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The influence of data quality on the detectability of sea-level height variations
van Onselen, K.L. (2000). The influence of data quality on the detectability of sea-level height variations. Publications on Geodesy, 49. [S.n.]: [s.l.]. ISBN 90-6132-273-1. XVI, 203 pp.
Part of: Publications on Geodesy. Netherlands Geodetic Commission (NCG): Delft. ISSN 0165-1706, more

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Keywords
    Analysis; Measurement; Sea level data; Sea level variations; Tide gauges; Marine

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  • van Onselen, K.L.

Abstract
    For low-lying areas like the Netherlands, an ever-increasing sea level can become a serious threat. Thisis especially true if sea level rise accelerates, e.g., due to greenhouse-gas induced warming. To anticipatepotential troubles, it is important to have a good estimate of the expected behaviour of future sea levels.This requires an accurate description of the present-day sea level variation curve and of foreseeablechanges in this "natural" pattern in the near future. These changes in the behaviour of future sea levelscan be based, c.g., on models predicting global change, hut this is beyond the scow of this thesis.Much simplified, sea level rise over the last century could he described bv a linear regression line.Accelerations of this "natural" pattern have occurred if the slope value of the regression line increases,or higher order regression coefficients arc required to describe the sea-level rise curve. The better thenatural sea level variation curve (as has occurred over the last century) can be determined, t he easier itwill be to detect a significant divergence from this curve. The objective of this thesis is to dotcrmino howwell patterns in sea level height variations can be detected, given the limited quality of the data available.The objective of this thesis requires long sea level height time series. Therefore, only tide gauge data hasbeen used and altiiuetrv SPa level hoight series have not been considered. Tide gauges measure sea levelheights relative to the tide gauge bench marks. Consequently, the resulting sea level height time seriesshow both variations in absolute sea level and vertical movements of the tide gauge bench marks. Bymonitoring the height changes between the tide gauge bench marks and a stable reference height, theserelative sea level heights can (in principle) be converted into absolute sea level changes. Unfortunately,locating a reference point which is truly stable over long time spans will be extremely difficult, if notimpossible.How well a specific sea level variation pattern can be detected depends on the sea level variations themselves,the quality of the tide gauge measurements and, if applicable, the quality of geodetic measurementsused to connect the tide gauge bench marks in height. Based on existing literature, it has been tried togain a dear understanding of these various aspects. Unfortunately, in the literature studied on processeswhich can influence relative sea-level heights, (almost) no mention is made of long-periodic processes(periods over 20 years), while analysis of tide gauge records shows that long-periodic fluctuations withsignificant amplitudes do occur in sea level height time series.Sea level heights as used in this thesis are annual mean sea levels. The quality of these annual meanvalues not only depends on the quality of the tide gauge measurements, but also on the frequency of thesemeasurements. Not only the quality of state-of-the-art techniques is important, but also of tide gaugesand measuring frequencies which were used in the past. Since estimating long-term sea level variationcurves requires long sea level height series, historical measurements have to be used as well. In chapter 3,an overview is given of the measuring precision and systematic errors and limitations characteristic forthe six tide gauge systems commonly used during the last century. Based on information available forDutch tide gauges, an estimate is given of how much the quality of annual mean sea levels deteriorates ifmean values are based on, e.g., mean tide levels instead of on hourly measurements.If data for a number of tide gauges is available, a common sea level variation curve, e.g., applying tothe Dutch coast, can be estimated. Since tide gauge measurements are relative to the local tide gaugebench mark, any vertical movements of the tide gauges relative to one another will have introducedinconsistencies between the individual time series. These inconsistencies reduce the quality of a commonsea level variation curve based on these tide gauge series.As long as tide gauges experience only secular height movements relative to one another, the commonoscillation pattern can still be discerned using techniques like SVD. However, the slope of the estimatedcommon variation curve is determined by the rate of vertical movements of the individual tide gauges.If tide gauges undergo vertical movements which vary in rate and over time, the common oscillationpattern will be affected as well. By relating all sea level height series to the same reference frame (e.g.,NAP) internal differences in relative sea level due to vertical movements of the tide gauge bench marksare removed from the data sets. Ideally, permanent monitoring of the tide gauge bench marks is applied.Nowadays, this can be achieved by means of GPS. However, in the past height differences were usuallybased on spirit levelling.In chapter 6, the quality of three geodetic techniques, i.e., GPS, gravimetry, and spirit levelling isdescribed. In addition, limitations of these techniques when applied to monitoring height changes of tidegauge bench marks are discussed. Since changes in local gravity represent both variations in mass andchanges in station height, gravimetry is not well suited for determining height differences. Uncertaintiesin height differences obtained by GPS can be reduced to within 1 cm. However, the quality of thesemeasurements might be less in harbour areas (e.g., due to signal interference). GPS has the advantagethat it allows for permanent monitoring over large distances, but measurements are only available forthe last few decades. Spirit levelling can produce high precision height differences (over short distances),but is time consuming and prone to systematic errors (especially over long distances). However, levelledheight differences are often the only type of height information available.In the past, tide gauge bench marks have (hopefully) been connected to a local reference frame. Betweensome neighbouring local height datums, height differences have occasionally been obtained as well.However, only since the second European levelling network (UELN-73), the height difference between thecontinent of Europe and Scandinavia and Great Britain respectively is available. These height connectionsconsist of only a single connection line and, consequently, errors in these height differences cannotbe detected by testing. In chapter 8, an indirect method is introduced for connecting vertical datums,which results in dynamic height differences between the fundamental stations in the various height datumzones. An advantage of this method is that quality information (both precision and reliability) of theestimated height differences can de determined as well. Unfortunately, a high quality potential coefficientmodel is required. As a result, only if a new model (to be obtained from the planned GaCE mission)becomes available, height differences between datum zones could be derived with standard deviations of1 cm.The quality of sea level variation curves depends on the method used to estimate these curves. Anumber of data analysing techniques have been tested for their suitability for working with sea level heightdata. Sea level height time series have a number of specific characteristics, for instance non-stationarity,data quality which is not constant for the complete time series, and a wide range of periodic fluctuationswith sometimes variable frequencies and amplitudes. As a result, most of the techniques examined donot work well when applied to sea level height data. It is found that the best techniques for smoothingsea level height series are moving average smoothing and Singular Spectrum Analysis, while estimates offuture sea level heights should be based on either AR(I)MA modelling or regression.To determine how well specific sea level variation patterns can be detected, experiments with a largevariety of simulated sea level height time series have been performed. These simulated time series consistof the curve which needs to be detected (e.g., a linear trend), periodic fluctuations (based on actual tidegauge data) and simulated additional errors. This can either be inaccuracies introduced by the tide gaugeequipment or the height measurements, or (uncorrected for) height variations between tide gauge benchmarks. By applying regression to the simulated time series, it is examined whether or not the originalsea level variation curve can be recovered. It should be noted that statistical significance of estimatedregression coefficients is no guarantee that the "true" sea level variation curve is detected. For example,if linear regression is applied to a sea level series following a quadratic curve, the estimated trend valuecan still be statistically significant. For this reason, often trend estimates are shown as a function of anincreasing number of observations. For the above mentioned example, estimated trend values will steadilyincrease with an increasing number of included observations. Only if the model (of a linear regressionline) fits the data, and if enough observations are available, estimated trend values will stabilise aroundthe trend value actually present in the data set.First, experiments have been performed with sea level height data for a single tide gauge. In this case,the original data relative to the tide gauge bench mark can be used. If (based on external knowledgeof the behaviour of the local sea level) long-periodic fluctuations could be eliminated from the data set,the detectability of a single linear regression line depends on the trend value and the noise level of themeasurements. For sea level data with a trend of 1.5 mm/yr, even if a noise level of 5 cm applies, thistrend can be detected if 35 observations are available. If a simulated time series contains long-periodicfluctuations based on data for tide gauge Den Helder, of the order of 90 years of observations are requiredbefore trend estimates stabilise around the actual trend value on which the data set is based. Therefore,it is concluded that long-periodic fluctuations are the main factor in determining the amount of datarequired to detect a linear trend in a sea level height time series.In chapter 7, using six tide gauge data sets, a common sea level variation curve for the Dutch coastis estimated. In order to eliminate deviations from this common curve caused by height variations of thetide gauge bench marks relative to one another, all tide gauges have to be connected in height to the localreference system (NAP). Inaccuracies in the required height connections introduce inconsistencies betweenthe time series. Since the actual height connection history for the tide gauges is unknown, a number ofscenarios have been used to simulate height connection errors. Experiments show that the quality of theestimated common variation curve not only depends on the precision of the height measurements, butalso on the time span between subsequent height connections. For higher levels of connection noise, it ismore pronounced that the larger the time span between subsequent connections, the less dependable theestimated trend values will be. In order to detect future sea level rise accelerations, historical data has tobe used as well. Experiments show that, iflong periods have elapsed between historic height connections,the precision of future height connections is of almost no importance. Increasing the standard deviation offuture height measurements from 5 mm to 2 cm, or increasing the time span between height connectionsfrom one to 10 years, hardly influences the results.Finally, for the North Sea area, the quality of spatial variation patterns which can be derived basedon trend values for 18 tide gauges, is examined. A spatial pattern in sea level height variations shouldbe based on real differences in trend values for the various locations and not on variations resultingfrom measuring errors and height changes between tide gauge bench marks. Based on experiments withsimulated time series, the following conclusions have been made. If height connections to a local referenceframe are performed every 10 years, ranges of errors in trend estimates (as a function of latitude andlongitude) are three times as large as results based on annual connection of heights. As a result of, e.g.,post-glacial rebound, fundamental stations in the different datum zones can experience height changesrelative to one another. If the individual time series (connected to the local datums) are not correctedfor these relative vertical movements, this will result in large errors in the estimated spatial variationpattern. If height differences between vertical datum zones are based on results derived for Europeanlevelling networks, resulting errors in trend values (as a function of latitude and longitude) will be muchlarger than those caused by the post-glacial rebound movements (of the selected fundamental stations:Amsterdam, Newlyn, and Helsingborg) itself. This same holds for differences in vertical movementsobtained by GPS measurements with a standard deviation of the order of 1 mm/yr.

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