11/9/20121ESPM 129 BiometeorologyLecture 30, Stomatal Conductance, Part 3, theory• Phenomenological Stomatal Conductance Models– The multiplicative model of PG Jarvis– Transpiration Conductance Theories of Mott and Parkhurst, Monteith• Coupled Photosynthesis-Stomatal Conductance Models– Norman/Wong, stomata operate to keep ci/Ca constant– Ball Berry Algorithm– Pieruschka and Berry, PNAS 2010– Leuning• Optimal Carbon Gain for Water Use Models– Cowan/Farquhar theory– Optimal use of water with time, Makela, Farquhar• Coupled Soil Moisture Models– Tardieu et al. (ABA)– Williams and Tuzet et al models (link to Soil water potential)11/9/2012ESPM 111 Ecosystem EcologyMathematical Representation:Model Algorithms1. Empirical, Regression Based1. Multiplicative2. Additive2. Mechanistic/Diagnostic3. Prognostic (,)dcfctdtftxy aft bfx cfy(, , ) () ( ) ( )ftxy aft bfx cfy(, , ) () ( ) ( )Rn H E G11/9/20122ESPM 111 Ecosystem EcologyModel Pitfalls• Garbage In = Garbage Out• Watch out for Non-Linearities– Apply at Proper Time-Step and Space-Scale • Validate, Validate, Validate• Don’t Parameterize Model Algorithms with the Same data used to Validate• Equifinality, a combination of parameters yield the same answer– An appeal to Multiple Constraints• Avoid Auto-Correlation, y =f(y)• Avoid Extrapolating Empirical Regression models beyond the range of the dataset• Use Mechanistic and Prognostic Models to predict the future and to upscale information• Closure: Equal number of Equations and Unknowns is neededESPM 129 BiometeorologyPAR (mol m-2 s-1)0 500 1000 1500 2000 2500normalized stomatal conductance0.00.20.40.60.81.01.2Tair (C)0 10203040vapor pressure deficit (kPa)012345normalized stomatal conductance0.00.20.40.60.81.01.2MPa)-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.50.0Concepts of Jarvis Model11/9/20123ESPM 129 BiometeorologyggI fTfDf fCspa()()()()()gIgIIppp()maxgI kIpp() exp( )1fTTTTTTTTTaaholhahoTTTThool() /FHGIKJFHGIKJfT kT Ta() ( )max 12fD kD()1fD kD( ) exp( )fn()( ( ))/1121ESPM 129 Biometeorologyssg=m A rhC+g0Ball-Berry-Collatz ModelA: photosynthesisRh: relative humidityCs: CO2 at leaf surface11/9/20124ESPM 129 BiometeorologyData from Ball’s DissertationESPM 129 BiometeorologyTonzi oak leaf, tree #92, Li-Cor 6400 measurement, 2001 ARH/Ca (mol m-2s-1)0.00 0.01 0.02 0.03 0.04 0.05gs (mol m-2s-1)0.00.10.20.30.40.5Xu and Baldocchi, 2003 Tree Physiol11/9/20125ESPM 129 BiometeorologyTonzi oak leaf, tree #92, Li-Cor 6400 measurement, 2001 ARH/Ca (mol m-2s-1)0.001 0.01gs (mol m-2s-1)0.00.10.20.30.40.5Xu and Baldocchi, 2003 Tree PhysiolESPM 129 BiometeorologygenusPinusP. baPinusP. maGlycinPiceaP. abQuercAcer PiceaT. aesPinusPinusArbutQuercAcer sFagusBetulaPiceaP artrP. vivPrunuZea mBall-Berry coefficient051015202530Survey of Ball-Berry Coef’sMean is 10.0 +/- 3.811/9/20126ESPM 129 BiometeorologyggACDDsss001[( )( )]Leuning ModelD=es(T)(1-rh).ESPM 129 BiometeorologyMott-Parkhurst Helox Experiment• Found that the response of stomata to D is actually a response to transpiration. • HELOX is an inert gas with different diffusivities than air. • By using HELOX and CO2rather than air and CO2, one is able to alter the molecular diffusivities of CO2and H2O – the ratio increased by a factor of 2.3. • For fixed CO2levels, assimilation rates were 27% higher in hypostomatous and 7% higher in amphistomatous leaves. • Does this suffer from Autocorrelation??– Stomatal conductance is inferred from cuvette measurements of transpiration11/9/20127ESPM 129 BiometeorologygabEsggEEsmm1Stomatal Conductance scales with evaporationESPM 129 BiometeorologyPieruschka et al. 2010 PNASPieruschka and Berry Model11/9/20128ESPM 129 Biometeorology0 100 200 300 400 50023242526Temperatures [?C]?C TeTair0 100 200 300 400 50022.533.5Vapor PressurekPa eeeair0 100 200 300 400 500-50510x 10-3Transpirationmol m-2 s1 EoutEin0 100 200 300 400 50000.511.5Conductancemol m-2 s1 gTgs0 100 200 300 400 5000.811.21.4VPDkPa VPD0 100 200 300 400 500-1-0.500.51PSIJ kg-1 PSIePieruschka and Berry Model, f(Rabs), absorbed radiationESPM 129 Biometeorology-1000 -800 -600 -400 -200 020222426Temperatures [?C]?C -1000 -800 -600 -400 -200 01.522.533.5Vapor PressurekPa -1000 -800 -600 -400 -200 0-50510x 10-3Transpirationmol m-2 s1 -1000 -800 -600 -400 -200 000.511.5Conductancemol m-2 s1 -1000 -800 -600 -400 -200 011.21.41.61.8VPDkPa -1000 -800 -600 -400 -200 0-1000-5000PSIJ kg-1 TeTaireeeairEoutEingTgsVPD PSIePieruschka and Berry Model = f(water potential)11/9/20129ESPM 129 Biometeorology((,) ) ((,) ) minE s t E A s t A dsdtST zz00EgAgEAss//220Farquhar-Cowan Transpiration-Photosynthesis OptimizationBorrow Idea of Economic Minimization and Lagrange MultiplierESPM 129 BiometeorologyShortcomings:What value is economizing water if it can be used by its competitors? Predicts Typical Diurnal Behavior11/9/201210ESPM 129 BiometeorologyEtdt Wt() ()z00dWdtEt ()Makela Model, Optimizing stomatal conductance and soil moistureESPM 129 BiometeorologyBall-Berry model0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.20.000.050.100.150.200.250.30gs mol m-2 s-1Ci/CaAC g C Cas ia/(/)1Ci/Ca is constantCi/Ca=0.7, C3Ci/Ca=0.4, C411/9/201211ESPM 129 Biometeorologygs0.0 0.1 0.2 0.3 0.4 0.5Ci/Ca0.40.60.81.0The Signal that Produces a Discrimination in Stable Isotope, 13C4.4 ‰ (27.5-4.4) ‰ iaCC ESPM 129 Biometeorologyg g ABAss l,minexp([ ] exp( )JRwroot leafplant()[]ABAJJbaJbabawrootwTardieu ABA theory11/9/201212ESPM 129 BiometeorologyTuzet et alSummary• Jarvis Model– Multiplicative functions of environmental drivers• Ball-Berry-Collatz– Gs is a function of photosynthesis, relative humidity and CO2• Pieruschka et al– Consider water balance of Epidermis• Farquhar Model– Uses economic theory regarding minimizing water used for carbon gained.• Makela Model– Considers water balance and water use efficiency• Tardieu and Davies– Considers the role of ABA on stomata• Tuzet and Leuning– Considered coupled plant soil system and feedbacks with water potential.ESPM 129
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