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Ninth USA/Europe Air Traffic Management Research and Development Seminar (ATM2011) Generating Probabilistic Capacity Profiles from weather forecast: A design-of-experiment approach Gurkaran Buxi Mark Hansen National Centre of Excellence for Aviation Operations Research NEXTOR, University of California Berkeley Berkeley, CA gkb@berkeley.edu National Centre of Excellence for Aviation Operations Research NEXTOR, University of California Berkeley Berkeley, CA mhansen@ce.berkeley.edu Abstract—It is common understanding that weather plays an important role in determining the capacity of an airport. Severe weather causes capacity reductions, creating a capacity demand imbalance, leading to delays. The role of air traffic flow management (ATFM) measures is to reduce these delay costs by aligning the demand with the capacity. Ground delay program (GDP) is one such measure. Though the GDP is initiated in poor weather conditions, and weather forecasts are subject to errors, present GDP planning procedures are essentially deterministic in nature. Forecast weather is translated into deterministic capacity predictions on which GDP planning is based. Models which employ probabilistic capacity profiles for planning GDPs have been developed, but their application has been limited by the inability to create such profiles from weather forecasts. This paper develops probabilistic profiles for three airports, BOS, LAX and SFO using the Terminal Aerodrome Forecast and San Francisco Marine Initiative. The profiles are inputs to a static stochastic GDP model to simulate ATFM strategies. A design of experiments approach has been employed to determine profiles which minimize the total average costs. The average cost of the methodologies is evaluated against realized capacities to determine the benefit of the forecast. It is shown that inclusion of weather forecasts reduces the cost of delays. It is shown for SFO that on average TAF offers similar benefit in controlling cost of delay when compared to STRATUS. Careful use of the TAF indicates that other airports would also benefit from using TAF in planning of operations. Keywords-ground delay program;terminal aerodrome forcast ;STRATUS;Design of experiments;Response surface methodology;Dynamic time warping I. INTRODUCTION Adverse weather conditions in the vicinity of an airport often reduce its operational capacity, leading to an imbalance between capacity and demand. This capacity-demand imbalance may lead to delays, and, in the absence of traffic management initiatives, holding in the terminal area, increased controller workload, and excessive fuel burn. To mitigate these impacts, the Federal Aviation Administration (FAA) often implements Ground Delay Programs (GDPs). GDPs mitigate the terminal weather-induced airspace congestion by metering the arrival of aircraft to the destination airport. The metering matches the number of flights arriving in a period with the arrival capacity forecast or the “airport acceptance rate” (AAR) forecast. The metering of flights is achieved by delaying inbound flights on ground at the origin airport prior to their departure. If the AAR forecast is perfectly accurate, the metering from the GDP ensures that the total delay costs are minimized. It is common understanding that the AAR is primarily influenced by the weather in the vicinity of the airport and thus AAR forecasting necessitates a terminal weather forecast. The weather forecasts are seldom accurate in perfectly predicting the conditions and can thus lead to inaccurate predictions of the AAR. There has been considerable research on how to plan GDPs so as to take into account uncertainty about airport capacity. GDP models found in the literature incorporate the uncertainty in the AAR and can be classified in two broad categories: dynamic models and static models. In dynamic models, as information about realized capacity is updated, ground holding decisions are revised, incorporating a wait-andsee strategy. Most dynamic models require scenario trees to represent the uncertainty in the AAR. Conversely, in a static model, decisions made once are not revised. Static models require probabilistic capacity profiles as inputs. Reference [1] contains more details on the types of GDP models. Most of the literature on these models has taken the capacity profiles or scenario trees as given, assuming that in real-world application these could somehow be extracted from weather forecasts and the expertise of traffic management specialists. There is considerably less literature on the development of specific dayof-operation probabilistic capacity profiles. Accordingly, this paper focuses on the development of probabilistic capacity profiles from a day-of-operation weather forecast using a design-of-experiments (DOE) methodology. This methodology determines the best input parameter values which lower the costs in a GDP. Such profiles, when used in conjunction with appropriate GDP planning models, could lead to better GDPs, with lower realized costs as a result of reducing either excessive ground delays or airborne delay. This paper develops probabilistic capacity profiles from weather forecasts for three United States (US) airports: San Francisco International Airport (SFO), Boston Logan International Airport (BOS) and Los Angeles International Airport (LAX). The weather forecast used for constructing the profiles for the three airports is the Terminal Aerodrome Forecast (TAF) which is issued for all the major US Airport. TAF contains forecast information on visibility, ceiling, winds, and other meteorological variables for the entire day. Amongst the above airports SFO is unique because it is issued another forecast, SFO Marine Stratus Forecast System (STRATUS) along with the TAF. STRATUS is a forecast project created specifically for SFO, because it experiences a low altitude marine stratus cloud layer during the summer which reduces the airport capacity. STRATUS forecasts the “burn-off” time of these marine clouds i.e. the time when the capacity would increase. We construct probabilistic capacity profiles from the TAF for all the three airports and also construct profiles for SFO using the STRATUS forecast. The contribution of this paper is that it provides techniques which use several statistical methodologies to convert weather forecasts into specific day-of-operation probabilistic capacity profiles using a design-of-experiments (DOE) approach. The profiles are provided as inputs to a static stochastic GDP model that determines the optimal arrival rate for an airport. The DOE approach determines parameters which generate probabilistic profiles minimizing the total realized costs. We compare the realized costs of the simulated outcomes from the GDP model based on the different methods of scenario generation from weather forecasts against two other reference cases. In the first, the GDP is based on perfect information about the capacity, while in the second profiles are developed from historical capacity data without use of the day-ofoperation weather forecast. This paper develops probabilistic capacity profiles based on the realized capacity and the weather forecast for the summer months (May-September) of 2004 to 2006 for the three airports. In total, the data set included D=446 days for SFO, D=432 days for BOS and D=450 days for LAX for which the TAF weather forecast and the realized capacity were both available. The STRATUS forecast for SFO was available for only 150 days because they become available when marine clouds are forecast in the in the terminal area. We construct probabilistic profiles which represents capacity for every 15 minutes (period) from 7am to 10pm as the bulk of the traffic is occurs in this time period. The reported results are based on three airports for 45 historical days but the methods for generating capacity profiles from the TAF can be applied at any other airport for which a TAF is available. This paper proceeds as follows. Section 2 provides the literature review. Section 3 presents the GDP model Section 4 describes the weather forecasts and the several techniques for generating probabilistic capacity profiles using the design of experiment approach. Section 5 presents a cost comparison of the strategies obtained from the profiles developed in Section 4. Section 6 offers conclusions. II. LITERATURE REVIEW The current National Airspace System (NAS) rarely incorporates uncertainty of the weather forecasts into strategic decisions. Operations planning assume a deterministic approach using expected weather conditions [2]. Since it is difficult to accurately predict AAR, several researchers have formulated GDP models which require probabilistic capacity profiles or scenario trees for AAR as inputs [1], [3], [4]. A probabilistic capacity profile is a time series of capacity values (typically based on a quarter-hour time unit) and an associated probability. For a given airport and day there will typically be several profiles depicting different possible evolutions of capacity. Thus the set of stochastic profiles capture the uncertainty in the future arrival capacity. Methods for generating these profiles have focused on developing them from historical data without specific reference to a particular day-of-operation [5]. Other scenario-generation methods have been developed to support the application of stochastic programs in finance [6]. Reference [5] formulates a methodology for developing stochastic profiles from historical AAR data for various airports in the United States. The profiles are the centroids of the clusters obtained after K-means clustering the AAR time series. Their approach in profile construction is devoid of any weather forecast information. Reference [7] presents a GDP model based on the SFO Marine Stratus Initiative (STRATUS) forecast. They model the time of fog burn off as a random variable with the probability distribution obtained from STRATUS. They assume at fog burn-off the landing capacity of SFO increases sharply. Refence [8] gauged the imprecision of the forecast weather information with the actual weather by calculating avoidable delays. First they matched the realized historical weather in a period with the capacity of the airport in that period. Using this developed relationship, they predicted the AAR from the Terminal Aerodrome Forecast (TAF) and the Meteorological Aviation Report (METAR) for every period. From a queuing model, they determined the delays between the scheduled arrivals and AAR predicted from TAF and AAR predicted from METAR. This deterministic approach ignores the uncertainty concerning the TAF. Reference [9] uses the day-of-operation weather forecast to generate probabilistic capacity profiles for SFO but have not addressed how to choose the parameters which influence the probabilities and the number of the profiles. Their approach does not produce probabilistic profiles which give the lowest realized costs in a GDP simulation. While there is previous research that addresses the development probabilistic capacity profiles from historical capacity data and which translates a TAF forecast into a deterministic capacity forecast, the problem of developing probabilistic capacity scenarios from a TAF forecast that give the lowest costs has yet to be addressed. The research presented here fills that gap. III. BALL ET AL. STATIC STOCHASTIC GDP MODEL This section describes Ball et al. [3] static stochastic model which requires probabilistic capacity profiles as inputs. This model determines ground delays by minimizing the total expected costs of delay in a GDP by determining the optimal rate at which aircraft should land at the destination airport. This rate is termed as the Planned Airport Arrival Rate (PAAR), for each time period. As mentioned in the introduction, uncertainty of the AAR is captured by probabilistic capacity profiles. In the model the cost of air delay ca is assumed to be greater than cost of ground delay cg (if ca ≤ cg there would not be a need to delay the aircraft on the ground). The model takes the following form: