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NASA NTRS2000

Design of a 2-Hour Prebreathe Protocol for Space Walks (EVAs) from the International Space Station (ISS)

The majority of extravehicular activities (EVAs) performed from the shuttle use a 10.2 psi staged decompression. The International Space Station (ISS) will operate at 14.7 psi, requiring crews to "campout" in the airlock at 10.2 psi. The constraints associated with campout (crew isolation, oxygen usage, and waste management), provided the rationale to develop a 2-hour prebreathe protocol from 14.7 psi. Previous studies on the affect of microgravity and exercise during prebreathe suggested the feasibility of this approach. Various combinations of adynamia (nonwalking subjects), prebreathe exercise doses, and space suit donning options (10.2 vs. 14.7 psi) were analyzed against timeline and consumable constraints. Prospective decompression sickness (DCS) and venous gas emboli (VGE) accept/reject criteria were defined from statistical analysis of historical DCS data, combined with risk management of DCS under ISS mission circumstances. Maximum operational DCS levels were defined based on protecting for EVA capability with two crew members at 95% confidence, throughout ISS lifetime (within the constraints of NASA DCS disposition policy JPG 1800.3). The accept / reject limits were adjusted for greater safety (including Grade IV VGE criteria) based on analysis of related medical factors. Monte-Carlo simulation was performed to design a closed sequential, multi-center laboratory trial, including the capability of rejecting the primary protocol and testing at least one alternate exercise dose, within the 2-hour prebreathe. The 2-hour protocol incorporates 0, breathing for 5 0 min at 14.7 psi, including 10 min dual cycle ergometry at 75%VO(2max). It requires an additional 30 minO2breathing during depress from 14.7 to 10.2 psi, followed by a 30-60 min suit donning break at 10.2 psi/26.5% O2. It concludes with a 40 min in-suit O2 prebreathe. The protocol would be accepted for operations, if the incidence of DCS was less than 15% and Grade IV VGE less than 20%, both at 95% confidence. The above protocol and accept/reject limits were implemented in a multi-center study.

Gernhardt, M. L.↗
NASA NTRS2000

Design and Testing of a 2-Hour Oxygen Prebreathe Protocol for Space Walks from the International Space Station

To develop and test a 2-hour prebreathe protocol for performing extravehicular activities (EVAs) from the International Space Station (ISS). Combinations of adynamia (non-walking), prebreathe exercise, and space suit donning options (10.2 vs. 14.7 psi) were evaluated, against timeline and consumable contraints to develop an operational 2- hour prebreathe protocol. Prospective accept/reject criteria were defined for decompression sickness (DCS) and venous gas emboli (VGE) from analysis of historical DCS data, combined with risk management of DCS under ISS mission circumstances. Maximum operational DCS levels were defined based on protecting for EVA capability with two crew-members at 95% confidence, throughout ISS lifetime (within the constraints of NASA DCS disposition policy JPG 1800.3). The accept/reject limits were adjusted for greater safety based on analysis of related medical factors. Monte-Carlo simulation was performed to design a closed sequential, multi-center human trial. Protocols were tested with 4 different prebreathe exercises (Phases I-IV), prior to exposure to 4.3 psi for 4 hrs. Subject selection, Doppler monitoring for VGE, test termination criteria, and DCS definitions were standardized. Phase I: upper and lower body exercises using dual-cycle ergometry (75% VO2 max for 10 min). Phase II: ergometry plus 24 min of light exercise (simulating space-suit preparations). Phase III: same 24 min of light exercise but no ergometry, and Phase IV: 56 min of light exercise without ergometry. A prebreathe procedure was accepted if, at 95% confidence, the incidence of DCS was less than 15% (with no Type II DCS), and Grade IV VGE was less than 20%.

Gernhardt, Michael L.↗
NASA NTRS1995

Reliability Stress-Strength Models for Dependent Observations with Applications in Clinical Trials

We consider the applications of stress-strength models in studies involving clinical trials. When studying the effects and side effects of certain procedures (treatments), it is often the case that observations are correlated due to subject effect, repeated measurements and observing many characteristics simultaneously. We develop maximum likelihood estimator (MLE) and uniform minimum variance unbiased estimator (UMVUE) of the reliability which in clinical trial studies could be considered as the chances of increased side effects due to a particular procedure compared to another. The results developed apply to both univariate and multivariate situations. Also, for the univariate situations we develop simple to use lower confidence bounds for the reliability. Further, we consider the cases when both stress and strength constitute time dependent processes. We define the future reliability and obtain methods of constructing lower confidence bounds for this reliability. Finally, we conduct simulation studies to evaluate all the procedures developed and also to compare the MLE and the UMVUE.

Kushary, Debashis↗
NASA NTRS2000

Direct Measurement of the Supernova Rate in Starburst Galaxies

Supernovae play a key role in the dynamics, structure, and chemical evolution of galaxies. The massive stars that end their lives as supernovae live for short enough times that many are still associated with dusty star formation regions when they explode, making them difficult to observe at visible wavelengths. In active star forming regions (galactic nuclei and starburst regions), dust extinction is especially severe. Thus, determining the supernova rate in active star forming regions of galaxies, where the supernova rate can be one or two orders of magnitude higher than the average, has proven to be difficult. From observations of SN1987A, we know that the [NiII] 6.63 micrometer emission line was the strongest line in the infrared spectrum for a period of a year and half after th explosion. Since dust extinction is much less at 6.63 micrometers than at visible wavelengths (A(sub 6.63)/A(sub V) = 0.025), the [NiII] line can be used as a sensitive probe for the detection of recent supernovae. We have observed a sample of starburst galaxies at 6.63 micrometers using ISOCAM to search for the [NiII] emission line characteristic of recent supernovae. We did not detect any [NiII] line emission brighter than a 5-sigma limit of 5 mJy. We can set upper limits to the supernova rate in our sample, scaled ot the rate in M82, of less than 0.3 per year at the 90% confidence level using Bayesian methods. Assuming that a supernova would have a [NiII] line with the same luminosity as observed in SN1987A, we find less than 0.09 and 0.15 per year at the 50% and 67% confidence levels. These rates are somewhat less if a more normal type II supernovae has a [NiII] line luminosity greater than the line in SN1987A.

Bregman, J. D.↗
NASA NTRS2001

Galaxy Cluster Gas Mass Fractions From Sunyaev-Zel'dovich Effect Measurement: Constraints on Omega_M

Using sensitive centimeter-wave receivers mounted on the Owens Valley Radio Observatory and Berkeley-Illinois-Maryland-Association millimeter arrays, we have obtained interferometric measurements of the Sunyaev-Zei'dovich (SZ) effect toward massive galaxy clusters. We use the SZ data to determine the pressure distribution of the cluster gas and, in combination with published X-ray temperatures, to infer the gas mass and total gravitational mass of 18 clusters. The gas mass fraction, f~g, is calculated for each cluster, and is extrapolated to the fiducial radius r_{500} using the results of numerical simulations. The mean f_g within r_{500} is 0.081 + 0.009 - 0.011/(h_{100} (statistical uncertainty at 68% confidence level, assuming OmegaM=0.3, OmegaL=0.7). We discuss possible sources of systematic errors in the mean f 9 measurement. We derive an upper limit for OmegaM from this sample under the assumption that the mass composition of clusters within r_{500} reflects the universal mass composition: Omega_M h <Omega_B/f_g.The gas mass f on cosmology through the angular diameter distance and the r_{500} correction factors. For a flat universe (Omegal, = 1 - OmegaM) and h=0.7, we find the measured gas mass fractions are consistent with OmegaM less than 0.40, at 68% confidence. Including estimates of the baryons contained in galaxies and the baryons which failed to become bound during the cluster formation process, we find OmegaM\approximately 0.25.

Grego, Laura↗
NASA NTRS2001

Modeling Nitrogen Oxides in the Lower Stratosphere

This talk will focus on the status of current understanding (not a historical review) as regards modeling nitrogen oxides (NOy) in the lower stratosphere (LS). The presentation will be organized around three major areas of process understanding: 1) NOy sources, sinks, and transport to the LS, 2) NOy species partitioning, and 3) polar multiphase processes. In each area, process topics will be identified with an estimate of the degree of confidence associated with their representation in numerical models. Several exotic and/or speculative processes will also be discussed. Those topics associated with low confidence or knowledge gaps, weighted by their prospective importance in stratospheric chemical modeling, will be collected into recommendations for further study. Suggested approaches to further study will be presented for discussion.

Kawa, S. Randy↗
NASA NTRS2001

Galaxy Cluster Gas Mass Fractions From Sunyaev-Zeldovich Effect Measurements: Constraints on Omega(M)

Using sensitive centimeter-wave receivers mounted on the Owens Valley Radio Observatory and Berkeley-Illinois-Maryland-Association millimeter arrays, we have obtained interferometric measurements of the Sunyaev-Zeldovich(SZ) effect toward massive galaxy clusters. We use the SZ data to determine the pressure distribution of the cluster gas and, in combination with published X-ray temperatures, to infer the gas mass and total gravitational mass of 18 clusters. The gas mass fraction, f(g), is calculated for each cluster and is extrapolated to the fiducial radius r(500) using the results of numerical simulations. The mean f(g) within r(500) is 0.081(+ 0.009 / - 0.011) per h(100) (statistical uncertainty at 68% confidence level, assuming Omega(M) = 0.3, Omega(Lambda) = 0.7). We discuss possible sources of systematic errors in the mean f(sub g) measurement. We derive an upper limit for Omega(M) from this sample under the assumption that the mass composition of clusters within r(500) reflects the universal mass composition: Omega(M)h is less than or equal to Omega(B)/f(g). The gas mass fractions depend on cosmology through the angular diameter distance and the r(500) correction factors. For a flat universe (Omega(Lambda) is identical with 1 - Omega(M)) and h = 0.7, we find the measured gas mass fractions are consistent with Omega(M) is less than 0.40, at 68% confidence. Including estimates of the baryons contained in galaxies and the baryons which failed to become bound during the cluster formation process, we find Omega(M) is approximately equal to 0.25.

Grego, Laura↗
NASA NTRS2001

BATSE Observations of the Piccinotti Sample of AGN II: Variability and Spectral Analysis

The Piccinotti sample is the hard x-ray-selected sample of active galactic nuclei (AGNs) best studied at energies below approximately 10 keV. It represents the only unbiased and complete high-energy survey of the sky down to a limiting flux of 3.1 x 10(exp -11) per square erg per second. As such, it has been used to study AGN properties such as X-ray spectral characteristics, log N-log S relation, and luminosity function. The BATSE data provide, for the first time, a systematic coverage of the whole sample at high energies. BATSE data from nearly four years of observations (1993 November - 1997 September) were analyzed using standard BATSE occultation analysis software to extract a signal from sources in the Piccinotti sample. Although the BATSE sensitivity for individual source measurements is relatively poor on short time scales, the near all-sky coverage and long CGRO lifetime allows us to improve our sensitivity considerably by sumrr~ng data over many years. This significantly reduces our statistical errors at the expense of loss of temporal information. However, the systematic errors associated with the summation of data over such a long period are not negligible, and the study of systematic effects was a major part of our effort. We evaluated two types of systematic error: those affecting the overall normalization (which are important for comparison with other instruments) and those affecting the size of the fluctuations (which are relevant for estimating the confidence level of a detection). The former was studied by comparison of BATSE data with other instruments, primarily CGRO/OSSE. The results indicate that our absolute flux values maybe overestimated by as much as 35% for some sources. However, since this does not affect our estimation of the detection confidence, we made no corrections to our flux estimates.

Paciesas, William S.↗
NASA NTRS2002

Two Outs, Bottom of the Ninth

It was eight months before launch when my second Flight Operations Team lead said he was leaving the project for another job. Six months earlier, the original lead had said he was leaving. I was stunned--but I remained confident that we would recover. I didn't expect to lose the second lead. After all, lightning is not supposed to strike twice in the same place. This time, with only eight months until launch, I was very much concerned. No, 'concerned' is probably too mild a word. Let's get it right: I was sweating. Losing a lead at any stage presents problems, but two losses within 6 months of each other can definitely shake the confidence of an inexperienced Flight Ops Team.

Snow, Frank↗
NASA NTRS2002

Non-Thermal Hard X-Ray Emission in Galaxy Clusters Observed with the BeppoSAX PDS

We studied the X-ray emission in a sample of clusters using the BeppoSAX PDS instrument in the 20 -- 80 keV energy band. We estimated the non-thermal cluster emission (HXR) by modeling the thermal contribution from the cluster gas and the non-thermal contamination from the AGN in the field, and propagating the corresponding uncertainties. We also evaluated and propagated the systematic uncertainties due to the background fluctuations. The resulting non-thermal component is detected at a sigma level in approx. 50 % of the non-significantly AGN-contaminated clusters, i.e. in clusters A2142, A2256, A3376, Coma, Ophiuchus and Virgo. Furthermore, Virgo is detected at a 4 sigma level. All the clusters detected at a 2 sigma level exhibit some degree of merger signatures, i.e. deviations from the azimuthally symmetric brightness and temperature distributions, while the relaxed clusters are detected at a lower confidence. The data are consistent with a scenario whereby relaxed clusters have no non-thermal hard X-ray component, whereas merger clusters do, with a 20 -- 80 keV luminosity of approx. 10(exp 42-44)((h(sub 50))(exp -2))(erg/s). Consistent with merger boosting of cluster temperatures, the non-thermal luminosity increases by 2-3 orders of magnitude between the average cluster temperatures 2 and 10 keV, as L(sub NTE) is proportional to T(sup j) with j = 2.4+/-0.3. These results corroborate the assumption which is the essential element in most non-thermal hard X-ray emission models. The co-added spectrum of all non-significantly AGN-contaminated clusters indicates a power-law spectrum for the non-thermal component with a photon index of 1.5+/-0.25 at 1 sigma confidence level. Unless there is a high energy cut-off in the electron velocity distribution, the total spectrum implies that Inverse Compton scatter of Cosmic Microwave Background photons from electron population dominates over the non-thermal bremsstrahlung in producing hard X-rays in clusters on the merger shock acceleration of electrons in clusters.

Nevalainen, Jukka H.↗
NASA NTRS2002

Application of Modern Design of Experiments to CARS Thermometry in a Model Scramjet Engine

We have applied formal experiment design and analysis to optimize the measurement of temperature in a supersonic combustor at NASA Langley Research Center. We used the coherent anti-Stokes Raman spectroscopy (CARS) technique to map the temperature distribution in the flowfield downstream of an 1160 K, Mach 2 freestream into which supersonic hydrogen fuel is injected at an angle of 30 degrees. CARS thermometry is inherently a single-point measurement technique; it was used to map thc flow by translating the measurement volume through the flowfield. The method known as "Modern Design of Experiments" (MDOE) was used to estimate the data volume required, design the test matrix, perform the experiment and analyze the resulting data. MDOE allowed us to match the volume of data acquired to the precision requirements of the customer. Furthermore, one aspect of MDOE, known as response surface methodology, allowed us to develop precise maps of the flowfield temperature, allowing interpolation between measurement points. An analytic function in two spatial variables was fit to the data from a single measurement plane. Fitting with a Cosine Series Bivariate Function allowed the mean temperature to be mapped with 95% confidence interval half-widths of +/- 30 Kelvin, comfortably meeting the confidence of +/- 50 Kelvin specified prior to performing the experiments. We estimate that applying MDOE to the present experiment saved a factor of 5 in data volume acquired, compared to experiments executed in the traditional manner. Furthermore, the precision requirements could have been met with less than half the data acquired.

Danehy, P. M.↗
NASA NTRS2002

Probabilistic Analysis and Density Parameter Estimation Within Nessus

This NASA educational grant has the goal of promoting probabilistic analysis methods to undergraduate and graduate UTSA engineering students. Two undergraduate-level and one graduate-level course were offered at UTSA providing a large number of students exposure to and experience in probabilistic techniques. The grant provided two research engineers from Southwest Research Institute the opportunity to teach these courses at UTSA, thereby exposing a large number of students to practical applications of probabilistic methods and state-of-the-art computational methods. In classroom activities, students were introduced to the NESSUS computer program, which embodies many algorithms in probabilistic simulation and reliability analysis. Because the NESSUS program is used at UTSA in both student research projects and selected courses, a student version of a NESSUS manual has been revised and improved, with additional example problems being added to expand the scope of the example application problems. This report documents two research accomplishments in the integration of a new sampling algorithm into NESSUS and in the testing of the new algorithm. The new Latin Hypercube Sampling (LHS) subroutines use the latest NESSUS input file format and specific files for writing output. The LHS subroutines are called out early in the program so that no unnecessary calculations are performed. Proper correlation between sets of multidimensional coordinates can be obtained by using NESSUS' LHS capabilities. Finally, two types of correlation are written to the appropriate output file. The program enhancement was tested by repeatedly estimating the mean, standard deviation, and 99th percentile of four different responses using Monte Carlo (MC) and LHS. These test cases, put forth by the Society of Automotive Engineers, are used to compare probabilistic methods. For all test cases, it is shown that LHS has a lower estimation error than MC when used to estimate the mean, standard deviation, and 99th percentile of the four responses at the 50 percent confidence level and using the same number of response evaluations for each method. In addition, LHS requires fewer calculations than MC in order to be 99.7 percent confident that a single mean, standard deviation, or 99th percentile estimate will be within at most 3 percent of the true value of the each parameter. Again, this is shown for all of the test cases studied. For that reason it can be said that NESSUS is an important reliability tool that has a variety of sound probabilistic methods a user can employ; furthermore, the newest LHS module is a valuable new enhancement of the program.

Godines, Cody R.↗
NASA NTRS2002

Dynamical Approach Study of Spurious Numerics in Nonlinear Computations

The last two decades have been an era when computation is ahead of analysis and when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems and non-traditional fields. Ensuring a higher level of confidence in the predictability and reliability (PAR) of these numerical simulations could play a major role in furthering the design, understanding, affordability and safety of our next generation air and space transportation systems, and systems for planetary and atmospheric sciences, and in understanding the evolution and origin of life. The need to guarantee PAR becomes acute when computations offer the ONLY way of solving these types of data limited problems. Employing theory from nonlinear dynamical systems, some building blocks to ensure a higher level of confidence in PAR of numerical simulations have been revealed by the author and world expert collaborators in relevant fields. Five building blocks with supporting numerical examples were discussed. The next step is to utilize knowledge gained by including nonlinear dynamics, bifurcation and chaos theories as an integral part of the numerical process. The third step is to design integrated criteria for reliable and accurate algorithms that cater to the different multiscale nonlinear physics. This includes but is not limited to the construction of appropriate adaptive spatial and temporal discretizations that are suitable for the underlying governing equations. In addition, a multiresolution wavelets approach for adaptive numerical dissipation/filter controls for high speed turbulence, acoustics and combustion simulations will be sought. These steps are corner stones for guarding against spurious numerical solutions that are solutions of the discretized counterparts but are not solutions of the underlying governing equations.

Yee, H. C.↗
NASA NTRS2001

Wilkinson Microwave Anisotropy Probe (WMAP) First Year Observations: TE Polarization

The Wilkinson Microwave Anisotropy Probe (WMAP) has mapped the full sky in Stokes I, Q, and U parameters at frequencies 23, 33, 41, 61, and 94 GHz. We detect correlations between the temperature and polarization maps significant at more than 10 standard deviations. The correlations are inconsistent with instrument noise and are significantly larger than the upper limits established for potential systematic errors. The correlations are present in all WAMP frequency bands with similar amplitude from 23 to 94 GHz, and are consistent with a superposition of a CMB signal with a weak foreground. The fitted CMB component is robust against different data combinations and fitting techniques. On small angular scales (theta less than 5 deg), the WMAP data show the temperature-polarization correlation expected from adiabatic perturbations in the temperature power spectrum. The data for l greater than 20 agree well with the signal predicted solely from the temperature power spectra, with no additional free parameters. We detect excess power on large angular scales (theta greater than 10 deg) compared to predictions based on the temperature power spectra alone. The excess power is well described by reionization at redshift 11 is less than z(sub r) is less than 30 at 95% confidence, depending on the ionization history. A model-independent fit to reionization optical depth yields results consistent with the best-fit ACDM model, with best fit value t = 0.17 +/- 0.04 at 68% confidence, including systematic and foreground uncertainties. This value is larger than expected given the detection of a Gunn-Peterson trough in the absorption spectra of distant quasars, and implies that the universe has a complex ionization history: WMAP has detected the signal from an early epoch of reionization.

Kogut, A.↗
NASA NTRS2003

A Measure from Line-of-Sight Magnetograms for Prediction of Coronal Mass Ejections

From a sample of 17 vector magnetograms of 12 bipolar active regions, we have recently found (1) that a measure of the overall nonpotentiality (the overall twist and shear in the magnetic field) of an active region is given by the strong-shear length L(sub SS), the length of the portion of the main neutral line on which the observed transverse fields is strong (greater than 150 G) and strongly sheared (shear angle greater than 45 deg), and (2) that L(sub SS) is well correlated with the CME productivity of the active regions during the +/- 2-day time window centered on the day of the magnetogram. In the present paper, from the same sample of 17 vector magnetograms, we show that there is a viable proxy for L(sub SS) that can be measured from a line-of-sight magnetogram. This proxy is the strong-gradient length L(sub SG), the length of the portion of the main neutral line on which the potential transverse field is strong (greater than 150 G) and the gradient of the line-of-sight field is sufficiently steep (greater than or approximately 50 G/Mm). In our sample of active regions, L(sub SG) is statistically significantly correlated with L(sub SS) (correlation confidence level greater than 95%), and L(sub SG) is as strongly correlated with active-region CME productivity as is L(sub SS)(correlation confidence level approximately 99.7%). Because L(sub SG) can be measured from line-of-sight magnetograms obtained from conventional magnetographs, such as the magnetograph mode of the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO), it is a dependable substitute for L(sub SS) for use in operational CME forecasting. In addition, via measurement of L(sub SG), the years-long, nearly continuous sequence of 1.5-hour-cadence full-disk line-of-sight magnetograms from MDI can be used to track the growth and decay of the large-scale nonpotentiality in active regions and to examine the role of this evolution in active-region CME productivity.

Falconer, D. A.↗
NASA NTRS2003

Real-Time Stability and Control Derivative Extraction From F-15 Flight Data

A real-time, frequency-domain, equation-error parameter identification (PID) technique was used to estimate stability and control derivatives from flight data. This technique is being studied to support adaptive control system concepts currently being developed by NASA (National Aeronautics and Space Administration), academia, and industry. This report describes the basic real-time algorithm used for this study and implementation issues for onboard usage as part of an indirect-adaptive control system. A confidence measures system for automated evaluation of PID results is discussed. Results calculated using flight data from a modified F-15 aircraft are presented. Test maneuvers included pilot input doublets and automated inputs at several flight conditions. Estimated derivatives are compared to aerodynamic model predictions. Data indicate that the real-time PID used for this study performs well enough to be used for onboard parameter estimation. For suitable test inputs, the parameter estimates converged rapidly to sufficient levels of accuracy. The devised confidence measures used were moderately successful.

Smith, Mark S.↗
NASA NTRS2003

Remote Sensing of Liquid Water and Ice Cloud Optical Thickness and Effective Radius in the Arctic: Application of Airborne Multispectral MAS Data

A multispectral scanning spectrometer was used to obtain measurements of the reflection function and brightness temperature of clouds, sea ice, snow, and tundra surfaces at 50 discrete wavelengths between 0.47 and 14.0 microns. These observations were obtained from the NASA ER-2 aircraft as part of the FIRE Arctic Clouds Experiment, conducted over a 1600 x 500 km region of the north slope of Alaska and surrounding Beaufort and Chukchi Seas between 18 May and 6 June 1998. Multispectral images of the reflection function and brightness temperature in 11 distinct bands of the MODIS Airborne Simulator (MAS) were used to derive a confidence in clear sky (or alternatively the probability of cloud), shadow, and heavy aerosol over five different ecosystems. Based on the results of individual tests run as part of the cloud mask, an algorithm was developed to estimate the phase of the clouds (water, ice, or undetermined phase). Finally, the cloud optical thickness and effective radius were derived for both water and ice clouds that were detected during one flight line on 4 June. This analysis shows that the cloud mask developed for operational use on MODIS, and tested using MAS data in Alaska, is quite capable of distinguishing clouds from bright sea ice surfaces during daytime conditions in the high Arctic. Results of individual tests, however, make it difficult to distinguish ice clouds over snow and sea ice surfaces, so additional tests were added to enhance the confidence in the thermodynamic phase of clouds over the Beaufort Sea. The cloud optical thickness and effective radius retrievals used 3 distinct bands of the MAS, with the newly developed 1.62 and 2.13 micron bands being used quite successfully over snow and sea ice surfaces. These results are contrasted with a MODIS-based algorithm that relies on spectral reflectance at 0.87 and 2.13 micron.

King, Michael D.↗
NASA NTRS2002

Statistical Sampling of Tide Heights Study

The goal of the study was to determine if it was possible to reduce the cost of verifying computational models of tidal waves and currents. Statistical techniques were used to determine the least number of samples required, in a given situation, to remain statistically significant, and thereby reduce overall project costs. Commercial, academic, and Federal agencies could benefit by applying these techniques, without the need to 'touch' every item in the population. For example, the requirement of this project was to measure the heights and times of high and low tides at 8,000 locations for verification of computational models of tidal waves and currents. The application of the statistical techniques began with observations to determine the correctness of submitted measurement data, followed by some assumptions based on the observations. Among the assumptions were that the data were representative of data-collection techniques used at the measurement locations, that time measurements could be ignored (that is, height measurements alone would suffice), and that the height measurements were from a statistically normal distribution. Sample means and standard deviations were determined for all locations. Interval limits were determined for confidence levels of 95, 98, and 99 percent. It was found that the numbers of measurement locations needed to attain these confidence levels were 55, 78, and 96, respectively.

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