High and Dry: Trading Water Vapor, Fuel andObserving Time for Airborne Infrared Astronmomy

Jeremy FrankNASA Ames Research Center

Mail Stop N269-3 Moffett Field, CA 94035-1000Email: frank@email.arc.nasa.gov

Elif KurkluQSS Group Inc

NASA Ames Research CenterMail Stop N269-3 Moffett Field, CA 94035-1000

Email: ekurklu@email.arc.nasa.gov

Abstract— Scheduling astronomy observations for the Strato-spheric Observatory for Infrared Astronomy (SOFIA) requiresassessing tradeoffs between the percentage of scheduled obser-vations, the Line Of Sight Water Vapor (LOS-WV) achievedon those observations, and fuel consumption. This trade spaceis complex, depending on time of year and specific mixes ofobservations, and cannot be effectively analyzed by hand. Wedemonstrate the complexity of these tradeoffs and show that anAutomated Flight Planner (AFP) is a crucial part of trade spaceanalysis during flight planning.

The Stratospheric Observatory for Infrared Astronomy(SOFIA) is NASA’s next generation airborne astronomicalobservatory. The facility consists of a 747-SP modified toaccommodate a 2.5 meter telescope. SOFIA is expected tofly an average of 140 science flights per year over its 20year lifetime, and will commence operations in early 2005.The SOFIA telescope is mounted aft of the wings on the portside of the aircraft and is articulated through a range of 20◦

to 60◦ of elevation. A significant problem in future SOFIAoperations is that of scheduling Facility Instrument (FI) flightsin support of the SOFIA General Investigator (GI) program.GIs are expected to propose small numbers of observations,and many observations must be grouped together to makeup single flights. Approximately 70 GI flight per year areexpected, with 5-15 observations per flight.

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Fig. 1. Variation in csc(h) in the interval h = [20◦, 60◦].

An important goal of flight planning for SOFIA is to ensurethat line-of-sight water vapor (LOS WV) is minimized during

observing [?]. This can be accomplished in one of threeways. It has long been known that water vapor decreases withaltitude, thus observing at higher altitude reduces LOS WV.If we analyze csc(h) where h is the telescope elevation in therange 20◦ ≤ h ≤ 60◦ (shown in Figure ??), we see that it takeson values in the range [2, 5.7]; thus, choosing the position andtime for observing at high telescope elevations reduces LOSWV. Finally, Becklin and Horn [?] showed that, in general,atmospheric water vapor is lower near the poles (as shown inFigure ??); thus, LOS WV can be reduced by repositioningthe aircraft.

Fig. 2. 5 year average of Water Vapor Overburden at 216.626 hPa(approximately FL 370) over the entire Earth for 31 December. Data providedcourtesy of the Wind and temperature data from European Center for MediumRange Weather Forecasting, file provided courtesy of Michael A. K. Gross.For comparison, at 147.474 hPa (approximately FL 450) WV overburden isuniformly below 10µ.

As an airborne observatory, SOFIA allows great flexibilityin optimizing any single observation. Judicious choice of take-off time, altitude selection and observatory position can ensurethat LOS WV is minimized for one observation. Unfortunately,there are complex tradeoffs between the takeoff fuel weight,flight duration, percentage of requested observations that canbe performed, and average LOS WV for a flight. Duringflight, aircraft altitude is limited by aircraft weight. The morefuel carried, the longer the flight, but also the more limitedthe aircraft’s initial operating altitude. Fuel is costly (JPAcosting $3.00 a gallon in April of 2005) so using it wiselyis important. Furthermore, repositioning the aircraft to seek

drier air or maximize telescope elevation will generally requirepreparatory ”dead-legs” (during which no observations areperformed); this will reduce time for observing.

Orion p2 Elvis p2

(1) Observation Order

P(Elvis, p2)=0.2/0.9

P(Orion, p2)=0.7/0.9

(5) Choose New Order

M74(2) Construct the Flight SgrA M82

M74 SgrA M82Elvis Orion

(3) Candidate Reordering of Rejects

(4) Net Benefit Analysis

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Fig. 3. A schematic view of the inner loop of the Automated Flight Planner.The AFP begins with an ordered list of the observations (1). The Constructorrapidly processes the observations to produce a flight out of a subset of theobservations (2). The Critic first determines which observations can be viewedif reordered (3). Net-benefit analysis is then performed (4), and finally someobservations are reordered (5) after which the cycle is performed again.

The constraints governing legal flights are complex enoughthat it is not possible to analyze the tradeoffs up front; one hasto generate flight plans and compare them to see the tradeoffsmanifested. Furthermore, the tradeoffs cannot be analyzed justonce. The trade space will look different for different sets ofobservations, due to the complex nature of the aircraft’s groundtrack (for more information see [?]). The trade space will alsolook different at different times of year; temperature and watervapor change throughout the year, affecting fuel consumptionand LOS WV. Finally, the price of fuel is not constant, sooperators’ propensity to trade science for operations costs willalso change. These tradeoffs are made even more complexbecause the quantities that are traded are usually incomparable.It is clear that lowering operations costs is valuable, but it isnot feasible to put a dollar value on the science output of theentire observatory. Similarly, it is not possible (or at least quitedifficult) to determine whether it is worthwhile to sacrifice oneobservation for lower LOS WV on another observation.

When building schedules for problems such as these, it isoften the case that schedule A “dominates” schedule B in thesense that A is more desirable than B by every measure. Thus,a flight A that used less fuel, scheduled the same (or the samenumber) of observations, and achieved lower LOS WV thana flight B dominates B in this sense. If A does not dominateB, then further care must be taken to decide which one tochoose. In the economics literature, this notion of dominancewas formalized by V. Pareto, and the set of schedules that donot dominate each-other is called the Pareto Frontier [?].

The SOFIA Automated Flight Planner (AFP) [?] enablesrapid exploration of the Pareto Frontier. Figure ?? showspictorally how the algorithm works. The AFP takes as input apermutation (1) of tasks to schedule. A fast procedure called a

SWO(MaxFlights,MaxRepeats)# F is current flight plan# B is best flight plan# P is a permutation of observations# R is rejected observations# U is candidate reorderingsfor MaxRepeats

(1) Generate observation order Pfor MaxFlights

(2) Construct the flightConstruct(P,R, F )Update best flight plan Bif R = ∅ return Felse

(3) Candidate reordering of rejectsfor all observations r in R,positions p and end times θ after observations in F

if (Feasible(o, p, θ))(4) Net Benefits analysis of new orderingC = net benefit of starting r at p, θUpdate U with < (r, p, θ), C >

end ifend for(5) Choose new orderForm biased probability from URevise order P

end elseend for #MaxFlights

end for #MaxRepeatsreturn B

Fig. 4. Pseudocode of the Automated Flight Planner.

Constructor (2) that treats each observation in order, ultimatelyscheduling or rejecting them. The permutation and its resultingflight are then analyzed by a Critic (3) to construct a newpermutation that schedules observations that were previouslyrejected. Since this might lead to other observations being“pushed out” of the schedule, the AFP estimates the net-benefit “score” (4) of revising the permutation. This scoreis used to randomly decide how to modify the permutation(5). The cycle is repeated until all tasks are scheduled orfor a fixed number of iterations. Figures ?? and ?? are apseudocode description of the AFP algorithm the reader isreferred to [?] for more details. Wind and temperature datafrom European Center for Medium Range Weather Forecasting(www.ecmwf.int) are used to calculate ground tracks andfuel consumption. We use data from the National GeospatialIntelligence Agency’s Digital Aeronautical Flight InformationFile to check for Special Use Airspace (SUAs).

We demonstrated the utility of AFP in a study performed on19 hours of requested observations for three days in December,and 31 hours of requested observations for five days in June;both flights originate and terminate at Moffett Field, CA.

Construct(P,R, F )Select the takeoff time θ# p is the current position of aircraft in F#θ is time aircraft at p in Ffor observation o ∈ P

if Feasible(o, p, θ)Add p to FUpdate p, θ

else add p to Rend for

Feasible(o, p, θ)# o is the observation# p is the current position# D is maximum dead leg duration(b, d, z) = FindDeadLeg(o, p, θ)# b = heading, d = duration, z = SUA zoneif the dead-leg crosses any SUA zone z

#Revise dead legs to avoid SUAb′ is closest heading s.t. all z not crossedd′ is new durationd = d′; b = b′

if d > D return falseif observation starts and ends in darkness

if dead leg home possible following oreturn true

return false

Fig. 5. Subroutines Construct(P, R, F ) and Feasible(o, p, θ) of the Auto-mated Flight Planner.

These observations form an initial “wish list” of science fromastronomers interested in using SOFIA, and thus constitutea good test case. Figure ?? shows the Right Ascension andDeclination of the requested observations, as well as the totalrequested time for each observation. Long observations (e.g.8.7 hours on Sagittarius A W. Arch Filaments in June) werebroken up into smaller requests of under two hours each.

The AFP was used to generate the Pareto Frontier for threedifferent fuel loads. These three fuel loads were originallydeveloped in [?] under the assumption of standard atmosphereand used to assess SOFIA’s ability to observe in the Northernhemisphere. These fuel loads are described in Figure ??.

Figure ?? and Figure ?? show the percentage of scheduledrequests, fuel load and LOS WV of the schedules found by theAFP. We desire flights with low LOS WV and high percent-ages of scheduled observations. Thus, the Pareto Frontier inthis case is the set of schedules in the upper left hand cornerof the figures. We see that there are tradeoffs between takeofffuel load, percentage of requested observations scheduled, andLOS WV. These tradeoffs are prominent in both the Decemberand June flight scenarios. We see “inflection points” where thethe number of scheduled observations needed to reduce LOSWV dramatically decreases; these appear to be natural oper-

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Fig. 6. The 3 fuel loads analyzed in the trade study. The shape of the iconin the middle of the profile denotes the icon used in Figures ?? - ?? to plotthe tradeoff between LOS WV and the percentage of scheduled observations.

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Alpha Lyr (3 hrs)

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Fig. 7. . The observation requests and observation durations. The top chartshows the Right Ascension and Declinations (coordinates) and requested timefor objects to be observed in December, while the bottom chart shows theobjects to be observed in June.

ating points for SOFIA. If operations staff can live with therelatively higher LOS WV, then the choice for SOFIA is to usethe Medium fuel load. If the instrument is insensitive to LOSWV and maximizing the science corresponds to maximizingthe number of scheduled observations, then using the Heavyfuel load is the best choice. However, for instruments that arevery sensitive to LOS WV, the operations staff can choose theLight fuel load.

The previous graphs showed that adjusting the fuel loadleads to a tradeoff between the LOS WV and the percentageof requested observations scheduled. However, as previouslystated, the AFP has the ability to reduce LOS WV by in-creasing the minimum telescope elevation angle. Doing so canhave unintended consequences; ensuring that the observationsare viewed at the best telescope elevation will generallyrequire longer setup steps, leading to less efficient flights at aminimum, and fewer scheduled observations at worst. Figures?? and ?? shows the flights in Figures ?? and ?? as wellas flights in which the AFP optimizes the telescope elevation

Fuel/Water vapor/Observation Tradeoff

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Fig. 8. Tradeoff between takeoff fuel load, LOS WV and fraction of requestedobservations scheduled for December flight series.

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Fig. 9. Tradeoff between takeoff fuel load, LOS WV and fraction of requestedobservations scheduled for December flight series, including results in whichAFP aggressively reduces LOS WV by increasing the telescope elevationangle.

angle to minimize LOS WV (these are plotted with the samefuel load icon, but are dark-filled). The AFP user can selecthow aggressively to optimize the telescope elevation; in ourtrade study we used 3 settings, but only present results for themost aggressive setting.

Optimizing the telescope elevation angle does not pay whenusing the Heavy fuel load for the December or June flightseries since generally, as good or better flights are foundwithout optimizing the telescope elevation. Further, for theDecember flights, optimizing the telescope elevation angledoes not qualitatively affect the characteristics of the flightsusing the Medium or Light fuel loads (Figure ??). By contrast,for the June flights (Figure ??), optimizing the telescopeelevation angle can lead to better tradeoffs between LOSWV and the percentage of scheduled requests when the fuelload is Medium or Light. However, the number of scheduledobservations is generally quite low when using the Light fuelload (it rarely exceeds 50% and when it does there is usuallya better flight using the Medium fuel load).

Flight planning for the previous generation airborne obser-

Fuel/Water vapor/Observation Tradeoff

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Fig. 10. Tradeoff between takeoff fuel load, LOS WV and fraction ofrequested observations scheduled for June flight series.

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Fig. 11. Tradeoff between takeoff fuel load, LOS WV and fraction ofrequested observations scheduled for June flight series, including resultsin which AFP aggressively reduces LOS WV by increasing the telescopeelevation angle.

vatory, the Kuiper Airborne Observatory (KAO), was done byhand; annecdotal evidence suggests this required roughly 8hours to generate one flight plan. When analyzing the Decem-ber and June flight series used in this paper, the AFP currentlygenerated 600 flight plans in roughly 50 hours of computationtime, a feat beyond the capabilities of human flight planners.The rate at which the AFP can generate flights enables humansto assess and analyze complex tradeoffs between fuel, LOSWV and the percentage of scheduled observations. Due tothe changing nature of SOFIA scheduling problems, thisfunctionality will play a crucial role in optimizing science andminimizing costs during operations.

REFERENCES

[1] E. Becklin and J. Horn, “High-latitude observations on sofia,” Publica-tions of the Astronomical Society of the Pacific, vol. 113, no. 786, 2001.

[2] J. Frank and E. Kurklu, “Mixed discrete and continuous algorithms forscheduling airborne astronomy observations,” in Proceedings of the 1st

International Conference on Constraint Programming, Artificial Intelli-gence and Operations Research, 2005.

[3] V. T’Kindt and J. C. Billaut, Multicriteria Scheduling. Springer Verlag,2002.