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

Previous studies have reported that human influences are required to explain the observed global warming using a linear model (LM) Δ T = λ L M Δ F that relates change in solar forcing Δ F to change in global mean temperature (GMT) Δ T . This model has the shortcoming of assuming a given Δ F causes the same Δ T irrespective of the value of the initial global warming rate( d T / d y ) i . Analysis of the GMT data showed that this warming rate has been increasing linearly since steady state ( ( d T / d y ) o = 0 for year y o = 1864.5 ) as given by d T / d y = ( d T / d y ) i + a T ( y − y i ) , where a T = 7.1954 × 1 0 − 5°C/year 2 is the secular GMT acceleration and y − y i 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/ m 2 (0.08% of Total Solar Irradiance) was expressed as Δ F = 0.18 × 0.19 ( y − y i ) / 11 . Defining the climate sensitivity as λ = Δ ( d T / d y ) / Δ F = a T / ( 0.18 × 0.19 / 11 ) = 0.023143 °C/year per W/ m 2 removed the shortcoming of the LM and integration of the model for d T / d y above and then simplifying gave a secular GMT‐solar forcing model given by Δ T = ( d T / d y ) i ( y − y i ) + ( λ 2 / ( 2 a T ) )( Δ F ) 2 that explained all of the observed global warming and increase in atmosphericC O 2 , 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.