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NASA NTRS2004

Implementation of Coupled Skin Temperature Analysis and Bias Correction in a Global Atmospheric Data Assimilation System

The NASA/NCAR Finite Volume GCM (fvGCM) with the NCAR CLM (Community Land Model) version 2.0 was integrated into the NASA/GMAO Finite Volume Data Assimilation System (fvDAS). A new method was developed for coupled skin temperature assimilation and bias correction where the analysis increment and bias correction term is passed into the CLM2 and considered a forcing term in the solution to the energy balance. For our purposes, the fvDAS CLM2 was run at 1 deg. x 1.25 deg. horizontal resolution with 55 vertical levels. We assimilate the ISCCP-DX (30 km resolution) surface temperature product. The atmospheric analysis was performed 6-hourly, while the skin temperature analysis was performed 3-hourly. The bias correction term, which was updated at the analysis times, was added to the skin temperature tendency equation at every timestep. In this presentation, we focus on the validation of the surface energy budget at the in situ reference sites for the Coordinated Enhanced Observation Period (CEOP). We will concentrate on sites that include independent skin temperature measurements and complete energy budget observations for the month of July 2001. In addition, MODIS skin temperature will be used for validation. Several assimilations were conducted and preliminary results will be presented.

Radakovich, Jon↗
NASA NTRS2001

Sensitivity Study of the Wall Interference Correction System (WICS) for Rectangular Tunnels

An off-line wall version of the Wall Interference Correction System (WICS) has been implemented for the NASA Langley National Transonic Facility. The correction capability is currently restricted to corrections for solid wall interference in the model pitch plane for MAch numbers less than 0.45 due to limitation in tunnel calibration data. A study to assess output sensitivity to measurement uncertainty was conducted to determine standard operational procedures and guidelines to ensure data quality during the testing process.

Walker, Eric L.↗
NASA NTRS2004

Analysis Of AVIRIS Data From LEO-15 Using Tafkaa Atmospheric Correction

We previously developed an algorithm named Tafkaa for atmospheric correction of remote sensing ocean color data from aircraft and satellite platforms. The algorithm allows quick atmospheric correction of hyperspectral data using lookup tables generated with a modified version of Ahmad & Fraser s vector radiative transfer code. During the past few years we have extended the capabilities of the code. Current modifications include the ability to account for within scene variation in solar geometry (important for very long scenes) and view geometries (important for wide fields of view). Additionally, versions of Tafkaa have been made for a variety of multi-spectral sensors, including SeaWiFS and MODIS. In this proceeding we present some initial results of atmospheric correction of AVIRIS data from the 2001 July Hyperspectral Coastal Ocean Dynamics Experiment (HyCODE) at LEO-15.

Montes, Marcos J.↗
NASA NTRS2006

Developing Formal Correctness Properties from Natural Language Requirements

This viewgraph presentation reviews the rationale of the program to transform natural language specifications into formal notation.Specifically, automate generation of Linear Temporal Logic (LTL)correctness properties from natural language temporal specifications. There are several reasons for this approach (1) Model-based techniques becoming more widely accepted, (2) Analytical verification techniques (e.g., model checking, theorem proving) significantly more effective at detecting types of specification design errors (e.g., race conditions, deadlock) than manual inspection, (3) Many requirements still written in natural language, which results in a high learning curve for specification languages, associated tools and increased schedule and budget pressure on projects reduce training opportunities for engineers, and (4) Formulation of correctness properties for system models can be a difficult problem. This has relevance to NASA in that it would simplify development of formal correctness properties, lead to more widespread use of model-based specification, design techniques, assist in earlier identification of defects and reduce residual defect content for space mission software systems. The presentation also discusses: potential applications, accomplishments and/or technological transfer potential and the next steps.

requirements engineering↗
NASA NTRS2006

Skin Temperature Analysis and Bias Correction in a Coupled Land-Atmosphere Data Assimilation System

In an initial investigation, remotely sensed surface temperature is assimilated into a coupled atmosphere/land global data assimilation system, with explicit accounting for biases in the model state. In this scheme, an incremental bias correction term is introduced in the model's surface energy budget. In its simplest form, the algorithm estimates and corrects a constant time mean bias for each gridpoint; additional benefits are attained with a refined version of the algorithm which allows for a correction of the mean diurnal cycle. The method is validated against the assimilated observations, as well as independent near-surface air temperature observations. In many regions, not accounting for the diurnal cycle of bias caused degradation of the diurnal amplitude of background model air temperature. Energy fluxes collected through the Coordinated Enhanced Observing Period (CEOP) are used to more closely inspect the surface energy budget. In general, sensible heat flux is improved with the surface temperature assimilation, and two stations show a reduction of bias by as much as 30 Wm(sup -2) Rondonia station in Amazonia, the Bowen ratio changes direction in an improvement related to the temperature assimilation. However, at many stations the monthly latent heat flux bias is slightly increased. These results show the impact of univariate assimilation of surface temperature observations on the surface energy budget, and suggest the need for multivariate land data assimilation. The results also show the need for independent validation data, especially flux stations in varied climate regimes.

Bosilovich, Michael G.↗
NASA NTRS2008

Atmospheric Correction at AERONET Locations: A New Science and Validation Data Set

This paper describes an AERONET-based Surface Reflectance Validation Network (ASRVN) and its dataset of spectral surface bidirectional reflectance and albedo based on MODIS TERRA and AQUA data. The ASRVN is an operational data collection and processing system. It receives 50x50 square kilometer subsets of MODIS L1B data from MODAPS and AERONET aerosol and water vapor information. Then it performs an accurate atmospheric correction for about 100 AERONET sites based on accurate radiative transfer theory with high quality control of the input data. The ASRVN processing software consists of L1B data gridding algorithm, a new cloud mask algorithm based on a time series analysis, and an atmospheric correction algorithm. The atmospheric correction is achieved by fitting the MODIS top of atmosphere measurements, accumulated for 16-day interval, with theoretical reflectance parameterized in terms of coefficients of the LSRT BRF model. The ASRVN takes several steps to ensure high quality of results: 1) cloud mask algorithm filters opaque clouds; 2) an aerosol filter has been developed to filter residual semi-transparent and sub-pixel clouds, as well as cases with high inhomogeneity of aerosols in the processing area; 3) imposing requirement of consistency of the new solution with previously retrieved BRF and albedo; 4) rapid adjustment of the 16-day retrieval to the surface changes using the last day of measurements; and 5) development of seasonal back-up spectral BRF database to increase data coverage. The ASRVN provides a gapless or near-gapless coverage for the processing area. The gaps, caused by clouds, are filled most naturally with the latest solution for a given pixels. The ASRVN products include three parameters of LSRT model (k(sup L), k(sup G), k(sup V)), surface albedo, NBRF (a normalized BRF computed for a standard viewing geometry, VZA=0 deg., SZA=45 deg.), and IBRF (instantaneous, or one angle, BRF value derived from the last day of MODIS measurement for specific viewing geometry) for MODIS 500m bands 1-7. The results are produced daily at resolution of 1 km in gridded format. We also provide cloud mask, quality flag and a browse bitmap image. The new dataset can be used for a wide range of applications including validation analysis and science research.

Wang, Yujie↗
NASA NTRS2008

A Vegetation Correction Methodology for Time Series Based Soil Moisture Retrieval From C-band Radar Observations

A methodology is presented to correct backscatter (sigma(sup 0)) observations for the effect of vegetation. The proposed methodology is based on the concept that the ratio of the surface scattering over the total amount of scattering (sigma(sup 0)(sub soil)/sigma(sup 0)) is only affected by the vegetation and can be described as a function of the vegetation water content. Backscatter observations sigma(sup 0) from the soil are not influenced by vegetation. Under bare soil conditions (sigma(sup 0)(sub soil)/sigma(sup 0)) equals 1. Under low to moderate biomass and soil moisture conditions, vegetation affects the observed sigma(sup 0) through absorption of the surface scattering and contribution of direct scattering by the vegetation itself. Therefore, the contribution of the surface scattering is smaller than the observed total amount of scattering and decreases as the biomass increases. For dense canopies scattering interactions between the soil surface and vegetation elements (e.g. leaves and stems) also become significant. Because these higher order scattering mechanisms are influenced by the soil surface, an increase in (sigma(sup 0)(sub soil)/sigma(sup 0)) may be observed as the biomass increases under densely vegetated conditions. This methodology is applied within the framework of time series based approach for the retrieval of soil moisture. The data set used for this investigation has been collected during a campaign conducted at USDA's Optimizing Production Inputs for Economic and Environmental Enhancement OPE-3) experimental site in Beltsville, Maryland (USA). This campaign took place during the corn growth cycle from May 10th to 0ctober 2nd, 2002. In this period the corn crops reached a vegetation water content of 5.1 kg m(exp -2) at peak biomass and a soil moisture range varying between 0.00 to 0.26 cubic cm/cubic cm. One of the deployed microwave instruments operated was a multi-frequency (C-band (4.75 GHz) and L-band (1.6 GHz)) quad-polarized (HH, HV, VV, VH) radar which was mounted on a 20 meter long boom. In the OPE-3 field campaign, radar observations were collected once a week at nominal times of 8 am, 10 am, 12 noon and 2 pm. During each data run the radar acquired sixty independent measurements within an azimuth of 120 degrees from a boom height of 12.2 m and at three different incidence angles (15,35, and 55 degrees). The sixty observations were averaged to provide one backscatter value for the study area and its accuracy is estimated to be 51.0 dB. For this investigation the C-band observations have been used. Application of the proposed methodology to the selected data set showed a well-defined relationship between (sigma(sup 0)(sub soil)/sigma(sup 0)) and the vegetation water content. It is found that this relationship can be described with two experimentally determined parameters, which depend on the sensing configuration (e.g. incidence angle and polarization). Through application of the proposed vegetation correction methodology and the obtained parameterizations, the soil moisture retrieval accuracy within the framework of a time series based approach is improved from 0.033 to 0.032 cubic cm/cubic cm, from 0.049 to 0.033 cubic cm/cubic cm and from 0.079 to 0.047 cubic cm/cubic cm for incidence angles of 15,35 and 55 degrees, respectively. Improvement in soil moisture retrieval due to vegetation correction is greater at larger incidence angles (due to the increased path length and larger vegetation effects on the surface signal at the larger angles).

Joseph, Alicia T.↗
NASA NTRS2007

Fault Detection and Correction for the Solar Dynamics Observatory Attitude Control System

The Solar Dynamics Observatory is an Explorer-class mission that will launch in early 2009. The spacecraft will operate in a geosynchronous orbit, sending data 24 hours a day to a devoted ground station in White Sands, New Mexico. It will carry a suite of instruments designed to observe the Sun in multiple wavelengths at unprecedented resolution. The Atmospheric Imaging Assembly includes four telescopes with focal plane CCDs that can image the full solar disk in four different visible wavelengths. The Extreme-ultraviolet Variability Experiment will collect time-correlated data on the activity of the Sun's corona. The Helioseismic and Magnetic Imager will enable study of pressure waves moving through the body of the Sun. The attitude control system on Solar Dynamics Observatory is responsible for four main phases of activity. The physical safety of the spacecraft after separation must be guaranteed. Fine attitude determination and control must be sufficient for instrument calibration maneuvers. The mission science mode requires 2-arcsecond control according to error signals provided by guide telescopes on the Atmospheric Imaging Assembly, one of the three instruments to be carried. Lastly, accurate execution of linear and angular momentum changes to the spacecraft must be provided for momentum management and orbit maintenance. In th~sp aper, single-fault tolerant fault detection and correction of the Solar Dynamics Observatory attitude control system is described. The attitude control hardware suite for the mission is catalogued, with special attention to redundancy at the hardware level. Four reaction wheels are used where any three are satisfactory. Four pairs of redundant thrusters are employed for orbit change maneuvers and momentum management. Three two-axis gyroscopes provide full redundancy for rate sensing. A digital Sun sensor and two autonomous star trackers provide two-out-of-three redundancy for fine attitude determination. The use of software to maximize chances of recovery from any hardware or software fault is detailed. A generic fault detection and correction software structure is used, allowing additions, deletions, and adjustments to fault detection and correction rules. This software structure is fed by in-line fault tests that are also able to take appropriate actions to avoid corruption of the data stream.

Starin, Scott R.↗
NASA NTRS2008

Accuracy Assessment and Correction of Vaisala RS92 Radiosonde Water Vapor Measurements

Relative humidity (RH) measurements from Vaisala RS92 radiosondes are widely used in both research and operational applications, although the measurement accuracy is not well characterized as a function of its known dependences on height, RH, and time of day (or solar altitude angle). This study characterizes RS92 mean bias error as a function of its dependences by comparing simultaneous measurements from RS92 radiosondes and from three reference instruments of known accuracy. The cryogenic frostpoint hygrometer (CFH) gives the RS92 accuracy above the 700 mb level; the ARM microwave radiometer gives the RS92 accuracy in the lower troposphere; and the ARM SurTHref system gives the RS92 accuracy at the surface using 6 RH probes with NIST-traceable calibrations. These RS92 assessments are combined using the principle of Consensus Referencing to yield a detailed estimate of RS92 accuracy from the surface to the lowermost stratosphere. An empirical bias correction is derived to remove the mean bias error, yielding corrected RS92 measurements whose mean accuracy is estimated to be +/-3% of the measured RH value for nighttime soundings and +/-4% for daytime soundings, plus an RH offset uncertainty of +/-0.5%RH that is significant for dry conditions. The accuracy of individual RS92 soundings is further characterized by the 1-sigma "production variability," estimated to be +/-1.5% of the measured RH value. The daytime bias correction should not be applied to cloudy daytime soundings, because clouds affect the solar radiation error in a complicated and uncharacterized way.

Whiteman, David N.↗
NASA NTRS1938

Correction of Profile-Drag Results from Variable-Density Tunnel and the Effect on the Choice of Wing-Section Thickness

Profile-drag coefficients published from tests in the N.A.C.A. variable-density tunnel (Technical Reports Nos. 460, 537, 586, and 610, references 1 to 4) have tended to appear high as compared with results from the N.A.C.A. full-scale tunnel (Technical Report No. 530, reference 5) and from foreign sources (references 6 to 8). Such discrepancies were considered in Technical Report No. 586, and corrections for turbulence and tip effects were derived that tended to reduce the profile-drag coefficients, particularly for the thicker airfoils. The corrected profile-drag coefficients, designated by the lower-case symbol cdo as contrasted with the older CDO, have been employed in the airfoil reports published since Technical Report No. 460, but even these corrected results continued to appear high, particularly for the thicker sections. The important practical result is that a smaller increase of drag with airfoil thickness is indicated, which may be of primary importance to the airplane designer in choosing the optimum airfoil sections for actual wings. Further investigations of this subject were, of course, undertaken, one of the most important being an investigation of three symmetrical sections N.A.C A. 0009, 0012, and 0018 under conditions of low turbulence in the full-scale tunnel. Preliminary results from this investigation also indicate a smaller increase in drag with airfoil thickness than the results from the variable-density tunnel. Furthermore, comparative tests made in the two tunnels by applying strings to the surface of the N.A.C.A. 0012 airfoil to move the transition point to a predetermined position indicated that the effective reynolds Number concept would account approximately for the drag as affected by the position of transition from laminar to turbulent flow in the boundary layer.

Jacobs, Eastman N.↗
NASA NTRS2007

Active Correction of Aberrations of Low-Quality Telescope Optics

A system of active optics that includes a wavefront sensor and a deformable mirror has been demonstrated to be an effective means of partly correcting wavefront aberrations introduced by fixed optics (lenses and mirrors) in telescopes. It is envisioned that after further development, active optics would be used to reduce wavefront aberrations of about one wave or less in telescopes having aperture diameters of the order of meters or tens of meters. Although this remaining amount of aberration would be considered excessive in scientific applications in which diffraction-limited performance is required, it would be acceptable for free-space optical- communication applications at wavelengths of the order of 1 m. To prevent misunderstanding, it is important to state the following: The technological discipline of active optics, in which the primary or secondary mirror of a telescope is directly and dynamically tilted, distorted, and/or otherwise varied to reduce wavefront aberrations, has existed for decades. The term active optics does not necessarily mean the same thing as does adaptive optics, even though active optics and adaptive optics are related. The term "adaptive optics" is often used to refer to wavefront correction at speeds characterized by frequencies ranging up to between hundreds of hertz and several kilohertz high enough to enable mitigation of adverse effects of fluctuations in atmospheric refraction upon propagation of light beams. The term active optics usually appears in reference to wavefront correction at significantly lower speeds, characterized by times ranging from about 1 second to as long as minutes. Hence, the novelty of the present development lies, not in the basic concept of active or adaptive optics, but in the envisioned application of active optics in conjunction with a deformable mirror to achieve acceptably small wavefront errors in free-space optical communication systems that include multi-meter-diameter telescope mirrors that are relatively inexpensive because their surface figures are characterized by errors as large as about 10 waves. Figure 1 schematically depicts the apparatus used in an experiment to demonstrate such an application on a reduced scale involving a 30-cm-diameter aperture.

Hemmati, Hamid↗
NASA NTRS2007

Ground-Based Correction of Remote-Sensing Spectral Imagery

Software has been developed for an improved method of correcting for the atmospheric optical effects (primarily, effects of aerosols and water vapor) in spectral images of the surface of the Earth acquired by airborne and spaceborne remote-sensing instruments. In this method, the variables needed for the corrections are extracted from the readings of a radiometer located on the ground in the vicinity of the scene of interest. The software includes algorithms that analyze measurement data acquired from a shadow-band radiometer. These algorithms are based on a prior radiation transport software model, called MODTRAN, that has been developed through several versions up to what are now known as MODTRAN4 and MODTRAN5 . These components have been integrated with a user-friendly Interactive Data Language (IDL) front end and an advanced version of MODTRAN4. Software tools for handling general data formats, performing a Langley-type calibration, and generating an output file of retrieved atmospheric parameters for use in another atmospheric-correction computer program known as FLAASH have also been incorporated into the present soft-ware. Concomitantly with the soft-ware described thus far, there has been developed a version of FLAASH that utilizes the retrieved atmospheric parameters to process spectral image data.

Alder-Golden, Steven M.↗
NASA NTRS2010

Wavefront Correction for Large, Flexible Antenna Reflector

A wavefront-correction system has been proposed as part of an outer-space radio communication system that would include a large, somewhat flexible main reflector antenna, a smaller subreflector antenna, and a small array feed at the focal plane of these two reflector antennas. Part of the wavefront-correction system would reside in the subreflector, which would be a planar patch-element reflectarray antenna in which the phase shifts of the patch antenna elements would be controlled via microelectromechanical systems (MEMS) radio -frequency (RF) switches. The system would include the following sensing-and-computing subsystems: a) An optical photogrammetric subsystem built around two cameras would estimate geometric distortions of the main reflector; b) A second subsystem would estimate wavefront distortions from amplitudes and phases of signals received by the array feed elements; and c) A third subsystem, built around small probes on the subreflector plane, would estimate wavefront distortions from differences among phases of signals received by the probes. The distortion estimates from the three subsystems would be processed to generate control signals to be fed to the MEMS RF switches to correct for the distortions, thereby enabling collimation and aiming of the received or transmitted radio beam to the required precision.

Imbriale, William A.↗
NASA NTRS2011

Aperiodicity Correction for Rotor Tip Vortex Measurements

The initial roll-up of a tip vortex trailing from a model-scale, hovering rotor was measured using particle image velocimetry. The unique feature of the measurements was that a microscope was attached to the camera to allow much higher spatial resolution than hitherto possible. This also posed some unique challenges. In particular, the existing methodologies to correct for aperiodicity in the tip vortex locations could not be easily extended to the present measurements. The difficulty stemmed from the inability to accurately determine the vortex center, which is a prerequisite for the correction procedure. A new method is proposed for determining the vortex center, as well as the vortex core properties, using a least-squares fit approach. This approach has the obvious advantage that the properties are derived from not just a few points near the vortex core, but from a much larger area of flow measurements. Results clearly demonstrate the advantage in the form of reduced variation in the estimated core properties, and also the self-consistent results obtained using three different aperiodicity correction methods.

Ramasamy, Manikandan↗
NASA NTRS2010

An Illumination Correction ALgorithm on Landsat-TM Data

In this paper, a new illumination correction model, the rotation model, is introduced. The model is based on the empirical correlation between reflectance and the illumination condition (IL). The model eliminates the dependency of reflectance on IL through rotating the data in IL-reflectance space. This model is compared with widely used cosine model and C model over a sample forest region. We found that the newly developed rotation model consistently performs best on both atmospheric uncorrected and corrected Landsat images. Index Terms Landsat, illumination correction, change detection, LEDAPS

Tan, Bin↗
NASA NTRS2011

Phase-Controlled Magnetic Mirror for Wavefront Correction

Typically, light interacts with matter via the electric field and interaction with weakly bound electrons. In a magnetic mirror, a patterned nanowire is fabricated over a metallic layer with a dielectric layer in between. Oscillation of the electrons in the nanowires in response to the magnetic field of incident photons causes a re-emission of photons and operation as a "magnetic mirror." By controlling the index of refraction in the dielectric layer using a local applied voltage, the phase of the emitted radiation can be controlled. This allows electrical modification of the reflected wavefront, resulting in a deformable mirror that can be used for wavefront control. Certain applications require wavefront quality in the few-nanometer regime, which is a major challenge for optical fabrication and alignment of mirrors or lenses. The use of a deformable magnetic mirror allows for a device with no moving parts that can modify the phase of incident light over many spatial scales, potentially with higher resolution than current approaches. Current deformable mirrors modify the incident wavefront by using nano-actuation of a substrate to physically bend the mirror to a desired shape. The purpose of the innovation is to modify the incident wavefront for the purpose of correction of fabrication and alignment-induced wavefront errors at the system level. The advanced degree of precision required for some applications such as gravity wave detection (LISA - Laser Interferometer Space Antenna) or planet finding (FKSI - Fourier-Kelvin Stellar Interferometer) requires wavefront control at the limits of the current state of the art. All the steps required to fabricate a magnetic mirror have been demonstrated. The modification is to apply a bias voltage to the dielectric layer so as to change the index of refraction and modify the phase of the reflected radiation. Light is reflected off the device and collected by a phase-sensing interferometer. The interferometer determines the initial wavefront of the device and fore optics. A wavefront correction is calculated, and voltage profile for each nanowire strip is determined. The voltage is applied, modifying the local index of refraction of the dielectric under the nanowire strip. This modifies the phase of the reflected light to allow wavefront correction.

Hagopian, John↗
NASA NTRS2006

Three-Dimensional Thermal Boundary Layer Corrections for Circular Heat Flux Gauges Mounted in a Flat Plate with a Surface Temperature Discontinuity

Three-dimensional Navier-Stokes computational fluid dynamics (CFD) analysis has been performed in an effort to determine thermal boundary layer correction factors for circular convective heat flux gauges (such as Schmidt-Boelter and plug type)mounted flush in a flat plate subjected to a stepwise surface temperature discontinuity. Turbulent flow solutions with temperature-dependent properties are obtained for a free stream Reynolds number of 1E6, and freestream Mach numbers of 2 and 4. The effect of gauge diameter and the plate surface temperature have been investigated. The 3-D CFD results for the heat flux correction factors are compared to quasi-21) results deduced from constant property integral solutions and also 2-D CFD analysis with both constant and variable properties. The role of three-dimensionality and of property variations on the heat flux correction factors has been demonstrated.

Kandula, M.↗
NASA NTRS2011

Multiangle Implementation of Atmospheric Correction (MAIAC): 2. Aerosol Algorithm

An aerosol component of a new multiangle implementation of atmospheric correction (MAIAC) algorithm is presented. MAIAC is a generic algorithm developed for the Moderate Resolution Imaging Spectroradiometer (MODIS), which performs aerosol retrievals and atmospheric correction over both dark vegetated surfaces and bright deserts based on a time series analysis and image-based processing. The MAIAC look-up tables explicitly include surface bidirectional reflectance. The aerosol algorithm derives the spectral regression coefficient (SRC) relating surface bidirectional reflectance in the blue (0.47 micron) and shortwave infrared (2.1 micron) bands; this quantity is prescribed in the MODIS operational Dark Target algorithm based on a parameterized formula. The MAIAC aerosol products include aerosol optical thickness and a fine-mode fraction at resolution of 1 km. This high resolution, required in many applications such as air quality, brings new information about aerosol sources and, potentially, their strength. AERONET validation shows that the MAIAC and MOD04 algorithms have similar accuracy over dark and vegetated surfaces and that MAIAC generally improves accuracy over brighter surfaces due to the SRC retrieval and explicit bidirectional reflectance factor characterization, as demonstrated for several U.S. West Coast AERONET sites. Due to its generic nature and developed angular correction, MAIAC performs aerosol retrievals over bright deserts, as demonstrated for the Solar Village Aerosol Robotic Network (AERONET) site in Saudi Arabia.

Lyapustin, A.↗