DIY Twilight Photometer: Estimate Ozone Peak Height?

No, a DIY twilight photometer cannot directly estimate the ozone layer’s peak height. It can measure the brightness of the twilight sky at different solar depression angles, and from that you can infer the average altitude of the scattering layer, but the ozone peak height itself requires a different technique (like satellite limb sounding or lidar). This article explains what a twilight photometer actually measures, how you can build one, and what you can realistically learn about the atmosphere from it.

Formula

The simple geometric relation used in twilight photometry is:

h = R * (1 / cos(θ) – 1)

where:

• h = altitude of the scattering layer (km)
• R = Earth’s radius (6371 km)
• θ = solar depression angle (degrees)

For small angles, this simplifies to h ≈ 4.5 * θ (with θ in degrees, h in km). This approximation is what the calculator uses. The solar depression angle is the angle of the Sun below the horizon, which you can estimate from time after sunset (roughly 1 degree per 4 minutes at mid-latitudes).

Worked Example

Using the defaults: time after sunset = 30 minutes, solar depression angle = 6°.

1. Convert depression angle to radians: 6° × π/180 = 0.1047 rad
2. Compute 1/cos(0.1047) = 1.0055
3. Subtract 1: 0.0055
4. Multiply by Earth’s radius: 6371 × 0.0055 = 35.0 km

The calculator gives 4.5 × 6 = 27 km, which is the small-angle approximation. The exact value is 35 km. The approximation works well for angles under 10°, but deviates significantly above that. For a typical twilight measurement, the scattering layer (where sunlight is still illuminating the upper atmosphere) is around 20–40 km high.

What a Twilight Photometer Actually Measures

A twilight photometer measures the brightness of the sky at a specific wavelength (often blue or red) as the Sun sets. The intensity of twilight decays exponentially as the Sun goes lower, and the rate of decay depends on the altitude of the scattering layer (mainly aerosols and air molecules). By measuring the brightness at different depression angles, you can derive the scale height of the atmosphere in that region, but not the ozone concentration itself.

Ozone affects twilight mainly through absorption in the Chappuis band (around 600 nm) and the Hartley band (UV). If you measure at a wavelength where ozone absorbs strongly, you can detect its total column amount, but the altitude distribution is hard to extract from ground-based twilight data alone.

How to Build a Simple DIY Twilight Photometer

You don’t need a lab-grade instrument. A basic twilight photometer can be made with:

• A light sensor (a photodiode or a light-dependent resistor)
• A narrow-band filter (e.g., 500 nm or 600 nm) to isolate a wavelength
• A microcontroller (like an Arduino) to log readings
• A tripod to point it at the zenith (straight up)

You record the voltage (or resistance) every minute after sunset. Convert the readings to relative intensity, then plot log(intensity) vs. solar depression angle. The slope of that curve gives the scale height of the scattering layer.

How to Estimate Scattering Layer Height from Your Data

If you have a series of intensity measurements, you can fit a straight line to the log-intensity vs. depression angle. The slope (in log units per degree) relates to the scale height H of the atmosphere (not the ozone peak). The relationship is approximately:

H ≈ 4.5 / slope (when slope is in log10 per degree)

For example, if the slope is 0.1 per degree, H ≈ 45 km. That’s the scale height, not the peak height. The peak height of the scattering layer (where most of the twilight signal originates) is roughly 4.5 times the depression angle at which the intensity drops to half its initial value. So if the intensity halves at 6° depression, the scattering layer is around 27 km high.

Common Problems and Misconceptions

Misconception: Twilight photometry can measure ozone layer height. In reality, ground-based twilight measurements are far more sensitive to aerosols and air density than to ozone. To get ozone altitude profiles, you need satellite instruments that look at the limb (edge) of the atmosphere, or ground-based lidar that measures backscattered laser light.

Problem: Clouds and haze ruin measurements. Even thin cirrus clouds scatter light unpredictably. Only measure on clear, haze-free evenings.

Problem: The small-angle approximation fails. For depression angles above 10°, use the full spherical formula, not the linear approximation.

Costs and Alternatives

A DIY photometer with an Arduino and a photodiode costs around $20–$50 in parts. Commercial twilight photometers (used in atmospheric research) cost thousands of dollars. If you’re interested in ozone specifically, alternatives include:

• Using a simple UV index meter to measure total column ozone (not altitude)
• Participating in a citizen science project that provides calibrated instruments
• Accessing satellite ozone data (e.g., from NASA’s OMI or ESA’s Sentinel-5P) for free online

Safety and Accuracy Notes

Always point the photometer at the zenith (straight up) to avoid direct sunlight, which can damage the sensor. Never look at the Sun through any optical device. For accurate results, calibrate your sensor against a known light source if possible. The calculator gives a rough estimate; for research-grade results, use a full radiative transfer model.

Frequently Asked Questions

Can I measure ozone layer height with a DIY photometer? No, not directly. The twilight brightness is dominated by air scattering and aerosols. Ozone absorption is a small effect and cannot be separated from a single-wavelength measurement.

What is the typical altitude of the ozone layer? The ozone layer peaks at about 20–30 km in the stratosphere, but the twilight scattering layer is usually higher (30–80 km) depending on the depression angle.

How do I know the solar depression angle without a calculator? Roughly, the Sun sets at 0°, and each 4 minutes after sunset adds about 1° of depression at mid-latitudes. This varies with latitude and season.

Why does the calculator use 4.5 km per degree? It’s a geometric approximation from the spherical Earth model. For small angles, the altitude of the shadow height is proportional to the depression angle, and the constant is about 4.5 km/degree.

What wavelengths are best for twilight photometry? Blue (400–500 nm) is good for Rayleigh scattering, while red (600 nm) is less affected by ozone absorption. Using two wavelengths can help separate ozone from aerosol effects, but it’s still not enough to get height profiles.

Can I use a smartphone as a photometer? Yes, with a light meter app, but the response is not linear and the sensor is not calibrated. You can still see relative changes, but absolute altitude estimates will be rough.

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in t | Time after sunset | min | 30 | 0 | 180
in a | Solar depression angle | deg | 6 | 0 | 18
out alt | Scattering layer altitude | km | 4.5 * a | 1