arctic ocean circulation patterns revealed by grace abstractmeasurements of ocean bottom pressure obp anomalies from the satellite mission gravity recovery and climate experiment grace complemented by information from two ocean models are used to investigate the variations and distribution of the arctic ocean mass from 2002 through 2011 the forcing and dynamics associated with the observed obp changes are explored major findings are the identification of three primary temporal spatial modes of obp variability at monthly to interannual time scales with the following characteristics mode 1 50 of the variance is a wintertime basin coherent arctic mass change forced by southerly winds through fram strait and to a lesser extent through bering strait these winds generate northward geostrophic current anomalies that increase the mass in the arctic ocean mode 2 20 reveals a mass change along the siberian shelves driven by surface ekman transport and associated with the arctic oscillation mode 3 10 reveals a mass dipole with mass decreasing

buoyancy driven interannual sea level changes in the southeast tropical pacific 1 it is commonly held that interannual to decadal sea level variability patterns mainly represent the ocean s response to wind forcing this view is based in part on modeling studies of wind driven sea level changes along the tropical pacific however because buoyancy forcing and other generating mechanisms are usually ignored this paradigm may overemphasize the role of winds focusing on the southeast tropical pacific we use a data constrained ocean state estimate to demonstrate that distinct mechanisms including the ocean s response to buoyancy forcing as well as nonlinear processes can also contribute to interannual sea level variability contrary to the notion that buoyancy driven sea level changes are dynamically passive such changes exhibit a strongly nonlocal dynamically active character made manifest in westward propagating waves as similar findings apply elsewhere accurate modeling of interannual to decadal regional sea level changes requires consideration of a variety of forcing mechanisms including but not limited to the winds

low frequency variability in coastal sea level from tide gauges and altimetry 1 long sea level observations are fundamental for studies of the low frequency changes in ocean circulation and climate tide gauges provide records several decades long but their locations are geographically sparse and confined to the coastline to assess the extent to which tide gauge point measurements represent broader scale conditions in the adjacent ocean we compare tide gauge records to altimeter data in their vicinity for the period 1993 2008 the analysis is based on detrended annual mean series and focuses on interannual variability the best agreement between tide gauge and altimeter series is found for mid ocean islands in the tropical pacific and indian oceans and along the coast of western australia elsewhere along most continental coasts root mean square differences between the two sea level estimates can be substantial when compared to the observed variability or the expected measurement noise with the worst correspondence found in western south america japan and eastern australia differences in magnitude as well as poor correlations between the tide gauge and altimeter estimates are involved although land motions and measurement errors can be a factor results point to the presence of considerable short spatial structure in coastal sea level at interannual time scales which can be related to the low frequency dynamics of coastally trapped circulations western boundary currents and associated eddy regimes or response to river runoff knowing whether coastal sea level variability becomes more spatially homogeneous at longer time scales must await longer sea level records

nonseasonal fluctuations of the arctic ocean mass observed by the grace satellites 1 time variable gravity observations from the grace satellites reveal strong nonseasonal fluctuations of bottom pressure in the arctic ocean on the time scales from 2 to 6 months and a record high bottom pressure anomaly in february of 2011 here we examine the nature and driving forces behind those fluctuations we find that the nonseasonal variability of the arctic ocean mass is strongly coupled to wind forcing the zonal wind pattern is correlated with a dipole pattern of arctic ocean mass changes westerly wind intensification over the north atlantic at about 60 n as well as over the russian arctic continental shelf break cause the ocean mass to decrease in the nordic seas and in the central arctic and to increase over the russian arctic shelf basin wide arctic ocean mass fluctuations are correlated with northward wind anomalies over the northeastern north atlantic and nordic seas and over the bering sea we show that positive negative arctic ocean mass anomalies are associated with anticyclonic cyclonic anomalies of the large scale ocean circulation pattern based on ocean model simulations we conclude that the observed nonseasonal arctic ocean mass variability is mostly explained by the net horizontal wind driven transports and the contribution of fresh water fluxes is negligible we demonstrate that transport anomalies across both the atlantic and pacific gateways were equally important for generating large arctic ocean mass anomalies in 2011

modal variability in the southeast pacific basin energetics of the 2009 event abstract we study the barotropic variability in the southeast pacific basin in particular focusing on the extreme event during the fourth quarter of 2009 a 3 year integration of a barotropic shallow water model forced with wind stress anomalies generates localized variability that is similar in spatial extent and amplitude as the observed anomalous event an eigenmode analysis of the same model shows the presence of several free modes in the southeast pacific but projection of the modal patterns on the model output shows that their amplitudes are low instead the mode is interpreted as an almost free mode the modal excitation accounts for a considerable fraction 23 on average of the kinetic energy input by the wind stress in the southeast pacific basin increasing to 38 for the anomalous event in 2009 surprisingly a similar but weaker event during the third quarter of 2008 appears to have been more significant from an energetics point of view with almost 50 of the energy being input into the mode key areas of energetic dissipation appear to be the eltanin fracture zone the crest of the east pacific rise and the chile rise east pacific rise intersection

detecting processes contributing to interannual halosteric and thermosteric sea level variability abstracton interannual time scales regional sea level variability is largely determined by changes in the steric component the relation between the thermosteric and halosteric components is studied by separating the components into contributions from the mixed layer and below the mixed layer into the part that is related to isopycnal motion and that contributes to the steric sea level and the inactive part related to changes of spiciness the decomposition provides a simple diagnostic to detect and understand physical mechanisms leading to regional sea level changes in most areas of the world s oceans steric sea level variability is dominated by the contribution from isopycnal motion to the thermosteric sea level while halosteric variability relates more to spiciness because of the salinity minimum at middepth different spatial salinity gradients above and below the minimum lead to opposing contributions and thus to a small contribution from isopycnal motion to the halosteric sea level in nonpola

low frequency variability of the north pacific ocean the roles of boundary and wind driven baroclinic rossby waves 1 the effects of the sea level variability along the eastern boundary of the north pacific ocean including those associated with el nino southern oscillation have been considered an important factor in determining the low frequency large scale variability of the ocean interior through rossby waves generated at the eastern boundary this hypothesis is examined in this study using 8 years worth of the sea surface height observations made by the topex poseidon satellite the timescales of interest are longer than 90 days with the annual cycle removed the results indicate that the influence of the eastern boundary of the north pacific ocean has limited offshore extent varying from 3000 4000 km at 10 n to 200 300 km at 50 n the variability in the ocean interior is primarily driven by wind with only a minor influence from the boundary simulations of a linear two layer model of the ocean driven by wind stress curl are correlated with the observations the effects of wind forcing accumulate along the characteristics of long nondispersive rossby waves in the time longitude domain these wind driven rossby waves overwhelm the boundary driven waves in the ocean interior where there are only some small residual effects of the boundary driven waves however these small effects become clearer after the simulated wind driven variability is removed from the observations index terms 4556 oceanography physical sea level variations 4504 oceanography physical air sea interactions 0312 4215 oceanography general climate and interannual variability 3309 keywords rossby waves satellite altimetry el nino north pacific eastern boundary

evaluation of new grace time variable gravity data over the ocean 1 monthly grace gravity field models from the three science processing centers csr gfz and jpl are analyzed for the period from february 2003 to april 2005 over the ocean the data are used to estimate maps of the mass component of sea level at smoothing radii of 500 km and 750 km in addition to using new gravity field models a filter has been applied to estimate and remove systematic errors in the coefficients that cause erroneous patterns in the maps of equivalent water level the filter is described and its effects are discussed the grace maps have been evaluated using a residual analysis with maps of altimeter sea level from jason 1 corrected for steric variations using the world ocean atlas 2001 monthly climatology the mean uncertainty of grace maps determined from an average of data from all 3 processing centers is estimated to be less than 1 8 cm rms at 750 km smoothing and 2 4 cm at 500 km smoothing which is better than was found previously using the first generation grace gravity fields

geographical variability of the first baroclinic rossby radius of deformation global 1 83 18 climatologies of the first baroclinic gravity wave phase speed c1 and the rossby radius of deformation l1 are computed from climatological average temperature and salinity profiles these new atlases are compared with previously published 5 83 58 coarse resolution maps of l1 for the northern hemisphere and the south atlantic and with a 1 83 18 fine resolution map of c1 for the tropical pacific it is concluded that the methods used in these earlier estimates yield values that are biased systematically low by 5 15 owing to seemingly minor computational errors geographical variations in the new high resolution maps of c1 and l1 are discussed in terms of a wkb approximation that elucidates the effects of earth rotation stratification and water depth on these quantities it is shown that the effects of temporal variations of the stratification can be neglected in the estimation of c1 and l1 at any particular location in the world ocean this is rationalized from consideration of the wkb approximation

recent progress in the application of satellite altimetry to observing the mesoscale variability and general circulation of the oceans recent progress in the application of satellite altimetry from seasat and geos 3 to the observation of the oceanic mesoscale variability and general circulation is reviewed the lack of accurate geoid models has been the major obstacle in the study of the general ocean circulation from altimetry the use of geoid independent methods that utilize the temporal differences in altimetric measurements taken at fixed locations however has made significant contributions to our knowledge of the mesoscale variability of the ocean the mesoscale energies of the sea surface height and geostrophic current have been mapped on a global basis their distributions in wave number space have also been analyzed because of many of the deficiencies of existing altimeter data short duration inadequate orbit poor accuracy etc most of these results describe only a small portion of the frequency wave number spectrum of the variability but they have nonetheless demonstrated the great value of an optimally designed altimetric mission in advancing our knowledge of the global mesoscale variability the current technology allows satellite altimetry to detect oceanic variability at periods from a few days to 3 5 years and wavelengths from 50 to 10 000 km determining the time averaged general ocean circulation from altimetry is more problematic because an accurate geoid is indispensable the currently available global geoid models have useful accuracies only at wavelengths greater than about 7000 km there have been several attempts at mapping the global ocean circulation at those scales using existing altimeter data and geoids when these results are compared with hydrographic surveys some qualitative agreement can be observed but the quantitative differences are mostly inconclusive because of the geoid and orbit errors it has been suggested however that an altimetric mission that is optimally designed with the current technology when complemented by a state of the art gravimetric mission to map the earth s gravity field is able to determine the ocean circulation quantitatively at scales from the ocean basin to about 200 km

satellite derived interannual ocean bottom pressure variability and its relation to sea level 1 knowledge of the relationship between bottom pressure pb and sea level is important for understanding ocean circulation and climate we use recent gravity recovery and climate experiment grace release 05 data along with altimetry to investigate the relationship between and pb over long periods 1 year and large scales 750 km elevated pb signals are observed over deep extratropical regions e g southern ocean basins and shallow or semi enclosed areas e g indonesian and nordic seas in these places considerable variance is explained by pb variance correlation between and pb is significant in many regions including instances of significant negative correlation suggestive of active baroclinic processes results exemplify the good quality of grace release 05 data and demonstrate that contemporary regional variability cannot always be interpreted in terms of steric changes alone

ocean dynamics associated with rapid j2 fluctuations importance of circumpolar modes and identification of a coherent arctic mode 1 fluctuations of the earth s dynamic oblateness j2 are a measure of global redistributions of mass between equatorial and polar regions sensitive to the component which is symmetric about the equator cox and chao recently published a time series of monthly values of j2 based on satellite orbit determination which showed rapid fluctuations from month to month as well as a large change in j2 in 1997 1998 we here investigate the ocean dynamics associated with these rapid fluctuations using a barotropic ocean model forced by atmospheric wind stress and pressure we find that the model has significant skill in reproducing the observations though not the change in 1997 1998 much of the model variability is related to coherent circumpolar fluctuations in arctic and antarctic bottom pressure which despite their apparent symmetry are forced by quite different mechanisms the antarctic mode is forced by circumpolar winds whereas the arctic mode is forced by northward winds over the entrances to the polar sea comparison with in situ observations shows that the model has skill in reproducing the polar modes arctic tide gauge records confirm the presence of a coherent mode at short periods and at long periods over at least the eurasian arctic shelf if barotropic and representative of the whole arctic this would be large enough to make a major contribution to measured j2 fluctuations but does not account for the 1997 1998 event

channel degradation and slope adjustment in steep streams controlled through bed sills general parallel and rotational degradation and the effect of bed sills are investigated with the aid of historical field data and laboratory experiments the case under consideration is a system of two tributaries and a main river in northeast spain characterized by its short length steepness and ephemeral nature the comparison of bed profiles since 1962 revealed an incision greater than 5 5 m the main causes of degradation are thought to be channelization width reduction and urban growth the equilibrium slopes with and without sills were obtained in 111 live bed flume tests it is demonstrated that the bed slope is milder with sills than without sills under the same flow and sediment rates the equations for the calculation of equilibrium slopes scaled to prototype are applied to the case study with good agreement copyright 2008 john wiley and sons ltd

joint inversion of rayleigh wave phase velocity and ellipticity using usarray constraining velocity and density structure in the upper crust rayleigh wave ellipticity or h v ratio observed on the surface is particularly sensitive to shallow earth structure in this study we jointly invert measurements of rayleigh wave h v ratio and phase velocity between 24 100 and 8 100 sec period respectively for crust and upper mantle structure beneath more than 1000 usarray stations covering the western united states upper crustal structure in particular is better constrained by the joint inversion compared to inversions based on phase velocities alone in addition to imaging vs structure we show that the joint inversion can be used to constrain vp vs and density in the upper crust new images of uppermost crustal structure 3 km depth are in excellent agreement with known surface features with pronounced low vs low density and high vp vs anomalies imaged in the locations of several major sedimentary basins including the williston powder river green river denver and san juan basins these results demonstrate not only the consistency of broadband h v ratios and phase velocity measurements but also that their complementary sensitivities have the potential to resolve density and vp vs variations

a simple model of the decadal response of the ocean to stochastic wind forcing abstract a simple linear model is used to estimate the decadal response of the extratropical ocean to wind stress forcing assuming a flat bottom a mean state at rest and no dissipation the barotropic fields are governed by a time dependent sverdrup balance the baroclinic ones by the long rossby wave equation the ocean is bounded by a coast in the east and a radiation condition is used in the west at each frequency the baroclinic response consists of a forced response plus a rossby wave generated at the eastern boundary for zonally independent forcing the response propagates westward at twice the rossby phase speed the wind stress is assumed to be stochastic with a white frequency spectrum so the model represents the continuous excitation of the ocean interior by the weather fluctuations the model predicts the shape and level of the frequency spectra of the oceanic pressure field and their variation with longitude and latitude the baroclinic response is spread over a continuum of frequencies

large scale variability in the midlatitude subtropical and subpolar north pacific ocean observations and causes abstract altimetric data from the 8 yr topex poseidon t p mission oct 1992 jul 2000 are used to investigate large scale circulation changes in the three current systems of the midlatitude north pacific ocean the north pacific current npc the alaska gyre and the western subarctic gyre wsg to facilitate the understanding of the observed changes a two layer ocean model was adopted that includes first mode baroclinic rossby wave dynamics and barotropic sverdrup dynamics the npc intensified steadily over the t p period from 1992 to 1998 much of this intensification is due to the persistent sea surface height ssh drop on the northern side of the npc a similar ssh trend is also found in the interior of the alaska gyre both of these ssh changes are shown to be the result of surface wind stress curl forcing accumulated along the baroclinic rossby wave characteristics initiated from the eastern boundary in addition to the interior ssh signals the intensity of the alaska gyre is shown to depend

the partition of regional sea level variability abstract the existing altimetric record offers an unprecedented view of sea level variability on a global scale for more than 2 decades optimal inference from the data involves appropriate partition of signal and noise in terms of relevant scales physical processes and forcing mechanisms such partition is achieved here through fitting a general circulation model to altimeter and other datasets to produce a best estimate of variability directly forced by the atmosphere the signal of primary interest here in this context noise comes primarily from instrument errors and meso scale eddies as expected but spatial smoothing effectively reduces this noise a separate constraint is thus formulated to measure the fit to monthly large scale altimetric variability that unlike the daily pointwise constraint shows a high signal to noise ratio the estimate is explored to gain insight into dynamics forcing and other factors controlling variability contributions from thermo steric halo steric and bottom pressure terms are all important depending on region but slopes of steric spectra red and bottom pressure spectra white are nearly invariant with latitude much variability can be represented by a seasonal cycle and linear trend plus a few eofs that can be associated with known modes of climate variability and or with topographic controls both wind and buoyancy forcing are important the response is primarily basin bound in nature but uneven patterns of propagation across basin boundaries are clearly present with the pacific being able to affect large portions of the indian and atlantic basins but the atlantic affecting mostly the arctic

interpretation of the propagation of surface altimetric observations in terms of planetary waves and geostrophic turbulence 1 the interpretation of surface altimetric signals in terms of rossby waves is revisited rather than make the long wave approximation the horizontal scale of the waves is adjusted to optimally fit the phase speed predicted by linear theory to that observed by altimetry assuming a first baroclinic mode vertical structure it is found that in the tropical band the observations can be fit if the wavelength of the waves is assumed to be large of order 600 km or so however poleward of 30 it is more difficult to fit linear theory to the observations and the fit is less good than at lower latitudes the required scale of the waves must be reduced to about 100 km somewhat larger than the local deformation wavelength it is argued that these results can be interpreted in terms of rossby wave baroclinic instability and turbulence theory at low latitudes there is an overlap between geostrophic turbulence and rossby wave timescales and so an upscale energy transfer from baroclinic instability at the deformation scale produces waves at high latitudes there is no such overlap and waves are not produced by upscale energy transfer these ideas are tested by using surface drifter data to infer turbulent velocities and timescales that are compared to those of linear rossby waves a transition from a field dominated by waves to one dominated by turbulence occurs at about 30 broadly consistent with the transition that is required to fit linear theory to altimetric observations

the response of the north pacific ocean to decadal variability in atmospheric forcing wind versus buoyancy forcing abstract both wind and buoyancy forcing result in variability in the north pacific ocean thermocline a vertical modal analysis of the density deviations in a 30 yr run of an ocean general circulation model of the north pacific forced by atmospheric variability is used to identify the spatial and temporal patterns of the different baroclinic modes the different dynamic vertical modes show distinct propagation characteristics with the first baroclinic mode exhibiting consistent westward propagation at all latitudes the higher baroclinic modes show westward phase propagation at low latitudes but propagate eastward at higher latitudes the propagation characteristics of each mode can be understood by the inclusion of the zonal mean flow in the vertical structure equation evaluation of the ekman pumping and diapycnal fluxes in the quasigeostrophic potential vorticity equation for each dynamic vertical mode distinguishes their effects on the thermocline variability wind variability dominantly forces the f

multidecadal sea level and gyre circulation variability in the northwestern tropical pacific ocean abstractsea level rise with the trend 10 mm yr 1 has been observed in the tropical western pacific ocean over the 1993 2009 period this rate is 3 times faster than the global mean value of the sea level rise analyses of the satellite altimeter data and repeat hydrographic data along 137 e reveal that this regionally enhanced sea level rise is thermosteric in nature and vertically confined to a patch in the upper ocean above the 12 c isotherm dynamically this regional sea level trend is accompanied by southward migration and strengthening of the north equatorial current nec and north equatorial countercurrent necc using a 1 layer reduced gravity model forced by the ecmwf reanalysis wind stress data the authors find that both the observed sea level rise and the nec necc s southward migrating and strengthening trends are largely attributable to the upper ocean water mass redistribution caused by the surface wind stresses of the recently strengthened atmospheric walker circulation based on the lo

an almost free barotropic mode in the australian antarctic basin 1 the australian antarctic basin aab is known for its high levels of intraseasonal variability sea surface height variability exceeds background values by factors of 2 over thousands of kilometers this paper addresses the hypothesis that this variability is caused by trapping of barotropic energy by the basin geometry analysis of a multi year integration of a shallow water model shows that the variability is dominated by a single large scale statistical mode that is highly coherent over the entire aab the flow associated with this mode is northwestward along the southeast indian ridge southward in the kerguelen abyssal plain and eastward in the southern aab the mode is interpreted as an almost free topographically trapped mode as it is confined by contours of potential vorticity that almost entirely enclose the aab the apex of the wilkes abyssal plain represents the strongest barrier to the modal circulation here velocities are strongest making it a key area for dissipation of kinetic energy through bottom friction and eddy viscosity

el nino modoki and its possible teleconnection 1 using observed data sets mainly for the period 1979 2005 we find that anomalous warming events different from conventional el nino events occur in the central equatorial pacific this unique warming in the central equatorial pacific associated with a horseshoe pattern is flanked by a colder sea surface temperature anomaly ssta on both sides along the equator empirical orthogonal function eof analysis of monthly tropical pacific ssta shows that these events are represented by the second mode that explains 12 of the variance since a majority of such events are not part of el nino evolution the phenomenon is named as el nino modoki pseudo el nino modoki is a classical japanese word which means a similar but different thing the el nino modoki involves ocean atmosphere coupled processes which include a unique tripolar sea level pressure pattern during the evolution analogous to the southern oscillation in the case of el nino hence the total entity is named as el nino southern oscillation enso modoki the enso modoki events significantly influence the temperature and precipitation over many parts of the globe depending on the season the impacts over regions such as the far east including japan new zealand western coast of united states etc are opposite to those of the conventional enso the difference maps between the two periods of 1979 2004 and 1958 1978 for various oceanic atmospheric variables suggest that the recent weakening of equatorial easterlies related to weakened zonal sea surface temperature gradient led to more flattening of the thermocline this appears to be a cause of more frequent and persistent occurrence of the enso modoki event during recent decades

an ocean resonance in the indian sector of the southern ocean 1 satellite altimeter observations of sea surface height show an extensive region of long wavelength fluctuations in the indian sector of the southern ocean a previous study showed that a similar feature found in the south pacific is due to a trapped geostrophic mode of the ocean here we investigate the feature in the indian sector and find that it is due to a similar mode with a decay time of approximately 3 5 days these previously unsuspected large scale modes of the ocean will have a significant effect locally on the satellite based gravity measurements currently underway

global ocean circulation during 1992 1997 estimated from ocean observations and a general circulation model 1 a three dimensional oceanic state is estimated for the period 1992 1997 as it results from combining large scale ocean data sets with a general circulation model at the cost of increased computational load the estimation assimilation method is chosen specifically so that the resulting state estimate is consistent with the model equations having no artificial sources or sinks to bring the model into close agreement with observations its initial temperature and salinity conditions are permitted to change as are the time dependent surface fluxes of momentum heat and freshwater resulting changes of these control vectors are largely consistent with accepted uncertainties in the hydrographic climatology and meteorological analyses the assimilation procedure is able to correct for many of the traditional shortcomings of the flow field by changing the surface boundary conditions changes in the resulting flow field are predominantly on the gyre scale and affect many features that are often poorly simulated in traditional numerical simulations such as the strengths of the gulf stream and its extension the azores current and the anticyclonic circulation associated with the labrador sea tests of the results and their consistency with prior error assumptions show that the constrained model has moved considerably closer to the observations imposed as constraints but has also moved closer to independent data from the world ocean circulation experiment not used in the assimilation procedure in some regions where the comparisons remain indeterminate not enough ocean observations are available and it is difficult to ascribe the residuals to either the model or the observations although problems remain a useful first solution to the global time dependent ocean state estimation problem has been found the estimates will continue to improve through the evolution of numerical models computer power increases more data and more efficient estimation methods

a near uniform fluctuation of ocean bottom pressure and sea level across the deep ocean basins of the arctic ocean and the nordic seas across the arctic ocean and the nordic seas a basin wide mode of ocean bottom pressure and sea level fluctuation is identified using satellite and in situ observations in conjunction with a global ocean circulation model and its adjoint the variation extends across the interconnected deep ocean basins of these semi enclosed arctic seas collectively called the arctic mediterranean with spatially near uniform amplitude and phase the basin wide fluctuation is barotropic and dominates the region s large scale variability from sub monthly to interannual timescales the fluctuation results from bifurcating coastally trapped waves generated by winds along the continental slopes of the arctic mediterranean and its neighboring seas including the north atlantic ocean the winds drive ekman transport across the large bathymetric gradients forcing mass divergence between the shallow coastal area and the deep ocean basins and creating ocean bottom pressure anomalies of opposite signs in the two regions the anomalies rapidly propagate away as barotropic coastally trapped waves with the coast and continental slope as respective boundaries the waves subsequently bifurcate at the shallow straits connecting the arctic mediterranean with the rest of the globe the straits transmit the shallow anomalies but not the deep variations thereby inhibiting the anomalies mutual cancelation by geographically separating the two anomalies that enter the deep arctic basins equilibrate uniformly across the domain characterized by a homogeneous depth integrated planetary potential vorticity distribution the potential vorticity s steep gradient that borders the basins shields the region from neighboring shallow variations giving rise to the observed spatially confined fluctuation compensating anomalies outside the arctic adjust similarly across the rest of the globe but are comparatively negligible in amplitude because of the global ocean s larger area relative to that of the deep arctic mediterranean the study from a technical perspective illustrates the utility of a model s adjoint in identifying causal mechanisms underlying a complex system