Zenith angle treatment in the biog/hrbeis*

[cjcoats]

The original (late-1980's) biogenics code had a computation of the form:

Compute COSZEN = cos( zenith angle ) in terms of latitude, longitude,
and time

Compute ZEN = arccos( COSZEN )

Compute vertical attenuation VATTEN in terms of ambient conditions

Attenuation ATTEN = VATTEN / COS( ZEN )

The PhD mathematician who wrote the original SMOKE noticed this,
together with the fact that unneccessary cos( arccos ( COSZEN ) )
adds only extra round-off error, extra computational cost, and some
degree of obscurity. He simplified this code to:

Compute COSZEN = cos( zenith angle ) in terms of latitude, longitude,
and time

Compute vertical attenuation VATTEN in terms of ambient conditions

Attenuation ATTEN = VATTEN / COSZEN

In all of the current biog/hrbeis routines, someone has replaced this formulation by the following:

Compute COSZEN = cos( zenith angle ) in terms of latitude, longitude,
and time

Compute ZEN = arccos( COSZEN )

Compute vertical attenuation VATTEN in terms of ambient conditions

Attenuation ATTEN = VATTEN * SQRT( 1.0 + TAN( ZEN ) )

Note for this last, that one of the most obscure Pythagorean identities from
trigonometry is

1/cos(A)^2 = 1 + tan(A)^2

so that this last step is mathematically equivalent to ATTEN = VATTEN / COSZEN.
Not only is this new form much worse for round-off error and computational cost,
it is also much more obscure. It needs to be fixed.

[cseppan]

Edited to remove gratuitous insults. Please refrain from personal attacks when submitting issues.

[cjcoats]

What do you call replacing expressions foo/cosz by foo*SQRT(1.0+COS(ACOS(COSZ))**2) ??

My Ph.D. is in mathematics (MIT: 1978) and I spent a decade as a math professor, so the "incompetent" is definitely a matter of fact within the scope of my professional competence; it is not within yours to nay-say me on this.