1 | INTRODUCTION
Gross primary production (GPP) represents the highest flux in the carbon (C) budget of a forest ecosystem. GPP has been commonly estimated using many approaches, such as eddy covariance (EC), empirical models, and upscaling ecophysiological measurements at stand scale (Baldocchi, 2003; Beer et al., 2010; Peichl, Brodeur, Khomik, & Arain, 2010). However, there are still some uncertainties in these GPP estimates (Campbell et al., 2017). For example, accurate EC estimates are based on a set of assumptions, such as homogeneous flat terrain and turbulent mixing of air (e.g. Baldocchi, 2003). Because the assumptions are not always met, the estimates are prone to ~20% uncertainty (Jocher et al., 2017; Keenan et al., 2019; Wehr et al., 2016).
Assuming that the EC assumptions are met, a semi-empirical model such as PRELES (PREdict Light-use efficiency, Evapotranspiration and Soil water) can estimate GPP (GPPPRELES) in a given forest ecosystem using the EC data for model parameterisation (Mäkelä et al. , 2008; Peltoniemi, Pulkkinen, Aurela, Pumpanen, Kolari, & Mäkelä, 2015). PRELES can subsequently be used for gap-filling the EC data that have been filtered out or are otherwise missing. One of the advantages of PRELES is that it estimates ecosystem fluxes (GPP and evapotranspiration) by using routinely measured weather data. It means that GPPPRELES can be estimated everywhere with no additional measurement than weather conditions (Tian et al., 2020). This approach allows one to go back in time for estimating GPP of the boreal forest in years for which EC are not available (Minunno et al., 2016).
The weakness of GPP estimates from PRELES is that its estimates are often unanchored by methods that are independent of EC. Previous studies that compared between biometric/component fluxes and GPP from EC (GPPEC) data have found that the GPP trends agreed reasonably well over several years, but often failed to find the same absolute values at annual scales (Curtis et al., 2002; Ehman et al., 2002; Peichl, Khomik, & Arain, 2010). These studies underlined two main kinds of errors, one due to EC measurements and the other due to the allometric equations and component fluxes. Thus, neither PRELES, EC nor biometric methods can be considered an absolute standard.
A third, alternative approach for estimating GPP is to scale up tree-level ecophysiological measurements to the stand level. This approach requires the scaling of component fluxes such as leaf photosynthesis or sap flux. For example, the Conductance Constrained Carbon Assimilation model (4C-A) combined sap flux-based stomatal conductance with light-dependent photosynthetic parameters to produce vertically explicit photosynthesis estimates in both single- and multi-species stands (Kim, Oren, & Hinckley, 2008; Schäfer et al., 2003). These parameters were used to estimate the vertically explicit ratio between internal C concentration in the stomatal cavity, (Ci) and atmospheric C concentration (Ca) (Ci/Ca) or, weighted by vertical leaf area distribution, a canopy-scale effective Ci/Ca at diurnal resolution. Although it described photosynthesis well (Schäfer et al., 2003), the method required detailed information on canopy architecture and gas exchange properties, which are not straightforward to obtain.
A simpler way forward is to infer intrinsic water use efficiency (WUEi) from δ13C (Cernusak et al., 2013; Ehleringer & Farquhar, 1993). WUEi represents the ratio between net photosynthesis and the stomatal conductance (gS) to water vapour (Flexas et al., 2016). It is also equivalent to the CO2 diffusion gradient between the atmosphere and the substomatal cavity when considering gS for CO2 (Farquhar, O’Leary, & Berry, 1982). The WUEi can be estimated from δ13C in phloem (δ13Cp) contents, which estimates WUEi, at the tree scale (Ubierna & Marshall, 2011; Werner et al., 2012). Tree-scale WUEi can be upscaled to the stand by measuring several trees representing the area of interest. The δ13Cp measurement integrates the signal from the whole canopy, and therefore improves on Hu, Moore, Riveros‐Iregui, Burns, & Monson. (2010), who used a similar approach, but based their δ13C estimates on sugar extracts from foliage. The elimination of photosynthetic parameters, the phloem sampling, and the long time-step reduce error propagation as we scale up the whole tree measurements to the stand. The scale of the calculated WUEi thus matches the scale of the transpiration estimate.
Some studies using δ13C to estimate WUEi (Seibt, Rajabi, Griffiths, & Berry, 2008; Wingate, Seibt, Moncrieff, Jarvis, & Lloyd, 2007) and GPP (Hu et al., 2010; Klein, Rotenberg, Tatarinov, & Yakir, 2016) have highlighted the importance of mesophyll conductance (gm). The gm describes the ease with which CO2 can diffuse from the substomatal cavity to the chloroplasts, where carbon assimilation actually occurs (Flexas, Ribas-Carbó, Diaz-Espejo, Galmès, & Medrano, 2008; Warren & Adams, 2006). Because gm is finite, assuming that it is infinite leads to an overestimation of WUEi (Seibt et al., 2008; Wingate et al., 2007). There is as yet no agreement about how to model gm, but it has often been estimated from gS (Warren, 2008).
We present a new GPP model, hereafter called GPPiso/SF,combining sap flux, δ13Cp, and mesophyll conductance based on approaches developed previously (Hu et al., 2010; Kim et al., 2008; Klein et al., 2016; Schäfer et al., 2003), and compare it to estimates from PRELES. We estimated GPPiso/SF of whole trees at a daily time step and then scaled it up to the stand level. The sap flow/isotopic method would, however, only consider the tree contribution to the ecosystem GPP, in contrast to PRELES, which considers the contribution of the whole ecosystem, including understorey and overstorey species. The understorey contribution from PRELES is in the process of being analysed. However, understorey GPP represents rather little of ecosystem GPP in a closed-canopy boreal forest (Kulmala et al., 2011; Palmroth et al., 2019, Tian et al, under review). PRELES and the sap flow/isotopic method should therefore give similar results. The GPPiso/SFmethod can also provide information on how GPPiso/SFresponds to fertilisation in terms of assimilation and gS.
A boreal forest is particularly suited for such method comparison because of its simple species composition (Hänninen, 2016; Högberg, 2007). Moreover, because this biome is strongly nitrogen (N)-limited (Du et al., 2020) adding extra N induces a strong response in terms of growth and C fluxes (From, Lundmark, Mörling, Pommerening, & Nordin, 2016; Högberg, 2007; Hyvönen et al., 2008; Kergoat, Lafont, Arneth, Le Dantec, & Saugier, 2008; Nohrstedt, 2001; Tamm, 1991). These increases should be captured by all methods. However, a positive N-fertilisation effect on GPP was not always observed. At our site, previous studies showed no effect of N supply on GPP (Lim et al., 2015; Tarvainen, Räntfors, Näsholm, & Wallin, 2016) but Tian et al (under review) found a higher GPP in the fertilised plot than in the reference plot.
The method we propose in this paper aims to provide an alternative stand-scale estimate of GPP that is independent of eddy covariance. Our first objective here was to compare estimates of GPP based on stable isotopes and sap flux against GPP based on PRELES, a process-based model parameterised with eddy covariance data. The second objective was to determine how fertilisation treatment influenced the canopy GPP with the sap flux/isotope method. Finally, the third objective explores alternative methods for incorporating an empirical gmestimate and how these alternatives influence the GPP estimate.