Determination of the Sun‐Climate Relationship Using Empirical Mathematical Models for Climate Data Sets

Abstract

Abstract Previous studies have reported that human influences are required to explain the observed global warming using a linear model (LM) ΔT=λLMΔF that relates change in solar forcing ΔF to change in global mean temperature (GMT) ΔT. This model has the shortcoming of assuming a given ΔF causes the same ΔT irrespective of the value of the initial global warming rate (dT/dy)i. Analysis of the GMT data showed that this warming rate has been increasing linearly since steady state ((dT/dy)o=0 for year yo=1864.5) as given by dT/dy=(dT/dy)i+aT(y−yi), where aT=7.1954×10−5 °C/year2 is the secular GMT acceleration and y−yi is the number of years of the change. The secular solar forcing due to 18% of the 11 yr solar cycle forcing of 0.19 W/m2 (0.08% of Total Solar Irradiance) was expressed as ΔF=0.18×0.19(y−yi)/11. Defining the climate sensitivity as λ=Δ(dT/dy)/ΔF=aT/(0.18×0.19/11)=0.023143 °C/year per W/m2 removed the shortcoming of the LM and integration of the model for dT/dy above and then simplifying gave a secular GMT‐solar forcing model given by ΔT=(dT/dy)i(y−yi)+(λ2/(2aT))(ΔF)2 that explained all of the observed global warming and increase in atmospheric CO2, sea level and ocean heat content. Therefore, for this nonlinear empirical model, invoking human influences to explain climate change was not required. The annual GMT model predicts a pause in global warming until 2040.

Keywords

• global mean temperature
• empirical mathematical modeling
• atmospheric CO2
• sea level
• ocean heat content
• solar forcing