Reviews of Geophysics

Các ứng dụng của giả thuyết đóng cửa độ hỗn loạn bậc hai đối với các vấn đề dòng chảy địa vật lý đã phát triển nhanh chóng kể từ năm 1973, khi mà khả năng dự đoán thực sự trong việc giải quyết các ảnh hưởng của sự phân tầng đã được chứng minh. Mục đích ở đây là tổng hợp và tổ chức các tài liệu đã xuất hiện trong một số bài báo và thêm các tài liệu hữu ích mới để một mô tả đầy đủ (và cải tiến) về một mô hình độ hỗn loạn từ khái niệm đến ứng dụng được cô đọng trong một bài báo duy nhất. Hy vọng rằng điều này sẽ là một tài liệu tham khảo hữu ích cho người sử dụng mô hình để ứng dụng cho các tầng biên khí quyển hoặc đại dương.

If model parameterizations of unresolved physics, such as the variety of upper ocean mixing processes, are to hold over the large range of time and space scales of importance to climate, they must be strongly physically based. Observations, theories, and models of oceanic vertical mixing are surveyed. Two distinct regimes are identified: ocean mixing in the boundary layer near the surface under a variety of surface forcing conditions (stabilizing, destabilizing, and wind driven), and mixing in the ocean interior due to internal waves, shear instability, and double diffusion (arising from the different molecular diffusion rates of heat and salt). Mixing schemes commonly applied to the upper ocean are shown not to contain some potentially important boundary layer physics. Therefore a new parameterization of oceanic boundary layer mixing is developed to accommodate some of this physics. It includes a scheme for determining the boundary layer depth h, where the turbulent contribution to the vertical shear of a bulk Richardson number is parameterized. Expressions for diffusivity and nonlocal transport throughout the boundary layer are given. The diffusivity is formulated to agree with similarity theory of turbulence in the surface layer and is subject to the conditions that both it and its vertical gradient match the interior values at h. This nonlocal “K profile parameterization” (KPP) is then verified and compared to alternatives, including its atmospheric counterparts. Its most important feature is shown to be the capability of the boundary layer to penetrate well into a stable thermocline in both convective and wind‐driven situations. The diffusivities of the aforementioned three interior mixing processes are modeled as constants, functions of a gradient Richardson number (a measure of the relative importance of stratification to destabilizing shear), and functions of the double‐diffusion density ratio, R_ρ. Oceanic simulations of convective penetration, wind deepening, and diurnal cycling are used to determine appropriate values for various model parameters as weak functions of vertical resolution. Annual cycle simulations at ocean weather station Papa for 1961 and 1969–1974 are used to test the complete suite of parameterizations. Model and observed temperatures at all depths are shown to agree very well into September, after which systematic advective cooling in the ocean produces expected differences. It is argued that this cooling and a steady salt advection into the model are needed to balance the net annual surface heating and freshwater input. With these advections, good multiyear simulations of temperature and salinity can be achieved. These results and KPP simulations of the diurnal cycle at the Long‐Term Upper Ocean Study (LOTUS) site are compared with the results of other models. It is demonstrated that the KPP model exchanges properties between the mixed layer and thermocline in a manner consistent with observations, and at least as well or better than alternatives.

A survey is given of the dimensions and composition of the present continental crust. The abundances of immobile elements in sedimentary rocks are used to establish upper crustal composition. The present upper crustal composition is attributed largely to intracrustal differentiation resulting in the production of granites senso lato. Underplating of the crust by ponded basaltic magmas is probably a major source of heat for intracrustal differentiation. The contrast between the present upper crustal composition and that of the Archean upper crust is emphasized. The nature of the lower crust is examined in the light of evidence from granulites and xenoliths of lower crustal origin. It appears that the protoliths of most granulite facies exposures are more representative of upper or middle crust and that the lower crust has a much more basic composition than the exposed upper crust. There is growing consensus that the crust grows episodically, and it is concluded that at least 60% of the crust was emplaced by the late Archean (ca. 2.7 eons, or 2.7 Ga). There appears to be a relationship between episodes of continental growth and differentiation and supercontinental cycles, probably dating back at least to the late Archean. However, such cycles do not explain the contrast in crustal compositions between Archean and post‐Archean. Mechanisms for deriving the crust from the mantle are considered, including the role of present‐day plate tectonics and subduction zones. It is concluded that a somewhat different tectonic regime operated in the Archean and was responsible for the growth of much of the continental crust. Archean tonalites and trond‐hjemites may have resulted from slab melting and/or from melting of the Archean mantle wedge but at low pressures and high temperatures analogous to modern boninites. In contrast, most andesites and subduction‐related rocks, now the main contributors to crustal growth, are derived ultimately from the mantle wedge above subduction zones. The cause of the contrast between the processes responsible for Archean and post‐Archean crustal growth is attributed to faster subduction of younger, hotter oceanic crust in the Archean (ultimately due to higher heat flow) compared with subduction of older, cooler oceanic crust in more recent times. A brief survey of the causes of continental breakup reveals that neither plume nor lithospheric stretching is a totally satisfactory explanation. Speculations are presented about crustal development before 4000 m.y. ago. The terrestrial continental crust appears to be unique compared with crusts on other planets and satellites in the solar system, ultimately a consequence of the abundant free water on the Earth.

Geophysical, petrological, and geochemical data provide important clues about the composition of the deep continental crust. On the basis of seismic refraction data, we divide the crust into type sections associated with different tectonic provinces. Each shows a three‐layer crust consisting of upper, middle, and lower crust, in which P wave velocities increase progressively with depth. There is large variation in average P wave velocity of the lower crust between different type sections, but in general, lower crustal velocities are high (>6.9 km s⁻¹) and average middle crustal velocities range between 6.3 and 6.7 km s⁻¹. Heat‐producing elements decrease with depth in the crust owing to their depletion in felsic rocks caused by granulite facies metamorphism and an increase in the proportion of mafic rocks with depth. Studies of crustal cross sections show that in Archean regions, 50–85% of the heat flowing from the surface of the Earth is generated within the crust. Granulite terrains that experienced isobaric cooling are representative of middle or lower crust and have higher proportions of mafic rocks than do granulite terrains that experienced isothermal decompression. The latter are probably not representative of the deep crust but are merely upper crustal rocks that have been through an orogenic cycle. Granulite xenoliths provide some of the deepest samples of the continental crust and are composed largely of mafic rock types. Ultrasonic velocity measurements for a wide variety of deep crustal rocks provide a link between crustal velocity and lithology. Meta‐igneous felsic, intermediate and mafic granulite, and amphibolite facies rocks are distinguishable on the basis of P and S wave velocities, but metamorphosed shales (metapelites) have velocities that overlap the complete velocity range displayed by the meta‐igneous lithologies. The high heat production of metapelites, coupled with their generally limited volumetric extent in granulite terrains and xenoliths, suggests they constitute only a small proportion of the lower crust. Using average P wave velocities derived from the crustal type sections, the estimated areal extent of each type of crust, and the average compositions of different types of granulites, we estimate the average lower and middle crust composition. The lower crust is composed of rocks in the granulite facies and is lithologically heterogeneous. Its average composition is mafic, approaching that of a primitive mantle‐derived basalt, but it may range to intermediate bulk compositions in some regions. The middle crust is composed of rocks in the amphibolite facies and is intermediate in bulk composition, containing significant K, Th, and U contents. Average continental crust is intermediate in composition and contains a significant proportion of the bulk silicate Earth's incompatible trace element budget (35–55% of Rb, Ba, K, Pb, Th, and U).

In the past, studies of stratosphere‐troposphere exchange of mass and chemical species have mainly emphasized the synoptic‐ and small‐scale mechanisms of exchange. This review, however, includes also the global‐scale aspects of exchange, such as the transport across an isentropic surface (potential temperature about 380 K) that in the tropics lies just above the tropopause, near the 100‐hPa pressure level. Such a surface divides the stratosphere into an “overworld” and an extratropical “lowermost stratosphere” that for transport purposes need to be sharply distinguished. This approach places stratosphere‐troposphere exchange in the framework of the general circulation and helps to clarify the roles of the different mechanisms involved and the interplay between large and small scales. The role of waves and eddies in the extratropical overworld is emphasized. There, wave‐induced forces drive a kind of global‐scale extratropical “fluid‐dynamical suction pump,” which withdraws air upward and poleward from the tropical lower stratosphere and pushes it poleward and downward into the extratropical troposphere. The resulting global‐scale circulation drives the stratosphere away from radiative equilibrium conditions. Wave‐induced forces may be considered to exert a nonlocal control, mainly downward in the extratropics but reaching laterally into the tropics, over the transport of mass across lower stratospheric isentropic surfaces. This mass transport is for many purposes a useful measure of global‐scale stratosphere‐troposphere exchange, especially on seasonal or longer timescales. Because the strongest wave‐induced forces occur in the northern hemisphere winter season, the exchange rate is also a maximum at that season. The global exchange rate is not determined by details of near‐tropopause phenomena such as penetrative cumulus convection or small‐scale mixing associated with upper level fronts and cyclones. These smaller‐scale processes must be considered, however, in order to understand the finer details of exchange. Moist convection appears to play an important role in the tropics in accounting for the extreme dehydration of air entering the stratosphere. Stratospheric air finds its way back into the troposphere through a vast variety of irreversible eddy exchange phenomena, including tropopause folding and the formation of so‐called tropical upper tropospheric troughs and consequent irreversible exchange. General circulation models are able to simulate the mean global‐scale mass exchange and its seasonal cycle but are not able to properly resolve the tropical dehydration process. Two‐dimensional (height‐latitude) models commonly used for assessment of human impact on the ozone layer include representation of stratosphere‐troposphere exchange that is adequate to allow reasonable simulation of photochemical processes occurring in the overworld. However, for assessing changes in the lowermost stratosphere, the strong longitudinal asymmetries in stratosphere‐troposphere exchange render current two‐dimensional models inadequate. Either current transport parameterizations must be improved, or else, more likely, such changes can be adequately assessed only by three‐dimensional models.

Recent advances in theory and experimentation motivate a thorough reassessment of the physics of debris flows. Analyses of flows of dry, granular solids and solid‐fluid mixtures provide a foundation for a comprehensive debris flow theory, and experiments provide data that reveal the strengths and limitations of theoretical models. Both debris flow materials and dry granular materials can sustain shear stresses while remaining static; both can deform in a slow, tranquil mode characterized by enduring, frictional grain contacts; and both can flow in a more rapid, agitated mode characterized by brief, inelastic grain collisions. In debris flows, however, pore fluid that is highly viscous and nearly incompressible, composed of water with suspended silt and clay, can strongly mediate intergranular friction and collisions. Grain friction, grain collisions, and viscous fluid flow may transfer significant momentum simultaneously. Both the vibrational kinetic energy of solid grains (measured by a quantity termed the granular temperature) and the pressure of the intervening pore fluid facilitate motion of grains past one another, thereby enhancing debris flow mobility. Granular temperature arises from conversion of flow translational energy to grain vibrational energy, a process that depends on shear rates, grain properties, boundary conditions, and the ambient fluid viscosity and pressure. Pore fluid pressures that exceed static equilibrium pressures result from local or global debris contraction. Like larger, natural debris flows, experimental debris flows of ∼10 m³ of poorly sorted, water‐saturated sediment invariably move as an unsteady surge or series of surges. Measurements at the base of experimental flows show that coarse‐grained surge fronts have little or no pore fluid pressure. In contrast, finer‐grained, thoroughly saturated debris behind surge fronts is nearly liquefied by high pore pressure, which persists owing to the great compressibility and moderate permeability of the debris. Realistic models of debris flows therefore require equations that simulate inertial motion of surges in which high‐resistance fronts dominated by solid forces impede the motion of low‐resistance tails more strongly influenced by fluid forces. Furthermore, because debris flows characteristically originate as nearly rigid sediment masses, transform at least partly to liquefied flows, and then transform again to nearly rigid deposits, acceptable models must simulate an evolution of material behavior without invoking preternatural changes in material properties. A simple model that satisfies most of these criteria uses depth‐averaged equations of motion patterned after those of the Savage‐Hutter theory for gravity‐driven flow of dry granular masses but generalized to include the effects of viscous pore fluid with varying pressure. These equations can describe a spectrum of debris flow behaviors intermediate between those of wet rock avalanches and sediment‐laden water floods. With appropriate pore pressure distributions the equations yield numerical solutions that successfully predict unsteady, nonuniform motion of experimental debris flows.

Volcanic eruptions are an important natural cause of climate change on many timescales. A new capability to predict the climatic response to a large tropical eruption for the succeeding 2 years will prove valuable to society. In addition, to detect and attribute anthropogenic influences on climate, including effects of greenhouse gases, aerosols, and ozone‐depleting chemicals, it is crucial to quantify the natural fluctuations so as to separate them from anthropogenic fluctuations in the climate record. Studying the responses of climate to volcanic eruptions also helps us to better understand important radiative and dynamical processes that respond in the climate system to both natural and anthropogenic forcings. Furthermore, modeling the effects of volcanic eruptions helps us to improve climate models that are needed to study anthropogenic effects. Large volcanic eruptions inject sulfur gases into the stratosphere, which convert to sulfate aerosols with an e‐folding residence time of about 1 year. Large ash particles fall out much quicker. The radiative and chemical effects of this aerosol cloud produce responses in the climate system. By scattering some solar radiation back to space, the aerosols cool the surface, but by absorbing both solar and terrestrial radiation, the aerosol layer heats the stratosphere. For a tropical eruption this heating is larger in the tropics than in the high latitudes, producing an enhanced pole‐to‐equator temperature gradient, especially in winter. In the Northern Hemisphere winter this enhanced gradient produces a stronger polar vortex, and this stronger jet stream produces a characteristic stationary wave pattern of tropospheric circulation, resulting in winter warming of Northern Hemisphere continents. This indirect advective effect on temperature is stronger than the radiative cooling effect that dominates at lower latitudes and in the summer. The volcanic aerosols also serve as surfaces for heterogeneous chemical reactions that destroy stratospheric ozone, which lowers ultraviolet absorption and reduces the radiative heating in the lower stratosphere, but the net effect is still heating. Because this chemical effect depends on the presence of anthropogenic chlorine, it has only become important in recent decades. For a few days after an eruption the amplitude of the diurnal cycle of surface air temperature is reduced under the cloud. On a much longer timescale, volcanic effects played a large role in interdecadal climate change of the Little Ice Age. There is no perfect index of past volcanism, but more ice cores from Greenland and Antarctica will improve the record. There is no evidence that volcanic eruptions produce El Niño events, but the climatic effects of El Niño and volcanic eruptions must be separated to understand the climatic response to each.

Atmospheric gravity waves have been a subject of intense research activity in recent years because of their myriad effects and their major contributions to atmospheric circulation, structure, and variability. Apart from occasionally strong lower‐atmospheric effects, the major wave influences occur in the middle atmosphere, between ∼ 10 and 110 km altitudes because of decreasing density and increasing wave amplitudes with altitude. Theoretical, numerical, and observational studies have advanced our understanding of gravity waves on many fronts since the review by Fritts [1984a]; the present review will focus on these more recent contributions. Progress includes a better appreciation of gravity wave sources and characteristics, the evolution of the gravity wave spectrum with altitude and with variations of wind and stability, the character and implications of observed climatologies, and the wave interaction and instability processes that constrain wave amplitudes and spectral shape. Recent studies have also expanded dramatically our understanding of gravity wave influences on the large‐scale circulation and the thermal and constituent structures of the middle atmosphere. These advances have led to a number of parameterizations of gravity wave effects which are enabling ever more realistic descriptions of gravity wave forcing in large‐scale models. There remain, nevertheless, a number of areas in which further progress is needed in refining our understanding of and our ability to describe and predict gravity wave influences in the middle atmosphere. Our view of these unknowns and needs is also offered.

This paper reviews the many developments in estimates of the direct and indirect global annual mean radiative forcing due to present‐day concentrations of anthropogenic tropospheric aerosols since Intergovernmental Panel on Climate Change [1996]. The range of estimates of the global mean direct radiative forcing due to six distinct aerosol types is presented. Additionally, the indirect effect is split into two components corresponding to the radiative forcing due to modification of the radiative properties of clouds (cloud albedo effect) and the effects of anthropogenic aerosols upon the lifetime of clouds (cloud lifetime effect). The radiative forcing for anthropogenic sulphate aerosol ranges from −0.26 to −0.82 W m⁻². For fossil fuel black carbon the radiative forcing ranges from +0.16 W m⁻² for an external mixture to +0.42 W m⁻² for where the black carbon is modeled as internally mixed with sulphate aerosol. For fossil fuel organic carbon the two estimates of the likely weakest limit of the direct radiative forcing are −0.02 and −0.04 W m⁻². For biomass‐burning sources of black carbon and organic carbon the combined radiative forcing ranges from −0.14 to −0.74 W m⁻². Estimates of the radiative forcing due to mineral dust vary widely from +0.09 to −0.46 W m⁻²; even the sign of the radiative forcing is not well established due to the competing effects of solar and terrestrial radiative forcings. A single study provides a very tentative estimate of the radiative forcing of nitrates to be −0.03 W m⁻². Estimates of the cloud albedo indirect radiative forcing range from −0.3 to approximately −1.8 W m⁻². Although the cloud lifetime effect is identified as a potentially important climate forcing mechanism, it is difficult to quantify in the context of the present definition of radiative forcing of climate change and current model simulations. This is because its estimation by general circulation models necessarily includes some level of cloud and water vapor feedbacks, which affect the hydrological cycle and the dynamics of the atmosphere. Available models predict that the radiative flux perturbation associated with the cloud lifetime effect is of a magnitude similar to that of the cloud albedo effect.