1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
|
<!DOCTYPE html>
<html class="writer-html5" lang="en" >
<head>
<meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>solar hour angle derivations — HARP 1.16 documentation</title>
<link rel="stylesheet" href="../../_static/pygments.css" type="text/css" />
<link rel="stylesheet" href="../../_static/css/theme.css" type="text/css" />
<link rel="stylesheet" href="../../_static/custom.css" type="text/css" />
<!--[if lt IE 9]>
<script src="../../_static/js/html5shiv.min.js"></script>
<![endif]-->
<script data-url_root="../../" id="documentation_options" src="../../_static/documentation_options.js"></script>
<script src="../../_static/jquery.js"></script>
<script src="../../_static/underscore.js"></script>
<script src="../../_static/_sphinx_javascript_frameworks_compat.js"></script>
<script src="../../_static/doctools.js"></script>
<script src="../../_static/sphinx_highlight.js"></script>
<script async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<script src="../../_static/js/theme.js"></script>
<link rel="index" title="Index" href="../../genindex.html" />
<link rel="next" title="solar zenith angle derivations" href="solar_zenith_angle.html" />
<link rel="prev" title="solar elevation angle derivations" href="solar_elevation_angle.html" />
</head>
<body class="wy-body-for-nav">
<div class="wy-grid-for-nav">
<nav data-toggle="wy-nav-shift" class="wy-nav-side">
<div class="wy-side-scroll">
<div class="wy-side-nav-search" >
<a href="../../index.html" class="icon icon-home"> HARP
</a>
<div class="version">
1.16
</div>
</div><div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="Navigation menu">
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="../../install.html">Installation</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../conventions/index.html">Conventions</a></li>
<li class="toctree-l1 current"><a class="reference internal" href="../index.html">Algorithms</a><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="../definitions.html">Definitions</a></li>
<li class="toctree-l2"><a class="reference internal" href="../formula.html">Common formula</a></li>
<li class="toctree-l2 current"><a class="reference internal" href="../index.html#variable-conversions">Variable Conversions</a><ul class="current">
<li class="toctree-l3"><a class="reference internal" href="../common.html">common derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="aerosol_extinction_coefficient.html">aerosol extinction coefficient derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="aerosol_optical_depth.html">aerosol optical depth derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="angstrom_exponent.html">angstrom exponent derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="altitude.html">altitude derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="altitude_bounds.html">altitude bounds derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="cloud_height.html">cloud height derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="column_mass_density.html">column mass density derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="column_mass_mixing_ratio.html">column mass mixing ratio derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="column_number_density.html">column number density derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="column_number_density_avk.html">column number density averaging kernel derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="column_volume_mixing_ratio.html">column volume mixing ratio derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="datetime.html">datetime derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="datetime_bounds.html">datetime bounds derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="datetime_length.html">datetime length derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="datetime_start.html">datetime start derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="datetime_stop.html">datetime stop derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="degrees_of_freedom_for_signal.html">degrees of freedom for signal</a></li>
<li class="toctree-l3"><a class="reference internal" href="frequency.html">frequency derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="geopotential.html">geopotential derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="geopotential_height.html">geopotential height derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="gravity.html">gravity derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="latitude.html">latitude derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="latitude_bounds.html">latitude bounds derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="longitude.html">longitude derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="longitude_bounds.html">longitude bounds derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="mass_density.html">mass density derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="mass_mixing_ratio.html">mass mixing ratio derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="molar_mass.html">molar mass derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="number_density.html">number density derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="number_density_avk.html">number density averaging kernel derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="partial_pressure.html">partial pressure derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="pressure.html">pressure derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="pressure_bounds.html">pressure bounds derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="relative_azimuth_angle.html">relative azimuth angle derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="relative_humidity.html">relative humidity derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="scattering_angle.html">scattering angle derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="sensor_azimuth_angle.html">sensor azimuth angle derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="sensor_elevation_angle.html">sensor elevation angle derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="sensor_zenith_angle.html">sensor zenith angle derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="solar_azimuth_angle.html">solar azimuth angle derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="solar_declination_angle.html">solar declination angle derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="solar_elevation_angle.html">solar elevation angle derivations</a></li>
<li class="toctree-l3 current"><a class="current reference internal" href="#">solar hour angle derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="solar_zenith_angle.html">solar zenith angle derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="temperature.html">temperature derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="viewing_azimuth_angle.html">viewing azimuth angle derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="viewing_elevation_angle.html">viewing elevation angle derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="viewing_zenith_angle.html">viewing zenith angle derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="virtual_temperature.html">virtual temperature derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="volume_mixing_ratio.html">volume mixing ratio derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="volume_mixing_ratio_avk.html">volume mixing ratio averaging kernel derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="wavelength.html">wavelength derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="wavenumber.html">wavenumber derivations</a></li>
<li class="toctree-l3"><a class="reference internal" href="wind_velocity.html">wind velocity derivations</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../../operations.html">Operations</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../ingestions/index.html">Ingestion definitions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../libharp.html">C library</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../idl.html">IDL interface</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../matlab.html">MATLAB interface</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../python.html">Python interface</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../R.html">R interface</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../tools.html">Command line tools</a></li>
</ul>
</div>
</div>
</nav>
<section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" >
<i data-toggle="wy-nav-top" class="fa fa-bars"></i>
<a href="../../index.html">HARP</a>
</nav>
<div class="wy-nav-content">
<div class="rst-content">
<div role="navigation" aria-label="Page navigation">
<ul class="wy-breadcrumbs">
<li><a href="../../index.html" class="icon icon-home"></a> »</li>
<li><a href="../index.html">Algorithms</a> »</li>
<li>solar hour angle derivations</li>
<li class="wy-breadcrumbs-aside">
</li>
</ul>
<hr/>
</div>
<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
<div itemprop="articleBody">
<section id="solar-hour-angle-derivations">
<h1>solar hour angle derivations</h1>
<blockquote>
<div></div></blockquote>
<ol class="arabic" id="derivation-solar-hour-angle-from-datetime-and-longitude">
<li><p>solar hour angle from datetime and longitude</p>
<table class="docutils align-default">
<colgroup>
<col style="width: 19%" />
<col style="width: 23%" />
<col style="width: 26%" />
<col style="width: 32%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>symbol</p></th>
<th class="head"><p>description</p></th>
<th class="head"><p>unit</p></th>
<th class="head"><p>variable name</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p><span class="math notranslate nohighlight">\(EOT\)</span></p></td>
<td><p>equation of time</p></td>
<td><p><span class="math notranslate nohighlight">\(minutes\)</span></p></td>
<td></td>
</tr>
<tr class="row-odd"><td><p><span class="math notranslate nohighlight">\(t\)</span></p></td>
<td><p>datetime (UTC)</p></td>
<td><p><span class="math notranslate nohighlight">\(s\)</span> since 2000-01-01</p></td>
<td><p><cite>datetime {time}</cite></p></td>
</tr>
<tr class="row-even"><td><p><span class="math notranslate nohighlight">\(\eta\)</span></p></td>
<td><p>orbit angle of the
earth around the sun</p></td>
<td><p><span class="math notranslate nohighlight">\(rad\)</span></p></td>
<td></td>
</tr>
<tr class="row-odd"><td><p><span class="math notranslate nohighlight">\(\lambda\)</span></p></td>
<td><p>longitude</p></td>
<td><p><span class="math notranslate nohighlight">\(degE\)</span></p></td>
<td><p><cite>longitude {time}</cite></p></td>
</tr>
<tr class="row-even"><td><p><span class="math notranslate nohighlight">\(\omega\)</span></p></td>
<td><p>solar hour angle</p></td>
<td><p><span class="math notranslate nohighlight">\(deg\)</span></p></td>
<td><p><cite>solar_hour_angle {time}</cite></p></td>
</tr>
</tbody>
</table>
<div class="math notranslate nohighlight">
\begin{eqnarray}
A & = & 2\pi \left( \frac{t + 10 \cdot 86400}{365.2422 \cdot 86400} - \lfloor \frac{t + 10 \cdot 86400}{365.2422 \cdot 86400} \rfloor \right) \\
B & = & A + 2 \cdot 0.0167 \sin( 2\pi \left( \frac{t - 2 \cdot 86400}{365.2422 \cdot 86400} - \lfloor \frac{t - 2 \cdot 86400}{365.2422 \cdot 86400} \rfloor \right) ) \\
C & = & \frac{A - \arctan(\frac{\tan(B)}{cos(\frac{\pi}{180} 23.44)})}{\pi} \\
EOT & = & 720 \left( C - \lfloor C + 0.5 \rfloor \right) \\
\omega & = & \lambda + 360 \left( \frac{t}{86400} - \lfloor \frac{t}{86400} \rfloor + \frac{EOT}{24 \cdot 60} \right) - 180
\end{eqnarray}</div><p>The solar hour angle will be mapped to [-180,180].</p>
</li>
</ol>
</section>
</div>
</div>
<footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
<a href="solar_elevation_angle.html" class="btn btn-neutral float-left" title="solar elevation angle derivations" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
<a href="solar_zenith_angle.html" class="btn btn-neutral float-right" title="solar zenith angle derivations" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a>
</div>
<hr/>
<div role="contentinfo">
<p>© Copyright 2015-2022 S[&]T, The Netherlands.</p>
</div>
</footer>
</div>
</div>
</section>
</div>
<script>
jQuery(function () {
SphinxRtdTheme.Navigation.enable(true);
});
</script>
</body>
</html>
|
