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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Ultraviolet DIAL measurements of O3 profiles in regions of spatially inhomogeneous aerosols

The differential absorption lidar (DIAL) technique generally assumes that atmospheric optical scattering is the same at the two laser wavelengths used in the DIAL measurement of a gas concentration profile. Erros can arise in this approach when the wavelengths are significantly separated, and there is a range dependence in the aerosol scattering distribution. This paper discusses the errors introduced by large DIAL wavelength separations and spatial inhomogeneity of aerosols in the atmosphere. A Bernoulli solution for determining the relative distribution of aerosol backscattering in the UV region is presented, and scattering ratio boundary values for these solutions are discussed. The results of this approach are used to derive a backscatter correction to the standard DIAL analysis method. It is shown that for the worst cases of severe range dependence in aerosol backscattering, the residual errors in the corrected DIAL O3 measurements were less than 10 ppbv for DIAL wavelengths at 286 and 300 nm.

Browell, E. V.↗
NASA NTRS1994

Differential absorption lidar measurements of atmospheric water vapor using a pseudonoise code modulated AlGaAs laser

Lidar measurements using pseudonoise code modulated AlGaAs lasers are reported. Horizontal path lidar measurements were made at night to terrestrial targets at ranges of 5 and 13 km with 35 mW of average power and integration times of one second. Cloud and aerosol lidar measurements were made to thin cirrus clouds at 13 km altitude with Rayleigh (molecular) backscatter evident up to 9 km. Average transmitter power was 35 mW and measurement integration time was 20 minutes. An AlGaAs laser was used to characterize spectral properties of water vapor absorption lines at 811.617, 816.024, and 815.769 nm in a multipass absorption cell using derivative spectroscopy techniques. Frequency locking of an AlGaAs laser to a water vapor absorption line was achieved with a laser center frequency stability measured to better than one-fifth of the water vapor Doppler linewidth over several minutes. Differential absorption lidar measurements of atmospheric water vapor were made in both integrated path and range-resolved modes using an externally modulated AlGaAs laser. Mean water vapor number density was estimated from both integrated path and range-resolved DIAL measurements and agreed with measured humidity values to within 6.5 percent and 20 percent, respectively. Error sources were identified and their effects on estimates of water vapor number density calculated.

Rall, Jonathan A. R.↗
NASA NTRS1980

Windfield retrieval from Doppler lidar observations

An approach to the retrieval of a vector wind field from Doppler lidar observations is developed in general terms. The field of radial velocity measurements from each look angle is modeled by a smooth surface, the parameters of the model being determined from the data by least squares techniques. The vector wind field and higher-order fields are obtained from the two modeled surfaces. Estimated measurement errors are taken into account, and error estimates are available for all output data sets.

Lee, R. W.↗
NASA NTRS2008

High Vertically Resolved Atmospheric and Surface/Cloud Parameters Retrieved with Infrared Atmospheric Sounding Interferometer (IASI)

The Joint Airborne IASI Validation Experiment (JAIVEx) was conducted during April 2007 mainly for validation of the IASI on the MetOp satellite. IASI possesses an ultra-spectral resolution of 0.25/cm and a spectral coverage from 645 to 2760/cm. Ultra-spectral resolution infrared spectral radiance obtained from near nadir observations provide atmospheric, surface, and cloud property information. An advanced retrieval algorithm with a fast radiative transfer model, including cloud effects, is used for atmospheric profile and cloud parameter retrieval. This physical inversion scheme has been developed, dealing with cloudy as well as cloud-free radiance observed with ultraspectral infrared sounders, to simultaneously retrieve surface, atmospheric thermodynamic, and cloud microphysical parameters. A fast radiative transfer model, which applies to the cloud-free and/or clouded atmosphere, is used for atmospheric profile and cloud parameter retrieval. A one-dimensional (1-d) variational multi-variable inversion solution is used to improve an iterative background state defined by an eigenvector-regression-retrieval. The solution is iterated in order to account for non-linearity in the 1-d variational solution. It is shown that relatively accurate temperature and moisture retrievals are achieved below optically thin clouds. For optically thick clouds, accurate temperature and moisture profiles down to cloud top level are obtained. For both optically thin and thick cloud situations, the cloud top height can be retrieved with relatively high accuracy (i.e., error < 1 km). Preliminary retrievals of atmospheric soundings, surface properties, and cloud optical/microphysical properties with the IASI observations are obtained and presented. These retrievals will be further inter-compared with those obtained from airborne FTS system, such as the NPOESS Airborne Sounder Testbed - Interferometer (NAST-I), dedicated dropsondes, radiosondes, and ground based Raman Lidar. The capabilities of satellite ultra-spectral sounder such as the IASI are investigated indicating a high vertical structure of atmosphere is retrieved.

Zhou, Daniel K.↗
NASA NTRS2008

Current Sounding Capability From Satellite Meteorological Observation With Ultraspectral Infrared Instruments

Ultraspectral resolution infrared spectral radiance obtained from near nadir observations provide atmospheric, surface, and cloud property information. The intent of the measurement of tropospheric thermodynamic state and trace abundances is the initialization of climate models and the monitoring of air quality. The NPOESS Airborne Sounder Testbed-Interferometer (NAST-I), designed to support the development of future satellite temperature and moisture sounders, aboard high altitude aircraft has been collecting data throughout many field campaigns. An advanced retrieval algorithm developed with NAST-I is now applied to satellite data collected with the Atmospheric InfraRed Sounder (AIRS) on the Aqua satellite launched on 4 May 2002 and the Infrared Atmospheric Sounding Interferometer (IASI) on the MetOp satellite launched on October 19, 2006. These instruments possess an ultra-spectral resolution, for example, both IASI and NAST-I have ~0.25 cm-1 and a spectral coverage from 645 to 2760 cm-1. The retrieval algorithm with a fast radiative transfer model, including cloud effects, is used for atmospheric profile and cloud parameter retrieval. The physical inversion scheme has been developed, dealing with cloudy as well as cloud-free radiance observed with ultraspectral infrared sounders, to simultaneously retrieve surface, atmospheric thermodynamic, and cloud microphysical parameters. A fast radiative transfer model, which applies to the clouded atmosphere, is used for atmospheric profile and cloud parameter retrieval. A one-dimensional (1-d) variational multi-variable inversion solution is used to improve an iterative background state defined by an eigenvector-regression-retrieval. The solution is iterated in order to account for non-linearity in the 1-d variational solution. It is shown that relatively accurate temperature and moisture retrievals can be achieved below optically thin clouds. For optically thick clouds, accurate temperature and moisture profiles down to cloud top level are obtained. For both optically thin and thick cloud situations, the cloud top height can be retrieved with relatively high accuracy (i.e., error less than 1 km). Retrievals of atmospheric soundings, surface properties, and cloud microphysical properties with the AIRS and IASI observations are obtained and presented. These retrievals are further inter-compared with those obtained from airborne FTS system, such as the NPOESS Airborne Sounder Testbed? Interferometer (NAST I), dedicated dropsondes, radiosondes, and ground based Raman Lidar. The capabilities of satellite ultra-spectral sounder such as the AIRS and IASI are investigated. These advanced satellite ultraspectral infrared instruments are now playing an important role in satellite meteorological observation for numerical weather prediction.

Zhou, Daniel K.↗
NASA NTRS2018

Observational Constraint on Cloud Susceptibility Weakened by Aerosol Retrieval Limitations

Aerosol-cloud interactions remain a major uncertainty in climate research. Studies have indicated that model estimates of cloud susceptibility to aerosols frequently exceed satellite estimates, motivating model reformulations to increase agreement. Here we show that conventional ways of using satellite information to estimate susceptibility can serve as only a weak constraint on models because the estimation is sensitive to errors in the retrieval procedures. Using instrument simulators to investigate differences between model and satellite estimates of susceptibilities, we find that low aerosol loading conditions are not well characterized by satellites, but model clouds are sensitive to aerosol perturbations in these conditions. We quantify the observational requirements needed to constrain models, and find that the nighttime lidar measurements of aerosols provide a better characterization of ten- uous aerosols. We conclude that observational uncertainties and limitations need to be accounted for when assessing the role of aerosols in the climate system.

Ma, Po-Lun↗
NASA NTRS1992

Lidar Measurement of Stratospheric Ozone at Hohenpeissenberg: an Improved Evaluation Method

In 1987, the schedule of long-term ozone monitoring at the Meteorological Observatory Hohenpeissenberg was extended by operational DIAL measurements. A detailed description of the system is given in earlier works. An improved evaluation method will be described, which allows the calculation of stratospheric ozone distribution up to 50 km. A good balance between precision and range resolution is achieved. The evaluation begins with the calculation of the relative error for each channel in accordance with the Poisson distribution. During the following evaluation an error calculation is performed according to the Gaussian error propagation. After normalization of the backscatter profiles to count per shot and kilometer, an empirical function is applied to correct non-linearities of the photomultipliers.

Vandersee, W.↗
NASA NTRS2011

Simulation Studies of Satellite Laser CO2 Mission Concepts

Results of mission simulation studies are presented for a laser-based atmospheric CO2 sounder. The simulations are based on real-time carbon cycle process modeling and data analysis. The mission concept corresponds to ASCENDS as recommended by the US National Academy of Sciences Decadal Survey. Compared to passive sensors, active (lidar) sensing of CO2 from space has several potentially significant advantages that hold promise to advance CO2 measurement capability in the next decade. Although the precision and accuracy requirements remain at unprecedented levels of stringency, analysis of possible instrument technology indicates that such sensors are more than feasible. Radiative transfer model calculations, an instrument model with representative errors, and a simple retrieval approach complete the cycle from "nature" run to "pseudodata" CO2. Several mission and instrument configuration options are examined, and the sensitivity to key design variables is shown. Examples are also shown of how the resulting pseudo-measurements might be used to address key carbon cycle science questions.

Kawa, Stephan Randy↗
NASA NTRS2012

Simulation Framework to Estimate the Performance of CO2 and O2 Sensing from Space and Airborne Platforms for the ASCENDS Mission Requirements Analysis

The Active Sensing of CO2 Emissions over Nights Days and Seasons (ASCENDS) mission recommended by the NRC Decadal Survey has a desired accuracy of 0.3% in carbon dioxide mixing ratio (XCO2) retrievals requiring careful selection and optimization of the instrument parameters. NASA Langley Research Center (LaRC) is investigating 1.57 micron carbon dioxide as well as the 1.26-1.27 micron oxygen bands for our proposed ASCENDS mission requirements investigation. Simulation studies are underway for these bands to select optimum instrument parameters. The simulations are based on a multi-wavelength lidar modeling framework being developed at NASA LaRC to predict the performance of CO2 and O2 sensing from space and airborne platforms. The modeling framework consists of a lidar simulation module and a line-by-line calculation component with interchangeable lineshape routines to test the performance of alternative lineshape models in the simulations. As an option the line-by-line radiative transfer model (LBLRTM) program may also be used for line-by-line calculations. The modeling framework is being used to perform error analysis, establish optimum measurement wavelengths as well as to identify the best lineshape models to be used in CO2 and O2 retrievals. Several additional programs for HITRAN database management and related simulations are planned to be included in the framework. The description of the modeling framework with selected results of the simulation studies for CO2 and O2 sensing is presented in this paper.

Plitau, Denis↗
NASA NTRS2014

Assessment of NASA GISS CMIP5 and Post-CMIP5 Simulated Clouds and TOA Radiation Budgets Using Satellite Observations. Part I: Cloud Fraction and Properties

Although many improvements have been made in phase 5 of the Coupled Model Intercomparison Project (CMIP5), clouds remain a significant source of uncertainty in general circulation models (GCMs) because their structural and optical properties are strongly dependent upon interactions between aerosol/cloud microphysics and dynamics that are unresolved in such models. Recent changes to the planetary boundary layer (PBL) turbulence and moist convection parameterizations in the NASA GISS Model E2 atmospheric GCM(post-CMIP5, hereafter P5) have improved cloud simulations significantly compared to its CMIP5 (hereafter C5) predecessor. A study has been performed to evaluate these changes between the P5 and C5 versions of the GCM, both of which used prescribed sea surface temperatures. P5 and C5 simulated cloud fraction (CF), liquid water path (LWP), ice water path (IWP), cloud water path (CWP), precipitable water vapor (PWV), and relative humidity (RH) have been compared to multiple satellite observations including the Clouds and the Earth's Radiant Energy System-Moderate Resolution Imaging Spectroradiometer (CERES-MODIS, hereafter CM), CloudSat- Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO; hereafter CC), Atmospheric Infrared Sounder (AIRS), and Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E). Although some improvements are observed in the P5 simulation on a global scale, large improvements have been found over the southern midlatitudes (SMLs), where correlations increased and both bias and root-mean-square error (RMSE) significantly decreased, in relation to the previous C5 simulation, when compared to observations. Changes to the PBL scheme have resulted in improved total column CFs, particularly over the SMLs where marine boundary layer (MBL) CFs have increased by nearly 20% relative to the previous C5 simulation. Globally, the P5 simulated CWPs are 25 gm22 lower than the previous C5 results. The P5 version of the GCM simulates PWV and RH higher than its C5 counterpart and agrees well with the AMSR-E and AIRS observations. The moister atmospheric conditions simulated by P5 are consistent with the CF comparison and provide a strong support for the increase in MBL clouds over the SMLs. Over the tropics, the P5 version of the GCM simulated total column CFs and CWPs are slightly lower than the previous C5 results, primarily as a result of the shallower tropical boundary layer in P5 relative to C5 in regions outside the marine stratocumulus decks.

General circulation models↗
NASA NTRSDate not supplied

TPSAS-NF1676L-29931-DND

The ACE science working group satellite concept calls for a combination of high spectral resolution aerosol lidar and a polarimeter able to determine vertical profiles of aerosol extinction and clouds. Here we discuss why an HSRL lidar is required to achieve these requirements. The primary advantage of an HSRL over an elastic backscatter lidar is that the HSRL channel allows for the independent retrieval of vertically resolved aerosol extinction without constraint. Not requiring a constraint means greater availability of retrievals in polar regions, on the night side, and in broken cloud situations, plus greater accuracy particularly in the lowest part of the atmosphere and in scenes with aerosol heterogeneity. Advantages go beyond the extinction products. Unlike attenuated backscatter, which is an integrated quantity, the aerosol backscatter coefficient depends only on the aerosol at a specific level in the atmosphere, making it preferable for use in quantitative applications. The aerosol backscatter coefficient is more accurate from an HSRL system compared to the retrieval from a single-channel system. This is because errors in both extinction and backscatter from a single-channel system increase with decreasing altitude, due to the need to accurately characterize the overlying attenuation. This means that an HSRL will also have more valid data in and near the boundary layer where aerosol is of primary interest for air quality and weather applications and for many climate objectives including aerosol-cloud interaction studies. Even cloud properties that do not directly use the HSRL capability (cloud phase and thin cirrus retrievals) benefit from the more accurate calibration of an HSRL system. The improved accuracy of backscatter and extinction also lead to better capabilities for aerosol typing, improved retrievals of aerosol radiative effect, and increased information content for combined lidar + polarimeter retrievals of profiles of microphysical properties such as vertically resolved effective radius.

S P Burton↗
NASA NTRS1983

Differential absorption lidar technique for measurement of the atmospheric pressure profile

A new two-wavelength lidar technique for remotely measuring the pressure profile using the trough absorption region between two strong lines in the oxygen A band is described. The theory of integrated vertical path, differential ranging, and horizontal-path pressure measurements is given, with methods to desensitize and correct for temperature effects. The properties of absorption troughs are described and shown to reduce errors due to laser frequency jitter by up to two orders of magnitude. A general analysis, including laser bandwidth effects, demonstrates that pressure measurements with an integrated-vertical-path technique are typically fifty times more accurate than with a differential ranging technique. Simulations show 0.1-0.3 percent accuracy for ground and Shuttle-based pressure-profile and surface-pressure experiments.

Korb, C. L.↗
NASA NTRS2022

Robust Vision-based Multi-spacecraft Guidance Navigation and Control using CNN-based Pose Estimation

In this paper, we present an end-to-end simulation framework for tracking an uncooperative Target spacecraft in Low Earth Orbit using a CubeSat-class Ego spacecraft outfitted with a camera. Currently, capturing high-fidelity realistic images in space for this scenario is difficult and exorbitantly expensive. Therefore, we developed a framework to simulate the spacecraft orbits in Basilisk software and generate high-fidelity realistic images of spacecraft in Unreal Engine, including the effects from Sun, Earth, Moon and stars. The Ego spacecraft uses cameras to capture images of the uncooperative Target and estimates its position and attitude using a CNN based 6DOF pose estimation pipeline, eliminating need for large SWAP-C(Size, Weight, Power and Cost) sensors like LIDAR or reliance on inter-spacecraft communication, This CNN, which is motivated by ESA’s Pose Estimation challenge of 2019, is trained using simulated data from our end-to-end simulation framework. We compare the performance of two distinct CNNbased algorithms for pose estimation along a nominal trajectory. In presence of non-Gaussian modeling uncertainties, the statedependent estimation error is characterized with a quadratic upper-bound. The quadratically-bounded error can be used by a robust controller to maneuver

Rahmani, Amir↗
NASA NTRS2018

CALIPSO Lidar Level 3 Aerosol Profile Product: Version 3 Algorithm Design

The CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) level 3 aerosol profile product reports globally gridded, quality-screened, monthly mean aerosol extinction profiles retrieved by CALIOP (the Cloud-Aerosol Lidar with Orthogonal Polarization). This paper describes the quality screening and averaging methods used to generate the version 3 product. The fundamental input data are CALIOP level 2 aerosol extinction profiles and layer classification information (aerosol, cloud, and clear-air). Prior to aggregation, the extinction profiles are quality-screened by a series of filters to reduce the impact of layer detection errors, layer classification errors, extinction retrieval errors, and biases due to an intermittent signal anomaly at the surface. The relative influence of these filters are compared in terms of sample rejection frequency, mean extinction, and mean aerosol optical depth (AOD). The “extinction QC flag” filter is the most influential in preventing high-biases in level 3 mean extinction, while the “misclassified cirrus fringe” filter is most aggressive at rejecting cirrus misclassified as aerosol. The impact of quality screening on monthly mean aerosol extinction is investigated globally and regionally. After applying quality filters, the level 3 algorithm calculates monthly mean AOD by vertically integrating the monthly mean quality-screened aerosol extinction profile. Calculating monthly mean AOD by integrating the monthly mean extinction profile prevents a low bias that would result from alternately integrating the set of extinction profiles first and then averaging the resultant AOD values together. Ultimately, the quality filters reduce level 3 mean AOD by −24 and −31 % for global ocean and global land, respectively, indicating the importance of quality screening.

Tackett, Jason L.↗
NASA NTRSDate not supplied

Snow Depth from AMSR-2 Using Multispectral Satellite Data in an Artificial Neural Network

By using diffusion theory and Monte Carlo lidar radiative transfer simulations, Hu et al. (2022b) has derived snow depth from the first-, second- and third-order moments of the lidar backscattering pathlength distribution. Lu et al. (2022) calculated the snow depth by applying the methods to the satellite ICESat-2 lidar measurements over the Arctic sea ice, as well as land surfaces of Northern Hemisphere. In this paper, an artificial neural network (ANN) algorithm, employing several channels from Advanced Microwave Scanning Radiometer 2 (AMSR-2) and the humidity vertical profiles from Global Modeling and Assimilation Office (GMAO) Goddard Earth Observing System for Instrument Teams (GEOS-IT) product, is trained to determine snow depth identified by time and geolocation matched 2019 ICESat-2 snow-depth data during winter months over the Arctic sea ice. The trained ANN snow-depth was applied to 2018 AMSR-2 clear pixel data, although the algorithms perform reasonably well in thinner clouds. The validation data (different from the training set) of ANN snow depth from AMSR-2 showed a good agreement with time matched and co-located snow-depth values from ICESat-2. The bias was near zero, with mean absolute error (MAE) 0.05 cm and a root-mean-square-error (RMSE) 0.08 cm. Prior applying the trained ANN snow depth to AMSR-2 data, a cloud screening algorithm was developed with a similar approach. A separate ANN cloud mask was trained to determine an AMSR-2 pixel is clear or cloudy with time and geolocation matched 2015 CALIOP Vertical Feature Mask (VFM) over Arctic sea ice. The ANN cloud mask from AMSR-2 under-estimated cloud fraction by 3-6% compared to CALIOP . The additional research is needed to conclusively evaluate the ANN cloud mask accuracy. Finally, this paper will lay the foundation for a sustained long-term snowfall and snow-storm monitoring system. The future Cloud Aerosol LIdar for Global scale Observations of the ocean-Land Atmosphere system (CALIGOLA) mission will provide a means to calculate snow depth from the lidar backscattering pathlength distribution, benefiting from the UV, visible and infrared pulses. With the calculated snow depth as the truth one could develop a machine learning algorithm, as it was done in this paper, using a passive microwave instrument available at that time to generate a wide range of snow depth data, covering extensive spatial areas in the cross-orbit direction.

Neural Network↗
NASA NTRS2008

Laser Frequency Stabilization for Coherent Lidar Applications using Novel All-Fiber Gas Reference Cell Fabrication Technique

Compact hollow-core photonic crystal fiber (HC-PCF)gas frequency reference cell was constructed using a novel packaging technique that relies on torch-sealing a quartz filling tube connected to a mechanical splice between regular and hollow-core fibers. The use of this gas cell for laser frequency stabilization was demonstrated by locking a tunable diode laser to the center of the P9 line from the (nu)1+(nu)3 band of acetylene with RMS frequency error of 2.06 MHz over 2 hours. This effort was performed in support of a task to miniaturize the laser frequency stabilization subsystem of JPL/LMCT Laser Absorption Spectrometer (LAS) instrument.

Laser Absorption Spectrometer (LAS)↗
NASA NTRS1988

Predictions of silicon avalanche photodiode detector performance in water vapor differential absorption lidar

Performance analyses are presented which establish that over most of the range of signals expected for a down-looking differential absorption lidar (DIAL) operated at 16 km the silicon avalanche photodiode (APD) is the preferred detector for DIAL measurements of atmospheric water vapor in the 730 nm spectral region. The higher quantum efficiency of the APD's, (0.8-0.9) compared to a photomultiplier's (0.04-0.18) more than offsets the higher noise of an APD receiver. In addition to offering lower noise and hence lower random error the APD's excellent linearity and impulse recovery minimize DIAL systematic errors attributable to the detector. Estimates of the effect of detector system parameters on overall random and systematic DIAL errors are presented, and performance predictions are supported by laboratory characterization data for an APD receiver system.

Kenimer, R. L.↗
NASA NTRS2007

Using MODIS and GLAS Data to Develop Timber Volume Estimates in Central Siberia

The boreal forest is the Earth's largest terrestrial biome, covering some 12 million km2 and accounting for about one third of this planet's total forest area. Mapping of boreal forest's type, structure parameters and biomass are critical for understanding the boreal forest's significance in the carbon cycle, its response to and impact on global climate change. Ground based forest inventories, have much uncertainty in the inventory data, particularly in remote areas of Siberia where sampling is sparse and/or lacking. In addition, many of the forest inventories that do exist for Siberia are now a decade or more old. Thus, available forest inventories fail to capture the current conditions. Changes in forest structure in a particular forest-type and region can change significantly due to changing environment conditions, and natural and anthropogenic disturbance. Remote sensing methods can potentially overcome these problems. Multispectral sensors can be used to provide vegetation cover maps that show a timely and accurate geographic distribution of vegetation types rather than decade old ground based maps. Lidar sensors can be used to directly obtain measurements that can be used to derive critical forest structure information (e.g., height, density, and volume). These in turn can used to estimate biomass components using allometric equations without having to use out dated forest inventory. Finally, remote sensing data is ideally suited to provide a sampling basis for a rigorous statistical estimate of the variance and error bound on forest structure measures. In this study, new remote sensing methods were applied to develop estimates timber volume using NASA's MODerate resolution Imaging Spectroradiometer (MODIS) and unique waveform data of the geoscience laser altimeter system (GLAS) for a 10 deg x 10 deg area in central Siberia. Using MODIS and GLAS data, maps were produced for cover type and timber volume for 2003, and a realistic variance (error bound) for timber volume was calculated for the study area. In this 'study we used only GLAS footprints that had a slope value of less than 10 deg. This was done to avoid large errors due to the effect of slope on the GLAS models. The method requires the integration of new remote sensing methods with available ground studies of forest timber volume conducted in Russian forests. The results were compared to traditional ground forest inventory methods reported in the literature and to ground truth collected in the study area.

Ranson, K. Jon↗