Balloon-borne two-channel infrared spectral photometer for observation of atmospheric greenhouse effect by undergraduates

The atmospheric greenhouse effect¹ is a significant component of the Earth's climate system.² However, the typical physics curriculum rarely includes an experimental investigation of the effect. As discussed by Bell,³ previously published benchtop demonstrations that purport to demonstrate this effect^4–6 are in fact more sensitive to convective rather than radiative heat transfer, so that they fail to illustrate greenhouse effect-induced warming.^7,8 One exception is Sieg et al.⁹ who do demonstrate the absorption of IR radiation by CO₂ gas, which is one component of the greenhouse effect. To overcome the limitations of benchtop experiments, we developed an in situ experiment in the Earth's atmosphere to demonstrate this crucial aspect of the Earth's climate to students. It can be performed by undergraduates, providing that they have access to a high-altitude balloon. In our case, we benefited from the Louisiana Space Grant Consortium's Louisiana Aerospace Catalyst Experience for Students (LaACES) Program.¹⁰ 

To understand how the greenhouse effect is essential to explain the temperature at the Earth's surface, let us first assume that the atmosphere does not play any role. In this first very simple model, the Earth absorbs approximately $ϕ q=$ 235 W/m² of heat from the Sun in the form of ultraviolet (UV), visible (VIS), and near-infrared (IR) radiation.² In the steady state, the Earth re-radiates this heat back to space in the form of mid- to far-IR thermal radiation with an effective temperature T of 254 K, which can be inferred from the Stefan-Boltzmann law, $ϕ q= 5.67 × 10 − 8 W m − 2 K − 4 T 4$⁠. In this model, the average temperature of the Earth's surface would be $T≈254 K$⁠. This first simplistic model, therefore, cannot account for the actual average surface temperature of the Earth, which is 287 K.¹¹ 

To be more realistic, one can devise a second model, where the Earth is in radiative equilibrium with a single atmospheric layer containing greenhouse gasses that absorb none of the UV, VIS, and near-IR radiation from the Sun, but do absorb a fraction f of the mid- to far-IR thermal radiation from the Earth. The thermal energy absorbed by the atmosphere is re-radiated equally upward to space and downward to the Earth, so that this additional heat flux raises the Earth's surface temperature. In this model, an average surface temperature of 287 K is obtained if f = 77%,¹² whereas the actual value is closer to f = 90%.² 

Furthermore, to accurately describe the observed altitudinal dependence of the effective IR radiation temperature, one needs a more realistic model that considers the atmosphere to be composed of multiple atmospheric layers containing greenhouse gasses in radiative-convective equilibrium.¹³ The temperature of the atmospheric layers decreases with altitude due to adiabatic cooling of rising air parcels in response to the hydrostatic decrease in atmospheric pressure with altitude. At higher altitudes, the absorbed IR radiation is, therefore, re-radiated at lower temperatures. Observing the decrease in effective radiation temperature with altitude is the first objective of this experiment.

The second objective of this experiment is to demonstrate the spectral effect of greenhouse gasses on the effective radiation temperature. In the [8–12] μm wavelength band, the IR transmittance from the surface of the Earth to space is very high in the absence of clouds. This wavelength band is referred to as the atmospheric IR window. At slightly shorter wavelengths, IR radiation is strongly absorbed by water vapor, and at slightly longer wavelengths, IR radiation is strongly absorbed by carbon dioxide.¹⁴ These two gasses are predominantly responsible for the absorption of IR radiation in the atmosphere. In our experiment, we measure separately the effective radiation temperature in the IR window and the absorption bands. We expect that the effective radiation temperature to space will be higher in the atmospheric window than in the absorption bands, since radiation to space then originates from deeper (and warmer) layers of the atmosphere.

Our method for observing the greenhouse effect directly was to have a balloon lift a downward-pointing infrared thermometer from the surface of the Earth up to an altitude of at least 25 km, to observe the decrease in the effective temperature of the radiation coming from the surface of the Earth. The payload measured the IR heat flux using Arduino-controlled MLX90614 infrared thermometers.¹⁸ The MLX90614 has an integrated IR filter with a passband between 5.5 and 14.0 μm. The field of view of the sensor 1.87 sr. The thermometer is factory-calibrated to read out the effective radiation temperature based on the incoming heat flux in this wavelength range and for this solid angle. In our experimental conditions, the quoted accuracy of the radiation temperature measurements is ±0.5 K. The MLX90614 also reads out the temperature of the sensor itself, T_s, which is used in our data analysis.

Figure 3 is a schematic of the instrument, and Fig. 4 shows photographs of the instrument. The instrument comprises three ML90614 sensors, designated as S1, S2, and S3. S1 and S2 both directly measure the overall IR radiation temperature directly. In front of S3 is placed an additional external IR filter which acts as a passband between 8.0 and 12.0 μm, with a transmissivity t = 0.859, per the manufacturer's datasheet. Therefore, S3 measures the radiation temperature in the atmospheric IR window. The instrument also comprises a GPS receiver for time and altitude data, an SD card drive for data storage for post-flight analysis, and two LED status indicators. An Arduino Mega 2560 microcontroller controls all of these devices. Batteries provide power, and a 3-cm thick polystyrene housing provides mechanical support and thermal insulation. Because the high-altitude balloon carries several experiments suspended vertically below the balloon, the sensors are mounted at an angle of 30° with respect to the nadir direction, so as to avoid having their field of view obstructed by one of the experiments suspended below ours. As long as, we can approximate the surface of the Earth and the atmospheric strata as flat planes and, as long as, the entire field of view of the sensors remains below the horizon; the orientation of the sensors does not affect the heat flux received.¹⁹ This is due to two competing effects: The first is that blackbody surfaces radiate in accordance with Lambert's law,²⁰ which states that the intensity of the radiation coming from a unit area decreases as the cosine of the viewing angle with respect to the surface normal. The second is that the radiating surface within the field of view of the sensor is a conic section (a circle or an ellipse) whose area increases as the reciprocal of the cosine of the viewing angle. Therefore, as the viewing angle increases, the increase in visible horizontal area exactly offsets the decrease in intensity per unit surface area, resulting in a heat flux to the sensors that is the same at all viewing angles.

The instrument was launched by high-altitude balloon, launched from 30.4773000°N longitude, 92.6936333°W latitude at 16:17:03 UTC (10:17:03 local standard time) on August 3, 2020. The surface temperature was 34 °C (307 K), and there were scattered cumulus clouds present. The instrument ascended to an altitude of 27 419 m and then returned to the surface of the Earth by parachute. Atmospheric temperature and pressure versus altitude as measured by our companion instrument, which we built and launched on the same balloon flight, are shown in Fig. 6. The data gathered during the flight for this experiment are shown in Fig. 7.

The results of analyzing our data using Eqs. (2)–(10) are shown in Figs. 8 and 9. Figure 8 shows that the overall radiation emission temperature, T_o, decreases with altitude in qualitative agreement with the results derived from our MODTRAN simulations, thus illustrating the greenhouse effect. The observed difference in radiation temperature between the surface and the highest altitude is $310 K−276 K=34 K$⁠. The measured and modelled effective radiation temperatures are in quantitative agreement up to an altitude of 7 km. Above that altitude, the measured effective radiation temperature shows a significant deviation from the model that peaks at a deviation of about −12 K at around 15 km in altitude. This is possibly due to a loss of accuracy when the sensor temperature is changing, as implied by the datasheet for the MLX90614.¹⁸ We intend to reduce this effect in future experiments by shading the sensors before launch and by locating the sensors outside of the insulating housing. This should prevent the sensor temperature from reaching such a high temperature before launch. Indeed, waste heat from the electronics typically raises the temperature inside the housing to 50 °C before launch. In our case, as seen in Fig. 7, the sensor temperature T_S was (325 K = 52 °C) at launch (altitude = 0 km). Reducing the initial sensor temperature would reduce the rate of cooling during the flight. It is also possible that atmospheric turbulence around the tropopause (at an altitude around 15 km) caused the sensor look direction to deviate from its designed direction.²³ While a downward oscillation would not affect the IR flux received by the sensor, upward oscillations greater than 15° would cause at least part of the sensor field of view to rise above the horizon and reduce the IR flux received. The net effect would be to bias the IR flux measurements downward.

As seen in Fig. 9, the qualitative result that the IR radiation temperature in the IR window, T_w, is higher than the radiation temperature in the absorption bands, T_a, is clear. The radiation temperatures in the IR window band, and the absorption bands are also in quantitative agreement with their corresponding models up to an altitude of 7000 m, with significant deviations above that altitude.

The performance of the developed instrument was sufficient to demonstrate the greenhouse effect. The decrease in the Earth's effective radiation temperature with altitude was qualitatively correct and in quantitative agreement with the model predictions up to an altitude of 7 km. Additionally, we observed that T_w in the IR window was greater than the overall effective radiation temperature T_o and, conversely, we showed that T_a in the absorption bands was smaller than T_o. These results were also in rough quantitative agreement with the model predictions.

One could also adapt this instrument to perform ground-based experiments. For example, if the sensors were oriented toward the sky, the instrument would measure the IR heat flux from the atmosphere to the Earth. The IR heat flux from a clear sky is concentrated in the absorption bands, with very little radiation from the atmospheric window. This would appear as a higher effective temperature in the absorption band than in the atmospheric window. In contrast, clouds radiate with the same effective temperatures in both bands.

In performing the experiment described in this article, the group of undergraduate physics students gained a practical understanding of an important part of the global climate system as well as the experience of designing their own instrument. Planned improvements in this instrument include the addition of an array of upward-facing thermometers to measure the downward IR heat flux and, therefore, the net heat flux as a function of altitude. With those sensors, we intend to observe the difference between net heat flux in the IR window and the absorption bands. Additionally, a triple-axis accelerometer will be included to determine the sensor nadir/zenith angle and payload motion at all time. Another group of undergraduates developed such an instrument, which flew on June 12, 2021. Initial results show improved accuracy in the radiation temperature measurements, indicating that placing the temperature sensors outside of the insulating housing is the better design option.

This work was supported in part by the National Aeronautics and Space Administration (NASA) Grant and Cooperative Agreement No. NNX15AH82H with Louisiana State University and A&M College through Subaward Agreement No. PO-0000107279 with Southeastern Louisiana University.

We list the best-fit parameters in Table II. We note that our use of a second order polynomial is only a mathematical convenience, and we attribute no physical significance to this particular functional form.

The total cost of materials for this project—not including the balloon vehicle—as detailed in Table III was $939. We do not list vendors for materials that are widely available.