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NASA NTRS2019

GOES-17 Magnetometer On-Orbit Calibration Design and Results

The Geostationary Operational Environmental Satellite-R (GOES-R) is a series of four NOAA weather satellites. Each spacecraft flies a Magnetometer instrument which includes two boom mounted fluxgate sensors located 6.3 and 8.5 meters from the spacecraft. Sensor readings are corrupted by both internal (bias and scale factor) and external (spacecraft emitted fields and misalignments) error sources. In order to estimate the bias, an on-orbit calibration is performed, slewing the spacecraft about multiple axes and then performing a fit of the data to determine zero offset and misalignment terms. The first satellite in the series, GOES-16 was launched in November 2016. Its magnetometer calibration maneuver was found to be inadequate providing insufficient rotation about orthogonal axes. The uncertainty in the estimated biases was found to be in the 3-5 nanotesla range, exceeding the magnetometer accuracy requirement of 1.0 nanotesla. Based on lessons learned, the maneuver was redesigned to provide multiple 360 degree rotations about two orthogonal axes, providing optimal visibility into bias and misalignment. Varying ambient fields over the duration of the calibration maneuvers, corrupts the ability to accurately determine parameters of interest. To address this issue, rather than assuming a constant field for the duration of the maneuver, a non-linear least squares filter was employed that uses a series of spline functions to better fit the ambient field. The number of splines can be varied to minimize the least squares filter residuals. Simulations were performed using 360 days of GOES-16 data to bound the uncertainty in the biases for given residuals of the fit to the ambient field. Following the launch of the second satellite in the series, GOES-17 in March 2018, the new calibration maneuver and enhanced bias estimation algorithm were exercised twice. Based on the residuals of the fit, the uncertainty of the estimated zero offset was reduced by an order of magnitude from 3-5 nanotesla to approximately 0.4 nanotesla per axis. This paper provides details of the maneuver design and the innovative algorithm used to estimate the GOES-17 biases and misalignments.

GOES-17↗

DOE OSTI2022

Dark Energy Survey Year 3 results: calibration of lens sample redshift distributions using clustering redshifts with BOSS/eBOSS

ABSTRACT We present clustering redshift measurements for Dark Energy Survey (DES) lens sample galaxies used in weak gravitational lensing and galaxy clustering studies. To perform these measurements, we cross-correlate with spectroscopic galaxies from the Baryon Acoustic Oscillation Survey (BOSS) and its extension, eBOSS. We validate our methodology in simulations, including a new technique to calibrate systematic errors that result from the galaxy clustering bias, and we find that our method is generally unbiased in calibrating the mean redshift. We apply our method to the data, and estimate the redshift distribution for 11 different photometrically selected bins. We find general agreement between clustering redshift and photometric redshift estimates, with differences on the inferred mean redshift found to be below |Δz| = 0.01 in most of the bins. We also test a method to calibrate a width parameter for redshift distributions, which we found necessary to use for some of our samples. Our typical uncertainties on the mean redshift ranged from 0.003 to 0.008, while our uncertainties on the width ranged from 4 to 9 per cent. We discuss how these results calibrate the photometric redshift distributions used in companion papers for DES Year 3 results.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2019

GOES-16 ABI Solar Reflective Channel Validation for Earth Science Application

This paper presents the validation results of GOES-16 Satellite's Advanced Baseline Imager (ABI) obtained from a reflectance-based field campaign undertaken at the Salar de Uyuni in Bolivia in June 2017. In situ ground measurements are used to characterize the surface reflectance and the atmosphere in order to constrain the radiative transfer code and predict at-sensor reflectance (also referred to as top-of-atmosphere (TOA) reflectance) to compare with concurrent GOES-16 ABI measurements. The five-day field campaign provided repeated TOA reflectance estimates, allowing assessment not only of the calibration accuracy of the ABI reflective channels 1, 2, 3, 5 and 6, but also of its stability over the duration of the campaign. The results show that the accuracy of the ABI reflective channels calibration is within specification for channels 1, 3, 5, and 6 - average biases within 2%; for channel 2 the bias is 5%. The estimated uncertainty on the derived biases is 2–2.4%. Some calibration stability issues were present in the ABI calibration at the time of the campaign: (i) a jump on the order of 2% in channels 1 and 6, coincident with an ABI solar calibration event, reflects an instability of the ABI gains in these channels, and (ii) short-term variability in channels 1 and 2 is due to striping (ABI detector-todetector calibration differences). Continued validation and subsequent reprocessing of ABI reflectance imagery would allow Earth scientists to fully benefit from the high spatial and spectral fidelity of the GOES-16 ABI diurnal measurements at the continental scale.

Joel McCorkel↗

NASA NTRS2020

MODIS TEB Calibration Algorithm Improvements for Future L1B Collection

Terra and Aqua MODIS have provided continuous global observations for scientific applications for more than 20 and 18 years, respectively. The radiometric calibration of the MODIS thermal emissive bands (TEB) is based on a quadratic approximation of the instrument response. The calibration coefficients look-up tables (LUTs) are updated using the response of the MODIS on-board blackbody (BB)with the response background subtracted by space view. The quarterly on-board BB warm-up and cool-down activity temperature ranges from 270 K to 315 K, and the derived offset has a relatively large uncertainty. Electronic cross-talk, an artifact that affects both instrument calibration and Earth view (EV) radiance retrievals, is corrected based on lunar observations. Calibration assessments using EV observations (e.g. ocean, desert, Antarctic Dome Concordia, and deep convective clouds) provide useful information to evaluate the impact of the Terra safe mode (February 2016) and Aqua MODIS formatter reset (January 2018) events on both MODIS instruments. This study focuses on the TEB radiometric calibration algorithm improvements for future collections based on calibration assessments using EV measurements and analytical modeling. Measurement stability and consistency over specific Earth scenes with a wide temperature range, as well as their brightness temperature (BT) dependency, are used for bias estimations in the calibration coefficients. Calibration coefficients are derived and updated after adjusting the current fitting algorithm. Thereafter, using the test LUTs, their impact on the Level 1B (L1B) data for different EV scenes is analyzed.

MODIS↗

NASA NTRS2019

Soil Moisture Active/Passive (SMAP) L-Band Microwave Radiometer Post-Launch Calibration Upgrade

The Soil Moisture Active/Passive (SMAP) microwave radiometer is a fully polarimetric L-band radiometer flown on theSMAP satellite in a 6 AM/6 PM sun-synchronous orbit at 685 km altitude. After the SMAP L1B_TB data product version 3 was released in 2016, the radiometer has been undergoing further calibration and validation with the goal of reducing both the bias in the cold-sky measurements and calibration drift in the global ocean measurements experienced during eclipse seasons in data product version 3. The post-launch calibration algorithm has been upgraded by using new estimates of the reflector emissivity as well as using multiple scenes to calibrate the radiometer internal reference sources and antenna gain simultaneously. In addition, a correction offset is applied to the ocean roughness model for horizontal polarization based on nadir observations. Test and validation results show that the goal is achieved (e.g., biases are removed and the calibration stability achieved for data release version 4 is 0.1 K(rms) over both the global ocean and CS).

Calibratio↗

NASA NTRS1996

Calibration improvements to electronically scanned pressure systems and preliminary statistical assessment

Orifice-to-orifice inconsistencies in data acquired with an electronically-scanned pressure system at the beginning of a wind tunnel experiment forced modifications to the standard, instrument calibration procedures. These modifications included a large increase in the number of calibration points which would allow a critical examination of the calibration curve-fit process, and a subsequent post-test reduction of the pressure data. Evaluation of these data has resulted in an improved functional representation of the pressure-voltage signature for electronically-scanned pressures sensors, which can reduce the errors due to calibration curve fit to under 0.10 percent of reading compared to the manufacturer specified 0.10 percent of full scale. Application of the improved calibration function allows a more rational selection of the calibration set-point pressures. These pressures should be adjusted to achieve a voltage output which matches the physical shape of the pressure-voltage signature of the sensor. This process is conducted in lieu of the more traditional approach where a calibration pressure is specified and the resulting sensor voltage is recorded. The fifteen calibrations acquired over the two-week duration of the wind tunnel test were further used to perform a preliminary, statistical assessment of the variation in the calibration process. The results allowed the estimation of the bias uncertainty for a single instrument calibration; and, they form the precursor for more extensive and more controlled studies in the laboratory.

Everhart, Joel L.↗

NASA NTRS2018

Soil Moisture Active/Passive (SMAP) L-Band Microwave Radiometer Post-Launch Calibration Upgrade

Current performance and existing problems in SMAP radiometer L1B_TB version 3 data product are described. The post-launch calibration algorithm has been updated by calibrating the three calibration parameters (the equivalent noise temperature of the noise diode, the offset of the reference load, and the antenna gain) jointly by using the global ocean and CS with both 110o and 180o pitch maneuvers after the reflector emissivity is calibrated. The results show that both calibration drift during eclipse season and bias over CS are removed. The RMSDs of the calibration drift over both the global ocean and CS are less than 0.1 K, and the goals of the calibration algorithm upgrade are achieved for coming L1B_TB version 4 data release.

Validation↗

DOE OSTI2020

Dealing with Measurement Uncertainties as Nuisance Parameters in Bayesian Model Calibration

In the presence of model discrepancy, the calibration of physics-based models for physical parameter inference is a challenging problem. Lack of identifiability between calibration parameters and model discrepancy requires additional identifiability constraints to be placed on the model discrepancy to obtain unique physical parameter estimates. If these assumptions are violated, the inference for the calibration parameters can be systematically biased. In many applications, such as in dynamic material property experiments, many of the calibration inputs refer to measurement uncertainties. Here, we develop a metric for identifying overfitting of these measurement uncertainties, propose a prior capable of reducing this overfitting, and show how this leads to a diagnostic tool for validation of physical parameter inference. The approach is demonstrated for a benchmark example and applied for a material property application to perform inference on the equation of state parameters of tantalum.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Detection and Calibration of Low-Energy Nuclear Recoils for Dark Matter and Neutrino Scattering Experiments

Detection of low-energy nuclear recoil events plays a central role in searches for particle dark matter interactions with atomic matter and studies of coherent neutrino scatters. Precise nuclear recoil calibration data allow the responses of these dark matter and neutrino detectors to be characterized and enable in situ evaluation of an experiment's sensitivity to anticipated signals. This article reviews the common methods for detection of nuclear recoil events and the wide variety of techniques that have been developed to calibrate detector response to nuclear recoils. We summarize the main experimental factors that are critical for accurate nuclear recoil calibrations, investigate mitigation strategies for different backgrounds and biases, and discuss how the presentation of calibration results can facilitate comparison between experiments. Lastly, we discuss the challenges for future nuclear recoil calibration efforts and the physics opportunities they may enable.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2009

An Empirical Approach to Ocean Color Data: Reducing Bias and the Need for Post-Launch Radiometric Re-Calibration

A new empirical approach is developed for ocean color remote sensing. Called the Empirical Satellite Radiance-In situ Data (ESRID) algorithm, the approach uses relationships between satellite water-leaving radiances and in situ data after full processing, i.e., at Level-3, to improve estimates of surface variables while relaxing requirements on post-launch radiometric re-calibration. The approach is evaluated using SeaWiFS chlorophyll, which is the longest time series of the most widely used ocean color geophysical product. The results suggest that ESRID 1) drastically reduces the bias of ocean chlorophyll, most impressively in coastal regions, 2) modestly improves the uncertainty, and 3) reduces the sensitivity of global annual median chlorophyll to changes in radiometric re-calibration. Simulated calibration errors of 1% or less produce small changes in global median chlorophyll (less than 2.7%). In contrast, the standard NASA algorithm set is highly sensitive to radiometric calibration: similar 1% calibration errors produce changes in global median chlorophyll up to nearly 25%. We show that 0.1% radiometric calibration error (about 1% in water-leaving radiance) is needed to prevent radiometric calibration errors from changing global annual median chlorophyll more than the maximum interannual variability observed in the SeaWiFS 9-year record (+/- 3%), using the standard method. This is much more stringent than the goal for SeaWiFS of 5% uncertainty for water leaving radiance. The results suggest ocean color programs might consider less emphasis of expensive efforts to improve post-launch radiometric re-calibration in favor of increased efforts to characterize in situ observations of ocean surface geophysical products. Although the results here are focused on chlorophyll, in principle the approach described by ESRID can be applied to any surface variable potentially observable by visible remote sensing.

Gregg, Watson W.↗

NASA NTRS1998

Observations from Long-Term Performance Monitoring of the TOPEX Radar Altimeter

From its August 1992 launch to the present, we have performed performance analysis and engineering assessment for the TOPEX radar altimeter. We continually update databases containing: (1) on-board engineering parameters such as temperatures, voltages, and currents; (2) internal calibration mode indications of bias changes in range and power estimates; and (3) global over-ocean averages of geophysical quantities such as significant waveheight (SWH) and ocean surface radar backscattering cross-section (sigmaO). For some time now we have seen an apparent increase in the TOPEX cycle-average SWH, amounting now to an increase of about 10% from our earlier mission value of about 2.8 m. Recently several investigators have reported that the TOPEX SWH is increasing relative to ERS-2 and to ocean buoy measurements. We examined the past six years of waveform data from an internal calibration mode (Cal 1) which samples the altimeter's point target response (ptr), and found that the ptr sidelobes are apparently greater now than at start of mission. Modeling studies indicate that the sidelobe enhancement can account for most of the increase in the TOPEX SWH estimate; that is, the SWH increase is not real but result of some drift within the altimeter. Our modeling indicates that the TOPEX range estimates will change less than a centimeter for ptr changes seen to date. An approximate recipe for correcting the TOPEX SWH values will be made available on our web site (http://topex.wffnasa.gov/). We emphasize that a radar altimeter is a complex system requiring continuing calibration and monitoring throughout its entire lifetime.

Hayne, G. S.↗

DOE OSTI2023

Hyper Suprime-Cam Year 3 results: Measurements of clustering of SDSS-BOSS galaxies, galaxy-galaxy lensing, and cosmic shear

Here we utilize the Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey (SDSS-BOSS) galaxies and its overlap with approximately 416 sq degrees of deep grizy-band imaging from the Subaru Hyper Suprime-Cam Survey (HSC). We perform measurements of three two-point correlations which form the basis of the cosmological inference presented in our companion papers, Miyatake et al. and Sugiyama et al. We use three approximately volume limited subsamples of spectroscopic galaxies by their i-band magnitude from the SDSS-BOSS: LOWZ (0.1 < z < 0.35), CMASS1 (0.43 < z < 0.55) and CMASS2 (0.55 < z < 0.7), respectively. We present high signal-to-noise ratio measurements of the projected correlation functions of these galaxies, which is expected to be proportional to the projected matter correlation function on large scales with a proportionality constant dependent on the bias of galaxies. In order to help break the degeneracy between the amplitude of the matter correlation and the bias of these spectroscopic galaxies, we use the distortions of the shapes of fainter galaxies in HSC due to weak gravitational lensing, to measure the galaxy-galaxy lensing signal, which probes the projected galaxy-matter cross-correlation function of the SDSS-BOSS galaxies. We also measure the cosmic shear correlation functions from HSC galaxies which is related to the projected matter correlation function. We demonstrate the robustness of our measurements by subjecting each of them to a variety of systematic tests. Our use of a single sample of HSC source galaxies is crucial to calibrate any residual systematic biases in the inferred redshifts of our galaxies. We also describe the construction of a suite of mocks: (i) spectroscopic galaxy catalogs which obey the clustering and abundance of each of the three SDSS-BOSS subsamples, and (ii) galaxy shape catalogs which obey the footprint of the HSC survey and have been appropriately sheared by the large-scale structure expected in a Lambda Cold Dark Matter model. Finally, we use these mock catalogs to compute the covariance of each of our observables.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2008

Provenance in Data Interoperability for Multi-Sensor Intercomparison

As our inventory of Earth science data sets grows, the ability to compare, merge and fuse multiple datasets grows in importance. This requires a deeper data interoperability than we have now. Efforts such as Open Geospatial Consortium and OPeNDAP (Open-source Project for a Network Data Access Protocol) have broken down format barriers to interoperability; the next challenge is the semantic aspects of the data. Consider the issues when satellite data are merged, cross-calibrated, validated, inter-compared and fused. We must match up data sets that are related, yet different in significant ways: the phenomenon being measured, measurement technique, location in space-time or quality of the measurements. If subtle distinctions between similar measurements are not clear to the user, results can be meaningless or lead to an incorrect interpretation of the data. Most of these distinctions trace to how the data came to be: sensors, processing and quality assessment. For example, monthly averages of satellite-based aerosol measurements often show significant discrepancies, which might be due to differences in spatio- temporal aggregation, sampling issues, sensor biases, algorithm differences or calibration issues. Provenance information must be captured in a semantic framework that allows data inter-use tools to incorporate it and aid in the intervention of comparison or merged products. Semantic web technology allows us to encode our knowledge of measurement characteristics, phenomena measured, space-time representation, and data quality attributes in a well-structured, machine-readable ontology and rulesets. An analysis tool can use this knowledge to show users the provenance-related distrintions between two variables, advising on options for further data processing and analysis. An additional problem for workflows distributed across heterogeneous systems is retrieval and transport of provenance. Provenance may be either embedded within the data payload, or transmitted from server to client in an out-of-band mechanism. The out of band mechanism is more flexible in the richness of provenance information that can be accomodated, but it relies on a persistent framework and can be difficult for legacy clients to use. We are prototyping the embedded model, incorporating provenance within metadata objects in the data payload. Thus, it always remains with the data. The downside is a limit to the size of provenance metadata that we can include, an issue that will eventually need resolution to encompass the richness of provenance information required for daata intercomparison and merging.

Lynnes, Chris↗

NASA NTRS2015

Helium Mass Spectrometer Leak Detection: A Method to Quantify Total Measurement Uncertainty

In applications where leak rates of components or systems are evaluated against a leak rate requirement, the uncertainty of the measured leak rate must be included in the reported result. However, in the helium mass spectrometer leak detection method, the sensitivity, or resolution, of the instrument is often the only component of the total measurement uncertainty noted when reporting results. To address this shortfall, a measurement uncertainty analysis method was developed that includes the leak detector unit's resolution, repeatability, hysteresis, and drift, along with the uncertainty associated with the calibration standard. In a step-wise process, the method identifies the bias and precision components of the calibration standard, the measurement correction factor (K-factor), and the leak detector unit. Together these individual contributions to error are combined and the total measurement uncertainty is determined using the root-sum-square method. It was found that the precision component contributes more to the total uncertainty than the bias component, but the bias component is not insignificant. For helium mass spectrometer leak rate tests where unit sensitivity alone is not enough, a thorough evaluation of the measurement uncertainty such as the one presented herein should be performed and reported along with the leak rate value.

error analysis↗

NASA NTRS2015

Evaluating a New Homogeneous Total Ozone Climate Data Record from GOME/ERS-2, SCIAMACHY/Envisat, and GOME-2/MetOp-A

The European Space Agency's Ozone Climate Change Initiative (O3-CCI) project aims at producing and validating a number of high-quality ozone data products generated from different satellite sensors. For total ozone, the O3-CCI approach consists of minimizing sources of bias and systematic uncertainties by applying a common retrieval algorithm to all level 1 data sets, in order to enhance the consistency between the level 2 data sets from individual sensors. Here we present the evaluation of the total ozone products from the European sensors Global Ozone Monitoring Experiment (GOME)/ERS-2, SCIAMACHY/Envisat, and GOME-2/MetOp-A produced with the GOME-type Direct FITting (GODFIT) algorithm v3. Measurements from the three sensors span more than 16 years, from 1996 to 2012. In this work, we present the latest O3-CCI total ozone validation results using as reference ground-based measurements from Brewer and Dobson spectrophotometers archived at the World Ozone and UV Data Centre of the World Meteorological Organization as well as from UV-visible differential optical absorption spectroscopy (DOAS)/Système D′Analyse par Observations Zénithales (SAOZ) instruments from the Network for the Detection of Atmospheric Composition Change. In particular, we investigate possible dependencies in these new GODFIT v3 total ozone data sets with respect to latitude, season, solar zenith angle, and different cloud parameters, using the most adequate type of ground-based instrument. We show that these three O3-CCI total ozone data products behave very similarly and are less sensitive to instrumental degradation, mainly as a result of the new reflectance soft-calibration scheme. The mean bias to the ground-based observations is found to be within the 1 plus or minus 1 percent level for all three sensors while the near-zero decadal stability of the total ozone columns (TOCs) provided by the three European instruments falls well within the 1-3 percent requirement of the European Space Agency's Ozone Climate Change Initiative project.

Satellite sensors↗

DOE OSTI2025

Calibration and Validation of the SAIL Radar

Calibration of a weather radar is not a simple process, as is well described and documented in several articles (Chandrasekar, V, L Baldini, N Bharadwaj, and PL Smith. 2015. "Calibration procedures for global precipitation-measurement ground-validation radars." URSI Radio Science Bulletin 2015(355): 45–73, https://10.23919/URSIRSB.2015.7909473.). Direct hardware-based characterization is called calibration whereas indirect check with other sources such as disdrometer, or comparison with other radars or indirect means, is called validation. The validation process has its own measurement error and the comparison should fall within its limit. In the following we describe calibration and validation processes for the SAIL radar. Based on the comparison of calibration and validation, an addition of 2 dB is suggested for the SAIL radar observations, with a nuanced Z dr calibration correction, as presented. If a fixed Z dr calibration is preferred, a bias addition of 0.5 dB is suggested.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

The DECADE cosmic shear project II: photometric redshift calibration of the source galaxy sample

We present the photometric redshift characterization and calibration for the Dark Energy Camera All Data Everywhere (DECADE) weak lensing dataset: a catalog of 107 million galaxies observed by the Dark Energy Camera (DECam) in the northern Galactic cap. The redshifts are estimated from a combination of wide-field photometry, deep-field photometry with associated redshift estimates, and a transfer function between the wide field and deep field that is estimated using a source injection catalog. We construct four tomographic bins for the galaxy catalog, and estimate the redshift distribution, $n(z)$, within each one using the Self-organizing Map Photo-Z (SOMPZ) methodology. Our estimates include the contributions from sample variance, zeropoint calibration uncertainties, and redshift biases, as quantified for the deep-field dataset. The total uncertainties on the mean redshifts are $σ_{\langle}$$_z$$_{\rangle} ≈ 0.01$. The SOMPZ estimates are then compared to those from the clustering redshift method, obtained by cross-correlating our source galaxies with galaxies in spectroscopic surveys, and are shown to be consistent with each other.

Anbajagane, D. [Univ. of Chicago, IL (United State↗

DOE OSTI2022

Supporting hierarchical soil biogeochemical modeling: version 2 of the Biogeochemical Transport and Reaction model (BeTR-v2)

Abstract. Reliable soil biogeochemical modeling is a prerequisite for credible projections of climate change and associated ecosystem feedbacks. This recognition has called for frameworks that can support flexible and efficient development and application of new or alternative soil biogeochemical modules in Earth system models (ESMs). The the Biogeochemical Transport and Reaction model version 1 (BeTR-v1) code (i.e., CLM4-BeTR) is one such framework designed to accelerate the development and integration of new soil biogeochemistry formulations into ESMs and to analyze structural uncertainty in ESM simulations. With a generic reactive transport capability, BeTR-v1 can represent multiphase (e.g., gaseous, aqueous, and solid), multi-tracer (e.g., nitrate and organic carbon), and multi-organism (e.g., plants, bacteria, and fungi) dynamics. Here, we describe the new version, Biogeochemical Transport and Reaction model version 2 (BeTR-v2), which adopts more robust numerical solvers for multiphase diffusion and advection and coupling between biogeochemical reactions and improves code modularization over BeTR-v1. BeTR-v2 better supports different mathematical formulations in a hierarchical manner by allowing the resultant model be run for a single topsoil layer or a vertically resolved soil column, and it allows the model to be fully coupled with the land component of the Energy Exascale Earth System Model (E3SM). We demonstrate the capability of BeTR-v2 with benchmark cases and example soil biogeochemical (BGC) implementations. By taking advantage of BeTR-v2's generic structure integrated in E3SM, we then found that calibration could not resolve biases introduced by different numerical coupling strategies of plant–soil biogeochemistry. These results highlight the importance of numerically robust implementation of soil biogeochemistry and coupling with hydrology, thermal dynamics, and plants – capabilities that the open-source BeTR-v2 provides. We contend that Earth system models should strive to minimize this uncertainty by applying better numerical solvers.

58 GEOSCIENCES↗