Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “ocean model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Impact of Pacific Ocean Heatwaves on Phytoplankton Community Composition

Since 2013, marine heatwaves have become recurrent throughout the equatorial and northeastern Pacific Ocean and are expected to increase in intensity relative to historic norms. Among the ecological ramifications associated with these high temperature anomalies are increased mortality of higher trophic organisms such as marine mammals and seabirds, which are likely triggered by changes in the composition of phytoplankton, the base of the marine trophic food web. Here, we assimilated satellite ocean color data into an ocean biogeochemical model to describe changes in the abundance of phytoplankton functional types (PFTs) during the last decade’s (2010s) warm anomalies in the equatorial and northeastern Pacific Ocean. We find important changes associated with the “Blob” warm anomaly in the Gulf of Alaska, where reduced silica supply led to a switch in community composition from diatoms to dinoflagellates, resulting in an increase in surface ocean chlorophyll during the Summer–Fall of 2014. A more dramatic change was observed in the equatorial Pacific, where the extreme warm conditions of the 2016 El Niño resulted in a major decline of about 40% in surface chlorophyll, which was associated with a nearly total collapse in diatoms.

Lionel A Quintero↗
NASA NTRSDate not supplied

Impact of Pacific Ocean Heatwaves on Phytoplankton Community Composition

Since 2013, marine heatwaves have become recurrent throughout the equatorial and northeastern Pacific Ocean and are expected to increase in intensity relative to historic norms. Among the ecological ramifications associated with these high temperature anoma- lies are increased mortality of higher trophic organisms such as marine mammals and sea- birds, which are likely triggered by changes in the composition of phytoplankton, the base of the marine trophic food web. Here, we assimilated satellite ocean color data into an ocean biogeochemical model to describe changes in the abundance of phytoplankton functional types (PFTs) during the last decade’s (2010s) warm anomalies in the equatorial and northeastern Pacific Ocean. We find important changes associated with the “Blob” warm anomaly in the Gulf of Alaska, where reduced silica supply led to a switch in community composition from diatoms to dinoflagellates, resulting in an increase in surface ocean chlorophyll during the Summer–Fall of 2014. A more dramatic change was observed in the equatorial Pacific, where the extreme warm conditions of the 2016 El Niño resulted in a major decline of about 40% in surface chlorophyll, which was associated with a nearly total collapse in diatoms.

Lionel A. Arteaga↗
NASA NTRS1993

The influence of orography on the transport of atmospheric constituents

Given the fact that martian orography varies over a range of two scale heights (cf., about one scale height on Earth), it is thought that on Mars some aspects of the circulation should be affected to a large degree by the presence of orography. Initial results from two numerical models are presented that illustrate the effect of orography on cross-equatorial transport on Mars. On Earth, western boundary currents are found not only in the oceans as one would expect, but also in the troposphere, the most notable example being the East African Jet, which has an important effect on the monsoon circulation of the Eastern Indian Ocean. Two models were used for this investigation: a simple GCM (hereafter referred to as the SGCM); and a simple one-level barotropic model (BM). The SGCM solves the hydrostatic primitive equations on a sphere by representing model variables by spherical harmonics in the horizontal, with nonlinear terms being calculated in grid-point space. In the vertical, the model uses the sigma coordinate system in finite-difference form. The model represents the radiative processes in the atmosphere by a Newtonian relaxation to a specified zonal mean temperature state and surface drag by Rayleigh friction in the lowest model level.

Joshi, Manoj M.↗
NASA NTRS2016

Effect of Atmospheric Organics on Bioavailable Fe Lifetime in the Oceans

The deposition of atmospheric aerosols is an important supply pathway of soluble iron (sol-Fe) to the global oceans influencing marine ecosystem processes and climate. Previous studies have shown that natural and anthropogenic acidic trace gases, when mixed with mineral dust, can lead to production of sol-Fe, leading to considerable increase in dust-Fe solubility. Recent studies have further highlighted the importance of atmospheric organic compounds/ligands in the production of sol-Fe during atmospheric transport and transformation of mineral aerosols. However, the actual scope of this aerosol sol-Fe for stimulating the primary productivity in the oceans is determined by both: the total atmospheric fluxes of sol-Fe and the lifetime of sol-Fe after its deposition to the ocean. In this study several atmospheric organic ligands were investigated for their effect on the lifetime of sol-Fe after mixing with seawater. Organic ligands were selected based on their abundance in the marine boundary layer and rainwater and their ability to form bidentate complexes with Fe. The results reveal that the tested organics had minor influence on Fe(II) lifetime in seawater. However, results also show that some organic acid considerably extended the lifetime of colloidal and aqueous Fe(III). Using these results we simulate aerosol sol-Fe lifetime in the ocean for different mineral dust deposition events in the presence and the absence of atmospheric organic ligands. The calculations suggest that when a large dust plume is assumed to contain Fe(II) alone, less than 15% of aerosol sol-Fe gets complexed with marine organic ligands. However, this fraction increases to over 90% when atmospheric Fe is allowed to bond with atmospheric organic acids prior to deposition to the oceans. Calculations also show that for the conditions when seawater organic ligands get titrated by Fe released from dust aerosol particles, retention of sol-Fe in the ocean depends on surface ocean mixing, i.e., replenishing rates for Fe-bonding ligands from below. This study suggests that in future ocean biogeochemistry models more attention should be devoted to better quantification of the role of atmospheric organic acids in the lifetime of aerosol sol-Fe after its deposition to the ocean and the improvements of upper ocean turbulence parameterizations.

Oceans↗
NASA NTRS2019

Satellite Salinity Observing System: Recent Discoveries and the Way Forward

Advances in L-band microwave satellite radiometry in the past decade, pioneered by ESA's SMOS and NASA's Aquarius and SMAP missions, have demonstrated an unprecedented capability to observe global sea surface salinity (SSS) from space. Measurements from these missions are the only means to probe the very-near surface salinity (top cm), providing a unique monitoring capability for the interfacial exchanges of water between the atmosphere and the upper-ocean, and delivering a wealth of information on various salinity processes in the ocean, linkages with the climate and water cycle, including land-sea connections, and providing constraints for ocean prediction models. The satellite SSS data are complimentary to the existing in situ systems such as Argo that provide accurate depiction of large-scale salinity variability in the open ocean but under-sample mesoscale variability, coastal oceans and marginal seas, and energetic regions such as boundary currents and fronts. In particular, salinity remote sensing has proven valuable to systematically monitor the open oceans as well as coastal regions up to approximately 40 km from the coasts. This is critical to addressing societally relevant topics, such as land-sea linkages, coastal-open ocean exchanges, research in the carbon cycle, near-surface mixing, and air-sea exchange of gas and mass. In this paper, we provide a community perspective on the major achievements of satellite SSS for the aforementioned topics, the unique capability of satellite salinity observing system and its complementarity with other platforms, uncertainty characteristics of satellite SSS, and measurement versus sampling errors in relation to in situ salinity measurements. We also discuss the need for technological innovations to improve the accuracy, resolution, and coverage of satellite SSS, and the way forward to both continue and enhance salinity remote sensing as part of the integrated Earth Observing System in order to address societal needs.

Vinogradova, Nadya↗
NASA NTRS1979

A model for the microwave emissivity of the ocean's surface as a function of wind speed

A quanitative model is presented which describes the ocean surface as a ensemble of flat facets with a normal distribution of slopes. The variance of the slope distribution is linearly related to frequency up to 35 GHz and constant at higher frequencies. These facets are partially covered with an absorbing nonpolarized foam layer. Experimental evidence is presented for this model.

Wilheit, T. T.↗
NASA NTRS1979

A model for the microwave emissivity of the ocean's surface as a function of wind speed

A quantitative model is presented, which describes the ocean surface as an ensemble of flat facets with a normal distribution of slopes. The variance of the slope distribution is linearly related to frequency up to 35 GHz and constant at higher frequencies. These facets are partially covered with an absorbing nonpolarized foam layer. Experimental evidence is presented for this model.

Wilheit, T. T., Jr.↗
NASA NTRS1996

Evaluation of the Emergency Response Dose Assessment System(ERDAS)

The emergency response dose assessment system (ERDAS) is a protype software and hardware system configured to produce routine mesoscale meteorological forecasts and enhanced dispersion estimates on an operational basis for the Kennedy Space Center (KSC)/Cape Canaveral Air Station (CCAS) region. ERDAS provides emergency response guidance to operations at KSC/CCAS in the case of an accidental hazardous material release or an aborted vehicle launch. This report describes the evaluation of ERDAS including: evaluation of sea breeze predictions, comparison of launch plume location and concentration predictions, case study of a toxic release, evaluation of model sensitivity to varying input parameters, evaluation of the user interface, assessment of ERDA's operational capabilities, and a comparison of ERDAS models to the ocean breeze dry gultch diffusion model.

Evans, Randolph J.↗
NASA NTRS2013

Global Monitoring of Terrestrial Chlorophyll Fluorescence from Moderate-Spectral-Resolution Near-Infrared Satellite Measurements: Methodology, Simulations, and Application to GOME-2

Globally mapped terrestrial chlorophyll fluorescence retrievals are of high interest because they can provide information on the functional status of vegetation including light-use efficiency and global primary productivity that can be used for global carbon cycle modeling and agricultural applications. Previous satellite retrievals of fluorescence have relied solely upon the filling-in of solar Fraunhofer lines that are not significantly affected by atmospheric absorption. Although these measurements provide near-global coverage on a monthly basis, they suffer from relatively low precision and sparse spatial sampling. Here, we describe a new methodology to retrieve global far-red fluorescence information; we use hyperspectral data with a simplified radiative transfer model to disentangle the spectral signatures of three basic components: atmospheric absorption, surface reflectance, and fluorescence radiance. An empirically based principal component analysis approach is employed, primarily using cloudy data over ocean, to model and solve for the atmospheric absorption. Through detailed simulations, we demonstrate the feasibility of the approach and show that moderate-spectral-resolution measurements with a relatively high signal-to-noise ratio can be used to retrieve far-red fluorescence information with good precision and accuracy. The method is then applied to data from the Global Ozone Monitoring Instrument 2 (GOME-2). The GOME-2 fluorescence retrievals display similar spatial structure as compared with those from a simpler technique applied to the Greenhouse gases Observing SATellite (GOSAT). GOME-2 enables global mapping of far-red fluorescence with higher precision over smaller spatial and temporal scales than is possible with GOSAT. Near-global coverage is provided within a few days. We are able to show clearly for the first time physically plausible variations in fluorescence over the course of a single month at a spatial resolution of 0.5 0.5. We also show some significant differences between fluorescence and coincident normalized difference vegetation indices (NDVI) retrievals.

Fluorescence↗
NASA NTRS2013

Global Monitoring of Terrestrial Chlorophyll Fluorescence from Moderate-spectral-resolution Near-infrared Satellite Measurements: Methodology, Simulations, and Application to GOME-2

Globally mapped terrestrial chlorophyll fluorescence retrievals are of high interest because they can provide information on the functional status of vegetation including light-use efficiency and global primary productivity that can be used for global carbon cycle modeling and agricultural applications. Previous satellite retrievals of fluorescence have relied solely upon the filling-in of solar Fraunhofer lines that are not significantly affected by atmospheric absorption. Although these measurements provide near-global coverage on a monthly basis, they suffer from relatively low precision and sparse spatial sampling. Here, we describe a new methodology to retrieve global far-red fluorescence information; we use hyperspectral data with a simplified radiative transfer model to disentangle the spectral signatures of three basic components: atmospheric absorption, surface reflectance, and fluorescence radiance. An empirically based principal component analysis approach is employed, primarily using cloudy data over ocean, to model and solve for the atmospheric absorption. Through detailed simulations, we demonstrate the feasibility of the approach and show that moderate-spectral-resolution measurements with a relatively high signal-to-noise ratio can be used to retrieve far-red fluorescence information with good precision and accuracy. The method is then applied to data from the Global Ozone Monitoring Instrument 2 (GOME-2). The GOME-2 fluorescence retrievals display similar spatial structure as compared with those from a simpler technique applied to the Greenhouse gases Observing SATellite (GOSAT). GOME-2 enables global mapping of far-red fluorescence with higher precision over smaller spatial and temporal scales than is possible with GOSAT. Near-global coverage is provided within a few days. We are able to show clearly for the first time physically plausible variations in fluorescence over the course of a single month at a spatial resolution of 0.5 deg × 0.5 deg. We also show some significant differences between fluorescence and coincident normalized difference vegetation indices (NDVI) retrievals.

remote sensing↗
NASA NTRS2019

Estuarine Dissolved Organic Carbon Flux From Space: With Application to Chesapeake and Delaware Bays

This study uses a neural network model trained with in situ data, combined with satellite data and hydrodynamic model products, to compute the daily estuarine export of dissolved organic carbon (DOC) at the mouths of Chesapeake Bay (CB) and Delaware Bay (DB) from 2007 to 2011. Both bays show large flux variability with highest fluxes in spring and lowest in fall as well as interannual flux variability (0.18 and 0.27 Tg C/year in 2008 and 2010 for CB; 0.04 and 0.09 Tg C/year in 2008 and 2011 for DB). Based on previous estimates of total organic carbon (TOCexp) exported by all Mid-Atlantic Bight estuaries (1.2 Tg C/year), the DOC export (CB + DB) of 0.3 Tg C/year estimated here corresponds to 25% of the TOCexp. Spatial and temporal covariations of velocity and DOC concentration provide contributions to the flux, with larger spatial influence. Differences in the discharge of fresh water into the bays (74 billion cu. m/year for CB and 21 billion cu. m/year for DB) and their geomorphologies are major drivers of the differences in DOC fluxes for these two systems. Terrestrial DOC inputs are similar to the export of DOC at the bay mouths at annual and longer time scales but diverge significantly at shorter time scales (days to months). Future efforts will expand to the Mid-Atlantic Bight and Gulf of Maine, and its major rivers and estuaries, in combination with coupled terrestrial-estuarine-ocean biogeochemical models that include effects of climate change, such as warming and CO2 increase.

Estuarine DOC export↗
NASA NTRS2015

Ocean Heat and Carbon Uptake in Transient Climate Change: Identifying Model Uncertainty

Global warming on decadal and centennial timescales is mediated and ameliorated by the oceansequestering heat and carbon into its interior. Transient climate change is a function of the efficiency by whichanthropogenic heat and carbon are transported away from the surface into the ocean interior (Hansen et al. 1985).Gregory and Mitchell (1997) and Raper et al. (2002) were the first to identify the importance of the ocean heat uptakeefficiency in transient climate change. Observational estimates (Schwartz 2012) and inferences from coupledatmosphere-ocean general circulation models (AOGCMs; Gregory and Forster 2008; Marotzke et al. 2015), suggest thatocean heat uptake efficiency on decadal timescales lies in the range 0.5-1.5 W/sq m/K and is thus comparable to theclimate feedback parameter (Murphy et al. 2009). Moreover, the ocean not only plays a key role in setting the timing ofwarming but also its regional patterns (Marshall et al. 2014), which is crucial to our understanding of regional climate,carbon and heat uptake, and sea-level change. This short communication is based on a presentation given by A.Romanou at a recent workshop, Oceans Carbon and Heat Uptake: Uncertainties and Metrics, co-hosted by US CLIVARand OCB. As briefly reviewed below, we have incomplete but growing knowledge of how ocean models used in climatechange projections sequester heat and carbon into the interior. To understand and thence reduce errors and biases inthe ocean component of coupled models, as well as elucidate the key mechanisms at work, in the final section we outlinea proposed model intercomparison project named FAFMIP. In FAFMIP, coupled integrations would be carried out withprescribed overrides of wind stress and freshwater and heat fluxes acting at the sea surface.

periodic variations↗
NASA NTRS2016

The Chlorine Isotopic Composition Of Lunar UrKREEP

Since the long standing paradigm of an anhydrous Moon was challenged there has been a renewed focus on investigating volatiles in a variety of lunar samples. Numerous studies have examined the abundances and isotopic compositions of volatiles in lunar apatite, Ca5(PO4)3(F,Cl,OH). In particular, apatite has been used as a tool for assessing the sources of H2O in the lunar interior. However, current models for the Moon's formation have yet to fully account for its thermal evolution in the presence of H2O and other volatiles. For ex-ample, in the context of the lunar magma ocean (LMO) model, it is anticipated that chlorine (and other volatiles) should have been concentrated in the late-stage LMO residual melts (i.e., the dregs enriched in incompatible elements such as K, REEs (Rare Earth Elements), and P, collectively called KREEP, and in its primitive form - urKREEP, given its incompatibility in mafic minerals like olivine and pyroxene, which were the dominant phases that crystallized early in the cumulate pile of the LMO. When compared to chondritic meteorites and terrestrial rocks, lunar samples have exotic chlorine isotope compositions, which are difficult to explain in light of the abundance and isotopic composition of other volatile species, especially H, and the current estimates for chlorine and H2O in the bulk silicate Moon (BSM). In order to better understand the processes involved in giving rise to the heavy chlorine isotope compositions of lunar samples, we have performed a comprehensive in situ high precision study of chlorine isotopes in lunar apatite from a suite of Apollo samples covering a range of geochemical characteristics and petrologic types.

Barnes, J. J.↗
NASA NTRS2009

Timing of Crystallisation of the Lunar Magma Ocean Constrained by the Oldest Zircon

The presently favoured concept for the early evolution of the Moon involves consolidation of debris from a giant impact of a Mars sized body with Earth forming a primitive Moon with a thick global layer of melt referred to as the Lunar Magma Ocean1 . It is widely accepted that many significant features observed on the Moon today are the result of crystallisation of this magma ocean. However, controversy exists over the precise timing and duration of the crystallisation process. Resolution of this problem depends on the establishment of precise and robust key crystallisation time points. We report a 4417 6 Myr old zircon in lunar breccia sample 72215,195, which provides a precisely determined younger limit for the solidification of the Lunar Magma Ocean. A model based on these data, together with the age of the Moon forming giant impact, defines an exponential time frame for crystallisation and suggests formation of anorthositic crust after about 80-85% of the magma ocean was solidified. In combination with other zircon ages the 4417 +/- 6 Myr age also suggests that the very small (less than a few per cent) residual portion of the magma ocean continued to solidify during the following 300-500 m.y.

Nemchin, A.↗
NASA NTRS2013

Sensitivity of the Atmospheric Response to Warm Pool El Nino Events to Modeled SSTs and Future Climate Forcings

Warm pool El Nino (WPEN) events are characterized by positive sea surface temperature (SST) anomalies in the central equatorial Pacific. Under present-day climate conditions, WPEN events generate poleward propagating wavetrains and enhance midlatitude planetary wave activity, weakening the stratospheric polar vortices. The late 21st century extratropical atmospheric response to WPEN events is investigated using the Goddard Earth Observing System Chemistry-Climate Model (GEOSCCM), version 2. GEOSCCM simulations are forced by projected late 21st century concentrations of greenhouse gases (GHGs) and ozone-depleting substances (ODSs) and by SSTs and sea ice concentrations from an existing ocean-atmosphere simulation. Despite known ocean-atmosphere model biases, the prescribed SST fields represent a best estimate of the structure of late 21st century WPEN events. The future Arctic vortex response is qualitatively similar to that observed in recent decades but is weaker in late winter. This response reflects the weaker SST forcing in the Nino 3.4 region and subsequently weaker Northern Hemisphere tropospheric teleconnections. The Antarctic stratosphere does not respond to WPEN events in a future climate, reflecting a change in tropospheric teleconnections: The meridional wavetrain weakens while a more zonal wavetrain originates near Australia. Sensitivity simulations show that a strong poleward wavetrain response to WPEN requires a strengthening and southeastward extension of the South Pacific Convergence Zone; this feature is not captured by the late 21st century modeled SSTs. Expected future increases in GHGs and decreases in ODSs do not affect the polar stratospheric responses to WPEN.

stratosphere↗
NASA NTRS2019

Soil Moisture Active/Passive (SMAP) L-Band Microwave Radiometer Post-Launch Calibration Upgrade

The Soil Moisture Active/Passive (SMAP) microwave radiometer is a fully polarimetric L-band radiometer flown on theSMAP satellite in a 6 AM/6 PM sun-synchronous orbit at 685 km altitude. After the SMAP L1B_TB data product version 3 was released in 2016, the radiometer has been undergoing further calibration and validation with the goal of reducing both the bias in the cold-sky measurements and calibration drift in the global ocean measurements experienced during eclipse seasons in data product version 3. The post-launch calibration algorithm has been upgraded by using new estimates of the reflector emissivity as well as using multiple scenes to calibrate the radiometer internal reference sources and antenna gain simultaneously. In addition, a correction offset is applied to the ocean roughness model for horizontal polarization based on nadir observations. Test and validation results show that the goal is achieved (e.g., biases are removed and the calibration stability achieved for data release version 4 is 0.1 K(rms) over both the global ocean and CS).

Calibratio↗
NASA NTRS1978

On isostatic geoid anomalies

In regions of slowly varying lateral density changes, the gravity and geoid anomalies may be expressed as power series expansions in topography. Geoid anomalies in isostatically compensated regions can be directly related to the local dipole moment of the density-depth distribution. This relationship is used to obtain theoretical geoid anomalies for different models of isostatic compensation. The classical Pratt and Airy models give geoid height-elevation relationships differing in functional form but predicting geoid anomalies of comparable magnitude. The thermal cooling model explaining ocean floor subsidence away from mid-ocean ridges predicts a linear age-geoid height relationship of 0.16 m/m.y. Geos 3 altimetry profiles were examined to test these theoretical relationships. A profile over the mid-Atlantic ridge is closely matched by the geoid curve derived from the thermal cooling model. The observed geoid anomaly over the Atlantic margin of North America can be explained by Airy compensation. The relation between geoid anomaly and bathymetry across the Bermuda Swell is consistent with Pratt compensation with a 100-km depth of compensation.

Haxby, W. F.↗
NASA NTRS2008

A Multi-Season Study of the Effects of MODIS Sea-Surface Temperatures on Operational WRF Forecasts at NWS Miami, FL

Studies at the Short-term Prediction Research and Transition (SPORT) Center have suggested that the use of Moderate Resolution Imaging Spectroradiometer (MODIS) sea-surface temperature (SST) composites in regional weather forecast models can have a significant positive impact on short-term numerical weather prediction in coastal regions. Recent work by LaCasse et al (2007, Monthly Weather Review) highlights lower atmospheric differences in regional numerical simulations over the Florida offshore waters using 2-km SST composites derived from the MODIS instrument aboard the polar-orbiting Aqua and Terra Earth Observing System satellites. To help quantify the value of this impact on NWS Weather Forecast Offices (WFOs), the SPORT Center and the NWS WFO at Miami, FL (MIA) are collaborating on a project to investigate the impact of using the high-resolution MODIS SST fields within the Weather Research and Forecasting (WRF) prediction system. The project's goal is to determine whether more accurate specification of the lower-boundary forcing within WRF will result in improved land/sea fluxes and hence, more accurate evolution of coastal mesoscale circulations and the associated sensible weather elements. The NWS MIA is currently running WRF in real-time to support daily forecast operations, using the National Centers for Environmental Prediction Nonhydrostatic Mesoscale Model dynamical core within the NWS Science and Training Resource Center's Environmental Modeling System (EMS) software. Twenty-seven hour forecasts are run dally initialized at 0300, 0900, 1500, and 2100 UTC on a domain with 4-km grid spacing covering the southern half of Florida and adjacent waters of the Gulf of Mexico and Atlantic Ocean. Each model run is initialized using the Local Analysis and Prediction System (LAPS) analyses available in AWIPS. The SSTs are initialized with the NCEP Real-Time Global (RTG) analyses at 1/12deg resolution (approx.9 km); however, the RTG product does not exhibit fine-scale details consistent with its grid resolution. SPORT is conducting parallel WRF EMS runs identical to the operational runs at NWS MIA except for the use of MODIS SST composites in place of the RTG product as the initial and boundary conditions over water, The MODIS SST composites for initializing the SPORT WRF runs are generated on a 2-km grid four times daily at 0400, 0700, 1600, and 1900 UTC, based on the times of the overhead passes of the Aqua and Terra satellites. The incorporation of the MODIS SST data into the SPORT WRF runs is staggered such that SSTs are updated with a new composite every six hours in each of the WRF runs. From mid-February to July 2007, over 500 parallel WRF simulations have been collected for analysis and verification. This paper will present verification results comparing the NWS MIA operational WRF runs to the SPORT experimental runs, and highlight any substantial differences noted in the predicted mesoscale phenomena for specific cases.

Case, Jonathan L.↗