as it appears that the restriction impacted the calculation of the floor.

Recent research also identified biases in the recordings of relative humidity at high altitudes. The correction model needs to be investigated and applied as appropriate.