Deducing Geothermal

I used to be a fan of Joseph Postma before I realized he’s very stubborn and on the wrong track headed for a dead end. I hope he turns around.

I highly recommend that everyone read his great series … The Fraud of the Greenhouse Effect (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19). You will learn a lot!

Today I will be critiquing Joseph Postma’s paper A Discussion on the Absence of a Measurable Greenhouse Effect in light of what I know about his current view. I take no issue with his central proposition that there is no Greenhouse Effect, but I do take issue with his current personal conclusion that the sun, and the sun alone, is enough to explain the surface temperature. His latent heat doesn’t occur until there’s energy to evaporate water first, and the only energy he has is from the sun. My goal is to show that in fact the sun is not enough, and Postma’s implicit hypothesis is in error, though his paper is still very good and highly recommended reading.

We will use some basic data from NASA:

Solar irradiance (W/m2): 1361

Bond albedo: 0.306

Average temperature: 15°C

Diurnal temperature range: 10°C to 20°C

— NASA’s Earth Fact Sheet

See code in the addendum. To run first part of analysis:

> source gmodel.sh && require && download && justsun

Sphere     ... Hard Way: 236.1329 W/m^2 , Easy Way: 236.1335 W/m^2
Hemisphere ... Hard Way: 472.2659 W/m^2 , Easy Way: 472.2659 W/m^2

The hard way performs the actual integration (approximation), while easy way just uses divisor (1/2 for sphere and 1/4 for hemisphere). The hard way is needed to create data of average of insolation across all latitudes as a function of local time. An average location on Earth will see this kind of daily insolation, averaged for the year. Keep in mind that this is an average value for a typical year and therefore my code purposefully disregards the math for Earth’s tilt and resulting seasonal daylight variation. It’s just not necessary. Resulting graph:

Global Average Insolation, using standard Albedo of ~0.3

It should be noted that we can’t use the standard albedo of ~0.3, because this albedo is an average for the entire surface+atmosphere ensemble. We need to know the actual portion of solar radiation that reaches the surface. This is different from the official standard albedo.

> absorbs
Surface Absorption: 0.4874

Flux data from NASA’s ISCCP Project (1983-2004 data here), yields a surface absorption of 0.4874, while NASA’s “official” energy budget [2008] shows: 163.3 / 340.3 = 0.4799. I am just going to choose an “albedo” of 0.52 (1-0.4799). We re-run with an ALB parameter set to 0.52:

> ALB=0.52 justsun
Sphere     ... Hard Way: 163.3196 W/m^2 , Easy Way: 163.3200 W/m^2
Hemisphere ... Hard Way: 326.6392 W/m^2 , Easy Way: 326.6392 W/m^2

Daily Insolation @ Surface for Average Location, Annually Averaged

Now we’re ready to move on to serious analysis. Postma has provided the only formula we will need:

Equation 11 (Page 13)

where C(t) is literally a climate term which could be either positive or negative (adding heat or taking heat away) in total, or composed of several unique contributions depending on if there is an additional heat source such as the “greenhouse effect”, or chemical and geologic sources, etc.

— A.d.o.t.A.o.a.M.G.E, Page 13

“emis = 1.0; % emissivity, using 1.0 for surface” [ I will use the same ]

— Same, Page 63

The following code snippets (see addendum) summarize this formula (emis = 1):

$1+ADD                          # As in Current Flux += ADD  # ADD = C(t)
T = T + ($1 - SIG*T^4)/TAU      # As in Tnew = Told + (Current Flux - SIG*Told^4)/TAU

We must choose a value for τ (TAU) that will produce a diurnal difference of 10°K (or °C) as shown in NASA’s Earth Fact Sheet above. The needed TAU equals 12940.

> TAU=12940; ADD=0; manydays; lastday

24HR  Sun ... 163.32 W/m2	
Day   Sun ... 326.64 W/m2	
Day   Max ... 236.64 K    -36.52 C	
Night Min ... 226.64 K    -46.52 C	
Max - Min ...  10.00 K     10.00 C	
24HR  Avg ... 231.59 K    -41.57 C	
24HR Flux ... 163.10 W/m2

We start off at T=0, and after 40 days we get to a stable typical day:

Note the result: Max – Min … 10.00 K. We have satisfied one of the criteria, but notice that our 24HR average is : –41.57°C. That’s not the 15°C we need. Obviously the sun is not enough! And the diurnal temperature does not go from a night average of -46.5°C to a day average of -36.5°C. We must satisfy all 4 temperature criteria in NASA’s Fact Sheet shown above, not just 1.

Postma spends a part of the paper analyzing a “C(t)” value of 324 W/m² (what is claimed for GHG backradiation) along with arbitrary (though intelligently guessed) τ values. He then dismisses the results for fairly good reasons. However he missed the crucial point: the sun is not enough. I’m going to show you what values he should have used. I have a parameter in my program (ADD) that is equivalent to C(t). I have found the necessary parameters to be TAU=12895, ADD=227.66. ADD is what I believe to be the radiative component of geothermal.

> TAU=12895; ADD=227.66; manydays; lastday

24HR  Sun ... 390.98 W/m2	
Day   Sun ... 781.96 W/m2	
Day   Max ... 293.21 K     20.05 C	
Night Min ... 283.21 K     10.05 C	
Max - Min ...  10.00 K     10.00 C
24HR  Avg ... 288.11 K     14.95 C	
24HR Flux ... 390.67 W/m2	

Geothermal (Green) + Solar (Yellow)

Geothermal (Green) + Solar (Yellow)

Notice that we satisfied all criteria set forth in NASA’s Earth Fact Sheet (with only 0.05°C error):

Day Max … 20.05 C
Night Min … 10.05 C
Max – Min … 10.00 K
24HR Avg … 14.95 C

But we’re not done. ADD is just the radiative component of geothermal. Let’s add Sensible and Latent Heat from NASA’s “official” energy budget [2008]:

227.66 + 18.4 + 86.4 = 332.46 W/m²

This result is not much different than the 335.64 W/m² result I got here: Measuring Geothermal, using NCEP Reanalysis data.

332.46 vs 335.64 ! What’s the significance of this? I was able to approximately get the same geothermal emergent radiative flux from a very simple model! I don’t know about you, but I’m impressed.

How about Postma? Where’s his mind today?

Yah…that’s definitely my Zoe…one of my most attractive stalkers for sure [Zoe: How sweet, TY] . She thinks that the flat Earth theory model is all totally fine [Zoe: strawman; no one presents an actual flat earth model, including those that print maps on flat paper rather than globes]…but backradiation isn’t from the atmosphere “because that’s impossible, but it is from geothermal.”

So…she wants to keep the flat Earth theory [Zoe: Two hemisphere 24hr heat capacity theory, actually] accounting where the Sun can’t heat the Earth or create and sustain the weather/climate, and where there’s some additional energy source which provides twice more energy than the Sun…but instead of it being “backradiation” she wants it to be geothermal….providing twice the energy than the Sun. She went on about this here for months…finally banned her…because the heat from geothermal is known and measured…and flat Earth theory would be the WRONG way to try to incorporate it anyway!

These people are sick, sick demented freaks, and they seem to really want to keep their flat Earth theory no matter what mechanisms need to change to make it work.

— Joseph Postma

Stalker means you are criticizing a public scientist for their ideas. I agree with him that there is no Greenhouse Effect, but he goes too far – way too far. As you can see he still thinks the sun, and the sun alone, is enough to explain surface temperatures and their diurnal variation – and everyone who disagrees is a flat earther!

One thing from his publication I found very interesting:

Solar forcing acts directly only on the top few millimeters of surface soil itself (the penetration depth is larger for ocean water and some heating occurs directly in the atmosphere via extinction), and this is where the incoming short wave radiant energy performs work and raises the temperature. This heat energy will then conduct its way down into the subsurface until it merges with the geothermal temperature at a depth of somewhere around, say, 5 to 10 meters and temperature of approximately 5°C to 10°C [Zoe: I found 0 to 10] … and this much larger thermal-mass system will respond much more slowly, in aggregate, to the solar variation. This low-frequency [Zoe: Goes to nil frequency] aggregate response will provide a baseline upon which the daily variations will oscillate at the top …

— A.d.o.t.A.o.a.M.G.E, Page 16

A baseline you say? Maybe this baseline would exist without the sun? Maybe this baseline is capable of its own thermal action and emission? Too bad he did not pursuit this line of thought. But thanks for reaffirming my intuition at the time.

I hope you’ve enjoyed this article.

Love, -Zoe

Update

Guys I just had several dozen notifications come through of Zoe trying to link to my blog from what is apparently her new blog.

WHAT A FN STALKER! [Zoe: You made yourself a public scientist so stop playing the victim]

“Zoe’s geothermal insights” or some retardation.

“Flat Earth is OK! [Zoe: usual strawman]. We just need to use geothermal to make up the temperature instead!”

Basic bitch. [Zoe: How lovely]

— Joseph E Postma says:2020/02/25 at 8:24 AM

Nice! Joseph, your solar-only theory can’t explain observations. It would be great if you could rejoin reality and continue to make contributions to science, as you did in the past.

Addendum

Code gmodel.sh:

# source gmodel.sh
# Zoe Phin, 2020/02/20

plothead="set term png size 740,550 font 'arial,12'; unset key
	set xtics 360 out nomirror; set mxtics 6; set grid xtics ytics
	set xtics add ('0h' 0,'6h' 360,'12h' 720,'18h' 1080,'24h' 1440)
	set yrange [0 to 800]; set ytics 100,100,800
"

require() { sudo apt-get install gnuplot; }

download() {
	wget -O sdn.bin -c https://isccp.giss.nasa.gov/pub/data/FC/FDAVGANN__SWFLSRFDW
	wget -O sup.bin -c https://isccp.giss.nasa.gov/pub/data/FC/FDAVGANN__SWFLSRFUW
}

absorbs() {
	od='od -An -f -w4 --endian=big'; $od sup.bin > .sup; $od sdn.bin > .sdn
	paste .sdn .sup | awk '{S+=$1-$2} END { 
		printf "Surface Absorption: %.4f\n", (S/NR)/(1361/4) }'
}

justsun() {
	[ -z $ALB ] && ALB=0.306
	seq -89.875 0.25 89.875 | awk -vA=$ALB 'BEGIN {pi = atan2(0,-1); r=pi/180} {
		CONVFMT="%.8f"; if ($1 < 0) $1 = 0 - $1
		a = sin(r*($1+0.125))-sin(r*($1-0.125))
		for (m=0; m<1440; m++) {
			y = cos((m-720)*pi/720)
			print m" "$1" "a/2" "1361*(1-A)*cos($1*pi/180)*((y<0)?0:y)
		}
	}' | awk '{ M[$1]+=$3*$4 } END {
		for (i in M) print M[i]
	}' | tee solar.dat | awk -vA=$ALB '$1>0 { S+=$1 } END { CONVFMT="%.4f"
		HW = S/720; EW = 1361*(1-A)/2
		print "Sphere     ... Hard Way: " HW/2 " W/m^2 , Easy Way: " EW/2 " W/m^2"
		print "Hemisphere ... Hard Way: " HW   " W/m^2 , Easy Way: " HW   " W/m^2" }'

	echo "$plothead set title 'Solar Flux (W/m²)'
	plot 'solar.dat' u (\$1==0?-1:\$1) w filledcu above fc 'yellow',\\
	     513.085*cos((x-720)*pi/720) w lines lc rgb 'orange' lt 8 lw 3
#	     741.835*cos((x-720)*pi/720) w lines lc rgb 'orange' lt 8 lw 3
	" | gnuplot > justsun.png
}

manydays() {
	[ -z $ADD ] && ADD=0; [ -z $DAYS ] && DAYS=15
	for n in `seq $DAYS`; do cat solar.dat | awk -vADD=$ADD '{ 
		printf "%7.3f\n", $1+ADD }'
	done | awk -vTAU=$TAU 'BEGIN { SIG=5.67e-8 } { 
		T=T+($1-SIG*T^4)/TAU
		printf "%10.6f %10.6f %10.6f\n", $0, T, SIG*T^4
	}' > many.dat

	echo "$plothead set key samplen 0; set title '$DAYS Days of Flux (W/m²)'
	set xtics format ''; set xtics 1440 in mirror; unset mxtics
	plot 'many.dat' u (\$1==0?-1:\$1) title '' w filledcurves above y=$ADD fc 'yellow',\\
	$ADD t '' w filledcu above y=0 fc 'dark-green' fs solid 0.8 border lt 2 lw 4,\\
	'' u 3 t 'τ = $TAU' w lines lw 2 lc 8" | gnuplot > many-t${TAU}.png
}

lastday() {
        tail -n 1440 many.dat | nl | tee last.dat | awk 'BEGIN { MIN=999 }
                   $3 > MAX { MAX=$3 }
                   $3 < MIN { MIN=$3 }
                        $2>0 { S+=$2 }
        NR >360 && NR <=1080 { D+=$3 }
        NR<=360 || NR > 1080 { N+=$3 }
        END { SIG=5.67e-8; D24 = (D+N)/1440; C=273.16
                printf "24HR  Sun ... %6.2f W/m2        \n", S/1440
                printf "Day   Sun ... %6.2f W/m2        \n", S/720
                printf "Day   Max ... %6.2f K %9.2f C   \n", MAX, MAX-C
                printf "Night Min ... %6.2f K %9.2f C   \n", MIN, MIN-C
                printf "Max - Min ... %6.2f K %9.2f C   \n", MAX-MIN, MAX-MIN
#               printf "Day   Avg ... %6.2f K %9.2f C   \n", D/720, D/720-C
#               printf "Night Avg ... %6.2f K %9.2f C   \n", N/720, N/720-C
#               printf "D-N Delta ... %6.2f K           \n", (D-N)/720
                printf "24HR  Avg ... %6.2f K %9.2f C   \n", D24, D24-C
                printf "24HR Flux ... %6.2f W/m2        \n", SIG*D24^4
        }'

        echo "$plothead set key samplen 0
        set ylabel 'Flux (W/m²)'; set y2label 'Temperature (K)'
        set ytics out 50 nomirror; set mytics 5; 
        set y2tics 210,10,800; set my2tics 2
        set link y2 via (y/5.67e-8)**0.25 inverse 5.67e-8*(y**4)

        plot $ADD t '' w filledcu above y=0 fc 'dark-green' fs solid 0.8 border lt 2 lw 4,\\
        'last.dat' u 1:2 t '' w filledcu above y=$ADD+1 fc 'yellow' fs solid 1 border lt 5 lw 4,\\
        '' u 1:3 t 'Surface T (τ=$TAU)' w lines lw 3 lc 8 axes x1y2" | gnuplot > last.png
}