Nikolay Diansky

Evaluation of Arctic sea ice thickness simulated by Arctic Ocean Model Intercomparison Project models

Six AOMIP model simulations are compared with estimates of sea ice thickness derived from pan-arctic satellite freeboard measurements (2004-2008), airborne electromagnetic measurements (2001-2009), ice-draft data from moored instruments in Fram Strait, the Greenland Sea and the Beaufort Sea (1992- 2008) and from submarines (1975-2000), drill hole data from the Arctic basin, Laptev and East Siberian marginal seas (1982-1986) and coastal stations (1998-2009). Despite an assessment of six models that differ in numerical methods, resolution, domain, forcing, and boundary conditions, the models generally overestimate the thickness of measured ice thinner than ~2 m and underestimate the thickness of ice measured thicker than about ~2 m. In the regions of flat immobile land-fast ice (shallow Siberian Seas with depths less than 25-30 m), the models generally overestimate both the total observed sea ice thickness and rates of September and October ice growth from observations by more than four times and more than one standard deviation, respectively. The models do not reproduce conditions of fast-ice formation and growth. Instead, the modeled fast-ice is replaced with pack ice which drifts, generates ridges of increasing ice thickness, in addition to thermodynamic ice growth. Considering all observational data sets, the better correlations and smaller differences from observations are from the ECCO2 and UW models.

Simulation and prediction of climate changes in the 19th to 21st centuries with the Institute of Numerical Mathematics, Russian Academy of Sciences, model of the Earth’s climate system

This paper presents results from a simulation of climate changes in the 19th–21st centuries with the Institute of Numerical Mathematics Climate Model Version 4 (INMCM4) in the framework of the Coupled Model Intercomparison Project, phase 5 (CMIP5). Like the previous INMCM3 version, this model has a low sensitivity of 4.0 K to a quadrupling of CO2 concentration. Global warming in the model by the end of the 21st century is 1.9 K for the RCP4.5 scenario and 3.4 K for RCP8.5. The spatial distribution of temperature and precipitation changes driven by the enhanced greenhouse effect is similar to that derived from the INMCM3 model data. In the INMCM4 model, however, the heat flux to the ocean and sea-level rise caused by thermal expansion are roughly 1.5 times as large as those in the INMCM3 model under the same scenario. A decrease in sea-ice extent and a change in heat fluxes and meridional circulation in the ocean under global warming, as well as some aspects of natural climate variability in the model, are considered.

Numerical Simulation of the World Ocean Circulation and Its Climatic Variability for 1948-2007 Using the INMOM

The results of simulating global ocean circulation and its interannual variability in 1948–2007 using INM RAS ocean general circulation model INMOM (Institute of Numerical Mathematics Ocean Model) are presented. One of the INMOM versions is also used for the Black Sea dynamics simulation. The CORE datasets were used to set realistic atmospheric forcing. Sea ice area decrease by 2007 was reproduced in the Arctic Ocean that is in good agreement with observations. The interdecadal climatic variability was revealed with significant decrease of Atlantic thermohaline circulation (ATHC) and meridional heat transport (MHT) in North Atlantic (NA) since the late 1990’s. MHT presents decrease of heat transport from NA to the atmosphere since the mid-1990’s. Therefore the negative feedback is revealed in the Earth climate system that leads to reducing of climate warming caused primarily by anthropogenic factor for the last decades. Long-term variability (60 years) of ATHC is revealed as well which influences NA thermal state with 10 year delay. The assumption is argued that this mechanism can make a contribution in the ATHC own long-term variability.

Numerical model of the circulation of the Black Sea and the Sea of Azov

The problem of mathematical modelling of the dynamics of the Black Sea and the Sea of Azov is considered with the use of the INMOM model developed at the Institute of Numerical Mathematics (INM) of the Russian Academy of Sciences. The model is based on the equations of general circulation written in a spherical σ -system of coordinates with a free surface boundary in the hydrostatics and Boussinesq approximations. The equations of sea dynamics are written in a symmetrized form. The numerical algorithm is based on the method of multicomponent splitting and has a flexible modular structure. Splitting with respect to physical processes and spatial coordinates is used. The problem is split into a series of energy-balanced subsystems called modules. Each particular module can be split further into modules of a simpler structure. The numerical experiment consists in the calculation of hydrophysical fields of the Black Sea and the Sea of Azov with the spatial resolution of ∼ 4 km, and 40 σ -levels non-uniformly distributed in depth are used in the vertical direction. Atmospheric forcing is calculated according to the EraInterim data, the calculation period is 3 years, from 2006 to 2008. The results of numerical simulation demonstrate good concordance with the observation data and also with the calculation of the Black Sea dynamics by the model of the Marine Hydrophysical Institute of the National Academy of Sciences of Ukraine. It is proposed to use the model presented here in the development of a monitoring system and for real-time forecast of water circulation in the Black Sea and the Sea of Azov. The problem of operative forecast [16] becomes nowadays one of the central problems of the mathematical modelling of seas and oceans. The base of real-time forecasts is a water circulation model for a given basin. At present, the system of modelling and real-time forecast for the dynamics of the Black Sea has been developed at the Marine Hydrophysical Institute of the National Academy of Sciences of Ukraine (MHI NASU) [16]. A finite difference model with explicit time integration schemes is used for this purpose (see [8–10]). The model adequately represents the structure of hydrophysical fields and is supplied with a block of observation data assimilation (see [10, 16]). The observation data assimilation is based on the application of the ∗Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow 119333, Russia †Marine Hydrophysical Institute of the National Academy of Sciences of Ukraine, Sevastopol 99011, Ukraine The work was supported by the Program of the Presidium of the Russian Academy of Sciences No. 21.1 ‘The Black Sea as a simulation ocean model’, by the Federal Target Program ‘Scientific and Pedagogical Staff for Innovative Russia’, by grants of the Russian Foundation for Basic Research and by the Grant Council of the President of the Russian Federation. 96 V. B. Zalesny et al. Kalman filter. The system gives satisfactory forecast accuracy in an open sea with the largest errors near the frontal zones. The further improvement of the forecast accuracy requires the use of more efficient numerical calculation methods, modern schemes of observation data assimilation, and the ability to perform calculations on remote computers. The products of the Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS) in the field of sea circulation modelling based on the methods of splitting and adjoint equations [18] seem to be very promising for the prognostic system of the Black Sea. The application of such models allows one to improve the stability of calculations, increase the spatial resolution of the model, develop an efficient method of four-dimensional variational data assimilation. As the result, this should lead to a qualitative improvement of operative forecasts. The use of modern numerical methods, in particular, non-structured grids [7] may also provide us with the ability for an environment evolution prognosis in the coastal zone of the Black Sea within the framework of an integrated model. At present, simulation methods for the sea and ocean dynamics and algorithms of variational assimilation of observation data based on methods of splitting and adjoint equations are developed at the INM RAS (see [3, 18, 19, 27, 30]). The method of splitting has the two basic functions: first, it allows one to solve the problem in time efficiently; second, to construct a flexible, hierarchically developed information computing system (see [3, 20, 30]). The essence of the method is the representation of a complicated problem as a set of simpler modules. The model can be simplified, or physically enriched by rejecting or adding some modules. The method of adjoint equations is the base of analysis of complex systems (see [3, 19]). It essentially decreases the dimension of the space of solutions in the problem of the optimal choice of the initial parameters of the model aimed at bringing the model solution closer to the observation data. However, the following essential difficulty arises in the use of the method: it is necessary to construct and implement an adjoint model whose equations have a more complicated form comparing to the direct prognostic system. If the method of solution of the prognostic problem, or the form of equations, or their spatial approximation are changed, we have to change the adjoint analogue of the model too. This is rather laborious from the technological viewpoint. In our approach combining two methods, i.e., splitting and adjoint equations techniques, we are able to solve the variational assimilation problem more efficiently. We have to construct an adjoint analogue to a particular split module of the direct model. The direct model is composed from direct split problems. The adjoint one is composed from the corresponding modules of adjoint subproblems. Our approach simplifies the construction of the adjoint model and gives us the ability to calculate an algebraically precise gradient of the minimized cost function. In this paper we present the direct prognostic circulation model of the Black Sea and the Sea of Azov. Further we will construct the model of four-dimensional assimilation of observation data on its base. Numerical model of the circulation 97 1. Circulation model of the Black Sea and the Sea of Azov The model of hydrodynamics of the Black Sea and the Sea of Azov is the extension of the basic general circulation model of the World Ocean developed at the INM RAS (see [11, 30]). Let us present here a brief description of the problem of the dynamics of the Black Sea and the Sea of Azov and the methods of its solution. The dimensionless variable σ ∈ [0,1] is used in the model as the vertical coordinate: σ = z−ζ (x,y, t) H(x,y)−ζ (x,y, t) (1.1) where z is the vertical depth coordinate measured from the unperturbed sea surface towards the center of the Earth, H(x,y) is the depth of the sea, ζ (x,y, t) is the sea level deviation from its unperturbed state, (x,y) are the horizontal coordinates, in our case these are the longitude and latitude, respectively. It is worth noting that in the general case, INMOM can utilize any orthogonal coordinates, including those with a grid refinement in given subdomains. t is the time. In the notation of the system of primitive sea dynamics equations in the σ -system of coordinates, it is useful to introduce the function of geopotential surfaces expressed according to (1.1) as Z = (H−ζ )σ +ζ , Zσ ≡ ∂Z ∂σ . (1.2) Then the system of sea hydrothermodynamic equations takes the following form in this system of coordinates: Dtu−Zσ (l+ξ) v =− Zσ ρ0rx [ ∂ ∂x ( p− g

Simulations of currents and pollution transport in the coastal waters of Big Sochi

We suggested a method for modelling the transport of pollutants over the Black Sea water basin adjacent to Big Sochi. The model is based on the application of the Institute of Numerical Mathematics Ocean Model (INMOM) over the entire basin of Big Sochi in two versions: M1 and M2. In the first version, we use uniform spatial resolution of the model with a step of ∼4 km; in the M2 version, the resolution is not uniform. The step decreases to 50 m in the basin of Big Sochi. The M2 version is used only in the periods when pollution transport is simulated, for which the initial hydrothermodynamic state is specified from the M1 version. Both versions reflect a complex character of Black Sea circulation; however, the M2 version more adequately reproduces the eddy circulation in its eastern part, where the horizontal resolution of the M2 version is higher. A conclusion is made on this basis that, in order to reproduce the eddy structure of the Black Sea circulation, the resolution of the model should be on the order of 1.5 km and the main factor of the formation of the quasi-stationary Batumi anticyclonic eddy is the topographic peculiarities in this part of the sea. The pollution spreading from the Sochi, Khosta, and Mzymta rivers and from 18 pipes of deep-water sewage was simulated for the flood periods from April 1, 2007, to April 30, 2007. It was shown that mesoscale eddy formations that form a complex three-dimensional structure of pollution spreading make the greatest contribution to the spread of pollution.

On the correlation between oscillations of the Caspian Sea level and the North Atlantic climate

Correlations between the changes in the climate of the Caspian Sea region and in its level and the variations in the North Atlantic climate are studied. The indices of North Atlantic oscillation (NAO), Atlantic multidecadal oscillation (AMO), the intensity of Atlantic thermohaline circulation (ATHC), and the air humidity above the North Atlantic are used as basic indicators of climatic variations that influence the Caspian Sea. Results of an experiment for reproducing the World Ocean circulation and the parameterization of cyclic climate peculiarities made it possible to reveal their impact on the formation of Eurasian climatic variability and on the level regime of the Caspian Sea. This impact is studied through the variability of ATHC, the NAO index, and a composite index of moisture transport (CIMT) that is proposed as a result of the studies.

Simulation of seasonal anomalies of atmospheric circulation using coupled atmosphere-ocean model

A coupled atmosphere-ocean model intended for the simulation of coupled circulation at time scales up to a season is developed. The semi-Lagrangian atmospheric general circulation model of the Hydrometeorological Centre of Russia, SLAV, is coupled with the sigma model of ocean general circulation developed at the Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), INMOM. Using this coupled model, numerical experiments on ensemble modeling of the atmosphere and ocean circulation for up to 4 months are carried out using real initial data for all seasons of an annual cycle in 1989–2010. Results of these experiments are compared to the results of the SLAV model with the simple evolution of the sea surface temperature. A comparative analysis of seasonally averaged anomalies of atmospheric circulation shows prospects in applying the coupled model for forecasts. It is shown with the example of the El Niño phenomenon of 1997–1998 that the coupled model forecasts the seasonally averaged anomalies for the period of the nonstationary El Niño phase significantly better.

Simulation of the present-day climate with the climate model INMCM5

In this paper we present the fifth generation of the INMCM climate model that is being developed at the Institute of Numerical Mathematics of the Russian Academy of Sciences (INMCM5). The most important changes with respect to the previous version (INMCM4) were made in the atmospheric component of the model. Its vertical resolution was increased to resolve the upper stratosphere and the lower mesosphere. A more sophisticated parameterization of condensation and cloudiness formation was introduced as well. An aerosol module was incorporated into the model. The upgraded oceanic component has a modified dynamical core optimized for better implementation on parallel computers and has two times higher resolution in both horizontal directions. Analysis of the present-day climatology of the INMCM5 (based on the data of historical run for 1979–2005) shows moderate improvements in reproduction of basic circulation characteristics with respect to the previous version. Biases in the near-surface temperature and precipitation are slightly reduced compared with INMCM4 as well as biases in oceanic temperature, salinity and sea surface height. The most notable improvement over INMCM4 is the capability of the new model to reproduce the equatorial stratospheric quasi-biannual oscillation and statistics of sudden stratospheric warmings.

Numerical simulation of water circulation in the central part of the Sea of Japan and study of its long-term variability in 1958–2006

The response of circulation in the Sea of Japan (SJ) to the CORE-calculated real atmospheric forcing for 1958–2006 is reconstructed using the general ocean circulation model developed at the Institute of Computational Mathematics, Russian Academy of Sciences (ICM RAS). Features of the interannual variability of the circulation in the intermediate and deep layers of the central part of SJ are studied from the numerical simulation results. For this, the spatiotemporal variability of the relative vorticity is calculated. Frequency spectra of this variability are calculated at depths of 500 and 800 m and the layer-average between these levels. The spectra have a quasi-discrete structure with maxima in vicinities of 4–5, 7, and 10-year periods. Coincidence is ascertained between frequencies corresponding to these periods and earlier determined frequencies of the inter-annual variability of the temperature field observed in the intermediate layer of the SJ in the second half of the 20th century.

Simulation of modern climate with the new version of the INM RAS climate model

The INMCM5.0 numerical model of the Earth’s climate system is presented, which is an evolution from the previous version, INMCM4.0. A higher vertical resolution for the stratosphere is applied in the atmospheric block. Also, we raised the upper boundary of the calculating area, added the aerosol block, modified parameterization of clouds and condensation, and increased the horizontal resolution in the ocean block. The program implementation of the model was also updated. We consider the simulation of the current climate using the new version of the model. Attention is focused on reducing systematic errors as compared to the previous version, reproducing phenomena that could not be simulated correctly in the previous version, and modeling the problems that remain unresolved.