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Corresponding author: Patrick Minnis, MS 420, NASA Langley Research Center, Hampton, VA 23681, USA. (email@example.com)
 Radiative forcing due to linear-shaped jet contrails is calculated over the Northern Hemisphere for four seasonal months using 2006 Aqua Moderate-resolution Imaging Spectroradiometer cloud and contrail property retrieval data in a radiative transfer model. The 4 month mean shortwave, longwave, and net radiative forcings normalized to 100% contrail cover are −5.7, 14.2, and 8.5 Wm−2. Mean total net forcing over the northern half of the globe varies from 9.1 mW m−2 during October to 12.1 mW m−2 in January and is only representative at 01:30 and 13:30 LT in nonpolar regions. In some dense flight traffic corridors, the mean net forcing approaches 80 mW m−2. Scaling the 4 month average of 10.6 mW m−2 to the Southern Hemisphere air traffic yields global mean net forcing of 5.7 mW m−2, which is smaller than most model estimates. Nighttime net forcing is 3.6 times greater than during daytime, when net forcing is greatest over low clouds. Effects from contrail cirrus clouds that evolve from linear contrails are not considered in these results.
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 Contrail impacts on global climate are estimated most simply in terms of the parameter contrail radiative forcing (CRF), which is the change in the radiation balance at the top of the atmosphere (TOA) caused by the presence of contrails. The CRF over any given location depends on many factors [Meerkötter et al. 1999], including the background radiation field and contrail properties such as coverage CC, visible optical depth τ, ice crystal effective diameter D, ice crystal habit [Yang et al., 2010], and temperature T or pressure P. Because of the difficulty in distinguishing contrails from natural cirrus clouds and the tenuous nature of contrails, direct measurement of CRF is extremely challenging. Thus, it has been estimated in several ways using pure modeling approaches or various combinations of data with model calculations. Some pure modeling approaches specify any number of the above contrail parameters, while others allow the model to compute them [e.g., Ponater et al. 2002]. The mixed data-model techniques [e.g., Minnis et al., 1999; DeLeon et al., 2012] compute monthly mean CRF by using climatological cloud, surface, and atmospheric data to compute the background radiation field using a radiative transfer model (RTM) and then add specified values of CC, T, D, and τ on top of the clear and cloudy atmospheres for each grid box. The results are differenced with the contrail-free radiation field to obtain CRF. Because the actual contrail properties and their background radiation fields are poorly known and the models produce a wide range of values, the most recent assessment of aircraft climate effects [Lee et al., 2009] has an uncertainty of more than 100% in the net CRF (NCRF) of linear contrails in terms of the global mean. Thus, more accurate measurements of contrail properties and CRF are needed to improve our understanding of contrails' influence on climate.
 To date, objective measurements of contrail properties and CRF have been confined to regional analyses of satellite data. Meyer et al.  analyzed NOAA-14 Advanced Very High Resolution Radiometer (AVHRR) data over Europe and found average values of 0.11 for τ. They also estimated the normalized (CRF for CC = 100%) NCRF to be ~7.9 W m−2 based on RTM calculations using the observed optical depths over a cloud-free background. Palikonda et al.  used the same approach and found a mean τ of 0.27 from NOAA-15 and 16 AVHRR data over the United States. They used a direct method that accounts for the variable background to estimate the normalized longwave CRF (LCRF) at ~15.5 W m−2 but were unable to determine the normalized shortwave CRF (SCRF) and, hence, NCRF with the same type of approach. The differences in τ between the two analyses are striking and are indicative of the uncertainty in the global NCRF. They may be due to different sensitivities in the AVHRRs used in the two studies or to actual regional variations in τ. To obtain a better estimate of the regional variation in τ and NCRF, it is desirable to use a consistent dataset and analysis procedure over the globe and to estimate both longwave and shortwave CRF using the actual background radiation fields below the contrails. To address this need, this study uses a RTM to compute the CRF by employing as input the contrail coverage and properties and related cloud parameters derived from 2006 Aqua Moderate-resolution Imaging Spectroradiometer (MODIS) data by Duda et al.  and Bedka et al. . The global estimates of CRF are then obtained by averaging the results over the Northern Hemisphere (NH) and scaling by air traffic to the remainder of the Earth.
2 Data and Methodology
 The 2006 Aqua MODIS pixels over the NH identified as contrails by Duda et al.  are used to define the contrails in this study. Only the pixels from the flight-track screened, sensitive mask, Mask B, as defined by Duda et al. , are used here for the four seasonal months: January, April, July, and October, denoted as JAJO hereafter. This mask captures mostly linear features and not diffuse, spreading contrails that are difficult to distinguish from natural cirrus clouds. The results of the contrail mask were screened using advected air traffic waypoint data for the same period according to the likelihood of having been located close enough to a passing aircraft [Duda et al., 2013]. That screening reduces the number of false detections and is especially useful at eliminating tropical cirrus streamers that are often misidentified as contrails. To further screen out noncontrail pixels here, contrail pixels having τ > 3.0 are eliminated on the assumption that such large values are likely to occur only for natural ice clouds given the lack of reliable observations of contrails with τ > 2.0. Nearly a third of the contrail pixels had τ < 0.1, while only 8% had τ > 1.0 [Bedka et al., 2013]. This secondary filter eliminated ~0.5% of the contrail pixels originally detected with Mask B and remaining after the flight-track screening.
 For each contrail pixel assumed to be completely covered by a contrail, the radiative forcing is defined to be
where Fconf and Fcon are the upward TOA shortwave or longwave fluxes for contrail-free and contrail-covered conditions, respectively. The Fu-Liou (FL) RTM [Fu and Liou, 1993; Fu et al., 1998] is used here to compute these fluxes. Fcon is derived assuming an atmosphere with contrail-covered conditions where a contrail layer and background cloud, if applicable, are inserted at the relevant altitudes. Fconf is computed for the contrail-free situation for the same background conditions but without the contrail layer. Finally, SCRF and LCRF are computed using equation ((1)) as well as NCRF, which is the sum of SCRF and LCRF. The contrail properties, τ, D, and P, retrieved by Bedka et al.  are used to define the contrail layer for each pixel calculation. The contrail ice crystals and background ice clouds are assumed to have a smooth surface and an aspect ratio, AR ≈ 1.1, parameters that must be specified in the FL RTM [Fu, 2007]. The liquid cloud model, used in some background scenes, is described by Hu and Stamnes .
 To specify the background conditions, all of the Aqua MODIS 1 km data used in the contrail analyses of Duda et al.  were processed with the algorithms of Minnis et al.  to classify every pixel as either clear or cloudy. The cloud properties, including thermodynamic phase, optical depth, pressure, and effective particle size, were determined for each cloudy pixel using the methods of Minnis et al. . To define the background conditions, the dominant scene for the surrounding pixels is first determined as clear or cloudy, as in Bedka et al. . When the dominant background type is determined to be clear, no cloud layer is inserted below the contrail. Otherwise, the dominant cloud phase is used, and the mean particle size, optical depth, and pressure of the dominant cloud type are used to specify the cloud layer used in the calculations of both Fconf and Fcon.
 The atmospheric temperature and humidity profiles were taken from the 0.5° × 0.67° Modern Era Retrospective Analysis for Research and Applications analyses [Rienecker et al., 2011]. A continental aerosol type was specified with an optical depth of 0.2. Surface albedo was specified for land as in Rutan et al.  and for ocean as in Jin et al. . Surface longwave emissivities were taken from Wilber et al. . Snow and ice cover was assigned using maps from the Interactive Multisensor Snow and Ice Mapping System [Ramsay1998].
 For each image, a partially filled 1° × 1° NH map of CRF and CC was produced. This follows from obtaining the pixel means in each grid box, CRFg = ΣCRFi/Nc and CCg = Nc/N , where N is the total number of pixels, Nc is the number of contrail pixels, subscript i is the contrail pixel index, and g indicates a gridded quantity. The JAJO mean normalized CRF and CC for each grid box were computed from ΣCRFgj/Ng and ΣCCgj/Ng, respectively, where Ng is the number of JAJO samples, and subscript j is an image index. Total mean CRF (TCRF) for each grid box is derived from Σ[CRFgj × CCgj]/Ng. The overall mean NH TCRF was computed by integrating over the hemisphere using a cosine-of-latitude weighting. The TCRF takes into account the contrail-free pixels, which have CRF = 0. The averaging was performed for night and day scenes separately and according to dominant background type. This process should yield a realistic estimate of contrail radiative forcing at the times of the Aqua overpasses at ~01:30 and 13:30 local time (LT).
3 Results and Discussion
 The 2006 JAJO TOA CRF values were computed using the FL model for a total of nearly 62 million Aqua MODIS pixels. The mean JAJO geographical distributions of CRF are shown in Figure 1. To minimize the visual impact of noisy observations, the results are plotted only for regions having a mean contrail fraction of, at least, 10% of the 0.13% NH average. The normalized shortwave CRF (Figure 1a) is strongest over parts of the Arctic Ocean and Tibet with values between −8 and −18 W m−2 and weakest over the Horn of Africa and midlatitudes between 50° and 70°N. The large negative values over the Arctic are due to the combination of high solar zenith angles and mean τ (~0.4) twice the hemispherical average, while those over Tibet are due to the large mean τ (~0.5) and the lack of snow during 2006. The large τ values may be due to erroneous detection or the highly variable background. For LCRF (Figure 1b), the values are greatest over the Arctic Ocean and from 20° to 40°N latitude, especially over the deserts, where the hot clear background contrasts with the cold contrail. LCRF values in these regions are in the 14–24 W m−2 range. Again, the large values over the Arctic are due to the greater mean τ. The areas of greatest LCRF expand northward in July and diminish with a southward retreat during January (not shown). Adding the shortwave and longwave components leads to small NCRF (Figure 1c) over the tropical oceans and in some areas north of 60°N. The greatest values of NCRF, between 8 and 18 W m−2, occur over northern Africa and Saudi Arabia.
 Table 1 summarizes the results for each month and diurnally. The magnitudes of SCRF and LCRF move together seasonally. The former varies from −4.9 W m−2 during January to −6.8 W m−2 in July, while the latter ranges from 13.7 to 15.3 W m−2. These variations cancel each other such that NCRF shows negligible (~3%) seasonal change at an average of 8.5 W m−2. During the day, SCRF offsets much of the LCRF, resulting in a mean value of 3.9 W m−2. At night, the LCRF is 0.7 W m−2 less than the daytime mean, presumably due to a cooler surface. Also, at night, the NCRF is equal to the LCRF and, therefore, is ~3.6 times larger than its daytime counterpart.
Table 1. Pixel Mean Normalized Contrail Radiative Forcing and Number of Contrail Pixels for Each Seasonal Month of 2006
 The normalized results provide a measure of sensitivity to the presence of contrails but do not provide an estimate of the overall contrail forcing. This is characterized by total net CRF (TNCRF), which is plotted in Figure 2 for JAJO 2006. During the day (Figure 2a), the flight corridors over the north Atlantic, north Pacific, southwest Asia, and eastern Europe and Russia stand out remarkably well with TNCRF values of 20–60 mW m−2, as well as some extreme values up to 70 mW m−2. Most areas have positive daytime TNCRF, but a significant number of areas in the Tropics have negative or zero TNCRF. Without the reflected sunlight, TNCRF is dramatically enhanced at night (Figure 2b) with many areas over the North Atlantic, southern Asia, and central North America having values exceeding 80 mW m−2 up to 160 mW m−2. The corridors between both Europe and South America and Europe and southern Asia become quite visible at night. Combining the day and night results yields a pattern in total TNCRF (Figure 2c) that is most similar to that at night. The greatest values of TNCRF are evident over the North Atlantic, the Persian Gulf, and Malaysia. The few areas having zero or negative TNCRF are over the central Pacific where air traffic is sparse and the impact is negligible.
 The NH total CRF means are listed in Table 2. The total shortwave CRF (TSCRF) varies from −6.0 mW m−2 in October to −8.1 mW m−2 in April, while total longwave CRF (TLCRF) ranges from 15.0 to 19.6 mW m−2 for the respective months. The maximum TNCRF during January drops 3 mW m−2 to a minimum during October, yielding a NH JAJO mean of 10.6 mW m−2. This 28% seasonal change is driven by the CC, which shows a 25% decrease relative to the JAJO mean between the same 2 months. During the daytime, TNCRF averages only 4.6 mW m−2 but increases to 16.7 mW m−2 at night. The nocturnal contrail coverage accounts for 47.5% of the total coverage, so it is clear that flights occurring in the dark are responsible for much of the net climate impact of contrails.
Table 2. Monthly and Estimated 2006 Mean Total Contrail Radiative Forcings and Contrail Coverage
 Assuming that the NH forcing computed here is representative of the globe, then the global radiative forcing can be estimated by scaling the TCRF by relative amounts of air traffic in the two hemispheres. Based on the waypoint data used by Duda et al. , 93% of the high altitude air traffic takes place in the Northern Hemisphere. Thus, the global TSCRF, TLCRF, and TNCRF are estimated to be −3.9, 9.6, and 5.7 mW m−2, respectively, for the linear contrails detected by mask B assuming the average air traffic density is the same for both hemispheres. A sensitivity analysis using other assumptions suggests that the global TNCRF is certain to within −0.1 and +0.3 mW m−2. The JAJO 2006 mean global contrail coverage is estimated to be 0.070%.
 The frequency distributions of CRF provide another measure of contrail effects that should be valuable for model evaluation. Figure 3 shows the normalized JAJO CRF frequency distributions for all scenes. This histogram is similar to those for specific background types (not shown). The most common SCRF value is between 0 and 5 W m−2, which is primarily due to night pixels. SCRF frequency decreases almost exponentially with decreasing SCRF. Values of SCRF < −10 W m−2 are nearly twice as common over clear backgrounds as over cloudy scenes because of the generally low surface albedos (not shown). The LCRF frequency peaks at ~7.5 W m−2 for all scene types and drops exponentially to a minimum near 40 W m−2. Essentially, LCRF is always positive. Maximum NCRF frequency is evident between 0 and 5 W m−2 and decreases exponentially to 40 W m−2, but ~12% of the pixels have slightly negative values.
 Although the histograms for the various scene types are similar to those in Figure 3, subtle differences combine to produce variations in the average values for each background type. Table 3 lists the mean CRF values for the three background conditions. During daytime, the magnitude of SCRF is greatest for clear scenes and least for water cloud backgrounds, reflecting the difference in relative mean albedos of the scene types. LCRF is also greatest for clear scenes but is larger over water cloud than over ice clouds. As a result, the magnitude of NCRF is greatest over water clouds, which are highly reflective and warm, and is least over ice clouds, which are often similar to the contrails overlying them. Water cloud backgrounds occur most often or 45% of the time, while clear backgrounds are only seen for 24% of the pixels. At night, the greatest NCRF occurs over clear backgrounds, where the mean value is 5.9 W m−2 larger than the average over ice clouds. These results suggest that flying over or within extant ice clouds would minimize CRF.
Table 3. Mean Pixel Normalized Contrail Radiative Forcing over Different Background Types from NH Aqua MODIS Data for Four Seasonal Months of 2006
SCRF (W m−2)
LCRF (W m−2)
NCRF (W m−2)
LCRF/NCRF (W m−2)
 The results presented here only represent the CRF at the Aqua overpass times, twice per day in most areas, although ~4–6 overpasses occur per day in the Arctic, where contrail cover is sparse. The time of day for computing CRF is important for several reasons. Air traffic undergoes a large diurnal cycle with more than 60% occurring during daylight [Stuber and Forster, 2007]. Additionally, the SCRF depends on the time of day because of the solar zenith angle dependence of contrail albedo [Myhre and Stordal, 2001]. The contrail coverage at night is not entirely proportional to the nocturnal air traffic relative to the daytime, probably because the heavier air traffic during the day and more variable background make detection of individual contrails more difficult than shortly after local midnight when flights are less likely to overlap [Duda et al., 2013]. Many of the undetected contrails during the day fall into the contrail cirrus category and are likely to increase the overall CRF. The question of whether the averaged day and night overpasses represent the true 24 h average CRF of linear contrails will require further study.
 Assuming that the global average, 5.7 mW m−2, presented here is representative of a 24 h mean, it can be compared to previous model estimates. It is less than the 8.4 mW m−2 estimate of Marquart et al.  for 2015; the difference can be partially explained by differences in contrail coverage. Rap et al.  employed the Ponater et al.  contrail scheme and found a global average TNCRF of 7.7 mW m−2 for 2002 air traffic for contrail coverage of 0.11% and τ = 0.2. Yi et al.  used the same approach as Rap et al.  in a different climate model and obtained a value of TNCRF that is double the result found here but comparable to that reported by Lee et al. . The best estimate from Minnis et al.  for τ = 0.3 and CC = 0.09% produced TNCRF = 17 mW m−2. All but 3 mW m−2 of the discrepancy with the current results can be explained by the larger τ and slightly greater CC used in the earlier report. The remainder is likely due to the differences in the treatment of the contrail pressure and background. In general, it appears that the current estimate is somewhat lower than many of the model results of the past decade. Since linear contrail coverage is defined only by the satellite mask, it is possible that the models' definitions include more spreading contrails than detected by the contrail mask used here.
4 Concluding Remarks
 This study has estimated, for the first time, the hemispherical radiative forcing of linear contrails based on simultaneous observations of contrails and their environment. The TOA CRFs normalized to 100% contrail cover show a warming effect of ~8.5 W m−2. Taking the contrail coverage into account, this translates to a NH TNCRF mean of 10.6 mW m−2 with a seasonal range of 9.1–12.1 mW m−2. The greatest warming effect occurs during winter when contrail coverage peaks. Some areas, such as the North Atlantic air corridor, experience TNCRF values ranging up to 80 mW m−2. The nocturnal contribution to the average TNCRF is ~3.6 times the daytime value. Assuming that the Northern Hemisphere results are representative of other parts of the globe, it is estimated that the net contrail radiative forcing is 5.7 mW m−2, which is generally smaller than most climate model results.
 The CRF results presented here are based on the sensitive contrail mask (mask B) of Duda et al.  and considered to be a best estimate of the net warming effects on the Earth-atmosphere system due to linear contrails. Contrail cirrus was not considered here. Including it would significantly increase the contrail fractions, and a more pronounced warming effect would be seen for most areas in the Northern Hemisphere, especially along the main flight corridors. For example, using the most sensitive contrail mask (mask C) of Duda et al.  would lead to a factor of 3 increase in the total mean net CRF. But it is not clear if the number of false contrails detected in that mask balances the missed contrail cirrus (e.g., Minnis et al., Linear contrail and contrail cirrus properties derived from satellite data, submitted to Geophysical Research Letters, 2013). Additional research is needed to assess the contrail cirrus effects. The most conservative estimate of contrail effects based on the conservative mask (mask A) would halve the CRF values reported in this study. To determine if the results presented here for 4 months of Aqua data are representative for linear contrails, it will be necessary to apply the methods used here to additional months of Aqua data and to data from Terra MODIS to better cover the diurnal cycle of air traffic and clouds. The current results, however, are useful for model validation and should reduce the uncertainty in our knowledge of linear contrail effects.
 This work was supported by the Aviation Climate Change Research Initiative (ACCRI) under contract DTRT57-10-X-70020 with the DOT. 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 US DOT Volpe Center, the US FAA, or EUROCONTROL.