MATHEMATICAL MODELLING CLIMATE AND CLIMATE CHANGE: REGIONAL ASPECTS - - PowerPoint PPT Presentation

International Conference and Young Scientists School

• n Computational Information Technologies

for Environmental Sciences: “CITES-2007” Tomsk, Russia, 14-25 July, 2007

MATHEMATICAL MODELLING CLIMATE AND CLIMATE CHANGE: REGIONAL ASPECTS

V.N. Lykosov Russian Academy of Sciences Institute for Numerical Mathematics, Moscow E-mail: lykossov@inm.ras.ru lykossov@inm.ras.ru

Climate Change 2007: The Physical Science Basis

Working Group I Contribution to the IPCC Fourth Assessment Report Presented by R.K. Pachauri, IPCC Chair and Bubu Jallow, WG 1 Vice Chair Nairobi, 6 February 2007

Global mean temperatures are rising faster with time

100 0.074±0.018 50 0.128±0.026

Warmest 12 years:

1998,2005, 2003, 2002,2004, 2006, 2001,1997, 1995, 1999,1990, 2000 Period Rate Years °/decade

SST Land

Land surface temperatures are rising faster than SSTs

Smoot hed annual anomalies f or pr ecipit at ion (%) over land f r om 1900 t o 2005; ot her r egions ar e dominat ed by var iabilit y.

Land precipitation is changing significantly over broad areas I ncreases Decreases

Snow cover and Arctic sea ice are decreasing

Spring snow cover shows 5% stepwise drop during 1980s Arctic sea ice area decreased by 2.7% per decade (Summer:

• 7.4%/decade)

Glaciers and Frozen Ground

Area of seasonally frozen ground in NH has decreased by 7% from 1901 to 2002 Increased Glacier retreat since the early 1990s

Physics

• f the Climate System

The climate system is characterized by a finite set of parameters whose values at a fixed time determine its state. Climate is an ensemble of states passed by the climate system during a sufficiently long time interval. In general case, the ensemble is considered to mean a set of states and a certain probability measure given on this set, determining the probability that the climate system may be located on a certain subset of the given set. The central problem of the modern theory of climate is prediction

• f it changes caused by anthropogenic activities. In view of specific

peculiarities of the climate system, this problem cannot be solved with the use of the conventional methods repeatedly tested in natural sciences. The basic (but not single) tool to study the climate system dynamics is mathematical (numerical) modeling.

Objectives of climate modeling

• To reproduce both “climatology” (seasonal and monthly means)

and statistics of variability: intra-seasonal (monsoon cycle, characteristics of storm-tracks, etc.) and climatic (dominated modes of inter-annual variability such as El-Nino phenomenon or Arctic Oscillation)

• To estimate climate change due to anthropogenic activity
• To reproduce with high degree of details regional climate:

features of hydrological cycle, extreme events, impact of global climate change on regional climate, environment and socio- economic relationships

• Fundamental question: what climatic parameters and in what

accuracy must by reproduced by a mathematical model of the climate system to make its sensitivity to small perturbations of external forcing close to the sensitivity of the actual climate system?

Meehl, G.A., T.F. Stocker, W.D. Collins, P. Friedlingstein, A.T. Gaye, J.M. Gregory, A. Kitoh, R. Knutti, J.M. Murphy, A. Noda, S.C.B. Raper,I.G. Watterson, A.J. Weaver and Z.-C. Zhao, 2007: Global Climate Projections. In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Solomon, S.,D. Qin, M. Manning, Z. Chen, M. Marquis, K.B. Averyt, M. Tignor and H.L. Miller (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA.

CMIP

– Coupled Model Intercomparison Project http://www-pcmdi.llnl.gov/cmip

CMIP collects output from global coupled ocean- atmosphere general circulation models (about 30 coupled GCMs). Among other usage, such models are employed both to detect anthropogenic effects in the climate record of the past century and to project future climatic changes due to human production of greenhouse gases and aerosols.

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.

|| Non-flux-adjusted coupling ||

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 climate model and experiments (Dymnikov et al., 2005, Volodin & Diansky, 2006) http://ksv.inm.ras.ru/index

Near-the-surface winter air temperature: simulation (top) and observations (bottom)

Annually mean precipitation (mm/day) as follows from

• bservations (top), CMIP models averaged results (middle) and

INM simulation (bottom).

Comparison of observed changes in global-average surface air temperature

• ver the 20-th century with that from an ensemble of climate model

simulations (http://www.grida.no/climate/ipcc_tar/vol4/english/022.htm)

Regional scale modeling and assessment

• Atmospheric modeling, e.g. using global climate model with improved

spatial resolution in the region under consideration and non-hydrostatic mesoscale models: parameterization of mesoscale variability

• Catchment modeling, e.g. constructing models of river dynamics:

parameterization of hydrological cycle

• Vegetation modeling, e.g. models of vegetation dynamics: parameterization
• f biogeochemical and hydrological cycles
• Soil (including permafrost) modeling, e.g. models of snow and frozen

ground mechanics: parameterization of hydrological and biogeochemical cycles

• Coupled regional models
• Air and water quality modeling
• Statistical and dynamic downscaling (e.g. regional projections of global

climate change patterns)

Ob: P and P-E annual means (1960-1989)

0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 2 Serreze BCCR-BCM2.0 CCSM3 CGCM3.1(T47) CGCM3.1(T63) CNRM-CM3 CSIRO-Mk3.0 ECHAM5/MPI-OM ECHO-G GFDL-CM2.0 GFDL-CM2.1 GISS-AOM GISS-EH GISS-ER INM-CM3.0 IPSL-CM4 MIROC3.2(hires) MIROC3.2(medres) MRI-CGCM2.3.2 PCM UKMO-HadCM3 UKMO-HadGEM1 mean-21 mean-19 mm/day P P-E

Kattsov, V.M., J.E. Walsh, W.L. Chapman, V.A. Govorkova, T.V. Pavlova, and X. Zhang, 2007: Simulation and projection of arctic freshwater budget components by the IPCC AR4 global climate models. J.Hydrometeor.

T.J. Philips et al. (2002). Large-Scale Validation of AMIP II Land-Surface Simulations

Растительность, гидрология поверхности и речной сток

Пример ячейки сетки, занятой хвойным лесом, широколиственным лесом, травой и голой поверхностью Гидрология поверхности – уравнение водного баланса поверхности и почвы:

( )

can sn i i prc v g surunoff drng i

W W z q E E q q t θ + + = − − − −

∑

    

Гидрология речного стока – распределенные модели ландшафтного типа (TOPMODEL, TOPOG, MPATH, MODFLOW )

The presence of different types

• f surfaces (forests, lakes, hills, etc.)

Thermal contrasts: “forest – bare soil”, “land – sea” urban “heat islands”, etc. Local atmospheric circulations: breezes, urban breezes, slope winds

• 5

5 15 25 35 45 55 65 75 85 95 105 115 125 135 145

• 150
• 100
• 50

50 100 150

• 150
• 100
• 50

50 100 150

Uncertainties

The precise magnitude of “climatic” change in regime of land surface is unknown (and unknowable?)

• Climate uncertainty (climate scenarios, climatic

sensitivity, regional climatic response, etc.)

• Land surface model uncertainty
• Process uncertainty

Current development of mathematical models of climate is characterized by a permanent increase of its spatial resolution and by the rejection the hydrostatic approximation (at least in regional models). These tendencies cause new problems in the parameterization of subgrid-scale processes. In particular, one of crucial importance is the interaction of the atmosphere with hydrologically heterogeneous land surface – the territory, occupied by a dense network of water bodies (lakes, rivers, wetlands, etc.), covering a significant fraction of the total area (e.g. Western Siberia, Karalee, and North America). Strunin and Hiyama (2005a) have analyzed the aircraft observations carried out

• ver the Lena River in the vicinity of the city of Yakutsk. Two phenomena over a cold

water surface (a river more than 10 km wide) are detected: 1) the mesoscale thermal internal boundary layer, whose profiles of vertical turbulent heat and moisture fluxes differed radically from the background profiles; 2) a local breeze circulation, which significantly changed the structure of horizontal advection up to the occurrence of reverse-airflow layer. The use of the wavelet transform (Strunin and Hiyama, 2005b) allowed to separate air-mass motions within the atmospheric boundary layer into: 1) turbulent (with scales

• f 20 m to 2 km) and 2) mesoscale (with scales of 2 to 20 km) motions. All turbulent

fluxes monotonically decreased with height, while the contribution of mesoscale motions increased with height and became maximal in the middle of the boundary layer.

Goal: Goal: Numerical simulation Numerical simulation

• f atmospheric circulations
• f atmospheric circulations

induced by thermal contrast induced by thermal contrast

• f the underlying surface
• f the underlying surface

(e.g. breezes, internal boundary layers (e.g. breezes, internal boundary layers and slope winds) and slope winds) Tasks Tasks: : Development and verification of land surface model (LSM) Development and verification of land surface model (LSM) Incorporation of LSM into the atmospheric model Incorporation of LSM into the atmospheric model Verification of capability of joint atmosphere Verification of capability of joint atmosphere -

• land surface

land surface model to simulate local circulations and parameterization model to simulate local circulations and parameterization It needs: It needs:

• atmospheric model

atmospheric model

• soil model

soil model

• inland water model

inland water model

• etc.

etc.

Soil Moisture Processes (E. Blyth, 2007)

• Gravity
• Surface tension
• Drainage
• Upward flow
• Groundwater
• Evaporation
• Soil Freezing
• Vapour Flow
• Soil swelling/cracking
• Macropores
• Organic soils
• Chalk Soils

Snow pack depth: from results of modeling for Valdai station, February – April, 1977. Contours: snow density (Volodina, Bengtsson and Lykosov, 2000)

Mean annual cycle of observed and simulated water - equivalent snowdepth (cm). Solid lines show observations. Dashed, dotted and dot-dashed lines show results of simulation (Volodina, Benhtsson and Lykosov, 2000)

From Point to Spatial (E. Blyth)

Infiltration of rainfall into frozen soil (55-60% of soil freezes in winter in the northern hemisphere) At a point, rainfall does not infiltrate a frozen soil At the catchment scale rainfall does penetrate a frozen soil

(Niu G.-Y. and Z.-L. Yang, Effects of Frozen Soil on Snowmelt Runoff and Soil Water Storage at a Continental Scale, Journal of Hydrometeorology, 2006, v. 7, 937-952).

Instruction Report EL-02-1 August 2002

CE-QUAL-W2: A Two-Dimensional, Laterally Averaged, Hydrodynamic and Water Quality Model, Version 3.1 User Manual

by Thomas M. Cole Environmental Laboratory U.S. Army Corps of Engineers Waterways Experiment Station Vicksburg, MS 39180-6199 and Scott A. Wells Department of Civil and Environmental Engineering Portland State University Portland, OR 97207-0751 Draft Report

Not approved for public release (Supersedes Instruction Report E-95-1

DRAFT

Prepared for U.S. Army Corps of Engineers Washington, DC 20314-1000

Pushistov et al., 2006: Modeling of hydrodynamics of Severnaya Sos’va river

Streamwise velocity

U max 1.39

Temperature

T max 11.43

Snow “Upper” ice Water Ground “Lower” ice U H,LE Es Ea S

Therm odynam ics of Shallow Reservoir ( Stepanenko & Lykosov, 2 0 0 5 )

1) One-dimensional approximation. 2) On the upper boundary: fluxes

• f 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 velocity H – sensible heat flux LE – latent heat flux S – shirt-wave radiation Ea – 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 dh T T dh T T I ñ c c t h dt h h dt z λ ξ ρ ρ ρ ξ ξ ξ ∂ ∂ ∂ ∂ ∂ = + − − ∂ ∂ ∂ ∂ ∂

h z = ξ

. ,

fr fr

F z t W LF z T z t T с − ∂ ∂ − = ∂ ∂ + ∂ ∂ ∂ ∂ = ∂ ∂ γ ρ λ ρ

. , ,

i i W i i W T

F t I F z z W z t W F L z W T c z T z t T c = ∂ ∂ − ∂ ∂ − ∂ ∂ ∂ ∂ = ∂ ∂ +               − ∂ ∂ + ∂ ∂ ∂ ∂ = ∂ ∂ γ λ ρ γ λ ρ λ ρ

• 48 -24

24 48 72 96 120 144 168 192 216 240 264 288 312 336 19 20 21 22 23 24 25 26

Observations FLAKE LAKE Temperature, С Time, h

Verification of the lake model against observations Verification of the lake model against observations

Lake Kossenblatter, Germany, June, 1998 Monte-Novo lake, Portugal, 1999 - 2002 Tiksi, July, 2002

• P. Viterbo et al. The representation of soil moisture

freezing and its impact on the stable boundary layer. – Q.J.R. Meteorol. Soc., 1999, v. 125, 2401-2426.

• A positive feedback exists in the land surface

boundary-layer coupling: if the surface is cooled too much the boundary layer becomes too stable, reducing the downward heat flux and making the surface even colder.

• The process of soil freezing turns out to be an

important damping mechanism on the seasonal temperature cycle: in winter the freezing prevents the boundary layer from becoming too stable.

• It is quite possible that mesoscale variability plays a

key role in the transport of heat and moisture towards the surface.

Mesoscale atmospheric model (Miranda, 1991)

Governing equations in σ-coordinates (Miller, White, 1984)

( ) ( )

2 * * * * * * * * 2 * * * * * * * * * * * * * * *

' ' , ' ' , ' '

u u v v v r w s

up u p vup up p p fvp p D R t x y x x vp uvp v p vp p p fup p D R t x y y y wp uwp vwp wp S p p g q p D t x y σ φ φ σ σ σ σ φ φ σ σ σ σ φ θ σ σ θ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + + + = − + + + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + + + = − + − + + ∂ ∂ ∂ ∂ ∂ ∂ ∂   ∂ ∂ ∂ ∂ ∂ + + + = − + − +   ∂ ∂ ∂ ∂ ∂   & & % % % &%

( ) ( ) ( ) ( )

( )

* * * * * * * * * * * * * * * * * * * *

, ' ' ' ' , 0, ,

v v

w k s v v p v v v v q q c c c

R L p p u p v p p S wp p COND EVAP p D R t x y c p p up vp p t x y q p uq p vq p q p p EVAP COND p D R t x y q p uq p vq p t x y

θ θ

θ θ θ θ σθ σ σ σ σ σ σ +   ∂ ∂ ∂ ∂ ∂ + + + = − + − + +   ∂ ∂ ∂ ∂ ∂   ∂ ∂ ∂ ∂ + + + = ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ + + + = − + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ + + ∂ ∂ ∂ & % & &

( )

( )

( )

( )

* * * * * * * * *

, .

c c r r

c q q r r r r r r q q

q p p COND AUTO COL p D R q p uq p vq p q p V q p AUTO COL EVAP g p D R t x y σ σ σ ρ σ σ ∂ + = − − + + ∂ ∂ ∂ ∂ ∂ ∂ + + + = + − − + + ∂ ∂ ∂ ∂ ∂ & &

• 10

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 20 40 60 80 100 20 40 60 80 100 120

West Siberia, 54.5-58.6° N, 63.1-66.6 ° E, topography and inland waters, grid resolution 3.7 km

Wind velocity Wind velocity

• 150
• 100
• 50

50 100 150

X, км

• 150
• 100
• 50

50 100 150

Y, км 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 |U|, м/с

Fraction of wetlands in Russia: 0,76 mln km^2, e.g. 0,35 mln km^2 in permafrost regions Fraction of wetlands in Russia: 0,76 mln km^2, e.g. 0,35 mln km^2 in permafrost regions

15 % - 30 % 15 % - 30 % 30 % - 50 % 30 % - 50 % 5 % - 15 % 5 % - 15 % 50 % - 85 % 50 % - 85 % 0 % - 5 % 0 % - 5 %

Глобальное потепление/Измен ения климата

Влажность почвы Температура Фотосинтез Дыхание растений Частота пожаров Атмосферный углекислый газ Запасенный углерод растений Азот и его соединения Бактериальное разложение в почве Почвенная респирация Углерод почвы

Углерод экосистемы

Carbon dioxide feedback in ecosystems (Lashof et al., 1997)

+

• +/-

+ + + +/- + +

• +
• +/-

+ + +

• +

+ +

Глобальное потепление/ Изменения климата

Атмосферный метан Потребление метана Продукция метана Температура почвы Влажность почвы Изменения ландшафта

Methane feedback (Lashof et al., 1997)

• 1. Vegetation and topography
• 2. Hydrology
• 3. Degradation of permafrost (5 – 65 Mt CH4 /year, Hogan, 1993)
• 4. Mechanics of frozen ground (thermokarsts)

+ +/- + + + + + +

• +

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