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Andrews, R. W., Pollard, A. & Pearce, J. M. The effects of snowfall on solar photovoltaic performance. Solar Energy
92, 8497 (2013). DOI: http://dx.doi.org/10.1016/j.solener.2013.02.014
The Effects of Snowfall on Solar Photovoltaic Performance
Rob W. Andrewsa, Andrew Pollarda, Joshua M. Pearceb,∗
aDepartment of Mechanical and Materials Engineering, Queen’s University, Canada
bDepartment of Materials Science and Engineering and Department of Electrical and Computer Engineering, Michigan Technological
University, USA
Abstract
Solar photovoltaic (PV) systems are frequently installed in climates with significant snowfall. To better understand the
effects of snowfall on the performance of PV systems, a multi-angle, multi-technology PV system was commissioned and
monitored over two winters. A novel methodology was introduced and validated with this system, which allows for the
determination of snowfall losses from time-series performance data with correlated meteorological observations down to
a 5-minute resolution. In addition, a new method for determining the probability distribution of snow deposition on a
module from image data was developed. It was found that the losses due to snowfall are dependent on the angle and
technology being considered and the effects of increased albedo in the surroundings of a PV system can increase expected
yields, particularly in the case of high tilt angle systems. Existing methods for predicting losses due to snowfall were
investigated, and were found to provide overly conservative estimates of snow losses. Overall the results show that the
proper assessment of snow related losses can help improve system performance and maintenance. It is concluded that
proper characterization of the snowfall effect on PV system performance can influence better systems optimization for
climates experiencing snowfall.
Keywords: snow, photovoltaics, snow losses, snow albedo, time series analysis, snow loss prediction
1. Introduction
As the costs of solar photovoltaic (PV) systems
continue to decline the levelized cost of solar electricity
becomes increasingly attractive in a widening group of
areas throughout the globe including those in
sub-optimal latitudes and climates (Branker et al.,
2011a). As such, in 2009 nearly three-quarters of PV
resources were installed in countries that experience some
amount of snowfall, namely Germany, Czech Republic,
Japan, and most recently Canada (SolarBuzz, 2010).
Depending on the orientation and tilt angle of the PV
modules and meteorological factors, previous studies
have indicated that snow losses on a PV system can be
as high as 15% for a low profile system in Truckee
California to 0.3%-2.7% for a highly exposed 28 degree
roof mount system in Germany (Townsend and Powers,
2011; Becker et al., 2008; Marion et al., 2005; Yoshioka
et al., 2003; Yoshio et al., 1999; Ross, 1995; Brench,
1979). In order to optimize both the economic (Branker
et al., 2011a,b; Ren et al., 2009; Mondol et al., 2009) and
environmental outcomes (Laleman et al., 2011; Kenny
et al., 2010; Pearce, 2002; Nieuwlaar and Alsema, 1997)
from PV systems (Parida et al., 2011), proper prediction
of systems yields is critical and requires in-depth and
∗601 M and M Building 1400 Townsend Drive Houghton, MI
49931-1295 906-487-1466
Email address: pearce@mtu.edu (Joshua M. Pearce )
accurate accounting of all loss mechanisms (Mani and
Pillai, 2010; Thevenard et al., 2010). Therefore, a test
site has been commissioned in Ontario, Canada to
investigate this question, and the results from two years
of study are presented. The purpose of this study is to
provide a comparison of energy yields from a wide variety
of technologies and module configurations to provide a
better understanding of the effects of system design on
snow related losses, gains and shedding. In addition, a
novel methodology to determine snowfall losses from
time-series data is introduced.
2. Background
Snowfall accumulation on modules is strongly affected
by the ambient temperature, wind speeds, inclination
from the horizontal, and surface properties (Pfister and
Schneebeli, 1999). At temperatures below -3◦Ca snow
crystal that impacts the surface of a module will bounce
on the surface. As the temperature decreases the
possibility of this bouncing increases, and as the angle of
the module to the horizontal increases, the possibility of
this bouncing causing the particle to slide along the
surface increases. In addition, the hydrophobicity of the
surface has been shown in some cases to increase the
propensity of the snow particle to slide on the surface
(Kako et al., 2004). At temperatures above -3◦C
bouncing action is reduced, and the snow particle will
Andrews, R. W., Pollard, A. & Pearce, J. M. The effects of snowfall on solar photovoltaic performance. Solar Energy
92, 8497 (2013). DOI: http://dx.doi.org/10.1016/j.solener.2013.02.014
tend to adhere immediately to the module face (Pfister
and Schneebeli, 1999). Once the particles adhere to the
face of the module, cohesion between snow particles will
cause the snow mass to increase on the module.
Once a layer of snow has accumulated on the face of a
PV module, some light can still penetrate the snowpack
and reach the PV module. This is an exponential
relationship, which is described by Giddings and
LaChappelle (Giddings and LaChapelle, 1961) and the
Bouger-Lambert law. Both of these predict that
approximately 20% of incident radiation will be available
at 2cm snow depth, and 3-4% is available at 10cm depth.
These correlations have been demonstrated empirically to
be a reasonably good fit to experimental data (O’Neill
and Gray, 1972; Curl et al., 1972). The light transmitted
is primarily short-wave radiation, and thus does not
necessarily align with an ideal spectrum for PV
electricity production, which of course depends on the
bandgap of the photovoltaic material; however, this
transmitted light can be important for shedding
phenomenon, which will be explained below.
An important property of snow residing on a module
is its insulation properties as fresh snow can have a
thermal conductivity as low as 0.04 W/mK, which is
equivalent to that of fibreglass insulation (Ross, 1995).
Therefore, the snow will act as an insulating layer, and
protect the surface of the module from convective heat
loss. This will allow the module to retain the heat
generated from incoming radiation and conductive
sources, which in turn increases energy transfer into
heating the snow-module layer to produce a water layer
that can promote snow sliding.
Snow shedding can occur in two major forms, either
sheet sliding or pure melting. The clearing mode depends
heavily upon the physical arrangement of the modules.
For example, if there is room for the snow to slide it
generally will; however, if the sliding process is impeded
by physical obstructions (e.g. a close packed multi-row
flat roof PV system) the snow cover will have to melt
directly on the modules in order to clear.
2.1. Module Control Volume
Assume the module as a control volume, the energy
influx to a snow-covered module can occur in three ways:
diffusion of short wave radiation through the snow pack,
albedo reflection to the exposed rear of the module, and
conduction from other parts of the PV array that are not
covered with snow. The amount of albedo reflection onto
the rear of the modules can be 25% (Ross, 1995) or more
(Townsend and Powers, 2011) of incident global
radiation; however, this is highly dependent on the
physical orientation of the modules. A ground mount
system, such as could be seen in an industrial PV
installation will typically have modules arranged in such
a way as to have a large view factor between the rear of
the module and the snow-covered ground and array. A
residential roof mount will have virtually no albedo
reflection to the rear of the module.
In addition, the emissivity of the rear face of the
module will affect its ability to convert this reflected
radiation to heat. A high spectral emissivity at the back
of the module will allow the reflected radiation from the
snow to heat the modules. Once the snow on the ground
melts due to warmer temperatures, the ambient albedo
will be reduced from 0.5-0.7 to around 0.2 and therefore
there will not be available a large amount of reflected
radiation, and thus the module temperature will not be
raised significantly in the summer. This effect was
studied in detail analytically for a more complicated
system utilizing a sealed convection chamber that
increases the efficiency of albedo absorption (Ross, 1995).
2.2. Previous studies of snow effects on PV systems
There are notable studies on the effects of snowfall on
PV systems. The first was performed in 1979 at the
Natural Bridges National Monument and had an
apparatus similar to that used in the present study. The
author utilized a simple linear empirical correlation to
determine expected PV output, and used this metric to
determine snowfall losses. However, 56% of the data were
discarded due to issues with the pyranometer being
obscured by snow or data logger reliability issues. Thus,
a yearly estimation of snowfall loss was not determined;
however, the following energy loss averages were
determined from the remaining data and are presented in
Table 1
Table 1: Daily loss predictions from 1979 study (Brench, 1979).
30◦module angle 40◦module angle
Snow depth >1” <1” >1” <1”
Daily loss 45% 11% 26% 5%
A theoretical study of snow shedding was performed
by Ross in 1995, with the goal of improving the battery
charging performance of remote sites. A new passive
melting technology, based on the reflection of light onto
the rear surface of the module was developed, and C++
code was developed to aid in the development of this
technology (Ross, 1995). The code predicts the
temperature of a module as it is covered with snow, and
is based on the assumption that when the module reaches
a temperature of 0◦Cthe module will begin to clear.
While this assumption is dubious, the simulation lead to
some interesting conclusions. For example, it predicted
that a light dusting of snow (<3cm) will actually increase
the rate of snow shedding from the module as the added
insulation by this layer will reduce heat losses from the
Andrews, R. W., Pollard, A. & Pearce, J. M. The effects of snowfall on solar photovoltaic performance. Solar Energy
92, 8497 (2013). DOI: http://dx.doi.org/10.1016/j.solener.2013.02.014
module, which allows it to more rapidly reach a higher
temperature.
Another study was performed in 2008 using six years
of data from the New Munich Trade Fair Centre (Becker
et al., 2008). Snowfall losses range from 0.3%-2.7% from
1999 to 2006, however, the methodology for determining
these losses was not specified. Interestingly, snow clearing
can be observed to occur from module temperatures of
+30◦Cto −10◦C, with the higher module temperatures
occurring at higher insolation. This finding invalidates
the assumptions used in the modelling performed by
Ross that assumed that snow would clear from a module
once the temperature reaches 0◦C.
An attempt to utilize satellite imaging to identify
times when a PV plant is covered with snow has been
documented. There were two major error sources from
this form of detection (i) false alarm, where satellite
imagery shows the plant to be uncovered, when it is in
fact covered and (ii) under prediction, stemming from an
overestimation of times of snow cover. These two error
mechanisms had values of 26% and 23% respectively,
which indicated the probability of errors in prediction
occurring from this system. In addition, there was a low
data availability of around 65% which could limit the use
of this technique as a consistent monitoring methodology.
(Wirth et al., 2010) However, it was shown to be a
potentially useful tool for monitoring the performance of
distributed systems when local irradiation monitoring is
not available.
Most recently, data from two test sites were obtained,
one which had a set of modules that were consistently
cleared of snow, and the other was an operating fixed tilt
system with no module clearing regimen (Townsend and
Powers, 2011). These sites were located in Truckee ,CA,
which receives on average 5m (200in) of snow per year.
Snow losses were recorded on a monthly basis, and
ranged up to 100% of expected yield for a flat low profile
system. On an annual basis losses were found to be 6%
for the fixed tilt system, and 13%, 17% ,and 26% for a
low profile system of angles 39◦, 24◦, and 0◦respectively.
A model was developed to estimate snow losses based on
meteorological data, which displayed some ability to
predict monthly energy loss from a system, and it was
applied to other locations that experience some level of
snowfall, however it has not yet been validated.
The current study overcomes the limitations of the
previous snow studies by providing novel measurement
methodologies and multiple co-located module
technologies and orientations, and attempts to validate
the work of Townsend and Powers (Townsend and
Powers, 2011).
(a) 2011
(b) 2012
Figure 1: OSOTF in the spring of 2011 and 2012. The modules
outlined in white were included in the quantitative analysis, and all
modules were included in the visual analysis
3. Methodology
A system was developed to test the effect of snowfall
on PV modules oriented at a variety of tilt angles with
a variety of technologies and front coatings. The system,
called the Open Source Outdoors Test Field (OSOTF),
was designed on open source principles (Pearce et al.,
2012). All system documentation, commissioning reports
and system data are available freely in the public domain
1.
A total of 70 modules of both amorphous silicon
(a-Si:H) and crystalline silicon (c-Si) are monitored for
short-circuit current(Isc) and back temperature at
5-minute intervals, and a full meteorological station is
co-located at the roof including secondary standard
heated and ventilated pyranometers (Pearce et al.,
2012). The modules used in this study were set at angles
of 5◦, 10◦, 15◦, 20◦, 40◦, and 60◦. There are multiple
modules at each angle, and each represents a module
that has been specifically modified with a surface
treatment or is from a specific manufacturer. Future
publications will look specifically at the effects of these
surface treatments on the performance of the modules.
An exception is the panels installed at 30◦which are all
nominally identical panels. Figure 1 shows a layout of
the test site and the relative locations of the modules.
The site was expanded over the summer of 2011, and the
modules that are included in each year of study are
shown as those outlined in white. It should be noted that
the spacing of the modules was maintained such that
inter-row shading losses would be the same for all rows.
For the two winters being considered, (Isc ) was used
as a representative performance metric. Isc is heavily
1The live web cam is accessible at snowstudy.ati.sl.on.ca,
the design and operations documentation is available at www.
appropedia.org/SEARC_OSOTF_Design_and_Operations_Manual and
the data stream is available at searckingston.ati.sl.on.ca/
selectData.php
Andrews, R. W., Pollard, A. & Pearce, J. M. The effects of snowfall on solar photovoltaic performance. Solar Energy
92, 8497 (2013). DOI: http://dx.doi.org/10.1016/j.solener.2013.02.014
Gt
Dt
Meteorological
Data
Module
Performance
Module
Temperature
Power Tolerance, spectral,
degradation and
temperature correction
(Andrews et al., 2012)
Compare predicted
to actual output
Derive snow losses
and modeling error
Ambient Temp
Relative Humidity
Wind Speed
Precipitation
Figure 2: Data processing flowchart, Gtand Dtrepresent the time
series of measured global and diffuse irradiation respectively. Module
performance in this case is defined as a timeseries of Isc.
influenced by the amount of effective irradiation
(including spectral effects) that reaches the cell. At
constant temperature Isc is related linearly to effective
irradiation under no or low levels of concentration (Wolf
and Rauschenbach, 1963; Fabero and Chenlo, 1991) and
is only comparatively weakly affected by temperature,
which is corrected during system modelling. Therefore a
change in the Isc will have a proportional change on the
power output of a module, as it represents the level of
light reaching the modules, making it an appropriate
performance metric, while effectively isolating against the
effects of temperature on the results.
3.1. System Modelling
A baseline data set of a PV system performance is
first required against which its actual performance under
the effects of snow may be compared. In order to do this,
a methodology was developed to accurately predict the
Isc of a PV module based on meteorological
measurements (Andrews et al., 2012). This was adapted
from the Sandia performance model (King et al., 2004)
to be applicable to high temporal resolutions.
The general analysis methodology used here is given in
Figure 2. The goal is to apply high-resolution modelling
techniques to predict the ˆ
Isc, which is the modelled short
circuit current. Comparison of the predicted to the actual
output enables the effects of snow to be determined. A
useful metric for identifying these effects is the modelled
output ratio (MOR ), which is defined as:
MOR =Isc
ˆ
Isc
(1)
Albedo was assumed to be a constant value of 0.7 if
snowfall was present and 0.2 if not, which are relatively
standard values (Warren, 1972; Gardner and Sharp,
2010; Thevenard, 2006)2. Therefore, any albedo
2Recent work has shown, however, that higher values for albedo
are likely appropriate for snow, when the spectral sensitivity of the
receiving surface is considered (Andrews and Pearce, 2012)
reflection which is effectively greater than this amount
(Andrews and Pearce, 2012) would lead to the modules
over-producing current relative to their expected outputs.
Thus, increased albedo reflection is measurable using this
methodology.
3.2. Identifying the Snow Effect
Once the system has been modelled, a time series of
so-called “synthetic days” can be assembled. The goal
of these synthetic days is to model the output of the PV
module without the addition of external, stochastic factors
such as dust and snow accumulation. The yearly snow
effect is defined as the summation of the difference between
the actual and synthetic output, and the error associated
with this measure is the Mean Bias Error (MBE) (defined
in Equation 2) of the model applied to an entire year of
collected data.
MBE =
¯
ˆ
Isc −¯
Isc
¯
Isc
(2)
3.2.1. Determining Module Clearance
Another important metric to account for snowfall
effects is the time required to clear a module after a snow
event. A filtering algorithm was employed to identify
periods when modules were covered and cleared of snow.
First, for each module, marker points which matched the
following characteristics were identified:
i. MOR(t). . . MO R(t+ 20min)<70%
ii. |Isc −ˆ
Isc|>Isco
12
Where Isco is the module rated Isc at 1000W/m2,25◦,
and a spectrum of AM1.5G (STC conditions). This point
identifies a location where there is a clear deficiency
between actual and modelled output, which is persistent
over at least 20 minutes. This eliminates variations in
cloud cover, short term shading and other effects (which
are presumed negligible). This marker point represents a
clearly identifiable loss due to snowfall; however, is not
necessarily the beginning of snow coverage on a panel.
The beginning of snow coverage is then located by
searching backwards from the identified point for the
point where Gt<10W/m2(Global Irradiation) or
MOR(t). . . MO R(t−20) >85% with the assumption
being that either the nearest morning, or point where the
output ratio reaches near to ideal, indicates the
beginning of the snow coverage.
To determine the point at which the module is assumed
to be clear a forward search locates the point where
i. MOR(t). . . MO R(t+ 20min)>85%
ii. MOR(t). . . MO R(t+ 20min)<120%
OR
i. |Isc(t)−ˆ
Isc(t)|. . . |Isc (t+ 20min)−ˆ
Isc(t+ 20min)|<
Isco
35
ii. AirM ass < 4
Andrews, R. W., Pollard, A. & Pearce, J. M. The effects of snowfall on solar photovoltaic performance. Solar Energy
92, 8497 (2013). DOI: http://dx.doi.org/10.1016/j.solener.2013.02.014
The first set of requirements locates the point where the
panel has returned to operation within 85% of predicted
output, which indicates that the panel has substantially
cleared. The upper threshold on performance ratio is
implemented to provide stability in the cases where the
output magnitude is small (such as at the beginning and
end of the day) which can cause asymptotic behaviour in
the performance ratio. The second set of conditions is
utilized to identify points where, due to low light levels,
the use of the modelled output ratio characteristic
becomes unstable, and Air Mass represents the thickness
of air through which the radiation must travel,
normalized by the actual atmospheric thickness. Using
this algorithm, each point where the module is obscured
by snow can be identified, and the length of time that it
takes to clear can be measured.
3.3. Image Analysis
Time-lapse digital photography was also taken at five
minute intervals to track the accumulation and shedding
of snow on the modules. Each photograph was imported
and aligned to a sup-pixel accuracy using a Fourier
transform based luminance optimization algorithm to a
baseline image (Guizar-Sicairos et al., 2008) to eliminate
effects of camera vibrations and creep. Each frame was
then converted to grayscale and thresholded using an
unbounded Otsu Adaptive algorithm (Nobuyuki, 1979)
to identify snow on modules. Each module in the frame
was then isolated, and a three dimensional histogram
that indicates the relative likelihood of snow
accumulating at a point on the module was constructed
by summing through each pixel of the module. A
flowchart illustrating each stage of this process is shown
in Figure 3. The resolution of the camera was upgraded
halfway through the winter of 2010/2011, and therefore
two separate graphics were produced, one from the low
resolution dataset and one from the high resolution set,
as the module histograms were incompatible.
4. Presentation of Results
The main results from this study are shown in
Figure 4 and 5, which demonstrate as a percentage of
total yearly production, the magnitude of losses due to
snowfall in the winters of 2010/2011 and 2011/2012.
Measurements for the winter of 2010/2011 began on
January 7, 2011, however as can be noted from Table 2
there was not a significant accumulation of snow earlier
in the year, and therefore the data may be considered
representative for the year. Because of the small
magnitude of the total snow in the winter of 2010/2011
at the test site compared to historical averages, the
annualized losses due to snowfall are not statistically
significant. However, it is still possible to utilize
information related to individual snow events to
characterize snow clearing events.
Identify each module
using a mask
Extract individual module
images showing snow distribution
Import Array Image
and allign it to a baseline
Threshold Image
Combine all images from a module
through time into a 3D histogram
Figure 3: Data processing for image analysis flowchart
Andrews, R. W., Pollard, A. & Pearce, J. M. The effects of snowfall on solar photovoltaic performance. Solar Energy
92, 8497 (2013). DOI: http://dx.doi.org/10.1016/j.solener.2013.02.014
Table 2: Average monthly snowfall accumulation and temperature
from the Kingston Climate station.
Yearly total Dec Jan
Year cm ◦Ccm ◦Ccm ◦C
2010/2011 58 -4.2 2 -3.8 30 -9.3
2011/2012 49 -1.0 8 -0.5 22 -3.9
Historical Avg. Feb Mar
Year cm ◦Ccm ◦Ccm ◦C
2010/2011 180.9 -1.7 17 -6.7 9 -1.1
2011/2012 12 -2.2 2 1.6
10 20 40 60
0 %
1 %
2 %
3 %
4 %
5 %
Panel Angle(o)
Yearly yeild loss attributable to snow
(a) Crystalline
10 20 40 60
0 %
0.5 %
1 %
1.5 %
2 %
2.5 %
3 %
3.5 %
4 %
Panel Angle(o)
Yearly yeild loss attributable to snow
(b) Amorphous
Figure 4: Losses attributable to snow in the winter of 2010/2011,
the different shaded bars represent a different module manufacturer
or surface treatment
5 10 15 20 30 40 60
0 %
0.5 %
1 %
1.5 %
2 %
Panel Angle(o)
Yearly yeild loss attributable to snow
(a) Crystalline
5 10 15 20 40 60
0 %
0.2 %
0.4 %
0.6 %
0.8 %
1 %
Panel Angle(o)
Yearly yeild loss attributable to snow
(b) Amorphous
Figure 5: Losses attributable to snow in the winter of 2011/2012, the
different coloured bars represent a different module manufacturer or
surface treatment. Error bars are not shown on this plot, as they are
greater in magnitude than the measured results.
Figure 6 presents surface plots of the difference between
actual and modelled daily Iscproduction. The height and
duration of the peaks in the first winter the snow losses
are dominant; however, in the second, much milder, winter
they are less pronounced.
To put these snowfall losses in perspective, Table 2
gives information on the snow accumulation measured at
a nearby weather station, Kingston
Climate (EnvironmentCanada, 2012), for the period of
the study and compared it to historical norms.
4.1. Time to clear snow from cell surface
Another method to identify the effects of snowfall on
modules is the time that it takes to clear the surface.
Data showing the mean time to shed for each module is
(a) Crystalline (b) Amorphous
Figure 6: A summary of daily module losses from January 7,2011 to
March 9,2012, positive represents module under production. a and
b show a top view of c-Si and a-Si:H, respectively.
10 20 40 60
0
5
10
15
20
25
30
35
40
Panel Angle(o)
Avg time required to clear panels(hr)
(a) Crystalline
10 20 40 60
0
10
20
30
40
50
Panel Angle(o)
Avg time required to clear panels(hr)
(b) Amorphous
5 10 15 20 30 40 60
0
2
4
6
8
10
Panel Angle(o)
Avg time required to clear panels(hr)
(c) Crystalline
5 10 15 20 40 60
0
2
4
6
8
10
Panel Angle(o)
Avg time required to clear panels(hr)
(d) Amorphous
Figure 7: Mean time to clear for c-Si, (a) and (c) and a-Si:H, (b)
and (d) for the winter of 2010/2011 (a),(c) and 2011/2012 (b),(d)
respectively. The colour of the bar represents a module from a
specific manufacturer
shown in Figure 7, and is further expanded into box plots
representing the entire dataset in Figure 8. These box
plots show the variability in each dataset, with the thick
box representing the lower and upper quartiles, the
central dot representing the median, the thin lines
showing the extent of the largest and smallest values in
the set, and any isolated points representing outliers from
the dataset. In addition, Figure 9 shows the correlation
between module angle, temperature and atmospheric
relative humidity and shedding times.
To demonstrate how these shedding times were
derived, a selection of time series data which
demonstrated the differences in shedding profiles for the
various modules is shown in Figure 10.
Andrews, R. W., Pollard, A. & Pearce, J. M. The effects of snowfall on solar photovoltaic performance. Solar Energy
92, 8497 (2013). DOI: http://dx.doi.org/10.1016/j.solener.2013.02.014
10 20 40 60
0
20
40
60
80
100
120
140
160
180
Panel Angle(o)
Time required to clear panels (hr)
(a) Crystalline
10 20 40 60
0
20
40
60
80
100
120
140
160
180
Panel Angle(o)
Time required to clear panels (hr)
(b) Amorphous
5 10 15 20 30 40 60
0
5
10
15
20
25
Panel Angle(o)
Time required to clear panels (hr)
(c) Crystalline
5 10 15 20 40 60
0
2
4
6
8
10
Panel Angle(o)
Time required to clear panels (hr)
(d) Amorphous
Figure 8: Box plots representing all recorded shedding events for c-
Si, (a) and (c) and a-Si:H, (b) and (d) for the winter of 2010/2011
(a),(c) and 2011/2012 (b),(d) respectively. The colour of the bar
represents a module from a specific manufacturer
−15 −10 −5 0 5
0
10
20
30
40
50
60
70
80
Panel Temperature(
oC)
Time to clear panel(h)
(a) Crystalline
30 % 40 % 50 % 60 % 70 %
0
10
20
30
40
50
60
70
80
Time to clear panel(h)
Relative Humidity
Panel Angle( o )
10
20
30
40
50
60
(b) Crystalline
−20 −15 −10 −5 0 5
0
10
20
30
40
50
60
70
80
90
Temperature(
oC)
Time to clear panel(h)
(c) Amorphous
30 % 40 % 50 % 60 % 70 %
0
10
20
30
40
50
60
70
80
90
Time to clear panel(h)
Relative Humidity
Panel Angle( o )
10
20
30
40
50
60
(d) Amorphous
Figure 9: Correlation of the time to clear for c-Si,(a) and (b) and
a-Si:H (c) and (d) modules to average daily temperature and relative
humidity, for the winter of 2010/2011 (a, c) and 2011/2012 (b, d)
respectively
4.2. Image analysis
The results of the image analysis are shown in
Figure 11, which represents a three dimensional
histogram of snow accumulation on each module. This
figure indicates areas where snow is most likely to collect
on the surface of a module. The colour scale for these
11−02−06 11−02−07
0
1
2
3
Date
Isc(A)
(a) February 2011
12−01−14 12−01−15
0
2
4
6
8
Date
Isc(A)
(b) January 2012
Figure 10: Time series showing snow shedding over two days
figures is based on the median of snow intensity from
each module, therefore a darker red colour represents a
higher probability of snow accumulating in this area, but
does not necessarily represent a higher total
accumulation of snow as compared to other modules.
4.3. Application of existing snow loss algorithms
The correlation suggested by Townsend (Townsend
and Powers, 2011) was applied to the collected dataset,
using meterological data collected on site or taken from
the Kingston Climate station (EnvironmentCanada,
2012) and a value of γ=1. The results of its application
to the output of the modules tested in the winter of
2010/2011 are shown in Figure 12.
5. Analysis and Discussion
From the given data some inferences about the nature
of the effect of snowfall on PV systems can be derived. It
should be noted initially that because of the low
magnitude of these effects, in some cases the results are
not statistically significant. The error for each estimation
has been derived from the MBE of the underlying model
used to predict the snowfall losses, assessed during the
period where no snowfall was present. Though this
modelling technique has a high degree of accuracy (<1%
in many cases) it is still in some cases of the same order
of magnitude of the snowfall effect, especially in the
second measured (mild) winter.
Andrews, R. W., Pollard, A. & Pearce, J. M. The effects of snowfall on solar photovoltaic performance. Solar Energy
92, 8497 (2013). DOI: http://dx.doi.org/10.1016/j.solener.2013.02.014
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
5−10
15−20
30−40
50−60
Panel Angle, degrees from horizontal
(a) January 2011
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
5−10
15−20
30−40
50−60
Panel Angle, degrees from horizontal
(b) Feb-March 2011
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
5−10
15−20
30−40
50−60
Panel Angle, degrees from horizontal
(c) Winter 2011/2012
Figure 11: Image analysis results for three sections of time-lapse
photos. Each module is scaled by the median of its intensity values,
thus the gradients do not represent the magnitude of coverage, rather
the normalized distribution on the surface of the module. Each row
consists of modules at two angles, which are labelled on the y-axis
and divided by the dashed line.
5.1. Albedo Effects
From the analysis of Figure 6 it can be seen that the
effects of snowfall on the performance of a PV device is
not always negative and could be used to optimize system
design in certain climates. Because of the increased view
factor of the modules with the ground at higher tilt
angles, the ambient albedo will tend to improve the
performance of higher angle modules, which may mask
the true snowfall losses when long term averages are
taken. Therefore Figure 13 shows the magnitude of this
albedo effect on the performance of the modules, as a
percentage improvement of yearly yield over that with
10 20 40 60
0 %
0.5 %
1 %
1.5 %
Panel Angle(o)
Yearly yeild loss attributable to snow
Figure 12: BEW algorithm applied to the output of modules
studied for the winter of 2010/2011, showing predicted yield losses
attributable to snow. The colour of the bar represents a module from
a specific manufacturer
the expected albedo value of 70%. As can be expected
the albedo effect increases with module inclination angle,
which is due to the increased view factor from the
module to the snow surface. An explanation for the
higher average level of albedo is given in (Andrews and
Pearce, 2012), which describes that snow albedo, which is
spectrally weighted to the response of a module, will have
a higher effective albedo than would be expected from
fully spectrally integrating the reflectivity of the surface.
10 20 40 60
0 %
0.2 %
0.4 %
0.6 %
0.8 %
1 %
Panel Angle(o)
Approximate Albedo effect
(a) Crystalline
5 10 15 20 30 40 60
0 %
0.2 %
0.4 %
0.6 %
0.8 %
1 %
1.2 %
1.4 %
1.6 %
Panel Angle(o)
Approximate Albedo effect
(b) Crystalline
5 10 15 20 40 60
0 %
0.5 %
1 %
1.5 %
Panel Angle(o)
Effect of Albedo on yearly yeild
(c) Amorphous
5 10 15 20 40 60
0 %
0.1 %
0.2 %
0.3 %
0.4 %
0.5 %
Panel Angle(o)
Effect of Albedo on yearly yeild
(d) Amorphous
Figure 13: Gains in performance attributable to snow albedo for
c-Si and a-Si:H modules from both winters. The colour of the bar
represents a module from a specific manufacturer
Andrews, R. W., Pollard, A. & Pearce, J. M. The effects of snowfall on solar photovoltaic performance. Solar Energy
92, 8497 (2013). DOI: http://dx.doi.org/10.1016/j.solener.2013.02.014
5.2. Angular dependence
Overall, it can be seen that losses due to snowfall
tend to decrease as module angle increases, and the same
trend is apparent in the observed shedding times.
However, in the second winter this angle dependence is
less pronounced, both in the shedding times and in the
energy yields. A possible explanation is because of higher
average temperatures during the winter, the main
shedding mechanism was melting rather than sliding of a
snow sheet. Thus, the effects of gravity would be less
prominent in this form of shedding mechanism, and this
effect is investigated more thoroughly with the image
analysis results.
In analysing the box plots of shedding times presented
in Figure 8 it can be seen that in the first winter, the
variability of shedding times tends to decrease as the panel
angle increases. Notably, the position of the upper bound
outliers shows a clear angular dependence, indicating that
lower angles are more likely to have on average greater
times to clear, in addition to a higher likelihood of being
covered for an extended period of time, beyond what would
be expected from the statistical distribution.
5.3. Snowfall loss correlations
The correlation of shedding times to daily average
temperature and relative humidity given in Figure 9,
indicate some weak trends. It appears that a higher
relative humidity would tend to increase the residence
time of snow on a module. Shedding events under 24
hours lower module temperatures can be seen to increase
shedding times. Generally, however it can be observed
that the shedding of snow from the surface of a module is
a complex phenomenon that is not easily predicted from
individual atmospheric variables. However, it can be
noted that snow shedding occurs at module temperatures
as low as −15◦C, as was also seen in (Becker et al.,
2008).
To investigate the use of exiting algorithms to predict
the effects due to snowfall, the methodology introduced
by Townsend was also applied to the meteorological data
from the winter of 2010/2011, and was shown in
Figure 12. It was found that this algorithm tended to
under-predict the effects of snowfall on the system.
Because of the vastly different snowfall accumulations
between the site where the model was developed and the
present site, such variation probably may be expected.
This methodology could be a useful method of
conservatively determining the yearly snowfall losses.
5.4. Accumulation of snowfall on a module
The different methods of shedding can be seen in
Figure 11 over the two years of study. It can be seen that
in the winter of 2010/2011 angles from 15◦to 40◦tend to
display a gradient of snow accumulation, with the snow
more likely to remain at the base of the module. This
effect has been observed in previous studies, and
indicated that the snow sheets that slide off the modules
are obstructed by the bottom edge of the modules. At
angles of 10◦and below, depending on the time of year
and module, gradients are still observable. Snow
accumulation, however, is generally more evenly
distributed over the whole face of the module, indicating
that snow is not sliding from the face of the module but
is rather melting into its face. Interestingly, for modules
13, 14 and 15 in Figure 11.b snow is most likely to
accumulate in the centre of the module, and there is not
the same bottom edge accumulation as seen in other
modules at the comparable angle. Across all winters, it
can be seen that modules at angles of 50◦and 60◦have a
bias of snow accumulation towards the top of the
module, and is variable over the face of the module than
those at lower angles. Because these modules are more
exposed to ambient winds, it is likely that the added
momentum of the snow impacting the module in those
areas that are not sheltered from the wind by the row in
front will give greater adhesion of the snow to these areas
of the modules. Also, because the higher angle modules
clear more quickly than their lower angle counterparts,
the effects of a sheet of snow covering a portion of the
module are less pronounced.
In the winter of 2011/2012, it can be seen that
though shedding gradients are still present, the
distribution is more even over the face of the module.
Due to the faster speed of clearing, and higher ambient
temperatures at the time of snowfall in this year, it can
be seen that the main method of module clearing is in
melting, rather than sheet sliding.
5.5. Effects on module performance
As can be seen from all the visual data, there is a
gradient in snow coverage that can be expected at most
practical installation angles. Thus, in designing systems
it is important to consider the orientation of diode
protected strings within a module. With the current
installation, the majority of c-Si based modules installed
had a series of three overlapping bypass diodes, with
strings parallel to the long edge of the module.
Therefore, if a gradient of snow coverage was present on
a portrait installed module (as the modules installed in
the study were), photocurrent could not be generated as
the entire string would be limited by its least producing
(most snow covered element), which would magnify the
effects of snow coverage. If the modules were installed in
landscape, there is a chance that the snow gradient may
impact the performance of the bottom string of cells,
however, the upper unshaded strings would still be able
to produce power.
It is also interesting to note the effects of module type
on the distribution of snow cover. It can be seen in
Figure 11 that the distribution of snow cover changes
Andrews, R. W., Pollard, A. & Pearce, J. M. The effects of snowfall on solar photovoltaic performance. Solar Energy
92, 8497 (2013). DOI: http://dx.doi.org/10.1016/j.solener.2013.02.014
even between modules which are installed beside each
other at the same angle. It can be seen from this that in
a string architecture, uneven snow loading between
modules in a string could cause string losses due to
limitations of the most shaded module. However, this
imbalance would cause a reverse bias current through the
most affected module, which would increase its
temperature and may promote snow clearing. More work
is required in order to determine the overall effects of
uneven snow loading on string architectures.
5.6. Effects on system payback
The decrease in energy output due to snow coverage
over the winter will have an effect on the financial
performance of the system. Looking at the simple (zero
debt) payback period as a metric of financial payback
given as:
SP B =CC
EIdeal (1 −)(3)
Where SP B is the simple payback period, C C is the
installed capital cost of the system, EI deal is the ideal
energy output of a system with no snow losses, and is
the snow loss as a percentage of yearly energy yield.
Thus, the ratio of S P B of an ideal system to one
experiencing snow losses is proportional to 1
(1−). Thus,
assuming an arbitrary but realistic 7 year payback period
and the worst case measured yearly snow energy loss of
3.5%, the payback time will be increased by
approximately 13 weeks.
However, solar can now be considered to be a financial
investment due to its growing recognition as a
low-technical risk and long term asset(Branker et al.,
2011a). It is therefore more appropriate to use an
investment metric such as Return on Investment(ROI),
which more fully embodies the total benefits of long term
solar investments (Pearce et al., 2009). Assuming a
system lifetime between 25 and 50 years, and a base
payback period of 7 years, the ROI of a system would be
decreased by 0.56% to 0.50% (absolute) due to the
potential effects of snowfall.
6. Future work
Overall, this study has shown the detailed effects of
snowfall on the DC performance of photovoltaic modules.
It should be recognized that the effects of snowfall are
highly dependant on system topology, and future work
should look into the effects of snowfall on various PV
topologies. In addition, generalizable methods to predict
the effects of snowfall on a PV system from routinely
collected weather data should be created. Future work is
also needed to investigate methods to mitigate snowfall
losses such as surface coatings, texturing, or snow
clearing systems. Finally, these models and methods
must be evaluated into the future taking in account the
effects of climate change on snowfall characteristics.
7. Conclusions
This study introduced a methodology that can be
used to derive snowfall losses and time to clear of snow
from a time series of module performance data, a metric
commonly collected at PV installation sites. In addition,
a methodology to analyse snow shedding patterns from
image data was introduced, and showed the variability of
snow distribution patterns depending on module type
and orientation. Overall it was seen that snowfall will
tend to settle in a vertical gradient on the surface of the
module.
It was found that the losses due to snowfall are
dependent on the angle and technology being considered.
Over the two years studied, which had low levels of
snowfall when compared to historic data, the losses
ranged from 3.5%-1% of expected yearly yield for sites in
south-eastern Ontario. It was also found that the effect
of increased spectrally responsive albedo can cause an
increase of approximately 1% over projected yields on
modules with higher inclinations from the horizontal. An
attempt was made to correlate the time required to shed
snow to module temperature and relative humidity, and
though some weak trends are apparent: that a lower
temperature and higher relative humidity will tend to
increase the time to shed, they were not significant.
Overall it was found that the proper assessment of snow
related losses can help improve system performance and
maintenance. In addition, proper characterization of the
snowfall effect can influence better systems optimization
for climates experiencing snowfall. Future work is also
needed to investigate system design to better utilize
albedo augmentation techniques.
8. Acknowledgements
The authors would like to acknowledge the work of H.
McLaren, J. Fairborn, Q. Bentley, D. Carter and A.
Babasola and the support of the Sustainable Energy
Applied Research Centre at St. Lawrence College, and to
the forward-looking industry partners of this project who
made it possible. In addition we acknowledge support
from the Natural Sciences and Engineering Research
Council of Canada and a Social Sciences and Humanities
Research Council of Canada Strategic Research Grant on
Environmental Issues. In addition, the support of the
on-line communities for both Matlab and L
A
T
E
X.
Andrews, R. W., Pollard, A. & Pearce, J. M. The effects of snowfall on solar photovoltaic performance. Solar Energy
92, 8497 (2013). DOI: http://dx.doi.org/10.1016/j.solener.2013.02.014
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