Making accurate estimations of daily and annual

Respiration is the second most important flux in ecosystems after
photosynthesis, in terms of the quantities of exchange and the contribution
to the total carbon cycle (Schlesinger and Andrews, 2000). Within ecosystem
respiration, soil respiration (

Soil respiration has been reported to differ across temporal and spatial
scales (Jia et al., 2006; Li et al., 2008; Vargas et al., 2010) as a result
of changes in soil temperature (Lloyd and Taylor, 1994; Subke and Bahn,
2010), soil moisture (Bown et al., 2014; Gaumont-Guay et al., 2006),
vegetation (Bahn et al., 2010; Buchmann, 2000), topography (Kang et al.,
2003), soil texture (Dilustro et al., 2005; Pumpanen et al., 2008), and
primary productivity (Bahn et al., 2010, 2008; Högberg et al., 2001;
Vargas et al., 2011). Among these variables, temperature and soil moisture
are the most widely used in empirical prediction models of

Sampling schemes of studies where annual

Soil respiration can be measured with alkali traps or infrared gas analysers
(IRGAs), the latter being the current reference for CO

Temperate forests present ecosystems with a high shaded area compared to
ecosystems with sparser vegetation, including agricultural land uses.
Nevertheless, variations of

Commonly researchers select times of the day during the morning, to get the
estimates of daily

Based on the estimation of seasonal or annual

Using a high-frequency sampling scheme (24 measurements per day) during
1 year in a temperate rainforest, we aimed to answer the still open questions
of when and how many measurements per day and per year should be performed in
order to adequately estimate

Location of the Senda Darwin Biological Station (marked with a star) at Chiloé Island.

The study was carried out in a temperate rainforest at the Senda Darwin
Biological Station (Carmona et al., 2010), a long-term socio-ecological
research site located 15 km east of Ancud, in Chiloé Island, Chile
(41

Mean long-term (1999–2012) (black) and August 2013–August 2014 (white) monthly precipitation (bars) and air temperature (circles).

The variability in forest conditions was preliminary assessed in terms of
canopy cover and other stand-related parameters. According to this, three
soil respiration chambers were installed to cover the range of these
variables, which were assessed in 3 m radius plots around each chamber.
Table 2 shows the basic statistical parameters of the forest stand, soil and
annual

Soil temperature (

For analysing the effects of making a different number of measurements per
day and including or not night-time measurements on the performance of daily

The partial-data series were then generated by randomly selecting
measurements. This process was different for the two sampling types defined
in 4):

For the day–night sampling, after randomly selecting one day (out of the 357 possibilities), the initial time of sampling was also randomly selected (out of the 24 possibilities); the other time(s) of measurement was selected equidistantly from this initial value, maximizing the time distance between samplings to fit the number of measurements in one day. In the case of one measurement per day, the time of measurement was the same as the initial time of sampling.

For the day sampling, to maintain the number of measurements per day and to make them as equidistant as possible, the times of measurements were randomly selected from windows of time, as shown in Fig. 3.

Characteristics of the forest stand, soil (30 cm) and annual

We defined different frequencies of sampling assuming that the most common
sampling schemes are seasonal (summer, autumn, winter and spring), every two months,
monthly, fortnightly or weekly. These frequencies implied 4, 6, 12, 26 and 52
measurements per year, respectively, which represented our partial-data
series. The best estimate of the annual

Once the selection of daily and annual measurements was done, we used two
different approaches to estimate the annual

Windows of time for randomly selecting measurements of different sampling frequencies, for the only daytime sampling. The lines represent the windows of time and the dots represent the exact time of measurements.

Daily mean

For estimating the performance of the estimations of

All three parameters were calculated for each sampling frequency based on
10 000 partial-data series, which were generated as described in Sects. 2.3
and 2.4. The bias of the daily estimation for each frequency of sampling was
calculated as

The precision was estimated as the standard deviation (SD) of the
partial-data series estimations of the daily flux, using the values selected
in Eq. (1):

The daily

The same pattern was observed for

The difference in

Statistics of the estimation of daily

In the scenario where only daytime measurements were considered, the bias was
always positive, around 0.35 g CO

The precision (SD) of the daytime scenario was around
4.2 g CO

The RMSE for only daytime measurements showed an important decrease when
comparing the frequencies of one and two measurements per day (1.45 and
0.82 g CO

Bias

The precision of daily measures of

Figure 6 shows the statistical parameters for the annual estimations of

In summary, regardless of the annual frequency of sampling, making
measurements only during daytime represented a positive bias (overestimation)
of the annual

The SD of only daytime measurements moved from a maximum around
0.52 kg CO

Because the parameter we used to represent the precision of the annual estimation (SD) accumulates the difference between observed and modelled values, the magnitude of the error associated to precision was much larger than the bias, making the value of precision almost identical to the accuracy parameter (Fig. 6c and d compared to Fig. 6e and f).

The RMSE of the daytime scenario showed a decreasing trend when increasing
the frequency of sampling from 4 to 6, 12, 26 and 52 days per year, with mean
values of 0.42, 0.34, 0.26, 0.22 and 0.20 kg CO

If sampling was done only once a day, sampling once a month was the minimum
frequency required for obtaining accurate estimates of annual

The effect of sampling more times per day on the error of annual

Table 1 shows that there is great variability in both daily and annual
frequency of sampling in studies that measured

We tested both linear interpolation and modelling based on soil temperature
as gap filling approaches, expecting that the latter would yield lower error
in the annual

Unfortunately, we cannot compare our results with the studies summarized in
Table 1, because no information is given about the level of accuracy of the
daily or annual estimations of

Finally, we agree with Gomez-Casanovas et al. (2013), in relation to the need
of improving and standardizing the techniques to estimate the annual

According to our observations in a temperate rainforest site, if the
research question seeks accurate daily estimations of

In general, the accuracy of most combinations of daily and annual sampling
frequencies used for modelling annual

The decrease in error when using modelling instead of linear interpolation
for estimating

As a general measure for reducing the errors originated from partial sampling
of

The complete data can be found in the Supplement.

The authors are grateful for the funding from the National Commission for Scientific & Technological Research of Chile (grants FONDEQUIP AIC-37 and FONDECYT 1130935). They also thank the administration and personnel at the Senda Darwin Biological Station and Richard Plant for his valuable comments on a preliminary version of the manuscript. Edited by: J.-A. Subke Reviewed by: two anonymous referees