helium and carbon fluxes in lake nyos cameroon constraint on next gas burst on 21 august 1986 a lethal gas burst issued from lake nyos in cameroon western africa killing at least 1700 people although the consensus is that the victims died of asphyxiation by co2 of magmatic origin the frequency of such catastrophic degassing events is still unknown the co2 flux at the bottom of lake nyos is estimated based on the measurement of3he4he and4he20ne ratios and the chemical composition of gases exsolved from the lake water the calculated co2 flux at the bottom of lake nyos is 4 4 2 3 1013cm3stp year combined with the estimated release in the august 1986 event of 8 2 1014 cm3 stp the co2 flux suggests that the gas burst may happen about once in18 10 years although the significant uncertainty should be taken into account for the frequency resulting from assumptions such as steady state fluxes in the lake and small fractionization of the c he ratio during the degassing event several yearly measurements of hypolimnetic fluxes and seasonal measurements of epilimnetic fluxes are needed to constrain better the recurrence interval in addition the results of a regional3he4he survey of carbonated mineral springs in northwestern cameroon are discussed in the context of the regional geotectonics

mantle helium flux from the bottom of lake mashu japan abstract most of the 52 water samples from lake mashu hokkaido japan show large anomalies in their3he 4he ratios up to 4 6 times the atmospheric ratio and4he 20ne ratios indicating continuous injection of mantle he due to hot spring activity at the lake bottom the3he 4he ratio of the injected mantle he is estimated at3he 4he 9 43 0 17 10 6 which is close to the highest value reported for volcanic gases from the japanese islands accumulation of mantle he in the near bottom water can be reasonably explained by a diffusion process with a constant he flux from the lake bottom off4he 9 2 107 atoms cm2 s andf3he 8 7 102 atoms cm2 s the heat 3he ratio 1 7 10 7j atom falls in the range of values reported for submarine hydrothermal systems 0 4 26 10 7 j atom whereas the c3he ratio 1 8 1011 is about two orders of magnitude higher than the morb average 2 109 the mantle he injected from the lake bottom has a fairly short mean residence time in the lake water and is estimated at about 2 4 years overturn of the lake water which occurs twice a year probably plays an important role in the rapid transportation of the mantle he from the bottom to the surface

tritium and helium 3 in the northeastern atlantic ocean during the 1983 topogulf cruise this study is part of the topogulf program in which tracer measurements were closely associated with the hydrological data the sampled area was located near the azores islands on the both sides of the mid atlantic ridge the tritium content of the surface waters reveals a strong front along the azores current the 3he distributions are used to identify some areas where ventilation processes are active at depth the spatial distribution of tritium is studied along isopycnals in the thermocline it is essentially the anticyclonic gyre which is responsible for the northeast southwest gradient in tritium concentrations the respective influences of the labrador sea water and the mediterranean water are noticeable through the tritium data the mediterranean water seems to be an end member responsible for a decrease of the tritium contents in the north and for an increase in the south by mixing a quantitative approach using a mixing model is used to check the validity of the 3he 3h age the model leads to two extreme values of the time scales for the middepth circulation in the studied area 35 years for the ventilation time of the labrador sea water and around 200 years for the residence time of the oldest waters in the southeastern area

modeling deep water renewal in lake baikal temperature dissolved oxygen nutrients and chlorofluorocarbon 12 data obtained from lake baikal are used to describe deep water renewal in a deep temperate latitude lake observations are used to propose the physical mechanism governing convection and to formulate a model of deep ventilation the key physical mechanism governing deep water renewal is the so called thermobaric instability because the temperature of maximum density decreases with depth a lake can become conditionally unstable if the base of the cold mixed layer is displaced to a depth at which its temperature matches the local temperature of maximum density thereby resulting in sinking plumes an important consequence of this phenomenon is that deep temperate lakes such as baikal do not completely mix twice yearly instead deep ventilation is episodic a two dimensional model of a wind and buoyancy driven lake shows many strong mixing events and a fairly realistic seasonal cycle indicating that the hypothesis is physically realizable a filling box model is used to deduce the annually averaged fluxes necessary to produce a steady vertical distribution of tracers as observed good fits are obtained to oxygen and chlorofluorocarbon distributions by this model about 50 of the world s liquid freshwater is contained in the large deep lakes located in the temperate latitudes between 45 and 65 n see hutchinson 1957 of fundamental importance to such lakes is their ventilation time the time scale associated with renewal of deep water for it is the deep convection process that most strongly controls the internal redistribution of scalar properties such as dissolved oxygen nutrients and anthropogenic pollutants see wiiest et al 1988 however surprisingly few attempts to study and quantify ventilation in deep

sources and sinks of methane in lake baikal a synthesis of measurements and modeling we studied the methane ch4 budget of lake baikal the most voluminous lake in the world and the only freshwater body with known occurrences of methane hydrates in the sediments ch4 concentrations were measured in water samples taken during six expeditions between october 2002 and june 2004 these expeditions covered the entire lake volume a one dimensional model was applied to 1 estimate the large scale vertical ch4 fluxes within the south basin of lake baikal 2 determine the exchange with the atmosphere and 3 constrain the ch4 inputs from seeps and mud volcanoes to the deep water fluxes were generally several orders of magnitude below previous estimates the annual internal source of ch4 to the pelagic surface mixed layer was roughly estimated to be 40 mg ch4 a large part of this input diffuses downwards and is consumed in the water column with a ch4 residence time of about 4 yr the input of ch4 from deep gas seeps and mud volcanoes is less than a few 10 mg ch4 yr21 most of which is oxidized before reaching the surface the net ch4 flux between the atmosphere and the main waterbody distant from shallow areas is negligible and not significantly different from zero however occasional high ch4 concentrations both in the surface water and in the atmosphere indicate that the region near the selenga delta is a local ch4 source to the atmosphere ch4 fluxes in the central basin are very similar to those in the south basin whereas in the north basin the shallow ch4 sources are weaker

processes of deep water renewal in lake baikal deep water renewal in lake baikal siberia the world s deepest lake and largest lake by volume is relatively fast water age calculated from tritium and helium as well as from chlorofluorocarbons does not exceed 19 yr relative saturation of dissolved oxygen typically exceeds 80 the equation of state of baikal water was determined including the effect of dissolved ions and silicic acid based on nearly 600 ctd profiles taken between 1993 and 1995 two mechanisms of deep water mixing were identified 1 in spring cold and relatively saline water from the selenga the major inflow to the lake forms a density plume that reaches the bottom of the central basin during april and early may due to entrainment of lake water the plume transports about 125 km of water per year to the deepest part of the basin later in spring the river water forms the thermal bar observed along the eastern shore there are indications that parts of the selenga are also plunging to the deep part of the southern basin 2 at academician ridge separating the cold and saline water of the central basin from the warmer and slightly less saline water of the northern basin horizontal mixing results in a water mass that can sink on either side of the sill whereas in the central basin the water mass stays at intcrmediatc depth in the northern basin it sinks to the decpcst part more detailed data are needed to quantify this density flux no indication of a wind induced thermobaric instability was found

initiation and arrest of earthquake ruptures due to elongated overstressed regions the initiation of natural and induced earthquakes is promoted in fault areas where the shear stress is close to fault strength in many important situations these overstressed fault areas or asperities are very elongated for example in the case of a fault intersecting a reservoir subject to fluid injection or the stress concentration along the bottom of a seismogenic zone induced by deep fault creep theoretical estimates of the minimum overstressed asperity size leading to runaway rupture and of the final size of self arrested ruptures are only available for 2d problems and for 3d problems with an asperity aspect ratio close to one in this study we determine how the nucleation of ruptures on elongated asperities and their ensuing arrest depend on the size and aspect ratio of the asperity and on the background stress based on a systematic set of 3d dynamic rupture simulations assuming linear slip weakening friction we find that if the shortest asperity side is smaller than the 2d critical length the problem effectively reduces to a 2d problem in which rupture nucleation and arrest are controlled by the shortest length of the asperity otherwise nucleation and rupture arrest are controlled by the asperity area with a minor exception for asperities with shortest side slightly larger than the 2d critical length arrested ruptures are smaller than predicted by the asperity area the fact that rupture arrest is dominantly controlled by area even for elongated asperities corroborates the finding that observed maximum magnitudes of earthquakes induced by fluid injection are consistent with the theoretical relation between the magnitude of the largest self arrested rupture and the injected volume galis et al 2017 in context of induced seismicity our simulations provide plausible scenarios that could be either favourable or challenging for traffic light systems and provide mechanical insights into the conditions leading to these situations

a time series of environmental tracer data from deep meromictic lake lugano switzerland an 11 yr 1990 2001 time series of tritium helium 3 3h 3he apparent water ages as well as one sulfur hexafluoride sf6 profile were used to study the development of the vertical mixing dynamics of the deep meromictic northern basin of lake lugano the density stratification of the water column was dominated by an increase in dissolved ions with depth which remained approximately constant during the 1990s the deep water temperature increased steadily during this period passing a threshold above which cooling of the surface water could force convection however increasingly mild winter temperatures prevented the occurrence of a turnover until 2005 the maximum apparent 3h 3he water age increased from about 16 yr in 1990 to 23 yr in 2001 the maximum apparent sf6 age in 2001 was 12 8 yr the large difference between the apparent 3h 3he and sf6 ages is at least partly due to nonlinear effects of mixing causing sf6 ages to underestimate the true mean deep water residence time whereas 3h 3he ages overestimate it the decreasing concentrations of 3h and 3he are more reliable indicators of the continuous deep water exchange in the lake than are the apparent ages budget calculations using the tracer concentrations reveal an annual renewal of the deep water below 100 m in depth by about 8 and enable the calculation of long term mean profiles of the effective vertical turbulent diffusivity kz no trend in the mixing intensity during the 1990s could be determined the radiogenic he flux into the lake is comparable to estimates of the whole crustal degassing flux

bottomwater formation due to hydrothermal activity in frolikha bay lake baikal eastern siberia hydrothermal water enters frolikha bay a well known site of high geothermal heat flux in the northern part of lake baikal at 400 m depth on the basis of ctd profiles the hydrothermal water is identified as forming an anomalous bottom layer with a higher temperature 0 15 c and salinity 2 5 mg kg 1 than the overlying water due to the entrainment of lake water a distinct dense water layer up to 40 m thick stabilised by its slightly higher salinity becomes established close to the bottom of the bay the density current thus generated flows out of the bay towards the deeper parts of the basin since helium isotope analysis shows that the geochemical characteristics of the hydrothermal water are similar to those of water from nearby hot springs on land the bottomwater of frolikha bay is easily interpreted in terms of the mixing of ordinary fresh water from the lake and hydrothermal water carrying isotopically heavy he from the continental crust because of its high crustal he content a similar hydrothermal component may even be identified in the open water of the northern basin

the major and minor element geochemistry of lake baikal funding for u s participation in the fieldwork and sample collection was provided by the u s national science foundation funding for the analytical work was obtained by various means

a three dimensional numerical model of deep ventilation in temperate lakes because of the variation in the temperature of maximum density with depth it is known that the upper above 250 m and lower water columns circulate separately in deep temperate lakes while near surface water overturns twice per year the deep waters often mix only partially during a complete annual cycle it is believed that deep convection is triggered by storm surge forcing of some of the relatively cold upper water column downward through its compensation depth so that it becomes unstable and sinks the scale and intensity of the resulting deep water forming plumes are studied numerically a high resolution model based on the nonhydrostatic boussinesq equations is used deep water formation is initiated by applying a statically unstable initial temperature profile over various regions of the domain at depths below 300 m the grid spacing is small enough to resolve individual plumes which carry surface water to the lake bottom the domain of study is also large enough that the geostrophic eady 1949 wave breakup of newly formed deep water can be observed it is found that when the initial instability is applied in midbasin remote from the solid sidewalls relatively little fresh deep water is formed and the fluid quickly reaches a geostrophic and hydrostatic balance vigorous vertical mixing ceases after 4 days and the resulting baroclinic fluid has a well defined and predictable scale in contrast when the initial instability is applied immediately adjacent to a solid boundary vigorous plume motion continues for the duration of the numerical simulations 12 days producing a much greater volume of fresh deep water a parametric study investigates the scale and intensity of this boundary mixing it is found that reduced surface water temperature coriolis acceleration or higher horizontal diffusion coefficients increase the rate of deep water renewal

interpreting noble gas concentrations as proxies for salinity and temperature in the world s largest soda lake lake van turkey in this work we present noble gas concentration profiles measured in the water column and in the sediment pore water of the earth s largest soda lake lake van eastern anatolia turkey the concentrations of noble gases in particular ar kr and xe in the water body deviate significantly from the expected equilibrium concentrations calculated from the in situ temperature and salinity using existing solubility functions for seawater the specific chemical composition of the water of the soda lake seems to be responsible for the observed deviations our measurements allow the identification and quantification of salinity factors that can be applied to correctly calculate the noble gas equilibrium concentrations for the lake these salinity factors provide a solid and robust empirical basis for the interpretation of noble gas concentration signals measured in the sediment pore water of lake van in terms of palaeosalinity and palaeotemperature

ventilation rates of the waters in the nansen basin of the arctic ocean derived from a multitracer approach tritium sup 3 he sup 14 c and helium neon data from a station located in the central nansen basin of the arctic ocean are reported and discussed it is demonstrated that sup 3 he is a valuable tracer for studies of the upper water column and together with tritium sup 3 he provides a rough time scale of the ventilation of these waters the apparent tritium sup 3 he age is about 7 years in the surface water and about 14 years in the lower part of the halocline water of atlantic origin defined by a temperature maximum shows tritium sup 3 he ages between 7 and 9 years this variation of ages indicates that the circulation of the individual water layers of the upper water column is largely decoupled and occurs on different time scales tritium sup 3 he ages observed in the arctic intermediate water suggest a ventilation on a time scale of 15 to 20 years depth 1 000 m the mean age of the eurasian basin bottom water is estimated on the basis of sup 14 c data to approximately 200 to 250 years there is no indication of noble gas fractionation due to sea ice formation below the surface layer from analysis of the sup 3 he backgroundmore it appears that there is a small primordial sup 3 he component in eurasian basin bottom water less

3h and 3he in the beta triangle observations of gyre ventilation and oxygen utilization rates abstract isopycnal maps of 3h 3he age with about 100 km resolution have been obtained for a 1000 km scale area in the eastern subtropical north atlantic the midscale texture of the maps is consistent with isopycnal diffusivities of order 500 m 2 s 1 analysis of the distributions within the context of advection diffusion equations reveals that the larger scale 3h 3he age gradients observed within the area are not seriously affected by mixing on those surfaces that outcrop in the region of ekman downwelling thus isopycnal velocities can be estimated from 1 but record only the velocity component normal to the outcrop the velocities thus obtained agree well with geostrophic estimates although the comparison is flawed by the fundamental mismatch in timescales between the two techniques backward extrapolation of the maps to zero age outcrop positions indicate that the contribution of unventilated older recirculated water to the gyre flow above 600 m depth is small in this area no more than 20

variations of the monsoon regime during the upper quaternary evidence from carbon isotopic record of organic matter in north indian ocean sediment cores abstract the 13 c 12 c ratios and contents of organic carbon in deep sea sediment cores of the north indian ocean have been compared for the different climatic stages as determined by oxygen isotope stratigraphy using the differences in the 13 c values between marine and terrestrial organic matter the terrestrial contribution to the eastern gulf of bengal and the andaman sea has been determined for modern and glacial times the geographical distribution of the terrestrial organic carbon linked to sea surface circulation shows that during the last glacial period the ne monsoon circulation was the dominant feature the organic carbon abundance within the sediment which is related to local productivity was greater during glacial times in the areas where production depends on the ne monsoon strength coast of north india in the arabian sea and andaman sea suggesting its reinforcement

quantification of gas fluxes from the subcontinental mantle the example of laacher see a maar lake in germany abstract vertical and horizontal distributions of helium and neon isotopes were measured in the water of laacher see a maar lake in the east eifel volcanic field in germany neon is in approximate atmospheric equilibrium throughout the lake but the concentrations of both helium isotopes increase with depth and reach values of up to 10 4 he and 50 3 he times the atmospheric equilibrium concentration the isotopic ratio of the helium excess r ex 3 he ex 4 he ex is 7 42 0 03 10 6 i e r ex r a 5 36 0 02 where r a 1 384 10 6 is the isotopic ratio in air this indicates the presence of mantle derived helium laacher see is thermally stratified during the summer it acts as an almost perfect trap for injected gases the helium concentration in the hypolimnion deep water approximately doubled from may to september 1991 yielding a mean 4 he flux of 10 2 10 12 atoms m 2 s 1 this value is 30 times smaller than in lake nyos cameroon but 20 times larger than in crater lake usa release of bubbles of nearly pure co 2 99 observable in shallow waters at the eastern shore as well as detected by divers in about 30 m depth was identified as an important source of the helium excess in the lake if carefully sampled by divers to avoid air contamination the bubbles exhibit mantle influenced isotopic signatures not only for helium but also for neon and argon 20 ne 22 ne 9 92 0 03 40 ar 36 ar 391 4 based on the elemental ratios of carbon neon and argon to 3 he the fluxes of volatiles from the mantle into laacher see are determined as 7 4 10 7 atoms m 2 s 1 for 3 he 13 10 7 atoms m 2 s 1 for 20 ne 26 10 7 atoms m 2 s 1 for 361 ar and 6 4 10 17 molecules m 2 s 1 for co 2 non atmospheric neon was also found in the well wallenborn in the west eifel volcanic field with a 20 ne 22 ne ratio as high as 11 21 0 06

deep water renewal in lake issyk kul 1 the deep water renewal rates of lake issyk kul are studied using the time dependent anthropogenically produced tracers sulfur hexafluoride sf 6 chlorofluorocarbons cfcs and tritium helium 3 sf 6 and the cfcs are used to calibrate a mixing model from which the vertical age distribution is calculated and found to be comparable to the sf 6 apparent ages based on this model the mean age of the water below 100 m depth is 6 1 yrs the mean oxygen consumption rate for the same depth range is 6 4 mol kg 1 yr 1 and the mean remineralization rates for nitrate phosphate and silicate are 0 53 0 003 and 0 67 mol kg 1 yr 1 respectively

deep ventilation of lake baikal waters due to spring thermal bars increase of density due to mixing cabbeling instability in a spring thermal bar in lake baikal results in the sinking of cold surface water t 3 2 3 4 c w 0 3 cm s 1 below the profile of tmd this density increase generates forced convection and subsequent movement of cold water along the underwater slope to maximum depths cooling of deep and near bottom waters caused by forced convection is compensated during other seasons of the year by eddy heat flux directed toward the bottom on a long term basis vertical temperature profiles in deep waters remain constant

helium isotope fluxes and groundwater ages in the dogger aquifer paris basin the dogger aquifer of the paris basin has been shown to be first order homogeneous in its helium concentration and its helium isotopic ratio although slight differences are noted in relation to specific chemical water types the helium isotopic composition of the dogger aquifer contains a small component of mantle helium that is associated with a magmatic input although the heat accompanying this magma is small constraints on the age of the overlying albien aquifer are used to calculate the flux of helium out of the dogger this constraint allows a calculation of the residence time of waters in the dogger aquifer of 4 myr 50 which is significantly longer than estimates derived from hydrologic models and hydrologic testing it is possible that the hydrologic ages and the helium ages can be reconciled by a vertically layered dogger aquifer with gradients in he salinity and fluid flow vertical profiles of fluid composition helium concentration and permeability are required in the paris basin to resolve this question

distribution of helium and tritium in lake baikal the 3 h 3 he age of a water mass is a measure of the time that has passed since the water mass was last in contact with the atmosphere between 1992 and 1995 a detailed study of 3 h 3 he ages was conducted in lake baikal the deepest and largest lake by volume on earth to investigate deep water renewal in its three major basins maximum 3 h 3 he ages are 14 17 years in the southern basin 16 18 years in the central basin and 10 11 years in the northern basin rates of renewal of deep water with surface water deduced from volume weighted mean 3 h 3 he ages below 250 m depth are about 10 yr 1 in the southern and central basins and 15 yr 1 in the northern basin in the southern basin the mean 3 h 3 he age below 250 m depth increased steadily from 9 6 years in 1992 to 11 years in 1995 indicating a slight diminution in deep water renewal during this time bottom water renewal by large scale advection was estimated from the mass balance of 3 he in the 200 m thick bottom layer of each basin bottom water renewal rates in the northern basin were found to be between 80 and 150 km 3 yr 1 and in the central basin between 10 and 20 km 3 yr 1 whereas in the southern basin they were practically zero correlating oxygen and dissolved helium 4 concentrations with 3 h 3 he age allowed us to determine the mean hypolimnetic oxygen depletion rate in the water column 4 5 mol l 1 yr 1 as well as mean helium fluxes from the lake bottom 2 8 x 10 11 atoms m 2 s 1 in the northern basin and 1 3 x 10 11 atoms m 2 s 1 in the central and southern basins the helium isotope ratio of the terrigenic helium component injected from the lake bottom determined from measurements of water from hydrothermal springs in the vicinity of the lake was found to be 2 2 x 10 7

impact of lake level change on deep water renewal and oxic conditions in deep saline lake van turkey 1 changes in the hydrological regime of the saline closed basin lake van a large deep lake in eastern turkey resulted in a lake level increase by about 2 m between 1988 and 1995 followed by a 1 5 m decrease until 2003 and a relatively constant lake level thereafter based on measurements of transient tracers sulfur hexafluoride cfc 12 3h 3he 4he ne dissolved oxygen light transmission conductivity temperature depth profiles and thermistor data we investigate the implications associated with lake level fluctuations for deep water renewal and oxygenation our data suggest that deep water renewal was significantly reduced in lake van between 1990 and 2005 this change in mixing conditions resulted in the formation of a more than 100 m thick anoxic deep water body below 325 m depth apparently the freshwater inflows responsible for the lake level rise between 1988 and 1995 decreased the salinity of the surface water sufficiently that the generation of density plumes during winter cooling was substantially reduced compared to that in the years before the lake level rise significant renewal and oxygenation of the deep water did not occur until at least 2005 although by 2003 the lake level was back to almost the same level as in 1988 this study suggests that short term changes in the hydrological regime resulting in lake level changes of a couple of meters can lead to significant and long lasting changes in deep water renewal and oxic conditions in deep saline lakes

injection of mantle type helium into lake van turkey the clue for quantifying deep water renewal helium neon and tritium concentrations have been measured to study long term vertical mixing and deep water renewal in lake van eastern turkey the largest soda lake on earth helium excesses were found in the water column of lake van although neon concentrations were close to air saturation the excesses of both isotopes are strictly correlated and increase with depth in the bottom water 4he supersaturation is about 20 and the corresponding 3he concentration is 2 5 times the air saturation value the mean excess 3he 4he ratio of 1 1 2 10 5 is slightly higher than the morb ratio found in lake nemrut a neighbouring volcanic crater lake in which a large input of mantle helium was detected mantle helium accounts for the majority of the helium excesses in lake van although part of the 3he excess is attributed to the presence of tritium a one dimensional lake model was used which describes tritium input vertical mixing and gas exchange to reconstruct the evolution of the helium isotopes and the tritium as a conclusion the model based on the measured 3he and 4he profiles shows that 1 the vertical exchange of deep water occurs within 1 2 yr 2 the flux of mantle helium into the lake averaged over the total cross section of lake van is 0 23 0 35 cm3 stp m 2 yr 1 2 3 1011 atoms m 2 s 1 the present estimate of the global mantle helium flux averaged over the total surface area of the earth is 3 9 109 atoms m 2 s 1 the flux into lake van would account for at least 0 04 0 06 of this

density driven exchange between the basins of lake lucerne switzerland traced with the 3h 3he method lake lucerne is divided by sills into four major and two minor basins during winter differential vertical mixing due to non uniform wind exposure and different total dissolved solid concentrations in the main tributaries of the lake cause considerable interbasin density gradients these gradients induce density driven currents across the sills that contribute significantly to the deep water exchange in the basins and gradually reduce the density gradients during summer over a period of 2 yr 1990 1992 the spatial and temporal evolution of water density and water age measured by the 3 h 3 he method was investigated variation in water age between the different basins and the occasional occurrence of age inversions older water overlying younger one can be explained in terms of the observed density distribution and the exchange flows the density gradients cause water age provides an integral measure of the magnitude of deep water renewal which in some basins can be roughly separated into contributions from density driven currents and wind induced vertical mixing by correlating water age with dissolved helium and oxygen concentrations radiogenic helium fluxes and average oxygen depletion rates were determined for the main basins of the lake the helium flux was between 1 and 2x10 10 atoms m 2 s 1 indicating dynamic equilibrium with helium production in the underlying crust oxygen depletion rates per unit sediment area were roughly equal in all basins between 220 and 290 g m 2 yr 1 whereas volumetric depletion rates varied from 1 8 g m 3 yr 1 in the deepest basin to 10 g m 3 yr 1 in the shallowest