Numerical modeling of internal mixing and greenhouse gas dynamics in - PowerPoint PPT Presentation

Numerical modeling of internal mixing and greenhouse gas dynamics in boreal lakes Stepanenko, Victor 1 Mammarella, Ivan 2 Glazunov, Andrey 3 , 1 Lykosov, Vasily 3 , 1 1 Lomonosov Moscow State University, Moscow, Russia 2 University of Helsinki, Helsinki, Finland 3 Institute of Numerical Mathematics, RAS, Moscow, Russia International Conference on Computational Information Technologies for Environmental Sciences, Tomsk, Russia, 26-30 June 2015 Lake greenhouse gas modeling Stepanenko et al. (MSU) Tomsk, Russia, June 2015 1 / 26

Outline The role of lakes in a global carbon cycle LAKE model: basic 1D version Extended 1D lake modeling framework, surface seiche parameterization Biochemistry model for O 2 , CO 2 , CH 4 Kuiv¨ aj¨ arvi Lake: site description Testing applicability of 1D model approach for the lake Model performance in lake temperature and gases concentrations Estimates of possible contribution of basin-scale seiches to the vertical gas transport Outlook Lake greenhouse gas modeling Stepanenko et al. (MSU) Tomsk, Russia, June 2015 2 / 26

Freshwaters in global carbon cycle (Tranvik et al. 2009) (Bastviken et al. 2011) Total freshwater methane emission is 104 Tg yr − 1 , i.e. 50% of global wetland emission (177-284 Tg yr − 1 , IPCC, 2013) greenhouse warming potentials from freshwater-originating CO 2 and CH 4 are roughly equal Lake greenhouse gas modeling Stepanenko et al. (MSU) Tomsk, Russia, June 2015 3 / 26

CH 4 and CO 2 production and vertical transport in a lake Vertical gas transport mechanisms: Ebullition Surface mixed-layer turbulence → driven by wind forcing and surface heat balance Thermocline → very strong stratification with intermittent turbulence. Possible mixing mechanisms are K-H instability, nonlinear wave breaking, and marginal shear induced by seiches. Hypolimnion → governed by gravity currents and seiche-induced turbulence Typical summer stratification in a temperate lake High CH 4 production in shallow sediments Low CH 4 production in deep sediments Lake greenhouse gas modeling Stepanenko et al. (MSU) Tomsk, Russia, June 2015 4 / 26

Thermodynamics and hydrodynamics of LAKE model 1D version 1D heat and momentum equations k − ǫ turbulence closure Monin-Obukhov similarity for surface fluxes Beer-Lambert law for shortwave radiation attenuation Momentum flux partitioning between wave development and currents (Stepanenko et al., 2014) Soil heat and moisture transfer including phase transitions Multilayer snow and ice models (not relevant in this study) 1D concept does not suffice the greenhouse gas modeling task, as it does not take into account differences between CH 4 & CO 2 emissions at deep and shallow sediments Lake greenhouse gas modeling Stepanenko et al. (MSU) Tomsk, Russia, June 2015 5 / 26

Extended ( 1 D + ) modeling framework Traditional 1D model concept 1 D + model concept 1 D + model includes friction, heat and mass exchange at the lateral boundaries Heat, moisture and gas transfer are solved for each soil column independently In 1 D + model horizontally averaged quantity f obeys the equation: ∂f 1 ∂ ∂f 1 dA ∂t = ∂z A k f ∂z + F ( z, t, f, A ) + H f dz . A A Lake greenhouse gas modeling Stepanenko et al. (MSU) Tomsk, Russia, June 2015 6 / 26

Soil columns in the model Horizontal projection Soil columns are geometric figures of the same vertical dimension confined by adjacent isobaths in horizontal: y z = 0 z = z 1 z = z 2 z = z 3 z = z 4 z = h x Lake greenhouse gas modeling Stepanenko et al. (MSU) Tomsk, Russia, June 2015 7 / 26

Coupling 1 D + lake model to soil columns z s 0 z s 0 T s 1 T s 1 F s 1 F s 1 Lake body z s 1 z s 1 T s 2 T s 2 Soil column 1 F s 2 F s 2 Soil column 1 z s 2 T s 3 z s 2 T s 3 F s 3 F s 3 z s 3 T s 4 z s 3 T s 4 Soil column 2 Soil column 2 z s 4 z s 4 F s 4 F s 4 Soil column 3 Soil column 3 Soil column 4 Soil column 4 Boundary conditions: at soil-water interface Soil column 5 Continuity of temperature (gas) Continuity of flux Lake greenhouse gas modeling Stepanenko et al. (MSU) Tomsk, Russia, June 2015 8 / 26

Parameterization of barotropic seiches y z Barotropic Lake surface Vertical cross-section, y = 0 (surface) seiches Wind are lake surface h x 2 and related L x, 0 v h x 1 u L y, 0 velocity oscillations u after strong wind events. x x Turbulent kinetic energy profile � dh N dt A 0 ( t ) = 2 � 1 dt A 0 ( t ) = − dh S (modeled), June 2013, Kuivajarvi 0 vL W − E hdξ, Lake, seiches produce TKE near Mass conservation dt A 0 ( t ) = 2 � 1 dh E dt A 0 ( t ) = − dh W bottom 0 uL S − N hdξ, � ∂x ≈ gπ 2 g ∂h s h E − h W L W − E, 0 , 4 Barotropic pressure gradient force ∂y ≈ gπ 2 g ∂h s h N − h S L S − N, 0 . 4 Surface oscillations in the model Lake greenhouse gas modeling Stepanenko et al. (MSU) Tomsk, Russia, June 2015 9 / 26

Biochemistry of the model Photosynthesis, Sinks and sources of gases in a lake respiration and BOD are Biochemical empirical functions of oxygen temperature and Chl-a O 2 demand (Stefan and Fang, 1994) (BOD) Oxygen uptake by sediments (SOD) is Photosynthesis Sedimentary controlled by O 2 oxygen concentration and Methane Respiration demand temperature (Walker and production (SOD) Snodrgass, 1986) Methane Methane production ∝ P 0 q T − T 0 oxidation , P 0 is 10 CO 2 CH 4 calibrated (Stepanenko et al., 2011) Turbulent diffusion Methane oxidation follows Michaelis-Menthen Bubble transport equation Lake greenhouse gas modeling Tomsk, Russia, June 2015 Stepanenko et al. (MSU) 10 / 26

Bubble model For shallow lakes (several meters), bubbles reach water surface not affected, for deeper lakes bubble dissolution has to be taken into account. v b Five gases are considered in a bubble: CH 4 , CO 2 , O 2 , N 2 , Ar r b Bubbles are composed of CH 4 and N 2 when they are M i , P i emitted from sediments The velocity of bubble, v b , is determined by balance dissolution, exsolution between buoyancy and friction C i The molar quantity of i -th gas in a bubble, M i , changes according to gas exchange equation (McGinnis et al., 2006): Methane ebullition from different soil columns dM i ∂M i = − 4 πr 2 = v b b K i ( H i ( T ) P i − C i ) . dt ∂z Gas exchange with solution is included in conservation equation for i -th gas : = 1 1 ∂AB C i ∂C i ∂z Ak ∂C i ∂ ∂z + + ∂t A A ∂z F ( z, t, C i , A ) + ( H C i − B C i ,b ) 1 dA dz . A Lake greenhouse gas modeling Tomsk, Russia, June 2015 Stepanenko et al. (MSU) 11 / 26

Kuiv¨ aj¨ arvi Lake (Finland) Mesotrophic, dimictic lake Area 0.62 km 2 (length 2.6 km, modal fetch 410 m) Altitude 142 m a.s.l. Maximal depth 13.2 m, average depth 6.4 m, depth at the point of measurements 12.5 m Catchment area 9.4 km 2 Secchi depth 1.2 – 1.5 m Point of measurements Lake greenhouse gas modeling Tomsk, Russia, June 2015 Stepanenko et al. (MSU) 12 / 26

Observations Measurement raft Conducted since 2009 by University of Helsinki Ultrasonic anemometer USA-1, Metek GmbH Enclosed-path infrared gas analyzers, LI-7200, LI-COR Inc. Footprint of the Four-way net radiometer (CNR-1) raft measurements relative humidity at the height of 1.5 m (MP102H-530300, Rotronic AG) thermistor string of 16 Pt100 resistance thermometers (depths 0.2, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 6.0, 7.0, 8.0, 10.0 and 12.0 m) Turbulent fluxes were calculated from 10 Hz raw data by EddyUH software Lake greenhouse gas modeling Tomsk, Russia, June 2015 Stepanenko et al. (MSU) 13 / 26

Validity of 1D approximation for Kuiv¨ aj¨ arvi Lake Wedderburn and Lake numbers Running means Wedderburn number W = g ∆ ρh 2 1 ρ 0 u 2 ∗ L W cr ≈ 1 2 Shintani et al., 2010 Lake number L N = 2( z m − z v ) V ρ 0 gh 1 z v τA 0 L L N,cr ≈ 1 Thermocline displacement is negligible compared to mixed-layer depth Imerito, 2015 Lake greenhouse gas modeling Tomsk, Russia, June 2015 Stepanenko et al. (MSU) 14 / 26

Significance of Coriolis force for Kuiv¨ aj¨ arvi Lake √ gρ − 1 ∆ ρ h ML Rossby deformation radius, λ = NH 0 ≈ f f The lake’s length Rotational effects are comparable with those of stratification. Lake greenhouse gas modeling Tomsk, Russia, June 2015 Stepanenko et al. (MSU) 15 / 26

Water temperature Measurements Model Mixed layer depth and surface temperature are well reproduced Stratification strength in the thermocline is overestimated Model results lack frequent temperature oscillations in the thermocline Lake greenhouse gas modeling Tomsk, Russia, June 2015 Stepanenko et al. (MSU) 16 / 26

Oxygen Measurements Model Seasonal pattern is well captured: oxygen is produced in the mixed layer and consumed below Oxygen concentration in the mixed layer is underestimated by 1-1.5 mg/l , and more significantly during autumn overturn Lake greenhouse gas modeling Tomsk, Russia, June 2015 Stepanenko et al. (MSU) 17 / 26

Carbon dioxide Measurements Model Seasonal pattern is simulated realistically: carbon dioxide is consumed by photosynthesis in the mixed layer and produced in the thermocline and hypolimnion Sudden CO 2 increase prior to autumn overturn is absent in the model Lake greenhouse gas modeling Tomsk, Russia, June 2015 Stepanenko et al. (MSU) 18 / 26