Search NASA⌕ Search

SEARCH · Search NASA

Results for “Standard deviation modeling”

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 253 records · Page 14

Utilizing Mars Global Reference Atmospheric Model (Mars-GRAM 2005) to Evaluate Entry Probe Mission Sites

The Mars Global Reference Atmospheric Model (Mars-GRAM 2005) is an engineering-level atmospheric model widely used for diverse mission applications. An overview is presented of Mars-GRAM 2005 and its new features. The "auxiliary profile" option is one new feature of Mars-GRAM 2005. This option uses an input file of temperature and density versus altitude to replace the mean atmospheric values from Mars-GRAM's conventional (General Circulation Model) climatology. Any source of data or alternate model output can be used to generate an auxiliary profile. Auxiliary profiles for this study were produced from mesoscale model output (Southwest Research Institute's Mars Regional Atmospheric Modeling System (MRAMS) model and Oregon State University's Mars mesoscale model (MMM5) model) and a global Thermal Emission Spectrometer (TES) database. The global TES database has been specifically generated for purposes of making Mars-GRAM auxiliary profiles. This data base contains averages and standard deviations of temperature, density, and thermal wind components, averaged over 5-by-5 degree latitude-longitude bins and 15 degree Ls bins, for each of three Mars years of TES nadir data. The Mars Science Laboratory (MSL) sites are used as a sample of how Mars-GRAM' could be a valuable tool for planning of future Mars entry probe missions. Results are presented using auxiliary profiles produced from the mesoscale model output and TES observed data for candidate MSL landing sites. Input parameters rpscale (for density perturbations) and rwscale (for wind perturbations) can be used to "recalibrate" Mars-GRAM perturbation magnitudes to better replicate observed or mesoscale model variability.

Justh, Hilary L.↗

Effects of Natural Variability on the Use of Standard Deviation to Represent Measurement Uncertainties in Atmospheric Composition Studies

Measurement uncertainty is defined as a “non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand”. It is most common that the uncertainties of GAW hourly measurements, such as greenhouse gas measurements, are reported as standard deviations derived from individual sampling at a higher time resolution (e.g., 1 min). In contrast, the uncertainties of GAW measurements of reactive gases and aerosol properties are reported in percentiles covering the same probability. A quick look at hourly CO 2 data from Cape Grim, Australia yielded some interesting findings: the hourly standard deviation is, on average, more than a factor of 10 higher for the measurements under non-background conditions (over 50% observations), while the difference in average CO 2 amount fraction was less than 2 ppm. The dramatic contrast cannot be explained by the difference in measurement uncertainties, but can largely be attributed the natural variability, or episodic ambient CO 2 variation reflecting changes in meteorological conditions or emissions. These initial findings motivated a more in-depth analysis of the ground-based measurements of trace gases and aerosol properties. This analysis will be using continuous 1 min ground site observations to construct time averaged statistical indicators to evaluate whether the standard deviation is adequate to represent the dispersion, especially under marked influence by natural variability. The suitability of this representation can be determined by examining the difference between the standard deviation and percentiles encompassing the same probability. We will examine time intervals of 1 hour, 3 hours, and 24 hours, with the latter time intervals chosen to match those commonly used in model assessments. We will also investigate how natural variability can alter the probability distribution of the measurands and how adequate the quadrature propagation of uncertainties is under these conditions. The results will include several trace gases (e.g., CO 2 , CO, O 3 , and NO 2 ) with a range of measurement techniques (e.g., PANDORA, in situ), atmospheric lifetimes, and aerosol properties (e.g. scattering coefficient). The findings from this analysis should provide some useful feedback on the best practices for uncertainty reporting.

Measurement Uncertainty↗

Retrieval of Snow Freeboard of Antarctic Sea Ice Using Waveform Fitting of CryoSat-2 Returns

In this paper we develop a CryoSat-2 algorithm to retrieve the surface elevation of the air–snow interface over Antarctic sea ice. This algorithm utilizes a two-layer physical model that accounts for scattering from a snow layer atop sea ice as well as scattering from below the snow surface. The model produces waveforms that are fit to CryoSat-2 level 1B data through a bounded trust region least-squares fitting process. These fit waveforms are then used to track the air–snow interface and retrieve the surface elevation at each point along the CryoSat-2 ground track, from which the snow freeboard is computed. To validate this algorithm, we compare retrieved surface elevation measurements and snow surface radar return power levels with those from Operation IceBridge, which flew along a contemporaneous CryoSat-2 orbit in October 2011 and November 2012. Average elevation differences (standard deviations) along the flight lines (IceBridge Airborne Topographic Mapper, ATM – CryoSat-2) are found to be 0.016 cm (29.24 cm) in 2011 and 2.58 cm (26.65 cm) in 2012. The spatial distribution of monthly average pan-Antarctic snow freeboard found using this method is similar to what was observed from NASA's Ice, Cloud, and land Elevation Satellite (ICESat), where the difference (standard deviation) between October 2011–2017 CryoSat-2 mean snow freeboard and spring 2003–2007 mean freeboard from ICESat is 1.92 cm (9.23 cm). While our results suggest that this physical model and waveform fitting method can be used to retrieve snow freeboard from CryoSat-2, allowing for the potential to join laser and radar altimetry data records in the Antarctic, larger (∼30 cm) regional differences from ICESat and along-track differences from ATM do exist, suggesting the need for future improvements to the method. Snow–ice interface elevation retrieval is also explored as a potential to obtain snow depth measurements. However, it is found that this retrieval method often tracks a strong scattering layer within the snow layer instead of the actual snow–ice interface, leading to an overestimation of ice freeboard and an underestimation of snow depth in much of the Southern Ocean but with promising results in areas such as the East Antarctic sector.

Fons, Steven W.↗

Analysis of daily latitude variations

The daily latitude measurements of the International Polar Motion Service are analyzed. The annual oscillation in the data was modeled by separate oscillations in each observatory's latitude data. The separate oscillations varied in amplitude from 0.05 sec to 0.15 sec with standard deviations of about 0.007 sec. Within the resolution of the latitude residuals (150 cm), there is no indication of the sharp changes which might be associated with earthquake effects. Then, applying Schuster's test to a periodogram of the residuals indicates that there are probably several processes occurring at amplitudes between 0.007 sec and 0.03 sec whose solution awaits a more precise measurement technique.

Graber, M. A.↗

Characteristics of vertical and lateral tunnel turbulence measured in air in the Langley Transonic Dynamics Tunnel

Preliminary measurements of the vertical and lateral velocity components of tunnel turbulence were obtained in the Langley Transonic Dynamics Tunnel test section using a constant-temperature anemometer equipped with a hot-film X-probe. For these tests air was the test medium. Test conditions included tunnel velocities ranging from 100 to 500 fps at atmospheric pressure. Standard deviations of turbulence velocities were determined and power spectra were computed. Unconstrained optimization was employed to determine parameter values of a general spectral model of a form similar to that used to describe atmospheric turbulence. These parameters, and others (notably break frequency and integral scale length), were determined at each test condition and compared with those of Dryden and Von Karman atmospheric turbulence spectra. When the data were discovered to be aliased, the spectral model was modified to account for and 'eliminate' the aliasing.

Sleeper, Robert K.↗

Evaluating Mars Science Laboratory Landing Sites with the Mars Global Reference Atmospheric Model (Mars-GRAM 2005)

The Mars Global Reference Atmospheric Model (Mars-GRAM) is an engineering-level atmospheric model widely used for diverse mission applications. Mars-GRAM s perturbation modeling capability is commonly used, in a Monte-Carlo mode, to perform high fidelity engineering end-to-end simulations for entry, descent, and landing (EDL) [1]. From the surface to 80 km altitude, Mars-GRAM is based on the NASA Ames Mars General Circulation Model (MGCM). Mars-GRAM and MGCM use surface topography from Mars Global Surveyor Mars Orbiter Laser Altimeter (MOLA), with altitudes referenced to the MOLA areoid, or constant potential surface. Traditional Mars-GRAM options for representing the mean atmosphere along entry corridors include: (1) Thermal Emission Spectrometer (TES) mapping years 1 and 2, with Mars-GRAM data coming from NASA Ames Mars General Circulation Model (MGCM) results driven by observed TES dust optical depth or (2) TES mapping year 0, with user-controlled dust optical depth and Mars-GRAM data interpolated from MGCM model results driven by selected values of globally-uniform dust optical depth. Mars-GRAM 2005 has been validated [2] against Radio Science data, and both nadir and limb data from TES [3]. There are several new features included in Mars-GRAM 2005. The first is the option to use input data sets from MGCM model runs that were designed to closely simulate conditions observed during the first two years of TES observations at Mars. The TES Year 1 option includes values from April 1999 through January 2001. The TES Year 2 option includes values from February 2001 through December 2002. The second new feature is the option to read and use any auxiliary profile of temperature and density versus altitude. In exercising the auxiliary profile Mars-GRAM option, values from the auxiliary profile replace data from the original MGCM databases. Some examples of auxiliary profiles include data from TES nadir or limb observations and Mars mesoscale model output at a particular location and time. The final new feature is the addition of two Mars-GRAM parameters that allow standard deviations of Mars-GRAM perturbations to be adjusted. The parameter rpscale can be used to scale density perturbations up or down while rwscale can be used to scale wind perturbations.

Justh, H. L.↗

A Final Approach Trajectory Model for Current Operations

Predicting accurate trajectories with limited intent information is a challenge faced by air traffic management decision support tools in operation today. One such tool is the FAA's Terminal Proximity Alert system which is intended to assist controllers in maintaining safe separation of arrival aircraft during final approach. In an effort to improve the performance of such tools, two final approach trajectory models are proposed; one based on polynomial interpolation, the other on the Fourier transform. These models were tested against actual traffic data and used to study effects of the key final approach trajectory modeling parameters of wind, aircraft type, and weight class, on trajectory prediction accuracy. Using only the limited intent data available to today's ATM system, both the polynomial interpolation and Fourier transform models showed improved trajectory prediction accuracy over a baseline dead reckoning model. Analysis of actual arrival traffic showed that this improved trajectory prediction accuracy leads to improved inter-arrival separation prediction accuracy for longer look ahead times. The difference in mean inter-arrival separation prediction error between the Fourier transform and dead reckoning models was 0.2 nmi for a look ahead time of 120 sec, a 33 percent improvement, with a corresponding 32 percent improvement in standard deviation.

Gong, Chester↗

Determining the Probability of Violating Upper-Level Wind Constraints for the Launch of Minuteman III Ballistic Missiles at Vandenberg Air Force Base

The 30th Operational Support Squadron Weather Flight (30 OSSWF) provides comprehensive weather services to the space program at Vandenberg Air Force Base (VAFB) in California. One of their responsibilities is to monitor upper-level winds to ensure safe launch operations of the Minuteman Ill ballistic missile. The 30 OSSWF tasked the Applied Meteorology Unit (AMU) to analyze VAFB sounding data with the goal of determining the probability of violating (PoV) their upper-level thresholds for wind speed and shear constraints specific to this launch vehicle, and to develop a tool that will calculate the PoV of each constraint on the day of launch. In order to calculate the probability of exceeding each constraint, the AMU collected and analyzed historical data from VAFB. The historical sounding data were retrieved from the National Oceanic and Atmospheric Administration Earth System Research Laboratory archive for the years 1994-2011 and then stratified into four sub-seasons: January-March, April-June, July-September, and October-December. The AMU determined the theoretical distributions that best fit the maximum wind speed and maximum wind shear datasets and applied this information when calculating the averages and standard deviations needed for the historical and real-time PoV calculations. In addition, the AMU included forecast sounding data from the Rapid Refresh model. This information provides further insight for the launch weather officers (LWOs) when determining if a wind constraint violation will occur over the next few hours on the day of launch. The AMU developed an interactive graphical user interface (GUI) in Microsoft Excel using Visual Basic for Applications. The GUI displays the critical sounding data easily and quickly for LWOs on day of launch. This tool will replace the existing one used by the 30 OSSWF, assist the LWOs in determining the probability of exceeding specific wind threshold values, and help to improve the overall upper winds forecast for the launch customer. This presentation will describe how the AMU calculated the historical and real-time PoV values for the specific upper-level wind launch constraints and outline the development of the interactive GUI display.

Shafer, Jaclyn A.↗

Using the Flow-3D General Moving Object Model to Simulate Coupled Liquid Slosh - Container Dynamics on the SPHERES Slosh Experiment: Aboard the International Space Station

The SPHERES Slosh Experiment (SSE) is a free floating experimental platform developed for the acquisition of long duration liquid slosh data aboard the International Space Station (ISS). The data sets collected will be used to benchmark numerical models to aid in the design of rocket and spacecraft propulsion systems. Utilizing two SPHERES Satellites, the experiment will be moved through different maneuvers designed to induce liquid slosh in the experiment's internal tank. The SSE has a total of twenty-four thrusters to move the experiment. In order to design slosh generating maneuvers, a parametric study with three maneuvers types was conducted using the General Moving Object (GMO) model in Flow-30. The three types of maneuvers are a translation maneuver, a rotation maneuver and a combined rotation translation maneuver. The effectiveness of each maneuver to generate slosh is determined by the deviation of the experiment's trajectory as compared to a dry mass trajectory. To fully capture the effect of liquid re-distribution on experiment trajectory, each thruster is modeled as an independent force point in the Flow-3D simulation. This is accomplished by modifying the total number of independent forces in the GMO model from the standard five to twenty-four. Results demonstrate that the most effective slosh generating maneuvers for all motions occurs when SSE thrusters are producing the highest changes in SSE acceleration. The results also demonstrate that several centimeters of trajectory deviation between the dry and slosh cases occur during the maneuvers; while these deviations seem small, they are measureable by SSE instrumentation.

Schulman, Richard↗

Evaluation of the Seasat altimeter time tag bias

Two methods were used in analyses of Seasat altimeter data, aimed at the corroboration of an inherent altimeter microprocessor delay compensation value of -79.4 msec, which benefited from a global data distribution in the oceanic areas: (1) the crossover method, using altimeter data differenced at points where the Seasat ground track intersected with itself, and (2) the direct use of the altimeter data. Because the former method is independent of errors in the geoid model, it is considered the more reliable. For all crossover method results, the adopted value of -79.4 msec is within the bounds of the standard deviation associated with the estimates, of which -78.1 + or - 2.0 msec is considered the best representative.

Schutz, B. E.↗

Thermal sensing of cryogenic wind tunnel model surfaces Evaluation of silicon diodes

Different sensors and installation techniques for surface temperature measurement of cryogenic wind tunnel models were investigated. Silicon diodes were selected for further consideration because of their good inherent accuracy. Their average absolute temperature deviation in comparison tests with standard platinum resistance thermometers was found to be 0.2 K in the range from 125 to 273 K. Subsurface temperature measurement was selected as the installation technique in order to minimize aerodynamic interference. Temperature distortion caused by an embedded silicon diode was studied numerically.

Daryabeigi, K.↗

Thermal sensing of cryogenic wind tunnel model surfaces - Evaluation of silicon diodes

Different sensors and installation techniques for surface temperature measurement of cryogenic wind tunnel models were investigated. Silicon diodes were selected for further consideration because of their good inherent accuracy. Their average absolute temperature deviation in comparison tests with standard platinum resistance thermometers was found to be 0.2 K in the range from 125 to 273 K. Subsurface temperature measurement was selected as the installation technique in order to minimize aerodynamic interference. Temperature distortion caused by an embedded silicon diode was studied numerically.

Daryabeigi, Kamran↗

Application of High-Resolution Thermal Infrared Remote Sensing and GIS to Assess the Urban Heat Island Effect

Day and night airborne thermal infrared image data at 5 m spatial resolution acquired with the 15-channel (0.45 micron - 12.2 micron) Advanced Thermal and Land Applications Sensor (ATLAS) over Alabama, Huntsville on 7 September, 1994 were used to study changes in the thermal signatures of urban land cover types between day and night. Thermal channel number 13 (9.6 micron - 10.2 micron) data with the best noise-equivalent temperature change (NEAT) of 0.25 C after atmospheric corrections and temperature calibration were selected for use in this analysis. This research also examined the relation between land cover irradiance and vegetation amount, using the Normalized Difference Vegetation Index (NDVI), obtained by ratioing the difference and the sum of the red (channel number 3: 0.60-0.63 micron) and reflected infrared (channel number 6: 0.76-0.90 micron) ATLAS data. Based on the mean radiance values, standard deviations, and NDVI extracted from 351 pairs of polygons of day and night channel number 13 images for the city of Huntsville, a spatial model of warming and cooling characteristics of commercial, residential, agricultural, vegetation, and water features was developed using a GIS approach. There is a strong negative correlation between NDVI and irradiance of residential, agricultural, and vacant/transitional land cover types, indicating that the irradiance of a land cover type is greatly influenced by the amount of vegetation present. The predominance of forests, agricultural, and residential uses associated with varying degrees of tree cover showed great contrasts with commercial and services land cover types in the center of the city, and favors the development of urban heat islands. The high-resolution thermal infrared images match the complexity of the urban environment, and are capable of characterizing accurately the urban land cover types for the spatial modeling of the urban heat island effect using a GIS approach.

Lo, C. P.↗

Real-Time Detection of Dust Devils from Pressure Readings

A method for real-time detection of dust devils at a given location is based on identifying the abrupt, temporary decreases in atmospheric pressure that are characteristic of dust devils as they travel through that location. The method was conceived for use in a study of dust devils on the Martian surface, where bandwidth limitations encourage the transmission of only those blocks of data that are most likely to contain information about features of interest, such as dust devils. The method, which is a form of intelligent data compression, could readily be adapted to use for the same purpose in scientific investigation of dust devils on Earth. In this method, the readings of an atmospheric- pressure sensor are repeatedly digitized, recorded, and processed by an algorithm that looks for extreme deviations from a continually updated model of the current pressure environment. The question in formulating the algorithm is how to model current normal observations and what minimum magnitude deviation can be considered sufficiently anomalous as to indicate the presence of a dust devil. There is no single, simple answer to this question: any answer necessarily entails a compromise between false detections and misses. For the original Mars application, the answer was sought through analysis of sliding time windows of digitized pressure readings. Windows of 5-, 10-, and 15-minute durations were considered. The windows were advanced in increments of 30 seconds. Increments of other sizes can also be used, but computational cost increases as the increment decreases and analysis is performed more frequently. Pressure models were defined using a polynomial fit to the data within the windows. For example, the figure depicts pressure readings from a 10-minute window wherein the model was defined by a third-degree polynomial fit to the readings and dust devils were identified as negative deviations larger than both 3 standard deviations (from the mean) and 0.05 mbar in magnitude. An algorithm embodying the detection scheme of this example was found to yield a miss rate of just 8 percent and a false-detection rate of 57 percent when evaluated on historical pressure-sensor data collected by the Mars Pathfinder lander. Since dust devils occur infrequently over the course of a mission, prioritizing observations that contain successful detections could greatly conserve bandwidth allocated to a given mission. This technique can be used on future Mars landers and rovers, such as Mars Phoenix and the Mars Science Laboratory.

Wagstaff, Kiri↗

The Atacama Cosmology Telescope: DR4 maps and cosmological parameters

We present new arcminute-resolution maps of the Cosmic Microwave Background temperature and polarization anisotropy from the Atacama Cosmology Telescope, using data taken from 2013{2016 at 98 and 150 GHz. The maps cover more than 17,000 deg(^2), the deepest 600 deg(^2) with noise levels below 10µK-arcmin. We use the power spectrum derived from almost 6,000 deg(^2) of these maps to constrain cosmology. The ACT data enable a measurement of the angular scale of features in both the divergence-like polarization and the temperature anisotropy, tracing both the velocity and density at last-scattering. From these one can derive the distance to the last-scattering surface and thus infer the local expansion rate, H0. By combining ACT data with large-scale information from WMAP we measure H0 = 67:6±1:1 km/s/Mpc, at 68% confidence, in excellent agreement with the independently measured Planck satellite estimate (from ACT alone we find H0 = 67:9± 1:5 km/s/Mpc). The ΛCDM model provides a good fit to the ACT data, and we find no evidence for deviations: both the spatial curvature, and the departure from the standard lensing signal in the spectrum, are zero to within 1σ; the number of relativistic species, the primordial Helium fraction, and the running of the spectral index are consistent with ΛCDM predictions to within 1.5{2.2σ. We compare ACT, WMAP, and Planck at the parameter level and find good consistency; we investigate how the constraints on the correlated spectral index and baryon density parameters readjust when adding CMB large-scale information that ACT does not measure. The DR4 products presented here will be publicly released on the NASA Legacy Archive for Microwave Background Data Analysis.

Simone Aiola↗

Utilization of Airborne Observations to Assess Model Parametrizations of Critical RH Profiles in the Arctic Ocean

Observational paucity is a reality in the Arctic Ocean. This is especially true for near-surface variables such as temperature, moisture, heat fluxes and BL clouds. As a result, modeling has become one of the major avenues for understanding current and future Arctic trends. Reanalyses are frequently used to force global ocean circulation and sea-ice models. But in northern high latitudes, model integrations and reanalyses are known to have large uncertainties in temperature and humidity profiles, and in boundary layer cloudiness. These are common sources of error in the surface radiative budget terms.An important way to diagnose these biases spatially and temporally is by using satellite remote sensing data. However, remotely-sensed observations also have large uncertainties, especially in near-surface temperature and relative humidity profiles.In situ observational studies are important in bridging our knowledge gap in regions such as the Arctic Ocean. Here, we utilize airborne and ship observations from the ARISE, ACME-IV, and ASCOS campaigns to construct critical relative humidity (RH) profiles over the Beaufort Sea. Such profiles are used as parameterization inputs in the NASA GOES global model to derive the total water condensate in a model grid-box, which determines the cloud fraction. Currently, the critical RH profiles are derived by global AIRS data, relaying mostly on mid-latitude regions, which are not necessarily relevant to the Arctic.We derive campaign-wide mean, standard deviation, and critical RH values, for grid size of 50x50 km and altitude bins between 50 to 400 m, covering both open-ocean and sea-ice covered regions. We compare profiles over open ocean and sea-ice, and look at correlations between the observed critical RH values and water condensate (by cloud number concentration) from observations versus the modeled ones. We then input our calculated values of minimal critical RH values into a set of GEOS single column model (SCM) simulations over the ARISE and ASCOS regions and compare the differences between the predicted values of cloud liquid water path (LWP), ice water path (IWP) and surface fluxes with the observed ones under the range of input parameterizations. Finally, we discuss the implications on surface radiative budget predictions in this region.

Segal-Rozenhaimer, Michal↗

Development Of FIAT-Based Parametric Thermal Protection System Mass Estimating Relationships For NASA's Multi-Mission Earth Entry Concept

An integrated tool called the Multi Mission System Analysis for Planetary Entry Descent and Landing (M-SAPE) is being developed as part of NASAs In-Space Propulsion Technology (ISPT) program. Part of M-SAPEs development requires the formulation of mass estimating relationships (MERs) to determine the vehicle's Thermal Protection System (TPS) material and required thickness for safe Earth entry. The objective of this study was to develop MERs using simple correlations that were non-ITAR and matched as accurately as possible NASAs high-fidelity ablation modeling tool, the Fully Implicit Ablation and Thermal Analysis Program (FIAT ). These MERs would be a first-estimate for feasibility studies; it is understood that higher-fidelity modeling like FIAT would be necessary once a proposed trajectory was down-selected. The trajectory space for these MERS consisted of 840 different trajectories, and a materials heating limit was the main constraint for an allowable trajectory. MERs for the vehicle fore body included the ablating materials Phenolic Impregnated Carbon Ablator (PICA ) and Carbon Phenolic atop Advanced Carbon-Carbon. For the backshell the materials were Silicone Impregnated Reusable Ceramic Ablator (SIRCA ), Acusil II, SLA-561V, and LI-900. The MERFIAT ratio indicates MERs are accurate to within 14 percent (at one standard deviation) of FIAT prediction, and the most any MER can under-predict TPS thickness is 18.7 percent of FIAT prediction. This poster focuses on the development of these MERs, the resulting equations, model limitations, and model accuracy.

thermal protection system↗

The linear polarization of lunar thermal emission at 3.1 mm wavelength

Several observations of the distribution of linearly polarized lunar thermal emission were made at a wavelength of 3.1 mm with 4.88 m parabolic reflector from February to March 1971. A shadow corrected rough surface thermal emission model was least squares fitted to the data. Results indicate an effective lunar dielectric constant of 1.34 + or -.08 with surface roughness characterized by a standard deviation of surface slopes of 18 deg + or - 2 deg. A comparison of these results with previously published values at other wavelengths suggests that the effective lunar dielectric constant decreases with decreasing wavelength.

White, T. L.↗