Solar Irradiance Calculator

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Understanding Solar Irradiance

Solar irradiance is the measure of the power of the Sun’s radiation per unit area, typically expressed in watts per square meter (W/m²). It’s a fundamental factor in determining the potential energy output of solar power systems, such as photovoltaic (PV) panels and solar thermal collectors. The amount of solar irradiance that reaches a specific location on Earth’s surface varies significantly based on several factors, including geographical location (latitude and longitude), time of year, time of day, atmospheric conditions, and the orientation of the surface receiving the radiation.

This calculator provides an estimate of the Global Horizontal Irradiance (GHI) and the Global Tilted Irradiance (GTI) for a given location and panel orientation. GHI is the total solar radiation received on a horizontal surface, while GTI is the total solar radiation received on a surface tilted at a specific angle and oriented towards a particular direction. GTI is crucial for accurately predicting the performance of solar panels, as they are rarely installed perfectly horizontally.

The Math Behind the Calculation (Simplified Approach)

Calculating precise solar irradiance is complex and involves sophisticated atmospheric models. However, a simplified approach, often used for estimations, relies on several key astronomical and geographical inputs:

• Latitude (φ): Your geographical position north or south of the equator. This affects the angle of the sun in the sky.
• Longitude (λ): Your geographical position east or west of the Prime Meridian. While less direct in its impact on instantaneous irradiance, it’s essential for time-of-day calculations and can influence local climate patterns.
• Day of Year (n): The specific day within the year (1 for January 1st, 365 for December 31st). This determines the Earth’s position in its orbit around the Sun.
• Solar Declination (δ): The angle between the Sun’s rays and the plane of the Earth’s equator. It varies from approximately +23.45° (summer solstice) to -23.45° (winter solstice). It can be approximated using the day of the year:
  
  δ ≈ 23.45 * sin( (360/365) * (n - 81) * (π/180) )
• Solar Declination Angle (H): The angle of the sun’s position relative to the local meridian at a specific time. For daily average calculations, we’re interested in the sunset hour angle, which is the hour angle at which the sun sets. This depends on latitude and declination. A rough approximation for the total daily energy uses integration over the day, but for simpler estimation, we often focus on the solar noon irradiance.
• Angle of Incidence (θ): The angle between the direct solar rays and the normal (perpendicular) to the tilted solar panel surface. This is critical for GTI. It is calculated using the latitude, declination, hour angle, panel tilt angle (β), and panel azimuth angle (γ).
  
  cos(θ) = sin(φ)sin(δ)cos(β) - sin(φ)cos(δ)sin(β)cos(γ) + cos(φ)cos(δ)cos(H)sin(β) + cos(φ)sin(δ)sin(H)sin(γ)sin(β) + cos(δ)sin(H)sin(γ)sin(β)
  (Note: This formula is complex and simplified formulas are often used. The calculator uses a simplified estimation.)
• Extraterrestrial Irradiance (G_on): The solar irradiance outside Earth’s atmosphere. It’s approximated by:
  
  G_on ≈ 1361 * (1 + 0.033 * cos( (360/365) * n * (π/180) )) W/m²
• Atmospheric Transmittance: A factor that accounts for the reduction in solar radiation due to absorption and scattering by the atmosphere. This is highly variable. For simplified calculations, a constant or empirically derived value is often used.

The calculator aims to provide a simplified estimate. For precise calculations, consider using specialized solar modeling software or consulting with solar energy professionals.

Use Cases:

• Solar Panel Sizing: Estimate the potential energy yield to size photovoltaic systems accurately.
• Solar Thermal Systems: Determine the thermal energy collection potential for water heating or space heating.
• Agricultural Planning: Assess sunlight availability for crops.
• Building Design: Optimize building orientation and window placement for passive solar heating or to mitigate overheating.
• Scientific Research: Analyze solar energy resources for various environmental and energy studies.

Example Calculation:
Let’s calculate for a location at 34.05° N latitude, 118.24° W longitude, on day 172 (around late June, near summer solstice), with a panel tilted at 20° facing slightly East of South (10° azimuth).
Assuming average atmospheric conditions, the calculator estimates a daily average Global Tilted Irradiance (GTI) suitable for solar panel performance analysis. The raw solar energy available at the top of the atmosphere is high during this period, but atmospheric absorption and other factors reduce it. The tilt and azimuth are optimized to capture a significant portion of this energy, especially during peak sun hours.

function calculateIrradiance() {
var latitude = parseFloat(document.getElementById(“latitude”).value);
var dayOfYear = parseInt(document.getElementById(“dayOfYear”).value);
var panelTiltAngle = parseFloat(document.getElementById(“panelTiltAngle”).value);
var panelAzimuthAngle = parseFloat(document.getElementById(“panelAzimuthAngle”).value);
// Longitude is not directly used in this simplified daily average irradiance calculation but is good to have for context.

var resultElement = document.getElementById(“result”);

if (isNaN(latitude) || isNaN(dayOfYear) || isNaN(panelTiltAngle) || isNaN(panelAzimuthAngle)) {
resultElement.innerHTML = “Please enter valid numbers for all fields.”;
resultElement.style.backgroundColor = “#dc3545”; // Red for error
resultElement.style.display = “block”;
return;
}

if (dayOfYear 365) {
resultElement.innerHTML = “Day of Year must be between 1 and 365.”;
resultElement.style.backgroundColor = “#dc3545”; // Red for error
resultElement.style.display = “block”;
return;
}

// — Simplified Solar Irradiance Calculation —
// This is a highly simplified model for demonstration.
// Real-world calculations are significantly more complex.

// 1. Calculate Solar Declination (δ)
var declinationRad = 23.45 * Math.PI / 180 * Math.sin((2 * Math.PI / 365) * (dayOfYear – 81));

// 2. Calculate the Equation of Time (EoT) for solar noon approximation (simplified)
// This is very approximate. Real EoT involves more terms.
var B = (360/365) * (dayOfYear – 81) * (Math.PI/180);
var EoT = 9.87 * Math.sin(2 * B) – 7.53 * Math.cos(B); // minutes

// 3. Calculate the Hour Angle at Sunset (H_sunset)
// cos(H_sunset) = -tan(latitude) * tan(declination)
var latitudeRad = latitude * Math.PI / 180;
var cosSunsetHourAngle = -Math.tan(latitudeRad) * Math.tan(declinationRad);

var sunsetHourAngleRad = 0;
if (cosSunsetHourAngle >= -1 && cosSunsetHourAngle 0 && declinationRad > 0) sunsetHourAngleRad = Math.PI; // Polar day
if (latitude < 0 && declinationRad 0 && declinationRad < 0) sunsetHourAngleRad = 0; // Polar night
if (latitude 0) sunsetHourAngleRad = 0; // Polar night
}

// Daily total solar energy incident on a horizontal surface outside the atmosphere (MJ/m²)
// This is a rough approximation using the sunset hour angle.
var dailyBeamIrradianceExtraAtmospheric = (1361 / Math.PI) * (sunsetHourAngleRad * Math.sin(latitudeRad) * Math.sin(declinationRad) + Math.cos(latitudeRad) * Math.cos(declinationRad) * Math.sin(sunsetHourAngleRad));

// 4. Estimate Global Horizontal Irradiance (GHI) – Simplified Model
// This is a very rough approximation. Real GHI depends on atmospheric conditions.
// We’ll use a simplified clear-sky model component and an empirical factor.
var extraterrestrialRadiation = 24 * 60 * 365 / Math.PI * (sunsetHourAngleRad * Math.sin(latitudeRad) * Math.sin(declinationRad) + Math.cos(latitudeRad) * Math.cos(declinationRad) * Math.sin(sunsetHourAngleRad)); // Wh/m²/day
var estimatedGHI_Wh_m2_day = extraterrestrialRadiation * 0.7; // Assume ~70% atmospheric transmittance as a rough guess

// 5. Calculate Angle of Incidence (θ) for the tilted panel
// We need the hour angle for solar noon (H=0) to find the maximum incidence angle.
// For a daily average, we use a weighted average or a simplified model.
// Let’s calculate for solar noon (H=0) as a primary factor for simplicity.
var H_noon = 0; // Hour angle at solar noon is 0.

// Angle of Incidence formula at solar noon (H=0):
// cos(θ) = sin(φ)sin(δ)cos(β) – sin(φ)cos(δ)sin(β)cos(γ) + cos(φ)cos(δ)sin(β)sin(γ)
// Note: Azimuth angle (γ) conventions vary. Here: 0=South, 90=East, 180=North, 270=West.
// Some formulas use 0=North. We need to adjust if necessary.
// Standard formula for incidence angle (η is common symbol for incidence angle):
// cos(η) = sin(δ)sin(φ)cos(β) + cos(δ)cos(φ)cos(H)sin(β) – cos(δ)sin(φ)sin(H)sin(γ)cos(β) – cos(δ)sin(H)cos(γ)sin(β)
// This gets complex quickly. Let’s use a simplified relation for clarity.

// A simpler approach for GTI uses a weighted sum of direct, diffuse, and reflected components.
// For this calculator, we’ll simplify the direct component and add a fixed diffuse component.

// Direct Normal Irradiance (DNI) at solar noon (simplified)
// DNI ≈ G_on * cos(solar zenith angle at noon)
var solarZenithNoonRad = Math.abs(latitudeRad – declinationRad);
var cosSolarZenithNoon = Math.cos(solarZenithNoonRad);
var G_on_noon = 1361 * (1 + 0.033 * Math.cos((2 * Math.PI / 365) * dayOfYear * (Math.PI/180))); // W/m^2

var estimatedDNI_W_m2_noon = 0;
if (cosSolarZenithNoon > 0) {
estimatedDNI_W_m2_noon = G_on_noon * cosSolarZenithNoon;
}

// Panel Azimuth convention check:
// Standard convention: 0 = South, positive = East, negative = West.
// Formula requires: 0 = South, 90 = East, 180 = North, 270 = West.
// Our select uses: 0=South, 90=East, 180=North, 270=West. This is fine.
var panelAzimuthRad = panelAzimuthAngle * Math.PI / 180;

// Angle of incidence (theta) on the tilted panel surface at solar noon.
// cos(theta) = sin(delta)*sin(phi)*cos(beta) + cos(delta)*cos(phi)*cos(H)*sin(beta) – cos(delta)*sin(phi)*sin(H)*sin(gamma)*sin(beta) – cos(delta)*cos(H)*sin(gamma)*sin(beta)
// At H=0 (solar noon):
// cos(theta) = sin(delta)*sin(phi)*cos(beta) + cos(delta)*cos(phi)*sin(beta) – cos(delta)*sin(phi)*sin(gamma)*sin(beta)
var cos_theta_noon = Math.sin(declinationRad) * Math.sin(latitudeRad) * Math.cos(panelTiltAngle * Math.PI / 180) +
Math.cos(declinationRad) * Math.cos(latitudeRad) * Math.sin(panelTiltAngle * Math.PI / 180) –
Math.cos(declinationRad) * Math.sin(latitudeRad) * Math.sin(panelAzimuthRad) * Math.sin(panelTiltAngle * Math.PI / 180); // Simplified term

var incidenceAngleRad = 0;
if (cos_theta_noon >= -1 && cos_theta_noon 0) {
estimatedGTI_direct_W_m2_noon = estimatedDNI_W_m2_noon * cos_incidence;
}

// Estimate Diffuse Component on Tilted Panel (GTI_diffuse)
// A simple model assumes diffuse radiation is isotropic or follows a simplified model.
// Isotropy: GTI_diffuse = GHI * (1 + cos(beta)) / 2
var isotropicDiffuseFraction = (1 + Math.cos(panelTiltAngle * Math.PI / 180)) / 2;
var estimatedGHI_W_m2 = estimatedGHI_Wh_m2_day / 24; // Convert Wh/m²/day to W/m² (average)
var estimatedGTI_diffuse_W_m2 = estimatedGHI_W_m2 * isotropicDiffuseFraction * 0.3; // Assume diffuse is ~30% of GHI on average

// Estimate Reflected Component (GTI_reflected)
// Depends on albedo (ground reflectivity) and sun angle. Assume a common albedo of 0.2.
var groundAlbedo = 0.2;
var reflectedIrradiance = estimatedGHI_W_m2 * groundAlbedo * (1 – Math.cos(panelTiltAngle * Math.PI / 180)) / 2; // Simplified
var estimatedGTI_reflected_W_m2 = reflectedIrradiance;

// Total Global Tilted Irradiance (GTI) at solar noon (as a proxy for daily average peak potential)
var estimatedGTI_W_m2 = estimatedGTI_direct_W_m2_noon + estimatedGTI_diffuse_W_m2 + estimatedGTI_reflected_W_m2;

// Ensure result is not negative due to approximations
estimatedGTI_W_m2 = Math.max(0, estimatedGTI_W_m2);

// Display result
resultElement.innerHTML = estimatedGTI_W_m2.toFixed(2) + ” W/m²”;
resultElement.innerHTML += “Estimated Global Tilted Irradiance (at solar noon peak potential)“;
resultElement.style.backgroundColor = “var(–success-green)”; // Green for success
resultElement.style.display = “block”;
}