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At least 397 records · Page 22

Study of MPLNET-Derived Aerosol Climatology over Kanpur, India, and Validation of CALIPSO Level 2 Version 3 Backscatter and Extinction Products

The level 2 aerosol backscatter and extinction profiles from the NASA Micropulse Lidar Network (MPLNET) at Kanpur, India, have been studied from May 2009 to September 2010. Monthly averaged extinction profiles from MPLNET shows high extinction values near the surface during October March. Higher extinction values at altitudes of 24 km are observed from April to June, a period marked by frequent dust episodes. Version 3 level 2 Cloud Aerosol Lidar with Orthogonal Polarization (CALIOP) aerosol profile products have been compared with corresponding data from MPLNET over Kanpur for the above-mentioned period. Out of the available backscatter profiles, the16 profiles used in this study have time differences less than 3 h and distances less than 130 km. Among these profiles, four cases show good comparison above 400 m with R2 greater than 0.7. Comparison with AERONET data shows that the aerosol type is properly identified by the CALIOP algorithm. Cloud contamination is a possible source of error in the remaining cases of poor comparison. Another source of error is the improper backscatter-to-extinction ratio, which further affects the accuracy of extinction coefficient retrieval.

extinction profiles↗

High-Resolution Forest Canopy Height Estimation in an African Blue Carbon Ecosystem

Mangrove forests are one of the most productive and carbon dense ecosystems that are only found at tidally inundated coastal areas. Forest canopy height is an important measure for modeling carbon and biomass dynamics, as well as land cover change. By taking advantage of the flat terrain and dense canopy cover, the present study derived digital surface models (DSMs) using stereophotogrammetric techniques on high-resolution spaceborne imagery (HRSI) for southern Mozambique. A mean-weighted ground surface elevation factor was subtracted from the HRSI DSM to accurately estimate the canopy height in mangrove forests in southern Mozambique. The mean and H100 tree height measured in both the field and with the digital canopy model provided the most accurate results with a vertical error of 1.18-1.84 m, respectively. Distinct patterns were identified in the HRSI canopy height map that could not be discerned from coarse shuttle radar topography mission canopy maps even though the mode and distribution of canopy heights were similar over the same area. Through further investigation, HRSI DSMs have the potential of providing a new type of three-dimensional dataset that could serve as calibration/validation data for other DSMs generated from spaceborne datasets with much larger global coverage. HSRI DSMs could be used in lieu of Lidar acquisitions for canopy height and forest biomass estimation, and be combined with passive optical data to improve land cover classifications.

HRSI↗

Simulating nonlinear optical processes on a superconducting quantum device

Simulating plasma physics on quantum computers is difficult because most problems of interest are nonlinear, but quantum computers are not naturally suitable for nonlinear operations. In weakly nonlinear regimes, plasma problems can be modelled as wave–wave interactions. In this paper, we develop a quantization approach to convert nonlinear wave–wave interaction problems to Hamiltonian simulation problems. We demonstrate our approach using two qubits on a superconducting device. Unlike a photonic device, a superconducting device does not naturally have the desired interactions in its native Hamiltonian. Nevertheless, Hamiltonian simulations can still be performed by decomposing required unitary operations into native gates. To improve experimental results, we employ a range of error-mitigation techniques. Apart from readout error mitigation, we use randomized compilation to transform undiagnosed coherent errors into well-behaved stochastic Pauli channels. Moreover, to compensate for stochastic noise, we rescale exponentially decaying probability amplitudes using rates measured from cycle benchmarking. We carefully consider how different choices of product-formula algorithms affect the overall error and show how a trade-off can be made to best utilize limited quantum resources. This study provides an example of how plasma problems may be solved on near-term quantum computing platforms.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Rayleigh/raman Lidars: Intercomparisons and Validation

Vertical sounding of the atmosphere by Rayleigh lidar was exclusively used in France to study the structure, the dynamics as well as the long term trend of the middle atmosphere. More recently, the addition of a rotational-Raman mode fills the gap between the ground and 30 km in such a way that the whole altitude range from ground up to 90-100 km can be studied with a unique instrument. The growing need of absolute measurement of temperature with high precision for climatic purpose led us to perform critical review of all the sources of error which can occur in this type of measurement. This is the subject of a recent paper which shows that the increase of the performances of the instrument in the last decade was successfully obtained without compromising the accuracy. It is briefly reviewed. Concern is with the presentation of the recent improvements of the technique and of the results of intercomparisons and validation of new satellites data.

Chanin, Marie-Lise↗

Merging IceSAT GLAS and Terra MODIS Data in Order to Derive Forest Type Specific Tree Heights in the Central Siberian Boreal Forest

Mapping of boreal forest's type, biomass, and other structural parameters are critical for understanding of the boreal forest's significance in the carbon cycle, its response to and impact on global climate change. We believe the nature of the forest structure information available from MISR and GLAS can be used to help identify forest type, age class, and estimate above ground biomass levels beyond that now possible with MODIS alone. The ground measurements will be used to develop relationships between remote sensing observables and forest characteristics and provide new information for understanding forest changes with respect to environmental change. Lidar is a laser altimeter that determines the distance from the instrument to the physical surface by measuring the time elapsed between the pulse emission and the reflected return. Other studies have shown that the returned signal may identify multiple returns originating from trees, building and other objects and permits the calculation of their height. Studies using field data have shown that lidar data can provide estimates of structural parameters such as biomass, stand volume and leaf area index and allows remarkable differentiation between primary and secondary forest. NASA's IceSAT Geoscience Laser Altimeter System (GLAS) was launched in January 2003 and collected data during February and September of that year. This study used data acquired over our study sites in central Siberia to examine the GLAS signal as a source of forest height and other structural characteristics. The purpose of our Siberia project is to improve forest cover maps and produce above-ground biomass maps of the boreal forest in Northern Eurasia from MODIS by incorporating structural information inherent in the Terra MISR and ICESAT Geoscience Laser Altimeter System (GLAS) instruments. A number of forest cover classifications exist for the boreal forest. We believe the limiting factor in these products is the lack of structural information, particularly in the vertical dimension. The emphasis of this project is to improve upon satellite maps of boreal forest structure parameters (i.e. height and biomass) using temporal, multi-angle, and vertical profile information of GLAS data. The existing and near future lidar data is useful for demonstrating these techniques and pursuing current estimates. Future lidar missions may be several years in the future, so we will work other new data sets that may aide in biomass estimates such as ALOS PALSAR We will continue this work to produce an accurate map of current above ground forest phytomass/carbon storage possible for the study area. We plan to develop, test, and integrate remote sensing methods for extracting forest canopy structure measures. We are compiling our field measurements and will compare them with the remote sensing methods where possible. We also be able to produce a realistic error bound on the remotely sensed carbon estimates.

Ranson, K. Jon↗

Shape from spectra

We introduce a new unified atmospheric–topographic correction approach that estimates surface geometry directly from the radiance measurement. Surface topography influences the at-sensor radiance measurement, making precise topography modeling critical in applications like vegetation or snow studies in mountainous terrain. Currently, elevation maps are used to derive topographic variables such as the slope and sky-view factor. This process is error-prone since static global digital elevation models do not generally achieve the accuracy required, and even minor mismatches in spatial resolution can introduce significant artifacts in downstream processing. Here we demonstrate that it is possible to estimate topographic parameters directly from spectral data, ensuring perfect physical consistency, temporal coincidence, and spatial alignment. We present experiments estimating topographic slope in two scenes in Southern California, with data from NASA’s Next Generation Airborne Visible/Near Infrared Imaging Spectrometer (AVIRIS-NG). We compared our radiance-based estimates against high-resolution lidar datasets. Our initial validation result showed a correlation of R 2 = 0.864 (n = 160) over the homogeneous surface of Beckman Auditorium’s cone-shaped roof on the Caltech campus in Pasadena, California. We then validate the model over a larger study site near Santa Clarita, California, finding R 2 = 0.923 (n = 40,000) in a 350 x 350m area. The accuracy of our model estimates, combined with its systematic advantages over the alternative, show the potential of the approach for use in both airborne campaigns and orbital missions.

Nimrod Carmon↗

Potential Basin-Scale Estimates of Arctic Snow Depth with Sea Ice Freeboards from CryoSat-2 and ICESat-2: An Exploratory Analysis

The potential of deriving snow depth estimates using differences in freeboard heights from CryoSat-2 (CS-2) and ICESat-2 (IS-2) is examined. In our analysis, we use lidar freeboard from the Airborne Topographic Mapper (ATM) on Operation IceBridge (OIB) as proxy of IS-2 total (snow plus ice) freeboard. Snow depths are estimates from the OIB snow radar. Differences in height between the total (ATM) and ice (CS-2) freeboards are related to snow depth by the refractive index of the snow layer, which is dependent on snow density. For two years (2014 and 2015), regression of the ATM and CS-2 freeboard differences against OIB snow depth gives correlations of approximately 0.80, estimated eta (sub s) of 1.21, and standard errors of 8 centimeters. The resulting refractive index, eta (sub s), can be compared to that expected of the Arctic snow cover in early spring (1.25 plus or minus 0.05). The expected biases and variability in the regression analysis are discussed. Results suggest that snow depth can be estimated from the freeboard differences. The benefits of adjusting the orbit of CS-2 for providing more optimized overlaps between IS-2 and CS-2 are considered.

Sea ice↗

Regime Characterization of Offshore Wind Resource Using Unsupervised Learning

Predictability of wind resource conditions is critical for offshore wind design and operations. While many studies of extreme wind conditions focus on specific events such as low-level jets or ramps, these rely on threshold definitions that limit generality. Here we present a data-driven framework that combines principal component analysis (PCA), self-organizing maps (SOM), and k-means clustering to classify wind resource conditions as typical and anomalous from climatological data. Anomalies are defined not by fixed thresholds but by flagging samples located far from SOM node centers inside the baseline SOM structure. This reframes extremes as rare ebents and hence, likely difficult to anticipate by numerical weather prediction models. We applied this approach to 23 years (2000–2022) of hourly profiles from the NOW-23 hindcast model at the Humboldt Wind Energy Area. Classification is conducted on a feature space consisting of 10 m wind speed and direction, bulk shear and veer across 30–270 m, and a low-level jet index. Dimensionality reduction is achieved through PC. A 2 × 3 OM lattice trained on the PCA vectors identified six baseline regimes spanning weak to strong flow states. High quantization-error profiles are identified and re-clustered into four anomalous regimes. The baseline regimes exhibited clear seasonal and diurnal cycles. Meanwhile, the anomalous regimes represented <10 % of all hours but showed distinct combinations of speed, shear, and veer, when compared to the baseline regimes. Anomalous regimes are typically short-lived (~few hours), yet their transitions can lead to hub-height wind changes of −18 to +9 m s -1 . For a representative 15 MW turbine, these shifts imply rapid swings in capacity factor from near-full output to negligible generation. Validation with lidar buoy data showed 51% agreement in SOM labels across ~6,000 overlapping hours, with most mismatches confined to adjacent speed classes. HRRR comparisons further revealed that anomalous regimes were disproportionately associated with forecast biases exceeding 5 m s -1 . Together, these results reframe extremes in offshore wind from absolute maxima or minima to weather states that are difficult to anticipate from models.

17 WIND ENERGY↗

Can reanalysis products outperform mesoscale numerical weather prediction models in modeling the wind resource in simple terrain?

Mesoscale numerical weather prediction (NWP) models are generally considered more accurate than reanalysis products in characterizing the wind resource at heights of interest for wind energy, given their finer spatial resolution and more comprehensive physics. However, advancements in the latest ERA-5 reanalysis product motivate an assessment on whether ERA-5 can model wind speeds as well as a state-of-the-art NWP model – the Weather Research and Forecasting (WRF) Model. We consider this research question for both simple terrain and offshore applications. Specifically, we compare wind profiles from ERA-5 and the preliminary WRF runs of the Wind Integration National Dataset (WIND) Toolkit Long-term Ensemble Dataset (WTK-LED) to those observed by lidars at a site in Oklahoma, United States, and in a United States Atlantic offshore wind energy area. We find that ERA-5 shows a significant negative bias (~-1ms-1) at both locations, with a larger bias at the land-based site. WTK-LED-predicted wind speed profiles show a limited negative bias (~-0.5ms-1) offshore and a slight positive bias (~+0.5ms-1) at the land-based site. On the other hand, we find that ERA-5 outperforms WTK-LED in terms of the centered root-mean-square error (cRMSE) and correlation coefficient, for both the land-based and offshore cases, in all atmospheric stability conditions. We find that WTK-LED's higher cRMSE is caused by its tendency to overpredict the amplitude of the wind speed diurnal cycle. At the land-based site, this is partially caused by wind plant wake effects not being accurately captured by WTK-LED.

17 WIND ENERGY↗

Space-based Doppler lidar sampling strategies: Algorithm development and simulated observation experiments

Lidar Atmospheric Wind Sounder (LAWS) Simulation Models (LSM) were developed to evaluate the potential impact of global wind observations on the basic understanding of the Earth's atmosphere and on the predictive skills of current forecast models (GCM and regional scale). Fully integrated top to bottom LAWS Simulation Models for global and regional scale simulations were developed. The algorithm development incorporated the effects of aerosols, water vapor, clouds, terrain, and atmospheric turbulence into the models. Other additions include a new satellite orbiter, signal processor, line of sight uncertainty model, new Multi-Paired Algorithm and wind error analysis code. An atmospheric wind field library containing control fields, meteorological fields, phenomena fields, and new European Center for Medium Range Weather Forecasting (ECMWF) data was also added. The LSM was used to address some key LAWS issues and trades such as accuracy and interpretation of LAWS information, data density, signal strength, cloud obscuration, and temporal data resolution.

Emmitt, G. D.↗

Tolerancing the LITE optical system

This paper describes the optical system used in the Lidar In-Space Technology Experiment (LITE) and presents the results of a study designed to generate a tolerance budget for the LITE, using the combination of manual and Monte Carlo tolerancing techniques utilizing the SYNOPSYS optical analysis program. The tolerance budget derived for LITE, including the contributions of both the fabrication and the alignment of the optical-path elements, are presented. It is shown that the nature of the design allows for typical optical shop tolerances of about 5 mils of despace and decenter, 0.1 deg of tilt, and about 5 fringes of surface figure error.

Wilson, Mark E.↗

Global Monitoring of Clouds and Aerosols Using a Network of Micro-Pulse Lidar Systems

Long-term global radiation programs, such as AERONET and BSRN, have shown success in monitoring column averaged cloud and aerosol optical properties. Little attention has been focused on global measurements of vertically resolved optical properties. Lidar systems are the preferred instrument for such measurements. However, global usage of lidar systems has not been achieved because of limits imposed by older systems that were large, expensive, and logistically difficult to use in the field. Small, eye-safe, and autonomous lidar systems are now currently available and overcome problems associated with older systems. The first such lidar to be developed is the Micro-pulse lidar System (MPL). The MPL has proven to be useful in the field because it can be automated, runs continuously (day and night), is eye-safe, can easily be transported and set up, and has a small field-of-view which removes multiple scattering concerns. We have developed successful protocols to operate and calibrate MPL systems. We have also developed a data analysis algorithm that produces data products such as cloud and aerosol layer heights, optical depths, extinction profiles, and the extinction-backscatter ratio. The algorithm minimizes the use of a priori assumptions and also produces error bars for all data products. Here we present an overview of our MPL protocols and data analysis techniques. We also discuss the ongoing construction of a global MPL network in conjunction with the AERONET program. Finally, we present some early results from the MPL network.

Welton, Ellsworth J.↗

MODIS 3 Km Aerosol Product: Applications over Land in an Urban/suburban Region

MODerate resolution Imaging Spectroradiometer (MODIS) instruments aboard the Terra and Aqua satellites have provided a rich dataset of aerosol information at a 10 km spatial scale. Although originally intended for climate applications, the air quality community quickly became interested in using the MODIS aerosol data. However, 10 km resolution is not sufficient to resolve local scale aerosol features. With this in mind, MODIS Collection 6 is including a global aerosol product with a 3 km resolution. Here, we evaluate the 3 km product over the Baltimore/Washington D.C., USA, corridor during the summer of 2011, by comparing with spatially dense data collected as part of the DISCOVER-AQ campaign these data were measured by the NASA Langley Research Center airborne High Spectral Resolution Lidar (HSRL) and a network of 44 sun photometers (SP) spaced approximately 10 km apart. The HSRL instrument shows that AOD can vary by up to 0.2 within a single 10 km MODIS pixel, meaning that higher resolution satellite retrievals may help to characterize aerosol spatial distributions in this region. Different techniques for validating a high-resolution aerosol product against SP measurements are considered. Although the 10 km product is more statistically reliable than the 3 km product, the 3 km product still performs acceptably, with more than two-thirds of MODIS/SP collocations falling within the expected error envelope with high correlation (R > 0.90). The 3 km product can better resolve aerosol gradients and retrieve closer to clouds and shorelines than the 10 km product, but tends to show more significant noise especially in urban areas. This urban degradation is quantified using ancillary land cover data. Overall, we show that the MODIS 3 km product adds new information to the existing set of satellite derived aerosol products and validates well over the region, but due to noise and problems in urban areas, should be treated with some degree of caution.

MODIS↗

Calibration and Validation of Landsat Tree Cover in the Taiga-Tundra Ecotone

Monitoring current forest characteristics in the taiga-tundra ecotone (TTE) at multiple scales is critical for understanding its vulnerability to structural changes. A 30 m spatial resolution Landsat-based tree canopy cover map has been calibrated and validated in the TTE with reference tree cover data from airborne LiDAR and high resolution spaceborne images across the full range of boreal forest tree cover. This domain-specific calibration model used estimates of forest height to determine reference forest cover that best matched Landsat estimates. The model removed the systematic under-estimation of tree canopy cover greater than 80% and indicated that Landsat estimates of tree canopy cover more closely matched canopies at least 2 m in height rather than 5 m. The validation improved estimates of uncertainty in tree canopy cover in discontinuous TTE forests for three temporal epochs (2000, 2005, and 2010) by reducing systematic errors, leading to increases in tree canopy cover uncertainty. Average pixel-level uncertainties in tree canopy cover were 29.0%, 27.1% and 31.1% for the 2000, 2005 and 2010 epochs, respectively. Maps from these calibrated data improve the uncertainty associated with Landsat tree canopy cover estimates in the discontinuous forests of the circumpolar TTE.

Montesano, Paul Mannix↗

Lidar observation of ozone over Tsukuba (36 deg N, 140 deg E)

An ozone lidar system was installed at the National Institute for Environmental Studies (NIES) in Tsukuba, Japan in March 1988 and has been measuring vertical profiles of ozone (15 - 45 km) since September 1988. The lidar system consists of a XeCl (308 nm) excimer laser, its deuterium Raman shifter (339 nm), a XeF excimer laser (351 nm), a 2 m telescope, a receiving system and a data processing system. The precision of the derived ozone concentration is about 10 percent of an altitude of 40 km for a 4 hr observation. Temperature profiles (30 - 80 km) are also obtained from the Rayleigh scattering signals at 351 nm. Approximate 50 ozone measurements are carried out in a year and variations of vertical profiles of ozone such as seasonal variations and shorter-term variations are observed. Systematic errors due to aerosols had been negligible until the arrival of the stratospheric aerosols injected by the eruption of Mt. Pinatubo. Effects of the volcanic aerosols on ozone measurements depend on the differences between wavelengths used as the on- and off-resonance.

Nakane, H.↗

Surface Irradiances Consistent With CERES-Derived Top-of-Atmosphere Shortwave and Longwave Irradiances

The estimate of surface irradiance on a global scale is possible through radiative transfer calculations using satellite-retrieved surface, cloud, and aerosol properties as input. Computed top-of-atmosphere (TOA) irradiances, however, do not necessarily agree with observation-based values, for example, from the Clouds and the Earth's Radiant Energy System (CERES). This paper presents amethod to determine surface irradiances using observational constraints of TOA irradiance from CERES. A Lagrange multiplier procedure is used to objectively adjust inputs based on their uncertainties such that the computed TOA irradiance is consistent with CERES-derived irradiance to within the uncertainty. These input adjustments are then used to determine surface irradiance adjustments. Observations by the Atmospheric Infrared Sounder (AIRS), Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO), CloudSat, andModerate Resolution Imaging Spectroradiometer (MODIS) that are a part of the NASA A-Train constellation provide the uncertainty estimates. A comparison with surface observations from a number of sites shows that the bias [root-mean-square (RMS) difference] between computed and observed monthlymean irradiances calculated with 10 years of data is 4.7 (13.3) W/sq m for downward shortwave and 22.5 (7.1) W/sq m for downward longwave irradiances over ocean and 21.7 (7.8) W m22 for downward shortwave and 21.0 (7.6) W/sq m for downward longwave irradiances over land. The bias andRMS error for the downward longwave and shortwave irradiances over ocean are decreased from those without constraint. Similarly, the bias and RMS error for downward longwave over land improves, although the constraint does not improve downward shortwave over land. This study demonstrates how synergetic use of multiple instruments (CERES,MODIS, CALIPSO, CloudSat, AIRS, and geostationary satellites) improves the accuracy of surface irradiance computations.

Kato, Seiji↗

Radioactive Source Localization via Bayesian Particle Filter

In the event of a misplaced radioactive source or other emergency situation, measuring a radiation field, mapping its distribution, and determining a source location are essential tasks to ameliorating the situation. However, radiation fields may be extremely hazardous to human surveyors and minimizing received radiation doses is just as essential. Robots appear to be a potential solution to these problems. Beyond simply measuring radiation, the robot's computer processing capabilities offer a way to apply complex data analysis methods to radiation measurements in real-time. Methods which predict likely source locations can then feed this information into other processes, potentially improving path planning and enabling more efficient measurements. Given a robot mounted with a gamma-ray detector, can we: develop a methodology to account for detector performance across a wide range of source angles, distances, and photon energies? operate an autonomously navigating robot to effectively survey and characterize an area of interest? implement a data analysis method, conventionally used in measurements of motion, for source localization purposes? An open-source TurtleBot 3 robot, running Robot Operating System (ROS) on Ubuntu 16.04 LTS, was fitted with a Kromek GR1{sup R} Cadmium Zinc Telluride (CZT) solid-state gamma-ray detector. As a part of ROS, the packages OpenSlam, gmapping, and amcl were used to perform Simultaneous Localization and Mapping (SLAM), determining the robot's position and mapping the surrounding area. Data was acquired via Lidar mounted on top the TurtleBot 3. Detector Calibration Fit: The equation was fit to 365 counts of various energies, distances, and angles. A MATLAB{sup R} program was written to simulate measurements taken a robot on a random walk, with count data and positions discretized into finite element pixels. Using this program, a sample of 100 runs was performed on a map with a simulated source at the center, with a total of 200 of 2 pixels each. Similarly, multiple runs of the filter were performed on recorded robot measurement data. In both simulation and real tests, when corrected for errors (particles placed outside of bounds or on the robot, and simulation-specific errors), corresponding t-tests of predicted x and y-coordinates were within a 95% confidence interval of the actual position. For the real trial, these positions are slightly skewed right in the x-axis as the robot remained mainly to the left side of the source within the sample area. These simulations demonstrate potential validity for the usage of a particle filter as method of radioactive source localization. In the future, true real-time implementation and data fusion may further augment the performance of the robot to localize lost sources. Additionally, identification of multiple sources, determination of source types, and usage of a collimator are areas to potentially be explored.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Asteroid approach covariance analysis for the Clementine mission

The Clementine mission is designed to test Strategic Defense Initiative Organization (SDIO) technology, the Brilliant Pebbles and Brilliant Eyes sensors, by mapping the moon surface and flying by the asteroid Geographos. The capability of two of the instruments available on board the spacecraft, the lidar (laser radar) and the UV/Visible camera is used in the covariance analysis to obtain the spacecraft delivery uncertainties at the asteroid. These uncertainties are due primarily to asteroid ephemeris uncertainties. On board optical navigation reduces the uncertainty in the knowledge of the spacecraft position in the direction perpendicular to the incoming asymptote to a one-sigma value of under 1 km, at the closest approach distance of 100 km. The uncertainty in the knowledge of the encounter time is about 0.1 seconds for a flyby velocity of 10.85 km/s. The magnitude of these uncertainties is due largely to Center Finding Errors (CFE). These systematic errors represent the accuracy expected in locating the center of the asteroid in the optical navigation images, in the absence of a topographic model for the asteroid. The direction of the incoming asymptote cannot be estimated accurately until minutes before the asteroid flyby, and correcting for it would require autonomous navigation. Orbit determination errors dominate over maneuver execution errors, and the final delivery accuracy attained is basically the orbit determination uncertainty before the final maneuver.

Ionasescu, Rodica↗