A newly developed model for estimating snow depth in ungauged areas

Full text

Physics and Chemistry of the Earth 134 (2024) 103588
Available online 24 March 2024
1474-7065/© 2024 Elsevier Ltd. All rights reserved.
A newly developed model for estimating snow depth in ungauged areas
Firooze Hashemireza
a
, Ahmad Sharafati
a
,
b
,
*
, Tayeb Raziei
c
, Yusef Kheyruri
a
a
Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
b
New Era and Development in Civil Engineering Research Group, Scientic Research Center, Al-Ayen University, Thi-Qar, Nasiriyah, 64001, Iraq
c
Soil Conservation and Watershed Management Research Institute (SCWMRI), Agricultural Research, Education and Extension Organization (AREEO), Tehran, Iran
ARTICLE INFO
Keywords:
Snow depth
Dual sigmoidal-Boltzmann equation (DSBE)
Double sigmoid model
ABSTRACT
The presence of snow signicantly affects the hydrological cycle and soil moisture globally. Nowadays, with the
expansion of science, different satellites can measure snow depth all over the world. By establishing a conditional
relationship between mean temperature and the Proportion of Snowfall to Total Precipitation (PSTP), this study
proposes a method for snow depth estimation for ungauged stations. The case study of this research is Iran. Most
of Iran’s climate is arid due to its location in the Middle East, making it one of the countries with the lowest
rainfall worldwide. On the other hand, this country enormously depends on water resources. Consequently, an
accurate and valid estimate of snow amounts in Iran is essential. To reach this goal, we analyzed daily data from
12 synoptic and climatological stations between 1970 and 2020, including rainfall, snow depth, and mean
temperature. For each station, the PSTP at 0.5 ◦C air temperature intervals was determined and tted to a double
sigmoid model that allows snow depth estimation. The evaluation of the snow depth approximated by the double
sigmoid model was done using R
2
, RRMSE, EF, and Bias statistics against the observational data. R
2
values in the
Era-5 dataset in all stations are lower than 0.5. Additionally, it should be noted that in certain stations, the bias
values surpass 20 mm. Furthermore, in 75 percent of the stations, the RRMSE values exceed 0.6. By utilizing the
DSBE model, it is possible to achieve a reduction of 122.4 and 0.7 in Bias and RRMSE values, respectively. The R
2
between observed and estimated snow depth was estimated between 0.81 and 1 in ten of the studied stations and
0.65 and 0.8 in the other two stations. Moreover, the ndings imply that the proposed model is a suitable
technique for estimating snow depth in remote areas lacking snowfall measurement.
1. Introduction
Snow signicantly regulates the global climate and hydrological
cycle (Qian et al., 2009). Moreover, since snow is a temporary water
source, its changes affect soil moisture, evaporation, and precipitation.
As a result, snow depth and snow cover signicantly impact the envi-
ronment (Jonas et al., 2009). Also, widespread and continuous snow can
cause natural disasters such as avalanches, leading to signicant loss of
wealth, health, and lives (J. Wang et al., 2020).
Currently, a wide range of satellite products have been developed,
leading to the expansion of data utilization in various elds. the
following can be mentioned: drought assessment (Dimyati et al., 2024;
Kheyruri et al., 2023a; Lakshmi et al., 2023), water quality (A. P. Mishra
et al., 2023; Moghadam et al., 2021; Tian et al., 2023), climate change
(Agbor et al., 2023; Nielsen-Englyst et al., 2023; Paranunzio and Marra,
2024), land cover (Horry et al., 2023; K. Mishra and Garg, 2023; Pande
et al., 2023), hydrology (Ali et al., 2023; Eini et al., 2023; Ibrahim et al.,
2022), adaptation (Jain et al., 2023; Liang et al., 2023; Zhao et al.,
2023), agriculture science (Antonijevi´
c et al., 2023; Kheyruri et al.,
2023b; Xiao et al., 2023), remote sensing (Asadollah et al., 2023; Chen
et al., 2023; Guo et al., 2024), ocean science (Joshi et al., 2023; G. Li
et al., 2023; J. Wu et al., 2024), wave energy (J. Liu et al., 2023; Sardana
et al., 2024; Z. Yang et al., 2023), solar (Nie et al., 2024; Paletta et al.,
2023; Tajjour et al., 2023), and etc.
Snow depth for water resources issues is critical since it will lead to
an incorrect estimation of snow water equivalent if it is not recognized;
therefore, it will lead to many problems, including not identifying the
load entering the dam, ooding, and several other troubles (Behroz
et al., 2019).
Nowadays, much research has been done on the trend of snow cover
changes, including the studies conducted by R. D. Brown and Mote
(2009); D´
ery and Brown (2007); Hern´
andez-Henríquez et al. (2015); A.
Wang et al. (2018). However, little research has been carried out on
estimating snow depth or snow water equivalent methods (L. Dai and
* Corresponding author. Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.
E-mail addresses: asharafati@srbiau.ac.ir, asharafati@gmail.com (A. Sharafati).
Contents lists available at ScienceDirect
Physics and Chemistry of the Earth
journal homepage: www.elsevier.com/locate/pce
https://doi.org/10.1016/j.pce.2024.103588
Received 2 November 2023; Received in revised form 26 February 2024; Accepted 22 March 2024

Physics and Chemistry of the Earth 134 (2024) 103588
2
Che, 2022). For instance, using a GNSS single-frequency signal collected
by a ground receiver, Li et al. (2019) showed that the snow depth in at
regions deviates from the measured data by 2–6 cm, as indicated by the
RMSE value.
Several methods have been proposed to solve the problem of the lack
of snow depth observational data in meteorological stations, one of
which is the measurement of snow depth through on-site devices (Ras-
mussen et al., 2012). However, these methods cannot depict the features
of spatiotemporal changes in snow depth using scattered stations (J.
Wang et al., 2020). Today, satellite remote sensing and reanalysis data
are widely used. For example, Dai et al. (2015) assessed snow depth
using passive microwave remote sensing data from SMMR, SSM/I, and
SSMI/S. Using ERA5 and ERA5-Land reanalysis, Lei et al. (2022) showed
that, in the Tibetan Plateau, the reanalysis data overestimates the actual
snow depth. However, there are some limitations to each of the
mentioned methods. Coarse spatial resolution, typically at the kilometer
level, characterizes passive microwave remote sensing data. Therefore,
it cannot meet the research need of hydrological snow processes at the
basin scale. In contrast, active microwave remote sensing has an
appropriate spatial resolution and higher sensitivity to snow parameters
(Y. Liu et al., 2017). Nevertheless, the active microwave mechanism of
remote sensing has a complex process of forward model-based inversion
that happens in the spread of the snow, the underneath surface covered
by snow, and land coverage (e.g., vegetation). When applied to moun-
tainous areas with relatively complex surface conditions, it is not easy to
distinguish backscatter information that returns to SAR Sensor. This
algorithm, being available under certain circumstances, is not generally
applied. There shall be more investigation into its global application (Y.
Liu et al., 2017).
In recent decades, techniques such as Lidar and Interferometric
synthetic aperture radar (InSAR) have been extensively used to measure
snow depth (L. Dai and Che, 2022). The utilization of the Lidar tech-
nique is constrained as a result of the limited availability of satellite data
and the absence of data in certain locations and specic time periods
(Currier et al., 2019). Costly methods are rarely used in developing
countries. Snow depth is quantied using InSAR by analyzing the phase
disparity between areas with and without snow cover (Deeb et al.,
2011). Given the inuence of snow depth, snowpack structure, and
surface roughness, there are notable uncertainties associated with these
estimates. Therefore, its use in measuring snow depth was far less than
lidar. There is also uncertainty regarding the reanalysis data obtained by
combining the results of short-term estimates of Numerical Weather
Prediction models (NWP) with observational data. (Hu et al., 2022). The
investigations show that the snow depth data estimated with the help of
remote sensing and reanalysis data do not have enough accuracy, and no
product performs best in all regions (L. Dai and Che, 2022; Durand et al.,
2024) evaluated snow depth values by the SWE model. The exhibition
demonstrated the potential of the SWE method to enormously enhance
the accuracy of snow data, resulting in a 20 percent improvement. This
algorithm is a very adequate algorithm for enhancing snow data (Zheng
et al., 2023). Improved snow depth data in China. This study displayed,
the algorithms that utilized in that research could improve correlation
values (R) and decrease Root-mean-square deviation (RMSE)values be-
tween satellite and observation snow depth data. (He et al., 2024)
estimated snow depth with various algorithms. The ndings indicate
that algorithms are effective in estimating snow depth during the winter
season, and these models have the capability to predict snow depth from
October to April. (J¨
a¨
askel¨
ainen et al., 2024) evaluated snow depth by
the new method. According to the research results, this method dem-
onstrates enhanced performance in detecting snow depth and can be
utilized for identifying occurrences of snowfall.
Consequently, in order to obtain a more precise assessment of snow
depth across various regions worldwide, it becomes imperative to
explore alternative methodologies.
When analyzing the connection between snowfall and air tempera-
ture, scientists rely on this information to determine if the precipitation
is falling as rain or snow (Hashemireza et al., 2023), the present study
intends to utilize this relationship to estimate snow depth in stations
with no snow measurements. Hashemireza et al. (2023) showed that the
dual sigmoidal-Boltzmann equation (DSBE) model could be used to es-
timate mean temperature thresholds and snow depth using the fre-
quency of snow events at air temperature lower than the T-snow
threshold which is the air temperature below which all precipitation
occurs in the form of snow.
Taking into account the fact that a substantial portion of Iran is
comprised of mountainous regions that receive abundant rainfall in
winter. The process of obtaining snow depth information in moun-
tainous areas is arduous. Hence, it is essential to investigate various
models for obtaining snow depth data in areas that are hard to reach.
The primary goal of this ongoing research is to employ a particular
regression technique to calculate and approximate the snow depth at
multiple stations under investigation. The focus of the proposed method
is on tting the DSBE model to the ratio or Proportion of Snow to Total
Precipitation (PSTP), rather than the frequency of snow events. By
employing sigmoid models like the DSBE model, this approach allows
for the determination of snow’s contribution to the overall precipitation
within each 0.5 ◦C air temperature interval. The effectiveness of the
proposed approach was subsequently assessed through a comparison of
the approximate snow depth with regression method with both the
observed snow depth data and the Era5-land reanalysis data.
2. Case study
Iran located in the Middle east with 1640000 km
2
(25–38 N and
44–64 E). The country is geographically situated in such a way that its
northern border is shared with the Caspian Sea, while its southern
border is shared with both the Persian Gulf and the Oman Sea.Iran has
two mountains with names Alborz and Zagros. The impact of these
mountains on the various climates in Iran is signicant.
The Alborz Mountains, which span from east to west, are accompa-
nied by the Zagros Mountains, which contract in the west. The highest
point in Iran is the Damavand crest in the Alborz mountain range,
Table 1
The length of the data period and the height of the studied stations.
Station ID Station name Latitude Longitude Record length (years) Elevation (m) Tmin (C) Tave (C) Tmax (C) Snow depth (mm)
S
1
Khoy 38.54 44.95 50 1103.4 5.24 10 17.24 124.84
S
2
Ardabil 38.22 48.33 44 1335.2 3.64 9 16.01 142.65
S
3
Sarab 37.93 47.53 34 1682 1.89 9 16.49 112.41
S
4
Piranshahr 36.70 45.15 34 1443.5 7.47 13 18.77 228.95
S
5
Saqez 36.22 46.31 50 1522.8 3.6 12 19.36 187.58
S
6
Firuzkuh 35.75 52.73 27 1976 2 11 16.91 98.37
S
7
Kamyaran 34.80 46.93 14 1404 6.5 16 22.29 238.31
S
8
Hamedan 34.87 48.53 44 1740.8 4 12 19.92 149.78
S
9
Arak 34.07 49.78 50 1702.8 7.55 14.02 21.11 149.29
S
10
Dorud 32.97 50.37 20 1522.3 4.52 11 17.76 194.69
S
12
Daran 33.52 49.00 28 2290 10.52 17 22.68 266.29
S
12
Sharekord 32.29 50.84 50 2048.9 3.09 12.19 20.52 232.35
F. Hashemireza et al.

Physics and Chemistry of the Earth 134 (2024) 103588
3
standing at an altitude of 5610 m. The Dasht-e Kavir is considered the
lowest. Zagros mountains receive rainfall in winter and west and
northwest of iran has freezing temperature in winter. An other hand
central platu of iran has warm and arid climate and receive less than 50
mm rainfall in year (Papi et al., 2022).
Yearly average of precipitation in iran is 250 mm and the minimum
temperature occure in south west in summer with 50 C, and max tem-
perature occurs in north west in winter with −30 C (Kheyruri et al.,
2023).
Due to the climatic conditions and the presence of the Zagros
mountains and the minimum temperature values, the amount of snow-
fall is the highest in the northwest and west of Iran, and in the winter
season, we see heavy snowfall in these areas. In most of the stations
investigated in this research, which were located in the western half of
Iran, at least 60% of the winter days in these stations had temperatures
below zero. Also, in all the investigated years, at least one day with a
snow depth of more than 10 cm was recorded in the stations.
For a better understanding of the climatic conditions and parameters
affecting the depth of snow, the height of the stations and the average
values of minimum, maximum, average temperature and snow depth in
the winter season are given in Table 1.
3. Data
The daily average air temperature, precipitation, and snow depth
data corresponding to 12 synoptic and the Iranian Meteorological Or-
ganization service provided the climatological stations used in this
study, which were obtained from their website at www.irimo.ir. These
data are available to the public on a daily, monthly and yearly basis
since the beginning of the establishment of the station. In addition, this
organization provides researchers with data on maximum and minimum
temperature, humidity, and wind speed and direction.
The considered stations are located in the highlands of Zagros and
Alborz mountain ranges and have a longer snow season and snow oc-
currences in Iran(Hashemireza et al., 2023). Fig. 1 illustrates the spatial
distribution of these stations as depicted on the map of Iran. In addition,
Fig. 1. Distribution of studied stations and Era5-land points on the map of Iran.
Fig. 2. a) The scatterplot of snow depth versus average daily air temperature, b) the scatter plot of average snow depth versus average daily air temperature with a
temperature interval of 0.5
◦C, c) the PSTP for average daily air temperature, and d) the PSTP for average daily air temperature with a temperature interval of 0.5.
F. Hashemireza et al.

Physics and Chemistry of the Earth 134 (2024) 103588
4
Table 1 provides a visual representation of the names of the stations,
their respective elevations above sea level, and the duration of their
recorded snow depth data.
In addition to possessing longer records of snow depth, the chosen
stations also have the highest frequency of days with air temperatures
equal to or below the snowfall air temperature threshold, as well as the
greatest proportion of snowfall in relation to the overall annual
precipitation.
The ECMWF reanalysis has recently introduced ERA5 as its fth-
generation version. It is built upon the foundation of the Integrated
Forecasting System (IFS) Cy41r2. The integration of measurements from
various observation systems (such as satellites and in-situ data) into the
atmospheric model is achieved through the utilization of a 4D-Var
scheme. Moreover, it enables a comprehensive and physically accurate
assessment of both land and ocean surfaces by combining the atmo-
spheric portion of the IFS with the HTESSEL land-surface model and the
WAM ocean wave model. The atmosphere is represented by ERA5
through the utilization of 137 hybrid sigma/pressure (model) levels,
extending from the surface to 1 Pa. The grid resolution is 31 km
(0.218125◦). Hourly data is at your disposal, encompassing analysis and
concise forecasts, executed twice daily at 06 and 18 UTC. Additionally,
at a reduced spatial and temporal resolution, uncertainty estimates are
provided for all variables. From 1950 to the present, ERA5 ensures
complete global spatial coverage. This database has been used in many
researches (Gomis-Cebolla et al., 2023; Shahbazdashti et al., 2024; Tan
et al., 2023; H. Wu et al., 2023).
This research involved a comparison of the daily snow depth data
from ERA5-Land reanalysis (https://www.ecmwf.int/) with both the
observational snow depth data of the studied stations and the estimated
data on snow depth was obtained using the method that was proposed.
The daily snow depth data from the ERA5-Land dataset were
downloaded from the ECMEF website. ERA5-Land is a downsized
variant of the ERA5 product, specically designed for enhanced preci-
sion in land-related applications. It is produced by integrating remote
sensing and at-site observations into the Cy4lr2 Integrated Forecast
System model to quantify climate conditions on a four-dimensional
matrix. ERA5-Land theoretically bridges simulation and observational
data in reanalyzing the observations. It may present insights regarding
areas where observational data is unavailable (Baker et al., 2021).
Fig. 1 illustrates the distribution of the studied stations and Era5 grid
points over the map of Iran. As the gure illustrates, the high spatial
resolution (0.1◦×0.1◦) of Era5-land data provides a dense network of
points with a relatively short distance from each of the stations, being
favorable for comparative analysis.
4. Method
In order to determine whether precipitation is in the form of snow or
rain, one can analyze the connection between snow events and air
temperature (Auer and Resources, 2010; A. Dai, 2008; Jennings et al.,
2018), it can be used to estimate snow depth in stations with or without
snow depth records. Fig. 2-a illustrates the distribution of snow depth
versus the average daily air temperature at Firuzkoh station. This scatter
plot shows a clear relationship between the snow depth and the average
daily air temperature. Fig. 2-b shows that by binning the 9600 records of
snow depth in 0.5 ◦C air temperature bins, the considered relationship
becomes much smoother. Fig. 2-b shows an exponential relationship
between average snow depth and average air temperature in the
considered bins, with higher temperatures resulting in lower snow
depth. However, as is seen in Fig. 2-b, since some points deviate from the
hypothetical exponential curve, instead of using the average snowfall in
the bins, their probability was plotted in Fig. 2-c. As depicted, as the air
temperature decreases, the probability of precipitation in the form of
snow increases. Nonetheless, as is seen, this shape is not smooth and no
model can be tted to it. Therefore, using Eqs. (1) and (2), the Propor-
tion of snowfall to total precipitation (rain +Snow Water
Equivalent/SWE) in air temperature intervals of 0.5 ◦C is calculated and
shown in Fig. 2-d. As can be seen, the distribution of the points follows a
very smooth curvy shape, favorable for tting a model to the points, to
be used for estimating snow depth for the days with missing snow depth
data (Pomeroy et al., 1995)
probability(SWE) = SWE(mm)
SWE(mm) + Rainfall(mm)∗100 (1)
SWE(mm) = 0.01 ∗SDcm ∗
ρ
s(2)
SWE represents snow water equivalent in mm, while
ρ
s represents
the density of fresh snow in kg/m3. Since the density of fresh snow is not
measured in the stations, in this research, it is considered 100 kg/m3.
Assuming a density of 100 kg/m3, the depth of 1 cm of snow will equal 1
mm of SWE (Pomeroy et al., 1995).
The following procedure describes how to estimate the snow depth
using the proposed method.
i. Collect daily snow depth, precipitation, and mean air tempera-
ture; This data can be measured and recorded at all meteoro-
logical stations.
ii. Selecting the stations with a signicant period of snow depth
records.
iii. Drawing a sigmoidal curve; For each station, the snow probability
in 0.5 ◦C air temperature bins is calculated using the station’s
observational data and Eqs. (1) and (2). For example, if the snow
depth between −1 and −1.5 ◦C is 100 cm (equivalent to 100 mL
of SWE), and the total height of rain is 300 mm, the probability of
snow (100/(100 +300) ×100) for that bin will be 25%. By
plotting the calculated snowfall probability versus air tempera-
ture bins, a sigmoidal curve like that shown in Fig. 2-d can be
obtained and used to predict the PSTP for any desired air tem-
perature bin.
iv. Fitting the proposed model, as in Hashemireza et al. (2023); in
this research,
v. The DSBE was applied to the PSTP conditioned on air tempera-
ture in 0.5 ◦C bins. The model consists of two logistic regressions.
It includes parameters for 2 centers, 2 rates, and 3 slopes (Lip-
ovetsky, 2010). Hashemireza et al. (2023) showed that the DSBE
model is more exible than the single logistic model with two
turning points, resulting in a better t to the data.
Sp(T) = S0
+SmaxpA+expT−x1
k1−1
+ (1−p)A+expT−x2
k2−1(3)
The equation uses Sp for snow probability and T for mean air tem-
perature (in Celsius). S
0
is the left asymptote of S
p
(the smallest value of
Fig. 3. Fitting the DSBE model to the snow probability data of Ardabil station
(Hashemireza et al., 2023).
F. Hashemireza et al.

Physics and Chemistry of the Earth 134 (2024) 103588
5
S
p
), and S
max
is the right asymptote of S
p
(the most signicant value of
S
p
). The slope factors denoted by k1 and k2 in the equation are constant
values that govern the elevation of the primary and secondary stages,
whereas ×1 and ×2 signify the central points of phases 1 and 2 of the
curve.
Fig. 3 shows the parameters of the DSBE model, and how it ts the
snow probability conditioned on air temperature.
The parameters in Fig. 3 are similar to the parameters of Fig. 2 in
Hashemireza et al. (2023) but they differ in the y-axis. The y-axis in this
Figure corresponds to the snow depth proportion obtained from Eq. (3),
while it represents the snowfall frequency in Fig. 2 of Hashemireza et al.
(2023).
vi. Estimating the probability of snow depth; the DSBE model ob-
tained from step 4 is an air temperature-based model by which it
is possible to estimate the probability of snow depth or SWE as a
variable dependent on average daily air temperature.
vii. Estimating the snow depth; if we multiply the probability of SWE
at any air temperature bin by the total precipitation recorded at
that bin, it is possible to obtain SWE or snow depth as they are
convertible to each other using Eq. (2).
viii. Evaluating the model; the precision of the DSBE model in esti-
mating snowfall was assessed using R2, RRMSE, BIAS, and EF
statistics. These measures are widely used to compare the pre-
dictions of a model with observational data (Moriasi et al., 2007).
Fig. 4. Snow depth estimation owchart.
F. Hashemireza et al.

Physics and Chemistry of the Earth 134 (2024) 103588
6
4.1. Statistical evaluation
The coefcient of determination (R
2
) is one of the most critical
evaluation criteria that shows the relationship between two variables
and is shown in the dimensionless format. The strength of the rela-
tionship between the variables increases as the coefcient of determi-
nation approaches one. RRMSE measures deviation between predicted
and actual values to determine model accuracy, with lower values
indicating higher accuracy (Eq. (4)).
RRMSE =
1
n
n
i
(SDobs −SDest)2

n
i
(SDest)2







(4)
The zero Bias value indicates that the model can perfectly predict the
observed values while positive and negative values indicate over- and
under-estimation of the model, respectively (Eq (5)).
BIAS =1
n
n
i=1
(SDest −SDobs)(5)
The Efciency Coefcient (EF) value, shown in a dimensionless
format, varies from negative innity and one. The negative value of this
coefcient indicates a very low model accuracy in predicting observed
values, and the closer it is to one, the higher the model’s accuracy (Eq.
(6)).
EF =1−
n
i=1
(SDobsi −SDesti)2

n
i=1
(SDobsi −SDobs)2
(6)
In the above equations, SD
obs
and SD
est
are the observed data and pre-
dicted data values, respectively, and n is the amount of data.
The owchart depicted in Fig. 4 provides a comprehensive expla-
nation of the steps involved in estimating the snow depth using the
proposed method. One of the basic steps after snow depth modeling is
the calibration and validation of the model. The proposed model was
calibrated using 70% of the randomly selected data. To validate the
model, the calibrated parameters were used to t it to the remaining
30% of the data. The Leave-One-Out Cross-Validation (LOOC) method
was employed to assess the accuracy of the proposed model in esti-
mating snow depth at stations without available data. This approach
involved tting the DSBE model to a dataset comprising records from
multiple stations, with the exception of the data records associated with
the particular station. N-1 iterations of this process were performed,
with N denoting the number of stations. Each time, the tted model was
used to estimate the amount of snow depth for the station that was
excluded from the analysis. Subsequently, a comparison was made be-
tween the estimated snow depth for the station that was excluded from
the analysis and the observed data of that particular station, employing
the R
2
statistic.
5. Results
5.1. Model calibration and validation
The DSBE model was tted to 70% of the data from 12 selected
stations. Table 2 shows the estimated parameters for each station.
Within Tables 2 and ×1 and ×2 denote the midpoint of the curve
formed in the initial and subsequent stages, respectively. The placement
of the critical value in the geometric transition is determined by A, with
k1 and k2 as slope factors. The parameter x
2
is negative in cases when
one phase is at an air temperature below zero while the other is above
zero. Since k
1
has a higher value compared to k
2
, the changes in the rst
phase are slower than in the second phase of the curve (Hashemireza
et al., 2023).
The model performance needs to be validated after estimating the
parameters of the DSBE model. The reliability and accuracy of the
estimated snow depth are very important due to its wide range of usage.
Thus, evaluating the model’s accuracy is necessary to obtain the ex-
pected results and check whether the model is satisfactory. This stage of
the model test is known as validation. In validation, model outputs are
compared with experimental observations not used in the model
development (30% of data).
As presented in Fig. 5, the lowest and highest RRMSE value for the
calibration period is 0.81 and 1.12, respectively, with an average
RRMSE =0.91, while the lowest and highest R
2
are 0.804 and 0.935,
respectively, with an average equals 0.893. For the validation period,
the lowest and highest RRMSE are 0.88 and 1.22, respectively, and the
lowest and highest R
2
values are 0.647 and 0.913, respectively (average
RRMSE =1.23, and average R
2
=0.849). The results indicate that the
RRMSE and R
2
values of the validation period are not different from
those of the calibration.
5.2. Fitting model to the ratio of snow depth to total precipitation
By tting the DSBE model to the PSTP versus air temperature in each
of the 12 stations, the PSTP at each air temperature bin is estimated. The
correlation coefcient between the PSTP estimated by the DSBE model
(Eq. (3)) is used to evaluate the proximity of the proposed method in
estimating snow depth. Then the observed snow depth was obtained for
the 30% of the data used in the validation period as demonstrated in
Fig. 6.
When compared to the observational data, the tted curve on the
PSTP in Khoy and Saqez stations exhibits the highest R
2
value of 0.99, as
depicted in Fig. 6. The lowest R
2
value is 0.88 for the Dorud station,
where the number of snow depth records is the lowest among the sta-
tions. In other stations, this value is between 0.97 and 0.98, which
suggests a strong compatibility between the DSBE model and the
snowfall probability data of this station.
5.3. Evaluation of the estimated snow depth
In Fig. 7, the snow depth estimated using the DSBE model is
compared to the observed snow depth during the validation period,
which accounts for 30% of the data. The maps in this gure present the
spatial distribution of various measures comparing the estimated values
with observation across the stations.
Fig. 7 shows that the R
2
value between the predicted and the
observed values is between 0.8 and 1 in most of the stations, which
indicates a good correlation between the observed and estimated data. It
is less than 0.8 in the Kamyaran and Dorud stations, which can be due to
the lower number of data records in that station used for the correlation
analysis. The total number of daily data in this station is 7300, of which
only 250 days present snow depth records. Therefore, 30% of the data
used in the validation stage comprises a small number of snow depth
records compared to other stations to determine the correlation coef-
cient. (Fig. 7-a).
Table 2
Estimated parameters of the DSBE model for the calibration period.
Station name K1 k2 p A X1 x2
Khoy 2.533 0.149 0.721 1.012 −0.786 3.524
Ardebil 3.746 1.071 0.425 0.997 −3.133 3.921
Sarab 2.439 0.006 0.660 1.014 −1.245 3.150
Piranshar 0.012 2.299 0.034 0.999 −8.312 2.862
Saqez 1.374 1.516 0.191 1.003 −6.361 2.139
Firuzkoh 1.302 1.529 0.209 1.005 −5.519 2.759
Kamyaran 0.8246 1.051 0.269 1.009 −3.582 1.701
Hamedan 3.236 0.817 0.483 1.002 −2.160 1.922
Arak 2.523 0.018 0.828 1.008 −1.371 2.719
Durod 0.126 2.070 0.401 1.002 −1.117 0.620
Daran 0.010 2.193 0.151 1.003 0.231 0.835
Shahrekord 1.990 0.489 0.864 1.003 −0.831 4.439
F. Hashemireza et al.

Physics and Chemistry of the Earth 134 (2024) 103588
7
Fig. 5. Relationship between the observed and estimated snow depth with the DSBE model for the calibration (70% of the data) and validation (30% of the data)
periods represented by red and black circles distributed along the regression line, respectively. (For interpretation of the references to colour in this gure legend, the
reader is referred to the Web version of this article.)
F. Hashemireza et al.

Physics and Chemistry of the Earth 134 (2024) 103588
8
According to Fig. 7-b, the EF statistics are more signicant than 0.8
in 10 stations, which conrms a good relationship between the esti-
mated and observed snow depth values. The lowest coefcient of
determination is between 0.6 and 0.8 which is related to Dorud and
Kamyaran stations.
Fig. 7-c shows the Bias statistics between the observed and estimated
snow depth. According to the gure, the bias in 11 stations is between
−0.8 and 0.9 mm. However, this value is between −1.4 and −0.9 mm in
Arak station, which shows a slight deviation of predicted from observed
values.
According to Fig. 7-d, in most of the stations (11 stations), the
RRMSE value is between 0.25 and 0.7, indicating a slight difference
Fig. 6. Fitting the DSBE model to the proportion of snowfall to total precipitation versus air temperature in the 12 studied stations, using 30% of the data for
the validation.
F. Hashemireza et al.

Physics and Chemistry of the Earth 134 (2024) 103588
9
Fig. 7. Comparison of the estimated and observed snow depth in the studied stations using a) Coefcient of Determination b) Nash–Sutcliffe model efciency
coefcient c) Bias d) Relative Root Mean Squared Error.
Fig. 8. Comparison of the estimated and the Era5-land snow depth in the studied stations using a) Coefcient of Determination, b) Nash–Sutcliffe model efciency
coefcient, c) Bias, d) Relative Root Mean Squared Error.
F. Hashemireza et al.

Physics and Chemistry of the Earth 134 (2024) 103588
10
between the predicted and observed values, but it is higher (between
0.85 and 0.9) in Kamyaran station.
5.4. Evaluation of Era5-land data
To better evaluate the snow depth estimated with the DSBE model, it
was compared with Era5 snow depth data in each of the 12 studied
stations. For this purpose, the Era5 snow depth data of the nearest grid to
Fig. 9. scatter plots of snow depth estimates by Era5-land and the DSBE model versus daily observed snow depth in the studied stations.
F. Hashemireza et al.

Physics and Chemistry of the Earth 134 (2024) 103588
11
each of the stations were compared with the observed and predicted
snow depth data as demonstrated in Fig. 8.
Fig. 8 shows that the R
2
value between the Era5-land and observa-
tional snow depth data is less than 0.5 in all stations (Fig. 8-a), indicating
a low correlation between Era5-land estimates and observational snow
depth data. Fig. 8-b shows that the EF value is less than −4 in 50% of the
stations and between −4 and −0.1 in the others. The ndings indicate a
limited association between the Era5-land snow depth data and the
recorded snow depth at the studied stations.
As in Fig. 8-c, the bias is higher than 120 mm in 3 stations, between
60 and 120 mm in 6 stations, and between 14 and 60 mm in the other 3
stations. These high biases point to a signicant difference between
Era5-land snow depth estimation and observed snow depth at the sta-
tions. According to Fig. 8-d, the RRMSE value is between 0.6 and 1.0 in 7
of the stations, and between 1.01 and 1.5 in 4 other stations, which is
much higher than that of between observation and estimations provided
by the proposed approach. These high RRMSE values show a signicant
difference between the Era5-land snow depth estimations and observa-
tion at the studied stations.
According to Figs. 7 and 8, it can be concluded that Era5-land snow
depth data is signicantly different from observation, while a strong
agreement was observed between the snow depth estimated by the DSBE
model and the observations in all the stations. In addition to the statis-
tical measures shown in Figs. 7 and 8 for the validation stage, Fig. 9
illustrates the regression analysis established between the observed
snow depth and the snow depth predicted by Era5-land and the DSBE
model. Based on the data presented in Fig. 9, it can be observed that the
snow depth estimated by the DSBE model exhibits a distribution closely
aligned with the 1:1 regression line across all stations. This correspon-
dence suggests a strong correlation between the observed snow depth
and the snow depth estimated using the DSBE model. In contrast, the
distribution of snow depth estimates by Era5-land deviates signicantly
from the 1:1 line. This indicates that the snow depth estimates provided
by Era5-land are considerably higher than the actual observed snow
depth in most stations, with the exception of the Arak and Hamedan
(airport) stations, where it is lower than the observed data. Despite the
regression line closely aligning with the 1:1 line in Arak, Hamedan,
Khoy, and Ardabil stations, the data points remain signicantly distant
from the line, indicating a minimal correlation between the Era5-land
snow depth estimates and observed snow depth.
5.5. Evaluation of the proposed method for predicting snow depth in
stations with no snowfall records
Fig. 6 suggests that the PSTSs of all stations follow approximately the
same sigmoidal pattern. This issue will be better illustrated if the curves
of all 12 stations are overlaid in one graph as presented in Fig. 10. This
gure suggests that it is possible to take the average of the 12 sigmodal
curves and use it to predict snow depth in stations with no snow depth
records. The purpose of constructing such a global model is to use it to
estimate the snow depth in stations with no snowfall data.
To conrm that the constructed global model performs well in esti-
mating snow depth in stations with no snow depth records, the leave-
one-out cross-validation method was used to evaluate this hypothesis.
This cross-validation method was applied to all 12 studied stations and
the results are presented in Fig. 11.
According to Fig. 11 and the corresponding R
2
value computed be-
tween the observed data of a given station not incorporated into the
construction of the global model and the estimated data for that station
by the global model, it can be concluded that, with an average R
2
value
of 0.86, the constructed global model has an acceptable performance in
estimating snow depth in stations with no data.
6. Discussion
Snow depth is one of the critical hydrological variables, particularly
in mountains. As a result of difculties encountered in measuring snow
at climatological stations, especially in remote areas, a signicant
portion of the region remains devoid of snow measurement data.
However, having information about snow depth is one of the most basic
requirements in determining the hydrological cycle of watershed basins.
This study aims to estimate snow depth by tting a DSBE sigmoidal
model. The evaluation of the results involved obtaining the coefcients
of the DSBE model during the calibration stage and estimating the snow
depth, which were then compared against observational and Era5-land
data. The DSBE model accurately estimated the snow depth at the 12
selected stations, with an average R
2
value of 0.97 during validation.
The DSBE model’s estimation of snow depth during the validation stage
shows a minimal deviation from the observational data of 12 stations,
unlike the Era5-land data. The maximum value of Bias and RRMSE of the
DSBE model with observational data in stations is between −1.4 mm and
0.88, respectively, and for Era5-land data, 121 mm and5.57. Also, the
minimum values of R
2
and EF of the DSBE model with observational
data are 0.65 and 0.63 mm, respectively, and for Era5-land data, they
are 0.2 and −42 mm.
For a more in-depth investigation, the snow depth records measured
at all stations, which accounted for 100% of the available data, were
compared to the estimated snow depth values derived from the DSBE
model and Era5-land data. The results show that Era5-land data predicts
the snow depth much higher than the actual value compared to the DSBE
model (Fig. 7). The large positive biases of the Era5-land data observed
herein are compatible with the results obtained by Lei et al. (2022); Q. Li
et al. (2022) for other parts of the world. Lei et al. (2022) showed that
the Era5-land data overestimates snow depth on the Tibetan Plateau,
especially for deep snow. Also, Q. Li et al. (2022)proved that Era5-land
data overpredicted snow depth in the Tianshan Mountains at altitudes
greater than 1000 m.
The DSBE model has performed satisfactorily compared to ERA-5. So
the correlation obtained with the DSBE model is between 0.6 and 0.7 in
the worst station, while the correlation values with ERA-5 data are
0.2–0.25 in the worst case. On the other hand, the difference between
the RRMSE values between the DSBE model and ERA-5 is massive, for
example, in Khoy station, the DSBE model has been able to reduce the
RRMSE by 520%, which indicates the favorable performance of the
Fig. 10. Fitting the DSBE model to the 30% of PSTP data of the stud-
ied stations.
F. Hashemireza et al.

Physics and Chemistry of the Earth 134 (2024) 103588
12
DSBE model compared to ERA-5. These results are similar to the results
of (Daudt et al., 2023; J. Wang et al., 2020; J. W. Yang et al., 2021)
The double Boltz DSBE model is a regression model based on the data
of snow depth and average air temperature data recorded in the synoptic
stations, and its parameters are calculated by tting the model to the
data. Hence, it is unsurprising that the snow depth derived from the
DSBE model exhibits greater proximity to the observed data. Further-
more, the model’s accuracy is signicantly impacted by the quantity and
scale of recorded snow depth data. Moreover, one of the most important
results of this research is the construction of a global model to be used
for estimating snow depth in any location across the entire study area.
The utilization of this global model is applicable for the estimation of
snow depth in stations lacking snow measurement or with inadequate
snow depth records for the tting of the DBSE model to the data.
Fig. 11. The results of the leave-one-out-cross-validation for the studied stations.
F. Hashemireza et al.

Physics and Chemistry of the Earth 134 (2024) 103588
13
7. Conclusion
In this research, we have analyzed the snow depth data in 12 stations
in Iran. In this research, the estimation of snow depth data has been
investigated using the DBSE model, and its performance has been
evaluated with ERA-5 data using R2, EF, Bias, and RRMSE indices.
The comparison of DSBE model and ERA-5 shows that the DSBE
model has a much better performance than ERA-5 and it has been
checked in domestic stations that a very good correlation in DSBE model
is higher than ERA-5 and also this model model that can be installed. It
reduces the error indicators considerably.
Based on the results of this study, it can be concluded that the pro-
posed model is a viable approach for estimating snow depth in remote
areas where snowfall measurements are not available. However, further
investigations are needed to evaluate the accuracy of the proposed
method in estimating snow depth data in other parts of the world. Since
this study has considered a xed snow density value for fresh snow in all
studied stations, to obtain more accurate results, it is suggested to
consider the exact snow density of the snow depth records where
available.
In conducting this research, we faced various limitations, which can
be mentioned as follows.
1. Lack of observation stations in mountains and rainy regions.
2. The absence of a consistent long-term dataset across all examined
stations resulted in varying statistical periods.
3. The presence of bulky gaps in the time series of observation data,
which has lessened the number of stations in this research.
Funding
No funding.
Availability of data and materials
Please contact the corresponding author for data requests.
Code availability
Please contact the corresponding author for code requests.
Ethics approval
Not applicable.
Consent to participate
Not applicable.
Consent for publication
Not applicable.
CRediT authorship contribution statement
Firooze Hashemireza: Software, Writing – original draft. Ahmad
Sharafati: Supervision, Validation, Writing – review & editing. Tayeb
Raziei: Data curation, Writing – review & editing, Conceptualization.
Yusef Kheyruri: Formal analysis, Investigation, Writing – original draft.
Declaration of competing interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgments
The authors would like to reveal their gratitude and appreciation to
the data provider, the Iranian Meteorological Organization.
References
Agbor, M.E., Udo, S.O., Ewona, I.O., Nwokolo, S.C., Ogbulezie, J.C., Amadi, S.O., 2023.
Potential impacts of climate change on global solar radiation and PV output using
the CMIP6 model in West Africa. Cleaner Engineering and Technology 13, 100630.
https://doi.org/10.1016/J.CLET.2023.100630.
Ali, M.H., Popescu, I., Jonoski, A., Solomatine, D.P., 2023. Remote sensed and/or global
datasets for distributed hydrological modelling: a review. Remote Sensing 2023 15
(6), 1642. https://doi.org/10.3390/RS15061642.
Antonijevi´
c, O., Jeli´
c, S., Bajat, B., Kilibarda, M., 2023. Transfer learning approach based
on satellite image time series for the crop classication problem. Journal of Big Data
10 (1), 1–19. https://doi.org/10.1186/S40537-023-00735-2/TABLES/6.
Asadollah, S.B.H.S., Sharafati, A., Saeedi, M., Shahid, S., 2023. Estimation of soil
moisture from remote sensing products using an ensemble machine learning model:
a case study of Lake Urmia Basin, Iran. Earth Science Informatics 17 (1), 385–400.
https://doi.org/10.1007/S12145-023-01172-8/METRICS.
Auer, A.H., Resources, A., 2010. The rain versus snow threshold temperatures.
Weatherwise 27 (February 2015), 3–4. https://doi.org/10.1080/
00431672.1974.9931684.
Baker, J.C.A., Castilho de Souza, D., Kubota, P.Y., Buermann, W., Coelho, C.A.S.,
Andrews, M.B., Gloor, M., Garcia-Carreras, L., Figueroa, S.N., Spracklen, D.V., 2021.
An assessment of land–atmosphere interactions over South America using satellites,
reanalysis, and two global climate models. J. Hydrometeorol. 22 (4), 905–922.
Behroz, S. safari, Habibeh, N., Aliakbar, R., Saeid, J., Iman, B., 2019. Modeling and
spatial analysis of snow depth in Northern Iran. Physical Geography Research
Quarterly 51 (4), 651–671.
Brown, R.D., Mote, P.W., 2009. The response of Northern Hemisphere snow cover to a
changing climate. J. Clim. 22 (8), 2124–2145. https://doi.org/10.1175/
2008JCLI2665.1.
Chen, K., Liu, C., Chen, H., Zhang, H., Li, W., Zou, Z., Shi, Z., 2023. In: RSPrompter:
Learning to Prompt for Remote Sensing Instance Segmentation Based on Visual
Foundation Model. https://doi.org/10.1109/TGRS.2024.3356074.
Currier, W.R., Pug, J., Mazzotti, G., Jonas, T., Deems, J.S., Bormann, K.J., Painter, T.H.,
Hiemstra, C.A., Gelvin, A., Uhlmann, Z., 2019. Comparing aerial lidar observations
with terrestrial lidar and snow-probe transects from NASA’s 2017 SnowEx campaign.
Water Resour. Res. 55 (7), 6285–6294.
Dai, A., 2008. In: Temperature and Pressure Dependence of the Rain-Snow Phase
Transition over Land and Ocean, 35, pp. 1–7. https://doi.org/10.1029/
2008GL033295.
Dai, L., Che, T., 2022. Estimating snow depth or snow water equivalent from space.
Sciences in Cold and Arid Regions 14 (2), 79–90. https://doi.org/10.3724/SP.
J.1226.2022.21046.
Dai, L., Che, T., Ding, Y., 2015. Inter-calibrating SMMR, SSM/I and SSMI/S data to
improve the consistency of snow-depth products in China. Rem. Sens. 7 (6),
7212–7230. https://doi.org/10.3390/rs70607212.
Daudt, R.C., Wulf, H., Hafner, E.D., Bühler, Y., Schindler, K., Wegner, J.D., 2023. Snow
depth estimation at country-scale with high spatial and temporal resolution. ISPRS J.
Photogrammetry Remote Sens. 197, 105–121. https://doi.org/10.1016/J.
ISPRSJPRS.2023.01.017.
Deeb, E.J., Forster, R.R., Kane, D.L., 2011. Monitoring snowpack evolution using
interferometric synthetic aperture radar on the North Slope of Alaska, USA. Int. J.
Rem. Sens. 32 (14), 3985–4003.
D´
ery, S.J., Brown, R.D., 2007. Recent Northern Hemisphere snow cover extent trends
and implications for the snow-albedo feedback. Geophys. Res. Lett. 34 (22) https://
doi.org/10.1029/2007GL031474.
Dimyati, M., Rustanto, A., Ash Shidiq, I.P., Indratmoko, S.Siswanto, Dimyati, R.D.,
Nurlambang, T., Zubair, A., Fakhruddin, A., Siddiq, A., Adhanto, D.H., Maulidina, K.,
Auni, R., 2024. Spatiotemporal relation of satellite-based meteorological to
agricultural drought in the downstream Citarum watershed, Indonesia.
Environmental and Sustainability Indicators 22, 100339. https://doi.org/10.1016/J.
INDIC.2024.100339.
Durand, M., Johnson, J.T., Dechow, J., Tsang, L., Borah, F., Kim, E.J., 2024. Retrieval of
snow water equivalent from dual-frequency radar measurements: using time series
to overcome the need for accurate a priori information. Cryosphere 18 (1), 139–152.
https://doi.org/10.5194/TC-18-139-2024.
Eini, M.R., Massari, C., Piniewski, M., 2023. Satellite-based soil moisture enhances the
reliability of agro-hydrological modeling in large transboundary river basins. Sci.
Total Environ. 873, 162396 https://doi.org/10.1016/J.SCITOTENV.2023.162396.
Gomis-Cebolla, J., Rattayova, V., Salazar-Gal´
an, S., Franc´
es, F., 2023. Evaluation of
ERA5 and ERA5-Land reanalysis precipitation datasets over Spain (1951–2020).
Atmos. Res. 284, 106606 https://doi.org/10.1016/J.ATMOSRES.2023.106606.
Guo, Y., Li, H., Liang, P., Xiong, R., Chaozhong, H., Xu, Y., 2024. Preliminary report of
coseismic surface rupture (part) of Türkiye’s MW7.8 earthquake by remote sensing
F. Hashemireza et al.

Physics and Chemistry of the Earth 134 (2024) 103588
14
interpretation. Earthquake Research Advances 4 (1), 100219. https://doi.org/
10.1016/J.EQREA.2023.100219.
Hashemireza, F., Sharafati, A., Raziei, T., Nazif, S., 2023. A double sigmoidal model for
snow-rain phase separation. J. Hydrol. 617 (PC), 129153 https://doi.org/10.1016/j.
jhydrol.2023.129153.
He, L., Xue, B., Hui, F., Xu, S., Chen, Z., Cheng, X., 2024. Towards daily snow depth
estimation on arctic sea ice during the whole winter season from passive microwave
radiometer data. IEEE Trans. Geosci. Rem. Sens. https://doi.org/10.1109/
TGRS.2024.3358340.
Hern´
andez-Henríquez, M.A., D´
ery, S.J., Derksen, C., 2015. Polar amplication and
elevation-dependence in trends of Northern Hemisphere snow cover extent, 1971-
2014. Environ. Res. Lett. 10 (4), 44010 https://doi.org/10.1088/1748-9326/10/4/
044010.
Horry, M.J., Chakraborty, S., Pradhan, B., Shulka, N., Almazroui, M., 2023. Two-speed
deep-learning ensemble for classication of incremental land-cover satellite image
patches. Earth Systems and Environment 7 (2), 525–540. https://doi.org/10.1007/
S41748-023-00343-3/FIGURES/10.
Hu, Y., Che, T., Dai, L., Zhu, Y., Xiao, L., Deng, J., Li, X., 2022. A long-term daily gridded
snow depth dataset for the Northern Hemisphere from 1980 to 2019 based on
machine learning. Earth Syst. Sci. Data Discuss. (March), 1–33.
Ibrahim, A.H., Molla, D.D., Lohani, T.K., 2022. Performance evaluation of satellite-based
rainfall estimates for hydrological modeling over Bilate river basin, Ethiopia. World
Journal of Engineering 21 (1), 1–15. https://doi.org/10.1108/WJE-03-2022-0106/
FULL/XML.
J¨
a¨
askel¨
ainen, E., Kouki, K., Riihel¨
a, A., 2024. Detecting snowfall events over the arctic
using optical and microwave satellite measurements. Hydrol. Earth Syst. Sci.
Discuss. 1–26. https://doi.org/10.5194/HESS-2023-278.
Jain, H., Dhupper, R., Shrivastava, A., Kumar, D., Kumari, M., 2023. AI-enabled
strategies for climate change adaptation: protecting communities, infrastructure, and
businesses from the impacts of climate change. Computational Urban Science 3 (1),
1–17. https://doi.org/10.1007/S43762-023-00100-2/FIGURES/3.
Jennings, K.S., Winchell, T.S., Livneh, B., Molotch, N.P., 2018. Spatial variation of the
rain-snow temperature threshold across the Northern Hemisphere. Nat. Commun. 9
(1) https://doi.org/10.1038/s41467-018-03629-7.
Jonas, T., Marty, C., Magnusson, J., 2009. Estimating the snow water equivalent from
snow depth measurements in the Swiss Alps. J. Hydrol. 378 (1–2), 161–167. https://
doi.org/10.1016/j.jhydrol.2009.09.021.
Joshi, I.D., Stramski, D., Reynolds, R.A., Robinson, D.H., 2023. Performance assessment
and validation of ocean color sensor-specic algorithms for estimating the
concentration of particulate organic carbon in oceanic surface waters from satellite
observations. Rem. Sens. Environ. 286, 113417 https://doi.org/10.1016/J.
RSE.2022.113417.
Kheyruri, Y., Nikaein, E., Sharafati, A., 2023. Spatial monitoring of meteorological
drought characteristics based on the NASA POWER precipitation product over
various regions of Iran. Environ. Sci. Pollut. Control Ser. 1–22. https://doi.org/
10.1007/S11356-023-25283-3, 2023.
Kheyruri, Y., Sharafati, A., Neshat, A., 2023a. Predicting agricultural drought using
meteorological and ENSO parameters in different regions of Iran based on the LSTM
model. Stoch. Environ. Res. Risk Assess. https://doi.org/10.1007/S00477-023-
02465-6.
Kheyruri, Y., Sharafati, A., Neshat, A., 2023b. The socioeconomic impact of severe
droughts on agricultural lands over different provinces of Iran. Agric. Water Manag.
289 https://doi.org/10.1016/j.agwat.2023.108550.
Lakshmi, V., Le, M.H., Gofn, B.D., Besnier, J., Pham, H.T., Do, H.X., Fang, B.,
Mohammed, I., Bolten, J.D., 2023. Regional analysis of the 2015–16 Lower Mekong
River basin drought using NASA satellite observations. J. Hydrol.: Reg. Stud. 46,
101362 https://doi.org/10.1016/J.EJRH.2023.101362.
Lei, Y., Pan, J., Xiong, C., Jiang, L., Shi, J., 2022. Snow depth and snow cover over the
Tibetan Plateau observed from space in against ERA5: matters of scale. Clim. Dynam.
https://doi.org/10.1007/s00382-022-06376-0.
Li, G., Cheng, L., Pan, Y., Wang, G., Liu, H., Zhu, J., Zhang, B., Ren, H., Wang, X., 2023.
A global gridded ocean salinity dataset with 0.5◦horizontal resolution since 1960 for
the upper 2000 m. Front. Mar. Sci. 10, 1108919 https://doi.org/10.3389/
FMARS.2023.1108919/BIBTEX.
Li, Q., Yang, T., Li, L., 2022. Evaluation of snow depth and snow cover represented by
multiple datasets over the Tianshan Mountains: remote sensing, reanalysis, and
simulation. Int. J. Climatol. 42 (8), 4223–4239. https://doi.org/10.1002/joc.7459.
Li, Y., Chang, X., Yu, K., Wang, S., Li, J., 2019. Estimation of snow depth using
pseudorange and carrier phase observations of GNSS single-frequency signal. GPS
Solut. 23 (4), 1–13. https://doi.org/10.1007/s10291-019-0912-5.
Liang, C., Cheng, B., Xiao, B., Dong, Y., 2023. Unsupervised domain adaptation for
remote sensing image segmentation based on adversarial learning and self-training.
Geosci. Rem. Sens. Lett. IEEE 20. https://doi.org/10.1109/LGRS.2023.3278448.
Lipovetsky, S., 2010. Double logistic curve in regression modeling. J. Appl. Stat. 37 (11),
1785–1793. https://doi.org/10.1080/02664760903093633.
Liu, J., Meucci, A., Liu, Q., Babanin, A.V., Ierodiaconou, D., Xu, X., Young, I.R., 2023.
A high-resolution wave energy assessment of south-east Australia based on a 40-year
hindcast. Renew. Energy 215, 118943. https://doi.org/10.1016/J.
RENENE.2023.118943.
Liu, Y., Li, L., Yang, J., Chen, X., Hao, J., 2017. Estimating snow depth using multi-source
data fusion based on the D-InSAR method and 3DVAR fusion algorithm. Rem. Sens. 9
(11) https://doi.org/10.3390/rs9111195.
Mishra, A.P., Khali, H., Singh, S., Pande, C.B., Singh, R., Chaurasia, S.K., 2023. An
assessment of in-situ water quality parameters and its variation with landsat 8 level 1
surface reectance datasets. Int. J. Environ. Anal. Chem. 103 (18), 6344–6366.
https://doi.org/10.1080/03067319.2021.1954175.
Mishra, K., Garg, R.D., 2023. Assessing variations in land cover-land use and surface
temperature dynamics for Dehradun, India, using multi-time and multi-sensor
landsat data. Environ. Monit. Assess. 195 (3), 1–31. https://doi.org/10.1007/
S10661-023-10945-Z/TABLES/24.
Moghadam, S.V., Sharafati, A., Feizi, H., Marjaie, S.M.S., Asadollah, S.B.H.S., Motta, D.,
2021. An efcient strategy for predicting river dissolved oxygen concentration:
application of deep recurrent neural network model. Environ. Monit. Assess. 193
(12) https://doi.org/10.1007/S10661-021-09586-X.
Moriasi, D.N., Arnold, J.G., Van Liew, M.W., Bingner, R.L., Harmel, R.D., Veith, T.L.,
2007. Model evaluation guidelines for systematic quantication of accuracy in
watershed simulations. Transactions of the ASABE 50 (3), 885–900.
Nie, Y., Li, X., Paletta, Q., Aragon, M., Scott, A., Brandt, A., 2024. Open-source sky image
datasets for solar forecasting with deep learning: a comprehensive survey. Renew.
Sustain. Energy Rev. 189, 113977 https://doi.org/10.1016/J.RSER.2023.113977.
Nielsen-Englyst, P., Høyer, J.L., Kolbe, W.M., Dybkjær, G., Lavergne, T., Tonboe, R.T.,
Skarpalezos, S., Karagali, I., 2023. A combined sea and sea-ice surface temperature
climate dataset of the Arctic, 1982–2021. Rem. Sens. Environ. 284, 113331 https://
doi.org/10.1016/J.RSE.2022.113331.
Paletta, Q., Arbod, G., Lasenby, J., 2023. Omnivision forecasting: combining satellite and
sky images for improved deterministic and probabilistic intra-hour solar energy
predictions. Appl. Energy 336, 120818. https://doi.org/10.1016/J.
APENERGY.2023.120818.
Pande, C.B., Moharir, K.N., Varade, A.M., Abdo, H.G., Mulla, S., Yaseen, Z.M., 2023.
Intertwined impacts of urbanization and land cover change on urban climate and
agriculture in Aurangabad city (MS), India using google earth engine platform.
J. Clean. Prod. 422, 138541 https://doi.org/10.1016/J.JCLEPRO.2023.138541.
Papi, R., Kakroodi, A.A., Soleimani, M., Karami, L., Amiri, F., Alavipanah, S.K., 2022.
Identifying sand and dust storm sources using spatial-temporal analysis of remote
sensing data in Central Iran. Ecol. Inf. 70, 101724 https://doi.org/10.1016/J.
ECOINF.2022.101724.
Paranunzio, R., Marra, F., 2024. Open gridded climate datasets can help investigating the
relation between meteorological anomalies and geomorphic hazards in mountainous
areas. Global Planet. Change 232, 104328. https://doi.org/10.1016/J.
GLOPLACHA.2023.104328.
Pomeroy, J.W., Gray, D.M., Canada, N.H.R.I., 1995. Snowcover accumulation, relocation
and management. National Hydrology Research Institute.
Qian, Y., Gustafson Jr, W.I., Leung, L.R., Ghan, S.J., 2009. Effects of soot-induced snow
albedo change on snowpack and hydrological cycle in western United States based
on Weather Research and Forecasting chemistry and regional climate simulations.
J. Geophys. Res. Atmos. 114 (D3).
Rasmussen, R., Baker, B., Kochendorfer, J., Meyers, T., Landolt, S., Fischer, A.P.,
Black, J., Th´
eriault, J.M., Kucera, P., Gochis, D., Smith, C., Nitu, R., Hall, M.,
Ikeda, K., Gutmann, E., 2012. How well are we measuring snow: the NOAA/FAA/
NCAR winter precipitation test bed. Bull. Am. Meteorol. Soc. 93 (6), 811–829.
https://doi.org/10.1175/BAMS-D-11-00052.1.
Sardana, D., Kumar, P., Rajni, 2024. Inuence of climate variability modes over wind-sea
and swell generated wave energy. Ocean Eng. 291, 116471 https://doi.org/
10.1016/J.OCEANENG.2023.116471.
Shahbazdashti, R., Sharafati, A., Kheyruri, Y., Ghasemzadeh, F., Mohajeri, S.H., 2024.
Enhancing the TRMM precipitation product in diverse regions of Iran through an
intelligent-based post-processing approach. Acta Geophys. 1–16. https://doi.org/
10.1007/S11600-023-01280-5/METRICS.
Tajjour, S., Chandel, S.S., Alotaibi, M.A., Malik, H., Garcia Marquez, F.P.,
Afthanorhan, A., 2023. Short-term solar irradiance forecasting using deep learning
techniques: a comprehensive case study. IEEE Access 11, 119851–119861. https://
doi.org/10.1109/ACCESS.2023.3325292.
Tan, M.L., Armanuos, A.M., Ahmadianfar, I., Demir, V., Heddam, S., Al-Areeq, A.M.,
Abba, S.I., Halder, B., Cagan Kilinc, H., Yaseen, Z.M., 2023. Evaluation of NASA
POWER and ERA5-Land for estimating tropical precipitation and temperature
extremes. J. Hydrol. 624, 129940 https://doi.org/10.1016/J.
JHYDROL.2023.129940.
Tian, S., Guo, H., Xu, W., Zhu, X., Wang, B., Zeng, Q., Mai, Y., Huang, J.J., 2023. Remote
sensing retrieval of inland water quality parameters using Sentinel-2 and multiple
machine learning algorithms. Environ. Sci. Pollut. Control Ser. 30 (7), 18617–18630.
https://doi.org/10.1007/S11356-022-23431-9/METRICS.
Wang, A., Xu, L., Kong, X., 2018. Assessments of the Northern Hemisphere snow cover
response to 1.5 and 2.0 ◦C warming. Earth System Dynamics 9 (2), 865–877. https://
doi.org/10.5194/esd-9-865-2018.
Wang, J., Yuan, Q., Shen, H., Liu, T., Li, T., Yue, L., Shi, X., Zhang, L., 2020. Estimating
snow depth by combining satellite data and ground-based observations over Alaska:
a deep learning approach. J. Hydrol. 585 (February), 124828 https://doi.org/
10.1016/j.jhydrol.2020.124828.
Wu, H., Xu, X., Luo, T., Yang, Y., Xiong, Z., Wang, Y., 2023. Variation and comparison of
cloud cover in MODIS and four reanalysis datasets of ERA-interim, ERA5, MERRA-2
and NCEP. Atmos. Res. 281, 106477 https://doi.org/10.1016/J.
ATMOSRES.2022.106477.
Wu, J., Lee, Z., Goes, J., Gomes, H. do R., Wei, J., 2024. Evaluation of three contrasting
models in estimating primary production from ocean color remote sensing using
long-term time-series data at oceanic and coastal sites. Rem. Sens. Environ. 302,
113983 https://doi.org/10.1016/J.RSE.2023.113983.
Xiao, J., Aggarwal, A.K., Rage, U.K., Katiyar, V., Avtar, R., 2023. Deep learning-based
spatiotemporal fusion of unmanned aerial vehicle and satellite reectance images for
crop monitoring. IEEE Access 11, 85600–85614. https://doi.org/10.1109/
ACCESS.2023.3297513.
Yang, J.W., Jiang, L.M., Lemmetyinen, J., Pan, J.M., Luojus, K., Takala, M., 2021.
Improving snow depth estimation by coupling HUT-optimized effective snow grain
F. Hashemireza et al.

Physics and Chemistry of the Earth 134 (2024) 103588
15
size parameters with the random forest approach. Rem. Sens. Environ. 264, 112630
https://doi.org/10.1016/J.RSE.2021.112630.
Yang, Z., García Medina, G., Neary, V.S., Ahn, S., Kilcher, L., Bharath, A., 2023. Multi-
decade high-resolution regional hindcasts for wave energy resource characterization
in U.S. coastal waters. Renew. Energy 212, 803–817. https://doi.org/10.1016/J.
RENENE.2023.03.100.
Zhao, S., Luo, Y., Zhang, T., Guo, W., Zhang, Z., 2023. A domain specic knowledge
extraction transformer method for multisource satellite-borne SAR images ship
detection. ISPRS J. Photogrammetry Remote Sens. 198, 16–29. https://doi.org/
10.1016/J.ISPRSJPRS.2023.02.011.
Zheng, N., Chai, H., Chen, L., Ma, Y., Tian, X., 2023. Snow depth retrieval by using robust
estimation algorithm to perform multi-SNR and multi-system fusion in GNSS-IR.
Adv. Space Res. 71 (3), 1525–1542. https://doi.org/10.1016/J.ASR.2022.10.014.
F. Hashemireza et al.