FIGURE 1: MAUNA LOA CO2 CONCENTRATION PPM FOR EACH CALENDAR MONTH

FIGURE 2: THE ATMOSPHERIC CO2 SEASONAL CYCLE 1959-2017

FIGURE 3: AMPLITUDE OF THE SEASONAL CYCLE IN GTC

FIGURE 4: SEASONAL CYCLE IN CO2 RADIATIVE FORCING 2000-2010 (FELDMAN 2015)

FIGURE 5: SEASONAL CYCLE IN THE RATE OF WARMING 1979-2017

FIGURE 6: WARMING TREND AND RADIATIVE FORCING SEASONAL CYCLES COMPARED

FIGURE 6A: SEASONAL CYCLES 1960-2018

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1. It is well known and well understood in terms of the theory of anthropogenic climate change that atmospheric CO2 concentration data from Mauna Loa 1959-2017 show a strong upward trend as seen in Figure 1 where all twelve calendar months are plotted. In Figure 1, the source data are shown on the left and the detrended series appear on the right. The differences among the calendar months is difficult to see in the source data due to the large range of values but they are somewhat clearer in the detrended series.
2. The seasonal cycles and their amplitudes for each calendar month are shown separately in Figure 2 and Figure 3. Here we see that atmospheric CO2 concentrations tend to be highest in late spring and early summer (April, May and June) where it is about 3 ppm above average and lowest in early autumn (September and October) where it is about 3 ppm below average. The amplitude for each year is computed as the difference between the May/June average and the Sep/Oct average in each year. It is shown in Figure 3 converted to gigatonnes of carbon equivalent (GTC) computed as GTC = 2.14*ppm. The amplitude is very volatile and an overall trend is apparent. It appears to be increasing over time.
3. It is postulated (Feldman 2015) that the observed seasonal differences are driven by the large swings in photosynthesis between the boreal spring and summer (when photosynthesis is active), and the boreal fall and winter (when photosynthesis is not active). This cycle does not exist in the Tropics and it is exactly reversed in the Southern Hemisphere, but it is argued that the preponderance of of boreal land mass and forests forces the atmospheric CO2 cycle. If that is the case, the upward trend seen in the amplitude of the seasonal cycle may imply increasing photosynthesis activity over the span of the data.The validity of the boreal forest driven photosynthesis cycle is found in the seasonal cycle in GHG forcing reported by Feldman et al 2015 shown in Figure 4 but not seen in the CO2 cycle in Figure 3.
4. The CO2 data do not show a pattern consistent with changes driven by seasonal differences in boreal photosynthesis. In the seasonal cycle of atmospheric CO2 concentration we find the highest levels in the Northern late spring and summer when boreal photosynthesis is most active and the lowest levels in September and October when boreal photosynthesis is not active. (Figure 2).
5. Feldman, Daniel R., et al. “Observational determination of surface radiative forcing by CO 2 from 2000 to 2010.” Nature519.7543 (2015): 339. The climatic impact of CO₂ and other greenhouse gases is usually quantified in terms of radiative forcing¹, calculated as the difference between estimates of the Earth’s radiation field from pre-industrial and present-day concentrations of these gases. Radiative transfer models calculate that the increase in CO₂ since 1750 corresponds to a global annual-mean radiative forcing at the tropopause of 1.82 ± 0.19 W m⁻²(ref. 2). However, despite widespread scientific discussion and modelling of the climate impacts of well-mixed greenhouse gases, there is little direct observational evidence of the radiative impact of increasing atmospheric CO₂. Here we present observationally based evidence of clear-sky CO₂ surface radiative forcing that is directly attributable to the increase, between 2000 and 2010, of 22 parts per million atmospheric CO₂. The time series of this forcing at the two locations—the Southern Great Plains and the North Slope of Alaska (SGP & NSA) —are derived from Atmospheric Emitted Radiance Interferometer spectra³together with ancillary measurements and thoroughly corroborated radiative transfer calculations⁴. The time series both show statistically significant trends of 0.2 W m⁻² per decade (with respective uncertainties of ±0.06 W m⁻² per decade and ±0.07 W m⁻² per decade) and have seasonal ranges of 0.1–0.2 W m⁻². This is approximately ten per cent of the trend in downwelling longwave radiation^5,6,7. These results confirm theoretical predictions of the atmospheric greenhouse effect due to anthropogenic emissions, and provide empirical evidence of how rising CO₂ levels, mediated by temporal variations due to photosynthesis and respiration, are affecting the surface energy balance.
6. The essence of the paper is that rising GHG forcing as measured with spectral analysis explains and confirms human caused global warming  by way of fossil fuel emissions. In this regard, the authors state that “Increasing atmospheric CO2 concentrations between 2000 and 2010 have led to increases in clear-sky surface radiative forcing of over 0.2Wm2 at mid- and high-latitudes. Fossil fuel emissions and fires contributed substantially to the observed increase”. With respect to the seasonal cycle in GHG forcing, Feldman et al find that the time series of measured CO2 surface forcing shows clear and increasing trends in radiative surface forcing and seasonal variability. The least-squares trend in the long-term forcing is 0.260.06Wm22 per decade and differs significantly (P,0.003) from zero. The seasonal amplitude of the forcing is 0.1–0.2Wm22, closely tracking the independently assessed pattern in the average CO2 concentration”.
7. Figure 4 above is a reproduction of Figure 4 in the Feldman 2015 paper (page 342). It shows the seasonal cycle in GHG forcing derived from the seasonal cycle in atmospheric CO2 concentration shown in Figure 2. The acronyms SGP (Southern Great Plains) and NSA (North Slope of Alaska) refer to the two sites where the spectral measurements were made. The implication of the Feldman 2015 findings in the context of this work is that the warming trends seen in the calendar months should be unequal and the pattern of these warming trends should be consistent with the differences in GHG forcing. In particular we should find that the rate of warming is highest in May and June and lowest in September and October.
8. The inequality of warming trends in the calendar months is confirmed in Figure 5 which shows warming trends by calendar month for CMIP5 projections in the RCP8.5 business as usual scenario computed from theoretical forcings as well as for four observational data series in the satellite era 1979-2018 for the early calendar months and 1979-2017 for the later calendar months. For each data series, the minimum trend is highlighted in yellow and the maximum is highlighted in red.
9. Figure 6 compares the shapes of the seasonal cycle in warming trends in five different temperature series in the period 1979-2017 (IN RED) with the average radiative forcing seasonal cycle for 1979-2017 computed as the natural logarithm of mean atmospheric CO2 concentration (IN WHITE). The comparison does not show that the observational temperature data are consistent with seasonal cycle in GHG radiative forcing. Surprisingly, not even the theoretical RCP8.5 projections show the expected seasonal cycle in warming rates.
10. Figure 6A compares the shapes of the seasonal cycle for CO2 for each year from 1960 to 2018. No consistent pattern is seen in the shapes of these curves that would indicate that they are driven by seasonal changes in temperature or by photosynthesis. It is likely that other variables may play a part in particular, geological sources and seasonal changes in anthropogenic emissions.
11. From the shape of the seasonal cycle in atmospheric CO2 it is tempting to suggest that it is a Henry’s Law cycle of CO2 exchange between atmosphere and ocean with high atmosCO2 in summer and low atmosCO2 in winter. Yet that is not the case exactly. The high level in the seasonal cycle occurs in late boreal spring and early boreal summer and declines into boreal midsummer. The low level is found in September and October and it rises in the boreal winter above the September low. The relevant consideration is that at the global level, as an average of the two hemispheres, there is no seasonal cycle in temperature.
12. We conclude from the above that the data are not consistent with the observed seasonal cycle in CO2 radiative forcing reported in Feldman 2015.

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