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\begin{document}

\title{Solar zenith angle-based calibration of Himawari-8 land surface
temperature based on MODIS spatiotemporal characteristics}



\author[1]{Yi Yu}%
\author[2]{Luigi J. Renzullo}%
\author[3]{Tim R. McVicar}%
\author[4]{Thomas G. Van Niel}%
\author[3]{Dejun Cai}%
\author[2]{Siyuan Tian}%
\author[5]{Yichuan Ma}%
\affil[1]{Fenner School of Environment \& Society, The Australian National University, Canberra, ACT 2601, Australia}%
\affil[2]{Bureau of Meteorology, Canberra, ACT 2600, Australia}%
\affil[3]{CSIRO Environment, Canberra, ACT 2601, Australia}%
\affil[4]{CSIRO Environment, Wembley, WA 6913, Australia}%
\affil[5]{Hubei Key Laboratory of Quantitative Remote Sensing of Land and Atmosphere, School of Remote Sensing and Information Engineering, Wuhan University, Wuhan 430079, China}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\selectlanguage{english}
\begin{abstract}
The geostationary Himawari-8 satellite offers a unique opportunity to
monitor sub-daily thermal dynamics over Asia and Oceania, and several
operational land surface temperature (LST) retrieval algorithms have
been developed for this purpose. However, studies have reported
inconsistency between LST data obtained from geostationary and
polar-orbiting platforms, particularly for daytime LST, which usually
shows directional artefacts and can be strongly impacted by viewing and
illumination geometries and shadowing effects. To overcome this
challenge, Solar Zenith Angle (SZA) serves as an ideal physical variable
to quantify systematic differences between platforms. Here we presented
an SZA-based Calibration (SZAC) method to operationally calibrate the
daytime component of a split-window retrieved Himawari-8 LST (referred
to here as the baseline). SZAC describes the spatial heterogeneity and
magnitude of diurnal LST discrepancies from different products. The SZAC
coefficient was spatiotemporally optimised against highest-quality
assured (error \textless{} 1 K) pixels from the MODerate-resolution
Imaging Spectroradiometer (MODIS) daytime LST between 01/Jan/2016 and
31/Dec/2020. We evaluated the calibrated LST data, referred to as the
Australian National University LST with SZAC (ANU\textsubscript{SZAC}),
against MODIS LST and the Visible Infrared Imaging Radiometer Suite
(VIIRS) LST, as well as \emph{in-situ} LST from the OzFlux network. Two
peer Himawari-8 LST products from Chiba University and the Copernicus
Global Land Service were also collected for comparisons. The median
daytime bias of ANU\textsubscript{SZAC} LST against Terra-MODIS LST,
Aqua-MODIS LST and VIIRS LST was 1.52 K, 0.98 K and -0.63 K,
respectively, which demonstrated improved performance compared to
baseline (5.37 K, 4.85 K and 3.02 K, respectively) and Chiba LST (3.71
K, 2.90 K and 1.07 K, respectively). All four Himawari-8 LST products
showed comparable performance of unbiased root mean squared error
(ubRMSE), ranging from 2.47 to 3.07 K, compared to LST from
polar-orbiting platforms. In the evaluation against \emph{in-situ} LST,
the overall mean values of bias (ubRMSE) of baseline, Chiba, Copernicus
and ANU\textsubscript{SZAC} LST during daytime were 4.23 K (3.74 K),
2.16 K (3.62 K), 1.73 K (3.31 K) and 1.41 K (3.24 K), respectively,
based on 171,289 hourly samples from 20 OzFlux sites across Australia
between 01/Jan/2016 and 31/Dec/2020. In summary, the SZAC method offers
a promising approach to enhance the reliability of geostationary LST
retrievals by incorporating the spatiotemporal characteristics observed
by accurate polar-orbiting LST data. Furthermore, it is possible to
extend SZAC for LST estimation by using data acquired by geostationary
satellites in other regions, e.g., Europe, Africa and Americas, as this
could improve our understanding of the error characteristics of
overlapped geostationary imageries, allowing for targeted refinements
and calibrations to further enhance applicability.

\par\null

\textbf{Keywords}

Land surface temperature; Geostationary; Himawari-8; Diurnal temperature
cycle; Calibration; Solar zenith angle; MODIS; VIIRS%
\end{abstract}%



\sloppy


\section*{1. Introduction}

{\label{introduction}}

Land surface temperature (LST) plays an important role in the Earth's
surface energy budget, and is widely used in hydrology, meteorology and
climatology (Li et al., 2013; Cao et al., 2019). LST undergoes rapid
fluctuations over time, exhibiting distinct diurnal and seasonal
patterns. The increasing quantity of LST observations obtained from
various satellite missions has been important to comprehend the
spatiotemporal dynamics of longwave radiation (Hu et al., 2020a). Such
observations have been utilised in numerous scientific fields, including
but not limited to agriculture (e.g., Ekinzog et al., 2022), drought
monitoring (e.g., Zhang et al., 2017; Hu et al., 2020b),
evapotranspiration estimation (e.g., Semmens et al., 2016) and ecology
(e.g., Jim\selectlanguage{ngerman}énez-Muñoz et al., 2013).

Remotely sensed LST can be routinely retrieved using data provided by
polar-orbiting and geostationary satellite missions (Yu et al., 2009).
Some well-known polar-orbiting platforms that provide LST retrievals
include the Advanced Very High Resolution Radiometer (AVHRR; Kerr et
al., 1992), the MODerate-resolution Imaging Spectroradiometer (MODIS;
Wan and Li, 1997), the Advanced Spaceborne Thermal Emission and
Reflection Radiometer (ASTER; Gillespie et al., 1998) and the Visible
Infrared Imaging Radiometer Suite (VIIRS; Islam et al., 2016). They have
a global coverage and relatively fine spatial resolution (e.g., 1 km for
MODIS and VIIRS) but low temporal frequency, e.g., 4 times per day
maximum for MODIS (less when considering cloud; Wilson and Jetz, 2016).
As a comparison, geostationary platforms acquire LST over the complete
diurnal cycle, with so-called `new generation' geostationary instruments
acquiring imagery at sub-hourly frequency (e.g., every 10 or 15
minutes), but with relatively coarse spatial resolution (usually
equivalent to, or coarser than, 2 km). Examples of geostationary
satellites include Himawari-8 (Bessho et al., 2016), the Geostationary
Operational Environmental Satellite (GOES-R; Schmit et al., 2008), the
Meteosat Second Generation (MSG; Schmetz et al., 2002), the Feng Yun
meteorological satellites (FY-4A; Yang et al., 2017), the Indian
National Satellite (INSAT-3D; Singh et al., 2016) and the Russian
meteorological satellites (Elektro-L; Uspenskii et al., 2015). However,
each geostationary satellite only observes a longitudinally defined
hemisphere. To overcome this limitation, Freitas et al. (2013) fused
data from multiple geostationary satellites to generate a
global-coverage LST product with hourly frequency, known as the
Copernicus Global Land Service (CGLS) project, but with a spatial
resolution that is coarser than the individually retrieved geostationary
LST products.

Over the past decades, there have been marked efforts to develop LST
retrieval algorithms (Wan and Dozier, 1996; Sobrino et al., 2004;
Yamamoto et al., 2018). Provided that land surface emissivity (LSE) is
known \emph{a priori} , the retrieval algorithms can be mainly
classified by three categories, including (i) single-channel methods;
(ii) multi-channel methods; and (iii) multi-angle methods (Li et al.,
2013). Firstly, the single channel method, alternatively known as the
model emissivity method (Hook et al., 1992), utilises radiance measured
by the sensor in a single thermal infrared channel. An accurate
estimation of LST through this approach requires a high-fidelity
atmospheric transmittance/radiance code, extensive familiarity with the
channel LSE, an accurate atmospheric profile, and an appropriate
consideration of the topographic impacts (Sobrino et al., 2004).
Secondly, due to the inherent challenges in either pre-establishing
radiative transfer models or accurately estimating atmospheric profiles,
linear split-window (SW) algorithms have been devised for the retrieval
of sea surface temperature (SST; Barton et al., 1989; Niclòs et al.,
2007). These algorithms leverage data from two adjacent channels centred
at \textasciitilde{} 11 and 12 \selectlanguage{greek}\emph{μ} \selectlanguage{english}m. This linear approach serves
as a typical multi-channel method and has been subsequently extended to
LST studies, which was shown to be highly effective (e.g., Price, 1984;
Coll et al., 1994; Wan and Dozier, 1996). Due to the SW algorithm's
versatility and compatibility with almost all geostationary sensors, it
is a popular choice for geostationary satellite products (Yu et al.,
2007; Yu et al., 2009; Freitas et al., 2013; Li et al., 2020), with the
exception of GOES 13/15 imagers, which have only one thermal band.
Multi-channel methods can also employ nonlinear terms (Atitar and
Sobrino, 2008) or utilise more than two adjacent channels (Yamamoto et
al., 2018). Thirdly and finally, similar to the underlying principle of
the multi-channel method, the multi-angle method relies on differential
atmospheric absorption resulting from distinct path-lengths, which
occurs when the same object is viewed from varying angles in a
particular channel (Sobrino et al., 2004; Li et al., 2013). The outcomes
of this method may surpass those of the SW algorithm, provided that the
spectral and angular characteristics of LSE are well-determined (Li et
al., 2013). However, a crucial concern in the multi-angle method is the
angular dependence of LSE as the angular behaviour of natural surfaces
(e.g., soils and rocks) is typically not well understood at the spatial
scale of satellite observations (Sobrino and Jim\selectlanguage{ngerman}énez-Muñoz, 2005). As a
result, multi-angle methods are generally limited to homogeneous areas
(e.g., sea surface or densely vegetated forests) under optimal
atmospheric conditions, hence there has been limited use of
multi-channel methods in most scenarios, particularly in heterogeneous
environments.

Regardless of the specific retrieval algorithms utilised, studies have
reported inconsistencies between LST obtained from geostationary and
polar-orbiting missions. Trigo et al. (2021) demonstrated a difference
of approximately ±1 K between LST products from the AVHRR sensor onboard
Metop polar-orbiting satellites and the Spinning Enhanced Visible and
Infrared Imager (SEVIRI) onboard the MSG geostationary platform.
Pérez-Planells et al. (2023) reported that Terra- and Aqua-MODIS LST
products (i.e., MOD11 and MYD11, respectively) were around 2 K cooler
than the LST datasets from the European Space Agency's Climate Change
Initiative (ESA CCI) across all land cover classes. Similarly, Li et al.
(2020) found MYD11 LST generally showed lower values than their SW
algorithm-retrieved Himawari-8 LST over southeast China and Australia.
Comparatively, their product displayed better agreement with MYD21 LST,
a successor to MYD11 LST, which Hulley et al. (2017) developed using a
Temperature and Emissivity Separation (TES) algorithm. The pronounced
discrepancy between MYD11 and MYD21 LST was attributed to the
differences in the emissivity calculation methods used in the retrievals
(Hulley et al., 2017).

The discrepancy between polar-orbiting and geostationary LST can be
particularly high during the daytime (Wang and Liang, 2009; Li et al.,
2014; Li et al., 2021; Trigo et al., 2021; Yamamoto et al., 2022), due
to variations in viewing and illumination angles (Ermida et al., 2017;
Trigo et al., 2021). For example, daytime LST derived from
polar-orbiting (i.e., MODIS) and geostationary (i.e., SEVIRI) platforms
can have a difference of up to 12 K due to directional effects
(Guillevic et al., 2013). This demonstrates that daytime geostationary
LST measurements require further recalibration to better align with
ground observations. Researchers have directed their investigations
towards the conspicuous directional characteristics of LST and have
developed correction and harmonisation methodologies, in which the solar
zenith angle (SZA) plays a pivotal role (Vinnikov et al., 2012; Ermida
et al., 2017; Ermida et al., 2018; Jiang et al., 2021).

SZA represents the angle formed between the Sun's rays and the vertical
direction. It is important in various meteorological and climatological
calculations, including the determination of radiant temperature (Di
Napoli et al., 2019; Vanos et al., 2021), and in the computation of
thermal and heat indices such as the Universal Thermal Climate Index
(UTCI; Di Napoli et al., 2021). SZA has also found extensive utility in
rectifying and harmonising discrepancies in daytime LST acquired from
different platforms. Specifically, Vinnikov et al. (2012) introduced an
LST anisotropy model that incorporates an SZA-based kernel, representing
the influence of directional heterogeneity on observed LST, in
conjunction with isotropic and emissivity kernels, which showed improved
agreements with ground-based observations. Ermida et al. (2017)
calibrated this model against satellite-observed LST acquired at varying
viewing angles, and derived spatially varying coefficients for the
SZA-based kernel, which encapsulated the characteristics of terrain and
vegetation cover. The application of this model ameliorated disparities
in LST observed by different satellites, as well as between satellite
observations and ground measurements, offering utility to harmonise LST
products (Vinnikov et al., 2012; Ermida et al., 2017). Furthermore, Duan
et al. (2014) used SZA as a predictor to normalise Terra-MODIS LST
during daylight hours, ensuring consistency with local solar time and
facilitating the generation of temporally consistent LST products. To
normalise the temporal effects of MODIS LST, Zhao et al. (2019)
estimated cumulative incident solar radiation by incorporating the
cosine value of the SZA, while also considering atmospheric
transmittance and path length. Their normalised LST showed reduced
uncertainty against MSG-SEVIRI LST. Jiang et al. (2021) compared the
performances of 11 kernel-driven models in simulating daytime urban
thermal radiation directionality (UTRD), where SZA was used to assess
the impact of city latitude and to simulate parametric kernels for UTRD.
They found that dual-kernel models achieved a best performance against
forward-modelling and satellite data. Wang et al. (2023) also employed
the SZA as a key parameter to establish an angular normalisation model
to convert MODIS off-nadir LST values to nadir values, which yielded
better consistencies with Sentinel-3A nadir LST. As summarised in Table
1, these diverse applications of SZA underscore its effectiveness in
rectifying LST discrepancies arising from multiple observational
platforms.\selectlanguage{english}
\begin{table}[H]
\centering
\normalsize\begin{tabulary}{1.0\textwidth}{CCCCCC}
\selectlanguage{english}Reference & Satellite platforms & Summary of key objective(s) & Usage of SZA & Key results & Potential limitations \\
Vinnikov et al. (2012) & GOES-EAST and GOES-WEST & Proposed a statistical model for evaluation and adjustment of angularity of LST. & SZA was used to simulate a solar kernel that represents directional inhomogeneity of LST. & Evaluations against observations from 5 SURFRAD stations showed bias within \selectlanguage{ngerman}±0.5 K and RMSE of 1.2-1.4 K. & All 5 SURFRAD stations are located within limited range of VZA between 43 \selectlanguage{ngerman}° and 66 °. The study also lacked observations of SZA < 10.75 °. \\
Duan et al. (2014) & Terra-MODIS and MSG-SEVIRI & Proposed a temporal normalisation method of daytime LST. & SZA was used as a regression predictor to estimate the slope of LST versus local solar time. & Difference between Terra-MODIS and MSG-SEVIRI LST reduced from ~ 1.5 K to ~ 0.5 K after normalisation. & The regression was established using data from only 4 months (January, April, July, and October) in 2010. No ground-based evaluations were performed. \\
Ermida et al. (2017) & Terra-, Aqua-MODIS and MSG-SEVIRI & Calibrated Vinnikov et al. (2012) model with LST acquired at different view angles to characterise LST anisotropy. & Same with Vinnikov et al. (2012). & Cross-validation showed the RMSE between SEVIRI and MODIS daytime (nighttime) reduced from 3.5 K (1.5 K) to 2.3 K (1.3 K). Evaluations against in-situ daytime LST showed a reduced RMSE from 4.6 K (2.0 K) to 3.8 K (1.9 K) for MODIS (SEVIRI). & Seasonal variations of vegetation-shaded fraction may impact the values of SZA-based kernel but was not considered. There was no observation of azimuth angles from north but was expected to have minor impacts as SZA-based kernel is symmetric to relative azimuth angles. \\
Zhao et al. (2019) & Terra-MODIS and MSG-SEVIRI & Normalised the temporal effects of MODIS LST using a random forest regression. & SZA was used to estimate the cumulative incident solar radiation, with the consideration of atmospheric transmittance and path length. & Normalised LST showed reduced bias (RMSE) of 1.66 K (1.23 K) against MSG-SEVIRI LST compared to the original MODIS LST. & The estimation of solar radiation factor may be affected by the simplification of spatial variability of atmospheric transmittance. No ground-based evaluations were performed. \\
Jiang et al. (2021) & Quasi-simultaneous multi-angle MODIS LST produced by Hu et al. (2016) & Simulated daytime urban thermal radiation directionality (UTRD) using 11 kernel-driven models. & SZA was used to assess the impact of city latitude and to simulate parametric kernels for UTRD. & Dual-kernel models achieved a best performance of RMSE against forward-modelling and satellite data, being 0.49 K and 0.77 K, respectively. & All models used herein were originally developed for vegetated surfaces, without considerations of urban surface types and environmental conditions. No ground-based evaluations were performed. \\
Wang et al. (2023) & Terra-, Aqua-MODIS and Sentinel-3A & Developed an angular normalisation method for converting global MODIS off-nadir LST to nadir over vegetated surface. & SZA was used to estimate sensor-object-solar geometry and kernel functions. & Normalised daytime LST showed bias (RMSE) of 0 K (1.57 K) against in-situ LST, and bias (RMSE) of -1.2 K (2.26\selectlanguage{ngerman} K) against Sentinel-3A nadir LST, while those of MODIS off-nadir LST being \selectlanguage{english}-2.15 K (3.01 K). & This study only focused on the vegetated surfaces. The cross-platform validation (i.e., against Sentinel-3A) was only performed for 4 days in 2020. \\
Our study & Terra-, Aqua-MODIS, VIIRS and Himawari-AHI & Proposed a calibration approach to reduce the daytime LST discrepancies between polar-orbiting and geostationary platforms. & SZA was used to construct an empirical function representing spatial heterogeneity of surface heating and the magnitude of LST discrepancies from different products. & Calibrated daytime LST showed improved bias (1.52 K, 0.98 K and -0.63 K, respectively) than baseline (5.37 K, 4.85 K and 3.02 K, respectively) against Terra-, Aqua-MODIS and VIIRS LST. It also had the best bias (ubRMSE) of 1.41 K (3.24 K) in evaluations against in-situ LST compared to other three Himawari-8 LST products. & The utilised observations of SZA were concentrated between 20 \selectlanguage{ngerman}° and 70 °. The method did not consider elevation and seasonal variations of vegetation. \\
\end{tabulary}
\caption{{An overview of studies representing the major types of methods using SZA
for LST correction or normalisation. Studies are ordered chronologically
by year of publication (oldest to newest). Our study is added for
completeness. The following abbreviations are used: AHI (Advanced
Himawari Imager); SURFRAD (SURFace RADiation budget observing network);
VZA (Viewing Zenith Angle).
{\label{535455}}%
}}
\end{table}Based on the summary of previous studies presented in Table 1, it is
evident that certain limitations exist within the body of research, such
as a lack of cross-platform validation, absence of ground-based
evaluations, and focus on a limited range of land cover types. These
factors collectively suggest that the full potential of SZA has not been
explored to maximise the consistency of LST across multiple platforms.
Additionally, to enhance the synchronisation of daytime and nighttime
observations, it is imperative to gain a comprehensive understanding of
the diurnal patterns of LST (Sharifnezhadazizi et al., 2019;
Azarderakhsh et al., 2020). While some studies have employed
multi-parameter models to simulate the diurnal cycle patterns of LST
using sparsely sampled observations from polar-orbiting satellites (Duan
et al., 2012; Hu et al., 2020a; Lu and Zhou, 2021), there have been
minimal efforts to quantify the diurnal characteristics of error
performance of geostationary LST products (Vinnikov et al., 2008; Holmes
et al., 2015). Hence, there is a need to address this scientific gap and
to investigate the diurnal error dynamics of geostationary LST products,
thus further improving accuracy of geostationary LST products.

Accordingly, our objectives were to: (i) calibrate the daytime component
of an SW algorithm-retrieved Himawari-8 LST product using an SZA-based
calibration approach that incorporates the spatiotemporal
characteristics of polar-orbiting MODIS LST; (ii) evaluate the diurnal
error characteristics of calibrated LST and collected Himawari-8 LST
peer products against \emph{in-situ} LST across different seasons; and
(iii) compare the spatial pattern and derive pixelwise metrics of
calibrated LST and Himawari-8 LST peer products against VIIRS LST.

\section*{2. Data and study area}

{\label{data-and-study-area}}

The remotely sensed data and ground measurements used herein are
itemised in Table 2. The Himawari-8 brightness temperature
(T\textsubscript{B}) was used as input, along with the emissivity, to
retrieve LST through an SW algorithm. Two peer Himawari-8 LST products
(i.e., (i) Chiba and (ii) Copernicus) were used for evaluations
against~\emph{in-situ} LST derived from ground-based longwave radiation
and polar-orbiting LST products. The MOD11A1 and MYD11A1 LST products
(Collection 6) were employed for pixelwise calibration of SW retrieved
Himawari-8 LST and assessment of model performance. The VNP21A1D LST
acquired by the VIIRS mission was used for spatiotemporal evaluations of
multi-sourced Himawari-8 LST through pixelwise metrics. The longwave
radiation obtained from the OzFlux network was used to
derive~\emph{in-situ} LST for ground-based evaluation. The MOD13A1
enhanced vegetation index (EVI), MCD15A2H leaf area index (LAI) and
MCD43A3 albedo products (all Collection 6) were used for evaluations of
the spatial patterns of the calibration coefficient of Himawari-8 LST.\selectlanguage{english}
\begin{table}[H]
\centering
\normalsize\begin{tabulary}{1.0\textwidth}{CCCCCC}
\selectlanguage{english}Categories & Datasets & Spatial resolution & Temporal      frequency & Period & References \\
Input & Himawari-8 TB & 2 km & 10-min & 01/Jan/2016 -- 31/Dec/2020 & Bureau of Meteorology (2021) \\
 & UW baseline fit emissivity & 5 km & Long-term monthly & 01/Jan/2003 -- 31/Dec/2016 & Seemann et al. (2008) \\
Himawari-8 LST products & Chiba & 2 km & Hourly & 01/Jan/2016 -- 31/Dec/2020 & Yamamoto et al. (2018) \\
 & Copernicus & ~ 4.5 km & Hourly & 01/Jan/2016 -- 31/Dec/2020 & Freitas et al. (2013) \\
Polar-orbiting LST products & MOD11A1 and MYD11A1 & 1 km & Daily & 01/Jan/2016 -- 31/Dec/2020 & Wan (2014) \\
 & VNP21A1D & 1 km & Daily & 01/Jan/2016 -- 31/Dec/2020 & Islam et al. (2016) \\
Ground measurements & OzFlux Longwave radiation & Point & 30-min & 01/Jan/2016 -- 31/Dec/2020 & Beringer et al. (2016) \\
Surface reflectance products & MOD13A1 & 500 m & 16-day & 01/Jan/2016 -- 31/Dec/2020 & Huete et al. (2002) \\
 & MCD15A2H & 500 m & 8-day & 01/Jan/2016 -- 31/Dec/2020 & Myneni et al. (2002) \\
 & MCD43A3 & 500 m & Daily & 01/Jan/2016 -- 31/Dec/2020 & Schaaf et al. (2002) \\
\end{tabulary}
\caption{{Summary of data used herein. The spatial resolution of OzFlux
measurements is not strictly a point, rather an aggregation of local
area fluxes in the vicinity of the flux tower. This means the values of
flux towers are representative of a specific region, while the area
depends on localised settings in the vicinity of each flux tower
station. The contribution from flux tower can range from meters to
kilometres and can be considered comparable to remotely sensed data (Chu
et al., 2021; Qin et al., 2022). UW denotes University of Wisconsin.
{\label{405032}}%
}}
\end{table}\subsection*{2.1 UW baseline fit
emissivity}

{\label{uw-baseline-fit-emissivity}}

The University of Wisconsin (UW) Baseline Fit Emissivity Database is a
global database of infrared land surface emissivity derived using an
operational MODIS product (MOD11) (Seemann et al., 2008). The database
fills in the spectral gaps of MOD11 and provides emissivity at 10
wavelengths, ranging from 3.6 to 14.3 \selectlanguage{greek}\emph{μ} \selectlanguage{english}m, with 0.05 degree
spatial resolution (\textasciitilde{} 5 km at the equator). We acquired
the emissivity at 10.8 and 12.1 \selectlanguage{greek}\emph{μ} \selectlanguage{english}m wavelengths (selected to
match the wavelengths used in baseline LST retrieval, see Section 3.1)
for each month over 2003-2016 and calculated monthly values by averaging
them over the 14-year period.

\subsection*{2.2 Himawari-8 LST}

{\label{himawari-8-lst}}

The Himawari-8 geostationary satellite was launched by the Japan
Meteorological Agency in October 2014 and has been operational since
July 2015 (Bessho et al., 2016). It carries the Advanced Himawari Imager
(AHI) with capabilities comparable to the Advanced Baseline Imager (ABI)
on board GOES-R (Schmit et al., 2005; Schmit et al., 2008). Himawari-8
is located above the equator at longitude of 140.7 \selectlanguage{ngerman}°E and observes
east/southeast Asia and Oceania. The AHI has 16 observation bands,
including 3 visible bands at wavelengths centred at 0.47, 0.51 and
0.64\selectlanguage{greek}\emph{μ} \selectlanguage{english}m (B1 -- B3), 3 near-infrared (NIR) bands at wavelengths
centred at 0.86, 1.61, and 2.25 \selectlanguage{greek}\emph{μ} \selectlanguage{english}m (B4 -- B6), and 10 infrared
(IR) bands with central wavelengths ranging from 3.9 to 13.3 \selectlanguage{greek}\emph{μ} \selectlanguage{english}m
(B7 -- B16). The resolution of observation bands ranges from 0.5 to 2 km
at the sub-satellite point. The observation cycle occurs every 10 min
for the full disk. Himawari-8 data are available through the collection
of Australian Bureau of Meteorology Satellite Observations (Bureau of
Meteorology, 2021).

\subsubsection*{2.1.1 Chiba LST}

{\label{chiba-lst}}

The LST retrieval from Chiba University, Japan, uses a three-band
algorithm developed by Yamamoto et al. (2018), herein denoted as the YAM
algorithm, which employs several nonlinear terms to improve the LST
estimation accuracy over a wide temperature range (Yamamoto et al.,
2022). It requires 3 bands of Himawari-8 T\textsubscript{B}, 3 bands of
LSEs and precipitable water (PW) as inputs. The wavelengths of 3
required TIR bands (T\textsubscript{B13}, T\textsubscript{B14} and
T\textsubscript{B15}) are 10.4, 11.2 and 12.4~\selectlanguage{greek}\emph{μ} \selectlanguage{english}m, respectively.
LSEs (\selectlanguage{greek}ε\selectlanguage{english}\textsubscript{B13}, \selectlanguage{greek}ε\selectlanguage{english}\textsubscript{B14}, and
\selectlanguage{greek}ε\selectlanguage{english}\textsubscript{B15}) are estimated using an NDVI threshold approach
developed by Yamamoto and Ishikawa (2018), while PW are total column
water vapour values from the European Centre for Medium-Range Weather
Forecasts (ECMWF) ReAnalysis version 5 (ERA5; Hersbach et al., 2020). We
collected Chiba LST for 01/Jan/2016 -- 31/Dec/2020 with a spatial
resolution of 2 km and an hourly frequency (i.e., on the hour mark). The
Chiba LST data are distributed by the Center for Environmental Remote
Sensing (CEReS), Chiba University, Japan, and are freely available at
\url{ftp://modis.cr.chiba-u.ac.jp/yyamamoto/AHILST/v0/}~(Accessed
05/Oct/2023).

\subsubsection*{2.1.2 Copernicus LST}

{\label{copernicus-lst}}

The Copernicus LST dataset is a global-coverage LST product using input
data from various geostationary satellites, including MSG, GOES and
Himawari-8 (Freitas et al., 2013). It employs a generalised SW algorithm
to accommodate different characteristics from each geostationary
satellite imager, which utilises two adjacent channels within the
thermal infrared domain to retrieve LST. We collected Copernicus LST
covering 01/Jan/2016 -- 31/Dec/2020 with a spatial resolution of
\textasciitilde{} 4.5 km at an hourly frequency (i.e., on the hour
mark). We acquired the Copernicus LST data from the CGLS project
(\url{https://land.copernicus.eu/global/products/lst}; accessed
05/Oct/2023).~

\subsection*{2.3 MODIS LST}

{\label{modis-lst}}

MODIS is aboard the Terra and Aqua satellites launched by the National
Aeronautics and Space Administration (NASA) in 1999 and 2002,
respectively (Justice et al., 1998). These satellites are in
sun-synchronous orbits, where Terra has a nominal descending node at
approximately 10:30 local solar time, while Aqua has an ascending node
at approximately 13:30 local solar time. The MODIS LST is retrieved
through a generalised SW algorithm with a reported accuracy of
approximately 2.0 K (Wan, 2014). We collected the MOD11A1 (Terra) and
MYD11A1 (Aqua) datasets (both Collection 6) covering 01/Jan/2016 --
31/Dec/2020 with a spatial resolution of 1 km and daily temporal
frequency. These data were acquired from the NASA Earthdata Search
platform (\url{https://search.earthdata.nasa.gov/search}; accessed
05/Oct/2023).~

\subsection*{2.4 VIIRS LST}

{\label{viirs-lst}}

VIIRS is a scanning radiometer on the Suomi National Polar-orbiting
Partnership (Suomi-NPP) satellite launched by NASA in October 2011
(Islam et al., 2016). It operates in a sun-synchronous orbit, with an
equatorial crossing time at the ascending node of approximately 13:30
local solar time. The VIIRS LST \& Emissivity (LST\&E) product (VNP21)
is retrieved using a physics-based Temperature and Emissivity Separation
(TES) algorithm, providing the simultaneous retrieval of LST and
emissivity from the thermal infrared bands. We obtained the VNP21A1D
dataset (Collection 1) for 01/Jan/2016 to 31/Dec/2020 with a spatial
resolution of 1 km and daily temporal frequency. The data were acquired
from the NASA Earthdata Search platform
(\url{https://search.earthdata.nasa.gov/search}; accessed 05/Oct/2023).~

\subsection*{\texorpdfstring{2.5 Study area and
\emph{in-situ~}measurements}{2.5 Study area and in-situ~measurements}}

{\label{study-area-and-in-situ-measurements}}

The observation area of Himawari-8 covers the longitude of 85 \selectlanguage{ngerman}°E -- 155
°W and latitude of 60 °S -- 60 °N (Fig. 1a). We chose a subset (112 °E
-- 154 °E and 45 °S -- 10 °S) covering the Australian continent as the
study area. Fig. 1 (b) shows the land cover of Australia (Lymburner et
al., 2015) and locations of 20 flux tower sites from the OzFlux network
(Beringer et al., 2016). Table 3 provides the details of the 20 flux
tower sites.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figures/Figure-1/Figure-1}
\caption{{(a) LST of the full-disk Himawari-8 observation area on 01/Jan/2016
00:00 GMT with clouds and oceans masked out; and (b) the land cover map
of Australia (Lymburner et al., 2015) and the distribution of 20 OzFlux
sites. The study site is provided by the black rectangle bounding
Australia in (a).
{\label{844365}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{table}[H]
\centering
\normalsize\begin{tabulary}{1.0\textwidth}{CCCCCC}
\selectlanguage{english}Site name & Latitude (\selectlanguage{ngerman}°N) & Longitude (\selectlanguage{ngerman}°E) & Land cover & Annual rainfall (mm/year) & Standard time zone \\
Alice Springs Mulga & -22.28 & 133.25 & Semi-arid mulga & 306 & ACST  \\
Calperum & -34.0 & 140.59 & Recovering woodland & 240 & ACST  \\
Cape Tribulation & -16.11 & 145.38 & Tropical rainforest & 5700 & AEST  \\
Cow Bay & -16.1 & 145.45 & Complex mesophyll vine forest & 4000 & AEST  \\
Cumberland Plain & -33.62 & 150.72 & Dry sclerophyll & 800 & AEST  \\
Daly Uncleared & -14.16 & 131.39 & Woodland savanna & 1170 & ACST \\
Dry River & -15.26 & 132.37 & Open forest savanna & 895 & ACST \\
Gingin & -31.38 & 115.71 & Coastal health & 641 & AWST  \\
 &  &  & woodland &  &  \\
Great Western Woodlands & -30.19 & 120.65 & Temperate woodland, shrubland and mallee & 240 & AWST  \\
Ridgefield & -32.51 & 116.97 & Dryland agriculture & 446 & AWST \\
Riggs Creek & -36.65 & 145.58 & Dryland agriculture & 650 & AEST \\
Robson Creek & -17.12 & 145.63 & Complex mesophyll vine forest & 2236 & AEST  \\
Samford & -27.39 & 152.88 & Improved pasture & 1102 & AEST  \\
Sturt Plains & -17.15 & 133.35 & Low lying plain dominated by grass & 640 & ACST \\
Ti Tree East & -22.29 & 133.64 & Grassy mulga woodland and savanna & 305 & ACST  \\
Tumbarumba & -35.66 & 148.15 & Wet temperate sclerophyll eucalypt & 1000 & AEST \\
Warra & -43.1 & 146.65 & Eucalyptus obliqua forest & 1700 & AEST \\
Whroo & -36.67 & 145.03 & Box woodland & 558 & AEST  \\
Wombat State Forest & -37.42 & 144.09 & Dry sclerophyll eucalypt forest & 650 & AEST  \\
Yanco & -34.99 & 146.29 & Various soils and cropland & 465 & AEST \\
\end{tabulary}
\caption{{Summary of 20 sites from the OzFlux network. The land cover and annual
rainfall information are from \url{https://ozflux.org.au/} (Accessed
05/Oct/2023). The following abbreviations are used in the `standard time
zone' column: ACST (Australian Central Standard Time; GMT+9.5); AEST
(Australian Eastern Standard Time; GMT+10); AWST (Australian Western
Standard Time; GMT+8).
{\label{622746}}%
}}
\end{table}We estimated the \emph{in-situ} LST using the ground-level upwelling and
downwelling longwave radiation (Level 3) data observed at the OzFlux
stations. By manipulating the traditional equation governing longwave
radiation balance (Allen et al., 1998; Trebs et al., 2021) an
approximation of the \emph{in-situ} LST was derived as:

\[\begin{equation}
\begin{matrix}LST_{in-situ}=\left(\frac{F^{\uparrow}-\left(1-\varepsilon_{\mathrm{b}}\right)F^{\downarrow}}{\sigma\varepsilon_{\mathrm{b}}}\right)^{1/4}\#\left(1\right)\\
\end{matrix}\nonumber \\
 \end{equation}\]

where \(LST_{in-situ}\) is \emph{in-situ} LST (K),~\(F^{\uparrow}\)
is the upwelling longwave radiation (W/m\textsuperscript{2}),
\(F^{\downarrow}\) is the downwelling longwave radiation
(W/m\textsuperscript{2}), \(\varepsilon_{b}\) is the surface broadband
emissivity (unitless), and \(\sigma\) is the Boltzmann constant
(5.67 \selectlanguage{ngerman}× 10\selectlanguage{english}\textsuperscript{-8} W
m\selectlanguage{english}\textsuperscript{-2}K\selectlanguage{english}\textsuperscript{-4}).

\subsection*{2.6 MODIS surface reflectance-derived
indices}

{\label{modis-surface-reflectance-derived-indices}}

We collected three MODIS surface reflectance-derived products, including
the 500 m resolution 16-day MOD13A1 EVI (Huete et al., 2002), the 500 m
resolution 8-day MCD15A2H LAI (Myneni et al., 2002) and the 500 m
resolution daily MCD43A3 albedo (Schaaf et al., 2002) products (all
Collection 6), covering 01/Jan/2016 -- 31/Dec/2020. We calculated the
pixelwise median values of each product for the Australian continent
throughout the 5-year period. These data were acquired from the NASA
Earthdata Search platform
(\url{https://search.earthdata.nasa.gov/search}; accessed 05/Oct/2023).~

\section*{3. Methodology}

{\label{methodology}}

Fig. 2 presents the experimental design employed herein, comprising
three key steps. Firstly, we retrieved the baseline LST through an SW
algorithm (Yu et al., 2012) using Himawari-8 T\textsubscript{B} and
emissivity from the UW Baseline Fit Emissivity Database (Section 3.1
Baseline algorithm). Secondly, we conducted the Solar Zenith Angle-based
Calibration (SZAC) using all available scenes of Terra- and Aqua-MODIS
daytime LST for the Australian continent between 01/Jan/2016 and
31/Dec/2020. To ensure the highest data quality, we applied quality
assurance (QA) flags to select MODIS LST pixels with an expected
retrieval error of less than 1.0 K (Wan, 2013). We selected MODIS QA
flags with numeric values of 0, 5, 17 and 21. By using the time series
of both MODIS best-quality LST and baseline LST, we derived a spatial
distribution of optimised coefficient of SZAC for Australia, which
allowed us to calibrate the daytime component of baseline LST. This step
is denoted as Section 3.2 Solar Zenith Angle-based Calibration (SZAC).
Thirdly and finally, we evaluated the performance of calibrated LST,
referred to as the Australian National University LST with SZAC
(ANU\textsubscript{SZAC} LST), against \emph{in-situ} LST and all
available pixels from MODIS and VIIRS LST data between 01/Jan/2016 and
31/Dec/2020, while utilising the performances of three Himawari-8 LST
datasets (baseline, Chiba, and Copernicus) as comparisons (Section 3.3
Multi-platform evaluation).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.84\columnwidth]{figures/Figure-2/Figure-2}
\caption{\selectlanguage{ngerman}{Experimental design for this research. The SZAC process was conducted
using the time series of every 2 × 2 km pixel throughout the Australian
continent.
{\label{769120}}%
}}
\end{center}
\end{figure}\selectlanguage{ngerman}

\subsection*{3.1 Baseline algorithm}

{\label{baseline-algorithm}}

We employed an SW algorithm (Yu et al., 2009) with coefficients from Yu
et al. (2012) to retrieve LST, referred to as the baseline Himawari-8
LST retrieval herein, taking the following forms:

\(\begin{gathered}L S T_{\text {day }}=30.022546+1.018212 T_{11}+1.263787\left(T_{11}-T_{12}\right)-39.387858 \varepsilon \\ +0.609744\left(T_{11}-T_{12}\right)\left(\sec \theta_{\text {view }}-1\right) \#(2)\end{gathered}\)

\(\begin{gathered}
L S T_{\text {night }}=36.160667+1.012895 T_{11}+1.022203\left(T_{11}-T_{12}\right)-38.909505 \varepsilon \\
+0.669541\left(T_{11}-T_{12}\right)\left(\sec \theta_{\text {view }}-1\right) \#(3)
\end{gathered}\)

where \(LST_{\text{day}}\) and \(LST_{\text{night}}\) represent LST (K) during
daytime and nighttime, respectively, which are defined as when SZA (\selectlanguage{ngerman}°)
is lower/higher than 85 °; \(T_{11}\) and~\(T_{12}\) are
T\textsubscript{B} (K) at \textasciitilde{} 11 and \textasciitilde{} 12
\selectlanguage{greek}\emph{μ} \selectlanguage{english}m wavelength (i.e., Himawari-8 bands 14 and 15, respectively);
\(\varepsilon\) is broadband emissivity
(unitless);~\(\theta_{\text{view}}\) is the viewing zenith angle (VZA; \selectlanguage{ngerman}°) of
Himawari-8. The Yu et al. (2012) LST coefficients were originally
developed for GOES-ABI and with Himawari-AHI having essentially
identical spectral and radiometric characteristics at bands 14 and 15
(Schmit et al., 2008; Bessho et al., 2016) they were applied to
Himawari-8 data.

\subsection*{3.2 Solar Zenith Angle-based Calibration
(SZAC)}

{\label{solar-zenith-angle-based-calibration-szac}}

SZA has underscored its effectiveness in rectifying LST discrepancies
arising from multiple observational platforms (see Table 1). SZA can
serve as a proxy for the amount of solar energy that reaches the ground
surface, and its consequent impact on LST can be analysed through
statistical approaches (Cresswell et al., 1999). Theoretically, SZA
should remain consistent across all platforms, serving as an ideal
bridging parameter to quantify systematic differences between them. This
is preferable to VZA, as the scanning strategies of polar-orbiting and
geostationary platforms are fundamentally distinct. This facilitates a
spatially coherent approach for achieving the necessary spatiotemporal
calibration.

Here we introduce the concept of SZAC to calibrate the daytime component
of Himawari-8 baseline LST using an empirical function of SZA on a
pixelwise basis. In SZAC, a fundamental assumption is that the diurnal
variations of clear-sky LST are continuous and can be simulated using
discrete observations (Duan et al., 2012; Lu and Zhou, 2021). SZAC is a
calibration factor (K) to be subtracted from daytime baseline LST, which
involves the application of a logarithm on the cosine of SZA and is
given as:

\[\begin{equation}
\begin{matrix}SZAC(x_{i},y_{i},t)=Coeff(x_{i}, y_{i})\times log\left(\cos\theta_{\text{solar}}(x_{i},y_{i},t)+1\right)\#\left(4\right)\\
\end{matrix}\nonumber \\
 \end{equation}\]\begin{equation}
\begin{matrix}\cos{\theta_{\text{solar}}\left(x_{i},y_{i},t\right)}=\sin{\Phi\left(x_{i},y_{i}\right)}\sin{\delta\left(x_{i},y_{i},t\right)}+\cos{\Phi\left(x_{i},y_{i}\right)}\cos{\delta\left(x_{i},y_{i},t\right)}\cos{h\left(x_{i},y_{i},t\right)}\#\left(5\right)\\
\end{matrix}\nonumber \\
 \end{equation}

where \((x_{i},\ y_{i})\) is the geolocation of a given pixel
\(i\);~\(t\) is the given time;
SZAC is the calibration factor (K);~Coeff
is an empirical coefficient (K) to be optimised;~\(\theta_{\text{solar}}\) is
SZA (\selectlanguage{ngerman}°); \(\Phi\) is the latitude;~\(\delta\) is the
current declination of Sun; and \(h\) is the hour angle in
local solar time.

SZAC can be conceptualised as the magnitude of LST disparities between
different platforms during the heating period of surface. The cosine of
SZA represents the diurnal variations of shadowed area in relation to
the total surface area, serving as an effective measure of the solar
radiance (not considering topographic adjustment) reaching the Earth's
surface (Yeom et al., 2012), with the application of a logarithmic
filter to attenuate potential overfitting of regression. Additionally,
this filtering ensures the curve approaches near-zero values during the
day-night transition and not adversely affect nighttime LST retrievals.
We employed LST from both Terra- and Aqua-MODIS as reference for
optimising the coefficient of SZAC. Fig. 3 (a) provides a scatterplot
example illustrating the baseline-MODIS difference plotted against SZA
at the Wombat State Forest site during 1/Jan/2016-31/Dec/2020. The
majority of samples cluster within the range of 20 - 70 ° SZA, which
corresponds to the MODIS overpass times of approximately 10:30 am and
1:30 pm local solar time for Terra and Aqua, respectively. Fig. 3 (b)
shows the temporal variation of SZAC throughout a day. SZAC attains its
maximum value when SZA is lowest (i.e., around midday) and reaches its
minimum value when SZA is approximately 85 ° (i.e., sunrise or sunset).
This ensures that SZAC has minimal impact on the day-night transition
and does not affect the nighttime LST retrievals.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figures/Figure-3/Figure-3}
\caption{{(a) Schematic of SZAC at the Wombat State Forest site and; (b) an
example to show the temporal variation (using a bin size of 60 minutes)
of SZAC during daytime on 02/Jan/2016. The location of Wombat State
Forest is shown on Fig. 1. (b) with additional details provided in Table
3.
{\label{838867}}%
}}
\end{center}
\end{figure}

We employed the Brent (2013) local optimisation approach to determine
the coefficient of SZAC for each matched cloud-free baseline-MODIS LST
time series during 1/Jan/2016-31/Dec/2020 on a pixelwise basis. This
minimised the difference between all coincident baseline Himawari LST
and MODIS LST observations over the full 5-year period on a pixelwise
basis. The objective function was the root mean square error (RMSE)
between the baseline LST and MODIS LST. Then the daytime baseline LST
for each pixel was calibrated using the single coefficient along with
the temporal variations of SZA, which was denoted as the calibrated LST
(i.e., ANU\textsubscript{SZAC}):

\[\begin{equation}
\begin{matrix}LST_{day,ZAC}(x_{i}, y_{i},t)=LST_{day}(x_{i},y_{i},t)-SZAC(x_{i},y_{i},t)\#\left(6\right)\\
\end{matrix}\nonumber \\
 \end{equation}\]

where \(LST_{day,ZAC}\) is the calibrated daytime LST
and~\(LST_{day}\) is the baseline daytime LST.

\subsection*{3.3 Multi-platform
evaluation}

{\label{multi-platform-evaluation}}

\subsubsection*{3.3.1 Cross-satellite matching
strategy}

{\label{cross-satellite-matching-strategy}}

Geostationary and polar-orbiting satellites have different surface
scanning strategies. The Terra, Aqua and Suomi-NPP satellites do not
have a constant overpass time, e.g., the data acquisition time of Terra
ranges from 10:00 to 12:10 local solar time (Hu et al., 2014). To
standardise the acquisition times of MODIS and VIIRS LST records and
make them comparable with those of Himawari-8 LST, we converted the
MODIS and VIIRS `view time' layer, which is expressed in local solar
time, to the GMT format, which is given as:

\[\begin{equation}
\begin{matrix}T_{polar,GMT}(x_{i}, y_{i},t)=T_{polar,solar}(x_{i}, y_{i},t)-Lon/15\#\left(7\right)\\
\end{matrix}\nonumber \\
 \end{equation}\]

where \(T_{polar,GMT}\) is the MODIS or VIIRS view time in GMT
format,~\(T_{polar,solar}\) is the MODIS or VIIRS view time in local
solar time, and Lon is the longitude in decimal of a
given pixel. Then we utilised a one-hour temporal window (i.e., \selectlanguage{ngerman}± 30
minutes) to match Himawari-8 time (GMT) and MODIS time (GMT) on a
pixelwise basis:

\[\begin{equation}
\begin{matrix}T_{H8,GMT}(x_{i},y_{i},t)-30\ min\leq T_{polar,GMT}(x_{i},y_{i},t)\leq T_{H8, GMT}(x_{i},y_{i},t)+30\ min\#\left(8\right)\\
\end{matrix}\nonumber \\
 \end{equation}\]

where \(T_{H8,GMT}\) is the time stamp of Himawari-8 in GMT format.
This matching strategy allowed us to derive comparable LST records from
Himawari-8 and polar-orbiting satellites (MODIS or VIIRS).

\subsubsection*{\texorpdfstring{3.3.2 \emph{In-situ} matching
strategy}{3.3.2 In-situ matching strategy}}

{\label{in-situ-matching-strategy}}

We employed the \emph{in-situ} LST derived from OzFlux longwave
radiation to evaluate Himawari-8 LST. Flux towers from the OzFlux
network (see Fig. 1 (b) for locations and Table 3 for additional
information) measure longwave radiation at half-hour intervals. We also
implemented a one-hour temporal window (i.e., \selectlanguage{ngerman}± 30 minutes) strategy,
similar to Eq. 8, to match Himawari-8 time (GMT) and \emph{in-situ} time
(converted to GMT). We calculated the mean in cases where
two~\emph{in-situ} records are present within the hour. By adopting this
approach, direct comparisons between Himawari-8 LST observations and
corresponding ground-level measurements were made, disregarding
individual time zones of flux towers.

\subsubsection*{3.3.3 Evaluation metrics}

{\label{evaluation-metrics}}

We utilised bias and unbiased root mean square error (ubRMSE) to
evaluate the performance of Himawari-8 LST data against the
corresponding reference LST:

\[\begin{equation}
\begin{matrix}Bias=\frac{\sum\left(LST_{H8}-LST_{ref}\right)}{N}\#\left(9\right)\\
\end{matrix}\nonumber \\
 \end{equation}\]\[\begin{equation}
\begin{matrix}ubRMSE=\sqrt{\frac{\sum\left(\left(LST_{H8}-\mu\left(LST_{H8}\right)\right)-\left(LST_{ref}-\mu\left(LST_{ref}\right)\right)\right)^{2}}{N}}\#\left(10\right)\\
\end{matrix}\nonumber \\
 \end{equation}\]

where \(LST_{H8}\) is the time series of Himawari-8 (i.e.,
baseline, Chiba, Copernicus or ANU\textsubscript{SZAC})
LST;~\(LST_{\text{ref}}\) is the time series of reference
(i.e.,~\emph{in-situ}, MODIS or VIIRS) LST; \(N\) is the
number of individual observations in each reference time series.

\section*{4. Results}

{\label{results}}

\subsection*{4.1 Assessment of MODIS-based SZAC's
performance}

{\label{assessment-of-modis-based-szacs-performance}}

Fig. 4 (a) shows the spatial distribution of SZAC coefficient for the
Australian continent. Lower values of the coefficient (less than 4 K)
were observed over the eastern edge, whereas higher values (exceeding 8
K) were concentrated in central and northern Australia. This means that
the Himawari-8 baseline LST was more consistent with MODIS LST in
Australia's eastern coastal regions, yet tended to overestimate LST in
central and northern Australia when compared to MODIS LST. Notably, the
area of Lake Eyre, the largest salt-lake in inland Australia, exhibited
the lowest coefficient value (\textasciitilde{}2 K), which could be
attributed to the absence of canopies within these highly reflective
salt-lake regions. A more detailed analysis of the spatial pattern of
SZAC coefficient is elucidated in Fig. 15. The distribution of the SZAC
coefficient was also influenced by the scanning strategy employed by the
MODIS instrument during its orbit which resulted in MODIS-induced strips
in the SZAC coefficient. Nevertheless, as SZAC functions as a
calibration factor to be subtracted from the Himawari-8 baseline LST, it
introduces certain offsets associated with the emissivity artifacts
within the baseline LST. This phenomenon is further elucidated in Fig.
5.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-4/Figure-4}
\caption{\selectlanguage{ngerman}{(a) Spatial distribution of the SZAC coefficient for the Australian
continent during 01/Jan/2016 -- 31/Dec/2020. The `light-green / yellow'
region just west of Himawari's longitude (140.7 °E represented by the
red dashed line) exhibiting the lowest coefficient values of
\textasciitilde{} 2 K, is associated with Lake Eyre and other salt lakes
within inland Australia.
{\label{144759}}%
}}
\end{center}
\end{figure}\selectlanguage{ngerman}

Fig. 5 presents the spatial distribution of input emissivity, SZAC
values, baseline and ANU\textsubscript{SZAC} LST at 02:00 GMT (i.e.,
12:00 AEST) on (a-d) 20/Mar/2016 (austral autumn equinox); (e-h)
21/Jun/2016 (austral winter solstice); (i-l) 23/Sep/2016 (austral spring
equinox); and (m-p) 21/Dec/2016 (austral summer solstice). The SZAC
values showed seasonal variations, being highest at the summer solstice
(Fig. 5 n), moderate and comparable at the spring and autumn equinoxes
(Fig. 5 b and j), and lowest at the winter solstice (Fig. 5 f). This
variation signifies that the disparities between the baseline LST and
MODIS LST were most pronounced in the summer, a period when incoming
radiation peaks and necessitate a stronger correction. The systematic
differences between the Himawari-8 baseline and MODIS LST in inland and
northern Australia were always higher than other regions. Furthermore,
both input emissivity (Fig. 5; first column) and SZAC values (Fig. 5;
second column) exhibited artefacts associated with MODIS scanning
effects. However, these artefacts were effectively removed by the
calibration process as seen in both baseline (Fig. 5; third column) and
ANU\textsubscript{SZAC} LST (Fig. 5; fourth column).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.84\columnwidth]{figures/Figure-5/Figure-5}
\caption{{Respective spatial distribution of emissivity, SZAC values, baseline and
ANU\textsubscript{SZAC} LST at 02:00 GMT on (a-d) 20/Mar/2016 (austral
autumn equinox); (e-h) 21/Jun/2016 (austral winter solstice); (i-l)
23/Sep/2016 (austral spring equinox); and (m-p) 21/Dec/2016 (austral
summer solstice). The oceans and seas surrounding Australia are white in
all parts, with Himawari cloud contaminated pixels being white over land
in the two columns on the right.
{\label{806944}}%
}}
\end{center}
\end{figure}

Fig. 6 presents the spatial distribution of bias (a-b) and ubRMSE (c-d)
of baseline and ANU\textsubscript{SZAC} LST against best-quality MODIS
LST for the Australian continent between 01/Jan/2016 and 31/Dec/2020.
This evaluation assesses the fitting performance of
ANU\textsubscript{SZAC} LST by comparing to the training set. The median
bias of baseline LST against MODIS\textsubscript{best} LST for the
Australian continent is 5.09 K while the median bias of
ANU\textsubscript{SZAC} LST was reduced to 1.07 K. Both baseline and
ANU\textsubscript{SZAC} LST demonstrated comparable levels of ubRMSE
performance, being 2.50 K and 2.53 K, respectively. In general, both LST
products exhibited the lowest ubRMSE values (ranging from 1 to 2 K) for
much of inland Australia. However, over coastal regions, the ubRMSE
increased to 2 to 3 K for both products (Fig. 6 b and e). The evaluation
based on the training set demonstrated that SZAC could reduce the bias
performance while maintaining a similar ubRMSE level.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figures/Figure-6/Figure-6}
\caption{{Spatial distribution of bias and ubRMSE of baseline and
ANU\textsubscript{SZAC} LST against best-quality (i.e., expected error
\textless{} 1 K) MODIS (both MOD11A1 and MYD11A1) LST for the Australian
continent between 01/Jan/2016 and 31/Dec/2020. The oceans and seas
surrounding Australia are white in all parts.
{\label{285685}}%
}}
\end{center}
\end{figure}

Fig. 7 presents the spatial distribution of bias (a-d) and ubRMSE (e-h)
of baseline, Chiba, Copernicus and ANU\textsubscript{SZAC} LST against
all available LST pixels from Terra-MODIS (i.e., MOD11A1) for the
Australian continent at \textasciitilde{} 10:30 local solar time between
01/Jan/2016 and 31/Dec/2020. The median bias of baseline, Chiba,
Copernicus LST against Terra-MODIS LST for the Australian continent was
5.37, 3.71, 3.25 K, respectively, while the median bias of
ANU\textsubscript{SZAC} LST was only 1.52 K, less than half of the
second-best other result (i.e., Copernicus LST). This indicates that
ANU\textsubscript{SZAC} LST outperformed the other LST products in terms
of bias, demonstrating an improved agreement against the
\textasciitilde{} 10:30 local solar time Terra-MODIS LST. The median
ubRMSE of baseline, Chiba, Copernicus LST was 2.47, 2.56 and 2.55 K,
respectively, while the ubRMSE of ANU\textsubscript{SZAC} LST was 2.75 K
and showed more spatial variability.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figures/Figure-7/Figure-7}
\caption{{Spatial distribution of bias and ubRMSE of baseline, Chiba, Copernicus
and ANU\textsubscript{SZAC} LST against all available LST pixels from
Terra-MODIS (i.e., MOD11A1) for the Australian continent at
\textasciitilde{} 10:30 local solar time between 01/Jan/2016 and
31/Dec/2020. The oceans and seas surrounding Australia are white in all
parts.
{\label{383033}}%
}}
\end{center}
\end{figure}

Fig. 8 presents the spatial distribution of bias (a-d) and ubRMSE (e-h)
of baseline, Chiba, Copernicus and ANU\textsubscript{SZAC} LST against
all available LST pixels from Aqua-MODIS (i.e., MYD11A1) for the
Australian continent at \textasciitilde{} 13:30 local solar time between
01/Jan/2016 and 31/Dec/2020. The median bias of baseline, Chiba,
Copernicus LST against Aqua-MODIS LST for Australian was 4.85, 2.90 and
2.28 K, respectively. In contrast, ANU\textsubscript{SZAC} LST exhibited
a reduced median bias of 0.98 K, which was less than half of the
second-best other result (i.e., Copernicus LST). This indicated that all
Himawari-8 LST products showed better agreement in the afternoon
(\textasciitilde{} 13:30 local solar time) than the morning
(\textasciitilde{} 10:30 local solar time), while
ANU\textsubscript{SZAC} LST had a superior bias performance compared to
the three other LST products in both the morning and afternoon. The
median ubRMSE of baseline, Chiba, Copernicus and
ANU\textsubscript{SZAC}LST was 2.42, 2.37, 2.48 and 2.44 K,
respectively. Both baseline and ANU\textsubscript{SZAC} LST displayed
relatively lower ubRMSE values (\textasciitilde{} 2 K) for inland
regions with relatively higher values (\textasciitilde{} 3 K) in the
north. The differences in the direction of strips seen in Fig. 8
compared to Fig. 7 are attributed to the differences of orbits of Terra
(descending at \textasciitilde{} 10:30 local solar time) and Aqua
(ascending at \textasciitilde{} 13:30 local solar time) satellites.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figures/Figure-8/Figure-8}
\caption{{Spatial distribution of bias and ubRMSE of baseline, Chiba, Copernicus
and ANU\textsubscript{SZAC} LST against all available LST pixels from
Aqua-MODIS (i.e., MYD11A1) for Australia at \textasciitilde{} 13:30
local solar time between 01/Jan/2016 and 31/Dec/2020. The oceans and
seas surrounding Australia are white in all parts.
{\label{225316}}%
}}
\end{center}
\end{figure}

\subsection*{\texorpdfstring{4.2 Evaluation against \emph{in-situ} LST
during
2016-2020}{4.2 Evaluation against in-situ LST during 2016-2020}}

{\label{evaluation-against-in-situ-lst-during-2016-2020}}

Fig. 9 presents the annual and seasonal boxplots of bias of baseline,
Chiba, Copernicus and ANU\textsubscript{SZAC} LST against
the~\emph{in-situ} LST derived at the 20 OzFlux sites (see Fig. 1 (b)
for their locations) at different times (i.e., all day, daytime and
nighttime) between 01/Jan/2016 and 31/Dec/2020. Regarding the all-day
metrics (Fig. 9 a), the overall mean values of bias of baseline, Chiba,
Copernicus and ANU\textsubscript{SZAC} LST were 1.87 K, -0.29 K, -0.57 K
and 0.60 K, respectively. For the daytime evaluation (Fig. 9 b), the
overall mean values of bias of baseline, Chiba, Copernicus and
ANU\textsubscript{SZAC} LST were 4.23 K, 2.16 K, 1.73 K and 1.41 K,
respectively. ANU\textsubscript{SZAC} LST exhibited better performance
than baseline LST and outperformed Chiba and Copernicus in almost all
seasons during daytime; while ANU\textsubscript{SZAC} LST was comparable
with Copernicus LST in winter. For the nighttime evaluation (i.e., Fig.
9 c), the overall mean values of bias of baseline, Chiba, Copernicus and
ANU\textsubscript{SZAC} LST against \emph{in-situ} LST were 0.06 K,
-2.29 K, -2.45 K and -0.06 K, respectively. As no SZAC was applied at
the night, the baseline and ANU\textsubscript{SZAC} LST exhibit
identical performance during nighttime. Both baseline and
ANU\textsubscript{SZAC} LST consistently outperformed Chiba and
Copernicus LST in all seasons during nighttime evaluations. It is
notable that the superior all-day bias metrics of Chiba and Copernicus
LST were due to the daytime and nighttime bias metrics essentially
cancelling each other out. For detailed metrics of the individual 20
OzFlux sites, see Table S1 in the Supplementary material.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figures/Figure-9/Figure-9}
\caption{{Annual and seasonal boxplots of bias of baseline, Chiba, Copernicus and
ANU\textsubscript{SZAC} LST against in-situ LST at different times
(i.e., all day, daytime and nighttime) between 01/Jan/2016 and
31/Dec/2020. For the southern hemisphere spring is from September to
November, summer from December to February, autumn from March to May,
and winter from June to August. The dark horizontal line within the
boxplots represents the median value; the upper and lower lines defining
the coloured rectangle are the interquartile range (i.e., the 75\% and
25\% values) respectively; the upper and lower whiskers extend from the
box represent the maximum and minimum values excluding any outliers. The
red numbers at the bottom of each plot are the overall mean values of
bias. The unit of bias is K. ~
{\label{585386}}%
}}
\end{center}
\end{figure}

Fig. 10 presents the annual and seasonal boxplots of ubRMSE of baseline,
Chiba, Copernicus and ANU\textsubscript{SZAC} LST against
\emph{in-situ~}LST at different times (i.e., all day, daytime and
nighttime) between 01/Jan/2016 and 31/Dec/2020 for the 20 OzFlux sites.
Regarding the all-day metrics (Fig. 10 a), the overall mean values of
ubRMSE of baseline, Chiba, Copernicus and ANU\textsubscript{SZAC} LST
were 3.98 K, 3.89 K, 3.69 K and 3.24 K, respectively.
ANU\textsubscript{SZAC} LST displayed a narrowed spread of ubRMSE in all
seasons, which indicated that ANU\textsubscript{SZAC} LST had the best
overall agreement with~\emph{in-situ} LST. For the daytime evaluation
(Fig. 10 b), the overall mean values of ubRMSE of baseline, Chiba,
Copernicus and ANU\textsubscript{SZAC} LST were 3.74 K, 3.62 K, 3.31 K
and 3.24 K, respectively. ANU\textsubscript{SZAC} LST demonstrated
narrowed spread than baseline throughout all seasons. For the nighttime
evaluation (Fig. 10 c), the overall mean values of ubRMSE of baseline,
Chiba, Copernicus and ANU\textsubscript{SZAC} LST against \emph{in-situ}
LST were 2.77 K, 2.57 K, 2.54 K and 2.77 K, respectively. The nighttime
measurements of all four LST products were generally comparable across
all seasons, with Copernicus LST showing a slightly greater uncertainty
in the spread of ubRMSE. For detailed metrics of the individual 20
OzFlux sites, see Table S2 in the Supplementary material.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figures/Figure-10/Figure-10}
\caption{{Annual and seasonal boxplots of ubRMSE of baseline, Chiba, Copernicus
and ANU\textsubscript{SZAC} LST against in-situ LST at different times
(i.e., all day, daytime and nighttime) between 01/Jan/2016 and
31/Dec/2020. The explanation of seasonal division and boxplot features
are the same as in the Fig. 9 caption. The red numbers at the bottom of
each plot are the overall mean values of ubRMSE. The unit of ubRMSE is
K.
{\label{958429}}%
}}
\end{center}
\end{figure}

Fig. 11 presents the hourly boxplots over the diurnal cycle of bias of
baseline, Chiba, Copernicus and ANU\textsubscript{SZAC} LST
against~\emph{in-situ} LST in local standard time zone between
01/Jan/2016 and 31/Dec/2020. During the daytime, ANU\textsubscript{SZAC}
LST showed smaller bias values compared to baseline LST. This was
evident as the bias of ANU\textsubscript{SZAC} LST was closer to the
zero-bias line, indicating a reduced systematic error. Additionally, the
spread of boxplots representing the variation of bias at different sites
was also narrowed for ANU\textsubscript{SZAC} LST. The biggest
improvement in bias of ANU\textsubscript{SZAC} LST was observed around
midday (i.e., 10:00-12:00 local standard time), corresponding to the
time when the SZAC coefficients reach their maximum thus the calibration
had the strongest effects (see Fig. 3 a). On the other hand, both Chiba
and Copernicus LST showed better bias performance than baseline during
the daytime. However, both Chiba and Copernicus LST exhibited negative
bias during the nighttime, indicating an underestimation of LST values
compared to \emph{in-situ} measurements. In contrast, during the
nighttime the median values of baseline and ANU\textsubscript{SZAC} LST
were close to the zero-bias line. Overall, the calibration process
applied to ANU\textsubscript{SZAC} LST effectively mitigated most
systematic errors, resulting in improved accuracy during daytime hours.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figures/Figure-11/Figure-11}
\caption{{Hourly boxplots over the diurnal cycle of bias of baseline, Chiba,
Copernicus and ANU\textsubscript{SZAC} LST against in-situ LST in local
standard time zone between 01/Jan/2016 and 31/Dec/2020. The boxplot
features are fully explained in the Fig. 9 caption.
{\label{648011}}%
}}
\end{center}
\end{figure}

Fig. 12 presents four examples of temporal variation of baseline, Chiba,
Copernicus, ANU\textsubscript{SZAC} and \emph{in-situ} LST in local
standard time zone at (a) Cumberland Plain, (b) Daly Uncleared, (c)
Gingin and (d) Tumbarumba sites within a 150-hour temporal window (see
Fig. 1 (b) for the locations of these OzFlux sites). All four Himawari-8
LST products showed consistent diurnal cycles with \emph{in-situ} LST
measurements. Among them, the baseline LST was generally overestimated
during daytime (a-c), which has been effectively resolved in
ANU\textsubscript{SZAC} LST. As a comparison, ANU\textsubscript{SZAC}LST
exhibited similar temporal patterns with Chiba and Copernicus LST during
daytime, aligning more closely with their diurnal cycles. However,
ANU\textsubscript{SZAC} LST retained the nighttime component of baseline
LST, which generally demonstrates better agreement with~\emph{in-situ}
LST during nighttime, aligning more closely with the observed LST values
in most cases.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figures/Figure-12/Figure-12}
\caption{{Four examples of temporal variation of baseline, Chiba, Copernicus,
ANU\textsubscript{SZAC} and in-situ LST in local standard time zone at
(a) Cumberland Plain, (b) Daly Uncleared, (c) Gingin and (d) Tumbarumba
OzFlux sites within a 150-hour window. The legend in (d) applies to all
other parts. The locations of the four sites are shown in Fig. 1 (b)
with additional site information provided in Table 3.
{\label{850331}}%
}}
\end{center}
\end{figure}

\subsection*{4.3 Spatial comparison against VIIRS LST during
2016-2020}

{\label{spatial-comparison-against-viirs-lst-during-2016-2020}}

Fig. 13 presents the spatial distribution of bias and ubRMSE of
baseline, Chiba, Copernicus and ANU\textsubscript{SZAC} LST against all
available LST pixels from VIIRS (i.e., VNP21A1D) for the Australian
continent at \textasciitilde{} 13:30 local solar time between
01/Jan/2016 and 31/Dec/2020. The median bias of baseline, Chiba,
Copernicus and ANU\textsubscript{SZAC} LST against VIIRS LST was 3.02,
1.07, 0.33 and -0.63 K, respectively. This indicates that all Himawari-8
LST products demonstrated less bias when compared against VIIRS LST than
when compared against Aqua-MODIS LST (which was 4.85, 2.90, 2.28 and
0.98 K, respectively; see Fig. 8). Notably, both VIIRS and Aqua-MODIS
have an overpass time of \textasciitilde{} 13:30 local solar time making
this comparison essentially free of diurnal cycle influences. The median
ubRMSE of baseline, Chiba, Copernicus and ANU\textsubscript{SZAC} LST
against VIIRS LST was 3.07, 2.84, 2.92 and 2.94 K, respectively.
ANU\textsubscript{SZAC} LST exhibited reduced values of ubRMSE in
northern and mid-eastern regions of Australia compared to the baseline
LST. In general, ANU\textsubscript{SZAC} LST was more comparable to
Copernicus LST than the two other products in terms of bias and ubRMSE
metrics. However, ANU\textsubscript{SZAC} offered the additional
advantage of higher spatial resolution (i.e., 2 km for
ANU\textsubscript{SZAC} and \textasciitilde{} 4.5 km for Copernicus) and
better temporal frequency (i.e., 10 min for ANU\textsubscript{SZAC} and
1 hour for Copernicus); see Table 2.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figures/Figure-13/Figure-13}
\caption{{Spatial distribution of bias and ubRMSE of baseline, Chiba, Copernicus
and ANU\textsubscript{SZAC} LST against all available LST pixels from
VIIRS (i.e., VNP21A1D) for Australia at \textasciitilde{} 13:30 local
solar time between 01/Jan/2016 and 31/Dec/2020. The oceans and seas
surrounding Australia are white in all parts.
{\label{978885}}%
}}
\end{center}
\end{figure}

Fig. 14 presents two examples of spatial pattern comparison of baseline,
Chiba, Copernicus and ANU\textsubscript{SZAC} LST against VIIRS LST at
04:00 GMT (i.e., equivalent to 14:00 AEST, 13:30 ACST or 12:00 AWST) on
20/Jun/2019 (austral winter) and 20/Dec/2019 (austral summer),
respectively. On both days, the four Himawari-8 LST products exhibit
similar spatial patterns, though differences are observed. On
20/Jun/2019, the baseline LST generally showed higher values in the
north-western regions; while on 20/Dec/2019, the baseline LST displayed
higher values in eastern regions. In contrast,
ANU\textsubscript{SZAC}LST demonstrated more similarity with Chiba,
Copernicus on both days, showing reduced discrepancies with the
reference VIIRS LST product. On 20/Jun/2019, the differences of Chiba,
Copernicus and ANU\textsubscript{SZAC} LST against VIIRS were visually
similar (Fig. 14, second column from left). On 20/Dec/2019, Chiba LST
showed slightly higher values while ANU\textsubscript{SZAC} LST
exhibited slightly lower values compared to VIIRS LST (Fig. 14, right
most column). The spatial comparisons presented in Fig. 14 were
consistent with the pixelwise metrics indicated in Fig. 13.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figures/Figure-14/Figure-14}
\caption{{Two examples of spatial comparison of baseline, Chiba, Copernicus and
ANU\textsubscript{SZAC} LST against VIIRS LST at 04:00 GMT on
20/Jun/2019 and 20/Dec/2019, respectively. The first and third columns
from the left are LST from the four Himawari products with VIIRS being
the bottom row. The first four rows of the second and fourth columns
from the left are differences (denoted `LST\textsubscript{diff}' in the
legend) between each Himawari-8 LST product (in turn) and the VIIRS LST.
The last rows of the second and fourth columns from the left are the
VIIRS view time strips (in GMT). The oceans and seas surrounding
Australia, cloud contaminated pixels and areas beyond the VIIRS swath
are white in all parts.
{\label{336859}}%
}}
\end{center}
\end{figure}

\section*{5. Discussion}

{\label{discussion}}

\subsection*{5.1 Distribution of SZAC coefficient and its physical
implications}

{\label{distribution-of-szac-coefficient-and-its-physical-implications}}

Numerous studies have noted discrepancies between LST acquired at
essentially the same time from both geostationary and polar-orbiting
platforms (e.g., Li et al., 2020; Trigo et al., 2021; P\selectlanguage{ngerman}érez-Planells et
al., 2023). Nighttime LST products exhibit good agreement across various
viewing configurations, whereas daytime observations have discrepancies
attributed to the influence of shadows and temperature gradients within
the landscape cover (Guillevic et al., 2013). As a result, SZA in
conjunction with emissivity has been extensively applied to rectify the
angular effects and enhance agreement of LST products acquired from
different platforms (Vinnikov et al., 2012; Ermida et al., 2017; Ermida
et al., 2018). Herein, we examined the diurnal patterns of baseline LST
errors and proposed the SZAC approach, which leverages the dynamics of
SZA (which mainly changes as a function of latitude, time-of-day and
day-of-year) to spatiotemporally correct the daytime component of
baseline LST measurements. There are four insights gleaned from this
research.

Firstly, the effectiveness of SZA as an input for spatial correction
lies in its cosine value, which is associated with the ratio of shadowed
area to the total surface area. This property makes SZA a representative
measure of the solar radiance reaching the Earth's surface (Yeom et al.,
2012). Vinnikov et al. (2012) also emphasised that an SZA-based kernel
is closely tied to the spatial inhomogeneity in surface heating and
shadowing across diverse regions of the land surface and its cover.
Moreover, the variability of SZA is linked to diurnal changes, seasonal
fluctuations, and latitudinal differences. Consequently, it serves as a
valuable bridging parameter to quantify the systematic differences
between diverse LST products, which were developed using different
underlying assumptions and showed systematic differences (see Table 1).

Secondly, the SZAC coefficient revealed negative associations with
vegetation cover characteristics and exhibited a greater degree of
uniformity within inland regions, where calibration effects exerted a
more pronounced influence. Fig. 15 shows (a-d) the continental-scale and
(e-t) zoomed comparisons between the spatial patterns of SZAC
coefficient and 5-year median values of MODIS EVI, LAI and albedo
between 01/Jan/2016 and 31/Dec/2020 for four chosen regions,
respectively. The greater uniformity observed in inland arid regions was
attributed to their predominantly homogeneous and larger patches of
vegetation (Fig. 15 a-d). In contrast, pixels along the eastern
coastlines exhibited greater heterogeneity (Region A and C; Fig. 15 e-h
and q-t), characterised by denser vegetation and relatively mountainous
terrain. This coastal area, where more population reside, featured more
heterogeneous landscapes. Additionally, in forests, the closed canopy
leads to a more even distribution, reducing internal shadowing compared
to woodland areas with lower tree density. Furthermore, the SZAC
coefficient and all three MODIS indices manifested distinct boundary
effects within the Nullarbor Plain area (Region B; Fig. 15 i-l), an
important biogeographic region as defined by the Australian Government
(DCCEEW, 2020). Finally, it is noteworthy that for the Lake Eyre area
(Region C; Fig. 15 m-p), the SZAC coefficient demonstrated strong
connections with the masked area of LAI, which were all salt lakes,
signifying the absence of canopies. The albedo of region C was also the
highest within Australia, demonstrating a distinctive characteristic of
highly reflective surfaces in this area.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.84\columnwidth]{figures/Figure-15/Figure-15}
\caption{\selectlanguage{ngerman}{(a-d) Continental-scale and (e-t) zoomed comparisons between the spatial
patterns of SZAC coefficient and 5-year median values of MODIS EVI, LAI
and albedo between 01/Jan/2016 and 31/Dec/2020 for region A, B, C and D,
respectively. Region A spans 142-147 °E and 10-20 ° S; region B spans
123-134 ° E and 28-33 °S; region C spans 135-141 °E and 24-32 °S; and
region D spans 148-154 °E and 25-35 °S.
{\label{316460}}%
}}
\end{center}
\end{figure}\selectlanguage{ngerman}

Fig. 16 presents violin plots illustrating the values of the SZAC
coefficient within four equal-value-range quantiles for (a) EVI, (b)
LAI, and (c) albedo between 01/Jan/2016 and 31/Dec/2020. For both EVI
and LAI, the SZAC coefficient exhibited similar decreasing trend with
increasing vegetation indices. As depicted in Fig. 16 (a) and (b), when
EVI (LAI) was concentrated within the range of 0-0.15 (0-1.75), the
median values of SZAC coefficient were 7.97 K (7.75 K); conversely, when
EVI (LAI) was concentrated within the range of 0.45-0.60 (5.25-7.00),
the median values of SZAC coefficient decreased to 4.87 K (4.71 K). This
trend aligns with the observations in Fig. 15 (a-c), where higher SZAC
coefficient values were associated with sparser vegetation (inland
Australia), while lower values were linked to denser vegetation and more
complex landscapes (eastern coastal Australia). Concerning albedo, the
SZAC coefficient demonstrated a positive relationship when albedo was
lower than 0.30. However, when albedo was concentrated within the range
of 0.30-0.40, the SZAC coefficient exhibited high uncertainties,
indicating a lack of strong connections between them in such scenarios.
These findings reinforce the relationship between the spatial pattern of
SZAC coefficient and vegetation cover characteristics.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.98\columnwidth]{figures/Figure-16/Figure-16}
\caption{{Violin plots of the values of SZAC coefficient within four
equal-value-range quantiles for (a) EVI; (b) LAI; and (c) albedo,
respectively, between 01/Jan/2016 and 31/Dec/2020. The red dots within
violins represent the median value; the bold vertical black lines within
violins are the interquartile range (i.e., the 75\% and 25\% values,
respectively); the upper and lower limits of violins represent the
maximum and minimum values excluding any outliers; the distribution of
violins represent the kernel density of sample numbers within each
quantile. The red decimal numbers (percentage) at the bottom of each
plot are the median values (percentage of overall sample numbers) of
SZAC coefficient within each quantile.
{\label{814403}}%
}}
\end{center}
\end{figure}

Thirdly, it is noteworthy that the distribution of the SZAC coefficient
may be influenced by VZA of the employed satellites (Himawari-8, Terra
and Aqua), although VZA was not explicitly incorporated into the
calibration process. In Fig. 4, a discernible pattern in SZAC dependence
was observed, particularly in relation to the longitudinal position of
140.7\selectlanguage{ngerman}° E (i.e., the longitude of Himawari-8). It becomes evident that
SZAC values are lower in southern regions near this longitude and higher
in areas situated farther away, such as those in Western Australia (WA)
and western South Australia (SA). This pattern could be attributed to
the fixed VZA of Himawari-8, where a shorter atmospheric path (or lower
VZA values) tends to enhance the accuracy of LST retrievals.
Additionally, the distribution of the SZAC coefficient is also
influenced by the viewing geometries of MODIS satellites (see Fig. 4),
specifically the Terra descending and Aqua ascending orbits.

Fourthly and finally, in alignment with various parametric modelling
approaches, such as diurnal temperature cycle (DTC) models, the SZAC
coefficient holds physical interpretations and implications. Yamamoto et
al. (2023) recently explored DTC models using Himawari-8 LST data as
inputs, revealing that the maximum daily LST (T\textsubscript{max}) and
its diurnal temperature range (DTR) emerged as particularly informative
parameters for monitoring vegetation drying signals under heatwave. This
was attributed to heightened sensitivity of T\textsubscript{max} to
geometric conditions of sun-target-observer, its stability in model
fitting, and its correlations with other environmental variables like
vegetation indices and soil moisture. In this research, the SZAC
coefficient was derived based on SZA values ranging from 20 to 70 ° and
can be conceptualised as representing the `magnitude of LST disparities
between different platforms during the heating period of surface'. Fig.
3 illustrated when SZA approaches its minimum value (around midday), the
magnitude of LST differences (and correction effect of SZAC) attains its
maximum extent. Given that SZA represents the angle formed between the
Sun's rays and the vertical direction, this phenomenon signifies a vital
relationship between the extent of shadowing and the observed variations
in LST. Moreover, the SZAC approach is consistent with previous studies
that modelled DTC models by relying on sparse polar-orbiting LST
observations (Duan et al., 2012; Hu et al., 2020a; Lu and Zhou, 2021).
However, the performance of SZAC within `twilight times' may require
further re-evaluation due to limited available data during the time of
day-to-night transition (and vice versa). The lack of data during
day-night transitions can potentially introduce uncertainties in
performance of SZAC, especially when dealing with rapid temperature
changes and complex atmospheric conditions within twilight zones
(Kurihara et al., 2016; Eytan et al., 2020).

\subsection*{5.2 Usage and prospects of
SZAC}

{\label{usage-and-prospects-of-szac}}

SZAC has demonstrated robustness and operational capability in reducing
systematic bias when compared to MODIS, VIIRS and \emph{in-situ} LST
measurements. Additionally, the ANU\textsubscript{SZAC} LST derived from
the SZAC approach showed a reduction of \textasciitilde{} 0.5 K in
ubRMSE compared to the baseline LST when evaluated against
daytime~\emph{in-situ} LST (Fig. 10). When compared to MODIS-Aqua and
VIIRS LST, ANU\textsubscript{SZAC} LST maintained a similar level of
ubRMSE with the other three Himawari-8 LST products (i.e., baseline,
Chiba, Copernicus). These findings underscore SZAC's capability to
reduce error deviations (as demonstrated by the ubRMSE statistics
against~\emph{in-situ} LST) while aligning LST values more closely with
those obtained from polar-orbiting platforms (see the bias statistics).
It demonstrates consistency with LSTs from both new generation
geostationary satellites, thereby offering additional choices for
researchers and practitioners who rely on LST snapshots from MODIS and
VIIRS. For applications needing high temporal frequency thermal
observations, ANU\textsubscript{SZAC} LST emerges as a valuable
alternative or complement to the polar-orbiting MODIS and VIIRS.

The ANU\textsubscript{SZAC} LST did exhibit a higher ubRMSE than the
other three products when compared against Terra-MODIS. This heightened
uncertainty may stem from variations in SZA, particularly when SZA
surpasses 50 ° (see Fig. 3 a), where the Himawari-8 baseline-MODIS
difference and SZA becomes more variable under these circumstances. This
increased variability of baseline-MODIS difference may be attributed to
the weaker incoming solar radiance during the Terra overpass time
(compared to Aqua and Suomi-NPP), diminishing the relative importance of
SZA. Liu et al. (2009) similarly highlighted that global solar
measurements may experience degradation due to cosine errors when SZA
becomes large. Moreover, higher SZA values indicate an extended solar
atmospheric path length, amplifying the potential impact of minor errors
in precipitable water parameterisation on both baseline LST and SZAC
correction attempts. Consequently, SZAC may introduce more uncertainties
and spatial variabilities during Terra overpass time. However,
considering the wavelength-dependent drift in reflectance, particularly
with a drop of up to 8\% in the shortest wavelength region observed in
Terra-MODIS NIR spectral bands (Wu et al., 2013), it becomes crucial to
prioritise consistency with Aqua-MODIS and VIIRS LST, where
ANU\textsubscript{SZAC} has demonstrated commendable performance.

The coefficient of SZAC was optimised against best-quality LST pixels
from MOD/MYD11 series, which may warrant reconsideration or improvements
in the future, given the dynamic nature of remote sensing data and
advancements in satellite missions. As the Terra-MODIS mission was
discontinued since November 2022, this would impact the availability of
MODIS data and raise questions about the long-term sustainability of
using MOD/MYD11 LST for calibration and evaluation. Alternative
satellite missions and/or newer generation sensors should be considered
to maintain the ongoing accuracy of the SZAC algorithm. Meanwhile,
studies have reported certain limitations of the MOD/MYD11 LST product,
particularly its tendency to underestimate LST during daytime in certain
regions (Li et al., 2014). Inconsistencies have been identified between
MOD/MYD11 and their successor VNP21, with MYD11 LST typically being 2 K
cooler than VNP21 LST (Hulley et al., 2017). To address this issue, NASA
produced two LST\&E products (i.e., MOD/MYD21) to ensure data continuity
among these platforms, with the bias of MYD21 LST against VNP21 LST
narrowed to \textasciitilde{} 0.4 K. Though ANU\textsubscript{SZAC} LST
has already demonstrated acceptable consistencies with MOD/MYD11 and
VNP21 LST, it is crucial to consider further comparisons of
ANU\textsubscript{SZAC} against MOD/MYD21. Moreover, future calibrations
might simultaneously incorporate MYD21 and VNP21, necessitating ongoing
evaluations. It would be beneficial to compare
ANU\textsubscript{SZAC}LST with other new generation LST products, e.g.,
the ECOsystem Spaceborne Thermal Radiometer Experiment on Space Station
(ECOSTRESS) LST (Fisher et al., 2020). However, caution must be
exercised when designing the experiments and comparison workflow due to
the inherent spatiotemporal variability of LST. ECOSTRESS LST, with its
irregular revisit frequency and 70 m spatial resolution, may not be
suitable for direct comparison purposes. To address this, a matching
strategy and spatial downscaling techniques (e.g., Yu et al., 2023)
could be thoughtfully implemented in the comparison process to ensure
meaningful and accurate assessments.

SZAC has shed light on potential LST calibration methods for the future,
suggesting the need for spatially varied coefficients to better
accommodate localised conditions. The SZAC coefficient is highly
relevant to the diurnal pattern of LST error variations for a specific
region and can be optimised for observation areas of different
geostationary satellites. Using MODIS LST data covering Australia, we
presented a pixelwise optimisation strategy that ensured
ANU\textsubscript{SZAC} LST incorporated MODIS LST spatial variability
over the entire continent. However, LST also has considerable temporal
variability and is highly dependent on localised conditions (Van De
Kerchove et al., 2013; Sekertekin et al., 2016). Thus, this optimisation
strategy could be extended temporally to derive seasonally dependent
sets of coefficients, which may improve the accuracy of
ANU\textsubscript{SZAC} LST in capturing the seasonal variability of
LST. However, strategies would need to be enlisted to ensure artificial
step-changes in LST aren't introduced across the seasonal boundaries.
Furthermore, implementing SZAC on LST using data acquired by other
geostationary satellites, such as the GOES series in the Americas and
the Meteosat series over Europe and Africa, may be a promising direction
for future research. Developing a globally adaptive SZAC coefficient set
could potentially improve our understanding of the error characteristics
of overlapping geostationary satellites and enable the creation of a new
global-coverage geostationary LST product, similar to the Copernicus
LST. It will also help identify any potential regional biases and/or
limitations of the current SZAC approach, allowing for targeted
refinements and calibrations to improve accuracy and applicability. This
could enhance our ability to monitor and study LST globally and aid in
applications such as weather forecasting, climate modelling, and
ecological and agricultural monitoring.

\section*{6. Conclusion}

{\label{conclusion}}

Numerous studies have reported the discrepancies between LST obtained
from geostationary platforms and those from polar-orbiting missions,
which can be particularly high (e.g., 12 K) during the daytime due to
variations in viewing angles and shadowing effects. To overcome this
challenge, SZA serves as a bridging parameter to systematically quantify
differences between platforms. We proposed SZAC to operationally
calibrate the daytime component of a Himawari-8 SW algorithm retrieved
LST. SZAC is an empirical function based on the variations of SZA,
describing the spatial heterogeneity and magnitude of LST discrepancies
from different products.

We evaluated the calibrated LST product (ANU\textsubscript{SZAC})
against MODIS LST and VIIRS LST, as well as \emph{in-situ} LST
measurements from the OzFlux network. We also compared
ANU\textsubscript{SZAC} LST with three Himawari-8 LST datasets
(baseline, Chiba and Copernicus) over 01/Jan/2016 to 31/Dec/2020. The
median values of bias of ANU\textsubscript{SZAC} LST during daytime
against Terra-MODIS LST, Aqua-MODIS LST and VIIRS LST were 1.52 K, 0.98
K and -0.63 K, respectively. In contrast, the other three Himawari-8 LST
products had at least doubled bias against MODIS LST datasets.
Additionally, the baseline and Chiba LST displayed higher bias than
ANU\textsubscript{SZAC} LST against VIIRS LST, whereas Copernicus LST
showed good agreement with VIIRS LST, being a bias of 0.33 K. All four
Himawari-8 LST products showed comparable ubRMSE when compared to LST
from polar-orbiting platforms (i.e., MODIS and VIIRS). In the evaluation
against daytime \emph{in-situ} LST, the overall mean values of bias
(ubRMSE) of baseline, Chiba, Copernicus and ANU\textsubscript{SZAC} LST
were 4.23 K (3.74 K), 2.16 K (3.62 K), 1.73 K (3.31 K) and 1.41 K (3.24
K), respectively. This demonstrated the lower bias of
ANU\textsubscript{SZAC} LST, and similar deviation of uncertainty
(represented by ubRMSE), when evaluated against peer products.

Overall, SZAC demonstrated robustness and operational capability in
reducing systematic bias in comparison to MODIS, VIIRS
and~\emph{in-situ} LST measurements. It has shed light on potential
calibration methods for the future, suggesting the need for spatially
varying coefficients to better accommodate localised conditions. It is
possible to extend SZAC using data acquired from other geostationary
satellites, such as the GOES series in the Americas and the Meteosat
series over Europe and Africa. This should improve our understanding of
the error characteristics of overlapped geostationary imageries,
allowing for targeted refinements and calibrations to further enhance
applicability.

\section*{Acknowledgement}

{\label{acknowledgement}}

This research was performed as part of a PhD by the first author (YY)
under an academic collaboration between the Australian National
University (ANU) and the Commonwealth Scientific and Industrial Research
Organisation (CSIRO). This research was undertaken while supported by
the ANU University Research Scholarship and an ANU-CSIRO Digital
Agriculture PhD Supplementary Scholarship through the Centre for
Entrepreneurial Agri-Technology (CEAT). We thank the continued support
of the TERN Landscapes Observatory
(\url{https://www.tern.org.au/tern-observatory/tern-landscapes/}), a
sensing platform of the Terrestrial Ecosystem Research Network (TERN;
\url{https://www.tern.org.au/}), which is supported and enabled by the
Australian Government through the National Collaborative Research
Infrastructure Strategy (NCRIS). We acknowledge the resources and
services provided by the National Computational Infrastructure (NCI),
which is also supported by the Australian Government through NCRIS. This
research was supported by resources and expertise provided by CSIRO IMT
Scientific Computing.~

\section*{Code availability}

{\label{code-availability}}

The key scripts for the development and operation of Himawari-ANU LST
dataset (i.e., ANU\textsubscript{SZAC}) are publicly available at
\url{https://github.com/yuyi13/Himawari-ANU}, with a permalink
registered at Zenodo (DOI will be provided once the manuscript is
formally published).~

\section*{Data availability}

{\label{data-availability}}

The Himawari-ANU LST dataset (i.e., ANU\textsubscript{SZAC}) is publicly
available from the TERN Data Discovery Portal (DOI) and NCI Data
Catalogue (DOI will be provided once the manuscript is formally
published).

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