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At least 145 records · Page 8

Integrated design and manufacturing for the high speed civil transport (a combined aerodynamics/propulsion optimization study)

This report documents the efforts of a Georgia Tech High Speed Civil Transport (HSCT) aerospace student design team in completing a design methodology demonstration under NASA's Advanced Design Program (ADP). Aerodynamic and propulsion analyses are integrated into the synthesis code FLOPS in order to improve its prediction accuracy. Executing the integrated product and process development (IPPD) methodology proposed at the Aerospace Systems Design Laboratory (ASDL), an improved sizing process is described followed by a combined aero-propulsion optimization, where the objective function, average yield per revenue passenger mile ($/RPM), is constrained by flight stability, noise, approach speed, and field length restrictions. Primary goals include successful demonstration of the application of the response surface methodolgy (RSM) to parameter design, introduction to higher fidelity disciplinary analysis than normally feasible at the conceptual and early preliminary level, and investigations of relationships between aerodynamic and propulsion design parameters and their effect on the objective function, $/RPM. A unique approach to aircraft synthesis is developed in which statistical methods, specifically design of experiments and the RSM, are used to more efficiently search the design space for optimum configurations. In particular, two uses of these techniques are demonstrated. First, response model equations are formed which represent complex analysis in the form of a regression polynomial. Next, a second regression equation is constructed, not for modeling purposes, but instead for the purpose of optimization at the system level. Such an optimization problem with the given tools normally would be difficult due to the need for hard connections between the various complex codes involved. The statistical methodology presents an alternative and is demonstrated via an example of aerodynamic modeling and planform optimization for a HSCT.

Baecher, Juergen↗

A Multi-Wavelength Study of the Hot Component of the Interstellar Medium

This research focuses on the kinematics and evolution of the hot phase of the interstellar medium in the Galaxy. The plan was to measure the UV spectra of all hot stars observed with IUE, in order to identify and measure the main component and any high velocity components to the interstellar lines. Collection of data from higher resolution instruments on HST has been proposed for some of the interesting lines of sight. IUE spectra of 240 stars up to 8 kpc in 2 quadrants of the galactic plane have been examined to (1) estimate the total column density per kpc as a function of direction and distance, and (2) to obtain a lower limit to the number of high velocity components to the interstellar lines, thus giving an approximation of the number of conductive interfaces encountered per line of sight. By determining an approximation to the number of components per unit distance we aim to derive statistics on interfaces between hot and cold gas in the Galaxy. We find that 20% of the stars in this sample show at least one high velocity component in the C IV interstellar line. Two successful FUSE programs address this research and collected data for several of the lines of sight identified as locations of hot, expanding gas with the IUE data. One FUSE program is complete for the Vela SNR region. Data from another FUSE program to investigate the Cygnus superbubble region are being analyzed.

Oliversen, Ronald J.↗

Summertime Coincident Observations of Ice Water Path in the Visible/Near-IR, Radar, and Microwave Frequencies

Accurate representation of the physical and radiative properties of clouds in climate models continues to be a challenge. At present, both remote sensing observations and modeling of microphysical properties of clouds rely heavily on parameterizations or assumptions on particle size distribution (PSD) and cloud phase. In this study, we compare Ice Water Path (IWP), an important physical and radiative property that provides the amount of ice present in a cloud column, using measurements obtained via three different retrieval strategies. The datasets we use in this study include Visible/Near-IR IWP from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument flying aboard the Aqua satellite, Radar-only IWP from the CloudSat instrument operating at 94 GHz, and NOAA/NESDIS operational IWP from the 89 and 157 GHz channels of the Microwave Humidity Sounder (MHS) instrument flying aboard the NOAA-18 satellite. In the Visible/Near-IR, IWP is derived from observations of optical thickness and effective radius. CloudSat IWP is determined from measurements of cloud backscatter and assumed PSD. MHS IWP retrievals depend on scattering measurements at two different, non-water absorbing channels, 89 and 157 GHz. In order to compare IWP obtained from these different techniques and collected at different vertical and horizontal resolutions, we examine summertime cases in the tropics (30S - 30N) when all 3 satellites are within 4 minutes of each other (approximately 1500 km). All measurements are then gridded to a common 15 km x 15 km box determined by MHS. In a grid box comparison, we find CloudSat to report the highest IWP followed by MODIS, followed by MHS. In a statistical comparison, probability density distributions show MHS with the highest frequencies at IWP of 100-1000 g/m(exp 2) and CloudSat with the longest tail reporting IWP of several thousands g/m(exp 2). For IWP greater than 30 g/m(exp 2), MODIS is consistently higher than CloudSat, and it is higher at the lower IWPs but lower at the higher IWPs that overlap with MHS. Some of these differences can be attributed to the limitations of the measuring techniques themselves, but some can result from the assumptions made in the algorithms that generate the IWP product. We investigate this issue by creating categories based on various conditions such as cloud type, precipitation presence, underlying liquid water content, and surface type (land vs. ocean) and by comparing the performance of the IWP products under each condition.

Pittman, Jasna V.↗

A case study of the energy dissipation of the gravity wave field based on satellite altimeter measurements

Wave breaking is proposed as the primary energy dissipation mechanism for the gravity wave field. The energy dissipation rate is calculated based on the statistical model proposed by Longuet-Higgins (1969) with a modification of the breaking criterion incorporating the surface stress according to Phillips and Banner (1974). From this modified model, an analytic expression is found for the wave attenuation rate and the half-life time of the wave field which depend only on the significant slope of the wave field and the ratio of friction velocity to initial wave phase velocity. These expressions explain why the freshly generated wave field does not last long, but why swells are capable of propagating long distances without substantial change in energy density. It is shown that breaking is many orders of magnitude more effective in dissipating wave energy than the molecular viscosity, if the significant slope is higher than 0.01. Limited observational data from satellite and laboratory are used to compare with the analytic results, and show good agreement.

Huang, N. E.↗

NuSTAR Observation of GROJ1744−28 at Low Mass Accretion Rate

Context.Neutron stars in low-mass X-ray binaries (LMXBs) are important systems to study the physics of accretion onto compact ob-jects. The system GRO J1744−28 is particularly interesting, as it usually shows clear pulsations as well as X-ray bursts. Additionally,there are claims for a magnetic field of 5×1011G through the detection of a Cyclotron Resonant Scattering Feature (CRSF).Aims.We present the spectral analysis of GRO J1744−28 using∼29 ks of NuSTAR data taken in 2017 February at a low luminosityof 3.2×1036erg s−1(3–50 keV). Our goal is to study the variability of the source spectrum with pulse phase and to search for the claimed CRSF. Methods.The continuum spectrum is modeled with an absorbed power-law with exponential cut-off, and an additional iron line component. We find no obvious indications for a CRSF and therefore perform a detailed cyclotron line search using statistical methods.We perform this search on pulse phase-averaged as well as phase-resolved spectra. Results.GRO J1744−28 was observed at one of the lowest luminosities studied so far. The previously detected Type II X-ray bursts re absent. Clear pulsations at a period of 2.141124(9) Hz are detected. The pulse profile shows an indication of a secondary peak,which was not seen at higher flux. The 4σupper limit for the strength of a CRSF in the 3–20 keV band is 0.07 keV, lower than the strength of the line found at higher luminosity. Conclusions.The detection of pulsations shows that the source did not enter the “propeller” regime, even though the source flux of4.15×10−10erg cm−2s−1was almost one order of magnitude below the threshold for the propeller regime claimed in previous studies on this source. The transition into the propeller regime in GRO J1744−28 must therefore be below a luminosity of 3.2×1036erg s−1(3–50 keV), which implies a surface magnetic field.2.9×1011G and mass accretion rate.1.7×1016g s−1. A change of the CRSF depth as function of luminosity is not unexpected and has been observed in other sources. This result possibly implies a change in emission geometry as function of mass accretion rate to reduce the depth of the line below our detection limit.

Ole König↗

Plasmaspheric H+, He+, O+, He++, and O++ Densities and Temperatures

Thermal plasmaspheric densities and temperatures for five ion species have recently become available, even though these quantities were derived some time ago from the Retarding Ion Mass Spectrometer onboard the Dynamics Explorer 1 satellite over the years 1981-1984. The quantitative properties will be presented. Densities are found to have one behavior with lessor statistical variation below about L=2 and another with much greater variability above that Lshell. Temperatures also have a behavior difference between low and higher L-values. The density ratio He++/H+ is the best behaved with values of about 0.2% that slightly increase with increasing L. Unlike the He+/H+ density ratio that on average decreases with increasing Lvalue, the O+/H+ and O++/H+ density ratios have decreasing values below about L=2 and increasing average ratios at higher L-values. Hydrogen ion temperatures range from about 0.2 eV to several 10s of eV for a few measurements, although the bulk of the observations are of temperatures below 3 eV, again increasing with L-value. The temperature ratios of He+/H+ are tightly ordered around 1.0 except for the middle plasmasphere between L=3.5 and 4.5 where He+ temperatures can be significantly higher. The temperatures of He++, O+, and O++ are consistently higher than H+.

Gallagher, D. L.↗

Plasmaspheric H+, He+, He++, O+, and O++ Densities and Temperatures

Thermal plasmaspheric densities and temperatures for five ion species have recently become available, even though these quantities were derived some time ago from the Retarding Ion Mass Spectrometer onboard the Dynamics Explorer 1 satellite over the years 1981-1984. The quantitative properties will be presented. Densities are found to have one behavior with lessor statistical variation below about L=2 and another with much greater variability above that Lshell. Temperatures also have a behavior difference between low and higher L-values. The density ratio He++/H+ is the best behaved with values of about 0.2% that slightly increase with increasing L. Unlike the He+/H+ density ratio that on average decreases with increasing Lvalue, the O+/H+ and O++/H+ density ratios have decreasing values below about L=2 and increasing average ratios at higher L-values. Hydrogen ion temperatures range from about 0.2 eV to several 10s of eV for a few measurements, although the bulk of the observations are of temperatures below 3 eV, again increasing with L-value. The temperature ratios of He+/H+ are tightly ordered around 1.0 except for the middle plasmasphere between L=3.5 and 4.5 where He+ temperatures can be significantly higher. The temperatures of He++, O+, and O++ are consistently higher than H+.

Gallagher, G. L.↗

Local Versus Remote Contributions of Soil Moisture to Near-Surface Temperature Variability

Soil moisture variations have a straightforward impact on overlying air temperatures, wetter soils can induce higher evaporative cooling of the soil and thus, locally, cooler temperatures overall. Not known, however, is the degree to which soil moisture variations can affect remote air temperatures through their impact on the atmospheric circulation. In this talk we describe a two-pronged analysis that addresses this question. In the first segment, an extensive ensemble of NASA/GSFC GEOS-5 atmospheric model simulations is analyzed statistically to isolate and quantify the contributions of various soil moisture states, both local and remote, to the variability of air temperature at a given local site. In the second segment, the relevance of the derived statistical relationships is evaluated by applying them to observations-based data. Results from the second segment suggest that the GEOS-5-based relationships do, at least to first order, hold in nature and thus may provide some skill to forecasts of air temperature at subseasonal time scales, at least in certain regions.

Koster, R.↗

Time-Frequency Analysis of Rocket Nozzle Wall Pressures During Start-up Transients

Surveys of the fluctuating wall pressure were conducted on a sub-scale, thrust- optimized parabolic nozzle in order to develop a physical intuition for its Fourier-azimuthal mode behavior during fixed and transient start-up conditions. These unsteady signatures are driven by shock wave turbulent boundary layer interactions which depend on the nozzle pressure ratio and nozzle geometry. The focus however, is on the degree of similarity between the spectral footprints of these modes obtained from transient start-ups as opposed to a sequence of fixed nozzle pressure ratio conditions. For the latter, statistically converged spectra are computed using conventional Fourier analyses techniques, whereas the former are investigated by way of time-frequency analysis. The findings suggest that at low nozzle pressure ratios -- where the flow resides in a Free Shock Separation state -- strong spectral similarities occur between fixed and transient conditions. Conversely, at higher nozzle pressure ratios -- where the flow resides in Restricted Shock Separation -- stark differences are observed between the fixed and transient conditions and depends greatly on the ramping rate of the transient period. And so, it appears that an understanding of the dynamics during transient start-up conditions cannot be furnished by a way of fixed flow analysis.

Baars, Woutijn J.↗

Determination of Uncertainties for Analytically Derived Material Properties to Be Used in Monte Carlo Based Orion Heatshield Sizing

Ablative materials are often used for spacecraft heatshields to protect underlying structures from the extreme environments associated with atmospheric reentry. NASA's Orion EM-1 capsule has been designed to use a molded Avcoat material system. In order to determine the required heatshield thickness, a Monte Carlo approach to the sizing process was proposed. To perform the Monte Carlo simulation, statistical uncertainties on all material property input parameters were required. Obtaining these values for measured properties is straightforward, however input parameters that are derived analytically have historically used uncertainties based on engineering judgment. A MATLAB program was created to use laboratory generated thermogravimetric analysis (TGA) data to calculate uncertainties on the Arrhenius parameters for molded Avcoat. Uncertainties associated with the normalized ablation rate and pyrolysis gas enthalpy were also generated using a wrapper script and the ACE code. These uncertainties could then be tied directly to measured values of individual elemental constituents. The resulting uncertainty values will allow for a probabilistic sizing approach on molded Avcoat with a higher level of confidence in the input parameters.

material property uncertainties↗

Population Pharmacokinetics of Intranasal Scopolamine

Introduction: An intranasal gel dosage formulation of scopolamine (INSCOP) was developed for the treatment of Space Motion Sickness (SMS).The bioavailability and pharmacokinetics (PK) was evaluated using data collected in Phase II IND protocols. We reported earlier statistically significant gender differences in PK parameters of INSCOP at a dose level of 0.4 mg. To identify covariates that influence PK parameters of INSCOP, we examined population covariates of INSCOP PK model for 0.4 mg dose. Methods: Plasma scopolamine concentrations versus time data were collected from 20 normal healthy human subjects (11 male/9 female) after a 0.4 mg dose. Phoenix NLME was employed for PK analysis of these data using gender, body weight and age as covariates for model selection. Model selection was based on a likelihood ratio test on the difference of criteria (-2LL). Statistical significance for base model building and individual covariate analysis was set at P less than 0.05{delta(-2LL)=3.84}. Results: A one-compartment pharmacokinetic model with first-order elimination best described INSCOP concentration ]time profiles. Inclusion of gender, body weight and age as covariates individually significantly reduced -2LL by the cut-off value of 3.84(P less than 0.05) when tested against the base model. After the forward stepwise selection and backward elimination steps, gender was selected to add to the final model which had significant influence on absorption rate constant (ka) and the volume of distribution (V) of INSCOP. Conclusion: A population pharmacokinetic model for INSCOP has been identified and gender was a significant contributing covariate for the final model. The volume of distribution and Ka were significantly higher in males than in females which confirm gender-dependent pharmacokinetics of scopolamine after administration of a 0.4 mg dose.

Wu, L.↗

Allowables for Structural Composites

In order to obtain the most benefit from building a structure with composite laminates, the strength of the laminate must be known. Based on the "weakest link" theory, the lower strength numbers obtained from testing are the ones to be used for design and analysis. The strength value to be used is determined by a statistical analysis of the test data, and is known as an allowable. MIL-HDBK- 17 outlines procedures to follow for determining these allowables. There are two types of statistically determined allowables, A- Basis and B-Basis. A-Basis is defined as a strength value at which only 1 in 100 specimens will fail with a 95% confidence level. B-Basis is a strength value at which only 10 in 100 specimens will fail with a 95% confidence level. As more specimens are tested a higher value of strength can be used as a valid allowable. Composites are highly process dependent and show much strength variation with environment, so it is critical to test materials and environments that are representative of hardware. Either using data obtained from a previous test series, or extrapolation to a certain temperature is highly discouraged.

Nettles, Alan T.↗

Motion sickness and proprioceptive aftereffects following virtual environment exposure

To study the potential aftereffects of virtual environments (VE), tests of visually guided behavior and felt limb position (pointing with eyes open and closed) along with self-reports of motion sickness-like discomfort were administered before and after 30 min exposure of 34 subjects. When post- discomfort was compared to a pre-baseline, the participants reported more sickness afterward (p < 0.03). The change in felt limb position resulted in subjects pointing higher (p < 0.038) and slightly to the left, although the latter difference was not statistically significant (p = 0.08). When findings from a second study using a different VE system were compared, they essentially replicated the results of the first study with higher sickness afterward (p < 0.001) and post- pointing errors were also up (p < 0.001) and to the left (p < 0.001). While alternative explanations (e.g. learning, fatigue, boredom, habituation, etc.) of these outcomes cannot be ruled out, the consistency of the post- effects on felt limb position changes in the two VE implies that these recalibrations may linger once interaction with the VE has concluded, rendering users potentially physiologically maladapted for the real world when they return. This suggests there may be safety concerns following VE exposures until pre-exposure functioning has been regained. The results of this study emphasize the need for developing and using objective measures of post-VE exposure aftereffects in order to systematically determine under what conditions these effects may occur.

NASA Discipline Neuroscience↗

The metallicity of M4: Accurate spectroscopic fundamental parameters for four giants

High-quality spectra, covering the wavelength range 5480 to 7080 A, have been obtained for four giant stars in the intermediate-metallicity CN-bimodal globular cluster M4 (NGC 6121). We have employed a model atmosphere analysis that is entirely independent from cluster parameters, such as distance, age, and reddening, in order to derive accurate values for the stellar parameters effective temperature, surface gravity, and microturbulence, and for the abundance of iron relative to the Sun, (Fe/H), and of calcium, Ca/H, for each of the four stars. Detailed radiative transfer and statistical equilibrium calculations carried out for iron and calcium suggest that departures from local thermodynamic equilibrium are not significant for the purposes of our analysis. The spectroscopically derived effective temperatures for our program stars are hotter by about 200 K than existing photometric calibrations suggest. We conclude that this is due partly to the uncertain reddening of M4 and to the existing photometric temperature calibration for red giants being too cool by about 100 K. Comparison of our spectroscopic and existing photometric temperatures supports the prognosis of a significant east-west gradient in the reddening across M4. Our derived iron abundances are slightly higher than previous high-resolution studies suggested; the differences are most probably due to the different temperature scale and choice of microturbulent velocities adopted by earlier workers. The resulting value for the metallicity of M4 is (Fe/H )(sub M4) = -1.05 + or - 0.15. Based on this result, we suggest that metallicities derived in previous high-dispersion globular cluster abundance analyses could be too low by 0.2 to 0.3 dex. Our calcium abundances suggest an enhancement of calcium, an alpha element, over iron, relative to the Sun, in M4 of (Ca/H) = 0.23.

Drake, J. J.↗

Monitoring of MLS Measurements for Ozone Data Assimilation

The ozone data assimilation system at the NASA Goddard Space Flight Center Data Assimilation Office (DAO) has operationally provided near real time global three dimensional analyzed ozone fields since December 1999. Presently, 4 system assimilates both total column ozone and profile measurements from the NOAA - 16 SBUV/2 instrument into an off-line transport model using a physical space statistical analysis scheme (PS AS). Recently, this system was modified to investigate a possible impact from including MLS profile observations. Over a period from December 13, 1991 to March 1, 1992 the system assimilated both NOAA 11 SBUV/2 profile measurements and TOMS total column measurements. Short term ozone forecasts were produced and compared to MLS observations. The resulting observed -minus -forecast (O-F) residuals were studied regionally (by both latitude bands and pressure levels) in order to explore the potential impact of MLS observations on the assimilation and sensitivity to the UARS yaw maneuver and other instrument and algorithm characteristics. In addition, MLS profiles were compared to nearest neighbor SBUV and analysis profiles. In the tropics, analyzed ozone values tend to be too high from 1-3 hPa and too low from 10-20 hPa. MLS measurements in these regions tend be lower and higher (respectively) than forecast ozone values. This indicates that assimilating MLS measurements may improve, analysis results in these areas. Further, nearest neighbor profile comparisons in the southern high latitudes indicate that laminar features present in the analysis but not present in SBUV measurements, are also present in MLS measurements. This, together with the availability of MLS measurements in polar night regions indicates that assimilating MLS measurements in polar night regions indicates that assimilating MLS measurements may improve analyzed ozone values in high latitudes.

Winslow, Nathan↗

Evaluation of Standard Gear Metrics in Helicopter Flight Operation

Each false alarm made by a machine monitoring system carries a high price tag. The machine must be taken out of service, thoroughly inspected with possible disassembly, and then made ready for service. Loss of use of the machine and the efforts to inspect it are costly. In addition, if a monitoring system is prone to false alarms, the system will soon be turned off or ignored. For aircraft applications, one growing concern is that the dynamic flight environment differs from the laboratory environment where fault detection methods are developed and tested. Vibration measurements made in flight are less stationary than those made in a laboratory, or test facility, and thus a given fault detection method may produce more false alarms in flight than might be anticipated. In 1977. Stewart introduced several metrics, including FM0 and FM4, for evaluating the health of a gear. These metrics are single valued functions of the vibration signal that indicate if the signal deviates from an ideal model of the signal. FM0 is a measure of the ratio of the peak-to-peak level to the harmonic energy in the signal. FM4 is the kurtosis of the signal with the gear mesh harmonics and first order side bands removed. The underlying theory is that a vibration signal from a gear in good condition is expected to be dominated by a periodic signal at the gear mesh frequency. If one or a small number of gear teeth contain damage or faults, the signal will change, possibly showing increased amplitude, local phase changes or both near the damaged region of the gear. FM0 increases if a signal contains a local increase in amplitude. FM4 increases if a signal contains a local increase in amplitude or local phase change in a periodic signal. Over the years, other single value metrics were also introduced to detect the onset and growth of damage in gears. These various metrics have detected faults in several gear tests in experimental test rigs. Conditions in these tests have been steady state in the sense that the rpm, torque and forces on the gear have been held steady. For gears used in a dynamic environment such as that occurring in aircraft, the rpm, torque and forces on the gear are constantly changing. The authors have measured significant variation in rpm and torque in the transmissions of helicopters in controlled steady flight conditions flown by highly proficient test pilots. Statistical analyses of the data taken in flight show significant nonstationarity in the vibration measurements. These deviations from stationarity may increase false alarms in gear monitoring during aircraft flight. In the proposed paper, the authors will study vibration measurements made in flight on an AH- 1 Cobra and an OH-58C Kiowa helicopters. The primary focus will be the development of a methodology to assess the impact of nonstationarity on false alarms. Issues to be addressed include how time synchronous averages are constructed from raw data as well as how lack of stationarity effects the behavior of single value metrics. Emphasis will be placed on the occurrence of false alarms with the use of standard metrics. In order to maintain an acceptable level of false alarms in the flight environment, this study will also address the determination of appropriate threshold levels, which may need to be higher than for test rigs.

Mosher, M.↗

Flare Statistics for Young Stars from a Convolutional Neural Network Analysis of TESS Data

All-sky photometric time-series missions have allowed for the monitoring of thousands of young (t(age) < 800 Myr) stars in order to understand the evolution of stellar activity. Here, we developed a convolutional neural network (CNN), stella, specifically trained to find flares in Transiting Exoplanet Survey Satellite (TESS) short-cadence data. We applied the network to 3200 young stars in order to evaluate flare rates as a function of age and spectral type. The CNN takes a few seconds to identify flares on a single light curve. We also measured rotation periods for 1500 of our targets and find that flares of all amplitudes are present across all spot phases, suggesting high spot coverage across the entire surface. Additionally, flare rates and amplitudes decrease for stars t(age) > 50 Myr across all temperatures T(eff) ≥ 4000 K, while stars from 2300 ≤ T(eff) < 4000 K show no evolution across 800 Myr. Stars of T(eff) ≤ 4000 K also show higher flare rates and amplitudes across all ages. We investigate the effects of high flare rates on photoevaporative atmospheric mass loss for young planets. In the presence of flares, planets lose 4%–7% more atmosphere over the first 1 Gyr. stella is an open-source Python toolkit hosted on GitHub and PyPI.

Adina D. Feinstein↗

Comments on Lambeck and Coleman - 'The earth's shape and gravity field: A report of progress from 1958 to 1982'

The accuracy and validation of global gravity models based on satellite data are discussed, responding to the statistical analysis of Lambeck and Coleman (1983) (LC). Included are an evaluation of the LC error spectra, a summary of independent-observation calibrations of the error estimates of the Goddard Earth Models (GEM) 9 and L2 (Lerch et al., 1977, 1979, 1982, 1983, and 1985), a comparison of GEM-L2 with GRIM-3B (Reigber et al., 1983), a comparison of recent models with LAGEOS laser ranging, and a summary of resonant-orbit model tests. It is concluded that the accuracy of GEMs 9, 10, and L2 is much higher than claimed by LC, that the GEMs are in good agreement with independent observations and with GRIM-3B, and that the GEM calibrations were adequate. In a reply by LC, a number of specific questions regarding the error estimates are addressed, and it is pointed out that the intermodel discrepancies of the greatest geophysical interest are those in the higher-order coefficients, not discussed in the present comment. It is argued that the differences among the geoid heights of even the most recent models are large enough to call for considerable improvements.

Lerch, F. J.↗