Diurnal Variations of Infrared Land Surface Emissivity in the Taklimakan Desert: An Observational Analysis

Abstract

This study’s field observations of Light Source Efficiency (LSE) in the Taklamakan Desert have unveiled significant daily average variations across different wavelengths, with LSE values ranging from 0.827 at 9.1 μm to a peak of 0.969 at 12.1 μm, and notably, a substantial daily variation (DV) of Δε = 0.080 in the 14.3 μm band. These findings underscore the necessity for wavelength-specific analysis in LSE research, which is crucial for enhancing the precision of remote sensing applications and climate models. This study’s high-temporal-resolution FTIR field observations systematically reveal the diurnal dynamics of infrared surface emissivity in the desert for the first time, challenging existing satellite-based inversion products and highlighting the limitations of traditional temperature–emissivity separation algorithms in arid regions. The diurnal fluctuations are governed by three primary mechanisms: the amplification of lattice vibrations in quartz minerals under high daytime temperatures, changes in the surface topography due to thermal expansion and contraction, and nocturnal radiative cooling effects. The lack of a significant correlation between environmental parameters and the emissivity change rate suggests that microclimate factors play a dominant indirect regulatory role. Model comparisons indicate that sinusoidal functions outperform polynomial fits across most wavelengths, especially at 12.1 μm, confirming the significant influence of diurnal forcing. The high sensitivity of the 14.3 μm band makes it an ideal indicator for monitoring desert surface–atmosphere interactions. This study provides three key insights for remote sensing applications: the development of dynamic emissivity correction schemes, the prioritization of the long-wave infrared band for surface temperature inversion in arid regions, and the integration of ground-based observations with geostationary high-spectral data to construct spatiotemporally continuous emissivity models. Future research should focus on multi-angle observation experiments and the exploration of machine learning’s potential in cross-scale emissivity modeling.

1. Introduction

The Taklimakan Desert (TD), being the largest desert in China, holds a pivotal position within the global climate system, attributed to its distinctive geographical and climatic attributes. Investigating the Intrinsic Land Surface Emissivity (LSE) of the TD bears substantial scientific significance across various dimensions. Firstly, in the context of refining climate models, LSE serves as a crucial parameter for the land surface energy balance, directly influencing the energy exchange mechanisms between the land surface and the atmosphere. The precise determination of the LSE in the TD can significantly bolster the capacity of climate models to simulate the energy balance in desert regions, thereby enabling more accurate forecasts of regional and global climate change [1]. Secondly, within the realm of land surface energy balance studies, the characteristics of the LSE in the TD encapsulate the cumulative effects of multiple factors, including the land surface temperature, humidity, and dust activity. By examining its diurnal variation (DV) patterns, a more profound comprehension of the dynamic processes of the underlying land surface energy balance in deserts can be attained, furnishing a robust scientific foundation for the conservation and management of desert ecosystems. Additionally, in terms of expanding remote sensing applications, the LSE constitutes a fundamental basis for the remote sensing inversion of parameters such as the land temperature surface and soil moisture. In the harsh environment of the TD, acquiring accurate emissivity data can enhance the precision of remote sensing technology applications in desert areas and broaden its scope in environmental monitoring, disaster early warning, and other related fields [2]. Lastly, regarding regional environmental change monitoring, alterations in the LSE of the TD are closely correlated with the distribution of surrounding oases and the desertification process. The long-term surveillance of its emissivity variations can aid in assessing the impact of desertification on the regional ecological environment and provide essential data for devising rational ecological protection strategies. In conclusion, studying the LSE of the TD is not only vital for elucidating the climate and ecological processes in desert regions, but also furnishes a crucial data foundation and theoretical underpinning for scientific research and practical applications in associated fields.

With the rapid advancement of remote sensing technology, the retrieval of large-area Intrinsic Land Surface Emissivity (LSE) and temperature has emerged as a global research hotspot. The use of thermal infrared spectroscopy and microwave remote sensing for land surface temperature retrieval has become a common method for regional or global land surface temperature monitoring [2]. For instance, the MODIS/Terra Land Surface Temperature/Emissivity product (MOD11A2) provides global 8-day composites at a 1 km resolution, yet its reliance on static emissivity values for bare soil in arid regions has been shown to overestimate emissivity, leading to systematic biases in temperature retrievals [3]. Remote sensing satellites must perform Temperature and Emissivity Separation (TES) to accurately retrieve the land surface temperature. However, since both the LSE and temperature are unknown parameters, the information obtained from the N channels of a sensor comprises N unknown emissivity and one land surface temperature. Mathematically, the ill-conditioned equations consisting of N equations with only one unknown have no unique solution. Therefore, it is necessary to rely on some artificial prior knowledge as a constraint to make the equations solvable [4]. This reliance introduces inversion errors and uncertainties in the LSE obtained from the inversion of land cover types observed by satellite remote sensing. Studies by Liu Dongqi et al. [5] and Zhang Renhua [6] have shown that a 0.01 change in the typical LSE within the 8–12 μm band can result in a 2 K difference in the land surface temperature retrieved by remote sensing. In arid and semi-arid regions, the low emissivity of bare soil often causes the retrieved values to be higher than the actual LSE, significantly reducing the accuracy of the net radiation estimation in these areas [6]. Recent advancements in microwave remote sensing, such as physics-based methods for retrieving the LSE from FengYun-3D Microwave Radiation Imager (MWRI) data [7] and machine learning algorithms for a desert microwave emissivity estimation [8], offer promising alternatives to mitigate these limitations by leveraging multi-sensor synergies. Additionally, long-term emissivity datasets, such as the 40-year AVHRR-derived time series for Fennoscandia [9], highlight the importance of capturing temporal variability to improve the climate model accuracy. Despite these advances, existing LSE products often lack a high temporal resolution or fail to account for diurnal cycles, particularly in hyper-arid environments like the Taklimakan Desert. For example, global microwave emissivity datasets derived from FY-3D/MWRI measurements [10] reveal significant spatial heterogeneity in desert regions, underscoring the need for localized, time-resolved observations to validate satellite retrievals.

Satellite-retrieved LSE data typically provide monthly averages, lacking detailed DV information. Mira et al. [11] found that laboratory measurements indicate a significant increase in emissivity, ranging from 1.7% to 16%, when the soil moisture content rises, especially in sandy soils within the 8.2–9.2 mm range. This increase in emissivity with the higher soil moisture has also been documented in other studies utilizing both laboratory experiments and satellite remote sensing techniques [12]. Jackson et al. [13] observed a clear diurnal pattern in soil moisture, characterized by a decrease during the day and a recovery (or increase) at night. Given these observations, it is anticipated that the LSE would exhibit DV in areas where soil moisture undergoes diurnal changes at the surface; particularly in desert regions, the LSE within the 8.2–9.2 mm range is expected to be higher at night and lower during the day. Many numerical weather prediction (NWP) and climate models continue to employ static maps that assign a limited number of possible emissivity values per surface type.

A substantial quantity of accurate and reliable ground verification data are essential to evaluate the applicability of these parameterization schemes in the TD, located in Northwest China. In this study, high-resolution field measurements of the surface radiation spectrum within the 8–14 μm thermal infrared atmospheric window were conducted using a Fourier transform thermal infrared spectrometer (FTIR). The observations were performed at the Tazhong station, situated in the heart of the TD, on 20–21 June 2023. Measurements were taken hourly, with each set comprising three repetitions. After calibration using cold and hot blackbodies and a diffuse gold plate, the LSE spectrum for this wavelength range was calculated, and the broadband LSE was subsequently derived. This methodology facilitated the acquisition of a high-precision dataset capturing the diurnal variation in the LSE for the TD. Based on these observations, this study has ascertained the LSE in the central region of the TD. The statistical characteristics of the observational data were analyzed by calculating the mean, standard deviation, and root mean square error. The DV characteristics of the LSE in the infrared band were examined and the potential causes of these diurnal changes were explored [14].

2. Materials and Methods

2.1. LSE Field Observation Experiments

To ensure the highest quality of infrared land surface emissivity (LSE) observational data (EOBS), this study conducted field observation experiments under clear and dry weather conditions with light wind. Cloudy weather conditions were avoided due to their tendency to introduce observational errors and diminish measurement precision. The experimental period was specifically selected to span from 12:00 UTC on 20 June to 12:00 UTC on 21 June 2023. The observation site was situated near the Tazhong station, in the central region of the TD. The precise locations, observational environments, and underlying surface conditions are depicted in Figure 1.

A Fourier Transform Infrared Spectrometer (FTIR) manufactured by Thermo Fisher Scientific, located in Madison, Wisconsin, USA, was employed in the experiment. This instrument is highly sensitive to thermal infrared radiance (TIR) and blackbody radiation under both cold and warm conditions. Additionally, a gold diffuse calibration plate was used. LSE measurements in the 8–14 μm band were performed hourly from 12:00 UTC on 20 June to 12:00 UTC on 21 June 2023. Each measurement comprised three repetitions. Typically, more than three sets of EOBS data were obtained through LSE spectral measurements in each experiment. The average values of these datasets were utilized to analyze the DV characteristics of the LSE.

To ensure the accuracy of the emissivity measurements, the 102F spectrometer was calibrated with a blackbody prior to each set of observations. The cold blackbody temperature was set 10 K below the ambient temperature, while the hot blackbody temperature was set 10 K above the local surface temperature (LST) at the same location. Once the blackbody temperatures were properly initialized, their actual temperatures were promptly measured and recorded. The precision of the blackbody emissivity measurement is ±0.002, with a temperature precision of ±0.1 K. Under this setup, the error introduced by the blackbody is less than 0.004. The temperature fluctuation range of the interferometer is maintained below 0.1 K, and the error of the blackbody itself is within 0.002. To reduce equipment noise signal interference, the overlap count of the scanning spectrum was typically set to 10, and the mean value during the overlap period was ultimately used by the interferometer.

The missing LSE observations for the observation times 2023062107, 2023062109, 2023062110, and 2023062111 were due to excessively high ground and ambient temperatures. These conditions exceeded the operational limits of the equipment, leading to a temporary suspension of the data collection to prevent potential damage and ensure the integrity of the measurement system. Such high temperatures can affect the calibration process and the accuracy of the spectrometer, necessitating a pause in observations until conditions returned to within safe operational parameters.

Table 1. The comprehensive observation data table of soil moisture and meteorological parameters at the observation point during LSE observation times.

Observation Time (UTC)	RH_0.5m (%)	TA_0.5m (°C)	Soiltemp_0cm (°C)	WS_0.5m (m/s)	Soilmoist_5cm (g/kg)
2023062012	21.00	27.70	50.80	1.56	0.00
2023062013	19.73	27.60	42.44	2.02	0.00
2023062014	21.00	26.90	40.00	1.31	0.00
2023062015	25.18	25.10	32.70	0.21	0.00
2023062016	30.93	23.30	28.92	0.30	0.00
2023062017	26.83	24.80	26.43	1.46	0.00
2023062018	26.57	25.00	25.29	1.95	1.00
2023062019	28.83	23.70	24.36	1.72	0.00
2023062020	34.08	21.45	24.14	0.28	1.00
2023062021	42.03	18.80	22.76	0.29	1.00
2023062022	39.42	19.80	21.65	0.39	0.00
2023062023	47.72	18.40	19.53	0.11	0.00
2023062100	48.67	17.95	20.01	0.09	0.00
2023062101	30.45	23.63	19.26	2.09	0.00
2023062102	26.27	25.65	17.61	2.35	0.00
2023062103	22.23	27.93	22.35	2.80	0.00
2023062104	16.75	30.18	30.54	2.90	0.00
2023062105	15.03	31.53	38.02	3.14	0.00
2023062106	15.07	31.72	46.12	1.67	0.00
2023062108	13.82	33.43	59.29	3.22	2.00

presents data on various meteorological and soil parameters during the observation period. The average relative humidity at 0.5 m (RH_0.5m) ranges from 13.82% to 48.67%, showing fluctuations throughout the observation period. The average air temperature at 0.5 m (TA_0.5m) varies from 18.40 °C to 33.43 °C, indicating a moderate temperature range. The soil temperature at 0 cm (Soiltemp_0cm) also fluctuates, with values ranging from 17.61 °C to 59.29 °C, suggesting significant variations in the ground temperature. The average wind speed at 0.5 m (WS_0.5m) shows a range from 0.09 m/s to 3.22 m/s, indicating relatively low wind speeds. The soil moisture at 5 cm (Soilmoist_5cm) is generally low, with most values at 0 g/kg, except for a few instances where it reaches up to 2.00 g/kg. Overall, the data reveal a pattern of variability in environmental conditions, with some parameters showing more significant fluctuations than others.

In the field measurement process, the following three steps were followed to obtain EOBS as accurately as possible. First, the radiation of the cold blackbody and the hot blackbody as well as the diffuse gold plate was measured. Second, thermal radiation was measured vertically with 0° as its zenith angle. Third, the first step was repeated. The diffuse gold plate was 5 × 5 inches in size and was developed by Lab sphere, an American company. Its emissivity is approximately 0.04, and the factory calibration value was used in the observation process of field experiments. To avoid any possible negative impact of weather-related variations on the emissivity of the instrument itself that would further impact the precision of the EOBS, the three steps were completed as swiftly as possible, and a single sampling process was hence shortened to within 10 min.

A credible LST measurement method is critical for LSE calibration. A module has been integrated into the 102F spectrometer softwar, which is capable of fitting the land-surface radiation spectrum from the blackbody radiation spectrum via the Planck function, which can calculate the LST; this is called blackbody fitting for short. It is suggested that the maximum emissivity of the fitting wavelength band in 7.45 to 7.65 μm should be 0.995 for the desert ground surface [2]. The LST obtained by the blackbody fitting method in this wavelength band is quite realistic, with its calculated LSE error generally smaller than 0.008. The fitted LST is thus also used to calculate the emissivity spectra at all wavelengths [15]. The blackbody fitting methodology is efficient and helps to obtain the LST and facilitates the infrared LSE calculation for a wavelength range of 8–14 μm in the TD, which has also been proven by the field experiments referred to in this study.

The FTIR-based emissivity is computed based on the following equation:

$$\mathrm{e}\left(\lambda \right)={\displaystyle \frac{L_{sample}\left(\lambda \right)-L_{dwr}\left(\lambda \right)}{L_{bb}\left(\lambda \right)-L_{dwr}\left(\lambda \right)}}$$

(1)

where $e\left(\lambda \right)$ denotes the Land Surface Emissivity (LSE) of the sample as a function of the wavelength $\lambda$, representing the ratio of the thermal infrared radiation emitted by the sample to that emitted by a perfect blackbody at the same temperature. $L_{sample}\left(\lambda \right)$ is the calibrated radiance of the sample at wavelength $\lambda$, which is the measured thermal infrared radiance from the surface being studied. $L_{dwr}\left(\lambda \right)$ represents the calibrated radiance of the downwelling radiance at wavelength $\lambda$, accounting for the thermal infrared radiance coming from the atmosphere towards the surface. Finally, $L_{bb}\left(\lambda \right)$ is the Planck function at the sample temperature, providing a reference for the maximum possible radiance at a given temperature and wavelength, representing the radiance that would be emitted by a perfect blackbody at the same temperature as the sample.

2.2. Methodologies

Fitting work is undertaken to understand and predict the behavior of complex systems based on empirical data. In the context of emissivity measurements, fitting sinusoidal and polynomial models helps to uncover underlying patterns that may not be immediately apparent. This analysis is crucial for interpreting how emissivity varies with time and across different wavelengths, potentially revealing insights into the physical or environmental factors influencing these measurements.

The fitting process involved the application of both sinusoidal and polynomial functions to the emissivity data against time (UTC). The quality of the fits was assessed by how closely the models followed the data points. The sinusoidal fits generally adhered more closely to the data, suggesting a periodic nature in emissivity that could be influenced by the experimental setup or environmental conditions. The fitting was executed using a least-squares approach, aiming to minimize the difference between the observed data and the values predicted by the models.

The sinusoidal functions used here are defined as:

$${\mathrm{y}}_{sin}=\mathrm{a} \ast \sin \left(\mathrm{b}\mathrm{x}+\mathrm{c}\right)+\mathrm{d}$$

(2)

where each component plays a distinct role: a, the amplitude, signifies the peak oscillation extent from the centerline (y = d), representing the wave’s height from its mean position; b, the angular frequency, dictates the wave’s oscillation speed, with a larger b indicating a quicker oscillation and a shorter period, given by T = 2π/b; c, the phase shift, influences the wave’s horizontal alignment along the x-axis, with positive values shifting the wave leftward and negatives rightward, reflecting a deviation from the standard sine function’s starting phase; and d, the vertical shift or DC offset, establishes the baseline around which the wave fluctuates, affecting its position relative to the x-axis.

Collectively, these parameters enable the sinusoidal function to accurately model a variety of natural and artificial periodic phenomena across physics, engineering, and signal processing, including sound and light waves, as well as alternating currents.

The polynomial functions that characterize a periodic wave pattern are defined in Equation (3).

$${\mathrm{y}}_{poly}=\mathrm{a}{x}^3+\mathrm{b}{x}^2+cx+d$$

(3)

where the parameters have distinct roles in shaping the polynomial curve. a, b, and c are the coefficients of the polynomial terms that determine the curvature and the inflection points of the polynomial function. These coefficients influence the overall shape of the polynomial, allowing it to fit a variety of complex patterns. d is the y-intercept, which sets the baseline or the vertical shift of the polynomial function. It determines where the curve crosses the y-axis.

It is important to note that unlike the sinusoidal function, the polynomial function does not inherently represent a periodic wave. Instead, it provides a flexible mathematical tool to approximate complex trends through its adjustable coefficients. The polynomial function can be particularly useful when the data do not exhibit a clear periodic nature or when a more general trend is required.

The quality of the fits was assessed by how closely the models followed the data points. The sinusoidal fits generally adhered more closely to the data, suggesting a periodic nature in emissivity that could be influenced by the experimental setup or environmental conditions. The fitting was executed using a least-squares approach, aiming to minimize the difference between the observed data and the values predicted by the models. The goodness-of-fit was quantified using the coefficient of determination (R²), which measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s). The R² values reported in this study were calculated based on the entire dataset used for model fitting and evaluation.

3. Results

3.1. The Difference of LSE Observations Between Different Wavelengths

The spectral distributions of Land Surface Emissivity (LSE) across the 8–13 μm wavelength range are presented for multiple acquisition dates in Figure 2. Each trace corresponds to a distinct acquisition date (see legend), demonstrating significant temporal variations in emissivity characteristics under different environmental conditions. Both diurnal and nocturnal measurements reveal consistent spectral features, particularly a prominent absorption feature centered at approximately 9 μm that persists across all observation dates.

A marked contrast in variability profiles emerges between nocturnal (Figure 2a) and diurnal (Figure 2b) measurements. Night-time data exhibit remarkable spectral consistency (σ < 0.02 across all wavelengths), while daytime measurements demonstrate increased variability (σ = 0.03–0.05), particularly within the 10–12 μm atmospheric window region. This enhanced daytime variability likely results from transient surface–atmosphere interactions and differential solar loading effects.

Boxplot distributions (Figure 3) quantify LSE variability across wavelengths, delineating median values, interquartile ranges (IQRs), and data extrema (1.5 × IQR whiskers). A significant positive correlation exists between the LSE and wavelength (Spearman’s ρ = 0.82, p < 0.01), with the peak median emissivity at 12.1 μm and 14.3 μm (0.93 ± 0.02), coinciding with atmospheric transmission bands. The measurement dispersion increases monotonically with the wavelength: IQRs expand from 0.04 (8 μm) to 0.12 (14.3 μm), while whisker ranges widen from 0.08 to 0.23 (R² = 0.94 for IQR-wavelength regression). Tukey-identified outliers (red circles) reflect wavelength-specific anomalies in nonparametric distributions. These outliers may be influenced by transient meteorological disturbances such as sudden changes in the wind speed, relative humidity, or surface temperature, which can temporarily alter emissivity values. Additionally, localized surface conditions, including variations in soil moisture or surface roughness due to diurnal thermal expansion and contraction, could also contribute to these anomalies.

These findings provide critical empirical insights into the diurnal spectral behavior of Land Surface Emissivity (LSE), particularly relevant for radiative transfer modeling in the thermal infrared spectrum, the validation of satellite-derived emissivity products, and the optimization of ground-based light source deployment strategies. The persistent 9 μm absorption feature, indicative of mineralogical influences on emissivity characteristics, coupled with observed diurnal variability in spectral signatures, highlights the imperative for implementing time-specific emissivity corrections during field radiometric measurements to account for dynamic surface–atmosphere interactions.

3.2. The Daily Variation of LSE

The diurnal variation (DV) of the average emissivity across wavelengths (8.3–14.3 μm) is illustrated in Figure 4, with shaded regions denoting night-time (14:00–22:00 UTC, 20 June 2023). All wavelengths exhibit systematic diurnal cycles: emissivity declines from 19:00 UTC, reaching minima at 21:00 UTC (Δε = −0.05 ± 0.01), followed by gradual recovery until 22:00 UTC (Figure 4a). The 12.1 μm and 14.3 μm bands maintain peak emissivity (ε = 0.975 ± 0.005), while the 8.3 μm band shows minimal values (ε = 0.825 ± 0.008). Notably, the 10.8 μm band demonstrates unique behavior with a transient peak at 21:00 UTC (ε = 0.945) before converging with other bands’ recovery trends.

The dynamics of emissivity are driven by two interconnected processes, as depicted in Figure 4b. Firstly, temperature-dependent mineralogy plays a significant role; quartz-dominated surfaces experience a 1–3% increase in emissivity within the 8–9.5 μm bands under daytime thermal stress conditions of 60–70 °C. This enhancement is attributed to amplified lattice vibrations. Although night-time cooling to temperatures between 10 and 20 °C theoretically should decrease the emissivity, the observed increases suggest the presence of competing mechanisms. Secondly, microstructural reconfiguration occurs due to diurnal thermal expansion and contraction, which smoothens the surface topography during the day, reducing scattering and thus increasing the emissivity, and generates micro-cracks at night. Interestingly, despite expectations, the specular reflection at fresh fracture interfaces actually reduces the effective emissivity. However, the overall night-time emissivity values remain elevated due to the enhanced thermal radiation efficiency. The dawn transition exhibits a biphasic behavior where rapid surface heating initially suppresses emissivity due to the dominance of Planck’s law, followed by a partial recovery as thermal expansion reactivates quartz vibrations and reduces surface roughness, leading to the mid-day stabilization of emissivity.

The daily average Land Surface Emissivity (LSE) values in the Taklimakan Desert exhibit wavelength-dependent stability, ranging from 0.827 at 9.1 μm to 0.969 at 12.1 μm (

Table 2. Daily average, maximum, and minimum LSE Values for different wavelengths.

Wavelength (μm)	Daily Average	Maximum	Minimum	DV Amplitude	Night-Time Average	Daytime Average
8.3	0.851	0.866	0.828	0.037	0.848	0.852
8.6	0.858	0.872	0.835	0.037	0.857	0.860
9.1	0.827	0.843	0.807	0.036	0.825	0.828
10.6	0.940	0.959	0.921	0.037	0.938	0.940
10.8	0.945	0.965	0.923	0.042	0.943	0.944
11.3	0.952	0.974	0.925	0.049	0.950	0.951
12.1	0.969	0.998	0.933	0.065	0.965	0.968
14.3	0.956	0.989	0.909	0.080	0.953	0.955

). This consistency suggests minimal temporal fluctuations for individual wavelengths under typical desert conditions. However, diurnal ranges—the difference between the maximum and minimum daily values—reveal significant spectral variability. The 14.3 μm band demonstrates the largest diurnal range (Δε = 0.080), attributed to its heightened sensitivity to temperature-driven lattice vibrations in quartz minerals and microstructural changes from thermal expansion/contraction. In contrast, the 9.1 μm band shows the smallest variation (Δε = 0.036), likely due to its position within the quartz Reststrahlen band where emissivity is inherently less responsive to environmental fluctuations. The quartz Reststrahlen band refers to the wavelength range in the infrared region (primarily 8–9.5 µm) where quartz exhibits strong reflectance peaks due to the interaction between lattice vibrations (phonons) and photons. This phenomenon occurs when the frequency of light approaches the natural vibration frequency of the quartz crystal lattice, resulting in high reflectivity and low transmissivity. In the context of this study, the Reststrahlen band is particularly significant for understanding the diurnal variations in infrared land surface emissivity (LSE) in the Taklimakan Desert. The high reflectivity within this band means that emissivity is inherently less responsive to environmental fluctuations, making it a stable reference for monitoring surface processes in arid regions. This band is also crucial for interpreting the observed diurnal patterns of emissivity, as it provides a baseline against which changes in other wavelengths can be compared. In interdisciplinary contexts, the Reststrahlen band remains significant for mineral identification in geology, monitoring the land surface temperature and soil moisture in remote sensing, and developing materials with specific optical properties in materials science.

Day–night deviations further highlight spectral differences, with 12.1 μm and 14.3 μm exhibiting the highest average discrepancies (0.010). These variations correlate with distinct physical mechanisms: daytime heating amplifies quartz lattice vibrations (increasing the emissivity by 1–3% in 8–9.5 μm), while nocturnal radiative cooling (an RH increase of 7.38% and a temperature drop of 3.67 °C) stabilizes the boundary layer, reducing the emissivity variability (σ = 0.0067 at night vs. 0.0138 daytime). Notably, the 10.8 μm band displays unique transient behavior, peaking at 21:00 UTC before converging with other bands, suggesting complex interactions between the thermal inertia and surface roughness effects.

The observed dynamics challenge traditional satellite-based LSE retrievals [16], which often underestimate diurnal variations by 12–15% due to algorithmic assumptions of temporal invariance. Field measurements reveal that existing Temperature–Emissivity Separation (TES) methods struggle in hyper-arid environments, particularly for longer wavelengths (12.1–14.3 μm) where atmospheric window characteristics enhance sensitivity to surface–atmosphere interactions. This discrepancy underscores the need for dynamic correction schemes in climate models and remote sensing applications, especially for land surface temperature estimation where a 0.01 emissivity error can induce 2 K biases.

These findings advocate for wavelength-specific approaches in LSE research. The 14.3 μm band emerges as a prime candidate for monitoring desert surface processes due to its large diurnal signal and atmospheric transparency, while shorter wavelengths (8.3–9.1 μm) serve as stable references. The integration of ground-based FTIR observations with geostationary satellite data (e.g., FY-4A/GIIRS) could bridge scale gaps, enabling spatiotemporally continuous emissivity models. Future work should prioritize multi-angle measurements and machine learning techniques to address residual variability unexplained by environmental parameters (|ρ| < 0.3, p > 0.05 for RH/TA correlations), ultimately refining energy balance calculations in arid regions.

The correlation analysis conducted in this study explored the relationship between the rate of change (RC) of the 9.1 µm long-wave emissivity (LSE) and environmental parameters (Figure 4c). The results indicated that the correlation between RC and the environmental parameters was not significant. Specifically, the correlation coefficients between the RC and the relative humidity (RH_0.5m) and air temperature (TA_0.5m) were 0.248 and −0.269, respectively, with corresponding p-values of 0.2923 and 0.2515. These results suggest that there is no significant correlation between these parameters and the RC (p > 0.05).

A further analysis of lagged correlations suggested that the relationship between environmental parameters and the RC might be influenced by time lags (Figure 4d). For the relative humidity (RH_0.5m), the correlation coefficients varied between 0.203 and 0.276 within a time lag range of 0 to 3 h, but the p-values remained above 0.05, indicating no significant correlation. Similarly, for the air temperature (TA_0.5m), the correlation coefficients ranged from −0.300 to 0.307, and the significance levels did not reach p < 0.05. This indicates that within the examined time lag range, there is no significant lagged correlation between the environmental parameters and RC.

The day–night comparison analysis revealed differences in the RC between the daytime and night-time periods (Figure 4d). During the daytime (non-night period), the mean value of the RC was −0.001250 with a standard deviation of 0.013840. In contrast, during the night-time period, the mean value of the RC was 0.002273, and the standard deviation was 0.006661. This suggests that the RC exhibited less variability at night and had a slightly higher mean value compared to the daytime. Additionally, the mean values of the relative humidity (RH_0.5m) and air temperature (TA_0.5m) were 30.54% and 23.21 °C at night, respectively, compared to 25.16% and 26.88 °C during the day. The higher relative humidity and lower air temperature at night may be associated with increased atmospheric stability and radiative cooling processes during the night-time hours.

The results showed that neither the relative humidity nor air temperature exhibited significant correlations or lagged correlations with the RC. However, the day–night comparison analysis indicated that the RC had less variability at night, with higher relative humidity and a lower air temperature, which may be related to the thermal and dynamic characteristics of the night-time atmosphere.

3.3. A Comprehensive Analysis of Emissivity Temporal Trends Using Various Models

During the fitting process, parameters a, b, c, and d—each with distinct physical significance—were optimized as key unknowns. The sinusoidal and polynomial fitting algorithms yielded wavelength-specific solutions. Representative equations for 9.1 µm and 14.3 µm are given as Equations (4) and (5), respectively:

$${\mathrm{y}}_{sin}=-46.41525332 \ast \sin \left(-0.06622688\mathrm{x}+1.58550611\right)+47.36227211$$

(4)

$${\mathrm{y}}_{poly}=0.27668241x^3-0.23997515x^2+0.06488117x+0.94539607$$

(5)

Figure 5 illustrates the average emissivity measurements across the wavelengths (8.3–14.3 µm) as a function of UTC time. Data points (distinct markers per wavelength) are fitted with both sinusoidal and polynomial models to characterize temporal emissivity variations. Key statistical metrics for all wavelengths are summarized below:

The sinusoidal model captures periodic trends (e.g., diurnal cycles), while the polynomial fit resolves nonlinear dynamics. Statistical metrics indicate a moderate performance across the wavelengths (NMSE: 0.44–0.79, Std. Dev.: 0.0045–0.0124), with polynomial fits generally outperforming sinusoidal models in shorter wavelengths (8.3–10.6 µm). The shaded background denotes the night-time, during which the emissivity variability increased by 15–30% compared to in the daytime (

Table 3. Comparison of polynomial and sinusoidal models for LSE at different wavelengths.

Wavelength (µm)	Model	NMSE	Rel. Bias (%)	Std. Dev.
8.3	Polynomial	0.707	0.00	0.0052
	Sinusoidal	0.621	0.00	0.0049
8.6	Polynomial	0.785	0.00	0.0050
	Sinusoidal	0.661	0.00	0.0045
9.1	Polynomial	0.687	0.00	0.0055
	Sinusoidal	0.642	−0.00	0.0053
10.6	Polynomial	0.602	−0.00	0.0059
	Sinusoidal	0.598	0.00	0.0058
10.8	Polynomial	0.587	0.00	0.0065
	Sinusoidal	—	—	—
11.3	Polynomial	0.538	0.00	0.0075
	Sinusoidal	0.568	0.00	0.0077
12.1	Polynomial	0.438	0.00	0.0092
	Sinusoidal	0.465	0.00	0.0095
14.3	Polynomial	0.531	−0.00	0.0119
	Sinusoidal	0.576	0.00	0.0124

).

This study systematically evaluated the performance of polynomial and sinusoidal models across wavelengths by integrating quantitative metrics (NMSE, relative bias, and standard deviation) and conducting comparative analyses. Key findings include negligible relative bias values (<0.01%), indicating a minimal systematic error, and elevated standard deviations at longer wavelengths (e.g., 14.3 µm, Std. Dev. = 0.0124), reflecting increased thermal noise. Notably, sinusoidal fitting failed to converge for the 10.8 µm wavelength, a limitation explicitly highlighted in the analysis. In general, the sinusoidal fits, generally following the data points more closely, suggest a potential periodic behavior in emissivity that could be influenced by daily cycles, such as temperature fluctuations or solar radiation impacts. The polynomial fits offer an alternative view, capturing the overall trend with a less strict periodic assumption. Notably, wavelengths like 8.3 and 8.6 μm exhibit a strong fit, with emissivity values ranging from approximately 0.925 to 0.975 and 0.925 to 0.950, respectively, indicating a relatively stable emissivity pattern during both the day and night. In contrast, the 9.1-micron wavelength shows a more dispersed pattern with values from about 0.850 to 0.925, hinting at possibly higher variability influenced by environmental factors or measurement specifics.

During daylight hours, wavelengths 10.6 and 12.1 μm display good fits with emissivity values from about 0.925 to 0.975, suggesting a consistent behavior across these wavelengths. The 10.8-micron wavelength demonstrates a consistent increase in emissivity, also ranging from approximately 0.925 to 0.975, which might be associated with the increasing solar input. The 11.3- and 14.3-micron wavelengths have good fits, with emissivity values ranging from about 0.850 to 0.925, potentially reflecting different material responses or atmospheric interactions at these wavelengths.

Figure 6 reveals that sinusoidal fits generally achieve higher R-squared values across most wavelengths compared to polynomial fits. The bar chart presents a comparative analysis of the coefficient of determination (R²) for sinusoidal and polynomial fits across various wavelengths, ranging from 8.3 to 14.3 micrometers (µm). The R² values serve as a measure of the goodness-of-fit, indicating the proportion of variance in the dependent variable that is predictable from the independent variable(s). The R² values here are calculated based on the entire dataset used for model fitting and evaluation, rather than being specifically divided into training or test sets. This approach ensures that the R² values reflect the overall model performance in capturing the diurnal dynamics of land surface emissivity without partitioning the data.

The sinusoidal fits are represented by the light blue bars. The R² values generally increase with the wavelength, starting from approximately 0.38 at 8.3 µm and peaking at about 0.53 at 12.1 µm, before slightly decreasing to around 0.42 at 14.3 µm. This trend suggests that sinusoidal models are more effective at capturing the periodic nature of emissivity variations at longer wavelengths, which may be associated with stronger diurnal cycles.

In contrast, the polynomial fits, depicted by the orange bars, show a more varied performance across wavelengths. The R² values for polynomial fits start at around 0.30 at 8.3 µm, increase gradually, and reach a maximum of approximately 0.55 at 12.1 µm, similar to the sinusoidal fits. However, the polynomial fits exhibit a less consistent pattern, with values fluctuating more between wavelengths, such as seen at 9.1 µm where the R² value is notably lower at about 0.32.

Overall, both models demonstrate moderate-to-high R² values, indicating a reasonable fit to the data across the measured wavelengths. However, the sinusoidal fits tend to perform slightly better, particularly at longer wavelengths, which aligns with the expectation that sinusoidal models would be more effective at capturing periodic trends like diurnal cycles. The polynomial fits, while also performing well, show more variability in their fit quality across different wavelengths, which may reflect their flexibility in modeling non-periodic or more complex trends. This analysis underscores the importance of the model choice in accurately representing the diurnal dynamics of land surface emissivity.

The residuals, which are the differences between the observed and model-predicted values, are plotted for both sinusoidal (Sin) and polynomial (Poly) fits across various wavelengths ranging from 8.3 to 14.3 µm (Figure 7). The data points are marked distinctly for each wavelength, with sinusoidal fits represented by dashed lines and polynomial fits by solid lines.

Analyzing the residuals, it is evident that the sinusoidal fits generally follow the data points more closely, especially during the night-time hours, as indicated by the smaller residuals for most wavelengths. The polynomial fits, while also performing reasonably well, show slightly larger residuals, particularly noticeable in the 8.3 µm and 9.1 µm bands. This suggests that sinusoidal models might be more effective in capturing the underlying periodic behavior of emissivity changes, which could be influenced by daily cycles such as temperature fluctuations or solar radiation impacts. The polynomial fits offer an alternative view, capturing the overall trend with a less strict periodic assumption, which might be more suitable when the data do not exhibit a clear periodic nature or when a more general trend is required.

Additionally, the graph reveals significant fluctuations in the residuals for both models during certain time periods, especially around 08:00 UTC, indicating a potential decrease in the predictive capability during these times. The range of residuals also differs across wavelengths, with some wavelengths showing smaller residuals, suggesting better fitting outcomes, while others display larger residuals, which may require further model refinement or the consideration of additional influencing factors. This analysis underscores the importance of model choice in accurately representing the diurnal dynamics of land surface emissivity and highlights the need for dynamic correction schemes in climate models and remote sensing applications, especially for land surface temperature estimation where small emissivity errors can induce significant biases.

4. Discussion

In this study, we have systematically evaluated the diurnal fluctuations in infrared land surface emissivity (LSE) across various wavelengths in the Taklimakan Desert. Our findings provide critical insights into the spectral properties of the LSE and underscore the necessity for wavelength-specific analysis in LSE research. However, it is important to address the limitations and seasonal applicability of our results.

One key limitation, is that our dataset is based on a 24 h period in June 2023, which may limit the seasonal generalizability of our findings. The measurement instrument (FTIR) operates within a working air temperature range of 10–40 °C. However, the diurnal temperature variation in the Taklimakan Desert’s hinterland can exceed 35 °C, and the diurnal variation in the surface temperature is even more extreme, with maximum sand surface temperatures reaching 70–80 °C during the daytime, while dropping below 0 °C at night. These constraints restrict field campaigns to a narrow seasonal window—typically late spring to early summer or late summer to early autumn—when temperature extremes remain within the instrument’s operational limits. Additionally, the harsh desert environment poses logistical challenges for extended observations.

Despite these limitations, we hypothesize that the underlying physical mechanisms governing emissivity diurnal variations, such as thermal inertia and quartz Reststrahlen band effects, remain applicable across seasons, albeit with potential magnitude differences. This hypothesis is based on the fundamental physical properties of the materials and processes involved, which are not expected to change significantly with seasons. However, to validate this assumption, future studies will prioritize multi-season measurements to validate the temporal generalizability of our findings. These efforts should be coupled with the development of improved emissivity parameterization schemes for climate models, which currently oversimplify diurnal variations (e.g., using fixed emissivity values for deserts). Our results demonstrate that such simplifications can introduce significant biases (e.g., up to 2 K errors in LST retrievals per 0.01 emissivity error), highlighting the need for dynamic emissivity representations in models like WRF or CESM. Furthermore, operational remote sensing programs (e.g., MODIS or VIIRS) could benefit from adopting our proposed wavelength-specific correction methods, especially for the 14.3 μm band, which exhibits the highest sensitivity to diurnal forcing (Δε = 0.080).

We explicitly address this temporal limitation and its implications in the Discussion section. By acknowledging these limitations, we aim to provide a clear understanding of the context within which our results should be interpreted. We also highlight the need for further research to explore the seasonal variability of the LSE in the Taklimakan Desert and other similar arid regions. This will be crucial for developing more robust and universally applicable models of the LSE that can enhance the precision of remote sensing applications and climate modeling in desert environments.

Meanwhile, some existing monthly LSE databases also do not account for angular variations, which were discovered and demonstrated previously [17,18]. Some other previous studies also endeavored to develop a model to produce the LST with angular LSE and LST corrections [16] or to investigate several LSE angular variation models for vegetation canopies [18]. While further efforts are still needed in this study to address angular variations of the existing LSE database, extensive LSE field measurements can be made to comprehensively understand how the LSE changes with viewing angles over different desert surface types and in different weather conditions. Quantitatively understanding the angular and temporal variations in the desert LSE can be used to develop an LSE model. An LSE database with adequate temporal and angular variations will make it possible to assimilate surface channel radiances, which contain important information for the boundary layer. Note that LSE models do not yet exist, while IR emissivity models over the ocean have been developed [19].

In addition, experiments similar to those described in this study have shown that the emissivity measurements from CAMEL provide an excellent background for the solution of the inverse problem, which returns results that agree with the measurements from the ground within the limits of instrumental error [14,20]. Furthermore, the emissivity of the CAMEL database has recently been used to define an index that shows an interesting correlation with evapotranspiration measured from ground stations [21]. Speaking of the inverse problem, thanks to the remarkable quality of the measurements and the appropriate mathematical methods over the last 10 years, the scientific community has overcome the complexity of solving the inverse problem despite the issues of the unknown LSE [14].

5. Conclusions

Field observations of the Light Source Efficiency (LSE) in the Taklimakan Desert (TD) have uncovered distinct daily average values across various wavelengths, emphasizing the significant variability of the LSE with the wavelength. At 8.3 μm, the LSE is 0.851, and at 14.3 μm, it is 0.956, while intermediate wavelengths show daily averages of 0.858 at 8.6 μm, 0.827 at 9.1 μm, 0.940 at 10.6 μm, 0.945 at 10.8 μm, 0.952 at 11.3 μm, and 0.967 at 12.1 μm. These findings underscore the critical role of wavelength-specific analysis in LSE research, which is essential for remote sensing applications and climate models. This study, through high-temporal-resolution FTIR field observations, systematically reveals the diurnal dynamics of the infrared surface emissivity (LSE) of the Taklimakan Desert for the first time. The daily average emissivity exhibits significant wavelength dependence, ranging from 0.827 at 9.1 μm to 0.969 at 12.1 μm, with the 14.3 μm band showing the largest daily variation (Δε = 0.080). The observed increase in daytime emissivity (1–3% higher than in the night-time) contradicts conclusions from existing satellite-based inversion products, highlighting the limitations of traditional temperature–emissivity separation algorithms in extremely arid regions. These detailed measurements deepen our understanding of the spectral properties of LSE and emphasize the necessity for wavelength-specific analysis in LSE research.

The diurnal dynamics are regulated by three mechanisms: the amplification of lattice vibrations in quartz minerals under high daytime temperatures (60–70 °C) enhances the emissivity in the 8–9.5 μm band; the surface topography changes due to thermal expansion and contraction, leading to reduced scattering during the day; and the nocturnal radiative cooling effect (RH increases by 7.38%, TA decreases by 3.67 °C) stabilizes the atmospheric boundary layer, thereby reducing emissivity variability (σ = 0.0067). Notably, there is no significant correlation between environmental parameters (RH/TA) and the emissivity change rate (RC) (|ρ| < 0.3, p > 0.05), indicating that indirect regulation by microclimate factors is dominant.

Model comparisons show that sinusoidal functions outperform polynomial fits in most bands (NMSE: 0.44–0.79), especially at 12.1 μm where there is a significant difference (R² increases by 23%), confirming the dominant role of diurnal forcing. The high sensitivity of the 14.3 μm band (Δε = 0.080), coupled with atmospheric window characteristics, makes it an ideal indicator for monitoring desert surface–atmosphere interactions.

This study offers three insights for remote sensing applications: (1) dynamic emissivity correction schemes need to be developed to compensate for the underestimation of daily variation (12–15%) by static databases; (2) the long-wave infrared band (e.g., 14.3 μm) should be prioritized for surface temperature inversion in arid regions; and (3) there is an urgent need to integrate ground-based observations with geostationary high-spectral data (such as FY-4A/GIIRS) to construct spatiotemporally continuous emissivity models. Future research should focus on conducting multi-angle observation experiments and exploring the potential of machine learning in cross-scale emissivity modeling. Additionally, we propose actionable recommendations to advance climate models and remote sensing applications: (1) refining emissivity parameterization in climate models by incorporating dynamic diurnal variations observed in this study, particularly for arid regions like the Taklimakan Desert; (2) developing wavelength-specific emissivity databases to replace static values in satellite-based algorithms (e.g., MODIS), thereby improving the land surface temperature retrieval accuracy; and (3) integrating ground-based FTIR observations with geostationary satellite data (e.g., FY-4A/GIIRS) to construct spatiotemporally continuous emissivity models, overcoming limitations of current low-temporal-resolution products.