Oh God Why: Day Three: IT'S LOOOOOOSE (18/30)

It's a group of multiple equations, taken with the differential every hour. The first equation is the Stephan-Boltzmann Law, where the blackbody irradiance is equal to σT⁴ W/m². The second part is the capacity of the atmosphere for heat, found by the pressure of the air (10332.3 kg/m²) times its specific heat (1006 J/gK) plus the albedo for greenhouse gas (55% times the first value). These two are divided to get temperature change per second (all units cancel out, leaving KW/J = K/s). This is multiplied by 3600 to get the loss per hour. The equation for daily temperature was found in this study by Satterlund et al., using the coastal April values. The official formulae that I use in my spreadsheet are below the spoiler:

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SpoilerColumn A: Time since start of night (hours)
Formula: A_n=A_n-1+1

Column B: Mean Temperature (Kelvin)
Formula: B_n=B_n-1-3600*E_n-1

Column C: Output Irradiance (Watts per meter squared)
Formula: C_n=(273.15+L_n)⁴*5.6704*10^-8

Column D: Heat Capacity (Kilojoules per Kelvin Meter Squared)
Formula: D_n=10332.3*1006+550*C_n

Column E: Temperature Differential (Kelvin per second)
Formula: E_n=C_n / D_n

Column F: Mean Temperature in Fahrenheit
Formula: F_n=1.8*(G_n+40)-40

Column G: Mean Temperature in Celsius
Formula: G_n=B_n-273.15

Column H: Valid Forecast Date
Column I: Valid Forecast Hour

Column J: Displacement from Maximum (Hours)
Formula: J_n=(I_n+19.3)%24-12

Column K: Current Temperature in Fahrenheit
Formula: K_n=(F_n-B_n/18)+(B_n/9)*(e^{If J_n>0: -.72, -.2;*J_n}*(1+J_n/14.7)^{If J_n>0: .72*14.7, .2*14.7;})
Excel® Formula {for cell K3}: =(F3-B3/18)+B3/9*(EXP(IF(J3>0,-0.72,-0.2)*J3)*(1+J3/14.7)^IF(J3>0,0.72*14.7,0.2*14.7))

Column L: Current Temperature in Celsius
Formula: L_n=5/9*(K_n+40)-40

Now, you might be asking why I am putting so much effort into this instead of the mafia game. Well, a mafia game has days and nights, so I'd put more in if we had one.

Also, with the corrections from when I last said, tonight's (18-19 Apr) low is expected to be -17.4°C (.6°F). Tomorrow's high should be around -3.9°C (25.0°F).

YOUR FIVE-DAY FORECAST, ASSUMING NIGHT DOESN'T END

Code:

DAY        HIGH      LOW
18 APR:      X      -17.4
19 APR:    -3.9     -19.6
20 APR:    -6.3     -21.7
21 APR:    -8.4     -23.7
22 APR:    -10.5    -25.7
23 APR:    -12.5    -27.6