Search NASA⌕ Search

SEARCH · Search NASA

Results for “Sampling error”

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 145 records · Page 8

Absorption of Solar Radiation by Clouds: Interpretations of Satellite, Surface, and Aircraft Measurements

To investigate the absorption of shortwave radiation by clouds, we have collocated satellite and surface measurements of shortwave radiation at several locations. Considerable effort has been directed toward understanding and minimizing sampling errors caused by the satellite measurements being instantaneous and over a grid that is much larger than the field of view of an upward facing surface pyranometer. The collocated data indicate that clouds absorb considerably more shortwave radiation than is predicted by theoretical models. This is consistent with the finding from both satellite and aircraft measurements that observed clouds are darker than model clouds. In the limit of thick clouds, observed top-of-the-atmosphere albedos do not exceed a value of 0.7, whereas in models the maximum albedo can be 0.8.

Cess, R. D.↗

Optimal Scales for Comparing Satellite and Rain-Gauge Rainfall Estimates for Verification Purposes

In spite of all their problems, rain gauges measure rainfall in such a direct way when compared with other methods of estimating rainfall that comparing their totals to satellite estimates remains an essential tool in the validation of satellite products. Some disagreement between averages of satellite data and rain-gauge data is expected because of the very different sampling patterns of the two systems--the satellite provides only occasional snapshots of large areas, whereas rain gauges provide continuous measurements over very small areas. The comparison of the two requires that some quantitative measure be supplied for the amount of disagreement that can be tolerated due to the differences in sampling. As part of an effort to determine the sampling error of satellite averages, a space-time model for rainfall statistics was developed and its parameters fit to radar data from a field experiment conducted near the Inter-Tropical Convergence Zone (ITCZ) in the eastern Atlantic (GATE). Although the model was intended to represent the statistics of relatively large scale fluctuations of rain, it is surprisingly consistent with the very different scales on which rain gauges observe. It can therefore be used to study some of the issues involved with comparing rain-gauge averages to satellite averages. Its implications for the best time and space scales for comparing the two will be discussed.

Bell, Thomas L.↗

Use of TRMM Data to Test an Improved Parameterization of Stratiform Precipitation

By incorporating the TRMM satellite orbital information into the most recent geodesic version of the Colorado State University General Circulation Model (CSU GCM), we are able to fly a satellite in the GCM, and sample the simulated atmosphere in the same way as the TRMM sensors sample the real atmosphere. The TRMM sampling statistics of precipitation and radiative fluxes at annual, intra-seasonal, monthly-mean and composited diurnal time scales are evaluated by comparing the satellite-sampled against fully-sampled simulated atmospheres. This information provides a valuable guidance for efficient usage of TRMM data and future satellite mission planning. We have also evaluated the effects of TRMM sampling errors on the inferred tropical-mean hydrologic cycle and radiative fluxes. We have found that there are strong spurious oscillations associated with the TRMM orbital geometry, with periods of 23 days and 3-4 months, in tropical-mean daily and monthly precipitation. Caution must therefore be used when applying TRMM observations of tropical-mean precipitation to interpret climate variations at intraseasonal and interannual scales.

Randall, David A.↗

Scale Dependence of Statistics of Spatially Averaged Rain Rate Seen in TOGA COARE Comparison with Predictions from a Stochastic Model

A characteristic feature of rainfall statistics is that they in general depend on the space and time scales over which rain data are averaged. As a part of an earlier effort to determine the sampling error of satellite rain averages, a space-time model of rainfall statistics was developed to describe the statistics of gridded rain observed in GATE. The model allows one to compute the second moment statistics of space- and time-averaged rain rate which can be fitted to satellite or rain gauge data to determine the four model parameters appearing in the precipitation spectrum - an overall strength parameter, a characteristic length separating the long and short wavelength regimes and a characteristic relaxation time for decay of the autocorrelation of the instantaneous local rain rate and a certain 'fractal' power law exponent. For area-averaged instantaneous rain rate, this exponent governs the power law dependence of these statistics on the averaging length scale $L$ predicted by the model in the limit of small $L$. In particular, the variance of rain rate averaged over an $L \times L$ area exhibits a power law singularity as $L \rightarrow 0$. In the present work the model is used to investigate how the statistics of area-averaged rain rate over the tropical Western Pacific measured with ship borne radar during TOGA COARE (Tropical Ocean Global Atmosphere Coupled Ocean Atmospheric Response Experiment) and gridded on a 2 km grid depends on the size of the spatial averaging scale. Good agreement is found between the data and predictions from the model over a wide range of averaging length scales.

Kundu, Prasun K.↗

Comparing Satellite Rainfall Estimates with Rain-Gauge Data: Optimal Strategies Suggested by a Spectral Model

Validation of satellite remote-sensing methods for estimating rainfall against rain-gauge data is attractive because of the direct nature of the rain-gauge measurements. Comparisons of satellite estimates to rain-gauge data are difficult, however, because of the extreme variability of rain and the fact that satellites view large areas over a short time while rain gauges monitor small areas continuously. In this paper, a statistical model of rainfall variability developed for studies of sampling error in averages of satellite data is used to examine the impact of spatial and temporal averaging of satellite and gauge data on intercomparison results. The model parameters were derived from radar observations of rain, but the model appears to capture many of the characteristics of rain-gauge data as well. The model predicts that many months of data from areas containing a few gauges are required to validate satellite estimates over the areas, and that the areas should be of the order of several hundred km in diameter. Over gauge arrays of sufficiently high density, the optimal areas and averaging times are reduced. The possibility of using time-weighted averages of gauge data is explored.

Bell, Thomas L.↗

Optimal Strategies for Validating TRMM Rainfall Estimates with Rain-Gauge Data

In spite of all their problems, rain gauges measure rainfall in such a direct way when compared with other methods of estimating rainfall that comparing their totals to satellite estimates remains an essential tool in the validation of satellite products. Some disagreement between averages of satellite data and rain-gauge data is expected because of the very different sampling patterns of the two systems--the satellite provides only occasional snapshots of large areas, whereas rain gauges provide continuous measurements over very small areas. A quantitative estimate of the expected level of disagreement due to the differences in sampling is needed in order for comparisons of the two kinds of averages to be informative. As part of an earlier effort to determine the sampling error of satellite averages, a space-time model for rainfall statistics was developed. Sets of parameter values for the model have been obtained for which the model statistics are found to agree quite well with those of radar data taken over the Atlantic during GATE and the western Pacific during TOGA COARE. Although the model was intended to represent the statistics of relatively large scale fluctuations of rain, it is surprisingly consistent with the very different scales on which rain gauges observe. Implications for maximizing the benefit in comparisons of rain gauge averages and TRMM estimates are derived using the model predictions.

Bell, Thomas L.↗

Lidar Measurements of Wind, Moisture, and Boundary Layer Evolution in a Dry Line during 1HOP 2002

Variability in the convective boundary layer moisture, wind and temperature fields and their importance in the forecasting and understanding of storms have been discussed in the literature. These . variations have been reported in relation to frontal zones, stationary boundaries and during horizontal convective rolls. While all three vary substantially in the convective boundary layer, moisture poses a particular challenge. Moisture or water vapor concentration (expressed as a mass mixing ratio, g/kg), is conserved in all meteorological processes except condensation and evaporation. The water vapor mixing ratio often remains distinct across an air-mass boundary even when the temperature difference is indistinct. These properties make it an ideal choice in visualizing and understanding many of the atmosphere's dynamic features. However, it also presents a unique measurement challenge because water vapor content can vary by more than three orders of magnitude in the troposphere. Characterization of the 3D-distribution of water vapor is also difficult as water vapor observations can suffer from large sampling errors and substantial variability both in the vertical and horizontal. This study presents ground-based measurements of wind, boundary layer structure and water vapor mixing ratio measurements observed by three co-located lidars. This presentation will focus on the evolution and variability of moisture and wind in the boundary layer during a dry line event that occurred on 22 May 2002. These data sets and analyses are unique in that they combine simultaneous measurements of wind, moisture and CBL structure to study the detailed thermal variability in and around clear air updrafts during a dryline event. It will quantify the variation caused by, in and around buoyant plumes and across a dryline. The data presented here were collected in the panhandle of Oklahoma as part of the International H2O Project (MOP-2002), a field experiment that took place over the Southern Great Plains (SGP) of the United States from 13 May to 30 June 2002. The chief goal of MOP-2002 is to improve characterization of the four-dimensional (4-D) distribution of water vapor and its application to improving the understanding and prediction of convection

Demoz, Belay↗

Lidar Measurements of Wind, Moisture and Boundary Layer Evolution in a Dryline During IHOP2002

Variability in the convective boundary layer moisture, wind and temperature fields and their importance in the forecasting and understanding of storms have been discussed in the literature. These variations have been reported in relation to frontal zones, stationary boundaries and during horizontal convective rolls. While all three vary substantially in the convective boundary layer, moisture poses a particular challenge. Moisture or water vapor concentration (expressed as a mass mixing ratio, g/kg), is conserved in all meteorological processes except condensation and evaporation. The water vapor mixing ratio often remains distinct across an air -mass boundary even when the temperature difference is indistinct. These properties make it an ideal choice in visualizing and understanding many of the atmosphere's dynamic features. However, it also presents a unique measurement challenge because water vapor content can vary by more than three orders of magnitude in the troposphere. Characterization of the 3D-distribution of water vapor is also difficult as water vapor observations can suffer from large sampling errors and substantial variability both in the vertical and horizontal. This study presents groundbased measurements of wind, boundary layer structure and water vapor mixing ratio measurements observed by three co-located lidars. This presentation will focus on the evolution and variability of moisture and wind in the boundary layer during a dry line event that occurred on 22 May 2002. These data sets and analyses are unique in that they combine simultaneous measurements of wind, moisture and CBL structure to study the detailed thermal variability in and around clear air updrafts during a dryline event. It will quantify the variation caused by, in and around buoyant plumes and across a dryline. The data presented here were collected in the panhandle of Oklahoma as part of the International BO Project (IHOP-2002), a field experiment that took place over the Southern Great Plains (SGP) of the United States from 13 May to 30 June 2002. The chief goal of IHOP-2002 is to improve characterization of the four-dimensional (4-D) distribution of water vapor and its application to improving the understanding and prediction of convection

Demoz, Belay↗

Calculating Statistical Orbit Distributions Using GEO Optical Observations with the Michigan Orbital Debris Survey Telescope (MODEST)

NASA's Orbital Debris measurements program has a goal to characterize the small debris environment in the geosynchronous Earth-orbit (GEO) region using optical telescopes ("small" refers to objects too small to catalog and track with current systems). Traditionally, observations of GEO and near-GEO objects involve following the object with the telescope long enough to obtain an orbit suitable for tracking purposes. Telescopes operating in survey mode, however, randomly observe objects that pass through their field of view. Typically, these short-arc observation are inadequate to obtain detailed orbits, but can be used to estimate approximate circular orbit elements (semimajor axis, inclination, and ascending node). From this information, it should be possible to make statistical inferences about the orbital distributions of the GEO population bright enough to be observed by the system. The Michigan Orbital Debris Survey Telescope (MODEST) has been making such statistical surveys of the GEO region for four years. During that time, the telescope has made enough observations in enough areas of the GEO belt to have had nearly complete coverage. That means that almost all objects in all possible orbits in the GEO and near- GEO region had a non-zero chance of being observed. Some regions (such as those near zero inclination) have had good coverage, while others are poorly covered. Nevertheless, it is possible to remove these statistical biases and reconstruct the orbit populations within the limits of sampling error. In this paper, these statistical techniques and assumptions are described, and the techniques are applied to the current MODEST data set to arrive at our best estimate of the GEO orbit population distribution.

Matney, M.↗

Advanced Precipitation Radar Antenna to Measure Rainfall From Space

To support NASA s planned 20-year mission to provide sustained global precipitation measurement (EOS-9 Global Precipitation Measurement (GPM)), a deployable antenna has been explored with an inflatable thin-membrane structure. This design uses a 5.3 5.3-m inflatable parabolic reflector with the electronically scanned, dual-frequency phased array feeds to provide improved rainfall measurements at 2.0-km horizontal resolution over a cross-track scan range of up to 37 , necessary for resolving intense, isolated storm cells and for reducing the beam-filling and spatial sampling errors. The two matched radar beams at the two frequencies (Ku and Ka bands) will allow unambiguous retrieval of the parameters in raindrop size distribution. The antenna is inflatable, using rigidizable booms, deployable chain-link supports with prescribed curvatures, a smooth, thin-membrane reflecting surface, and an offset feed technique to achieve the precision surface tolerance (0.2 mm RMS) for meeting the low-sidelobe requirement. The cylindrical parabolic offset-feed reflector augmented with two linear phased array feeds achieves dual-frequency shared-aperture with wide-angle beam scanning and very low sidelobe level of -30 dB. Very long Ku and Ka band microstrip feed arrays incorporating a combination of parallel and series power divider lines with cosine-over-pedestal distribution also augment the sidelobe level and beam scan. This design reduces antenna mass and launch vehicle stowage volume. The Ku and Ka band feed arrays are needed to achieve the required cross-track beam scanning. To demonstrate the inflatable cylindrical reflector with two linear polarizations (V and H), and two beam directions (0deg and 30deg), each frequency band has four individual microstrip array designs. The Ku-band array has a total of 166x2 elements and the Ka-band has 166x4 elements with both bands having element spacing about 0.65 lambda(sub 0). The cylindrical reflector with offset linear array feeds reduces the complexity from "NxN" transmit/receive (T/R) modules of a conventional planar-phased array to just "N" T/R modules. The antenna uses T/R modules with electronic phase-shifters for beam steering. The offset reflector does not provide poor cross-polarization like a double- curved offset reflector would, and it allows the wide scan angle in one plane required by the mission. Also, the cylindrical reflector with two linear array feeds provides dual-frequency performance with a single, shared aperture. The aperture comprises a reflective surface with a focal length of 1.89 m and is made from aluminized Kapton film. The reflective surface is of uniform thickness in the range of a few thousandths of an inch and is attached to the chain-link support structure via an adjustable suspension system. The film aperture rolls up, together with the chain-link structure, for launch and can be deployed in space by the deployment of the chain-link structure.

Rahmat-Samii, Yahya↗

A Critical Look at Deriving Monthly Aerosol Optical Depth from Satellite Data

Satellite-derived aerosol data sets, such as those provided by NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) instruments, are greatly improving our understanding of global aerosol optical depth (AOD). Yet, there are sampling issues. MODIS specific orbital geometry, convolved with the need to avoid bright surfaces (glint, desert, clouds, etc.), means that AOD can be under- or over-sampled in places. When deriving downstream products, such as daily or monthly gridded AOD, one must consider the spatial and temporal density of the measurements relative to the gradients of the true AOD. Additionally, retrieval confidence criteria should be considered. Averaged products are highly dependent on choices made for data aggregation and weighting, and sampling errors can be further propagated when deriving regional or global mean AOD. Different choices for aggregation and weighting result in estimates of regional and global means varying by 30% or more. The impacts of a particular averaging algorithm vary by region and surface type and can be shown to represent different tolerance for clouds and retrieval confidence.

Levy, R. C.↗

Techniques for Down-Sampling a Measured Surface Height Map for Model Validation

This software allows one to down-sample a measured surface map for model validation, not only without introducing any re-sampling errors, but also eliminating the existing measurement noise and measurement errors. The software tool of the current two new techniques can be used in all optical model validation processes involving large space optical surfaces

Sidick, Erkin↗

An Experimental Study of Small-Scale Variability of Raindrop Size Distribution

An experimental study of small-scale variability of raindrop size distributions (DSDs) has been carried out at Wallops Island, Virginia. Three Joss-Waldvogel disdrometers were operated at a distance of 0.65, 1.05, and 1.70 km in a nearly straight line. The main purpose of the study was to examine the variability of DSDs and its integral parameters of liquid water content, rainfall, and reflectivity within a 2-km array: a typical size of Cartesian radar pixel. The composite DSD of rain events showed very good agreement among the disdrometers except where there were noticeable differences in midsize and large drops in a few events. For consideration of partial beam filling where the radar pixel was not completely covered by rain, a single disdrometer reported just over 10% more rainy minutes than the rainy minutes when all three disdrometers reported rainfall. Similarly two out of three disdrometers reported5%more rainy minutes than when all three were reporting rainfall. These percentages were based on a 1-min average, and were less for longer averaging periods. Considering only the minutes when all three disdrometers were reporting rainfall, just over one quarter of the observations showed an increase in the difference in rainfall with distance. This finding was based on a 15-min average and was even less for shorter averaging periods. The probability and cumulative distributions of a gamma-fitted DSD and integral rain parameters between the three disdrometers had a very good agreement and no major variability. This was mainly due to the high percentage of light stratiform rain and to the number of storms that traveled along the track of the disdrometers. At a fixed time step, however, both DSDs and integral rain parameters showed substantial variability. The standard deviation (SD) of rain rate was near 3 mm/h, while the SD of reflectivity exceeded 3 dBZ at the longest separation distance. These standard deviations were at 6-min average and were higher at shorter averaging periods. The correlations decreased with increasing separation distance. For rain rate, the correlations were higher than previous gauge-based studies. This was attributed to the differences in data processing and the difference in rainfall characteristics in different climate regions. It was also considered that the gauge sampling errors could be a factor. In this regard, gauge measurements were simulated employing existing disdrometer dataset. While a difference was noticed in cumulative distribution of rain occurrence between the simulated gauge and disdrometer observations, the correlations in simulated gauge measurements did not differ from the disdrometer measurements.

Tokay, Ali↗

Reply to Comment by Laprise on 'the Added Value to Global Model Projections of Climate Change by Dynamical Downscaling: a Case Study over the Continental U.S. Using the GISS-ModelE2 and WRF Models'

In his comment, Laprise raises several points that we agree merit consideration. His primary critique is that our study [Racherla et al., 2012] tested the ability of the WRF regional climate model to reproduce historical temperature and precipitation change relative to the driving global climate model (GCM) using only a single simulation rather than an ensemble. He asserts that the observed changes are smaller than the internal variability in the climate system (i.e., not statistically significant) and that thus a single simulation should not necessarily be able to capture the observations. Laprise points out that the statistical signal is reduced for a multi-decadal trend such as the one we analyzed in comparison with mean climatology and cites two studies showing that for particular climate parameters it can take any years for a signal to be discerned over internal variability. He states that The results of theexperiment as designed were strongly influenced by the presence of internal variability and sampling errors,which masked the rather small climate changes that may have occurred as a consequence of changes inforcing during the period considered. While Laprise discusses statistics in general terms at some length, for the actual climate trends examined in our study, he offers no evidence that the forced signal was smallcompared with internal variability. The two studies he cites [de Ela et al., 2013; Maraun, 2013] do not provide convincing evidence as they concern climate variables averaged over different times and areas. One in fact examines extreme precipitation events, which by definition are rare and thus have a lower significance level. We accept the general point that it is important to consider internal variability, and as noted in our paper we agree that an ensemble of simulations is in principle an optimal, though computationally expensive, approach. While we did not present the statistical significance of the observations in our original paper, we have now evaluated those for the regional temperature trends used in our study to evaluate the added value of WRF and thus can analyze data as to the magnitude of the trends with respect to internal variability.

climate↗

Advances and Limitations of Atmospheric Boundary Layer Observations with GPS Occultation over Southeast Pacific Ocean

The typical atmospheric boundary layer (ABL) over the southeast (SE) Pacific Ocean is featured with a strong temperature inversion and a sharp moisture gradient across the ABL top. The strong moisture and temperature gradients result in a sharp refractivity gradient that can be precisely detected by the Global Positioning System (GPS) radio occultation (RO) measurements. In this paper, the Constellation Observing System for Meteorology, Ionosphere & Climate (COSMIC) GPS RO soundings, radiosondes and the high-resolution ECMWF analysis over the SE Pacific are analyzed. COSMIC RO is able to detect a wide range of ABL height variations (1-2 kilometer) as observed from the radiosondes. However, the ECMWF analysis systematically underestimates the ABL heights. The sharp refractivity gradient at the ABL top frequently exceeds the critical refraction (e.g., −157 N-unit per kilometer) and becomes the so-called ducting condition, which results in a systematic RO refractivity bias (or called N-bias) inside the ABL. Simulation study based on radiosonde profiles reveals the magnitudes of the N-biases are vertical resolution dependent. The N-bias is also the primary cause of the systematically smaller refractivity gradient (rarely exceeding −110 N-unit per kilometer) at the ABL top from RO measurement. However, the N-bias seems not affect the ABL height detection. Instead, the very large RO bending angle and the sharp refractivity gradient due to ducting allow reliable detection of the ABL height from GPS RO. The seasonal mean climatology of ABL heights derived from a nine-month composite of COSMIC RO soundings over the SE Pacific reveals significant differences from the ECMWF analysis. Both show an increase of ABL height from the shallow stratocumulus near the coast to a much higher trade wind inversion further off the coast. However, COSMIC RO shows an overall deeper ABL and reveals different locations of the minimum and maximum ABL heights as compared to the ECMWF analysis. At low latitudes, despite the decreasing number of COSMIC RO soundings and the lower percentage of soundings that penetrate into the lowest 500-m above the mean-sea-level, there are small sampling errors in the mean ABL height climatology. The difference of ABL height climatology between COSMIC RO and ECMWF analysis over SE Pacific is significant and requires further studies.

COSMIC RO↗

A Non-Intrusive Algorithm for Sensitivity Analysis of Chaotic Flow Simulations

We demonstrate a novel algorithm for computing the sensitivity of statistics in chaotic flow simulations to parameter perturbations. The algorithm is non-intrusive but requires exposing an interface. Based on the principle of shadowing in dynamical systems, this algorithm is designed to reduce the effect of the sampling error in computing sensitivity of statistics in chaotic simulations. We compare the effectiveness of this method to that of the conventional finite difference method.

Blonigan, Patrick J.↗

Random Variables with Moment-Matching Staircase Density Functions

This paper proposes a family of random variables for uncertainty modeling. The variables of interest have a bounded support set, and prescribed values for the first four moments. We present the feasibility conditions for the existence of any of such variables, and propose a class of variables that conforms to such constraints. This class is called staircase because the density of its members is a piecewise constant function. Convex optimization is used to calculate their distributions according to several optimality criteria, including maximal entropy and maximal log-likelihood. The flexibility and efficiency of staircases enable modeling phenomena having a possibly skewed and/or multimodal response at a low computational cost. Furthermore, we provide a means to account for the uncertainty in the distribution caused by estimating staircases from data. These ideas are illustrated by generating empirical staircase predictor models. We consider the case in which the predictor matches the sample moments exactly (a setting applicable to large datasets), as well as the case in which the predictor accounts for the sampling error in such moments (a setting applicable to sparse datasets). A predictor model for the dynamics of an aeroelastic airfoil subject to flutter instability is used as an example. The resulting predictor not only describes the system's response accurately, but also enables carrying out a risk analysis for safe flight.

Luis G. Crespo↗

Satellite Salinity Observing System: Recent Discoveries and the Way Forward

Advances in L-band microwave satellite radiometry in the past decade, pioneered by ESA's SMOS and NASA's Aquarius and SMAP missions, have demonstrated an unprecedented capability to observe global sea surface salinity (SSS) from space. Measurements from these missions are the only means to probe the very-near surface salinity (top cm), providing a unique monitoring capability for the interfacial exchanges of water between the atmosphere and the upper-ocean, and delivering a wealth of information on various salinity processes in the ocean, linkages with the climate and water cycle, including land-sea connections, and providing constraints for ocean prediction models. The satellite SSS data are complimentary to the existing in situ systems such as Argo that provide accurate depiction of large-scale salinity variability in the open ocean but under-sample mesoscale variability, coastal oceans and marginal seas, and energetic regions such as boundary currents and fronts. In particular, salinity remote sensing has proven valuable to systematically monitor the open oceans as well as coastal regions up to approximately 40 km from the coasts. This is critical to addressing societally relevant topics, such as land-sea linkages, coastal-open ocean exchanges, research in the carbon cycle, near-surface mixing, and air-sea exchange of gas and mass. In this paper, we provide a community perspective on the major achievements of satellite SSS for the aforementioned topics, the unique capability of satellite salinity observing system and its complementarity with other platforms, uncertainty characteristics of satellite SSS, and measurement versus sampling errors in relation to in situ salinity measurements. We also discuss the need for technological innovations to improve the accuracy, resolution, and coverage of satellite SSS, and the way forward to both continue and enhance salinity remote sensing as part of the integrated Earth Observing System in order to address societal needs.

Vinogradova, Nadya↗