International Conference on Environmental Observations, International Conference on Environmental Observations, Modeling and Information Systems ENVIROMIS-2004Modeling and Information Systems ENVIROMIS-2004

17-25 July 2004, Tomsk, Russia17-25 July 2004, Tomsk, Russia

Modeling of present and assessing of Modeling of present and assessing of future climate variations in Siberiafuture climate variations in Siberia

V.N. Lykosov,V.N. Lykosov,Institute for Numerical Mathematics, Institute for Numerical Mathematics,

Russian Academy of Sciences, MoscowRussian Academy of Sciences, Moscow

E-mail: lykossov@inm.ras.ruE-mail: lykossov@inm.ras.ru

The central direction of the climate sensitivity studies:

mathematical modeling

Problems:

1. The identification of models by sensitivity.

2. Is it possible to determine the sensitivity of the climate

system to small external forcing using single trajectory?

AGCM - Finite difference model with spatial resolution 5°x4° and 21 levels in sigma-coordinates from the surface up to 10 hPa. - In radiation absorption of water vapour, clouds, CO2, O3, CH4, N2O, O2 and aerosol are taken into account. Solar spectrum is divided by 18 intervals, while infrared spectrum is divided by 10 intervals. - Deep convection, orographic and non-orographic gravity wave drag are considered in the model. Soil and vegetation processes are taken into account.

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Non-flux-adjusted coupling

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OGCM -The model is based on the primitive equations of the ocean dynamics in spherical sigma-coordinate system. It uses the splitting-up method in physical processes and spatial coordinates. Model horizontal resolution is 2.5°x2°, it has 33 unequal levels in the vertical with an exponential distribution. -An other version: 50m upper ocean layer with ice

INM coupled atmosphere - ocean general

circulation model

Response to the increasing of CO2CMIP models (averaged)

INM model

Analysis of some extreme weather Analysis of some extreme weather situations in Russia for the present-day situations in Russia for the present-day

climate and under COclimate and under CO22 doubling doubling

E.M. VolodinE.M. VolodinInstitute for Numerical Mathematics, Russian Institute for Numerical Mathematics, Russian

Academy of sciences, MoscowAcademy of sciences, MoscowE-mail: volodin@inm.ras.ruE-mail: volodin@inm.ras.ru

DJF T(2m) – NCEPobserved

DJF T(2m) – INMsimulated

JJA T(2m) – NCEPobserved

JJA T(2m) – INMsimulated

Present-day climate

Max positive DJF T(2m) anomaly

observed

Max positive DJF T(2m) anomaly

simulated

Max negative DJFT(2m) anomaly

observed

Max negative DJFT(2m) anomaly

simulated

Present-day climate

T(2m) climate change under CO2 doubling

DJF averaged

DJF most warm

DJF most cold

T(2m) climate change under CO2 doubling

JJA averaged

JJA most warm

JJA most cold

Present-day climate

DJF precipitationobserved

DJF precipitationsimulated

JJA precipitationobserved

JJA precipitationsimulated

Present-day climate

Normalized RMSD of precipitationDJF - observed

Normalized RMSD of precipitationDJF - simulated

Normalized RMSD of precipitationJJA - observed

Normalized RMSD of precipitationJJA - simulated

Precipitation climate change (normalized) under CO2 doubling

DJF

JJA

Preliminary conclusions Preliminary conclusions

The INM climate model quite well reproduces the present-day The INM climate model quite well reproduces the present-day climatic distribution of themperature and precipitation as well climatic distribution of themperature and precipitation as well as their seasonal variability and climatic extremesas their seasonal variability and climatic extremes

When COWhen CO2 2 is increasing, winter extremes are, in general, less is increasing, winter extremes are, in general, less intensiveintensive

However, summer extremes (caused by positive anomalies of However, summer extremes (caused by positive anomalies of the air temperature and decreased amount of precipitation) the air temperature and decreased amount of precipitation) are more intensive in the southern part of Russia and less are more intensive in the southern part of Russia and less intensive in the northern Russia.intensive in the northern Russia.

The increase of northern precipitation and the decrease of The increase of northern precipitation and the decrease of southern precipitation is mainly caused by increase of the southern precipitation is mainly caused by increase of the Arctic Oscillation index. Arctic Oscillation index.

Sensitivity of the climate Sensitivity of the climate system to small perturbations system to small perturbations

of of external forcingexternal forcing

(invited lecture at the World Climate (invited lecture at the World Climate Conference, Moscow, 29 September – 3 October, Conference, Moscow, 29 September – 3 October,

2003)2003)

V.P. Dymnikov, E.M. Volodin, V.Ya. Galin, A.S. Gritsoun, A.V. Glazunov, N.A. Diansky, V.N. Lykosov

Institute of Numerical Mathematics RAS, Moscow

The Arctic Oscillation

(constructed using NCEP/NCAR data and output of AGCM of INM RAS)

AO (1EOF of surface pressure) calculated using DJF NCEP/NCAR data

AO (1EOF of surface pressure) calculated using output of AGCM of INM RAS

1. Formulation of model equations

2. Proof of the existence and uniqueness theorems

3. Attractor existence theorem, dimension estimate

4. Stability of the attractor (as set) and measure on it

5. Finite-dimensional approximations and correspondent

convergence theorems

),,( tuFdtdu

Mathematical theory of climate

Mathematical theory of climate(sensitivity)

6. Construction of the response operator for measure and its moments

(“optimal perturbation”, inverse problems,….)

7. Methods of approximation for

8. Numerical experiments

fMu

M

Response operator for 1st moment (linear theory)

Linear model for the low-frequency variability of the original system:

( A is stable, is white noise in time)

Perturbed system

)(tAudtdu

ftuAdtud

)(

)(t

Stationary response

For covariance matrix we have

and response operator M could be obtained as

fMfAu

uuu

1

)0()exp()( CAC

dCCM )0()( 1

0

CCM0 (E.J.Pitcher et.al., J.Atmos.Sci., (1982), v.40., p.580)

1) 9 levels in -coordiante

2) prognostic variables: horizontal velocity divergence, vertical component of the

relative vorticity, temperature, relative humidity, surface pressure

3) Parameterizations of convection, condensation, latent and explicit heat fluxes,

radiation, vertical and horizontal diffusion

4) Galerkin method for space approximation. Basis functions - spherical harmonics,

R15 truncation. Phase space dimension - 18352

Numerical experiments

Construction of the approximate response operator (A.S.Gritsoun,G.Branstator, V.P.Dymnikov, R.J.Numer.Analysis&M.Model, (2002), v.17,p. 399)

CCM0 (right) and M-operator (left) responses to the “sinusoidal” heating anomaly at (60E, 00N). First row – at sigma=0.336, second row - at sigma=0.811

Reconstruction of the CCM0 response to the sinusoidal heating anomaly

Reconstruction of the low-level heating anomalies using

the inverse response operator

Real heating anomalies at sigma=0.991 (in K/day) are shown on the left, reconstructed ones - on the right. Positions of the anomalies are (30E,40N) and (45E,40N).

Procedure for the construction of the approximate response operator is analogues to (A.S.Gritsoun, G.Branstator, V.P.Dymnikov, R.J.Numer. Analysis&M.Model, (2002), v.17,p. 399)

Optimal perturbation for AO (1EOF of PS)calculated using NCEP/NCAR reanalysis data(zonal average)

Optimal perturbation for AO (1EOF of PS)calculated using output of AGCM of INM RAS(zonal average)

Some questions on assessment of climate change Some questions on assessment of climate change impact on regional environmentimpact on regional environment

RAS/NASA Northern Eurasia (NEA) Earth Science Partnership Initiative RAS/NASA Northern Eurasia (NEA) Earth Science Partnership Initiative (NEESPI):(NEESPI):

- are mathematical models capable of simulating observed climate changes in - are mathematical models capable of simulating observed climate changes in

NEA and their feedback effects on global climate? NEA and their feedback effects on global climate?

- what are the direct and feedback effects on environmental changes in NEA - what are the direct and feedback effects on environmental changes in NEA on the Earth climate system?on the Earth climate system?

Permafrost changes in Siberia may have a substantial effect on the Permafrost changes in Siberia may have a substantial effect on the chemical deposition of the atmosphere such as carbon dioxide and methanechemical deposition of the atmosphere such as carbon dioxide and methane

Are stand-alone permafrost models forced by climate change scenarios Are stand-alone permafrost models forced by climate change scenarios produced by global climate models (which, in general, do not describe produced by global climate models (which, in general, do not describe explicitly processes in the frozen ground) capable of correct assessing explicitly processes in the frozen ground) capable of correct assessing environmental changes in Siberia?environmental changes in Siberia?

Snow

“Upper” ice

Water

Ground

“Lower” ice

U

H,LE Es

EaS

Thermodynamics of shallow reservoir

1) One-dimensional approximation.

2) On the upper boundary: fluxes of momentum, sensible and latent heat, solar and long-wave radiation are calculated On the lower boundary: fluxes are prescribed

3) Water and ice: heat transport Snow and ground: heat- and moisture transport

U – wind velocityH – sensible heat fluxLE – latent heat fluxS – shirt-wave radiationEa – incoming long-wave radiation Es – outgoing long-wave radiation

Mathematical formulation

- for water and ice:

, - heat conductivity

- for snow:

- temperature

- liquid water

- for ground:

- temperature

- liquid water

- ice

2

2 2

1 dhT T dh T T Iñ c c

t h dt h h dt z

h

z

.

,

fr

fr

Fzt

W

LFz

T

zt

Tс

.

,

,

i

iW

iiWT

Ft

I

Fzz

W

zt

W

FLz

WTc

z

T

zt

Tc

Atmospheric forcing

- air-water interface:

- empirical formula for radiative fluxes

- sensible and latent heat fluxes from the Monin-Obukhov similarity theory

Routine observational data set on meteorological stations is used

)()sin( 4awwwasun TcLPRECLEHTEhSD

z

T

.

,

22

22

sE

sHp

qqVLCLE

VCcH

Simulated snow cover depth for station ValdaiSimulated snow cover depth for station Valdai

((February – April, 1977)February – April, 1977) Contours: snow densityContours: snow density

Snow cover height in YakutskSnow cover height in Yakutsk: : 19701970/71 /71 (а), 1971(а), 1971/72 /72 (б), 1972(б), 1972//73 (в).73 (в).

Computed Sep-Oct-Nov mean 2-m air temperature (0С) along 720 N (top) и 600 N (bottom) versus observed one (the curve with open circles). Notation: the curve with closed circles – simplified version of the snow model; the curve with quadrants – improved snow model.

SimulatedSimulated ( (solidsolid) ) and observedand observed ( (Franklin Bluffs, Alaska – dotted) Franklin Bluffs, Alaska – dotted) ground temperature at depth 40 cm and 80 cmground temperature at depth 40 cm and 80 cm for 1988 (top) and 1990 (bottom) time period for 1988 (top) and 1990 (bottom) time period

Five numerical experiments with the INM global climate model, in which there were varied: 1) the depth of computa-tional domain with the frozen ground (10 m or 60 m), 2) the depth of organic matter with low heat conductivity (1 cm as in standard version of the model or 8 cm). Experiments are ordered accordingly to the following table:

10 m 60 m 1 cm - everywhere 1 2

8 cm - for tundra, 1 cm - for the rest of land 3 4 8 cm everywhere 5

Total ice content (mm) from results of different numerical experiments (1986 – 1995). Notation: curve without symbols – exp. 1; curve with closed circles – exp. 2; curve with quadrants – exp. 3; curve with diamonds – exp. 4; curve with crosses – exp. 5.

Instead conclusion:Instead conclusion:THANK YOUTHANK YOU

for YOURfor YOUR ATTENTIONATTENTION