Appendix S2: Description of gap filling methods
For all gap filling methods, raw Rsoil data were screened to remove unreasonable values
caused by instrument malfunction or biologically anomalous conditions (e.g., plants growing
inside the collars). For all methods involving linear or cubic interpolation, if half-hourly Rsoil
values were missing for the first and last half-hour period of each year, the missing Rsoil values
were set to zero to avoid unrealistic predicted Rsoil values.
SIMPLE ALGORITHM METHODS:
Linear interpolation method
In this method, half-hourly missing Rsoil values were extrapolated using the following
equation,
𝑅𝑠𝑜𝑖𝑙 = 𝑅𝑠𝑜𝑖𝑙 (t 0 ) + (t − t 0 )
𝑅𝑠𝑜𝑖𝑙 (t1 )−𝑅𝑠𝑜𝑖𝑙 (t0 )
t1 −t0
;
[4]
where Rsoil (t0) and Rsoil (t1) represented the Rsoil values adjacent to the missing value.
Cubic interpolation method
This method is based on a cubic Hermite interpolation, a mathematical technique to interpolate
data points using polynomials. The interpolation is piecewise, i.e., performed on a moving
window over the time series. The advantage of this method for gap filling purposes is that the
local shape of the curve around gaps is preserved during the extrapolation.
Monthly average method
Half-hourly missing Rsoil values were replaced by the average of Rsoil data for the current
month for gap window sizes bellow 30 days. If monthly Rsoil averages for a current month were
missing (except for the first and last month of each year), monthly Rsoil averages were linearly
extrapolated from adjacent months. If Rsoil data for the first and last month of the year was
missing, monthly Rsoil average was assumed to be 0.
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SOIL TEMPERATURE-DEPENDENCE METHODS:
The soil temperature dependent methods used in this study were based on Equation 1
(manuscript). In this equation, Tref and T0 were set at 10°C and -46°C, respectively (Lloyd &
Taylor 1994). The E0 and Rsoil parameters were calculated according to each soil temperature
dependence method as shown in Table 1. For the soil temperature dependence methods,
biologically unrealistic E0 and Rref values were avoided by setting lower and upper limits for
these parameters. This biologically unrealistic E0 and Rref values are often associated with
confounding factors that affect the temperature sensitivity of Rsoil (Davidson et al., 2006;
Anderson-Teixeira et al., 2008) and result in abnormally high predicted Rsoil values. The lower
and upper limits for these parameters were set for these temperature dependent methods at 0 and
1000 K-1 for E0, and 0-4 μmol m-2 s-1 for Rref (previously determined to represent reasonable
range at this site).
T:annual method
For the T:annual method, E0 and Rref were assumed to be constant and calculated by
fitting a single relationship between Rsoil and temperature for the entire year.
T:cE0 method
For the T:cE0 method, E0 was assumed to be constant for the entire year (308.56 K-1; Lloyd and
Taylor, 1994). In this method, Rref was calculated from Rsoil for each half-hour record. Missing
Rref values were linearly interpolated extrapolated from the calculated Rref values.
T:min_time method
For the T:min_time method, E0 and Rref (Eq. 1) were estimated for 5 lengths of time
periods (1 day, 1 week, 1 month, 3 months and 1 year). At time frames less than one year, a
minimum of 25% of half-hourly records was considered sufficient for reasonable parameter
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estimation. For each half-hour period, Rsoil values were calculated based upon estimates of E0
and Rref (Eq. 1) for all time periods over which equation 1 was fit, and the first reasonable
estimate (moving from short- to long-fitting time frames) was selected. Rsoil estimates where
considered reasonable when they differed from a linearly interpolated record of Rsoil by a factor
of less than two (i.e., <2*LI estimate or > ½*LI estimate). If the Rsoil estimate from fitting at the
annual time scale was determined to be unreasonable, the model defaulted to the linearly
interpolated Rsoil estimate. Estimated Rsoil values that exceeded the maximum observed value in
the dataset were replaced with that maximum value.
SOIL TEMPERATURE- AND MOISTURE-DEPENDENCE METHODS:
The soil temperature-and moisture- dependence methods predict Rsoil based on the
relationship between Rsoil and soil temperature and moisture. The RSWC was calculated using the
following equation,
𝑅𝑆𝑊𝐶 =
𝑆𝑊𝐶
𝑆𝑊𝐶𝐹𝐶
;
[5]
where RSWC is the soil moisture at any given half-hour period (SWC, m m-3) and SWCFC (m m-3)
is the soil moisture content at field capacity. SWCFC was calculated as the soil moisture content
after 3 days of drainage after maximum soil moisture content was reached as described in
Reichstein et al. (2003). Values of RSWC at or below 0 and soil temperature values at or below 1
°C were excluded from the analyses, as unrealistic Rsoil values were obtained.
Soil temperature and moisture dependence methods with soil temperature and moisture
interaction.
Artificially created half-hourly Rsoil values were gap filled using Equation 2 and 5. In this
Equation, Tref and T0 were set at 10ºC and -46 ºC. Values of RSWC at or below 0 and soil
temperature values at or below 1 °C were excluded from the analyses.
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For the TxSWC:annual method, the parameter Rref was calculated by fitting a single
relationship between Rsoil and temperature for the entire year. The parameter E0(RSWC) was
calculated by fitting a relationship between E0 and RSWC for the entire year as in Reichstein et
al. (2003).
For the TxSWC:min_time, E0 and Rref were estimated as in the T:min_time method. In
addition, this method assumed that E0 was dependent on changes in soil moisture and therefore
was calculated as in the TxSWC:annual method. If RSWC ½ (SWC where half-maximal
respiration at a given temperature occurs; Reichstein et al., 2003) for the shortest possible time
period could not be calculated, the annual RSWC ½ was used.
Soil temperature and moisture dependence methods without soil temperature and moisture
interaction.
The soil temperature and moisture dependence method without interaction (T+SWC:cE0)
was calculated using Equation 1. However, the parameter Rref was calculated by assuming a
linear dependency of Rref on the RSWC for each half-hour record. Missing Rref values were
linearly interpolated extrapolated from the calculated Rref values. The parameter E0 was assumed
to be constant for the entire year (308.56 K-1; Lloyd and Taylor, 1994). For this method, Tref and
T0 were set at 10°C and -46°C.
In addition to the soil temperature-moisture dependence method with no interaction, Rsoil
was calculated using Equation 2 and 5, but assuming a constant E0 for the entire year (308.56K-1;
Lloyd and Taylor, 1994). However, this method yielded poor ΣRsoil estimates (data not shown).
4