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At least 253 records · Page 14

Cloud Impacts on Photochemistry: Building a Climatology of Photolysis Rates from the Atmospheric Tomography Mission

Measurements from actinic flux spectroradiometers on board the NASA DC-8 during the Atmospheric Tomography (ATom) mission provide an extensive set of statistics on how clouds alter photolysis rates (J values) throughout the remote Pacific and Atlantic Ocean basins. J values control tropospheric ozone and methane abundances, and thus clouds have been included for more than three decades in tropospheric chemistry modeling. ATom made four profiling circumnavigations of the troposphere capturing each of the seasons during 2016–2018. This work examines J values from the Pacific Ocean flights of the first deployment, but publishes the complete Atom-1 data set (29 July to 23 August 2016). We compare the observed J values (every 3 s along flight track) with those calculated by nine global chemistry– climate/transport models (globally gridded, hourly, for a mid-August day). To compare these disparate data sets, we build a commensurate statistical picture of the impact of clouds on J values using the ratio of J -cloudy (standard, sometimes cloudy conditions) to J -clear (artificially cleared of clouds). The range of modeled cloud effects is inconsistently large but they fall into two distinct classes: (1) models with large cloud effects showing mostly enhanced J values aloft and or diminished at the surface and (2) models with small effects having nearly clear-sky J values much of the time. The ATom-1 measurements generally favor large cloud effects but are not precise or robust enough to point out the best cloud-modeling approach. The models here have resolutions of 50–200 km and thus reduce the occurrence of clear sky when averaging over grid cells. In situ measurements also average scattered sunlight over a mixed cloud field, but only out to scales of tens of kilometers. A primary uncertainty remains in the role of clouds in chemistry, in particular, how models average over cloud fields, and how such averages can simulate measurements.

actinic flux spectroradiometers↗

Saturn Atmospheric Dynamics One Year After Cassini: Long-Lived Features and Time Variations in the Drift of the Hexagon

We examine Saturn's atmospheric dynamics with observations in the visible range from ground-based telescopes and Hubble Space Telescope (HST). We present a detailed analysis of observations acquired during 2018 obtaining drift rates of major meteorological systems from the equator to the North polar hexagon. A system of polar storms that appeared in the planet in March 2018 and remained active with a complex phenomenology at least until September is analyzed elsewhere [Sanchez-Lavega et al., 2019]. Many of the regular cloud features visible in 2018 are long-lived and can be identified in Saturn images in 2017, and in some cases, for up to a decade using also Cassini ISS images. Without considering the polar storms, the most interesting long-lived cloud systems are: i) A bright white spot in the Equatorial Zone that can be tracked continuously since 2014 with minimal changes in its zonal velocity, which was 444:3 +or- 3:1 ms(exp -1) in 2014 and 452:4 + or - 1:7 ms(exp -1) in 2018. This velocity is remarkably different from the zonal winds at the cloud level at its latitude during the Cassini mission, and is closer to zonal winds obtained at the time of the Voyagers flybys and to zonal winds from Cassini VIMS infrared images of the lower atmosphere. ii) A large long-lived Anticyclone Vortex, here AV, that formed after the Great White Spot of 2010-2011. This vortex has changed significantly in visual contrast, drift rate and latitude with minor changes in size over the last years. iii) A system of subpolar vortices at latitudes 60-65N present at least since 2011. These vortices and additional atmospheric features here studied follow drift rates consistent with zonal winds obtained by Cassini. We also present a study of the positions of the vertices of Saturn's North polar hexagon from 2015 to 2018. These measurements are compared with previous analyses during the Cassini mission (2007-2014), observations with HST in the 90s, and data from the Voyagers in 1980-1981 to explore the long term variability of the hexagon's drift rate. We find variations in the drift rate of the hexagon through these epochs that can not be fit by seasonal changes in the polar area. Instead, the different drift rates reinforce the role of the North Polar Spot that was present in the Voyager epoch and in the early 90s to cause a faster drift rate of the hexagon at that time compared with the current slower one.

R Hueso↗

Comparative Study of Active Flow Control Strategies for Lift Enhancement of a Simplified High-Lift Configuration

Numerical simulations have been performed for a simplified high-lift (SHL) version of the Common Research Model (CRM) configuration, where the Fowler flaps of the conventional high-lift (CRM-HL) configuration are replaced by a set of simple hinged flaps. These hinged flaps are equipped with integrated modular active flow control (AFC) cartridges on the suction surface, and the resulting geometry is known as the CRM-SHL-AFC configuration. The main objective is to make use of AFC devices on the CRM-SHL-AFC configuration to recover the aerodynamic performance (lift) of the CRM-HL configuration. In the current paper, a Lattice Boltzmann method-based computational fluid dynamics (CFD) code, known as PowerFLOWQ® is used to simulate the entire flow field associated with the CRM-SHL-AFC configuration equipped with several different types of AFC devices. The transonic version of the PowerFLOWQ® code that has been validated for high speed flows is used to accurately simulate the flow field generated by the high-momentum actuators required to mitigate reversed flow regions on the suction surfaces of the main wing and the flap. The numerical solutions predict the expected trends in aerodynamic forces as the actuation levels are increased. More efficient AFC systems and actuator arrangements emerged based on the parametric studies performed prior to a Fall 2018 wind tunnel test. Preliminary comparisons of the numerical solutions for lift and surface pressures are presented here with the experimental data, demonstrating the usefulness of CFD for predicting the flow field and lift characteristics of AFC-enabled high-lift configurations.

Vatsa, Veer N.↗

CALIPSO Level 3 Stratospheric Aerosol Product: Version 1.00 Algorithm Description and Initial Assessment

In August 2018,the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) project released a new level 3 stratospheric aerosol profile data product derived from nearly 12 years of measurements acquired by the space-borne Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP).This monthly averaged, gridded level 3 product is based on version 4.2 of the CALIOP level 1 and level 2 data products, which feature significantly improved calibration that now makes it possible to reliably retrieve profiles of stratospheric aerosol extinction and backscatter coefficients. This paper describes the science algorithm and data handling techniques that were developed to generate the CALIPSO version 1.00 level 3 stratospheric aerosol profile product. Further, we show that the retrieved extinction profiles capture the major stratospheric perturbations over the last decade resulting from volcanic eruptions, extreme smoke events, and signatures of stratospheric dynamics. Initial assessment of the product by inter-comparison with the stratospheric aerosol retrievals from the Stratospheric Aerosol and Gas Experiment III (SAGE III) on the International Space Station (ISS) indicates good agreement in the tropical stratospheric aerosol layer (30oN-30oS),where the average difference between zonal mean extinction profiles is typically less than 25% between 20km and 30km. However, differences can exceed 100% in the very low aerosol loading regimes found above 25 km at higher latitudes.

Jayanta Kar↗

Astrobee On-Orbit Commissioning

The Astrobee free flying robots operate in the interior of the International Space Station (ISS) under supervisory control of a ground operator or ISS crew. They replace the Synchronized Position Hold Engage and Reorient Experimental Satellites (SPHERES) as research platforms for zero-g free-flying robotics. Astrobee also provides a tool for improving the efficiency of ISS operations as a mobile camera/sensor platform available to flight and payload controllers. The Astrobee system consists of three robots with perching arms, a docking station, and a ground data system. Development began in late-2014, and flight hardware has been deployed to ISS on several launches starting in November 2018 and concluding in October 2019. Shortly after the first two robots arrived on ISS in April, we began a series of "commissioning" activities to validate both space and ground segments. We plan to complete commissioning and become an operational facility available to guest scientists by the end of 2019. This paper provides an overview of the Astrobee system, a description of the on-orbit activities, and commissioning results.

ISS↗

S-NPP and N20 VIIRS RSB Bands Detector-to-Detector Calibration Differences Assessment Using a Homogeneous Ground Target

The S-NPP and N20 satellites have successfully operated since their launches on October 28, 2011 and November 18, 2017, respectively. This paper provides an assessment of the detector calibration stability for the reflective solar bands (RSBs) observed from both S-NPP and N20 VIIRS. Top-of-atmosphere radiances from near-nadir observations over the homogeneous Libya 4 desert site are extracted from the S-NPP VIIRS Collection 1 and N20 Collection 2 Level-1B products. The radiances from individual detectors per Half‐angle Mirror side are studied. The comparisons of the normalized radiance to all detector average values indicate that the detector calibration differences are wavelength dependent. The S-NPP detector differences have been slowly increasing in the past 8.5 years and bands M1-M4 have 1.3%- 2.2% detector differences in 2019. N20 detector differences are stable and small in the past two years except SWIR M bands. N20 M10 and M11 have 1.3% and 2.1% detector differences, respectively. S-NPP DNB detector differences are about 0.8% and N20 DNB detector differences are about 0.5%. Most bands HAM side differences are less than 0.25% in the past years except N20 VIIRS M1 HAM side differences are 0.57% in 2018 and 0.54% in 2019. The Libya 4 images have small but noticeable striping in S-NPP M1-M4 data as well as in N20 M1, M8, M10, and M11 data. These study results have been applied in the S-NPP Collection 2 new algorithm to remove the detector differences. This research help scientists and VIIRS users better understand detector calibration differences in different version VIIRS products.

Libya 4↗

Astrobee On-Orbit Commissioning

The Astrobee free flying robots operate in the interior of the International Space Station (ISS) under supervisory control of a ground operator or ISS crew. They replace the Synchronized Position Hold Engage and Reorient Experimental Satellites (SPHERES) as research platforms for zero-g free-flying robotics. Astrobee also provides a tool for improving the efficiency of ISS operations as a mobile camera/sensor platform available to flight and payload controllers. The Astrobee system consists of three robots with perching arms, a docking station, and a ground data system. Development began in late-2014, and flight hardware has been deployed to ISS on several launches starting in November 2018 and concluding in October 2019. Shortly after the first two robots arrived on ISS in April, we began a series of “commissioning” activities to validate both space and ground segments. This paper provides an overview of the Astrobee system, a description of the on-orbit activities, and commissioning results.

Astrobee↗

Environmental Benefits Assessment of the Traffic Aware Strategic Aircrew Requests Concept

Reduction of greenhouse gas emissions has been a focus area of the scientific community for the past several years. Specifically, the aviation industry has set goals to reduce greenhouse gas emissions, providing a sustainable transportation mechanism with minimal impacts on the environment. This reduction must be accomplished through several means, including advanced technology, sustainable propulsion, efficient air traffic management, and improved operations. A potential solution for improving operations in an efficient air traffic management system is the Traffic Aware Strategic Aircrew Requests (TASAR) concept. The TASAR concept applies onboard automation for the purpose of advising the pilot of route modifications that would be beneficial to the flight, leading to a decrease in direct operating costs through fuel burn reduction and shorter flight times. This report discusses analyses that provide an estimate of the potential environmental benefits that result from the application of the TASAR concept. The data used for this benefits assessment was gathered during an operational evaluation on revenue flights with an airline partner between July 2018 and April 2019. The analyses in this report determined that there are impactful potential environmental benefits to be realized using the TASAR concept.

TASAR, Digital TASAR, 4D TASAR, SATM, Green Aviati↗

Retrievals of Aerosol Optical Depth and Spectral Absorption from DSCOVR EPIC

A new algorithm is described for joint retrievals of the aerosol optical depth and spectral absorption from EPIC observations in the UV—Vis spectral range. The retrievals are illustrated on examples of the wildfire smoke events over North America, and dust storms over greater Sahara region in 2018. An initial evaluation of single scattering albedo (SSA) at 443 nm over these regions shows a good agreement with AERONET data, generally within the uncertainty of AERONET SSA of ± 0.03. A particularly good agreement is achieved for dust with R∼0.62, rmse∼0.02, negligible bias, and 85% points within the expected error. This new capability is part of version 2 MAIAC EPIC algorithm. The v2 algorithm has recently completed reprocessing of the EPIC record covering the period of 2015–2020.

EPIC↗

Global Total Ozone Recovery Trends Attributed to Ozone-Depleting Substance (ODS) Changes Derived From Five Merged Ozone Datasets

We report on updated trends using different merged zonal mean total ozone datasets from satellite and ground-based observations for the period from 1979 to 2020. This work is an update of the trends reported in Weber et al. (2018) using the same datasets up to 2016. Merged datasets used in this study include NASA MOD v8.7 and NOAA Cohesive Data (COH) v8.6, both based on data from the series of Solar Backscatter Ultraviolet (SBUV), SBUV-2, and Ozone Mapping and Profiler Suite (OMPS) satellite instruments (1978–present), as well as the Global Ozone Monitoring Experiment (GOME)-type Total Ozone – Essential Climate Variable (GTO-ECV) and GOME-SCIAMACHY-GOME-2 (GSG) merged datasets (both 1995–present), mainly comprising satellite data from GOME, SCIAMACHY, OMI, GOME-2A, GOME-2B, and TROPOMI. The fifth dataset consists of the annual mean zonal mean data from ground-based measurements collected at the World Ozone and Ultraviolet Radiation Data Centre (WOUDC). Trends were determined by applying a multiple linear regression (MLR) to annual mean zonal mean data. The addition of 4 more years consolidated the fact that total ozone is indeed slowly recovering in both hemispheres as a result of phasing out ozone-depleting substances (ODSs) as mandated by the Montreal Protocol. The near-global (60° S–60° N) ODS-related ozone trend of the median of all datasets after 1995 was 0.4 ± 0.2 (2σ) %/decade, which is roughly a third of the decreasing rate of 1.5 ± 0.6 %/decade from 1978 until 1995. The ratio of decline and increase is nearly identical to that of the EESC (equivalent effective stratospheric chlorine or stratospheric halogen) change rates before and after 1995, confirming the success of the Montreal Protocol. The observed total ozone time series are also in very good agreement with the median of 17 chemistry climate models from CCMI-1 (Chemistry-Climate Model Initiative Phase 1) with current ODS and GHG (greenhouse gas) scenarios (REF-C2 scenario). The positive ODS-related trends in the Northern Hemisphere (NH) after 1995 are only obtained with a sufficient number of terms in the MLR accounting properly for dynamical ozone changes (Brewer–Dobson circulation, Arctic Oscillation (AO), and Antarctic Oscillation (AAO)). A standard MLR (limited to solar, Quasi-Biennial Oscillation (QBO), volcanic, and El Niño–Southern Oscillation (ENSO)) leads to zero trends, showing that the small positive ODS-related trends have been balanced by negative trend contributions from atmospheric dynamics, resulting in nearly constant total ozone levels since 2000.

Total Column Ozone Trends↗

Springtime SEA Air Is Consistently Both Smoky and Humid, but This Relationship (and Its Radiative Effects) Varies Spatially and Seasonally

The atmosphere over the southeast Atlantic Ocean (SEA) sees a consistent springtime biomass burning (BB) smoke from widespread agricultural fires on the African continent. This smoke layer is initially lofted high in a continental mixed layer (~5-6km) and is then transported westward in the free troposphere, where it overlies and ultimately mixes into the SEA stratocumulus-topped oceanic boundary layer. Coincident with this smoke is an elevated humidity signal which is present from the time a given airmass is over the continental source region. ORACLES (ObseRvations of Aerosols above CLouds and their intEractionS) was a NASA Earth Venture Suborbital mission with the goal of measuring aerosol, cloud, and atmospheric properties over this region during three deployments in September 2016, August 2017, and October 2018. A previous study discussed the spatial characteristics of the water vapor-BB plume observations in the September 2016 flight data and their degree of agreement with several atmospheric reanalyses and models. In the present work, we first discuss atmospheric chemistry, structure, and aerosol results from all three ORACLES deployments to place these results in a broader seasonal context. Despite the differing locations and season of each deployment, we show that there continues to be good agreement between the airborne ORACLES dataset and large-scale reanalyses, specifically the ECMWF ERA5 and CAMS reanalyses. Other reanalyses (specifically NASA's MERRA-2) preserved the observed correlation between meteorology and biomass burning conditions, but, as was seen for 2016, was frequently displaced spatially relative to the observations. The CAMS reanalysis performs better with water vapor than with CO. Results comparing CAMS column AOD to the field measurements show slight overestimates, consistent with previous analysis, but the good relationship observed between AOD and inlet-based aerosol extinction demonstrates this metric's utility to broader studies. The good ERA5/CAMS/ORACLES agreement allows us to next examine the multi-year seasonal patterns and trends beyond the three ORACLES deployment periods. Looking at seven years of reanalysis data for the BB season, we find distinct variations between each month/deployment in terms of vertical smoke distribution and correlation to atmospheric specific humidity, due to changing conditions through the BB season. Using k-means clustering of these climatological reanalysis, we identify six canonical atmospheric profile types of varying total atmospheric humidity and vertical structure and describe their changing incidence spatially and throughout the season, and six analogous profile types for carbon monoxide, allowing us to characterize the atmospheric structure of both vapor and BB over time throughout the SEA region. This classification will allow for a more complete analysis of the broader radiative and dynamical effects of humid aerosols overlying stratocumulus clouds.

Kristina Marie Myers Pistone↗

Key Perseverance Sampling Locations for the Ancient Martian Crust and Implications for Mars Science

Since Feb 2021, the Perseverance rover has collected samples in the Jezero crater. The plan baselined at the 2018 landing site selection, subsequently further developed by the Mars-2020 team, and presented to the Decadal Survey included the exploration and sampling of the Jezero crater rim and the Nili Planum area, a rock record that is important to preserving the science return of the endeavor. Specifically, the science team identified the following prioritized science objectives aligned with community objectives that are not covered by the current sample cache: 1) Investigate the habitable environments with potential biosignatures from a more ancient time interval and from a diverse set of geological environments (incl. exposed subsurface) than the Jezero crater sedimentary deposits (Fig. 2). (2) Determine radioisotopic ages for well-defined craterretaining surfaces and/or the Isidis basin impact event. (3) Characterize ancient aqueous environments to study climate, environmental transitions, and habitability on ancient Mars. (4) Investigate planetary accretion, crustal evolution, and dynamo activity through analysis and sampling of igneous lithologies. (5) Study the geology of basin-forming impacts. In addition, for the Jezero rim and any Jezero ejecta: (6) Analyze Jezero impactites for potentially habitable hydrothermal environments and radioisotopic dating of the Jezero crater formation. From 2018 to now, we used a combination of High Resolution Imaging Experiment (HiRISE) and Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) data to further characterize Jezero rim and Nili Planum, culminating in our prioritized sample location recommendations: (1) Monument Valley and (2) Northwest Jezero rim.

Mars sample return↗

A Note on the Temporary Misregistration of Landsat-8 Operational Land Imager (OLI) and Sentinel-2 Multi Spectral Instrument (MSI) Imagery

The Landsat-8 and Sentinel-2 sensors provide multi-spectral image data with similar spectral and spatial characteristics that together provide improved temporal coverage globally. Both systems are designed to register Level 1 products to a reference image framework, however, the Landsat-8 framework, based upon the Global Land Survey images, contains residual geolocation errors leading to an expected sensor-to-sensor misregistration of 38 m (2sigma). These misalignments vary geographically but should be stable for a given area. The Landsat framework will be readjusted for consistency with the Sentinel-2 Global Reference Image, with completion expected in 2018. In the interim, users can measure Landsat-to-Sentinel tie points to quantify the misalignment in their area of interest and if appropriate to reproject the data to better alignment.

Storey, James↗

Clouds Around the World: How a Simple Citizen Science Data Challenge Became a Worldwide Success

Citizen science is often recognized for its potential to directly engage the public in science, and is uniquely positioned to support and extend participants’ learning in science. In March 2018, the Global Learning and Observations to Benefit the Environment (GLOBE) Program, NASA’s largest and longest-lasting citizen science program about Earth, organized a month-long event that asked people around the world to contribute daily cloud observations and photographs of the sky (15 March–15 April 2018). What was considered a simple engagement activity turned into an unprecedented worldwide event that garnered major public interest and media recognition, collecting over 55,000 observations from 99 different countries, in more than 15,000 locations, on every continent including Antarctica. The event was called the “Spring Cloud Challenge” and was created to 1) engage the general public in the scientific process and promote the use of the GLOBE Observer app, 2) collect ground-based visual observations of varying cloud types during boreal spring, and 3) increase the number and locations of ground-based visual cloud observations collocated with cloud-observing satellites. The event resulted in roughly 3 times more observations than during the historic and highly publicized 2017 North American total solar eclipse. The dataset also includes observations over the Drake Passage in Antarctica and reports from intense Saharan dust events. This article describes how the challenge was crafted, outreach to volunteer scientists around the world, details of the data collected, and impact of the data.

GLOBE↗

Joint Observation Estimates of XCO2

Localized, correlated biases exist in OCO-2 (Orbiting Carbon Observatory-2) data. These biases do not improve with averaging. These have been noted by O'Dell (various OCO-2 telecons), Worden (2017), Kulawik (2018). We propose to utilize information from adjacent observations to reduce this bias. This works on the assumption that grouping the observations allows the system to find a better, global minimum. Pooling adjacent observations could allow more accurate characterization of interferents (e.g. retrieving additional albedo parameters), reducing entanglement with CO2.

Kulawik, Susan S.↗

The High-Energy Emission from HD 93129A Near Periastron

We conducted an observational campaign towards one of the most massive and luminous colliding wind binaries in the Galaxy, HD 93129A, close to its periastron passage in 2018. During this time the source was predicted to be in its maximum of high-energy emission. Here we present our data analysis from the X-ray satellites Chandra and NuSTAR and the γ-ray satellite AGILE. High-energy emission coincident with HD 93129A was detected in the X-ray band up to 18 keV, whereas in the γ-ray band only upper limits were obtained. We interpret the derived fluxes using a non-thermal radiative model for the wind-collision region. We establish a conservative upper limit for the fraction of the wind kinetic power that is converted into relativistic electron acceleration, f(NT,e) < 0.02. In addition, we set a lower limit for the magnetic field in the wind-collision region as BWCR > 0.3 G. We also argue a putative interpretation of the emission from which we estimate f(NT,e) ≈ 0.006 and B(WCR) ≈ 0.5 G. We conclude that multi-wavelength, dedicated observing campaigns during carefully selected epochs are a powerful tool for characterising the relativistic particle content and magnetic field intensity in colliding wind binaries.

S del Palacio↗

Algorithm Theoretical Basis Document (ATBD) - Stream Stage Measurements: V2.5.1 Water Level Products from Satellite Radar Altimetry

In response to the 2018 NASA ROSES Applied Sciences/Water Resources (NASA HQ Program Official: Dr. Brad Doorn) call for proposals, the “Integration of Remotely Sensed Streamflow Data into Alaska Water Resource Management Agency Operations” project with Principal Investigator (PI) Jack Eggleston USGS, was successful, and had the ultimate goal of creating a series of remotely sensed or derived Alaska river parameters for integration into NWIS. These parameters included surface water height and average reach surface water slope (from altimetry), average reach width (from Landsat imagery), and an associated river discharge derived via theoretical means. The surface water height products were required to have both archival and near real time components, noting the availability of ~25years of potential measurements, and accepting the temporal resolution (10-35days) of the suite of radar altimeters. Each surface water level product was expected to be a continuous time series of observation with a sufficient accuracy to highlight monthly, seasonal and interannual variation. The designated set of river reaches were chosen for their geographical distribution, their reach width, and the presence of a radar altimeter mission satellite overpass. This document describes the procedure associated with the creation of these altimetric surface water level products and is relevant to product Version 2.5.1 available from the Global Water Monitor (GWM) web portal.

Altimetry↗

Radiometric Stability in 16 years of AIRS Hyperspectral Infrared Data (SPIE OP-431-20)

With global warming at the rate of 10 mK/yr, it is important to at least characterize any trend in the AIRS data, which may impact the use of AIRS data for climate change research. We evaluated the stability of the AIRS v5 calibration for seven atmospheric window channels between 2002 and 2018 under tropical ocean clear conditions. Trends for the channels between 961, 1128 and 1231 cm-1 channels are typically +3 mK/yr; for 790 and 901 cm-1 the trend is 6 mK/yr, i.e. the observations are increasingly getting warmer than expected. The trends are day/night consistent. The trend for the 2508 and 2616 cm-1 channels is close to 10 mK/yr at night, but closer to 6 mK/yr during the day. On an absolute scale these trends are small, but not when viewed in the context of global warming at a 10 mK/yr rate. While the warming trends are consistent with increased scattering from the scan mirrors, which create an error in reading the Onboard Blackbody Calibration, the resulting changes in the gain are a factor of about five larger than observed changes in the gain. The effects of scattering due to scan mirror contamination are evident at extremely cold temperatures, but scattering does not produce the observed warming at warm temperatures. It is possible that much of the observed warming in the AIRS window channels is a geophysical effect related to the warming of the oceans, resulting in a shift in the diurnal cycle and skin effect correction. This requires more careful evaluation.

Manning, Evan M.↗