Thermische Energieflüsse an der Wasseroberfläche: Beispiel Sempachersee

Data collected every 20 minutes for 18 months by a meteorological buoy moored on Lake Sempach in Switzerland (maximum depth 86 m, surface area 14.1 km²) are used to calculate different processes contributing to the net heat flux between water and atmosphere. The processes considered are shortwave and longwave radiation, evaporation/condensation and sensible heat transfer. The temporal resolution of the measurements allows the evaluation of the processes occurring on three different time scales: diurnal variations, weather events of a few days and yearly cycles. The heat content of the lake is calculated from quasi-continuous measurements of water temperature at different depths. The yearly amplitude of the heat content is 1100·10⁶ J/m². Short-time variations of the heat flux determined from water temperature analysis agree well with the flux variations modeled using meteorological data. However, the latter generally underestimates the measured net heat flux in the long term. Wind measurements, together with the net heat flux, are used to calculate the Flux Richardson Number and the Monin-Obukov Length. Examples are given to show the predominant influence of the wind on the stratification of the upper water column and thus on the surface water temperature.      

Heat flow in the Ozark Plateau, Arkansas and Missouri: relationship to groundwater flow

Heat flow values were calculated from direct measurements of temperature and thermal conductivity at thirteen sites in the Arkansas-Missouri Ozark Plateau region. These thirteen values are augmented by 101 estimates of heat flow, based on thermal conductivity measurements and temperature gradients extrapolated from bottom-hole temperatures. The regional heat flow profile ranges from 9 mW m⁻² to over 80 mW m⁻², but at least two distinct thermal regimes have been identified. Seven new heat flow determinations are combined with three previously published values for the St. Francois Mountains (SFM), a Precambrian exposure of granitic and rhyolitic basement rocks, average 47 mW m⁻². Radioactive heat production of 76 samples of the exposed rocks in the SFM averages 2.4 μW m⁻² and a typical continental basement contribution of 14 mW m⁻² is implied. Conversely, the sedimentary rock sequence of the plateau is characterized by an anomalously low heat flow, averaging approximately 27 mW m⁻². Groundwater transmissivity values that are based on data from 153 wells in deep regional aquifers demonstrate an inverse relationship to the observed heat flow patterns. The areas of high transmissivity that correspond to areas of low total heat flux suggest that the non-conservative vertical heat flow within the Ozark sedimentary sequence can be attributed to the effects of groundwater flow.     

Graphical analysis of enthalpy-composition relationships in mixed magmas

Enthalpy-composition diagrams (H^*-X) calculated from existing temperature-composition (T-X) phase diagrams and thermodynamic data provide a simple and effective means for evaluating the enthalpy-temperature effects of magma mixing. If athermal mixing is assumed, adiabatic mixing lines on H^*-X diagrams are straight lines because enthalpy, unlike temperature, is an extensive property of a system. Comparison of binary T-X diagrams with their derivative H^*-X diagrams shows that incorrect predictions can be obtained when T-X diagrams are used to analyze mixing problems.An H^*-X diagram calculated using experimentally determined phase equilibria for anhydrous basalt-rhyolite mixtures predicts that adiabatic mixing of basalt and rhyolite at their respective liquidus temperatures will result in small amounts of crystallization ( < 2 wt.% ). Because the phase equilibria of hydrous basalt-rhyolite mixtures have not yet been determined, an H^*-X diagram for such mixtures cannot be constructed. However, existing hydrous phase equilibria can be used to predict whether adiabatic mixtures of anhydrous basalt and hydrous rhyolite will be super- or subliquidus. Calculations at P_total = 200 MPa show that on an H^*-X diagram a mixing chord drawn between anhydrous basalt and water-saturated rhyolite at their respective liquidus temperatures lies below the enthalpy values calculated for a Paricutin andesite and Mt. St. Helens dacite at their estimated liquidus temperatures. This indicates that the liquidus for mixtures of anhydrous basalt and water-saturated rhyolite is noticeably convex upward, suggesting that larger amounts of crystallization will occur than in the anhydrous case.     

Double origin of hydrothermal convective flux variations in the Fossa of Vulcano (Italy)

Soil-temperature measurements can provide information on the distribution of degassing fissures, their relationship to the internal structure of the volcano, and the temporal evolution of the system. At Vulcano Island (Italy), heat flux from a <3 km-deep magma body drives a hydrothermal system which extends across the main Fossa crater. This heat flux is also associated with variable magmatic gas flow. A high-density map of soil-temperatures was made in 1996 at a constant depth of 30 cm on the central and southern inner flanks of the Fossa crater. These measurements extended over an area covering about 0.04 km², across which the heat flux is predominantly associated with a shallow boiling aquifer. The map shows that hot zones relate to structures of higher permeability, mainly associated with a fissure system dating from the last eruptive cycle (1888–1890). From 1996 to January 2005, we studied the evolution of the heat flux for the high temperature part of the map, both by repeating our measurements as part of 14 visits, during which temperatures were measured at a constant depth, and using data from permanent stations which allowed soil-temperatures to be continuously measured for selected vertical profiles. These data allowed us to calculate the heat flux, and its variation, with good precision for values lower than about 100 W m⁻², which is generally the case in the study area. Above 100 W m⁻², although the heat flux value is underestimated, its variations are recorded with an error less than 10%. During the period 1996–2004, two increases in the thermal flux were recorded. The first one was related to the seismic crisis of November 1998 which opened existing or new fissures. The second, in November 2004, was probably due to magma migration, and was associated with minor seismic activity.     

基于同步观测信息利用的高寒湖泊湍流通量数据插补方法

源区划分和质量过滤提高湖面涡动相关通量数据可靠性的同时,却降低了通量时间序列的连续性.为此,本文基于TensorFlow机器学习框架构建了一种超宽人工神经网络(ANN)模型.在选择输入ANN模型的特征变量信息时,我们采取了尽可能获取湍流输送过程中热力、动力学同步观测背景强迫信息的原则.通过ANN模型模拟通量的插补,本文实现了通量时间序列连续性的优化,插补后的羊卓雍错湖面通量数据的时间覆盖率从不足0.40提升至超过0.98.基于10次折叠交叉验证的ANN模型通量模拟性能检验则表明,各个检验组之间ANN模型的模拟误差波动较小,这显示出了较好的稳健性.具体地讲,感热通量、潜热通量和水汽通量原始观测平均值分别约为18.8 W/m~2、81.5 W/m~2和1.84 mmol/(s·m~2),10组交叉验证的插补感热通量、潜热通量和水汽通量平均绝对误差分别为5.4 W/m~2、15.7 W/m~2和0.35 mmol/(s·m~2).这表明本文所探索的ANN建模结构和同步观测变量筛选原则可更充分地利用观测点局地同步观测信息估算通量强度,有效地优化湍流通量数据的时间连续性,从而提升通量数据的可分析性.     

Estimation of spatially distributed surface energy fluxes using remotely‐sensed data for agricultural fields

Land surface energy fluxes are required in many environmental studies, including hydrology, agronomy and meteorology. Surface energy balance models simulate microscale energy exchange processes between the ground surface and the atmospheric layer near ground level. Spatial variability of energy fluxes limits point measurements to be used for larger areas. Remote sensing provides the basis for spatial mapping of energy fluxes. Remote‐sensing‐based surface energy flux‐mapping was conducted using seven Landsat images from 1997 to 2002 at four contiguous crop fields located in Polk County, northwestern Minnesota. Spatially distributed surface energy fluxes were estimated and mapped at 30 m pixel level from Landsat Thematic Mapper and Enhanced Thematic Mapper images and weather information. Net radiation was determined using the surface energy balance algorithm for land (SEBAL) procedure. Applying the two‐source energy balance (TSEB) model, the surface temperature and the latent and sensible heat fluxes were partitioned into vegetation and soil components and estimated at the pixel level. Yield data for wheat and soybean from 1997 to 2002 were mapped and compared with latent heat (evapotranspiration) for four of the fields at pixel level. The spatial distribution and the relation of latent heat flux and Bowen ratio (ratio of sensible heat to latent heat) to crop yield were studied. The root‐mean‐square error and the mean absolute percentage of error between the observed and predicted energy fluxes were between 7 and 22 W m⁻² and 12 and 24% respectively. Results show that latent heat flux and Bowen ratio were correlated (positive and negative) to the yield data. Wheat and soybean yields were predicted using latent heat flux with mean R² = 0·67 and 0·70 respectively, average residual means of −4·2 bushels/acre and 0·11 bushels/acre respectively, and average residual standard deviations of 16·2 bushels/acre and 16·6 bushels/acre respectively (1 bushel/acre ≈ 0·087 m³ ha⁻¹). The flux estimation procedure from the SEBAL‐TSEB model was useful and applicable to agricultural fields. Copyright © 2005 John Wiley & Sons, Ltd.     

Geophysical evidence on the structure of the Taupo Volcanic Zone and its hydrothermal circulation

The Taupo Volcanic Zone (TVZ) of New Zealand is characterised by extensive volcanism and by high rates of magma production. Associated with this volcanism are numerous high-temperature (> 250 °C) geothermal systems through which the natural heat output of 4200 ± 500 MW is channelled. Outside the geothermal fields the heat flow is negligible. The average heat flux from the central 6000 km² of the TVZ, which contains most of the geothermal fields, is 700 mW/m³. This heat flux appears to be more concentrated along the eastern margin of the TVZ.Schlumberger resistivity measurements (AB/2 of 500 m and 1000 m) have identified 17 distinct geothermal fields with natural heat outputs greater than 20 MW. An additional six, low-heat-output geothermal fields also occur, and may represent formerly more active systems now in decline. Two extinct fields have also been identified. The average spacing between fields is 10–15 km. The distribution of geothermal fields does not appear to be directly associated with individual volcanic features except for the geothermal system that occurs within Lake Taupo and which occupies the vent of the 1800 yr.B.P. Taupo eruption. The positions of the geothermal fields do not appear to have varied for at least the last 200,000 years. These data are consistent with a model of large-scale convection occurring throughout the TVZ, in which the geothermal fields represent the upper portion of the rising, high-temperature, convective plumes. The majority of the recharge to the convection system is provided by the downward movement of cold meteoric water between the fields which suppresses the heat flow in these regions.Gravity measurements indicate that to a depth of about 2.5 km the upper layers of the TVZ consist of low-density pyroclastic infill. A seismic refraction interface with velocity change from 3.2 km/s to 5.5 km/s occurs at a similar depth. The cross-sectional area of the convection plumes (identified electrically) appears to increase at depths of 1–2 km, consistent with a decrease in permeability at the depth at which the velocity and density increase.The seismicity is dominated by swarm activity which accounts for about half of all earthquakes and is highly variable in both space and time. The small number of seismic events (and swarms) that have well determined depths show a cut off of seismicity at depths of 7–9 km. The depth of the transition from brittle to ductile behaviour of the rocks is identified with the transition from a regime where heat is transported by (hydrothermal) convection and pore pressures are near-hydrostatic to a regime where heat transport is dominantly conductive and pore pressures are lithostatic. Within the convective region, temperatures are moderated by the circulation of water so that the depth of the transition from convective to conductive heat transfer can be linked to the bottom of the seismogenic zone. Rocks must become ductile within about 1 km of the bottom of the overlying convective zone.Seismic refraction studies suggest that the crust beneath the TVZ is highly thinned with a seismic velocity of about 7.5 km/ s, typical of the upper mantle, occurring at depth of 15 km. Seismological studies indicate the upper mantle is highly attenuating beneath the TVZ. Conductive heat transfer between the bottom of the convective system, at about 8 km, and the base of the material with crustal velocities, at 15 km, is not able to provide all the heat that is discharged at the surface. Repeated intrusion from the mantle may provide the additional heat transport required.     

Estimation of the high-latitude topside electron heat flux using DMSP plasma density measurements

The high-latitude ionosphere interfaces with the hot, tenuous, magnetospheric plasma, and a heat flow into the ionosphere is expected, which has a large impact on the plasma densities and temperatures in the high-latitude ionosphere. The value of this magnetospheric heat flux is unknown. In an effort to estimate the value of the magnetospheric heat flux into the high-latitude ionosphere, and show its effect on the high-latitude ionospheric plasma densities, we ran an ensemble of model runs using the Ionosphere Forecast Model (IFM) with different values of the heat flux through the upper boundary. These model runs included heating from both auroral and solar sources. Then, for each heat flux value, the plasma densities obtained from the model runs, at 840 km, were compared to the corresponding values measured by the DMSP F13 satellite. The heat flux value that gave the best comparison between the measured and calculated plasma densities was considered to be the best estimate for the topside heat flux. The comparison was conducted for a 1-year data set of the DMSP F13 measured plasma densities (4300 consecutive orbits). Our systematic IFM/DMSP plasma density comparisons indicate that when a zero magnetospheric downward heat flux is assumed at the upper boundary of the IFM model, on the average, the IFM underestimates the measured plasma densities by a factor of 2. A good IFM/DMSP plasma density comparison was achieved for each month in 1998 when for each month a constant heat flux was assumed at the upper boundary of the model. For the 12-month period, the heat flux values that gave the best IFM/DMSP plasma density comparisons varied on the average from −0.5×10¹⁰ to −1.5×10¹⁰ eV cm⁻² s⁻¹.     

Ground-based thermal imaging of lava lakes at Erebus volcano,Antarctica

Mount Erebus, a large intraplate stratovolcano dominating Ross Island, Antarctica, hosts the world's only active phonolite lava lakes. The main manifestation of activity at Erebus volcano in December 2004 was as the presence of two convecting lava lakes within an inner crater. The long-lived Ray Lake, ~ 1400 m² in area, was the site of up to 10 small Strombolian eruptions per day. A new but short-lived, ~ 1000–1200 m² lake formed at Werner vent in December 2004 sourced by lava flowing from a crater formed in 1993 by a phreatic eruption. We measured the radiative heat flux from the two lakes in December 2004 using a compact infrared (IR) imaging camera. Daily thermal IR surveys from the Main Crater rim provide images of the lava lake surface temperatures and identify sites of upwelling and downwelling. The radiative heat outputs calculated for the Ray and Werner Lakes are 30–35 MW and 20 MW, respectively. We estimate that the magma flux needed to sustain the combined heat loss is ~ 250–710 kg s^− 1, that the minimum volume of the magma reservoir is 2 km³, and that the radius of the conduit feeding the Ray lake is ~ 2 m.     

A detailed energy budget analysis of river supercooling and the importance of accurately quantifying net radiation to predict ice formation

River supercooling and ice formation is a regular occurrence throughout the winter in northern countries. The resulting frazil ice production can obstruct the flow through intakes along the river, causing major problems for hydropower and water treatment facilities, among others. Therefore, river ice modellers attempt to calculate the river energy budget and predict when supercooling will occur in order to anticipate and mitigate the effects of potential intake blockages. Despite this, very few energy budget studies have taken place during freeze-up, and none have specifically analysed individual supercooling events. To improve our understanding of the freeze-up energy budget detailed measurements of air temperature, relative humidity, barometric pressure, wind speed and direction, short- and longwave radiation, and water temperature were made on the Dauphin River in Manitoba. During the river freeze-up period of late October to early November 2019, a total of six supercooling events were recorded. Analysis of the energy budget throughout the supercooling period revealed that the most significant heat source was net shortwave radiation, reaching up to 298 W/m², while the most significant heat loss was net longwave radiation, accounting for losses of up to 135 W/m². Longwave radiation was also the most significant heat flux overall during the individual supercooling events, accounting for up to 84% of the total heat flux irrespective of flux direction, highlighting the importance of properly quantifying this flux during energy budget calculations. Five different sensible (Q_h) and latent (Q_e) heat flux calculations were also compared, using the bulk aerodynamic method as the baseline. It was found that the Priestley and Taylor method most-closely matched the bulk aerodynamic method on a daily timescale with an average offset of 8.5 W/m² for Q_h and 10.1 W/m² for Q_e, while a Dalton-type equation provided by Webb and Zhang was the most similar on a sub-daily timescale with average offsets of 20.0 and 14.7 W/m² for Q_h and Q_e, respectively.     

Seasonal variations between sampling and classical mean turbulent heat flux estimates in the eastern North Atlantic

The two commonly used statistical measures of the air-sea heat flux, the sampling and classical means, have been compared using hourly reports over a 7-year-period from a weather ship stationed in the NE Atlantic. The sampling mean is the average over all flux estimates in a given period, where individual flux estimates are determined from ship reports of meteorological variables using the well-known bulk formulae. The classical mean is the flux derived by substituting period-averaged values for each of the meteorological variables into the bulk formula (where the averaging period employed is the same as that over which the fluxes are to be determined). Monthly sampling and classical means are calculated for the latent and sensible heat fluxes. The monthly classical mean latent heat flux is found to overestimate the sampling mean by an amount which increases from 1–2 W m⁻² in summer to 7 W m⁻² in winter, on average, over the 7-year-period. In a given winter month, the excess may be as great as 15 W m⁻², which represents about 10% of the latent heat flux. For the sensible heat flux, any seasonal variation between the two means is of the order of 1 W m⁻² and is not significant compared to the interannual variation. The discrepancy between the two means for the latent heat flux is shown to arise primarily from a negative correlation between the wind speed and sea-air humidity difference, the effects of which are implicitly included in the sampling method but not in the classical. The influence of the dominant weather conditions on the sign and magnitude of this correlation are explored, and the large negative values that it takes in winter are found to depend on the typical track of the mid-latitude depressions with respect to the position sampled. In conclusion, it is suggested that sampling means should be employed where possible in future climatological studies.     

Verification of land surface evapotranspiration estimation from remote sensing spatial contextual information

Estimation of evapotranspiration (ET) is of great significance in modeling the water and energy interactions between land and atmosphere. Negative correlation of surface temperature (T_s) versus vegetation index (VI) from remote sensing data provides diagnosis on the spatial pattern of surface soil moisture and ET. This study further examined the applicability of T_s–VI triangle method with a newly developed edges determination technique in estimating regional evaporative fraction (EF) and ET at MODIS pixel scale through comparison with large aperture scintillometer (LAS) and high‐level eddy covariance measurements collected at Changwu agro‐ecological experiment station from late June to late October, 2009. An algorithm with merely land and atmosphere products from MODIS onboard Terra satellite was used to estimate the surface net radiation (R_n) and soil heat flux. In most cases, the estimated instantaneous R_n was in good agreement with surface measurement with slight overestimation by 12 W/m². Validation results from LAS measurement showed that the root mean square error is 0.097 for instantaneous EF, 48 W/m² for instantaneous sensible heat flux, and 30 W/m² for daily latent heat flux. This paper successfully presents a miniature of the overall capability of T_s–VI triangle in estimating regional EF and ET from limited number of data. For a thorough interpretation, further comprehensive investigation needs to be done with more integration of remote sensing data and in‐situ surface measurements. Copyright © 2011 John Wiley & Sons, Ltd.     

Comparison of three remote sensing based models for the estimation of latent heat flux over India

The aim of this work is to compare three remote sensing based models: two contextual and one physically-based single-pixel model for the estimation of daytime integrated latent heat flux without the use of any ground measurements over Indian ecosystems. Satellite datasets from the MODIS sensors aboard the Terra and the Aqua satellites were used. The latent heat flux estimated from the remote sensing models was compared with that estimated from Bowen ratio energy balance towers at five sites in India. The root mean square error (RMSE) of the latent heat flux estimated from the contextual and the physically-based models was found to be in the order of 40 and 70 W m^?2, respectively. The relatively inferior performance of the more complex physically-based model in comparison with the contextual models was found to be largely due to inaccurate parameterizations estimated only from remote sensing datasets without any ground data.     

A composite trans-Atlantic heat flow profile between 20°S and 35°S

Sixty new measurements together with published heat flow data in the South Atlantic between 20°S and 35°S latitude have been analyzed. Heat flux is greater through the eastern Mid-Atlantic Ridge flank and basin than their counterparts on the west but the standard deviation or spatial variation is greater on the west, contrary to expectation based on sediment thickness. The variance in the data indicates that this asymmetry in mean heat flux is statistically significant at 87% confidence level. A pair of ridge-flank minima appear in a composite trans-Atlantic profile of heat flux versus sea-floor age, suggesting hydrothermal circulation in the young oceanic crust. The Walvis Ridge has a mean excess heat flux of 28 mW m^?2 (0.7 μcal cm^?2 sec^?1) above the surrounding Cape and Angola Basins, and decreases along the ridge towards the northeast. Consistent with the apparent asymmetric distribution in the South Atlantic, it is also significantly higher than that of the Rio Grande Rise. We hypothesize that the trend and larger mean heat flux of the Walvis Ridge is best explained by a hot-spot origin, perhaps combined with higher radioactivity in the crust. However, the morphologic and heat flow differences between the Walvis Ridge and Rio Grande Rise suggest that these features have different geologic histories.     

Mantle heat flow and geotherms for major tectonic units in central Europe

The results of seismic measurements along the deep seismic sounding profile VII and terrestrial heat flow measurements used for construction of heat generation models for the crust in the Paleozoic Platform region, the Sudetic Mountains (Variscan Internides) and the European Precambrian Platform show considerable differences in mantle heat flow and temperatures. At the base of the crust variations from 440–510°C in the models of Precambrian Platform to 700–820°C for the Paleozoic Platform and the Variscan Internides (Sudets) are found. These differences are associated with considerable mantle heat flow variations.The calculated models show mantle heat flow of about 8.4–12.6 mW m^–2 for the Precambrian Platform and 31 mW m^–2 to 40.2 mW m^–2 for Paleozoic orogenic areas. The heat flow contribution originating from crustal radioactivity is almost the same for the different tectonic units (from 33.5 mW m^–2 to 37.6 mW m^–2). Considerable physical differences in the lower crust and upper mantle between the Precambrian Platform and the adjacent areas, produced by lateral temperature variations, could be expected. On the basis of carbon ratio data it can be concluded that the Carboniferous paleogeothermal gradient was much lower in the Precambrian Platform area than in the Paleozoic Platform region.     

On the interaction between convection and crystallization in cooling magma chambers

We investigate the interaction of thermal convection and crystallization in large aspect-ratio magma chambers. Because nucleation requires a finite amount of undercooling, crystallization is not instantaneous. For typical values of the rates of nucleation and crystal growth, the characteristic time-scale of crystallization is about 10³–10⁴ s. Roof convection is characterized by the quasi-periodic formation and instability of a cold boundary layer. Its characteristic time-scale depends on viscosity and ranges from about 10² s for basaltic magmas to about 10⁷ s for granitic magmas. Hence, depending on magma viscosity, convective instability occurs at different stages of crystallization. A single non-dimensional number is defined to characterize the different modes of interaction between convection and crystallization.Using realistic functions for the rates of nucleation and crystal growth, we integrate numerically the heat equation until the onset of convective instability. We determine both temperature and crystal content in the thermal boundary layer. Crystallization leads to a dramatic increase of viscosity which acts to stabilize part of the boundary layer against instability. We compute the effective temperature contrast driving thermal convection and show that it varies as a function of magma viscosity and hence composition.In magmas with viscosities higher than 10⁵ poise, the temperature contrast driving convection is very small, hence thermal convection is weak. In low-viscosity magmas, convective breakdown occurs before the completion of crystallization, and involves partially crystallized magma. The convective regime is thus characterized by descending crystal-bearing plumes, and bottom crystallization proceeds both by in-situ nucleation and deposition from the plumes. We suggest that this is the origin of intermittent layering, a form of rhythmic layering described in the Skaergaard and other complexes. We show that this regime occurs in basic magmas only at temperatures close to the liquidus and never occurs in viscous magmas. This may explain why intermittent layering is observed only in a few specific cases.     

The extraction of heat from magmas based on heat transfer mechanisms

Analytical heat transfer calculations are used to relate geological surface evidence to conditions that should exist in magma chambers for the purpose of improving estimates of possible commercial heat extraction rates. These calculations indicate that an upward-melting magma system necessarily is approximately equidimensional and that injected magmas with very high aspect (L/D) ratios are likely formed by a forced intrusion process which involves little if any melting or natural convection. Calculations along with surface heat flow measurements suggest that steady-state heat extraction rates for emplaced heat exchangers in currently suspected shallow magma chambers will probably be below 10 kW m⁻², a value that is low by engineering standards.     

Early spring turbulent mixing in an ice-covered Arctic fjord during transition to melting

Observations are presented of currents, hydrography and turbulence in a jet-type tidally forced fjord in Svalbard. The fjord was ice covered at the time of the experiment in early spring 2004. Turbulence measurements were conducted by both moored instruments within the uppermost 5 m below the ice and a microstructure profiler covering 3–60 m at 75 m depth. Tidal choking at the mouth of the fjord induces a tidal jet advecting relatively warmer water past the measurement site and dominating the variability in hydrography. While there was no strong correlation with the observed hydrography or mixing and the phase of the semidiurnal tidal cycle, the mean structure in dissipation of turbulent kinetic energy, work done under the ice and the mixing in the water column correlated with the current when conditionally sampled for tidal jet events. Observed levels of dissipation of turbulent kinetic energy per unit mass, 1.1×10⁻⁷ W kg⁻¹, and eddy diffusivity, 7.3×10⁻⁴ m² s⁻¹, were comparable to direct measurements at other coastal sites and shelves with rough topography and strong forcing. During spring tides, an average upward heat flux of 5 W m⁻² in the under-ice boundary layer was observed. Instantaneous (1 h averaged) large heat flux events were correlated with periods of large inflow, hence elevated heat fluxes were associated with the tidal jet and its heat content. Vertical heat fluxes are derived from shear-probe measurements by employing a novel model for eddy diffusivity [Shih et al., 2005. Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations. Journal of Fluid Mechanics 525, 193–214]. When compared to the direct heat flux measurements using the eddy correlation method at 5 m below the ice, the upper 4–6 m averaged heat flux estimates from the microstructure profiler agreed with the direct measurements to within 10%. During the experiment water column was stably, but weakly, stratified. Destabilizing buoyancy fluxes recorded close to the ice were absent at 5 m below the ice, and overall, turbulence production was dominated by shear. A scaling for dissipation employing production by both stress and buoyancy [Lombardo and Gregg, 1989. Similarity scaling of viscous and thermal dissipation in a convecting boundary layer. Journal of Geophysical Research 94, 6273–6284] was found to be appropriate for the under-ice boundary layer.     

A heat flow survey on anomaly M0 south of the Bermuda Rise

We have obtained a suite of 42 closely spaced, acoustically navigated, heat flow measurements on well-sedimented crust of anomaly M0 age (109 Ma) in the northwest Atlantic Ocean (25°N, 68°W; 950 km south of Bermuda). The mean and standard deviation of the values obtained are 1.13 HFU (μcal/cm² s) (47.3 mW/m²) and 0.05 HFU (2.1 mW/m²), respectively. Some of the variability is accounted for by refractive effects of the basement topography. Drill core data and our modelling suggest that the thermal conductivity contrast between sediments and basement rocks in this region is less than a factor of 1.6. The mean heat flow is close to the 1.1 HFU (46 mW/m²) predicted by both the plate and boundary layer cooling models of the oceanic lithosphere. This is the first detailed comparison with theoretical cooling models on old Atlantic Ocean crust. Since the difference in surface heat flow (0.15 HFU) predicted by the two cooling models for the oldest observed oceanic lithosphere (180 Ma) is also not much larger than the range of uncertainty in our observations, discrimination between the two models on the basis of surface heat flow data alone may prove difficult.     

Tidal motions in the Dover Straits as a variational inverse of the sea level and surface velocity data

The M₂ tidal component of the flow in the Dover Straits is reconstructed using a natural combination of two independent data sources: HF Ocean Surface Current Radar (HF OSCR) system and coastal tidal measurements. The method used is the variational data assimilation technique into a quasi-linearized finite element tidal model. The model uses triangular elements with horizontal resolution varying from 800 to 1200 m. It is controlled by the boundary conditions at open boundaries, which are adjusted to fit the available data in an optimal way. A “weak” formulation of the dynamical constraints is used. The interpolation scheme allows small (0.01%) deviations from the exact dynamics specified by the model. The optimal state of M₂ parameters (sea surface elevation and depth-averaged velocities) is used to map both the M₂ tidal flux through the strait and the M₂ energy flux. The respective values obtained are the tidal flux amplitude 1.18±0.09×10⁶ m³ s⁻¹, the net residual transport (Stoke's drift) 40±3×10³ m³ s⁻¹, and the net energy flux 1.19±0.09×10¹⁰ W. These figures within the statistically estimated error band are in the close agreement with those obtained by Prandle et al., 1993. A rigorous error analysis is performed using an explicit inversion of the Hessian matrix, associated with the assimilation scheme. As a result, error charts for M₂ velocities and sea surface elevation are obtained. It is shown that OSCR data combined with coastal level measurements and constrained by dynamics is able to provide quite accurate velocity estimates whose errors vary within the range of 0.05–0.45 m s⁻¹ depending upon the location. Error maps also enable us to determine areas requiring better coverage by data, thus forming a basis of optimization approach to the design of the HFR measurements. The use of variational assimilation technique in providing integrated interpolation patterns from various sources of data demonstrates its capabilities in relation to future oceanographic monitoring systems of shelf circulation.