where t k is the time at instant k, and b is the slope of the linear trend of the sample.
The slope is calculated as
b ¼
P n
k¼1
x k t k À
1
n
P n
k¼1
x k
P n
k¼1
t k
P n
k¼1
t k t k À
1
n
P n
k¼1
t k
P n
k¼1
t k
ð3:196Þ
The methods given for the calculation of the means are basically dependent on
the analysis of a given finite series of measured data. The sampling time depends on
the atmospheric stratification, the wind velocity, and the measurement height.
Calculating the means for corresponding covariances for time series of 30 min is
enough to encompass the effects of low frequency relative to all the eddies
responsible for the turbulent transport (Gash and Culf 1996; Aubinet et al. 2000;
Burba and Anderson 2010).
A sampling time of 30 min over the full daytime is considered as delivering no
significant measurement errors. For height measurements of 2−5 m, sampling
periods of 10–20 min would be required for daytime unstable stratification in
summer and about 30–60 min and perhaps 120 min would be required for
night-time stable stratification (Foken 2017).
(vii) Eddy covariance measurements are affected by peaks caused by environmental
factors such as the footprint changes or rapid changes in turbulence or instrumentation (e.g., heavy rain falling on the sonic anemometer or an open circuit
analyzer). All processes with fluctuations higher than 3.5r are considered as
spikes or high-frequency peaks. High-frequency peaks, affecting the instantaneous measurement, are removed by filtering before calculating covariance
means for half-hour periods. Typically, these half-hour periods are excluded
when the high-frequency peaks exceed 1% of total data (Foken 2017).
Peaks or oscillations in the time series of the mean values for half-hour periods
typical for non-turbulent phenomena affect the quality of gap-filled data. The
methodology used to determine these low-frequency events and consider them as
outliers is based on the position of each average value of the flux over a half-hour
period (e.g., the net ecosystem exchange NEE i or carbon budget) compared to
before and after adjacent periods, needed for the d i variable (Papale et al. 2006):
d i ¼ NEE i À NEE iÀ1
ð
Þ ÀNEE i þ 1 À NEE i
ð
Þ
ð 3:197Þ
where the value of NEE i is considered a low-frequency peak if
d i \Md À
zMAD
0:6745
or d i [ Md À
zMAD
0:6745
ð3:198Þ
3.7 Eddy Covariance Method
89
The slope is calculated as
b ¼
P n
k¼1
x k t k À
1
n
P n
k¼1
x k
P n
k¼1
t k
P n
k¼1
t k t k À
1
n
P n
k¼1
t k
P n
k¼1
t k
ð3:196Þ
The methods given for the calculation of the means are basically dependent on
the analysis of a given finite series of measured data. The sampling time depends on
the atmospheric stratification, the wind velocity, and the measurement height.
Calculating the means for corresponding covariances for time series of 30 min is
enough to encompass the effects of low frequency relative to all the eddies
responsible for the turbulent transport (Gash and Culf 1996; Aubinet et al. 2000;
Burba and Anderson 2010).
A sampling time of 30 min over the full daytime is considered as delivering no
significant measurement errors. For height measurements of 2−5 m, sampling
periods of 10–20 min would be required for daytime unstable stratification in
summer and about 30–60 min and perhaps 120 min would be required for
night-time stable stratification (Foken 2017).
(vii) Eddy covariance measurements are affected by peaks caused by environmental
factors such as the footprint changes or rapid changes in turbulence or instrumentation (e.g., heavy rain falling on the sonic anemometer or an open circuit
analyzer). All processes with fluctuations higher than 3.5r are considered as
spikes or high-frequency peaks. High-frequency peaks, affecting the instantaneous measurement, are removed by filtering before calculating covariance
means for half-hour periods. Typically, these half-hour periods are excluded
when the high-frequency peaks exceed 1% of total data (Foken 2017).
Peaks or oscillations in the time series of the mean values for half-hour periods
typical for non-turbulent phenomena affect the quality of gap-filled data. The
methodology used to determine these low-frequency events and consider them as
outliers is based on the position of each average value of the flux over a half-hour
period (e.g., the net ecosystem exchange NEE i or carbon budget) compared to
before and after adjacent periods, needed for the d i variable (Papale et al. 2006):
d i ¼ NEE i À NEE iÀ1
ð
Þ ÀNEE i þ 1 À NEE i
ð
Þ
ð 3:197Þ
where the value of NEE i is considered a low-frequency peak if
d i \Md À
zMAD
0:6745
or d i [ Md À
zMAD
0:6745
ð3:198Þ
3.7 Eddy Covariance Method
89