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1: Illustration of the water cycle (source: the official website of the United States Geological Survey, USGS, http://water.usgs.gov/edu/watercycle.html).
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The time-variable gravity fields from the Gravity Recovery and Climate Experiment (GRACE) satellite mission provide valuable information about total water storage variations on a global scale. This quantity is difficult to observe with in-situ measurements but important for understanding regional energy balance, as well as for agricultural, and wat...
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... the magnitude of propagated errors, for the trend component (IC1), the atmosphere error (gray lines) is dominant (IC1 in Fig. 5.11). For the other components, those of GRACE coefficients and the sampling error (black lines) are the dominant source of uncertainty (IC2, IC and IC4 in Fig. 5.11). The dominant behavior of the atmospheric error for IC1 is most likely due to the erroneous behavior of the atmospheric de-aliasing products over the polar regions (Forootan et al., ...
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... the magnitude of propagated errors, for the trend component (IC1), the atmosphere error (gray lines) is dominant (IC1 in Fig. 5.11). For the other components, those of GRACE coefficients and the sampling error (black lines) are the dominant source of uncertainty (IC2, IC and IC4 in Fig. 5.11). The dominant behavior of the atmospheric error for IC1 is most likely due to the erroneous behavior of the atmospheric de-aliasing products over the polar regions (Forootan et al., ...
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... first independent mode (spatial pattern of IC1 in Fig. 5.10 and IC1 in Fig. 5.11) captures the dominant linear trend that has been detected over polar regions such as Greenland, Alaska and Antarctica. IC1 thus represents a considerable ice-mass loss over the polar regions during the period of study (cf. Velicogna and Wahr, 2005). Some smaller mass decrease is also detected in the first independent mode such as the one over west of Australia (see also ). In contrast, signals of moderate mass increase have been detected over the northern part of South America, as well as crustal uplift in the northern part of the Canadian shield (Rangelova and Sideris, ...
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... This approach is found to be effective during geomagnetic storms because the pronounced temporal and spatial changes during these events enhance the model-data integration. An application of this technique during calm periods might be challenging because a comparable level of uncertainties in models and data reduces the efficiency of the decomposition techniques 29 . ...
Estimating global and multi-level Thermosphere Neutral Density (TND) is important for studying coupling processes within the upper atmosphere, and for applications like orbit prediction. Models are applied for predicting TND changes, however, their performance can be improved by accounting for the simplicity of model structure and the sampling limitations of model inputs. In this study, a simultaneous Calibration and Data Assimilation (C/DA) algorithm is applied to integrate freely available CHAMP, GRACE, and Swarm derived TND measurements into the NRLMSISE-00 model. The improved model, called ‘C/DA-NRLMSISE-00’, and its outputs fit to these measured TNDs, are used to produce global TND fields at arbitrary altitudes (with the same vertical coverage as the NRLMSISE-00). Seven periods, between 2003-2020 that are associated with relatively high geomagnetic activity selected to investigate these fields, within which available models represent difficulties to provide reasonable TND estimates. Independent validations are performed with along-track TNDs that were not used within the C/DA framework, as well as with the outputs of other models such as the Jacchia-Bowman 2008 and the High Accuracy Satellite Drag Model. The numerical results indicate an average 52%, 50%, 56%, 25%, 47%, 54%, and 63% improvement in the Root Mean Squared Errors of the short term TND forecasts of C/DA-NRLMSISE00 compared to the along-track TND estimates of GRACE (2003, altitude 490 km), GRACE (2004, altitude 486 km), CHAMP (2008, altitude 343 km), GOCE (2010, altitude 270 km), Swarm-B (2015, altitude 520 km), Swarm-B (2017, altitude 514 km), and Swarm-B (2020, altitude 512 km), respectively.
... This view is followed in this paper by proposing an alternative decomposition-based data assimilation (DDA) technique that takes advantage of PCA (Jolliffe 2005) for dimension reduction. This step can be replaced with more sophisticated techniques such as applying the independent component analysis (ICA) as in Forootan and Kusche (2012); Forootan (2014);and Forootan et al. (2018). Unlike many previous studies (e.g., Matsuo et al. 2001Matsuo et al. , 2005Matsuo et al. , 2012, the formulated DDA works based on the ensemble of model outputs and observations; thus, it contains the positive features of the EnKF-based techniques, which means that this new DDA formulation considers the uncertainty of model outputs. ...
... The differences between the NeQuick (TIEGCM) and DDA-NeQuick (DDA-TIEGCM) compared to the GIM/ CODE indicate that the reduction of error around EIA is found to be 50 (30)% approximately. • Statistical measures indicate that the DDA-NeQuick and DDA-TIEGCM perform better than the original models, compared to the final product GIM/CODE, in both This work can be extended by performing other decomposition techniques such as independent component analysis (ICA Forootan andKusche 2012, 2013). The DDA can be tested on irregular observations (not-gridded) such as scatter GNSS-derived VTEC estimates from the IGS stations. ...
An accurate estimation of ionospheric variables such as the total electron content (TEC) is important for many space weather, communication, and satellite geodetic applications. Empirical and physics-based models are often used to determine TEC in these applications. However, it is known that these models cannot reproduce all ionospheric variability due to various reasons such as their simplified model structure, coarse sampling of their inputs, and dependencies to the calibration period. Bayesian-based data assimilation (DA) techniques are often used for improving these model’s performance, but their computational cost is considerably large. In this study, first, we review the available DA techniques for upper atmosphere data assimilation. Then, we will present an empirical decomposition-based data assimilation (DDA), based on the principal component analysis and the ensemble Kalman filter. DDA considerably reduces the computational complexity of previous DA implementations. Its performance is demonstrated by updating the empirical orthogonal functions of the empirical NeQuick and the physics-based TIEGCM models using the rapid global ionosphere map (GIM) TEC products as observation. The new models, respectively, called ‘DDA-NeQuick’ and ‘DDA-TIEGCM,’ are then used to predict TEC values for the next day. Comparisons of the TEC forecasts with the final GIM TEC products (that are available after 11 days) represent an average \(42.46\%\) and \(31.89\%\) root mean squared error (RMSE) reduction during our test period, September 2017.
... The EOF vectors are orthogonal and reveal the spatial structure (x, y) of major factors of data; the PC is orthogonal and represents the temporal feature of the amplitude for each EOF. This technique has been applied to analysis of global or regional climate change, sea surface variability, and the Equivalent Water Height (EWH) of the grids from a time series of monthly estimates of the gravitational spherical harmonic coefficients (SHC) as outlined by Wahr et al. (1998), Forootan and Kusche (2012), Forootan (2014), or to the potential field (Löcher & Kusche, 2021). Talpe et al. (2017) directly applied the EOF analysis to the SHC from GRACE and SLR, and we provide a short review of the theory behind our application of the EOF analysis of the GRACE-based SHC to the SLR estimates. ...
It is essential that the Satellite Laser Ranging (SLR) estimates of C20 and C30 are as reliable as possible for GRACE and GRACE Follow‐on science applications. Experiments in combining SLR and GRACE data indicated that not accounting for the influence of the higher‐degree even zonal terms results in a lower trend for C20 and slightly overestimates the annual variation. The data are insufficient for separating C30 and C50 within a month from the five satellites used in GRACE Technical Note 11 (TN11) (Cheng & Ries, 2016, https://podaac‐tools.jpl.nasa.gov/drive/files/allData/grace/docs/TN‐11_C20_SLR.txt). LARES's eccentricity is extremely sensitive to the gravitational perturbations of C30 and plays an important role in the reliable determination of C30. Applying a time‐variable gravity (TVG) forward model (based on GRACE) for the higher‐degree coefficients improves the recovery of the lower‐degree coefficients, such as C30, C50, and C60 when a GRACE‐based empirical orthogonal function (EOF) analysis is also applied. A better time series of C20 and C30 (represented by TN11E as the updated TN11) was determined from seven satellites (including −1 and 2, Starlette, Ajisai, Stella, BEC, and LARES) and adjusting a degree and order 5 (5 × 5) field + C60, C61, and S61 based on the TVG model and an EOF analysis of GRACE. The estimated rate of the C20 is comparable with that from TN14 (Loomis et al., 2019, https://doi.org/10.1029/2019GL082929), but the seasonal variations appear to be better recovered from this study. The time series of C30 from this study is comparable with the GRACE RL06 solution for the period prior to March 2012 and appropriate for application to the GRACE‐FO mission.
... However, this method can only be used for reanalyzing and now-casting the thermosphere, and the reliability of these ratio fields, derived by a limited number of satellite tracks, might be treated with caution. (2) Statistical decomposition techniques ( [9]) have been used to extract the dominant structures of the upper atmosphere dynamics. Then, in the prediction step, state-space techniques such as the Kalman Filter (KF, [14]) are applied to forecast thermosphere variations. ...
In this report, the possibility of using the space-based along-track Thermospheric Neutral Density (TND) estimates for generating the European Space Agency (ESA)'s Level 3 (L3) global multi-level TND data products is assessed. For this, the TND estimates along the CHAMP, GRACE, and Swarm satellites are used as observation within the sequential Calibration and Data Assimilation (C/DA) framework proposed by (Forootan et al., 2020 & 2022: doi:10.1093/gji/ggaa507 & doi:10.1038/s41598-022-05952-y).
The C/DA approach is applied to re-calibrate four key parameters of the NRLMSISE-00 model, which are most sensitive to the thermospheric neutral mass and thermospheric temperature. The model with re-calibrated parameters is called 'C/DA-NRLMSISE-00', whose outputs fit to the space-based TNDs. The C/DA-NRLMSISE-00 is able to forecast TNDs and individual neutral mass compositions at any predefined vertical level (i.e., the same vertical coverage as the NRLMSISE-00) and arbitrary spatial-temporal resolution. Therefore, the C/DA method is tested to produce level 3 (L3) TND data consistent with space-based TND estimates.
Seven periods (October 2003, July 2004, March 2008, April 2010, March 2015, September 2017, and September 2020), associated with relatively high geomagnetic activity, are selected for investigating the L3 products because most of available models represent difficulties to provide reasonable TND estimations. Independent comparisons (validations) are performed with the space-based TNDs that were not used within the C/DA framework (from CHAMP, GRACE, GOCE and Swarm missions), as well as with the outputs of other thermosphere models such as the Jacchia-Bowman 2008 (JB08) and the High Accuracy Satellite Drag Model (HASDM).
The report is also available from ESA: https://earth.esa.int/eogateway/documents/20142/4335041/Swarm-DISC-Pre-Study-5-2_2023.pdf
... However, abnormal sites in the regional network can significantly affect the extraction of CME in such stacking methods. To extract CME more objectively and accurately, the statistical signal decomposition techniques widely utilized in geodetic research [22,23] were introduced to suppress CME. Dong et al. [24] proposed the Principal Component Analysis (PCA) approach for identifying and removing the CME for the southern California integrated GPS network. ...
Common Mode Error (CME) presents a kind of spatially correlated error that is widespread in regional Global Navigation Satellite System (GNSS) networks and should be eliminated during postprocessing of a GNSS position time series. Several spatiotemporal filtering methods have been developed to mitigate the effects of CME. However, such methodologies become inappropriate when missing and noisy data exists. In this research, we introduce a novel spatial filtering algorithm called Weighted Expectation Maximization Principal Component Analysis (WEMPCA) for detecting and removing CME from noisy GNSS position time series with missing values, among which formal errors of daily GNSS solutions are utilized to weight the input data. Compared with traditional PCA and the special case of EMPCA, simulation experiments demonstrate that the new WEMPCA algorithm always has outstanding performance over others. The WEMPCA algorithm was then successfully used to extract the CME from real noisy and missing GNSS position time series in Xinjiang province. Our results show that only the first principal component exhibits significant spatial response, with average values of 70.11%, 66.53%, and 52.45% for North, East, and Up (NEU) components, respectively, indicating that it represents the CME of this region. After removing CME, the canonical correlation coefficients and root mean square error of GNSS residual time series, as well as the amplitudes of power-law noises (PLN), are obviously decreased in all three directions. However, the white noise (WN) amplitudes are found to diminish exclusively in the North and East component, not in the Up components. Moreover, the average velocity differences before and after filtering CME are 0.19 mm/year, 0.03 mm/year, and −0.56 mm/year for the NEU components, respectively, indicating that CME has an influence on the GNSS station velocity estimation. The velocity uncertainty is also reduced by 43.51%, 38.64%, and 40.39% on average for the NEU components, respectively, implying that the velocity estimates are more reliable and accurate after removing CME. Therefore, we conclude that the new WEMPCA approach provides an efficient solution to detect and mitigate CME from the noisy and missing GNSS position time series.
... These profiles are shown by the grey and red lines, respectively, and they are associated with the latitude 0 • and longitude 0 • . These results indicate that by applying C/DA both profiles are modified, whereas the temperature during high (low) solar activity was on average increased by 34 www.nature.com/scientificreports/ is equivalent with 7.52 × 10 −12 ( 8.50 × 10 −12 ) changes in density estimates, respectively. It is worth mentioning that the changes in thermosphere are more complex during storms. ...
... To investigate the dominant spatial and temporal changes caused by applying the C/DA method, the principal component analysis (PCA) 34,74 method is applied on the hourly differences between NRLMSISE-00 and C/DA-NRLMSISE-00 during one day (i.e., February 8th, 2015) and entire February 2015. The mathematical details of PCA are described in the Supplementary file (Section S7 online). ...
... .34 (43.26) degree covering the altitude of 200 to 500 km. This ...
Global estimation of thermospheric neutral density (TND) on various altitudes is important for geodetic and space weather applications. This is typically provided by models, however, the quality of these models is limited due to their imperfect structure and the sensitivity of their parameters to the calibration period. Here, we present an ensemble Kalman filter (EnKF)-based calibration and data assimilation (C/DA) technique that updates the model’s states and simultaneously calibrates its key parameters. Its application is demonstrated using the TND estimates from on-board accelerometer measurements, e.g., those of the Gravity Recovery and Climate Experiment (GRACE) mission (at ∼410 km altitude), as observation, and the frequently used empirical model NRLMSISE-00. The C/DA is applied here to re-calibrate the model parameters including those controlling the influence of solar radiation and geomagnetic activity as well as those related to the calculation of exospheric temperature. The resulting model, called here ‘C/DA-NRLMSISE-00’, is then used to now-cast TNDs and individual neutral mass compositions for 3 h, where the model with calibrated parameters is run again during the assimilation period. C/DA-NRLMSISE-00 is also used to forecast the next 21 h, where no new observations are introduced. These forecasts are unique because they are available globally and on various altitudes (300–600 km). To introduce the impact of the thermosphere on estimating ionospheric parameters, the coupled physics-based model TIE-GCM is run by replacing the O2, O1, He and neutral temperature estimates of the C/DA-NRLMSISE-00. Then, the non-assimilated outputs of electron density (Ne) and total electron content (TEC) are validated against independent measurements. Assessing the forecasts of TNDs with those along the Swarm-A (∼467 km), -B (∼521 km), and -C (∼467 km) orbits shows that the root-mean-square error (RMSE) is considerably reduced by 51, 57 and 54%, respectively. We find improvement of 30.92% for forecasting Ne and 26.48% for TEC compared to the radio occulation and global ionosphere maps (GIM), respectively. The presented C/DA approach is recommended for the short-term global multi-level thermosphere and enhanced ionosphere forecasting applications.
... ICA (Independent Component Analysis) can extract the required source signals from multiple mixed signals from different source signals [6]. Then, the independent components will be extracted by the ICA method [7,8]. Compared with traditional filtering algorithms, ICA is an analysis method based on high-order statistical characteristics. ...
The Antarctic ice sheet change is one of the key factors affecting global climate change. The influence of climate factors obscures the understanding to elevation change of the ice sheet. Due to the lack of understanding of the quantitative relationship between climate events and elevation change of Antarctic ice sheet, we here combined climate factor data to quantify the impact of climate events on the elevation change of Antarctic ice sheet. A strong correlation between climate factors and elevation change of ice sheet was found. And the influence between them exists time delay in some extent. Meanwhile, the influence of climate factors in the Antarctic ice sheet change was separated from the ice sheet change based on the Independent Component Analysis (ICA) and multivariate linear regression model. The study also indicates that the influence of climate factors may be an important contribution for the accelerated decline of ice sheet elevation in the Amundsen Sea.
... The EOFs are data driven orthogonal basis functions that represent the maximum variance of a data set (Forootan, 2014). The EOFs in this study are obtained from the ERA5 0 s humidity and temperature data on 37 pressure levels. ...
The GNSS tomography provides the opportunity to estimate atmospheric wet refractivity, which is important for precise positioning and navigation, as well as for constraining weather and climate models. The GNSS-derived water vapor is often estimated by implementing voxel-based inversions, but this technique is numerically unstable due to the high number of unknown parameters especially in networks covering large areas or when the spatial resolution increases. To mitigate this problem, in this study, we introduce functional based 3 and 4 dimensional (3D and 4D) inversions. Here, the horizontal changes are modelled by the spherical cap harmonic functions. For the vertical component, empirical orthogonal functions derived from ERA5 (Empirical Reanalysis Fifth generation) are applied as background model. The time-dependency is accounted for by applying polynomial spline functions. Numerical results are based on a network of about 190 GPS stations in Germany during 15 days in summer and winter of 2018. Observations from 8 radiosonde stations are applied for comparisons. Our results indicate that the functional tomography is effective and retrieves wet refractivity indices with the mean RMSE (Root Mean Square Error) of about 1.9 ppm. These values are found to be up to 22% smaller than those derived by comparing ERA5 with the radiosonde data.
... 3) Separation of the GRACE TWS signals e.g., soil moisture, groundwater in recent studies is still an active research field and has many unresolved issues. Since inversion and statistical decomposition methods which were applied by Rietbroek (2014), Schmeer et al. (2012 and Forootan (2014) have some limitations in separating different GRACE TWS signals, assimilation of GRACE TWS data into hydrological models by considering the physics of the problem and climate input data provides a unique opportunity to separate different GRACE TWS components. Another important product which is used in DA is satellite or radar soil moisture products e.g., SMOS or AMSR-E, which usually measures top layer soil moisture (e. g., 0-5 cm). ...
Global climate change and anthropogenic impacts lead to alterations in the water cycle, water resource availability and the frequency and intensity of floods and droughts. As a result, developing effective techniques such as hydrological modeling is essential to monitor and predict water storage changes. However, inaccuracies and uncertainties in different aspects of modeling, due to simplification of meteorological physical processes, data limitations and inaccurate climate forcing data limit the reliability of hydrological models. Satellite remote sensing datasets, especially Terrestrial Water Storage (TWS) data which can be obtained from Gravity Recovery and Climate Experiment (GRACE), provide a new and valuable source of data which can augment our understanding of the hydrologic cycle. Merging these new observations with hydrological models can effectively enhance the model performance using advanced statistical and numerical methods, which is known as data assimilation. Assimilation of new observations constrain the dynamics of the model based on uncertainties associated with both model and data, which can introduce missing water storage signals e.g., anthropogenic and extreme climate change effects. Assimilation of GRACE TWS data into hydrological models is a challenging task as provision should be made for handling the errors and then merging them with hydrological models using efficient assimilation techniques. The goal of this paper is to provide an in-depth overview of recent studies on assimilating GRACE TWS data into hydrological models and shed light on their limitations, challenges and progress. We present a comprehensive review of some challenges with GRACE TWS data assimilation into a hydrological model including GRACE TWS errors e.g., the correlated noise of high-frequency mass variations and spatial leakage errors, and how to work with GRACE TWS data errors to use the potential of GRACE TWS data as much as possible. We provide a review of the benefits and limitations of available data assimilation techniques with emphasis on the capability of sequential methods for hydrological applications.
... Here, we prefer ICA over PCA, since it performs better to separate TWSC signal from noise [see, e.g., 45,46]. Besides, ICA's independent modes can better be related to physical phenomena as shown by e.g., [10,14,47]. Approach 1 follows a common data reconstruction procedure similar to [28] and [48], but in the spatial grid domain (TWSC), although Approach 2 is novel and formulated as an iterative ICA-based reconstruction, using the whole period of available GRACE and Swarm TWSC time series, covering 2003-2018. ...
Observing global terrestrial water storage changes (TWSCs) from (inter-)seasonal to (multi-)decade timescales is very important to understand the Earth as a system under natural and anthropogenic climate change. The primary goal of the Gravity Recovery And Climate Experiment (GRACE) satellite mission (2002-2017) and its follow-on mission (GRACE-FO, 2018-onward) is to provide time-variable gravity fields, which can be converted to TWSCs with ∼ 300 km spatial resolution; however, the one year data gap between GRACE and GRACE-FO represents a critical discontinuity, which cannot be replaced by alternative data or model with the same quality. To fill this gap, we applied time-variable gravity fields (2013-onward) from the Swarm Earth explorer mission with low spatial resolution of ∼ 1500 km. A novel iterative reconstruction approach was formulated based on the independent component analysis (ICA) that combines the GRACE and Swarm fields. The reconstructed TWSC fields of 2003-2018 were compared with a commonly applied reconstruction technique and GRACE-FO TWSC fields, whose results indicate a considerable noise reduction and long-term consistency improvement of the iterative ICA reconstruction technique. They were applied to evaluate trends and seasonal mass changes (of 2003-2018) within the world's 33 largest river basins.
