Abstract

# Introduction

The estimation of the net ecosystem exchange (NEE) by the eddy covariance (EC) technique is based on simplifications of the mass balance equation, and on its integration over a control volume that extends horizontally on a representative surface and vertically from the soil level to the measurement height (Finnigan et al., 2003; Foken et al., 2012). After Reynolds averaging, integrating over the control volume, ignoring horizontal turbulent flux divergence and the horizontal variation of the vertical flux, the equation can be written as (Aubinet et al., 2005; Feigenwinter et al., 2008):
EQUATION HERE [1]
where Vm is the molar volume of dry air, c is the CO2 molar fraction (μmolmol-1), t is time, z is the height of EC measurement, υi, with i = 1, 2, and 3, represents the wind velocity components in x, y, and z direction (namely u, v and w respectively). In the third term i indicates a summation over each value. The overbar denotes time averages and primes indicates related departures (turbulent fluctuations). The three terms on the RHS of equation (1) are the eddy flux, the storage change (Fc and Sc in the following), and the advection (horizontal for i = 1 and2, vertical for i = 3). In the prevalence of studies on long-term carbon budgets, either those involved in continental and global monitoring networks (e.g. ICOS, Neon, Fluxnet) or not, the advection term is neglected mainly because of the critical difficulties in measuring these fluxes with the required accuracy (Heinesch et al., 2007; Leuning et al., 2008; Moderow et al., 2011; Vickers et al., 2012). Under weak turbulence conditions, such exclusion causes an underestimation of the true ecosystem total flux, the severity of which is related to site-specific surface conditions (Kutsch et al., 2008; Mammarella et al., 2007; Novick et al., 2014). In this paper, the advection is explicitly not considered, referring the readers to ad-hoc bibliography (e.g. Canepa et al., 2010; Feigenwinter et al., 2008; Kang et al., 2017; Yi et al., 2000and aforementioned references). Here the focus is moved to the storage term because, as stated above and despite the missing CO2 problem, the bulk of carbon budgets studies quantify NEE by
EQUATION HERE [2]
The storage term Sc reflects the dynamics of CO2 in the air volume below the Fc measurement height. Assuming no horizontal advection, positive values are due to a source/accumulation of CO2 within the control volume while negative values mean a sink/depletion. In practical terms, Sc is the rate of change of CO2 given by the difference in the instantaneous profiles of concentration at the beginning and end of the averaging period, divided by the averaging period (Finnigan, 2006). While cumulating over time led to a nullification of Sc, it can be significant at short time periods such as half-hours or hours, especially around sunrise or sunset. Also during the night, when atmospheric stratification is strong and turbulence is suppressed Sc becomes important, equaling or even exceeding Fc. This has been demonstrated basically by all the studies in which Sc has been measured (references in the text). It follows that Sc cannot be ignored or misestimated in order to reduce the uncertainty in the NEE budget estimate, in particular the one related to the nighttime flux error (Aubinet et al., 2012). Besides on NEE long-term budgets (cumulative), this error propagates on further analysis like friction velocity (u*) threshold determination, NEE gap-filling and partitioning, and also on flux-climate functional modeling, inducing both random and systematic errors (Papale et al., 2006).
Assuming horizontal homogeneity, the typical approach to compute Sc is based on a single tower concentrations profile (one-dimensional integration) thought, ideally, it should be derived from profiles of space averaged concentrations (three-dimensional integration). Under non-ideal site conditions, as in cases of heterogeneity in the source/sink distribution, the error caused by this assumption can be large (Pattey et al., 2002; van Gorsel et al., 2009). Despite this evidence, is not unusual that Sc is computed basing solely on the temporal changes of the concentrations measured at the tower top assuming a constant gradient in the air column underneath. The error associated with this further assumption is proportional to the degree of decoupling between the CO2 measurement height (generally the EC system height) and the below canopy air space. Several studies reported similarity between profile and one-point Sc estimates (Greco and Baldocchi, 1996; Knohl et al., 2003; Lee et al., 1999; Priante-Filho et al., 2004) while others ascertained substantial underestimates (Gu et al., 2012; Iwata et al., 2005). The choice of one sampling design over another is essentially due to technical and cost-related aspects. Obviously by reducing the sampling intensity the accuracy of Sc it is also reduced, and this reduction is proportional to the source/sink spatial variability. It follows that a careful distribution of sampling points is crucial in order to avoid large misestimation. Some studies assayed the effect of profile vertical configuration on Sc and NEE estimates (Bjorkegren et al., 2015; Gu et al., 2012; Wang et al., 2016; Yang et al., 2007, 1999; Zhang et al., 2010)basing on a one-dimensional analysis (single vertical profile).
In this paper we expand the analysis achieved in the aforementioned works to a three-dimensional volume with the objective of 1) quantify the error in Sc measurements due to the spatial variability of CO2 concentration, 2) identify the most efficient measurement setup, and 3) quantify the impact of Sc error on NEE estimate and some related analysis. The data at the base of this study come from ADVEX, the CarboEurope-Integrated Project (CE-IP) advection campaigns (Feigenwinter et al., 2008).
It is worth to note that here the focus is on the spatial sampling error only. The other main source of uncertainty in Sc measurements, the temporal sampling error, is not considered (detail on this can be found in e.g. Cescatti et al., 2016; Marcolla et al., 2014; Siebicke et al., 2011; Wang et al., 2016; Yang et al., 2007)