Engineering topics

Bhartia, P. K.

Publications and source records attributed to Bhartia, P. K..

At least 37 records · Page 2

NASA NTRS2011

Estimation of Smoothing Error in SBUV Profile and Total Ozone Retrieval

Data from the Nimbus-4, Nimbus-7 Solar Backscatter Ultra Violet (SBUV) and seven of the NOAA series of SBUV/2 instruments spanning 41 years are being reprocessed using V8.6 algorithm. The data are scheduled to be released by the end of August 2011. An important focus of the new algorithm is to estimate various sources of errors in the SBUV profiles and total ozone retrievals. We discuss here the smoothing errors that describe the components of the profile variability that the SBUV observing system can not measure. The SBUV(/2) instruments have a vertical resolution of 5 km in the middle stratosphere, decreasing to 8 to 10 km below the ozone peak and above 0.5 hPa. To estimate the smoothing effect of the SBUV algorithm, the actual statistics of the fine vertical structure of ozone profiles must be known. The covariance matrix of the ensemble of measured ozone profiles with the high vertical resolution would be a formal representation of the actual ozone variability. We merged the MLS (version 3) and sonde ozone profiles to calculate the covariance matrix, which in general case, for single profile retrieval, might be a function of the latitude and month. Using the averaging kernels of the SBUV(/2) measurements and calculated total covariance matrix one can estimate the smoothing errors for the SBUV ozone profiles. A method to estimate the smoothing effect of the SBUV algorithm is described and the covariance matrixes and averaging kernels are provided along with the SBUV(/2) ozone profiles. The magnitude of the smoothing error varies with altitude, latitude, season and solar zenith angle. The analysis of the smoothing errors, based on the SBUV(/2) monthly zonal mean time series, shows that the largest smoothing errors were detected in the troposphere and might be as large as 15-20% and rapidly decrease with the altitude. In the stratosphere above 40 hPa the smoothing errors are less than 5% and between 10 and 1 hPa the smoothing errors are on the order of 1%. We validate our estimated smoothing errors by comparing the SBUV ozone profiles with other ozone profiling sensors.

Kramarova, N. A.↗

NASA NTRS2011

Fast Simulators for Satellite Cloud Optical Centroid Pressure Retrievals, 1. Evaluation of OMI Cloud Retrievals

We have developed a relatively simple scheme for simulating retrieved cloud optical centroid pressures (OCP) from satellite solar backscatter observations. We have compared simulator results with those from more detailed retrieval simulators that more fully account for the complex radiative transfer in a cloudy atmosphere. We used this fast simulator to conduct a comprehensive evaluation of cloud OCPs from the two OMI algorithms using collocated data from CloudSat and Aqua MODIS, a unique situation afforded by the A-train formation of satellites. We find that both OMI algorithms perform reasonably well and that the two algorithms agree better with each other than either does with the collocated CloudSat data. This indicates that patchy snow/ice, cloud 3D, and aerosol effects not simulated with the CloudSat data are affecting both algorithms similarly. We note that the collocation with CloudSat occurs mainly on the East side of OMI's swath. Therefore, we are not able to address cross-track biases in OMI cloud OCP retrievals. Our fast simulator may also be used to simulate cloud OCP from output generated by general circulation models (GCM) with appropriate account of cloud overlap. We have implemented such a scheme and plan to compare OMI data with GCM output in the near future.

Joiner, J.↗

NASA NTRS2010

A New ENSO Index Derived from Satellite Measurements of Column Ozone

Column Ozone measured in tropical latitudes from Nimbus 7 total ozone mapping spectrometer (TOMS), Earth Probe TOMS, solar backscatter ultraviolet (SBUV), and Aura ozone monitoring instrument (OMI) are used to derive an El Nino-Southern Oscillation (ENSO) index. This index, which covers a time period from 1979 to the present, is defined as the Ozone ENSO Index (OEI) and is the first developed from atmospheric trace gas measurements. The OEI is constructed by first averaging monthly mean column ozone over two broad regions in the western and eastern Pacific and then taking their difference. This differencing yields a self-calibrating ENSO index which is independent of individual instrument calibration offsets and drifts in measurements over the long record. The combined Aura OMI and MLS ozone data confirm that zonal variability in total column ozone in the tropics caused by ENSO events lies almost entirely in the troposphere. As a result, the OEI can be derived directly from total column ozone instead of tropospheric column ozone. For clear-sky ozone measurements a +1K change in Nino 3.4 index corresponds to +2.9 Dobson Unit (DU) change in the OEI, while a +1 hPa change in SOI coincides with a -1.7DU change in the OEI. For ozone measurements under all cloud conditions these numbers are +2.4DU and -1.4 DU, respectively. As an ENSO index based upon ozone, it is potentially useful in evaluating climate models predicting long term changes in ozone and other trace gases.

Ziemke, J. R.↗

NASA NTRS2010

Detection of Multi-Layer and Vertically-Extended Clouds Using A-Train Sensors

The detection of mUltiple cloud layers using satellite observations is important for retrieval algorithms as well as climate applications. In this paper, we describe a relatively simple algorithm to detect multiple cloud layers and distinguish them from vertically-extended clouds. The algorithm can be applied to coincident passive sensors that derive both cloud-top pressure from the thermal infrared observations and an estimate of solar photon pathlength from UV, visible, or near-IR measurements. Here, we use data from the A-train afternoon constellation of satellites: cloud-top pressure, cloud optical thickness, the multi-layer flag from the Aqua MODerate-resolution Imaging Spectroradiometer (MODIS) and the optical centroid cloud pressure from the Aura Ozone Monitoring Instrument (OMI). For the first time, we use data from the CloudSat radar to evaluate the results of a multi-layer cloud detection scheme. The cloud classification algorithms applied with different passive sensor configurations compare well with each other as well as with data from CloudSat. We compute monthly mean fractions of pixels containing multi-layer and vertically-extended clouds for January and July 2007 at the OMI spatial resolution (l2kmx24km at nadir) and at the 5kmx5km MODIS resolution used for infrared cloud retrievals. There are seasonal variations in the spatial distribution of the different cloud types. The fraction of cloudy pixels containing distinct multi-layer cloud is a strong function of the pixel size. Globally averaged, these fractions are approximately 20% and 10% for OMI and MODIS, respectively. These fractions may be significantly higher or lower depending upon location. There is a much smaller resolution dependence for fractions of pixels containing vertically-extended clouds (approx.20% for OMI and slightly less for MODIS globally), suggesting larger spatial scales for these clouds. We also find higher fractions of vertically-extended clouds over land as compared with ocean, particularly in the tropics and summer hemisphere.

Joiner, J.↗

NASA NTRS2009

Recent Biomass Burning in the Tropics and Related Changes in Tropospheric Ozone

Biomass burning is an important source of chemical precursors of tropospheric ozone. In the tropics, biomass burning produces ozone enhancements over broad regions of Indonesia, Africa, and South America including Brazil. Fires are intentionally set in these regions during the dry season each year to clear cropland and to clear land for human/industrial expansion. In Indonesia enhanced burning occurs during dry El Nino conditions such as in 1997 and 2006. These burning activities cause enhancement in atmospheric particulates and trace gases which are harmful to human health. Measurements from the Aura Ozone Monitoring Instrument (OMI) and Microwave Limb Sounder (MLS) from October 2004-November 2008 are used to evaluate the effects of biomass burning on tropical tropospheric ozone. These measurements show sizeable decreases approx.15-20% in ozone in Brazil during 2008 compared to 2007 which we attribute to the reduction in biomass burning. Three broad biomass burning regions in the tropics (South America including Brazil, western Africa, and Indonesia) were analyzed in the context of OMI/MLS measurements and the Global Modeling Initiative (GMI) chemical transport model developed at Goddard Space Flight Center. The results indicate that the impact of biomass burning on ozone is significant within and near the burning regions with increases of approx.10-25% in tropospheric column ozone relative to average background concentrations. The model suggests that about half of the increases in ozone from these burning events come from altitudes below 3 km. Globally the model indicates increases of approx.4-5% in ozone, approx.7-9% in NO, (NO+NO2), and approx.30-40% in CO.

Ziemke↗

NASA NTRS2008

Measurement of Atmospheric Composition from Geostationary Platforms

Satellite instruments flown since 1970 have had great success in elucidating the processes that control stratospheric ozone. In contrast, space-based data for tropospheric constituents that affect air quality and climate have only recently become available. While these datasets highlight the rapidly advancing capabilities of spacebased tropospheric sensors, they are also pointing to the limitations of sun-synchronous, low-earth orbiting (SSO/LEO) satellite platforms for making such measurements. In our talk we will highlight the science requirements for new missions and the technological and algorithmic approaches that we are developing to meet these requirements. From these studies a clear need for advanced atmospheric composition sensors has emerged that can be put on geostationary (GEO) platforms to provide 5 km horizontal resolution with 15-60 minutes repeat cycle. Such measurements have been high priority in the recently released Decadal Survey report by the US National Research Council. The need for GEO is driven not only by the science requirements to track rapidly changing pollution events but also by the need to provide altitude-resolved information about tropospheric constituents. Currently, with the exception of aerosols, it is not possible to derive profile information about lower tropospheric constituents from satellite measurements. New algorithmic approaches are being developed to obtain this information by combining UV and IR data, by monitoring the spatial and temporal structures of the constituents, and by using low-level clouds to separate boundary layer constituents from free troposphere. All these approaches require better spatial and temporal resolution than that provided by LEO sensors.

Bhartia, P. K.↗

NASA NTRS2008

A Sample of What We Have Learned from A-Train Cloud Measurements

The A-train active sensors CloudSat and CALIPSO provide detailed information about cloud vertical structure. Coarse vertical information can also be obtained from a combination of passive sensors (e.g. cloud liquid water content from AMSR-E, cloud ice properties from MLS and HIRDLS, cloud-top pressure from MODIS and AIRS, and UVNISINear IR absorption and scattering from OMI, MODIS, and POLDER). In addition, the wide swaths of instruments such as MODIS, AIRS, OMI, POLDER, and AMSR-E can be exploited to create estimates of the three-dimensional cloud extent. We will show how data fusion from A-train sensors can be used, e.g., to detect and map the presence of multiple layer/phase clouds. Ultimately, combined cloud information from Atrain instruments will allow for estimates of heating and radiative flux at the surface as well as UV/VIS/Near IR trace-gas absorption at the overpass time on a near-global daily basis. CloudSat has also dramatically improved our interpretation of visible and UV passive measurements in complex cloudy situations such as deep convection and multiple cloud layers. This has led to new approaches for unique and accurate constituent retrievals from A-train instruments. For example, ozone mixing ratios inside tropical deep convective clouds have recently been estimated using the Aura Ozone Monitoring Instrument (OMI). Field campaign data from TC4 provide additional information about the spatial variability and origin of trace-gases inside convective clouds. We will highlight some of the new applications of remote sensing in cloudy conditions that have been enabled by the synergy between the A-train active and passive sensors.

Joiner, Joanna↗

NASA NTRS2008

Absorption in Extended Inhomogeneous Clouds

The launch of several different sensors, including CloudSat, into the A-train constellation of satellites allows us for the first time to compute absorption that can occur in realistic vertically inhomogeneous clouds including multiple cloud decks. CloudSat data show that these situations are common. Therefore, understanding vertically inhomogeneous clouds is important from both climate and satellite atmospheric composition remote sensing perspectives. Satellite passive sensors that operate from the near IR to the UV often rely on radiative cloud pressures derived from absorption in oxygen bands (A, B, gamma, or O2-O2 bands) or from rotational-Raman scattering in order to retrieve information about atmospheric trace gases. The radiative cloud pressure is distinct from the physical cloud top derived from thermal infrared measurements. Therefore, the combination of information from different passive sensors yields some information about the cloud vertical profile. When either or both the clouds or atmospheric absorbers (trace gases and aerosols) are vertically inhomogeneous, the use of an effective cloud pressure derived from these approaches may lead to errors. Here, we focus on several scenarios (deep convective clouds and distinct two layer clouds) based on realistic cloud optical depth vertical profiles derived from the CloudSatfMODIS combination. We focus on implications for trace-gas column amount retrievals (specifically ozone and NO2) and derived surface UV irradiance from the Ozone Monitoring Instrument (OMI) on the Atrain Aura platform.

Joiner, Joanna↗

NASA NTRS2007

Identification of Stratospheric Waves in Ozone in the Tropics from OMI High Spectral Resolution Measurements

Previous studies using Total Ozone Mapping Spectrometer (TOMS) measurements have identified several types of tropical waves in the stratosphere. These waves include Kelvin waves, mixed Rossby-gravity waves, equatorial Rossby waves, and global normal modes. All of these detected waves occur when their zonal phase speeds are opposite the zonal winds in the low-mid stratosphere associated with the Quasi-biennial Oscillation (QBO). Peak-to-peak amplitudes in all cases are typically 5 DU. While total ozone data from TOMS is sensitive in detecting these tropical waves, they provide each day only a single horizontal cross-sectional map. The high spatial and spectral resolution of the Aura Ozone Monitoring Instrument (OMI) provides a unique means to evaluate 3D structure in these waves including their propagation characteristics. Ozone profiles retrieved from OMI radiances for wavelengths 270-310 nm are utilized to examine the nature of these wave disturbances extending from the lower to upper stratosphere.

Ziemke, J. R.↗

NASA NTRS2007

SHADOZ in the Aura Era

We present comparisons of observed tropical and sub-tropical ozone from the Southern Hemisphere Additional Ozonesondes (SHADOZ) project with satellite measurements using Aura's Ozone Monitoring Instrument (OMI) and Microwave Limb Sounder (MLS) instruments. Satellite products of total and derived tropospheric column ozone from OMI and profiles of ozone in the UT/LS region from MLS are used.

Witte, J. C.↗

NASA NTRS2007

Effects of the 2004 El Nino on Tropospheric Ozone and Water Vapor

The global effects of the 2004 El Nino on tropospheric ozone and H2O based on Aura OM1 and MLS measurements are analyzed. Although it was a weak El Nino from a historical perspective, it produced significant changes in these parameters in tropical latitudes. Tropospheric ozone increased by 10-20% over most of the western Pacific region and decreased by about the same amount over the eastern Pacific region. H2O in the upper troposphere showed similar changes but with opposite sign. These zonal changes in tropospheric ozone and H2O are caused by the eastward shift in the Walker circulation in the tropical pacific region during El Nino. For the 2004 El Nino, biomass burning did not have a significant effect on the ozone budget in the troposphere unlike the 1997 El Nino. Zonally averaged tropospheric column ozone did not change significantly either globally or over the tropical and subtropical latitudes.

Chandra, S.↗

NASA NTRS2006

Tropospheric Ozone Determined from Aura OMI and MLS: Evaluation of Measurements and Comparison with the Global Modeling Initiative's Chemical Transport Model

Ozone measurements from the OMI and MLS instruments on board the Aura satellite are used for deriving global distributions of tropospheric column ozone (TCO). TCO is determined using the tropospheric ozone residual method which involves subtracting measurements of MLS stratospheric column ozone (SCO) from OMI total column ozone after adjusting for intercalibration differences of the two instruments using the convective-cloud differential method. The derived TCO field, which covers one complete year of mostly continuous daily measurements from late August 2004 through August 2005, is used for studying the regional and global pollution on a timescale of a few days to months. The seasonal and zonal characteristics of the observed TCO fields are also compared with TCO fields derived from the Global Modeling Initiative's Chemical Transport Model. The model and observations show interesting similarities with respect to zonal and seasonal variations. However, there are notable differences, particularly over the vast region of the Saharan desert.

Ziemke, J. R.↗

NASA NTRS2006

Tropospheric Ozone from Assimilation of Aura Data using Different Definitions of the Tropopause

Ozone data from Aura OMI and MLS instruments were assimilated into the general circulation model (GCM) constrained by assimilated meteorological fields from the Global Modeling and Assimilation Office at NASA Goddard. Properties of tropospheric ozone and their sensitivity to the definition of the tropopause are investigated. Three definitions of the tropopause are considered: (1) dynamical (using potential vorticity and potential temperature), (2) using temperature lapse rate, and (3) using a fixed ozone value. Comparisons of the tropospheric ozone columns using these tropopause definitions will be presented and evaluated against coincident profiles from ozone sondes. Assimilated ozone profiles are used to identify possible tropopause folding events, which are important for stratosphere-troposphere exchange. Each profile is searched for multiple levels at which ozone attains the value typical of the troposphere-stratosphere transition in order to identify possible tropopause folds. Constrained by the dynamics from a global model and by assimilation of Aura ozone data every 3-hours, this data set provides an opportunity to study ozone evolution in the upper troposphere and lower stratosphere with high temporal resolution.

Stajner, Ivanka↗

NASA NTRS2006

Long-term Evolution of Upper Stratospheric Ozone at Selected Stations of the Network for the Detection of Stratospheric Change (NDSC)

The long-term evolution of upper stratospheric ozone has been recorded by lidars and microwave radiometers within the ground-based Network for the Detection of Stratospheric Change (NDSC), and by the space-borne Solar Backscatter Ultra-Violet instruments (SBUV), Stratospheric Aerosol and Gas Experiment (SAGE), and Halogen Occultation Experiment (HALOE). Climatological mean differences between these instruments are typically smaller than 5% between 25 and 50 km. Ozone anomaly time series from all instruments, averaged from 35 to 45 km altitude, track each other very well and typically agree within 3 to 5%. SBUV seems to have a slight positive drift against the other instruments. The corresponding 1979 to 1999 period from a transient simulation by the fully coupled MAECHAM4-CHEM chemistry climate model reproduces many features of the observed anomalies. However, in the upper stratosphere the model shows too low ozone values and too negative ozone trends, probably due to an underestimation of methane and a consequent overestimation of ClO. The combination of all observational data sets provides a very consistent picture, with a long-term stability of 2% or better. Upper stratospheric ozone shows three main features: (1) a decline by 10 to 15% since 1980, due to chemical destruction by chlorine; (2) two to three year fluctuations by 5 to 10%, due to the Quasi-Biennial Oscillation (QBO); (3) an 11-year oscillation by about 5%, due to the 11-year solar cycle. The 1979 to 1997 ozone trends are larger at the southern mid-latitude station Lauder (45 S), reaching 8%/decade, compared to only about 6%/decade at Table Mountain (35 N), Haute Provence/Bordeaux (approximately equal to 45 N), and Hohenpeissenberg/Bern(approximately equal to 47 N). At Lauder, Hawaii (20 N), Table Mountain, and Haute Provence, ozone residuals after subtraction of QBO- and solar cycle effects have levelled off in recent years, or are even increasing. Assuming a turning point in January 1997, the change of trend is largest at southern mid-latitude Lauder, +11%/decade, compared to +7%/decade at northern mid-latitudes. This points to a beginning recovery of upper stratospheric ozone. However, chlorine levels are still very high and ozone will remain vulnerable. At this point the most northerly mid-latitude station, Hohenpeissenberg/Bern differs from the other stations, and shows much less clear evidence for a beginning recovery, with a change of trend in 1997 by only +3%/decade. In fact, record low upper stratospheric ozone values were observed at Hohenpeissenberg/Bern, and to a lesser degree at Table Mountain and Haute Provence, in the winters 2003/2004 and 2004/2005.

Steinbrecht, W.↗

NASA NTRS2006

Observations over Hurricanes from the Ozone Monitoring Instrument

There is an apparent inconsistency between the total column ozone derived from the total ozone mapping spectrometer (TOMS) and aircraft observations within the eye region of tropical cyclones. The higher spectral resolution, coverage, and sampling of the ozone monitoring instrument (OMI) on NASA s Aura satellite as compared with TOMS allows for improved ozone retrievals by including estimates of cloud pressure derived simultaneously using the effects of rotational Raman scattering. The retrieved cloud pressures from OM1 are more appropriate than the climatological cloud-top pressures based on infrared measurements used in the TOMS and initial OM1 algorithms. We find that total ozone within the eye of hurricane Katrina is significantly overestimated when we use climatological cloud pressures. Using OMI-retrieved cloud pressures, total ozone in the eye is similar to that in the surrounding area. The corrected total ozone is in better agreement with aircraft measurements that imply relatively small or negligible amounts of stratospheric intrusion into the eye region of tropical cyclones.

Joiner, J.↗

NASA NTRS2006

Tropospheric and stratospheric ozone from assimilation of Aura data

Ozone is an atmospheric trace gas with multiple impacts on the environment. Global ozone fields are needed for air quality predictions, estimation of the ultraviolet radiation reaching the surface, climate-radiation studies, and may also have an impact on longer-term weather predictions. We estimate global ozone fields in the stratosphere and troposphere by combining the data from EOS Aura satellite with an ozone model using data assimilation. Ozone exhibits a large temporal variability in the lower stratosphere. Our previous work showed that assimilation of satellite data from limb-sounding geometry helps constrain ozone profiles in that region. We assimilated ozone data from the Aura Microwave Limb Sounder (MLS) and the Ozone Monitoring Instrument (OMI) into the ozone system at NASA's Global Modeling and Assimilation Office (GMAO). Ozone is transported within a general circulation model (GCM) which includes parameterizations for stratospheric photochemistry, tropospheric chemistry, and a simple scheme for heterogeneous ozone loss. The focus of this study is on the representation of ozone in the lower stratosphere and tropospheric ozone columns. We plan to extend studies of tropospheric ozone distribution through assimilation of ozone data from the Tropospheric Emission Spectrometer (TES). Comparisons with ozone sondes and occultation data show that assimilation of Aura data reproduces ozone gradients and variability in the lower stratosphere well. We proceed by separating the contributions to temporal changes in the ozone field into those that are due to the model and those that are due to the assimilation of Aura data. The impacts of Aura data are illustrated and their role in the representation of ozone variability in the lower stratosphere and troposphere is shown.

Stajner, I.↗

NASA NTRS2006

Exploration of OMI Products for Air Quality Applications Through Comparisons with Models and Observations

The Ozone Monitoring Instrument (OMI) on board NASA s Aura satellite was launched in July 2004, and is now providing daily global observations of total column ozone, NO2, and SO2, as well as aerosol information. Algorithms have also been developed to produce daily tropospheric ozone and NO2 products. The tropospheric ozone product reported here is a tropospheric residual computed through use of Aura Microwave Limb Sounder (MLS) ozone profile data to quantify stratospheric ozone. We are investigating the applicability of OMI products for use in air quality modeling, forecasting, and analysis. These investigations include comparison of the OMI tropospheric O3 and NO2 products with global and regional models and with lower tropospheric aircraft observations. Large-scale transport of pollution seen in the OM1 tropospheric O3 data is compared with output from NASA's Global Modeling Initiative global chemistry and transport model. On the regional scale we compare the OMI tropospheric O3 and NO2 with fields from the National Oceanic and Atmospheric Administration and Environmental Protection Agency (NOAA/EPA) operational Eta/CMAQ air quality forecasting model over the eastern United States. This 12-km horizontal resolution model output is roughly of equivalent resolution to the OMI pixel data. Correlation analysis between lower tropospheric aircraft O3 profile data taken by the University of Maryland over the Mid-Atlantic States and OMI tropospheric column mean volume mixing ratio for O3 will be presented. These aircraft data are representative of the lowest 3 kilometers of the atmosphere, the region in which much of the locally-generated and regionally-transported ozone exists.

Pickering, K. E.↗

NASA NTRS2005

Aerosol-Cloud-Precipitation Interactions over Indo-Gangetic Basin

About 60% of world population reside in Asia, in term of which sheer population density presents a major environmental stress. Economic expansion in this region is, in fact, accompanied by increases in bio-fuel burning, industrial pollution, and land cover and land use changes. With a growth rate of approx. 8%/yr for Indian economy, more than 600 million people from Lahore, Pakistan to Calcutta, India over the Indo-Gangetic Basin have particularly witnessed increased frequencies of floods and droughts as well as a dramatic increase in atmospheric loading of aerosols (i.e., anthropogenic and natural aerosol) in recent decades. This regional change (e.g., aerosol, cloud, precipitation, etc.) will constitute a vital part of the global change in the 21st century. Better understanding of the impacts of aerosols in affecting monsoon climate and water cycles is crucial in providing the physical basis to improve monsoon climate prediction and for disaster mitigation. Based on climate model simulations, absorbing aerosols (dust and black carbon) play a critical role in affecting interannual and intraseasonal variability of the Indian monsoon. An initiative on the integrated (aerosols, clouds, and precipitation) measurements approach over the Indo-Gangetic Basin will be discussed. An array of ground-based (e.g., AERONET, MPLNET, SMART-COMMIT, etc.) and satellite (e.g., Terra, A-Train, etc.) sensors will be utilized to acquire aerosol characteristics, sources/sinks, and transport processes during the pre-monsoon (April-May, aerosol forcing) season, and to obtain cloud and precipitation properties during the monsoon (May-June, water cycle response) season. Close collaboration with other international programs, such as ABC, CLIVAR, GEWEX, and CEOP in the region is anticipated.

Tsay, S.-C.↗