Overview
Location & panel geometry¶
To begin with, let's define the fundamental input parameters for our location of interest and a moment in time:
- Location: (Longitude, Latitude) = (8, 45)
- Elevation: 214 m
- A good, clear-sky day over our location is
2010-01-27 12:00:00.
Next, let us consider the basic geometry of a solar panel :
- Orientation of the panel : South which is 180 degrees counting clock-wise from due North.
- Tilt of the Panel : a horizontally flat panel which is 0 degrees.
Coordinates
In PVGIS, coordinates are provided in longitude, latitude order.
Symbols
- The ∡ symbol means we are reporting an inclined component!
- The calculations include atmospheric refraction (as described in Hofierka, 2002)1
- The albedo is set to 0.2
- The Linke Turbidity is set to 2
On the Linke Turbidity
By default, PVGIS does not use any Linke Turbidity input when it gets to read solar irradiance components from external datasets, such as for example SARAH-3 products.
Solar position¶
As a starting point, the command position, features a sub-command introduction which returns a text explaining the flow of calculations of the position of the sun and the agle between sun-rays and the solar collector surface.
Go ahead, try it out and skim through the text!
See also
Refer to the introduction to solar position how-to section.
Now that we have an overview, let's start with the basics:
Solar Position Overview
☉ ⛰
∢ 🕛 Hour ⦩ ⭮ ⭸ ⛰ Sun-Hori… 👁
Time Declina… Angle ⦭ Zenith Altitude Azimuth Incidence Horizon Position Visible
──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
2010-01… -20.904 6.297 66.923 23.077 185.881 22.442 0.0 Above True
12:00:00
╭────────────────────────────────────────────────────────────────╮
│ ⏳ Start Time ⏱ Frequency ⌛ End Time Timezone │
│ 2010-01-17 12:00 Single timestamp 2010-01-17 12:00 UTC │
╰────────────────────────────────────────────────────────────────╯
╭─────────────────────────────────────────────────────────────────────────────────────────────╮
│ Position longitude, latitude = 8.628, 45.812, Orientation : 180.0, Tilt : 45.0 Unitless │
│ Algorithms Timing : NOAA, Zone : UTC, Positioning : NA, Incidence : Iqbal, Shading : PVGIS │
│ Definitions Azimuth origin : North, Incidence angle : Sun-Vector-to-Surface-Normal │
╰───────────────────────────────────────────────────────────────────────────────── Reference ─╯
╭─────────────────────────────────────────────────────────╮
│ ∢ Declination ⦩ Altitude ⛰ Horizon 👁 Visible │
│ 🕛 Hour angle ⭮ Azimuth ☉ Sun │
│ ⦭ Zenith ⭸ Incidence - Loss │
╰──────────────────────────────────────────────── Legend ─╯
Info
The command
reads:
- execute
pvgiscommandpositionand sub-commandoverview - set
- the longitude to
8.628and the latitude to45.812 - the surface (panel) orientation to
180and the tilt to45degrees - the timestamp
2010-01-17 12:00
- the longitude to
- output the angle quantities in
degrees
Degrees or radians?
By default, PVGIS returns angle figures measured in radians. This extra bit
of -aou is required to get the reported numbers in degrees. Without it :
Solar Position Overview
☉ ⛰
∢ 🕛 Hour ⦩ ⭮ ⭸ ⛰ Sun-Hori… 👁
Time Declina… Angle ⦭ Zenith Altitude Azimuth Incidence Horizon Position Visible
──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
2010-01… -0.365 0.11 1.168 0.403 3.244 0.392 0.0 Above True
12:00:00
╭────────────────────────────────────────────────────────────────╮
│ ⏳ Start Time ⏱ Frequency ⌛ End Time Timezone │
│ 2010-01-17 12:00 Single timestamp 2010-01-17 12:00 UTC │
╰────────────────────────────────────────────────────────────────╯
╭─────────────────────────────────────────────────────────────────────────────────────────────╮
│ Position longitude, latitude = 0.151, 0.8, Orientation : 3.142, Tilt : 0.785 Unitless │
│ Algorithms Timing : NOAA, Zone : UTC, Positioning : NA, Incidence : Iqbal, Shading : PVGIS │
│ Definitions Azimuth origin : North, Incidence angle : Sun-Vector-to-Surface-Normal │
╰───────────────────────────────────────────────────────────────────────────────── Reference ─╯
╭─────────────────────────────────────────────────────────╮
│ ∢ Declination ⦩ Altitude ⛰ Horizon 👁 Visible │
│ 🕛 Hour angle ⭮ Azimuth ☉ Sun │
│ ⦭ Zenith ⭸ Incidence - Loss │
╰──────────────────────────────────────────────── Legend ─╯
Let's note down the solar zenith angle (in radians) : 1.16802
Altitude and Azimuth¶
The two solar position angles of interest are the solar altitude (also referred to as solar elevation) and the solar azimuth.
We can identify them individually:
Solar Altitude Series
Time ⦩ Altitude
──────────────────────────────────
2010-01-17 12:00:00 23.077
╭────────────────────────────────────────────────────────────────╮
│ ⏳ Start Time ⏱ Frequency ⌛ End Time Timezone │
│ 2010-01-17 12:00 Single timestamp 2010-01-17 12:00 UTC │
╰────────────────────────────────────────────────────────────────╯
╭─────────────────────────────────────────────────────────╮
│ Position longitude, latitude = 8.628, 45.812, Unitless │
│ Algorithms Timing : NOAA, Zone : UTC, Positioning : NA │
╰───────────────────────────────────────────── Reference ─╯
╭───────────────╮
│ ⦩ Altitude │
│ │
╰────── Legend ─╯
and
pvgis position azimuth \
8.628 45.812 \
'2010-01-17 12:00:00' \
-aou degrees \
--solar-position-model noaa
Solar Azimuth Series
Time ⭮ Azimuth
─────────────────────────────────
2010-01-17 12:00:00 185.881
╭────────────────────────────────────────────────────────────────╮
│ ⏳ Start Time ⏱ Frequency ⌛ End Time Timezone │
│ 2010-01-17 12:00 Single timestamp 2010-01-17 12:00 UTC │
╰────────────────────────────────────────────────────────────────╯
╭─────────────────────────────────────────────────────────╮
│ Position longitude, latitude = 8.628, 45.812, Unitless │
│ Algorithms Timing : NOAA, Zone : UTC, Positioning : NA │
│ Definitions Azimuth origin : North │
╰───────────────────────────────────────────── Reference ─╯
╭──────────────╮
│ ⭮ Azimuth │
│ │
│ │
╰───── Legend ─╯
Incidence angle¶
Nonetheless, the single-most important angle in the context of photovoltaics, is the solar incidence angle. Let's get it for a South-facing surface, tilted at 35 degrees
Solar Position Overview
Time ⭸ Incidence
───────────────────────────────────
2010-01-17 12:00:00 32.222
╭────────────────────────────────────────────────────────────────╮
│ ⏳ Start Time ⏱ Frequency ⌛ End Time Timezone │
│ 2010-01-17 12:00 Single timestamp 2010-01-17 12:00 UTC │
╰────────────────────────────────────────────────────────────────╯
╭─────────────────────────────────────────────────────────────────────────────────────╮
│ Position longitude, latitude = 8.628, 45.812, Unitless │
│ Algorithms Timing : NOAA, Zone : UTC, Positioning : NA, Incidence : Iqbal │
│ Definitions Azimuth origin : North, Incidence angle : Sun-Vector-to-Surface-Normal │
╰───────────────────────────────────────────────────────────────────────── Reference ─╯
╭────────────────╮
│ ⭸ Incidence │
│ │
│ │
╰─────── Legend ─╯
Orientation & tilt angles
The incidence command requires a surface orientation and tilt angle (see highlighted figures in the above example). Missing to provide these parameters, would cause the command to fail.
The solar radiation model presented by Hofierka (2002), defines as solar incidence the angle between the sun-rays and the plane of the solar surface. Or else : the angle between the position of the sun and the inclination of the panel.
Typically, solar incidence is defined as the angle between the sun-rays and the normal to the reference surface. It is important to disinguish between the two, hence, in PVGIS we call the Sun-To-Plane the complementary incidence angle, where as the Sun-to-Surface-Normal we call it the typical incidence angle.
To get the typical solar incidence angle, one can use the optional flag --sun-vector-to-surface-normal (or even --sun-to-normal) like so:
pvgis position overview \
8.628 45.812 180 45 \
'2010-01-17 12:00' \
-aou degrees \
--sun-vector-to-surface-normal
Solar Position Overview
☉ ⛰
∢ 🕛 Hour ⦩ ⭮ ⭸ ⛰ Sun-Hori… 👁
Time Declina… Angle ⦭ Zenith Altitude Azimuth Incidence Horizon Position Visible
──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
2010-01… -20.904 6.297 66.923 23.077 185.881 22.442 0.0 Above True
12:00:00
╭────────────────────────────────────────────────────────────────╮
│ ⏳ Start Time ⏱ Frequency ⌛ End Time Timezone │
│ 2010-01-17 12:00 Single timestamp 2010-01-17 12:00 UTC │
╰────────────────────────────────────────────────────────────────╯
╭─────────────────────────────────────────────────────────────────────────────────────────────╮
│ Position longitude, latitude = 8.628, 45.812, Orientation : 180.0, Tilt : 45.0 Unitless │
│ Algorithms Timing : NOAA, Zone : UTC, Positioning : NA, Incidence : Iqbal, Shading : PVGIS │
│ Definitions Azimuth origin : North, Incidence angle : Sun-Vector-to-Surface-Normal │
╰───────────────────────────────────────────────────────────────────────────────── Reference ─╯
╭─────────────────────────────────────────────────────────╮
│ ∢ Declination ⦩ Altitude ⛰ Horizon 👁 Visible │
│ 🕛 Hour angle ⭮ Azimuth ☉ Sun │
│ ⦭ Zenith ⭸ Incidence - Loss │
╰──────────────────────────────────────────────── Legend ─╯
Time series¶
The power of overview is exactly its capability to generate time series.
It suffices to provide a start-time and an end-time:
pvgis position overview \
8.628 45.812 180 45 \
--start-time '2010-01-17 06:00:00' \
--end-time '2010-01-17 18:00:00' \
-aou degrees
Solar Position Overview
☉ ⛰
∢ 🕛 Hour ⦩ ⭮ ⭸ ⛰ Sun-Hori… 👁
Time Declina… Angle ⦭ Zenith Altitude Azimuth Incidence Horizon Position Visible
──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
2010-01… -20.951 -83.682 100.617 -10.617 109.214 0.0 0.0 Below False
06:00:0…
2010-01… -20.943 -68.685 90.835 -0.835 119.86 0.0 0.0 Below False
07:00:0…
2010-01… -20.935 -53.689 82.456 7.544 130.795 56.576 0.0 Above True
08:00:0…
2010-01… -20.927 -38.692 75.342 14.658 143.013 43.501 0.0 Above True
09:00:0…
2010-01… -20.92 -23.696 70.07 19.93 156.623 31.655 0.0 Above True
10:00:0…
2010-01… -20.912 -8.7 67.152 22.848 171.55 23.203 0.0 Above True
11:00:0…
2010-01… -20.904 6.297 66.923 23.077 185.881 22.442 0.0 Above True
12:00:0…
2010-01… -20.896 21.293 69.411 20.589 201.079 29.967 0.0 Above True
13:00:0…
2010-01… -20.888 36.29 74.324 15.676 214.917 41.47 0.0 Above True
14:00:0…
2010-01… -20.88 51.286 81.172 8.828 227.372 54.428 0.0 Above True
15:00:0…
2010-01… -20.872 66.283 89.196 0.804 238.289 67.57 0.0 Low angle True
16:00:0…
2010-01… -20.864 81.279 98.975 -8.975 249.218 0.0 0.0 Below False
17:00:0…
2010-01… -20.856 96.276 109.039 -19.039 259.32 0.0 0.0 Below False
18:00:0…
╭───────────────────────────────────────────────────────────╮
│ ⏳ Start Time ⏱ Frequency ⌛ End Time Timezone │
│ 2010-01-17 06:00 Hourly 2010-01-17 18:00 UTC │
╰───────────────────────────────────────────────────────────╯
╭─────────────────────────────────────────────────────────────────────────────────────────────╮
│ Position longitude, latitude = 8.628, 45.812, Orientation : 180.0, Tilt : 45.0 Unitless │
│ Algorithms Timing : NOAA, Zone : UTC, Positioning : NA, Incidence : Iqbal, Shading : PVGIS │
│ Definitions Azimuth origin : North, Incidence angle : Sun-Vector-to-Surface-Normal │
╰───────────────────────────────────────────────────────────────────────────────── Reference ─╯
╭─────────────────────────────────────────────────────────╮
│ ∢ Declination ⦩ Altitude ⛰ Horizon 👁 Visible │
│ 🕛 Hour angle ⭮ Azimuth ☉ Sun │
│ ⦭ Zenith ⭸ Incidence - Loss │
╰──────────────────────────────────────────────── Legend ─╯
And what about every 30 minutes?
Ask this via the --frequency option:
pvgis position overview \
8.628 45.812 180 45 \
--start-time '2010-01-17 06:00:00' \
--end-time '2010-01-17 18:00:00' \
-aou degrees \
--frequency 30min
Solar Position Overview
☉ ⛰
∢ 🕛 Hour ⦩ ⭮ ⭸ ⛰ Sun-Hori… 👁
Time Declina… Angle ⦭ Zenith Altitude Azimuth Incidence Horizon Position Visible
──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
2010-01… -20.951 -83.682 100.617 -10.617 109.214 0.0 0.0 Below False
06:00:0…
2010-01… -20.951 -76.182 95.736 -5.736 114.346 0.0 0.0 Below False
06:30:0…
2010-01… -20.943 -68.685 90.835 -0.835 119.86 0.0 0.0 Below False
07:00:0…
2010-01… -20.943 -61.185 86.491 3.509 125.23 63.23 0.0 Above True
07:30:0…
2010-01… -20.935 -53.689 82.456 7.544 130.795 56.576 0.0 Above True
08:00:0…
2010-01… -20.935 -46.189 78.708 11.292 136.734 49.955 0.0 Above True
08:30:0…
2010-01… -20.927 -38.692 75.342 14.658 143.013 43.501 0.0 Above True
09:00:0…
2010-01… -20.927 -31.192 72.444 17.556 149.65 37.338 0.0 Above True
09:30:0…
2010-01… -20.92 -23.696 70.07 19.93 156.623 31.655 0.0 Above True
10:00:0…
2010-01… -20.92 -16.196 68.293 21.707 163.923 26.773 0.0 Above True
10:30:0…
2010-01… -20.912 -8.7 67.152 22.848 171.55 23.203 0.0 Above True
11:00:0…
2010-01… -20.912 -1.2 66.695 23.305 180.0 21.695 0.0 Above True
11:30:0…
2010-01… -20.904 6.297 66.923 23.077 185.881 22.442 0.0 Above True
12:00:0…
2010-01… -20.904 13.797 67.843 22.157 193.68 25.445 0.0 Above True
12:30:0…
2010-01… -20.896 21.293 69.411 20.589 201.079 29.967 0.0 Above True
13:00:0…
2010-01… -20.896 28.793 71.596 18.404 208.166 35.439 0.0 Above True
13:30:0…
2010-01… -20.888 36.29 74.324 15.676 214.917 41.47 0.0 Above True
14:00:0…
2010-01… -20.888 43.79 77.546 12.454 221.318 47.85 0.0 Above True
14:30:0…
2010-01… -20.88 51.286 81.172 8.828 227.372 54.428 0.0 Above True
15:00:0…
2010-01… -20.88 58.786 85.133 4.867 233.074 61.1 0.0 Above True
15:30:0…
2010-01… -20.872 66.283 89.196 0.804 238.289 67.57 0.0 Low angle True
16:00:0…
2010-01… -20.872 73.783 94.142 -4.142 244.024 0.0 0.0 Below False
16:30:0…
2010-01… -20.864 81.279 98.975 -8.975 249.218 0.0 0.0 Below False
17:00:0…
2010-01… -20.864 88.779 103.952 -13.952 254.282 0.0 0.0 Below False
17:30:0…
2010-01… -20.856 96.276 109.039 -19.039 259.32 0.0 0.0 Below False
18:00:0…
╭───────────────────────────────────────────────────────────╮
│ ⏳ Start Time ⏱ Frequency ⌛ End Time Timezone │
│ 2010-01-17 06:00 30min 2010-01-17 18:00 UTC │
╰───────────────────────────────────────────────────────────╯
╭─────────────────────────────────────────────────────────────────────────────────────────────╮
│ Position longitude, latitude = 8.628, 45.812, Orientation : 180.0, Tilt : 45.0 Unitless │
│ Algorithms Timing : NOAA, Zone : UTC, Positioning : NA, Incidence : Iqbal, Shading : PVGIS │
│ Definitions Azimuth origin : North, Incidence angle : Sun-Vector-to-Surface-Normal │
╰───────────────────────────────────────────────────────────────────────────────── Reference ─╯
╭─────────────────────────────────────────────────────────╮
│ ∢ Declination ⦩ Altitude ⛰ Horizon 👁 Visible │
│ 🕛 Hour angle ⭮ Azimuth ☉ Sun │
│ ⦭ Zenith ⭸ Incidence - Loss │
╰──────────────────────────────────────────────── Legend ─╯
Maybe we want shorter figures? We can limit the output numbers to 2 decimals:
pvgis position overview \
8.628 45.812 180 45 \
--start-time '2010-01-17 06:00:00' \
--end-time '2010-01-17 18:00:00' \
-aou degrees \
-r 2
Solar Position Overview
☉ ⛰
∢ 🕛 Hour ⦩ ⭮ ⭸ ⛰ Sun-Hori… 👁
Time Declina… Angle ⦭ Zenith Altitude Azimuth Incidence Horizon Position Visible
──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
2010-01… -20.95 -83.68 100.62 -10.62 109.21 0.0 0.0 Below False
06:00:0…
2010-01… -20.94 -68.69 90.84 -0.84 119.86 0.0 0.0 Below False
07:00:0…
2010-01… -20.94 -53.69 82.46 7.54 130.79 56.58 0.0 Above True
08:00:0…
2010-01… -20.93 -38.69 75.34 14.66 143.01 43.5 0.0 Above True
09:00:0…
2010-01… -20.92 -23.7 70.07 19.93 156.62 31.65 0.0 Above True
10:00:0…
2010-01… -20.91 -8.7 67.15 22.85 171.55 23.2 0.0 Above True
11:00:0…
2010-01… -20.9 6.3 66.92 23.08 185.88 22.44 0.0 Above True
12:00:0…
2010-01… -20.9 21.29 69.41 20.59 201.08 29.97 0.0 Above True
13:00:0…
2010-01… -20.89 36.29 74.32 15.68 214.92 41.47 0.0 Above True
14:00:0…
2010-01… -20.88 51.29 81.17 8.83 227.37 54.43 0.0 Above True
15:00:0…
2010-01… -20.87 66.28 89.2 0.8 238.29 67.57 0.0 Low angle True
16:00:0…
2010-01… -20.86 81.28 98.97 -8.97 249.22 0.0 0.0 Below False
17:00:0…
2010-01… -20.86 96.28 109.04 -19.04 259.32 0.0 0.0 Below False
18:00:0…
╭───────────────────────────────────────────────────────────╮
│ ⏳ Start Time ⏱ Frequency ⌛ End Time Timezone │
│ 2010-01-17 06:00 Hourly 2010-01-17 18:00 UTC │
╰───────────────────────────────────────────────────────────╯
╭─────────────────────────────────────────────────────────────────────────────────────────────╮
│ Position longitude, latitude = 8.63, 45.81, Orientation : 180.0, Tilt : 45.0 Unitless │
│ Algorithms Timing : NOAA, Zone : UTC, Positioning : NA, Incidence : Iqbal, Shading : PVGIS │
│ Definitions Azimuth origin : North, Incidence angle : Sun-Vector-to-Surface-Normal │
╰───────────────────────────────────────────────────────────────────────────────── Reference ─╯
╭─────────────────────────────────────────────────────────╮
│ ∢ Declination ⦩ Altitude ⛰ Horizon 👁 Visible │
│ 🕛 Hour angle ⭮ Azimuth ☉ Sun │
│ ⦭ Zenith ⭸ Incidence - Loss │
╰──────────────────────────────────────────────── Legend ─╯
Uniplot¶
We can also have a visual overview via the --uniplot option:
pvgis position overview \
8.628 45.812 180 45 \
--start-time '2010-01-17 06:00:00' \
--end-time '2010-01-17 18:00:00' \
-aou degrees \
--quiet \
--uniplot
Uniplot
Solar Position observed from (longitude, latitude) 8.628, 45.812000000000005
┌────────────────────────────────────────────────────────────────────────────────────────────────────────────┐
│ ▄▄▄▄▄▄▄▀▀▀▀│
│ ▄▄▄▄▄▄▄▀▀▀▀▀▀▀ │
│ ▗▄▄▄▄▄▞▀▀▀▀▀▀ │
│ ▄▄▄▄▄▞▀▀▀▀▘ │ 200 Unitless
│ ▄▄▄▄▄▀▀▀▀▀ │
│ ▗▄▄▄▄▞▀▀▀▀▀ │
│ ▄▄▄▄▄▞▀▀▀▀▘ │
│ ▗▄▄▄▄▄▄▀▀▀▀▀▀ │
│ ▗▄▄▄▄▄▄▞▀▀▀▀▀▀▘ │
│▀▀▘ │ 100 Unitless
│ │
│ ▗▄▄▄▄▖ │
│ ▗▞▀▀▀▄▄▄▄▄▄ ▗▄▄▄▄▄▞▀▀▀▀▀▘ ▝▀▄ │
│ ▗▄▀▘ ▀▀▀▀▀▀▄▄▄▄▄▄▄▄ ▗▄▄▄▄▄▄▄▞▀▀▀▀▀▘ ▀▄ │
│ ▄▞▘ ▗▄▄▄▄▄▄▄▄▄▄▄▄▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▚▄▄▄▄▄▄▄▄▄▄▄▄ ▀▄▖ │
│▄▄▄▄▄▄▄▄▄▄▄▄▀▀▀▀▀▀▀▀▀▘▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▀▀▀▀▀▀▀▀▀▚▄▄▄▄▄▄▄▖▝▚▄▄▄▄▄▄▄▄▄│ 0 Unitless
│▀▀▀▀ ▝▀▀▀▀▀▀▀▄▄▄▄│
└────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00
██ Sun-Vector-to-Surface-Normal Incidence (Iqbal) ██ altitude ██ azimuth North
We can zoom-out a bit to gain a better understanding :
pvgis position overview \
8.628 45.812 180 45 \
--start-time '2010-01-17' \
--end-time '2010-01-18' \
-aou degrees \
--quiet \
--uniplot
Uniplot
Solar Position observed from (longitude, latitude) 8.628, 45.812000000000005
┌────────────────────────────────────────────────────────────────────────────────────────────────────────────┐
│ ▄▄▀▌ │
│ ▄▄▄▀▀ ▐ │
│ ▄▄▄▄▞▀▀▀ ▝▖ │
│ ▄▄▄▄▄▞▀▀▀▀▀ ▌ │ 250 Unitless
│ ▗▄▄▄▄▞▀▀▀▀▘ ▐ │
│ ▄▄▄▄▀▀▀▀▘ ▝▖ │
│ ▗▄▄▄▞▀▀▀ ▌ │
│ ▄▄▄▄▀▀▀▘ ▐ │
│ ▄▄▄▄▄▀▀▀▀ ▝▖ │
│ ▗▄▄▄▄▄▀▀▀▀▀ ▌ │
│ ▗▄▄▄▄▞▀▀▀▀▘ ▐ │
│ ▄▄▄▀▀▀▘ ▄▖ ▗▄▄▄▄▀▄ ▝▖│
│ ▗▄▞▀▀ ▄▀ ▝▀▀▀▀▄▄▄▄▄▖ ▄▄▄▄▄▀▀▀▀▘ ▚▖ ▌│
│▞▀▘ ▄▗▄▄▄▄▄▄▄▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▚▄▄▄▄▄▄▄ ▝▚ ▐│
│▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▄▄▄▄▄▞▀▀▀▀▀▘▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▀▀▀▀▀▚▄▄▄▄▄▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀│ 0 Unitless
│ ▗▄▄▄▄▄▀▀▀▀▀ ▀▀▀▀▀▚▄▄▄▄▄ │
│▄▄▄▄▄▀▀▀▀▀▀▘ ▀▀▀▀▀▀▄▄▄▄▄▄▄▄▄│
└────────────────────────────────────────────────────────────────────────────────────────────────────────────┘
2010-01-17 2010-01-17T06:00 2010-01-17T12:00 2010-01-17T18:00 2010-01-18
██ Sun-Vector-to-Surface-Normal Incidence (Iqbal) ██ altitude ██ azimuth North
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Hofierka, J., and Suri, M. (2002). The solar radiation model for Open source GIS: implementation and applications. ResearchGate ↩