Corrections to Townsend snow model

[cwhanse]

Private communications with the model's author have turned up some issues with the pvlib implementation. Chief among the issues is this part of the calculation:

    lower_edge_height_clipped = np.maximum(lower_edge_height, 0.01)
    gamma = (
        slant_height
        * effective_snow_weighted_m
        * cosd(surface_tilt)
        / (lower_edge_height_clipped**2 - effective_snow_weighted_m**2)
        * 2
        * tand(angle_of_repose)
    )

    ground_interference_term = 1 - C2 * np.exp(-gamma)

When lower_edge_height_clipped < effective_snow_weighted_m, gamma < 0 and the ground_interference_term can become negative. In contrast, the author's intent is that C2 < ground_interference_terms < 1. The author recommends clipping the squared difference (lower bound being worked out but will be something like 0.01.).

Other issues appear to arise from the unit conversions. The published model uses inches for distance and snow depth. The pvlib code uses cm for snow depth (convenience for working with external snow data) and m for distances (for consistency with the rest of pvlib). After several steps, including the ground_interference_term calculation, the code converts from cm or m to inches to apply the final formula for loss (since the formula involves some coefficients determined by a regression). It would be easier to trace the pvlib code back to the paper if the internal unit conversions (from cm / m to inches) were done earlier.

[kandersolar]

Interestingly, clamping the difference of squares at 0.01 was part of the original PR but got lost along the way: #1251 (comment)

It would be great if the communication with the author results in improved tests as well as improved code.

[cwhanse]

After communications with the author, the pvlib code is missing two items:

• a lower bound on lower_edge_height_clipped**2 - effective_snow_weighted_m**2 which the author specifies should be 0.1 in^2.
• a factor that multiplies the monthly loss fraction, to represent the potential for a string of modules at the top of the slanted array to generate power while strings at lower positions are still affected by snow. This factor was brought up in Townsend model string orientation adjustment #1625

Neither is documented in the 2011 paper but should be added to 1) prevent unreasonably low loss values (item 1) and to better represent the loss for systems with multiple, horizontally-oriented strings.

Also, the author recommends advising users to enter 1/2 the total module width as the slant_height for single-axis tracked systems, which makes sense to me, as snow could slide off either surface depending on its rotation.

[wedize]

Hi everyone,
I am currently working with the Townsend snow model and have encountered a question regarding the determination of the number of snow events (N) within the model. I have reviewed the documentation, but I'm seeking further insight into the process of selecting this parameter.

Could someone please shed light on how the number of snow events (N) is determined in the Townsend snow model? Are there specific criteria, guidelines, or data sources that can help in making an informed decision about this parameter? I want to ensure I'm using an appropriate value for N in my application of the model.

Any guidance, references, or real-world examples related to this aspect of the Townsend snow model would be greatly appreciated.
Best regards,
Mberki

[cwhanse]

@wedize this question came up recently on the pvlib google group. https://groups.google.com/g/pvlib-python/c/j4FEErBul3U/m/W00HNritAAAJ

[wedize]

@cwhanse . Thank you. It was very helpful.