Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Phase Retrieval”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

621 records · Page 35
All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Validation of SMAP Surface Soil Moisture Products with Core Validation Sites

The NASA Soil Moisture Active Passive (SMAP) mission has utilized a set of core validation sites as the primary methodology in assessing the soil moisture retrieval algorithm performance. Those sites provide well calibrated in situ soil moisture measurements within SMAP product grid pixels for diverse conditions and locations.The estimation of the average soil moisture within the SMAP product grid pixels based on in situ measurements is more reliable when location specific calibration of the sensors has been performed and there is adequate replication over the spatial domain, with an up-scaling function based on analysis using independent estimates of the soil moisture distribution. SMAP fulfilled these requirements through a collaborative CalVal Partner program.This paper presents the results from 34 candidate core validation sites for the first eleven months of the SMAP mission. As a result of the screening of the sites prior to the availability of SMAP data, out of the 34 candidate sites 18 sites fulfilled all the requirements at one of the resolution scales (at least). The rest of the sites are used as secondary information in algorithm evaluation. The results indicate that the SMAP radiometer-based soil moisture data product meets its expected performance of 0.04 cu m/cu m volumetric soil moisture (unbiased root mean square error); the combined radar-radiometer product is close to its expected performance of 0.04 cu m/cu m, and the radar-based product meets its target accuracy of 0.06 cu m/cu m (the lengths of the combined and radar-based products are truncated to about 10 weeks because of the SMAP radar failure). Upon completing the intensive CalVal phase of the mission the SMAP project will continue to enhance the products in the primary and extended geographic domains, in co-operation with the CalVal Partners, by continuing the comparisons over the existing core validation sites and inclusion of candidate sites that can address shortcomings.

SMAP↗
NASA NTRSDate not supplied

166 GHz Ice Scattering Signal in Cold-Season Precipitating Cloud Systems

Surface snowfall can be produced by a variety of forcing mechanisms that are accompanied by different in-cloud physical processes and microphysical composition. For instance, shallow cumuliform snowfall forced by marine cold air outbreaks shows distinct geographic and seasonal signatures and plays in important role in annual snowfall production in many regions worldwide. Coincident CloudSat-CALIPSO observations confirm that oceanic regions exhibiting frequent shallow cumuliform snow are typically composed of mixed-phase cloud and precipitation particles and display passive microwave brightness temperature behavior that is dominated by cloud liquid water emission, while combined Global Precipitation Measurement (GPM) radiometer and surface radar studies of intense shallow cumuliform events indicate significant ice particle scattering signals at the highest GPM radiometer frequencies. Passive microwave imager channels in the 37 to 89 GHz range have long been used to detect precipitation-sized ice particle scattering signatures in clouds. Dual polarization plays an important role in distinguishing between scattering signatures and other background variability. The GPM Microwave Imager (GMI) is the first satellite radiometer to possess dual-polarized channels at 166 GHz. These high-frequency channels are more susceptible to emission and attenuation by cloud liquid water and water vapor than lower-frequency channels, but are also more sensitive to ice scattering. This research studies the ice scattering information contained in the 166 GHz channels compared to the historically used 85/89 GHz channels on previous sensors. A 166 GHz scattering index (SI) will be developed to understand how its correlation with non-precipitating ice scattering at higher altitudes also affects the 166 GHz scattering signature in cold-season precipitating cloud systems. The 166 GHz SI will be used to possibly isolate precipitation scattering signature for different snowfall modes (shallow convective vs. deep stratiform). The supercooled liquid water affecting shallow convective systems and drastically reducing the scattering signal could be detected and quantified, providing additional information for convective snow detection and quantification in solid precipitation retrieval algorithms.

Lisa Milani↗
NASA NTRS1999

A Study of Direct and Cloud-Mediated Radiative Forcing of Climate Due to Aerosols

The Intergovernmental Panel on Climate Change (IPCC) has reported that in the southeastern US and eastern China, the general greenhouse warming due to anthropogenic gaseous emissions is dominated by the cooling effect of anthropogenic aerosols. To verify this model prediction in eastern China and southeastern US, we analyzed regional patterns of climate changes at 72 stations in eastern China during 1951- 94 (44 years), and at 52 stations in the southeastern US during 1949-94 (46 years) to detect the fingerprint of aerosol radiative forcing. It was found that the mean rates of change of annual mean daily, maximum, minimum temperatures and diurnal temperature range (DTR) in eastern China were 0.8, -0.2, 1.8, and -2.0 C/100 years respectively, while the mean rates of change of annual mean daily, maximum, minimum temperatures and DTR in the southeastern US were -0.2, -0.6, 0.2, and -0.8 C/100 years, respectively. This indicates that the high rate of increase in annual mean minimum temperature in eastern China results in a slightly warming trend of daily temperature, while the high rate of decrease in annual mean maximum temperature and low rate of increase in annual mean minimum temperature lead to the cooling trend of daily temperature in the southeastern US. We found that the warming from the longwave forcing due to both greenhouse gases and aerosols was completely counteracted by the shortwave aerosol forcing in the southeastern US in the past 46 years. A slightly overall warming trend in eastern China is evident; winters have become milder. This finding is explained by hypothesizing that increasing energy usage during the past 44 years has resulted in more coal and biomass burning, thus increasing the emission of absorbing soot and organic aerosols in eastern China. Such emissions, in addition to well-known Asia dust and greenhouse gases, may be responsible for the winter warming trend in eastern China that we have reported here. The sensitivity of aerosol radiative properties to aerosol composition, size distribution, relative humidity (RH) is examined for the following aerosol systems: inorganic and organic ions (Cl-, Br-, NO3 -, SO4 2-, Na+, NH4 +, K+, Ca2+, Mg2+, HCOO-, CH3COO-, CH3CH2COO-, CH3COCOO-, OOCCOO2-, MSA-1); water-insoluble inorganic and organic compounds (elemental carbon, n-alkanes, SiO2, Al2O3, Fe2O3 and other organic compounds). The partial molar refraction method was used to calculate the real part of the refractive index. It was found that the asymmetry factor increased by approximately 48% with the real part varying from 1.40 to 1.65, and the single scattering albedo decreased by 24% with the imaginary part varying from -0.005 to -0.1. The asymmetry factor increased by 5.4 times with the geometric standard deviation varying from 1.2 to 3.0. The radiation transmission is very sensitive to the change in size distribution; other factors are not as significant. To determine the aerosol direct radiative forcing (ADRF), the aerosol optical depth (AOD) values at the three operational wavelengths (415, 500 and 673 nm) were determined at a regionally representative site, namely, Mt. Gibbs (35.78 deg N, 82.29 deg W, elevation 2006 m) in Mt. Mitchell State Park, NC, and a site located in an adjacent valley (Black Mountain, 35.66 deg N, 82.38 deg W, elevation 951 m) in the southeastern US. The two sites are separated horizontally by 10 km and vertically by 1 km. It was found that the representative total AOD values at 500 nm at the valley site for highly polluted (HP), marine (M) and continental (C) air masses were 0.68 +/- 0.33, 0.29 +/- 0.19 and 0.10 +/- 0.04, respectively. A search-graph method was used to retrieve the columnar size distribution (number concentration N, effective radius reff and geometric standard deviation=?g) from the optical depth observations at three operational wavelengths. The ground albedo, single scattering albedo and imaginary part of the refractive index were calculated using a mathematically unique procedure involving a Mie code and a radiative transfer code in conjunction with the retrieved aerosol size distribution, AOD, and diffuse-direct irradiance ratio. It was found that N, r(eff) and sigma(g) were in the ranges of 10 to 1.7 x 10(exp 4)/cubic cm, 0.09 to 0.68 micrometers and 1.12 to 2.95, respectively. The asymmetry factor and single scattering albedo were in the ranges of 0.63 to 0.75 and 0.74 to 0.97 respectively. The ground albedo for the forested terrain and imaginary part of refractive index were found to be in the ranges of 0.06 to 0.29 and 0.005 to 0.051 respectively. On the basis of these aerosol radiative properties obtained at the research sites and computations using the Column Radiation Model (CRM) of National Center of Atmospheric Research (NCAR) Community Climate Model (CCM3), it was found that the average cloud-free 24-hour ADRF values were -13 +/- 8, -8 +/- 3, -33 +/- 16 W/square m for marine, continental, and polluted air masses, respectively. On the assumption that the fractional coverage of clouds is 0.61, it was estimated that the annual mean ADRF was 7 +/- 2 W/square m in the southeastern US. The review with respect to the current knowledge of organic acids shows that aerosol formate and acetate concentrations range from 0.02 to 5.3 nmol/cubic m and from 0.03 to 12.4 nmol/cubic m respectively, and that between 34% to 77% of formate and between 21% to 66% of acetate are present in the fine fraction of aerosols. It was found that although most (98-99%) of these volatile organic acids were present in the gas phase, their concentrations in the aerosol particles were sufficient to make them a good candidate for cloud condensation nuclei (CCN). It is hypothesized that organic acids are at least one of the primary sources of CCN in the atmosphere due to their ubiquitous presence in the troposphere, especially over the continental forested areas. The results of our measurements at Palmer Station, Antarctica show that the daily average CCN concentrations at 0.3% and 1% supersaturations ranged from 0.3 to 160/cubic cm and from 4 to 168/cubic cm, respectively, during the period from 17 January to 26 February, 1994. New evidence for substantial and definitive CCN enhancement near and within cloud has been observed at Mt. Mitchell, North Carolina. The results show that the average monthly CCN concentrations were 460 +/- 217, 386 +/- 286, 429 +/- 228 and 238 +/- 134/cubic cm for in-cloud, overcast, clear and rainy conditions, respectively. The typical CCN spectra show that there were a lot of small CCN produced and the ion concentrations (especially H+ and SO4 2-) were very high during the CCN enhancement period. The significantly positive correlation between black carbon (BC) and CCN at 1% supersaturation indicates that a percentage of the BC measured at the site may be in the form of an internal mixture and participated in the formation of CCN.

Yu, Shao-Cai↗
NASA NTRS2005

Nighttime Cirrus Detection using Atmospheric Infrared Sounder Window Channels and Total Column Water Vapor

A method of cirrus detection at nighttime is presented that utilizes 3.8 and 10.4 (micro)m infrared (IR) window brightness temperature differences (dBT) and total column precipitable water (PW) measurements. This technique is applied to the Atmospheric Infrared Sounder (AIRS) and Advanced Microwave Sounding Unit A (AMSU-A) instrument suite on board EOS-Aqua, where dBT is determined from sets of carefully selected AIRS window channels, while PW is derived from the synergistic AIRS and AMSU-A water vapor retrievals. Simulated and observed dBT for a particular value of PW are not constant; several physical factors impact dBT, including the variability in temperature and relative humidity profiles, surface emissivity, instrument noise, and skin/ near-surface air temperature differences. We simulate clear-sky dBT over a realistic range of PWs using 8350 radiosondes that have varying temperature and relative humidity profiles. Thresholds between cloudy and uncertain sky conditions are derived once the scatter in the clear-sky dBT is determined. Simulations of optically thin cirrus indicate that this technique is most sensitive to cirrus optical depth in the 10 (micro)m window of 0.1-0.15 or greater over the tropical and subtropical oceans, where surface emissivity and skin/near-surface air temperature impacts on the IR radiances are minimal. The method at present is generally valid over oceanic regions only, specifically, the tropics and subtropics. The detection of thin cirrus, and other cloud types, is validated using observations at the Atmospheric Radiation Measurement (ARM) program site located at Manus Island in the tropical western Pacific for 89 coincident EOS-Aqua overpasses. Even though the emphasis of this work is on the detection of thin cirrus at nighttime, this technique is sensitive to a broad cloud morphology. The cloud detection technique agrees with ARM-detected clouds 82-84% of the time, which include thin cirrus, as well as other cloud types. Most of the disagreements are well explained by AIRS footprint-scale heterogeneity compared to ARM point measurements, cirrus overlying lower-layer water clouds, possible mixed phase microphysics in midlevel clouds, and significant IR channel noise for cold BT scenes over deep convective towers.

Atmospheric Radiation Measurement (RAM)↗
NASA NTRSDate not supplied

U.S. IMERG Status

The U.S. Science Team’s Integrated Multi-satellitE Retrievals for the Global Precipitation Measurement (GPM) mission (IMERG) product provides estimates of surface precipitation rate and related information on a global 0.1° half-hour grid. It is run three times at increasingly longer latency and higher information input to serve different communities. This presentation will briefly summarize the major upgrades included in Version 07. The Goddard Profiling (GPROF) algorithm (applied to passive microwave sensor data from the GPM virtual constellation) and the Combined Radar-Radiometer Algorithm (CORRA) that provide input to IMERG V07 are both improved, and the new Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks–Dynamic Infrared Rain Rate (PDIR) algorithm is being applied to infrared data, which employs an additional, warmer infrared temperature threshold than the previous infrared scheme and a deep neural network. V07 has improved bias performance as a result of calibrations that now employ the entire swath widths of CORRA and GPROF GPM Microwave Imager precipitation estimates. As well, time continuity in precipitation features is improved as a result of changes to the Kalman filter that approximately preserve the local histogram of precipitation rates (Scheme for Histogram Adjustment with Ranked Precipitation Estimates in the Neighborhood, or SHARPEN), and that better account for differences in sensor performance. A long-standing bug in the geolocation that shifted grid values 0.1° to the east in the latitude band 70°N-S has been corrected. Other changes in V07 include a hierarchical selection among motion vector sources to address deficiencies in the precipitation propagation near orography, an update to the precipitation phase specification for improved consistency with current inputs, and a renewed effort to implement climatological gauge adjustment to the near-real-time Runs. Early evaluations of V07 IMERG show interesting behavior across the TRMM orbit boost that is highly relevant to the planned orbit boost for the GPM Core observatory.

GPM↗
NASA NTRS2022

Identifying Chemical Aerosol Signatures Using Optical Suborbital Observations: How Much Can Optical Properties Tell us about Aerosol Composition?

Improvements in air quality and Earth’s climate predictions require improvements of the aerosol speciation in chemical transport models, using observational constraints. Aerosol speciation (e.g., organic aerosols, black carbon, sulfate, nitrate, ammonium, dust or sea salt) is typically determined using in situ instrumentation. Continuous, routine surface network aerosol composition measurements are not uniformly widespread over the globe. Satellites, on the other hand, can provide a maximum coverage of the horizontal and vertical atmosphere but observe aerosol optical properties (and not aerosol speciation) based on remote sensing instrumentation. Combinations of satellite-derived aerosol optical properties can inform on air mass aerosol types (AMTs e.g., clean marine, dust, polluted continental). However, these AMTs are subjectively defined, might often be misclassified and are hard to relate to the critical parameters that need to be refined in models. In this paper, we derive AMTs that are more directly related to sources and hence to speciation. They are defined, characterized, and derived using simultaneous in situ gas-phase, chemical and optical instruments on the same aircraft during the Study of Emissions and Atmospheric Composition, Clouds, and Climate Coupling by Regional Surveys (SEAC4RS, US, summer of 2013). First, we prescribe well-informed AMTs that display distinct aerosol chemical and optical signatures to act as a training AMT dataset. These in situ observations reduce the errors and ambiguities in the selection of the AMT training dataset. We also investigate the relative skill of various combinations of aerosol optical properties to define AMTs and how much these optical properties can capture dominant aerosol speciation. We find distinct optical signatures for biomass burning (from agricultural or wildfires), biogenic and dust-influence AMTs. Useful aerosol optical properties to characterize these signatures are the extinction angstrom exponent (EAE), the single scattering albedo, the difference of single scattering albedo in two wavelengths, the absorption coefficient, the absorption angstrom exponent (AAE), and the real part of the refractive index (RRI). We find that all four AMTs studied when prescribed using mostly airborne in situ gas measurements, can be successfully extracted from at least three combinations of airborne in situ aerosol optical properties (e.g., EAE, AAE and RRI) over the US during SEAC4RS. However, we find that the optically based classifications for BB from agricultural fires and polluted dust include a large percentage of misclassifications that limit the usefulness of results relating to those classes. The technique and results presented in this study are suitable to develop a representative, robust and diverse source-based AMT database. This database could then be used for widespread retrievals of AMTs using existing and future remote sensing suborbital instruments/networks. Ultimately, it has the potential to provide a much broader observational aerosol data set to evaluate chemical transport and air quality models than is currently available by direct in situ measurements. This study illustrates how essential it is to explore existing airborne datasets to bridge chemical and optical signatures of different AMTs, before the implementation of future spaceborne missions (e.g., the next generation of Earth Observing System (EOS) satellites addressing Aerosol, Cloud, Convection and Precipitation (ACCP) designated observables).

Meloe S F Kacenelenbogen↗
NASA NTRS1992

Canadian Space Agency Space Station Freedom utilization plans

Under the terms of the NASA/CSA Memorandum of Understanding, Canada will contribute the Mobile Servicing System and be entitled to use 3 percent of all Space Station utilization resources and user accommodations over the 30 year life of the Station. Equally importantly Canada, like NASA, can begin to exploit these benefits as soon as the Man-Tended Capability (MTC) phase begins, in early 1997. Canada has been preparing its scientific community to fully utilize the Space Station for the past five years; most specifically by encouraging, and providing funding, in the area of Materials Science and Applications, and in the area of Space Life Sciences. The goal has been to develop potential applications and an experienced and proficient Canadian community able to effectively utilize microgravity environment facilities such as Space Station Freedom. In addition, CSA is currently supporting four facilities; a Laser Test System, a Large Motion Isolation Mount, a Canadian Float Zone Furnace, and a Canadian Protein Crystallization Apparatus. In late April of this year CSA sent out a Solicitation of Interest (SOI) to potential Canadian user from universities, industry, and government. The intent of the SOI was to determine who was interested, and the type of payloads which the community at large intended to propose. The SOI will be followed by the release of an Announcement of Opportunity (AO) following governmental approval of the Long Term Space plan later this year, or early next year. Responses to the AO will be evaluated and prioritized in a fair and impartial payload selection process, within the guidelines set by our international partners and the Canadian Government. Payload selection is relatively simple compared to the development and qualification process. An end-to-end user support program is therefore also being defined. Much of this support will be provided at the new headquarters currently being built in St. Hubert, Quebec. It is recognized that utilizing the Space Station could be expensive for users; costing in many cases millions of dollars to get a payload from conception to retrieval. It is also recognized that some of the potential users cannot or will not invest a lot of money or effort into Space Station utilization, unless there is a perceived significant commercial potential. How best to fund Space Station payloads is under study. Space Station Freedom will provide the first opportunity for Canada to conduct experiments in a long-duration microgravity environment. CSA have been developing and funding potential users for some time, and considerable interest has been shown by the response to our SOI earlier this year. Canada can be one of the two earliest users for the Space Station, along with NASA. We hope to take full advantage of this opportunity.

Faulkner, James↗
NASA NTRS2010

Aerosol Observability and Predictability: From Research to Operations for Chemical Weather Forecasting. Lagrangian Displacement Ensembles for Aerosol Data Assimilation

A challenge common to many constituent data assimilation applications is the fact that one observes a much smaller fraction of the phase space that one wishes to estimate. For example, remotely sensed estimates of the column average concentrations are available, while one is faced with the problem of estimating 3D concentrations for initializing a prognostic model. This problem is exacerbated in the case of aerosols because the observable Aerosol Optical Depth (AOD) is not only a column integrated quantity, but it also sums over a large number of species (dust, sea-salt, carbonaceous and sulfate aerosols. An aerosol transport model when driven by high-resolution, state-of-the-art analysis of meteorological fields and realistic emissions can produce skillful forecasts even when no aerosol data is assimilated. The main task of aerosol data assimilation is to address the bias arising from inaccurate emissions, and Lagrangian misplacement of plumes induced by errors in the driving meteorological fields. As long as one decouples the meteorological and aerosol assimilation as we do here, the classic baroclinic growth of error is no longer the main order of business. We will describe an aerosol data assimilation scheme in which the analysis update step is conducted in observation space, using an adaptive maximum-likelihood scheme for estimating background errors in AOD space. This scheme includes e explicit sequential bias estimation as in Dee and da Silva. Unlikely existing aerosol data assimilation schemes we do not obtain analysis increments of the 3D concentrations by scaling the background profiles. Instead we explore the Lagrangian characteristics of the problem for generating local displacement ensembles. These high-resolution state-dependent ensembles are then used to parameterize the background errors and generate 3D aerosol increments. The algorithm has computational complexity running at a resolution of 1/4 degree, globally. We will present the result of assimilating AOD retrievals from MODIS (on both Aqua and TERRA satellites) from AERONET for validation. The impact on the GEOS-5 Aerosol Forecasting will be fully documented.

da Silva, Arlindo↗
NASA NTRSDate not supplied

Monitoring Airspace Complexity and Determining Contributing Factors

The national airspace has evolved over many years to accommodate increased traffic demand [1] while simultaneously maintaining one of the safest forms of transportation [2], [3]. One of the reasons for this success is the ability of the system and the operators to adapt and accommodate to situations that routinely disrupt optimal operations. These situations may include: adverse weather, delays, early arrivals, equipment outages, and other factors that are outside the operators ability to control. These factors can lead to states where automation is unable to properly handle these issues and therefore air traffic controllers and pilots have to intervene, ultimately increasing communication between operators resulting in higher workload. As controller workload increases to handle sub-optimal operating conditions this can be viewed as an increase in complexity. The reasoning for this is because humans are now required to make tactical decisions in response to external factors, resulting in a departure from the strategic plan where operations would be more efficiently managed. Human operators control airspace complexity under rigid regulations that are constantly changing. The airspace is divided into sectors and the number of aircraft assigned to each controller is limited for safe handling. There has been past work that devised airspace complexity metrics in commercial aviation and related these metrics to controller workload (e.g., [4],[5]). The upper bounds on the system load are pre-determined. Such bounds on complexity make for a safe system, but the system cannot scale and adapt to autonomous, dense, and heterogeneous traffic, including the many types of Unmanned Aerial Vehicles (UAVs) envisioned to be added to the operations. We hypothesize that, as traffic density and heterogeneity grow, and other key metrics change, there will be phase transitions at which the way traffic should be managed changes significantly [6]. We offer a method for in-time detection of contributing factors that lead to phase transitions, characterized by increased complexity. To the best of our knowledge, there is no tool similar to our proposed effort that identifies such contributing factors or precursor patterns. To define the scope we are proposing to measure complexity from the viewpoint of the Terminal Radar Approach Control Facilities (TRACON) controller’s perspective. In particular we are analyzing arrivals into KSFO. With safety as the top concern for airspace operators, it is important to recognize that as density and heterogeneity grow, the focus of the system will change. Times of the day when the airspace has low density and heterogeneity, the flights will follow more efficient paths where the aircraft move on established routes that are more or less directly to the destination. However, when density and heterogeneity increases, the system will begin changing focus to avoiding conflicts and collisions and route the flights in a more flexible way. Higher flexibility requires more communication and coordination between controllers and pilots which the current automation is unable to handle. This paper proposes a novel approach that monitors airspace complexity at multiple scales, uses a Machine Learning-based tool that predicts when operations will transition to a regime of greater complexity, and identifies actions that can reduce the complexity while still maintaining efficient and safe operations. We demonstrate our proposed approach using data from multiple complementary sources. This includes, but is not limited to: historical aircraft surveillance data from NASA’s Sherlock Data Warehouse [7], METAR weather data, and airport configuration data from Aviation System Performance Metrics (ASPM). The surveillance data flight paths are sampled at a variable sample rate — increasing as the aircraft approaches the airport. This is due to how Sherlock manages flight track stitching between different radar facilities which have different sampling rates. The weather and performance data are logged at defined intervals throughout the day at a courser refresh rate. In addition to the logged data and metrics, we leverage pre-defined Standard Terminal Arrival Routes (STARs) procedures to characterize the path of each flight. Each flight files for one of these routes in the flight plan well before entering the terminal airspace, and approximately follows the route until it leaves the STAR, typically on the final fix of a runway transition. However, most flights do not always fly the full STAR procedure to completion [8], but the majority do adhere to the fixes within the common route of the procedure. Our approach leverages fixes in the common route of each of the STARs to build a reference path to the airport. This allows us to characterize the flight paths in what we are defining as the “maneuvering area” (the airspace between the STAR and before the flight is lined up on the runway’s final approach) to determine how off nominal the flights are to calculate its complexity score. Determining airspace complexity is a concept that does not have a concrete answer. In designing this metric, we consider what increases the workload for the air traffic controllers. Consequently more specialized vectoring maneuvers results in higher workload. Accordingly, we start with a theory: each flight has a direct path it takes from the STAR’s common route to the final approach’s outer marker fix for the flight’s landing runway. It is important to note that the direct path is only used as a reference. If the majority of the flights have a large consistent offset as compared to other routes it does not necessarily mean that those flights have higher complexity. We are merely building a distribution based on this direct path for that particular STAR and runway pair to determine the normal mode of operations for that route. Flights that are in the upper tail of these distributions will result in higher complexity scores and flights that fly in the median will represent the normal mode of operations and therefore will have lower complexity scores. Since flights following each STAR route take different paths to the airport, we have a different distribution for each STAR route and therefore can model these distributions to compute a complexity score from their respective normalized distributions. To evaluate the effectiveness of our proposed airspace complexity metric we will compare against an established approach based on trajectory clustering [9]. This unsupervised learning technique consists of the following steps: (1) identify the general maneuvering areas (waypoints) by performing $\kappa$-means or DBSCAN clustering on locations where aircraft frequently turn based on the surveillance radar track data, (2) map flight trajectories onto sequences of waypoints, and (3) cluster the sequences based on their common subsequences. From a high-level perspective, this baseline model learns nominal operations in the airspace through the sequence of waypoints that are representative of where aircraft change direction and defines deviations from the nominal operations as “complex.” Therefore, more deviations from the nominal operations correspond to higher complexity values. For our validation, we re-implemented this technique and tune model hyper-parameters to correctly detect waypoints for the arrival traffic into the San Francisco bay area. We will compute the complexity measure over a one-year period using our proposed technique as well as the baseline. Our validation will be based on each technique’s ability to detect a set of undesirable outcomes (e.g., go-arounds, holding patterns, average time in the airspace, etc.). Since our current complexity metric is derived from the offset from the direct reference path, it’s important to understand what causes these offsets. In many of the flights with high offset distance, flights performing holding patterns and S turns can be observed. These maneuvering tactics are utilized to add distance between the aircraft and the destination runway to prevent multiple flights from having conflicting arrival times. In order to predict a rise in complexity (or the precursor to complexity), it’s necessary to be able to identify these potential conflicts (which in turn, result in higher offsets). To do this, we define a “representative flight” for each STAR route and runway pair. This flight is approximately the path the flight would take if there was a clear path with no other flights in the airspace — including the time remaining to the airport. We first identify the flights for a given STAR runway pair using the offset to the reference path distributions that fall between the 44-55 percentiles. This yields the flights that conform to the most normal mode of operation. Each of these flights is partitioned based on the percent complete from the entry point into the maneuvering areas from 0\% – 100\% complete. Then for each percent “bin”, we take the median value of the flight’s latitude/longitude coordinates, airspeed, and (non causal) time remaining to the airport to construct a lookup table for each percent complete bin on a given route. As a flight enters the maneuvering area, we can find the estimated arrival time of a flight to the airport by finding the closest point to the representative path’s percent complete bin (relative to the flight’s current position at any snapshot in the airspace) and therefore retrieve the corresponding remaining time left on the “representative path”. We assume that the flight will follow the representative path to completion when deriving these estimates. We can then compare these estimated arrival times against other flights for the same snapshot in time to identify potential conflicts. If more flights are estimated to arrive within a tolerance window than there are runways available, then we have a potential conflict. We can use this derived measure along with other factors expected to add disruption to the operation such as weather and runway configuration changes as an input to machine learning tools to detect precursors that increases in our complexity measure. This novel method will assist in uncovering insights into the contributing factors that lead to increased complexity that may allow for in-time responses to avoid reaching a high complexity state in the airspace.

complexity↗