Well, I don't know that I'm as close as I'd like to be, but I am getting better results now, even with the denser shades.
In short, what I did was roll all the suggestions into a new set of simulations. Specifically, I added:
render= -lw 1e-8 -av 0 0 0
... to my rif file, increased the ambient bounces to five, and normalized all my shade relfectances (20%). Here's what I got:
Test20 (no shade) 82,356 249.82
Test21 (10% shade) 82,350 30.89 10.00% 12.36% 24%
Test22 (05% shade) 82,343 16.32 5.00% 6.53% 31%
Test23 (01% shade) 82,346 1.38 1.00% 0.55% -45%
Test24 (10% + 05% shades) 82,338 0.80 0.50% 0.32% -36%
Test25 (10% + 01% shades) 82,354 0.35 0.10% 0.14% 40%
Test26 (01% + 01% shades) 82,348 0.01 0.01% 0.00% -60%
Data is as follows:
Column 1 - Exterior horizontal diffuse illuminance (Lux)
Column 2 - Interior horizontal diffuse illuminance (Lux)
Column 3 - "expected" light reduction from test 20 (no shade)
Column 4 - actual light reduction from test 20 (no shade)
Column 5 - "error". I'm certainly no statistician though, and maybe this value is being unfairly computed (COL4/COL3)-1. (?)
As you can see, there is still some wild fluctuation, but not nearly as bad as the original tests. I am confused as to why the accuracy of the 10% and 05% shades has suffered; in earlier tests they were very close, 04% and 08% "accurate" respectively.
OK, so then I tried Alex's trick of increasing the exterior illumination by a factor of ten, in hopes that the higher light levels that would now result in the interior space would be more accurately evaluated:
(HDI x 10)
Test20 (no shade) 832,317 2,528.67
Test21 (10% shade) 832,319 361.96 10.00% 14.31% 43%
Test22 (05% shade) 832,322 222.05 5.00% 8.78% 76%
Test23 (01% shade) 832,315 23.48 1.00% 0.93% -7%
Test24 (10% + 05% shades) 832,297 17.45 0.50% 0.69% 38%
Test25 (10% + 01% shades) 832,314 2.98 0.10% 0.12% 18%
Test26 (01% + 01% shades) 832,304 0.37 0.01% 0.01% 46%
~8-/
Now my 05% shade is the least accurate of the lot! I double checked the paramaters, and even re-ran the calc using five points in an array around the intitial calc point, but it averages to within .5 lux of this calc. I did a rendering of the 05% shade too, everything looks OK.
Hmmm. Even at these higher light levels, the 01% + 01% shade seems suspect. This combo had the greatest "swing" from the first simulation to the second (60% under-prediction to a 46% over prediction).
My co-worker & I have been thinking that maybe we should test the model with more transmissive shades, and simply apply a factor to those illuminance values to figure out what the shades should be, for this last gallery. It feels a lot like giving up, but I'm not sure I want to trust these numbers based on this test.
Either way we go, this has been very educational and I thank everyone who contributed to this thread.
-- OK, seconds before I was to press send, Carsten Bauer sent me an email. He's been doing some testing of his own with this model, with much better results. It seems that if we set -lw to zero, and not a really-really low number, you get results that match the math. The other big difference between his process and mine is that he's getting his values from a rendering (rpict) and I'm just rtracing values. So perhaps there's the missing link(s).
Maybe I won't give up just yet... Seems like there's just no way to know all there is to know about Radiance!
To be continued (?)