Linear contrail and contrail cirrus properties determined from satellite data



[1] The properties of contrail cirrus clouds are retrieved through analysis of Terra and Aqua Moderate Resolution Imaging Spectroradiometer data for 21 cases of spreading linear contrails. For these cases, contrail cirrus enhanced the linear contrail coverage by factors of 2.4–7.6 depending on the contrail mask sensitivity. In dense air traffic areas, linear contrail detection sensitivity is apparently reduced when older contrails overlap and thus is likely diminished during the afternoon. The mean optical depths and effective particle sizes of the contrail cirrus were 2–3 times and 20% greater, respectively, than the corresponding values retrieved for the adjacent linear contrails. When contrails form below, in, or above existing cirrus clouds, the column cloud optical depth is increased and particle size is decreased. Thus, even without increased cirrus coverage, contrails will affect the radiation balance. These results should be valuable for refining model characterizations of contrail cirrus needed to fully assess the climate impacts of contrails.

1 Introduction

[2] One of the outstanding uncertainties in our understanding of aviation effects on climate is the impact of aviation on cirrus clouds over and above that due to linear contrails [Lee et al., 2009; Burkhardt et al., 2010]. This additional impact is due to a combination of spreading contrails that are not recognized as such and increased ice nuclei in the upper troposphere due to aircraft soot emissions. The former effect is likely the most influential impact and has been examined using a variety of modeling and a few observational studies. As contrails age and spread, their properties and areal coverage change [e.g., Minnis et al., 1998], and consequently, the radiative effect will likely be different from that of linear contrails. To reduce the uncertainty in contrail cirrus climate effects, it is necessary to quantify both the coverage of spreading contrails and their microphysical and optical properties.

[3] The additional coverage caused by spreading can be quantified as the spreading factor SF, which is the ratio of total cirrus coverage from contrails (linear contrail plus contrail cirrus) to the linear contrail (Con) coverage. Contrail cirrus (CC) is defined here as the cirrus cover originating from contrails but not identified as linear contrails. Duda et al. [2004] performed a case study of spreading contrails over the Great Lakes and found SF ≈ 2. Total cirrus coverage from contrails was determined by manual inspection of Geostationary Operational Environmental Satellite (GOES) imagery, while Con coverage was obtained by an application of the contrail detection algorithm of Mannstein et al. [1999] to both GOES and Advanced Very High Resolution Radiometer imagery. Minnis et al. [2004] estimated that SF = 1.8 based on trends in cirrus clouds and an estimate of 1990 global Con coverage. Burkhardt and Kärcher [2011] simulated the life cycle of contrails over the globe using a parameterization along with flight track information in a global climate model. They found that SF ≈ 9 based on the age of young contrails rather than on linear contrails per se, but their model also produced reductions in natural cirrus clouds, partially offsetting the aircraft-induced clouds. Schumann [2012] developed a parameterization to compute cirrus and contrail coverage as well as their microphysical properties using numerical weather prediction model data and flight track information. Using that model, Schumann and Graf [2013] found that the impact of contrails, both via spreading and forming in extant cirrus, on cirrus cover and optical depth results in an order of magnitude more radiative forcing compared to linear contrails alone.

[4] Using a visible reflectance method applied to low-resolution satellite data, Duda et al. [2004] also determined that the effective particle diameter D of the Con and CC together decreased with contrail age while the optical depth τ initially increased, then diminished after a few hours. Burkhardt and Kärcher [2011] assumed that D and τ were the same for both Con and CC to estimate CC effects. Linear contrail microphysical properties are becoming fairly well defined as retrievals based on active [e.g., Iwabuchi et al., 2012] and passive infrared observations [e.g., Bedka et al., 2013] are providing converging results. However, the visible reflectance technique often overestimates τ for optically thin cirrus clouds [e.g., Minnis et al., 2011] and is very sensitive to the particle habit used in the retrieval. Thus, the sparse information currently available on CC optical properties is not very reliable and more data are needed to guide and validate models, such as those of Burkhardt and Kärcher [2011] and Schumann [2012].

[5] To begin addressing the paucity of information regarding the properties of contrail cirrus, this paper determines the properties of both cirrus and contrails over selected areas where it has been determined visually that only contrails produced the extant cirrus clouds. An optimal methodology applying two different techniques is used to derive D and τ from Moderate Resolution Imaging Spectroradiometer (MODIS) for both the Con and CC pixels. This approach minimizes the potentially large errors associated with the reflectance methods previously used [e.g., Minnis et al., 1998]. Additionally, the contrail and cirrus coverage is determined so that a value for SF is computed for all cases.

2 Data and Methodology

[6] The data sets used here include 4 km 10.8 µm images from GOES-13 and 1 km 0.64, 3.8, 10.8, and 12 µm radiances from MODIS on the Terra and Aqua satellites. Atmospheric and surface properties are the same as those used by Bedka et al. [2013].

[7] A set of 11 CC outbreaks was selected in the following manner. Sequences of GOES infrared imagery over North America were visually examined in conjunction with MODIS 10.8–12 µm brightness temperature differences (BTD) to determine areas where contrails formed and grew in otherwise clear air. Furthermore, areas were excluded from analysis if “natural” cirrus appeared to develop within or advect into the region. This necessarily subjective selection process does not always eliminate all noncontrail-induced cirrus cloudiness and bright background low-level clouds. For the selected days, an analysis region was defined for each of the available MODIS images containing the scene. The analysis regions change in each image because the areal extent of the Con and CC varies, the subject scene moves between images, the viewing zenith angles differ for each image, and ambient cloud cover may interfere with parts of the contrail-only area. The case selection process is discussed further in the supporting information of this paper.

[8] Figure 1 shows a developing CC scene in GOES-13 images taken 29 December 2010. By 13:15 UTC, a few small contrails have formed off over northern Florida and the adjacent Atlantic. The contrails continue forming and spreading at 14:15 UTC and an hour later cover parts of southern Georgia as well. At 16:15 UTC (Figure 1d), new contrails appear to have developed over both land and ocean as the older contrails spread and move eastward. This continues through at least 18:15 UTC. The area containing the Con and CC is seen clearly in the 16:30 UTC Terra 1 km BTD image, shown in Figure 2a. This image, an example of a large outbreak of a long-lived CC system, clearly shows the overlapping of new and old contrails resulting in nearly overcast skies off the coast. The system began dissipating as it moved eastward and was mostly gone by 23:00 UTC. To be more representative of the full range of CC, the selected cases include both small and large outbreaks. Table 1 lists the cases, with the latitudes and longitudes that encompass the areas used in the analyses for each satellite. The regions were selected to ensure a relatively uniform and cloud-free background. An attempt was made to track the same set of contrails for both Terra and Aqua, but because of changes in the background, it was not always possible to include all of the same contrails in each Terra and Aqua pair. The percentages of each area determined to be Con using mask C and CC (both described below) are included along with total number of pixels in the analysis domain. The nominal pixel resolution is 1 km, but increases with viewing zenith angle, which differs from image to image.

Figure 1.

Infrared (10.8 µm) images from GOES-13 over southeastern U.S. and adjacent Atlantic, 29 December 2010. Times are given in UTC.

Figure 2.

Terra MODIS (a) 10.8–12 µm brightness temperature differences and (b) contrail optical depths for mask C, 16:30 UTC, 29 December 2010. Red box indicates analysis region.

Table 1. Cases Used in Contrail Cirrus Analysis
Case #DateTime (UTC)Latitude Range (°N)Longitude Range (°W)SatelliteMask C (%)CC (%)Ntot
121 Jan 200616:4532.0–37.092.0–100.0Terra18.313.3209,792
2 20:0033.2–37.790.0–98.0Aqua8.841.6133,485
313 Feb 200616:5034.3–38.094.0–96.5Terra7.25.460,561
4 20:0533.1–37.191.4–94.1Aqua3.615.226,156
54 Nov 200617:4522.9–26.0101.6–108.6Terra10.74.7226,715
6 20:5522.6–26.5102.4–105.6Aqua4.823.435,802
75 Nov 200616:4530.2–32.682.4–87.0Terra8.420.576,343
8 18:2030.5–32.780.9–85.2Aqua4.721.857,943
9 18:2525.7–29.3106.6–111.1Terra8.39.690,298
10 20:0026.2–28.5105.5–110.9Aqua5.89.162,534
116 Nov 200615:5034.8–36.567.8–81.6Terra9.227.7192,610
12 19:0534.5–37.576.5–79.9Aqua16.164.028,517
1326 Dec 200617:1535.9–39.991.7–99.3Terra6.03.4270,067
14 18:5535.0–40.794.5–97.5Aqua14.95.845,087
1528 Dec 200617:0535.5–39.093.6–92.0Terra7.14.1199,666
16 18:4037.8–40.585.0–91.7Aqua16.75.0107,563
1731 Dec 200619:1532.5–36.5113.3–116.1Terra13.18.135,362
18 20:5033.4–36.2111.5–115.1Aqua12.82.293,777
197 Sep 201014:4533.0–35.128.0–32.0Aqua8.034.848,951
2029 Dec 201016:3028.3–32.578.3–80.3Terra23.941.424,755
21 18:0527.9–32.278.6–80.2Aqua14.946.134,646

[9] After defining the analysis regions, the method of Duda et al. [2013] was applied to the MODIS data to determine the linear contrail pixels at three different levels of sensitivity. The most conservative mask, A, detects the lowest number of linear contrail pixels, but has the fewest false contrail detections. Mask B detects more contrails at the expense of increasing false detections. It is assumed to be the best estimate of linear contrails, as it includes fewer very wide contrails that could be contrail cirrus. Mask C is the most sensitive mask and detects the most linear contrails and picks up some contrail cirrus coverage, but tends to misclassify many linear ambient cirrus clouds as contrails. All three masks are considered because the definitions of both linear contrails and contrail cirrus depend on the mask.

[10] The contrail properties, τCon and DCon, were retrieved using the infrared bispectral (10.8 and 12 µm) technique (IBT), which selects background radiances for each pixel by averaging the radiances for the surrounding noncontrail pixels. The IBT, described by Bedka et al. [2013], assumes a contrail temperature and iteratively solves for τCon and DCon. Figure 2b shows the retrievals of τCon for mask C applied to the Terra MODIS data taken 15 min after the case in Figure 1d. Many of the individual contrails outside the analysis region (red box) are detected, while in the region, 23.9% of the pixels are classified as contrails, yielding, on average, τCon = 0.208 ± 0.156 and DCon = 29.7 ± 18.1 µm. It is evident, however, that the detection algorithm misses a large amount of CC.

[11] To estimate the properties and coverage of the missed CC for all cases, the following procedure is used. All pixels in a given region are classified as clear or cloudy using the approach of Minnis et al. [2008], and the cloudy pixels are then analyzed with the visible infrared shortwave-infrared split-window technique (VISST) [Minnis et al., 2011] to retrieve τCC, DCC, and cloud temperature TCC. Given the propensity of visible channel techniques to overestimate τ for thin cirrus clouds, τCC and DCC are also retrieved for the CC using the IBT with the assumption that TCC is equal to the contrail temperature TCon and the background temperature is the clear-sky radiance field employed by the VISST. To further minimize the impact of the low-level clouds on the results, all pixels having τCC > 3 from either technique were eliminated from further analysis. These two retrievals provide a range of values. Contrail cirrus likely has a greater radiating temperature than the original contrails because contrails tend to spread by diffusion, precipitation, and vertical wind shear [e.g., Jensen et al., 1998], which drop the radiating center to a lower altitude. Thus, assuming that TCC = TCon could likely underestimate both τCC and DCC. Using the two methods together should constrain the ranges of τ and D for the CC.

[12] A best estimate of the CC properties was determined using the following procedure. The IBT result is used if DCC < 70 µm, because the differences in BTD between DCC = 70 and 130 µm are small compared to the uncertainty in the clear-sky background for small τCC. In those instances, the IBT retrieval usually tends toward the largest value and is likely to be highly uncertain. If DCC from the IBT exceeds 70 µm, then the VISST result is examined. In those cases, the VISST results replace the IBT results if the VISST phase is ice and |TCC − TCon| < 10 K. This test is used on the basis that the VISST retrieval is likely to be accurate if the retrieved temperature (height) is close to that of the contrail. Overestimates of τ by the VISST will always underestimate the cloud height and overestimate TCC. The ±10 K window is selected because the actual contrail temperature could differ from the assumed TCon value and the CC radiating temperature is likely to be greater than TCon, as noted earlier. A 10 K difference is roughly equivalent to a 1.5 km altitude difference, which is a conservative constraint given the potential uncertainty in TCon [Bedka et al., 2013] and the likelihood of contrail cirrus to extend more than 1 km below the original contrail height [e.g., Heymsfield et al., 1998]. Thus, CC are all ice cloud pixels in the domain having τCC < 3 and not classified as contrails. Thus, some of the pixels defined as contrails using mask C can be considered as contrail cirrus using mask A or B. As seen in Table 1, the CC coverage is sometimes less than the contrail coverage.

3 Results and Discussion

[13] Figure 3 shows an example of the analyses overlaid on the Aqua MODIS BTD image taken at 18:05 UTC for the case in Figure 1, more than 1.5 h after the Terra image (Figure 2). To minimize the uncertainties associated with the background radiance fields, the analysis region was restricted to open water east of the coast as indicated by the red box, similar to that in Figure 2. The BTD and retrievals of τCon for mask C are shown in Figures 3a and 3d, respectively, to illustrate the maximum linear contrail coverage and the contrail properties. The pixels for masks A and B are subsets of mask C and use the mask C background radiances. The retrieval results among the masks differ slightly because they use different numbers of pixels in the averaging. For this case, the contrail coverages are 4.6, 7.3, and 14.9% for masks A, B, and C, respectively. The corresponding averages for τCon are 0.165 ± 0.128, 0.147 ± 0.120, and 0.130 ± 0.111 and for DCon (not shown) are 33.2, 33.5, and 33.7 µm. The τCon means are statistically different from each other at the 99% level, while the DCon values are not statistically different. For this case, TCon = 220.5 K for all three masks. The linear contrail coverage is less than that seen earlier in the Terra image (Figure 2), while τCon from the mask C data is substantially smaller and DCon is 4 µm greater than the Terra counterparts. The smaller optical depths may be due to some saturation of air traffic levels with contrails, while DCon could be larger due to increased mixing with the greater amount of extant contrail cirrus, which is characterized by larger particles than the contrails, as seen below. Some of this difference may be due to the use of slightly different analysis regions.

Figure 3.

Contrail and cirrus properties retrieved from Aqua MODIS data off the Florida coast, 18:05 UTC, 29 December 2010. Red box indicates analysis region.

[14] The values of DCC determined using the IBT (Figure 3b) and VISST (Figure 3c) are shown as colors for values up to 70 µm and as raw BTD values for greater values. Blocky areas in the VISST retrieval arise from errors in the background radiances. Generally, DCC(VISST) is less than DCC(IBT). In the lower part of the box, where overlapped contrails are sparse, DCC(IBT) is typically less than 30 µm, but exceeds 60 µm for many of the pixels near the top of the box. Conversely, DCC(VISST) < 45 µm for a majority of the pixels. Remarkably, the VISST optical depths (Figure 3f) are quite similar to their IBT counterparts (Figure 3e). For this case, the average values of τCC(IBT) and DCC(IBT) are 0.387 and 56.1 µm, respectively, and τCC(VISST) and DCC(VISST) are 0.361 and 47.9 µm. After applying the filtering process described in the previous section, some of the IBT values were replaced with their VISST counterparts to obtain the best estimates of 0.388 and 46.0 µm for τCC and DCC, respectively, and CC = 48%. The best estimate of DCC for the Terra data in Figure 2 is 41.4 µm, while τCC = 0.306 and CC = 40.1%. Thus, all of the parameters except contrail coverage and τCon increased relative to the Terra results. The differences between the Terra and Aqua values of τCon, DCon, τCC, and DCC are all statistically different, having p-values < 10−8 that indicate there is essentially no probability that they are the same. All of the above averages of τCC and DCC were computed including only contrail cirrus and excluding linear contrails identified by mask C. In this case, both the CC optical depth and particle size are considerably greater than their linear contrail counterparts.

[15] The results for all 21 cases were averaged to estimate the properties for the linear contrails and CC accompanying each mask. Two different approaches were used to compute the CC properties, the first only includes pixels having a best estimate DCC < 70 µm, while the other includes all pixels having a retrieval. The percentage of CC pixels having DCC < 70 µm is denoted as FD<70. All of the means are presented in Table 2. The mean Con and CC temperatures are all ~219.8 K and, therefore, are not listed.

Table 2. Average Contrail and Contrail Cirrus Properties for All 21 Images Listed in Table 1a
MaskCon (%)CC (%)τConτCC Dci < 70 µmτCC Dci < 70 µmDCon (µm)DCC (µm) DCC < 70 µmDCC (µm) AllFD<70 (%)
  1. aValues in parentheses denote standard deviations.
A3.3221.30.167 (0.135)0.3180.38727.9 (18.2)37.667.966.3
B5.4719.10.155 (0.131)0.3290.40029.2 (19.8)38.971.254.0
C10.214.40.136 (0.124)0.3630.43130.5 (20.9)43.680.848.1

[16] Overall, the linear contrail coverage for each domain averaged from 3.3 to 10.2% for the three masks. Increasing contrail coverage is accompanied by decreasing τCon and slightly rising values of DCon. These trends are statistically significant given that the p-values are zero for any pair of masks for either parameter. This variation is, in part, due to mask A detecting mostly the core of the contrails where the particles are more concentrated and smaller, while mask C picks up more contrail edges along with the cores. Because of wind shear, the precipitate portion of the contrail will be located at one edge and will contain larger ice crystals than the contrail's core. Another possible effect giving rise to the difference is detection of partially contrail-filled pixels, which would appear to have a small τCon and large DCon. Also, mask C is the most sensitive, so it detects more thin contrails than the other masks. On average, τCon for these cases is ~30% smaller than the daytime mean of 0.218 found for the Northern Hemisphere [Bedka et al., 2013]. The particle effective diameters are roughly 20% smaller than the hemispherical mean.

[17] The CC coverage varies from 14 to 21% of the average scene depending on the linear contrail mask. These values convert to spreading factors between 2.4 for mask C to 7.4 for mask A. For the Terra results alone, SF = 2.1, while SF increases to 3.1 during the afternoon when only the results from the 10 corresponding Aqua cases are considered. Since, for these cases, the Aqua images occurred ~2.2 h after their Terra counterparts and the images generally cover areas with relatively continuous air traffic during the day, these SF differences suggest that detection of linear contrails is more difficult later in the day. Furthermore, the relationship (e.g., SF) between linear contrails and contrail cirrus depends on the temporal variation of the air traffic in addition to the meteorological conditions and particular contrail mask. This apparent decrease in detection sensitivity later in the day for heavy air traffic regions could help explain why the maximum linear contrail coverage was not observed over the areas with the greatest air traffic in the Aqua MODIS analyses of Duda et al. [2013].

[18] Pixels having DCC < 70 µm account for one half to two thirds of the retrievals, yielding optical depths nearly double the average τCon value. The mean value of DCC is 10–12 µm larger than DCon. Thus, it is not surprising that contrails forming in extant CC would tend to have larger values of DCon than those forming in otherwise clear skies. If the CC with larger particles are included, the mean retrieved τCC increases by ~20%, while DCC nearly doubles. This apparent doubling of DCC might be due to the diminished sensitivity of the IBT to changes in DCC for larger particles, as noted earlier. This interpretation is consistent with the differences in DCC retrieved by the IBT and VISST west of the box in Figures 3b and 3c. There, the VISST mostly retrieves DCC < 40 µm, where the IBT yields values greater than 70 µm (gray areas in Figure 3b). The VISST DCC retrievals in that part of the image are smaller than those in the box. Even though the VISST TCC values are slightly too high to pass the best estimate threshold, the optical depth results from the VISST would not be dramatically different than the IBT values. Thus, it is likely that the DCC averages for DCC < 70 µm are reasonable estimates for all of the CC pixels. Because τCon is primarily a function of the 10.8 µm brightness temperature, its retrieval is relatively insensitive to DCC, though it is susceptible to errors in the contrail and background temperatures. Assuming that those IBT values are correct, on average, then the values of τcc for all noncontrail ice cloud pixels should be representative of the CC in these cases. Thus, it is concluded that the best estimates of τCC should come from all of the pixels and the best values of DCC should be from only those pixels having DCC < 70 µm, respectively. The best estimates for mask C then are τCC = 0.431 and DCC = 43.6 µm, values that are roughly 3 and 1.4 times their respective Con counterparts.

[19] Another concern for aviation impacts is the effect of contrails forming in extant cirrus. While contrails will not increase the cirrus coverage when they form within existing cirrus clouds, they can potentially increase the optical depth of those clouds [e.g., Schumann and Graf, 2013] and have a measurable radiative forcing impact [Spangenberg et al., 2013]. The differences between τCC and τCon are consistent with a thickening of cirrus by linear contrails, if it is assumed that the CC constitutes existing cirrus clouds. However, the averages include contrails over both cloud-free and cirrus-covered backgrounds. To more carefully examine the differences between the contrail and the cirrus cloud with which it shares an atmospheric column, the values of τCon and τCC from the optimal retrieval are compared only for the contrail pixels in the northern halves of the domains in Figures 2 and 3, where the background is essentially all cirrus. For all of the mask C contrail pixels in the two truncated images, τCon = 0.176 and τCC = 0.384, while DCon = 27.9 µm and DCC = 29.8 µm. For contrail pixels, the CC parameters include both the contrail and cirrus contribution because they are computed relative to the clear-sky background. If the contrail portion is removed through subtraction with optical depth weighting for DCC, the true values of τCC and DCC are 0.206 and 40.6 µm, respectively. Thus, the linear contrails can increase the optical depth of existing cirrus and decrease the mean particle size, two effects that will change the radiative forcing of the affected cirrus clouds. This is important in estimating the impact of contrails because some studies suggest that increases in cloud cover due to contrails are limited [e.g., Burkhardt and Kärcher, 2011]. Thus, changes in the mean optical properties of cirrus clouds in air traffic regions should also be considered, even if cirrus coverage does not change.

4 Concluding Remarks

[20] The properties of contrail cirrus clouds formed during 11 different contrail outbreaks were determined in the context of objectively determined linear contrails and their properties. It was found that the ratio of contrail cirrus to linear contrails is heavily dependent on the satellite analysis algorithm used to define linear contrails and appears to be affected by the amount of overlapping contrails, which can obscure individual contrails. The contrail cirrus optical depths were found to be 2–3 times greater than their linear contrail counterparts and the associated ice crystal particle diameters were roughly 20% greater than the contrail particle sizes. The average contrail spreading factor for these cases varied from 2.4 to 7.4. Increases of this magnitude along with the greater optical depths have significant implications for aviation-induced radiative forcing. The results also demonstrate that even without an increase in cloudiness, contrails are likely to alter the properties of existing cirrus by decreasing the particle size and increasing the optical depth and, thereby, affecting the radiation balance to some degree.

[21] The results shown here should not be construed as representing all contrail cirrus relative to the contrail masks. The cases were selected because they occurred in mostly clear skies and could be seen developing in geostationary satellite images. Linear contrails observed from satellites do not always develop into long-lived contrail outbreaks and most often form in conjunction with other clouds, natural or contrail-generated [Bedka et al., 2013]. It is currently not possible to automatically distinguish natural from contrail-generated background cirrus clouds. Carleton et al. [2008] found that the probability of a contrail outbreak in mostly cloud-free conditions on a given day over the United States is between 0.3% over the southwest and 8.1% over the Midwest with an average size of ~3 × 105 km2. Given the findings of Schumann and Graf [2013] over the North Atlantic, such outbreaks may be more common over other parts of the globe. Additionally, outbreaks in cloudy skies may be just as effective in altering the cloud properties to produce additional forcing. Fully assessing the impact of contrail cirrus requires more than observations. However, observations are essential for validating and refining models that can take contrails and their changing environment into account [e.g., Burkhardt and Kärcher, 2011; Schumann, 2012]. This study has provided data that should be immediately valuable for further testing of such models.

[22] The retrievals were performed using relatively small signals in noisy environments and thus are encumbered by uncertainties that render some results unlikely (e.g., the extremely large CC particles). By using two different analysis techniques, it is possible to overcome some of those uncertainties. However, further refinement of both methods for this particular application and the background radiances will likely reduce the instantaneous errors in both optical depth and particle size. When combined with other analysis methods [e.g., Vazquez-Navarro et al., 2010] that can track contrail development along with the ambient meteorological conditions, the techniques developed here can be used to shed additional light on the development of cirrus from contrails.


[23] This work was supported by the Aviation Climate Change Research Initiative (ACCRI) under contract DTRT57-10-X-70020 with the DOT. The waypoint data used for this work were provided by U.S. DOT Volpe Center and are based on data provided by the U.S. FAA and EUROCONTROL in support of the objectives of the International Civil Aviation Organization Committee on Aviation Environmental Protection CO2 Task Group. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the U.S. DOT Volpe Center, the U.S. FAA, or EUROCONTROL.

[24] The Editor and authors thank two anonymous reviewers for their assistance in evaluating this paper.