Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “mesoscale convective system”

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 235 records · Page 13

Co-Occurring Atmospheric Features and Their Contributions to Precipitation Extremes

Object-based identification algorithms for atmospheric features are commonly utilized to attribute global precipitation. This study employs a systematic approach to examine feature co-occurrences and their relationships to mean and extreme precipitation. Four features are identified using existing data sets for atmospheric rivers (ARs), mesoscale convective systems (MCSs), low-pressure systems (LPSs), and fronts (FTs). Often, a single atmospheric phenomenon satisfies the criteria set by multiple feature identification algorithms, yielding an association between precipitation and multiple features. Over the extra-tropics, the number of features attributed to a single event typically increases with precipitation intensity. Over two-thirds of the precipitation is from co-occurring features, with a considerable fraction related to AR-FT co-occurrences. Over the tropics, about one-quarter of precipitation is associated with co-occurring features, with LPS-MCS co-occurrences contributing substantially in monsoon regions. MCSs are the leading single-feature contributors over tropical land and oceans. In the extra-tropics, FTs, ARs, and their co-occurrences account for over half of the total precipitation over oceans. AR-FT-MCS and FT-MCS co-occurrences contribute to extremes (precipitation exceeding the 95th percentile) over both oceans (over 30%) and land (over 20%). Any combination of features involving MCSs shows a larger contribution to high percentiles of precipitation intensity. A case analysis indicates that AR-FT-MCS co-occurrences exhibit convective instability and deep vertical motion, suggesting that the feature trackers and reanalysis are capturing physics relevant to both convective and frontal systems. The results here emphasize the need for simultaneous identifications of multiple features when attributing precipitation to atmospheric phenomena.

54 ENVIRONMENTAL SCIENCES↗

Mechanisms Behind the Long‐Distance Diurnal Offshore Precipitation Propagation in Northwestern South America

Abstract Northwestern South America (NWSA) is the rainiest region on Earth, with diurnal precipitation exhibiting extensive westward offshore propagation of up to about 1,200 km in boreal spring (March‐May). The diurnal offshore precipitation propagation begins slowly (3–10 m s −1 ) near the coast of NWSA (<200 km) but accelerates significantly (∼20 m s −1 ) and shows an afternoon enhancement far from the coast (>400 km). However, the driving mechanisms behind this long‐distance precipitation propagation remain unclear. Using a new cloud tracking and classification data set, we found that mesoscale convective systems (MCSs) are the dominant precipitation contributors in the offshore region of NWSA. Cloud tracking shows that the long‐distance propagation and the afternoon enhancement of diurnal precipitation primarily originate from MCSs initiated in the early morning, either over open oceans or from the coast of Central America. Composite tendency analysis shows that MCSs initiated near the coast of Central America have significant upward cooling and moistening signals starting from the surface before initiation. Further analysis of surface diurnal perturbation fields indicates that the land breeze is the primary driving mechanism for MCS initiation. Conversely, for MCSs initiated over open oceans, a significant downward cooling signal from 400 hPa is observed ∼7 hr before initiation, corresponding to the passage of diurnal gravity waves emitted from the Andes. Additionally, our findings highlight the critical role of lower and mid‐level moisture conditions in MCS initiation, alongside the influence of gravity waves.

Hu, Jingyi [Department of Meteorology and Atmosphe↗

The Impacts of Rotational Mixing on the Precipitation Simulated by a Convection Permitting Model

With increased availability of computational resources, regional and global scale convection-permitting model (CPM, Δx ~ 1–10 km) simulations are becoming more common. CPMs have improved accuracy in their representation of deep convection and mesoscale convective systems (MCSs) compared to coarser resolution models. However, CPMs still exhibit convective cloud and precipitation biases relative to observations, notably a lesser frequency of light precipitation rates and greater frequency of heavy precipitation rates. In this work we hypothesize that these CPM biases are related to under-resolved mixing between convective updrafts and their surrounding environment. To test this hypothesis, we introduce a parameterization to the Weather Research and Forecasting model (WRF) that adds a small angular rotation of the grid-scale flow about the axis perpendicular to the plane of convective drafts. This rotated flow is then allowed to alter advection of moisture and hydrometeors. The effects of such mixing on precipitation characteristics are evaluated in month-long 4-km grid spacing simulations over the Amazon. The enhanced mixing transports moisture and condensate from convective cores to other areas including downdrafts. This increases the frequency of low-precipitable water and light precipitation. It also decreases the frequency of intense precipitation from isolated deep convection and MCSs, increases cloud top temperatures, reduces radar echo-top heights, and increases overall precipitation by altering the relationship of precipitation with precipitable water, in better agreement with observations. The results suggest when optimized using multiple observations, such an approach may provide a path toward more accurate representation of convection and precipitation statistics in convection-permitting simulations.

54 ENVIRONMENTAL SCIENCES↗

Examining Clustered MCSs and Their Precipitation Significance Over Global Land MCS Hotspots

Multiple independent mesoscale convective systems (MCSs) can occur closely in space and time, subjecting common geographic regions to multiple precipitation events over short periods. Motivated by an earlier study highlighting significant hydrological impacts of clustered MCSs in the US, we extend the analysis to seven global continental MCS hotspots using a 20‐year global MCS data set. Our findings reveal that (a) 40%–80% of MCSs occur in clusters, depending on the region; (b) clustered MCSs exhibit larger rainfall areas and higher mean areal rainfall, with the highest values observed in Argentina and India; and (c) clustered MCSs contribute increasing fractions to more extreme 24‐ and 72‐hr precipitation events across all regions. Our results underscore the critical role of clustered MCSs in driving hydrological extremes over global land regions and highlight the need to better understand how their formation mechanisms differ from non‐clustered events across the globe.

Hu, Huancui [Pacific Northwest National Laboratory↗

Evaluation of Monin‐Obukhov Similarity Theory Wind Profiles in Convective Storm Environments and Cold Pools at the ARM Southern Great Plains Atmospheric Observatory

Monin-Obukhov similarity theory (MOST) is widely used in numerical weather prediction to model surface fluxes of momentum, heat, and water vapor. However, MOST is based on assumptions of steady state and horizontally homogeneous turbulence that can lead to prediction errors in and around convective storms. To understand the nature of these errors, we used wind and eddy covariance flux measurements from the Atmospheric Radiation Measurement Southern Great Plains Atmospheric Observatory to evaluate MOST wind profiles in fair-weather and convective storm environments, specifically those of mesoscale convective systems and ordinary thunderstorms. MOST wind profiles agreed well with observations in fair-weather cases, while in convective storm cases the theory systematically overestimated shear in cold pools after gust front passage. Surface layer stability was found to be important in assessing MOST within convective storm environments. The overestimation of wind shear in cold pools suggests the role of non-local fluxes in transferring momentum downward. We discuss reasons for differences and agreement with past studies, and conclude with recommendations to improve prediction of surface winds and fluxes in convective storm simulations.

58 GEOSCIENCES↗

Environmental Influences on Deep Convective Upscale Growth Rate in Central Argentina From a Convection‐Permitting Simulation

This study uses a convection‐permitting model simulation to describe the environmental conditions under which convective upscale growth occurs in central Argentina, particularly examining environmental parameters when deep convection initially forms that could differentiate the rate of initial upscale growth. Simulated mesoscale convective systems (MCSs) are separated into slow and rapid growth by the rate of spatial growth from convection initiation until reaching the MCS scale. A low‐level jet (LLJ) is found more frequently near the deep convection that experiences rapid growth to an MCS, but its presence alone is not predictive of rapid growth. Using spatially‐averaged parameters, we find that rapid growth to MCSs also occurs in environments that are significantly more thermodynamically favorable with greater low‐level moisture and instability. Fewer significant differences are found in the kinematic environment with only the 0–2 km vertical wind shear magnitude being significantly larger for rapid growth MCSs compared to slow growth MCSs, potentially related to LLJs often peaking near this height. When focusing only on MCSs with the slowest and fastest growth rates, elevated‐layer shear is significantly smaller for very rapid growth MCSs, suggesting elevated‐layer shear may help discriminate between the upper and lower bounds of growth rate. Finally, when upscale growth occurs near the Sierras de Córdoba (SDC) with a LLJ present, rapid growth is also supported by favorable wind shear orientation. However, this does not hold for upscale growth occurring away from the SDC, highlighting the importance of interpreting shear direction relative to the orientation of features initiating deep convection.

Sasaki, Clayton R. S. [Univ. of Washington, Seattl↗

An Optimized Parameterization of Sub‐Grid Scale Advection for Convection Permitting Models

Convection‐permitting models (CPMs) explicitly resolve deep convection yet under‐resolve the organized lateral exchanges among drafts and their environment that control entrainment/detrainment, precipitation efficiency, and mesoscale structure. In this work, we introduce the Optimized Advection Scheme (OAS), which introduces a small rotation of the Cartesian frame of reference for the horizontal winds relative to other variables used in advection that induces cross‐gradient transport to mimic under‐resolved convective mixing. The rotation angle is selected to minimize the Kullback–Leibler divergence between the simulated and satellite observed precipitation intensity distributions, yielding a physically consistent perturbation that is computationally inexpensive and portable. Optimized Advection Scheme is implemented in WRF and evaluated over Amazon (April 2014). It shifts precipitation–precipitable‐water joint distributions toward lighter rain, reduces overly intense rates, and improves mesoscale convective system (MCS) lifetime and propagation. Mechanistically, the added cross‐gradient transport promotes convective detrainment and environmental mixing, which cools and moistens the mid‐troposphere, weakens downward momentum transport, alleviates excessive downwelling shortwave biases, and warms the surface temperature. The optimized rotation angle yields comparable improvements at 4‐km and 1‐km grid spacing, demonstrating resolution‐independent benefits across the CPM gray zone. By targeting the dynamical root of under‐mixed convective circulations, rather than tuning model microphysics or closures, OAS delivers robust, scale‐aware improvements in precipitation statistics, cloud vertical structure, and characteristics of MCS (MCSs), offering a practical pathway to more reliable CPM simulations for weather and climate applications.

CPM↗

Differences in Lightning—Storm Microphysical Relationships in Subtropical South America Versus the Continental U.S. and Their Impact on Model Lightning Parameterizations

Satellite studies have shown that some of the deepest convection with high lightning flash rates occurs downstream of the Andes in subtropical South America (SSA). Using high resolution ground‐based observations in SSA, we explore the relationship between lightning and radar‐inferred storm microphysics. Results show these storms have significantly larger 35‐dBZ volumes and more graupel per lightning flash compared to storms in the U.S. We then test microphysics‐based lightning parameterizations for storms in SSA on a 1‐km convection‐permitting simulation of a mesoscale convective system. Results from the simulation match well with observed flash rates. If parameterizations based on U.S. storms had been applied, flash rates would have been overestimated by a factor of eight. These results suggest that storms in SSA are fundamentally different compared to storms in the U.S., and caution should be exercised when applying microphysics‐based lightning parameterizations in different regions of the world.

54 ENVIRONMENTAL SCIENCES↗

Aircraft observations in a tropical supercluster over the equatorial Indian Ocean during MISO-BOB field campaign

The Monsoon Intra-Seasonal Oscillations in the Bay of Bengal (MISO-BOB) field campaign was conducted in the Indian Ocean during the 2018 and 2019 summer monsoon seasons. WC-130J aircraft of the 53rd Weather Reconnaissance Squadron of the US Air Force participated in the campaign in June 2018. The dropsonde observations across a tropical supercluster showed zonal wind variations in association with the structure of the convectively coupled Kelvin wave (CCKW). Within the supercluster, easterlies (westerlies) were observed in the upper (lower) troposphere; this transformation occurred just below the 0° C level. The cold pool had an easterly component throughout, and it was coldest (by 2.5° C) at the center of the supercluster, deepest (~ 1000 m) at its rear/western end, and shallowest (~ 300 m) at the front/eastern end. The level of free convection (LFC) at the front end was at 897 m altitude. At the eastern flank of the supercluster, zonal convergence in the lower troposphere occurred between 500-1500 m levels above the surface between the westerlies within the supercluster and opposing ambient easterlies. Thus, the uplifting of conditionally unstable air parcels above LFC to the east of the supercluster was likely to occur due to this convergence rather than the cold pool influence. Conversely, the western flank of the supercluster had low-level zonal divergence. These observations support the notion of ‘self-similarity’ among the mesoscale convective systems and large-scale waves.

54 ENVIRONMENTAL SCIENCES↗

Sensitivity of organized convective storms to model grid spacing in current and future climates

Mesoscale convective systems (MCSs) are complexes of thunderstorms that become organized and cover hundreds of kilometres over several hours. MCSs are prolific rain producers in the tropics and mid-latitudes and are the major cause of warm-season flooding. Traditionally, climate models have difficulties in simulating MCSs partly due to the misrepresentation of complex process interactions that operate across a large range of scales. Significant improvements in simulating MCSs have been found in kilometre-scale models that explicitly simulate deep convection. However, these models operate in the grey zone of turbulent motion and have known deficiencies in simulating small-scale processes (e.g. entrainment, vertical mass transport). Here, we perform mid-latitude idealized ensemble MCS simulations under current and future climate conditions in three atmospheric regimes: hydrostatic (12 km horizontal grid spacing; Δx), non-hydrostatic (Δx = 4, 2 and 1 km) and large eddy scale (Δx = 500 m and 250 m). Our results show a dramatic improvement in simulating MCS precipitation, movement, cold pools, and cloud properties when transitioning from 12 km to 4 km Δx. Decreasing Δx beyond 4 km results in modest improvements except for up- and downdraft sizes, average vertical mass fluxes, and cloud top height and temperature, which continue to change. Most important for climate modelling is that Δx = 4 km simulations reliably capture most MCS climate change signals compared to those of the Δx = 250 m runs. Significantly different climate change signals are found in Δx = 12 km runs that overestimate extreme precipitation changes by up to 100%.

54 ENVIRONMENTAL SCIENCES↗

Utilizing a Storm-Generating Hotspot to Study Convective Cloud Transitions: The CACTI Experiment

The Cloud, Aerosol, and Complex Terrain Interactions (CACTI) field campaign was designed to improve understanding of orographic cloud life cycles in relation to surrounding atmospheric thermodynamic, flow, and aerosol conditions. The deployment to the Sierras de Córdoba range in north-central Argentina was chosen because of very frequent cumulus congestus, deep convection initiation, and mesoscale convective organization uniquely observable from a fixed site. The C-band Scanning Atmospheric Radiation Measurement (ARM) Precipitation Radar was deployed for the first time with over 50 ARM Mobile Facility atmospheric state, surface, aerosol, radiation, cloud, and precipitation instruments between October 2018 and April 2019. An intensive observing period (IOP) coincident with the RELAMPAGO field campaign was held between 1 November and 15 December during which 22 flights were performed by the ARM Gulfstream-1 aircraft. A multitude of atmospheric processes and cloud conditions were observed over the 7-month campaign, including numerous orographic cumulus and stratocumulus events; new particle formation and growth producing high aerosol concentrations; drizzle formation in fog and shallow liquid clouds; very low aerosol conditions following wet deposition in heavy rainfall; initiation of ice in congestus clouds across a range of temperatures; extreme deep convection reaching 21-km altitudes; and organization of intense, hail-containing supercells and mesoscale convective systems. These comprehensive datasets include many of the first ever collected in this region and provide new opportunities to study orographic cloud evolution and interactions with meteorological conditions, aerosols, surface conditions, and radiation in mountainous terrain.

54 ENVIRONMENTAL SCIENCES↗

Effective Visualization of Radar Data for Users Impacted by Color Vision Deficiency

Color vision deficiency (CVD) is a decreased ability to discern between particular colors. Eight percent of genetic males and half a percent of genetic females have some form of CVD, with many in the radar community falling into this group. When presenting data on a two-dimensional plane, it is common to use colors to represent values via a colormap. Colormap choice in the radar community is influenced by the ability to highlight scientifically interesting features in data, institutional choices, and domain dominance of legacy colormaps. The problem with these current colormaps is that many do not project well for those with CVD (i.e., green next to red). In working with the CVD community to address this problem, multiple colormaps for moments such as equivalent reflectivity factor and Doppler velocity were created for users with forms of CVD such as deuteranomaly, protanomaly, protanopia, and deuteranopia using Python tools such as colorspacious and viscm. We show how these colormaps can improve interpretability for four cases: a mesoscale convective system, a pyrocumulonimbus storm, a wintertime midlatitude cyclone, and widespread storms with a large bird migration. These new radar equivalent reflectivity factor, Doppler velocity, and polarization colormaps are designed to highlight rain, frozen precipitation, nonmeteorological targets, and velocity-based items, are perceptually uniform, and are visually friendly for those with CVD.

54 ENVIRONMENTAL SCIENCES↗

Two-Day Westward-Propagating Inertio-Gravity Waves during GoAmazon

The dynamical and thermodynamical features of Amazonian 2-day westward-propagating inertia–gravity (WIG) waves are examined. On the basis of a linear regression analysis of satellite brightness temperature and data from the 2014–15 Observations and Modeling of the Green Ocean Amazon (GoAmazon) field campaign, it is shown that Amazonian WIG waves exhibit structure and propagation characteristics consistent with the n = 1 WIG waves from shallow water theory. These WIG waves exhibit a pronounced seasonality, with peak activity occurring from March to May and a minimum occurring from June to September. Evidence is shown that mesoscale convective systems over the Amazon are frequently organized in 2-day WIG waves. Results suggest that many of the Amazonian WIG waves come from preexisting 2-day waves over the Atlantic, which slow down when coupled with the deeper, more intense convection over tropical South America. In contrast to WIG waves that occur over the ocean, Amazonian 2-day WIG waves exhibit a pronounced signature in surface temperature, moisture, and heat fluxes.

54 ENVIRONMENTAL SCIENCES↗

Atmosphere–Ocean Coupled Energy Budgets of Tropical Convective Discharge–Recharge Cycles

An energy budget combining atmospheric moist static energy (MSE) and upper ocean heat content (OHC) is used to examine the processes impacting day-to-day convective variability in the tropical Indian and western Pacific Oceans. Feedbacks arising from atmospheric and oceanic transport processes, surface fluxes, and radiation drive the cyclical amplification and decay of convection around suppressed and enhanced convective equilibrium states, referred to as shallow and deep convective discharge–recharge (D–R) cycles, respectively. The shallow convective D–R cycle is characterized by alternating enhancements of shallow cumulus and stratocumulus, often in the presence of extensive cirrus clouds. The deep convective D–R cycle is characterized by sequential increases in shallow cumulus, congestus, narrow deep precipitation, wide deep precipitation, a mix of detached anvil and altostratus and altocumulus, and once again shallow cumulus cloud types. Transitions from the shallow to deep D–R cycle are favored by a positive “column process” feedback, while discharge of convective instability and OHC by mesoscale convective systems (MCSs) contributes to transitions from the deep to shallow D–R cycle. Variability in the processes impacting MSE is comparable in magnitude to, but considerably more balanced than, variability in the processes impacting OHC. Variations in the quantity of atmosphere–ocean coupled static energy (MSE + OHC) result primarily from atmospheric and oceanic transport processes, but are mainly realized as changes in OHC. MCSs are unique in their ability to rapidly discharge both lower-tropospheric convective instability and OHC.

54 ENVIRONMENTAL SCIENCES↗

An Improved Convection Parameterization with Detailed Aerosol–Cloud Microphysics for a Global Model

Abstract A new microphysical treatment that includes aerosol–cloud interactions and secondary ice production (SIP) mechanisms is implemented in the convection scheme of the Community Atmosphere Model, version 6 (CAM6). The approach is to embed a 1D Lagrangian parcel model in the bulk convective plume of the existing deep convection parameterization. Aerosol activation, growth processes including collision/coalescence, and three processes of SIP mechanisms, two of which are normally overlooked in atmospheric models, are represented in this embedded parcel model. These microphysical processes are treated with a hybrid bin/bulk scheme and a high spatial and temporal resolution for the integration of the embedded parcel in 1D, allowing vertical velocity to determine the microphysical evolution following the in-cloud motion during ascent. Simulations of an observed case (Midlatitude Continental Convective Clouds Experiment) of a mesoscale convective system in Oklahoma, United States, with a single-column model (SCAM) version of CAM, are compared with aircraft in situ and ground-based observations of microphysical properties from the convection and precipitation. Results from the validation show the new microphysical scheme has a good representation of the ice initiation in the bulk convective plume, including the known and empirically quantified pathways of primary and secondary initiation, with benefits for the accuracy of properties of its supercooled cloud liquid. The sensitivity simulations and use of tagging tracers for the validated simulation confirm that the newly included SIP mechanisms are of paramount importance for convective microphysics and can be successfully treated in the global model.

54 ENVIRONMENTAL SCIENCES↗

Evaluating Diurnal and Semi-Diurnal Cycle of Precipitation in CMIP6 Models Using Satellite- and Ground-Based Observations

We report the diurnal and semi-diurnal cycle of precipitation simulated from CMIP6 models during 1996-2005 are evaluated globally between 60°S and 60°N, as well as at ten selected locations representing three categories of diurnal cycle of precipitation: (1) afternoon precipitation over land, (2) early morning precipitation over ocean, and (3) nocturnal precipitation over land. Three satellite-based and two ground-based rainfall products are used to evaluate the climate models. Globally, the ensemble mean of CMIP6 models shows a diurnal phase of 3 to 4 hours earlier over land and 1 to 2 hours earlier over ocean, when compared with the latest satellite products. These biases are in line with what were found in previous versions of climate models but reduced compared to the CMIP5 ensemble mean. Analysis at the selected locations complimented with in-situ measurements further reinforces these results. Several CMIP6 models have shown a significant improvement in the diurnal cycle of precipitation compared to their CMIP5 counterparts, notably on delaying afternoon precipitation over land. This can be attributed to the use of more sophisticated convective parameterizations. Most models are still unable to capture the nocturnal peak associated with elevated convection and propagating mesoscale convective systems, with a few exceptions that allow convection to be initiated above the boundary layer to capture nocturnal elevated convection. We also quantify an encouraging consistency between the satellite- and ground-based precipitation measurements despite differing spatiotemporal resolutions and sampling periods, which provides confidence in using them to evaluate the diurnal and semi-diurnal cycle of precipitation in climate models.

58 GEOSCIENCES↗

Understanding the distinct impacts of MCS and non-MCS rainfall on the surface water balance in the central US using a numerical water-tagging technique

Warm-season rainfall associated with mesoscale convective systems (MCSs) in the central US is characterized by higher intensity and nocturnal timing compared to rainfall from non-MCS systems, suggesting their potentially different footprints on the land surface. To differentiate the impacts of MCS and non-MCS rainfall on the surface water balance, a water tracer tool embedded in the Noah land surface model with multi-parameterization options (WT-Noah-MP) is used to numerically “tag” water from MCS and non-MCS rainfall separately during April to August (1997-2018) and track their transit in the terrestrial system. From the water-tagging results, over 50% of warm-season rainfall leaves the surface-subsurface system through evapotranspiration by the end of August, but non-MCS rainfall contributes a larger fraction. However, MCS rainfall plays a more important role in generating surface runoff. These differences are mostly attributed to the rainfall intensity differences. The higher intensity MCS rainfall tends to produce more surface runoff through infiltration excess flow and drives a deeper penetration of the rainwater into the soil. Over 70% of the top 10 percentile runoff is contributed by MCS rainfall, demonstrating its important contribution to local flooding. In contrast, lighter intensity non-MCS rainfall resides mostly in the top layer and contributes more to evapotranspiration through soil evaporation. Diurnal timing of rainfall has negligible effects on the flux partitioning for both MCS and non-MCS rainfall. Differences in soil moisture profiles for MCS and non-MCS rainfall and the resultant evapotranspiration suggest differences in their roles in soil moisture-precipitation feedbacks and ecohydrology.

Hu, Huancui↗

Columnar Vertical Profile (CVP) Methodology for Validating Polarimetric Radar Retrievals in Ice Using In Situ Aircraft Measurements

Abstract A novel way to process polarimetric radar data collected via plan position indicator (PPI) scans and display those data in a time–height format is introduced. The columnar vertical profile (CVP) methodology uses radar data collected via multiple elevation scans, limited to data within a set region in range and azimuth relative to the radar, to create vertical profiles of polarimetric radar data representative of that limited region in space. This technique is compared to others existing in the literature, and various applications are discussed. Polarimetric ice microphysical retrievals are performed on CVPs created within the stratiform rain region of two mesoscale convective systems sampled during two field campaigns, where CVPs follow the track of research aircraft. Aircraft in situ data are collocated to microphysical retrieval data, and the accuracy of these retrievals is tested against other retrieval techniques in the literature.

Engineering↗