I'm using mathematical notation as it is succinct ... it's still basic physics ... it's a shame you don't seem to understand what the notation means ... basic physics includes the difference between average and instantaneous ... we all know what average is, and that involves a time period ... I ask again ... what value do you give time period for your averages? ...
I'm asking for a demonstration ... you keep begging off like these nothing to demonstrate ... what about global mean temperature, ocean heat content, ice masses ... how does this change weather? ... or do you completely divorce the two subjects? ...
Of course Newton's 2nd Law applies ... basic physics ... it takes a one newton force to accelerate a one kilogram mass by one meter per second ... and we say this force perform one joule of work ... and that the object accelerated has gained a joule of kinetic energy ... or show me a different equation to use ...
If energy is moving ... there has to be a force ... no exceptions ...
... incoming solar minus outgoing infrared equals energy accumulation ...
Do you have a numerical value for this? ... you seem allergic to numbers ... and equations ... basic physics requires basic math ...
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
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