scholarly journals Spatiotemporal Large-Scale Networks Shaped by Air Mass Movements

2021 ◽  
Vol 6 ◽  
Author(s):  
M. Choufany ◽  
D. Martinetti ◽  
R. Senoussi ◽  
C. E. Morris ◽  
S. Soubeyrand
Keyword(s):  
Large Scale ◽  
Seasonal Pattern ◽  
Geographical Area ◽  
Three Dimensional ◽  
Mass Movements ◽  
Air Mass ◽  
Air Masses ◽  
Large Scale Networks ◽  
Definition Of ◽  
French Region

The movement of atmospheric air masses can be seen as a continuous flow of gases and particles hovering over our planet, and it can be locally simplified by means of three-dimensional trajectories. These trajectories can hence be seen as a way of connecting distant areas of the globe during a given period of time. In this paper we present a mathematical formalism to construct spatial and spatiotemporal networks where the nodes represent the subsets of a partition of a geographical area and the links between them are inferred from sampled trajectories of air masses passing over and across them. We propose different estimators of the intensity of the links, relying on different bio-physical hypotheses and covering adjustable time periods. This construction leads to a new definition of spatiotemporal networks characterized by adjacency matrices giving, e.g., the probability of connection between distant areas during a chosen period of time. We applied our methodology to characterize tropospheric connectivity in two real geographical contexts: the watersheds of the French region Provence-Alpes-Côte d’Azur and the coastline of the Mediterranean Sea. The analysis of the constructed networks allowed identifying a marked seasonal pattern in air mass movements in the two study areas. If our methodology is applied to samples of air-mass trajectories, with potential implications in aerobiology and plant epidemiology, it could be applied to other types of trajectories, such as animal trajectories, to characterize connectivity between different components of the landscape hosting the animals.

scholarly journals Analysis of a rapid increase of stratospheric ozone during late austral summer 2008 over Kerguelen (49.4° S, 70.3° E)

2011 ◽  
Vol 11 (1) ◽  
pp. 363-373 ◽  
Author(s):  
H. Bencherif ◽  
L. El Amraoui ◽  
G. Kirgis ◽  
J. Leclair De Bellevue ◽  
A. Hauchecorne ◽  
...  
Keyword(s):  
Potential Vorticity ◽  
Large Scale ◽  
Lower Stratosphere ◽  
Transport Model ◽  
Stratospheric Ozone ◽  
Three Dimensional ◽  
Austral Summer ◽  
Air Masses ◽  
Global Mapping ◽  
The Tropics

Abstract. This paper reports on an increase of ozone event observed over Kerguelen (49.4° S, 70.3° E) in relationship with large-scale isentropic transport. This is evidenced by ground-based observations (co-localised radiosonde and SAOZ experiments) together with satellite global observations (Aura/MLS) assimilated into MOCAGE, a Méteo-France model. The study is based on the analyses of the first ozonesonde experiment never recorded at the Kerguelen site within the framework of a French campaign called ROCK that took place from April to August 2008. Comparisons and interpretations of the observed event are supported by co-localised SAOZ observations, by global mapping of tracers (O3, N2O and columns of O3) from Aura/MLS and Aura/OMI experiments, and by model simulations of Ertel Potential Vorticity initialised by the ECMWF (European Centre for Medium-Range Weather Forecasts) data reanalyses. Satellite and ground-based observational data revealed a consistent increase of ozone in the local stratosphere by mid-April 2008. Additionally, Ozone (O3) and nitrous oxide (N2O) profiles obtained during January–May 2008 using the Microwave Limb Sounder (MLS) aboard the Aura satellite are assimilated into MOCAGE (MOdèle de Chimie Atmosphérique à Grande Echelle), a global three-dimensional chemistry transport model of Météo-France. The assimilated total O3 values are consistent with SAOZ ground observations (within ±5%), and isentropic distributions of O3 match well with maps of advected potential vorticity (APV) derived from the MIMOSA model, a high-resolution advection transport model, and from the ECMWF reanalysis. The event studied seems to be related to the isentropic transport of air masses that took place simultaneously in the lower- and middle-stratosphere, respectively from the polar region and from the tropics to the mid-latitudes. In fact, the ozone increase observed by mid April 2008 resulted simultaneously: (1) from an equator-ward departure of polar air masses characterised with a high-ozone layer in the lower stratosphere (near the 475 K isentropic level), and (2) from a reverse isentropic transport from the tropics to mid- and high-latitudes in the upper stratosphere (nearby the 700 K level). The increase of ozone observed over Kerguelen from the 16-April ozonesonde profile is thus attributed to a concomitant isentropic transport of ozone in two stratospheric layers: the tropical air moving southward and reaching over Kerguelen in the upper stratosphere, and the polar air passing over the same area but in the lower stratosphere.

scholarly journals Relationships between submicrometer particulate air pollution and air mass history in Beijing, China, 2004–2006

2008 ◽  
Vol 8 (20) ◽  
pp. 6155-6168 ◽  
Author(s):  
B. Wehner ◽  
W. Birmili ◽  
F. Ditas ◽  
Z. Wu ◽  
M. Hu ◽  
...  
Keyword(s):  
Air Pollution ◽  
Large Scale ◽  
Northwest China ◽  
Back Trajectory ◽  
Anthropogenic Aerosol ◽  
Air Mass ◽  
Air Masses ◽  
Rapid Economic Growth ◽  
Trajectory Classification ◽  
History Of

Abstract. The Chinese capital Beijing is one of the global megacities where the effects of rapid economic growth have led to complex air pollution problems that are not well understood. In this study, ambient particle number size distributions in Beijing between 2004 and 2006 are analysed as a function of regional meteorological transport. An essential result is that the particle size distribution in Beijing depends to large extent on the history of the synoptic scale air masses. A first approach based on manual back trajectory classification yielded differences in particulate matter mass concentration by a factor of two between four different air mass categories, including three main wind directions plus the case of stagnant air masses. A back trajectory cluster analysis refined these results, yielding a total of six trajectory clusters. Besides the large scale wind direction, the transportation speed of an air mass was found to play an essential role on the PM concentrations in Beijing. Slow-moving air masses were shown to be associated with an effective accumulation of surface-based anthropogenic emissions due to both, an increased residence time over densely populated land, and their higher degree of vertical stability. For the six back trajectory clusters, differences in PM1 mass concentrations by a factor of 3.5, in the mean air mass speed by a factor of 6, and in atmospheric visibility by a factor of 4 were found. The main conclusion is that the air quality in Beijing is not only degraded by anthropogenic aerosol sources from within the megacity, but also by sources across the entire Northwest China plain depending on the meteorological situation.

scholarly journals Exploring the inorganic composition of the Asian Tropopause Aerosol Layer using medium-duration balloon flights

2021 ◽  
Author(s):  
Hazel Vernier ◽  
Neeraj Rastogi ◽  
Hongyu Liu ◽  
Amit Kumar Pandit ◽  
Kris Bedka ◽  
...  
Keyword(s):  
Particle Size ◽  
Large Scale ◽  
Transport Model ◽  
Large Fraction ◽  
Western China ◽  
Aerosol Layer ◽  
Fire Event ◽  
Air Mass ◽  
Air Masses ◽  
Model Simulations

Abstract. Satellite observations have revealed an enhanced aerosol layer near the tropopause over Asia during the summer monsoon, called the Asian Tropopause Aerosol Layer (ATAL). In this work, aerosol particles in the ATAL were collected with a balloon-borne impactor near the tropopause region over India, using extended duration balloon flights, in summer 2017 and winter 2018. Their chemical composition was further investigated by quantitative analysis using offline ion chromatography. Nitrate (NO3−) and nitrite (NO2−) were found to be the dominant ions in the collected aerosols with values ranging between 87–343 ng/m3 STP during the summer campaign. In contrast, sulfate (SO42−) levels were found above the detection limit (> 10 ng/m3 STP) only in winter. In addition, we determined the origin of the air masses sampled during the flights through analysis of back trajectories along with convective influence. The results obtained therein were put into a context of large-scale transport and aerosol distribution with GEOS-Chem chemical transport model simulations. The first flight of summer 2017 which sampled air mass within the Asian monsoon anticyclone (AMA), influenced by convection over Western China, was associated with particle size radius (0.05–2 μm). In contrast, the second flight sampled air mass at the edge of the AMA associated with larger particle size radius (> 2 μm) with higher nitrite concentration. The sampled air masses in winter 2018 were likely affected by smoke from the Pacific Northwest fire event in Canada, which occurred 7 months prior to our campaign, leading to concentration enhancements of SO42− and Ca2+. Overall, our results suggest that nitrogen-containing particles represent a large fraction of aerosols populating the ATAL, in agreement with the results from aircraft measurements during the StratoClim campaign. Furthermore, GEOS-Chem model simulations suggest that lightning NOx emissions had a significant impact on the production of nitrate aerosols sampled during the summer 2017.

scholarly journals Inferring long-distance connectivity shaped by air-mass movement for improved experimental design in aerobiology

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Maria Choufany ◽  
Davide Martinetti ◽  
Samuel Soubeyrand ◽  
Cindy E. Morris
Keyword(s):  
Large Scale ◽  
Mass Movement ◽  
Geographical Area ◽  
Small World ◽  
Long Distance ◽  
Air Mass ◽  
Key Factor ◽  
Large Geographical Area ◽  
Spatio Temporal ◽  
Small World Property

AbstractThe collection and analysis of air samples for the study of microbial airborne communities or the detection of airborne pathogens is one of the few insights that we can grasp of a continuously moving flux of microorganisms from their sources to their sinks through the atmosphere. For large-scale studies, a comprehensive sampling of the atmosphere is beyond the scopes of any reasonable experimental setting, making the choice of the sampling locations and dates a key factor for the representativeness of the collected data. In this work we present a new method for revealing the main patterns of air-mass connectivity over a large geographical area using the formalism of spatio-temporal networks, that are particularly suitable for representing complex patterns of connection. We use the coastline of the Mediterranean basin as an example. We reveal a temporal pattern of connectivity over the study area with regions that act as strong sources or strong receptors according to the season of the year. The comparison of the two seasonal networks has also allowed us to propose a new methodology for comparing spatial weighted networks that is inspired from the small-world property of non-spatial networks.

Geodetic reference frames in the Netherlands

2005 ◽  
Author(s):  
Arnoud de Bruijne ◽  
Joop van Buren ◽  
Anton Kösters ◽  
Hans van der Marel
Keyword(s):  
The Netherlands ◽  
Reference System ◽  
Large Scale ◽  
Reference Frames ◽  
Three Dimensional ◽  
Geodetic Reference System ◽  
Geoid Model ◽  
Leading Role ◽  
Definition Of

Unambiguous and homogeneous geodetic reference frames are essential to the proper determination of locations and heights. The reference frames used in the Netherlands are the Rijksdriehoekmeting (RD) for locations and the Normaal Amsterdamse Peil (NAP) for heights. The RD has traditionally been managed by the Kadaster; the NAP by Rijkswaterstaat. The emergence of satellite positioning has resulted in drastic changes to these geodetic reference frames. A surveyor is now offered one instrument, GPS (the Global Positioning System), capable of the simultaneous determination of locations and heights. This is possible by virtue of one three-dimensional geodetic reference system - the European Terrestrial Reference System (ETRS89) - which in the Netherlands is maintained in a collaborative arrangement between the Kadaster and Rijkswaterstaat. GPS has been advanced as a practical measurement technique by linking the definition of the RD grid to ETRS89. Nevertheless the introduction of GPS also revealed distortions in the RD grid, which are modelled in the RDNAPTRANSTM2004 transformation. Furthermore, the use of the geoid model has become essential to the use of GPS in determining the height in comparison to NAP. Subsidence that has disrupted the backbone of the NAP gave cause to the need for a large-scale adjustment of the heights of the underground benchmarks and, in so doing, of the grid. Consequently new NAP heights have been introduced at the beginning of 2005; a new definition of the RD grid that had already been introduced in 2000 was once again modified in 2004. During the past few years two NCG subcommissions have devoted a great deal of time to these modifications. This publication lays down ETRS89, the RD and the NAP, together with their mutual relationships. In addition to reviewing the history of the reference frames and the manner in which they are maintained (including, for example, the use of AGRS.NL as the basis for the Dutch geometric infrastructure), the publication also discusses the status of the frames as at 1 January 2005. This encompasses the realisation of ETRS89 via AGRS.NL, the revision and new definition of the RD grid in 2004, and the new NAP publication in 2005. The publication also describes the mutual relationships between the frames in the modernized RDNAPTRANSTM2004 transformation consisting of the new NLGEO2004 geoid model and a model for the distortions of the RD grid. In conclusion, the publication also devotes attention to the future maintenance of the ETRS89, RD and NAP. The continuity of the link between the traditional frames and the three-dimensional frames is of great importance, and ETRS89 will continue to fulfil this linking role. The GPS base network and AGRS.NL reference stations will increasingly assume the leading role in the maintenance of the RD frame. The maintenance of the NAP will continue to be necessary, although during the coming decades the the primary heights will not need revision. In so doing the high quality of the geodetic reference frames required for their use in actual practice will continue to be guaranteed.

scholarly journals Air mass origins influencing TTL chemical composition over West Africa during 2006 summer monsoon

2010 ◽  
Vol 10 (22) ◽  
pp. 10753-10770 ◽  
Author(s):  
K. S. Law ◽  
F. Fierli ◽  
F. Cairo ◽  
H. Schlager ◽  
S. Borrmann ◽  
...  
Keyword(s):  
West Africa ◽  
Summer Monsoon ◽  
Large Scale ◽  
Lower Stratosphere ◽  
Deep Convection ◽  
Lower Troposphere ◽  
Trace Gas ◽  
Air Mass ◽  
Back Trajectories ◽  
Air Masses

Abstract. Trace gas and aerosol data collected in the tropical tropopause layer (TTL) between 12–18.5 km by the M55 Geophysica aircraft as part of the SCOUT-AMMA campaign over West Africa during the summer monsoon in August 2006 have been analysed in terms of their air mass origins. Analysis of domain filling back trajectories arriving over West Africa, and in the specific region of the flights, showed that the M55 flights were generally representative of air masses arriving over West Africa during the first 2 weeks of August, 2006. Air originating from the mid-latitude lower stratosphere was under-sampled (in the mid-upper TTL) whilst air masses uplifted from central Africa (into the lower TTL) were over-sampled in the latter part of the campaign. Signatures of recent (previous 10 days) origins were superimposed on the large-scale westward flow over West Africa. In the lower TTL, air masses were impacted by recent local deep convection over Africa at the level of main convective outflow (350 K, 200 hPa) and on certain days up to 370 K (100 hPa). Estimates of the fraction of air masses influenced by local convection vary from 10 to 50% depending on the method applied and from day to day during the campaign. The analysis shows that flights on 7, 8 and 11 August were more influenced by local convection than on 4 and 13 August allowing separation of trace gas and aerosol measurements into "convective" and "non-convective" flights. Strong signatures, particularly in species with short lifetimes (relative to CO2) like CO, NO and fine-mode aerosols were seen during flights most influenced by convection up to 350–365 K. Observed profiles were also constantly perturbed by uplift (as high as 39%) of air masses from the mid to lower troposphere over Asia, India, and oceanic regions resulting in import of clean oceanic (e.g. O3-poor) or polluted air masses from Asia (high O3, CO, CO2) into West Africa. Thus, recent uplift of CO2 over Asia may contribute to the observed positive CO2 gradients in the TTL over West Africa. This suggests a more significant fraction of younger air masses in the TTL and needs to taken into consideration in derivations of mean age of air. Transport of air masses from the mid-latitude lower stratosphere had an impact from the mid-TTL upwards (20–40% above 370 K) during the campaign period importing air masses with high O3 and NOy. Ozone profiles show a less pronounced lower TTL minimum than observed previously by regular ozonesondes at other tropical locations. Concentrations are less than 100 ppbv in the lower TTL and vertical gradients less steep than in the upper TTL. The air mass origin analysis and simulations of in-situ net photochemical O3 production, initialised with observations, suggest that the lower TTL is significantly impacted by uplift of O3 precursors (over Africa and Asia) leading to positive production rates (up to 2 ppbv per day) in the lower and mid TTL even at moderate NOx levels. Photochemical O3 production increases with higher NOx and H2O in air masses with O3 less than 150 ppbv.

scholarly journals Analysis of a rapid increase of stratospheric ozone during late austral summer 2008 over Kerguelen (49.4° S, 70.3° E)

2010 ◽  
Vol 10 (7) ◽  
pp. 17727-17751
Author(s):  
H. Bencherif ◽  
L. El Amraoui ◽  
G. Kirgis ◽  
J. Leclair De Bellevue ◽  
A. Hauchecorne ◽  
...  
Keyword(s):  
Potential Vorticity ◽  
Large Scale ◽  
Lower Stratosphere ◽  
Transport Model ◽  
Stratospheric Ozone ◽  
Three Dimensional ◽  
Austral Summer ◽  
Air Masses ◽  
Weather Forecasts ◽  
Global Mapping

Abstract. This paper reports on an increase of ozone event observed over Kerguelen (49.4° S, 70.3° E) in relationship with large-scale isentropic transport. It is evidenced from ground-based observations, together with satellite global observations and assimilated fields. The study is based on the analyses of the first ozonesonde experiment never recorded at the Kerguelen site in the framework of a French campaign called ROCK that took place from April to August 2008. Comparisons and interpretations of the observed event are supported by co-localised SAOZ observations, by global mapping of tracers (O3, N2O and columns of O3) from Aura/MLS and Aura/OMI experiments, and by model simulations of Ertel Potential Vorticity initialised by ECMWF (European Centre for Medium-Range Weather Forecasts) data reanalyses. Satellite and ground-based observational data revealed a consistent increase of ozone in the local stratosphere by mid-April 2008. Additionally, Ozone (O3) and nitrous oxide (N2O) profiles obtained during January–May 2008 by the Microwave Lamb Sounder (MLS) aboard the Aura satellite are assimilated into MOCAGE (MOdèle de Chimie Atmosphérique à Grande Echelle), a global three-dimensional chemistry transport model of Météo-France. The assimilated total O3 values are consistent with SAOZ ground observations (within ±5%), and isentropic distributions of O3 are matching well with maps of advected potential vorticity (APV) derived from the MIMOSA model, a high-resolution advection transport model, and from ECMWF reanalysis. The studied event seems to be related to isentropic transport of air masses that took place simultaneously in the lower- and middle-stratosphere, respectively from the polar region and from tropics to the mid-latitudes. In fact, the studied ozone increase by mid April 2008 results simultaneously: (1) from an equator-ward departure of polar air masses characterised with a high-ozone layer in the lower stratosphere (nearby the 475 K isentropic level), and (2) from a reverse isentropic transport from tropics to mid- and high-latitudes in the upper stratosphere (nearby the 700 K level). The increase of ozone observed over Kerguelen from the 16-April ozonesonde profile is then attributed to a concomitant isentropic transport of ozone in two stratospheric layers: the tropical air moving southward and reaches over Kerguelen in the upper stratosphere, and the polar air passing over the same area but in the lower stratosphere.

scholarly journals Relationships between submicrometer particulate air pollution and air mass history in Beijing, China, 2004–2006

2008 ◽  
Vol 8 (3) ◽  
pp. 11321-11362 ◽  
Author(s):  
B. Wehner ◽  
W. Birmili ◽  
F. Ditas ◽  
Z. Wu ◽  
M. Hu ◽  
...  
Keyword(s):  
Air Pollution ◽  
Large Scale ◽  
Northwest China ◽  
Back Trajectory ◽  
Anthropogenic Aerosol ◽  
Air Mass ◽  
Air Masses ◽  
Rapid Economic Growth ◽  
Trajectory Classification ◽  
History Of

Abstract. The Chinese capital Beijing is one of the global megacities where the effects of rapid economic growth have led to complex air pollution problems that are not well understood. In this study, ambient particle number size distributions in Beijing between 2004 and 2006 are analysed as a function of regional meteorological transport. An essential result is that the particle size distribution in Beijing depends to large extent on the history of the synoptic scale air masses. A first approach based on manual back trajectory classification yielded differences in particulate matter mass concentration (PM1 and PM10) by a factor of two between four different air mass categories, including three main wind directions plus the case of stagnant air masses. A back trajectory cluster analysis refined these results, yielding a total of six trajectory clusters. Besides the large scale wind direction, the transportation speed of an air mass was found to play an essential role on the PM concentrations in Beijing. Slow-moving air masses were shown to be associated with an effective accumulation of surface-based anthropogenic emissions due to both, an increased residence time over densely populated land, and their higher degree of vertical stability. For the six back trajectory clusters, differences in PM1 mass concentrations by a factor of 3.5, in the mean air mass speed by a factor of 6, and in atmospheric visibility by a factor of 4 were found. The main conclusion is that the air quality in Beijing is not only degraded by anthropogenic aerosol sources from within the megacity, but also by sources across the entire Northwest China plain depending on the meteorological situation.

scholarly journals Air mass origins influencing TTL chemical composition over West Africa during 2006 summer monsoon

2010 ◽  
Vol 10 (6) ◽  
pp. 15485-15536 ◽  
Author(s):  
K. S. Law ◽  
F. Fierli ◽  
F. Cairo ◽  
H. Schlager ◽  
S. Borrmann ◽  
...  
Keyword(s):  
West Africa ◽  
Summer Monsoon ◽  
Large Scale ◽  
Lower Stratosphere ◽  
Deep Convection ◽  
Lower Troposphere ◽  
Trace Gas ◽  
Air Mass ◽  
Back Trajectories ◽  
Air Masses

Abstract. Trace gas and aerosol data collected in the tropical tropopause layer (TTL) between 12–18.5 km by the M55 Geophysica aircraft as part of the SCOUT-AMMA campaign over West Africa during the summer monsoon in August 2006 have been analysed in terms of their air mass origins. Analysis of domain filling back trajectories arriving over West Africa, and in the specific region of the flights, showed that the M55 flights were generally representative of air masses arriving over West Africa during the first 2 weeks of August, 2006. Air originating from the mid-latitude lower stratosphere was under-sampled (in the mid-upper TTL) whilst air masses uplifted from central Africa (into the lower TTL) were over-sampled in the latter part of the campaign. Signatures of recent (previous 10 days) origins were superimposed on the large-scale westerly flow over West Africa. In the lower TTL, air masses were impacted by recent local deep convection over Africa at the level of main convective outflow (350 K, 200 hPa) and on certain days up to 370 K (100 hPa). Estimates of the fraction of air masses influenced by local convection vary from 10 to 50% depending on the method applied and from day to day during the campaign. The analysis shows that flights on 7, 8 and 11 August were more influenced by local convection than on 4 and 13 August allowing separation of trace gas and aerosol measurements into ''convective'' and ''non-convective'' flights. Strong signatures, particularly in short-lived species like CO, NO and fine-mode aerosols were seen during flights most influenced by convection up to 350–365 K. Observed profiles were also constantly perturbed by uplift (as high as 39%) of air masses from the mid to lower troposphere over Asia, India, and oceanic regions resulting in import of clean oceanic (e.g., O3-poor) or polluted air masses from Asia (high O3, CO, CO2) into West Africa. Thus, recent uplift of CO2 over Asia may contribute to the observed positive CO2 gradients in the TTL over West Africa. This suggests a more significant fraction of younger air masses in the TTL making it difficult to derive mean age of air from average gradients. Transport of air masses from the mid-latitude lower stratosphere had an impact from the mid-TTL upwards (20–40% above 370 K) during the campaign period importing air masses with high O3 and NOy. Ozone profiles show a less pronounced lower TTL minimum than observed previously by regular ozonesondes at other tropical locations. Concentrations are less than 100 ppbv in the lower TTL and vertical gradients less steep than in the upper TTL. The air mass origin analysis and simulations of in-situ net photochemical O3 production, initialised with observations, suggest that the lower TTL is significantly impacted by uplift of O3 precursors (over Africa and Asia) leading to positive production rates (up to 2 ppbv per day) in the lower and mid TTL even at moderate NOx levels. Photochemical O3 production increases with higher NOx and H2O in air masses with O3 less than 150 ppbv.

scholarly journals Approximational Projection of a Network with an Arbitrary Structure

2018 ◽  
Vol 7 (3.2) ◽  
pp. 550
Author(s):  
Valerii Usenko ◽  
Olga Kodak ◽  
Iryna Usenko
Keyword(s):  
Network Structure ◽  
Large Scale ◽  
System Parameters ◽  
Arbitrary Structure ◽  
Large Scale Networks ◽  
Definition Of

Improving the efficiency of the functioning of the engineering networks of cities involves solving the issues of expanding and deepening the process of studying the interconnection of its components.An approximate definition of the property of the network structure's connectivity belongs to the conceptual class of diminishing the dimension of the multiplicity of system parameters. It studies the structures of networks with arbitrary reliability of its constituent parts. The reflection of the reliability values of the components of a redundant engineering network structure is appropriate for large-scale networks. The multiplicity of the network is projected onto the subspace of its parameters with variable values of the argument of the function of the integrity of the connectivity.  

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