Continuous records of the atmospheric greenhouse gases (GHGs)
CO

Our knowledge of changes in the atmospheric mixing ratios of the important
greenhouse gases (GHGs) CO

All three GHG records have special features which need some attention during data compilation:

For some of the CO

Due to the dominance of CH

In situ production of N

Rapid changes are most pronounced in CH

In order for these issues to be overcome, careful data selection and
processing are required. Here, we document our assumptions during data
compilation and calculate continuous time series of CO

Previous splines (similar to our approach here but not identical in detail)
have also been proposed to be used in interglacial experiments of the
Holocene within PMIP4

As will be seen in detail in the next section, the mathematical formulation of
the spline smoothing method needs information on the uncertainties or errors in the data points supporting the spline. These data uncertainties represent
the precisions of individual measurements (

In the following, ages are either given in years CE (Common Era) or in years
BP (before present), where present is defined as 1950 CE. We define the
onset of anthropogenic activities at 1750 CE (or 200 BP), based on the
timing of the increase in CO

The numerical code for spline smoothing is based on

In a smoothing spline a cost function is minimised. This cost function
includes two terms: (i) the error-weighted deviation between the spline value
and the actual data value and (ii) the curvature of the spline, represented
by its second derivative. A parameter

According to Fourier, each time series can be represented by a sum of sine
functions. Since a smoothing spline acts as a low-pass filter, high
frequencies are dampened in the spline. The period at which the amplitude is
attenuated to 50 % is defined as the cutoff period

Let us assume input data are

In the following, we prescribe

Locations of the different data sources, ordered north to south.
Individual sites of the NOAA observational network are not explicitly
mentioned here, when they only contribute to global mean calculations. SH
CH

Notes:

Let us now assume we have a data set with variable data spacing, for which we
would like to apply different smoothing depending on

where

An intermediate product with

Data used to construct the CO

Notes:

The uncertainties of the final splines are calculated from the square root of
the sum of squares of three individual errors (

Data resolution error
(

Monte Carlo error (

Our GHG data compilations are based on various data sets from 13 global
distributed locations. An overview of the locations, including latitude and
longitude, is provided in Table

CO

Statistics of the CO

There are small offsets of a few parts per million in measured CO

Our CO

The CO

Comparison of our final spline data with values used for PMIP4
experiments for 21 kyr

Details of the CO

Our CO

The firn and ice data compilation of Law Dome, which also contains some
contributions from Cape Grim and the South Pole – available for the time from
1996 CE to 1 CE (

Data from the WDC ice core exist for the times of 11–1210 BP, or 1939–740 CE

EDC data exist between 350 BP and the Last Glacial Maximum (LGM)

Termination I is best covered by data from WDC

is 0.15 or 0.09 W m

Further back in time all ice core records used have some data overlap with their successive records.
There are some small offsets between the different records

From 104.3 to 156.3 kyr BP – the interval spanning the last glacial
inception, the last interglacial, Termination II, and the penultimate glacial
maximum (Fig.

For every supporting data point

The data selection as described above then leads to

To account for the variable temporal resolution of the data points
(Fig.

The total

The CO

The CO

Since spline smoothing is a low-pass filter, abrupt changes in CO

Data used to construct (or compare to) the Southern Hemisphere
CH

Notes:

Our data compilation of CH

Our data compilation starts with the beginning of the year 2016 CE (

CH

Details of the southern hemispheric CH

Statistics of the CH

From the NOAA network, the annual global mean concentration of CH

Ice core and firn air data from Law Dome and Cape Grim (SH) exist from
2005 CE back to 14 CE (

The discrete CH

We extend our SH CH

The NH Greenland composite of CH

Data used to construct the N

Notes:

The assigned data uncertainty (

Compiled data contain 30 214 data points, among which duplicate entries
exist for 39 ages. These duplicates are averaged giving

The whole data set is divided into seven intervals with different assigned
cutoff periods.

The total

N

Details of the N

Statistics of N

The SH CH

A comparison of our final spline with the GHG values chosen for the PMIP4
time slice experiments

For the data compilation of the third GHG, N

The compiled record starts at the beginning of the year 2016 CE
(

The data sets contributing to the N

There are two contributions of N

Law Dome and Cape Grim N

In the Holocene, N

The most highly resolved N

The last glacial interval is well resolved by N

Additional N

Calculated radiative forcing of CO

The generally assigned

The mean temporal resolution (11-point running mean) of the underlying N

The total

If compared with the N

The N

Data connected with this paper are available in the scientific database
PANGAEA (

In detail, for each of three GHGs the following data are available.

Final, compiled raw data (

Preprocessed raw data (averaging of duplicate entries for similar times).

Calculated splines with time steps of

Corresponding radiative forcing based on the simplified Eqs. (

When using these data, please consider citing the original publications from which the data underlying this compilation have been taken.

We have compiled available greenhouse gas records and, by calculating a
smoothing spline, we were able to provide continuous records over the last
glacial cycle, starting from the beginning of the year 2016 CE and going
back to 134 kyr BP (for N

We thank NOAA for the availability of the instrumental GHG data, specifically
Ed Dlugokencky and Pieter Tans, NOAA/ESRL
(