Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “surface mass variations”

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 109 records · Page 6

Systematics of the CHON and other light-element particle populations in Comet Halley

Based on chemical signatures measured by the PIA experiment during the Giotto flyby of comet Halley, particle classifications were designated. In addition to silicate-like grains and particles of mixed (cosmic) composition, there appear to be several light-element rich populations, including the CHON, (H,C), (H,C,O), and (H,C,N) particle types. These compositional classes are further distinguished by differences in mass distributions, a density indicator, and variations in relative abundance within the coma. These particle populations are evidence for chemical heterogeneity in the surface of the cometary nucleus. Particles found mainly in the inner coma may be volatile icy grains. Most of the N of the comet may be found in up to three different populations of grains; one or more of these may be responsible for the observation of cyanojets.

Clark, Benton↗

Polar Firn Properties in Greenland and Antarctica and Related Effects on Microwave Brightness Temperatures

In studying the mass balance of polar ice sheets, fluctuations of firn density near the surface is a major uncertainty. In this paper, we explore these variations at locations in the Greenland Ice Sheet and at the Dome C location in Antarctica. Borehole in situ measurements, Snow Radar echoes, microwave brightness temperatures, and modelling results from the Community firn model (CFM) are used. It is shown that firn density profiles can be represented using 3 processes: “long” and “short” length scale density variations and “refrozen layers”. Consistency with this description is observed in the dynamic range of airborne 0.5-2 GHz brightness temperatures and Snow Radar echo peaks in measurements performed in Greenland in 2017. Based on these insights, a new analytical partially coherent model is implemented to explain the microwave brightness temperatures using the three scale description of the firn. Short and long scale firn processes are modelled as a 3D continuous random medium with finite vertical and horizontal correlation lengths as opposed to past 1D random layered medium descriptions. Refrozen layers are described as deterministic sheets with planar interfaces, with the number of refrozen layer interfaces determined by radar observations. Firn density and correlation length parameters used in forward modelling to match measured 0.5-2 GHz brightness temperatures in Greenland show consistency with similar parameters in CFM predictions. Model predictions also are in good agreement with multi-angle 1.4 GHz vertically and horizontally polarized brightness temperature measured by the SMOS satellite at DOME C, Antarctica. This work shows that co-located active and passive microwave measurements can be used to infer polar firn properties that can be compared with predictions of the CFM. In particular, 0.5-2 GHz brightness temperature measurements are shown to be sensitive to long scale firn density fluctuations with density standard deviations in the range 0.01-0.06 g/cm^3 and vertical correlation lengths of 6-20 cm.

Haokui Xu↗

Photosynthetic fractionation of 13C and concentrations of dissolved CO2 in the central equatorial Pacific during the last 255,000 years

Carbon isotopically based estimates of CO2 levels have been generated from a record of the photosynthetic fractionation of 13C [is equivalent to epsilon(p)] in a central equatorial Pacific sediment core that spans the last approximately 255 ka. Contents of 13C in phytoplanktonic biomass were determined by analysis of C37 alkadienones. These compounds are exclusive products of Prymnesiophyte algae which at present grow most abundantly at depths of 70-90 m in the central equatorial Pacific. A record of the isotopic composition of dissolved CO2 was constructed from isotopic analyses of the planktonic foraminifera Neogloboquadrina dutertrei, which calcifies at 70-90 m in the same region. Values of epsilon(p), derived by comparison of the organic and inorganic delta values, were transformed to yield concentrations of dissolved CO2 [is equivalent to c(e)] based on a new, site-specific calibration of the relationship between epsilon(p) and c(e). The calibration was based on reassessment of existing epsilon(p) versus c(e) data, which support a physiologically based model in which epsilon(p) is inversely related to c(e). Values of PCO2, the partial pressure of CO2 that would be in equilibrium with the estimated concentrations of dissolved CO2, were calculated using Henry's law and the temperature determined from the alkenone-unsaturation index U(K/37). Uncertainties in these values arise mainly from uncertainties about the appropriateness (particularly over time) of the site-specific relationship between epsilon(p) and 1/c(e). These are discussed in detail and it is concluded that the observed record of epsilon(p) most probably reflects significant variations in delta pCO2, the ocean-atmosphere disequilibrium, which appears to have ranged from approximately 110 microatmospheres during glacial intervals (ocean > atmosphere) to approximately 60 microatmospheres during interglacials. Fluxes of CO2 to the atmosphere would thus have been significantly larger during glacial intervals. If this were characteristic of large areas of the equatorial Pacific, then greater glacial sinks for the equatorially evaded CO2 must have existed elsewhere. Statistical analysis of air-sea pCO2 differences and other parameters revealed significant (p<0.01) inverse correlations of delta pCO2 with sea surface temperature and with the mass accumulation rate of opal. The former suggests response to the strength of upwelling, the latter may indicate either drawdown of CO2 by siliceous phytoplankton or variation of [CO2]/[Si(OH)4] ratios in upwelling waters.

NASA Discipline Exobiology↗

Transport phenomena of reactive fluid flow in heterogeneous combustion processes.

A previously developed computer program was used to model two transient hybrid combustion processes involving tubes of solid Plexiglas. In the first study, representing combustion of a hybrid rocket, the oxidizing gas was oxygen, and calculations were continued sufficiently long to obtain steady-state values. Systematic variations were made in reaction rate constant, mass flow rate, and pressure, alternatively using constant and temperature dependent regression rate models for the fuel surface. Consistent results were obtained, as is evidenced by the values for the mass function of the reaction product and the flame temperature, for which plots are supplied. In the second study, fire initiation in a duct was studied, with an air mixture as the oxidizing gas. It was demonstrated that a satisfactory flame spread mechanism could be reproduced on the computer. In both of the above applications, the general, transient, two-dimensional conservation equations were represented, together with chemical reactions, solid-fuel interface conditions, and heat conduction in the solid fuel.

Hung, W. S. Y.↗

Understanding and Utilizing PBL Height Data from Multiple Observing Systems in the GEOS System

The accuracy of PBL height simulation is a key issue in many applications including forecasting near surface meteorology and air quality, however, it is a very challenging problem due to the lack of not only comprehensive, global Planetary Boundary Layer (PBL) observations but also a strategy and infrastructure to utilize PBL height data from a variety of sensors. Following the designation of PBL as an incubation class observable in the 2017 Decadal Survey, the PBL Incubation Study Team Report [14] made clear that “a future global PBL observing system requires modeling and data assimilation as essential components.” There is an urgent need for global modeling development in order to utilize Program of Record (POR) observations, assess their impacts, and identify gaps to be filled by future PBL missions. Our overall objective is to develop PBL data assimilation capabilities in the NASA Global Earth Observing System (GEOS), focusing on PBL height from multiple observing systems, to support the assessment and use of future PBL observations. The NASA GEOS system is composed of the GEOS global atmospheric general circulation model (AGCM) and the atmospheric data assimilation system (ADAS). The PBL parameterizations include the “Lock” K-profile scheme driven by surface and cloud-top buoyancy fluxes ([4]), and the “Louis” local scheme for stable conditions based on the Richardson number ([5]). Above the mixed layer defined by the Lock surface plume, shallow cumulus convection is represented by the mass flux scheme of [9]. Additional parameterizations are summarized in [1]. The ADAS employs the hybrid 4D Ensemble- Variational (EnVar) configuration ([15]), with the ensemble providing flow-dependent background error covariance information. The resultant analysis increments are fed back to the forecast model through the 4D incremental analysis update (IAU) approach ([11]). In this study, PBL height data are being or have been generated from radiosondes, GNSS RO, satellite (CATS, CALIPSO and ICESat-2) and ground-based (MPLNET) lidars, and wind profiler. Investigations have been conducted to specify quality marks for PBL height retrievals for the data assimilation purpose. These PBL height data have different strengths and weaknesses ([2], [3], [6], [7], [8], [10]), and the satellite PBL height data provide better global coverage and complement in-situ PBL height data. Radiosondes offer high accuracy and in situ measurement of temperature and humidity profiles, but with poor spatio-temporal sampling. The in-situ observing systems like MPLNET and wind profiler provide long history of PBL height records at each station. The GNSS RO based PBL height is retrieved based on the sharp gradients in refractivity profile that represent the fine vertical structure of temperature and moisture changes above the PBL. However, not all RO refractivity profiles reach the surface depending on location and regime, and RO refractivity retrievals can be negatively biased below 2km. The PBL height data from satellite lidars provide high resolution along track PBL height retrievals, but over land they are affected by previous day convective PBL aerosol and strongly associated with mixing layer and retrievals cannot be made below thick, attenuating clouds. A successful assimilation of PBL height data requires a thorough understanding of the observing method and the retrieval algorithm for each observing system in order to use the PBL height data from multiple observing systems properly. Due to the sensitivity of PBL height data to the observing method and choice of algorithm, it is important to use a model definition appropriate for each observation type to compute differences between PBL height data and model PBL height (OmFs). The GEOS model currently includes two PBL height definitions suitable for direct comparison with observed PBL height, and additional definitions are being added in this study. Evaluation of different model PBL height definitions is underway. Meanwhile, efforts have been made in the GEOS data assimilation system to develop PBL height data assimilation capability. PBL height data can be assimilated using two different approaches. The traditional approach is to construct an observation operator and its tangent linear and adjoint, which link control variables to PBL height data from each observing system. This observation operator can be very complicated, e.g., the lidar-based PBL height observation operator includes the backscatter lidar forward observation operator, the algorithm to derive PBL height from attenuated total backscatter, interpolation, and calculations handling the mismatch between observed and model scales. The other approach is to augment PBL height to the control variable vector, and it is adopted in this study. The latter approach was also used in previous studies, e.g., the assimilation of PBL height data from radiosonde and aircraft in the Real Time Mesoscale Analysis (RTMA) system for a dispersion modelling study ([13]); the PBL height assimilation study using lidar PBL height data at Greensburg, Kansas for a field campaign ([12]). The PBL height assimilation from multiple observing systems in this study allows us to take advantage of the diverse PBL height data that provide much better global coverage collectively under different meteorological conditions and with different temporal and spatial scales. As all the PBL heights are tightly coupled with the PBL thermodynamic variables, the strong correlations, which are provided by the 4D ensemble forecast, enable PBL height data from various sources to interact and combine coherently and provide additional information for PBL temperature and moisture fields. The results of comparisons among PBL height data from different sources and the evaluation of the model PBL height definitions with the PBL height data will be presented, and the PBL height data synergy strategies and preliminary results will also be discussed at the conference.

Y. Zhu↗

A combined surface/volume scattering retracking algorithm for ice sheet satellite altimetry

An algorithm that is based upon a combined surface-volume scattering model is developed. It can be used to retrack individual altimeter waveforms over ice sheets. An iterative least-squares procedure is used to fit the combined model to the return waveforms. The retracking algorithm comprises two distinct sections. The first generates initial model parameter estimates from a filtered altimeter waveform. The second uses the initial estimates, the theoretical model, and the waveform data to generate corrected parameter estimates. This retracking algorithm can be used to assess the accuracy of elevations produced from current retracking algorithms when subsurface volume scattering is present. This is extremely important so that repeated altimeter elevation measurements can be used to accurately detect changes in the mass balance of the ice sheets. By analyzing the distribution of the model parameters over large portions of the ice sheet, regional and seasonal variations in the near-surface properties of the snowpack can be quantified.

Davis, Curt H.↗

Viscous relaxation of a compressible spherical shell

Analytical solutions for analyzing viscous relaxation of a compressible mantle to surface loading are developed. Two different models are considered: one in which the density step of the core-mantle boundary is held fixed and the other in which the mass of the earth remains invariant with respect to variations of equation of state parameters. For thermodynamic parameters characteristic of the mantle, relaxation times of the fundamental and first overtone modes change by no more than about 30 percent for degree less than four. For a given initial depression, the ratio between the velocity in the lower mantle and that at the surface is bigger for incompressible models than for compressible models. Eigenfunctions between the two models also differ in appearance throughout the mantle, with the incompressible ones being larger for the second model. These results would suggest that the resolution of mantle viscosity may be impaired by the smaller excitation in the lower mantle due to effects of mantle compressibility.

Li, Guoying↗

Resonant absorption of Alfvenic surface waves and the heating of solar coronal loops

A first-order mass- and energy-balance model is developed for steady-state EUV 'coronal rain' loops that are not associated with postflare events and are often seen over sunspot umbrae. The model disregards variations in a loop's thermodynamic and magnetic properties along magnetic-field lines and yields average properties of the resonant absorption sheath, the boundary layer, and the loop's interior. Both irreversible heating by Alfvenic surface waves and energy transport via induced boundary-layer convection are taken into account in the analysis. Results that include predictions of the temperatures of the sheath and the boundary-layer plasma, the temperature of the interior plasma, the radiative output of the loop, and the filling factor associated with this radiation are given in terms of the period and velocity amplitude of the relevant surface wave as well as various parameters that characterize a typical 'coronal rain' loop. These results are shown to be consistent with the observed minimum and maximum temperatures as well as the radiative output of typical 'coronal rain' loops.

Ionson, J. A.↗

Growing season boundary layer climate and surface exchanges in a subarctic lichen woodland

Between June and August 1990, observations were made at two surface micrometeorological towers near Schefferville Quebec (54 deg 52 min N, 66 deg 40.5 min W), one in a fen and one in the subarctic lichen woodland, and at four surface climatological stations. Data from these surface stations were supplemented by regular radiosonde launches. Supporting measurements of radiative components and soil temperatures allowed heat and moisture balances to be obtained at two sites. The overall surface meteorological experiment design and results of micrometeorological observations made on a 30-m tower in the lichen woodland are presented here. Seasonal variation in the heat and water vapor transport characteristics illustrate the marked effect of the late summer climatological shift in air mass type. During the first half of the summer, average valley sidewalls only 100 m high are sufficient to channel winds along the valley in the entire convective boundary layer. Channeling effects at the surface, known for some time at the long-term climate station in Schefferville, are observed both at ridge top and in the valley, possibly the response of the flow to the NW-SE orientation of valleys in the region. Diurnal surface temperature amplitude at ridge top (approximately equal to 10 C) was found to be half that observed in the valley. Relatively large differences in precipitation among these stations and the climatological station at Schefferville airport were observed and attributed to the local topography. Eddy correlation observations of the heat, moisture and momentum transports were obtained from a 30-m tower above a sparse (approximately equal to 616 stems/ha) black spruce lichen woodland. Properties of the turbulent surface boundary layer agree well with previous wind tunnel studies over idealized rough surfaces. Daytime Bowen ratios of 2.5-3 are larger than those reported in previous studies. Surface layer flux data quality was assessed by looking at the surface layer heat balance. Diurnal and seasonal scale heat budget imbalances were found. We suggest that unmeasured surface heat storage may be responsible for some of the observed imbalance. The presence of the unexplained residual in this and other studies of energy balance over forests casts a note of caution on the interpretation of energy balance components obtained using heat residual methods.

Fitzjarrald, David R.↗

The Lunar Mass Spectrometer experiment.

The features of the Lunar Mass Spectrometer (LMS), the purpose of which will be to determine the global distributions and the diurnal variations of the lunar atmosphere from the lunar surface, are outlined. Particular attention is given to its configuration, design, and latest engineering refinements. A brief description is also given of the experiment operation and data return.

Ormsby, R. D.↗

Mass Redistribution in the Core and Time-varying Gravity at the Earth's Surface

The Earth's liquid outer core is in convection, as suggested by the existence of the geomagnetic field in much of the Earth's history. One consequence of the convection is the redistribution of mass resulting from relative motion among fluid parcels with slightly different densities. This time dependent mass redistribution inside the core produces a small perturbation on the gravity field of the Earth. With our numerical dynamo solutions, we find that the mass redistribution (and the resultant gravity field) symmetric about the equator is much stronger than that anti-symmetric about the equator. In particular, J(sub 2) component is the strongest. In addition, the gravity field variation increases with the Rayleigh number that measures the driving force for the geodynamo in the core. With reasonable scaling from the current dynamo solutions, we could expect that at the surface of the Earth, the J(sub 2) variation from the core is on the order of l0(exp -16)/year relative to the mean (i.e. spherically symmetric) gravity field of the Earth. The possible shielding effect due to core-mantle boundary pressure variation loading is likely much smaller and is therefore negligible. Our results suggest that time-varying gravity field perturbation due to core mass redistribution may be measured with modem space geodetic observations, which will result a new means of detecting dynamical processes in the Earth's deep interior.

Kuang, Wei-Jia↗

Assessment of climate variability of the Greenland Ice Sheet: Integration of in situ and satellite data

The proposed research involves the application of multispectral satellite data in combination with ground truth measurements to monitor surface properties of the Greenland Ice Sheet which are essential for describing the energy and mass of the ice sheet. Several key components of the energy balance are parameterized using satellite data and in situ measurements. The analysis will be done for a ten year time period in order to get statistics on the seasonal and interannual variations of the surface processes and the climatology. Our goal is to investigate to what accuracy and over what geographic areas large scale snow properties and radiative fluxes can be derived based upon a combination of available remote sensing and meteorological data sets. Operational satellite sensors are calibrated based on ground measurements and atmospheric modeling prior to large scale analysis to ensure the quality of the satellite data. Further, several satellite sensors of different spatial and spectral resolution are intercompared to access the parameter accuracy. Proposed parameterization schemes to derive key component of the energy balance from satellite data are validated. For the understanding of the surface processes a field program was designed to collect information on spectral albedo, specular reflectance, soot content, grain size and the physical properties of different snow types. Further, the radiative and turbulent fluxes at the ice/snow surface are monitored for the parameterization and interpretation of the satellite data. The expected results include several baseline data sets of albedo, surface temperature, radiative fluxes, and different snow types of the entire Greenland Ice Sheet. These climatological data sets will be of potential use for climate sensitivity studies in the context of future climate change.

Steffen, K.↗

Assessment of climate variability of the Greenland ice sheet: Integration of in situ and satellite data

The proposed research involves the application of multispectral satellite data in combination with ground truth measurements to monitor surface properties of the Greenland ice sheet which are essential for describing the energy and mass of the ice sheet. Several key components of the energy balance are parameterized using satellite data and in situ measurements. The analysis will be done for a ten year time period in order to get statistics on the seasonal and interannual variations of the surface processes and the climatology. Our goal is to investigate to what accuracy and over what geographic areas large scale snow properties and radiative fluxes can be derived based upon a combination of available remote sensing and meterological data sets. Data analysis showed the following results: (1)cloud classification based on longwave sky radiation revealed that overcast sky occurred for 25% of the time in winter, and for 15% in spring and summer respectively (winter and summer both show the same occurrence of clear sky of approximately 26%); (2) comparison of aerodynamic profile method with eddy correlation method to derive sensible and latent heat flux showed good agreement in the diurnal cycle and the turbulent fluxes were underestimated with the aerodynamic method by 10 - 30% as compared to the in situ eddy flux method; (3) the katabatic wind shows a distinct diurnal cycle with a maximum in the morning (7-9 h solar time) and a minimum in the later afternoon (18 h solar time); (4) snow grain size was modeled with a surface energy balance model (SNTHERM) and compared with in situ measurements. Sharp decreases in the modeled snow grain size, caused by accumulation events such as precipitation and deposition, could be verified with observational data; (4) radiative transfer modeling of firn supports our beliefs that the observed trends in 18 and 19 GHz passive microwave brightness temperatures are attributable to accumulation rate changes (modeling also indicates the above relationship is detectable because of the presence of depth hoar; (5) snow melt can be detected by a distinct signal in the passive microwave cross-polarized gradient ratio (19h-37v)/(19h+37v) and has been used for wet/dry snow classification; (6) top of the atmosphere (TOA) broadband albedos were derived from AVHRR visible and near infrared reflectances for the entire ice sheet from May 1990 - June 1991, and the highest albedo values are found along the southeast coast of the ice sheet which is consistent with the summer peak of precipitation due to onshore flow loaded with high water vapor content (TOA albedo values dropped to around 40% along the south-western coast during July and August due to bare ice surfaces); and (7) the net all-wave radiation balance at the top of the atmosphere is negative over the entire ice sheet except for the summer months - June-July-August (in June, the net radiation balance is slightly positive over the dry snow areas--15 W/m2).

Steffen, K.↗

Assessment of Climate Variability of the Greenland Ice Sheet: Integration of In Situ and Satellite Data

The proposed research involves the application of multispectral satellite data in combination with ground truth measurements to monitor surface properties of the Greenland Ice Sheet which are essential for describing the energy and mass of the ice sheet. Several key components of the energy balance are parameterized using satellite data and in situ measurements. The analysis has been done for a 6 to 17 year time period in order to analyze the seasonal and interannual variations of the surface processes and the climatology. Our goal was to investigate to what accuracy and over what geographic areas large scale snow properties and radiative fluxes can be derived based upon a combination of available remote sensing and meteorological data sets. For the understanding of the surface processes a field program was designed to collect information on spectral albedo, specular reflectance, soot content, grain size and the physical properties of different snow types. Further, the radiative and turbulent fluxes at the ice/snow surface were monitored for the parameterization and interpretation of the satellite data. Highlights include AVHRR time series and surface based radiation measurements, passive microwave time series, and geodetic results from the ETH/CU camp.

Steffen, K.↗

Two Successive Martian Years on the Orbit: Similarities and Differences of CO2 Seasonal Cycle from HEND/ODYSSEY Data

The three years of Mars Odyssey successful work on the martian orbit provide a lot of new information about peculiarities of long term variations of CO2 seasonal cycle. To start such analysis we have used observations of neutron albedo of Mars obtained by High Energy Neutron detector (HEND) mounted onboard Mars Odyssey spacecraft. The high latitude northern and southern regions of Mars are affected by global redistribution of atmospheric CO2 which resulted in 25% of atmospheric mass condensed on martian surface of these regions during winter period of time. The seasonal deposit is formed starting from 60N/60S latitudes and achieve its maximal thickness about 1 m at latitudes close to martian poles. Changes of CO2 deposit thickness is the reason for significant variations of neutron flux above martian poles from summer to winter seasons because CO2 frost effectively hides upper water rich surface layers from the orbit observations in neutrons and gamma-rays. This effect was used to estimate column density of CO2 deposit at different latitudes on North and South of Mars and reconstruct multidimensional model of CO2 deposit showing how snow depth varies as function of latitude, longitude and time. In this presentation we tried to make a next step in our study of martian seasonal CO2 cycle and look for similarities and differences between two successive martian years.

Litvak, M. L.↗

Oceanic Excitation of Polar Motion During 1992-1994

Two global ocean general circulation models have been used to compute the angular momentum of nontidal oceanic current and sea level height variations: (1) the Princeton Modular Ocean Model (MOM) having 22 vertical layers and a rigid lid, and (2) the Miami Isopycnic-Coordinate Ocean Model (MICOM) having 11 vertical layers with a mixed layer and a free surface. Both models were run on the same 2 degree longitude by 1 degree latitude grid spanning 80 S to 80 N latitude. Following a 10-year spin-up with climatological air-sea fluxes, both models were forced during 1992-1994 with daily wind and heat flux from the NCEP operational analysis and sea surface salinity restoring to Levitus climatology. After correcting for the effects of mass non-conservation in these models, they are shown to predict similar effects on polar motion excitation of sea level height variations, but the effect of currents predicted by MOM is much larger than that predicted by MICOM.

Gross, R.↗

Reflection of a shock wave from a thermally accommodating wall - Molecular simulation.

Reflection of a plane shock wave from a wall has been simulated on a microscopic scale using a direct simulation Monte Carlo technique of the type developed by Bird. A monatomic gas model representing argon was used to describe the fluid medium and a simple one-parameter accommodation coefficient model was used to describe the gas-surface interaction. The influence of surface accommodation was studied parametrically by varying the accommodation coefficient from zero to one. Results are presented showing the temporal variations of flow field density, and mass, momentum, and energy fluxes to the wall during the shock wave reflection process. The energy flux was used to determine the wall temperature history. Comparisons with experiment are found to be satisfactory where data are available.

Deiwert, G. S.↗

Notes on the meteorology of the intertropical convergence zone during the July 1977 experiment

The stratosphere and troposphere are large-scale open systems which exchange mass and trace constituents. If averaged over all longitudes, mass exchange can be expressed as products of the means and the mean of the product of the deviations from the mean. At high latitudes, the mass exchange is dominated by the deviations from the mean. At low latitudes, in the tropics, it is generally assumed that the mass exchange is caused by the mean motion. Figures are presented which depict: Northern Hemisphere mean motion; Convergence Zone motion; clouds and their motions; surface pressure variations; and meteorological parameters such as temperature, relative humidity, and ozone mixing ratios.

Danielson, E. F.↗