ClimatExam   Scientific analyses of the climate change and global warming by Dr. Antero Ollila

The climate sensitivity (CS) according absorption and longwave radiation changes

The author has also calculated the CS and lambda (L) values applying two simulation tools available in the network, namely Modtran (Berk et al., 2013) and the Spectral Calculator (Gats, 2014). The results are collected in Table 1. The all-sky conditions have been calculated by combining the clear and cloudy sky values (Bellouin et al., 2003; Ollila, 2013b):

(1-CL/100) * Fclear + (CL/100) * Fcloudy = Fall-sky         (7)

Where F is a radiation flux of a sky in question and CL is a cloudiness-%. Also temperatures of different skies are combined according to this equation.

The  average global atmosphere’s (AGA) surface temperature is 15 °C, and the concentrations of the anthropogenic GH gases measured in 2005 (AGA 2005) or in 2012 (AGA 2012) have been used. The GH gas concentrations (2005/2012) are: CO2 (379/393 ppm), CH4 (1.774/1.866 ppm), and N2O (0.319/0.324 ppm), as reported by IPCC (2007c, 2013). The graphs in Fig. 1 are based on the AGA 2005 gas concentrations are based on the AGA 2012 conditions. The parameters and choices applied in Modtran simulations, are depicted in Table 2.

The CS and L calculations are carried out to an altitude of 70 km. In these calculations, a few iterations are needed in both calculation tools in order to find the surface temperature, which compensates the increased absorption caused by a CO2 increase to 560 ppm, bringing the OLR flux exactly to the same the OLR flux caused by a CO2 concentration of 280 ppm. Because both the OLR change and the temperature change are calculated at the same time, the L value can be easily calculated. The cloudy sky values are calculated using the Modtran simulations, which show about 30 % lower OLR change than the clear sky simulations. This relationship has been used in estimating the cloudy sky values of Spectral Calculator simulations. IPCC’s report AR5 (2013) summarizes that according to several studies, the overall reduction of RF values in cloudy sky conditions is in average 25 % lower than the clear sky values.  The results of the simulations carried out by Modtran and Spectral Calculator are summarized in Table 2.

The change of CO2 concentration from 280 ppm to 560 ppm would increase the total absorption of shortwave (SW) radiation by 0.40 Wm-2 according to the 1D model simulations. This change alone would mean an essential warming impact, but the situation is not straightforward, because this absorption directly decreases the SW radiation reaching the surface.

Myhre et al. (1998) have concluded that the absorption of solar radiation in the troposphere yields a positive RF at the tropopause and a negative RF in the stratosphere contributing to a net cooling effect of CO2 absorption of -0.06 Wm-2 for the concentration change from 280 ppm to 381 ppm. On these bases the author has not included the solar radiation absorption changes of CO2 into his calculations. The net effect of solar radiation absorption would slightly decrease the RF values of CO2 according to the analyses of Myhre et al. (1998).

The clear sky OLR change 2.69 Wm-2 calculated by Spectral Calculator at the TOA is the sum of transmittance flux change 1.12 Wm-2 and the radiance flux change 1.57 Wm-2. The OLR changes and the warming values of different CO2 concentrations are summarized in Table 4.  The global warming caused by the CO2 concentration increase from 280 ppm to 393 ppm calculated through OLR change is 0.24 °C without water feedback.

The logarithmic fitting gives the following equation between RF values and CO2 concentrations:

RF = 3.12 * ln(C/280),                        (8)

Where RF is the radiative forcing in Wm-2, C is the CO2 concentration in ppm.

table 4. the radiative forcing and warming values of different co2 concentrations (reference level 280 ppm). the clear sky values are calculated by spectral calculator and cloudy skies by Modtran.

Analyses of different CS results

Using Spectral Calculator simulation, a CO2 concentration of 393 ppm gives the  L value 0.230 and 1,370 ppm gives the L value 0.269. According to several studies (Zhang et al., 2004; Bodas-Salcedo et al., 2008; Loeb et al., 2009), the OLR flux varies between 233-240 Wm2 and using Eq. (3) shows that RF value 233 Wm-2 gives L value 0.270, and RF value 240 Wm-2 gives L value 0.265. The variation of l is relatively small but l is not invariant. The L values vary in totality from 0.230 to 0.319 in simulations. If Eq. (3) is applied for OLR changes calculated by the dRF 2.16 Wm-2 of Spectral Calculator, the ECS is 0.576 °C and L is 0.267. The same values using the dRF=1.834 Wm-2 of Modtran, the ECS is 0.49 °C and L is 0.267. The Modtran calculations’ results are not as accurate and reliable as the Spectral Calculator results, because the atmospheric conditions of Modtran cannot be specified with the same accuracy as in Spectral Calculator.

The author has also calculated the ECS value utilizing the IR absorption in the clear atmosphere; this value is 0.46 °C. Some other researchers (Miskolczi and Mlynczak, 2004) have calculated almost the same value, namely 0.48 °C. The most reliable results and best estimates are the values calculated by energy balance equations: ECS = 0.576 °C and
L = 0.268 K/(Wm-2) with the uncertainty ranges of 0.46–0.6 °C and 0.23–0.32 K/(Wm-2).

Some researchers have paid attention to the fact that the temperatures simulated by General Circulation Models (GCM) have departed from the real temperatures since 1998. There are several new research studies, which show lower ECS values than those of IPCC. According to these results, the best estimates and minimum values for ECS are: (Aldrin, 2012) 2.0 °C / 1.1°C; (Bengtson & Schwartz, 2012) 2.0 °C / 1.15 °C; (Otto et al., 2013) 2.0 °C / 1.2 °C and (Lewis, 2012) 1.6 °C / 1.2 °C.  Common features of these studies are mathematical methods like Bayes’s theorem to analyze the impact of CO2 based on the measured global data of radiative forcing factors, temperatures and ocean heat content.

These studies’ minimum values of ECS are practically same in the range 1.1-1.2 °C. Bengtson & Schwartz (2012) draw a conclusion that this value is the same as the no-feedback Planck sensitivity. An interesting point is that the ECS value of this study without any feedback mechanisms (including the Planck sensitivity calculation which is the same as equation (3)) is in the range 0.559…0.584 °C, and with water feedback the ECS according to the Plank’s equation is 1.1 °C. Is this a coincidence? There could be a very simple explanation. All the referred studies use the radiative forcing value of 3.7 Wm-2 for CO2 and they do not mention, whether or not water feedback has been used in their analyses.

The author’s conclusion is that the researchers of these studies have applied the RF value of 3.7 Wm-2 as in the study of Bengtson & Schwartz (2012). If this RF value has been calculated in the atmosphere, where is constant relative humidity, it would mean that it includes the positive water feedback duplicating the warming values.