French-Russian A.M.Liapunov Institute in Computer Science and Applied Mathematics.
INRIA --- Moscow State University.

Project No 4

Predictability of atmospheric and oceanic circulations.

Fourth Extended conference

September, 2-4 1998,
Moscow, Russia


The conference was supported by


Brief report is available in Russian (koi8 encoding)

Procedings are published by French-Russian A.M.Liapunov Institute on Applied Mathematics and Computer Science.


Abstracts and full text articles.

Numerical Modeling of Kinetic Processes of Gaseous Pollutants and Aerosols in the Atmosphere

A.E. Aloyan, V.O. Arutyunyan, P.I. Louzan

Institute of Numerical Mathematics RAS,
8 Gubkina str., 117333 Moscow, Russia

Two problems are considered in this work. (1) Numerical modeling of gaseous pollutants and aerosols in the atmosphere with consideration for photochemical transformations in the gas- and aqueous phases as well as aerosol formation processes due to condensation and coagulation. These mechanisms allow one to estimate the secondary pollution levels of the atmosphere along with the disperse phase formation (caused both by fluctuations and interaction with atmospheric nuclei). Here the problem is resolved combined with the mesoscale hydrodynamics model. The results of numerical experiments are provided for specific problems. (2) Numerical modeling of the transport of persistent organic pollutants in the Northern hemisphere. A representative of POP, lindane, was used in the calculations due to availability of European-source emission data. The transport of lindane in the atmosphere and soil, and accumulation in water is considered. A series of parametrization mechanisms for lindane exchange in the atmosphere and soil is used in the model. The numerical calculations were performed to obtain the spatial and temporal variability of lindane in the Northern hemisphere for one year period.

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A World ocean circulation model for climatic changes modelling.

Diansky N. A., Bagno A. V.

Institute of Numerical Mathematics RAS,
8 Gubkina str., 117333 Moscow, Russia
A World ocean circulation model with $2.5^0\times 2^0\times 16$levels space resolution was developed. The model can be used for solving various physical problems. The primitive equation system for momentum, stream function, heat and salinity use "sigma" coordinate system with realistic bottom topography. The numerical algorithm is based on splitting up in physical processes and geometrical variables, 2nd order accuracy approximation in space, implicit scheme for transport - diffusion - type equation.

A number of numerical experiments were carried out for 25 years with winter restoring surface boundary conditions, starting from Levitus climatology. The simulated currents are in a good agreement with observations and results of other models with same resolution. The Pacific equatorial current has maximum velocity of 100 cm/s, western boundary currents being twice slower. The sensitivity of simulated climate to the coefficients and type of horizontal diffusion was investigated.

Changing lateral diffusion from being directed along relief (according to "sigma" surfaces) to strictly horizontal (which is more complex in "sigma" coordinates) influences the width of Gulf Stream. The North Atlantic current becomes longer and realistically more northern directed, while barotropic streamfunction reveals more distinct mid latitude gyres with western boundary intensification.

The simulated surface heat flux in ocean was compared to the NCEP/NCAR reanalysis data. The meridional heat flux and overturning streamfunction were evaluated. The procedure of coupling the World ocean circulation model to atmospheric circulation model was developed for climate changes of coupled system study. The ocean model can be used for simulation of deep water circulation and cold water formation in North Atlantic as well.

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Inverse Problems in Satellite Meteorology

G. I. Marchuk, A. I. Chavro

Institute of Numerical Mathematics RAS,
8 Gubkina str., 117333 Moscow, Russia
A method is proposed for the determination of meteorological parameters in the system "underlying surface-atmosphere" using solutions of adjoint equations of the radiation transfer theory in the IR-spectrum. This method allows one to take into account variations of the main absorbing substances of atmosphere and emissivity of a surface and may be used for scanning satellite systems. Modern methods of mathematical stasistics and apriori statistical information are used for the parameterization and solution of an inverse problem.

Numerical experiments with using this method for the determinanion of vertical temperature profiles of atmosphere were carried out.

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On the predictability of climate changes

V.P. Dymnikov

Institute of Numerical Mathematics RAS,
8 Gubkina str., 117333 Moscow, Russia

In the paper the some problems of the predictability theory of climate changes are considered. It is assumed that "ideal model" of climatic system can be described by PDE system, which is dynamical system and has global attractor. The dynamics on this attractor is chaotic one and can be coded as stationary random process. The applicability of corresponding dissipation - fluctuation relationships to this dynamics is discussed.Using appropriate assumptions for construction of dynamical-stochastical model of low-frequency variability of atmospheric circulation the problem of maximal sensitivity of climate model to small external forcing is investigated. It is shown that the climate model can have hypersensitivity to some special external forcing if the first EOF of low-frequency variability of atmospheric circulation is hadly separated from anothers ( in dispersion). The results of numerical experiments with GCM are given.

Optimal intraseasonal sea surface temperature anomalies in the World Ocean.

V.V. Efimov, M.V. Shokurov and A.V. Prusov

Marine Hydrophysical Institute,
Ukrainian National Academy of Sciences, Ukraine.

Optimal intraseasonal sea surface temperature (SST) anomalies are analysed in terms of characteristics, specific to separate seasons of the year. For the analysis the method of local Lyapunov coefficients, calculated from the changes of the SST anomalies during one-month interval, was applied. Using monthly COAD-Set, the changes of Lyapunov exponents throughout the year were computed and periods of the most unstable and stable seasons revealed. Of most interest is the spring instability of SST anomalies in the tropical Pacific, being crucial for the existence of a predictability barrier for an El-Nino events. The regions and months of SST anomalies instability for the Atlantic were obtained. The application of this method for Mediterranean was also given.

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Some approaches towards the creation more effective program version of a general circulation model.

I.N. Esau

Institute of Numerical Mathematics RAS,
8 Gubkina str., 117333 Moscow, Russia

Peculiarities of the modern computers were examined. Different subroutines of real programs were analyzed with help of the Livermore's kernel test. It was demonstrated that the performance of scalar as well as vector computers varies according to an used calculation algorithm more than the order one. The general circulation model by INM was tuned with regard to the detected regularities, the most of which were well-known. Structures with conventional statements calculate the most of the program run-time. Such situation had its origin in a lot of physical parametrisation, which using empirical functions. One of the most expended subroutines is the convection, condensation and precipitation procedure. Sufficiently general approach was suggested. Its allows to replace the structures with conditional statements by a loops sequence with independent iterations. This approach gives a vectorized algorithms of the parametrisations. It was applied to the just listed subroutines and it tended to increase the important model performance for computers of different architecture.

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Stability of attractors of semidynamical systems

A.N. Filatov

Institute of Numerical Mathematics RAS,
8 Gubkina str., 117333 Moscow, Russia

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Simulation of atmosphere circulation response to North Atlantic SST anomalies in winter

Diansky N.A., A.V. Glazunov, V.P. Dymnikov

Institute of Numerical Mathematics RAS,
8 Gubkina str., 117333 Moscow, Russia

The interaction of atmosphere and ocean in the middle latitudes under winter conditions is studied. For this purpose three 360 month simulating time numerical experiments with atmosphere general circulation model (AGCM) of INM RAS was carried out for the condition of continuous January. In one of experiments an ocean upper layer model (OULM) was joined to AGCM. It was shown, as concerns the structure of leading empirical orthogonal functions (EOF) for interannual anomalies of 500mb geopotential height (H500), it was closer to observations in the coupled model (AGCM and OULM), than in the AGCM with prescribed climatic SST. It may point out to the better description of atmospheric low-frequency variability in the coupled model. Two experiments were performed with stationary positive and alternating (with the prescribed temporary course) SST anomalies in the North Atlantic. Spatial monopolar form of SST anomaly and its temporary course were selected to be concordant with the dynamics of atmosphere model using the results of the numerical experiment with the coupled model. It was shown, that the located response of the atmosphere model to SST anomaly has baroclinic structure. The spatial structure of this response to SST anomaly of monopolar configuration in the North Atlantic is such, that the arising atmosphere circulation seems to suppress SST anomaly thus realizing a negative feedback in model. It was found, that the stationary atmosphere response in H500 to a fixed in time SST anomaly beside located response in H500 may contain a global component. The spatial structure of this response component is determined by the spatial structure of the leading low-frequency EOFs.

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Sensitivity of January atmosphere circulation to the observed ozone depletion in low stratosphere

E.M. Volodin and V. Ya. Galin

Institute of Numerical Mathematics RAS,
8 Gubkina str., 117333 Moscow, Russia
The sensitivity of January circulation in two versions of INM AGCM to ozone depletion observed last decade is investigated. The response of one version is small and statistically insignificant, but for the second version the response is large, statistically significant and looks like the observed anomalies of winter circulation in 1989-1994. Both observed anomalies and model response almost coincide with the first EOF of low-frequency variability. It is shown that the reason of different sensitivity of model versions to the ozone depletion is the difference of the first EOFs of meridional circulation. For the sensitive version, the projection of the radiative heating rates due to ozone depletion to the first mode of zonal-mean vertical velocities is large, and for another version - not so large. The similar projection for the observations is as large as for the sensitive version of model

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Sensitivity of the average state of barotropic atmosphere model to the small constant perturbations. Theory and numerical experiments.

A.S. Gritsun, V.P.Dymnikov

Institute of Numerical Mathematics RAS,
8 Gubkina str., 117333 Moscow, Russia

The problem of maximum sensitivity forecast of the atmospheric circulation to the small external perturbations is very difficult. Therefore it is important to have a simple approximate method that can provide information about climate model response on such perturbations.

In this study we consider the barotropic model of low-frequency atmospheric variability obtained from the barotropic vorticty equation on the sphere with the help of Galerkin method. For this model by means of direct method we construct the operator, that describes the model response on small constant perturbations. It is shown, that this operator can be considered as linear with high accuracy. Moreover the maximum response of the system is close to the first low-frequency EOF.

Next we investigate the possibility to describe the response of the original model by means of its linear dynamical-stochastic analogues. The two models are considered. The linear operator of the first one is constructed according to the fluctuation-dissipation theorem using data produced by original model. In the second model the linearized operator of original model with additional Rayleigh dissipation is used.

It is shown that the first linear model can predict maximum response vector of the original model with the correlation 0.9. The accuracy of optimal excitation vector prediction is also sufficiently good ( 0.85). The coefficient of the optimal excitation growth turns to be slightly higher than in reality ( 145 and 100 respectively ). The use of the second linear model gives rise to the worse results.

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Unstable periodic orbits and Attractor of the Lorenz Model.

E. Kazantsev

INRIA-Lorraine, projet NUMATH,
615, rue du Jardin Botanique, BP101,
54602, Villers-lès-Nancy, Cedex, France.

Numerical method for detection of unstable periodic orbits on attractors of nonlinear dynamical systems is proposed. This method requires the similar techniques as the data assimilation does. This fact facilitates its implementation for geophysical models. Some low-period orbits of the Lorenz model have been calculated explicitely using this method.

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Finite dimensional approximation of the barotropic ocean model and its attractor.

Ch. Kazantsev.

Departement de Mathematiques, Universite Nancy 1,
BP239, 54506 Vandoeuvre-les-Nancy Cedex, France.

The structure of attractor of barotropic ocean model is studied in this paper. Theorems of the existence of the attractor for the finite dimensional approximation of this model are proved as well as its convergence to the attractor of the model itself. Some properties of stationary solutions of this model and their stability are discussed.

Eddy-wave turbulence on a beta-plane

Korotaev G.K., Dorofeev V.L.

Well-known result of the theory of two-dimensional turbulence is formation of eddies from a random initially field. Following evolution of a turbulent field consists from collision of eddies and concentration of vorticity in vortices of increasing scale. This scenario of evolution of turbulent field can be applied for geophysics if the energy of turbulence is high enough and beta- effect is suppressed. However for example in the open ocean non- linearity of turbulent field has the same order as beta-effect and specific process of eddy-wave interaction is responsible for evolution of turbulence. We show in our report that eddies in turbulence on a beta-plane radiate Rossby waves and also extract energy from random wave field. As a result mean lifetime of eddies increases in comparison with a single vortex. An eddy interacts with Rossby waves only in the case when special synchronism condition is satisfied. This condition depends fron phase of Rossby waves. Since Rossby wave field has random phases resulting trajectory of edies is also random which is shown by means of numerical simulation. Thus the predictability of an individual vortex trajectory depends from accuracy of prediction of phases of Rossby waves. Additional numerical simulations show that shear of currents or inhomogenity of bottom topography act on a vortex similarly to beta-effect and waves or wavelike perturbations may induce complicate propagation of each individual vortex.

Vegetation - atmosphere CO2 exchange simulated by land surface model forced by ECSib climate model

Vladimir Krupchatnikoff

Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Prospect Lavrentieva, 6, 630090, Novosibirsk 90, RUSSIA
tel.:+7 -3832 -344367 fax:+7 -3832 -324259

Vegetation is important for many ecological studies because it determines the rate of CO2 during photosynthesis and is important for hydrologic and atmospheric studies because of its effect on the latent heat flux. The most detailed parameterizations of vegetation are often found in the land surface models used with atmospheric models. It may be summarized as follows: effects of leaf area on the absorption of solar radiation at the surface sensible heat flux and latent heat flux biochemical fluxes and the soil heat fluxes, which are important due to the effects of soil temperature on biochemical fluxes the surface energy budget and soil hydrology. The land surface model considered in this report is an extansion of this earlier model development and built upon the work of Sellers P.J.,, (1986) and Bonan G.B.,(1995). Proposed version of the land surface model combines a rather complete accounting for phisical factors to assess the interaction of the atmosphere with the surface and availability for including in the general circulation model ECSib (Fomenko A., Krupchatnikoff V.,Yantzen A., (1996). The atmospheric model ECSib has been developed from ECMWF model (therefore the first part of its name is EC) and dynamical package and some physical subroutines developed at Novosibirsk Computing Center Siberian Branch of the RAS. The current state of the atmosphere (monthly mean parameters simulated by ECSib model wich is forced by the climatology of the annual cycle SST) is used to force the surface model. Required surface data for each land drid cell derived from Olson et. al's (1983), soil colors were taken from Dickinson, sand ,silt and clay data were derived from Webb et. al's(1993), inland water data were derived from Cogley (1991) and overlayed onto the NCAR CCM (128 x 64) grid (file 'fsurdat'). This dataset were used to carry out experiments,where the model was running in uncoupled mode.

The simulation of CO2 exchange for the West - Siberia is presented

The important feature of the given model of a surface is the description, except common physical processes, biophysical (account of physiology of plants) and biochemical (photosynthesis, respiration of plants and manufacture of primary production) processes on a surface. This feature of model bring closer together its with ecological models of a surface and also allows to carry out joint modeling of dynamics of a climate and ecosystem.

This work was supported by the RFFR 97 -05 -65194 and INTAS 96-1935.

Finite Element Method in Ocean Circulation Models

Prof. Victor I.Kuzin

Institut of Numerical Mathematics and Mathematical Geophysics SD RAS

In the paper the experience gainned in the construction of the Finite Element Method (FEM) Ocean Circulation Models is presented. These algorithms are sufficiently based on the use of various modifications of the splitting method for the realisation with respect to time.This allows one to use the implicit and semi-implicit schemes.The splitting in the models is done at two levels: in the differential formwith rwspect to the physical processes and for multipoint FEM grid operatorsto reduce them to a series of three-point operators. For discretization different grid meshes ( A-quazi-regular grid, B-,E- regular grids) as well as the different finite elements ( conforming, non-conforming elements) are used for different models. With the use of these numerical models the circulation of the North Pasific,Sea of Japan as well as in the Kuroshio region South of Japan were simulated. Some of these results are discussed in the paper.

Surface Fluxes in Climate System. A New EU Project "SFINCS" (the years 1998-2000)

Soeren Larsen, S. Zilitinkevich,

Wind Energy and Atmospheric Physics Departament, Risoe National Laboratory,
P.O. Box49, DK-4000 Rosklide, Denmark
Programme of Meteorology, Uppsala University,
Vallavagen 16, S-752 36 Uppsala, Sweden

This Project focuses on parametrization of the sub-grid scale air-sea/air-land turbulent fluxes of heat, momentum and passive scalars (henceforth flux-parametrization) for use in climate, weather prediction and other atmospheric models. the project participants are Risoe National Laboratory (Denmark, Co-ordinator) Max Planck Institute for Meteorology (Germany) Uppsala University (Sweden), Swedish Meteorological and Hydrological Istitute (Sweden) National Observatory of Athens (Greece). The sub-contractors (to Uppsala University) are FOA-- Departament of NBC Defence (Sweden), FIAMS-- Flinders University (Australia), and A.M. Obukhov Institute for Atmospheric Physics (Russia). The overall goal is to fill the gap between modern knowledge on the physical nature of turbulence and currently employed old-fashioned flux-parametrization.

Speed up of modern computers has inspired rapidly increasing spatial resolution and accuracy of operational models. This progress, howevar, is empedded by the lack of flux-parametrization that reflects non-logical properties of the planetary boundary layer (PBL) turbulence. The convectional surface-layer similarity theory as well as turbulence closures in operational use are both unable to reproduce non-local transport of momentum, heat and passive scalars. as a result the surface fluxes are ill-founded in extreme cases of strong convection and strong static stability. The key role in this problem is played by large-scale semi-organised structures, disregarded within the traditional concept of a turbulent flow as composed universally of fully organised (mean) and fully chaotic components.

Advanced theoretical concepts of the PBL turbulence together with recent evidence from field measurements and numerical large-eddy simulation studies provide sufficient basis for better understanding and realistic parametrization of the effects of non-universal semi-organised structures on the vertical transport. Moderen generation of the climate and weather prediction models provide convenient tools for incorporation and testing of new modules such as the flux parametrization. In the scope of Project SFINCS, the above recent achievements are further extended to develop an improved parametrization of turbulent fluxes at the air-sea/air-land interface in the interests of modelling the atmosphere and sea. This work includes:

In both micrometeorological experimental studies and case studies with climate and weather prediction models particular attention is paid to the Baltic Sea and Mediterranean Sea areas.

Modelling the heat and moisture transport in the "ABL - VEGETATION - SNOW - SOIL" system: an overview

V.N. Lykossov,

Institute of Numerical Mathematics RAS,
8 Gubkina str., 117333 Moscow, Russia

The problem of simulation of the air - land interaction is considered. A special attention is paid to the problem of heat and moisture transport in the atmospheric boundary layer (ABL) and in the soil. It is assumed that the interface surface could be covered by vegetation and/or snow. The overall objective of this study is to construct models which will be suitable for the use as parameterization schemes for the climate models.

The problem of turbulence closure for convective boundary layers (CBLs) is discussed. Due to the presence of semi-organized coherent structures, the nature of the vertical transport of heat and moisture across the CBL is essentially non-local. Such effects are also important for the surface layer. A brief overview is given of various closure schemes.

A special attention is paid to the description of the soil water dynamics for the cold season when (i) the heat and moisture exchange between the atmosphere and land is very much influenced by the presence of the snow cover, and (ii) the upper layer of the soil is frozen. The summer season case is also considered.

The description of a local one-dimensional model of the heat and moisture transport in the ``ABL - vegetation - snow - soil" system is given. To verify the model, data from different field experiments carried out in India, France, the Netherlands and Sweden have been used. To simulate the process of the autumn-winter soil, the input data are extracted from the measurements at the Russian meteorological stations. The results of model calculations compare favorable with data.

The model is used as a revised land surface parameterization within the atmospheric general circulation model developed in the Institute for Numerical Mathematics of Russian Academy of Sciences. It is shown that the suggested parameterization is perspective for the use in climate modelling.

This work is financinally supported by RFBR (Grant 98-05-64210) and INTAS (Grant INTAS-96-1935).

Numerical study of the World ocean climatic variability

Ch. Kazantsev, Moshonkin S.N., Zalesny V.B.

Institute of Numerical Mathematics RAS,
8 Gubkina str., 117333 Moscow, Russia

A three-dimensional primitive equation World ocean model in $\sigma$-coordinates with 5*4*10 resolution, real topography, is presented. The model basin includes the Arctic ocean and two-dimensional representation of the Mediterranean sea. The computational algorithms are based on the decomposition of the space operator and implicit splitting schemes. The model is applied to calculate a climatic equilibrium thermohaline circulation under momentum flux and prescribed temperature and salinity at the sea surface. Model. The model uses the evolutionary symmetrized form of governing equations. The computational algorithms are based on the decomposition of a space operator and implicit splitting schemes. The system of equations is transformed into the evolutionary form by eliminating the pressure and vertical velocity. The obtained system of evolutionary equations is rewritten in special symmetrized form. This form is chosen so that it is convenient to represent the operator of the differential problem as a sum of suboperators of a simpler structure. Each suboperator must be positive definite in the norm that is defined by the law of conservation of total energy. The space approximation of the model equations is realized on different staggered grids: the combinations of grids A, B, and C are used. Results. The global ocean circulation is computed for a number of model conditions: a) for two versions of the equation of sea water state, b) with and without Mediterranean sea, c) with and without mixed derivatives in horizontal turbulent diffusivity. Generally, the all simulated velocity fields satisfactory reproduce the principal properties of the observed ocean circulation. The global distributions of temperature and salinity are consistent with observations. The differences between the solutions depending on different model conditions are analyzing.

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Adjoint problems for diagnostic research and estimation of stability and predictability of numerical models of atmospheric hydrodynamics


ICMMG SB RAS, Novosibirsk

Conceptual and constructive aspects of numerical modeling for the solution of the problems connected with estimations of climatic and ecological future of industrial regions forced by natural and ecological factors are considered. The problems of sensitivity, stability and predictability are the fundamental ones as for the statements of the class of problems as for the organization of numerical models. As an example the model of hydrodynamics and transport of pollutants in climatic system of the region is described. Taking into account a huge number of inner and outer degrees of freedom, a set of general characteristics and quality criteria described by functionals on the set of the state functions is introduced to analyze the behavior of modeling processes and numerical models in diagnostic and prognostic regimes .

The methodology of investigations are constructed on the principles of direct and inverse modeling, variational approach and optimization technique. Five basic elements are involved in the methodology: algorithms for the solution of direct and adjoint problems, a basic algorithm of the inverse modeling, algorithms of sensitivity functions calculation and the sensitivity theory formulas for the given set of functionals.

The methods of inverse modeling are of diagnostic nature . They allow us to bring to light the key parameters which are responsible for the possibility to reach the desired result. Their use in prognostic goals gives an estimation of tendency of perturbations influence of input parameters and initial data. The algorithms operating with functionals have definite advantages over that of distributed state functions. With this approach the sensitivity estimations of large scale "output" parameters of the system to all disturbances of input parameters as a whole are derived directly and the contribution of each parameters are explicitly given off.

If input influences of natural and anthropogenic factors have uncertainties they are described with the help of scenarious. The method is discussed for the formulation of appropriate collection of scenarious. Then the results are considered as if they were determinate ones.

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Parameterization of turbulent fluxes in 3-D HIRLAM on the base of turbulent kinetic energy--dissipation approach

V. Perov, K.-I. Ivarsson

Swedish Meteorological and Hydrological Institute,
Folkborgsvägen 1, S-60176 Norrköping, Sweden

The parameterization scheme of subgrid-scale vertical turbulent fluxes on base of the nonlocal turbulent kinetic energy (E) - dissipation ($\epsilon$) approach has been developed and installed in 3-D HIRLAM (High Resolution Limited Area Model). The scheme uses two full prognostic equations for E and $\epsilon$, including horizontal and vertical advection for E, $\epsilon$ and no mixing length assumption. A stable implicit numerical method of a Crank-Nicholson type has been used for the E, $\epsilon$prognostic equations in the vertical. A semi-Lagrangian semi-implicit numerical scheme has been used for horizontal and vertical advection of E and $\epsilon$. Some case studies based on results of 48 hours weather forecasts by 31 vertical levels and 0.3o horizontal resolution HIRLAM model (versions 4.1) are described. The main attention in these experiments were: verification of model data against observations, the role of the advection of E, $\epsilon$ and the role of the nonlocal turbulence terms. The results of the case studies for summer and winter periods are discussed. The proposed new scheme demonstrates advantages against the first order K-theory schemes in numerical weather forecasts by HIRLAM.

Statistical analysis of air temperature anomalies formation in the lake Baikal region


Limnological Institute, Russian Academy of Science,Siberian Branch.

Global arrays of surface temperature anomalies is used for the statistical analysis of East Siberia anomalies formation. Empirical orthogonal functions of global anomalies field are calculated. Statistical estimation of Grin function is used for "influence function" calculation for Lake Baikal region.

Interest to the problem of Earth surface temperature anomalies formation is growing during last years. This is valid due, from the one hand, to forecast of global warming (see, for example, Hasselmann, 1997). From the other hand, more deep studies of El-Ninio event in Pacific ocean and changes of global atmosphere circulation correlating with it (Mitchell and Wallace, 1996) enhance the interest to irregular climate variability. In the same time, problem is still actual to study climatic cycles of different time scale from millions to few years (Hansen and Lebedeff, 1987).

Lake Baikal area is, seemingly, the most far eastern Eurasia region, that is under the influence of the Atlantic air masses. It means, however, that transport of air masses of Atlantic, Arctic or Polar origin is controlled by processes of Indo-Pacific atmosphere circulation. Position and state of Siberian (Northern Asian) anticyclone is depending on the positions of high and low pressure main centres over the Pacific (Aleut depression, Hawaii maximum, etc.) and on the monsoons circulation. Proper Pacific air masses reach Baikal region very seldom (less then 1 Structure and resources, 1977). This geographical position forms lack of direct correlation between East Siberia climate, from one side, and East Europe and Atlantic, from another, as it was noted by some researchers (Structure and esources, 1977, Barnett et al., 1984).

In the presented study we propose an application of two multivariate statistical analysis methods for the analysis of surface temperature variability in the East Siberia region in the neighbourhood of lake Baikal. Method of empirical orthogonal function (EOF) gives a possibility to calculate main global modes of surface temperature variability and to estimate an impact of every mode in anomalies formation for Baikal region. Solution of the inverse problem for general heat transport equation in the form of Grin function (Piterbarg and Semovski, 1985) can be used for so called "influence function" calculation. The notion of influence function was firstly coined by G.I.Marchuk (1984). The calculation of this functional makes possible to estimate relative "energy-activity" of different area with reference to the region under study. In this instance, influence function estimation shows the regions position, for which temperature anomalies are systematically preceded to Baikal area anomalies. The further analysis can produce the result for long-time forecast.

Thermal bar in lake Baikal: nature research and numerical modeling

Shimaraev M.N., Granin N.G., Zhdanov A.A., Tsekhanovsky V.V., Gnatovsky R.Yu.,

Limnological Institute of RAS SB, Irkutsk

Tsvetova Ye.A.

Institute of Computational Mathematics and Mathematical Geophysics of RAS SB, Novosibirsk

Thermal bar as a thermal, density and dynamical front is a phenomenon having an important role for the processes occuring in freshwater lakes of temperate latitudes of the Earth. Its appearence in spring and in autumn is due to abnormal behaviour of fresh water density (with maximum on the surface about 4®C) and with unequal heating (cooling) of deep lacustrine and near-shore sites. Thanks to experiments in 1991-1995 an exceptional originality of this phenomenon in large Baikal depths (maximal one is 1636 m, middle one is 730 m) was found out. Due to the decrease of temperature of maximal water density Tmd with increase of hydrostatic pressure (0.021 ®? per 1 bar) a free temperature convection and thermal bar development are limited by the depth of winter mesothermal (intermediate) maximum z with Tmm (z)= Tmd (z) (Shimaraev, Granin, 1991). Above the depth z ?(à) passes via Tmd (à) value twice a year, and stratification sign changes. In the majority of large lakes z>? max, thermal bar front is spread up to the bottom and is a natural barrier causing difficulties in heat and mass exchange of near-shore and lacustrine waters (Tikhomirov, 1959, 1982 Boyarinov, Petrov: 1991 Rodgers, 1975).

Unlike all other lakes, main water mass in Lake Baikal is concentrated below mesothermal maximum (z=200-250 m). Here, as in marine waters, ?(à) is always greater than ?md(à), and free temperature convection and thermal bar cannot exist. By experimental data, in early spring a quick penetration of thermal bar front to the depths of 400-600 m creates particular pecularities for heat and mass exchange in all water column (Shimaraev et al., 1993). In the upper layer 0-250 m condensation taking place during mixing of lacustrine (with ?<3-3,5 ®?) and near-shore waters (with ?>4 ®?) on thermal bar front results in waters convergence and sinking at both sides of the front.

Sinking of cold lacustrine waters in the convergence zone below the depth z generates a deep forced temperature convection causing large-scale near-slope circulation with the average sinking velocity 0.2-0.4 cm/c. It promotes the exchange of upper and deep and near-bottom waters and provides interaction of near-shore and lacustrine waters below the front boundaries. It results in more active aeration of deep waters by oxygen and acceleration of circulation of biogenic elements and organic matter at the sites of near-shore thermal bars in comparison with lake pelagic area (Shimaraev et al., 1995 Likhoshway et al., 1996). Due to large horizontal gradients of temperature (density) near the shore, a strong (up to 20 cm/s) geostrophic current causing a cyclonic circulation in the lake, appears.

Measurements of lake's thermal bar are accompanied by theoretical investigations with the help of mathematical modeling. For the description of the phenomenon a numerical model of hydrodynamics of compressible fluid with non-hydrostatic approximation is developed (Tsvetova, 1995,1997). The system of equation consists of three motion equations, continuity , state equations and equation describing the redistribution of heat . Coriolis force is presented by two components. The state equation gives the density behavior depending on temperature, pressure and salt content. The system of equations is completed by the usual boundary and initial conditions. The topography is taken into account. The results of numerical experiments show that the model reproduces the main features of the phenomenon. Due to the heat flux through the surface the front is formed which separates the near shore regions and open lake. This front gradually moves from the shore to the centre of the domain an intensive downwelling is in the convergent zone while upwellings occur near the far boundaries of the convective cells. In the report measured data and results of numerical experiments are given to illustrate the theory and the phenomenon under investigation. The work reported is supported by Russian Founation for Basic Research under grants ü96-05-65494, ü97-05-96521, ü97-05-96511.

Global semi-Lagrangian atmospheric model based on compact finite-differences

Mikhail Tolstykh

Institute of Numerical Mathematics RAS,
8 Gubkina str., 117333 Moscow, Russia

The semi-Lagrangian atmospheric model on the sphere based on compact finite differences is presented. Fourth-order compact finite differences are used to discretize first- and second-order derivatives. The 3D version of the model uses the absolute vorticity as one of the prognostric variables and the vertical $\sigma$-coordinate, with the perspective of using quasipotential vorticity along with the hybrid $\sigma$-isentropic vertical coordinate. It includes the parametrizations of the subgrid-scale processes from the Météo-France operational numerical weather prediction model and pre- and postprocesing from the model of the Russian Hydrometeorological Center. The results and discussion of the model validation using the series of five days forecasts using ECMWF data are presented.

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Ensemble Seasonal Climate Prediction.

Elena Yulaeva

Due to the chaotic nature of the atmospheric dynamics, the future behavior of the atmosphere on both weather and climate timescales should be described in probabilistic terms. Our research approaches the problem of probabilistic climate forecasting by assessing and comparing ensemble forecast skills of the following atmospheric general circulation models (GCMs) runs: -45 years of 10-member ensemble of Max-Planck-Institute for Meteorology, Hamburg ECHAM-3 model -45 years of 13-member ensemble NCEP model -16 years of 9-member ensemble COLA model. The models were forced with the observed sea surface temperature anomalies (SSTA). Using a new method to effectively expand the ensemble size, we calculated maximum likelihood estimates of parameters for theoretical probability density functions (PDFs) of the ensemble seasonal integrations from these GCMs. This approach to the description of the predicted state of the atmosphere is shown to be much more informative and useful than the conventional ensemble mean diagnostics. Probabilistic skill score distributions (including the newly suggested Relative Operating Characteristics) and internal ensemble consistency are studied for different geographical regions. In related work, t tests have been applied to interannual variabilities on seasonal timescales to estimate theoretical effective ensemble sizes for the chosen regions. To validate these estimates, a 100-member ensemble simulation was conducted with the ECHAM-3 model, and the information and forecast skill scores from these ensemble seasonal integrations were compared to those from 10-member ensemble subsets. The optimal regional ensemble sizes were evaluated. The results of this research show to what degree the new methodology can expand traditional seasonal climate forecast ensemble sizes, and how this information can be used to provide more complete and skillful climate prediction.

Procedings of the conference have been published by French-Russian A.M.Liapunov Institute on Applied Mathematics and Computer Science.

Eugene Kazantsev
Last modified the 30th of March 1999.