Townsend monthly

Method

Townsend fitted the monthly energy lost to snow at test arrays in the Sierra Nevada. The model counts the month's effective snowfall from the snowfall and the number of snow events (1), weights it with the previous month's, January taking December's (2), and reduces the snow's sliding when the snow piled on the ground reaches the lower edge of the modules (3). The loss rises with the snowfall, the cosine of the tilt squared and the humidity, and falls with the absolute temperature squared and with the month's insolation (4); it is held between 0 and 1, and a month without insolation loses nothing. The model works in inches and kelvin; the inputs are converted. Each timestep then loses its month's fraction of the module power, after the spectral row and before the flat derates.

Values the model fills in or derives. The monthly mean temperature is the mean of the weather file's temperature over the month. The monthly relative humidity is the mean of the weather file's humidity; when the file has none, it is the Site tab's monthly humidity, and without either the option is not available. The insolation is the month's front plane-of-array insolation: the mean day over the days the weather file covers in that month, times the month's days, so a file of part of a month or of several years gives one month's value; on a bifacial system the rear irradiance is added and the loss is scaled by the front share, as Townsend and Previtali 2023 recommend. The geometry comes from the racking: fixed rows and rooftops use the tilt and the collector width as the slant height; trackers use the largest rotation angle and half the collector width, the distance from the axis to the module edge, as the model's author recommends for trackers. The lower-edge height, the string factor and the angle of repose are the Site tab's values, 1.0 m, 1 and 40° if not given. A snow event is a day with more than 2.54 cm (1 inch) of snow.

Settings

Setting	Value
Coefficient $C_{T1}$	5.7 × 10⁴
Coefficient $C_{T2}$	0.51
Smallest squared distance under the lower edge	0.1 in²

The math

1. Effective snowfall
2. Weighted snowfall
3. Ground interference
4. Monthly loss

$$S_e = \begin{cases} \tfrac{1}{2}\,S_{snow}\left(1 + \dfrac{1}{N_{ev}}\right) & N_{ev} > 0 \\ 0 & N_{ev} = 0 \end{cases} \tag{1}$$ $$S_w = \tfrac{1}{3}\,S_{e,prev} + \tfrac{2}{3}\,S_e \tag{2}$$ $$\Gamma = \frac{s\,S_w\cos\beta}{\max(0.1,\ H^2 - S_w^2)}\cdot 2\tan \kappa \tag{3}$$ $$s_m = \min\!\left(1,\ \max\!\left(0,\ \frac{C_{T1}\,S_w\cos^2\beta\,(1 - C_{T2}\,e^{-\Gamma})\,RH}{\bar T_a^2\,E_{POA}^{0.67}}\,f_s\,f_{front}\right)\right) \tag{4}$$

where

Symbol	Meaning	Unit
$S_e$	the effective snowfall of the month	inches
$S_{snow}$	the snowfall of the month	inches
$N_{ev}$	the number of snow events in the month	—
$S_w$	the weighted snowfall	inches
$S_{e,prev}$	the effective snowfall of the previous month, December for January	—
$\Gamma$	the ground-interference term	—
$s$	the slant height	inches
$H$	the height of the lower edge above the ground	inches
$\kappa$	the angle of repose of piled snow	degrees
$\beta$	the tilt of the module plane from the horizontal	degrees
$s_m$	the fraction of the month's energy lost to snow	—
$RH$	the monthly mean relative humidity, a fraction	—
$\bar T_a$	the monthly mean ambient temperature	K
$E_{POA}$	the month's plane-of-array insolation	kWh/m²
$f_s$	the string factor	—
$f_{front}$	the front share of the insolation, 1 on a monofacial system	—

References

1. Townsend & Powers 2011, Photovoltaics and snow: An update from two winters of measurements in the SIERRA, IEEE 37th Photovoltaic Specialists Conference
2. Townsend 2013, Predicting PV Energy Loss Caused by Snow, Solar Power International
3. Townsend & Previtali 2023, A Fresh Dusting: Current Uses of the Townsend Snow Model, Photovoltaic Reliability Workshop 2023, NREL/CP-5900-87918
4. pvlib-python 0.16.1 source code (github.com/pvlib/pvlib-python), reference implementation: pvlib/snow.py, loss_townsend()

API

site.snow_model = townsend, site.snowfall_monthly_cm, site.snow_events_monthly

Symbols follow the symbol registry.