High-frequency fluctuations of surface temperatures in an urban environment

Abstract

This study presents an attempt to resolve fluctuations in surface temperatures at scales of a few seconds to several minutes using time-sequential thermography (TST) from a ground-based platform. A scheme is presented to decompose a TST dataset into fluctuating, high-frequency, and long-term mean parts. To demonstrate the scheme’s application, a set of four TST runs (day/night, leaves-on/leaves-off) recorded from a 125-m-high platform above a complex urban environment in Berlin, Germany is used. Fluctuations in surface temperatures of different urban facets are measured and related to surface properties (material and form) and possible error sources. A number of relationships were found: (1) Surfaces with surface temperatures that were significantly different from air temperature experienced the highest fluctuations. (2) With increasing surface temperature above (below) air temperature, surface temperature fluctuations experienced a stronger negative (positive) skewness. (3) Surface materials with lower thermal admittance (lawns, leaves) showed higher fluctuations than surfaces with high thermal admittance (walls, roads). (4) Surface temperatures of emerged leaves fluctuate more compared to trees in a leaves-off situation. (5) In many cases, observed fluctuations were coherent across several neighboring pixels. The evidence from (1) to (5) suggests that atmospheric turbulence is a significant contributor to fluctuations. The study underlines the potential of using high-frequency thermal remote sensing in energy balance and turbulence studies at complex land–atmosphere interfaces.

Appendix: Quantification of error sources

In addition to true changes in surface temperature, the radiance signal could fluctuate due to signal noise of the microbolometer focal plane array (“Appendix A1”), changing temperature gradients (signal drift) across the array as the array progressively warms up or cools down (“Appendix A2”), changing absorption along the LOS (“Appendix A3”), effects of moving objects (“Appendix A4”), vibration of the camera platform (“Appendix A5”), and effects of reflection (“Appendix A6”). Those effects will be separately quantified and/or discussed.

1.1 A1 Signal noise of the microbolometer array

To test the noise of the microbolometer array, the same equipment was operated in a controlled temperature chamber at 16°C for 80 min, recording the temperature of a uniformly warm concrete slab (50 × 50 × 4.5 cm) using the same housing, calibration, and recoding settings as outdoors. The measured $\sigma_{{\rm ftotal}}^{\prime}$ in the center of the array was determined as 0.169 K which corresponds to approximately 40–50% of the average $\sigma_{{\rm ftotal}}^{\prime}$ in the daytime runs and 70–75% of the average $\sigma_{{\rm ftotal}}^{\prime}$ in the N1 and N2 runs in form of a random background noise. This means that random inter-pixel noise of the Peltier cooled array is a dominant effect that adds noise on top of the energy-balance driven changes. Nevertheless, sensor noise should not correlate to any specific surfaces in the FOV. Based on the spectral results presented, noise dominates fluctuations in the high-frequency part (P < 30 s), where ensemble-averaged spectra of all facet classes converge, and surface effects cannot be separated (see Fig. 8).

1.2 A2 Differential warming or cooling of the microbolometer array

The effect of differential warming or cooling across the array is expected to be eliminated constantly by the internal calibration (shutter) but might add additional high-frequency noise at higher frequencies than the shutter. Differential warming or cooling is expected to cause more variability on the corners of the array compared to its thermally more stable center. Indeed, N1 and N2 runs show a radial pattern with slightly lower $\sigma_{ftotal}^{\prime}$ in the center compared to the corners (Fig. 4). In the temperature controlled chamber run, $\sigma_{ftotal}^{\prime}$ increases by 0.050 K from 0.169 K in the center to 0.219 K in the corners, which corresponds ~15% of the average signal of $\sigma_{ftotal}^{\prime}$ during the day and ~24% during night. The effect is more evident in higher frequencies, i.e., the spectral analysis (Fig. 7, N1 and N2) reveals this radial effect clearly at a period of 5 s.

Patterns in the cross-correlation functions $C_{ftotal}^{\prime}$ that relate to the image geometry could be a further indicator of fluctuations caused preferably in certain regions of the image (e.g., corners). Although interesting patterns relating to the actual surface objects are revealed by $C_{ftotal}^{\prime}$ (Section 3.1.4 and Fig. 9), none of the patterns shows a dependence on distance from image center or in any specific direction across the array.

1.3 A3 Absorption in the turbulent atmosphere along the line of sight

To estimate the effect of air temperature and humidity fluctuations along the LOS, an atmospheric radiative transfer model (MODTRAN 5.2; Berk et al. 2005) was combined with the sensor’s known spectral sensitivity (see Meier et al. 2011 for details). Using measured standard deviations of temperature and humidity fluctuations (see Section 2.1.3 and Table 2), an upper limit of the effect of a turbulent atmosphere was estimated as follows: The maximal error is considered as the difference between modeled atmospheric absorption for two temperatures that were offset by σ _Tair at absolute air temperature T _air. The estimated effect of air temperature fluctuations along the median path length of 234 m is 0.018 K for N1 and 0.012 K for N2. During daytime, due to a strongly convective atmosphere, stronger fluctuations of T _air are observed that cause maximum fluctuations of 0.068 and 0.073 K for D1 and D2, respectively. This corresponds in all cases to less than 10% of the measured signal of $\sigma_{ftotal}^{\prime}$. Note that the calculation assumes that air temperatures will change instantaneously along the entire line of sight as expressed by σ _Tair. But realistically, temperature variations (eddies) will cause the spatially integrated value of σ _Tair along the LOS to be much smaller than the single-point measurement of σ _Tair. Similarly, the effect of humidity fluctuations was estimated as the difference between modeled atmospheric absorption for the same temperature, but different absolute humidity (offset by $\sigma_{\rho_v}$, see Table 2) at the measured absolute humidity ρ _v . Effects of humidity fluctuations along the path are in all cases < 3% of measured $\sigma_{ftotal}^{\prime}$.

1.4 A4 Moving objects along the LOS

The approach presented in this study assumes that all objects in the FOV are fixed and not moving. However, in an urban environment, cars and pedestrians (which are usually warmer) trace temperature signals that are either directly resolved or cause sub-pixel variation. Higher-order moments and the spectral analysis at high frequencies (Fig. 7 at P = 5 s) indeed indicate extreme values along road lanes that are attributable to moving traffic. Also ensemble spectra of road surface temperatures are higher in the range of 1–30 s compared to any other surfaces (Fig. 8).

Further, wind causes flexible objects (trees) to move. A displacement, even in the sub-pixel scale, would change the signal emitted from pixels and can also alter the geometry of surface objects. Tree movement was not monitored, but studies indicate that at the observed wind speed of ~2.5 m s^− 1, the unimodal swaying of typical coniferous trees is less than 1 m at 15-m height (Schindler et al. 2010).

1.5 A5 Moving of the camera

Finally, the camera itself (mounted on a 3-m boom) or the entire high-rise building might sway relative to the ground. This would lead pixels that are on strong mean gradients (such as edges) to show higher $\sigma_{ftotal}^{\prime}$ due to contamination by neighboring pixels, yet affect the entire image. Evidence for this effect is observed in Figs. 4 (D2) and 7 (D2, and N1, most clearly visible at 5 s). To quantify this error, an edge detection filter was applied to calculate the spatial standard deviation of mpattern in a 3 × 3 neighborhood (σ _3×3), which is an indication of the sharpness of nearby “edges.” σ _3×3 was then compared to the temporal $\sigma_{ftotal}^{\prime}$ on a pixel-by-pixel basis. For the entire image, there is positive relationship between σ _3×3 and $\sigma_{ftotal}^{\prime}$ with slopes of 0.008 K K^− 1 (r ² = 0.01) in D1, 0.044 K K^− 1 (r ² = 0.32) in D2, 0.025 K K^− 1 (r ² = 0.07) in N1, and 0.009 K K^− 1 (r ² = 0.03) in N2. These relationships are estimated to explain 2.6% of $\sigma_{ftotal}^{\prime}$ in D1, 6.4% in D2, 9.0% in N1, and 1.6% in N2. This matches the visual interpretation of the images, where runs D2 and N1 are more affected by this error. While wind speed was similar during the two daytime and the two nighttime runs, wind direction was changing from along the boom (view direction, 325° in D1 and N2) to perpendicular in N1 and N2 (Table 1). A perpendicular wind is expected to cause more lateral swaying of the boom and/or building and hence more displacement. If the same procedure is applied only to the masked areas that are at least 1 pixel away from any facet edge, the explained error is reduced to 1.2% (D1), 4.5% (D2), 4.7% (N1), and 0.7% (N2) of $\sigma_{ftotal}^{\prime}$ because sharp edges are excluded.

1.6 A6 Reflectivity

Most materials studied have emissivities <1.0 and part of the signal in the apparent surface temperature might be caused by reflection of fluctuating radiance from nearby objects or the sky. As large fluctuations of the long-wave emittance (originating from nearby objects, the sky or the long-wave part of the direct solar irradiance) are not expected, an error from reflection is likely small. The only exception could be a non-Lambertian behavior of a surface (e.g., metal roof) in combination with a changing solar position over 20 min. Evidence for this effect was not found in the current dataset.