That is part of it, but some of the early morning examples are up to 500% 
different, although with very small values.  In those cases I still suspect 
there is extra scattered radiation from the surroundings, whether it be 
trees or buildings.
I wonder also if the sensor type may change results slightly.
There may also be a calibration error, due to the different spectral energy 
distribution comparing dawn and midday, or perhaps even simple nonlinearity 
near zero output. These are not research-grade instruments that most of us 
are using.
If you add all that in with ozone, water vapour and particulates of 
different sizes, all of which change seasonally and daily, you will never 
expect precise agreement.

Here's another example - I left the RS and Bras models with the same values 
as previous, and changed the BH model to ignore just ozone, water vapour 
and particulates.
That gave the solid line. Then I set albedo for the full snow cover and the 
result was  the dashed line.

So, the "theoretical curve" for around Boston is anywhere in that range of 
curves, or it could be even lower in moderately polluted skies.
On Wednesday, 23 December 2020 at 10:51:08 pm UTC+10 tke...@gmail.com wrote:

> Very useful, Cameron.
>
> It looks like the R-S curve is quite a bit lower, maybe as much as 20% 
> lower, at dawn and dusk, which seems to be when people are experiencing 
> values higher than maxSolarRad.
>
> On Wed, Dec 23, 2020 at 1:19 AM Cameron D <cgo...@davidsoncj.id.au> wrote:
>
>> And then I forgot the attachment!
>>
>>
>> On Wednesday, 23 December 2020 at 7:18:31 pm UTC+10 Cameron D wrote:
>>
>>> I should have looked a bit more closely before posting!  I used the 
>>> solrad excel code from Uni Washington.
>>> I had adjusted my B&H parameters to represent quite clean air but forgot 
>>> to match the Bras and RS code from default.
>>> If I:
>>>
>>>    1. reset the BH turbidity params to default,
>>>    2. adjust the Bras param down to 1.6 and
>>>    3. adjust the RS param to 0.84,
>>>
>>>  then the curves are close to normalised at peak.  The RS curve is still 
>>> a somewhat poor representation at dawn and dusk, while Bras is probably 
>>> close enough to BH that it's not worth the extra effort.  
>>> The main advantage with B&H is the atmospheric moisture, which I think 
>>> contributes significantly, but differently from the atmospheric turbidity 
>>> parameters and changes the shape of the curve. So a single parameter cannot 
>>> account for all variables.
>>> The safest bet might be to adjust the parameter for clear skies and then 
>>> say that is an upper limit.
>>>
>>> On Wednesday, 23 December 2020 at 6:31:47 pm UTC+10 Cameron D wrote:
>>>
>>>> So the weewx python code says it is using the Ryan and 
>>>> Stolzenbach model, which has a few approximations that don't work well in 
>>>> some cases, and it looks like this is one of them.
>>>>
>>>> I've attached a plot comparing 3 insolation models predicting global 
>>>> horizontal irradiation.
>>>> Bird and Hulstrom 1991
>>>> Bras 1992
>>>> and  Ryan and Stolzenbach  1972
>>>>
>>>> B&H has a lot more parameters to account for, but I have just thrown in 
>>>> the date/location for Boston, using whatever parameters were in the 
>>>> spreadsheet, and come up with the following comparison.
>>>> I used the B&H predictions for modelling my solar PV system and found 
>>>> it gives very close results - or at least it did before my system got a 
>>>> bit 
>>>> older.  However R&S also gives results that aren't too bad in my location.
>>>>
>>>> I have the code in php, but no spare time at the moment to convert to 
>>>> python.
>>>>
>>>> On Tuesday, 22 December 2020 at 2:19:29 am UTC+10 t...@tom.org wrote:
>>>>
>>>>> kk, glad you corroborated my observations. I am no expert in this for 
>>>>> sure. I am just tired of all of the comments I get from visitors to the 
>>>>> website about how my readings exceed theoretical max. I could remove the 
>>>>> max, but that doesn't seem fun.
>>>>>
>>>>> I do not have the expertise to validate the way weewx calculates it 
>>>>> nor am I even competent in Python, but for those who may, here is a link 
>>>>> to 
>>>>> the code:
>>>>>
>>>>>
>>>>> https://github.com/weewx/weewx/blob/d91635f3bc429f906d1f084c6a6bc8ee09fa1a27/bin/weewx/wxformulas.py#L332
>>>>>
>>>>>
>>>>>
>>>>> On Sunday, December 20, 2020 at 1:26:31 PM UTC-5 kk44...@gmail.com 
>>>>> wrote:
>>>>>
>>>>>> I found that thread interesting, so I added the column "maxSolarRad", 
>>>>>> too. 
>>>>>>
>>>>>> [image: dayradiation.png]
>>>>>> Readings of the console and the WeatherLinkLive device are quite the 
>>>>>> same. And the readings of "radiation" are higher than "maxSolarRad". The 
>>>>>> values I upload to the local weather network are well in the range of 
>>>>>> other 
>>>>>> stations nearby.
>>>>>>
>>>>>>
>>>>>> Greg Troxel schrieb am Sonntag, 20. Dezember 2020 um 17:58:01 UTC+1:
>>>>>>
>>>>>>>
>>>>>>> Greg Troxel <g...@lexort.com> writes: 
>>>>>>>
>>>>>>> > Can someone share how to add maxSolarRad (when it is in the db) to 
>>>>>>> the 
>>>>>>> > graphs for the traditional skin? Can I graph radiation, max 
>>>>>>> (observed), 
>>>>>>> > and theory all at once, having three? 
>>>>>>>
>>>>>>> The answer is to just add it and label it; it comes out in green 
>>>>>>> after 
>>>>>>> radiation in blue and max in red. Pro Tip: add it after 
>>>>>>> radiation_max, 
>>>>>>> which is the max of local observations, and don't stick the line 
>>>>>>> after 
>>>>>>> the radiation_max header and the 4 lines defining how max should be. 
>>>>>>>
>>>>>>>
>>>>>>> [[[dayradiation]]] 
>>>>>>> [[[[radiation]]]] 
>>>>>>> [[[[radiation_max]]]] 
>>>>>>> data_type = radiation 
>>>>>>> aggregate_type = max 
>>>>>>> aggregate_interval = 3600 
>>>>>>> label = max 
>>>>>>> [[[[maxSolarRad]]]] 
>>>>>>> label = theory 
>>>>>>>
>>>>>> -- 
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