Net CO_{2} fluxes*, F*, provided by flux-tower measurements represent the difference between two fundamental processes of gross photosynthesis, *P _{g}*, and ecosystem respiration,

*R*. In general, factors of photosynthesis and respiration at the stand level are not the same (though overlap), and the patterns of their response to a given factor are not identical. Decomposition of the

_{e}*F*data into photosynthesis and respiration is an essential part of flux-tower data processing, required for understanding the dynamics of CO

_{ }_{2}exchange and prediction of its response to climatic change and anthropogenic management. While in the earlier period of flux data analysis partitioning was based on night-time

*fluxes, derivation of day-time*

**respiration from day-time**

**measurements became a dominant approach later (Gilmanov et al 2005; Reichstein et al 2005; Lasslop et al 2010). A crucial feature of the daytime CO**

_{2}exchange utilized in partitioning algorithms based on daylight measurements is that the decrease of

*F*is directly associated with the increase of respiration

*R*, which, in its turn, is closely related to temperature. The problem is that the decrease of

_{e}*F*may also be caused by decreasing photosynthesis

_{ }*P*, e.g. resulting from water stress. A number of methods to incorporate water-stress were proposed in the literature (e.g., Gilmanov et al 2003; Lasslop et al 2010). In this presentation we describe a physiologically based approach

_{g}**incorporating combined effects of photosynthetically active radiation**

**(**

*Q*), soil temperature (

*T*), and vapor pressure deficit

_{s}**(**

*VPD*) according Gilmanov (2011).

Analysis of the tower CO_{2} exchange data in a wide range of non-forest terrestrial ecosystems led us to the partition equation:

*F(**Q, T _{s}, VPD) = P_{g}(Q, VPD) - R_{e}(T_{s}),*

provided that for modeling the net flux *F*, only the one day 30-min data on radiation *Q*, soil temperature *T _{s}*, and vapor pressure deficit

*VPD*are used. This assumption excludes the need to introduce factors slowly changing within a day such as soil water content, soil nutrients concentrations, and leaf area. To allow variation of the convexity of the light-response at the canopy level we have selected nonrectangular hyperbolic light-response function with convexity parameter

*q*:

*F(**Q,T _{s},VPD*

*; a, A*

_{max}, q, r_{0}, k_{T}) = [a Q + A_{max }– SQRT((a Q + A_{max})^{2}– 4 a A_{max }q Q)]* * f(VPD; VPD _{cr}, s)/(2 q) – r_{0 }Exp(k_{T}_{ }T_{s})*

*f**(VPD; VPD _{cr}, s) = If[VPD < VPD_{cr}, 1, Exp(–((VPD – VPD_{cr})/s)^{2})]*

where the normalized *VPD*-response function *f(VPD; VPD _{cr}, s)* depends on two parameters: critical value

*VPD*, below which water deficit doesn't affect photosynthesis (

_{cr}*f = 1 for VPD < VPD*and

_{cr}),*the standard deviation parameter*

*s*(typically, 1 <

*s*< 20) with lower values describing strong water-stress effect, and the higher values - weak effect. Though, generally speaking, the values of parameter

_{ }*VPD*may vary between crops and ecosystems, following El-Sharkaway et al (1984), at this stage of analysis we assumed a general value

_{cr}*VPD*= 1 kPa and considered a one-parametric

_{cr}*VPD*-response function in the form

*f(*

*VPD; s)*.

Because in non-forest ecosystems soil respiration is not directly linked to *VPD*, it was possible to describe ecosystem respiration by only temperature-dependent term* r _{0} Exp(k_{T} T_{s}*), where

*r*=

_{0}*R*and

_{e}(0),*k*is the temperature response coefficient.

_{T}Equations above were applied to a range of grassland and crop flux-tower data sets from several continents. Parameters *a, A _{max}, q, *

*s, r*, and

_{0}*k*were numerically estimated for every day of the season with available data using the optimization tools of the "Mathematica" system (Wolfram Research 2011). E.g., for DOY=182 of the year 2009 at the Brookings, SD, grassland site, the estimates (st. errors) were:

_{T}*a*= 0.00128 (0.00014) mg CO

_{2 }μmol

^{-1},

*A*= 1.15 (0.092) mg CO

_{max}_{2 }m

^{-2 }s

^{-1},

*q*= 8.6 « 10

^{-9}(0.0075) (dimensionless)

*, r*, = 0.0383 (0.0298) mg CO

_{0}_{2}m

^{-2}s

^{-1};

*k*= 0.068 (0.041) (°C)

_{T}^{-1};

*s*= 2.676 (1.483) kPa.

The method was quite robust when applied to the data from a wide range of non-forest terrestrial ecosystems, demonstrating convergence and generating consistent parameter estimates under different meteorological conditions. One of the reasons for the robustness is due to our choice of light, top-soil temperature and air *VPD*, as flux predictors. At the 30-min time scale this set of variables has a much lower multicollinearity, than light, air temperature and air *VPD* often used by other authors.

Knowing dynamics of the parameters for most of the growing season serves as an effective tool for gap-filling and reconstruction of the long-term dynamics of the CO_{2} exchange at the ecosystem level as illustrated by the 7-year data set for the Brookings grassland (Figure 1).

Figure 1. Seasonal and year-to-year dynamics of CO_{2} exchange at the Brookings grassland site, 2004-2010: *P _{g}*, – photosynthesis,

*R*– respiration,

_{e}*F*– net CO

_{2}exchange,

*iNEP*– integrated net ecosystem production.

REFERENCES

El-Sharkaway MA et al (1984) Crop Science 24, 503-507.

Gilmanov TG (2011) http://www.nacarbon.org/meeting_ab_presentations/2011/2011_Poster_Gilmanov_A_12_21.pdf

Gilmanov TG et al (2010) Rangeland Ecology and Management 63:16-39.

Gilmanov TG et al (2003) Basic and Applied Ecology 4:167-183.

Gilmanov TG et al (2005) Global Ecology and Biogeography 14:271-292.

Lasslop G et al (2010) Global Change Biology 16:187 - 208.

Reichstein M et al (2005) Global Change Biology 11:1424-1439.

Wolfram Research (2011) Mathematica portal: http://www.wolfram.com/