# Partitioning algorithm

## Problem

The eddy covariance method measures the net ecosystem exchange. However, particularly for CO2 exchange a lot more understanding of the ecosystem is gained, when the net flux is partitioned into the main components: gross carbon uptake (GPP) and ecosystem respiration (Reco).

Currently, there are two alternative methods implemented:

- Reichstein 2005: Respiration is estimated from night-time and exptrapolated to daytime
- Lasslaop 2010: Respiration is estimated from fitting the Light-Response Curve (NEE ~ Radiation)

## Reichstein 2005: night-time based Flux-partitioning algorithm

The flux partitioning algorithms follows three steps: First, the temperature sensitivity E_{0} is estimated for the whole dataset. Second, the seasonal course of the reference temperature R_{ref} throughout the year is estimated with a seven-day sliding window in steps of four days. Periods where no R_{ref} could be found are linearly interpolated. Third, using the estimates of E_{0} and R_{ref}, the net ecosystem fluxes NEE_f are partitioned into the gross primary production GPP_f and ecosystem respiration R_{eco}.

## Data selection

Only original data (non gap-filled with a quality flag of 0) is used for the estimation of the reference temperature. The other data (i.e. the gap-filled data) is used only for the partitioning step in the end.

To filter the ecosystem respiration (R_{eco}) from the night-time data, only half-hours are selected with a global radiation Rg of less that 10 W m-2 and cross-checked against sunrise and sunset data derived from the local time and the potential radiation calculated from standard sun-geometrical routines. Next, the data set is split into consecutive periods of length x (configurable, default 14 days), and for each period it is checked where there are more than six data points available and whether the temperature range is more than 5 °C. Only under these conditions reasonable regressions of R_{eco} versus temperature can be expected.

### Fitting the ecosystem respiration model

First an activation energy parameter, E_{0,avg} is estimated for the entire period in the following manner: For each of those periods where the criteria are met, the Lloyd-and-Taylor (1994) regression model is fitted to the scatter of ecosystem respiration (R_{eco}) versus either soil or air temperature (T). While the regression parameter T0 is kept constant at -46.02°C as in Lloyd and Taylor (1994), the activation-energy parameter (E_{0}), was allowed to vary. The reference temperature (T_{ref}) is set to 15°C :

For each period, the regression parameters and statistics are kept in memory and evaluated after regressions for all periods that have been performed. The three estimates of E_{0} with the smallest standard error are then assumed to best represent the short-term temperature response of R_{eco} and are averaged resulting in an E_{0} value for the whole data set.

Subsequently, the seasonal course of the respiration at reference temperature (R_{eco,ref}) is estimated from the night time data for consecutive intervals of four days using non-linear regression of the R_{eco} data versus temperature according to Eq. 1, where E_{0} is fixed to the E_{0,avg} value (for a total window size of seven days). The estimated value R_{eco,ref} is then assigned to the central time-point of the period and linearly interpolated between periods.

Eventually, R_{eco} can be estimated as a function of the temperature, because for each half hour the parameters E_{0} and R_{eco,ref} are available.

## Day-time based Flux-partitioning algorithm (Lasslop et al., 2010)

The daytime flux partitioning algorithms implemented is based on Lasslop et al., 2010. NEE was modelled using the common rectangular hyperbolic light–response curve (Falge et al., 2001):

where NEE is net ecosystem exchange, α (μmol C J^{-1}) is the canopy light utilization efficiency and represents the initial slope of the light–response curve, β (μmol C m^{-2} s^{-1}) is the maximum CO2 uptake rate of the canopy at light saturation, γ (μmol C m^{-2} s^{-1}) is the ecosystem respiration and Rg is the global radiation (W m^{-2}). The hyperbolic light–response curve is modified to account for the temperature dependency of respiration after Gilmanov et al. (2003) by replacing the constant respiration γ with a respiration model, in this case the Lloyd & Taylor model (Lloyd & Taylor, 1994) as given in Eqn (1)

Tref and T0 were fixed as in the nighttime data-based approach. The other parameters (E_{0}, R_{b}, α, β) of the model are estimated as follow: E_{0} is estimated using nighttime data (Rg<4 W m^{-2}), then E_{0} was fixed and rb, α, β were derived from daytime data. The threshold for the definition of nighttime data (Rg<4 W m^{-2}) is lower here than in the nighttime data based approach, as excluding all data with Rg<20 W m^{-2} leads to long gaps for high latitude sites. The hyperbolic light response curve accounts for the VPD limitation of GPP. Here, the fixed parameter β in Eqn (3) was replaced with an exponential decreasing function (Körner, 1995) for β at high VPD:

The k parameter was estimated for each 4-day data window to quantify the response of the maximum carbon uptake to VPD. Since we found that the parameter k was not well constrained after including the VPD0 in the optimization, the VPD0 threshold was set to 10 hPa in accordance with earlier findings at the leaf level (Körner, 1995), at this point ignoring potential vegetation specific differences.

The settings for the parameters (first guess and rejection criteria) during the estimation procedure are described in Lasslop et al., 2010 (See Table A1).

The steps of the partitioning procedure are:

- Reference temperature sensitivity E
_{0}is estimated for a moving window from night-time data. - The E
_{0}estimates smoothed across successive windows. - Parameters of the rectangular hyperbolic light–response curve are fitted using only day-time data for a moving window using the previously determined temperature sensitivity (E
_{0}). - For each NEE_f record GPP and R
_{eco}are estimated with the parameter set of the previous window and the parameters of the next window and results are interpolated linearly by the time difference to the window centers.

## References

Falge, E, Baldocchi, D, Olson, R et al. (2001) Gap filling strategies for defensible annual sums of net ecosystem exchange. Agricultural and Forest Meteorology, 107, 43–69.

Gilmanov, TG, Johnson, DA, Saliendra, NZ (2003) Growing season CO2 fluxes in a sagebrush-steppe ecosystem in Idaho: bowen ratio/energy balance measurements and modeling. Basic and Applied Ecology, 4, 167–183.

Körner, C (1995) Leaf diffusive conductances in the major vegetation types of the globe. In: Ecophysiology of photosynthesis (eds SchulzeE-D, CaldwellMM), pp. 463–490. Springer Verlag, Berlin.

Lasslop G, Reichstein M, Papale D, Richardson A, Arneth A, Barr A, Stoy P & Wohlfahrt G (2010) Separation of net ecosystem exchange into assimilation and respiration using a light response curve approach: critical issues and global evaluation. Global Change Biology, Wiley Online Library, 16, 187-208

Lloyd, J and Taylor, JA (1994) On the temperature dependence of soil respiration. Functional Ecology 8(3): 315-323.

Reichstein M, Falge E, Baldocchi D et al. (2005) On the separation of net ecosystem exchange into assimilation and ecosystem respiration: review and improved algorithm. Global Change Biology, 11, 1424-1439.