Comparison of accelerometer data calibration methods used in thermospheric neutral density estimation

Ultra-sensitive space-borne accelerometers on board of low Earth orbit (LEO) satellites are used to measure non-gravitational forces acting on the surface of these satellites. These forces consist of the Earth radiation pressure, the solar radiation pressure and the atmospheric drag, where the first two are caused by the radiation emitted from the Earth and the Sun, respectively, and the latter is related to the thermospheric density. On-board accelerometer measurements contain systematic errors, which need to be mitigated by applying a calibration before their use in gravity recovery or thermospheric neutral density estimations. Therefore, we improve, apply and compare three calibration procedures: (1) a multi-step numerical estimation approach, which is based on the numerical differentiation of the kinematic orbits of LEO satellites; (2) a calibration of accelerometer observations within the dynamic precise orbit determination procedure and (3) a comparison of observed to modeled forces acting on the surface of LEO satellites. Here, accelerometer measurements obtained by the Gravity Recovery And Climate Experiment (GRACE) are used. Time series of bias and scale factor derived from the three calibration procedures are found to be different in timescales of a few days to months. Results are more similar (statistically significant) when considering longer timescales, from which the results of approach (1) and (2) show better agreement to those of approach (3) during medium and high solar activity. Calibrated accelerometer observations are then applied to estimate thermospheric neutral densities. Differences between accelerometer-based density estimations and those from empirical neutral density models, e.g., NRLMSISE-00, are observed to be significant during quiet periods, on average 22 % of the simulated densities (during low solar activity), and up to 28 % during high solar activity. Therefore, daily corrections are estimated for neutral densities derived from NRLMSISE-00. Our results indicate that these corrections improve model-based density simulations in order to provide density estimates at locations outside the vicinity of the GRACE satellites, in particular during the period of high solar/magnetic activity, e.g., during the St. Patrick's Day storm on 17 March 2015

Comparisons of atmospheric data and reduction methods for the analysis of satellite gravimetry observations

[1] The Gravity Recovery and Climate Experiment (GRACE) derived gravity solutions contain errors mostly due to instrument noise, anisotropic spatial sampling, and temporal aliasing. Improving the quality of satellite gravimetry observations, in terms of using more sensitive sensors and/or increasing the spatial isotropy, has been discussed in the context of the designed scenarios of future satellite gravimetry missions. Temporal aliasing caused by incomplete reducing of background models, however, is still a factor that affects the quality of the gravity field solutions. This paper specifically explores the possible physical, geometrical, and numerical modifications of the three‒dimensional (3‒D) integration approach to eliminate the high‒frequency atmospheric effects from satellite gravimetry observations. The new modified 3‒D approach is then applied to compute new sets of atmospheric dealiasing products, using atmospheric fields from the European Centre for Medium‒Range Weather Forecasts (ECMWF) operational analysis model and ERA‒Interim reanalysis. Impacts of modifications are compared to the prelaunch baseline and the current error‒curve of GRACE as well as an error‒curve of a Bender‒type multiorbit satellite configuration. Specifically, we found that using latitude‒dependent radius, latitude‒ and altitude‒dependent gravity accelerations along with numerical modifications have a considerable impact on the 3‒D integral. Comparing the new products to those of GRACE Atmosphere and Ocean Dealiasing level‒1B shows a nonnegligible difference with respect to the prelaunch baseline of GRACE and a possible Bender‒type mission up to harmonic degrees 13 and 50, respectively. A big difference is also found between the derived dealiasing products from ECMWF operational analysis and ERA‒Interim indicating the importance of input parameters on the final atmospheric dealiasing products

Comparing multi-objective optimization techniques to calibrate a conceptual hydrological model using in situ runoff and daily GRACE data

Hydrological models are necessary tools for simulating the water cycle and for understanding changes in water resources. To achieve realistic model simulation results, real-world observations are used to determine model parameters within a “calibration” procedure. Optimization techniques are usually applied in the model calibration step, which assures a maximum similarity between model outputs and observations. Practical experiences of hydrological model calibration have shown that single-objective approaches might not be adequate to tune different aspects of model simulations. These limitations can be as a result of (i) using observations that do not sufficiently represent the dynamics of the water cycle, and/or (ii) due to restricted efficiency of the applied calibration techniques. To address (i), we assess how adding daily Total Water Storage (dTWS) changes derived from the Gravity Recovery And Climate Experiment (GRACE) as an extra observations, besides the traditionally used runoff data, improves calibration of a simple 4-parameter conceptual hydrological model (GR4J, in French: mod`ele du G´enie Rural `a 4 param`etres Journalier) within the Danube River Basin. As selecting a proper calibration approach (in ii) is a challenging task and might have significant influence on the quality of model simulations, for the first time, four evolutionary optimization techniques, including the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the Multi-objective Particle Swarm Optimization (MPSO), the Pareto Envelope-Based Selection Algorithm II (PESA-II), and the Strength Pareto Evolutionary Algorithm II (SPEA-II) along with the Combined objective function and Genetic Algorithm (CGA) are tested to calibrate the model in (i). A number of quality measures are applied to assess cardinality, accuracy, and diversity of solutions, which include the Number of Pareto Solutions (NPS), Generation Distance (GD), Spacing (SP), and Maximum Spread (MS). Our results indicate that according toMS and SP, NSGA-II performs better than other techniques for calibrating GR4J using GRACE dTWS and in situ runoff data. Considering GD as a measure of efficiency, MPSO is found to be the best technique. CGA is found to be an efficient method, while considering the statistics of the GR4J’s 4 calibrated parameters to rank the optimization techniques. The Nash-Sutcliffe model efficiency coefficient is also used to assess the predictive power of the calibrated hydrological models, for which our results indicate satisfactory performance of the assessed calibration experiments

Improving the recovery of monthly regional water storage using one year simulated observations of two pairs of GRACE-type satellite gravimetry constellation

Increasing the spatial sampling isotropy is a major issue in designing future missions dedicated to continue the task of the Gravity Recovery And Climate Experiment (GRACE) mission. From various possible future satellite gravimetry scenarios, the two-pair multi-orbit satellite configuration (Bender-type in the sequence), consisting of a coupled semi-polar pair (the same as GRACE) and an inclined pair of satellites seems to be an optimal mission choice. This contribution examines the performance of a Bender-type scenario at altitudes of 335 km and 352 km and inclinations of 89° and 63°, respectively, for improving the regional recovery of hydrological signals. To this end, we created one full year of simulated observations of the GRACE and Bender-type configurations. Our investigations include: 1) evaluating the feasible spatial resolution for the recovery of terrestrial water storage (TWS) changes in the presence of realistic instrumental noise and errors in the background models; 2) assessing the influence of aliasing errors in the TWS recovery and its separation from instrumental noise and introduced hydrological signals; and 3) analyzing the regional quality of the gravity-derived TWS results by assessing water storage changes over the 33 world major river basins. From our simulations, the Bender-derived spectral error curves indicate that, in spite of the instrumental noise, aliasing errors still contaminate the gravity fields above geopotential spherical harmonic coefficient (SHC) degree and order (d/o) 80 till 100. Regarding to the TWS recovery, we found notable improvements for the Bender-type configuration results in medium and small-scale basins, such as the Brahmaputra, Euphrates, Ganges, Indus, Mekong basins in Asia and the Yellow and Orange basins in South Africa. These results were achieved without applying post-processing, which was unachievable using simulations of one pair of GRACE-like configuration. Comparing the magnitudes of errors in the Bender-derived solutions with those of GRACE indicate that the accuracy derived from the Bender-type fields is about two times better than that of GRACE, specifically at medium spatial resolutions of 250 km (SHC d/o 80). We truncated the TWS recovery up to SHC d/o 80 in the spectral domain, whereas all comparisons are demonstrated in the spatial domain after a truncation of the solutions and WGHM field at d/o 60, since beyond this range; a relatively strong instrumental and aliasing errors contaminate the solutions. Our numerical results indicate that the spatial resolution of the Bender-type TWS recovery can be even higher for the basins with strong temporal water storage variations such as the Amazon basin. Short wavelength mass variations in basins with relatively weaker temporal TWS magnitude, such as the Murray basin, might still need the application of a filter with small averaging kernel

Comparisons of atmospheric mass variations derived from ECMWF reanalysis and operational fields, over 2003 to 2011

There are two spurious jumps in the atmospheric part of the Gravity Recovery and Climate Experiment-Atmosphere and Ocean De-aliasing level 1B (GRACE-AOD1B) products, which occurred in January-February of the years 2006 and 2010, as a result of the vertical level and horizontal resolution changes in the ECMWFop (European Centre for Medium-Range Weather Forecasts operational analysis). These jumps cause a systematic error in the estimation of mass changes from GRACE time-variable level 2 products, since GRACE-AOD1B mass variations are removed during the computation of GRACE level 2. In this short note, the potential impact of using an improved set of 6-hourly atmospheric de-aliasing products on the computations of linear trends as well as the amplitude of annual and semi-annual mass changes from GRACE is assessed. These improvements result from 1) employing a modified 3D integration approach (ITG3D), and 2) using long-term consistent atmospheric fields from the ECMWF reanalysis (ERA-Interim). The monthly averages of the new ITG3D-ERA-Interim de-aliasing products are then compared to the atmospheric part of GRACE-AOD1B, covering January 2003 to December 2010. These comparisons include the 33 world largest river basins along with Greenland and Antarctica ice sheets. The results indicate a considerable difference in total atmospheric mass derived from the two products over some of the mentioned regions. We suggest that future GRACE studies consider these through updating uncertainty budgets or by applying corrections to estimated trends and amplitudes/phases

Developing a Complex Independent Component Analysis (CICA) technique to extract non-stationary patterns from geophysical time series

In recent decades, decomposition techniques have enabled increasingly more applications for dimension reduction, as well as extraction of additional information from geophysical time series. Traditionally, the principal component analysis (PCA)/empirical orthogonal function (EOF) method and more recently the independent component analysis (ICA) have been applied to extract, statistical orthogonal (uncorrelated), and independent modes that represent the maximum variance of time series, respectively. PCA and ICA can be classified as stationary signal decomposition techniques since they are based on decomposing the autocovariance matrix and diagonalizing higher (than two) order statistical tensors from centered time series, respectively. However, the stationarity assumption in these techniques is not justified for many geophysical and climate variables even after removing cyclic components, e.g., the commonly removed dominant seasonal cycles. In this paper, we present a novel decomposition method, the complex independent component analysis (CICA), which can be applied to extract non-stationary (changing in space and time) patterns from geophysical time series. Here, CICA is derived as an extension of real-valued ICA, where (a) we first define a new complex dataset that contains the observed time series in its real part, and their Hilbert transformed series as its imaginary part, (b) an ICA algorithm based on diagonalization of fourth-order cumulants is then applied to decompose the new complex dataset in (a), and finally, (c) the dominant independent complex modes are extracted and used to represent the dominant space and time amplitudes and associated phase propagation patterns. The performance of CICA is examined by analyzing synthetic data constructed from multiple physically meaningful modes in a simulation framework, with known truth. Next, global terrestrial water storage (TWS) data from the Gravity Recovery And Climate Experiment (GRACE) gravimetry mission (2003–2016), and satellite radiometric sea surface temperature (SST) data (1982–2016) over the Atlantic and Pacific Oceans are used with the aim of demonstrating signal separations of the North Atlantic Oscillation (NAO) from the Atlantic Multi-decadal Oscillation (AMO), and the El Niño Southern Oscillation (ENSO) from the Pacific Decadal Oscillation (PDO). CICA results indicate that ENSO-related patterns can be extracted from the Gravity Recovery And Climate Experiment Terrestrial Water Storage (GRACE TWS) with an accuracy of 0.5–1 cm in terms of equivalent water height (EWH). The magnitude of errors in extracting NAO or AMO from SST data using the complex EOF (CEOF) approach reaches up to ~50% of the signal itself, while it is reduced to ~16% when applying CICA. Larger errors with magnitudes of ~100% and ~30% of the signal itself are found while separating ENSO from PDO using CEOF and CICA, respectively. We thus conclude that the CICA is more effective than CEOF in separating non-stationary patterns

Over exploitation of groundwater in the centre of Amman Zarqa Basin-Jordan: evaluation of well data and GRACE satellite observations

Jordan faces a sincere water crisis. Groundwater is the major water resource in Jordan and most of the ground water systems are already exploited beyond their estimated safe yield. The Amman Zarqa Basin is one of the most important groundwater systems in Jordan, which supplies the three largest cities in Jordan with drinking and irrigation water. Based on new data the groundwater drawdown in the Amman Zarqa Basin is studied. This basin is the most used drainage area in Jordan. Groundwater drawdown in eight central representative monitoring wells is outlined. Based on almost continuous data for the last 15 years (2000–2015) an average drawdown for the whole basin in the order of 1.1 m·a−1 is calculated. This result is in accordance with results of previous studies in other areas in Jordan and shows that, until now, no sustainable water management is applied. Groundwater management in such a basin presents a challenge for water managers and experts. The applicability of satellite data for estimating large-scale groundwater over exploitation, such as gravity products of the Gravity Recovery and Climate Experiment (GRACE) mission, along with supplementary data, is discussed. Although the size of the basin is below the minimum resolution of GRACE, the data generally support the measured drawdown

Updating ESA's Earth System Model for gravity mission simulation studies: 1. Model description and validation

The ability of any satellite gravity mission concept to monitor mass transport processes in the Earth system is typically tested well ahead of its implementation by means of various simulation studies. Those studies often extend from the simulation of realistic orbits and instrumental data all the way down to the retrieval of global gravity field solution time-series. Basic requirement for all these simulations are realistic representations of the spatio-temporal mass variability in the different sub-systems of the Earth, as a source model for the orbit computations. For such simulations, a suitable source model is required to represent (i) high-frequency (i.e., subdaily to weekly) mass variability in the atmosphere and oceans, in order to realistically include the effects of temporal aliasing due to non-tidal high-frequency mass variability into the retrieved gravity fields. In parallel, (ii) low-frequency (i.e., monthly to interannual) variability needs to be modelled with realistic amplitudes, particularly at small spatial scales, in order to assess to what extent a new mission concept might provide further insight into physical processes currently not observable. The new source model documented here attempts to fulfil both requirements: Based on ECMWF’s recent atmospheric reanalysis ERA-Interim and corresponding simulations from numerical models of the other Earth system components, it offers spherical harmonic coefficients of the time-variable global gravity field due to mass variability in atmosphere, oceans, the terrestrial hydrosphere including the ice-sheets and glaciers, as well as the solid Earth. Simulated features range from sub-daily to multiyear periods with a spatial resolution of spherical harmonics degree and order 180 over a period of 12 years. In addition to the source model, a de-aliasing model for atmospheric and oceanic high-frequency variability with augmented systematic and random noise is required for a realistic simulation of the gravity field retrieval process, whose necessary error characteristics are discussed. The documentation of the updated ESA Earth System Model (updated ESM) for gravity mission simulation studies is organized as follows: The characteristics of the updated ESM along with some basic validation is presented in Volume 1. A detailed comparison to the original ESA ESM (Gruber et al., 2011) is provided in Volume 2, while Volume 3 contains the description of a strategy to derive realistic errors for the de-aliasing model of high-frequency mass variability in atmosphere and ocean