# Evaluation of six satellite- and model-based surface soil temperature datasets using global ground-based observations

Hongliang Ma, Jiangyuan Zeng, Xiang Zhang, Peng Fu, Donghai Zheng,

Wigneron J.-P., Nengcheng Chen, Dev Niyogi

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► To cite this version:

Hongliang Ma, Jiangyuan Zeng, Xiang Zhang, Peng Fu, Donghai Zheng, et al.. Evaluation of six
satellite- and model-based surface soil temperature datasets using global ground-based observations.

Remote Sensing of Environment, 2021, 264, 10.1016/j.rse.2021.112605. hal-03612029

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# Evaluation of six satellite- and model-based surface soil temperature datasets using global ground-based observations

Hongliang Ma<sup>a,e</sup>, Jiangyuan Zeng<sup>d</sup>, Xiang Zhang<sup>a,b,c,*</sup>, Peng Fu<sup>f</sup>, Donghai Zheng<sup>g</sup>, Jean-Pierre Wigneron<sup>e</sup>, Nengcheng Chen<sup>a,b,c</sup>, Dev Niyogi<sup>h</sup>

<figure><img src="image_4.png" /></figure>

## ARTICLE INFO

### Keywords:

Surface soil temperature

GEOS-5

GLDAS

MERRA-2

ERA-interim

ERA5

AMSR2 LPRM

Evaluation

## ABSTRACT

The comprehensive evaluation of model- and satellite-based surface soil temperature (ST) products is a pre-requisite for applications of these datasets in hydrology, ecology, and climate change, as well as in passive microwave soil moisture retrieval algorithms. Distinguished from existing regional validations, this study used ground soil temperature observations of approximately 800 stations from 5 sparse and 15 dense networks worldwide to fully assess six model- and satellite-based surface ST products from April 2015 to December 2017. The products consist of five model-based ST from the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2), the Goddard Earth Observing System Model version 5 Forward Processing (GEOS-5 FP), the Global Land Data Assimilation System (GLDAS) Noah, the ERA-Interim and the newly released ERA5 produced by the European Centre for Medium Range Weather Forecasts (ECMWF), and one satellite-based ST retrieved from the Advanced Microwave Scanning Radiometer 2 (AMSR2) by using the Land Parameter Retrieval Model (LPRM). The accuracy of these products was comprehensively assessed per availability of ground networks, soil temperature interval, soil moisture interval, land cover, climate zone, and elevation. The results show that the GEOS-5 exhibits the smallest averaged unbiased root mean square difference (ubRMSD) of 1.84 K among all the surface ST products. All model-based products show a high skill in capturing the temporal trend of ground observations with an averaged correlation coefficient larger than 0.97. The ERA5 surface ST obtains visible improvements compared to its predecessor ERA-Interim by showing smaller ubRMSD and absolute bias values. All model-based surface ST products generally show lower values than ground ST, while their bias tends to be warmer as soil temperature and soil moisture increase except for the highest temperature and moisture conditions. Moreover, unstable performance of most model-based products in shrubland and grassland, tropical, arid and cold climate, and high elevation regions is also demonstrated by larger ubRMSD values. The averaged ubRMSD of the satellite-based LPRM ST is 3.04 K, and more attentions should be paid to the impacts of elevations and underlying surfaces on improving this product. These new findings will be valuable for future refinement of ST datasets, algorithms used to estimate soil moisture from satellite data, and applications in various disciplines.

## 1. Introduction

Surface soil temperature (ST) is a crucial physical variable of soil and has been widely used to facilitate the understanding of land-atmosphere

interaction and climate change (e.g., extreme climate) (Bond-Lamberty and Thomson, 2010; Seneviratne et al., 2006). Over the past few decades, dedicated efforts have been made to disseminate global surface ST products estimated from satellite observations, global land model

<footnote><sup>a</sup> State Key Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan University, Wuhan 430079, China</footnote>

<footnote><sup>b</sup> National Engineering Research Center of Geographic Information System, China University of Geosciences (Wuhan), Wuhan, 430074, China.</footnote>

<footnote><sup>c</sup> School of Geography and Information Engineering, China University of Geosciences (Wuhan), Wuhan, 430074, China.</footnote>

<footnote><sup>d</sup> State Key Laboratory of Remote Sensing Science, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100101, China</footnote>

<footnote><sup>e</sup> Interactions Sol Plante Atmosphère (ISPA), Unité Mixte de Recherche 1391, Institut National de la Recherche Agronomique (INRAE), CS 20032, 33882 Villenave d'Ornon CEDEX, France</footnote>

<footnote><sup>f</sup> Department of Plant Biology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA</footnote>

<footnote><sup>g</sup> National Tibetan Plateau Data Center, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing 100101, China</footnote>

<footnote><sup>h</sup> Department of Agronomy, Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, West Lafayette, IN 47907, USA</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: zhangxiangsw@whu.edu.cn (X. Zhang).</footnote>
simulations, and data assimilation approaches. The Modern-Era Retro-
spective Analysis for Research and Applications, version 2 (MERRA-2)
and the Goddard Earth Observing System Model version 5 Forward
Processing (GEOS-5 FP) are both developed by the National Aeronautics
and Space Administration (NASA) Global Modeling and Assimilation
Office (GMAO) (Gelaro et al., 2017; Lucchesi, 2013), and have been used
by the community for studying land-atmosphere interactions (Gelaro
et al., 2017; Gupta et al., 2020; Koster et al., 2015). Similarly, the ERA5
and ERA-Interim are global atmospheric reanalyses produced by the
European Centre for Medium-Range Weather Forecasts (ECMWF) (Ber-
risford et al., 2011; Hersbach et al., 2019). Developed together by the
National Oceanic and Atmospheric Administration (NOAA), NASA, and
other related agencies, the Global Land Data Assimilation System
(GLDAS) Noah has provided global ST datasets retrospectively since
1948 (Rodell et al., 2004). With regard to satellite temperature products,
the Moderate Resolution Imaging Spectroradiometer (MODIS) land
surface temperature (LST) dataset has been distributed and extensively
applied in various applications (Beale et al., 2019; Ermida et al., 2018).
Though MODIS can provide LST products at a global scale (both for land
and sea surface), the products are limited to clear-sky conditions since
they are retrieved from the thermal infrared (TIR) data which are sus-
ceptible to the clouds and weather conditions (Duan et al., 2017; Huang
et al., 2019; Long et al., 2020). Moreover, they can only represent the
effective temperature conditions on the land surface (e.g., the vegetation
surface temperature in densely vegetated areas), but not necessarily the
true conditions of soil temperature. Additionally, utilizing the passive
microwave satellite observations at large scales and all-weather condi-
tions, the Advanced Microwave Scanning Radiometer-Earth Observing
System (AMSR-E) and its successor AMSR2 also provide ST retrievals at
a global scale (Holmes et al., 2009; Owe et al., 2008).

It is imperative to comprehensively understand the accuracy of these
products as they continue to be widely used in hydrometeorological and
climatic applications. Additionally, ST is required for microwave
radiometer-based retrieval of soil moisture. For reliable soil moisture
estimation from passive microwave observations, the contributions of
ST to brightness temperature need to be carefully accounted for. In many
passive microwave-based soil moisture retrieval algorithms, both sat-
ellite- and model-based surface ST products are adopted. For example,
Zeng et al. (2015a, 2015b) found that the errors of AMSR-E Land
Parameter Retrieval Model (LPRM) soil moisture product in the Tibetan
Plateau are partially caused by the errors in surface temperature
retrieved from the AMSR-E Ka-band brightness temperature. Recent
studies also reported that the underestimation of surface temperature
derived from GEOS-5 and ECMWF, which are used as the inputs in the
Soil Moisture Active Passive (SMAP) and Soil Moisture and Ocean
Salinity (SMOS) soil moisture algorithms respectively, contributes to the
general dry bias found in the SMAP and SMOS soil moisture products
(Chen et al., 2018; Cui et al., 2018; Ma et al., 2019; Zheng et al., 2018).
Thus, comprehensive evaluations on current satellite- and model-based
surface ST products are of crucial importance for accurate remote
sensing soil moisture retrievals and further enhancements of soil moist-
ture products.

Some primary evaluation studies concerning several surface ST
products have been recently reported (Huang et al., 2019; Krishnan
et al., 2015; Niclós et al., 2018; Yang and Zhang, 2018; Zhou et al.,
2017). Holmes et al. (2012) evaluated three surface ST products from
Numerical Weather Prediction (NWP) systems using ground observa-
tions over Oklahoma. Albergel et al. (2015) compared soil temperature
produced by ECMWF with ground observations over the United States
and Europe. Hu et al. (2019) evaluated three ST reanalysis datasets over
the Tibetan Plateau from 1980 to 2015. However, most evaluation
studies have focused only on a few surface ST products and a regional
scale. The systematic evaluation of current surface ST products, partic-
ularly for the newly released ERA5 product at a global scale, in which
diverse climate, land cover types, and various elevation conditions can
be simultaneously assessed has been lacking. In addition, to our

knowledge, few studies, if any, considered the effect of the variation of
in situ ST itself when validating the surface ST products, and, we
postulate, may affect the performance of surface ST products. The effects
of soil moisture conditions on the accuracy of satellite- and model-based
surface ST products are also often overlooked though these ST datasets
are often used for radiometer-based soil moisture retrievals.

Furthermore, in the ongoing intensive evaluation campaigns con-
cerning the remotely sensed or modeled soil moisture products, ground-
based soil moisture observations from extensive in situ stations estab-
lished across the globe, have been adopted (Chan et al., 2018; Colliander
et al., 2017; Dorigo et al., 2011a, 2011b; Ma et al., 2019; Zeng et al.,
2015b). These in situ stations also provide valuable ST measurements,
which enable a comprehensive assessment of the satellite- and model-
based surface ST products at global scales to be feasible. Moreover,
most conventional evaluations of surface ST products were conducted
only via ground observations from sparse networks. The advantage of
sparse networks is that they often cover a wide range of ground condi-
tions. However, the spatial inconsistencies between the point-based
ground observations and the grid-based (~tens of kilometers) model
and satellite products often introduce some uncertainties in the evalu-
ation results (Jackson et al., 2010). In contrast, in situ measurements
from dense networks can significantly alleviate the spatial-mismatch
issue, but they cover only a limited land cover types (Chan et al.,
2016a, 2016b; Zeng et al., 2016). Thus, it is essential to combine the
advantages of in situ observations from sparse and dense networks for a
comprehensive evaluation of surface ST products.

In this study, five model-based surface ST products, i.e., GEOS-5 FP, MERRA-2, GLDAS Noah, ERA-Interim and ERA5, and one satellite-based ST, i.e., AMSR2 LPRM, were firstly evaluated against approximately 800 ground stations worldwide from 5 sparse and 15 dense networks. The objectives of this study were to: 1) fully understand the performance of six satellite- and model-based surface ST products at the global scale for diverse land cover types and climate types; 2) evaluate the impacts of soil temperature, moisture conditions and elevation on the performance of surface ST products, which have been often overlooked in previous studies; 3) provide suggestions for the possible enhancements of satellite soil moisture retrievals. This paper is structured as follows. Descriptions of six surface ST products, in situ observations, and auxiliary datasets are presented in Section 2. Section 3 introduces the methodology adopted in this study. The results are covered and discussed in Section 4, and the conclusions are presented in Section 5.

2. Datasets

2.1. Model- and satellite-based surface ST products

2.1.1. GEOS-5 FP

The GEOS-5 FP products used in this study are generated by GMAO,
which provides forecasts and assimilation products for near-real-time
production. The ST datasets in GEOS-5 FP are distributed in hourly in-
tervals at a spatial resolution of 0.3125° by 0.25°. In this study, ST at the
first layer (0–5 cm) was selected. More information about the GEOS-5 FP
datasets can be found in Lucchesi (2013). The datasets used in this study
were downloaded from https://portal.nccs.nasa.gov/datashare/gmao
_ops/pub/fp/das/.

2.1.2. MERRA-2

The MERRA-2 is a widely used atmospheric reanalysis dataset for the
modern satellite era by NASA. The ST included in ‘MERRA-2
tavg1_2d_lnd_Nx: 2d’ is available with a spatial resolution of 0.5°*0.625°
and an hourly sampling interval for a period post-1980. MERRA-2 is an
intermediate project between the previous MERRA data and the new
generation of Earth system analysis data, into which several observa-
tions are assimilated (Gelaro et al., 2017). The ST datasets derived from
MERRA-2 are freely available at https://disc.gsfc.nasa.gov/datasets. In
this study, soil temperature at the depth of 0–5 cm was adopted for
evaluation. More detailed information on MERRA-2 can be referred to
Gelaro et al. (2017).

2.1.3. GLDAS Noah

The GLDAS is a global assimilation and modeling system, which is
developed jointly by NASA, Goddard Space Flight Center (GSFC), and
NOAA (Rodell et al., 2004). This system provides land surface infor-
mation in near-real time by driving four land surface models (LSMs), in
which the ground and satellite observations have been included. In this
study, ST from the first soil depth (0–10 cm) generated by the GLDAS
Noah model with a spatial grid resolution of 0.25°*0.25° and a temporal
resolution of 3-h was selected for the assessment. More information
about the GLDAS products can be found in Rodell et al. (2004), and Rui
and Beaudoing (2018).

2.1.4. ERA-interim

The ERA-Interim is a global atmospheric reanalysis dataset devel-
oped based on the Integrated Forecast System (IFS) Cy31r2 and
distributed by ECMWF. The ERA-Interim has made improvements on the
previous ECMWF's reanalysis datasets, ERA-40, and provides the data-
sets since 1979 (Berrisford et al., 2011). The ST from the first soil layer
(0–7 cm) at six-hourly intervals with a spatial grid sampling of
0.25°*0.25° was available. The ERA-Interim product is freely accessed at
https://apps.ecmwf.int/datasets and more details regarding this prod-
uct can be found in Dee et al. (2011).

2.1.5. ERA5

The ERA5 is the fifth generation ECMWF atmospheric reanalysis dataset and has been considered as the successor of ERA-Interim (Hersbach et al., 2019). Distinguished with its predecessor at six-hourly output resolution, the ERA5 can afford estimates for each hour of the day based on the 4D-Var assimilation approach. The ST data of ERA5 adopted in this study were derived from the 'ERA5 hourly estimates of variables on single levels' with horizontal resolution of 0.25°*0.25° and can be freely downloaded from https://cds.climate.copernicus.eu/. 'Soil temperature level 1' representing the ST on topsoil (0–7 cm) was selected for the assessment.

2.1.6. AMSR2 LPRM

In addition to five model-based ST, the satellite-based ST derived
from the AMSR2 LPRM was also adopted in this study. The LPRM ST,
which has been used for temperature correction in the LPRM AMSR2 soil
moisture retrieval algorithm, is derived from the AMSR2 Ka-band (36.5
GHz) V-pol brightness temperature by using an empirical model
(Holmes et al., 2009). This model has been integrated in the LPRM
which can retrieve soil moisture, vegetation optical depth and soil
temperature simultaneously (Owe et al., 2008). The AMSR2 LPRM ST
product is provided at a grid resolution of 0.25°*0.25° and is freely
available at https://disc.gsfc.nasa.gov/datasets. It was selected in this
study for the following reasons: (i) compared to optical or thermal
infrared remote sensing (e.g., MODIS, SEVIRI, VIIRS, and SLSTR),
AMSR2 LPRM is capable of providing ST estimations for 24-h and nearly
all-weather coverage; (ii) LPRM ST and soil moisture are derived from
the same microwave sensors, and they have the same spatial and tem-
poral resolutions. Thus, the representativeness errors (usually from the
ancillary data in general soil moisture retrieval algorithms) can be
minimized (Holmes, 2003); (iii) among current satellite-based temper-
ature products, AMSR2 LPRM ST has the retrieval depth closest to
model-based surface ST products of the top-soil layer, which can be
adopted for corrections of temperature impacts in current passive mi-
crowave soil moisture retrieval algorithms.

2.2. In-situ ST datasets

In this study, 15 dense observation networks and 5 sparse observa-
tion networks across the globe were used to assess the six surface ST

products. All in situ observations were acquired from three main sources (Ma et al., 2019): the International Soil Moisture Network (ISMN), the United States Department of Agriculture (USDA), and the Murrumbidgee River Catchment in Australia (Dorigo et al., 2011a, 2011b; Smith et al., 2012). It is noteworthy that the ISMN is widely recognized as a centralized soil moisture data hosting facility, and extensive validations concerning satellite- or model-based soil moisture products have been conducted (Dorigo et al., 2011a, 2011b; Ma et al., 2019). Moreover, the ISMN not only offers ground-based surface soil moisture, but also provides ST measurements, while previous ST validation studies paid limited attention on these valuable data. Similarly, USDA and Murrumbidgee River Catchment also provide ST datasets. In this study, a total of 572 validation pixels (0.25°) corresponding to approximately 800 ground stations distributed globally (Fig. 1) were used for the assessment of the six surface ST products. More detailed information concerning global in situ observation networks was listed in Table 1. Additionally, to reduce the spatial resolution non-conformity of the model or satellite products and in situ data as much as possible, only the 0.25° cells comprising more than three ground stations were taken into account for the dense network averaging.

2.3. Auxiliary datasets

To evaluate the impacts of elevation, climate zone, and land cover on
the performance of surface ST products, the Global Land One-kilometer
Base Elevation Digital Elevation (GLOBE DEM) (GLOBE Task Team and
others and Hastings, 1999), the MODIS IGBP land cover (Sulla-Menashe
and Friedl, 2018), and the Köppen-Geiger climate classification dataset
(Peel et al., 2007; Kottek et al., 2006) were used in this study. Moreover,
the evaluation pixels were divided into several groups after labeling
them by these factors such as (station elevation, climate types, and land
cover types). The details regarding the pre-processing approaches are
presented in the following section.

3. Methodology

3.1. Pre-processing

To make a fair assessment of the six surface ST products, essential
pre-processing steps were undertaken for the model- and satellite-based
surface ST products as well as ground observations. On one hand, since
there is slight spatial inconsistency (all within the scope of tens of ki-
lometers and around 0.25° grid resolution) among different surface ST
products, to make a consistent comparison for these products, the grid
resolution of model- and satellite-based ST datasets was resampled into
0.25 degree by using the nearest-neighbor interpolation method, which
is a feasible sampling approach and extensively adopted in existing
validation studies (Al-Yaari et al., 2014; Cui et al., 2018; Zeng et al.,
2015b; Ma et al., 2019). On the other hand, with regard to various
temporal sampling intervals of these assessed products (i.e., 1-, 3-, and
6-hourly or daily), it cannot be neglected that some uncertainties due to
significant diurnal variation in ST might hinder the impartial evaluation
of the ST products. Thus, all model-based ST datasets at four overlapping
time points (i.e., 00:00, 06:00, 12:00 and 18:00 universal coordinated
time) per day were selected (corresponding to 6-hourly sampling in-
terval) and then fairly processed into daily average before evaluation. As
the GEOS-5 and MERRA-2 are hourly disseminated at each half o'clock
(e.g., 00:30, 01:30, ..., 22:30, 23:30), the selection and processing were
finished by averaging the values of two intervals before and after the
four selected points of time. This unified selection and average pro-
cessing is supposed to effectively reduce the uncertainty resulting from
possible large diurnal variation of ST and has been widely used in pre-
vious studies (Yang et al., 2020; Hu et al., 2019). Additionally, the
performance of all model-based ST datasets at the four individual time
points (00:00, 06:00, 12:00 and 18:00) were also examined.

As for LPRM ST, taking increased thermal equilibrium conditions of
<figure><img src="image_5.png" /><figcaption>Fig. 1. The spatial distribution of global ST evaluation stations. The legend of the color map represents the MODIS IGBP global land cover classes.</figcaption></figure>

<table><caption>**Table 1**
The information of global in situ ST networks used in this study.</caption><thead><tr><th>Network Type</th><th>Network Name</th><th>Country</th><th>No. of Station Used</th><th>Depth Used (cm)</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="15">Dense Network</td><td>Little Washita</td><td>America</td><td>20</td><td>5</td><td>(Cosh et al., 2006)</td></tr><tr><td>Walnut Gulch</td><td>America</td><td>19</td><td>5</td><td>(Keefer et al., 2008)</td></tr><tr><td>Little River</td><td>America</td><td>33</td><td>5</td><td>(Bosch et al., 2007)</td></tr><tr><td>Fort Cobb</td><td>America</td><td>15</td><td>5</td><td>(Cosh et al., 2014)</td></tr><tr><td>South Fork</td><td>America</td><td>21</td><td>5</td><td>(Coopersmith et al., 2015)</td></tr><tr><td>St. Joseph's</td><td>America</td><td>15</td><td>5</td><td>(Heathman et al., 2012)</td></tr><tr><td>Reynolds Creek</td><td>America</td><td>20</td><td>5</td><td>(Seyfried et al., 2001)</td></tr><tr><td>Yanco</td><td>Australia</td><td>37</td><td>0-5</td><td>(Panciera et al., 2014)</td></tr><tr><td>RISMA</td><td>Canada</td><td>14</td><td>0-5</td><td>(Ojo et al., 2015)</td></tr><tr><td>CTP_SMTMN</td><td>China</td><td>53</td><td>5</td><td>(Yang et al., 2013)</td></tr><tr><td>HOBE</td><td>Denmark</td><td>28</td><td>0-5</td><td>(H. Jensen and Illangasekare, 2011)</td></tr><tr><td>FMI</td><td>Finland</td><td>19</td><td>5</td><td>(Zeng et al., 2016)</td></tr><tr><td>TERENO</td><td>Germany</td><td>4</td><td>5</td><td>(Zacharias et al., 2011)</td></tr><tr><td>BIEBRZA-S-1</td><td>Poland</td><td>18</td><td>5</td><td>http://www.igik.edu.pl/en</td></tr><tr><td>REMEDHUS</td><td>Spain</td><td>20</td><td>0-5</td><td>(Martinez Fernandez and Ceballos, 2005)</td></tr><tr><td>USCRN</td><td>America</td><td>97</td><td>5</td><td>(Bell et al., 2013)</td></tr><tr><td>SNOTEL</td><td>America</td><td>208</td><td>5</td><td>https://www.wcc.nrcs.usda.gov/</td></tr><tr><td>SCAN</td><td>America</td><td>157</td><td>5</td><td>(Schaefer et al., 2007)</td></tr><tr><td>SMOSMANIA</td><td>France</td><td>15</td><td>5</td><td>(Albergel et al., 2008)</td></tr><tr><td>RSMN</td><td>Romania</td><td>20</td><td>0-5</td><td>(Zeng et al., 2016)</td></tr><tr><td>Sparse Network</td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

the near-surface air, vegetation canopy, and surface soil during night time into account (Cui et al., 2018; Zeng et al., 2015a), the datasets derived from AMSR2 descending overpass time (i.e., the AMSR2 scan-time, which is close to the nominal 1:30 A.M. local solar time but varies with locations) were used for evaluation. It should be noted that at nighttime (e.g., descending scantime for AMSR2 adopted in our study) or morning time, previous studies have pointed out that in the absence of immediate precipitation, soil profile can approach a thermal equilibrium condition (Owe et al., 2008; Zeng et al., 2015a). At nighttime or morning time, the thermal equilibrium builds up among the vegetation, air, and topsoil, which can minimize the temperature gradients within the soil and canopy. Under this condition the soil profile within the top 5 cm of the soil is uniform (Jackson et al., 2010). The assumption that vegetation temperature and topsoil temperature are equal is commonly made in various soil moisture retrieval algorithms (Njoku et al., 2003; Owe et al., 2008; Chan et al., 2016a, 2016b). Moreover, all the selected models (i.e., GEOS-5, MERRA-2, GLDAS, ERA-Interim and ERA5) provide ST at several layers. Since the passive microwave soil moisture retrieval

algorithms usually need the topsoil temperature (commonly 0–5 cm depending on the observation frequency and soil moisture condition) (Zeng et al., 2015b; Li et al., 2020b), as well as most in situ ST measurements are available only over the top soil layer, only the model- or satellite-based temperature products on topsoil were analyzed in this study. Different from conventional validation studies focusing on ST at multi-layers (Xia et al., 2013; Li et al., 2020a), in which necessary interpolation method (e.g., linear interpolation) was adopted to facilitate comparison with model-based products at deep layers (i.e., >20 cm), we only focused on evaluating ST products at topsoil surface (within the scope of 0–10 cm). With regard to AMSR2 LPRM, the sampling depth is generally recognized as 0–1 cm. Thus, the AMSR2 LPRM temperature has been considered as the land surface temperature in general case (Holmes, 2008; Holmes et al., 2009). Taking the thermal equilibrium conditions at night into consideration, the LPRM temperature at descending overpass time, can be approximately regarded as surface ST together with other model-based ST products (all within the scope of 0–10 cm) in the present study to facilitate the comparison. The
similarity has already been demonstrated by previous study (Zhang et al., 2011), in which in situ surface infrared temperature records and topsoil temperature are very close at nighttime and ground temperature observations at topsoil layer can be reasonably used to assess the performance of LPRM ST. The model-based soil temperature products at the first layer (i.e., 0–5 cm for GEOS-5 and MERRA-2, 0–7 cm for ERA-Interim and ERA5, and 0–10 cm for GLDAS Noah) were selected for the assessment. Considering the availability of in situ observations at the global scale and previous comparison studies concerning the topsoil (Cui et al., 2018; Ding et al., 2018; Liu et al., 2015), although it is acceptable to fairly assess these ST products against in situ observations at the depth of 5 cm or 0–5 cm, a slight depth mismatch between different model- or satellite-based ST products and the in situ observations still inevitably exists. The uncertainty caused by this depth inconsistency should be considered by taking necessary error metric and is discussed in the following sections.

For ground observations, although most ground observations were obtained from the ISMN, in which the in situ datasets spreading over the world are harmonized, these datasets may still have some uncertainties due to the measurement device and installation placement of sensors (Dorigo et al., 2013). Thus, to achieve a more stable and fair assessment of these ST products, the quality of in situ datasets should be strictly inspected and further processed. The pre-processing was conducted as follows: (1) assessment period was set from April 1st, 2015 to December 31st, 2017 due to the availability of consistent global in situ observations, which covered more than two and a half years; (2) only the ground based ST on the top soil (i.e., 5 cm or 0–5 cm) was used (see Table 1); (3) the in situ observations were strictly evaluated against evaluated surface ST products using timestamps (UTC time for model-based ST products and satellite overpass time for satellite-based ST products) (4) the evaluation sites were filtered by the evaluation error metrics (presented in detail in Section 3.3).

## 3.2. Grouping evaluation pixels

As mentioned in Section 2.3, the DEM, land cover and climate type datasets were used to examine the accuracy of the ST datasets per elevation, land cover, and climate zone. Specifically, as presented in Table 2, by using the global DEM, all the evaluation pixels at the global scale were categorized into four types, in which DEM-I represented the lowest elevation condition and DEM-IV indicated the highest elevation condition. With regard to land cover, in order to more conveniently describe the performance of ST products under various land conditions, the MODIS IGBP land cover categories were combined and re-classified into six dominant land use types (i.e., forest, grassland, shrubland, savanna, agriculture and others). Similarly, five main climate types (i.e., tropical, arid, temperate, cold, and polar) were adopted for the labeling of evaluation pixels. Furthermore, based on the in situ ST and soil moisture observations at the evaluation period, the evaluation series used for calculating error metrics were re-classified into four categories

with regard to the intensity of soil temperature (from cold to hot) or moisture (from dry to wet). In this case, the impacts of soil temperature or moisture on the performance of diverse soil temperature products can be exhaustively evaluated. (See Table 2.)

## 3.3. Error metrics

To quantify the evaluation results, three commonly used error metrics, i.e., the unbiased root mean square difference (ubRMSD), the Bias, and the Pearson correlation coefficient (R), were selected:

$$ubRMSD = \sqrt{E\{[(\theta_{product} - E[\theta_{product}]) - (\theta_{in-situ} - E[\theta_{in-situ}])]^2\}} \quad (1)$$

$$Bias = E[\theta_{product} - \theta_{in situ}] \quad (2)$$

$$R = \frac{E[(\theta_{product} - E[\theta_{product}]) (\theta_{in-situ} - E[\theta_{in-situ}])]}{\sigma_{product} \sigma_{in-situ}} \quad (3)$$

where $E[\bullet]$ donates the mean operator, $\theta_{product}$ represents model- or satellite-based ST, and $\theta_{in-situ}$ represents the ground based ST. The correlation coefficient can assess the capability of model- and satellite-based products to capture the temporal trend of ground measurements (Zeng et al., 2020). The Bias is computed as the difference between ground observations and model- and satellite-based products. It should be noted that distinguished with previous studies in which the root mean square difference (RMSD) is used for assessing ST products (Gupta et al., 2020; Hu et al., 2019), the ubRMSD was adopted in the study to consider the impacts of spatial and depth mismatch between in situ data and selected products. This is because the RMSD metric may be severely compromised in the presence of bias (due to sampling depth mismatch for instance), which can be removed by the ubRMSD metric (Entekhabi et al., 2014; Zeng et al., 2016). Moreover, as mentioned in Section 3.1, in situ evaluation sites were excluded if (i) these evaluation sites have fewer than 20 samples, and (ii) the results did not satisfy the requirement of R-value with p-value <0.01.

# 4. Results and discussion

## 4.1. Evaluation of surface ST products against observations from dense networks

For evaluation of six satellite- and model-based surface ST products by using global dense networks, the three error metrics were calculated and the results are shown in Table 2. With regard to measuring the temporal values of ground surface ST observations, five model-based surface ST products have similar performance, in which the GEOS-5 exhibits the lowest ubRMSD of 1.84 K. The microwave satellite-based LPRM ST exhibits an averaged ubRMSD of 3.04 K and thus needs further improvement compared to the model-based ST. This conclusion

<table><caption>**Table 2**
The classification principles of sparse evaluation sites used in the study.</caption><thead><tr><th>DEM Value (m)</th><th>Pixel Type</th><th>In situ ST (K)</th><th>ST Type</th><th>In situ SM (m<sup>3</sup> m<sup>-3</sup>)</th><th>SM Type</th></tr></thead><tbody><tr><td>33.918 ≤ DEM &lt; 635.523</td><td>DEM -I</td><td>ST &lt; 278.15</td><td>ST-I</td><td>0 &lt; SM &lt; 0.1</td><td>SM-I</td></tr><tr><td>635.523 ≤ DEM &lt; 1237.128</td><td>DEM -II</td><td>278.15 ≤ ST &lt; 285.15</td><td>ST-II</td><td>0.1 ≤ SM &lt; 0.25</td><td>SM-II</td></tr><tr><td>1237.128 ≤ DEM &lt; 1838.733</td><td>DEM -III</td><td>285.15 ≤ ST &lt; 293.15</td><td>ST-III</td><td>0.25 ≤ SM &lt; 0.4</td><td>SM-III</td></tr><tr><td>1838.733 ≤ DEM ≤ 3041.943</td><td>DEM -IV</td><td>ST ≥ 293.15</td><td>ST-IV</td><td>0.4 ≤ SM &lt; 1</td><td>SM-IV</td></tr></tbody></table><table><thead><tr><th>IGBP Land Cover</th><th>Land Cover</th><th>IGBP Land Cover</th><th>Land Cover</th><th>Climates</th><th>Description</th></tr></thead><tbody><tr><td>Broadleaf Evergreen Forest</td><td rowspan="5">Forest</td><td>Closed Shrublands</td><td rowspan="5">Shrubland</td><td>A</td><td>Tropical</td></tr><tr><td>Broadleaf Deciduous Forest</td><td>Open Shrublands</td><td>B</td><td>Arid</td></tr><tr><td>Needleleaf Evergreen Forest</td><td>Woody Savannas</td><td>C</td><td>Temperate</td></tr><tr><td>Needleleaf Deciduous Forest</td><td>Savannas</td><td>D</td><td>Cold</td></tr><tr><td>Mixed Forest</td><td>Croplands</td><td>E</td><td>Polar</td></tr><tr><td>Grasslands</td><td>Grassland</td><td>Cropland/Natural Vegetation Mosaic</td><td>Agriculture</td><td></td><td></td></tr><tr><td>Others</td><td>Others</td><td></td><td></td><td></td><td></td></tr></tbody></table>
<table><caption>**Table 2**
The evaluation results for daily averaged model-based ST (GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah), and satellite-based AMSR2 LPRM ST at descending overpass time against observations from global dense networks. Bold numbers in the table represent the best results corresponding to each error metric.</caption><thead><tr><th>Metrics</th><th>Dense Networks</th><th>HOBE</th><th>BS-1</th><th>TERENO</th><th>RISMA</th><th>RC</th><th>SF</th><th>SJ</th><th>REMEDHUS</th><th>FC</th><th>LW</th><th>CS</th><th>WG</th><th>LR</th><th>Yanco</th><th>FMI</th><th>Average</th></tr></thead><tbody><tr><td rowspan="6">ubRMSD (K)</td><td>GEOS-5</td><td>1.04</td><td>2.02</td><td>1.33</td><td>1.94</td><td>2.31</td><td>1.84</td><td>2.20</td><td>1.45</td><td>1.98</td><td>2.23</td><td>1.77</td><td>2.37</td><td>1.65</td><td>2.10</td><td>1.41</td><td>1.84</td></tr><tr><td>MERRA-2</td><td>1.02</td><td>2.11</td><td>1.48</td><td>1.98</td><td>2.52</td><td>2.00</td><td>2.41</td><td>1.40</td><td>1.98</td><td>2.10</td><td>1.86</td><td>2.22</td><td>1.38</td><td>1.91</td><td>1.49</td><td>1.86</td></tr><tr><td>ERA-Interim</td><td>1.09</td><td>2.13</td><td>1.47</td><td>2.05</td><td>3.33</td><td>1.85</td><td>2.21</td><td>1.37</td><td>2.28</td><td>2.29</td><td>1.88</td><td>1.92</td><td>1.46</td><td>1.86</td><td>3.23</td><td>2.03</td></tr><tr><td>ERA5</td><td>1.03</td><td>2.23</td><td>2.33</td><td>1.99</td><td>3.51</td><td>1.74</td><td>2.20</td><td>1.35</td><td>2.16</td><td>2.42</td><td>1.57</td><td>1.74</td><td>1.40</td><td>1.83</td><td>2.02</td><td>1.97</td></tr><tr><td>GLDAS</td><td>1.10</td><td>2.05</td><td>1.44</td><td>2.98</td><td>2.31</td><td>2.59</td><td>2.35</td><td>2.23</td><td>2.31</td><td>1.72</td><td>2.29</td><td>1.40</td><td>2.03</td><td>2.76</td><td>2.07</td></tr><tr><td>LPRM</td><td>2.47</td><td>2.68</td><td>2.33</td><td>3.20</td><td>2.88</td><td>5.26</td><td>3.75</td><td>2.65</td><td>3.47</td><td>3.48</td><td>2.66</td><td>3.02</td><td>2.58</td><td>2.86</td><td>2.37</td><td>3.04</td></tr><tr><td rowspan="6">Bias (K)</td><td>GEOS-5</td><td>-1.18</td><td>-1.05</td><td>-0.47</td><td>-0.97</td><td>1.37</td><td>-1.29</td><td>-0.30</td><td>-0.66</td><td>-0.09</td><td>-3.94</td><td>-3.99</td><td>-1.86</td><td>-1.89</td><td>-0.94</td><td>-1.35</td></tr><tr><td>MERRA-2</td><td>-1.10</td><td>-1.21</td><td>-0.24</td><td>-0.74</td><td>2.12</td><td>-0.83</td><td>0.26</td><td>-0.48</td><td>-0.21</td><td>-2.52</td><td>-3.21</td><td>-2.26</td><td>-1.00</td><td>-1.11</td><td>-1.01</td></tr><tr><td>ERA-Interim</td><td>-0.26</td><td>0.06</td><td>0.60</td><td>-0.90</td><td>3.81</td><td>0.72</td><td>2.07</td><td>-0.37</td><td>0.40</td><td>1.05</td><td>-3.18</td><td>-1.18</td><td>-2.37</td><td>-0.86</td><td>-2.90</td><td>-0.29</td></tr><tr><td>ERA5</td><td>-0.54</td><td>-0.01</td><td>-0.35</td><td>-0.46</td><td>5.04</td><td>0.38</td><td>1.32</td><td>-1.50</td><td>0.29</td><td>0.39</td><td>-2.74</td><td>-0.38</td><td>-0.70</td><td>-0.95</td><td>-1.61</td><td>-0.12</td></tr><tr><td>GLDAS</td><td>-0.91</td><td>-1.25</td><td>-0.28</td><td>-1.08</td><td>-0.95</td><td>-1.21</td><td>-0.21</td><td>-2.61</td><td>0.07</td><td>0.21</td><td>-1.16</td><td>-1.37</td><td>-2.20</td><td>-0.63</td><td>-2.75</td><td>-1.09</td></tr><tr><td>LPRM</td><td>0.34</td><td>0.74</td><td>-0.61</td><td>0.73</td><td>2.40</td><td>-1.62</td><td>-0.48</td><td>-2.18</td><td>0.78</td><td>0.63</td><td>-1.80</td><td>-2.76</td><td>-2.30</td><td>1.61</td><td>2.95</td><td>-0.10</td></tr><tr><td rowspan="6">R</td><td>GEOS-5</td><td>0.984</td><td>0.973</td><td>0.979</td><td>0.982</td><td>0.968</td><td>0.981</td><td>0.980</td><td>0.988</td><td>0.988</td><td>0.980</td><td>0.974</td><td>0.962</td><td>0.979</td><td>0.968</td><td>0.971</td><td>0.977</td></tr><tr><td>MERRA-2</td><td>0.985</td><td>0.974</td><td>0.980</td><td>0.983</td><td>0.966</td><td>0.981</td><td>0.980</td><td>0.988</td><td>0.983</td><td>0.981</td><td>0.970</td><td>0.966</td><td>0.981</td><td>0.973</td><td>0.970</td><td>0.977</td></tr><tr><td>ERA-Interim</td><td>0.988</td><td>0.965</td><td>0.971</td><td>0.983</td><td>0.962</td><td>0.983</td><td>0.981</td><td>0.988</td><td>0.988</td><td>0.977</td><td>0.971</td><td>0.976</td><td>0.974</td><td>0.975</td><td>0.943</td><td>0.974</td></tr><tr><td>ERA5</td><td>0.987</td><td>0.969</td><td>0.980</td><td>0.982</td><td>0.963</td><td>0.983</td><td>0.980</td><td>0.987</td><td>0.976</td><td>0.975</td><td>0.980</td><td>0.979</td><td>0.980</td><td>0.976</td><td>0.965</td><td>0.977</td></tr><tr><td>GLDAS</td><td>0.983</td><td>0.976</td><td>0.976</td><td>0.971</td><td>0.964</td><td>0.962</td><td>0.968</td><td>0.983</td><td>0.974</td><td>0.970</td><td>0.965</td><td>0.975</td><td>0.965</td><td>0.971</td><td>0.966</td><td>0.971</td></tr><tr><td>LPRM</td><td>0.887</td><td>0.894</td><td>0.910</td><td>0.892</td><td>0.925</td><td>0.735</td><td>0.845</td><td>0.949</td><td>0.893</td><td>0.885</td><td>0.736</td><td>0.914</td><td>0.906</td><td>0.917</td><td>0.864</td><td>0.877</td></tr></tbody></table>

1 Some abbreviated names of global dense networks were adopted in this table due to the limitation of display window: BS-1: BIEBRZA-S-1; RC: Reynolds Creek; SF: South Fork; SJ: St. Joseph's; FC: Fort Cobb; LW: Little Washita; CS: CTP_SMTMN; WG: Walnut Gulch; LR: Little River

is in line with the findings reported in Cui et al. (2018), who similarly found that the model ST simulations show lower ubRMSD value than the satellite-based LPRM ST by using two dense networks in the United States and Spain, and in turn yield more accurate soil moisture retrievals when the soil moisture algorithms adopt the model ST for temperature correction. With respect to the newly developed ERA5 surface ST, it can be observed that some improvements have been achieved compared to its predecessor, with an averaged ubRMSD of 1.97 K compared to the value of 2.03 K by ERA-Interim. This result is consistent with recent evaluation campaigns concerning ERA5 surface ST conducted in limited regional areas (Li et al., 2020a; Yang et al., 2020) and our study firstly demonstrate this upgrade by using global dense networks.

The five model surface ST products all generally exhibit lower temperature values in relative to the in situ surface ST with negative bias values. The underestimation of GLDAS Noah at the global scale is consistent with previous studies, which highlights a known issue with the underestimation of downward longwave radiation from the model forcing data (Wang et al., 2016). Specifically, the underestimation of MERRA-2 is smaller than that of GEOS-5 and GLDAS, with the bias value of -1.01 K. Moreover, the ERA5 shows a small bias value of -0.12 K, which demonstrates the improvement compared to the ERA-Interim surface ST product with bias value of -0.29 K. Although LPRM ST also yields a relatively small averaged absolute bias value, it cannot be concluded that the LPRM ST has better performance than other model-based products. This is due to the occurrence of both significant positive and negative biases among the different data networks considered (e.g., overestimation in Reynolds Creek, Yanco and FMI, and underestimation in REMEDHUS, Walnut Gulch and Little River as shown in Table 2). Although the depth mismatch between the LPRM and in situ observations partial contributes to the bias, this performance suggests that the accuracy of the LPRM ST is affected by underlying surfaces, which is consistent with previous studies (Holmes et al., 2009; Zeng et al., 2015a). In terms of capturing the temporal variations of ground-based ST, the GEOS-5, MERRA-2 and ERA5 are marginally superior to other surface ST products.

Moreover, it should be noted that, despite the essential measures for fair assessment considered (described in Section 3.1), the error sources of the surface ST products could partly be due to the mismatch of in-situ ST measuring depth and the sampling depth of the selected satellite- and model-based surface ST products (Zeng et al., 2015b). Taking the diurnal variability of ST into consideration, five model-based ST products were also evaluated at four UTC time points (i.e., 0:00, 6:00, 12:00 and 18:00) and the averaged error metrics computed from the global dense networks are shown in Table 3 (the specific results at four UTC time points for all dense networks are presented in Appendix section). From these averaged error metrics, the GEOS-5 ST performs slightly better than other model-based ST products by showing smaller ubRMSD and higher correlation coefficients at four UTC time points. More particularly, it can be seen that ERA5 performs better than ERA-Interim with smaller ubRMSD, absolute bias and higher *R* values at the four UTC time points. The main conclusions drawn here are quite consistent with the results obtained by daily averaged processing (Table 2). Additionally, it can be noticed that all model-based products perform slightly better by daily averaged processing than by considering the four separate UTC time points, which demonstrates the uncertainties of ST products may be partially reduced through daily averaged processing.

## 4.2. Performance of surface ST products at diverse temperature intervals

The surface ST datasets are being increasingly used to study covariance of extreme climatic conditions (Miralles et al., 2012; Sen- evratne et al., 2006); hence it is pertinent to pay more attention to the performance of Surface ST products under 'extreme' ST conditions. Fig. 2 (for bias) and Fig. 3 (for ubRMSD) show the evaluation results of the six surface ST products at different temperature intervals (the classification of temperature intervals can be seen in Table 2).
<caption>**Table 3**</caption>

Averaged evaluation results of five model-based ST products using global dense networks at four UTC time points. Bold numbers in the table represent the best results corresponding to each error metric.

<table><thead><tr><th>UTC time</th><th>Error metrics</th><th>GEOS-5</th><th>MERRA-2</th><th>ERA-Interim</th><th>ERA5</th><th>GLDAS</th></tr></thead><tbody><tr><td rowspan="3">0:00</td><td>ubRMSD (K)</td><td>2.34</td><td>2.36</td><td>2.67</td><td>2.41</td><td>2.52</td></tr><tr><td>Bias (K)</td><td>-1.38</td><td>-0.84</td><td>-0.31</td><td>-0.12</td><td>-0.97</td></tr><tr><td>R</td><td>0.965</td><td>0.964</td><td>0.957</td><td>0.965</td><td>0.961</td></tr><tr><td rowspan="3">6:00</td><td>ubRMSD (K)</td><td>2.06</td><td>2.16</td><td>2.19</td><td>2.08</td><td>2.30</td></tr><tr><td>Bias (K)</td><td>-1.54</td><td>-1.00</td><td>-0.95</td><td>-0.79</td><td>-1.40</td></tr><tr><td>R</td><td>0.967</td><td>0.966</td><td>0.962</td><td>0.966</td><td>0.961</td></tr><tr><td rowspan="3">12:00</td><td>ubRMSD (K)</td><td>2.04</td><td>2.16</td><td>2.46</td><td>2.12</td><td>2.32</td></tr><tr><td>Bias (K)</td><td>-1.54</td><td>-1.00</td><td>-0.95</td><td>-0.79</td><td>-1.40</td></tr><tr><td>R</td><td>0.967</td><td>0.966</td><td>0.955</td><td>0.965</td><td>0.958</td></tr><tr><td rowspan="3">18:00</td><td>ubRMSD (K)</td><td>2.32</td><td>2.36</td><td>2.78</td><td>2.60</td><td>2.56</td></tr><tr><td>Bias (K)</td><td>-0.90</td><td>-0.35</td><td>1.01</td><td>0.84</td><td>-0.67</td></tr><tr><td>R</td><td>0.966</td><td>0.966</td><td>0.961</td><td>0.964</td><td>0.960</td></tr></tbody></table>

With regard to bias, it is interestingly found that the performance of all the model surface ST products have the similar trend (i.e., colder in lower temperature, and warmer in higher temperature and the bias increases as the temperature increases except for the highest temperature conditions). In the highest temperature conditions, all model-based surface ST exhibit lower temperature values than the ground ST observations. This pattern is in line with a more recent study that adopted the quantile regression analysis approach (Li et al., 2020a). On the contrary, the satellite LPRM ST yields the adverse pattern compared to the model-based ST for different ST conditions (i.e., overestimation in lower ST conditions and underestimation in the higher ones). As mentioned in Section 4.1, MERRA-2, ERA-Interim and ERA5 are generally colder compared to ST observations from global dense networks, while somewhat inconsistent performance was observed under diverse ST conditions. Regardless of the underestimation in lower ST, in medium or high ST environments (i.e., ST-II and ST-III), the MERRA-2, ERA-Interim and ERA5 tend to be warmer and show positive averaged bias values.

In terms of ubRMSD, most model-based surface ST products perform better with the increase of ST in Fig. 3. In the lowest temperature condition (ST-I), all ST products are observed to have unsatisfied performance by exhibiting larger ubRMSD values than those of ST products in

other conditions, indicating that further improvement of the ST products is needed in this situation. Although larger underestimation occurs for all model-based surface ST products in the highest temperature condition, satisfactory performance of these products with smaller ubRMSD values (i.e., averaged ubRMSD value of 2.05 K for GEOS-5, 2.09 K for MERRA-2, 2.10 K for ERA-Interim, 2.14 K for GLDAS and 2.01 K for ERA5) can be also found, in which the new ERA5 performs better than other surface ST products. These findings are supposed to attract enough attentions from the extreme climate researchers since in their studies, the accuracy of adopted surface ST products in lower and higher temperature conditions is dominantly vital. The temperature-dependent bias would likely exaggerate the uncertainties in some hydro-meteorology applications, and needs to be corrected in extreme climate studies. With regard to LPRM ST, the slightly larger absolute bias values can be partially explained by the low penetration depth of Kaba band (Holmes, 2003; Holmes, 2008), although the thermal equilibrium condition has been taken into account in this study. The degraded performance of LPRM in medium and higher temperature conditions, in which larger uncertainty of ubRMSD can be obtained, should be paid attentions and this satellite-based ST products should be further improved in such cases.

<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Bias results of daily averaged model-based ST (GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah), and satellite-based AMSR2 LPRM ST at descending overpass time under diverse ST conditions.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Fig. 3. ubRMSD results of daily averaged model-based ST (GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah), and satellite-based AMSR2 LPRM ST at descending overpass time under diverse ST conditions.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 4. Bias results of daily averaged model-based ST (GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah), and satellite-based AMSR2 LPRM ST at descending overpass time for diverse soil moisture conditions.</figcaption></figure>

### 4.3. Performance of surface ST products at diverse moisture intervals

Similar to Section 4.2, the performance of six surface ST products was further evaluated under diverse soil moisture conditions, as shown in Figs. 4 and 5, which is expected to provide potential suggestions for satellite soil moisture retrieval in various moisture conditions. Similar to the patterns in diverse ST conditions, the bias of most surface ST products (even the AMSR2 LPRM) tends to be warmer as the soil moisture

gets wetter except for the highest moisture condition (i.e., SM-IV). Specifically, the GEOS-5 and GLDAS Noah ST generally show lower values than in situ observations in most soil moisture conditions by showing negative averaged bias values. However, the ERA-Interim, ERA5 and MERRA-2 ST products exhibit slightly higher values than ground ST in medium soil moisture conditions, in which the ERA5 performs better than the other surface ST products. Taking the results of ubRMSD into consideration (Fig. 5), the performance of most model-
<figure><img src="image_9.png" /><figcaption>Fig. 5. ubRMSD results of daily averaged model-based ST (GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah), and satellite-based AMSR2 LPRM ST at descending overpass time for diverse soil moisture conditions.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 6. Bias results of daily averaged model-based ST (GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah), and satellite-based AMSR2 LPRM ST at descending overpass time for diverse land cover types.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 7. ubRMSD results of daily averaged model-based ST (GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah), and satellite-based AMSR2 LPRM ST at descending overpass time for diverse land cover types.</figcaption></figure>

based products in medium SM conditions are worse compared to that in other moisture conditions, and such result should be paid more attention before related applications.

With regard to the highest SM condition, the underestimations of most model-based surface ST products become larger while the ubRMSD values are smaller, which indicates that these products have higher accuracy in wetter soil conditions after removing the mean bias. However, from the perspective of satellite soil moisture retrieval, since an overestimation (underestimation) of soil temperature inputs used in the soil moisture retrieval algorithms will lead to an overestimation (underestimation) of soil moisture estimations (Chen et al., 2018; Cui et al., 2018), the bias of the surface ST products should be carefully corrected to obtain more reliable soil moisture retrievals.

## 4.4. Impacts of land cover

With regard to diverse land covers, as shown in Figs. 6 and 7, most model-based surface ST products show lower temperature values than the ground surface ST in savanna and agricultural lands by showing negative bias values, which is in line with the findings obtained in dense networks. However, in forest and grassland, the model-based surface ST products tend to be warmer (i.e., getting smaller underestimations or even obtaining some overestimations), which indicates the impacts of vegetation might partially contribute to the bias variations in different

land cover types and should be considered for the model refinement. In terms of the ubRMSD shown in Fig. 7, it cannot be neglected that in grassland and shrubland, the performance of most model-based surface ST products is unsatisfactory by exhibiting larger mean ubRMSD values. Additionally, this phenomenon might be possibly linked with variations of soil organic matter in diverse land cover types (Hao et al., 2016), which is beyond the scope of the current study and should be carefully investigated in the future for the improvements of these model-based products.

## 4.5. Impacts of diverse climate zones

In terms of diverse climate zones, most model-based surface ST products perform better in temperate climate areas, with smaller absolute bias values and ubRMSD values as shown in Figs. 8 and 9 respectively. All model-based surface ST products show slightly higher values than the ground observations in tropical areas by showing general positive bias values, which is different from the results (i.e., general underestimation) obtained in dense networks presented in Section 4.1. Moreover, in arid and cold climate types, relative unstable performance of most model-based surface ST products is noticed with larger ubRMSD values and deviations of the ubRMSD (Fig. 9). Compared with ERA-Interim, the advancements of the new ERA5 can be observed in diverse climate areas, especially in tropical climate areas, which is in
<figure><img src="image_12.png" /><figcaption>Fig. 8. Bias results of daily averaged model-based ST (GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah), and satellite-based AMSR2 LPRM ST at descending overpass time for diverse climate types.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 9. ubRMSD results of daily averaged model-based ST (GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah), and satellite-based AMSR2 LPRM ST at descending overpass time for diverse climate types.</figcaption></figure>

line with the findings in Section 4.1.

## 4.6. *Impacts of elevation*

The effect of elevation on the accuracy of surface ST products was evaluated and presented in Figs. 10 and 11. With the elevation increasing, all the surface ST products show more unstable performance by exhibiting longer boxes concerning both bias and ubRMSD. It

suggests the impacts of altitude on the surface ST might be one of the crucial error sources and should be carefully taken into account for further improvement of the surface ST products. Specifically, most model-based surface ST products have better performance in lower DEM conditions by showing smaller ubRMSD values, though with negative bias values. In medium DEM conditions, all the model-based products tend to be warmer and some products (e.g., MERRA-2, ERA-Interim and ERA5) even present higher temperature values than the in situ surface
<figure><img src="image_14.png" /><figcaption>Fig. 10. Bias results of daily averaged model-based ST (GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah), and satellite-based AMSR2 LPRM ST at descending overpass time for different elevation intervals.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 11. ubRMSD results of daily averaged model-based ST (GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah), and satellite-based AMSR2 LPRM ST at descending overpass time for different elevation intervals.</figcaption></figure>

ST. With regard to LPRM ST, noticeable impacts of elevation on ST could be seen in Fig. 10(f), in which underestimation in low elevation and overestimation in medium or high elevation (i.e., DEM-III and DEM-IV) are observed. This is consistent with the results noted for different land cover and the limitations of modeling based on regional in situ observations (Holmes et al., 2009). Zeng et al. (2015a, 2015b) have pointed out that since the ground observations used to establish the LPRM empirical temperature model are from the United States and several

European countries, the model may be regionally calibrated. They also found that the LPRM ST has larger errors in the Tibetan Plateau with a very high elevation, which is consistent with our results as well.

From Sections 4.2 to 4.6, the impacts of surface condition in terms of ST and soil moisture, land cover, climate types and elevation on the performance of surface ST products were fully discussed. We can see the performance of satellite-based ST and model-based ST is slightly different under different environmental conditions. It is noteworthy that
it is not our intention to conclude the LPRM ST is inferior to model-based ST. The LPRM ST has its own unique advantages in soil moisture retrieval algorithms (e.g., avoid reliance on ancillary data) and provides an important supplement for remote sensing ST (or LST) products. It also should be noted that the uncertainties associated with the ST products under various ground conditions can be also partially caused by the slightly horizontal and vertical mismatch between model (or satellite)-based products and in situ measurements, and the mismatch-induced bias can be relieved to some extent by the ubRMSD metric (Zeng et al., 2016). Besides, we should be aware that the uncertainties of the model-based ST products are supposed to be related to the model driving data, model structure and model parameters (Bi et al., 2016), which is worthy to be further investigated but out of the scope of this manuscript.

## 4.7. Suggestions for satellite soil moisture enhancements

As stated before, for the retrieval of surface soil moisture from passive microwave observations, the impacts of surface ST on the brightness temperature must be carefully taken into account (Wigneron et al., 2017; Wigneron et al., 2021). Thus, based on the comprehensive assessment of the state-of-the art surface ST products made in this study, it is possible to provide some potential suggestions for the satellite soil moisture enhancements: (i) since it is demonstrated in previous studies that the bias of surface ST might partially contribute to the bias of some remotely sensed soil moisture products (Chen et al., 2018; Cui et al., 2018; Ma et al., 2019), the bias of the surface ST found in this study, especially in colder and wetter soil, tropical climate types, should be necessarily taken into account before applying them in soil moisture retrieval algorithms; (ii) the advancements of surface ST might provide some promising directions for the enhancements of satellite soil moisture retrievals. For instance, it is observed in this study that the newly developed ERA5 surface ST gains visible upgrades compared to its predecessor ERA-Interim, which has been adopted for the SMOS-L3/IC soil moisture retrieval (Li et al., 2020b). Thus, it is expected to enhance the SMOS soil moisture products via adopting ERA5 surface ST product; (iii) the large bias found in the LPRM ST product may have a detrimental impact on the LPRM ST retrievals. Moreover, it should be noted that in some retrieval algorithms, such as SMOS-IC, the ST value is combined with temperature at depth to compute an effective soil temperature (Wigneron et al., 2007), and thus the bias computed in ST will not be translated directly in a bias in SM.

Finally, it is worth noting too that, although essential processing of the in situ measurements for the fair evaluation was taken, the error sources of the evaluated surface ST products might be partly due to the mismatch of in situ ST measuring depth and the sampling depth of the selected satellite- and model-based surface ST products, as well as the well-known spatial mismatch between them (Zeng et al., 2015b, 2016). Note however, that as the reference temperature value used to compute the bias in this study corresponds to a sampling depth of ~0–5 cm, which is close to the sampling depth of microwave observations at low frequencies (e.g., L-band), results obtained here should be particularly relevant for soil moisture retrieval studies at these low frequencies. As for the depth and spatial mismatch, with the increasing abundance of soil temperature networks and increasing density of soil observation stations, this issue is expected to be further mitigated in the future.

## 5. Conclusions

The comprehensive assessment of surface ST products made in this study provides suggestions for the users of ST products on meteorological or ecological applications, and also contributes to the improvements of remote sensing soil moisture retrievals. In this study, five model-based surface ST products (GEOS-5, MERRA-2, GLDAS Noah, ERA-Interim and ERA5), and one satellite-based ST product (AMSR2 LPRM), were firstly evaluated against extensive ground observations from approximate 800 sites worldwide. The in situ observations from

both dense and sparse networks were used for the assessment to obtain a comprehensive understanding of the accuracy of these products. To gain a deeper insight into the skill of the six surface ST products, various potential impact factors including land cover, climate type, elevation, the ST and soil moisture conditions were taken into account. To the best of our knowledge, it is the first time to examine the effects of ST itself and soil moisture conditions on the accuracy of satellite- and model-based surface ST products.

The results using ST observations from dense networks highlight that the GEOS-5 shows the smallest ubRMSD of 1.84 K among all the evaluated surface ST products. All model-based surface ST products generally exhibit lower temperature values than the ground ST and show a high skill in capturing the temporal trend of ground observations with an averaged coefficient correlation more than 0.97. The newly produced ERA5 surface ST product was found, for the first time to our knowledge, to achieve visible improvements compared to ERA-Interim by using global dense networks. The ubRMSD of AMSR2 LPRM ST product is 3.16 K, and it is more sensitive to the impacts of underlying surfaces (e. g., land cover and elevation) compared to model-based ST.

Taking the ground ST conditions into account, all the model-based surface ST products show a similar trend: the bias increases from colder to warmer except for the highest temperature conditions. Most model-based products (e.g., the MERRA-2, ERA-Interim and ERA5) show slightly higher temperature values than the in situ data in moderate temperature conditions while they exhibit lower values than the ground measurements in low ST conditions. In the highest ST conditions, however, all the model-based surface ST products seriously demonstrate lower temperature values than the ground ST observations but show smaller ubRMSD values. Similarly, most surface ST products tend to be warmer as the soil moisture gets wetter except for the highest moisture condition, but show larger underestimations in the highest moisture condition. In terms of different land cover areas, it is found that most model-based surface ST products are more obviously affected in shrubland and forest. With regard to the climate types, most model-based ST products perform better in temperate climate types than in arid and cold climate types by showing smaller absolute bias and ubRMSD values. Additionally, the impacts of elevation on LPRM ST product should be taken into consideration for its future refinement, particularly in high elevation regions.

With regard to the enhancements of satellite soil moisture retrievals, since improvements of the newly developed ERA5 surface ST product have been demonstrated in this study, it is recommended to replace ERA-Interim for the further improvement of satellite soil moisture retrievals (e.g., the enhancements of SMOS-L3/IC products). Although the uncertainties of selected ST products were investigated in terms of the perspectives of ST interval, soil moisture interval, land cover, climate and elevation, more in-depth physical explanations concerning these uncertainties should be given in further studies. The findings in this study are expected to provide useful guidance for the improvement of model- and satellite-based surface ST products, which will benefit the satellite soil moisture retrievals as well as hydrometeorological applications.

### CRediT author statement

Hongliang Ma and Jiangyuan Zeng conceived and designed the research and wrote the manuscript. Hongliang Ma did the experiments. Xiang Zhang, Nengcheng Chen and Jean-Pierre Wigneron provided essential supporting and supervisions. All authors contributed to the editing of the manuscript.

### Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
## Acknowledgements

The authors thank Goddard Earth Sciences (GES) Data and Information Services Center (DISC), NASA and ECMWF for providing surface ST products, and the USDA, the OzNet network and the ISMN for supporting in situ ST datasets. This research was supported by the National Key R&D Program (No. 2018YFB2100500), National Natural Science

Foundation of China program (No. 41971317, 41801339, 41890822) and Creative Research Groups of Natural Science Foundation of Hubei Province of China (No. 2016CFA003). Jiangyuan Zeng was supported by the Youth Innovation Promotion Association CAS (No. 2018082), and Hongliang Ma was sponsored by China Scholarship Council (No. 202006270077).

## Appendix A

<caption>Table A1</caption>

The evaluation results at UTC 0:00 for GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah against observations from global dense networks. Bold numbers in the table represent the best results corresponding to each error metric.

<table><caption>Table A2</caption><thead><tr><th rowspan="2">Metrics</th><th colspan="5">ubRMSD (K)</th><th colspan="5">Bias (K)</th><th colspan="5">R (p-value < 0.01)</th></tr><tr><th>GEOS-5</th><th>MERRA-2</th><th>ERA-Interim</th><th>ERA5</th><th>GLDAS</th><th>GEOS-5</th><th>MERRA-2</th><th>ERA-Interim</th><th>ERA5</th><th>GLDAS</th><th>GEOS-5</th><th>MERRA-2</th><th>ERA-Interim</th><th>ERA5</th><th>GLDAS</th></tr></thead><tbody><tr><td>HOBE</td><td>1.75</td><td>1.83</td><td>1.75</td><td><strong>1.72</strong></td><td>1.73</td><td>-1.60</td><td>-1.35</td><td><strong>-0.79</strong></td><td>-1.54</td><td>-1.37</td><td>0.944</td><td>0.937</td><td>0.943</td><td><strong>0.946</strong></td><td>0.945</td></tr><tr><td>BIEBRZA-S-1</td><td><strong>1.81</strong></td><td>1.96</td><td>2.10</td><td>1.85</td><td>1.85</td><td>-1.84</td><td><strong>-1.65</strong></td><td>-1.66</td><td>-2.21</td><td>-1.85</td><td><strong>0.961</strong></td><td>0.944</td><td>0.931</td><td>0.959</td><td>0.960</td></tr><tr><td>TERENO</td><td>1.74</td><td><strong>1.71</strong></td><td>2.00</td><td>1.80</td><td>1.75</td><td>-0.87</td><td>0.14</td><td><strong>-0.03</strong></td><td>-0.71</td><td>-0.74</td><td>0.957</td><td>0.955</td><td>0.935</td><td><strong>0.959</strong></td><td>0.955</td></tr><tr><td>RISMA</td><td>2.94</td><td>3.06</td><td>3.21</td><td><strong>2.99</strong></td><td>3.87</td><td>-1.21</td><td><strong>-0.64</strong></td><td>-1.21</td><td>-0.68</td><td>-1.10</td><td><strong>0.967</strong></td><td><strong>0.967</strong></td><td>0.964</td><td>0.965</td><td>0.956</td></tr><tr><td>Reynolds Creek</td><td><strong>2.95</strong></td><td>3.17</td><td>4.24</td><td>4.97</td><td>3.19</td><td>2.59</td><td>3.55</td><td>6.36</td><td>8.62</td><td><strong>0.33</strong></td><td>0.962</td><td>0.960</td><td><strong>0.964</strong></td><td>0.961</td><td>0.960</td></tr><tr><td>South Fork</td><td>2.08</td><td>2.31</td><td>2.34</td><td><strong>2.01</strong></td><td>3.13</td><td><strong>-0.35</strong></td><td><strong>0.35</strong></td><td>1.49</td><td>1.18</td><td>-0.36</td><td>0.979</td><td>0.979</td><td>0.980</td><td><strong>0.981</strong></td><td>0.950</td></tr><tr><td>St. Joseph's</td><td>2.48</td><td>2.73</td><td>2.62</td><td><strong>2.43</strong></td><td>2.64</td><td>0.35</td><td>1.08</td><td>2.18</td><td>1.70</td><td><strong>0.32</strong></td><td><strong>0.978</strong></td><td><strong>0.978</strong></td><td>0.975</td><td><strong>0.978</strong></td><td>0.963</td></tr><tr><td>REMEDHUS</td><td>1.55</td><td>1.81</td><td>1.98</td><td><strong>1.50</strong></td><td>1.59</td><td>-3.49</td><td>-2.88</td><td><strong>-2.61</strong></td><td>-3.31</td><td>-3.11</td><td>0.985</td><td>0.980</td><td>0.978</td><td><strong>0.986</strong></td><td>0.983</td></tr><tr><td>Fort Cobb</td><td><strong>2.30</strong></td><td><strong>2.30</strong></td><td>2.98</td><td>2.57</td><td>2.69</td><td><strong>0.52</strong></td><td>0.85</td><td>2.04</td><td>1.79</td><td>1.45</td><td><strong>0.975</strong></td><td>0.976</td><td>0.965</td><td>0.966</td><td>0.970</td></tr><tr><td>Little Washita</td><td>2.44</td><td><strong>2.26</strong></td><td>2.87</td><td>2.64</td><td>2.64</td><td>0.93</td><td><strong>0.84</strong></td><td>2.39</td><td>1.75</td><td>1.48</td><td><strong>0.978</strong></td><td><strong>0.978</strong></td><td>0.967</td><td>0.970</td><td>0.964</td></tr><tr><td>CTP-SMTMN</td><td>2.62</td><td>2.15</td><td>2.34</td><td>2.62</td><td><strong>1.79</strong></td><td>-3.54</td><td>-1.78</td><td>-1.88</td><td>-2.52</td><td><strong>-0.61</strong></td><td>0.941</td><td>0.958</td><td>0.945</td><td>0.937</td><td><strong>0.971</strong></td></tr><tr><td>Walnut Gulch</td><td>3.53</td><td>3.32</td><td>3.05</td><td><strong>2.78</strong></td><td>3.27</td><td>-4.97</td><td>-4.16</td><td>-2.67</td><td><strong>-1.03</strong></td><td>-1.11</td><td>0.946</td><td>0.948</td><td>0.958</td><td><strong>0.963</strong></td><td>0.953</td></tr><tr><td>Little River</td><td>1.94</td><td>1.66</td><td>1.67</td><td>1.61</td><td><strong>1.59</strong></td><td>-1.60</td><td>-2.16</td><td>-2.99</td><td><strong>-0.84</strong></td><td>-1.68</td><td>0.970</td><td>0.972</td><td>0.968</td><td><strong>0.973</strong></td><td>0.971</td></tr><tr><td>Yanco</td><td>2.97</td><td><strong>2.51</strong></td><td>2.73</td><td>2.61</td><td>2.72</td><td>-4.32</td><td>-1.89</td><td><strong>-1.75</strong></td><td>-3.53</td><td>-3.21</td><td>0.953</td><td><strong>0.968</strong></td><td>0.956</td><td>0.961</td><td>0.954</td></tr><tr><td>FMI</td><td>1.35</td><td>2.00</td><td>3.45</td><td>1.44</td><td>2.58</td><td><strong>-0.86</strong></td><td>-1.98</td><td>-3.24</td><td>-1.05</td><td>-2.82</td><td><strong>0.967</strong></td><td>0.947</td><td>0.906</td><td>0.965</td><td>0.958</td></tr><tr><td>Average</td><td><strong>2.30</strong></td><td>2.32</td><td>2.62</td><td>2.37</td><td>2.47</td><td>-1.35</td><td>-0.78</td><td>-0.29</td><td><strong>-0.16</strong></td><td>-0.96</td><td>0.964</td><td>0.963</td><td>0.956</td><td><strong>0.965</strong></td><td>0.961</td></tr></tbody></table>

The evaluation results at UTC 6:00 for GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah against observations from global dense networks. Bold numbers in the table represent the best results corresponding to each error metric.

<table><thead><tr><th rowspan="2">Metrics</th><th colspan="5">ubRMSD (K)</th><th colspan="5">Bias (K)</th><th colspan="5">R (p-value < 0.01)</th></tr><tr><th>GEOS-5</th><th>MERRA-2</th><th>ERA-Interim</th><th>ERA5</th><th>GLDAS</th><th>GEOS-5</th><th>MERRA-2</th><th>ERA-Interim</th><th>ERA5</th><th>GLDAS</th><th>GEOS-5</th><th>MERRA-2</th><th>ERA-Interim</th><th>ERA5</th><th>GLDAS</th></tr></thead><tbody><tr><td>HOBE</td><td>1.71</td><td>1.75</td><td>1.77</td><td><strong>1.69</strong></td><td>1.80</td><td>-1.43</td><td>-0.78</td><td><strong>-0.21</strong></td><td>-1.39</td><td>-1.66</td><td>0.942</td><td>0.940</td><td><strong>0.944</strong></td><td>0.943</td><td>0.933</td></tr><tr><td>BIEBRZA-S-1</td><td>1.81</td><td>2.32</td><td>1.96</td><td>1.86</td><td><strong>1.79</strong></td><td>-1.71</td><td><strong>0.05</strong></td><td>-0.38</td><td>-1.99</td><td>-2.14</td><td>0.962</td><td><strong>0.965</strong></td><td>0.954</td><td>0.960</td><td>0.959</td></tr><tr><td>TERENO</td><td>1.69</td><td><strong>1.66</strong></td><td><strong>1.66</strong></td><td>1.70</td><td>1.69</td><td>-1.26</td><td><strong>-0.07</strong></td><td>-0.12</td><td>-1.18</td><td>-1.26</td><td>0.954</td><td>0.956</td><td>0.954</td><td><strong>0.958</strong></td><td>0.954</td></tr><tr><td>RISMA</td><td>2.06</td><td><strong>2.03</strong></td><td>2.20</td><td>2.36</td><td>3.31</td><td><strong>0.12</strong></td><td>-3.62</td><td>-0.29</td><td>0.31</td><td>0.19</td><td><strong>0.972</strong></td><td>0.967</td><td>0.968</td><td>0.970</td><td>0.959</td></tr><tr><td>Reynolds Creek</td><td><strong>2.28</strong></td><td>2.42</td><td>2.67</td><td>2.80</td><td>2.30</td><td><strong>0.53</strong></td><td>1.36</td><td>1.29</td><td>2.90</td><td>-1.62</td><td><strong>0.968</strong></td><td>0.966</td><td>0.961</td><td>0.964</td><td>0.965</td></tr><tr><td>South Fork</td><td>1.93</td><td>2.10</td><td><strong>1.73</strong></td><td>1.78</td><td>2.40</td><td>-1.60</td><td>-1.24</td><td><strong>-0.16</strong></td><td>-0.27</td><td>-1.27</td><td>0.978</td><td>0.978</td><td><strong>0.981</strong></td><td>0.980</td><td>0.968</td></tr><tr><td>St. Joseph's</td><td>2.31</td><td>2.45</td><td><strong>2.03</strong></td><td>2.28</td><td>2.34</td><td>-1.02</td><td>-0.57</td><td>0.82</td><td><strong>0.27</strong></td><td>-0.42</td><td>0.971</td><td>0.973</td><td><strong>0.975</strong></td><td>0.968</td><td>0.967</td></tr><tr><td>REMEDHUS</td><td>1.62</td><td>1.81</td><td>1.65</td><td><strong>1.54</strong></td><td>1.97</td><td>-3.96</td><td><strong>-2.88</strong></td><td>-2.94</td><td>-3.78</td><td>-4.32</td><td>0.979</td><td>0.980</td><td>0.978</td><td><strong>0.981</strong></td><td>0.970</td></tr><tr><td>Fort Cobb</td><td>2.07</td><td><strong>2.06</strong></td><td>2.10</td><td>2.17</td><td>2.29</td><td>-1.36</td><td>-1.19</td><td>-1.39</td><td>-1.40</td><td><strong>-0.32</strong></td><td>0.976</td><td><strong>0.980</strong></td><td>0.973</td><td>0.971</td><td>0.971</td></tr><tr><td>Little Washita</td><td>2.31</td><td>2.21</td><td><strong>2.17</strong></td><td>2.47</td><td>2.42</td><td>-0.82</td><td>-0.96</td><td>-0.76</td><td>-1.33</td><td><strong>-0.29</strong></td><td>0.975</td><td><strong>0.976</strong></td><td>0.972</td><td>0.966</td><td>0.968</td></tr><tr><td>CTP-SMTMN</td><td><strong>2.31</strong></td><td>2.64</td><td>2.86</td><td>2.42</td><td>2.52</td><td>-3.71</td><td>-2.26</td><td>-2.60</td><td>-2.04</td><td><strong>-1.81</strong></td><td><strong>0.952</strong></td><td>0.935</td><td>0.921</td><td>0.944</td><td>0.943</td></tr><tr><td>Walnut Gulch</td><td>1.95</td><td>1.88</td><td>1.77</td><td><strong>1.63</strong></td><td>1.81</td><td>-2.88</td><td>-2.10</td><td>-1.61</td><td>-0.39</td><td><strong>-0.37</strong></td><td>0.968</td><td>0.972</td><td>0.974</td><td><strong>0.979</strong></td><td>0.973</td></tr><tr><td>Little River</td><td>1.71</td><td><strong>1.47</strong></td><td>1.81</td><td>1.70</td><td>1.49</td><td>-2.41</td><td>-2.76</td><td>-3.52</td><td><strong>-1.84</strong></td><td>-2.78</td><td>0.975</td><td><strong>0.978</strong></td><td>0.959</td><td>0.968</td><td>0.971</td></tr><tr><td>Yanco</td><td>3.35</td><td>2.77</td><td><strong>2.60</strong></td><td>2.92</td><td>3.06</td><td>-3.36</td><td>-1.92</td><td><strong>-1.39</strong></td><td>-2.20</td><td>-1.63</td><td>0.955</td><td>0.966</td><td><strong>0.967</strong></td><td>0.960</td><td>0.953</td></tr><tr><td>FMI</td><td><strong>1.41</strong></td><td>2.37</td><td>3.38</td><td>1.53</td><td>2.73</td><td><strong>-0.72</strong></td><td>-1.32</td><td>-2.46</td><td>-0.91</td><td>-2.83</td><td><strong>0.966</strong></td><td>0.953</td><td>0.939</td><td>0.963</td><td>0.954</td></tr><tr><td>Average</td><td><strong>2.04</strong></td><td>2.13</td><td>2.16</td><td>2.05</td><td>2.26</td><td>-1.71</td><td>-1.35</td><td>-1.05</td><td><strong>-1.02</strong></td><td>-1.50</td><td><strong>0.966</strong></td><td><strong>0.966</strong></td><td>0.961</td><td>0.965</td><td>0.960</td></tr></tbody></table>
<caption>Table A3</caption>

The evaluation results at UTC 12:00 for GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah against observations from global dense networks. Bold numbers in the table represent the best results corresponding to each error metric.

<table><caption>Table A4</caption><thead><tr><th rowspan="2">Metrics<br>Dense<br>Networks</th><th colspan="4">ubRMSD (K)</th><th colspan="4">Bias (K)</th><th colspan="4">R (p-value < 0.01)</th></tr><tr><th>GEOS-5</th><th>MERRA-2</th><th>ERA-Interim</th><th>ERA5</th><th>GLDAS</th><th>GEOS-5</th><th>MERRA-2</th><th>ERA-Interim</th><th>ERA5</th><th>GLDAS</th><th>GEOS-5</th><th>MERRA-2</th><th>ERA-Interim</th><th>ERA5</th><th>GLDAS</th></tr></thead><tbody><tr><td>HOBE</td><td>2.21</td><td>2.39</td><td>2.45</td><td>2.22</td><td>2.45</td><td>-0.66</td><td>0.43</td><td>0.42</td><td>-0.53</td><td>-0.32</td><td><strong>0.934</strong></td><td><strong>0.934</strong></td><td>0.932</td><td><strong>0.934</strong></td><td>0.918</td></tr><tr><td>BIEBRZA-S-1</td><td>2.48</td><td>3.25</td><td>3.12</td><td>2.63</td><td>2.38</td><td>0.85</td><td>2.92</td><td>3.03</td><td>1.05</td><td><strong>0.28</strong></td><td><strong>0.960</strong></td><td>0.945</td><td>0.939</td><td><strong>0.960</strong></td><td>0.944</td></tr><tr><td>TERENO</td><td>2.14</td><td>2.49</td><td>2.58</td><td>2.36</td><td>2.18</td><td><strong>0.58</strong></td><td>2.23</td><td>2.47</td><td>0.96</td><td>1.00</td><td>0.948</td><td>0.944</td><td>0.933</td><td>0.945</td><td><strong>0.949</strong></td></tr><tr><td>RISMA</td><td>2.11</td><td>2.35</td><td>2.62</td><td>2.34</td><td>3.10</td><td><strong>0.02</strong></td><td>0.22</td><td>-0.34</td><td>-0.02</td><td>-0.29</td><td><strong>0.965</strong></td><td>0.959</td><td>0.946</td><td>0.962</td><td>0.948</td></tr><tr><td>Reynolds Creek</td><td>2.07</td><td>2.20</td><td>2.69</td><td>2.40</td><td>2.42</td><td>-0.28</td><td>0.34</td><td>0.41</td><td>1.03</td><td>-2.74</td><td><strong>0.963</strong></td><td>0.961</td><td>0.939</td><td>0.953</td><td>0.946</td></tr><tr><td>South Fork</td><td>2.03</td><td>2.14</td><td>2.29</td><td>1.86</td><td>2.32</td><td>-2.32</td><td>-2.15</td><td>-0.78</td><td>-0.91</td><td>-2.10</td><td>0.972</td><td>0.973</td><td>0.962</td><td><strong>0.976</strong></td><td>0.967</td></tr><tr><td>St. Joseph's</td><td>2.30</td><td>2.42</td><td>2.32</td><td><strong>2.30</strong></td><td>2.33</td><td>-1.37</td><td>-1.09</td><td>0.96</td><td><strong>0.07</strong></td><td>-0.95</td><td>0.969</td><td><strong>0.971</strong></td><td>0.964</td><td>0.967</td><td>0.963</td></tr><tr><td>REMEDHUS</td><td>1.90</td><td>2.00</td><td>2.06</td><td><strong>1.84</strong></td><td>2.25</td><td>-3.24</td><td>-0.12</td><td>0.37</td><td>-2.97</td><td>-2.84</td><td><strong>0.983</strong></td><td>0.980</td><td>0.978</td><td><strong>0.983</strong></td><td>0.969</td></tr><tr><td>Fort Cobb</td><td>2.03</td><td><strong>1.99</strong></td><td>2.33</td><td>2.13</td><td>2.19</td><td>-2.31</td><td>-2.31</td><td>-3.13</td><td>-2.30</td><td>-1.70</td><td>0.974</td><td><strong>0.979</strong></td><td>0.960</td><td>0.972</td><td>0.965</td></tr><tr><td>Little Washita</td><td>2.27</td><td><strong>2.19</strong></td><td>2.50</td><td>2.55</td><td>2.34</td><td>-1.72</td><td>-1.92</td><td>-2.25</td><td>-2.19</td><td>-1.60</td><td>0.974</td><td><strong>0.977</strong></td><td>0.956</td><td>0.965</td><td>0.963</td></tr><tr><td>CTP-SMTMN</td><td>2.35</td><td><strong>2.21</strong></td><td>2.47</td><td>2.60</td><td>2.32</td><td>-3.77</td><td>-3.41</td><td>-4.50</td><td>-2.04</td><td>-0.93</td><td>0.952</td><td><strong>0.954</strong></td><td>0.945</td><td>0.945</td><td>0.952</td></tr><tr><td>Walnut Gulch</td><td>1.81</td><td>1.75</td><td>1.62</td><td><strong>1.51</strong></td><td>1.88</td><td>-3.07</td><td>-2.26</td><td>-0.76</td><td>-0.14</td><td>-1.95</td><td>0.968</td><td>0.973</td><td>0.973</td><td><strong>0.982</strong></td><td>0.965</td></tr><tr><td>Little River</td><td>1.68</td><td><strong>1.47</strong></td><td>2.53</td><td>1.78</td><td>1.50</td><td>-2.80</td><td>-3.06</td><td>-3.34</td><td>-2.00</td><td>-3.44</td><td>0.980</td><td><strong>0.983</strong></td><td>0.951</td><td>0.972</td><td>0.970</td></tr><tr><td>Yanco</td><td>1.82</td><td><strong>1.78</strong></td><td>1.88</td><td>1.91</td><td>2.01</td><td><strong>0.00</strong></td><td>-0.44</td><td>-0.67</td><td>0.86</td><td>1.36</td><td>0.967</td><td>0.968</td><td>0.966</td><td><strong>0.971</strong></td><td>0.969</td></tr><tr><td>FMI</td><td><strong>1.55</strong></td><td>2.13</td><td>3.62</td><td>1.64</td><td>3.00</td><td><strong>-0.88</strong></td><td>-1.21</td><td>-2.68</td><td>-1.01</td><td>-2.44</td><td>0.971</td><td><strong>0.972</strong></td><td>0.951</td><td>0.971</td><td><strong>0.972</strong></td></tr><tr><td>Average</td><td><strong>2.05</strong></td><td>2.18</td><td>2.47</td><td>2.14</td><td>2.31</td><td>-1.40</td><td>-0.79</td><td>-0.72</td><td>-0.68</td><td>-1.24</td><td><strong>0.965</strong></td><td><strong>0.965</strong></td><td>0.953</td><td>0.964</td><td>0.957</td></tr></tbody></table>

The evaluation results at UTC 18:00 for GEOS-5, MERRA-2, ERA-Interim, ERA5 and GLDAS Noah against observations from global dense networks. Bold numbers in the table represent the best results corresponding to each error metric.

<table><thead><tr><th rowspan="2">Metrics<br>Dense<br>Networks</th><th colspan="4">ubRMSD (K)</th><th colspan="4">Bias (K)</th><th colspan="4">R (p-value < 0.01)</th></tr><tr><th>GEOS-5</th><th>MERRA-2</th><th>ERA-Interim</th><th>ERA5</th><th>GLDAS</th><th>GEOS-5</th><th>MERRA-2</th><th>ERA-Interim</th><th>ERA5</th><th>GLDAS</th><th>GEOS-5</th><th>MERRA-2</th><th>ERA-Interim</th><th>ERA5</th><th>GLDAS</th></tr></thead><tbody><tr><td>HOBE</td><td>2.12</td><td>2.12</td><td>2.13</td><td><strong>2.12</strong></td><td>2.23</td><td>-1.01</td><td>-0.49</td><td>-0.48</td><td>-0.91</td><td>-0.43</td><td>0.940</td><td>0.940</td><td><strong>0.942</strong></td><td>0.941</td><td>0.935</td></tr><tr><td>BIEBRZA-S-1</td><td>2.22</td><td>2.63</td><td>2.33</td><td>2.37</td><td>2.34</td><td>0.09</td><td>1.09</td><td>0.82</td><td><strong>0.04</strong></td><td><strong>0.04</strong></td><td><strong>0.966</strong></td><td>0.950</td><td>0.954</td><td>0.964</td><td>0.957</td></tr><tr><td>TERENO</td><td>2.03</td><td>2.05</td><td>2.01</td><td>2.24</td><td>1.93</td><td><strong>0.54</strong></td><td>1.47</td><td>0.98</td><td>0.87</td><td>0.59</td><td>0.958</td><td>0.957</td><td>0.955</td><td>0.956</td><td>0.962</td></tr><tr><td>RISMA</td><td>3.29</td><td>3.18</td><td><strong>2.99</strong></td><td>3.15</td><td>3.75</td><td>-2.57</td><td>-1.30</td><td>-1.58</td><td>-2.35</td><td>-2.95</td><td>0.961</td><td>0.965</td><td><strong>0.969</strong></td><td>0.963</td><td>0.954</td></tr><tr><td>Reynolds Creek</td><td>2.76</td><td>3.00</td><td>5.23</td><td>5.15</td><td><strong>2.63</strong></td><td>2.64</td><td>3.27</td><td>7.24</td><td>7.66</td><td>0.24</td><td><strong>0.963</strong></td><td>0.962</td><td>0.952</td><td>0.950</td><td>0.960</td></tr><tr><td>South Fork</td><td>1.97</td><td>2.12</td><td>2.62</td><td>2.30</td><td>3.16</td><td>-0.90</td><td>-0.30</td><td>-2.32</td><td>1.53</td><td>-1.12</td><td>0.979</td><td>0.980</td><td><strong>0.981</strong></td><td>0.978</td><td>0.945</td></tr><tr><td>St. Joseph's</td><td>2.54</td><td>2.78</td><td>3.30</td><td>2.99</td><td>2.77</td><td>0.84</td><td>1.59</td><td>4.34</td><td>3.23</td><td><strong>0.21</strong></td><td><strong>0.977</strong></td><td><strong>0.977</strong></td><td>0.971</td><td>0.974</td><td>0.955</td></tr><tr><td>REMEDHUS</td><td>2.13</td><td>1.85</td><td><strong>1.79</strong></td><td>2.06</td><td>2.14</td><td>-2.70</td><td>-1.17</td><td>-2.11</td><td>-2.44</td><td>-1.96</td><td>0.984</td><td>0.984</td><td><strong>0.986</strong></td><td>0.983</td><td>0.977</td></tr><tr><td>Fort Cobb</td><td>2.23</td><td>2.27</td><td>3.43</td><td>3.02</td><td>2.50</td><td><strong>0.49</strong></td><td>0.71</td><td>4.10</td><td>3.08</td><td>0.81</td><td>0.978</td><td><strong>0.981</strong></td><td>0.964</td><td>0.961</td><td>0.970</td></tr><tr><td>Little Washita</td><td>2.53</td><td><strong>2.38</strong></td><td>3.33</td><td>3.25</td><td>2.62</td><td>1.22</td><td><strong>1.20</strong></td><td>4.76</td><td>3.34</td><td>1.24</td><td>0.977</td><td><strong>0.979</strong></td><td>0.965</td><td>0.964</td><td>0.960</td></tr><tr><td>CTP-SMTMN</td><td>2.31</td><td>2.19</td><td>2.55</td><td>2.27</td><td><strong>1.72</strong></td><td>-3.78</td><td>-2.54</td><td>-2.80</td><td>-2.55</td><td>-0.32</td><td>0.952</td><td>0.955</td><td>0.932</td><td>0.953</td><td><strong>0.973</strong></td></tr><tr><td>Walnut Gulch</td><td>3.01</td><td>2.79</td><td>2.45</td><td><strong>2.05</strong></td><td>2.93</td><td>-5.05</td><td>-4.33</td><td>0.29</td><td><strong>0.03</strong></td><td>-2.06</td><td>0.959</td><td>0.962</td><td>0.970</td><td><strong>0.979</strong></td><td>0.962</td></tr><tr><td>Little River</td><td>1.82</td><td><strong>1.59</strong></td><td>1.68</td><td>2.00</td><td>1.78</td><td>-0.63</td><td>-1.04</td><td>0.39</td><td>1.87</td><td>-0.86</td><td><strong>0.974</strong></td><td><strong>0.974</strong></td><td>0.968</td><td>0.961</td><td>0.964</td></tr><tr><td>Yanco</td><td><strong>1.88</strong></td><td>1.90</td><td>1.96</td><td>1.98</td><td>2.09</td><td>-0.51</td><td>-0.37</td><td>-0.48</td><td>0.14</td><td><strong>0.13</strong></td><td>0.956</td><td>0.956</td><td>0.956</td><td><strong>0.958</strong></td><td>0.950</td></tr><tr><td>FMI</td><td><strong>1.62</strong></td><td>2.21</td><td>3.10</td><td>1.70</td><td>3.10</td><td><strong>-0.69</strong></td><td>-1.29</td><td>-2.61</td><td>-0.86</td><td>-2.31</td><td>0.970</td><td>0.966</td><td>0.952</td><td>0.970</td><td><strong>0.971</strong></td></tr><tr><td>Average</td><td><strong>2.30</strong></td><td>2.34</td><td>2.73</td><td>2.58</td><td>2.51</td><td>-0.80</td><td>-0.23</td><td>1.01</td><td>0.84</td><td>-0.58</td><td><strong>0.966</strong></td><td><strong>0.966</strong></td><td>0.961</td><td>0.964</td><td>0.960</td></tr></tbody></table>

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