Solar Radiation

longitude_rad(lon_deg)

Converts longitude from degrees to radians.

Parameters:: lon_deg (float) – longitude in degrees, \(\phi\) [deg]
Returns:: lon – longitude, \(\phi\) [rad]
Return type:: float

latitude_rad(lat_deg)

Converts latitude from degrees to radians.

Parameters:: lat_deg (float) – latitude in degrees, \(\lambda\) [deg]
Returns:: lat – latitude, \(\lambda\) [rad]
Return type:: float

slope_rad(slope_deg)

Converts slope from degrees to radians.

Parameters:: slope_deg (float) – slope in degrees, \(s\) [deg]
Returns:: slope – slope, \(\Delta\) [rad]
Return type:: float

aspect_rad(aspect_deg)

Converts aspect from degrees to radians.

Parameters:: aspect_deg (float) – aspect in degrees, \(s\) [deg]
Returns:: aspect – aspect (0 is north; pi is south), \(\alpha\) [rad]
Return type:: float

declination(doy)

Computes the solar declination which is the angular height of the sun above the astronomical equatorial plane in radians.

\[\begin{split}\\delta=0.409 \cdot \sin\left(\frac{2\pi \cdot J}{365}-1.39\right)\end{split}\]

Parameters:: doy (float) – julian day of the year, \(J\) [-]
Returns:: decl – declination, \(\\delta\) [rad]
Return type:: float

Examples

>>> import ETLook.solar_radiation as solrad
>>> solrad.declination(180)
0.40512512455439242

earth_sun_distance(doy)

Computes the earth sun distance in Angstrom Unit where 1 AU is 1.496e8 km.

\[d_{r}=1+0.033 \cdot \cos\left(\frac{2\pi \cdot J}{365}\right)\]

Parameters:: doy (float) – julian day of the year, \(J\) [-]
Returns:: ed – earth sun distance, \(d_{r}\) [AU]
Return type:: float

Examples

>>> import ETLook.solar_radiation as solrad
>>> solrad.earth_sun_distance(180)
0.96703055420162642

inverse_earth_sun_distance(doy)

Computes the inverse earth sun distance (iesd) in Angstrom Unit where 1 AU is 1.496e8 km.

\[d_{r}=1+0.033 \cdot \cos\left(\frac{2\pi \cdot J}{365}\right)\]

Parameters:: doy (float) – julian day of the year, \(J\) [-]
Returns:: iesd – inverse earth sun distance, \(d_{r}\) [AU]
Return type:: float

Examples

>>> import ETLook.solar_radiation as solrad
>>> solrad.inverse_earth_sun_distance(180)
0.96703055420162642

actual_earth_sun_distance(iesd)

Computes the earth sun distance (esd) in Angstrom Unit where 1 AU is 1.496e8 km.

\[d_{r}=1+0.033 \cdot \cos\left(\frac{2\pi \cdot J}{365}\right)\]

Parameters:: iesd (float) – inverse earth sun distance, \(J\) [AU]
Returns:: esd – earth sun distance, \(d_{r}\) [AU]
Return type:: float

Examples

>>> import ETLook.solar_radiation as solrad
>>> solrad.actual_earth_sun_distance(180)
1.034093489244084

seasonal_correction(doy)

Computes the seasonal correction for solar time in hours.

\[b=\frac{2\pi\left(J-81\right)}{365}\]

\[s_{c}= 0.1645 \cdot sin \left( 2b \right) - 0.1255 \cdot cos \left(b \right) - 0.025 \left(b\right)\]

Parameters:: doy (float) – julian day of the year, \(J\) [-]
Returns:: sc – seasonal correction, \(s_{c}\) [hours]
Return type:: float

Examples

>>> import ETLook.solar_radiation as solrad
>>> solrad.seasonal_correction(180)
-0.052343379605521212

sunset_hour_angle(lat, decl)

Computes the sunset hour angle.

\[\begin{split}w_{s}=\arccos(-\tan(\lambda)\cdot \tan(\\delta))\end{split}\]

Parameters:

decl (float) – solar declination, \(\\delta\) [rad]
lat (float) – latitude, \(\lambda\) [rad]

Returns:

ws – sunset hour angle, \(w_{s}\) [rad]

Return type:

float

hour_angle(sc, dtime, lon=0)

Computes the hour angle which is zero at noon and -pi at 0:00 am and pi at 12:00 pm

\[\omega=\left(\frac{\pi}{12}\right)\cdot \left(t+s_{c}-12\right)\]

Parameters:

sc (float) – seasonal correction, \(s_{c}\) [hours]
dtime (float) – decimal time, \(t\) [hours]
lon (float) – longitude, \(\phi\) [rad]

Returns:

ha – hour_angle, \(\omega\) [rad]

Return type:

float

Examples

>>> import ETLook.solar_radiation as solrad
>>> solrad.hour_angle(sc=solrad.seasonal_correction(75), dtime=11.4)
-0.19793970172084141

inst_solar_radiation_toa(csza, iesd)

Computes the instantaneous solar radiation at the top of the atmosphere [Wm-2].

\[S_{toa}^{i} = S_{sun} \cdot d_{r} \cdot \phi\]

Parameters:

csza (float) – cosine solar zenith angle, \(\phi\) [-]
iesd (float) – inverse earth sun distance, \(d_{r}\) [AU]

Returns:

ra_i_toa – instantaneous solar radiation at top of atmosphere, \(S_{toa}^{i}\) [Wm-2]

Return type:

float

Examples

>>> import ETLook.solar_radiation as solrad
>>> doy = 1
>>> sc = solrad.seasonal_correction(doy)
>>> ha = solrad.hour_angle(sc, dtime=12)
>>> decl = solrad.declination(doy)
>>> csza = solrad.cosine_solar_zenith_angle(ha, decl, 0)
>>> iesd = solrad.inverse_earth_sun_distance(doy)
>>> solrad.inst_solar_radiation_toa(csza, iesd)
1299.9181944414036

daily_solar_radiation_toa(sc, decl, iesd, lat, slope, aspect)

Computes the daily solar radiation at the top of the atmosphere.

\[S_{toa}=S_{sun} \cdot d_{r}\int_{i=-\pi}^{i=\pi}S_{toa}^{i}\]

Parameters:

iesd (float) – inverse earth sun distance, \(d_{r}\) [AU]
decl (float) – solar declination, \(\\delta\) [rad]
sc (float) – seasonal correction, \(s_{c}\) [hours]
lat (float) – latitude, \(\lambda\) [rad]
slope (float) – slope (0 is flat, 90 is vertical), \(\Delta\) [deg]
aspect (float) – aspect (0 is north; 180 is south), \(\alpha\) [deg]

Returns:

ra_24_toa – daily solar radiation at the top of atmosphere, \(S_{toa}\) [Wm-2]

Return type:

float

Examples

>>> import ETLook.solar_radiation as solrad
>>> from math import pi
>>> doy = 1
>>> sc = solrad.seasonal_correction(doy)
>>> decl = solrad.declination(doy)
>>> iesd = solrad.inverse_earth_sun_distance(doy)
>>> solrad.daily_solar_radiation_toa(sc, decl, iesd, lat=25*pi/180.0)
265.74072308978026

cosine_solar_zenith_angle(ha, decl, lat, slope=0, aspect_rad=0)

computes the cosine of the solar zenith angle [-].

\[\begin{split}\phi = & \sin\left(\\delta\right) \cdot \sin\left(\lambda\right) \cdot \cos\left(\Delta\right) - \\ & \sin\left(\\delta\right) \cdot \cos\left(\lambda\right) \cdot \sin\left(\Delta\right) + \\ & \cos\left(\\delta\right) \cdot \cos\left(\lambda\right) \cdot \cos\left(\Delta\right) \cdot \cos\left(\omega\right)+\\ & \cos\left(\\delta\right) \cdot \sin\left(\lambda\right) \cdot \sin\left(\Delta\right) \cdot \sin\left(\alpha\right) \cdot \cos\left(\omega\right)+\\ & \cos\left(\\delta\right) \cdot \sin\left(\Delta\right) \cdot \sin\left(\alpha\right) \cdot \sin\left(\omega\right)\end{split}\]

Parameters:

ha (float) – hour angle, \(\omega\) [rad]
decl (float) – declination, \(\\delta\) [rad]
lat (float) – latitude, \(\lambda\) [rad]
slope (float) – slope, \(\Delta\) [rad]
aspect_rad (float) – aspect (0 is north; pi is south), \(\alpha\) [rad]

Returns:

csza – cosine solar zenith angle, \(\phi\) [-]

Return type:

float

Examples

>>> import ETLook.solar_radiation as solrad
>>> sc = solrad.seasonal_correction(1)
>>> ha = solrad.hour_angle(sc, dtime=12)
>>> solrad.cosine_solar_zenith_angle(ha, decl=solrad.declination(1), lat=0)
0.92055394167363314

transmissivity(ra_24_flat, ra_24_toa_flat)

Computes the transmissivity (inverse of daily_solar_radiation_flat).

Parameters:

ra_24_flat (float) – daily solar radiation for a flat surface, \(S^{\downarrow}\) [Wm-2]
ra_24_toa_flat (float) – daily solar radiation at the top of atmosphere for a flat surface, \(S_{toa,f}\) [Wm-2]

Returns:

trans_24 – daily atmospheric transmissivity, :math:` au` [-]

Return type:

float

daily_solar_radiation_toa_flat(decl, iesd, lat, ws)

Computes the daily solar radiation at the top of the atmosphere for a flat surface.

\[\begin{split}S_{toa,f}=\frac{S_{sun}}{\pi} \cdot d_{inv,r} \cdot (w_{s} \cdot \sin(\lambda) \cdot \sin(\\delta) + \cos(\lambda)\cdot\cos(\\delta)\cdot\sin(w_{s}))\end{split}\]

Parameters:

decl (float) – solar declination, \(\\delta\) [rad]
iesd (float) – inverse earth sun distance, \(d_{inv,r}\) [AU]
lat (float) – latitude, \(\lambda\) [rad]
ws (float) – sunset hour angle, \(w_{s}\) [rad]

Returns:

ra_24_toa_flat – daily solar radiation at the top of atmosphere for a flat surface, \(S_{toa,f}\) [Wm-2]

Return type:

float

daily_solar_radiation_flat(ra_24_toa_flat, trans_24)

Computes the daily solar radiation at the earth’s surface.

\[\begin{split}S^{\\downarrow} = \tau \cdot S_{toa}\end{split}\]

Parameters:

ra_24_toa_flat (float) – daily solar radiation at the top of atmosphere for a flat surface, \(S_{toa}\) [Wm-2]
trans_24 (float) – daily atmospheric transmissivity, \(\tau\) [-]

Returns:

ra_24_flat – daily solar radiation for a flat surface, \(S^{\\downarrow}\) [Wm-2]

Return type:

float

diffusion_index(trans_24, diffusion_slope=-1.33, diffusion_intercept=1.15)

Computes the diffusion index, the ratio between diffuse and direct solar radiation. The results are clipped between 0 and 1.

\[I_{diff} = a_{diff}+b_{diff} \cdot \tau\]

Parameters:

trans_24 (float) – daily atmospheric transmissivity, \(\tau\) [-]
diffusion_slope (float) – slope of diffusion index vs transmissivity relationship, \(b_{diff}\) [-]
diffusion_intercept (float) – intercept of diffusion index vs transmissivity relationship, \(a_{diff}\) [-]

Returns:

diffusion_index – diffusion_index, \(I_{diff}\) [-]

Return type:

float

daily_total_solar_radiation(ra_24_toa, ra_24_toa_flat, diffusion_index, trans_24)

Computes the daily solar radiation at the earth’s surface taken diffuse and direct solar radiation into account.

\[\begin{split}S^{\\downarrow} = I_{diff} \cdot \tau \cdot S_{toa,f} +(1-I_{diff}) \cdot \tau \cdot S_{toa}\end{split}\]

Parameters:

ra_24_toa (float) – daily solar radiation at the top of atmosphere, \(S_{toa}\) [Wm-2]
ra_24_toa_flat (float) – daily solar radiation at the top of atmosphere for a flat surface, \(S_{toa,f}\) [Wm-2]
diffusion_index (float) – diffusion_index, \(I_{diff}\) [-]
trans_24 (float) – daily atmospheric transmissivity, \(\tau\) [-]

Returns:

ra_24 – daily solar radiation, \(S^{\\downarrow}\) [Wm-2]

Return type:

float