1. Introduction
The remotely sensed land surface temperature (LST) is the directional radiometric temperature of the ensemble of surfaces viewed by a thermal infrared (TIR) sensor during the image acquisition process [
1,
2]. This physical highly dynamic parameter is a key quantity for the surface energy balance and a key input to many applications, such as the study of the urban thermal environment and the hydrological cycle [
3,
4]. Presently, LST data are primarily obtained (after the correction of the atmospheric and emissivity effects [
1]) as a level-2 derivative of TIR satellite remote sensing [
5]. However, due to technical and physical constrains, the available TIR satellite sensors cannot offer LST data that match the characteristic scale [
6] of the LST diurnal cycle. This is due to the anti-correlation between the spatial and temporal resolution of a satellite sensor that prohibits the frequent acquisition (<1–2 h) of fine-scale (0.1–0.2 km [
7]) TIR data [
8]. This issue hampers the exploitability of satellite LST datasets and to address it many research efforts have focused on the statistical downscaling (also referred as thermal sharpening) of coarse scale, but frequently acquired, TIR data [
7,
8,
9,
10], e.g., geostationary TIR data.
The statistical downscaling of thermal satellite data is an effective technique for enhancing the spatial resolution of thermal imagery using spatially distributed, statistically correlated auxiliary data (usually referred to as predictors, disaggregation kernels, or scaling factors) [
11,
12]. According to Zhan et al. [
12], the core of the downscaling of thermal images can be understood as some inferential statistics that estimate the emitted spectral characteristic of surface targets with the use of features from the finer-scale disaggregation kernels [
12]. This scaling process can be performed on digital numbers (DN), TIR radiances or LST (this work focuses on LST and thus the terms LST downscaling and LST predictors will be used henceforth); it fundamentally relates to three primary laws [
13]: the Bayesian theorem, Tobler’s first law of geography [
14], and the surface energy balance equation; and it is based on four interrelated assumptions [
11,
12]. These assumptions are: (i) the assumption of additivity, i.e., that the energy flux interactions among components/pixels can be neglected; (ii) the assumption of separability, i.e., that the component values are statistically separable; (iii) the assumption of connectivity, i.e., that the DN/radiances/LST can be predicted from other ancillary data (i.e., the LST predictors); and (iv) the assumption of convertibility, i.e., that the conversion of spatial/spectral/temporal/angular information to another kind is possible.
In general, the workflow of a LST statistical downscaling scheme consists of three major operations [
15]. The first operation is the upscaling and co-registration of the fine-scale LST predictors to the coarse scale LST data. The second operation is the generation of a statistical model on the basis of the coarse-scale LST data and predictors; and finally, the last operation is the application of this model to the fine-scale LST predictors so as to generate the downscaled LST (DLST) data. The employed empirical model can be linear or nonlinear [
12,
13] depending mostly on the type and number of LST predictors employed (for downscaling TIR DN or radiances, the nonlinear factors of the atmospheric and emissivity effects should also be taken into consideration during this selection [
12]). Zhan et al. [
11] discuss that simple tools such as linear and quadratic tools are effective when the predictors’ number is low (e.g., [
9,
10,
16,
17]), while complex tools such as support vector regression machines (SVM) are better suited when multiple LST predictors are employed (e.g., [
18,
19,
20]). In principle, the LST is determined by numerous factors, including topography, vegetation abundance and vigor, soil moisture, land cover and meteorological conditions [
16]; and usually the relationship between the LST data and the LST predictors is nonlinear [
13]. However, this nonlinearity is so complex [
12,
16] that the derivation of explicit global models is not an easy task (a localization strategy can be carried out as in [
21,
22] and a linear relationship can be individually constructed for each group of adjacent pixels) and hence even to this date no strong evidence, that support whether the linearity or nonlinearity performs better, exist [
12].
Even more than the applied model, the set of LST predictors are a key element of every LST statistical downscaling scheme. This is because the LST predictors indicate the LST distribution in the fine spatial resolution and drive the empirical model [
12]. The composition and selection of appropriate LST predictors should refer to the understood relations of LST to other biophysical variables (e.g., vegetation cover, land surface albedo, topography and soil moisture status) [
20], which is a key for meeting the connectivity assumption [
11]. The choice of LST predictors should also consider: (i) the spatial scale, since the suitability of the kernel is partly determined by this factor (a key assumption for statistical downscaling studies is that the relationship between the LST data and the predictors is scale invariant [
15,
23]); (ii) the local particularities of the study area; and (iii) the temporal cycle (diurnal or annual) [
11,
15] because it might render some LST predictors less effective or even ineffective (e.g., the correlation between the Normalized Difference Vegetation Index (NDVI), which is a widely used LST predictor, and LST is not persistent in time due to seasonal variations in the vegetation cover [
24,
25]).
In recent literature several LST downscaling methods have been proposed utilizing various LST predictors—either individually or by combining them into larger sets—such as vegetation indices (VIs), topography data, impervious maps and visible/near-infrared (VNIR, 0.4–1.4 μm) or TIR images. For instance, Kustas et al. [
9] utilized the NDVI with a quadratic regression tool (this method is referred in literature as disTrad: disaggregation procedure for radiometric surface temperature), whereas Agam et al. [
10] used the fractional vegetation cover with a linear tool and also other variants of disTrad. Inamdar et al. [
16] employed the emissivity for downscaling GOES (Geostationary Environmental Satellite) LST data, while Essa et al. [
26] expanded the disTrad methodology and tested 15 remote sensing based indices (individually) as LST predictors (including soil, vegetation and built-up indices). Stathopoulou and Cartalis [
8] enhanced the spatial resolution of AVHHR (Advanced Very High Resolution Radiometer) LST data using as LST predictors the effective emissivity and a LST map retrieved from Landsat 5 data.
Downscaling methods that utilize large sets of LST predictors became available after 2009 as the study of Zhan et al. [
11] reveals. To that end, Zakšek and Oštir [
21] used a LST predictor set comprising VIs, albedo, emissivity, land cover, slope, aspect, and the sky view factor data to downscale LST images retrieved from SEVIRI (Spinning Enhanced Visible and Infrared Imager), while Keramitsoglou et al. [
19] employed a set of 17 LST predictors that included topography data, land cover data, VIs and emissivity data in conjunction with a SVM tool. Merlin et al. [
27] used the fractional photosynthetically active and non-photosynthetically active vegetation cover for downscaling MODIS (Moderate Resolution Imaging Spectroradiometer) thermal data, while Weng et al. [
18] utilized VIs, albedo, emissivity and elevation data to downscale GOES LST data. Lastly, Hutengs and Vohland [
20] used as LST predictors VNIR and SWIR (Shortwave Infrared Radiation, 1.4–3 μm) surface reflectance data, elevation data and derivatives (i.e., the solar incidence angle and the sky view factor), and a land cover map with a random forest regression tool.
It is clear from the above that the most widely used LST predictors are VNIR-based (e.g., the NDVI) or static (e.g., the altitude) and that little attention has been given into TIR-based LST predictors. However, TIR-based LST predictors can prove quite useful for downscaling diurnal LST data. This is because being derived from satellite thermal data they incorporate the location-specific seasonal thermal response as well as the thermal surface properties and thus perform more consistently over various land cover types and landscapes. In addition, TIR-based LST predictors can also provide information about how these patterns change with time. This is possible when TIR multitemporal LST predictors are employed, i.e., LST predictors that indicate the LST spatial distribution during different times of a day (e.g., morning, noon, afternoon, night) or seasons. The Annual Cycle Parameters (ACPs) [
28] are such multitemporal LST predictors. This data product, which is globally available and derived from multitemporal thermal satellite data, presents a continuous description of the thermal surface behavior and the thermal surface characteristics (i.e., the “thermal landscape”) using a set of five parameters [
28,
29]. These five parameters are: the mean annual surface temperature (MAST); the yearly amplitude of surface temperature (YAST); the phase shift of the sine function that approximates the LST annual cycle (Theta; it is estimated relative to the spring equinox); the number of clear-sky observations used for the fit (NCSA); and lastly the root-mean-square-error (RMSE) of the sine fit, which is a measure for the inter-diurnal and inter-annual LST variation. The estimation of these five predictors corresponds to the acquisition time of the satellite LST data. Thus for multiple acquisitions within a day, multiple sets of ACPs can be generated, i.e., ACPs that refer to morning, noon, afternoon or night hours. Some studies have used the ACPs for downscaling LST data [
7,
15,
30,
31]. However, the use of this dataset for downscaling diurnal LST data and its ability to provide information about the LST diurnal fluctuations has not been studied in great depth, mainly because it is a very recent data product.
This study investigates the use of the MAST, YAST and Theta as LST predictors for downscaling daytime and nighttime geostationary LST data. In particular, it focuses on the LST change between 10:30 and 22:30 UTC; and 13:30 and 01:30 UTC, and assesses the capacity of YAST, MAST and Theta to reproduce characteristics of the LST diurnal cycle in the downscaling process. Following this Introduction, in
Section 2 the employed LST data and LST predictors are described, as well as the research objective of this work and the performed experiment. In
Section 3 and
Section 4, the results obtained are presented and discussed, respectively, while, in
Section 5, the drawn conclusions are outlined.
4. Discussion
The results of this study suggest that the use of MAST, YAST and Theta as LST predictors improve the downscaling of coarse-scale LST data and the estimation of the diurnal range from the DLST data. MAST, YAST and Theta represent the thermal landscape of a region [
28,
29] and can be estimated for various times within a day (e.g., morning, noon, afternoon and night) depending on the overpass time of the satellite. Hence, these LST predictors can be very useful for the downscaling of geostationary diurnal LST data, which is a more demanding process than the downscaling of single scenes. This is because the spatiotemporal interrelationships of the LST data, which are driven by the thermodynamic characteristics of the surface materials the short-term meteorological conditions and the diurnal and annual cycle of heating and cooling, have to be preserved [
15].
In this work MAST, YAST and Theta improved the downscaling of both daytime and nighttime LST data as well as their interrelationship. The former is evident through the comparison with the corresponding MODIS data and the latter with the estimation of the DLST diurnal range, which is the main focus of this paper. The estimation of diurnal thermal differences, (e.g., daytime minus nighttime), is particularly useful for numerous studies such as: the assessment of regional and global climate change [
51,
52]; the estimation of evapotranspiration [
3,
27,
53]; the assessment and monitoring of the SUHI effect [
19,
21,
54]; the estimation of crop yield [
55]; and the assessment of excess heat effects to human health [
56] (for most of these studies a LST accuracy of 1 °C or better is required [
1]). The use of the three ACP components as LST predictors improved considerably the thermal spatial patterns of the nighttime data, which were influenced by the weakening of the LST predictors’ relationship with LST [
24]. In addition, MAST, YAST and Theta improved the estimation of the very low DLST values and the overall distribution of the DLST diurnal range. Usually downscaling schemes tend to be biased in the extreme LST ranges [
20], due to the small number of extreme LST pixels and the presence of outliers [
10].
The inconsistency in the performance of LST predictors, both in respect to time and location, is another important issue in the downscaling literature [
41,
57]. This is because it complicates or even prohibits the transfer of a downscaling scheme designed for a specific area to another area with different landscape and climatic characteristics [
15,
57]. For instance, NDVI-based downscaling schemes do not perform well over complex heterogeneous regions [
57] and for this reason alternative approaches have been proposed (e.g., [
20]). Such inconsistencies are also evident when working with different land cover types. This is because the explanatory power of an LST predictor varies in respect to land cover. For instance, the impervious surface cover is more appropriate for downscaling urban areas than NDVI [
26] and vice versa. To that end, MAST, YAST and Theta offer the advantage of a stable performance over various land cover types, landscapes and climatic conditions. This is because, being derived from LST data, they incorporate the location-specific variability, e.g., the effects of topographic shading [
28], and how this variability changes with time (when multitemporal MAST, YAST and Theta data are being used). This fact makes them especially useful for downscaling geostationary diurnal LST data. In addition, it also implies that the inclusion of YAST, MAST and Theta can help limit the size of the LST predictor set, which is more practical and performs better as some studies [
7,
41] suggest. However, the good performance of the ACPs depends on the multi-year time series of satellite LST data used for their estimation. Specifically, the employed time series should deliver a sufficient sample size that is not affected by short weather effects and does not cover substantial changes in the climatic or surface conditions (e.g., a burnt scar) in order to be accurate [
28,
29]. Otherwise, artifacts may occur [
28].
Another important issue that may prohibit the use of a dataset as LST predictors is the scale invariance assumption, i.e., the relationship between the LST data and LST predictors to be the same between the coarse and fine spatial scale [
7,
15,
23]. For NDVI it is known that as the spatial scale becomes finer the near-linear relationship with coarse-scale LST transforms to a trapezoid and weakens [
23]. In this work, the scale invariance assumption for MAST, YAST and Theta was validated for the 4 km and 1 km spatial scales. Strong evidence that support the validity of the scale invariance assumption for MAST, YAST and Theta for finer scale resolutions are available in [
7], where the ACPs were used in conjunction with other LST predictors to downscale a SEVIRI scene down to 100 m (RMSE = 2.2 °C). However, more detailed tests are still required.