I. IntroductionAircraft induced environmental impact has drawn attention in recent years. 1 The three largest emission impacts include direct emissions of greenhouse gases such as CO 2 , emissions of NOx, and persistent contrails.Contrails are clouds that are visible trails of water vapor made by the exhaust of aircraft engines.Contrails form when a mixture of warm engine exhaust gases and cold ambient air reaches saturation with respect to water, forming liquid drops which quickly freeze.They persist if the aircraft is flying in certain atmospheric conditions.Persistent contrails reduce incoming solar radiation and outgoing thermal radiation in a way that accumulates heat. 2 The global mean contrail cover in 1992 was estimated to double by 2015, and quadruple by 2050 due to an increase in air traffic. 3Studies suggest that the environmental impact from persistent contrail is estimated to be three to four times, 4 or even ten times 5 larger than the aviation induced emissions.Therefore, methods to reduce aircraft induced persistent contrails are needed to minimize the impact of aviation on climate.Efforts have been made in the past to reduce the persistent contrail formation.Gierens 6 and Noppel 7 reviewed various strategies for contrail avoidance.Mannstein 8 proposed a strategy to reduce the climate impact of contrails significantly by only small changes in individual flight altitude.Campbell 9 presented a methodology to optimally reroute aircraft trajectories to avoid the formation of persistent contrails with the use of mixed integer programming.Both methodologies require onboard contrail detection system and flight rerouting.Fichter 10 showed that the global annual mean contrail coverage could be reduced by downshifting the cruise altitude.Williams 11,12 proposed strategies for contrail reduction by identifying fixed and varying maximum altitude restriction policy.These restrictions generally imply more fuel burn, thus more emissions, and add congestion to the already crowded airspace at lower altitudes.The objective of this paper is to develop strategies to reduce persistent contrail formation with consideration to extra emissions and air space congestion.The concept of contrail frequency index is used to quantify the severity of contrail formation.The strategy for reducing persistent contrail formation is to reduce contrail frequency index by altering the aircraft's cruising altitude with minimal increase in emissions.A class of contrail reduction strategies that considers extra emissions is proposed.It provides a flexible way to trade off between contrail reduction and emissions.The results show that the contrail frequency index can be reduced with extra emissions and without adding congestion to airspace.The strategies provide a starting point for developing operational policies to reduce the impact of aviation on climate.The remainder of the paper is organized as follows.Section II provides descriptions of contrail model, definition of contrail frequency index, and the fuel burn and emission models.Next, contrail reduction strategies and the trade-offs between contrail reduction and emissions are described in Section III.Section IV shows the results.Finally, Section V presents a summary and conclusions. II. Data and Model II.A. Contrail ModelContrails are vapor trails caused by aircraft operating at high altitudes under certain atmospheric conditions.The contrail model in this paper uses atmospheric temperature and humidity data retrieved from the Rapid Updated Cycle (RUC) data, provided by the National Oceanic and Atmospheric Administration (NOAA).The horizontal resolution in RUC is 13-km.RUC data has 37 vertical isobaric pressure levels ranging between 100 and 1000 millibar (mb) in 25 mb increments.Since the vertical isobaric pressure levels do not correspond with 2,000 feet increments, linear interpolation was used to convert the RUC data to a vertical range from 26,000 feet to 44,000 feet with an increment of 2,000 feet.This range is chosen because it generally is too warm for contrails to form below 26,000 feet and most aircraft fly below 44,000 feet.Contrails form when a mixture of warm engine exhaust gases and cold ambient air reaches saturation with respect to water, forming liquid drops which quickly freeze.Contrails form in the regions of airspace that have ambient Relative Humidity with respect to Water (RHw) greater than a critical value r contr . 13Regions with RHw greater than or equal to 100% are excluded because clouds are already present. 14Contrails can persist when the environmental Relative Humidity with respect to Ice (RHi) is greater than 100%. 15In this paper, contrail favorable regions are defined as the regions of airspace that have r contr ≤ RHw < 100% and RHi ≥ 100%.The estimated critical relative humidity for contrail formation at a given temperature T (in Celsius) can be calculated asr contr = G(T -T contr ) + e liq sat (T contr ) e liq sat (T ) ,(1)where e liq sat (T ) is the saturation vapor pressure over water at a given temperature.The estimated threshold temperature for contrail formation at liquid saturation isT contr = -46.46 + 9.43ln(G -0.053) + 0.72ln 2 (G -0.053),(2)whereG = EI H2O C p P Q(1 -η) , (3)EI H2O is the emission index of water vapor (assumed to be 1.25); C p = 1004 (in JKg -1 K -1 ) is the isobaric heat capacity of air, P (in Pa) is the ambient air pressure, = 0.6222 is the ratio of molecular masses of water and dry air, Q = 43 • 10 6 (in JKg -1 ) is the specific combustion heat, and η = 0.3 is the average propulsion efficiency of the jet engine.The value of r contr is computed by Eq (1)-(3) using RUC measurements for RHw and temperatures.RHi is calculated by temperature and relative humidity using the following formula: 16 RHi = RHw • 6.0612e 18.102T /(249.52+T ) 6.1162e 22.577T /(237.78+T ) ,where T is the temperature in Celsius. Figure 1 shows the temperature, RHw, RHi, and contrail favorable regions at 8AM EDT on April 23, 2010 at an altitude of 34,000 feet. II.B. Contrail Frequency IndexContrail frequency index (CFI) is used to quantify the severity of contrail activities.This paper uses 13km RUC data instead of the 40km RUC data used in Ref. 17.The modified 13km RUC data divide the U.S. national airspace into a three dimensional grid with 337 elements along the latitude, 451 elements along the longitude, and 10 altitudes ranging from 26,000 feet to 44,000 feet.Air traffic in the U.S. can be mapped into the same volumetric grid.Contrail frequency index is the number of aircraft in a volumetric element which meets conditions for persistent contrail formation.Contrail frequency index is zero for volumetric elements which do not meet the conditions for persistent contrail formation.Precise definitions of contrail frequency index are provided by the following equations.The altitude level index l is defined as l = 1 . . . 10 corresponding to altitudes of 26, 000, 28, 000, . . ., 44, 000 feet.The persistent contrail formation matrix (contrail matrix) at time t at level l is defined asR l t =     r l 1,1,t r l 1,    ,(5)where r l i,j,t is 1 if r contr ≤ RHw < 100% and RHi ≥ 100% at grid (i, j), and 0 if the conditions are not met.The Center contrail frequency indices of twenty U.S. air traffic control centers at time t at level l are defined asC center,l,t = 337 i=1 451 j=1 r l i,j,t a l i,j,t c i,j ,(6)where a l i,j,t is the number of aircraft within RUC 13km grid (i, j) flying closest to altitude level l at time t, and c i,j is 1 when grid (i, j) is inside the center and 0 if not.The twenty U.S. air traffic control centers are listed in Table 1.The aircraft data were provided by the Federal Aviation Administration's Aircraft Situation Display to Industry (ASDI) data.For planning contrail reduction strategies, traffic flow managers need to know potentially high contrail regions in the next few hours.Therefore predicted contrail frequency indices are needed for contrail reduction strategies.Similar to the concept of Weather Impacted Traffic Index (WITI) introduced by Callaham et al. 18 and Sridhar, 19 and the three-dimensional index derived by Chen, 20 predicted contrail frequency index was defined as a convolution of predicted traffic data and forecast of atmospheric conditions.The index consists of the RUC forecast data and the predicted aircraft locations when t is a future time.The Center contrail frequency index can then be rewritten asC center,l,t =    337 i=1 451 j=1 r l i,j,t a l i,j,t c i,j if t <= t now , 337i=1451 j=1 rl i,j,t âl i,j,t c i,j if t > t now ,(7)where t now is the current time, rl i,j is defined in (5) with RUC forecast data, and âl i,j is the predicted number of aircraft within RUC 13km grid (i, j) flying closest to altitude level l at time t.Figure 2 illustrates how contrail frequency index is computed.The aircraft trajectories and contrail formations between 33,000 feet and 34,999 feet for the hour of 8AM EDT on April 23, 2010 are shown in Fig. 2a.An one-minute time interval is used.The blue polygons indicate the contrail favorable regions; grey dots are the aircraft between 33,000 feet and 34,999 feet.When the aircraft enter the blue polygons, contrails would form as indicated by blue dots.The number of blue dots is defined as the contrail frequency index.As shown in Fig. 2b, there are 148 blue dots for the hour in Kansas City Center.Therefore, the center contrail frequency index for Kansas City Center for the hour of 8AM EDT is 148.The total time, due to all aircraft that would form contrails during the hour, is 148 minutes.The Center contrail frequency indices for all 20 US air traffic control Centers at 34,000 feet at 8AM EDT on April 23, 2010 were computed and are shown in Fig. 3.As shown in the figure, Minneapolis Center (ZMP) and Chicago Center (ZAU) have high contrail frequency indices because there are large contrail favorable regions in the Centers and also high density of air traffic, as shown in Fig. 2a.Salt Lake City Center (ZLC) has large contrail favorable regions inside the Center but the contrail frequency index is low because not many aircraft fly through the Center.Contrail frequency index takes both atmospheric and air traffic data and quantifies the contrail activities.It will be used later in developing contrail reduction strategies. II.C. Fuel Burn and Emission ModelsThe computations of aircraft fuel burn and emissions are needed in order to study the trade-offs between contrail reductions and aircraft induced emissions.This paper uses the fuel consumption model in Eurocontrols Base of Aircraft Data Revision 3.7 (BADA). 21The air traffic data provide aircraft information including aircraft type, mass, altitude and speed to compute the fuel burn.There are five stages, climb, cruise, descent-idle, descent-approach, and descent-landing that are determined by the aircraft altitude and speed.Only climb, cruise, and descent-idle models are used in this paper since the other two are used at the low altitudes.For climb stage, the fuel burn is computed using the following equation,F B = SF C • T • ∆t, (8)where F B is the fuel burn in kilograms, SF C (kg/min•kN) is the thrust specific fuel consumption, T is the trust in Newtons, and ∆t is the elapse time in minutes.For cruise, the fuel burn isF B = SF C • T • C f cr • ∆t,(9)where C f cr is the cruise fuel flow factor.For descent-idle, the fuel burn isF B = C f 3 (1 - h C f 4 ),(10)where C f 3 and C f 4 are descent fuel flow coefficients, and h is the altitude in meters.SFC in ( 8) and ( 9) are formulated asJet: SF C = C f 1 (1 + V T AS C f 2 ), Turboprop: SF C = C f 1 (1 - V T AS C f 2 ) • (V T AS /1000),(11)where V T AS is the true air speed in meters per second, and C f 1 and C f 2 are thrust specific fuel consumption coefficients.The thrust in (8) for climb stage is formulated asJet: T climb = C T c,1 (1 - h C T c,2 + C T c,3 • h 2 ), Turboprop: T climb = C T c,1 (1 - h C T c,2 )/V T AS + C T c,3 ,(12)where C T c,1 , C T c,2 and C T c,3 are climb thrust coefficients.For cruise, thrust is set equal to drag.Drag is computed byD = C D • ρ • V 2 T AS • S 2 , (13)where D is the drag in Newtons, C D is the drag coefficient, ρ (kg/m 3 ) is the air density, and S (m 2 ) is the wing reference area.The emission model is based on a prototype of the Aviation Environmental Design Tool (AEDT) developed by the Federal Aviation Administration (FAA). 22Five emissions are computed including CO 2 , SO x , CO, HC and NO x .Emissions of CO 2 and SO x (modeled as SO 2 ) are modeled based on fuel consumption. 23he emissions are computed byE CO2 = 3155 • F B, E SO2 = 0.8 • F B,(14)where E CO2 and E SO2 are emissions of CO 2 and SO 2 in grams, and FB is fuel burn in kilograms.Emissions of CO, HC and NO x are modeled through the use of the Boeing Fuel Flow Method 2 (BFFM2). 24The emissions are determined by aircraft engine type, altitude, speed, and fuel burn and the coefficients in International Civil Aviation Organization (ICAO) emission data bank.In the models, fuel burn is corrected to sea-level reference temperature (273.15K) and pressure (14.696 psi): 3.8 amb exp(0.2MF B c = (F B/δ amb )[θwhere F B c is the corrected fuel flow, P amb is the at-altitude ambient pressure, T amb is the at-altitude ambient temperature, and M is the Mach number.where EICO, EIHC and EIN O x are emission indices of CO, HC and N O x , H is the humidity correction factor, and ω is the specific humidity.The emissions are computed byE CO = EICO • F B, E HC = EIHC • F B, E N Ox = EIN O x • F B,(17)where E CO , E HC and E N Ox are emissions in grams. III. Contrail Reduction Strategies III.A. Use of contrail frequency indexContrail frequency index (CFI) quantifies the contrail activities.The strategy for reducing the persistent contrail formations is to minimize contrail frequency index by altering the aircraft's cruising altitude.Assume the aircraft at altitude level l in a Center are made to fly at a different level l .Both l and l range from 1 to 10, corresponding to altitudes of 26, 000, 28, 000, . . ., 44, 000 feet.The definition of the contrail frequency index is changed from (6) toC l center,l,t = 337 i=1 451 j=1 r l i,j,t a l i,j,t c i,j ,(18)A contrail frequency index matrix is formed asC center,t =       C 1 1,where the diagonal term C l l,t is the contrail frequency index at level l before changing cruising altitude, and C l l,t is the contrail frequency index when guiding aircraft at level l to level l .The contrail reduction from level l to l is ∆C l l,t = C l l,t -C l l,t .Note that when l > l, not all aircraft have the ability to fly from level l to level l .If altitude level l is higher than an aircraft's maximal flight altitude, it stays at level l and is not counted in C l l,t .In addition, if an aircraft crosses a sector boundary and causes congestion, it stays at level l and does not add to C l l,t .Additional conditions can be added to satisfy other operational procedures.The strategy is to find the altitude that would form least contrails.In other words, find the smallest element in each column of C center,t .If the aircraft are limited to alter ∆l levels, the solution is the smallest elementin [C l-∆l l,t . . . C l l,t . . . C l+∆l l,t] T in each column.The solution is denoted as [ l1 . . .l10 ].Each li means aircraft at flight level i is flying at level li .If li = i, the aircraft at level i do not alter.The total contrail reduction at the given center at time t can be expressed asΣ∆C t = 10 i=1 ∆C li i,t .(21)Consider the traffic situation at Kansas City Center.For ∆l = 2, the CFI matrix at 8AM EDT on April 23, 2010 was computed,C ZKC =                    0 0 0 × × × × × × × 0 0 0 0 × × × × × × 0 0 0 0 0 × × × × × × 0 0 0 0 0 × × × × × × 61 89 148 387 233 × × × × × × 35 102 230 154 83 × × × × × × 104 213 141 65 0 × × × × × × 164 67 22 0 0 × × × × × × 137 17 0 0 × × × × × × × 18 0 0                    , (22)where the elements not used are marked as ×.The center is divided into sectors horizontally and vertically.An air traffic controller monitors traffic in each sector and maintains separation between aircraft.The number of aircraft in a sector is kept below a maximum, referred to as Monitor Alert Parameter (MAP) in the current U.S. air traffic system, to keep the controllers workload within limits. 25The MAP is used to define the airspace capacity.The contrail reduction moves will not change the sector counts unless they cross the sector boundaries.The strategies only allow the moves such that the aircraft count in a sector does not exceed the sector capacity after the moves.In the previous example, Kansas City Center has 15 high sectors and 11 super-high sectors.Among them, sector 31 has the highest sector count during the hour.Sector 31 has a lower bound of 37,000 feet and is on top of sector 28, 29 and 30, shown in Fig. 4. The move from level 6 (35,000-36,999 feet) to level 7 (37,000-38,999 feet) would move some aircraft in sector 28, 29 and 30 to sector 31.Sector 28, 29, 30 and 31 have the MAP values of 18, 18, 19 and 21 respectively.Figure 5 shows the MAP values and the sector counts in sector 28, 29, 30 and 31 before and after the moves.The aircraft counts in sector 28, 29 and 30 decrease because some aircraft have been moved up to sector 31; the sector count in sector 31 increases but is still lower than the sector capacity of 21.Thus the contrail reduction moves are applied without exceeding the capacity of the airspace.The altitudes of the aircraft are changed as they enter a new Center.The number of altitude changes is not expected to result in frequent climb and descents to affect current operations.However, if needed, additional constraints can be imposed on the number of altitude changes.Data from a 24-hour period on April 23, 2010 was analyzed.The contrail reduction strategies were applied and the results are shown in Fig. 6.The center CFIs before reduction are shown in blue bars.When the aircraft altitudes are allowed to alter by 2,000 feet, the center CFIs after reduction are shown in light blue bars.The total reduction among all centers is 62%.When the aircraft altitudes are allowed to alter by 4,000 feet, the total reduction is 88% as indicated in green bars.Since allowing aircraft to alter 4,000 feet would eliminate most of the contrail formation, the strategies in this paper limit the altitude changes to 4,000 feet. III.B. Tradeoff between contrails and emissionsAltering cruising altitudes changes the aircraft fuel consumption and emissions.In order to analyze the environmental impact of contrail reduction strategies, fuel consumption and emissions are considered in the strategies.Fuel burn and emissions computations are based on the models described in Sec.II.C. Define E l l,t as the emissions for all aircraft at level l at a given center at time t before contrail reduction, and E l l,t as the total emissions when guiding aircraft from level l to level l .When aircraft change their flying altitude from level l to l , the difference in emissions is∆E l l,t = E l l,t -E l l,t .(23)∆E l l,t < 0 implies emission reduction.Define the emission matrix as∆E center,t =         0 ∆E        .0This matrix helps to study the emissions trade-offs when applying contrail reduction strategies.For the contrail reduction solution of [ l1 . . .l10 ], the change in emissions can be expressed asΣ∆E t = 10 i=1 ∆E li i,t .(25)Consider the same example in the previous subsection and study the trade-offs between contrail reduction and CO 2 emissions.The emission matrix for CO 2 was computed based on the models described in Sec.II.C and is the following:∆E ZKC =                    0 484 1130 × × × × × × × -27 0 531 3562 × × × × × × -41 -31 0 1674 3169 × × × × × × -28 11 0 1417 4542 × × × × × × 55 237 0 2143 3462 × × × × × × 285 1331 0 1683 1042 × × × × × × 961 1237 0 420 2 × × × × × × 434 1892 0 0 0 × × × × × × 70 106 0 0 × × × × × × × 128 0 0                    ,(26)where the elements not used are marked as × and the unit is kilograms.Assuming the environmental impact of the contrail frequency index of 1 is equivalent to CO 2 emissions of 10 kg, the move from level 5 to 4 makes sense because a reduction of 148 in CFI is greater than the impact of additional CO 2 of 1417 kg (148 • 10 -1417 > 0).However, the move from level 6 to 4 is not worth while because the net impact is negative (230 • 10 -4542 < 0).Instead, the move from 6 to 8 is preferred because it has a CFI reduction of 66 with additional CO 2 emissions of 434 kg and reduces the net impact (66 • 10 -434 > 0).Similarly, the move from level 7 to 8 and from 8 to 9 are not preferred because of the net negative impacts.Aircraft at level 7 and 8 are not altered.The new solution can be denoted as [1 2 3 4 4 8 7 8 9 10], resulting in a CFI reduction of 214, with additional CO 2 emissions of 1851 kg.Compared with the maximal reduction strategy, this strategy achieves less contrail reduction, 40% versus 84%, but emits much less CO 2 emissions, 1, 851 kg vs 7, 957 kg (77% less).This example shows that the proposed contrail reduction strategies have the capability to trade off contrail reduction with emissions.Considering the relative environment impact of emissions and contrails, the strategy would move aircraft only if the contrails reduction benefits exceed the environmental impact of additional emissions.The aircraft would be guided from level l to l only if∆C l l,t > 1 α ∆E l l,t ,(27)where ∆C i,t and ∆E l,t are defined in (20) and (23) and α is a user-defined trade-off factor.It can be interpreted as the equivalent emissions in kg that has the same environmental impact as the contrail frequency index of 1.For the maximal contrail reduction strategy, the effect of emissions is ignored.In other words, α = ∞.Also, α = 0 simply means no reduction strategy is applied because (27) will never be true.Higher values of α means more contrail reduction and more emissions (closer to maximal reduction strategy); lower α means less contrail reduction and less emissions (closer to no reduction).In the previous example, α is 10.The appropriate value of α can be determined in two different ways.It is possible to monetize the value of both contrails and emissions as suggested in Ref. 26.Another approach is to consider contrails and emissions as disturbances to the global climate equilibrium and measure their impact as changes to the global mean surface temperature. 27However, both these methods are beyond the scope of this paper and the value of α will be considered as a user-preference weighting factor in the rest of the paper. IV. ResultsThis section presents the results of contrail reduction strategies and the trade-offs between contrail reduction and extra emissions over a 24-hour period on April 23, 2010.The 24-hour period starts at 4AM EDT and ends at 4AM the next day.The strategies allow aircraft to move 4,000 feet up or down within a center and use various user-defined α values to trade off between contrail reduction and emissions.This paper focuses on the trade-offs between contrails and CO 2 emissions while other emissions like NOx, SO 2 , HC and CO have a similar trend.Figure 7 shows the hourly variations in contrail reduction and extra emissions with different trade-off factors during a 24-hour period over the entire U.S. In Fig. 7a, the blue line shows the hourly CFI during the day with no reduction strategy applied (α = 0).When reduction strategies are applied, it is consistent that higher α results in lower CFI, meaning more reduction.The maximal reduction strategy (α = ∞), shown in the magenta line, has the lowest CFI at every hour.On the other hand, Fig. 7b shows that higher α results in higher extra CO 2 emissions, and the maximal reduction strategy has the highest CO 2 emissions.The results show that contrails reduction results in extra CO 2 emissions.Looking at the Center level, Fig. 8 shows the daily contrail reduction and extra emissions in twenty U.S. air traffic control centers.The blue bars in Fig. 8a are the daily center contrail frequency index for each Center.It is consistent that for all Centers, higher α values results in more contrail reduction and the maximal reduction strategy achieves most contrail reduction in all twenty Centers.On the other hand, higher α also results in more CO 2 emissions, as shown in Fig. 8b, while the maximal reduction strategy has the most CO 2 emissions.Table 2 summarizes the trade-offs between contrail reduction and extra CO 2 emissions over the entire U.S. on April 23, 2010.On that day, the maximal reduction strategy has an 88% contrail reduction rate with extra CO 2 emissions of 3778 megagram (Mg).A smaller value of α lowers the contrail reduction ratio but has less emissions.For α = 40, the contrail reduction rate is 73% with 2,621 Mg extra CO 2 emissions, 31% less than the emissions in the maximal reduction strategy.If CO 2 has more environmental impact, using α = 10 results in a contrail reduction of 21% with 100 Mg extra CO 2 emissions, 97% less than the emissions in the maximal reduction strategy.As for fuel burn, considering all aircraft flying between 26, 000 feet and 44, 000 feet on a day with large contrail favorable regions, an 80% reduction in contrails can be achieved with around 1% extra fuel.The increase in fuel would be less on a day with smaller contrail favorable regions.The main focus of this paper is to study the trade-offs between contrail reduction and extra emissions.Therefore, the factor of the extra fuel burn is not taken into account in the strategies.Figure 9 shows the contrail reduction versus extra CO 2 emissions with various α values.In the figure, more contrail reduction takes place from left to right and more CO 2 emissions occurs from bottom to top.At the lower-left point, no reduction strategy is applied.The upper-right point is the maximal reduction strategy.As the values of α increases, the curve moves from lower-left to upper-right.The user-defined trade-off factor α provides a flexible way to trade off between contrail reduction and extra emissions.Better understanding of the trade-offs between contrails and emissions and impact on the climate need to beRelative Humidity with respect to ice (d) Contrail favorable regions Figure 1 .1Figure 1.Atmospheric data and contrail favorable regions at 34,000 feet at 8AM EDT on April 23, 2010. entire U.S. airspace (b) Kansas City Center Figure 2 .Figure 3 .23Figure 2. Aircraft trajectories and contrail favorable regions at 8AM EDT on April 23, 2010. F B c is used in ICAO emission data bank to determine the reference emission index REIHC, REICO and REIN O x for HC, CO and NO x .The emission indices are computed by EICO = REICO(θ 3.3 amb /δ 1.02 amb ), EIHC = REIHC(θ 3.3 amb /δ 1.02 amb ), EIN O x = REIN O x [exp(H)](δ 1.02 amb /θ 3.3 amb ) 0.5 , H = -19.0(ω-0.0063), Figure 4 .4Figure 4. Kansas City Center sector 28, 29, 30 and 31. Figure 5 .5Figure 5. MAP values and sector counts before and after the contrail reduction strategies at 8AM EDT on April 23, 2010. Figure 6 .6Figure 6.Results of contrail reduction strategies on April 23, 2010. Figure 7 .7Figure 7. Hourly contrail reduction and extra CO2 emissions using different trade-off factors on April 23, 2010. Figure 9 .9Figure 9. Contrail reduction versus extra CO2 emissions on April 23, 2010. Table 1 .1Center index of twenty continental U.S. air traffic control centers.IndexNameIndexName1Seattle Center (ZSE)11Chicago Center (ZAU)2Oakland Center (ZOA)12Indianapolis Center (ZID)3Los Angeles Center (ZLA)13Memphis Center (ZME)4Salt Lake City Center (ZLC)14Cleveland Center (ZOB)5Denver Center (ZDV)15Washington D. C. Center (ZDC)6Albuquerque Center (ZAB)16Atlanta Center (ZTL)7Minneapolis Center (ZMP)17Jacksonville Center (ZJX)8Kansas City Center (ZKC)18Miami Center (ZMA)9Dallas/Fort Worth Center (ZFW)19Boston Center (ZBW)10Houston Center (ZHU)20New York Center (ZNY) 2 )], δ amb = P amb /14.696, θ amb = (T amb + 273.15)/273.15, The diagonal elements of the matrix show the current CFIs at various altitudes.First consider the case if the aircraft are allowed to move one level (2,000 feet) up or down to reduce contrail formation.All the aircraft between 33,000 feet and 34,999 feet (level 5) have a totalCFI of 148 (C ZKC (5, 5) = 148). Moving the aircraft to level 4 will result in zero CFI (C ZKC (4, 5) = 0), areduction of CFI by 148. Other contrail reduction moves include moving aircraft from level 6 to 7 (a CFIreduction of 17), 7 to 8 (a CFI reduction of 74) and 8 to 9 (a CFI reduction of 5). The solution is expressedas [1 2 3 4 4 7 8 9 9 10], resulting in a CFI reduction from 541 to 297, a 45% reduction. If the aircraft areallowed to move two levels up or down, even greater reductions can be achieved. The moves include movingaircraft from level 5 to 4, 6 to 4, 7 to 8 and 8 to 9. The solution is expressed as [1 2 3 4 4 4 8 9 9 10],resulting in a contrail reduction from 541 to 84, an 84% reduction. 4s shown in the matrix and in(22), moving aircraft from level 5 to 4 results in a CFI reduction of 148 with additional CO 2 emissions of 1,417 kg (∆E45,t = 1417); moving from level 6 to 4 results in a CFI reduction of 230 with additional CO 2 of 4,542 kg; moving from level 7 to 8 results in a CFI reduction of 74 with additional CO 2 of 1892 kg; moving from level 8 to 9 results in a CFI reduction of 5 with additional CO 2 of 106 kg.This solution achieves the most contrail frequency index reduction of 457 with additional CO 2 emissions of 7,957 kg. developed to fully utilize this class of contrail reduction strategies. V. ConclusionsA class of strategies for reducing persistent contrail formations with the capability to trade off between contrails and emissions has been developed.The concept of contrail frequency index is defined and used to quantify the contrail activities.The strategy of reducing the persistent contrail formations is to minimize the contrail frequency index by altering the aircraft's cruising altitude with consideration to extra emissions.The strategies use a user-defined factor to trade off between contrail reduction and extra emissions.The analysis results show that the contrails can be reduced with extra emissions and without adding congestion to airspace.For the day tested, the results show that the maximal contrail reduction strategy can achieve a contrail reduction of 88%.When a trade-off factor is used, the strategy can still achieve a 73% contrail reduction while emitting 31% less emissions compared to the maximal contrail reduction strategy, or achieve a 21% contrail reduction while only emitting 97% less emissions.The user-defined trade-off factor provides a flexible way to trade off between contrail reduction and extra emissions.Better understanding of the trade-offs between contrails and emissions and impact on the climate need to be developed to fully utilize this class of contrail reduction strategies.The strategies provide a starting point for developing operational policies to reduce the impact of aviation on climate. IWaitz JTownsend JCutcher-Gershenfeld EGreitzer JKerrebrock Report to the United States Congress: Aviation and the Environment, A National Vision, Framework for Goals and Recommended Actions London, UK December 2004 Tech. rep Partnership for AiR Transportation Noise and Emissions Reduction Waitz, I., Townsend, J., Cutcher-Gershenfeld, J., Greitzer, E., and Kerrebrock, J., "Report to the United States Congress: Aviation and the Environment, A National Vision, Framework for Goals and Recommended Actions," Tech. rep., Partnership for AiR Transportation Noise and Emissions Reduction, London, UK, December 2004. Radiative forcing by contrails RMeerkötter USchumann DRDoelling PMinnis TNakajima YTsushima 10.1007/s00585-999-1080-7 Annales Geophysicae Ann. Geophys. 1432-0576 17 8 1999 Copernicus GmbH Meerkotter, R., Schumann, U., Doelling, D. R., Minnis, P., Nakajima, T., and Tsushima, Y., "Radiative forcing by contrails," Annales Geophysicae, Vol. 17, 1999, pp. 1080-1094. Future Development of Contrail Cover, Optical Depth, and Radiative Forcing: Impacts of Increasing Air Traffic and Climate Change SMarquart MPonater FMager RSausen 10.1175/1520-0442(2003)016<2890:fdocco>2.0.co;2 Journal of Climate J. Climate 0894-8755 1520-0442 16 17 September 2003 American Meteorological Society Marquart, S., Ponater, M., Mager, F., and Sausen, R., "Future Development of Contrail Cover, Optical Depth, and Radiative Forcing: Impacts of Increasing Air Traffic and Climate Change," Journal of Climate, Vol. 16, September 2003, pp. 2890-2904. A Standing Royal Commission SusanOwens 10.1093/acprof:oso/9780198294658.003.0003 Knowledge, Policy, and Expertise London, UK Oxford University Press 2002 "The Environmental Effects of Civil Aircraft in Flight," Tech. rep., Royal Commission on Environmental Pollution, London, UK, 2002. Aircraft induced contrail cirrus over Europe HermannMannstein UlrichSchumann 10.1127/0941-2948/2005/0058 Meteorologische Zeitschrift metz 0941-2948 14 4 2005 Schweizerbart Mannstein, H. and Schumann, U., "Aircraft induced contrail cirrus over Europe," Meteorologische Zeitschrift, Vol. 14, No. 4, 2005, pp. 549-554. A Review of Various Strategies for Contrail Avoidance KlausGierens LingLim KostasEleftheratos 10.2174/1874282300802010001 The Open Atmospheric Science Journal TOASCJ 1874-2823 2 1 2008 Bentham Science Publishers Ltd. The Open Atmospheric Gierens, K., Limb, L., and Eleftheratos, K., "A Review of Various Strategies for Contrail Avoidance," The Open Atmo- spheric Science Journal, Vol. 2, 2008, pp. 1-7. Overview on Contrail and Cirrus Cloud Avoidance Technology FNoppel RSingh 10.2514/1.28655 Journal of Aircraft Journal of Aircraft 0021-8669 1533-3868 44 5 2007 American Institute of Aeronautics and Astronautics (AIAA) Noppel., F. and Singh, R., "Overview on Contrail and Cirrus Cloud Avoidance Technology," Journal of Aircraft, Vol. 44, No. 5, 2007, pp. 1721-1726. A note on how to avoid contrail cirrus HermannMannstein PeterSpichtinger KlausGierens 10.1016/j.trd.2005.04.012 Transportation Research Part D: Transport and Environment Transportation Research Part D: Transport and Environment 1361-9209 10 5 September 2005 Elsevier BV Mannstein, H., Spichtinger, P., and Gierens, K., "A note on how to avoid contrail cirrus," Transportation Research. Part D, Transport and environment, Vol. 10, No. 5, September 2005, pp. 421-426. An Optimal Strategy for Persistent Contrail Avoidance ScotCampbell NatashaNeogi MichaelBragg 10.2514/6.2008-6515 AIAA-2008-6515 AIAA Guidance, Navigation and Control Conference and Exhibit Honolulu, HI American Institute of Aeronautics and Astronautics August 2008 Campbell1, S. E., Neogi, N. A., and Bragg, M. B., "An Optimal Strategy for Persistent Contrail Avoidance," AIAA Guidance, Navigation and Control Conference, AIAA-2008-6515, AIAA, Honolulu, HI, August 2008. The impact of cruise altitude on contrails and related radiative forcing ChristineFichter SusanneMarquart RobertSausen DavidSLee 10.1127/0941-2948/2005/0048 Meteorologische Zeitschrift metz 0941-2948 14 4 August 2005 Schweizerbart Fichter, C., Marquart, S., Sausen, R., and Lee, D. S., "The impact of cruise altitude on contrails and related radiative forcing," Meteorologische Zeitschrift, Vol. 14, No. 4, August 2005, pp. 563-572. Reducing the climate change impacts of aviation by restricting cruise altitudes VictoriaWilliams RobertBNoland RalfToumi 10.1016/s1361-9209(02)00013-5 Transportation Research Part D: Transport and Environment Transportation Research Part D: Transport and Environment 1361-9209 7 6 November 2002 Elsevier BV Williams, V., Noland, R. B., and Toumi, R., "Reducing the climate change impacts of aviation by restricting cruise altitudes," Transportation Research. Part D, Transport and environment, Vol. 7, No. 5, November 2002, pp. 451-464. Variability of contrail formation conditions and the implications for policies to reduce the climate impacts of aviation VictoriaWilliams RobertBNoland 10.1016/j.trd.2005.04.003 Transportation Research Part D: Transport and Environment Transportation Research Part D: Transport and Environment 1361-9209 10 4 July 2005 Elsevier BV Williams, V. and Noland, R. B., "Variability of contrail formation conditions and the implications for policies to reduce the climate impacts of aviation," Transportation Research. Part D, Transport and environment, Vol. 10, No. 4, July 2005, pp. 269-280. Contrails in a comprehensive global climate model: Parameterization and radiative forcing results MichaelPonater SMarquart RSausen 10.1029/2001jd000429 Journal of Geophysical Research J. Geophys. Res. 0148-0227 107 D13 2002 American Geophysical Union (AGU) Ponater, M., Marquart, S., and Sausen, R., "Contrails in a Comprehensive Global Climate Model: Parameterization and Radiative Forcing Results," Journal of Geophysical Research, Vol. 107, No. D13, 2002, pp. ACL 2-1. Determination of humidity and temperature fluctuations based on MOZAIC data and parametrisation of persistent contrail coverage for general circulation models KMGierens USchumann HG JSmit MHelten GZängl 10.1007/s00585-997-1057-3 Annales Geophysicae Ann. Geophys. 1432-0576 15 8 1997 Copernicus GmbH Gierens, K. M., Schumann, U., Smit, H. G. J., Helten, M., and Zangl1, G., "Determination of humidity and temperature fluctuations based on MOZAIC data and parametrisation of persistent contrail coverage for general circulation models," Annales Geophysicae, Vol. 15, 1997, pp. 1057-1066. Estimated contrail frequency and coverage over the contiguous United States from numerical weather prediction analyses and flight track data DavidPDuda PatrickMinnis RabindraPalikonda 10.1127/0941-2948/2005/0050 Meteorologische Zeitschrift metz 0941-2948 14 4 June-July 2003 Schweizerbart Friedrichshafen at Lake Constance, Germany Duda, D. P., Minnis, P., Costulis, P. K., and Palikonda, R., "CONUS Contrail Frequency Estimated from RUC and Flight Track Data," European Conference on Aviation, Atmosphere, and Climate, Friedrichshafen at Lake Constance, Germany, June- July 2003. Improved Magnus Form Approximation of Saturation Vapor Pressure OlegAAlduchov RobertEEskridge 10.1175/1520-0450(1996)035<0601:imfaos>2.0.co;2 Journal of Applied Meteorology J. Appl. Meteor. 0894-8763 1520-0450 35 4 April 1996 American Meteorological Society Alduchov, O. A. and Eskridge, R. E., "Improved Magnus Form Approximation of Saturation Vapor Pressure," Journal of Applied Meteorology, Vol. 35, No. 4, April 1996, pp. 601-609. Prediction and Use of Contrail Frequency Index for Contrail Reduction Strategies NeilChen BanavarSridhar HokNg 10.2514/6.2010-7849 AIAA Guidance, Navigation, and Control Conference Toronto, Ontario American Institute of Aeronautics and Astronautics August 2010 Chen, N. Y., Sridhar, B., and Ng, H. K., "Prediction and Use of Contrail Frequency Index for Contrail Reduction Strategies," AIAA Guidance, Navigation, and Control Conference, Toronto, Ontario, August 2010. Assessing NAS Performance: Normalizing for the Effects of Weather MBCallaham JSDearmon ACooper JHGoodfriend DMoch-Mooney GSolomos 4th USA/Europe Air Traffic Management R&D Symposium Santa Fe, NM December 2001 Callaham, M. B., DeArmon, J. S., Cooper, A., Goodfriend, J. H., Moch-Mooney, D., and Solomos, G., "Assessing NAS Performance: Normalizing for the Effects of Weather," 4th USA/Europe Air Traffic Management R&D Symposium, Santa Fe, NM, December 2001. Relationship Between Weather, Traffic and Delay Based on Empirical Methods BanavarSridhar SeanSwei 10.2514/6.2006-7760 6th AIAA Aviation Technology, Integration and Operations Conference (ATIO) Wichita, KS American Institute of Aeronautics and Astronautics September 2006 Sridhar, B. and Swei, S., "Relationship between Weather, Traffic and Delay Based on Empirical Methods," 6th AIAA Aviation Technology, Integration and Operations Conference (ATIO), Wichita, KS, September 2006. Estimation of Air Traffic Delay Using Three Dimensional Weather Information NeilChen BanavarSridhar 10.2514/6.2008-8916 The 26th Congress of ICAS and 8th AIAA ATIO Anchrorage, AK; Washington, DC American Institute of Aeronautics and Astronautics September 2008. March 2009. October 2010 3 Aviation Environmental Design Tool (AEDT) User Guide: Beta1c Chen, N. Y. and Sridhar, B., "Estimation of Air Traffic Delay Using Three Dimensional Weather Information," 8th AIAA Aviation Technology, Integration and Operations Conference (ATIO), Anchrorage, AK, September 2008. 21 EUROCONTROL Validation Infrastructure Centre of Expertise, France, User manual for the base of aircraft data (BADA), 3rd ed., March 2009. 22 Federal Aviation Administration, Washington, DC, Aviation Environmental Design Tool (AEDT) User Guide: Beta1c, October 2010. The Characteristics of Future Fuels OJHadaller AMMomenthy 1989 Project Report D6-54940, Boeing publication Hadaller, O. J. and Momenthy, A. M., "The Characteristics of Future Fuels," Project Report D6-54940, Boeing publica- tion, 1989. Development of an EMF Measurements Database, EMF Rapid Program, Project #5, Interim Report: April 1995-December 1996 SBaughcuma TTritz SHenderson DPickett 10.2172/2440 NASA CR 4700 April 1996 Office of Scientific and Technical Information (OSTI) Project Report Baughcuma, S., Tritz, T., Henderson, S., and Pickett, D., "Scheduled Civil Aircraft Emission Inventories for 1992: Database Development and Analysis," Project Report NASA CR 4700, April 1996. Impact of Uncertainty on the Prediction of Airspace Complexity of Congested Sectors BanavarSridhar DeepakKulkarni KapilSheth 10.2514/atcq.19.1.1 Air Traffic Control Quarterly Air Traffic Control Quarterly 1064-3818 2472-5757 19 1 2011 American Institute of Aeronautics and Astronautics (AIAA) Sridhar, B., Kulkarni, D., and Sheth, K., "Impact of Uncertainty on the Prediction of Airspace Complexity of Congested Sectors," Air Traffic Control Quarterly, Vol. 19, No. 1, 2011, pp. 1-23. Methods for Evaluating Environmental and Performance Tradeoffs for Air Transportation Systems MGregoryO'neill Jean-MarieDumont TomReynolds JohnHansman 10.2514/6.2011-6816 11th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference Virginia Beach, VA American Institute of Aeronautics and Astronautics September 2011 ONeill, M., Dumont, J., Reynolds, T., and Hansman, J., "Methods for Evaluating Environmental and Performance Tradeoffs for Air Transportation Systems," 11th AIAA Aviation Technology, Integration and Operations Conference (ATIO), Virginia Beach, VA, September 2011. Transport impacts on atmosphere and climate: Metrics JSFuglestvedt KPShine TBerntsen JCook DSLee AStenke RBSkeie GJ MVelders IAWaitz 10.1016/j.atmosenv.2009.04.044 Atmospheric Environment Atmospheric Environment 1352-2310 44 37 December 2010 Elsevier BV Fuglestvedta, J., Shineb, K., Berntsen, T., Cook, J., Lee, D., Stenke, A., Skeie, R., Velders, G., and Waitz, I., "Transport impacts on atmosphere and climate: Metrics," Atmospheric Environment, Vol. 44, No. 37, December 2010, pp. 4648-4677.