scholarly journals Decorrelation of GRACE Time Variable Gravity Field Solutions Using Full Covariance Information

Geosciences ◽  
2018 ◽  
Vol 8 (9) ◽  
pp. 323 ◽  
Author(s):  
Alexander Horvath ◽  
Michael Murböck ◽  
Roland Pail ◽  
Martin Horwath
Keyword(s):  
Time Series ◽  
Gravity Field ◽  
Closed Loop ◽  
Real Data ◽  
Geoid Height ◽  
Covariance Matrices ◽  
Time Variable ◽  
Time Variable Gravity ◽  
Variable Gravity ◽  
The Impact

In this study the feasibility and performance of time variable decorrelation (VADER) filters derived from covariance information on decadal Gravity Recovery and Climate Experiment (GRACE) time series are investigated. The VADER filter is based on publicly available data that are provided by several GRACE processing centers, and does not need its own Level-2 processing chain. Numerical closed loop simulations, incorporating stochastic and deterministic error budgets, serve as basis for the design of the filter setup, and the resulting filters are subsequently applied for real data processing. The closed loop experiments demonstrate the impact of temporally varying error and signal covariance matrices that are used for the design of decorrelation filters. The results indicate an average reduction of cumulative geoid height errors of 15% using time-variable instead of static decorrelation. Based on the simulation experience, a real data filtering procedure is designed and set up. It is applied to the ITSG-Grace2014 time variable gravity field time series with its associated full monthly covariance matrices. To assess the validity of the approach, linear mass trend estimates for the Antarctic Peninsula are computed using VADER filters and compared to previous estimates from both, GRACE and other mass balance estimation techniques. The mass change results obtained show very good agreement with other estimates and are robust against variations of the filter strength. The DDK decorrelation filter serves as main benchmark for the assessment of the VADER filter. For comparable filter strengths the VADER filters achieve a better de-striping and deliver smaller formal errors than static filters like the DDK.

scholarly journals Time-variable gravity fields and ocean mass change from 37 months of kinematic Swarm orbits

2017 ◽  
Author(s):  
Christina Lück ◽  
Jürgen Kusche ◽  
Roelof Rietbroek ◽  
Anno Löcher
Keyword(s):  
Time Series ◽  
Gravity Field ◽  
Sea Level ◽  
Time Variable ◽  
Field Analysis ◽  
Time Variable Gravity ◽  
Ocean Mass ◽  
Grace Data ◽  
Swarm Satellites ◽  
Variable Gravity

Abstract. Measuring the spatiotemporal variation of ocean mass allows one to partition volumetric sea level change, sampled by radar altimeters, into a mass-driven and a steric part, the latter being related to ocean heat change and the current Earth’s energy imbalance. Since 2002, the Gravity Recovery and Climate Experiment (GRACE) mission provides estimates of the Earth’s time-variable gravity field, from which one can derive ocean mass variability. However, GRACE has reached the end of its lifetime with data degradation and several gaps during the last years, and there will be a prolonged gap until the launch of the follow-on mission GRACE-FO. Therefore, efforts focus on generating a long and consistent ocean mass time series by analyzing kinematic orbits from other low-flying satellites; i.e. extending the GRACE time series. Here we utilize data from the European Space Agency’s (ESA) Swarm Earth Explorer satellites to derive and investigate ocean mass variations. We investigate the potential to bridge the gap between the GRACE missions and to substitute missing monthly solutions. Our monthly Swarm solutions have a root mean square error (RMSE) of 4.0 mm with respect to GRACE, whereas directly estimating trend, annual and semiannual signal terms leads to an RMSE of only 1.7 mm. Concerning monthly gaps, our Swarm solution appears better than interpolating existing GRACE data in 13.5 % of all cases, for 80.0 % of all investigated cases of an 18-months-gap, Swarm ocean mass was found closer to the observed GRACE data compared to interpolated GRACE data. Furthermore, we show that precise modelling of non-gravitational forces acting on the Swarm satellites is the key for reaching these accuracies. Our results have implications for sea level budget studies, but they may also guide further research in gravity field analysis schemes, including non-dedicated satellites.

scholarly journals Simulation of the time-variable gravity field by means of coupled geophysical models

2011 ◽  
Vol 4 (1) ◽  
pp. 27-70 ◽  
Author(s):  
Th. Gruber ◽  
J. L. Bamber ◽  
M. F. P. Bierkens ◽  
H. Dobslaw ◽  
M. Murböck ◽  
...  
Keyword(s):  
Time Series ◽  
Gravity Field ◽  
Mass Distribution ◽  
Time Variable ◽  
Data Sets ◽  
Earth System ◽  
Time Variable Gravity ◽  
The Earth ◽  
Gravity Fields ◽  
Variable Gravity

Abstract. Time variable gravity fields, reflecting variations of mass distribution in the system Earth is one of the key parameters to understand the changing Earth. Mass variations are caused either by redistribution of mass in, on or above the Earth's surface or by geophysical processes in the Earth's interior. The first set of observations of monthly variations of the Earth gravity field was provided by the US/German GRACE satellite mission beginning in 2002. This mission is still providing valuable information to the science community. However, as GRACE has outlived its expected lifetime, the geoscience community is currently seeking successor missions in order to maintain the long time series of climate change that was begun by GRACE. Several studies on science requirements and technical feasibility have been conducted in the recent years. These studies required a realistic model of the time variable gravity field in order to perform simulation studies on sensitivity of satellites and their instrumentation. This was the primary reason for the European Space Agency (ESA) to initiate a study on "Monitoring and Modelling individual Sources of Mass Distribution and Transport in the Earth System by Means of Satellites". The goal of this interdisciplinary study was to create as realistic as possible simulated time variable gravity fields based on coupled geophysical models, which could be used in the simulation processes in a controlled environment. For this purpose global atmosphere, ocean, continental hydrology and ice models were used. The coupling was performed by using consistent forcing throughout the models and by including water flow between the different domains of the Earth system. In addition gravity field changes due to solid Earth processes like continuous glacial isostatic adjustment (GIA) and a sudden earthquake with co-seismic and post-seismic signals were modelled. All individual model results were combined and converted to gravity field spherical harmonic series, which is the quantity commonly used to describe the Earth's global gravity field. The result of this study is a twelve-year time-series of 6-hourly time variable gravity field spherical harmonics up to degree and order 180 corresponding to a global spatial resolution of 1 degree in latitude and longitude. In this paper, we outline the input data sets and the process of combining these data sets into a coherent model of temporal gravity field changes. The resulting time series was used in some follow-on studies and is available to anybody interested via a Website.

scholarly journals Time-variable gravity field recovery from kinematic positions of Low Earth Orbiting satellites

2021 ◽  
Author(s):  
Thomas Grombein ◽  
Martin Lasser ◽  
Daniel Arnold ◽  
Ulrich Meyer ◽  
Adrian Jäggi
Keyword(s):  
Time Series ◽  
Gravity Field ◽  
Time Variable ◽  
Kinematic Orbit ◽  
Time Variable Gravity ◽  
Gravity Field Recovery ◽  
The Earth ◽  
Leo Satellites ◽  
Variable Gravity ◽  
Gnss Data

<p>For the monitoring of mass transport and mass distribution in the Earth’s system, the gravity field and its temporal variations provide an important source of information. Dedicated satellite missions like GRACE and GRACE-FO allow to resolve the Earth’s time-variable gravity field based on ultra-precise inter-satellite ranging. In addition, any (non-dedicated) Low Earth Orbiting (LEO) satellite equipped with an on-board GNSS receiver may also serve as a gravity field sensor. For this purpose, the collected GNSS data is used to derive kinematic LEO orbit positions that can subsequently be utilized as pseudo-observations for gravity field recovery. Although this technique is less sensitive and restricted to the long wavelength part of the gravity field, it provides valuable information, particularly for those months where no inter-satellite ranging measurements are available from GRACE or GRACE-FO. Furthermore, the increasing number of operational LEO satellites makes it attractive to produce combined Multi-LEO gravity field solutions that will take advantage of the variety of complementary orbital configurations and can offer additional sensitivities to selected coefficients of solutions based on inter-satellite ranging.</p><p>At the Astronomical Institute of the University of Bern (AIUB) GPS-based kinematic orbits are routinely processed for various LEO satellites like missions dedicated to gravity (GOCE, GRACE/-FO), altimetry (Jason, Sentinel), or further constellations of Earth-observing satellites like SWARM. Beside conventional ambiguity-float orbits, also ambiguity-fixed orbits are recently being computed based on new phase bias and clock products of the Center for Orbit Determination in Europe (CODE). The kinematic orbit positions offer the opportunity to derive time series of monthly gravity field solutions for the different LEO satellites that are eventually combined on the level of normal equations.</p><p>In this contribution, we will present first results of our effort to generate a combined time series of monthly gravity field solutions based on the kinematic orbits of multiple LEO satellites. In a first step, the focus is laid on the GRACE/-FO missions that provide the longest time series in terms of collected GNSS data and that will therefore serve as a backbone for future combinations. We analyze the impact of accelerometer data on the recovery of time-variable mass variations. This will be particularly important for the handling of non-dedicated gravity missions, for which accelerometer measurements are usually not available. Furthermore, we study and compare the performance of gravity field recoveries based on ambiguity-float and ambiguity-fixed kinematic orbit solutions. We assess our results with respect to superior gravity field models based on inter-satellite ranging for selected areas with strong mass change signals like in Greenland, West-Antarctica or the Amazon river basin.</p>

scholarly journals Influence of the Low-Frequency Error of the Residual Orbit on Recovering Time-Variable Gravity Field from the Satellite-To-Satellite Tracking Mission

2021 ◽  
Vol 13 (6) ◽  
pp. 1118
Author(s):  
Lei Liang ◽  
Jinhai Yu ◽  
Changqing Wang ◽  
Min Zhong ◽  
Wei Feng ◽  
...  
Keyword(s):  
Gravity Field ◽  
Low Frequency ◽  
Real Data ◽  
Time Variable ◽  
Frequency Error ◽  
Perturbation Model ◽  
Time Variable Gravity ◽  
Residual Range ◽  
Variable Gravity ◽  
Range Rate

When using the dynamic approach to recover the time-variable gravity field, the reference orbit generated by the perturbation model and the non-conservative force observed from the accelerometer should be introduced at first, and then the observation equations of the residual orbit and the residual range rate are established. This introduces a perturbation model error and instrument noise. Thus, there are low-frequency errors in the residual orbit and the residual range rate. Currently, most studies only focus on the low-frequency error of the residual range rate, neglecting the influence of the low-frequency error in the residual orbit. Therefore, under the condition of the perturbation model error and instrument noise including the constant term and 1CPR term, the low-frequency error formulas of the residual orbit and residual range rate are derived according to the characteristics of the solution of the Hill equation. Then, the influence of the low-frequency error on the residuals is analyzed by using the simulation and the real data processing respectively. In the simulation and real data processing, the accuracy of the recovered gravity field can maintain a good consistency for different arc lengths by removing the low-frequency error in the residual orbit. Finally, the time-variable gravity field model UCAS-IGG (University of Chinese Academy of Sciences-Institute of Geodesy and Geophysics) was solved from January 2005 to February 2010 by removing the low-frequency error of the residual orbit and residual range rate. Compared with the official institutions, the UCAS-IGG presents a good consistency in the estimating time-variable gravity field signal. This study demonstrates how the effect of the low-frequency error of the residual orbit should be taken into consideration when the longer arc length is used to recover a time-variable gravity field. Using a long arc length can reduce the variables of the initial state and recover the influence of the small force.

scholarly journals Time-variable gravity fields and ocean mass change from 37 months of kinematic Swarm orbits

Solid Earth ◽  
2018 ◽  
Vol 9 (2) ◽  
pp. 323-339 ◽  
Author(s):  
Christina Lück ◽  
Jürgen Kusche ◽  
Roelof Rietbroek ◽  
Anno Löcher
Keyword(s):  
Time Series ◽  
Gravity Field ◽  
Sea Level ◽  
Time Variable ◽  
Time Variable Gravity ◽  
Ocean Mass ◽  
Grace Data ◽  
Swarm Satellites ◽  
Gravity Fields ◽  
Variable Gravity

Abstract. Measuring the spatiotemporal variation of ocean mass allows for partitioning of volumetric sea level change, sampled by radar altimeters, into mass-driven and steric parts. The latter is related to ocean heat change and the current Earth's energy imbalance. Since 2002, the Gravity Recovery and Climate Experiment (GRACE) mission has provided monthly snapshots of the Earth's time-variable gravity field, from which one can derive ocean mass variability. However, GRACE has reached the end of its lifetime with data degradation and several gaps occurred during the last years, and there will be a prolonged gap until the launch of the follow-on mission GRACE-FO. Therefore, efforts focus on generating a long and consistent ocean mass time series by analyzing kinematic orbits from other low-flying satellites, i.e. extending the GRACE time series. Here we utilize data from the European Space Agency's (ESA) Swarm Earth Explorer satellites to derive and investigate ocean mass variations. For this aim, we use the integral equation approach with short arcs (Mayer-Gürr, 2006) to compute more than 500 time-variable gravity fields with different parameterizations from kinematic orbits. We investigate the potential to bridge the gap between the GRACE and the GRACE-FO mission and to substitute missing monthly solutions with Swarm results of significantly lower resolution. Our monthly Swarm solutions have a root mean square error (RMSE) of 4.0 mm with respect to GRACE, whereas directly estimating constant, trend, annual, and semiannual (CTAS) signal terms leads to an RMSE of only 1.7 mm. Concerning monthly gaps, our CTAS Swarm solution appears better than interpolating existing GRACE data in 13.5 % of all cases, when artificially removing one solution. In the case of an 18-month artificial gap, 80.0 % of all CTAS Swarm solutions were found closer to the observed GRACE data compared to interpolated GRACE data. Furthermore, we show that precise modeling of non-gravitational forces acting on the Swarm satellites is the key for reaching these accuracies. Our results have implications for sea level budget studies, but they may also guide further research in gravity field analysis schemes, including satellites not dedicated to gravity field studies.

Intercomparison of signals and noise in time variable gravity field releases from an ice sheet perspective

2020 ◽  
Author(s):  
Andreas Groh ◽  
Ulrich Meyer ◽  
Martin Lasser ◽  
Christoph Dahle ◽  
Andreas Kvas ◽  
...  
Keyword(s):  
Time Series ◽  
Gravity Field ◽  
Regional Integration ◽  
Noise Level ◽  
Ice Sheets ◽  
Product Evaluation ◽  
Time Variable ◽  
Mass Change ◽  
Time Variable Gravity ◽  
Variable Gravity

<p align="justify">The International Combination Service for Time-variable Gravity Fields (COST-G), a product center of IAG’s International Gravity Field Service, aims on the combination of monthly global gravity field models. A consolidated gravity field series is derived from individual releases provided by different analysis centres (AC). COST-G’s Product Evaluation Group (PEG) assesses the combined gravity field series as well as the series provided by the ACs regarding their suitability for studying mass changes in the Earth’s subsystems (e.g. oceans, cryosphere, continental hydrosphere). Here we present results from the PEG’s assessment regarding mass changes of the ice sheets. Our study focuses on the COST-G RL01 series and the contributing releases AIUB RL02, GFZ RL06, ITSG-Grace2018, CSR RL06 and an unconstrained variant of GRGS RL05.</p> <p align="justify">Based on residual variations of the spherical harmonic (SH) coefficients with respect to a long-term and seasonal model, we quantify the noise level of the latest GRACE/GRACE-FO solutions series provided by COST-G and the contributing ACs. This assessment is performed both in the SH domain and in the space domain, focusing on the polar regions. A regional integration approach using tailored sensitivity kernels is applied to derive mass change time series for individual drainage basins and the entire ice sheets in Greenland (GIS) and Antarctica (AIS). A measure for the noise level of the different mass change time series is inferred from the residuals with respect to a climatology, corrected for remaining inter-annual mass changes. In this way we are able to assess if and to which extent mass change products for GIS and AIS can benefit from the combination of different solution series. Furthermore, we also quantify the signal content inherent to the individual mass change time series in terms of the seasonal signal and the linear trend (i.e. mass balance). Differences in the signal content between the releases are further investigated with respect to contributions from different parts of the SH spectrum. In addition to selected SH coefficients (e.g. C<sub>21</sub>, S<sub>21</sub>), we systematically attribute the differences to each SH degree and the corresponding SH orders.</p>

scholarly journals Simulation of the time-variable gravity field by means of coupled geophysical models

2011 ◽  
Vol 3 (1) ◽  
pp. 19-35 ◽  
Author(s):  
Th. Gruber ◽  
J. L. Bamber ◽  
M. F. P. Bierkens ◽  
H. Dobslaw ◽  
M. Murböck ◽  
...  
Keyword(s):  
Time Series ◽  
Gravity Field ◽  
Mass Distribution ◽  
Time Variable ◽  
Data Sets ◽  
Earth System ◽  
Time Variable Gravity ◽  
The Earth ◽  
Gravity Fields ◽  
Variable Gravity

Abstract. Time variable gravity fields, reflecting variations of mass distribution in the system Earth is one of the key parameters to understand the changing Earth. Mass variations are caused either by redistribution of mass in, on or above the Earth's surface or by geophysical processes in the Earth's interior. The first set of observations of monthly variations of the Earth gravity field was provided by the US/German GRACE satellite mission beginning in 2002. This mission is still providing valuable information to the science community. However, as GRACE has outlived its expected lifetime, the geoscience community is currently seeking successor missions in order to maintain the long time series of climate change that was begun by GRACE. Several studies on science requirements and technical feasibility have been conducted in the recent years. These studies required a realistic model of the time variable gravity field in order to perform simulation studies on sensitivity of satellites and their instrumentation. This was the primary reason for the European Space Agency (ESA) to initiate a study on ''Monitoring and Modelling individual Sources of Mass Distribution and Transport in the Earth System by Means of Satellites''. The goal of this interdisciplinary study was to create as realistic as possible simulated time variable gravity fields based on coupled geophysical models, which could be used in the simulation processes in a controlled environment. For this purpose global atmosphere, ocean, continental hydrology and ice models were used. The coupling was performed by using consistent forcing throughout the models and by including water flow between the different domains of the Earth system. In addition gravity field changes due to solid Earth processes like continuous glacial isostatic adjustment (GIA) and a sudden earthquake with co-seismic and post-seismic signals were modelled. All individual model results were combined and converted to gravity field spherical harmonic series, which is the quantity commonly used to describe the Earth's global gravity field. The result of this study is a twelve-year time-series of 6-hourly time variable gravity field spherical harmonics up to degree and order 180 corresponding to a global spatial resolution of 1 degree in latitude and longitude. In this paper, we outline the input data sets and the process of combining these data sets into a coherent model of temporal gravity field changes. The resulting time series was used in some follow-on studies and is available to anybody interested.

scholarly journals Earth’s Time-Variable Gravity from GRACE Follow-On K-Band Range-Rates and Pseudo-Observed Orbits

2021 ◽  
Vol 13 (9) ◽  
pp. 1766
Author(s):  
Igor Koch ◽  
Mathias Duwe ◽  
Jakob Flury ◽  
Akbar Shabanloui
Keyword(s):  
Gravity Field ◽  
Time Variable ◽  
Time Variable Gravity ◽  
Gravity Field Recovery ◽  
Variable Gravity ◽  
Earth’S System ◽  
Grace Mission ◽  
Insight Into ◽  
K Band

During its science phase from 2002–2017, the low-low satellite-to-satellite tracking mission Gravity Field Recovery And Climate Experiment (GRACE) provided an insight into Earth’s time-variable gravity (TVG). The unprecedented quality of gravity field solutions from GRACE sensor data improved the understanding of mass changes in Earth’s system considerably. Monthly gravity field solutions as the main products of the GRACE mission, published by several analysis centers (ACs) from Europe, USA and China, became indispensable products for quantifying terrestrial water storage, ice sheet mass balance and sea level change. The successor mission GRACE Follow-On (GRACE-FO) was launched in May 2018 and proceeds observing Earth’s TVG. The Institute of Geodesy (IfE) at Leibniz University Hannover (LUH) is one of the most recent ACs. The purpose of this article is to give a detailed insight into the gravity field recovery processing strategy applied at LUH; to compare the obtained gravity field results to the gravity field solutions of other established ACs; and to compare the GRACE-FO performance to that of the preceding GRACE mission in terms of post-fit residuals. We use the in-house-developed MATLAB-based GRACE-SIGMA software to compute unconstrained solutions based on the generalized orbit determination of 3 h arcs. K-band range-rates (KBRR) and kinematic orbits are used as (pseudo)-observations. A comparison of the obtained solutions to the results of the GRACE-FO Science Data System (SDS) and Combination Service for Time-variable Gravity Fields (COST-G) ACs, reveals a competitive quality of our solutions. While the spectral and spatial noise levels slightly differ, the signal content of the solutions is similar among all ACs. The carried out comparison of GRACE and GRACE-FO KBRR post-fit residuals highlights an improvement of the GRACE-FO K-band ranging system performance. The overall amplitude of GRACE-FO post-fit residuals is about three times smaller, compared to GRACE. GRACE-FO post-fit residuals show less systematics, compared to GRACE. Nevertheless, the power spectral density of GRACE-FO and GRACE post-fit residuals is dominated by similar spikes located at multiples of the orbital and daily frequencies. To our knowledge, the detailed origin of these spikes and their influence on the gravity field recovery quality were not addressed in any study so far and therefore deserve further attention in the future. Presented results are based on 29 monthly gravity field solutions from June 2018 until December 2020. The regularly updated LUH-GRACE-FO-2020 time series of monthly gravity field solutions can be found on the website of the International Centre for Global Earth Models (ICGEM) and in LUH’s research data repository. These operationally published products complement the time series of the already established ACs and allow for a continuous and independent assessment of mass changes in Earth’s system.

Combination Service for Time-variable Gravity Fields (COST-G): operational GRACE-FO combination and validation of Chinese GRACE time-series

2021 ◽  
Author(s):  
Ulrich Meyer ◽  
Martin Lasser ◽  
Adrian Jäggi ◽  
Christoph Dahle ◽  
Frank Flechtner ◽  
...  
Keyword(s):  
Time Series ◽  
Quality Assessment ◽  
International Association ◽  
Time Variable ◽  
Operational Mode ◽  
Time Variable Gravity ◽  
Gravity Fields ◽  
Variable Gravity ◽  
Processed Products ◽  
The Cost

<p>The Combination Service for Time-variable Gravity Fields (COST-G) of the International Association of Geodesy (IAG) provides combined monthly gravity fields of its associated and partner Analysis Centers (ACs). In November 2020, the combination of monthly GRACE-FO gravity fields started its operational mode, providing consolidated L2 (spherical harmonics) and L3 (gridded and post- processed) products with a latency of currently 3 months. We present an overview and quality assessment of the available products.</p><p>COST-G aims at the extension of its service to include further GRACE and GRACE-FO analysis centers. In January 2020 a collaboration with representatives of five Chinese ACs was initiated, who provided GRACE time-series according to the COST-G requirements. We present the results of a test combination with the Chinese AC models, including comparison and quality assessment of all contributing time-series and validation of the combined gravity fields.</p>

Combination Service for Time-variable Gravity Field Solutions (COST-G) – GRACE-FO operational combination

2020 ◽  
Author(s):  
Ulrich Meyer ◽  
Martin Lasser ◽  
Adrian Jäggi ◽  
Frank Flechtner ◽  
Christoph Dahle ◽  
...  
Keyword(s):  
Time Series ◽  
Quality Control ◽  
International Association ◽  
Time Variable ◽  
Polar Regions ◽  
Time Variable Gravity ◽  
Gravity Fields ◽  
River Hydrology ◽  
Variable Gravity ◽  
Combined Time Series

<p lang="en-US">We present the operational GRACE-FO combined time-series of monthly gravity fields of the Combination Service for Time-variable Gravity fields (COST-G) of the International Association of Geodesy (IAG). COST-G_GRACE-FO_RL01_operational is combined at AIUB and relies on operational monthly solutions of the COST-G Analysis Centers GFZ, GRGS, IfG, LUH and AIUB and the associated Analysis Centers CSR and JPL. All COST-G Analysis Centers have passed a benchmark test to ensure consistency between the different processing approaches and all of the contributing time-series undergo a strict quality control focusing on the signal content in river basins and polar regions with pronounced changes in ice mass to uncover any regularization that may bias the combination.</p> <p lang="en-US">The combination is performed by variance component estimation on the solution level, the relative monthly weights thus providing valuable and independent insight into the consistency and noise levels of the individual monthly contributions. The combined products then are validated internally in terms of noise, approximated by the non-secular, non-seasonal variability over the oceans. Once they have passed this quality control the combined gravity fields are assessed by an external board of experts who evaluate them in terms of orbit predictions, lake altimetry, river hydrology or oceanography.</p>

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