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At least 505 records · Page 28

A magnetic suspension system with a large angular range

The paper describes a small-scale laboratory system, called the Large-Angle Magnetic Suspension Test Fixture (LAMSTF), constructed at NASA Langley Research Center in order to explore and develop technology required for the magnetic suspension of objects over large ranges of orientation. The LAMSTF hardware comprises five electromagnets in a circular arrangement, each driven from a separate bipolar power amplifier. The suspended element is a cylindrical axially magnetized permanent magnet core, within an aluminum tube. The element, which is 'levitated' by repulsive forces, is stabilized in five degrees-of-freedom, with rotation about the cylinder axis not controlled. The controller accommodates the changes in magnetic coupling between the electromagnets and the suspended element by real-time adaptation of a decoupling matrix. The paper presents performance measurements demonstrating that the major design objective of the 360 deg rotation was accomplished.

Britcher, Colin P.↗

Cluster Observations of Multiple Dipolarization Fronts

We present Cluster observations of a series of dipolarization fronts (DF 1 to 6) at the central current sheet in Earth's magnetotail. The velocities of fast earthward flow following behind each DF 1-3, are comparable to the Alfven velocity, indicating that the flow bursts might have been generated by bursty reconnection that occurred tailward of the spacecraft. Based on multi-spacecraft timing analysis, DF normals are found to propagate mainly earthward at $160-335$ km/s with a thickness of 900-1500 km, which corresponds to the ion inertial length or gyroradius scale. Each DF is followed by significant fluctuations in the $x$ and $y$ components of the magnetic field whose peaks are found 1-2 minutes after the DF passage. These $(B_{x},B_{y} )$-fluctuations propagate dawnward (mainly) and earthward. Strongly enhanced field-aligned beams are observed coincidently with $(B_{x},B_{y})$ fluctuations, while an enhancement of cross-tail currents is associated with the DFs. From the observed pressure imbalance and flux-tube entropy changes between the two regions separated by the DF, we speculate that interchange instability destabilizes the DFs and causes the deformation of the mid-tail magnetic topology. This process generates significant field-aligned currents, and might power the auroral brightening in the ionosphere. However, this event is neither associated with the main substorm auroral breakup nor the poleward expansion, which might indicate that the observed multiple DFs have been dissipated before they reach the inner plasma sheet boundary.

Hwang, Kyoung-Joo↗

Prediction of Aerodynamic Coefficient using Genetic Algorithm Optimized Neural Network for Sparse Data

Wind tunnels use scale models to characterize aerodynamic coefficients, Wind tunnel testing can be slow and costly due to high personnel overhead and intensive power utilization. Although manual curve fitting can be done, it is highly efficient to use a neural network to define the complex relationship between variables. Numerical simulation of complex vehicles on the wide range of conditions required for flight simulation requires static and dynamic data. Static data at low Mach numbers and angles of attack may be obtained with simpler Euler codes. Static data of stalled vehicles where zones of flow separation are usually present at higher angles of attack require Navier-Stokes simulations which are costly due to the large processing time required to attain convergence. Preliminary dynamic data may be obtained with simpler methods based on correlations and vortex methods; however, accurate prediction of the dynamic coefficients requires complex and costly numerical simulations. A reliable and fast method of predicting complex aerodynamic coefficients for flight simulation I'S presented using a neural network. The training data for the neural network are derived from numerical simulations and wind-tunnel experiments. The aerodynamic coefficients are modeled as functions of the flow characteristics and the control surfaces of the vehicle. The basic coefficients of lift, drag and pitching moment are expressed as functions of angles of attack and Mach number. The modeled and training aerodynamic coefficients show good agreement. This method shows excellent potential for rapid development of aerodynamic models for flight simulation. Genetic Algorithms (GA) are used to optimize a previously built Artificial Neural Network (ANN) that reliably predicts aerodynamic coefficients. Results indicate that the GA provided an efficient method of optimizing the ANN model to predict aerodynamic coefficients. The reliability of the ANN using the GA includes prediction of aerodynamic coefficients to an accuracy of 110% . In our problem, we would like to get an optimized neural network architecture and minimum data set. This has been accomplished within 500 training cycles of a neural network. After removing training pairs (outliers), the GA has produced much better results. The neural network constructed is a feed forward neural network with a back propagation learning mechanism. The main goal has been to free the network design process from constraints of human biases, and to discover better forms of neural network architectures. The automation of the network architecture search by genetic algorithms seems to have been the best way to achieve this goal.

Rajkumar, T.↗

Cluster Observations of Multiple Dipolarization Fronts

We present Cluster observations of a series of dipolarization fronts (DF 1 to 6) at the central current sheet in Earth's magnetotail. The velocities of fast earthward flow following behind each DF 1.3 are comparable to the Alfven velocity, indicating that the flow bursts might have been generated by bursty reconnection that occurred tailward of the spacecraft. Based on multispacecraft timing analysis, DF normals are found to propagate mainly earthward at 160.335 km/s with a thickness of 900-1500 km, which corresponds to the ion inertial length or gyroradius scale. Each DF is followed by significant fluctuations in the x and y components of the magnetic field whose peaks are found 1.2 min after the DF passage. These (B(sub x), B(sub y)) fluctuations propagate dawnward (mainly) and earthward. Strongly enhanced field-aligned beams are observed coincidently with (B(sub x), B(sub y)) fluctuations, while an enhancement of cross-tail currents is associated with the DFs. From the observed pressure imbalance and flux tube entropy changes between the two regions separated by the DF, we speculate that interchange instability destabilizes the DFs and causes the deformation of the midtail magnetic topology. This process generates significant field-aligned currents and might power the auroral brightening in the ionosphere. However, this event is associated with neither the main substorm auroral breakup nor the poleward expansion, which might indicate that the observed multiple DFs have been dissipated before they reach the inner plasma sheet boundary.

Hwang, K.-J.↗

Upper-Ocean Heat Balance Processes and the Walker Circulation in CMIP5 Model Projections

Considerable uncertainty remains as to the importance of mechanisms governing decadal and longer variability of the Walker Circulation, its connection to the tropical climate system, and prospects for tropical climate change in the face of anthropogenic forcing. Most contemporary climate models suggest that in response to elevated CO2 and a warmer but more stratified atmosphere, the required upward mass flux in tropical convection will diminish along with the Walker component of the tropical mean circulation as well. Alternatively, there is also evidence to suggest that the shoaling and increased vertical stratification of the thermocline in the eastern Pacific will enable a muted SST increase there-- preserving or even enhancing some of the dynamical forcing for the Walker cell flow. Over the past decade there have been observational indications of an acceleration in near-surface easterlies, a strengthened Pacific zonal SST gradient, and globally-teleconnected dislocations in precipitation. But is this evidence in support of an ocean dynamical thermostat process posited to accompany anthropogenic forcing, or just residual decadal fluctuations associated with variations in warm and cold ENSO events and other stochastic forcing? From a modeling perspective we try to make headway on this question by examining zonal variations in surface energy fluxes and dynamics governing tropical upper ocean heat content evolution in the WCRP CMIP5 model projections. There is some diversity among model simulations; for example, the CCSM4 indicates net ocean warming over the IndoPacific region while the CSIRO model concentrates separate warming responses over the central Pacific and Indian Ocean regions. The models, as with observations, demonstrate strong local coupling between variations in column water vapor, downward surface longwave radiation and SST; but the spatial patterns of changes in the sign of this relationship differ among models and, for models as a whole, with observations. Our analysis focuses initially on probing the inter-model differences in energy fluxes / transports and Walker Circulation response to forcing. We then attempt to identify statistically the El Nino- / La Nina-related ocean heat content variability unique to each model and regress out the associated energy flux, ocean heat transport and Walker response on these shorter time scales for comparison to that of the anthropogenic signals.

Robertson, F. R.↗

Magnetic Flux Cancelation as the Buildup and Trigger Mechanism for CME-Producing Eruptions in Two Small Active Regions

We follow two small, magnetically isolated CME (Coronal Mass Ejection)-producing solar active regions (ARs) from the time of their emergence until several days later, when their core regions erupt to produce the CMEs. In both cases, magnetograms show: (a) following an initial period where the poles of the emerging regions separate from each other, the poles then reverse direction and start to retract inward; (b) during the retraction period, flux cancelation occurs along the main neutral line of the regions, (c) this cancelation builds the sheared core field/flux rope that eventually erupts to make the CME. In the two cases, respectively 30 percent and 50 percent of the maximum flux of the region cancels prior to the eruption. Recent studies indicate that solar coronal jets frequently result from small-scale filaments eruptions (Sterling et al. 2015), with those “minifilament” eruptions also being built up and triggered by cancelation of magnetic flux (Panesar et al. 2016). Together, the small-AR eruptions here and the coronal jet results suggest that isolated bipolar regions tend to erupt when some threshold fraction, perhaps in the range of 50 percent, of the region’s maximum flux has canceled. Our observed erupting filaments/flux ropes form at sites of flux cancelation, in agreement with previous observations. Thus, the recent finding that minifilaments that erupt to form jets also form via flux cancelation is further evidence that minifilaments are small-scale versions of the long-studied full-sized filaments. (Details are in Sterling et al. 2018, ApJ, 864, 68.) Supported by NASA's Heliophysics Guest Investigators (HGI) Program and the MSFC (Marshall Space Flight Center)/Hinode project.

Sterling, Alphonse C.↗

Streaming Instability with Multiple Dust Species – I. Favourable Conditions for the Linear Growth

A recent study suggests that the streaming instability, one of the leading mechanisms for driving the formation of planetesimals, may not be as efficient as previously thought. Under some disc conditions, the growth time-scale of the instability can be longer than the disc lifetime when multiple dust species are considered. To further explore this finding, we use both linear analysis and direct numerical simulations with gas fluid and dust particles tomutually validate and study the unstablemodes of the instability in more detail.We extend the previously studied parameter space by one order of magnitude in both the range of the dust-size distribution [Ts, min, Ts, max] and the total solid-to-gas mass ratio ε and introduce a third dimension with the slope q of the size distribution. We find that the fast-growth regime and the slow-growth regime are distinctly separated in the ε–Ts, max space, while this boundary is not appreciably sensitive to q or Ts, min.With a wide range of dust sizes present in the disc (e.g. Ts, min  10−3), the growth rate in the slow-growth regime decreases as more dust species are considered.With a narrow range of dust sizes (e.g. Ts, max/Ts, min = 5), on the other hand, the growth rate in most of the ε–Ts, max space is converged with increasing dust species, but the fast and the slow growth regimes remain clearly separated. Moreover, it is not necessary that the largest dust species dominate the growth of the unstable modes, and the smaller dust species can affect the growth rate in a complicated way. In any case, we find that the fast-growth regime is bounded by ε  1 or Ts, max  1, which may represent the favourable conditions for planetesimal formation.

Zhaohuan Zhu↗

Characteristics of wake vortex generated by a Boeing 727 jet transport during two-segment and normal ILS approach flight paths

A series of flight tests was conducted to evaluate the vortex wake characteristics of a Boeing 727 (B727-200) aircraft during conventional and two-segment ILS approaches. Twelve flights of the B727, which was equipped with smoke generators for vortex marking, were flown and its vortex wake was intentionally encountered by a Lear Jet model 23 (LR-23) and a Piper Twin Comanche (PA-30). Location of the B727 vortex during landing approach was measured using a system of photo-theodolites. The tests showed that at a given separation distance there were no readily apparent differences in the upsets resulting from deliberate vortex encounters during the two types of approaches. Timed mappings of the position of the landing configuration vortices showed that they tended to descend approximately 91 m(300 ft) below the flight path of the B727. The flaps of the B727 have a dominant effect on the character of the trailed wake vortex. The clean wing produces a strong, concentrated vortex but as the flaps are lowered, the vortex system becomes more diffuse. Pilot opinion and roll acceleration data indicate that 4.5 n.mi. would be a minimum separation distance at which roll control of light aircraft (less than 5,670 kg (12,500 lb) could be maintained during parallel encounters of the B727's landing configuration wake. This minimum separation distance is generally in scale with results determined from previous tests of other aircraft using the small roll control criteria.

Kurkowski, R. L.↗

Vorticity imbalance and stability in relation to convection

A complete synoptic-scale vorticity budget was related to convection storm development in the eastern two-thirds of the United States. The 3-h sounding interval permitted a study of time changes of the vorticity budget in areas of convective storms. Results of analyses revealed significant changes in values of terms in the vorticity equation at different stages of squall line development. Average budgets for all areas of convection indicate systematic imbalance in the terms in the vorticity equation. This imbalance resulted primarily from sub-grid scale processes. Potential instability in the lower troposphere was analyzed in relation to the development of convective activity. Instability was related to areas of convection; however, instability alone was inadequate for forecast purposes. Combinations of stability and terms in the vorticity equation in the form of indices succeeded in depicting areas of convection better than any one item separately.

Read, W. L.↗

Development of a Fatigue Crack Growth Coupon for Highly Plastic Stress Conditions

This paper presents an analytical approach used to develop a novel fatigue crack growth coupon for a highly plastic 3-D stress field condition. The flight hardware investigated in this paper is a large separation bolt that fractures using pyrotechnics at the appointed time during the flight sequence. The separation bolt has a deep notch that produces a severe stress concentration and a large plastic zone when highly loaded. For this geometry, linear-elastic fracture mechanics (LEFM) techniques are not valid due to the large nonlinear stress field. Unfortunately, industry codes that are generally available for fracture mechanics analysis and fatigue crack growth (e.g. NASGRO (11) are limited to LEFM and are available for only a limited number of geometries. The results of LEFM based codes are questionable when used on geometries with significant plasticity. Therefore elastic-plastic fracture mechanics (EPFM) techniques using the finite element method (FEM) were used to analyze the bolt and test coupons. scale flight hardware is very costly in t e r n of assets, laboratory resources, and schedule. Therefore to alleviate some of these problems, a series of novel test coupons were developed to simulate the elastic-plastic stress field present in the bolt.

Allen, Phillip A.↗

Dichroic Filter for Separating W-Band and Ka-Band

The proposed Aerosol/Cloud/Ecosystems (ACEs) mission development would advance cloud profiling radar from that used in CloudSat by adding a 35-GHz (Ka-band) channel to the 94-GHz (W-band) channel used in CloudSat. In order to illuminate a single antenna, and use CloudSat-like quasi-optical transmission lines, a spatial diplexer is needed to add the Ka-band channel. A dichroic filter separates Ka-band from W-band by employing advances in electrical discharge machining (EDM) and mode-matching analysis techniques developed and validated for designing dichroics for the Deep Space Network (DSN), to develop a preliminary design that both met the requirements of frequency separation and mechanical strength. First, a mechanical prototype was built using an approximately 102-micron-diameter EDM process, and tolerances of the hole dimensions, wall thickness, radius, and dichroic filter thickness measured. The prototype validated the manufacturing needed to design a dichroic filter for a higher-frequency usage than previously used in the DSN. The initial design was based on a Ka-band design, but thicker walls are required for mechanical rigidity than one obtains by simply scaling the Ka-band dichroic filter. The resulting trade of hole dimensions for mechanical rigidity (wall thickness) required electrical redesign of the hole dimensions. Updates to existing codes in the linear solver decreased the analysis time using mode-matching, enabling the electrical design to be realized quickly. This work is applicable to missions and instruments that seek to extend W-band cloud profiling measurements to other frequencies. By demonstrating a dichroic filter that passes W-band, but reflects a lower frequency, this opens up the development of instruments that both compare to and enhance CloudSat.

Epp, Larry W.↗

Recent Development Work with Self-Aligned Focusing Schlieren

A novel compact focusing schlieren instrument has recently been developed that eliminates the need for a separate source and cutoff grid. The technique works by projecting an image of a grid onto a retroreflective surface and then reimaging the projection back onto the original grid. By manipulating the polarization state of the light passing through the instrument, a single Rochon polarizing prism can be used to adjust the schlieren sensitivity by translating it along the instrument’s optical axis, which changes the in-plane offset between the reimaged projection and the original grid. This arrangement makes the instrument inherently self-aligned. Relative to conventional focusing schlieren instruments, which require alignment of a separate source grid and cutoff grid to achieve sensitivity, the setup time required in order to obtain high quality focusing schlieren images is significantly reduced. Further, the self-aligned nature of this instrument makes it insensitive to vibrations and allows for on-the-fly adjustments to field-of-view. In this paper we discuss recent work that has been performed to expand the capabilities of this self-aligned focusing schlieren instrument including: schlieren visualization at extreme angles for optically-restricted test facilities, 3D schlieren visualization using a light field camera, acquisition of high quality focusing schlieren images from facilities with low quality windows, and obtaining focusing schlieren images in full-scale ground test facilities.

Brett Bathel↗

Tidal and atmospheric forcing of the upper ocean in the Gulf of California. 2: Surface heat flux

Satellite infrared imagery and coastal meteorological data for March 1984 through February 1985 are used to estimate the net annual surface heat flux for the northern Gulf of California. The average annual surface heat flux for the area north of Guaymas and Santa Rosalia is estimated to be +74 W/sq m for the 1984-1985 time period. This is comparable to the +20-50 W/sq m previously obtained from heat and freshwater transport estimates made with hydrographic surveys from different years and months. The spatial distribution of the net surface heat flux shows a net gain of heat over the whole northern gulf. Except for a local maximum near San Esteban Island, the largest heat gain (+110-120 W/sq m) occurs in the Ballenas and Salsipuedes channels, where strong tidal mixing produces anomalously cold sea surface temperatures (SSTs) over much of the year. The lowest heat gain occurs in the Guayamas Basin (+40-50 W/sq m), where SSTs are consistently warmer. In the relatively shallow northern basin the net surface heat flux is farily uniform, with a net annual gain of approxmately +70 W/sq m. A local minimum in heat gain (approximately +60 W/sq m) is observed over the shelf in the northwest, where spring and summer surface temperatures are particularly high. A similar minimum in heat gain over the shelf was observed in a separate study in which historical SSTs and 7 years (1979-1986) of meteorological data from Puerto Penasco were used to estimate the net surface heat flux for the northern basin. In that study, however, the heat fluxes were higher, with a gain of +100 W/sq m over the shelf and +114 W/sq m in the northern basin. These larger values are directly attributable to the higher humidities in the 1979-1986 study compared to the 1984-1985 satellite study. High humidities reduce evaporation and the associated latent heat loss, promoting a net annual heat gain. In the norther Gulf of California, however, tidal mixing appears to play a key role in the observed gain of heat. Deep mixing in the island region produces a persistent pool of cold water which is mixed horizontally by the large-scale circulation, lowering surface temperatures over most of the northern gulf. These cold SSTs decrease evaporation by reducing the saturation vapor pressure of the overlying air. As a result, heat loss is substantially reduced, even when humidities are low. By removing heat from the surface, tidal mixing alters the time scale of air-sea interaction and reduces or possibly even inhibits the formation of deep water masses via convection.

Paden, Cynthia A.↗

Evaluation of ERTS-1 data for inventory of forest and rangeland and detection of forest stress

The author has identified the following significant results. Results of photointerpretation indicated that ERTS is a good classifier of forest and nonforest lands (90 to 95 percent accurate). Photointerpreters could make this separation as accurately as signature analysis of the computer compatible tapes. Further breakdowns of cover types at each site could not be accurately classified by interpreters (60 percent) or computer analysts (74 percent). Exceptions were water, wet meadow, and coniferous stands. At no time could the large bark beetle infestations (many over 300 meters in size) be detected on ERTS images. The ERTS wavebands are too broad to distinguish the yellow, yellow-red, and red colors of the dying pine foliage from healthy green-yellow foliage. Forest disturbances could be detected on ERTS color composites about 90 percent of the time when compared with six-year-old photo index mosaics. ERTS enlargements (1:125,000 scale, preferably color prints) would be useful to forest managers of large ownerships over 5,000 hectares (12,500 acres) for broad area planning. Black-and-white enlargements can be used effectively as aerial navigation aids for precision aerial photography where maps are old or not available.

Heller, R. C.↗

The optical and radiation field signatures produced by lightning return strokes

Typical examples of the signals that are produced by first and subsequent return strokes in cloud-to-ground lightning on a microsecond time scale are presented. Statistics on the structure of the waveforms and the radiance of the channels are given. The relationship between the light signals and the associated electric field signatures is discussed. It is shown that the initial light signal from a return stroke tends to be linear for about 15 microsec and then rises more slowly to a peak that is delayed by approximately 60 microsec from the electric field peak. It is thought that the transition between the fast linear portion and the slower rise may be due to the return stroke entering the cloud base. A small percentage of the records suggest that two different branches of the same stepped leader can initiate separate return strokes. The light pulses from cloud discharges tend to be smaller and to vary more slowly than those from return strokes.

Guo, C.↗

Definition of experiments to investigate fire suppressants in microgravity

Defined and justified here are the conceptual design and operation of a critical set of experiments expected to yield information on suppressants and on suppressant delivery systems under realistic spacecraft-fire conditions (smoldering). Specific experiment parameters are provided on the solid fuel (carbon), oxidants (habitable spacecraft atmospheres), fuel/oxidant supply, mixing mode, and rate (quiescent and finite; ventilated and replenishable), ignition mode, event, and reignition tendency, fire-zone size, fire conditions, lifetime, and consequences (toxicity), suppressants (CO2, H2O, N2) and suppressant delivery systems, and diagnostics. Candidate suppressants were identified after an analysis of how reduced gravity alters combustion, and how these alterations may influence the modes, mechanisms, and capacities of terrestrial agents to suppress unwanted combustion, or fire. Preferred spacecraft suppression concepts included the local, near-quiescent application of a gas, vapor, or mist that has thermophysical fire-suppression activity and is chemically inert under terrestrial (normal gravity) combustion conditions. The scale, number, and duration (about 1 hour) of the proposed low-gravity experiments were estimated using data not only on the limitations imposed by spacecraft-carrier (Shuttle or Space Station Freedom) accommodations, but also data on the details and experience of standardized smolder-suppression experiments at normal gravity. Deliberately incorporated into the conceptual design was sufficient interchangeability for the prototype experimental package to fly either on Shuttle now or Freedom later. This flexibility is provided by the design concept of up to 25 modular fuel canisters within a containment vessel, which permits both integration into existing low-gravity in-space combustion experiments and simultaneous testing of separate experiments to conserve utilities and time.

Reuther, James J.↗

A Novel Biomedical Device Utilizing Light Emitting Nano-Structures

This paper will discuss the development of a novel biomedical detection device that will be used to detect microorganisms with the use of infrared fluorochrome polymers attached to antibodies in fluids such as water. The fluorochrome polymers emit light in the near inferred region (NIR), approximately 805 nm, when excited by an NIR laser at 778 nm. The device could remarkably change the way laboratory testing is done today. The testing process is usually performed on a time scale of days while our device will be able to detect microorganisms in minutes. This type of time efficient analysis is ideal for use aboard the International Space Station and the Space Shuttle (ISS/SS) and has many useful commercial applications, for instance at a water treatment plant and food processing plants. With more research and experimentation the testing might also one day be used to detect bacteria and viruses in complex fluids such as blood, which would revolutionize blood analysis as it is performed today. My contribution to the project has been to develop a process which will allow an antibody/fluorescent dye pair to be conjugated to a specific bacteria or virus and than to to be separated from a sample body of water for detection. The antibody being used in this experiment is anti beta galactosidase and its complement enzyme is beta galactosidase, a non harmful derivative of E. Coli. The anti beta galactosidase has been conjugated to the fluorochrome polymer, IRDye800, which emits at approximately 806 nm. The dye when excited by the NIR laser emits a signal which is detected by a spectrometer and then is read by state of the art computer software. The state-of-the-art process includes incubating the anti beta galactosidase and beta galactosidase in a phosphate buffer solution in a test tube, allowing the antibody to bind to specific sites on the enzyme. After the antibody is bound to the enzyme, it is centrifuged in specific filters that will allow free antibody to wash away and leave the antibody-enzyme complexes on top in solution for testing and analysis. This solution is pipetted into a cuvette, a special plastic test tube, which will then be excited by the laser. The signal read will tell US that an antibody is present and since it is bound to the enzyme, that the bacteria is also present.

Varaljay, Vanessa A.↗

Spatial Correlation and Coherence of Boundary Layer Winds Near Cape Canaveral Florida

The spatial correlation and coherence of winds over separation distances from 8.5 to 31 km based on central Florida data from November 1999 through August 2001 are presented. The winds at altitudes from 500 to 3000 m were measured using a network of five radar wind profilers. The goal was to determine the extent to which the profilers may be considered independent data sources. Quality controlled profiles were produced every 15 minutes for up to sixty gates, each representing 101 m in altitude over the range from 130 m to 6089 m. Five levels, each containing three consecutive gates, were selected for analysis. These levels covered the range from 433 to 3059 m. The results show that the profilers are independent for features having time scales of less than one hour in the winter or two hours in the summer. This does not depend significantly on height. Because the size of the network coincides with the "spectral gap" in the boundary layer, the result also does not depend on the spacing of the profilers within the network.

Merceret, Francis J.↗