EXCHANGE VELOCITY APPROACH AND OBT FORMATION IN PLANTS DURING THE DAYTIME Anca Melintescu PhD “Horia Hulubei” National Institute of Physics and Nuclear Engineering, Bucharest - Magurele, ROMANIA ancameli@ifin.nipne.ro, melianca@yahoo.com Third Technical Meeting of the EMRAS II, Working Group 7, “Tritium” Accidents, Vienna, Austria, 24 - 28 January 2011
THE DRIVING EQUATIONS FOR TRITIUM TRANSFER IN ATMOSPHERE - SOIL- PLANT CONTINUUM Driving equation for the HTO transfer from atmosphere to leaves: C – HTO concentration in plant water (Bq/kg); depends on canopy resistance C air – HTO concentration in air (Bq/m 3 ); C s - HTO concentration in the sap water (Bq/kg); s - saturated air humidity at vegetation temp. (kg/m 3 ); dC V V - air humidity at reference level (kg/m 3 ); exc exc ( C 0 . 91 C ) ( ) C M w – water mass in plant on a unit soil surface (kg/m 2 ); air s s s dt M M V exc – exchange velocity from atmosphere to canopy (m/s) w w the transpiration flux - used for all canopy, ignoring the transfer of air HTO to steam, because the exchange velocity is smaller with one order of magnitude; - Ignores the initial diffusion of leaf water to steams The tritium dynamics at soil surface: depends on soil resistance dC V sw , 1 ex , s ( C 0 . 91 ( T ) C ) DF C sw,1 - HTO concentration in the first soil layer at the (Bq/kg); air sat s sw , 1 V ex,s - exchange velocity from atmosphere to soil (m/s); dt M sat (Ts) - saturated air humidity at soil surface temp. (kg/m 3 ); ws M ws – water mass in the surface soil layer; DF - HTO net flux at the bottom interface of the first soil layer
SIMPLIFIED EQUATION FOR TRITIUM TRANSFER BETWEEN AIR AND PLANTS If C air = ct and V exc = ct and ignoring the soil tritium transfer, a simple equation is obtained: C TFWT - HTO concentration in plant at the considered time t (Bq L -1 ); C ∞ - steady-state TFWT concentration (Bq L -1 ); k - constant rate for HTO uptake (h -1 ); t - time after the beginning of exposure (h); C ∞ =1.1* ρ a / ρ s C ah ρ s - water vapour density in leaf stomatal pore (g /m 3 ); ρ a - the water vapour density in atmosphere (g /m 3 ); C ah is the air water HTO concentration (Bq/L) k = ρ s /(1.1*W*r) W - water content of leaf (g /m 2 ); r - leaf resistance to water transport (h/m) The above relationships were used to explain the experimental data for various plants and environmental conditions.
M. Andoh Atarashi et al., 1997 Large variability between plants and environmental conditions → Need to consider the variability of exchange velocity
Y. Ichimasa et al., 1990, 1991, 1992 Large variability between plants and environmental conditions → Need to consider the variability of exchange velocity
Resistance Approaches for Deposition and Exchange • Similitude between water vapour transport Atmospheric source and electric circuits → in both cases the transport is due to specific gradients: - specific humidity for water Aerodynamic, R a - electric potential for electricity • Environmental resistances - analogy with electric resistances → both = the ratio between potential difference and flux Boundary, R b • R a - turbulence and wind speed • R b - turbulence, wind speed and surface Stomatal, R s properties Cuticular, R ct Total Surface, R c • Total surface resistance R c - split up into canopy and ground related resistance • Canopy resistance - surface properties, Ground, R g temperature, PAR, humidity, water content for various in soil surfaces • HT deposition → ground resistance depends on the rates of diffusion and oxidation in soil; 1 V - much lower than the canopy ex R R R resistance a b c ↓ exchange velocity at air to plant (soil) interface
Boundary layer Turbulent eddies - responsible for transporting material through the surface boundary layer Transport processes: - transfer of heat - mass modify the atmosphere’s properties - momentum Distinct aspect of the boundary layer → turbulent nature A force is needed to change momentum transfer from one level to another. This drag force or shear stress is also equivalent to the momentum flux density Visualization of momentum transfer Momentum must be transferred downward. Logarithmic wind profile: u* - friction velocity K – von Karmann’s constant (=0.40) z - height above the ground z 0 – roughness parameter = the effectiveness of a canopy to absorb momentum; valid only for very short vegetation and for a neutrally stratified atmosphere d - Zero-Plane Displacement Height = the level at which surface drag acts on the roughness elements or level which would be obtained by flattening out all the roughness elements into a smooth surface.
Atmospheric resistance (R a ) and boundary layer resistance (R b ) Turbulent eddies - responsible for transporting material through the surface boundary layer; R a - determines the rate that momentum, and other scalars, are transported between a given level in the atmosphere and the vegetation’s effective surface sink. ψ c - adiabatic correction function Boundary layer = that thin skin of unperturbed air which surrounds the surface of soil or vegetation z c - scalar roughness length; S c - Schmidt number; P r – Prandtl number; const - often assumed to be 2 over closed canopies, but it can be much larger over rough incomplete canopies • Heat and water vapor must be transferred through this layer through molecular diffusion (conduction). • The long timescale involved can be represented by a large resistance - the boundary layer resistance . • The magnitude of this resistance depends mainly on the depth of the boundary layer and is proportional to leaf size/wind speed.
CANOPY RESISTANCE IS PREDOMINANT R a , R b - affected by wind speed, crop height, leaf size, and FOREST atmospheric stability; - decrease with the increasing of wind speed and crop height • Smaller resistances - over the tall forests than over short grass; - under unstable atmospheric thermal stratification, than under neutral and stable stratification • For wind speed = 4 m s -1 → 60 s m -1 , for 0.1 m tall grass 20 s m -1 , for 1.0 m crop R b = 10 s m -1 , for 10 m conifer forest • R a , R b < 20 s m -1 - during the daytime over a temperate deciduous forest (exp. results) • R a ≥ 150 s m -1 – during the night time R a , R b ÷ 4 -18 s m -1 (turbulent mixing is reduced) R c ÷ 70 – 160 s m -1
Canopy resistance (R C ) • R c - function of: leaf area; - canopy stomatal resistance (R stom ) stomatal physiology; soil pH; - canopy cuticle resistance (R cuticle ) affected by: presence and chemistry of liquid - soil resistance (R soil ) drops and films • R stom , R cuticle , R soil act in parallel: • ‘Big-Leaf’ resistance models - electrical analogy - current flow (mass or energy flux density) is equal to the ratio between a potential and the sum of the resistances to the flow: C a – concentration of a scalar in the atmosphere over the vegetation C 0 – ‘internal’ concentration
Canopy resistance – physiological models Stomatal cavity → common pathway for water and CO 2 Leaf = Σ stomata E – evaporation ρ a – air density q q q in – saturated air vapour at leaf temp. in air E q air – air vapour in atmosphere a r r a c Scalling from leaf to canopy: - classic: R c = R leaf /LAI - big leaf: integral over all canopy as a single leaf - physiological approach
• Jarvis approach – light, temperature, water vapour deficit, and soil water deficit behave independently as modifying factors (0, 1) - minimal leaf resistance R c- min is plant characteristic • Ball-Berry scheme - uses m and b as semi-empirical coefficients → inconvenience • Physiological approach – link between water and CO 2 pathway to photosynthesis (A n ), taking into account different diffusion coefficients
Physiological approach (preferred and tested) - assumes that C conductance is determined by ratio between photosynthetic rate and the concentration difference of CO 2 for leaf surface and leaf interior g min, c - the cuticular conductance A g - the gross assimilation rate of leaf D s - the vapour pressure deficit at plant level g l,c – leaf C conductance; C s - the CO 2 concentration at the leaf surface g l,w – leaf water conductance; C i - the CO 2 concentration in the plant interior g c,c – C canopy conductance; f 0 - the maximum value of (C i - Γ )/(C s - Γ ) g c,w - water canopy conductance f min - the minimum value of (Ci - Γ )/(Cs - Γ ) D 0 - the value of Ds at which the stomata are closed Γ – CO 2 compensation point (Jacobs - Calvet) • For canopy - integrate on LAI • We use gross canopy photosynthesis rate from WOFOST • Data base exist → advantage
Recommend
More recommend
