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NASA NTRS2004

Random Matrix Approach to Quantum Adiabatic Evolution Algorithms

We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.

Boulatov, Alexei↗

NASA NTRS2020

Mechanisms Linked to Recent Ozone Decreases in the Northern Hemisphere Lower Stratosphere

Previous studies have robustly identified a decrease since 1998 in lower stratospheric (LS) ozone in the Northern Hemisphere (NH). While this ozone decrease is qualitatively explained as resulting from changes in the large‐scale circulation, there is not yet a quantitative mechanistic explanation of these changes. Here we explore the drivers of recent ozone changes using two different configurations of the Goddard Earth Observing System (GEOS) general circulation model. The first configuration of GEOS includes a full chemistry module and is constrained with meteorological fields from the Modern‐Era Retrospective analysis for Research and Applications, Version 2 (MERRA‐2). This configuration (M2GMI) is used to analyze an idealized tracer that covaries closely with ozone on interannual and decadal timescales, revealing that recent ozone decreases in the NH subtropics are associated with a poleward expansion of upwelling in the NH LS, with reduced (enhanced) downwelling over northern subtropics (midlatitudes). The second configuration of GEOS is a free‐running version of the GEOS Chemistry‐Climate Model (CCM) that is used to perform a ten‐member ensemble of free‐running simulations. Comparisons of the two configurations reveal that, while the free‐running model can produce negative ozone changes in the NH LS, the magnitude of these changes is significantly weaker, relative to both M2GMI and MERRA‐2; moreover, these weaker ozone decreases are consistent with weaker simulated changes in the residual circulation. Finally, we examine the GEOS model results in the broader context of the hindcast simulations performed as part of Phase 1 of the Chemistry Climate Modeling Initiative. We show that the majority of the free‐running simulations considered here also exhibit weaker long‐term residual circulation changes, compared to reanalyses.

Ozone↗

NASA NTRS1989

Numerical study of the current sheet and PSBL in a magnetotail model

The current sheet and plasma sheet boundary layer (PSBL) in a magnetotail model are discussed. A test particle code is used to study the response of ensembles of particles to a two-dimensional, time-dependent model of the geomagnetic tail, and test the proposition (Coroniti, 1985a, b; Buchner and Zelenyi, 1986; Chen and Palmadesso, 1986; Martin, 1986) that the stochasticity of the particle orbits in these fields is an important part of the physical mechanism for magnetospheric substorms. The realistic results obtained for the fluid moments of the particle distribution with this simple model, and their insensitivity to initial conditions, is consistent with this hypothesis.

Doxas, I.↗

DOE OSTI2023

Global nitrogen and sulfur deposition mapping using a measurement–model fusion approach

Abstract. Global reactive nitrogen (N) deposition has more than tripled since 1860 and is expected to remain high due to food production and fossil fuel consumption. Global sulfur emissions have been decreasing worldwide over the last 30 years, but many regions are still experiencing unhealthily high levels of deposition. We update the 2010 global deposition budget for reactive nitrogen and sulfur components with new regional wet deposition measurements from Asia, improving the ensemble results of 11 global chemistry transport models from the second phase of the United Nations Economic Commission for Europe's Task Force on Hemispheric Transport of Air Pollution (HTAP II). The observationally adjusted global N deposition budget is 114.5 Tg N, representing a minor increase of 1 % from the model-only derived values, and the adjusted global sulfur deposition budget is 88.9 Tg S, representing a 6.5 % increase from the modeled values, using an interpolation distance of 2.5∘. Regionally, deposition adjustments can be up to ∼ 73 % for nitrogen and 112 % for sulfur. Our study demonstrates that a global measurement–model fusion approach can improve N and S deposition model estimates at a regional scale, with sufficient availability of observations; however, in large parts of the world, alternative approaches need to be explored. The analysis presented here represents a step forward toward the World Meteorological Organization's goal of global fusion products for accurately mapping harmful air pollution deposition.

Rubin, Hannah J. (ORCID:0000000182226924)↗

DOE OSTI2024

Quantifying Drivers of Methane Hydrobiogeochemistry in a Tidal River Floodplain System

The influence of coastal ecosystems on global greenhouse gas (GHG) budgets and their response to increasing inundation and salinization remains poorly constrained. In this study, we have integrated an uncertainty quantification (UQ) and ensemble machine learning (ML) framework to identify and rank the most influential processes, properties, and conditions controlling methane behavior in a freshwater floodplain responding to recently restored seawater inundation. Our unique multivariate, multiyear, and multi-site dataset comprises tidal creek and floodplain porewater observations encompassing water level, salinity, pH, temperature, dissolved oxygen (DO), dissolved organic carbon (DOC), total dissolved nitrogen (TDN), partial pressure of carbon dioxide (pCO 2 ), nitrous oxide (pN 2 O), methane (pCH 4 ), and the stable isotopic composition of methane (δ 13 CH 4 ). Additionally, we incorporated topographical data, soil porosity, hydraulic conductivity, and water retention parameters for UQ analysis using a previously developed 3D variably saturated flow and transport floodplain model for a physical mechanistic understanding of factors influencing groundwater levels and salinity and, therefore, CH 4 . Principal component analysis revealed that groundwater level and salinity are the most significant predictors of overall biogeochemical variability. The ensemble ML models and UQ analyses identified DO, water level, salinity, and temperature as the most influential factors for porewater methane levels and indicated that approximately 80% of the total variability in hourly water levels and around 60% of the total variability in hourly salinity can be explained by permeability, creek water level, and two van Genuchten water retention function parameters: the air-entry suction parameter α and the pore size distribution parameter m. These findings provide insights on the physicochemical factors in methane behavior in coastal ecosystems and their representation in local- to global-scale Earth system models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2011

Multi-Scale Hydrometeorological Modeling, Land Data Assimilation and Parameter Estimation with the Land Information System

The Land Information System (LIS; http://lis.gsfc.nasa.gov) is a flexible land surface modeling framework that has been developed with the goal of integrating satellite-and ground-based observational data products and advanced land surface modeling techniques to produce optimal fields of land surface states and fluxes. As such, LIS represents a step towards the next generation land component of an integrated Earth system model. In recognition of LIS object-oriented software design, use and impact in the land surface and hydrometeorological modeling community, the LIS software was selected as a co-winner of NASA?s 2005 Software of the Year award.LIS facilitates the integration of observations from Earth-observing systems and predictions and forecasts from Earth System and Earth science models into the decision-making processes of partnering agency and national organizations. Due to its flexible software design, LIS can serve both as a Problem Solving Environment (PSE) for hydrologic research to enable accurate global water and energy cycle predictions, and as a Decision Support System (DSS) to generate useful information for application areas including disaster management, water resources management, agricultural management, numerical weather prediction, air quality and military mobility assessment. LIS has e volved from two earlier efforts -- North American Land Data Assimilation System (NLDAS) and Global Land Data Assimilation System (GLDAS) that focused primarily on improving numerical weather prediction skills by improving the characterization of the land surface conditions. Both of GLDAS and NLDAS now use specific configurations of the LIS software in their current implementations.In addition, LIS was recently transitioned into operations at the US Air Force Weather Agency (AFWA) to ultimately replace their Agricultural Meteorology (AGRMET) system, and is also used routinely by NOAA's National Centers for Environmental Prediction (NCEP)/Environmental Modeling Center (EMC) for their land data assimilation systems to support weather and climate modeling. LIS not only consolidates the capabilities of these two systems, but also enables a much larger variety of configurations with respect to horizontal spatial resolution, input datasets and choice of land surface model through "plugins". LIS has been coupled to the Weather Research and Forecasting (WRF) model to support studies of land-atmosphere coupling be enabling ensembles of land surface states to be tested against multiple representations of the atmospheric boundary layer. LIS has also been demonstrated for parameter estimation, who showed that the use of sequential remotely sensed soil moisture products can be used to derive soil hydraulic and texture properties given a sufficient dynamic range in the soil moisture retrievals and accurate precipitation inputs.LIS has also recently been demonstrated for multi-model data assimilation using an Ensemble Kalman Filter for sequential assimilation of soil moisture, snow, and temperature.Ongoing work has demonstrated the value of bias correction as part of the filter, and also that of joint calibration and assimilation.Examples and case studies demonstrating the capabilities and impacts of LIS for hydrometeorological modeling, assimilation and parameter estimation will be presented as advancements towards the next generation of integrated observation and modeling systems

Peters-Lidard, Christa D.↗

NASA NTRS2020

Evaluation of Arctic Warming in Mid-Pliocene Climate Simulations

Palaeoclimate simulations improve our understanding of the climate, inform us about the performance of climate models in a different climate scenario, and help to identify robust features of the climate system. Here, we analyse Arctic warming in an ensemble of 16 simulations of the mid-Pliocene Warm Period (mPWP), derived from the Pliocene Model Intercomparison Project Phase 2 (PlioMIP2). The PlioMIP2 ensemble simulates Arctic (60–90∘ N) annual mean surface air temperature (SAT) increases of 3.7 to 11.6 ∘C compared to the pre-industrial period, with a multi-model mean (MMM) increase of 7.2 ∘C. The Arctic warming amplification ratio relative to global SAT anomalies in the ensemble ranges from 1.8 to 3.1 (MMM is 2.3). Sea ice extent anomalies range from −3.0 to −10.4×106 km2, with a MMM anomaly of −5.6×106 km2, which constitutes a decrease of 53 % compared to the pre-industrial period. The majority (11 out of 16) of models simulate summer sea-ice-free conditions (≤1×106 km2) in their mPWP simulation. The ensemble tends to underestimate SAT in the Arctic when compared to available reconstructions, although the degree of underestimation varies strongly between the simulations. The simulations with the highest Arctic SAT anomalies tend to match the proxy dataset in its current form better. The ensemble shows some agreement with reconstructions of sea ice, particularly with regard to seasonal sea ice. Large uncertainties limit the confidence that can be placed in the findings and the compatibility of the different proxy datasets. We show that while reducing uncertainties in the reconstructions could decrease the SAT data–model discord substantially, further improvements are likely to be found in enhanced boundary conditions or model physics. Lastly, we compare the Arctic warming in the mPWP to projections of future Arctic warming and find that the PlioMIP2 ensemble simulates greater Arctic amplification than CMIP5 future climate simulations and an increase instead of a decrease in Atlantic Meridional Overturning Circulation (AMOC) strength compared to pre-industrial period. The results highlight the importance of slow feedbacks in equilibrium climate simulations, and that caution must be taken when using simulations of the mPWP as an analogue for future climate change.

Palaeoclimate simulations↗

DOE OSTI2020

Pairing Correlations across the Superfluid Phase Transition in the Unitary Fermi Gas

In the two-component Fermi gas with a contact interaction, a pseudogap regime can exist at temperatures between the superfluid critical temperature $T_c$ and a temperature $T^\ast > T_c$. This regime is characterized by pairing correlations without superfluidity. However, in the unitary limit of infinite scattering length, the existence of this regime is still debated. To help address this, we have applied finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods to study the thermodynamics of the superfluid phase transition and signatures of the pseudogap in the spin-balanced homogeneous unitary Fermi gas. We present results at finite filling factor $\textit{ν}$ ≃ 0.06 for the condensate fraction, an energy-staggering pairing gap, the spin susceptibility, and the heat capacity, and compare them to experimental data when available. In contrast to previous AFMC simulations, our model space consists of the complete first Brillouin zone of the lattice, and our calculations are performed in the canonical ensemble of fixed particle number. The canonical ensemble AFMC framework enables the calculation of a model-independent gap, providing direct information on pairing correlations without the need for numerical analytic continuation. We use finite-size scaling to estimate $T_c$ at the corresponding filling factor. In this work, we find that the energy-staggering pairing gap vanishes above $T_c$, showing no pseudogap effects, and that the spin susceptibility shows a substantially reduced signature of a spin gap compared to previously reported AFMC simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Estuarine hurricane wind can intensify surge-dominated extreme water level in shallow and converging coastal systems

Based on the projected increase in hurricane landfall frequency on the middle to lower US east coast, we examined the crucial role of the estuarine wind field in exacerbating coastal flooding. A regionally refined atmospheric and two high-resolution hydrology and ocean models are integrated to provide plausible and physically consistent ensembles of hurricane events and the associated flooding inside the Delaware Bay and River, a US mid-Atlantic estuary. Model results show that the hurricane propagation direction, estuarine geometry, remote surge from the open ocean, and direct nearshore upwind stress could magnify the flood magnitude. More specifically, inland-bound tracks that make landfall before reaching the mid-Atlantic coast produce a more significant surge within Delaware Bay than the shore-parallel tracks, where the estuarine wind direction plays the primary role in surge amplification. Ultimately, this study emphasized the need for integrated models to capture the nonlinear dynamics and interactions in flood hazard modeling.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1981

A numerical model study of long-term planetary wave predictability

A numerical model was developed to study planetary wave behavior over periods up to 4 months under the influences of stochastic and diffusive forcing by synoptic scale motions and of sea surface temperature anomalies. The model is suitable for Monte Carlo experiments which provide ensemble mean and variance predictions and permit the response to heating anomalies to be partly separated from random variability. The model incorporates the linear-balanced dynamical equations for wind at two tropospheric levels and temperature at one level. The model atmosphere is forced by semiempirical January heating linearly dependent on local air temperature. Topography and the lower boundary layer are represented by vertical motion and drag functions, respectively, of the lower level wind. The linear phase speeds of Rossby waves are modified to reflect the effect of the stratosphere.

Wobus, R. L.↗

NASA NTRS2019

Forecasting the Ambient Solar Wind with Numerical Models. I. On the Implementation of an Operational Framework

The ambient solar wind conditions in interplanetary space and in the near-Earth environment are determined by activity on the Sun. Steady solar wind streams modulate the propagation behavior of interplanetary coronal mass ejections and are themselves an important driver of recurrent geomagnetic storm activity. The knowledge of the ambient solar wind flows and fields is thus an essential component of successful space weather forecasting. Here, we present an implementation of an operational framework for operating, validating, and optimizing models of the ambient solar wind flow on the example of Carrington Rotation 2077. We reconstruct the global topology of the coronal magnetic field using the potential field source surface model (PFSS) and the Schatten current sheet model (SCS) and discuss three empirical relationships for specifying the solar wind conditions near the Sun, namely the Wang–Sheeley (WS) model, the distance from the coronal hole boundary model (DCHB), and the Wang-Sheeley–Arge (WSA) model. By adding uncertainty in the latitude about the sub-Earth point, we select an ensemble of initial conditions and map the solutions to Earth by the Heliospheric Upwind eXtrapolation (HUX) model. We assess the forecasting performance from a continuous variable validation and find that the WSA model most accurately predicts the solar wind speed time series (RMSE≈83 km/s). We note that the process of ensemble forecasting slightly improves the forecasting performance of all solar wind models investigated. We conclude that the implemented framework is well suited for studying the relationship between coronal magnetic fields and the properties of the ambient solar wind flow in the near-Earth environment.

Reiss, Martin A.↗

DOE OSTI2024

Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs

Abstract We show that the quantum approximate optimization algorithm (QAOA) for higher-order, random coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p = 1 up to p = 5, which allows for computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool. We show that the best quantum processors find lower energy solutions up to p = 2 or p = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2010

Prediction Activities at NASA's Global Modeling and Assimilation Office

The Global Modeling and Assimilation Office (GMAO) is a core NASA resource for the development and use of satellite observations through the integrating tools of models and assimilation systems. Global ocean, atmosphere and land surface models are developed as components of assimilation and forecast systems that are used for addressing the weather and climate research questions identified in NASA's science mission. In fact, the GMAO is actively engaged in addressing one of NASA's science mission s key questions concerning how well transient climate variations can be understood and predicted. At weather time scales the GMAO is developing ultra-high resolution global climate models capable of resolving high impact weather systems such as hurricanes. The ability to resolve the detailed characteristics of weather systems within a global framework greatly facilitates addressing fundamental questions concerning the link between weather and climate variability. At sub-seasonal time scales, the GMAO is engaged in research and development to improve the use of land information (especially soil moisture), and in the improved representation and initialization of various sub-seasonal atmospheric variability (such as the MJO) that evolves on time scales longer than weather and involves exchanges with both the land and ocean The GMAO has a long history of development for advancing the seasonal-to-interannual (S-I) prediction problem using an older version of the coupled atmosphere-ocean general circulation model (AOGCM). This includes the development of an Ensemble Kalman Filter (EnKF) to facilitate the multivariate assimilation of ocean surface altimetry, and an EnKF developed for the highly inhomogeneous nature of the errors in land surface models, as well as the multivariate assimilation needed to take advantage of surface soil moisture and snow observations. The importance of decadal variability, especially that associated with long-term droughts is well recognized by the climate community. An improved understanding of the nature of decadal variability and its predictability has important implications for efforts to assess the impacts of global change in the coming decades. In fact, the GMAO has taken on the challenge of carrying out experimental decadal predictions in support of the IPCC AR5 effort.

Schubert, Siegfried↗

NASA NTRSDate not supplied

The Role of Internal Variability and Feedbacks Controlling AMOC Stability

A bi-stable mode of the Atlantic Meridional Overturning Circulation (AMOC) is found in a 10-member ensemble simulation of the SSP2-4.5 scenario using the NASA GISS-E2-1-G climate model. Local feedbacks in the subpolar North Atlantic region in conjunction with internal variability in sea-ice transport and melt play a critical role in causing the divergent behavior of the AMOC in the ensemble members. While other fully coupled models have demonstrated the important role of surface freshening in leading to AMOC shutdown, either through hosing experiments or increased precipitation and greenhouse gas warming at high latitudes, in the GISS simulations, there are no external freshwater perturbations. This is the first time that a CMIP-class model has shown such a bifurcation across an initial condition ensemble.

Atlantic Meridional Overturning Circulation↗

DOE OSTI2024

An Entropy-Based Test and Development Framework for Uncertainty Modeling in Level-Set Visualizations

We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly influences the memory use, run time, and accuracy of an uncertainty visualization algorithm. We use an entropy calculation directly on ensemble data to establish an expected result and then compare the entropy from various probability models, including uniform, Gaussian, histogram, and quantile models. Our results verify that models matching the distribution of the ensemble indeed match the entropy. We further show that fewer bins in nonparametric histogram models are more effective whereas large numbers of bins in quantile models approach data accuracy.

Sisneros, Robert↗

DOE OSTI2024

Data-driven closure modeling for hypersonic turbulent flows

The Reynolds-averaged Navier–Stokes (RANS) equations remain a workhorse technology for simulating compressible fluid flows of practical interest. Due to model-form errors, however, RANS models can yield erroneous predictions that preclude their use on mission-critical problems. This report summarizes work performed from FY22-FY24 focused on improving RANS models for hypersonic flows using data-driven modeling and scientific machine learning. In this work we: 1. Investigate the current capabilities of RANS models in Sandia’s parallel aerodynamics and re-entry code (SPARC) for hypersonic flows with a focus on shock boundary layer interactions (SBLIs), 2. Assess several established corrections that exist in the literature aimed at improving predictions for SBLIs, 3. Develop improved models for the Reynolds stress tensor using tensor-basis neural networks, 4. Develop a neural-network-based variable turbulent Prandtl number model to reduce errors in wall heating in SBLIs. 5. Begin future investigations including employing the LIFE framework to improve wall heating predictions in SBLIs as well as the ensemble Kalman filter. We find that current RANS models in SPARC are deficient for complex SBLI flows. In particular, no current model jointly predicts wall heat flux, wall shear stress, and wall pressure with reasonable accuracy. Existing corrections help, but do not alleviate this issue altogether. The development of improved models for the Reynolds stress tensor via tensor-basis neural networks results in more predictive RANS models across a suite of low-speed and high-speed cases. For hypersonic boundary layers, the inclusion of the wall-normal Reynolds stress via TBNNs has an appreciable impact on the wall-normal momentum balance and wall quantities. However, we find that improvements to the Reynolds stress tensor do not address the over-prediction in wall heat flux in SBLIs. We find that a neural-network-based variable turbulent Prandtl number model systematically and substantially improves wall heating predictions for a range of SBLI cases.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1999

Potential Predictability of the Monsoon Subclimate Systems

While El Nino/Southern Oscillation (ENSO) phenomenon can be predicted with some success using coupled oceanic-atmospheric models, the skill of predicting the tropical monsoons is low regardless of the methods applied. The low skill of monsoon prediction may be either because the monsoons are not defined appropriately or because they are not influenced significantly by boundary forcing. The latter characterizes the importance of internal dynamics in monsoon variability and leads to many eminent chaotic features of the monsoons. In this study, we analyze results from nine AMIP-type ensemble experiments with the NASA/GEOS-2 general circulation model to assess the potential predictability of the tropical climate system. We will focus on the variability and predictability of tropical monsoon rainfall on seasonal-to-interannual time scales. It is known that the tropical climate is more predictable than its extratropical counterpart. However, predictability is different from one climate subsystem to another within the tropics. It is important to understand the differences among these subsystems in order to increase our skill of seasonal-to-interannual prediction. We assess potential predictability by comparing the magnitude of internal and forced variances as defined by Harzallah and Sadourny (1995). The internal variance measures the spread among the various ensemble members. The forced part of rainfall variance is determined by the magnitude of the ensemble mean rainfall anomaly and by the degree of consistency of the results from the various experiments.

Yang, Song↗

NASA NTRS2014

Development of Super Ensemble-Based Aviation Turbulence Guidance (SEATG) for Air Traffic Management

A new method for forecasting turbulence is developed and evaluated using the high resolution weather model and in situ turbulence observations from commercial aircraft. The new method is an ensemble of various turbulence metrics from multiple time-lagged ensemble forecasts created using a sequence of four procedures. These include weather modeling, calculation of turbulence metrics, mapping the metrics into a common turbulence-scale, and production of final forecast. The new method uses similar methodology as current operational turbulence forecast with three improvements. First, it uses a higher resolution ((delta)x = 3 km) weather model to capture cloud resolving scale phenomena. Second, it computes the metrics for multiple forecasts that are combined at the same valid time resulting in a time-lagged ensemble of multiple turbulence metrics. Finally, it provides both deterministic and probabilistic turbulence forecasts. Results show the new forecasts match well with observed radar reflectivity along a surface front as well as convectively induced turbulence outside the clouds on research period. Overall performance skill of the new turbulence forecast compared with the observed EDR data during the research period is superior to any single turbulence metric. The probabilistic turbulence forecast is used in an example air traffic management application for creating a wind-optimal route considering turbulence information. The wind-optimal route passing through areas of 50% potential for moderate-or-greater turbulence and the lateral turbulence avoidance routes starting from three different waypoints along the wind-optimal route from Los Angeles international airport to John F. Kennedy international airport are calculated using different turbulence forecasts. This example shows additional flight time is required to avoid potential turbulence encounters.

modeling↗