Tropospheric delays in ground-based GNSS Multipath Reflectometry – experimental evidence from coastal sites

Recent studies have demonstrated the utility of ground based GNSS Multipath Reflectometry (GNSS-MR) for sea level studies. Typical root-mean-square (RMS) differences of GNSS-MR derived sea level time series with respect to nearby tide gauges are on the order of 6 – 40 cm, sufficiently accurate to estimate tidal and secular sea level variations but are possibly biased due to delay of the signal through the troposphere. In this study we investigate the tropospheric effect from more than 20 GNSS coastal sites located from several meters up to 280 m above sea level. We find a bias in the estimated heights that is elevation and height dependent and can reach orders of 1 m for a 90 m site. Without correcting for tropospheric delay we find that GNSS-MR estimated tidal coefficients will be smaller than their true amplitudes by around 2% while phases seem unaffected. Correcting for the tropospheric delay also improves levelling results as a function of reflector height. Correcting for the tropospheric delay in GNSS-MR for sea level studies is therefore highly recommended for all sites no matter the height of the antenna above the sea surface as it manifests as a scale error

Water surface height determination with a GPS wave glider: a demonstration in Loch Ness, Scotland

A geodetic GPS receiver has been installed on a Wave Glider, an unmanned water surface vehicle. Using kinematic precise point positioning (PPP) GPS, which operates globally without directly requiring reference stations, surface heights are measured with ~0.05-m precision. The GPS Wave Glider was tested in Loch Ness, Scotland, by measuring the gradient of the loch’s surface height. The experiment took place under mild weather, with virtually no wind setup along the loch and a wave field made mostly of ripples and wavelets. Under these conditions, the loch’s surface height gradient should be approximately equal to the geoid slope. The PPP surface height gradient and that of the Earth Gravitational Model 2008 geoid heights do indeed agree on average along the loch (0.03 m km−1). Also detected are 1) ~0.05-m-sized height changes due to daily water pumping for hydroelectricity generation and 2) high-frequency (0.25–0.5 Hz) oscillations caused by surface waves. The PPP heights compare favorably (~0.02-m standard deviation) with relative carrier phase–based GPS processing. This suggests that GPS Wave Gliders have the potential to autonomously determine centimeter-precise water surface heights globally for lake modeling, and also for applications such as ocean modeling and geoid/mean dynamic topography determination, at least for benign surface states such as those encountered during the reported experiment

Changes in mean sea level around Great Britain over the past 200 years

We systematically assimilate a wide range of historical sea level data from around the coast of Great Britain, much of it previously unpublished, into a single comprehensive framework. We show that this greatly increased dataset allows the construction of a robust and extended Mean Sea Level curve for Great Britain covering a period of more than two centuries, and confirms that the 19th century trend was much weaker than that in the 20th century and beyond. As well as attempting to maximise the amount of newly recovered sea level observations, we have also recovered the levelling metadata necessary to connect this 19th and early 20th century data with modern records. We adjust this data for known sources of variability and estimate overall uncertainties over the entire period. Data are processed in 36 regional clusters, before recombining to compute national statistics. We investigate the advantages of extending and adjusting the time series on sea level rise trends and low order variability. Confidence limits are improved by better than 60%. The weighted linear trend since 1900 for the fully adjusted data points from all clusters when averaged annually and adjusted for Glacial Isostatic Adjustment is 2.12 mm/year ± 0.02 mm/year (1-sigma). The much lower trend estimated for the 19th Century alone is 0.24 ± 0.12 mm/yr. There is an acceleration of 0.012 mm/yr2 ± 0.003 mm/yr2 in the rate of rise over the period 1813 to 2018. These trends are quite sensitive to the GIA correction used, but their differences and accelerations are not

Improved and extended tide gauge records for the British Isles leading to more consistent estimates of sea level rise and acceleration since 1958

This paper describes methods of obtaining improved estimates of long-term sea level trends for the British Isles. This is achieved by lengthening the sea level records where possible, then removing known sources of variability, and then further adjusting for datum errors that are revealed by the previous processes after verification using metadata from archived sources. Local sea level variability is accounted for using a tide and surge model. Far field variability is accounted for using a “common mode”. This combination reduces the residual variability seen at tide gauges around the coast of the British Isles to the point that a number of previously unrecognised steps in individual records become apparent, permitting a higher level of quality control to be applied. A comprehensive data archaeology exercise was carried out which showed that these step-like errors are mostly coincident with recorded site-specific changes in instrumentation, and that in many cases the periodic tide gauge calibration records can be used to quantify these steps. A smaller number of steps are confirmed by “buddy-checking” against neighbouring tide gauges. After accounting for the observed steps, using levelling information where possible and an empirical fit otherwise, the records become significantly more consistent. The steps are not found to make a large difference to the trend and acceleration observed in UK sea level overall, but their correction results in much more consistent estimates of first order (Sea Level Rise) and second order (Sea Level Acceleration) trends over this 60-year period. We find a mean rate of sea level rise of 2.39 ± 0.27 mm yr−1, and an acceleration of 0.058 ± 0.030 mm yr−2 between Jan. 1958 and Dec. 2018. The cleaner dataset also permits us to show more clearly that the variability other than that derived from local meteorology is indeed consistent around the UK, and relates to sea level changes along the eastern boundary of the North Atlantic

Weighing the ocean with bottom-pressure sensors: robustness of the ocean mass annual cycle estimate

We use ocean bottom-pressure measurements from 17 tropical sites to determine the annual cycle of ocean mass. We show that such a calculation is robust, and use three methods to estimate errors in the mass determination. Our final best estimate, using data from the best sites and two ocean models, is that the annual cycle has an amplitude of 0.85 mbar (equivalent to 8.4 mm of sea level, or 3100 Gt of water), with a 95% chance of lying within the range 0.61–1.17 mbar. The time of the peak in ocean mass is 10 October, with 95% chance of occurring between 21 September and 25 October. The simultaneous fitting of annual ocean mass also improves the fitting of bottom-pressure instrument drift

Commentary on ‘Coastal Planning Should Be Based on Proven Sea Level Data' by A. Parker and C.D. Ollier (Ocean & Coastal Management, 124, 1–9, 2016)

A recent paper by A. Parker and C.D. Ollier (Ocean & Coastal Management, 124, 1–9, 2016), concerned with the use of 'proven’ sea-level data for coastal planning, contained a number of incorrect or misleading statements about sea-level data sets and measurement methods. In this commentary, we address aspects of sea-level records that could have been misunderstood by readers of that paper. While we agree with the main point made by the authors, that the best possible sea-level data are required by coastal planners, we suggest that planners should base their work on wider and better informed sources of sea-level information

Trends in UK mean sea level revisited.

This paper presents estimates of rates of mean sea level (MSL) change around the UK based on a larger tide gauge data set and more accurate analysis methods than have been employed so far. The spatial variation of the trend in MSL is found to be similar to that inferred from geological information and from advanced geodetic techniques, which is a similar conclusion to that arrived at in previous, less precise and complete studies. The tide gauge MSL trends for 1901 onwards are estimated to be 1.4 +/- 0.2 mm/year larger than those inferred from geology or geodetic methods, suggesting a regional sea level rise of climate change origin several 1/10s mm/year lower than global estimates for the 20th century. However, UK MSL change cannot be described in terms of a simple linear increase alone but includes variations on interannual and decadal timescales. The possible sources of variation in a ‘UK sea level index’ are explored. Air pressure is clearly one such possible source but its direct local forcing through the ‘inverse barometer’ accounts for only one third of the observed variability. A number of larger scale atmospheric and ocean processes must also play important roles, but modelling them satisfactorily and separating the individual contributions presents a major challenge. As regards future regional UK sea level changes, one concludes that there is no basis for major modification to existing projections for the 2080s included in the 2002 UK Climate Impacts Programme studies

Estimation of offsets in GPS time-series and application to the detection of earthquake deformation in the far-field.

Extracting geophysical signals from Global Positioning System (GPS) coordinate time-series is a well-established practice that has led to great insights into how the Earth deforms. Often small discontinuities are found in such time-series and are traceable to either broad-scale deformation (i.e. earthquakes) or discontinuities due to equipment changes and/or failures. Estimating these offsets accurately enables the identification of coseismic deformation estimates in the former case, and the removal of unwanted signals in the latter case which then allows tectonic rates to be estimated more accurately. We develop a method to estimate accurately discontinuities in time series of GPS positions at specified epochs, based on a so-called ‘offset series’. The offset series are obtained by varying the amount of GPS data before and after an event while estimating the offset. Two methods, a mean and a weighted mean method, are then investigated to produce the estimated discontinuity from the offset series. The mean method estimates coseismic offsets without making assumptions about geophysical processes that may be present in the data (i.e. tectonic rate, seasonal variations), whereas the weighted mean method includes estimating coseismic offsets with a model of these processes. We investigate which approach is the most appropriate given certain lengths of available data and noise within the time-series themselves. For the Sumatra–Andaman event, with 4.5 yr of pre-event data, we show that between 2 and 3 yr of post-event data are required to produce accurate offset estimates with the weighted mean method. With less data, the mean method should be used, but the uncertainties of the estimated discontinuity are larger