Accurate multi-point monitoring systems are required to
derive atmospheric measurements of greenhouse gas concentrations both for
the calculation of surface fluxes with inversion transport models and for
the estimation of non-turbulent components of the mass balance equation
(i.e. advection and storage fluxes) at eddy covariance sites. When a single
analyser is used to monitor multiple sampling points, the deployment of
buffer volumes (BVs) along sampling lines can reduce the uncertainty due to
the discrete temporal sampling of the signal. In order to optimize the use
of buffer volumes we explored various set-ups by simulating their effect on
time series of high-frequency CO

The increasing atmospheric greenhouse gas concentrations and the related
global warming are raising the demand for reliable and stable observations
of both greenhouse gas atmospheric concentrations and land–atmosphere
fluxes. In particular, measurement of CO

To our knowledge, the complex effect of BVs in multi-point sampling systems
has not been fully investigated and specific studies are required to explore
the potential and limitations of their application. For this purpose, in
this work we evaluate the effectiveness and optimal use of BVs in CO

The study site is located in an unmanaged forest stand in northern Italy
(45

The study site is located in a rice paddy field in the Po Valley
northern Italy (45

The study site is located in a maritime pine forest in central Italy
(Tuscany; 43

In order to analyse the impact of BVs on the error statistics of a
multi-point monitoring system, the high-frequency CO

For practical reasons in this study the theoretically infinite memory of BVs
is limited to half an hour. To accommodate this assumption the transfer
function Eq. (1) is normalized in order to sum to one when integrated over
1800 s, according to Eq. (2):

Frequency distributions of the bias between real and estimated
CO

According to the theoretical framework presented in the previous section,
the CO

For this purpose we propose to process the convoluted signal with a weighted averaging scheme based on the concept that the importance, and therefore the weight, of an instantaneous reading in determining the half-hourly average depends on the fraction of air build-up in the volume during the half hour of interest. According to this approach, readings at the beginning of the half hour have a low importance since they are mostly influenced by the air concentration of the previous half hour, while readings at the end of the averaging period have the highest weight. In parallel, a fraction of the signal originated in a given half-hour affects the convoluted signal in the following 1800 s, and this information has also to be considered in the estimation of the half-hourly statistics.

To formalize this methodology we define the following weighting functions
for the calculation of the mean:

In order to assess the effectiveness of this new weighed averaging scheme (hereinafter referred to as WAM), half-hourly average concentrations derived from the discrete sampling for different sites and simulated set-ups have been compared with the real concentration values derived from the half-hourly block average of the high-frequency signal.

Dependency of the mean absolute error (MAE) on

In parallel, error statistics have been computed for two alternative methodologies commonly used in multi-point monitoring systems: (i) set-up without BVs (NoVol) and half-hourly averages computed as arithmetic mean of the discrete sampling of the original signal at high frequency, (ii) set-up with BVs and half-hourly averages computed as arithmetic mean (AM) of the discrete sampling of the convoluted signal. Concerning the error sources, it needs to be pointed out that the present analysis focuses exclusively on the uncertainty due to the discrete sampling of a multi-point system and does not consider the instrumental error of the gas analyser and the associated uncertainty in high-frequency observations.

Finally, the performances of the three alternative methodologies (i.e.
NoVol, AM and WAM) are compared under different architectures of the
sampling system (i.e. number of points, temporal sampling scheme and

The analysis of experimental data is presented in the following two sections. In the first part, the mean error introduced by the discrete temporal sampling is analysed and its dependency on the variability of the concentration field both in space and time is explored using data collected at IT-Isp above and below canopy; in the second section, the analysis is extended to two other sites (IT-SR2 and IT-Cas) with the aim of generalizing the findings and proposing an empirical methodology for the selection of the optimal set-up for multi-point monitoring systems.

Dependency of the mean absolute error (MAE) on the standard
deviation of half-hourly CO

From the high-frequency time series of CO

We define as optimal set-up the one that minimizes the MAE of CO

In the present work we focus both the theoretical framework and the analysis
of the results on the concept of optimal residence time (

MAE as a function of the number of measurement points at three Fluxnet sites (IT-Isp above and below canopy, IT-Cas, IT-SR2) and for four sampling schemes (5 s purging and 1, 5, 10, 15 s reading).

The frequency distributions of the half-hourly errors were calculated for
the three averaging schemes (NoVol, AM, WAM) and four residence times (30,
60, 120, and 240 s) for above and below canopy at IT-Isp, simulating a
set-up with six points and a 5 s purging

The WAM approach outperforms the other methods for every value of residence
time and shows the lowest MAE for a

Optimal

The dependency of the mean absolute error on

For both above and below canopy measurements the error due to the discrete
sampling of the CO

In this section we aim at exploring the optimal set-ups of a multi-point monitoring system at three experimental sites located in different environments (i.e. plain, coastal and hills) and characterized by different vegetation cover (i.e. crop, evergreen and deciduous forests). Given the effectiveness of the WAM averaging scheme demonstrated in Sect. 3.1, in what follows we will limit the computation of half-hourly estimates to this methodology.

Optimal renewal frequency (at minimum MAE) of the buffer volume as a function of the sampling frequency for the different sites and sampling schemes. The WAM averaging scheme was used for computing half-hourly concentrations.

Figure 5 shows the trend of MAE as a function of the number of sampling
points for different sites and four alternative sampling schemes with fixed
purging time (5 s) and variable reading time (1, 5 ,10, 15 s). The MAE
obtained with the optimum BV is reported for each case. Results show that
MAE increases with the number of sampling points for all sites and for all
sampling schemes and that within each site it also increases with the length
of the reading time. In fact, thanks to the temporal correlation of the
convoluted signal, there is a clear advantage in shortening the reading time
and switching faster between lines. The ultimate effectiveness of this
strategy depends on the technical specification of the gas analyser and in
particular on the time interval required to obtain a stable signal. For fast
and accurate CO

The optimal

In the present work, high-frequency time series of CO

In conclusion, this analysis shows that, when the size of the volumes is
optimized and the data analysis is properly performed, BVs represent a
valuable technique to substantially reduce the error due to the discrete
temporal sampling in multi-point monitoring systems. Even if the present
work is focused on CO

Half hourly averages of meteorological variables and flux data of the three eddy covariance sites used
in the present paper are available at