To understand nature’s functioning, the look is devoted to the past – first to preindustrial times revealing undisturbed nature and second, to the industrial eon with significant anthropogenic contributions.
2.1 Atmospheric CO2 concentration
During the preindustrial past 800 thousand years (ka), the atmospheric CO2 concentration has followed temperature in the order of 20–25 ppmv/°C within the range of about 180–280 ppmv (ppmv, volume parts per million). – At preindustrial times, global waters have released 1.7 GtC/year into the atmosphere (cf. ). Apparently, terrestrial vegetation was prepared to consume these emissions leading to overall flux balance in first order. – During the industrial eon, the atmospheric CO2 concentration has approximately evolved from 280 ppmv to 420 ppmv. These measured concentrations can be related to the rather well known anthropogenic input if the latter is taken up by land and the oceans at a year-on-year rate of 3%/year .
2.2 Surface temperature
Also for the preindustrial past 800 ka, the temperature can be viewed determined by the atmospheric CO2 concentration and direct temperature effects, the latter driven by the solar irradiation and snow/ice albedo alteration. The CO2-temperature contribution is approximated by the ‘Eocene relationship’ with TCO2 = ln(𝑝CO2/22) * 6.68°C (TCO2, surface temperature in °C; 𝑝CO2, atmospheric CO2 volume mixing ratio in ppmv) , here the data of  used for 𝑝CO2. TCO2 comprises all related effects, e.g. from water vapor. When complemented by further driving forces, these are considered as correction terms, thus in turn also comprising all related effects. In the present studies, insolation is differentiated by the components eccentricity, obliquity, perihelion, flux at 65°N summer solstice, and global average . Albedo is assumed proportional to sea level and in turn, sea level to seawater-δ18O . The temperature contributions from insolation and snow/ice albedo are determined by fit to the temperature measurements through the past ca. 800 ka . At first, the subdivision between insolation and albedo is non-unique. In the present work, the relative contributions of albedo and CO2 are constrained by consistency between energy budget  and absorber density dependencies . In result, the effects from insolation and snow/ice albedo can be approximated by multiplying the CO2-temperature contribution of the Eocene relationship with 1.4. This factor has proven its applicability in previous computations .
The left part of Fig. 1 shows the measured temperatures (solid blue line) in comparison with the computation of the present work (dotted brown line). The measurement data are scaled to reflect a glacial-interglacial span of 4°C. The right part of Fig. 1 presents the decomposition into the CO2-temperature relationship (solid blue line) and the contributions from insolation (solid yellow line) and albedo (dotted red line). The insolation contributions of Fig. 1 are obtained from 65°N summer solstice superimposed by the global average. As a result, insolation cannot be found to significantly contribute to the gross glacial-interglacial temperature pattern. Notwithstanding, it certainly plays a major role for the cyclic reversals. As complementary note, the discussed temperature contributions relate to equilibrium states. Upon a disturbance from equilibrium, e.g. the CO2 concentration changing from a certain steady level to another, it takes in the order of ≳ 1000 years until the temperature asymptotically reaches the new equilibrium temperature .
The temperature contribution from atmospheric CO2 is considered well known from the Eocene relationship. For the present Late Quaternary, the second-next contribution originates from snow/ice albedo alteration, as rule of thumb amounting to 40% of the CO2 contribution.
2.3 Ocean heat content (OHC)
The oceans are a prominent energy store and at the same time, exhibit strong inertia to Earth energy variabilities. Thus, the ocean heat content and its time pattern strongly influence the surface temperature evolvement.
The (total global) ocean heat content (OHC) during the past 2000 years can be subdivided into four sections (Fig. 2, solid blue line) . – During the first 600 years, OHC increases almost linearly in time while temperature stays nearly constant (Fig. 2, dotted gray line ). Solar irradiance (Fig. 2, dashed red line) is in steady strong mode. – The period from years 600 to ~ 1000 is interpreted to reveal an equilibrated OHC state at about 1600 ZJ (1 ZJ = 1021 Joule). Insolation had left the stable high level. Constellations are such that surface temperature increases. – In the period 1000–1750, OHC decreases at about the same pace as it grew in the first period. Insolation variability is yet more pronounced than before. This time, temperature decreases together with OHC. – Since year 1750, OHC rises again, synchronously with temperature. Over the entire 2000-year period, OHC appears with a cyclic behavior posing a rising bias to the recent OHC development. – Since in absolute values, the slopes in the periods of years 0-600 and 1000–1750 are approximately equal, the indication may be inferred that the natural OHC trend (without anthropogenic influence) will extend to the future at the same pace, depicted with the dotted blue line in Fig. 2. During the industrial eon, ocean heat content has risen by 660 ZJ (solid blue line of Fig. 2) with the anthropogenic contribution estimated to 180 ZJ .
Most probably, natural processes bear a rising bias for the future OHC evolvement. A natural equilibrium state is interpreted existing at OHC in the order of 1600 ZJ.
2.4 Sea level
Between glacial and interglacial maxima for the preindustrial past about 400 ka, sea level has changed by roughly 100 m [4,12]. With an associated temperature span of 4°C, sea level has changed by 25 m per 1°C temperature change. During the recent glacial-to-interglacial transition, the pace reached the order of 1.3 m/century . These relationships are highly non-linear, particularly when approaching the turning conditions of the glacial and interglacial maxima. At present, temperature and sea level have attained levels characteristic for an interglacial maximum, the sea level rise revealed at about 0.2 m/century for the recent 9 ka  – just what has been experienced to date during the industrial eon.