Modelling sun and sky irradiance#

  • This notebook explain how to use astk functions to simulate the natural lighting of a scenesky irradiance for diiferent conditions.

Conventions#

  • Radiation fluxes are expressed in terms of irradiance of a horizontal unit placed at earth surface(total energetic flux passing through a square meter of ground).

  • The standard measurement of radiation at earth surface is the global horizontal irradiance (ghi, W.m-2 i.e. J.m-2.s-1), that captures radiations coming from the sun and from the sky in the shortwave domain (visible light)

  • The sun contribution is called direct normal irradiance (dni), whereas sky contribution is called diffuse horizontal irradiance (dhi)

Imports and setup location#

[1]:

from openalea.astk.data_access import montpellier_spring_2013
from openalea.astk.sky_irradiance import sky_irradiance

Specify a location on earth:

[2]:

Montpellier ={
'longitude': 3.87,
'latitude': 43.61,
'altitude': 56,
'timezone': 'Europe/Paris'}

Simulating clear sky conditions#

[3]:

 sky_irr = sky_irradiance(daydate='2000-06-21', **Montpellier)
 sky_irr

[3]:
azimuth zenith elevation ghi dni dhi ppfd
2000-06-21 07:00:00+02:00 65.222522 81.781574 8.218426 69.608228 133.668645 50.500666 167.643135
2000-06-21 08:00:00+02:00 74.723897 71.647009 18.352991 241.741681 432.873390 105.442654 528.836249
2000-06-21 09:00:00+02:00 84.230207 61.003100 28.996900 428.277428 708.490643 84.827871 897.324728
2000-06-21 10:00:00+02:00 94.525066 50.169169 39.830831 603.268306 781.227518 102.874099 1233.792552
2000-06-21 11:00:00+02:00 106.936113 39.517644 50.482356 751.612236 811.181337 125.843702 1515.360865
2000-06-21 12:00:00+02:00 124.101947 29.712676 60.287324 862.071318 805.824816 162.194835 1723.771894
2000-06-21 13:00:00+02:00 150.974668 22.305842 67.694158 926.637555 815.663749 172.009087 1845.290578
2000-06-21 14:00:00+02:00 189.036867 20.362593 69.637407 940.709766 813.385068 178.153651 1871.754717
2000-06-21 15:00:00+02:00 222.847350 25.217800 64.782200 903.290967 801.009537 178.621855 1801.370007
2000-06-21 16:00:00+02:00 244.565120 34.007293 55.992707 817.036014 809.396716 146.073338 1638.894191
2000-06-21 17:00:00+02:00 259.103202 44.316289 45.683711 688.127892 792.097153 121.387018 1395.154930
2000-06-21 18:00:00+02:00 270.327385 55.107908 34.892092 526.051805 757.091487 92.970738 1086.065369
2000-06-21 19:00:00+02:00 280.142111 65.894619 24.105381 343.602529 611.132818 94.005988 731.774188
2000-06-21 20:00:00+02:00 289.566812 76.349471 13.650529 158.912224 318.904517 83.651016 359.130268
2000-06-21 21:00:00+02:00 299.258754 86.099097 3.900903 15.621544 0.000000 15.621544 41.965131

Simulating cloudy conditions#

[4]:

 sky_irr = sky_irradiance(daydate='2000-06-21', attenuation=0.2,**Montpellier)
 sky_irr

[4]:
azimuth zenith elevation ghi dni dhi ppfd
2000-06-21 07:00:00+02:00 65.222522 81.781574 8.218426 13.921646 0.000000 13.921646 37.808178
2000-06-21 08:00:00+02:00 74.723897 71.647009 18.352991 48.348336 0.000000 48.348336 120.629656
2000-06-21 09:00:00+02:00 84.230207 61.003100 28.996900 85.655486 0.000000 85.655486 205.795668
2000-06-21 10:00:00+02:00 94.525066 50.169169 39.830831 120.653661 0.000000 120.653661 283.847764
2000-06-21 11:00:00+02:00 106.936113 39.517644 50.482356 150.322447 0.105614 150.240974 349.281690
2000-06-21 12:00:00+02:00 124.101947 29.712676 60.287324 172.414264 0.618064 171.877462 397.754979
2000-06-21 13:00:00+02:00 150.974668 22.305842 67.694158 185.327511 2.164173 183.325281 426.028282
2000-06-21 14:00:00+02:00 189.036867 20.362593 69.637407 188.141953 2.292383 185.992823 432.186277
2000-06-21 15:00:00+02:00 222.847350 25.217800 64.782200 180.658193 0.783678 179.949204 415.808807
2000-06-21 16:00:00+02:00 244.565120 34.007293 55.992707 163.407203 0.422203 163.057211 378.010644
2000-06-21 17:00:00+02:00 259.103202 44.316289 45.683711 137.625578 0.000000 137.625578 321.337452
2000-06-21 18:00:00+02:00 270.327385 55.107908 34.892092 105.210361 0.000000 105.210361 249.555017
2000-06-21 19:00:00+02:00 280.142111 65.894619 24.105381 68.720506 0.000000 68.720506 167.479703
2000-06-21 20:00:00+02:00 289.566812 76.349471 13.650529 31.782445 0.000000 31.782445 81.596061
2000-06-21 21:00:00+02:00 299.258754 86.099097 3.900903 3.124309 0.000000 3.124309 9.353447

Simulating actual irradiances#

In general, meteorological conditions are between overcast and clear sky conditions. The cursor between theses two extremes is a function of the ratio between actual irradiance (measured) and clear sky irradiance.

get some meteorological data

[5]:

meteo_db = montpellier_spring_2013()

[6]:

import pandas
when = pandas.date_range(start='2013-05-26', freq='h', periods=25,
                             tz='Europe/Paris')
observed = meteo_db.loc[when,'ghi']
observed

[6]:

2013-05-26 00:00:00+02:00      0.000000
2013-05-26 01:00:00+02:00      0.000000
2013-05-26 02:00:00+02:00      0.000000
2013-05-26 03:00:00+02:00      0.000000
2013-05-26 04:00:00+02:00      0.000000
2013-05-26 05:00:00+02:00      0.000000
2013-05-26 06:00:00+02:00     31.615385
2013-05-26 07:00:00+02:00    166.370370
2013-05-26 08:00:00+02:00    335.425926
2013-05-26 09:00:00+02:00    505.481481
2013-05-26 10:00:00+02:00    660.689655
2013-05-26 11:00:00+02:00    783.516667
2013-05-26 12:00:00+02:00    865.300000
2013-05-26 13:00:00+02:00    887.883333
2013-05-26 14:00:00+02:00    843.233333
2013-05-26 15:00:00+02:00    861.366667
2013-05-26 16:00:00+02:00    700.766667
2013-05-26 17:00:00+02:00    576.966667
2013-05-26 18:00:00+02:00    415.766667
2013-05-26 19:00:00+02:00    241.550000
2013-05-26 20:00:00+02:00     68.566667
2013-05-26 21:00:00+02:00      1.433333
2013-05-26 22:00:00+02:00      0.000000
2013-05-26 23:00:00+02:00      0.000000
2013-05-27 00:00:00+02:00      0.000000
Name: ghi, dtype: float64

[7]:

sky_irr = sky_irradiance(dates=observed.index, ghi=observed)
sky_irr

[7]:
azimuth zenith elevation ghi dni dhi ppfd
2013-05-26 07:00:00+02:00 67.394678 82.902288 7.097712 166.370370 382.539320 119.103104 372.883646
2013-05-26 08:00:00+02:00 76.998278 72.595513 17.404487 335.425926 708.145583 123.608595 712.692855
2013-05-26 09:00:00+02:00 86.670875 61.831377 28.168623 505.481481 756.869728 148.187460 1043.076789
2013-05-26 10:00:00+02:00 97.240796 50.953097 39.046903 660.689655 850.791955 124.727856 1339.890179
2013-05-26 11:00:00+02:00 110.082221 40.367996 49.632004 783.516667 882.613527 111.053233 1573.703322
2013-05-26 12:00:00+02:00 127.790259 30.809505 59.190495 865.300000 820.208961 160.843080 1729.864628
2013-05-26 13:00:00+02:00 154.619856 23.898554 66.101446 887.883333 676.893420 269.023929 1775.511620
2013-05-26 14:00:00+02:00 190.458560 22.437564 67.562436 843.233333 578.462848 308.562438 1695.371933
2013-05-26 15:00:00+02:00 222.025552 27.340165 62.659835 861.366667 669.045851 267.056253 1725.259707
2013-05-26 16:00:00+02:00 243.129279 36.027976 53.972024 700.766667 530.630224 271.630139 1425.687318
2013-05-26 17:00:00+02:00 257.658296 46.287318 43.712682 576.966667 510.687303 224.060075 1188.519867
2013-05-26 18:00:00+02:00 268.996379 57.092156 32.907844 415.766667 402.926728 196.860848 876.394984
2013-05-26 19:00:00+02:00 278.938942 67.937211 22.062789 241.550000 248.774528 148.104704 530.208075
2013-05-26 20:00:00+02:00 288.494733 78.476514 11.523486 68.566667 6.658009 67.236599 165.803474
2013-05-26 21:00:00+02:00 298.338059 88.229752 1.770248 1.433333 0.000000 1.433333 4.500906 
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