Atmospheric variations of carbon dioxide (CO

Combustion of fossil fuel and cement production represent the dominant
annual source of atmospheric

Many previous studies have used atmospheric measurements of

In the next section we describe measurements of

Figure

The NOAA/ESRL monitoring sites used in our

The maximum

Twin air samples are collected weekly at the sites and analysed for

The wavelet transform method (described below) requires a continuous time
series that is regularly spaced in time. To fill a missing value in a time
series we add a value from 7-year average seasonal cycle (calculated using
the 3

Figure

Reference weekly

Weekly (top)

We also use measurements of

We use the University of East Anglia Climate Research Unit TS3.10 land
temperature data set

To investigate large-scale vegetation change, we use the Global Inventory
Modeling and Mapping Studies normalized difference vegetation index (GIMMS
NDVI3g) data set derived from the NOAA Advanced Very High Resolution
Radiometer (AVHRR)

We use a wavelet transform to spectrally decompose the observed

In general a wavelet transform

The wavelet transform of a time series

Parameters used by the control wavelet transform for monthly and
weekly spectral decomposition of

We can recover the original time series from wavelet space using the
corresponding inverse transform

To minimize edge effects associated with the Fourier transform, we add synthetic data to pad the beginning and end of the time series. For our calculation we repeat the first (last) 3 years of the time series backwards (forwards) in time, accounting for continuity of the growth rate based on the following (preceding) years. The synthetic data used in the padding should be close to what we expect, but is essentially unknown, and this uncertainty penetrates the first and last year of the time series. We also “zero pad” the time series so that the number of points used is an integral power of 2, which further reduces edge effects and speeds up the transform. The padded data at the edges of the time series are removed post-wavelet decomposition and prior to analysis.

We quantify the numerical error associated with the wavelet transform by
applying it to synthetic time series, which are representative of

Additional uncertainties may arise in the long-term trend and detrended
seasonal cycle as a result of spectral power being assigned to the incorrect
frequency band. This could, for example, result in concentration changes
caused by anthropogenic emissions being misattributed to the natural
(seasonal) cycle of

Decadal mean

We find that for atmospheric

Figure

Global decadal mean growth rates (GR) and the corresponding growth
rate due to fossil fuel combustion (FF) and natural sources (GR–FF).
Units are ppm yr

By subtracting anthropogenic fossil fuel emission estimates from the
atmospheric

We use several metrics to interpret the

Figure

Based on

A schematic describing the metrics we use to characterize changes in
the amplitude and phase of atmospheric

To look at changes in phase, previous studies have used the zero-crossing
point (ZCP) of

The beginning of the period of net carbon uptake is difficult to determine
accurately using the seasonal cycle at high-latitude sites because small mole
fraction variations during the dormant period (which has a near-zero flux)
are sufficient to bring

The ability to isolate changes in the phase and amplitude of the seasonal
cycle with fidelity is critical for our analysis. We use Monte Carlo
numerical experiments to characterize the errors associated with
independently identifying changes in phase and amplitude that can result in
the misinterpretation of these data and/or underestimation of uncertainties
(Appendix

Figure

Scatterplots of the

Time series of the percentage change of peak uptake and release at four high northern latitude sites (see main text). Each panel shows the data as blue closed circles and the 25 % uncertainty interval. The dashed black line is the fitted linear trend that is reported inset of each panel.

Time series of phase changes and the corresponding change to the
carbon uptake period of

The concomitant observed changes in

Observed changes in amplitude at BRW (

We have used a wavelet transform to spectrally isolate changes in the
seasonal cycle of atmospheric

We found that the atmospheric growth rate of

Using the detrended

We reported an increase in amplitude of

We diagnosed phase changes using thresholds of

Our analysis does not provide direct evidence about the balance between
uptake and release of carbon, but changes in the
peak uptake and release together with an invariant growing period length
provides indirect evidence that high northern latitude ecosystems are
progressively taking up more carbon in spring and early summer. The period of
net carbon uptake has not lengthened but has become more intense. However, it
is possible that this increase may be offset by a prolonged period of
respiration due to warmer autumn temperatures. Changes in atmospheric

Figure

As discussed above, we use the spectrally decomposed data set to
interpret the observed variability of

Top row: weekly mean (black) and low-pass filtered (red, periods

We use synthetic

We use a simple box model based on the

Synthetic

The starting point of our numerical experiments is the detrended time
series of atmospheric

Wavelet analysis of

The following three broad set of experiments are designed to identify
the best metrics to describe changes in the contemporary cycle from
detrended

Figure

Same as Fig.

Figure

Figure

Same as Fig.

Same as Fig.

We find that the wavelet transform attributes the
0.70

Figure

Despite large interannual variability, there is a negligible trend in
the spring timing of

We find that the analysis of synthetic time series indicates that

We used an MCS to study the ability of the
wavelet transform to simultaneously determine the PU, PR, and changes
in phase. We generated 1000 synthetic time series with random
trends and variability such as the one illustrated in
Fig.

Figure

Probability densities of trends introduced as part of a 1000-member ensemble of synthetic time series generated for the Monte Carlo experiment where the black line is the fitted probability distribution.

Regression of expected and estimated linear trends for peak uptake
(PU), peak release (PR), and the

Scatterplot and associated linear regression coefficients of
the amplitude trend (

Figure

Our analysis of phase changes in the

Table

Estimated trends of downward and upward zero crossing points (DZCP
and UZCP respectively), peak uptake and release (PU and PR respectively),
and carbon uptake period (CUP) calculated from

Table

The warming-induced earlier onset of springtime carbon uptake is also
supported by observed increases in vegetation greenness described by
NDVI inferred from space-borne sensors

Figure

Figure

Temperature linear trend analysis (1970–2011) for the beginning and end of the thermal growing season.

Linear regression coefficients that describe the relationship
between changes in

Linear regression coefficients that describe the relationship
between changes in

We thank NOAA/ESRL for the