Is there a difference between the solar elevation angle and sun declination?

Is there a difference between the solar elevation angle and sun declination?

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I need to use the sunrise equation but one of the variables is the sun declination. On the other hand, I have the values for solar elevation angle that I need. Are they the same thing?

Elevation and Declination are from different co-ordinate systems, so solar elevation is given in Alt/Az co-ordinates and refers to the elevation above the local horizon. Sun declination is measured in RA/Dec co-ordinates (which is an equatorial co-ordinate system) and measures the Sun's inclination above or below the equator on the celestial sphere.

Is there a difference between the solar elevation angle and sun declination? - Astronomy

Angles of Elevation / Inclination and
Angles of Depression / Declination

Angles of elevation or inclination are angles above the horizontal, like looking up from ground level toward the top of a flagpole. Angles of depression or declination are angles below the horizontal, like looking down from your window to the base of the building in the next lot. Whenever you have one of these angles, you should immediately start picturing how a right triangle will fit into the description.

    Driving along a straight flat stretch of Arizona highway, you spot a particularly tall saguaro ("suh-WARH-oh") cactus right next to a mile marker. Watching your odometer, you pull over exactly two-tenths of a mile down the road. Retrieving your son's theodolite from the trunk, you measure the angle of elevation from your position to the top of the saguaro as2.4°. Accurate to the nearest whole number, how tall is the cactus?

Two-tenths of a mile is 0.2×5280 feet = 1056 feet, so this is my horizontal distance. I need to find the height h of the cactus. So I draw a right triangle and label everything I know:

The scale is not important I'm not bothering to get the angle "right". I'm using the drawing as a way to keep track of information the particular size is irrelevant.

What is relevant is that I have "opposite" and "adjacent" and an angle measure. This means I can create and solve an equation:

h/1056 = tan(2.4°)
h = 1056×tan(2.4°) = 44.25951345.

To the nearest foot, the saguaro is 44 feet tall.

  • You were flying a kite on a bluff, but you managed somehow to dump your kite into the lake below. You know that you've given out325feet of string. A surveyor tells you that the angle of declination from your position to the kite is15°. How high is the bluff where you and the surveyor are standing?

The horizontal line across the top is the line from which the angle of depression is measured. But by nature of parallel lines, the same angle is in the bottom triangle. I can "see" the trig ratios more easily in the bottom triangle, and the height is a bit more obvious. So I'll use this part of the drawing.

I have "opposite", hypotenuse, and an angle, so I'll use the sine ratio to find the height.

h/325 = sin(15°) Copyright © Elizabeth Stapel 2010-2011 All Rights Reserved
h = 325×sin(15°) = 84.11618966.

The bluff is about 84 feet above the lake.

  • A lighthouse stands on a hill100m above sea level. If&angACDmeasures60°and&angBCDis30°, find the height of the lighthouse.

I'm going to have to work this exercise in steps. I can't find the height of the tower, AB , until I have the length of the base CD . (Think of D as being moved to the right, to meet the continuation of AB , forming a right triangle.) For this computation, I'll use the height of the hill.

100/|CD| = tan(30°)
100/tan(30°) = |CD| = 173.2050808.

To minimize round-off error, I'll use all the digits from my calculator in my computations, and try to "carry" the computations in my calculator the whole way..

Now that I have the length of the base, I can find the total height, using the angle that measures the the elevation from sea level to the top of the tower.

h/173.2050808 = tan(60°)
h = 173.2050808×tan(60°) = 300

Excellent! By keeping all the digits and carrying the computations in my calculator, I got an exact answer. No rounding! But I do need to subtract, because " 300 " is the height from the water to the top of the tower. The first hundred meters of this total height is hill, so:

Is there a difference between the solar elevation angle and sun declination? - Astronomy

The excellent sun_position utility by Vincent Roy has been converted to an alternate library that accepts a [1XN] Julian vector in place of [Y,D,M,H,MI,S] and local hour offset and/or a [3XN] position vector in place of the location structure. Calculations with fixed time and varying location or fixed location and varying time can be used. Varying time and position calculations are suited for aircraft or satellite observations.

Cite As

Charles Rino (2021). Full Vectorization of Solar Azimuth and Elevation Estimation (, MATLAB Central File Exchange. Retrieved June 25, 2021 .

Comments and Ratings ( 11 )

Apparently only the issue in my last comment was implemented. Anyway - a much faster code is provided in the PV-Lib toolbox.
At least times 2 faster and also addresses the issues mentioned by the original author with messed up angles at low sun angles.

Ah man this comments system is messed up. I hope MathWorks sort it out. Anyway, nice and fast code. I am surprised though that when I download the .zip I seem to get a version that hasn't had John Wood's correction implemented. Any idea why that is?

Following on from G. M. Wolfe's 3rd comment. It is not that it is not obvious, it is that the instructions in the function are incorrect:

% Input parameters:
% jday= julian day at loc_llh Nx1 vector
% loc_llh: a 3xN vector containing

Another small mistake:
the topocentric local hour calculate R never gets called.

topocentric_local_hour = topocentric_local_hour_calculate(observer_local_hour, topocentric_sun_position)

topocentric_local_hour = topocentric_local_hour_calculateR(observer_local_hour, topocentric_sun_position)

I agree to John Wood. And I have the solution to his stated problem:

With the code in the zenith calculations, the vectorized apparent_elevation never adds the refraction:

% Apparent elevation
if(true_elevation > -5)
apparent_elevation = true_elevation + refraction_corr
apparent_elevation = true_elevation

Use instead:

This is certainly much faster than for-looping sun_position, and I am thankful for the effort. There are, however a few issues that could be easily remedied.

1) The one previously noted by John Wood, which I fixed in my copy.

2) It would have been easier to implement this if the inputs had not been changed from those in sun_position. I had to calculate julian days myself, requiring me to vectorize the julian_calculation sub-function.

3) It took a few tries to determine that the function expects row vectors, not column vectors. This is not obvious from the function description.

OK. The gross error in the zenith calculation is in line 7 of sun_topocentric_zenith_angle_calculateR. You are only using the first latitude value. This should read:
% Topocentric elevation, without atmospheric refraction
argument = (sin(loc_llh(1,:)* pi/180).*sin(topocentric_sun_position.declination * pi/180)) + .
(cos(loc_llh(1,:)* pi/180).*cos(topocentric_sun_position.declination * pi/180).*cos(topocentric_local_hour * pi/180))
true_elevation = asin(argument) * 180/pi

I haven't followed through the fine scale discrepancies, but I suspect they are due to errors in the Vincent Roy transcription of the Reda & Andreas algorithms that haven't been corrected yet.

Thank you for having a go at vectorising this function Charles, that would be very useful. However I found some unexpected outputs when I tried it out.
1. When I tried your test script SunAngleSpatialVariation, I found the solar altitude angle did not vary with latitude, which I don't think is right. I did a similar graph plotting the solar azimuth, and there were some discontinuities in this as well. So I think there is a bug somewhere in the calculation chain.
2. I started to test your function by comparing it with the original SunPosition calculations done within a for loop, but found that the original calculation chain in your files was broken (inconsistencies in the location definition). When I went back to the original Vincent Roy source, and compared his results with yours for your SunAngleLocalVariation script, I found a close agreement, but there were small differences in the calculated angles of the order of 0.03°, which may not be a problem in practice, but are 10 to 100 times the stated accuracy of the Roy algorithm.

If you could resolve these inconsistencies, this vectorised calculation would be extremely useful.

At an equinox, the Sun is overhead (at midday) at the equator.

Now I'm having a little trouble visualizing the situation .

If the Sun is overhead at midday at an equinox at the equator, it means that the solar altitude is 90 degrees. At the Tropics, which are at latitude 23.5 degrees, the solar altitude would be at 66.5 degrees (90 - 23.5) . is that right? If I'm visualizing it properly, it means that the Sun's declination is 23.5 degrees at the Tropics at an equinox, and 0 degrees at the equator.

But then I'm thinking that at the equinox, the Earth's rotation axis is perpendicular to the line of intersection between the ecliptic and the equator of the celestial sphere . so that's what makes me think that the Sun's declination is 0 degrees, because the Sun is also perpendicular to that line of intersection.

Have I totally misunderstood? I think I may have confused the Sun's declination with its altitude.

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Nontracking solar collection technologies for solar heating and cooling systems

4.4 Compound parabolic collectors

CPCs belong in the category of nonimaging concentrators as they do not form an image of the sun on the absorber. These are capable of reflecting to the absorber all of the incident radiation. The first designs of these collectors were developed by [19] thus sometimes they are also called Winston-type collectors. The basic idea is that the necessity of moving the concentrator to accommodate the diurnal apparent motion of the sun can be reduced by using a trough with two sections of a parabola facing each other, as shown in Fig. 4.6 .

Figure 4.6 . Possible absorber types for compound parabolic collectors and fin details.

Compound parabolic concentrators can accept incoming radiation over a relatively wide range of angles depending on the solar incidence angle by using one or multiple internal reflections. Any radiation that is entering the aperture, within the collector acceptance angle, will hit the absorber surface located at the bottom of the collector. If the reflectivity of the concentrating surface is not high, optical losses may be significant [22] . The absorber of a CPC can take a variety of shapes and as can be seen in Fig. 4.6 it can be flat, bifacial, wedge-shaped, or cylindrical. The first three are a fin type with pipes embedded on the fins (shown in details in Fig. 4.6 ).

Two basic types of CPCs have been developed: the symmetric, shown in Fig. 4.6 , and the asymmetric, which have shapes similar to those shown in the next section.

The collector can be stationary or tracking, depending on the acceptance angle. When tracking is used this is very coarse or intermittent as the concentration ratio is small. Solar radiation is collected and concentrated by one or more reflections on the parabolic surfaces. For higher temperature applications higher concentration ratios and more refined tracking are required.

CPCs can be designed either as one large unit with one opening and one receiver as shown in Fig. 4.6 or as a panel, which looks like an FPC, as shown in Fig. 4.7 .

Figure 4.7 . Detail of a panel compound parabolic collector with cylindrical absorbers.

In the following an optical and thermal analysis of CPCs is presented.

A Winston design CPC [20] is shown in Fig. 4.8 . This is a nonimaging concentrator. It is a linear two-dimensional concentrator consisting of two parabolas, A and B, the axes of which are inclined at the collector half-acceptance angle (±θc) on either side of the collector optical axis. The collector θc is defined as the angle through which a source of light can be moved from the normal to the collector axis and still converge at the absorber. CPCs have a constant acceptance angle over the entire aperture area [22] .

Figure 4.8 . Design details of a flat receiver compound parabolic collector (CPC).

A cylindrical receiver collector is shown in Fig. 4.9 . As was indicated earlier, the receiver of the CPC does not have to be flat and parallel but can be bifacial, wedge-shaped, or cylindrical. In the cylindrical receiver collector, the small lower portions of the reflector (AB and AC) are of circular shape and the upper portions (BD and CE) are of parabolic shape. In this design, it is required that, for the parabolic portion of the collector at any point X, the normal to the collector must bisect the angle between the tangent line to the receiver XY and the incident ray at point X at angle θc with respect to the collector axis, as shown. The side wall profile of fully developed CPCs may terminate when it becomes parallel to the optical axis. Usually very little concentration is lost by truncating these devices by some fraction (about 0.6–0.9) relative to their full height [22] . Therefore, a shorter version of the CPC is obtained with less reflective material, which affects marginally the acceptance angle but changes the height-to-aperture ratio, the concentration ratio, and the average number of reflections. As the reflectivity of the mirrored surfaces is affected by dust and other material deposits, CPCs are usually covered with glass.

Figure 4.9 . Schematic diagram of a compound parabolic collector with cylindrical receiver.

The orientation of a CPC is related to its acceptance angle. A two-dimensional CPC is an ideal concentrator, ie, it perfectly utilizes all rays within the acceptance angle 2θc. The collector can be stationary or tracking depending on the collector acceptance angle. Both north–south and east–west directions can be employed with respect to the orientation of its long axis. In both cases its aperture is tilted directly toward the equator at an angle equal to the latitude of the location.

When the collector axis is oriented along the north–south direction this must track the sun periodically by turning its axis so that the solar incidence is within the acceptance angle of the concentrator. Depending on the application (requirement over a certain time span) the collector can also be stationary but radiation will be received only during the hours when the sun is within the collector acceptance angle [6] .

When the concentrator is oriented with its long axis along the east–west direction, the collector is able to utilize the sun's rays effectively through its acceptance angle. For stationary CPCs mounted in this mode the minimum acceptance angle should be 47 degrees. This angle covers the declination of the sun from the summer to the winter solstice (2 × 23.5°). Bigger angles are used in practice with lower concentration ratio to enable the collector to also collect diffuse radiation. Small CPCs, with a concentration ratio less than 3, are of the greatest practical interest [10] . These are able to accept a large amount of diffuse radiation incident on their apertures and concentrate the beam radiation without the need of tracking the sun. As a general guideline, the required frequency of collector adjustment is related to the collector concentration ratio. For C ≤ 2 the collector can be steady, whereas for C = 3 the collector needs only biannual adjustment, and for C close to 10 it requires almost daily adjustment, and these systems are also called quasi-static [6] .

Tilt Fixed at Winter Angle

If your need for energy is highest in the winter, or the same throughout the year, you may want to just leave the tilt at the winter setting. This could be the case if, for instance, you are using passive solar to heat a greenhouse. Although you could get more energy during other seasons by adjusting the tilt, you will get enough energy without making any adjustment. The following tables assume that the tilt is set at the winter optimum all year long. They show the amount of insolation (in kWh/m 2 ) on the panel each day, averaged over the season.

Latitude 30° Tilt 50.7°
Season Insolation on panel % of winter insolation
Winter 5.6 100%
Spring, Autumn 6.0 107%
Summer 5.1 91%

Latitude 40° Tilt 59.6°
Season Insolation on panel % of winter insolation
Winter 4.7 100%
Spring, Autumn 5.8 123%
Summer 5.1 109%

Latitude 50° Tilt 68.5°
Season Insolation on panel % of winter insolation
Winter 3.4 100%
Spring, Autumn 5.4 158%
Summer 5.1 150%

Solar Radiation on a Tilted Surface

The power incident on a PV module depends not only on the power contained in the sunlight, but also on the angle between the module and the sun. When the absorbing surface and the sunlight are perpendicular to each other, the power density on the surface is equal to that of the sunlight (in other words, the power density will always be at its maximum when the PV module is perpendicular to the sun). However, as the angle between the sun and a fixed surface is continually changing, the power density on a fixed PV module is less than that of the incident sunlight.

The amount of solar radiation incident on a tilted module surface is the component of the incident solar radiation which is perpendicular to the module surface. The following figure shows how to calculate the radiation incident on a tilted surface (Smodule) given either the solar radiation measured on horizontal surface (Shoriz) or the solar radiation measured perpendicular to the sun (Sincident).

Tilting the module to the incoming light reduces the module output.

The equations relating Smodule, Shoriz and Sincident are:

&alpha is the elevation angle and
&beta is the tilt angle of the module measured from the horizontal.

The elevation angle has been previously given as:

where (phi) is the latitude and
(delta)is the declination angle previously given as:

where d is the day of the year. Note that from simple math (284+d) is equivalent to (d-81) which was used before. Two equations are used interchangeably in literature.

From these equations a relationship between Smodule and Shoriz can be determined as:

The following active equations show the calculation of the incident and horizontal solar radiation and that on the module. Enter only one of Smodule, Shoriz and Sincident and the program will calculate the others.

The tilt angle has a major impact on the solar radiation incident on a surface. For a fixed tilt angle, the maximum power over the course of a year is obtained when the tilt angle is equal to the latitude of the location. However, steeper tilt angles are optimized for large winter loads, while lower title angles use a greater fraction of light in the summer. The simulation below calculates the maximum number of solar insolation as a function of latitude and module angle.

The effect of latitude and module tilt on the solar radiation received throughout the year in W.h.m -2 .day -1 without cloud. On the x-axis, day is the number of days since January 1. The Module Power is the solar radiation striking a tilted module. The module tilt angle is measured from the horizontal. The Incident Power is the solar radiation perpendicular to the sun's rays and is what would be received by a module that perfectly tracks the sun. Power on Horizontal is the solar radiation striking the ground and is what would be received for a module lying flat on the ground. These values should be regarded as maximum possible values at the particular location as they do not include the effects of cloud cover. The module is assumed to be facing south in the northern hemisphere and north in the southern hemisphere. For some angles, the light is incident from the rear of the module and in these cases the module power drops to 0.

As can be seen from the above animation, for a module tilt of 0°, the Module Power and Power on Horizontal are equal since the module is lying flat on the ground. At a module tilt of 80°, the module is almost vertical. The Module Power is less than the Incident Power except when the module is perpendicular to the sun's rays and the values are equal. The module is orientated to the equator so it faces north in the Southern Hemisphere and south in the Northern Hemisphere. As module moves from the Northern to Southern Hemisphere (latitude = 0°), the module is turned to face in the opposite direction and so the Module Power curve flips. When the light is incident from the rear of the module the Module Power drops to zero . Try setting the latitude to your location and then varying the module tilt to see the effect on the amount of power received throughout the year.

The Role of Solar-Radiation Climatology in the Design of Photovoltaic Systems

5.4.1 Key angles describing the solar geometry

Two angles are used to define the angular position of the Sun as seen from a given point on Earth’s surface ( Fig. 20 ): solar altitude and solar azimuth.

Figure 20 . Definition of angles used to describe the solar position (γs and αs), the orientation and tilt of the irradiated plane (α and β), the angle of incidence (ν), and the horizontal shadow angle (α1).

From reference CIBSE Guide J. Weather, Solar and Illuminance Data, Chartered Institution of Building Services Engineers, 222 Balham High Road, London SW12 9BS, UK, 2002 [7] .

Solar altitude (γS) is the angular elevation of the center of the solar disk above the horizontal plane.

Solar azimuth (αS) is the horizontal angle between the vertical plane containing the center of the solar disk and the vertical plane running in a true north–south direction. It is measured from due south in the northern hemisphere, clockwise from the true north. It is measured from due north in the southern hemisphere, anticlockwise from true south. Values are negative before solar noon and positive after solar noon.

Four other important solar angles are the following:

The solar incidence angle on a plane of tilt α and slope β (ν(β,α)) is the angle between the normal to the plane on which the Sun is shining and the line from the surface passing through the center of the solar disk. The cosine of ν(β,α) is used to estimate the incident beam irradiance on a surface from the irradiance normal to the beam.

The vertical shadow angle, sometimes called the vertical profile angle (γp), is the angular direction of the center of the solar disk as it appears on a drawn vertical section of specified orientation (see Fig. 21 ).

Figure 21 . Definition of vertical shadow angle γp and the horizontal shadow angle αF.

From reference CIBSE Guide J. Weather, Solar and Illuminance Data, Chartered Institution of Building Services Engineers, 222 Balham High Road, London SW12 9BS, UK, 2002 [7] .

The wall solar azimuth angle, sometimes called the horizontal shadow angle (αF) is the angle between the vertical plane containing the normal to the surface and the vertical plane passing through the center of the solar disk. In other words it is the resolved angle on the horizontal plane between the direction of the Sun and the direction of the normal to the surface (see Fig. 21 ).

The sunset hour angle (ωs) is the azimuth angle at astronomical sunset. It is a quantity used in several algorithmic procedures.


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Watch the video: HW 2 Practice 1 MEE 473. RCL 573 - Elevation Angle and Azimuth Angle from Date, Time and Location. (June 2022).