Zonal mean and tidal dynamics from space: an empirical examination of aliasing and sampling issues

Interpretations of space-based measurements of atmospheric parameters in the mesosphere and thermosphere are complicated by large local-time variations at these altitudes. For this reason, satellite orbits are often preferred which precess through all local times one or more times per season. However, the local-time structure of the atmosphere is inherently non-stationary, which can lead to sampling and aliasing difficulties when attempting to deconvolve the measurements into zonal mean and tidal components. In the present study, hourly radar measurements of mesopause-region winds are used to form a mock data base which can be used to gain insight into implications of the aforementioned problems; the use of actual measurements introduces a realistic element of geophysical temporal variability. Assuming zonal symmetry (i.e., migrating tides superimposed on a zonal mean circulation), the radar measurements are sampled from the satellite perspective for orbital inclinations of 57° and 70°, and compared to the ground or true perspective. These comparisons provide realistic estimates of the errors to be expected when attempting to derive mean and tidal components from space-based measurements. For both diurnal and semidiurnal components, and the quoted satellite inclinations, acceptable errors (3–4 m/s rms) are obtained for data covering 24 h local time (i.e., ascending plus descending nodes); the corresponding errors for singlenode data (12 h local-time coverage) are of order 8–11 m/s, and therefore may not represent reliable estimates of the actual tidal components. There exist certain caveats in connection with the latter conclusion which are discussed.     

On the dynamics and morphology of extensive tidal mudflats: Integrating remote sensing data with an inundation model of Cook Inlet, Alaska

A new method of integrating satellite remote sensing data and inundation models allows the mapping of extensive tidal mudflats in a sub-Arctic estuary, Cook Inlet (CI), Alaska. The rapid movement of the shorelines in CI due to the large tides (~10 m range) is detected from a series of Landsat imagery taken at different tidal stages, whereas GIS tools are used to identify the water coverage in each satellite image and to extract the coordinates of the shoreline. Then, water level along the shoreline for each satellite image is calculated from the observed water level at Anchorage and the statistics of an inundation model. Several applications of the analysis are demonstrated: 1. studying the dynamics of a tidal bore and the flood/ebb processes, 2. identifying climatic changes in mudflats morphology, and 3. mapping previously unobserved mudflat topographies in order to improve inundation models. The method can be used in other regions to evaluate models and improve predictions of catastrophic floods such as those associated with hurricane storm surges and tsunamis.     

Coastal tides in West Greenland derived from tide gauge records

Based on pressure tide-gauge observations, sea-level records are derived for ten sites along the coast of West Greenland. The ocean tidal signal is extracted by a harmonic tidal analysis. The accuracy of the determined tidal constants is discussed in detail. The tides account for 85% of the observed sea-level standard deviation. The tide gauge records reveal significant shallow-water tidal effects, in particular compound and overtide amplitudes reaching 5 cm. The propagation of the tidal waves into the fjords depends strongly on local conditions and is in some cases accompanied by an amplification of the tidal amplitudes. The observed tidal signals are compared to the predictions of the global ocean tide model FES2004. At the outer coast, a good agreement is found. Inside the fjords, however, the model performs worse and tide gauge observations may still be indispensable when accurate tidal signals are required.     

An estimate of the suspended particulate matter (SPM) transport in the southern North Sea using SeaWiFS images,in situ measurements and numerical model results

A study is presented where satellite images (SeaWiFS), in situ measurements (tidal cycle and snapshot) and a 2D hydrodynamic numerical model have been combined to calculate the long term SPM (Suspended Particulate Matter) transport through the Dover Strait and in the southern North Sea. The total amount of SPM supplied to the North Sea through the Dover Strait is estimated to be 31.74×10⁶ t. The satellite images provide synoptic views of SPM concentration distribution but do not take away the uncertainty of SPM transport calculation. This is due to the fact that SPM concentration varies as a function of tide, wind, spring-neap tidal cycles and seasons. The short term variations (tidal, spring-neap tidal cycle) have not been found in the satellite images, however seasonal variations are clearly visible. Furthermore the SPM concentration in the satellite images is generally lower than in the in situ measurements. The representativness of SPM concentration maps derived from satellites for calculating long term transports has therefore been investigated by comparing the SPM concentration variability from the in situ measurements with those of the remote sensing data. The most important constraints of satellite images are related to the fact that satellite data is evidence of clear sky conditions, whereas in situ measurements from a vessel can be carried out also during rougher meteorological conditions and that due to the too low time resolution of the satellite images the SPM concentration peaks are often missed. It is underlined that SPM concentration measurements should be carried out during at least one tidal cycle in high turbidity areas to obtain representative values of SPM concentration.     

Sea level time series and ocean tide analysis from multipath signals at five GPS sites in different parts of the world

We present sea level observations derived from the analysis of signal-to-noise ratio (SNR) data recorded by five coastal GPS stations. These stations are located in different regions around the world, both in the northern and in the southern hemisphere, in different multipath environments, from rural coastal areas to busy harbors, and experience different tidal ranges.The recorded SNR data show periodic variations that originate from multipath, i.e. the interference of direct and reflected signals. The general assumption is that for satellite arcs facing the open sea, the rapid SNR variations are due to reflections off the sea surface. The SNR data recorded from these azimuth intervals were analyzed by spectral analysis with two methods: a standard analysis method assuming a static sea level during a satellite arc and an extended analysis method assuming a time dependent sea level during a satellite arc.The GPS-derived sea level results are compared to sea level records from co-located traditional tide gauges, both in the time and in the frequency domain. The sea level time series are highly correlated with correlation coefficients to the order of 0.89–0.99. The root-mean-square (RMS) difference is 6.2 cm for the station with the lowest tidal range of 165 cm and 43 cm for the station with the highest tidal range of 772 cm. The relative accuracy, defined as the ratio of RMS and tidal range, is between 2.4% and 10.0% for all stations.Comparing the standard analysis method and the extended analysis method, the results based on the extended analysis method agree better with the independent tide gauge records for the stations with a high tidal range. For the station with the highest tidal range (772 cm), the RMS is reduced by 47% when using the extended analysis method. Furthermore, the results also indicate that the standard analysis method, assuming a static sea level, can be used for stations with a tidal range of up to about 270 cm, without performing significantly worse than the extended analysis method.Tidal amplitudes and phases are derived by harmonic analysis of the sea level records. Again, a high level of agreement is observed between the tide gauge and the GPS-derived results. Comparing the GPS-derived results, the results based on the extended analysis method show a higher degree of agreement with the traditional tide gauge results for stations with larger tidal ranges. Spectral analysis of the residuals after the harmonic analysis reveals remaining signal power at multiples of the draconitic day. This indicates that the observed SNR data are to some level disturbed by additional multipath signals, in particular for GPS stations that are located in harbors.     

Thermal tides and studies to tune the mechanistic tidal model using UARS observations

Monthly simulations of the thermal diurnal and semidiurnal tides are compared to High-Resolution Doppler Imager (HRDI) and Wind Imaging Interferometer (WINDII) wind and temperature measurements on the Upper-Atmosphere Research Satellite (UARS). There is encouraging agreement between the observations and the linear global mechanistic tidal model results both for the diurnal and semidiurnal components in the equatorial and mid-latitude regions. This gives us the confidence to outline the first steps of an assimilative analysis/interpretation for tides, dissipation, and mean flow using a combination of model results and the global measurements from HRDI and WINDII. The sensitivity of the proposed technique to the initial guess employed to obtain a best fit to the data by tuning model parameters is discussed for the January and March 1993 cases, when the WINDII day and night measurements of the meridional winds between 90 and 110 km are used along with the daytime HRDI measurements. Several examples for the derivation of the tidal variables and decomposition of the measured winds into tidal and mean flow components using this approach are compared with previous tidal estimates and modeling results for the migrating tides. The seasonal cycle of the derived diurnal tidal amplitudes are discussed and compared with radar observation between 80 and 100 km and 40° S and 40°N.     

Earth tides observed by gravity and GPS in southeastern Alaska

We analyzed gravity data obtained in Juneau and global positioning system (GPS) data obtained from three PBO sites in southeastern Alaska (SE-AK), which are part of a US research facility called ‘EarthScope’, and we compared the obtained tidal amplitudes and phases with those estimated from the predicted tides including both effects of the body tide and ocean tide. Global tide models predict the ocean tides in this region of complex coastline and bathymetry. To improve the accuracy of prediction, we developed a regional ocean tide model in SE-AK.Our comparison results suggest: (1) by taking into account the ocean tide effect, the amplitude differences between the observation and the predicted body tide is remarkably reduced for both the gravity and displacement (e.g. for the M₂ constituent, 8.5–0.3 μGal, and 2.4–0.1 cm at the AB50 GPS site in Juneau in terms of the vector sum of three components of the north–south, east–west and up–down), even though the ocean tide loading is large in SE-AK. (2) We have confirmed the precise point positioning (PPP) method, which was used to extract the tidal signals from the original GPS time series, works well to recover the tidal signals. Although the GPS analysis results still contain noise due to the atmosphere and multipath, we may conclude that the GPS observation surely detects the tidal signals with the sub-centimeter accuracy or better for some of the tidal constituents. (3) In order to increase the accuracy of the tidal prediction in SE-AK, it is indispensable to improve the regional ocean tide model developed in this study, especially for the phase.     

Scales and structure of frontal adjustment and freshwater export in a region of freshwater influence

Sea surface temperature satellite imagery and a regional hydrodynamic model are used to investigate the variability and structure of the Liverpool Bay thermohaline front. A statistically based water mass classification technique is used to locate the front in both data sets. The front moves between 5 and 35 km in response to spring–neap changes in tidal mixing, an adjustment that is much greater than at other shelf-sea fronts. Superimposed on top of this fortnightly cycle are semi-diurnal movements of 5–10 km driven by flood and ebb tidal currents. Seasonal variability in the freshwater discharge and the density difference between buoyant inflow and more saline Irish Sea water give rise to two different dynamical regimes. During winter, when cold inflow reduces the buoyancy of the plume, a bottom-advected front develops. Over the summer, when warm river water provides additional buoyancy, a surface-advected plume detaches from the bottom and propagates much larger distances across the bay. Decoupled from near-bed processes, the position of the surface front is more variable. Fortnightly stratification and re-mixing over large areas of Liverpool Bay is a potentially important mechanism by which freshwater, and its nutrient and pollutant loads, are exported from the coastal plume system. Based on length scales estimated from model and satellite data, the erosion of post-neap stratification is estimated to be responsible for exporting approximately 19% of the fresh estuarine discharge annually entering the system. Although the baroclinic residual circulation makes a more significant contribution to freshwater fluxes, the episodic nature of the spring–neap cycle may have important implications for biogeochemical cycles within the bay.     

Investigation of the time variability of diurnal tides and resonant FCN period

The time variability of diurnal tides was investigated by analyzing gravity observations from global superconducting gravimeter (SG) stations with running time intervals. Through least-square and Bayesian approaches, FCN resonance parameters were estimated for each data section after obtaining the tidal parameters of mainly diurnal tidal waves. The correlation of the time variation in diurnal tidal waves and FCN period was discussed. For comparison, a similar method was used to analyze VLBI observations to study the time variability of nutation terms and FCN period. The variation trend of the FCN period totally depends on the Ψ1 wave in tidal gravity and on the retrograde annual term in nutation. We observed a similar variation trend in the FCN periods obtained from different SG stations worldwide and VLBI observations. The relation between diurnal tides and LOD variations is discussed and the possible mechanisms of the decadal variation in FCN periods were discussed.     

Sediment transport in distributary channels and its export to the pro-deltaic environment in a tidally dominated delta: Fly River, Papua New Guinea

Current metre deployments, suspended sediment measurements and surface sediment samples were collected from three locations within distributary channels of the tidally dominated Fly River delta in southern Papua New Guinea. Net bedload transport vectors and the occurrence of elongate tidal bars indicate that mutually evasive ebb- and flood-dominant transport zones occur in each of the distributary channels. Suspended sediment experiments at two locations show a phase relationship between tidal velocity and sediment concentration such that the net suspended sediment flux is directed seaward. Processes that control the export of fluid muds with concentrations up to 10 g l⁻¹ from the distributary channels across the delta front and onto the pro-delta are assessed in relation to the available data. Peak spring tidal current speeds (measured at 100 cm above the bed) drop off from around 100 cm s⁻¹ within the distributary channels to <50 cm s⁻¹ on the delta front. Gravity-driven, 2-m thick, fluid mud layers generated in the distributary channels are estimated to require at least 35 h to traverse the 20-km-wide, low-gradient (2×10⁻³ degrees) delta front. The velocities of such currents are well below those required for autosuspension. A 1-month time series of suspended sediment concentration and current velocity from the delta front indicates that tidal currents alone are unable to cause significant cross-delta mud transport. Wave-induced resuspension together with tides, storm surge and barotropic return-flow may play a role in maintaining the transport of fine sediment across the delta front, but insufficient data are available at present to make any reliable estimates.     

Earth tides observed by gravity and GPS in southeastern Alaska

We analyzed gravity data obtained in Juneau and global positioning system (GPS) data obtained from three PBO sites in southeastern Alaska (SE-AK), which are part of a US research facility called ‘EarthScope’, and we compared the obtained tidal amplitudes and phases with those estimated from the predicted tides including both effects of the body tide and ocean tide. Global tide models predict the ocean tides in this region of complex coastline and bathymetry. To improve the accuracy of prediction, we developed a regional ocean tide model in SE-AK.Our comparison results suggest: (1) by taking into account the ocean tide effect, the amplitude differences between the observation and the predicted body tide is remarkably reduced for both the gravity and displacement (e.g. for the M₂ constituent, 8.5–0.3 μGal, and 2.4–0.1 cm at the AB50 GPS site in Juneau in terms of the vector sum of three components of the north–south, east–west and up–down), even though the ocean tide loading is large in SE-AK. (2) We have confirmed the precise point positioning (PPP) method, which was used to extract the tidal signals from the original GPS time series, works well to recover the tidal signals. Although the GPS analysis results still contain noise due to the atmosphere and multipath, we may conclude that the GPS observation surely detects the tidal signals with the sub-centimeter accuracy or better for some of the tidal constituents. (3) In order to increase the accuracy of the tidal prediction in SE-AK, it is indispensable to improve the regional ocean tide model developed in this study, especially for the phase.     

Transverse structure of tidal and residual flow and sediment concentration in estuaries

An analytical and a numerical model are used to understand the response of velocity and sediment distributions over Gaussian-shaped estuarine cross-sections to changes in tidal forcing and water depth. The estuaries considered here are characterized by strong mixing and a relatively weak along-channel density gradient. It is also examined under what conditions the fast, two-dimensional analytical flow model yields results that agree with those obtained with the more complex three-dimensional numerical model. The analytical model reproduces and explains the main velocity and sediment characteristics in large parts of the parameter space considered (average tidal velocity amplitude, 0.1–1 m s^− 1 and maximum water depth, 10–60 m). Its skills are lower for along-channel residual flows if nonlinearities are moderate to high (strong tides in deep estuaries) and for transverse flows and residual sediment concentrations if the Ekman number is small (weak tides in deep estuaries). An important new aspect of the analytical model is the incorporation of tidal variations in the across-channel density gradient, causing a double circulation pattern in the transverse flow during slack tides. The gradient also leads to a new tidally rectified residual flow component via net advection of along-channel tidal momentum by the density-induced transverse tidal flow. The component features landward currents in the channel and seaward currents over the slopes and is particularly effective in deeper water. It acts jointly with components induced by horizontal density differences, Coriolis-induced tidal rectification and Stokes discharge, resulting in different along-channel residual flow regimes. The residual across-channel density gradient is crucial for the residual transverse circulation and for the residual sediment concentration. The clockwise density-induced circulation traps sediment in the fresher water over the left slope (looking up-estuary in the northern hemisphere). Model results are largely consistent with available field data of well-mixed estuaries.     

Suspended sediment transport in the German Wadden Sea—seasonal variations and extreme events

The German Wadden Sea (southern North Sea) sediments are composed of both cohesive and non-cohesive deposits. The spatial distribution patterns are mainly driven by wind-induced waves and tidal currents. Transport intensity and duration depend on the hydrodynamic conditions, which vary over time. In this paper, the transport of suspended sediment was investigated on seasonal, tidal and hourly time scales in the back-barrier system of Spiekeroog Island. Long- and short-term data of fair weather periods and two storm events were investigated based on stationary and mobile measurements of currents and waves by Acoustic Doppler Current Profiler (ADCP), in situ particle size and suspended sediment concentration (SSC) measurements by laser in situ scattering and transmissometry (LISST) as well as wind records. The ADCP backscatter intensities were calibrated by means of LISST volume concentration data in order to quantify longer term SSCs and fluxes in the back-barrier system. Values up to 120 mg l⁻¹ were recorded, but concentrations more commonly were below 60 mg l⁻¹. The long-term results confirm former observations of a balanced budget during low-energy (fair weather) conditions in the study area. In general, SSCs were higher during spring tides than during neap tides. The data also clearly show the remobilisation of sediment by tidal current entrainment. The records include two severe storm events, “Britta” (1st November 2006) and “Kyrill” (18th January 2007). The data reveal very complex temporal flow and transport patterns. During both storm events, the export of material was mainly controlled by the interaction of wind, waves and tidal phase. The typical ebb-dominance occurring during fair-weather conditions was temporarily neutralised and even reversed to a flood-dominated situation. During “Kyrill”, the wind and high-waves setup in conjunction with the tidal phase was even able to compress the duration of two successive ebb cycles by over 70%. Although SSCs increased during both storms and higher turbulence lifted particle clouds upwards, an export of suspended matter towards the North Sea was only observed under the conditions taking place during “Britta”. Such fluxes, however, are currently still difficult to quantify because the backscatter intensity during high energy events includes a substantial amount of noise produced by the high turbulence, especially near the water surface.     

Complex demodulation in VLBI estimation of high frequency Earth rotation components

The spectrum of high frequency Earth rotation variations contains strong harmonic signal components mainly excited by ocean tides along with much weaker non-harmonic fluctuations driven by irregular processes like the diurnal thermal tides in the atmosphere and oceans. In order to properly investigate non-harmonic phenomena a representation in time domain is inevitable. We present a method, operating in time domain, which is easily applicable within Earth rotation estimation from Very Long Baseline Interferometry (VLBI). It enables the determination of diurnal and subdiurnal variations, and is still effective with merely diurnal parameter sampling. The features of complex demodulation are used in an extended parameterization of polar motion and universal time which was implemented into a dedicated version of the Vienna VLBI Software VieVS. The functionality of the approach was evaluated by comparing amplitudes and phases of harmonic variations at tidal periods (diurnal/semidiurnal), derived from demodulated Earth rotation parameters (ERP), estimated from hourly resolved VLBI ERP time series and taken from a recently published VLBI ERP model to the terms of the conventional model for ocean tidal effects in Earth rotation recommended by the International Earth Rotation and Reference System Service (IERS). The three sets of tidal terms derived from VLBI observations extensively agree among each other within the three-sigma level of the demodulation approach, which is below 6 μas for polar motion and universal time. They also coincide in terms of differences to the IERS model, where significant deviations primarily for several major tidal terms are apparent. An additional spectral analysis of the as well estimated demodulated ERP series of the ter- and quarterdiurnal frequency bands did not reveal any significant signal structure. The complex demodulation applied in VLBI parameter estimation could be demonstrated a suitable procedure for the reliable reproduction of high frequency Earth rotation components and thus represents a qualified tool for future studies of irregular geophysical signals in ERP measured by space geodetic techniques.     

Interactions between tides and other frequencies in the Indonesian seas

Interactions of tidal constituents and the transfer of energy from the tidal frequencies to other frequencies are investigated using 3-D tidal simulations for the Indonesian seas, focusing on an area of active internal tides. Semidiurnal tides strongly affect diurnal tides; however, semidiurnal tides are essentially unaffected by diurnal tides. The semidiurnal and diurnal constituents interact with each other through non-linear interference, both destructive and constructive. Semidiurnal tides generate harmonics at nearly the diurnal frequency and higher vertical wavenumbers. In Ombai Strait, these harmonics are out of phase with the diurnal tides and interact destructively with the diurnal tides, effectively negating the diurnal response in some locations. However, this is not a general response, and interactions differ between locations. Energy is also transferred from both semidiurnal and diurnal tides to other frequencies across the spectrum, with more energy originating from semidiurnal tides. These energy transfers are not homogeneous, and the spectral responses differ between the Makassar and Ombai Straits, with the region east of Ombai showing a more active surface response compared to a more intense benthic response in Makassar. In deep water away from topography, velocity spectra generally follow the Garrett–Munk (GM) relation. However, in areas of internal tide generation, spectral density levels exceed GM levels, particularly between 4 and 8 cycles per day (cpd), indicating increased non-linear interactions and energy transfer through resonant interactions. The model indicates strong surface trapping of internal tides, with surface velocity spectra having significantly higher energy between 4 and 8 cpd even 100 km away from the prominent sill generating the internal tides.     

A climatology of nonmigrating semidiurnal tides from TIMED Doppler Interferometer (TIDI) wind data

With the launch of the TIMED satellite in December 2001, continuous temperature and wind data sets amenable to MLT tidal analyses became available. The wind measuring instrument, the TIMED Doppler Interferometer (TIDI), is operating since early 2002. Its day- and nighttime capability allows to derive tidal winds over a range of MLT altitudes. This paper presents climatologies (June 2002–June 2005) of monthly mean amplitudes and phases for six nonmigrating semidiurnal tidal components between 85 and 105 km altitude and between 45°S and 45°N latitude (westward propagating wave numbers 4, 3, 1; the standing oscillation s0; and eastward propagating wave numbers 1, 2) in the zonal and meridional wind directions.Amplitude errors are 15–20% (accuracy) and 0.8 m/s (precision). The phase error is 2 h. The TIDI analysis agrees well with 1991–1994 UARS results at 95 km. During boreal winter, amplitudes of a single component can reach 10 m/s at latitudes equatorward of 45°. Aggregate effects of nonmigrating tides can easily reach or exceed the amplitude of the migrating tide. Comparisons with the global scale wave model (GSWM) and the thermosphere–ionosphere–mesosphere–electrodynamics general circulation model (TIME-GCM) are partly inconclusive but they suggest that wave–wave interaction and latent heat release in the tropical troposphere both play an important role in forcing the semidiurnal westward 1, westward 3, and standing components. Latent heat release is the leading source of the eastward propagating components.     

Mapping nonlinear shallow-water tides: a look at the past and future

Overtides and compound tides are generated by nonlinear mechanisms operative primarily in shallow waters. Their presence complicates tidal analysis owing to the multitude of new constituents and their possible frequency overlap with astronomical tides. The science of nonlinear tides was greatly advanced by the pioneering researches of Christian Le Provost who employed analytical theory, physical modeling, and numerical modeling in many extensive studies, especially of the tides of the English Channel. Le Provost’s complementary work with satellite altimetry motivates our attempts to merge these two interests. After a brief review, we describe initial steps toward the assimilation of altimetry into models of nonlinear tides via generalized inverse methods. A series of barotropic inverse solutions is computed for the M tide over the northwest European Shelf. Future applications of altimetry to regions with fewer in situ measurements will require improved understanding of error covariance models because these control the tradeoffs between fitting hydrodynamics and data, a delicate issue in coastal regions. While M can now be robustly determined along the Topex/Poseidon satellite ground tracks, many other compound tides face serious aliasing problems. In memory of Christian Le Provost     

A numerical study of the barotropic tides and tidal energy distribution in the Indonesian seas with the assimilated finite volume coastal ocean model

The tides and tidal energetics in the Indonesian seas are simulated using a three-dimensional finite volume coastal ocean model. The high-resolution coastline-fitted model is configured to better resolve the hydrodynamic processes around the numerous barrier islands. A large model domain is adopted to minimize the uncertainty adjacent to open boundaries. The model results with elevation assimilation based on a simple nudge scheme faithfully reproduced the general features of the barotropic tides in the Indonesian Seas. The mean root-mean-square errors between the observed and simulated tidal constants are 2.3, 1.1, 2.4, and 1.5 cm for M₂, S₂, K₁, and O₁, respectively. Analysis of the model solutions indicates that the semidiurnal tides in the Indonesian Seas are primarily dominated by the Indian Ocean, whereas the diurnal tides in this region are mainly influenced by the Pacific Ocean, which is consistent with previous studies. Examinations of tidal energy transport reveal that the tidal energy for both of the simulated tidal constituents are transported from the Indian Ocean into the IS mainly through the Lombok Strait and the Timor Sea, whereas only M₂ energy enters the Banda Sea and continues northward. The tidal energy dissipates the most in the passages on both sides of Timor Island, with the maximum M₂ and K₁ tidal energy transport reaching about 750 and 650 kW m^–1, respectively. The total energy losses of the four dominant constituents in the IS are nearly 338 GW, with the M₂ constituent dissipating 240.8 GW. It is also shown that the bottom dissipation rate for the M₂ tide is about 1–2 order of magnitudes larger than that of the other three tidal components in the Indonesian seas.     

Lava discharge during Etna's January 2011 fire fountain tracked using MSG-SEVIRI

Etna's January 2011 eruption provided an excellent opportunity to test the ability of Meteosat Second Generation satellite's Spinning Enhanced Visible and InfraRed Imager (SEVIRI) sensor to track a short-lived effusive event. The presence of lava fountaining, the rapid expansion of lava flows, and the complexity of the resulting flow field make such events difficult to track from the ground. During the Etna's January 2011 eruption, we were able to use thermal data collected by SEVIRI every 15 min to generate a time series of the syn-eruptive heat flux. Lava discharge waxed over a ~1-h period to reach a peak that was first masked from the satellite view by a cold tephra plume and then was of sufficient intensity to saturate the 3.9-μm channel. Both problems made it impossible to estimate time-averaged lava discharge rates using the syn-eruptive heat flux curve. Therefore, through integration of data obtained by ground-based Doppler radar and thermal cameras, as well as ancillary satellite data (from Moderate Resolution Imaging Spectrometer and Advanced Very High Resolution Radiometer), we developed a method that allowed us to identify the point at which effusion stagnated, to allow definition of a lava cooling curve. This allowed retrieval of a lava volume of ~1.2 × 10⁶ m³, which, if emitted for 5 h, was erupted at a mean output rate of ~70 m³ s⁻¹. The lava volume estimated using the cooling curve method is found to be similar to the values inferred from field measurements.     

Time-domain modeling of global ocean tides generated by the full lunisolar potential

Traditionally, ocean tides have been modeled in frequency domain with a forcing from selected tidal constituents. It is a natural approach; however, it implicitly neglects non-linearities of ocean dynamics. An alternative approach is time-domain modeling with a forcing given by the full lunisolar potential, i.e., all tidal waves are a priori included. This approach has been applied in several ocean tide models; however, some challenging tasks still remain, for example, assimilation of satellite altimetry data. In this paper, we introduce the assimilative scheme applicable in a time-domain model, which is an alternative to existing techniques used in assimilative ocean tide models. We present results from DEBOT, a global barotropic ocean tide model, which has two modes: DEBOT-h, a purely hydrodynamical mode, and DEBOT-a, an assimilative mode. The accuracy of DEBOT in both modes is assessed through a series of tests against tide gauge data which demonstrate that DEBOT is comparable to state-of-the-art global ocean tide models for major tidal constituents. Furthermore, as signals of all tidal frequencies are included in DEBOT, we also discuss modeling of minor tidal constituents and non-linear compound tides. Our modeling approach can be useful for those applications where the frequency domain approach is not suitable.