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All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

Progress of the NASA ACE Mission Polarimeter Working Group Instrument Inter-Comparison

The NASA Aerosol-Cloud-Ecosystem (ACE) mission is a National Research Council Decadal Survey recommended mission that will contain an imaging polarimeter for remote sensing of aerosols and clouds. A variety of airborne polarimeter prototypes exist, so the ACE Polarimeter Working Group (ACEPWG) was formed to share information between groups and collectively work for improved measurement techniques, uncertainty characterization, and algorithm development. The initial focus has been on observations made during the Polarimeter Definition Experiment (PODEX), conducted in early 2013 in Southern California. Three ACE mission supported polarimeters were deployed on the high altitude ER-2 aircraft as it flew over a variety of targets. Two of those instruments to date have successfully produced Level 1 (geolocated radiance and polarization) data. Initial matched scene inter-comparisons found little radiometric, but significant polarimetric, bias. After improvement to geolocation in one instrument, and calibration in the other, polarimetric comparisons have improved significantly. We will describe these results, remaining unresolved issues, and future plans.

Polarimeter↗
DOE OSTI2025

Cosmological constraints from the Planck cluster catalogue with DES shear profiles and Chandra observations

We present cosmological constraints from the Planck PSZ2 cosmological cluster sample, using weak-lensing shear profiles from Dark Energy Survey (DES) data and X-ray observations from the Chandra telescope for the mass calibration. We compute hydrostatic mass estimates for all clusters in the PSZ2 sample with a scaling relation between their Sunyaev-Zeldovich signal and X-ray derived hydrostatic mass, calibrated with the Chandra data. We introduce a method to correct these masses with a hydrostatic mass bias using shear profiles from wide-field galaxy surveys. We simultaneously fit the number counts of the PSZ2 sample and the mass calibration with the DES data, finding $Ω_\text{m}=0.312^{+0.018}_{-0.024}$, $σ_8=0.777\pm 0.024$, $S_8\equiv σ_8 \sqrt{Ω_\text{m} / 0.3}=0.791^{+0.023}_{-0.021}$, and $(1-b)=0.844^{+0.055}_{-0.062}$ for our baseline analysis when combined with BAO data. When considering a hydrostatic mass bias evolving with mass, we find $Ω_\text{m}=0.353^{+0.025}_{-0.031}$, $σ_8=0.751\pm 0.023$, and $S_8=0.814^{+0.019}_{-0.020}$. We verify the robustness of our results by exploring a variety of analysis settings, with a particular focus on the definition of the halo centre used for the extraction of shear profiles. We compare our results with a number of other analyses, in particular two recent analyses of cluster samples obtained from SPT and eROSITA data that share the same mass calibration data set. We find that our results are in overall agreement with most late-time probes, in very mild tension with CMB results (1.6$σ$), and in significant tension with results from eROSITA clusters (2.9$σ$). We confirm that our mass calibration is consistent with the eROSITA analysis by comparing masses for clusters present in both Planck and eROSITA samples, eliminating it as a potential cause of tension.

Aymerich, G. [Orsay, IAS; AIM, Saclay] (ORCID:0009↗
DOE OSTI2025

Climate-extreme modeling framework for sustainable flood management in the Arabian Peninsula

Evaluating extreme precipitation events (EPEs) is essential for building climate-resilient water management strategies, but it remains a major challenge in ungauged basins. Using the 26,070 km 2 Wadi al-Rummah basin in central Saudi Arabia as a case study, we developed an alternative, reliable, cost-effective satellite-based framework that combines empirically derived EPE thresholds, imagery-calibrated 2D hydrodynamic modeling, GRACE water-storage diagnostics, and bias-corrected CMIP6 projections to assess flood hazards and recharge potential under current and future climate scenarios in ungauged basins. The integrated approach and the resulting findings followed four key steps: (1) Identified a 22.5 mm EPE threshold, the 80th percentile of 3-day GPM/IMERG rainfall (2000–2024), aligned with flood-triggering events (Nov 2018: 23–28 mm; Apr, 2023: 42 mm); (2) Developed and calibrated a RiverFlow2D model using Sentinel-2 and PlanetScope imagery for the November 2018 flood, accurately reproducing flood depth and extent (RMSE ≤0.31 m; fuzzy-Dice ≥0.91), and estimating runoff (41 %), infiltration (25 %), and evaporation (34 %); (3) Independently validated the model with the April 2023 event (RMSE ≤0.35 m; fuzzy-Dice ≥0.86); (4) Conducted climate projections (2025–2100) from five bias-corrected NEX-GDDP CMIP6 models that revealed a 34 % increase in EPE intensity under SSP2-4.5 and 48 % under SSP5-8.5 scenarios, relative to 20th-century baselines. Our findings indicate that while intensifying extremes in the 21st century increase flood risk, the results highlight the potential for episodic recharge if effective retention strategies are employed, and offer a transferable model for climate-informed planning in data-scarce arid regions.

CMIP6↗
NASA NTRS1994

Calibration of TOPEX/Poseidon at Platform Harvest

We present preliminary estimates for the mean bias of the TOPEX/Poseidon NASA altimeter (ALT) and the CNES altimeter (SSALT) using in situ data gathered at platform Harvest during the first 36 cycles of the mission. Data for 21 overflights of the ALT and 3 overflights of the SSALT have been analyzed.

TOPEX/Poseidon↗
NASA NTRS2016

Model Development for MODIS Thermal Band Electronic Crosstalk

MODerate-resolution Imaging Spectroradiometer (MODIS) has 36 bands. Among them, 16 thermal emissive bands covering a wavelength range from 3.8 to 14.4 m. After 16 years on-orbit operation, the electronic crosstalk of a few Terra MODIS thermal emissive bands developed substantial issues that cause biases in the EV brightness temperature measurements and surface feature contamination. The crosstalk effects on band 27 with center wavelength at 6.7 m and band 29 at 8.5 m increased significantly in recent years, affecting downstream products such as water vapor and cloud mask. The crosstalk effect is evident in the near-monthly scheduled lunar measurements, from which the crosstalk coefficients can be derived. The development of an alternative approach is very helpful for independent verification.In this work, a physical model was developed to assess the crosstalk impact on calibration as well as in Earth view brightness temperature retrieval. This model was applied to Terra MODIS band 29 empirically to correct the Earth brightness temperature measurements. In the model development, the detectors nonlinear response is considered. The impact of the electronic crosstalk is assessed in two steps. The first step consists of determining the impact on calibration using the on-board blackbody (BB). Due to the detectors nonlinear response and large background signal, both linear and nonlinear coefficients are affected by the crosstalk from sending bands. The second step is to calculate the effects on the Earth view brightness temperature retrieval. The effects include those from affected calibration coefficients and the contamination of Earth view measurements. This model links the measurement bias with crosstalk coefficients, detector non-linearity, and the ratio of Earth measurements between the sending and receiving bands. The correction of the electronic cross talk can be implemented empirically from the processed bias at different brightness temperature. The implementation can be done through two approaches. As routine calibration assessment for thermal infrared bands, the trending over select Earth scenes is processed for all the detectors in a band and the band averaged bias is derived at a certain time. In this case, the correction of an affected band can be made using the regression of the model with band averaged bias and then corrections of detector differences are applied. The second approach requires the trending for individual detectors and the bias for each detector is used for regression with the model. A test using the first approach was made for Terra MODIS band 29 with the biases derived from long-term trending of brightness temperature over ocean and Dome-C.

Chang, Tiejun↗
NASA NTRSDate not supplied

Evaluation of Aqua MODIS and S-NPP VIIRS Thermal Emissive Bands Calibration Stability Using Dome-C

Establishing the calibration consistency between satellite measurements is an essential step in the implementation of a long-term global monitoring plan, which often leads to sensor calibration improvements. The Suomi National Polar-Orbiting Partnership (S-NPP) Visible Infrared Imaging Radiometer Suite (VIIRS) is a polar-orbiting Earth remote sensing instrument built with a strong Moderate Resolution Imaging Spectroradiometer (MODIS) heritage. The center wavelengths of all VIIRS thermal emissive bands (TEBs) match well with those of MODIS with the exception of VIIRS TEB M15 (10.7μm). Previous work from the MODIS Characterization Support Team (MCST) at the NASA/GSFC used specific Earth surface targets to track the long-term consistency,stability, and relative bias between the two MODIS instruments onboard the Terra and Aqua satellites. Using similar methodologies, this paper evaluates the TEB calibration consistency between the MODIS instruments and S-NPP VIIRS over Dome Concordia (Dome-C). The Dome-C site is uniformly snow-covered and the atmospheric effects are small in the surrounding area. Near-surface air temperature measurements from an Automatic Weather Station (AWS) are used as a reference to track each sensor’s calibration stability and determine the relative bias between the MODIS and VIIRS instruments. The results of this study provide a quantitative assessment of the S-NPP VIIRS TEB mission-long performance.

MODIS↗
DOE OSTI2021

No Galaxy Left Behind: Measuring the Transfer Function of the Dark Energy Survey with Balrog

In this dissertation, we describe a calibration and diagnostic framework called Balrog which was used to directly sample the selection and photometric biases of the Dark Energy Survey (DES) Year 3 (Y3) dataset. We systematically inject onto the single-epoch images of a random 20% subset of the DES footprint an ensemble of nearly 30 million realistic galaxy models derived from DES Deep Field observations. These augmented images are analyzed in parallel with the original data to automatically inherit measurement systematics that are often too difficult to capture with traditional generative models. The resulting object catalog is a Monte Carlo sampling of the DES transfer function and is used as a powerful diagnostic and calibration tool for a variety of DES Y3 science, particularly for the calibration of the photometric redshifts of distant "source" galaxies and magnification biases of nearer "lens" galaxies. The recovered Balrog injections are shown to closely match the photometric property distributions of the fiducial Y3 GOLD catalog, particularly in color, and capture the number density fluctuations from observing conditions of the real data within 1% for a typical galaxy sample. We find that Y3 colors are extremely well calibrated, typically within ~1-8 millimagnitudes, but for a small subset of objects we detect significant magnitude biases correlated with large overestimates of the injected object size due to proximity effects and blending. Finally, we discuss approaches to extend the current methodology to capture more aspects of the transfer function for future analyses.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2012

A Nonlinear Adaptive Filter for Gyro Thermal Bias Error Cancellation

Deterministic errors in angular rate gyros, such as thermal biases, can have a significant impact on spacecraft attitude knowledge. In particular, thermal biases are often the dominant error source in MEMS gyros after calibration. Filters, such as J\,fEKFs, are commonly used to mitigate the impact of gyro errors and gyro noise on spacecraft closed loop pointing accuracy, but often have difficulty in rapidly changing thermal environments and can be computationally expensive. In this report an existing nonlinear adaptive filter is used as the basis for a new nonlinear adaptive filter designed to estimate and cancel thermal bias effects. A description of the filter is presented along with an implementation suitable for discrete-time applications. A simulation analysis demonstrates the performance of the filter in the presence of noisy measurements and provides a comparison with existing techniques.

Galante, Joseph M.↗
NASA NTRS2014

Optimization of a Radiative Transfer Forward Operator for Simulating SMOS Brightness Temperatures over the Upper Mississippi Basin, USA

The Soil Moisture and Ocean Salinity (SMOS) satellite mission is routinely providing global multi-angular observations of brightness temperature (TB) at both horizontal and vertical polarization with a 3-day repeat period. The assimilation of such data into a land surface model (LSM) may improve the skill of operational flood forecasts through an improved estimation of soil moisture (SM). To accommodate for the direct assimilation of the SMOS TB data, the LSM needs to be coupled with a radiative transfer model (RTM), serving as a forward operator for the simulation of multi-angular and multi-polarization top of atmosphere TBs. This study investigates the use of the Variable Infiltration Capacity (VIC) LSM coupled with the Community Microwave Emission Modelling platform (CMEM) for simulating SMOS TB observations over the Upper Mississippi basin, USA. For a period of 2 years (2010-2011), a comparison between SMOS TBs and simulations with literature-based RTM parameters reveals a basin averaged bias of 30K. Therefore, time series of SMOS TB observations are used to investigate ways for mitigating these large biases. Specifically, the study demonstrates the impact of the LSM soil moisture climatology in the magnitude of TB biases. After CDF matching the SM climatology of the LSM to SMOS retrievals, the average bias decreases from 30K to less than 5K. Further improvements can be made through calibration of RTM parameters related to the modeling of surface roughness and vegetation. Consequently, it can be concluded that SM rescaling and RTM optimization are efficient means for mitigating biases and form a necessary preparatory step for data assimilation.

SMOS↗
NASA NTRS1980

Viking Orbiter 75 in-flight pointing calibration of the high-gain antenna

An in-flight pointing calibration technique developed for the Viking Orbiter high-gain antenna has been validated through actual flight usage. The desired telecommunications performance dictated that the high-gain antenna pointing error be held at 0.7 deg, which would have been exceeded without calibration. The in-flight calibration methodology required the development of a stochastic model of the spacecraft rotational biases and earth-received signal strength measurements. The signal strength measurements, which were performed at X-band frequency, were used as observations to estimate the rotational biases and their corresponding uncertainties. Reducing the uncertainties of these parameters resulted in increased antenna pointing accuracy. The initial pointing offset was estimated to be in excess of 1 deg, and after in-flight calibration it was reduced to about 0.66 deg. About 50% of the original offset could not be calibrated, thus the improvement on the remaining offset is better than 50%.

Assefi, T.↗
DOE OSTI2021

The Simons Observatory: gain, bandpass and polarization-angle calibration requirements for B-mode searches

We quantify the calibration requirements for systematic uncertainties for next-generation ground-based observatories targeting the large-angle B-mode polarization of the Cosmic Microwave Background, with a focus on the Simons Observatory (SO). We explore uncertainties on gain calibration, bandpass center frequencies, and polarization angles, including the frequency variation of the latter across the bandpass. We find that gain calibration and bandpass center frequencies must be known to percent levels or less to avoid biases on the tensor-to-scalar ratio r on the order of Δ r∼10-3, in line with previous findings. Polarization angles must be calibrated to the level of a few tenths of a degree, while their frequency variation between the edges of the band must be known to O(10) degrees. Given the tightness of these calibration requirements, we explore the level to which residual uncertainties on these systematics would affect the final constraints on r if included in the data model and marginalized over. We find that the additional parameter freedom does not degrade the final constraints on r significantly, broadening the error bar by O(10%) at most. We validate these results by reanalyzing the latest publicly available data from the collaboration within an extended parameter space covering both cosmological, foreground and systematic parameters. Finally, our results are discussed in light of the instrument design and calibration studies carried out within SO.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS2004

Spitzer Instrument Pointing Frame (IPF) Kalman Filter Algorithm

This paper discusses the Spitzer Instrument Pointing Frame (IPF) Kalman Filter algorithm. The IPF Kalman filter is a high-order square-root iterated linearized Kalman filter, which is parametrized for calibrating the Spitzer Space Telescope focal plane and aligning the science instrument arrays with respect to the telescope boresight. The most stringent calibration requirement specifies knowledge of certain instrument pointing frames to an accuracy of 0.1 arcseconds, per-axis, 1-sigma relative to the Telescope Pointing Frame. In order to achieve this level of accuracy, the filter carries 37 states to estimate desired parameters while also correcting for expected systematic errors due to: (1) optical distortions, (2) scanning mirror scale-factor and misalignment, (3) frame alignment variations due to thermomechanical distortion, and (4) gyro bias and bias-drift in all axes. The resulting estimated pointing frames and calibration parameters are essential for supporting on-board precision pointing capability, in addition to end-to-end 'pixels on the sky' ground pointing reconstruction efforts.

calibration↗
DOE OSTI2023

Improved calibration of rf cavities for relativistic electron beams: Effects of secondary corrections and experimental verification

In the aspect of longitudinal beam bunching, the bunching strength can be controlled by the rf cavity phase and voltage. However, these machine parameters are different from those that interact with the beam itself. In order to gain control of the beam-cavity interaction, cavity calibration must be performed. Furthermore, it relies on fitting the beam energy gain versus cavity phase to a calibration function. Under the conventional assumption of relativistic beam conditions, the calibration function is a first harmonic sinusoidal function (a sinusoidal function with a period of 2π). However, this expression is insufficient for a high-voltage bunching cavity. Due to beam acceleration inside the cavity, an energy bias and a second harmonic function should be included to modify the conventional calibration function, even for a relativistic electron beam. In this paper, we will derive this modification and provide a comparison to both the Coherent Electron Cooling Experiment and the IMPACT T simulation, respectively.

43 PARTICLE ACCELERATORS↗
NASA NTRSDate not supplied

Inter-Calibrating CERES Instrument Fluxes Utilizing the CERES Instrument Geostationary Scan Mode Observations

The NASA Clouds and the Earth’s Radiant Energy System (CERES) project provides the scientific community observed top-of-atmosphere (TOA) fluxes to monitor the Earth’s energy imbalance and validate climate models. The CERES instruments onboard the Terra, Aqua, SNPP and NOAA-20 satellites need to be inter-calibrated to provide a continuous and consistent TOA flux record contained in the CERES Energy Balanced and Filled (EBAF) product. The SNPP and NOAA-20 satellites are positioned a half an orbit apart within the same sun-synchronous orbit (1:30 PM equatorial crossing time) thus preventing any direct time-matched observations. The CERES project designed the geostationary scan mode (GEOscan) to inter-calibrate the Geostationary Earth Radiation Budget (GERB) broadband measurement onboard the Meteosat 8-11 satellites. By rotating the orientation of the CERES instrument scan to match the angular configuration of the geostationary scan mode, the comparison of both angle and time matched observations suitable for inter-calibration is possible. To determine if the GEOscan mode is useful for inter-calibrating two CERES instruments placed in the same 16-day repeating orbit, the CERES project placed the Terra and Aqua CERES instruments in GEOscan mode once every 6 days over a rotation of five geostationary domains beginning in February 2023. The GEO imager narrowband to broadband derived radiances are used as transfer radiometers to compare the Terra and Aqua CERES observed radiances. Since both the Terra and Aqua CERES instruments are in GEOscan mode over the same GEO domain and day, the GEO imager calibration is expected to be consistent between the Terra and Aqua overpass times. Any GEO imager narrowband to broadband regional biases should be similar for the Terra and Aqua overpasses. The GEOscan mode Terra and Aqua CERES inter-calibration coefficients for both shortwave and longwave broadband radiances will be compared against the CERES instrument team’s coefficients to determine the viability of this approach. Improvements in the GEO imager narrowband to broadband approaches will also be investigated and verified within this framework.

Kyle Itterly↗
NASA NTRS2012

Inferring Land Surface Model Parameters for the Assimilation of Satellite-Based L-Band Brightness Temperature Observations into a Soil Moisture Analysis System

The Soil Moisture and Ocean Salinity (SMOS) satellite mission provides global measurements of L-band brightness temperatures at horizontal and vertical polarization and a variety of incidence angles that are sensitive to moisture and temperature conditions in the top few centimeters of the soil. These L-band observations can therefore be assimilated into a land surface model to obtain surface and root zone soil moisture estimates. As part of the observation operator, such an assimilation system requires a radiative transfer model (RTM) that converts geophysical fields (including soil moisture and soil temperature) into modeled L-band brightness temperatures. At the global scale, the RTM parameters and the climatological soil moisture conditions are still poorly known. Using look-up tables from the literature to estimate the RTM parameters usually results in modeled L-band brightness temperatures that are strongly biased against the SMOS observations, with biases varying regionally and seasonally. Such biases must be addressed within the land data assimilation system. In this presentation, the estimation of the RTM parameters is discussed for the NASA GEOS-5 land data assimilation system, which is based on the ensemble Kalman filter (EnKF) and the Catchment land surface model. In the GEOS-5 land data assimilation system, soil moisture and brightness temperature biases are addressed in three stages. First, the global soil properties and soil hydraulic parameters that are used in the Catchment model were revised to minimize the bias in the modeled soil moisture, as verified against available in situ soil moisture measurements. Second, key parameters of the "tau-omega" RTM were calibrated prior to data assimilation using an objective function that minimizes the climatological differences between the modeled L-band brightness temperatures and the corresponding SMOS observations. Calibrated parameters include soil roughness parameters, vegetation structure parameters, and the single scattering albedo. After this climatological calibration, the modeling system can provide L-band brightness temperatures with a global mean absolute bias of less than 10K against SMOS observations, across multiple incidence angles and for horizontal and vertical polarization. Third, seasonal and regional variations in the residual biases are addressed by estimating the vegetation optical depth through state augmentation during the assimilation of the L-band brightness temperatures. This strategy, tested here with SMOS data, is part of the baseline approach for the Level 4 Surface and Root Zone Soil Moisture data product from the planned Soil Moisture Active Passive (SMAP) satellite mission.

Reichle, Rolf H.↗
NASA NTRS1978

A new measurement of the cosmic ray electron spectrum from 10 GeV to 300 GeV

The spectrum of cosmic-ray electrons has been measured with an instrument that combines a transition-radiation detector with a shower detector. The transition-radiation detector provides unique identification of individual electrons and good discrimination against protons. At the same time, it allows the construction of a large-area instrument (0.48 sq m ? ster) and consequently makes possible a measurement of improved statistical accuracy. The instrument has been calibrated with electron beams of 5-300 GeV at Fermilab, thus eliminating energy-dependent biases. A first balloon flight yielded 30 hours of data at an altitude of 5 g/sq cm. The design of the instrument is described, along with the accelerator calibrations and the analysis of the balloon flight data. The spectrum of electrons is found to be significantly steeper than that of protons over the whole energy range.

Hartmann, G.↗
NASA NTRS2006

Inter-calibrating Brightness Temperatures of a Constellation of Radiometers

In 2010, the National Aeronautics and Space Agency (NASA) of the U.S.A. and the Japanese Exploration Agency (JAXA) of Japan in cooperation with other U.S. and international partners will launch the Global Precipitation Measurement (GPM) mission. The mission center-piece is a core U.S. provided satellite holding a scanning microwave imager provided by the U.S. A. and a dual-frequency precipitation radar provided by Japan. The core satellite is in a 65 deg inclination (the current Tropical Rainfall Measuring Mission -TRMM is in a 35 deg inclination). Joining the core satellite are a constellation of approximately 8 satellites containing scanning radiometers. The purpose of the constellation is to increase the global sampling capability of the mission. One constellation satellite will be provided by NASA. Some of the constellation radiometers will provided by other U.S. agencies with existing (e.g. SSMI/S) or planned (NPOESS) radiometer assets. International groups have also expressed interest in contributing to the GPM mission including providing radiometer data for the GPM constellation. The use of a heterogeneous group of scanning radiometers each with its own unique purpose, characteristics and calibration offers a significant challenge for combining brightness temperatures or rain retrievals to create meaningful combined global radiometer products. However, the availability of active dual precipitation radar on the GPM core in combination with a well-calibrated radiometer on the same platform offers the possibility of inter-calibrating the constellation radiometers using the core satellite as a calibrator. This paper describes a joint NASA/GSFC and Colorado State University prototype effort at inter-calibrating existing radiometers using such a core calibrator approach. In the prototype, existing radiometers (i.e. SSM/I and AMSR-E) are intercalibrated, as required, using the TRMM Precipitation Radar (PR) and TRMM Microwave Imager (TMI) as the calibration core. This prototype includes four basic steps: provide the data in a normalized-common logical radiometer format, convert all data to a granule that stops and starts at the southernmost latitude rather than at the equator, perform basic processing and finally inter-calibrate the radiometers with the TRMM core as appropriate. Basic processing includes quality control, cross-track bias correction as well as the core action of converting T(sub a), to T(sub b). The purpose of the inter-calibration step is to provide consistent brightness temperatures for the various SSMA sensors, TMI and AMSR-E. The C appended to the level of the product indicates common brightness temperature (T(sub c)). The paper provides a summary of each of these actions. The details of the processing as well as data format and tools can be obtained by connecting to the website at mrain.atmos.colostate.eduLEVEL1C .

Stocker, Erich Franz↗
NASA NTRS1976

Use of calibration maneuvers for improved performance of strapdown attitude reference systems

Conventional strapdown configurations require precise knowledge of the orientation of the gyro input axes as well as a moderately large, fast computer to provide inertial attitude. This paper presents the mechanization and discusses the operation and performance of an omnidirectional, strapdown pointing control system called All Sky Pointer which does not require precise gyro alignment or a sophisticated computer. Errors caused by gyro-optical sensor misalignment, gyro-integrator bias, and scale factor error are compensated for by the use of calibration maneuvers. Control and computation are provided by an electronics package utilizing technology similar to that found in hand-held calculators. Simulation results indicate that sub arc-minute pointing performance is possible and pointing errors are reduced by as much as an order of magnitude compared with uncompensated systems.

Lorell, K. R.↗