Storage flux uncertainty impact on eddy covariance net ecosystem exchange measurements

Abstract

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 *V*_{m}
is the molar volume of dry air, *c* is the
CO_{2} molar fraction (μmolmol^{-1}), *t* is time, *z* is the
height of EC measurement, *υ*_{i},
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 CO_{2} in the air volume below
the *Fc* measurement height. Assuming
no horizontal advection, positive values are due to a source/accumulation of CO_{2}
within the control volume while negative values mean a sink/depletion. In
practical terms, *Sc* is the rate of
change of CO_{2 }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 CO_{2} 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 CO_{2} 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)