scholarly journals Generation of a bending angle radio occultation climatology (BAROCLIM) and its use in radio occultation retrievals

2015 ◽  
Vol 8 (1) ◽  
pp. 109-124 ◽  
Author(s):  
B. Scherllin-Pirscher ◽  
S. Syndergaard ◽  
U. Foelsche ◽  
K. B. Lauritsen
Keyword(s):  
Radio Occultation ◽  
Weather Prediction ◽  
A Priori ◽  
A Priori Information ◽  
Bending Angle ◽  
Weather Forecasts ◽  
Global Statistics ◽  
Priori Information ◽  
Bending Angles

Abstract. In this paper, we introduce a bending angle radio occultation climatology (BAROCLIM) based on Formosat-3/COSMIC (F3C) data. This climatology represents the monthly-mean atmospheric state from 2006 to 2012. Bending angles from radio occultation (RO) measurements are obtained from the accumulation of the change in the raypath direction of Global Positioning System (GPS) signals. Best quality of these near-vertical profiles is found from the middle troposphere up to the mesosphere. Beside RO bending angles we also use data from the Mass Spectrometer and Incoherent Scatter Radar (MSIS) model (modified for RO purposes) to expand BAROCLIM in a spectral model, which (theoretically) reaches from the surface up to infinity. Due to the very high quality of BAROCLIM up to the mesosphere, it can be used to detect deficiencies in current state-of-the-art analysis and reanalysis products from numerical weather prediction (NWP) centers. For bending angles derived from European Centre for Medium-Range Weather Forecasts (ECMWF) analysis fields from 2006 to 2012, e.g., we find a positive bias of 0.5 to 1% at 40 km, which increases to more than 2% at 50 km. BAROCLIM can also be used as a priori information in RO profile retrievals. In contrast to other a priori information (i.e., MSIS) we find that the use of BAROCLIM better preserves the mean of raw RO measurements. Global statistics of statistically optimized bending angle and refractivity profiles also confirm that BAROCLIM outperforms MSIS. These results clearly demonstrate the utility of BAROCLIM.

scholarly journals Generation of a Bending Angle Radio Occultation Climatology (BAROCLIM) and its use in radio occultation retrievals

2014 ◽  
Vol 7 (8) ◽  
pp. 8193-8231 ◽  
Author(s):  
B. Scherllin-Pirscher ◽  
S. Syndergaard ◽  
U. Foelsche ◽  
K. B. Lauritsen
Keyword(s):  
Radio Occultation ◽  
Weather Prediction ◽  
A Priori ◽  
A Priori Information ◽  
Bending Angle ◽  
Weather Forecasts ◽  
Global Statistics ◽  
Priori Information ◽  
Bending Angles

Abstract. In this paper, we introduce a bending angle radio occultation climatology (BAROCLIM) based on Formosat-3/COSMIC (F3C) data. This climatology represents the monthly-mean atmospheric state from 2006 to 2012. Bending angles from radio occultation (RO) measurements are obtained from the accumulation of the change in the raypath direction of Global Positioning System (GPS) signals. Best quality of these near-vertical profiles is found from the middle troposphere up to the mesosphere. Beside RO bending angles we also use data from the Mass Spectrometer and Incoherent Scatter Radar (MSIS) model to expand BAROCLIM in a spectral model, which (theoretically) reaches from the surface up to infinity. Due to the very high quality of BAROCLIM up to the mesosphere, it can be used to detect deficiencies in current state-of-the-art analysis and reanalysis products from numerical weather prediction (NWP) centers. For bending angles derived from European Centre for Medium-Range Weather Forecasts (ECMWF) analysis fields from 2006 to 2012, e.g., we find a positive bias of 0.5% to % at 40 km, which increases to more than 2% at 50 km. BAROCLIM can also be used as a priori information in RO profile retrievals. In contrast to other a priori information (i.e., MSIS) we find that the use of BAROCLIM better preserves the mean of raw RO measurements. Global statistics of statistically optimized bending angle and refractivity profiles also confirm that BAROCLIM outperforms MSIS. These results clearly demonstrate the utility of BAROCLIM.

scholarly journals Retrieval of temperature profiles from CHAMP for climate monitoring: intercomparison with Envisat MIPAS and GOMOS and different atmospheric analyses

2007 ◽  
Vol 7 (13) ◽  
pp. 3519-3536 ◽  
Author(s):  
A. Gobiet ◽  
G. Kirchengast ◽  
G. L. Manney ◽  
M. Borsche ◽  
C. Retscher ◽  
...  
Keyword(s):  
High Altitude ◽  
Weather Prediction ◽  
A Priori ◽  
Michelson Interferometer ◽  
Altitude Range ◽  
A Priori Information ◽  
Climate Monitoring ◽  
Retrieval Scheme ◽  
Priori Information ◽  
Upper Boundary

Abstract. This study describes and evaluates a Global Navigation Satellite System (GNSS) radio occultation (RO) retrieval scheme particularly aimed at delivering bias-free atmospheric parameters for climate monitoring and research. The focus of the retrieval is on the sensible use of a priori information for careful high-altitude initialisation in order to maximise the usable altitude range. The RO retrieval scheme has been meanwhile applied to more than five years of data (September 2001 to present) from the German CHAllenging Minisatellite Payload for geoscientific research (CHAMP) satellite. In this study it was validated against various correlative datasets including the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) and the Global Ozone Monitoring for Occultation of Stars (GOMOS) sensors on Envisat, five different atmospheric analyses, and the operational CHAMP retrieval product from GeoForschungsZentrum (GFZ) Potsdam. In the global mean within 10 to 30 km altitude we find that the present validation observationally constrains the potential RO temperature bias to be <0.2 K. Latitudinally resolved analyses show biases to be observationally constrained to <0.2–0.5 K up to 35 km in most cases, and up to 30 km in any case, even if severely biased (about 10 K or more) a priori information is used in the high altitude initialisation of the retrieval. No evidence is found for the 10–35 km altitude range of residual RO bias sources other than those potentially propagated downward from initialisation, indicating that the widely quoted RO promise of "unbiasedness and long-term stability due to intrinsic self-calibration" can indeed be realised given care in the data processing to strictly limit structural uncertainty. The results thus reinforce that adequate high-altitude initialisation is crucial for accurate stratospheric RO retrievals. The common method of initialising, at some altitude in the upper stratosphere, the hydrostatic integral with an upper boundary temperature or pressure value derived from meteorological analyses is prone to introduce biases from the upper boundary down to below 25 km. Also above 30 to 35 km, GNSS RO delivers a considerable amount of observed information up to around 40 km, which is particularly interesting for numerical weather prediction (NWP) systems, where direct assimilation of non-initialised observed RO bending angles (free of a priori) is thus the method of choice. The results underline the value of RO for climate applications.

scholarly journals Analysis of ionospheric structure influences on residual ionospheric errors in GNSS radio occultation bending angles based on ray tracing simulations

2018 ◽  
Vol 11 (4) ◽  
pp. 2427-2440 ◽  
Author(s):  
Congliang Liu ◽  
Gottfried Kirchengast ◽  
Yueqiang Sun ◽  
Kefei Zhang ◽  
Robert Norman ◽  
...  
Keyword(s):  
Impact Parameter ◽  
Radio Occultation ◽  
Global Climate ◽  
Weather Prediction ◽  
Signal Propagation ◽  
Satellite System ◽  
Primary Role ◽  
Dual Frequency ◽  
Bending Angle ◽  
Bending Angles

Abstract. The Global Navigation Satellite System (GNSS) radio occultation (RO) technique is widely used to observe the atmosphere for applications such as numerical weather prediction and global climate monitoring. The ionosphere is a major error source to RO at upper stratospheric altitudes, and a linear dual-frequency bending angle correction is commonly used to remove the first-order ionospheric effect. However, the higher-order residual ionospheric error (RIE) can still be significant, so it needs to be further mitigated for high-accuracy applications, especially from 35 km altitude upward, where the RIE is most relevant compared to the decreasing magnitude of the atmospheric bending angle. In a previous study we quantified RIEs using an ensemble of about 700 quasi-realistic end-to-end simulated RO events, finding typical RIEs at the 0.1 to 0.5 µrad noise level, but were left with 26 exceptional events with anomalous RIEs at the 1 to 10 µrad level that remained unexplained. In this study, we focused on investigating the causes of the high RIE of these exceptional events, employing detailed along-ray-path analyses of atmospheric and ionospheric refractivities, impact parameter changes, and bending angles and RIEs under asymmetric and symmetric ionospheric structures. We found that the main causes of the high RIEs are a combination of physics-based effects – where asymmetric ionospheric conditions play the primary role, more than the ionization level driven by solar activity – and technical ray tracer effects due to occasions of imperfect smoothness in ionospheric refractivity model derivatives. We also found that along-ray impact parameter variations of more than 10 to 20 m are possible due to ionospheric asymmetries and, depending on prevailing horizontal refractivity gradients, are positive or negative relative to the initial impact parameter at the GNSS transmitter. Furthermore, mesospheric RIEs are found generally higher than upper-stratospheric ones, likely due to being closer in tangent point heights to the ionospheric E layer peaking near 105 km, which increases RIE vulnerability. In the future we will further improve the along-ray modeling system to fully isolate technical from physics-based effects and to use it beyond this work for additional GNSS RO signal propagation studies.

scholarly journals Unconstrained, robust Kalman filtering for GNSS troposphere tomography

2013 ◽  
Vol 6 (5) ◽  
pp. 9133-9162 ◽  
Author(s):  
W. Rohm ◽  
K. Zhang ◽  
J. Bosy
Keyword(s):  
Water Vapour ◽  
Kalman Filtering ◽  
Weather Prediction ◽  
A Priori ◽  
Real Data ◽  
Reference Station ◽  
A Priori Information ◽  
Dependent Observations ◽  
Integrated Water Vapour ◽  
Priori Information

Abstract. The mesoscale variability of water vapour (WV) in the troposphere is a highly complex phenomenon and modeling and monitoring the WV distribution is a very important but challenging task. Any observation technique that can reliably provide WV distribution is essential for both monitoring and predicting weather. GNSS tomography technique is a powerful tool that builds upon the critical ground-based GNSS infrastructure – Continuous Operating Reference Station (CORS) networks and can be used to sense the amount of WV. Previous research suggests that 3-D WV field from GNSS tomography has an uncertainty of 1 hPa. However all the models used in GNSS tomography heavily rely on a priori information and constraints from non-GNSS measurements. In this study, 3-D GNSS tomography models are investigated based on an unconstrained approach with limited a priori information. A case study is designed and the results show that unconstrained solutions are feasible by using a robust Kalman filtering technique and effective removal of linearly dependent observations and parameters. Discrepancies between reference wet refractivity data derived from the Australian Numerical Weather Prediction (NWP) model (i.e. ACCESS) and the GNSS tomography model using both simulated and real data are 4.2 ppm (mm km−1) and 6.5 ppm (mm km−1), respectively, which are essentially in the same order of accuracy. Therefore the accuracy of the integrated values should not be worse than 0.06 m in terms of zenith wet delay and the integrated water vapour is a fifth of this value which is roughly 10 mm.

scholarly journals Simultaneous Radio Occultation Predictions for Inter-Satellite Comparison of Bending Angle Profiles from COSMIC-2 and GeoOptics

2021 ◽  
Vol 13 (18) ◽  
pp. 3644
Author(s):  
Yong Chen ◽  
Xi Shao ◽  
Changyong Cao ◽  
Shu-peng Ho
Keyword(s):  
Radio Occultation ◽  
International System ◽  
Weather Prediction ◽  
Prediction Method ◽  
Low Earth Orbit ◽  
Weather Data ◽  
Bending Angle ◽  
System Of Units ◽  
Leo Satellites ◽  
Bending Angles

The Global Navigation Satellite System (GNSS) radio occultation (RO) is a remote sensing technique that uses International System of Units (SI) traceable GNSS signals for atmospheric limb soundings. The RO bending angle/sounding profiles are needed for assimilation in Numerical Weather Prediction (NWP) models, weather, climate, and space weather applications. Evaluating these RO data to ensure the high data quality for these applications is becoming more and more critical. This study presents a method for predicting radio occultation events, from which simultaneous radio occultation (SRO) for a pair of low-Earth-orbit (LEO) satellites on the limb to the same GNSS satellite can be obtained. The SRO method complements the Simultaneous Nadir Overpass (SNO) method (for nadir viewing satellite instruments), which has been widely used to inter-calibrate LEO to LEO and LEO to geosynchronous-equatorial-orbit (GEO) satellites. Unlike the SNO method, the SRO method involves three satellites: a GNSS and two LEO satellites with RO receivers. The SRO method allows for the direct comparison of bending angles when the simultaneous RO measurements for two LEO satellites receiving the same GNSS signal pass through approximately the same atmosphere within minutes in time and within less than 200 km of distance from each other. The prediction method can also be applied to radiosonde overpass prediction, and coordinate radiosonde launches for inter-comparisons between RO and radiosonde profiles. The main advantage of the SRO comparisons of bending angles is the significantly reduced uncertainties due to the much shorter time and smaller atmospheric path differences than traditional RO comparisons. To demonstrate the usefulness of this method, we present a comparison of the Constellation Observing System for Meteorology, Ionosphere, and Climate-2 (COSMIC-2) and GeoOpitcs RO profiles using SRO data for two time periods: Commercial Weather Data (CWD) data delivery order-1 (DO-1): 15 December 2020–15 January 2021 and CWD DO-2: 17 March 2021–31 August 2021. The results show good agreement in the bending angles between the COSMIC-2 RO measurements and those from GeoOptics, although systematic biases are also found in the inter-comparisons. Instrument and processing algorithm performances for the signal-to-noise ratio (SNR), penetration height, and bending angle retrieval uncertainty are also characterized. Given the efficiency of this method and the many RO measurements that are publicly and commercially available as well as the expansion of receiver capabilities to all GNSS systems, it is expected that this method can be used to validate/inter-calibrate GNSS RO measurements from different missions.

scholarly journals Quantifying residual ionospheric errors in GNSS radio occultation bending angles based on ensembles of profiles from end-to-end simulations

2015 ◽  
Vol 8 (7) ◽  
pp. 2999-3019 ◽  
Author(s):  
C. L. Liu ◽  
G. Kirchengast ◽  
K. Zhang ◽  
R. Norman ◽  
Y. Li ◽  
...  
Keyword(s):  
Solar Activity ◽  
Spherical Symmetry ◽  
Radio Occultation ◽  
Weather Prediction ◽  
High Latitudes ◽  
Ionospheric Correction ◽  
Bending Angle ◽  
End To End ◽  
Standard Deviations ◽  
Bending Angles

Abstract. The radio occultation (RO) technique using signals from the Global Navigation Satellite System (GNSS), in particular from the Global Positioning System (GPS) so far, is currently widely used to observe the atmosphere for applications such as numerical weather prediction and global climate monitoring. The ionosphere is a major error source in RO measurements at stratospheric altitudes, and a linear ionospheric correction of dual-frequency RO bending angles is commonly used to remove the first-order ionospheric effect. However, the residual ionospheric error (RIE) can still be significant so that it needs to be further mitigated for high-accuracy applications, especially above about 30 km altitude where the RIE is most relevant compared to the magnitude of the neutral atmospheric bending angle. Quantification and careful analyses for better understanding of the RIE is therefore important for enabling benchmark-quality stratospheric RO retrievals. Here we present such an analysis of bending angle RIEs covering the stratosphere and mesosphere, using quasi-realistic end-to-end simulations for a full-day ensemble of RO events. Based on the ensemble simulations we assessed the variation of bending angle RIEs, both biases and standard deviations, with solar activity, latitudinal region and with or without the assumption of ionospheric spherical symmetry and co-existing observing system errors. We find that the bending angle RIE biases in the upper stratosphere and mesosphere, and in all latitudinal zones from low to high latitudes, have a clear negative tendency and a magnitude increasing with solar activity, which is in line with recent empirical studies based on real RO data although we find smaller bias magnitudes, deserving further study in the future. The maximum RIE biases are found at low latitudes during daytime, where they amount to within −0.03 to −0.05 μrad, the smallest at high latitudes (0 to −0.01 μrad; quiet space weather and winter conditions). Ionospheric spherical symmetry or asymmetries about the RO event location have only a minor influence on RIE biases. The RIE standard deviations are markedly increased both by ionospheric asymmetries and increasing solar activity and amount to about 0.3 to 0.7 μrad in the upper stratosphere and mesosphere. Taking also into account the realistic observation errors of a modern RO receiving system, amounting globally to about 0.4 μrad (unbiased; standard deviation), shows that the random RIEs are typically comparable to the total observing system error. The results help to inform future RIE mitigation schemes that will improve upon the use of the linear ionospheric correction of bending angles and also provide explicit uncertainty estimates.

scholarly journals Quantifying residual ionospheric errors in GNSS radio occultation bending angles based on ensembles of profiles from end-to-end simulations

2015 ◽  
Vol 8 (1) ◽  
pp. 759-809 ◽  
Author(s):  
C. L. Liu ◽  
G. Kirchengast ◽  
K. Zhang ◽  
R. Norman ◽  
Y. Li ◽  
...  
Keyword(s):  
Solar Activity ◽  
Spherical Symmetry ◽  
Radio Occultation ◽  
Weather Prediction ◽  
High Latitudes ◽  
Ionospheric Correction ◽  
Bending Angle ◽  
Uncertainty Estimates ◽  
End To End ◽  
Bending Angles

Abstract. The radio occultation (RO) technique using signals from the Global Navigation Satellite System (GNSS), in particular from the Global Positioning System (GPS) so far, is meanwhile widely used to observe the atmosphere for applications such as numerical weather prediction and global climate monitoring. The ionosphere is a major error source in RO measurements at stratospheric altitudes and a linear ionospheric correction of dual-frequency RO bending angles is commonly used to remove the first-order ionospheric effect. However, the residual ionopheric error (RIE) can still be significant so that it needs to be further mitigated for high accuracy applications, especially above about 30 km altitude where the RIE is most relevant compared to the magnitude of the neutral atmospheric bending angle. Quantification and careful analyses for better understanding of the RIE is therefore important towards enabling benchmark-quality stratospheric RO retrievals. Here we present such an analysis of bending angle RIEs covering the stratosphere and mesosphere, using quasi-realistic end-to-end simulations for a full-day ensemble of RO events. Based on the ensemble simulations we assessed the variation of bending angle RIEs, both biases and SDs, with solar activity, latitudinal region, and with or without the assumption of ionospheric spherical symmetry and of co-existing observing system errors. We find that the bending angle RIE biases in the upper stratosphere and mesosphere, and in all latitudinal zones from low- to high-latitudes, have a clear negative tendency and a magnitude increasing with solar activity, in line with recent empirical studies based on real RO data. The maximum RIE biases are found at low latitudes during daytime, where they amount to with in −0.03 to −0.05 μrad, the smallest at high latitudes (0 to −0.01 μrad; quiet space weather and winter conditions). Ionospheric spherical symmetry or asymmetries about the RO event location have only a minor influence on RIE biases. The RIE SDs are markedly increased both by ionospheric asymmetries and increasing solar activity and amount to about 0.3 to 0.7 μrad in the upper stratosphere and mesosphere. Taking into account also realistic observation errors of a modern RO receiving system, amounting globally to about 0.4 μrad (un-biased; SD), shows that the random RIEs are typically comparable to the total observing system error. The results help to inform future RIE mitigation schemes that will improve upon the use of the linear ionospheric correction of bending angles and that will also provide explicit uncertainty estimates.

scholarly journals Analysis of ionospheric structure influences on residual ionospheric errors in GNSS radio occultation bending angles based on ray tracing simulations

2017 ◽  
Author(s):  
Congliang Liu ◽  
Gottfried Kirchengast ◽  
Yueqiang Sun ◽  
Kefei Zhang ◽  
Robert Norman ◽  
...  
Keyword(s):  
Impact Parameter ◽  
Radio Occultation ◽  
Global Climate ◽  
Weather Prediction ◽  
Signal Propagation ◽  
Satellite System ◽  
Primary Role ◽  
Dual Frequency ◽  
Bending Angle ◽  
Bending Angles

Abstract. The Global Navigation Satellite System (GNSS) radio occultation (RO) technique is widely used to observe the atmosphere for applications such as numerical weather prediction and global climate monitoring. The ionosphere is a major error source to RO at upper stratospheric altitudes and a linear dual-frequency bending angle correction is commonly used to remove the first-order ionospheric effect. However, the residual higher-order ionospheric error (RIE) can still be significant so that it needs to be further mitigated for high accuracy applications, especially from 30 km altitude upward where the RIE is most relevant compared to the decreasing magnitude of the atmospheric bending angle. In a previous study we quantified RIEs using an ensemble of about 700 quasi-realistic end-to-end simulated RO events, finding typical RIEs at the 0.1 to 0.5 μrad noise level, but were left with 26 exceptional events with anomalous RIEs at the 1 to 10 μrad level that remained unexplained. In this study, we focused on investigating the causes of the high RIE of these exceptional events, employing detailed along-raypath analyses of atmospheric and ionospheric refractivities, impact parameter changes, and bending angles and RIEs under asymmetric and symmetric ionospheric structures. We found that the main causes of the high RIEs are a combination of physics-based effects, where asymmetric ionospheric conditions play the primary role, more than the ionization level driven by solar activity, and technical ray tracer effects due to occasions of imperfect smoothness in ionospheric refractivity model derivatives. We also found that along-ray impact parameter variations of more than 10 to 20 m are well possible due to ionospheric asymmetries, and depending on prevailing horizontal refractivity gradients are positive or negative relative to the initial impact parameter at the GNSS transmitter. Furthermore, mesospheric RIEs are found generally higher than upper stratospheric ones, likely due to being closer in tangent point heights to the ionospheric E layer peaking near 105 km, which increases RIE vulnerability. In future we will further improve the along-ray modeling system to fully isolate technical from physics-based effects and to use it beyond this work for additional GNSS RO signal propagation studies.

scholarly journals Smoothing radio occultation bending angles above 40 km

2001 ◽  
Vol 19 (4) ◽  
pp. 459-468 ◽  
Author(s):  
S. B. Healy
Keyword(s):  
Radio Occultation ◽  
A Priori ◽  
Observation Data ◽  
Error Statistics ◽  
Background Error ◽  
Bending Angle ◽  
Radio Science ◽  
Composition And Structure ◽  
Optimal Approach ◽  
Bending Angles

Abstract. The 'statistically optimal' approach to smoothing bending angles derived from radio occultation (RO) measurements is outlined. This combines a measured bending angle profile with an a priori or background estimate derived from climatology, in order to obtain the most probable bending angle profile. However, the method is only optimal if the error statistics of both the measured and background profiles are known and applied accurately. In this work it is shown that correlations in the background estimate have a significant role in determining the degree of smoothing in the solution. We find that smooth profiles, consistent with the measured values, can be derived if the correlations are approximated analytically with a Gaussian, assuming a scale length of 6km. In regions where the observed and background error levels are comparable, the solutions take the general shape from the background estimate, centred on the observation data. The effects of correlated observation errors are also considered. It is shown that the quality of the temperature retrievals can be significantly affected by the choice of climatology used for background estimate.Key words. Atmosphere composition and structure (pressure, density and temperature) – Radio science (remote sensing)

scholarly journals Bayesian Perspective in the Selection of Bean Genotypes

2020 ◽  
Vol 12 (9) ◽  
pp. 173
Author(s):  
Tâmara Rebecca A. de Oliveira ◽  
Moysés Nascimento ◽  
Paulo R. Santos ◽  
Kleyton Danilo S. Costa ◽  
Thalyson V. Lima ◽  
...  
Keyword(s):  
Bayesian Method ◽  
Block Design ◽  
A Priori ◽  
A Priori Information ◽  
Bayesian Procedure ◽  
R Software ◽  
Randomized Block Design ◽  
Priori Information ◽  
Selection Of

Changes in the relative performance of genotypes have made it necessary for more in-depth investigations to be carried out through reliable analyses of adaptability and stability. The present study was conducted to compare the efficiency of different informative priors in the Bayesian method of Eberhart &amp; Russel with frequentist methods. Fifteen black-bean genotypes from the municipalities of Bel&eacute;m do S&atilde;o Francisco and Petrolina (PE, Brazil) were evaluated in 2011 and 2012 in a randomized-block design with three replicates. Eberhart &amp; Russel&rsquo;s methodology was applied using the GENES software and the Bayesian procedure using the R software through the MCMCregress function of the MCMCpack package. The quality of Bayesian analysis differed according to the a priori information entered in the model. The Bayesian approach using frequentist analysis had greater accuracy in the estimate of adaptability and stability, where model 1 which uses the a priori information, was the most suitable to obtain reliable estimates according to the BayesFactor function. The inference, using information from previous studies, showed to be imprecise and equivalent to the linear-model methodology. In addition, it was realized that the input of a priori information is important because it increases the quality of the adjustment of the model.

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