# A Simple Production Efficiency Model 1/18 Willem de Kooning (1904-1997) A Tree in Naples.

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A Simple Production Efficiency Model 1/18 Willem de Kooning (1904-1997) A Tree in Naples

About 2/18 A simple model to calculate Net Primary Production We shall call this a Production Efficiency Model (PEM) Applicable to Coarse Spatial Resolutions (example, 0.5x0.5 degree) Applicable to Coarse Temporal Resolutions (example, monthly) Used to generate MODIS NPP Products Reference: Heinsch et al., 2003, User’s Guide GPP and NPP (MOD17A2/A3) Products NASA MODIS Land Algorithm

Background 3/18 Monteith first proposed a conservative relationship between - Absorbed photosynthetically active radiation (APAR) and Net Primary Production (NPP). APAR depends on the geographic and seasonal variability of day length and incident radiation, as modified by cloud cover and aerosols, and the amount and geometry of displayed leaf material. This relation combines the meteorological constraint of available sunlight at a site with the ecological constraint of the amount of leaf-area capable of absorbing that solar energy.

The PEM Model 4/18 Annual NPP = Annual GPP - Annual Autotrophic_Respiration (kg C/m2/yr) (kg C/m2/yr) (kg C/m2/yr) Annual GPP = Annual Sum of Daily GPP (kg C/m2/yr) (kg C/m2/day) Step 1: Evaluate Daily GPP, save it and sum it over the year Step 2: Then worry about the Annual Autotrophic_Respiration term

Daily GPP 5/18 Daily GPP =   APAR (kg C/m2/day) (kg C/MJ) (Mega Joules/m2/day) APAR = IPAR  FPAR (MJ/m2/day) (MJ/m2/day) (dimensionless)  Efficiency of APAR conversion to GPP APAR PAR absorbed by vegetation IPAR PAR incident on the vegetation FPAR Fraction of IPAR absorbed by vegetation (from satellites) SWRAD Incident shortwave solar radiation (measured) PAR Photosynthetically Active Radiation (400-700 nm) IPAR = 0.45  SWRAD (MJ/m2/day)

Efficiency-01 6/18 The PAR conversion efficiency, ε, varies widely with different vegetation types. There are two principal sources of this variability. First, with any vegetation, some photosynthesis is immediately used for maintenance respiration. For the annual crop plants, these respiration costs are minimal, so ε is typically around 2 gC/MJ. Respiration costs, however, increase with the size of perennial plants. Published ε values for woody vegetation are much lower, from about 0.2 to 1.5 gC/MJ – this could be due to respiration of living cells in the sapwood of woody stems. The second source of variability in ε is attributed to suboptimal climatic conditions. Evergreen vegetation such as conifer trees or shrubs absorb PAR during the non-growing season, yet sub-freezing temperatures stop photosynthesis because leaf stomata are forced to close. Additionally, high vapor pressure deficits, > 2000Pa, have been shown to induce stomatal closure in many species, thereby reducing photosynthetic activity. These biome- and climate-induced ranges of ε must be taken into account in any global modeling of NPP.

Efficiency-02 7/18  =  max  TMIN_scalar  VPD_scalar (kg C/MJ) (kg C/MJ) (dimensionless) (dimensionless)  max Biome dependent maximum efficiency (Look-Up-Table) TMIN_scalar Minimum Temperature attenuation scalar VPD_scalar Vapor Pressure Deficit attenuation scalar

Temperature Attenuation Scalar 8/18 TMIN_scalar = 0, if TMIN < TMIN_min TMIN_scalar = 1, if TMIN > TMIN_max TMIN_scalar = (TMIN-TMIN_min)/(Range), else Range = (TMIN_max - TMIN_min) TMIN Daily Minimum Temperature (degrees C; measured) TMIN_min Daily minimum temperature at which ε=0 (any VPD; degrees C; LUT) TMIN_max Daily minimum temperature at which ε=ε max (optimal VPD; degrees C; LUT)

VPD Attenuation Scalar 9/18 VPD_scalar = 0, if VPD > VPD_max VPD_scalar = 1, if VPD < VPD_min VPD_scalar = (VPD_max-VPD)/(Range), else Range = (VPD_max - VPD_min) VPD Daylight average vapor pressure deficit (Pa; measured) VPD_min Daylight average VPD at which ε=0 (any TMIN; LUT) VPD_max Daylight average VPD at which ε=ε max (optimal TMIN; LUT)

Autotrophic Respiration 10/18 Annual NPP = Annual GPP - Annual Autotrophic_Respiration (kg C/m2/yr) (kg C/m2/yr) (kg C/m2/yr) Step 1: Evaluate Daily GPP, save it and sum it over the year Step 2: Then worry about the Annual Autotrophic_Respiration term Maintenance Respiration Growth Respiration LeafDailyAnnual Fine RootsDailyAnnual Live WoodAnnual Dead Wood-Annual

Daily Leaf Maintenance Respiration 11/18 Leaf_MR = Leaf_Mass  leaf_mr_base  Q10_mr [(Tavg-20)/10] (kg C/m2/day) (kg Leaf C/m2) (kg C/kg Leaf C/day) (dimensionless) Leaf_Mass = LAI / SLA (kg Leaf C/m2) (m2 Leaf /m2 ground) (m2 Leaf/kg Leaf C) Leaf_Mass Leaf mass as kg leaf carbon per m2 of ground area LAI Leaf area index defined as m2 of green leaf area per m2 of ground area (from satellites) SLA Specific Leaf Area defined as projected m2 of green leaf area per kg of leaf carbon (LUT) leaf_mr_base Maintenance respiration of leaves per unit leaf mass (kg C/kg C/day) at 20°C (LUT) Tavg Daily average temperature (degrees C; measured) Q10_mr Exponent shape parameter controlling respiration as a function of temperatrure (LUT)

Daily Fine root Maintenance Respiration 12/18 Froot_MR = Fine_Root_Mass  froot_mr_base  Q10_mr [(Tavg-20)/10] (kg C/m2/day) (kg Fine Roots C/m2) (kg C/kg Fine Roots C/day) (dimensionless) Fine_Root_Mass = Leaf_Mass  froot_leaf_ratio (kg Fine Roots C/m2) (kg Leaf C/m2) (kg Fine Roots C/kg Leaf C) Leaf_Mass Leaf mass as kg leaf carbon per m2 of ground area (LAI/SLA) froot_leaf_ratio Ratio of fine root mass in kg C to leaf mass in kg C (LUT) froot_mr_base Maintenance respiration of fine roots per unit fine root mass (kg C/kg Fine Roots C/day) at 20°C (LUT) Tavg Daily average temperature (degrees C; measured) Q10_mr Exponent shape parameter controlling respiration as a function of temperatrure (LUT)

Annual Live Wood Maintenance Respiration 13/18 Livewood_MR = Livewood_Mass  livewood_mr_base  annsum_mr_index (kg C/m2/day) (kg Livewood C/m2) (kg C/kg Livewood C/day) (dimensionless) Livewood_Mass = Ann_leaf_mass_max  livewood_leaf_ratio (kg Livewood C/m2) (kg Leaf C/m2) (kg Livewood C/kg Leaf C) ann_leaf_mass_max Annual maximum value of leaf mass as kg leaf carbon per m2 of ground area [Max(LAI/SLA)] livewood_leaf_ratio Ratio of live wood mass in kg C to leaf mass in kg C (LUT) livewood_mr_base Maintenance respiration of live wood per unit live wood mass (kg C/kg Livewood C/day) at 20°C (LUT) annsum_mr_index Annual sum of Q10_mr [(Tavg-20)/10] Tavg Daily average temperature (degrees C; measured) Q10_mr Exponent shape parameter controlling respiration as a function of temperatrure (LUT)

Maintenance Respiration 14/18 Daily_MR (kg C/m2/day) = Leaf_MR + Froot_MR + Livewood_MR/365 Annual_MR (kg C/m2/yr) = Annual sum of Leaf_MR + Annual Sum of Froot_MR + Livewood_MR

Annual Leaf Growth Respiration 15/18 Leaf_GR = ann_leaf_mass_max  ann_turnover_proportion  leaf_gr_base (kg C/m2/yr) (kg Leaf C/m2) (per year) (kg C/kg Leaf C) ann_leaf_mass_max Annual maximum value of leaf mass as kg leaf carbon per m2 of ground area [Max(LAI/SLA)] ann_turnover_proportion Annual proportion of leaves that turnover (per year) which indicates the proportion of newly grown leaves each year (LUT) leaf_mr_base Growth respiration of leaf per unit leaf mass (kg C/kg C) at 20°C (LUT)

Annual Growth Respiration 16/18 Annual_GR (kg C/m2/yr) = Leaf_GR + Froot_GR + Livewood_GR + Deadwood_GR Froot_GR = Leaf_GR  froot_leaf_gr_ratio Livewood_GR = Leaf_GR  livewood_leaf_gr_ratio Deadwood_GR = Leaf_GR  deadwood_leaf_gr_ratio froot_leaf_gr_ratio ratio of fine root growth respiration to leaf growth respiration (dimensionless; LUT) livedwood_leaf_gr_ratio ratio of live wood growth respiration to leaf growth respiration (dimensionless; LUT) deadwood_leaf_gr_ratio ratio of dead wood growth respiration to leaf growth respiration (dimensionless; LUT)

Net Primary Production 17/18 Daily_NPP (kg C/m2/day) = Daily_GPP - Daily_MR - (Annual_GR/365) Annual_NPP (kg C/m2/yr) = Annual GPP - Annual_MR + Annual_GR

Look-Up-Table 18/18

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