TUTORIAL 3 : The Sky class and computation of radiometric quantities#
In this final tutorial we shall explore the solrad.Sky.Sky class and see how it can be used to compute perform a simulation of solar radiation. We shall see how we can use the class Sky to calculate radiometric quantites such as spectral radiance, radiance, exposure vectors and absorbed energy. This tutorial builds upon the Site object initialized in a previous tutorial (see tutorial 2).
IMPORTATION OF LIBRARIES#
[1]:
import os
import solrad
import numpy as np
from solrad.Sky import Sky
from solrad.Site import Site
import matplotlib.pyplot as plt
import solrad.auxiliary_funcs as aux
from scipy.interpolate import interp1d
1) LOAD Site_obj#
We require a solrad.Site.Site class instance in order to initialize a Sky class instance. Therefore, we load the previously compute Site_obj instance from tutorial 2.
[2]:
# Change this path to where yoy have saved the 'example_Site_obj.pkl' object
# (see tutorial 2). Dont' leav as is.
EXAMPLES_PATH = os.path.join(os.path.dirname(os.path.dirname(solrad.__path__[0])), "examples")
Site_obj_path = os.path.join(EXAMPLES_PATH, "example_Site_obj.pkl")
Site_obj = aux.load_obj_with_pickle(path = Site_obj_path)
2) INITIALIZATION OF SKY OBJECT#
We may now initialize the sky object by passing in the loaded site object as well as the number of division we would like the sky to be discretised in.
[3]:
# Initialization of Sky object.
Sky_obj = Sky(Site_obj, num_divisions = 50)
# Visualize the discretised sky vault in 2D.
Sky_obj.plot_disk_patches(figsize=(12,12))
# Visualize the discretised sky vault in 3D.
Sky_obj.plot_sphere_patches(figsize=(12,12), axis_view=(25, 30))
# (NOTE: Naturally, the higher the number of divisions, the better results.)


3) DISCRETISATION OF THE SKY-VAULT#
Although, the sky is automatically discretised once we initialize the Sky_obj, we can always rediscretize it by calling the ‘self.discretise’ method.
[4]:
# Re-discretise sky-vault
Sky_obj.discretise(num_divisions = 400)
# Visualize the discretised sky vault in 2D.
Sky_obj.plot_disk_patches(figsize=(12,12))
# Visualize the discretised sky vault in 3D.
Sky_obj.plot_sphere_patches(figsize=(12,12), axis_view=(25, 30))
# NOTE: Doing calling this method after initialization will also errase all other radiation quantities computed up to that point.


4) ZONE_DATA AND PATCH_DATA#
After initialization, two important attributes within Sky_obj are created. These are self.zone_data and self.patch_data. These are dictionaries which store all relevant data of each zone and patch of the discretised sky. We call a ‘zone’, each sky ring that contains one or more sky patches. We call a ‘patch’, each cell that subdivides the sky.
[5]:
# Let us see the keys of 'self.zone_data' attribute.
print("--- ZONE KEYS ---")
print(Sky_obj.zone_data.keys())
# These keys are integers which identify each sky zone uniquely.
# The greater the number, the further away the zone is from the sky zenith and the closer
# it is to the sky horizon. We call these numbers 'zone_num'. Let us see the content for one
# of its keys.
print("--- ZONE[KEY] CONTENT ---")
print(Sky_obj.zone_data[5])
# Now, let us see they keys of 'self.patch_data':
print("--- PATCH KEYS ---")
print(Sky_obj.patch_data.keys())
# These keys are 2-tuples of integers which together identify each sky patch uniquely.
# The first number is the 'zone_num' each patch belongs to and the second number is its 'patch_num',
# i.e, a number identifying that patch (only) uniquely within that zone. Let us see the content for one
# of its keys.
print("--- PATCH[KEY] CONTENT ---")
print(Sky_obj.patch_data[(5,1)])
# If you whish to learn more about the specific contents of each dictionary, please
# see the documentation for the method "self.discretise".
--- ZONE KEYS ---
dict_keys([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17])
--- ZONE[KEY] CONTENT ---
{'num_patches': 16, 'inf_zen': 23.897688903972423, 'sup_zen': 28.979615255186545, 'inf_rad': 0.2927963517929051, 'sup_rad': 0.3538472300429355, 'azimuths': array([ 0. , 22.5, 45. , 67.5, 90. , 112.5, 135. , 157.5, 180. ,
202.5, 225. , 247.5, 270. , 292.5, 315. , 337.5, 360. ]), 'patch_area': 0.015503036623809485, 'zone_area': 0.24804858598095175}
--- PATCH KEYS ---
dict_keys([(0, 0), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 0), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (4, 0), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (4, 10), (4, 11), (4, 12), (5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (5, 7), (5, 8), (5, 9), (5, 10), (5, 11), (5, 12), (5, 13), (5, 14), (5, 15), (6, 0), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6), (6, 7), (6, 8), (6, 9), (6, 10), (6, 11), (6, 12), (6, 13), (6, 14), (6, 15), (6, 16), (6, 17), (7, 0), (7, 1), (7, 2), (7, 3), (7, 4), (7, 5), (7, 6), (7, 7), (7, 8), (7, 9), (7, 10), (7, 11), (7, 12), (7, 13), (7, 14), (7, 15), (7, 16), (7, 17), (7, 18), (7, 19), (7, 20), (8, 0), (8, 1), (8, 2), (8, 3), (8, 4), (8, 5), (8, 6), (8, 7), (8, 8), (8, 9), (8, 10), (8, 11), (8, 12), (8, 13), (8, 14), (8, 15), (8, 16), (8, 17), (8, 18), (8, 19), (8, 20), (8, 21), (8, 22), (8, 23), (9, 0), (9, 1), (9, 2), (9, 3), (9, 4), (9, 5), (9, 6), (9, 7), (9, 8), (9, 9), (9, 10), (9, 11), (9, 12), (9, 13), (9, 14), (9, 15), (9, 16), (9, 17), (9, 18), (9, 19), (9, 20), (9, 21), (9, 22), (9, 23), (9, 24), (9, 25), (10, 0), (10, 1), (10, 2), (10, 3), (10, 4), (10, 5), (10, 6), (10, 7), (10, 8), (10, 9), (10, 10), (10, 11), (10, 12), (10, 13), (10, 14), (10, 15), (10, 16), (10, 17), (10, 18), (10, 19), (10, 20), (10, 21), (10, 22), (10, 23), (10, 24), (10, 25), (10, 26), (10, 27), (11, 0), (11, 1), (11, 2), (11, 3), (11, 4), (11, 5), (11, 6), (11, 7), (11, 8), (11, 9), (11, 10), (11, 11), (11, 12), (11, 13), (11, 14), (11, 15), (11, 16), (11, 17), (11, 18), (11, 19), (11, 20), (11, 21), (11, 22), (11, 23), (11, 24), (11, 25), (11, 26), (11, 27), (11, 28), (11, 29), (12, 0), (12, 1), (12, 2), (12, 3), (12, 4), (12, 5), (12, 6), (12, 7), (12, 8), (12, 9), (12, 10), (12, 11), (12, 12), (12, 13), (12, 14), (12, 15), (12, 16), (12, 17), (12, 18), (12, 19), (12, 20), (12, 21), (12, 22), (12, 23), (12, 24), (12, 25), (12, 26), (12, 27), (12, 28), (12, 29), (12, 30), (13, 0), (13, 1), (13, 2), (13, 3), (13, 4), (13, 5), (13, 6), (13, 7), (13, 8), (13, 9), (13, 10), (13, 11), (13, 12), (13, 13), (13, 14), (13, 15), (13, 16), (13, 17), (13, 18), (13, 19), (13, 20), (13, 21), (13, 22), (13, 23), (13, 24), (13, 25), (13, 26), (13, 27), (13, 28), (13, 29), (13, 30), (13, 31), (13, 32), (14, 0), (14, 1), (14, 2), (14, 3), (14, 4), (14, 5), (14, 6), (14, 7), (14, 8), (14, 9), (14, 10), (14, 11), (14, 12), (14, 13), (14, 14), (14, 15), (14, 16), (14, 17), (14, 18), (14, 19), (14, 20), (14, 21), (14, 22), (14, 23), (14, 24), (14, 25), (14, 26), (14, 27), (14, 28), (14, 29), (14, 30), (14, 31), (14, 32), (14, 33), (15, 0), (15, 1), (15, 2), (15, 3), (15, 4), (15, 5), (15, 6), (15, 7), (15, 8), (15, 9), (15, 10), (15, 11), (15, 12), (15, 13), (15, 14), (15, 15), (15, 16), (15, 17), (15, 18), (15, 19), (15, 20), (15, 21), (15, 22), (15, 23), (15, 24), (15, 25), (15, 26), (15, 27), (15, 28), (15, 29), (15, 30), (15, 31), (15, 32), (15, 33), (15, 34), (16, 0), (16, 1), (16, 2), (16, 3), (16, 4), (16, 5), (16, 6), (16, 7), (16, 8), (16, 9), (16, 10), (16, 11), (16, 12), (16, 13), (16, 14), (16, 15), (16, 16), (16, 17), (16, 18), (16, 19), (16, 20), (16, 21), (16, 22), (16, 23), (16, 24), (16, 25), (16, 26), (16, 27), (16, 28), (16, 29), (16, 30), (16, 31), (16, 32), (16, 33), (16, 34), (17, 0), (17, 1), (17, 2), (17, 3), (17, 4), (17, 5), (17, 6), (17, 7), (17, 8), (17, 9), (17, 10), (17, 11), (17, 12), (17, 13), (17, 14), (17, 15), (17, 16), (17, 17), (17, 18), (17, 19), (17, 20), (17, 21), (17, 22), (17, 23), (17, 24), (17, 25), (17, 26), (17, 27), (17, 28), (17, 29), (17, 30), (17, 31), (17, 32), (17, 33), (17, 34)])
--- PATCH[KEY] CONTENT ---
{'inf_zen': 23.897688903972423, 'sup_zen': 28.979615255186545, 'inf_az': 22.5, 'sup_az': 45.0, 'patch_area': 0.015503036623809485, 'unit_vector': array([0.37020297, 0.24736172, 0.8954116 ])}
5) RADIANCES#
With this, we can now fairly easily compute an approximation of the sky’s spectral radiance, as well as its regular radiance, for a given date. To do this, we make use of the self.compute_radiances_for_a_date method.
[6]:
# (NOTE: the date chosen must be present in 'Site_obj.simulation_time_data.keys()')
# COMPUTE SPECTRAL RADIANCE AND RADIANCE
Sky_obj.compute_radiances_for_a_date(year = 2023,
month = 1,
day = 10,
nel = 46,
naz = 181,
num_iterations = 500,
use_site_horizon=True)
# The results are stored in the attribute 'self.radiance_res':
print(Sky_obj.radiances)
# We can also plot the results for a particular time of the date simulated.
# PLOT SPECTRAL RADIANCE
for nt in [15, 50, 100]:
Sky_obj.plot_spectral_radiance_for_a_date(component="direct", nt=nt)
Sky_obj.plot_spectral_radiance_for_a_date(component="diffuse", nt=nt)
# PLOT RADIANCE
for nt in [15, 50, 100]:
Sky_obj.plot_radiance_for_a_date(component="direct", nt=nt)
Sky_obj.plot_radiance_for_a_date(component="diffuse", nt=nt)
Sky_obj.plot_radiance_for_a_date(component="diffuse", nt=nt, projection = "sphere")
# PLOT IGAWA'S SKY INDEX
fig = plt.figure(figsize=(14,12))
plt.plot(Sky_obj.radiances["DatetimeIndex_obj"], Sky_obj.radiances["Siv"])
plt.xlabel("Time")
plt.ylabel("Siv [-]")
plt.title("Igawa's clear sky index across time")
C:\Users\PC-LENOVO\Desktop\solrad-project\src\solrad\radiation\diffuse_radiance_model.py:131: RuntimeWarning: invalid value encountered in divide
Ce = Gdh/Gh
C:\Users\PC-LENOVO\Desktop\solrad-project\src\solrad\radiation\diffuse_radiance_model.py:501: RuntimeWarning: divide by zero encountered in divide
gradation = 1 + a*np.exp(b/np.sin(El_))
{'Siv': array([0.98624458, 1.03452857, 1.07823171, 1.10125785, 1.11417061,
1.12158523, 1.1257394 , 1.12783628, 1.1285739 , 1.02863375,
0.98186586, 0.95029232, 0.92503881, 0.9029509 , 0.88265017,
0.86344879, 0.84496947, 0.8269899 , 0.80937167, 0.79202471,
0.77488839, 0.76380003, 0.75266546, 0.74149322, 0.73029141,
0.71906769, 0.70782938, 0.69658353, 0.68533692, 0.67409618,
0.66286781, 0.65165822, 0.64047381, 0.60485363, 0.57235054,
0.54217056, 0.51376277, 0.48673353, 0.46079526, 0.43573426,
0.41138976, 0.38764001, 0.36439272, 0.34157858, 0.31914688,
0.30991418, 0.30068086, 0.2914471 , 0.28221306, 0.27297894,
0.26374491, 0.2545112 , 0.24527801, 0.23604559, 0.22681421,
0.21758415, 0.20835576, 0.20461276, 0.20086815, 0.19712196,
0.19337423, 0.18962497, 0.18587421, 0.18212196, 0.17836823,
0.17461301, 0.1708563 , 0.16709808, 0.16333832, 0.17870895,
0.19515881, 0.21263108, 0.23110281, 0.25058021, 0.27109577,
0.2927072 , 0.31549802, 0.33957987, 0.36509704, 0.39223352,
0.42122401, 0.40233147, 0.38481509, 0.36861482, 0.35368605,
0.33999636, 0.32752278, 0.31624937, 0.30616495, 0.29726097,
0.28952944, 0.28296101, 0.27754325, 0.29004184, 0.30254233,
0.31504442, 0.32754784, 0.34005236, 0.35255778, 0.36506392,
0.3775706 , 0.39007769, 0.40258503, 0.41509251, 0.42760001,
0.46251985, 0.49773554, 0.53336005, 0.56956637, 0.60662664,
0.64498473, 0.68539908, 0.72924663, 0.7792417 , 0.84142565,
0.93242253, 1.13816097, 1.11128619, 1.08818287, 1.06764466,
1.04900117, 1.03183963, 1.01588971, 1.00096825, 0.98695009,
0.9737517 , 0.96132209, 0.94963838, 0.9387053 , 0.94595761,
0.95288469, 0.95938061, 0.96529853, 0.97043561, 0.97451736,
0.97719743, 0.97814674, 0.9775904 , 0.97939801, 0.99421324,
1.00454456]), 'Kc': array([0.0183847 , 0.02298068, 0.02757657, 0.03217237, 0.03676809,
0.04136373, 0.0459593 , 0.05055478, 0.0551502 , 0.07234696,
0.08954344, 0.10673964, 0.12393558, 0.14113126, 0.15832669,
0.17552187, 0.19271681, 0.20991153, 0.22710602, 0.2443003 ,
0.26149436, 0.27520463, 0.28891475, 0.30262473, 0.31633457,
0.33004429, 0.34375388, 0.35746336, 0.37117272, 0.38488198,
0.39859114, 0.41230021, 0.4260092 , 0.44735184, 0.46869432,
0.49003667, 0.51137889, 0.53272098, 0.55406296, 0.57540483,
0.59674661, 0.6180883 , 0.63942992, 0.66077147, 0.68211296,
0.69137443, 0.70063594, 0.7098975 , 0.7191591 , 0.72842075,
0.73768245, 0.74694422, 0.75620604, 0.76546794, 0.7747299 ,
0.78399194, 0.79325405, 0.79703225, 0.80081055, 0.80458896,
0.80836747, 0.81214609, 0.81592481, 0.81970365, 0.8234826 ,
0.82726166, 0.83104083, 0.83482012, 0.83859953, 0.82600131,
0.81340321, 0.80080522, 0.78820733, 0.77560954, 0.76301184,
0.75041423, 0.73781671, 0.72521925, 0.71262187, 0.70002456,
0.68742731, 0.69046696, 0.69350672, 0.69654659, 0.69958658,
0.70262668, 0.7056669 , 0.70870723, 0.71174768, 0.71478825,
0.71782894, 0.72086976, 0.7239107 , 0.71138851, 0.69886635,
0.68634419, 0.67382203, 0.66129987, 0.64877771, 0.63625552,
0.62373333, 0.6112111 , 0.59868885, 0.58616656, 0.57364423,
0.53948038, 0.50531625, 0.47115182, 0.43698708, 0.40282201,
0.36865659, 0.33449082, 0.30032467, 0.26615814, 0.2319912 ,
0.19782385, 0.16365606, 0.16039592, 0.15713575, 0.15387555,
0.15061533, 0.14735509, 0.14409481, 0.1408345 , 0.13757417,
0.1343138 , 0.13105339, 0.12779295, 0.12453248, 0.11415576,
0.10377887, 0.09340182, 0.08302459, 0.07264718, 0.06226959,
0.05189181, 0.04151384, 0.03113568, 0.02075732, 0.01037876,
0. ]), 'Cle': array([1.2 , 0.43543968, 0.28536202, 0.22521502, 0.19363109,
0.17454744, 0.16194612, 0.15308178, 0.14653456, 0.30862152,
0.39993035, 0.45663107, 0.49421151, 0.52029666, 0.53902834,
0.55282884, 0.56319911, 0.5711134 , 0.57722852, 0.58200135,
0.58575797, 0.57614036, 0.56745428, 0.55957547, 0.55240158,
0.54584738, 0.53984121, 0.53432222, 0.52923838, 0.52454484,
0.52020271, 0.51617806, 0.51244114, 0.56878609, 0.61962619,
0.66572156, 0.70770143, 0.7460908 , 0.78133084, 0.81379478,
0.84380026, 0.87161919, 0.89748558, 0.92160178, 0.94414362,
0.94433274, 0.94457125, 0.94485527, 0.94518124, 0.94554592,
0.94594637, 0.94637991, 0.94684414, 0.94733688, 0.94785619,
0.94840035, 0.94896782, 0.9488835 , 0.948842 , 0.94884142,
0.94888004, 0.94895638, 0.94906912, 0.94921712, 0.94939941,
0.94961521, 0.94986385, 0.95014482, 0.95045777, 0.92014212,
0.88892529, 0.85675955, 0.82359426, 0.78937558, 0.75404619,
0.71754494, 0.67980651, 0.64076101, 0.60033355, 0.55844374,
0.51500512, 0.55201747, 0.58876501, 0.62525778, 0.66150609,
0.69752057, 0.73331224, 0.76889253, 0.80427337, 0.83946725,
0.87448725, 0.90934718, 0.94406157, 0.94328877, 0.94252761,
0.94177928, 0.94104505, 0.94032634, 0.93962464, 0.93894157,
0.93827887, 0.93763835, 0.93702195, 0.93643166, 0.93586959,
0.91590917, 0.89296214, 0.86633608, 0.83511678, 0.79807339,
0.75351083, 0.69903152, 0.63113427, 0.54450388, 0.43067257,
0.27529341, 0.05199723, 0.07396981, 0.09717278, 0.12172728,
0.14777224, 0.17546823, 0.20500272, 0.23659714, 0.27051685,
0.30708528, 0.34670475, 0.38988774, 0.43730489, 0.44644183,
0.45739166, 0.47082574, 0.48777464, 0.50988084, 0.53989024,
0.5826953 , 0.6478173 , 0.75633254, 0.9654196 , 1.2 ,
1.2 ]), 'wavelengths': array([ 300. , 305. , 310. , 315. , 320. , 325. , 330. , 335. ,
340. , 345. , 350. , 360. , 370. , 380. , 390. , 400. ,
410. , 420. , 430. , 440. , 450. , 460. , 470. , 480. ,
490. , 500. , 510. , 520. , 530. , 540. , 550. , 570. ,
593. , 610. , 630. , 656. , 667.6, 690. , 710. , 718. ,
724.4, 740. , 752.5, 757.5, 762.5, 767.5, 780. , 800. ,
816. , 823.7, 831.5, 840. , 860. , 880. , 905. , 915. ,
925. , 930. , 937. , 948. , 965. , 980. , 993.5, 1040. ,
1070. , 1100. , 1120. , 1130. , 1145. , 1161. , 1170. , 1200. ,
1240. , 1270. , 1290. , 1320. , 1350. , 1395. , 1442.5, 1462.5,
1477. , 1497. , 1520. , 1539. , 1558. , 1578. , 1592. , 1610. ,
1630. , 1646. , 1678. , 1740. , 1800. , 1860. , 1920. , 1960. ,
1985. , 2005. , 2035. , 2065. , 2100. , 2148. , 2198. , 2270. ,
2360. , 2450. , 2500. , 2600. , 2700. , 2800. , 2900. , 3000. ,
3100. , 3200. , 3300. , 3400. , 3500. , 3600. , 3700. , 3800. ,
3900. , 4000. ]), 'Az': array([[ 0., 2., 4., ..., 356., 358., 360.],
[ 0., 2., 4., ..., 356., 358., 360.],
[ 0., 2., 4., ..., 356., 358., 360.],
...,
[ 0., 2., 4., ..., 356., 358., 360.],
[ 0., 2., 4., ..., 356., 358., 360.],
[ 0., 2., 4., ..., 356., 358., 360.]]), 'El': array([[ 0., 0., 0., ..., 0., 0., 0.],
[ 2., 2., 2., ..., 2., 2., 2.],
[ 4., 4., 4., ..., 4., 4., 4.],
...,
[86., 86., 86., ..., 86., 86., 86.],
[88., 88., 88., ..., 88., 88., 88.],
[90., 90., 90., ..., 90., 90., 90.]]), 'DatetimeIndex_obj': DatetimeIndex(['2023-01-10 06:20:00-05:00', '2023-01-10 06:25:00-05:00',
'2023-01-10 06:30:00-05:00', '2023-01-10 06:35:00-05:00',
'2023-01-10 06:40:00-05:00', '2023-01-10 06:45:00-05:00',
'2023-01-10 06:50:00-05:00', '2023-01-10 06:55:00-05:00',
'2023-01-10 07:00:00-05:00', '2023-01-10 07:05:00-05:00',
...
'2023-01-10 17:15:00-05:00', '2023-01-10 17:20:00-05:00',
'2023-01-10 17:25:00-05:00', '2023-01-10 17:30:00-05:00',
'2023-01-10 17:35:00-05:00', '2023-01-10 17:40:00-05:00',
'2023-01-10 17:45:00-05:00', '2023-01-10 17:50:00-05:00',
'2023-01-10 17:55:00-05:00', '2023-01-10 18:00:00-05:00'],
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C:\Users\PC-LENOVO\Desktop\solrad-project\src\solrad\Sky.py:1167: UserWarning: FixedFormatter should only be used together with FixedLocator
axs[nr,nc].set_yticklabels([80, 70, 60, 50, 40, 30, 20, 10, 0])






C:\Users\PC-LENOVO\Desktop\solrad-project\src\solrad\Sky.py:1245: UserWarning: FixedFormatter should only be used together with FixedLocator
ax.set_yticklabels([80, 70, 60, 50, 40, 30, 20, 10, 0])









[6]:
Text(0.5, 1.0, "Igawa's clear sky index across time")

6) (SPECTRAL) RADIANT EXPOSURE VECTORS#
We can now compute the spectral and regular exposure vectors for the discretised sky. Each sky patch has one spectral and one regular radiant exposure vectors. The magnitude of these vectors (be it spectral or regular) tells us the total amount energy (per unit area per unit wavelength in the first case, while and just per unit area in the second case) that is emitted by that sky patch, for a given time interval. The direction of these vectors points to the ‘center of radiation’ of the sky patch. That is, the weighted average of emission direction. We can use these vectors (be it spectral or regular) in order to perform computations of absorption and direction optimization, among other things.
[7]:
# We first delete the 'self.radiances' attribute in order to conserve memory space.
# Depending on your hardware this may or may not be necessary.
Sky_obj.radiances = None
# COMPUTE RADIANT EXPOSURE VECTORS (SPECRAL AND NOT SPECTRAL)
start_date = (2023, 1, 1)
end_date = (2023, 1, 31)
Sky_obj.compute_exposure_vectors_for_a_date_interval( start_date = start_date,
end_date = end_date,
nel = 46,
naz = 181,
num_iterations = 500,
use_site_horizon = False,
int_nzen = 20,
int_naz = 30)
# (NOTE: the dates chosen must be present in 'Site_obj.simulation_time_data.keys()')
# The results can be found in 2 places:
# 1) 'self.exposure_vectors' attribute
# 2) 'self.patch_data["exposure"]' attribute
print("--- self.exposure_vectors KEYS ---")
print(Sky_obj.exposure_vectors.keys())
print("--- self.patch_data['exposure'] KEYS ---")
print(Sky_obj.patch_data[(5,1)]["exposure"].keys())
# If you whish to learn more about the specific contents of each dictionary, please
# see the documentation for the method "self.compute_exposure_vectors_for_a_date_interval".
# PLOT RADIANT EXPOSURE (VECTOR MAGNITUDE, NOT SPECTRAL) FOR ALL SKY-PATCHES
for projection in ["disk", "sphere"]:
for mode in ["global", "direct", "diffuse"]:
config = {"projection":projection, "mode":mode, "n":1000}
Sky_obj.plot_exposures(config)
# PLOT RADIANT EXPOSURE (VECTOR MAGNITUDE, SPECTRAL) FOR SOME SKY PATCHES
wavelengths = Sky_obj.exposure_vectors["wavelengths"]
start_date = Sky_obj.time_integrated_spectral_radiance["start_date"]
end_date = Sky_obj.time_integrated_spectral_radiance["end_date"]
for key in [(0, 0), (1, 1), (3, 0), (3, 1), (3, 2), (3, 3), (5, 8), (5, 9), (5, 10), (5, 11), (7, 11), (7, 12), (7, 13)]:
zone_num, patch_num = key
direct_spectral_irrad_mag = Sky_obj.patch_data[key]["exposure"]["spectral_direct"]["magnitude"]
diffuse_spectral_irrad_mag = Sky_obj.patch_data[key]["exposure"]["spectral_diffuse"]["magnitude"]
global_spectral_irrad_mag = Sky_obj.patch_data[key]["exposure"]["spectral_global"]["magnitude"]
az_lims = [round(Sky_obj.patch_data[key]['inf_az'],2), round(Sky_obj.patch_data[key]['sup_az'],2)]
zen_lims = [round(Sky_obj.patch_data[key]['inf_zen'],2), round(Sky_obj.patch_data[key]['sup_zen'],2)]
fig = plt.figure(figsize=(16,12))
plt.plot(wavelengths, direct_spectral_irrad_mag, label="direct")
plt.plot(wavelengths, diffuse_spectral_irrad_mag, label="diffuse")
plt.plot(wavelengths, global_spectral_irrad_mag, label="global")
plt.suptitle(f"From date {start_date} to {end_date}")
plt.title(f"Spectral exposure of patch ({key[0]}, {key[1]}) with az_lims: {az_lims}°, zen_lims: {zen_lims}°")
plt.ylabel("Spectral exposure [Wh/m^2/nm]")
plt.xlabel("Wavelengths [nm]")
plt.xlim(300, 4000)
plt.ylim(0, 18)
plt.grid()
plt.legend()
plt.show()
C:\Users\PC-LENOVO\Desktop\solrad-project\src\solrad\radiation\diffuse_radiance_model.py:202: RuntimeWarning: divide by zero encountered in divide
Cle = (1 - Ce)/(1 - Ces)
C:\Users\PC-LENOVO\Desktop\solrad-project\src\solrad\radiation\diffuse_radiance_model.py:202: RuntimeWarning: invalid value encountered in divide
Cle = (1 - Ce)/(1 - Ces)
C:\Users\PC-LENOVO\Desktop\solrad-project\src\solrad\Sky.py:2008: RuntimeWarning: invalid value encountered in divide
local_direct_spectral_exposure_uvec_spectrally_avgd /=\
C:\Users\PC-LENOVO\Desktop\solrad-project\src\solrad\Sky.py:2384: RuntimeWarning: invalid value encountered in divide
new_direct_unit_vector = new_direct_vector/new_direct_magnitude
--- self.exposure_vectors KEYS ---
dict_keys(['spectral_direct', 'spectral_diffuse', 'spectral_global', 'spectral_direct_mag', 'spectral_diffuse_mag', 'spectral_global_mag', 'spectral_direct_unit_savgd', 'spectral_diffuse_unit_savgd', 'spectral_global_unit_savgd', 'wavelengths', 'direct', 'diffuse', 'global', 'direct_mag', 'diffuse_mag', 'global_mag', 'direct_unit', 'diffuse_unit', 'global_unit'])
--- self.patch_data['exposure'] KEYS ---
dict_keys(['spectral_direct', 'spectral_diffuse', 'spectral_global', 'wavelengths', 'direct', 'diffuse', 'global'])



















7) ABSORBED ENERGY#
We can also compute the incident and absorbed energies for a unit plane, given an an absorption fucntion, for a given radiation component.
[8]:
# DUMMY ABSORPTION FUNCTION FOR EXAMPLE
wavelengths = Sky_obj.exposure_vectors["wavelengths"]
func_array = np.logical_and(375 <= wavelengths, wavelengths <= 1000).astype(float)
func = interp1d(x = wavelengths, y = func_array, kind = "linear")
def absorption_func(arguments):
cos_aoi = np.cos(np.deg2rad(arguments[:,0]))
cos_aoi[cos_aoi<0] = 0
return cos_aoi*func(arguments[:,1])
aoi = np.full(len(wavelengths), 50)
arguments = np.stack([aoi,wavelengths], axis=1)
res = absorption_func(arguments)
plt.plot(wavelengths, res, label = f"aoi = {aoi[0]}°")
plt.ylim(0,1)
plt.show()
# UNIT NORMAL OF PLANE TO EVALUATE
n_uvec=[0,0,1] # (horizontal plane in this case)
# COMPUTE INCIDENT ENERGY (ABSORPTION = 1, FOR EVERY WAVELENGTH)
total_incident_energy =\
Sky_obj.compute_absorbed_energy_by_unit_plane(n_uvec=n_uvec, absorption_func=1, component="global")
# COMPUTE INCIDENT ENERGY (ABSORPTION VARIES WITH WAVELENGTH)
total_absorbed_incident_energy =\
Sky_obj.compute_absorbed_energy_by_unit_plane(n_uvec=n_uvec, absorption_func=absorption_func, component="global")
print(f"Total incident energy on unit horizontal plane: {total_incident_energy/1000} kWh")
print(f"Total absorbed incident energy on unit horizontal plane: {total_absorbed_incident_energy/1000} kWh")

Total incident energy on unit horizontal plane: 179.8235130823509 kWh
Total absorbed incident energy on unit horizontal plane: 95.12443476397864 kWh
8) OPTIMAL ORIENTATION#
Finally, we can find the plane orientation that maximizes energy absorption for a unit plane, given an an absorption fucntion, for a given radiation component.
[9]:
res =\
Sky_obj. compute_optimal_plane_orientation(absorption_func = 1, component = "global")
"""
res =\
Sky_obj. compute_optimal_plane_orientation(absorption_func = absorption_func, component = "global")
"""
print("--- OPTIMAL ORIENTATION RESULTS --- ")
print(res)
--- OPTIMAL ORIENTATION RESULTS ---
{'energy': 208422.72627443934, 'az': 179.83397990969368, 'zen': 32.109434537418075, 'n_uvec': [-0.5315358311644897, 0.0015401810467349133, 0.8470344078197877], 'el': 57.890565462581925, 'az_res': 8.26908594968082e-08, 'el_res': 0.3468305983166518}
[ ]: