Solar Radiation, Meteorology and Resource Assessment

Introduction

Solar-energy-system performance begins with a reliable description of the solar resource at a site. The resource is not simply “sunshine.” It is a time-varying combination of extraterrestrial radiation, atmospheric attenuation, cloud effects, terrain, orientation, shading, and local meteorological conditions. A photovoltaic or solar-thermal system can be well designed electrically and still underperform if the solar resource has been incorrectly estimated.

This chapter develops the foundation needed to assess solar resources at a specific location. It explains solar geometry, irradiance components, air mass, sun-path diagrams, orientation and shading, meteorological measurements, satellite and typical meteorological year (TMY) data, and uncertainty analysis. The emphasis is on methods appropriate for undergraduate engineering practice.

Learning Objectives

By the end of this chapter, a student should be able to:

1. Explain the distinction between irradiance, irradiation, and sunshine duration.
2. Calculate solar declination, solar time, solar altitude, and solar azimuth.
3. Distinguish direct, diffuse, and reflected radiation.
4. Explain air mass and atmospheric effects on solar radiation.
5. Interpret sun-path diagrams and evaluate orientation and shading.
6. Compare pyranometer, satellite, and modeled resource data.
7. Use TMY datasets appropriately and identify their limitations.
8. Estimate a plane-of-array solar resource and communicate uncertainty.

1. Solar Radiation Fundamentals

Solar radiation is electromagnetic energy emitted by the Sun. At the mean Earth–Sun distance, the average irradiance on a plane normal to the Sun’s rays outside the atmosphere is approximately 1,361 W/m². This value is called the solar constant, although the actual value varies slightly with Earth–Sun distance and solar activity.

Irradiance is instantaneous radiant power per unit area, measured in watts per square metre (W/m²). Irradiation is radiant energy received per unit area over a time interval, commonly expressed in Wh/m² or kWh/m². Thus, an irradiance of 800 W/m² maintained for 2 h produces 1.6 kWh/m² of irradiation, ignoring variation during the interval.

At the ground, global horizontal irradiance (GHI) is conventionally separated into:

• Direct normal irradiance (DNI): radiation arriving directly from the solar disk on a surface normal to the Sun’s rays.
• Diffuse horizontal irradiance (DHI): radiation scattered or reflected by the atmosphere and arriving from the sky dome, excluding the solar disk.
• Ground-reflected irradiance: radiation reflected from the ground or surrounding surfaces.

For a horizontal surface, the fundamental relationship is:

Here, θ_z is the solar zenith angle, measured from the vertical. DNI is defined on a plane normal to the rays, whereas GHI is defined on a horizontal plane. The equation assumes that the direct beam is above the horizon and that irradiance components are measured consistently.

For an inclined collector, the plane-of-array irradiance is commonly represented as:

where G_POA is irradiance on the collector plane, θ_i is the incidence angle between the Sun’s rays and the collector normal, DHI_i is diffuse irradiance incident on the inclined plane, ρ_g is ground albedo, and F_g is the fraction of the ground visible to the collector. The first term is the plane-of-array direct component. The diffuse term requires a sky model; the final term is a simplified isotropic ground-reflection contribution.

The equation is a model rather than a universal measurement identity. More advanced anisotropic models account separately for circumsolar brightness and horizon brightening.

2. Earth–Sun Geometry

Solar geometry describes the apparent position of the Sun relative to an observer. The principal angles are:

• Latitude, φ: angular position north or south of the equator; north is positive.
• Solar declination, δ: angular position of the Sun north or south of the equatorial plane.
• Hour angle, ω: angular displacement of the Sun east or west of the local solar meridian; it is negative in the morning and positive in the afternoon.
• Solar zenith angle, θ_z: angle between the Sun and the vertical.
• Solar altitude angle, α: angle between the Sun and the horizontal plane.
• Solar azimuth, γ_s: horizontal direction of the Sun, measured using a stated convention.

The solar altitude and zenith angles are complementary:

2.1 Declination

A commonly used approximation for solar declination is:

where n is the day number, with 1 January as n = 1. The approximation is suitable for preliminary engineering calculations. More precise solar-position algorithms account for leap years, orbital eccentricity, and time standards.

2.2 Solar Time and Hour Angle

Solar time differs from civil clock time because of longitude, time-zone meridian, and the equation of time. A practical conversion is:

where T_s is solar time in minutes, T_c is local standard clock time in minutes, L_st is the standard meridian for the time zone in degrees, L_loc is site longitude in degrees, and E_t is the equation of time in minutes. Longitudes must use a consistent sign convention; with east-positive longitude, the expression above is commonly applied with care to local standards.

The hour angle is:

Solar noon occurs when ω = 0°. Each hour from solar noon corresponds to approximately 15° of hour angle.

2.3 Solar Zenith and Azimuth

The solar zenith angle is obtained from:

This equation is valid for a spherical Earth and standard astronomical definitions. When θ_z ≥ 90°, the Sun is below the horizon and direct-beam irradiance on a horizontal surface is zero.

One useful azimuth formulation is:

The function atan2 is preferred because it preserves the correct quadrant. Since azimuth conventions differ—north-based clockwise, south-based, or mathematical east-based—the convention must always be stated. Software packages may report azimuth from north clockwise, whereas some solar-engineering texts measure it from south.

At solar noon, the Sun is due south in the northern hemisphere and due north in the southern hemisphere, except near and within the tropics where the noon direction can change seasonally.

2.4 Sunrise, Sunset, and Day Length

At sunrise and sunset, the idealized solar zenith angle is 90°. The corresponding sunset hour angle is:

The astronomical day length is:

where N is in hours if ω_s is expressed in degrees. Refraction and the finite apparent radius of the Sun cause observed sunrise and sunset to differ slightly from this geometric approximation.

3. Worked Solar-Geometry Example

Consider a site at latitude φ = 35° north on day n = 172, near the June solstice. At solar noon, ω = 0°.

First, estimate declination:

At solar noon:

Therefore:

The Sun is approximately 78.5° above the horizon at solar noon. The result is geometrically plausible: in summer, the noon Sun is high in the sky at a mid-latitude northern site.

For sunset:

Thus:

This is ideal geometric daylight duration, not necessarily the duration of useful irradiance at a specified threshold.

4. Air Mass and Atmospheric Attenuation

Air mass describes the relative path length of direct sunlight through the atmosphere. At sea level with the Sun directly overhead, the optical air mass is approximately 1, denoted AM1. At a zenith angle θ_z, a simple approximation is:

This plane-parallel approximation becomes inaccurate at large zenith angles. A widely used Kasten–Young form is:

for 0° ≤ θ_z < approximately 90°. The angle is in degrees in this empirical expression, and the result is dimensionless.

Air mass is not the only atmospheric variable. Absorption and scattering depend on:

• water vapour;
• aerosols and dust;
• ozone;
• cloud optical thickness;
• altitude and pressure;
• particle size and composition.

The terrestrial photovoltaic reference spectrum AM1.5 is associated with a specified atmospheric path and is used for standardized module testing. It should not be confused with a site’s annual average spectrum.

5. Sun-Path Diagrams, Orientation, and Shading

A sun-path diagram shows the Sun’s azimuth and altitude for different times and dates. Horizontal-axis diagrams often plot azimuth against altitude; stereographic or polar diagrams may plot the sky dome as viewed from above. Date curves show the daily path for selected days, while hour curves show solar position at selected solar times.

Sun-path diagrams support three practical tasks:

1. determining whether a nearby obstacle blocks the Sun;
2. selecting collector orientation and tilt;
3. identifying seasonal differences in shading and solar access.

For a fixed photovoltaic array, annual energy is generally maximized when the array faces the equator and has a tilt near the site latitude, although the exact optimum depends on latitude, weather, ground reflectance, system losses, and whether annual, summer, or winter output is being optimized. In the northern hemisphere, equator-facing means generally south-facing; in the southern hemisphere, it generally means north-facing.

The incidence angle θ_i for a tilted surface can be calculated from solar position and surface orientation. One common formulation uses surface tilt β and surface azimuth γ:

The exact signs depend on the azimuth convention. Therefore, this equation should be used only with its stated convention and validated against known cases, such as a horizontal surface where β = 0° and θ_i = θ_z.

For shading analysis, an obstacle is represented by its angular profile. If the obstacle elevation angle in a particular azimuth direction exceeds the Sun’s altitude at that time, direct radiation is blocked. Shading losses are often highly nonlinear because a small shaded area can activate bypass diodes or reduce the current of a series-connected module string.

A professional shading assessment may use:

• a compass and inclinometer for preliminary surveys;
• a fisheye photograph analyzed with a sun-path overlay;
• a solar-pathfinder-type instrument;
• 3D laser scanning, drone photogrammetry, or digital terrain models;
• time-step simulation using horizon profiles.

The assessment should include trees, buildings, poles, parapets, terrain, future construction, and seasonal vegetation changes.

6. Meteorological Measurements

Solar-resource assessment requires both radiometric and meteorological measurements. Important variables include GHI, DNI, DHI, ambient temperature, wind speed and direction, relative humidity, precipitation, pressure, snow cover, and soiling conditions.

Pyranometers and Pyrheliometers

A pyranometer measures hemispherical shortwave irradiance on a plane, commonly the horizontal plane. A shaded pyranometer can measure diffuse horizontal irradiance. A pyrheliometer uses a narrow field of view and a solar tracker to measure DNI.

Measurement quality depends on:

• calibration traceability;
• leveling and orientation;
• cosine response;
• spectral response;
• thermal offset;
• ventilation and heating;
• cleanliness and bird or insect protection;
• data logging interval and clock synchronization.

A secondary-standard pyranometer is commonly used for high-quality monitoring. Instruments should be inspected regularly, cleaned according to the manufacturer’s procedure, and recalibrated at defined intervals. A measurement is not automatically reliable merely because it was recorded by a sensor.

Data Quality Control

A basic quality-control procedure should identify:

• negative daytime irradiance beyond instrument offset;
• GHI values exceeding physically plausible clear-sky limits;
• inconsistent timestamps or daylight-saving changes;
• impossible relationships among GHI, DNI, and DHI;
• prolonged constant values indicating sensor or logger failure;
• spikes caused by clouds, reflections, or electrical noise.

For an unobstructed horizontal plane, a useful physical consistency test is:

Differences are expected because of sensor uncertainty, response time, spectral differences, and non-simultaneous sampling, but large persistent discrepancies require investigation.

7. Satellite, Reanalysis, and Ground Data

Ground stations provide direct measurements at a point. Satellite products infer surface irradiance from cloud imagery and atmospheric models over a grid. Reanalysis products combine observations with numerical weather models. Each source has advantages and limitations.

Satellite data are particularly useful where ground stations are absent. Their uncertainty may increase in mountainous, snowy, coastal, or highly aerosol-loaded regions. Good practice is to compare overlapping satellite and ground records and apply a documented bias correction when justified.

The annual irradiation at a site can be estimated by integrating irradiance:

where H is irradiation, G(t) is irradiance, and T is the assessment period. For discrete measurements at equal interval ∆t:

If Gᵢ is in W/m² and ∆t is in hours, divide by 1,000 to obtain kWh/m².

8. Typical Meteorological Year Data

A TMY is a synthetic 12-month sequence created by selecting representative months from a multiyear historical record. It is designed to produce typical long-term energy behavior, not to reproduce a particular calendar year. A TMY may include GHI, DNI, DHI, temperature, wind, humidity, and pressure.

TMY data are useful for:

• preliminary photovoltaic yield simulation;
• comparison of system designs;
• building-energy modeling;
• heating and cooling studies;
• estimating typical monthly production.

They are not appropriate alone for:

• extreme-event design;
• guaranteed production claims;
• probabilistic financing analysis;
• assessment of year-to-year variability;
• detailed battery autonomy during rare weather events.

When using a TMY, the analyst should record the dataset version, source, time convention, units, missing-value codes, irradiance definitions, and conversion methods. TMY selection can reduce persistence of unusual weather and may not preserve correlations across variables as faithfully as an actual historical year.

9. Resource Estimation and Uncertainty

A resource estimate should distinguish measurement uncertainty, natural variability, model uncertainty, and representativeness uncertainty. For example, a well-calibrated sensor may measure its local irradiance accurately, while the site’s long-term average remains uncertain because only two years were measured.

If independent quantities x and y are added or subtracted, the approximate combined standard uncertainty is:

For a quantity z = xy, the relative standard uncertainty is approximately:

These propagation formulas assume small uncertainties and approximate independence. Correlated errors require covariance terms.

For an annual irradiation estimate based on a sample mean, the standard error of the mean is:

where s is the sample standard deviation of annual irradiation and n is the number of independent years. Annual solar values may exhibit serial and climate correlations, so the apparent sample size can be smaller than n.

A practical resource report should provide:

• central estimate, such as P50 annual irradiation;
• plausible lower and upper cases, such as P90 and P10;
• data sources and periods;
• gap-filling and bias-correction methods;
• sensor and model uncertainties;
• shading and soiling assumptions;
• sensitivity to tilt, albedo, and orientation.

The notation P50 commonly means a value with a 50% probability of exceedance, whereas P90 is a more conservative value with a 90% probability of exceedance. Organizations may use different conventions, so the definition must be stated explicitly.

10. Applied Case: Preliminary Assessment for a Rooftop PV System

Background. An engineering team is evaluating a 100 kW rooftop photovoltaic system at 35° north latitude. A nearby meteorological station provides one year of quality-controlled GHI measurements. A satellite database provides a 15-year monthly record. The roof has a 10° tilt and a low parapet on its western edge.

Problem. The one-year ground record gives 1,720 kWh/m² of GHI, while the satellite long-term average gives 1,650 kWh/m². The team must determine a defensible resource estimate and assess the parapet’s effect.

Analysis. The ground year may have been sunnier than typical. The 15-year satellite value is more representative of long-term conditions but may contain regional bias. During the overlapping year, the satellite estimate is 3% lower than the ground measurement. If the difference is judged to be a stable bias after quality checks, a documented correction may be applied. However, one overlapping year is weak evidence; additional ground measurements would improve confidence.

A sun-path and horizon survey shows that the western parapet blocks the low western Sun during late afternoon in winter. Because low-altitude sunlight has a reduced projection on the array and winter irradiance is lower, the annual loss may be modest, but it must be simulated rather than assumed negligible. The engineer models hourly plane-of-array irradiance using DNI, DHI, GHI, array orientation, albedo, and the horizon profile.

Approach and solution. The recommended central estimate is based primarily on the long-term satellite record, adjusted only if the overlap analysis demonstrates a defensible bias. The one-year ground record is retained as validation evidence, not treated as a long-term average. Three simulations are prepared: unshaded, measured horizon, and measured horizon plus plausible future obstruction. Monthly results are reported because the western shading loss is seasonally dependent.

Outcome. The design decision is based on a long-term central estimate and a conservative production case rather than on the unusually favorable single year. The report identifies the principal uncertainty as long-term climate variability and satellite-to-ground bias, not the arithmetic of the energy simulation.

Learning points. Resource assessment is a chain of evidence. Data quality, temporal representativeness, geometric conversion, shading, and uncertainty are all necessary parts of the engineering result.

11. Best Practices, Limitations, and Professional Responsibility

Best practice begins with clearly defining the quantity being assessed: GHI, DNI, DHI, or plane-of-array irradiation. Units and time bases must be checked before calculations. Solar-position algorithms should be tested against known solar-noon and solstice cases. Sensor metadata should be preserved, and every adjustment to raw data should be documented.

Important limitations include imperfect sky models, changing albedo, vegetation growth, snow, soiling, sensor drift, missing data, and climate nonstationarity. Historical averages are not guarantees of future conditions. Climate change may alter cloud patterns, aerosols, temperature, and extreme events; therefore, long-lived projects should consider scenario-based sensitivity analysis.

Ethically, engineers must not select an optimistic dataset merely because it improves project economics. Resource reports should distinguish measured facts, model assumptions, and professional judgments. Data licensing and privacy rules must be respected when using proprietary satellite products, drone imagery, or high-resolution site surveys. Automated and AI-assisted quality control can identify anomalies, but its classifications require human review, traceable thresholds, and validation against physical principles.

Chapter Summary

Solar-resource assessment combines astronomy, atmospheric science, instrumentation, data analysis, and engineering judgment. Solar declination, hour angle, zenith angle, altitude, and azimuth describe the Sun’s position. Direct, diffuse, and reflected components determine irradiance on a collector, while air mass summarizes the atmospheric path length but does not fully describe atmospheric attenuation.

Sun-path diagrams and horizon profiles provide practical tools for orientation and shading assessment. Pyranometers and pyrheliometers supply ground observations, while satellite and reanalysis products extend coverage in space and time. TMY files are useful for typical simulations but do not represent actual years or rare extremes. A credible site-specific estimate requires quality control, cross-validation, documented assumptions, and explicit uncertainty.

Key Terms

Solar irradiance: Instantaneous radiant power per unit area, measured in W/m².

Solar irradiation: Radiant energy received per unit area over a time period.

GHI: Global horizontal irradiance, combining direct and diffuse horizontal components.

DNI: Direct normal irradiance measured normal to the Sun’s rays.

DHI: Diffuse horizontal irradiance from the sky dome.

Albedo: Fraction of incident radiation reflected by a surface.

Solar declination: Angular position of the Sun north or south of the equatorial plane.

Hour angle: Angular measure of time from the solar meridian.

Solar zenith angle: Angle between the Sun and the local vertical.

Solar altitude: Angle between the Sun and the horizontal plane.

Solar azimuth: Horizontal direction of the Sun under a stated convention.

Air mass: Relative atmospheric path length of direct sunlight.

Pyranometer: Instrument for measuring hemispherical shortwave irradiance.

Pyrheliometer: Instrument for measuring direct normal irradiance.

Sun-path diagram: Graphical representation of solar position over dates and times.

Plane-of-array irradiance: Irradiance incident on an inclined collector surface.

TMY: Synthetic typical meteorological year assembled from representative historical months.

P50/P90: Probabilistic resource values defined by stated probabilities of exceedance.

Uncertainty: Quantified lack of exact knowledge in a measurement or estimate.

Review Questions

5 Short Answer Questions

1. Distinguish irradiance from irradiation and state a unit for each.
2. What are DNI, DHI, and GHI?
3. Define solar declination and hour angle.
4. Why is a TMY not an actual historical year?
5. State two causes of uncertainty in a solar-resource assessment.

5 Long Answer Questions

1. Explain the calculation of solar zenith angle and discuss the assumptions behind the equation.
2. Describe how a sun-path diagram can be used to assess orientation and shading.
3. Compare ground, satellite, and reanalysis solar-resource data.
4. Explain the operation, maintenance, and quality-control requirements of pyranometers.
5. Discuss why air mass alone cannot fully characterize atmospheric attenuation.

3 Analytical / Application Questions

1. For a site at 30° north latitude on the equinox at solar noon, calculate the approximate solar zenith and altitude angles.
2. A horizontal surface receives DNI = 700 W/m² and DHI = 120 W/m² when θ_z = 40°. Calculate GHI.
3. A two-year site record gives annual irradiation values of 1,600 and 1,760 kWh/m². Calculate the arithmetic mean and explain why this mean should not automatically be treated as a long-term P50 estimate.

Multiple Choice Questions with Answers

Question 1

Which quantity is measured in W/m²?

A. Irradiance

B. Irradiation

C. Annual energy yield

D. Air mass

Correct Answer: A. Irradiance

Question 2

For a horizontal surface, which relationship is correct when the Sun is above the horizon?

A. GHI = DNI + DHI cos θ_z

B. GHI = DNI cos θ_z + DHI

C. GHI = DNI sin θ_z + DHI

D. GHI = DHI cos θ_z + DNI

Correct Answer: B. GHI = DNI cos θ_z + DHI

Question 3

At solar noon, the hour angle is:

A. −15°

B. 0°

C. 15°

D. 90°

Correct Answer: B. 0°

Question 4

The solar altitude angle is related to the solar zenith angle by:

A. α = θ_z

B. α = 180° − θ_z

C. α = 90° − θ_z

D. α = θ_z − 90°

Correct Answer: C. α = 90° − θ_z

Question 5

A pyrheliometer is primarily used to measure:

A. Diffuse horizontal irradiance

B. Direct normal irradiance

C. Ground albedo

D. Ambient temperature

Correct Answer: B. Direct normal irradiance

Question 6

Why does air mass generally increase when the Sun is near the horizon?

A. The solar constant increases

B. The atmospheric path becomes longer

C. The collector tilt increases

D. The Earth stops rotating

Correct Answer: B. The atmospheric path becomes longer

Question 7

A TMY dataset is best described as:

A. A guaranteed worst-case year

B. A synthetic year assembled from representative months

C. A real calendar year selected at random

D. A satellite image of one clear day

Correct Answer: B. A synthetic year assembled from representative months

Question 8

If DNI = 800 W/m², DHI = 100 W/m², and θ_z = 60°, what is GHI?

A. 400 W/m²

B. 500 W/m²

C. 800 W/m²

D. 900 W/m²

Correct Answer: B. 500 W/m²

Question 9

Which practice is most appropriate when a one-year ground record differs from a 15-year satellite record?

A. Always select the larger value

B. Discard both datasets

C. Investigate overlap, bias, and representativeness

D. Use the ground value as the guaranteed future value

Correct Answer: C. Investigate overlap, bias, and representativeness

Question 10

For independent small uncertainties in x and y that are added or subtracted, the approximate combined standard uncertainty is:

A. u_x + u_y

B. |u_x − u_y|

C. √(u_x² + u_y²)

D. u_xu_y

Correct Answer: C. √(u_x² + u_y²)