Analytical Workload Model for Estimating En Route Sector Capacity in Convective Weather* John Cho, Jerry Welch, and Ngaire Underhill 16 June 2011 *This work was sponsored by the Federal Aviation Administration under Air Force Contract No. FA8721-05-C-0002. Opinions, interpretations, Paper 33-1 conclusions, and recommendations are those of the authors and are not necessarily endorsed by the United States Government. JYNC 6/2/2011
Issues with Existing Airspace Capacity Models • Weather-impact models yield flow reduction relative to historical fair-weather traffic (fractional availability) – Route blockage model – Sector min-cut max-flow approach – Directional ray scanning method • Controller workload, which determines sector capacity, is not taken into account • Workload-based sector models give absolute capacity values but weather effects not included – Detailed simulation models – “Macroscopic” analytical models ⇒ Incorporate convective weather effects into analytical sector workload model Paper 33-2 JYNC 6/2/2011
Outline • Motivation • Sector capacity model without weather • Sector capacity model with weather • Results and issues • Summary Paper 33-3 JYNC 6/2/2011
Controller Workload Limits Traffic • Sector reaches capacity when the controller team is fully occupied • Queuing grows with three critical traffic-dependent event rates Conflict rate V 21 ∆ t λ c = (2 N 2 / Q ) M h M v V 21 Sector aircraft count N V 21 Sector airspace volume Q Miss distances M h , M v Mean closing speed V 21 M h Aircraft randomly located Monitor Alert Parameter (MAP) basis with density κ Recurring event (scanning/monitoring) rate Transit (boundary crossing) rate λ r = N/P λ t = N/T Sector aircraft count N Sector aircraft count N Recurrence period P Mean sector transit time T Paper 33-4 JYNC 6/2/2011
Task-Based Analytical Sector Workload Model G = G b + G c + G r + G t Sector Fraction of controller time workload intensity Recurring Conflict Transition Background Service times ( empirical ) G c = τ c [(2 N 2 / Q ) M h M v V 21 ] G r = τ r [ N/P ] G t = τ t [ N/T ] Occurrence rates ( calculated from airspace parameters ) • Determining the unknown service times – Live approach Measure controller performance – Regression approach Observe peak daily counts N p for many Welch et al., 2007: Macroscopic model for estimating en sectors route sector capacity, 7 th USA/Europe ATM R&D Seminar, Calculate corresponding model capacities N m Barcelona, Spain Find service times that best fit N m to N p bound Paper 33-5 JYNC 6/2/2011
Effect of Altitude Changes • Aircraft with vertical rates cause increased uncertainty • Adapt by increasing vertical miss distance M v ― Determine fraction F ca of aircraft with ≥ 2000 ft altitude change ― As F ca grows, increase M v linearly from 1000 ft to M vmax 2000 Mv , ft M vmax ≈ 1600 ft (for NAS) 1500 Vertical Miss Distance 1000 500 ∆ a 0 0 0.2 0.4 0.6 0.8 1 Fraction F ca of Aircraft with ∆ a > 2000 ft Paper 33-6 JYNC 6/2/2011
Fitted Capacities vs. Peak Counts (790 NAS Sectors July–August 2007) 30 25 NAS Model Capacity 20 15 10 5 0 0 5 10 15 20 25 30 Observed Peak Count Simple analytical model can bound data well and is suitable for real-time application Paper 33-7 JYNC 6/2/2011
Outline • Motivation • Sector capacity model without weather • Sector capacity model with weather • Results and issues • Summary Paper 33-8 JYNC 6/2/2011
Convective Weather Avoidance Model (CWAM) Creating the model ENSEMBLE OF CIWS WEATHER & ETMS TRAJECTORIES CLASSIFY TRAJECTORY VIL Non-deviation Mean Deviation DEVIATION DATABASE Threshold Classified Weather Encounters Deviation Actual Path Planned Path Begin Deviation End Deviation Non-Deviation Deviation Actual Path VIL Actual Path Planned Path Decision Point Data Editing Planned Path Edited Trajectories Actual Path Planned Path VIL Actual Path 2006-2008 Database IDENTIFY WEATHER ENCOUNTERS Total Weather Encounters: ~10000 Weather Encounters w/ Deviation: ~1500 Weather Encounters w/o Deviation: ~3500 Planned Path Planned Path ~5000 Weather Encounters Edited: End Encounter Begin Encounter Paper 33-9 JYNC 6/2/2011
Weather Avoidance Field (WAF) Applying the model CIWS WEATHER DATA WEATHER AVOIDANCE FIELD VIL Deviation Probability Lookup Table Spatial Filters Echo Top 90 th Percentile Flight Altitude – 16km EchoTop 60km VIL Area Coverage WAF Deviation Probability DEVIATION DATABASE Echo Top 90 th Percentile Flight Altitude – 16km Deviation Non-Deviation Statistical Pattern Classifier 60km VIL Area Coverage Paper 33-10 JYNC 6/2/2011
Weather Blockage Modification to Sector Workload Model τ τ τ BN = + + + + r t c G G N N ( N 1 ) No Weather max b P T Q τ + τ τ τ + ( F ) N N BN ( N 1 ) = + + + r w w t c G G With Weather − max b P T Q ( 1 F ) w F w = fraction of airspace blocked by weather τ w = time needed per reroute due to weather blockage • Compute F w from WAF data ― 80% WAF contours ― Integrate over WAF contours at 2000-ft altitude increments ― Fractional blockage of 3D sector volume Fit to observed sector peak counts during weather to obtain τ w • Compare to τ w = 45–60 s estimated by experienced air traffic ― controller Paper 33-11 JYNC 6/2/2011
Outline • Motivation • Sector capacity model without weather • Sector capacity model with weather • Results and issues • Summary Paper 33-12 JYNC 6/2/2011
Some Results Using Observed Weather Peak Count Peak Count Model capacity with τ w = 30 s Actual sector peak count Model capacity with τ w = 90 s Fair-weather model capacity Paper 33-13 JYNC 6/2/2011
Weather Effects on Sector Transit Time Slope = -0.5 • “Cutting corners” to avoid weather decrease mean sector transit time • Use fitted wx blockage- transit time relationship to ZDC32 adjust mean transit time in capacity forecast • F ca does not show dependence on weather blockage Paper 33-14 JYNC 6/2/2011
Model vs. Observed Peak Sector Count • Capacity model should bound sector peak count data • Still do not have a lot of heavy weather impact cases • For now set τ w = 45 s (consistent with subject matter expert estimate) 31 ARTCC-days worth of data used Paper 33-15 JYNC 6/2/2011
Some Results with Forecast Weather • Historical mean sector transit time and F ca per are used in forecast ― Transit time adjusted for weather blockage ― Better to use time-dependent forecast values of transit time and F ca if available Paper 33-16 JYNC 6/2/2011
Model Dependencies • Three workload components affected by weather ― Conflict resolution task (via available airspace reduction) ― Weather rerouting task ― Sector hand-off task (via mean transit time reduction) • The rerouting and hand-off tasks dominate the dependence of workload on weather except at very high weather blockages Paper 33-17 JYNC 6/2/2011
Capacity vs Weather Blockage Fraction Capacity dependence on weather blockage is nonlinear Paper 33-18 JYNC 6/2/2011
Sector Weather Blockage Forecast Errors • Sector weather blockage is scalar: Straightforward error analysis • Need to accumulate more data for heavy weather cases 22 ARTCC-days worth of data used Paper 33-19 JYNC 6/2/2011
Sector Capacity Forecast Errors Forecast F w , T , F ca Obs. F ca ; Forecast F w , T Obs. T , F ca ; Forecast F w • No sector capacity truth available • Comparison of model capacity using forecast data vs. observed data • Accurate forecast of sector transit time as important as weather forecast Paper 33-20 JYNC 6/2/2011
Directional Capacity Issue • Sector capacity (peak traffic count) is scalar—no differentiation based on flow direction • But flow capacity is directional – Sector transit time depends greatly on sector shape and travel direction – Weather blockage can be highly directional • Formulate workload model for directional capacity – Replace scalar F w with directional weather blockage in reroute term – Utilize existing directional blockage model • Scalar capacity depends on directional capacity and 4D flight trajectories—a difficult forecast problem Paper 33-21 JYNC 6/2/2011
Summary • Sector capacity model based on analytical workload model was modified to include weather effects • Difficult to validate because “truth” is not available – Model as upper bound—use statistics – Initial results are promising—need to analyze more data • Sector capacity forecast uncertainties arise from – Sector transit times – Weather • Weather forecast uncertainties are large at several hours in advance – Huge effort in developing complicated and ultradetailed capacity model may not be justified • Need to tackle directional capacity issue • Collaboration with MIT ORC and Metron to provide sector capacity input to air traffic flow optimization models Paper 33-22 JYNC 6/2/2011
Back-up Slides Paper 33-23 JYNC 6/2/2011
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