E. Rangelova

Analysis of Gravity Recovery and Climate Experiment time-variable mass redistribution signals over North America by means of principal component analysis

Four years of data provided by the NASA/German Aerospace Center Gravity Recovery and Climate Experiment (GRACE) satellite mission are analyzed over North America using principal component analysis (PCA). Three hydrology models [Global Land Data Assimilation System (GLDAS), Climate Prediction Center (CPC), and Land Dynamics (LaD)] are used to analyze the water mass changes over the same area and time period. The GRACE-observed and the hydrology models mass changes are compared spatially and temporally, and good agreement is observed. Two signal modes are found to represent more than 65% of the GRACE-observed mass variability. The first mode represents mainly mass changes related to the snow accumulation and melting and has maximum amplitude in the western Cordillera and Quebec-Labrador regions. The second mode comprises long-term positive mass changes in central and eastern Canada and negative mass changes in Alaska. In addition, two more spatiotemporal patterns that explain 14% of the GRACE-observed mass variability are extracted and studied, but no definite relation to hydrology is established. While the GLDAS model agrees very well with the GRACE observations, it is found that the CPC model also provides useful information for validating the GRACE-observed mass changes in North America. On the basis of the results of this study, we can state that principal component analysis is a useful technique for extracting and validating regional hydrology signals from GRACE gravity field data. The main advantage of PCA is the capability to extract interannual and nonperiodic mass changes in addition to long-term and periodic variations.

Assessment of the capabilities of the temporal and spatiotemporal ICA method for geophysical signal separation in GRACE data

We investigate the potential of two independent component analysis (ICA) methods, i.e., the temporal and spatiotemporal ICA, for separating geophysical signals in Gravity Recovery and Climate Experiment (GRACE) data. These methods are based on the assumption of the statistical independence of the signals and thus separate the GRACE-observed mass changes into maximal independent signals. These two ICA methods are compared to the conventional principal component analysis (PCA) method. We test the three methods with respect to their ability to separate a periodic hydrological signal from a trend signal originating in the solid Earth or the cryosphere with simulated and Center for Space Research GRACE mass changes for the time period of January 2003 to December 2010. In addition, we investigate whether the methods are capable of separating hydrological annual and semiannual mass variations. It is shown that both ICA methods are superior to PCA when non-Gaussian mass variations are analyzed. Furthermore, the spatiotemporal ICA resolves successfully the lack of full temporal and spatial independence of the geophysical signals observed by GRACE both in global and regional simulation scenarios. Although the temporal and spatiotemporal ICA are nearly equivalent, both superior to PCA in the global GRACE analysis, the spatiotemporal ICA proves to be more efficient in regional applications by recover more reliably the postglacial rebound trend in North America and the bimodal total water storage variability in Africa.

Spatiotemporal Analysis of the GRACE-Derived Mass Variations in North America by Means of Multi-Channel Singular Spectrum Analysis

We apply multi-channel singular spectrum analysis (MSSA) to infer the main spatiotemporal modes of mass variability in North America derived from GRACE monthly gravity field data. MSSA is a data-adaptive method for analyzing time lagged maps of variability on regional and global scales. The method proves useful in studying the annual and long-term continental water mass variations and the secular deformation signal associated with glacial isostatic adjustment (GIA) of the Earth.

The GBVP approach for vertical datum unification: recent results in North America

Two levelling-based vertical datums have been used in North America, namely CGVD28 in Canada and NAVD88 in the USA and Mexico. Although the two datums will be replaced by a common and continent-wide vertical datum in a few years, their connection and unification are of great interest to the scientific and user communities. In this paper, the geodetic boundary value problem (GBVP) approach is studied as a rigorous method for connecting two or more vertical datums through computed datum offsets from a global equipotential surface defined by a GOCE-based geoid. The so-called indirect bias term, the effect of the GOCE geoid omission error, the effect of the systematic levelling datum errors and distortions, and the effect of the geodetic data errors on the datum unification are four important factors affecting the practical implementation of this approach. These factors are investigated numerically using the GNSS-levelling and tide gauge stations in Canada, the USA, Alaska, and Mexico. The results show that the indirect bias term can be omitted if a GOCE-based global geopotential model is used in gravimetric geoid computations. The omission of the indirect bias term simplifies the linear system of equations for the estimation of the datum offset(s). Because of the existing systematic levelling errors and distortions in the Canadian and US levelling networks, the datum offsets are investigated in eight smaller regions along the Canadian and US coastal areas. Using GNSS-levelling stations in the US coastal regions, the mean datum offset can be estimated with a 1 cm standard deviation if the GOCE geoid omission error is taken into account by means of the local gravity and topographic information. In the Canadian Atlantic and Pacific regions, the datum offsets can be estimated with 2.3 and 3.5 cm standard deviation, respectively, using GNSS-levelling stations. However, due to the low number of tide gauge stations, the standard deviation of the CGVD28 and NAVD88 datum offsets can reach one decimetre in the Pacific regions. With the available GNSS-levelling stations in Alaska and Mexico, the NAVD88 datum offset can be estimated with a standard deviation below 3 cm. The numerical investigations of this study provide, for the first time, the datum offsets between North American vertical datums and their associated standard deviations with which the offsets can be estimated. The results of this study demonstrate the importance of the aforementioned four factors in the practical implementation of the GBVP approach for the unification of the levelling-based vertical datums.

First Results on Height System Unification in North America Using GOCE

We study the impact of GOCE on the North American height system unification by assessing different factors: the performance of the GOCE global geopotential models, the models’ omission error and its effect on the computed mean height datum offsets, and the effect of the biased local gravity data. Depending on the distribution of the data points, the omission error of the third release time-wise GOCE model used up to degree and order 180 contributes 13–15 cm to the computed mean offset of CGVD28 in Canada and only 2 cm to the mean offset of NAVD88 in the USA. The effect of the biased local gravity anomalies on the datum offsets is assessed by means of Stokes’s integration with the original and residual kernels in a regional simulation scenario. This effect is found to be negligible when GOCE geopotential models are used in the computation of the geoid heights.

Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models

Abstract The performance of GOCE-based geopotential models is assessed for the estimation of offsets for three regional vertical datums in Canada with respect to a global equipotential surface using the GNSS benchmarks from the first-order vertical control network. Factors that affect the computed value of the local vertical datum offset include the GOCE commission and omission errors, measurement errors, the configuration of the network of GNSS/levelling benchmarks, and systematic levelling errors and distortions propagated through the vertical control network. Among these various factors, the effect of the GOCE omission error on the datum offsets is investigated by extending the models with the high resolution gravity field model EGM2008 and by means of Canada’s official high resolution geoid model CGG2010. The effect of the GOCE commission error in combination with errors from the GNSS/levelling data is also examined, in addition to the effect of systematic levelling errors. In Canada, the effect of the GOCE omission error is at the dm-level when computing local vertical datum offsets. The effect of including accuracy information for the GNSS/levelling data and the GOCE geoid heights can be up to 4 cm over the Canadian mainland and at the dm-level for island regions. Lastly, the spatial tilts found in the levelling network can be modelled with a 2-parameter bias corrector model, which reduces the RMS of the adjusted geoid height differences by 4 cm when compared to the RMS of adjusted geoid height differences computed without the use of a bias corrector model. Thus, when computing local vertical datum offsets in Canada, it is imperative to account for GOCE commission and omission errors, ellipsoidal and levelling height errors, as well as the systematic levelling errors of the vertical control network.

Implementing a Dynamic Geoid as a Vertical Datum for Orthometric Heights in Canada

The geoid heights in Canada are subject to secular dynamic changes caused by the slow glacial isostatic adjustment of the viscoelastic Earth. As a result, the reference surface for orthometric heights changes with time at a level that is an order of magnitude smaller than the rate of change of heights. The objective of this paper is to provide a feasibility study on implementing the geoid as a dynamic vertical datum. For this purpose, the most accurate GPS ellipsoidal heights from the CBN (Canadian Base Network), orthometric heights from the most recent minimally constrained adjustment of the primary vertical control network and the latest geoid model for Canada are used. In this approach, the dynamic geoid is treated in the context of the combined adjustment of the ellipsoidal, orthometric and geoid heights.

North American height datums and their offsets: Evaluation of the GOCE-based global geopotential models in Canada and the USA

Abstract The Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission was launched on March 17, 2009. Three generations of global geopotential models have been computed and released based on the data collected by GOCE since then. The first generation of the models has been computed from the first two months of the data, and more observations, ranging from six to eight months, have been used in the computation of the second generation models. The third generation models are based on eighteen months of GOCE observations. The evaluation of these models is important in view of Canada’s and the USA’s decision to modernize and unify their vertical datums based on the geoid. In this paper, the released GOCE-based models are evaluated using 1315 and 18399 GNSS/levelling stations in Canada and the USA, respectively. In addition, three GRACE-based models and EGM2008 are included in the evaluation procedure as ’pre-GOCE era’ models to identify any improvements brought by the new GOCE-based models in the region. The results provide evidence that the third generation time-wise (go_cons_gcf_2_tim_r3) and direct approach (go_cons_gcf_2_dir_r3) GOCE models perform slightly better than the rest of the geopotential models in Canada and the USA

How Significant is the Dynamic Component of the North American Vertical Datum

Abstract One of the main current geodetic activities in North America is the definition and establishment of a geoid-based vertical datum that will replace the official CGVD28 and NAVD88 datums in Canada and the USA, respectively. The new datum will also have a time-dependent (dynamic) component required by the targeted one-centimetre accuracy of the datum. Heights of the levelling benchmarks are subject to temporal changes, which contribute to the degradation of the accuracy of the datum and increase the misfit of the geoid heights determined gravimetrically and by GNSS/levelling. The zero level surface, i.e., the geoid, also changes with time, most significantly due to postglacial rebound, climate-induced loss of polar ice masses and mountain glaciers, and hydrology variations. In this study, we examine the possible changes of the datum due to the aforementioned factors. We are mostly concerned with postglacial rebound as it can contribute more than 1 mm per year and more than 1 cm per decade to the geoid change. We also assess the significance of the temporal geoid and benchmark height changes and show that, compared to its current accuracy, the geoid change is only significant after a decade mostly in the flat areas of central Canada.

North American height datums and their offsets: The effect of GOCE omission errors and systematic levelling effects

Abstract One of the main scientific objectives of the Gravity field and steady state Ocean Circulation Explorer (GOCE) gravity field satellite mission is its contribution to the global unification of height systems. In this study, we compute the offsets of three height datums in North America (NAVD88, CGVD28 and Nov07) against a common equipotential surface. NAVD88 and CGVD28 are the official vertical datums for the USA and Canada, respectively. Nov07 is the latest unofficial adjustment of the first-order levelling network in Canada. This datum is only used for the validation of geoid models. The offset for each datum is determined from a combination of ellipsoidal, orthometric and geoid heights. The ellipsoidal heights on benchmarks come from the GNSS networks of Canada and the USA while geoid heights are computed from currently the best GOCE-based geopotential model in North America, i.e., go_cons_gcf_2_tim_r3. The orthometric heights of the GNSS stations are available from the adjustments of the vertical control networks of both countries. Among the various factors that contribute to the uncertainty of the computed datum offset, we investigate the effect of the omission error of the GOCE geoid by means of the EGM2008 model. In Canada, where GNSS/levelling stations are irregularly distributed over the landmass, the effect of the GOCE omission error on the computed offsets reaches one decimetre. Due to the much more densely distributed GNSS/levelling stations in the USA, the effect of the GOCE omission error on the offset of NAVD88 is 3 cm. Therefore, the effect of the omission error of GOCE-based geopotential models should be taken into account in the height datum unification on the North American continent if we aim at the one centimetre accuracy.