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NASA NTRS2025

Mind the Gap: Addressing Data Gaps and Assessing Noise Mismodeling in LISA

Due to the sheer complexity of the Laser Interferometer Space Antenna (LISA) space mission, data gaps arising from instrumental irregularities and/or scheduled maintenance are unavoidable. Focusing on merger-dominated massive black hole binary signals, we test the appropriateness of the Whittle-likelihood on gapped data in a variety of cases. From first principles, we derive the likelihood valid for gapped data in both the time and frequency domains. Cheap-to-evaluate proxies to p-p plots are derived based on a Fisher-based formalism, and verified through Bayesian techniques. Our tools allow to predict the altered variance in the parameter estimates that arises from noise mismodeling, as well as the information loss represented by the broadening of the posteriors. The result of noise mismodeling with gaps is sensitive to the characteristics of the noise model, with strong low-frequency (red) noise and strong high-frequency (blue) noise giving statistically significant fluctuations in recovered parameters. We demonstrate that the introduction of a tapering window reduces statistical inconsistency errors, at the cost of less precise parameter estimates. We also show that the assumption of independence between inter-gap segments appears to be a fair approximation even if the data set is inherently coherent. However, if one instead assumes fictitious correlations in the data stream, when the data segments are actually independent, then the resultant parameter recoveries could be inconsistent with the true parameters. The theoretical and numerical practices that are presented in this work could readily be incorporated into global-fit pipelines operating on gapped data.

LISA↗

NASA NTRS2007

High-Resolution WRF Forecasts of Lightning Threat

Tropical Rainfall Measuring Mission (TRMM)lightning and precipitation observations have confirmed the existence of a robust relationship between lightning flash rates and the amount of large precipitating ice hydrometeors in storms. This relationship is exploited, in conjunction with the capabilities of the Weather Research and Forecast (WRF) model, to forecast the threat of lightning from convective storms using the output fields from the model forecasts. The simulated vertical flux of graupel at -15C is used in this study as a proxy for charge separation processes and their associated lightning risk. Initial experiments using 6-h simulations are conducted for a number of case studies for which three-dimensional lightning validation data from the North Alabama Lightning Mapping Array are available. The WRF has been initialized on a 2 km grid using Eta boundary conditions, Doppler radar radial velocity and reflectivity fields, and METAR and ACARS data. An array of subjective and objective statistical metrics is employed to document the utility of the WRF forecasts. The simulation results are also compared to other more traditional means of forecasting convective storms, such as those based on inspection of the convective available potential energy field.

Goodman, S. J.↗

NASA NTRS2016

Connecting Paleo and Modern Oceanographic Data to Understand Atlantic Meridional Overturning Circulation Over Decades to Centuries

Modeling is an important tool for understanding AMOC on all timescales. Mechanistic studies of modern AMOC variability have been hampered by a lack of consistency between free-running models and the sensitivity of AMOC to resolution and parameterization. Recent work within the framework of the phase two Coordinated Ocean- Reference Experiments (CORE-II) addresses this issue head on, looking at model differences of AMOC mean state and interannual variability. One consistent feature across the models is that AMOC mean transport is related to mixed layer depths and Labrador Sea salt content, whereas interannual variability is primarily associated with Labrador Sea temperature anomalies. This is consistent with the hypothesized importance of salt balance for AMOC variability on geological timescales. The simulated relationships between AMOC and subsurface temperature anomalies in fully coupled climate models reveal subsurface AMOC fingerprints that could be used to reconstruct historical AMOC variations at low frequency.With the lack of long-term AMOC observations, models of ocean state that assimilate observational data have been explored as a way to reconstruct AMOC, but comparisons between models indicate they are quite variable in their AMOC representations. Karspeck et al. (2015) found that historical reconstructions of AMOC in such models are sensitive to the details of the data assimilation procedure. The ocean data assimilation community continues to address these issues through improved models and methods for estimating and representing error information.Two objectives of paleoclimate modeling are 1) to provide mechanistic information for interpretation of paleoclimate observations, and 2) to test the ability of predictive models to simulate Earth's climate under different background forcing states. In a good example of the first objective, Schmittner and Lund (2015) and Menviel et al. (2014) provided key information about the proxy signals expected under freshwater disturbance of AMOC, which were used to support the paleoclimate observations made by Henry et al. (2016). In an example of the second objective, Muglia and Schmittner (2015) analyzed Third Paleoclimate Modeling Intercomparison Project (PMIP3) models of the Last Glacial Maximum (LGM) and found consistently more intense and deeper AMOC transports relative to preindustrial simulations, counter to the paleoclimate consensus of LGM conditions, indicating that some processes are not well represented in the PMIP3 models. One challenge is to find adequate paleo observations against which to test these models. PMIP is now in phase 4 (part of CMIP6), which includes experiments covering five periods in Earth's history: the last millennium, last glacial maximum, last interglacial, and the mid-Pliocene. Newly compiled paleoclimate datasets from the PAGES2k project, more transient simulations, and participation of isotope enabled models planned for CMIP6PMIP4 will enable richer paleo data-model comparisons in the near future.

Kilbourne, Hali↗

NASA NTRS2007

The Impact on EOP Predictions of AAM Forecasts from the ECMWF and NCEP

Predictions of UT1 are improved when dynamical model-based forecasts of the axial component of atmospheric angular momentum (AAM) are used as proxy length-of-day (LOD) forecasts (Freedman et al. 1994; Johnson et al. 2005). For example, the accuracy of JPL's predictions of UT1 are improved by nearly a factor of 2 when AAM forecast data from the National Centers for Environmental Prediction (NCEP) are used. Given the importance of AAM forecasts on the accuracy of UT1 predictions, other sources of AAM forecasts should be sought. Here, the angular momentum of the forecasted wind fields from the European Centre for Medium-Range Weather Forecasts (ECMWF) are computed and used to predict UT1. The results are compared to those obtained using NCEP forecasts.

atmospheric angular momentum (AAM)↗

NASA NTRS1998

Study of Magnetic Structure in the Solar Photosphere and Chromosphere

This grant funded an observational and theoretical program to study the structure and dynamics of the solar photosphere and low chromosphere, and the spectral signatures that result. The overall goal is to learn about mechanisms that cause heating of the overlying atmosphere, and produce variability of solar emission in spectral regions important for astrophysics and space physics. The program exploited two new ground-based observational capabilities: one using the Swedish Solar Telescope on La Palma for very high angular resolution observations of the photospheric intensity field (granulation) and proxies of the magnetic field (G-band images); and the other using the Near Infrared Magnetograph at the McMath-Pierce Solar Facility to map the spatial variation and dynamic behavior of the solar temperature minimum region using infrared CO lines. We have interpreted these data using a variety of theoretical and modelling approaches, some developed especially for this project. Previous annual reports cover the work done up to 31 May 1997. This final report summarizes our work for the entire period, including the period of no-cost extension from 1 June 1997 through September 30 1997. In Section 2 we discuss observations and modelling of the photospheric flowfields and their consequences for heating of the overlying atmosphere, and in Section 3 we discuss imaging spectroscopy of the CO lines at 4.67 mu.

Noyes, Robert W.↗

NASA NTRS2019

Modeling a Carrington-Scale Stellar Superflare and Coronal Mass Ejection from K(exp 1) Cet

Observations from the Kepler mission have revealed frequent superﬂares on young and active solar-like stars. Superﬂares result from the large-scale restructuring of stellar magnetic ﬁelds, and are associated with the eruption of coronal material (a coronal mass ejection, or CME) and energy release that can be orders of magnitude greater than those observed in the largest solar ﬂares. These catastrophic events, if frequent, can signiﬁcantly impact the potential habitability of terrestrial exoplanets through atmospheric erosion or intense radiation exposure at the surface. We present results from numerical modeling designed to understand how an eruptive superﬂare from a young solar-type star, κ(exp 1)Cet, could occur and would impact its astrospheric environment. Our data-inspired, three- dimensional magnetohydrodynamic modeling shows that global-scale shear concentrated near the radial-ﬁeld polarity inversion line can energize the closed-ﬁeld stellar corona sufﬁciently to power a global, eruptive superﬂare that releases approximately the same energy as the extreme 1859 Carrington event from the Sun. We examine proxy measures of synthetic emission during the ﬂare and estimate the observational signatures of our CME-driven shock, both of which could have extreme space-weather impacts on the habitability of any Earth-like exoplanets. We also speculate that the observed 1986 Robinson-Bopp superﬂare from κ(exp 1)Cet was perhaps as extreme for that star as the Carrington ﬂare was for the Sun.

Lynch, Benjamin J.↗

NASA NTRSDate not supplied

Illustrating the Spatiotemporal Complexity of No2 Columns Using A Multi-Perspective Observing System: Moving Toward Geostationary Product Validation and Applications

As a precursor to secondary pollutants like ozone and PM2.5, nitrogen dioxide (NO2) is crucial to understand when addressing air quality issues. However, due to NO2’s short lifetime during the daytime and complexity of emission sources in urbanized regions, interpreting datasets from ground or satellite perspectives alone are challenged by variance in spatial and temporal resolutions. High resolution airborne mapping (< 1 km) of NO2 column densities across morning, midday, and afternoon add a unique perspective toward interpreting satellite data with respect to ground-measurements. This presentation focuses on the interpretation of spatiotemporal complexity of NO2 columns from the Synergistic TEMPO Air Quality Science Study (STAQS). The mission’s goal is to integrate geostationary observations from Tropospheric Emissions: Monitoring of Pollution (TEMPO) with traditional and enhanced air quality monitoring to improve the understanding of air quality science for increased societal benefit. We will demonstrate the interweaved perspective of NO2 columns from ground-based Pandora spectrometers and satellite-based observations (e.g., TROPOMI) as compared to high spatial resolution airborne observations from the GEOstationary Coastal and Air Pollution Events (GEO-CAPE) Airborne Simulator (GCAS). This includes the evaluation of each dataset through comparison to each other to identify potential biases in data products and the impact of heterogeneity on these comparisons. Airborne data will also be used as a proxy for geostationary observations with morning, midday, and afternoon raster maps collected over four cities (Los Angeles, Chicago, Toronto, and New York City). Finally, recent research outcomes will be presented to demonstrate how airborne and geostationary observations can be used to evaluate emission inventories and air quality models.

Laura Judd↗

NASA NTRSDate not supplied

Practical Considerations using Weighted-Acceleration Compensation Techniques for Dynamic Force Measurements in Wind Tunnels

Most wind tunnel force measurement systems are designed and calibrated for high-accuracy static measurements, but may have limited ability to sense dynamic forces and moments. As a means to improve the measurement bandwidth of dynamic forces, researchers have proposed using a weighted-acceleration technique, which uses accelerometer data to compensate and correct for system dynamics. The sum of weighted-accelerations method is attractive as the acceleration data applies a correction to the traditional static measurements. The focus of this paper is on practical aspects of implementing a weighted-acceleration technique in an experimental arrangement. A formulation of the weighted-acceleration methodology is validated on a reduced-order model and demonstrated on a tabletop experiment that serves as a proxy to a wind tunnel force measurement system. As part of this system, a two component normal force and pitching moment balance was designed and fabricated. A static and dynamic calibration of the system was performed, and the weighted-acceleration technique was used to reconstruct impact forces acting on the system. Practical considerations of the experimental design that improve the success of the methodology are discussed.

Dynamic force measurement↗

NASA NTRSDate not supplied

Practical Considerations using Weighted-Acceleration Compensation Techniques for Dynamic Force Measurements in Wind Tunnels

Dynamic force measurement↗

NASA NTRS2017

Meteoroid Bulk Density and Ceplecha Types

The determination of asteroid bulk density is an important aspect of Near Earth Object (NEO) characterization. A fraction of meteoroids originate from asteroids (including some NEOs), thus in lieu of mutual perturbations, satellites, or expensive spacecraft missions, a study of meteoroid bulk densities can potentially provide useful insights into the densities of NEOs and PHOs (Potentially Hazardous Objects). Meteoroid bulk density is still inherently difficult to measure, and is most often determined by modeling the ablation of the meteoroid. One approach towards determining a meteoroid density distribution entails using a more easily measured proxy for the densities, then calibrating the proxy with known densities from meteorite falls, ablation modelling, and other sources. An obvious proxy choice is the Ceplecha type, KB (Ceplecha, 1958), which is thought to indicate the strength of a meteoroid and often correlated to different bulk densities in literature. KB is calculated using the air density at the beginning height of the meteor, the initial velocity, and the zenith angle of the radiant; quantities more readily determined than meteoroid bulk density itself. Numerical values of K(sub B) are sorted into groups (A, B, C, etc.), which have been matched to meteorite falls or meteor showers with known composition such as the porous Draconids. An extensive survey was conducted to establish the strength of the relationship between bulk density and K(sub B), specifically looking at those that additionally determined K(sub B) for the meteors. In examining the modeling of high-resolution meteor data from Kikwaya et al. (2011), the correlation between K(sub B) and bulk density was not as strong as hoped. However, a distinct split by dynamical type was seen with Jovian Tisserand parameter (T(sub J)), with meteoroids from Halley Type comets (T(sub J) < 2) exhibiting much lower bulk densities than those originating from Jupiter Family comets and asteroids (T(sub J) > 2). Therefore, this work indicates that the dynamical classification of a meteoroid is a better indicator of the density than the strength proxy, a somewhat surprising result.

Blaauw, R. C.↗

NASA NTRS2011

Model, Proxy and Isotopic Perspectives on the East African Humid Period

Both North and East Africa experienced more humid conditions during the early and mid-Holocene epoch (11,000-5000yr BP; 11-5 ka) relative to today. The North African Humid Period has been a major focus of paleoclimatic study, and represents a response of the hydrological cycle to the increase in boreal summer insolation and associated ocean, atmosphere and land surface feedbacks. Meanwhile, the mechanisms that caused the coeval East African Humid Period are poorly understood. Here, we use results from isotopeenabled coupled climate modeling experiments to investigate the cause of the East African Humid Period. The modeling results are interpreted alongside proxy records of both water balance and the isotopic composition of rainfall. Our simulations show that the orbitally-induced increase in dry season precipitation and the subsequent reduction in precipitation seasonality can explain the East African Humid Period, and this scenario agrees well with regional lake level and pollen paleoclimate data. Changes in zonal moisture flux from both the Atlantic and Indian Ocean account for the simulated increase in precipitation from June through November. Isotopic paleoclimate data and simulated changes in moisture source demonstrate that the western East African Rift Valley in particular experienced more humid conditions due to the influx of Atlantic moisture and enhanced convergence along the Congo Air Boundary. Our study demonstrates that zonal changes in moisture advection are an important determinant of climate variability in the East African region.

Tierney, Jessica E.↗

NASA NTRS2022

Simulations of Firn Processes Over the Greenland and Antarctic Ice Sheets: 1980-2021

Conversion of altimetry-derived ice-sheet volume change to mass requires an understanding of the evolution of the combined ice and air content within the firn column. In the absence of suitable techniques to observe the changes to the firn column across the entirety of an ice sheet, the firn column processes are typically modeled. Here, we present new simulations of firn processes over the Greenland and Antarctic ice sheets (GrIS and AIS) using the Community Firn Model and atmospheric reanalysis variables for more than four decades. A data set of more than 250 measured depth–density profiles from both ice sheets provides the basis of the calibration of the dry-snow densification scheme. The resulting scheme results in a reduction in the rate of densification, relative to a commonly used semi-empirical model, through a decreased dependence on the accumulation rate, a proxy for overburden stress. The 1980–2020 modeled firn column runoff, when combined with atmospheric variables from MERRA-2, generates realistic mean integrated surface mass balance values for the Greenland (+390 Gt yr(exp −1)) and Antarctic (+2612 Gt yr(exp −1)) ice sheets when compared to published model-ensemble means. We find that seasonal volume changes associated with firn air content are on average approximately 2.5 times larger than those associated with mass fluxes from surface processes for the AIS and 1.5 times larger for the GrIS; however, when averaged over multiple years, ice and air-volume fluctuations within the firn column are of comparable magnitudes. Between 1996 and 2019, the Greenland Ice Sheet lost nearly 5% of its firn air content, indicating a reduction in the total meltwater retention capability. Nearly all (94 %) of the meltwater produced over the Antarctic Ice Sheet is retained within the firn column through infiltration and refreezing.

Greenland↗

NASA NTRS2014

New Approach to Monitor Transboundary Particulate Pollution over Northeast Asia

A new approach to more accurately monitor and evaluate transboundary particulate matter (PM) pollution is introduced based on aerosol optical products from Korea's Geostationary Ocean Color Imager (GOCI). The area studied is Northeast Asia (including eastern parts of China, the Korean peninsula and Japan), where GOCI has been monitoring since June 2010. The hourly multi-spectral aerosol optical data that were retrieved from GOCI sensor onboard geostationary satellite COMS (Communication, Ocean, and Meteorology Satellite) through the Yonsei aerosol retrieval algorithm were first presented and used in this study. The GOCI-retrieved aerosol optical data are integrated with estimated aerosol distributions from US EPA Models-3/CMAQ (Community Multi-scale Air Quality) v4.5.1 model simulations via data assimilation technique, thereby making the aerosol data spatially continuous and available even for cloud contamination cells. The assimilated aerosol optical data are utilized to provide quantitative estimates of transboundary PM pollution from China to the Korean peninsula and Japan. For the period of 1 April to 31 May, 2011 this analysis yields estimates that AOD as a proxy for PM2.5 or PM10 during long-range transport events increased by 117-265% compared to background average AOD (aerosol optical depth) at the four AERONET sites in Korea, and average AOD increases of 121% were found when averaged over the entire Korean peninsula. This paper demonstrates that the use of multi-spectral AOD retrievals from geostationary satellites can improve estimates of transboundary PM pollution. Such data will become more widely available later this decade when new sensors such as the GEMS (Geostationary Environment Monitoring Spectrometer) and GOCI-2 are scheduled to be launched.

Data Assimilation↗

NASA NTRS1999

Satellite Remote Sensing of Aerosol Forcing

The role of aerosol forcing remains one of the largest uncertainties in estimating man's impact on the global climate system. One school of thought suggests that remote sensing by satellite sensors will provide the data necessary to narrow these uncertainties. While satellite measurements of direct aerosol forcing appear to be straightforward, satellite measurements of aerosol indirect forcing will be more complicated. Pioneering studies identified indirect aerosol forcing using AVHRR data in the biomass burning regions of Brazil. We have expanded this analysis with AVHRR to include an additional year of data and assimilated water vapor fields. The results show similar latitudinal dependence as reported by Kaufman and Fraser, but by using water vapor observations we conclude that latitude is not a proxy for water vapor and the strength of the indirect effect is not correlated to water vapor amounts. In addition to the AVHRR study we have identified indirect aerosol forcing in Brazil at much smaller spatial scales using the MODIS Airborne Simulator. The strength of the indirect effect appears to be related to cloud type and cloud dynamics. There is a suggestion that some of the cloud dynamics may be influenced by smoke destabilization of the atmospheric column. Finally, this study attempts to quantify remote sensing limitations due to the accuracy limits of the retrieval algorithms. We use a combination of numerical aerosol transport models, ground-based AERONET data and ISCCP cloud climatology to determine how much of the forcing occurs in regions too clean to determine from satellite retrievals.

Remer, Lorraine↗

NASA NTRS1994

Phytoplankton production in the Sargasso Sea as determined using optical mooring data

Optical measurements from an untended mooring provide high-frequency observations of in-water optical properties and permit the estimation of important biological parameters continuously as a function of time. A 9-month time series, composed of three separate deployments, of optical data from the BIOWATT 1987 deep-sea mooring located in the oligotrophic waters of the Sargasso Sea at 34 deg N, 70 deg W are presented. These data have been tested using several bio-optical models for the purpose of providing a continuous estimate of phytoplankton productivity. The data are discussed in the context of contemporaneous shipboard observations and for future ocean color satellite observations. We present a continuous estimation of phytoplankton productivity for the 9-month time series. Results from the first 70-day deployment are emphasized to demonstrate the utility of optical observations as proxy measures of biological parameters, to present preliminary analysis, and to compare our bio-optical observations with concurrent physical observations. The bio-optical features show variation in response to physical forcings including diel variations of incident solar irradiance, episodic changes corresponding to wind forcing, variability caused by advective mesoscale eddy events in the vicinity of the mooring, and seasonal variability corresponding to changes in solar radiation, shoaling of the mixed layer depth, and succession of phytoplankton populations.

Waters, K. J.↗

NASA NTRS2017

Glyoxal Yield from Isoprene Oxidation and Relation to Formaldehyde: Chemical Mechanism, Constraints from SENEX Aircraft Observations, and Interpretation of OMI Satellite Data

Glyoxal (CHOCHO) is produced in the atmosphere by the oxidation of volatile organic compounds(VOCs). Like formaldehyde (HCHO), another VOC oxidation product, it is measurable from space by solar backscatter. Isoprene emitted by vegetation is the dominant source of CHOCHO and HCHO in most of the world. We use aircraft observations of CHOCHO and HCHO from the Southeast Nexus (SENEX) campaign over the southeast US in summer 2013 to better understand the CHOCHO time-dependent yield from isoprene oxidation, its dependence on nitrogen oxides (NO (sub x) triple bonded to NO plus NO2), the behavior of the CHOCHO-HCHO relationship, the quality of Ozone Monitoring Instrument (OMI) CHOCHO satellite observations, and the implications for using CHOCHO observations from space as constraints on isoprene emissions. We simulate the SENEX and OMI observations with the Goddard Earth Observing System chemical transport model (GEOSChem) featuring a new chemical mechanism for CHOCHO formation from isoprene. The mechanism includes prompt CHOCHO formation under low-NO (sub x) conditions following the isomerization of the isoprene peroxy radical (ISOPO2).The SENEX observations provide support for this prompt CHOCHO formation pathway, and are generally consistent with the GEOS-Chem mechanism. Boundary layer CHOCHO and HCHO are strongly correlated in the observations and the model, with some departure under low-NO (sub x) conditions due to prompt CHOCHO formation. SENEX vertical profiles indicate a free-tropospheric CHOCHO background that is absent from the model. The OMI CHOCHO data provide some support for this free-tropospheric background and show southeast US enhancements consistent with the isoprene source but a factor of 2 too low. Part of this OMI bias is due to excessive surface reflectivities assumed in the retrieval. The OMI CHOCHO and HCHO seasonal data over the southeast US are tightly correlated and provide redundant proxies of isoprene emissions. Higher temporal resolution in future geostationary satellite observations may enable detection of the prompt CHOCHO production under low-NO (sub x) conditions apparent in the SENEX data.

OMI↗

NASA NTRS2017

Climatic History of the Northeastern United States During the Past 3000 Years

Many ecosystem processes that influence Earth system feedbacks - vegetation growth, water and nutrient cycling, disturbance regimes - are strongly influenced by multidecadal- to millennial-scale climate variations that cannot be directly observed. Paleoclimate records provide information about these variations, forming the basis of our understanding and modeling of them. Fossil pollen records are abundant in the NE US, but cannot simultaneously provide information about paleoclimate and past vegetation in a modeling context because this leads to circular logic. If pollen data are used to constrain past vegetation changes, then the remaining paleoclimate archives in the northeastern US (NE US) are quite limited. Nonetheless, a growing number of diverse reconstructions have been developed but have not yet been examined together. Here we conduct a systematic review, assessment, and comparison of paleotemperature and paleohydrological proxies from the NE US for the last 3000 years. Regional temperature reconstructions (primarily summer) show a long-term cooling trend (1000BCE - 1700CE) consistent with hemispheric-scale reconstructions, while hydroclimate data show gradually wetter conditions through the present day. Multiple proxies suggest that a prolonged, widespread drought occurred between 550 and 750CE. Dry conditions are also evident during the Medieval Climate Anomaly, which was warmer and drier than the Little Ice Age and drier than today. There is some evidence for an acceleration of the longer-term wetting trend in the NE US during the past century; coupled with an abrupt shift from decreasing to increasing temperatures in the past century, these changes could have wide-ranging implications for species distributions, ecosystem dynamics, and extreme weather events. More work is needed to gather paleoclimate data in the NE US to make inter-proxy comparisons and to improve estimates of uncertainty in reconstructions.

Marlon, Jennifer R.↗

NASA NTRS1994

Estimating 11-year solar UV variations using 27-day response as a guide to isolate trends in total column ozone

The total column ozone response to 11-year solar ultraviolet (UV) variations is estimated here from the observed response to 27-day solar variations adjusted for the theoretical difference between the 27-day response and 11-year response. The estimate is tested by comparing two data sets where long-term drifts have been removed, the Nimbus 7 TOMS Version 6 total column ozone and the 280 nm core-to-wing ratio (a proxy for solar UV variations). The 365-day running means of data area-weighted between 40 deg N to 40 deg S latitude give a 1.9% ozone variation related to the 11-year solar cycle compared with the estimate of 1.8%. Estimates of linear trends were reduced by a factor of 2 by including solar effects. The standard deviation from the empirical model was reduced from 1.0 to 0.6 Dobson Units, by including the quasi-biennial oscillation (QBO), but the QBO did not significantly alter trend estimates. Both the ozone responses to 27-day and 11-year solar variations were considerably stronger than predicted by a 2-D theoretical model.

Keating, G. M.↗