In solar resource assessment and photovoltaic (PV) engineering, understanding the components of sunlight is critical for predicting energy yield. The Diffuse Horizontal Irradiance (DHI) represents the amount of solar radiation received per unit area by a horizontal surface that does not arrive on a direct path from the sun, but has been scattered by molecules and particles in the atmosphere.
The Fundamental Solar Irradiance Equation
To calculate DHI, we use the relationship between the three main components of solar radiation: Global Horizontal Irradiance (GHI), Direct Normal Irradiance (DNI), and the Solar Zenith Angle. The formula is expressed as:
GHI = DHI + DNI × cos(θ)
Rearranging this to solve for DHI:
DHI = GHI – (DNI × cos(θ))
Component Definitions
GHI (Global Horizontal Irradiance): The total amount of shortwave radiation received from above by a horizontal surface.
DNI (Direct Normal Irradiance): The amount of solar radiation received per unit area by a surface that is always held perpendicular (or normal) to the rays that come in a straight line from the direction of the sun.
Solar Zenith Angle (θ): The angle between the sun's rays and the vertical (zenith). When the sun is directly overhead, the zenith angle is 0°.
Practical Example Calculation
Imagine a solar farm located in a semi-arid region at solar noon. The sensors provide the following data:
Parameter
Value
Global Horizontal Irradiance (GHI)
1000 W/m²
Direct Normal Irradiance (DNI)
900 W/m²
Solar Zenith Angle
30°
Step-by-Step Logic:
Convert the Zenith Angle to Radians: 30° × (π / 180) = 0.5236 rad.
Calculate the cosine: cos(0.5236) ≈ 0.866.
Calculate the horizontal component of DNI: 900 × 0.866 = 779.4 W/m².
Subtract from GHI: 1000 – 779.4 = 220.6 W/m².
In this case, the DHI is 220.6 W/m², indicating the amount of scattered light hitting the panels.
Importance in Solar Energy
Accurate DHI data is vital for:
Bifacial Solar Panels: These panels capture reflected and diffuse light on their rear side; knowing DHI helps estimate back-side gain.
Concentrated Solar Power (CSP): CSP systems primarily use DNI. DHI tells engineers how much energy is being "lost" to atmospheric scattering.
Atmospheric Studies: High DHI values relative to GHI often indicate heavy cloud cover, pollution, or high aerosol optical depth.
function calculateDHI() {
var ghi = parseFloat(document.getElementById("ghiInput").value);
var dni = parseFloat(document.getElementById("dniInput").value);
var zenith = parseFloat(document.getElementById("zenithInput").value);
var resultBox = document.getElementById("resultBox");
var dhiDisplay = document.getElementById("dhiValue");
var errorNote = document.getElementById("errorNote");
// Reset displays
errorNote.innerHTML = "";
if (isNaN(ghi) || isNaN(dni) || isNaN(zenith)) {
alert("Please enter valid numeric values for all fields.");
return;
}
// Convert degrees to radians for JS Math.cos
var radians = zenith * (Math.PI / 180);
var cosTheta = Math.cos(radians);
// Calculate DHI: DHI = GHI – (DNI * cos(theta))
var dhi = ghi – (dni * cosTheta);
// Formatting result
dhiDisplay.innerHTML = dhi.toFixed(2) + " W/m²";
resultBox.style.display = "block";
// Logic Check: DHI cannot be greater than GHI, and GHI shouldn't be negative
if (dhi ghi) {
errorNote.innerHTML = "Note: Calculated DHI exceeds GHI. This is physically impossible and suggests an error in the input data.";
}
}