Vertical Velocity Estimates Research Articles

Time-varying observer of the supporting body velocity for vibration units

The problem of controlled passage through resonance zone for mechanical systems with several degrees of freedom is analyzed. Existing control algorithms based on speed-gradient method require measurement of the full state vector of the system. In this paper a novel control algorithm based on a time-varying partial observer for the supporting body vertical velocity estimation is designed. The proposed observer is based on the simplified nonlinear model of the two-mass oscillatory system. Efficiency of the controlled passage through resonance zone with the control algorithm based on the proposed observer is analyzed by means of computer simulation for full model of the mechanical system.

Estimation of vertical migration velocity of 137Cs in the Mount IDA/Kazdagi, Turkey

This paper presents the results obtained from a radioecological study carried out in the forest sites of Mount IDA (Kazdagi)/Edremit, Turkey. For 118 soil profiles, the depth distribution of 137Cs activity was established by fitting the experimental points to an exponential, a gaussian or a log-normal function. The relaxation lengths were in the range of 1.09–16.7 cm with a mean of 5.73 cm, showing a slow transport and a strong retention capacity of 137Cs even after the 26-y period of Chernobyl accident. From the data for the vertical distribution of 137Cs in soil profiles, the mean annual migration velocity of 137Cs was in the range of 0.11–0.62 cm year−1 with a mean of 0.30 cm year−1. Statistically significant correlations between the thickness of the humus layer and the mean annual velocity of 137Cs were found for both coniferous and mixed forest sites. The mean annual velocity of 137Cs in the forests sites with Pinus nigra var pallasiana was significantly higher than sites with Pinus brutia. External dose-rates from the 137Cs in forest soils were estimated using a conversion factor used in many studies and comprised with the external dose-rates determined according to the vertical distribution of 137Cs within the soil depth profiles. It is clearly seen that both levels and spatial distribution patterns of the external dose-rates from 137Cs were influenced considerably with the vertical migration rate and the vertical distribution of 137Cs.

Quantifying error of lidar and sodar Doppler beam swinging measurements of wind turbine wakes using computational fluid dynamics

Abstract. Wind-profiling lidars are now regularly used in boundary-layer meteorology and in applications such as wind energy and air quality. Lidar wind profilers exploit the Doppler shift of laser light backscattered from particulates carried by the wind to measure a line-of-sight (LOS) velocity. The Doppler beam swinging (DBS) technique, used by many commercial systems, considers measurements of this LOS velocity in multiple radial directions in order to estimate horizontal and vertical winds. The method relies on the assumption of homogeneous flow across the region sampled by the beams. Using such a system in inhomogeneous flow, such as wind turbine wakes or complex terrain, will result in errors. To quantify the errors expected from such violation of the assumption of horizontal homogeneity, we simulate inhomogeneous flow in the atmospheric boundary layer, notably stably stratified flow past a wind turbine, with a mean wind speed of 6.5 m s−1 at the turbine hub-height of 80 m. This slightly stable case results in 15° of wind direction change across the turbine rotor disk. The resulting flow field is sampled in the same fashion that a lidar samples the atmosphere with the DBS approach, including the lidar range weighting function, enabling quantification of the error in the DBS observations. The observations from the instruments located upwind have small errors, which are ameliorated with time averaging. However, the downwind observations, particularly within the first two rotor diameters downwind from the wind turbine, suffer from errors due to the heterogeneity of the wind turbine wake. Errors in the stream-wise component of the flow approach 30% of the hub-height inflow wind speed close to the rotor disk. Errors in the cross-stream and vertical velocity components are also significant: cross-stream component errors are on the order of 15% of the hub-height inflow wind speed (1.0 m s−1) and errors in the vertical velocity measurement exceed the actual vertical velocity. By three rotor diameters downwind, DBS-based assessments of wake wind speed deficits based on the stream-wise velocity can be relied on even within the near wake within 1.0 m s−1 (or 15% of the hub-height inflow wind speed), and the cross-stream velocity error is reduced to 8% while vertical velocity estimates are compromised. Measurements of inhomogeneous flow such as wind turbine wakes are susceptible to these errors, and interpretations of field observations should account for this uncertainty.

Geodetic vertical velocities affected by recent rapid changes in polar motion

Abstract Secular motion of Earth's rotation pole results in large-scale secular deformation of Earth. Here, we investigate the magnitude of the deformation that has resulted from the rapid motion of the rotation pole to the east since ∼2005. We show that geodetic (GNSS, DORIS, VLBI and SLR) estimates of vertical velocity since ∼2005 have been biased by up to ±0.38 mm yr–1 relative to the longer-term deformation pattern. The largest signals occur within regions that include the U.S. Pacific Coast, Europe and South Pacific islands where geodetic measurements provide essential measurements of tide-gauge vertical movement and important constraints on models of glacial isostatic adjustment. Consequently, geodetic vertical velocities based on recent data should not be interpreted as being identical to centennial or longer term vertical land movement. Since 2010 the effect is further amplified by the overprediction of the IERS polar motion model relative to the ongoing secular change in pole position—during this time geodetic vertical velocities based on the IERS pole tide model are not just biased relative to the long-term rates but also from actual post-2010 Earth deformation. For geophysical or reference frame studies seeking geodetic vertical velocities that are representative of decadal timescales, where interannual variation is considered noise, the correction for this non-linear effect is straightforward, requiring an elastic computation using a reference rate of polar motion that is linear over the timescales of interest.

Heat fluxes across the Antarctic Circumpolar Current in Drake Passage: Mean flow and eddy contributions

AbstractIn contrast to a long‐standing belief, observations in the Antarctic Circumpolar Current (ACC) show that mean velocity vectors rotate with depth, thus suggesting a possible importance of the time‐mean flow for the local poleward heat transport. The respective contributions of the eddy and mean flows to the heat flux across the ACC in Drake Passage (DP) are investigated using recently acquired and historical time series of velocity and temperature from a total of 24 current meter moorings and outputs of a high‐resolution (1/12°) model with realistic topography. Only 11 out of the 24 depth‐integrated eddy heat flux estimates are found to be significant, and they are poleward. Model depth‐integrated eddy heat fluxes have similar signs and amplitudes as the in situ estimates at the mooring sites. They are mostly poleward or nonsignificant, with amplitude decreasing to the south. The cross‐stream temperature fluxes caused by the mean flow at the moorings have a sign that varies with location and corresponds to the opposite of the vertical velocity estimates. The depth‐integrated temperature fluxes due to the mean flow in the model exhibit small spatial scales and are of opposite sign to the bottom vertical velocities. This suggests that the rotation of the mean velocity vectors with depth is mainly due to bottom topography. The rough hilly topography in DP likely promotes the small‐scale vertical velocities and temperature fluxes. Eddy heat fluxes and cross‐stream temperature fluxes are integrated over mass‐balanced regions defined by the model transport streamlines. The contribution of the mean flow to the ocean heat fluxes across the Southern ACC Front in DP (covering about 4% of the circumpolar longitudes) is about four times as large as the eddy heat flux contribution and the sum of the two represent on the order of 10% of the heat loss to the atmosphere south of 60°S.

Vadose zone lag time and potential 21st century climate change effects on spatially distributed groundwater recharge in the semi-arid Nebraska Sand Hills

Summary Deep drainage of water below plant root zones (potential groundwater recharge) will become groundwater recharge (GR) after a delay (or lag time) in which soil moisture traverses the vadose zone before reaching the water table. Depending on the thickness of the vadose zone, the magnitude of deep drainage, and soil hydraulic properties, lag times will vary broadly, exceeding decades to centuries in semi-arid and arid environments. Yet, studies of future climate change impacts to GR have typically avoided focusing on impacts beyond 100 years and often neglect to consider lag effects caused by the vadose zone. We investigate the effects of vadose zone lag time and potential 21st century climate change on the spatial distribution and timing of GR throughout the semi-arid Nebraska Sand Hills (NSH) region (∼50,000 km2). We propose a simple and rapid quantitative approach for assessment of the groundwater system response time to changes in climate. Understanding of such effects is needed for groundwater modeling, analysis of climate change impacts on groundwater, and the effective management and sustainability of future water resources. Lag time estimates are made using the pressure-based vertical velocity of soil moisture changes, equivalent to a kinematic wave approximation of Richards’ equation. The underlying assumptions (unit hydraulic gradient and relatively slow changes in climate) are supported by observations in the High Plains aquifer region, encompassing the NSH. The analysis relies on four sources of input data, including: Spatially distributed high resolution (1.1-km) GR rates (as the difference in 2000–2009 mean precipitation and evapotranspiration—estimated using a novel MODIS-based approach); thickness of the vadose zone—based on 30-m digital elevation models of the land surface and water table elevations; statistically downscaled estimates of future (2010–2099) potential GR rates from two hydroclimate model projections (WRCP CMIP3) with opposing GR trends; and estimates of hydraulic conductivity and vertical velocity of the vadose zone pressure changes using the van Genuchten–Mualem equation. We found that vadose zone lag times (with a mean GR rate of 78 mm/yr for 2000–2009) have an estimated spatial mean of 5.28 yrs (vertical velocity of 5.68 m/yr). End-of-century lag times (with mean potential GR rates of 128 and 61 mm/yr for 2090–2099) have estimated spatial means of 3.78 and 6.55 yrs (vertical velocities of 8.13 and 4.69 m/yr) for wet and dry scenarios, respectively. Findings suggest that the highly conductive materials (primarily sand deposits) and high potential GR rates in the NSH lead to relatively quick drainage of vadose zone water on the order of several years (less than a decade) for the entire 21st century. However, considerable spatial variations of lag times exist due to gradients in potential GR rates and the highly variable vadose zone thickness in the NSH.

A sensor fusion method for tracking vertical velocity and height based on inertial and barometric altimeter measurements.

A sensor fusion method was developed for vertical channel stabilization by fusing inertial measurements from an Inertial Measurement Unit (IMU) and pressure altitude measurements from a barometric altimeter integrated in the same device (baro-IMU). An Extended Kalman Filter (EKF) estimated the quaternion from the sensor frame to the navigation frame; the sensed specific force was rotated into the navigation frame and compensated for gravity, yielding the vertical linear acceleration; finally, a complementary filter driven by the vertical linear acceleration and the measured pressure altitude produced estimates of height and vertical velocity. A method was also developed to condition the measured pressure altitude using a whitening filter, which helped to remove the short-term correlation due to environment-dependent pressure changes from raw pressure altitude. The sensor fusion method was implemented to work on-line using data from a wireless baro-IMU and tested for the capability of tracking low-frequency small-amplitude vertical human-like motions that can be critical for stand-alone inertial sensor measurements. Validation tests were performed in different experimental conditions, namely no motion, free-fall motion, forced circular motion and squatting. Accurate on-line tracking of height and vertical velocity was achieved, giving confidence to the use of the sensor fusion method for tracking typical vertical human motions: velocity Root Mean Square Error (RMSE) was in the range 0.04–0.24 m/s; height RMSE was in the range 5–68 cm, with statistically significant performance gains when the whitening filter was used by the sensor fusion method to track relatively high-frequency vertical motions.

Nonparametric estimation of wave dispersion in high‐rise buildings by seismic interferometry

SUMMARYInterferometric identification and health monitoring of high‐rise buildings has been gaining increasing interest in recent years. The wave dispersion in the structure has been largely ignored in these efforts but needs to be considered to further develop these methods. In this paper, (i) the goodness of estimation of vertical wave velocity in buildings, as function of frequency, by two nonparametric interferometric techniques is examined, using realistic fixed‐base Timoshenko beam benchmark models. Such models are convenient because the variation of phase and group velocities with frequency can be derived theoretically. The models are those of the NS and EW responses of Millikan Library. One of the techniques, deconvolution interferometry, estimates the phase velocity on a frequency band from phase difference between motions at two locations in the structure, while the other one estimates it approximately at the resonant frequencies based on standing wave patterns. The paper also (ii) examines the modeling error in wave velocity profiles identified by fitting layered shear beam in broader band impulse response functions of buildings with significant bending flexibility. This error may affect inferences on the spatial distribution of damage from detected changes in such velocity profiles. Copyright © 2014 John Wiley & Sons, Ltd.

Variability in the vertical distribution and advective transport of eight mesozooplankton taxa in spring in Rivers Inlet, British Columbia, Canada

Zooplankton vertical distribution data and velocity estimates from a hydrodynamicmodel were employed to determine zooplankton daily exchange during four cruisesconducted from March to June 2010 in Rivers Inlet, a fjord in central BritishColumbia, Canada. Zooplankton transport rates varied temporally, being fastest inMarch when water velocities were highest. The active vertical movement of thezooplankton interacted with the vertically sheared flow field to influence zooplanktonadvection. Surface dwelling plankton such as Acartia longiremis and larvaceans experi-enced the highest advection losses of 20.4 and 20.5 day

Aerosol plume after the Chelyabinsk bolide

In this work, the bolide is studied as an atmospheric event causing significant release of meteoritic dust into the stratosphere. Ground-based pictures taken by eyewitnesses and images from the Japan geostationary satellite MTSAT-2 are used as a database. The analysis of the ground-based pictures allows the altitude of the main burst to be estimated as 22.9 ± 1.6 km. It is shown that the top of the cloud formed due to the main burst rose to 11 km for about 60–80 s due to convection, which provides an estimate of the maximum vertical velocity of 130–180 m/s. According to calculations, the upper part of the trail is affected by a strong wind drift and is located at an altitude of >53 km, in the mesosphere. The MTSAT-2 data show that the mesospheric part of the trail traveled southwestward, while the stratospheric part, northeastward, with velocities higher than 100 km/h.

Kinematic structure of a wildland fire plume observed by Doppler lidar

Wildland fires present a challenging environment to make meteorological measurements. Observations in the vicinity of wildland fires are needed to better understand fire‐atmosphere interactions and to provide data for the evaluation of coupled fire‐atmosphere models. An observational study was conducted during a low‐intensity prescribed fire in an area of complex terrain with grass fuels east of San José, California. A ground‐based scanning Doppler lidar acquired radial wind velocities and backscatter intensity in and around the fire plume from multiple horizontal and vertical scans. The development of a convergence zone was consistently observed to exist downwind of the plume and was indicated by a decrease in radial velocity of 3–5 m s−1. Divergence calculations made from the lidar radial velocities showed that the magnitude of convergence ranged between −0.06 and −0.08 s−1 downwind of the plumes, while a maximum of −0.14 s−1 occurred within the plume near the fire front. Increased radial velocities were observed at the plume boundary, indicating fire‐induced acceleration of the wind into the base of the convection column above the fire front. Thermodynamic measurements made with radiosondes showed the smoke plume had a potential temperature perturbation of 3.0 to 4.4 K and an increase in water vapor mixing ratio of 0.5 to 1.0 g kg−1. Plume heights determined from sequential range height indicator scans provided estimates of vertical velocity between 0.4 and 0.6 m s−1, representing the ambient background vertical velocity as the top of the plume likely reached equilibrium.

A unified equation for the vertical velocity of fluid parcels in the context of quasi-geostrophic potential-vorticity equations

Quasi-geostrophic potential-vorticity equations in the inertial regime are obtained by eliminating the ageostrophic vertical velocity from two coupled equations: a vorticity equation and a local conservation equation which depends on special properties of the fluid considered each time. In this paper, a unified equation governing the nondimensional ageostrophic vertical velocity for barotropic and baroclinic flows, in both the oceanic and atmospheric context is presented. Then, the results are applied to determine a wide variety of quasi-geostrophic potential-vorticity equations. Moreover, the estimate of the related dimensional vertical velocity is carried out on general grounds.

Estimates of vertical land motion along the southwestern coasts of Turkey from coastal altimetry and tide gauge data

The differences between coastal altimetry and sea level time series of tide gauges in between March 1993 and December 2009 are used to estimate the rates of vertical land motion at three tide gauge locations along the southwestern coasts of Turkey. The CTOH/LEGOS along-track coastal altimetry retrieves altimetric sea level anomalies closer to the coast than the standard along-track altimetry products. However, the use of altimetry very close to the coast is not found to improve the results. On the contrary, the gridded and interpolated AVISO merged product exhibits the best agreement with tide gauge data as it provides the smoothest variability both in space and time compared with along track altimetry data. The Antalya gauge to the south (in the Mediterranean Sea) and the Mentes/Izmir gauge to the west (in the Aegean Sea) both show subsidence while the Bodrum tide gauge to the south (in the Aegean Sea) shows no significant vertical land motion. The results are compared and assessed with three independent geophysical vertical land motion estimates like from GPS. The GIA effect in the region is negligible. The VLM estimates from altimetry and tide gauge data are in good agreement both with GPS derived vertical velocity estimates and those inferred from geological and archaeological investigations.

Aspects of CO2 advection measurements

Observations of vegetation–atmosphere exchange of carbon dioxide (CO2) by the eddy covariance (EC) technique are limited by difficult conditions such as nighttime and heterogeneous terrain. Thus, advective flux components are included into the net ecosystem exchange (NEE) budget. However, advection measurements are experimentally challenging and do not always help to solve the night flux problem of the EC technique. This study investigates alternative methods for the observation of horizontal advection, in particular horizontal concentration gradients, as well as different approaches to coordinate rotation and vertical advection. Continuous high-frequency measurements of the horizontal CO2 concentration field are employed and compared to the often used discontinuous sequential sampling. Significant differences were found in the case of 30-min mean concentration values between the conventional discontinuous sampling approach and the complete observation of the time series by continuous sampling. Estimates of vertical advection rely on accurate estimates of vertical wind velocity (\(\emph{w}\)). Therefore, different approaches to the planar fit coordinate rotation have been investigated. Sector-wise rotation was able to eliminate directional dependencies of mean \(\emph{w}\). Furthermore, the effect of the data set length used for rotation (window length) was investigated and was found to have significant impact on estimates of vertical advection, with larger window lengths yielding about 50% larger vertical advection. A sequential planar fit with controlled window length is proposed to give reproducible results. The different approaches to the measurement and calculation of horizontal and vertical advection presented are applied to data obtained during the exchange processes in mountainous region experiment at the FLUXNET site Waldstein–Weidenbrunnen (DE-Bay). Estimates of NEE including advection are compared to NEE from turbulent and storage flux alone without advection. NEE including vertical advection with sector-wise planar fit rotation and controlled window length and including horizontal advection from continuous gradient measurements, which were comprehensively bias corrected by a new approach, did compare well with the expected night flux error, with meteorological drivers of the fluxes and with soil chamber measurements. Unrealistically large and noisy values of horizontal advection from the conventional discontinuous sampling approach, which lead to unrealistic values of NEE, could be eliminated by the alternative approaches presented. We therefore suggest the further testing of those approaches at other sites in order to improve the accuracy of advection measurements and, subsequently, estimates of NEE.

Activity classification using a single chest mounted tri-axial accelerometer

Accelerometer-based activity monitoring sensors have become the most suitable means for objective assessment of mobility trends within patient study groups. The use of minimal, low power, IC (integrated circuit) components within these sensors enable continuous (long-term) monitoring which provides more accurate mobility trends (over days or weeks), reduced cost, longer battery life, reduced size and weight of sensor. Using scripted activities of daily living (ADL) such as sitting, standing, walking, and numerous postural transitions performed under supervised conditions by young and elderly subjects, the ability to discriminate these ADL were investigated using a single tri-axial accelerometer, mounted on the trunk. Data analysis was performed using M atlab ® to determine the accelerations performed during eight different ADL. Transitions and transition types were detected using the scalar (dot) product technique and vertical velocity estimates on a single tri-axial accelerometer was compared to a proven discrete wavelet transform method that incorporated accelerometers and gyroscopes. Activities and postural transitions were accurately detected by this simplified low-power kinematic sensor and activity detection algorithm with a sensitivity and specificity of 86–92% for young healthy subjects in a controlled setting and 83–89% for elderly healthy subjects in a home environment.

Merging GPS and Atmospherically Corrected InSAR Data to Map 3-D Terrain Displacement Velocity

A method to derive accurate spatially dense maps of 3-D terrain displacement velocity is presented. It is based on the merging of terrain displacement velocities estimated by time series of interferometric synthetic aperture radar (InSAR) data acquired along ascending and descending orbits and repeated GPS measurements. The method uses selected persistent scatterers (PSs) and GPS measurements of the horizontal velocity. An important step of the proposed method is the mitigation of the impact of atmospheric phase delay in InSAR data. It is shown that accurate vertical velocities at PS locations can be retrieved if smooth horizontal velocity variations can be assumed. Furthermore, the mitigation of atmospheric effects reduces the spatial dispersion of vertical velocity estimates resulting in a more spatially regular 3-D velocity map. The proposed methodology is applied to the case study of Azores islands characterized by important tectonic phenomena.

Evidence for a slow subsidence of the Tahiti Island from GPS, DORIS, and combined satellite altimetry and tide gauge sea level records

Monitoring vertical land motion is of crucial interest in observations of long-term sea level change and its reconstruction, but is among of the most, yet highly challenging, tasks of space geodesy. The aim of the paper is to compare the vertical velocity estimates of Tahiti Island obtained from five independent geophysical measurements, namely a decade of GPS and DORIS data, 17 years sea level difference (altimeter minus tide gauge (TG)) time series, ICE-5G (VM2 L90) Post-Glacial Rebound (PGR) model predictions, and coral reef stratigraphy. Except for the Glacial Isostatic Adjustment (GIA also known as PGR) model, all the techniques are in a good agreement and reveal a very slow subsidence of the Tahiti Island averaged at −0.5 mm/yr which is barely significant. Nevertheless, despite of that vertical motion, Tahiti remains an ideal location for the calibration of satellite altimeter measurements.

Expansion of the planar-fit method to estimate flux over complex terrain

An expanded planar-fit (PF) method over complex terrain is presented and applied to coordinate rotation of the eddy-covariance (EC) flux and vertical velocity estimation. Theoretical analysis indicates that PF coefficients depend on wind direction, and an expression of vertical velocity is deduced. We applied the theory using 1 year of observations from the KoFlux site in the Gwangneung Forest in Korea and investigated the influence of wind direction on the PF method. Then, we performed an expansion of the PF method to consider dependence of PF coefficients on wind direction and applied the PF method to every sector. The results show that the PF coefficients and tilt angles over complex terrain vary with wind direction. Two hundred 30-min data sets are sufficient to derive stable PF coefficients over hilly terrain for each sector. The relative difference in eddy-covariance flux between the general planar fit (GPF) and sector planar fit (SPF) is less than 10% for the scalar flux and about 18% for friction velocity. Vertical velocity and vertical advection (VA) terms were also calculated and compared using SPF and GPF methods, and a normal distribution and diurnal trend of real vertical velocity on clear days are presented.

Sea level at Saint Paul Island, southern Indian Ocean, from 1874 to the present

A data archeology exercise was carried out on sea level observations recorded during the transit of Venus across the Sun observed in 1874 from Saint Paul Island (38°41′S, 77°31 E) in the southern Indian Ocean. Historical (1874) and recent (1994–2009) sea level observations were assembled into a consistent time series. A thorough check of the data and its precise geodetic connection to the same datum was only possible thanks to the recent installation of new technologies (GPS buoy and radar water level sensor) and leveling campaigns. The estimated rate of relative sea level change, spanning the last 135 years at Saint Paul Island, was not significantly different from zero (−0.1 ± 0.3 mm yr−1), a value which could be reconciled with estimates of global average sea level rise for the 20th century assuming the DORIS vertical velocity estimate at Amsterdam Island (100 km distant) could be applied to correct for the land motion at the tide gauge. Considering the scarcity of long‐term sea level data in the Southern Hemisphere, the exercise provides an invaluable additional observational constraint for further investigations of the spatial variability of sea level change, once vertical land rates can be determined.

Twentieth century constraints on sea level change and earthquake deformation at Macquarie Island

SUMMARY Through the combination of rare historical sea level observations collected during Sir Douglas Mawson’s 1911–1914 Australasian Antarctic Expedition (AAE), together with modern sea level data, space geodetic estimates of crustal displacement and modelling of coseismic and post-seismic earthquake deformation, we present a contemporary analysis to constrain sea level and land level change over the twentieth century at Macquarie Island (54 ◦ 30 � S, 158 ◦ 57 � E). We combine 9 months of 1912–1913 sea level data with intermediate observations in 1969–1971, 1982 and 1998–2007 to estimate sea level rise relative to the land at +4.8 ± 0.6 mm yr −1 . Combined with estimates of global mean sea level rise, this value supports the geologically surprising notion of land subsidence, conflicting with longer term geological evidence that suggests uplift at ∼0.8 mm yr −1 over the last 400–300 Kyr. We investigate the current tectonic evolution of the Island through analysis of Global Positioning System (GPS) solutions that utilize data over the period 2000–2009. Importantly, this provides an opportunity to refine the source parameters of the M w ∼8.0 great earthquake of 2004 December 23 using estimates of coseismic displacements at regional GPS sites. We use the estimated earthquake source and GPS observations of four years of post-seismic deformation at Macquarie Island to infer the rheology of the oceanic upper mantle. We find that an asthenosphere bounded by stronger material above and below is required to produce the observed post-seismic deformation, particularly in the vertical component. Assuming a Maxwell rheology, the best fit is given by an asthenospheric viscosity of 3×10 19 Pa s. The inferred rheology determined from the 2004 earthquake is used to model long period post-seismic deformation from M w ∼8.0 earthquakes of 1989 and 1924. The 1924 earthquake is the closest of the three great earthquakes to Macquarie Island, and our modelling suggests that the majority of the vertical deformation at the tide gauge over the subsequent 80 years is related to ongoing viscoelastic relaxation from this thrust earthquake that ruptured south from an epicentre south of Macquarie Island. Assimilated time-series of land level change from the earthquake modelling (suggesting ongoing subsidence) constrained by the GPS estimate of vertical velocity of −2.46 ± 0.64 mm yr −1 combine with the relative sea level time-series to yield an estimate of absolute sea level change of +2.0 ± 0.8 mm yr −1 over the twentieth century. We conclude this is consistent with the upper bound of the global average rate of absolute sea level rise over the same period. This represents one of few estimates of observed sea level change in the Southern Ocean, re-emphasizing the importance of historical data and continued geodetic and oceanographic observation in remote areas.