You want numbers? Good. Let’s use them.
Climate averages are typically defined over 30 years by the WMO. That’s long enough to smooth ENSO, volcanic noise, and short term variability. You can use 50 or 100 years; the warming trend still shows up.
Energy imbalance? Yes. Measured at roughly +0.5 to +1.0 W/m2 over recent decades. That’s satellite TOA radiation data plus ocean heat uptake. Multiply that by Earth’s surface area (5.1×10¹⁴ m²) and you get on the order of 10²² joules per year accumulating in the system. Over 90% of that is going into the oceans. That’s directly measured via Argo floats.
Newton’s 2nd Law: F = ma applies to mechanical acceleration of mass. Climate change is primarily governed by radiative transfer and thermodynamics. The relevant framework is: ΔE = Ein − Eout. If outgoing infrared is reduced by greenhouse gases, you get a positive energy imbalance. No mechanical push required; radiative flux differences are energy transfer. Photons carry momentum, yes, but the governing equations are from radiative physics, not rigid-body mechanics.
“If energy is moving, there must be a force” is not correct in the way you’re applying it. Heat flow is driven by temperature gradients. Radiative transfer is governed by the SB law and absorption spectra, not Newtonian acceleration of a bulk mass.
Weather is the instantaneous state. Climate is the statistical distribution of those states. When the distribution shifts, weather events shift accordingly.
You asked for equations and numbers. The numbers are measured. The equations are standard thermodynamics. The energy accumulation is observed. The only question left is whether you accept measurements that don’t fit your prior mode
I'm fine if you want to use 30 year averages ... just be advised that the
NOAA temperature trace gives periods of global cooling between 1880 and 1910, warming between 1910 and 1940, then cooling again during WWII and the rebuilding afterward, then our current period of warming ... that would stand as a counter-example to the theory CO
2 is the dominating factor ... seems you're not smoothing short term variability very well ... I'm not arguing against global warming, I'm against this notion of climate change that seems to be invisible to all except the cool people ...
I'm with you at 10^22 joules ... but why did you stop? ... did you divide by the number of grams in the ocean ... 10^27 in case you're curious ... 100,000 years for 1ºC warming ...
Basic physics says it's the electromagnetic force that's responsible for electromagnetic radiation ... this isn't a casual mistake ... more of a sign of partial understanding ... the watt unit is defined as a newton meter per second ... newton is the unit of force, either gravity or electromagnetic ... zero force means zero watts, pretty cool eh? ... basic physics teaches the interrelationship between all these values ... force, power, energy, work ... something you apparently are missing somehow ...
SB Law is derived from Planck and not Newton, "irradiation is proportional to temperature raised to the fourth power" ... have you ever used it? ... I used your 1.0 W/m^2 radiative forcing value and only got a 0.2ºC increase ... [yawn] ... if that's your governing equation, then all your climate change is invisible ... because 0.2º doesn't change weather, so it doesn't change average weather, so it doesn't change climate ...
You're moving energy around with electromagnetic radiation without involving the electromagnetic force ... really? ...