Analysis of Snow Cover in the Sibillini Mountains in Central Italy

Abstract

Research on solid precipitation and snow cover, especially in mountainous areas, suffers
from problems related to the lack of on-site observations and the low reliability of measurements,
which is often due to instruments that are not suitable for the environmental conditions. In this
context, the study area is the Monti Sibillini National Park, and it is no exception, as it is a mountainous
area located in central Italy, where the measurements are scarce and fragmented. The purpose of this
research is to provide a characterization of the snow cover with regard to maximum annual snow
depth, average snow depth during the snowy period, and days with snow cover on the ground in
the Monti Sibillini National Park area, by means of ground weather stations, and also analyzing
any trends over the last 30 years. For this research, in order to obtain reliable snow cover data,
only data from weather stations equipped with a sonar system and manual weather stations, where
the surveyor goes to the site each morning and checks the thickness of the snowpack and records,
it were collected. The data were collected from 1 November to 30 April each year for 30 years,
from 1991 to 2020; six weather stations were taken into account, while four more were added as
of 1 January 2010. The longer period was used to assess possible ongoing trends, which proved to
be very heterogeneous in the results, predominantly negative in the case of days with snow cover
on the ground, while trends were predominantly positive for maximum annual snow depth and
distributed between positive and negative for the average annual snow depth. The shorter period,
2010–2022, on the other hand, ensured the presence of a larger number of weather stations and was
used to assess the correlation and presence of clusters between the various weather stations and,
consequently, in the study area. Furthermore, in this way, an up-to-date nivometric classification
of the study area was obtained (in terms of days with snow on the ground, maximum height of
snowpack, and average height of snowpack), filling a gap where there had been no nivometric study
in the aforementioned area. The interpolations were processed using geostatistical techniques such as
co-kriging with altitude as an independent variable, allowing fairly precise spatialization, analyzing
the results of cross-validation. This analysis could be a useful tool for hydrological modeling of the
area, as well as having a clear use related to tourism and vegetation, which is extremely influenced
by the nivometric variables in its phenology. In addition, this analysis could also be considered a
starting point for the calibration of more recent satellite products dedicated to snow cover detection,
in order to further improve the compiled climate characterization.

Full text

Citation: Gentilucci, M.; Catorci, A.;
Panichella, T.; Moscatelli, S.; Hamed,
Y.; Missaoui, R.; Pambianchi, G.
Analysis of Snow Cover in the
Sibillini Mountains in Central Italy.
Climate 2023,11, 72. https://doi.org/
10.3390/cli11030072
Academic Editor: Nir Y. Krakauer
Received: 28 February 2023
Revised: 15 March 2023
Accepted: 17 March 2023
Published: 19 March 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
climate
Article
Analysis of Snow Cover in the Sibillini Mountains in Central Italy
Matteo Gentilucci 1, * , Andrea Catorci 2, Tiziana Panichella 2, Sara Moscatelli 2, Younes Hamed 3,4,
Rim Missaoui 3,5 and Gilberto Pambianchi 1
1School of Science and Technology, Geology Division, University of Camerino, 62032 Camerino, Italy
2School of Biosciences and Veterniary Medicine, University of Camerino, 62032 Camerino, Italy
3Department of Earth Sciences, Laboratory for the Application of Materials to the Environment,
Water and Energy (LAM3E), University of Gafsa, Gafsa 2112, Tunisia
4Department of Earth and Atmospheric Sciences, University of Houston, Science and Research Building 1,
3507 Cullen Blvd, Room 312, Houston, TX 77204, USA
5Higher Institute of the Sciences and Techniques of Waters of Gabes (ISSTEG), Department of Water Sciences,
University of Gabes, Gabes 6072, Tunisia
*Correspondence: matteo.gentilucci@unicam.it; Tel.: +39-3474100295
Abstract:
Research on solid precipitation and snow cover, especially in mountainous areas, suffers
from problems related to the lack of on-site observations and the low reliability of measurements,
which is often due to instruments that are not suitable for the environmental conditions. In this
context, the study area is the Monti Sibillini National Park, and it is no exception, as it is a mountainous
area located in central Italy, where the measurements are scarce and fragmented. The purpose of this
research is to provide a characterization of the snow cover with regard to maximum annual snow
depth, average snow depth during the snowy period, and days with snow cover on the ground in
the Monti Sibillini National Park area, by means of ground weather stations, and also analyzing
any trends over the last 30 years. For this research, in order to obtain reliable snow cover data,
only data from weather stations equipped with a sonar system and manual weather stations, where
the surveyor goes to the site each morning and checks the thickness of the snowpack and records,
it were collected. The data were collected from 1 November to 30 April each year for 30 years,
from 1991 to 2020; six weather stations were taken into account, while four more were added as
of
1 January 2010
. The longer period was used to assess possible ongoing trends, which proved to
be very heterogeneous in the results, predominantly negative in the case of days with snow cover
on the ground, while trends were predominantly positive for maximum annual snow depth and
distributed between positive and negative for the average annual snow depth. The shorter period,
2010–2022, on the other hand, ensured the presence of a larger number of weather stations and was
used to assess the correlation and presence of clusters between the various weather stations and,
consequently, in the study area. Furthermore, in this way, an up-to-date nivometric classification
of the study area was obtained (in terms of days with snow on the ground, maximum height of
snowpack, and average height of snowpack), filling a gap where there had been no nivometric study
in the aforementioned area. The interpolations were processed using geostatistical techniques such as
co-kriging with altitude as an independent variable, allowing fairly precise spatialization, analyzing
the results of cross-validation. This analysis could be a useful tool for hydrological modeling of the
area, as well as having a clear use related to tourism and vegetation, which is extremely influenced
by the nivometric variables in its phenology. In addition, this analysis could also be considered a
starting point for the calibration of more recent satellite products dedicated to snow cover detection,
in order to further improve the compiled climate characterization.
Keywords: snow cover; snow depth; co-kriging; climate; snow pack
Climate 2023,11, 72. https://doi.org/10.3390/cli11030072 https://www.mdpi.com/journal/climate

Climate 2023,11, 72 2 of 17
1. Introduction
1.1. Aim of the Study and State of the Art
Snow cover is a variable that has an important influence on vegetation, the hydro-
logical regime, and slope stability, but also on the tourism of an area. Vegetation depends
strongly, in certain areas and at certain altitudes, on the melting of the snow pack, which
enables the start of the growing season and has a great influence on the germination of both
forest species and fruit plants [
1
–
3
]. Similarly, snow cover affects the hydrological cycle,
so much so that it is extremely important for hydrological modeling and water supply,
which is reduced due to global warming. This causes early snowmelt, resulting in more
frequent winter floods and summer droughts [
4
,
5
]. The early melting of snow cover is
also detrimental to slope stability, as shown by a piece of recent research in Japan, which
showed that an increasing snow cover improves the safety factor and consequently reduces
the landslide movement, especially if superficial and small in size [
6
]. Therefore, it was
pointed out that the reduction in snow cover due to global warming is very damaging to
the area and even more so if one considers the decrease in winter tourism, which in areas
such as the study area, represents an important source of income [
7
]. In this context, it
is essential to understand the trends taking place, both in terms of the days with snow
cover on the ground and in terms of the maximum and average snow depth, for a dual
purpose: on the one hand, to understand the processes that are underway, and on the other,
to mitigate the effects of climate change. The evaluation of snow cover trends is fundamen-
tal to assessing the effect of global warming on this important variable. There are many
analyses for various places on Earth, but very often, they make use of satellite products
that are not always calibrated and reliable, especially with regard to quantities, although in
some cases, distinctions can be made if there are continuous snow cover surveys, such as
in the European Alps [
8
,
9
]. In some areas such as the one in our study, which considers
a small portion of the Apennine chain in central Italy, no detailed or trend studies have
been carried out to define a snow cover regime. Snow cover data are often subject to rather
large gaps, in some cases recorded manually and only in rare cases automatically with
snow measuring weather stations, so that data reconstructions are often necessary [10,11].
In addition, satellite survey data are not always reliable, both in terms of quantity and in
terms of the presence or absence of the snow event, so major calibrations with weather
stations are necessary, which do not always lead to acceptable results [
12
–
14
]. In particular,
products such as IMERG, MERRA-2, or ERA sometimes show a certain underestimation of
the snowpack, which makes these instruments unreliable for the purposes of a detailed
analysis of snow depths [
15
,
16
]. Similarly, it is also complex for heated rain gauges to
be able to count the snow water equivalent (SWE), since there are interactions with the
wind that can generate underestimates in quantity when not properly shielded by special
devices [
17
–
19
]. Precisely in relation to the possibility of snowfall being blown away by the
wind, there are studies evaluating the preferential accumulation of wind-borne snow in
mountain or glacial environments [
20
]. Because of these problems in accurately counting
snow, recent efforts are being made to create models that can simulate snow cover and in
some cases, predict it in relation to other climatic variables [
21
]. Statistical and geostatistical
techniques are also used to predict the distribution of snow cover over an area from a
few recorded points of data [
22
,
23
]. The aim of this research is to define a current climate
characterization of snow cover by generating interpolations that can quantify the average
snow cover, maximum snow cover, and days with snow cover on the ground, also by
evaluating possible clusters of weather stations resulting from their geographical location
in relation to local atmospheric dynamics. At the same time, in order to test the presence
of a trend over the last 30 years in order to understand the evolution of snow variables
in the study area, an area, that of the Monti Sibillini National Park, which has never been
analyzed before from this point of view, has been chosen for this study. Snow cover is very
important but it is also complex, both to detect and to study, and because of this, there are
still too many areas that are periodically snow-covered, but are not adequately analyzed in
terms of a detailed climatic characterization.

Climate 2023,11, 72 3 of 17
1.2. Geographical Framework
Central Italy is bordered by two seas, the Tyrrhenian Sea and the Adriatic Sea, which
are the arms of the Mediterranean Sea; however, depending on their size, they influence
the climate of the inland areas to a greater or lesser extent. The Monti Sibillini National
Park is located between two Italian regions, Marche and Umbria, and its territory consists
of sixteen municipalities belonging to four different provinces. The extent of the study area
is approximately 697 km
2
, which includes numerous mountains above 2000 m, the highest
of which is Monte Vettore at 2476 m, where the average altitude of the area is 1173 m a.s.l.
(Figure 1). The park is the source of four main rivers, including the Aso, the Tenna, and the
Fiastrone, which flow into the Adriatic Sea to the east, and the Nera, which flows into the
Tyrrhenian Sea, as well as numerous other minor watercourses.
Climate 2023, 10, x FOR PEER REVIEW 3 of 18
area, that of the Monti Sibillini National Park, which has never been analyzed before from
this point of view, has been chosen for this study. Snow cover is very important but it is
also complex, both to detect and to study, and because of this, there are still too many
areas that are periodically snow-covered, but are not adequately analyzed in terms of a
detailed climatic characterization.
1.2. Geographical Framework
Central Italy is bordered by two seas, the Tyrrhenian Sea and the Adriatic Sea, which
are the arms of the Mediterranean Sea; however, depending on their size, they influence
the climate of the inland areas to a greater or lesser extent. The Monti Sibillini National
Park is located between two Italian regions, Marche and Umbria, and its territory consists
of sixteen municipalities belonging to four different provinces. The extent of the study
area is approximately 697 km2, which includes numerous mountains above 2000 m, the
highest of which is Monte Vettore at 2476 m, where the average altitude of the area is 1173
m a.s.l. (Figure 1). The park is the source of four main rivers, including the Aso, the Ten-
na, and the Fiastrone, which flow into the Adriatic Sea to the east, and the Nera, which
flows into the Tyrrhenian Sea, as well as numerous other minor watercourses.
Figure 1. Map of the study area and positioning of weather stations.
2. Materials and Methods
Figure 1. Map of the study area and positioning of weather stations.

Climate 2023,11, 72 4 of 17
2. Materials and Methods
The snow cover data were collected from two different databases, that of the Func-
tional Multiple Risk Centre of the Civil Protection of the Marche Region and that of the
METEOMONT service, which are responsible for monitoring the snowpack and avalanche
risk in Italy. Ten weather stations were considered for the period 2010–2022, while for
the period 1991–2020, six stations were available in the area (Table 1). In particular, the
4 stations from the Functional Multiple Risk Centre (Monte Prata, Monte Bove, Pintura
di Bolognola, and Sassotetto) are equipped with a sonar that measures the snow depth
on the ground every 30 min, while the remaining 6 weather stations are manual weather
stations, where the surveyor goes to the site and by means of a graduated rod notes the
measurement once a day. With these two detection methods, the measurement errors are
significantly reduced compared to other methods such as the heated rain gauge, which is
exposed to wind problems, especially in mountain environments.
Table 1. Name
, name of the weather stations,
Long.
, longitude,
Lat.
, latitude,
Alt.
, altitude, presence
in the period 1991–2020, presence in the period 2010–2022.
Name Alt. Lon. Lat. 1991–2020 2010–2022
Colle 1036 13.30 42.84 X X
Forca di Gualdo 1496 13.19 42.86 X X
La Valletta 1352 13.24 42.99 X X
Monte Bicco 1450 13.16 42.92 X X
Monte Bove 1917 13.19 42.91 X
Monte Prata 1813 13.21 42.87 X
Parco Guarnieri 980 13.33 42.90 X X
Pintura di Bolognola 1360 13.24 42.99 X
Rifugio Perugia 1500 13.18 42.77 X X
Sassotetto 1365 13.24 43.01 X
Data were collected for each year from the beginning of November to the end of
April and were evaluated on both a monthly and annual scale. The variables of interest
for the snowpack were identified in 3 main ones: days with snow cover on the ground,
average snow depth, and maximum snow depth. Concerning days with snow cover on
the ground, days with snow on the ground were counted for each calendar year, while
for average snow depths, an average was taken for each year of all daily values, even
those without snow on the ground. Finally, the maximum snow depth in the interval
between November and April was isolated for each year. As far as quality control is
concerned, gross error check was put into practice, as the only error that the two weather
station detection systems can make is in typing, as well as the assessment of internal
consistency with melt rates not exceeding the calculated threshold value per day, which
can only occur if a zero is mistakenly entered in place of the missing data. Therefore, daily
snowfall values of more than 250 cm and melts of more than 50 cm per day, which were
assessed as statistically impossible for the study area, were eliminated, and of course, they
were always verified with neighboring weather stations. Homogenization was conducted
using the standard normal homogeneity test (SNHT) test; however, it resulted in null
hypotheses, which is evidence that the weather stations had no perturbations that could
cause inhomogeneity in the analyzed time series. In this context, it is very interesting to
evaluate the possible correlation of weather stations in order to understand which areas
are homogeneous and to prepare spatial procedures for validating data in the future, in
cases of more uncertain detections. Therefore, the first of all the correlations between
the various weather stations in the period 2010–2022 was evaluated using two methods,
Pearson’s and the Kendall tau, both at an alpha significance level of 0.05. On the other

Climate 2023,11, 72 5 of 17
hand, agglomerative hierarchical clustering (AHC) made it possible to identify preferential
associations between the various mountain weather stations and was performed using the
statistical software XL Stat. The AHC works with dissimilarities, and one of the products
is the dendrogram, which shows the progressive grouping of data based on similarity
and distance; two objects that minimize a certain agglomeration criterion when grouped
together are grouped together, thus creating a class that includes these
two objects
, and
this is conducted until the groups defined on the basis of the agglomeration criterion are
defined. In this case, Kendall’s tau method was used for similarity assessment due to its
robustness against possible outliers. For both the correlation calculation and the AHC, daily
snow cover data were used. The weather stations from 1991 to 2020 were mainly used for
trend significance analysis, evaluating them using the Mann–Kendall test. The purpose of
the Mann–Kendall (MK) test is to statistically assess whether there is a monotonic upward
trend, that is, the variable studied increases, or a downward trend, that is, the variable
studied decreases over time. MK tests whether to reject the null hypothesis and accept
the alternative hypothesis, where hypothesis H
0
states that no monotonic trend is present,
while in the case of hypothesis Hathere is a monotonic trend.
signTi−Tj=


1i f Ti−Tj>0
0i f Ti−Tj=0
−1i f Ti−Tj<0


(1)
This tells us the difference between the measurements at time iand j, which are
positive, negative, or zero.
Ti=previous data
Tj=following data
S=∑n−1
k=1∑n
j=k+1signTi−Tj(2)
The sum of these results determines the Svalue and this value can be entered into
the Z test.
Z=
S−1
√VAR(S)i f S >0
0i f S =0
S−1
√VAR(S)i f S <0
(3)
The variance of Sis calculated using the following equation:
VAR(S)=1
18 hn(n−1)(2n+5)−∑g
i=1tptp−12tp+5i(4)
g=numb er o f ti des grou ps
tp=numb er o f observati ons in t he p-th grou p
Sen’s test assesses the true slope of a trend line only if the trend can be assumed to be
linear of the following form:
f(t)=Qt +B(5)
Q=slope o f the line
B=constant
t=time series of data
Qi=xj−xk
j−k(6)
xjand xkare data values at time jand k, respectively.
Finally, geostatistical interpolations were required to obtain a spatialization of the
point data functional to a characterization of the snow cover variables identified. Given the
good correlation between snow cover and altitude, the latter was chosen as the independent

Climate 2023,11, 72 6 of 17
variable. In particular, ordinary co-kriging with altitude as an independent variable was
used, as the analysis of statistical indices showed better values than methods based on
geostatistical interpolation alone, without a correlated independent variable.
In this case, ordinary co-kriging (OCK) was used instead of simple co-kriging, as
the assumption that the mean is known over the entire area being interpolated cannot
be considered correct, due to the non-pervasive coverage of the area because of the low
number of weather stations present.
ZOCK (u)=∑n1(u)
α1=1λOCK
α1(u)Z1(uα1)+∑n2(u)
α2=1λOCK
α2(u)Z1(uα2)(7)
Z(u)=primary variable
uα1=location α1
uα2=location α2
λα=kriging weight for the αprimary data sample
In order to be able to assess the goodness of an interpolative method, the cross-validation
procedure with the one-leave-out method was used, which resulted in
four statistical
indices:
mean standardized error (MSE), root mean square error standardized (RMSSE), root mean
square error (RMSE), and average standard error (ASE) [24].
Root mean square error (RMSE): This is the standard deviation between observed
and predicted values: t. This statistical index enables an assessment of the prediction
errors for different weather stations. However, RMSE is not an absolute statistical
index, since it is impossible to compare different variables with the RMSE. However, it
can be useful to compare within the same data set. The value of RMSE should be the
smallest possible and similar to the ASE (average standard error). In this way, when it is
predicting a value at a point without observation points, it has only the ASE to assess
the uncertainty of the prediction.
s∑n
i=1[ˆ
Z(si)−z(si)]2
n(8)
ˆ
z(si)=estimated value
z(si)=observed value
n=sample size
Average standard error (ASE): This statistical tool is known to be similar to the stan-
dard deviation from the mean and is used to estimate the standard deviation of a sampling
distribution. The ASE is an estimator of the bias of the RMSE (i.e., the standard deviation
of the estimation error). A value close to zero and similar to RMSE represents a very low
error in the estimation of the variability of the sampling distribution.
r∑n
i=1ˆ
σ2(si)
n(9)
ˆ
σ2=variance
Mean standardized error (MSE): This is similar to the mean error in that it calculates
the difference between measured and predicted values; however, MSE values are not related
to single variables but can be used to compare different variables. The standardization
procedure leads a variable with mean of xand variance
ˆ
σ2
, to another with mean of zero
and variance equal to 1, in order to allow comparison between different variables. The
mean standardized error is represented by the ratio between the mean absolute error and
the standard deviation of the estimation error.
∑n
i=1[ˆ
ˆ
Z(si)−z(si)]/ˆ
σ(si)
n(10)

Climate 2023,11, 72 7 of 17
ˆ
σ(si)=standard deviation
Root mean square standardized error (RMSSE): The RMSSE enables the assessment of
the goodness of the prediction models; it is desirable to have a value close to 1. If the value
of RMSSE is less than 1, the variability is overestimated; otherwise, it is underestimated.
This is a dimensionless statistical tool, independent from the considered variable. It is the
most significant instrument to evaluate the interpolative model with other variables.
s∑n
i=1[ˆ
Z(si)−z(si)/ˆ
σ(si)]2
n(11)
3. Results
3.1. Correlation of Snow between Different Weather Stations
In order to obtain a good snow characterization of an area, it is necessary to under-
stand the correlation and presence of possible clusters, as the local atmospheric dynamics
are greatly influenced by the topography, which inevitably shields certain air masses,
creating differential snow depth even in apparently homogeneous areas. The correlation
was tested using Pearson’s and Kendall’s tau methods for the period 2010–2022 for
daily snow depths data on the ground, as the data are almost complete for the entire
period and all weather stations analyzed are present at the same time (Tables 2and 3).
The reason for using two methods to assess the correlation is that they provide a better
characterization of the time series analyzed, as the Pearson correlation, being based on
the mean, is rather sensitive to outliers.
Table 2.
Correlation matrix performed with Pearson’s method between weather stations for daily
snow depth data; the stations with a significant 95% correlation between them are in bold.
Name M. Prata F. di
Gualdo M. Bove M. Bicco P. di
Bolognola La Valletta Sassotetto Rif.
Perugia P. Guarnieri Colle
M. Prata 1.00 0.53 0.83 0.80 0.17 0.00 0.14 0.55 −0.06 −0.05
F. di Gualdo 0.53 1.00 0.73 0.70 0.39 0.44 0.44 0.66 0.02 0.05
M. Bove 0.83 0.73 1.00 0.82 0.32 0.23 0.24 0.59 −0.09 −0.08
M. Bicco 0.80 0.70 0.82 1.00 0.00 0.01 0.11 0.24 −0.32 −0.34
P. di Bolognola 0.17 0.39 0.32 0.00 1.00 0.86 0.68 0.53 0.76 0.78
La Valletta 0.00 0.44 0.23 0.01 0.86 1.00 0.59 0.52 0.74 0.76
Sassotetto 0.14 0.44 0.24 0.11 0.68 0.59 1.00 0.26 0.41 0.45
Rif. Perugia 0.55 0.66 0.59 0.24 0.53 0.52 0.26 1.00 0.19 0.25
P. Guarnieri −0.06 0.02 −0.09 −0.32 0.76 0.74 0.41 0.19 1.00 0.96
Colle −0.05 0.05 −0.08 −0.34 0.78 0.76 0.45 0.25 0.96 1.00
Table 3.
Correlation matrix performed with Kendall’s tau method between weather stations for daily
snow depth data; the stations with a significant 95% correlation between them are in bold.
Name M. Prata F. di
Gualdo M. Bove M. Bicco P. di
Bolognola La Valletta Sassotetto Rif.
Perugia P. Guarnieri Colle
M. Prata 1.00 0.33 0.62 0.61 0.16 0.02 0.21 0.31 0.04 0.00
F. di Gualdo 0.33 1.00 0.52 0.51 0.29 0.38 0.32 0.41 0.11 0.12
M. Bove 0.62 0.52 1.00 0.63 0.26 0.19 0.32 0.34 −0.05 −0.05
M. Bicco 0.61 0.51 0.63 1.00 0.08 0.09 0.20 0.16 −0.16 −0.18
P. di Bolognola 0.16 0.29 0.26 0.08 1.00 0.64 0.67 0.35 0.51 0.55
La Valletta 0.02 0.38 0.19 0.09 0.64 1.00 0.67 0.36 0.45 0.50
Sassotetto 0.21 0.32 0.32 0.20 0.67 0.67 1.00 0.34 0.45 0.48
Rif. Perugia 0.31 0.41 0.34 0.16 0.35 0.36 0.34 1.00 0.13 0.20
P. Guarnieri 0.04 0.11 −0.05 −0.16 0.51 0.45 0.45 0.13 1.00 0.80
Colle 0.00 0.12 −0.05 −0.18 0.55 0.50 0.48 0.20 0.80 1.00

Climate 2023,11, 72 8 of 17
Agglomerative hierarchical clustering was crucial in order to be able to identify the
associations between different weather stations regarding snow depths over the period
2010–2022. In this first analysis, it is interesting to note that only the closest weather
stations are similar to each other, especially those that occupy the same slopes. This is clear
evidence of the influence of topography on local atmospheric dynamics (Figure 2). Daily
ground snow data were used to evaluate agglomerative hierarchical clustering in order
to identify whether there may be clusters of weather stations that show similar trends in
ground snow cover and consequently are exposed to the same atmospheric dynamics. The
first group includes Forca di Gualdo, Monte Bicco, Monte Bove, and Monte Prata, while
the
second group
includes Colle, La Valletta, Parco Guarnieri, Pintura di Bolognola, and
Sassotetto, while Rifugio Perugia is the only weather station facing the Tyrrhenian slope in
its own group (Figure 2).
Climate 2023, 10, x FOR PEER REVIEW 8 of 18
Agglomerative hierarchical clustering was crucial in order to be able to identify the
associations between different weather stations regarding snow depths over the period
2010–2022. In this first analysis, it is interesting to note that only the closest weather sta-
tions are similar to each other, especially those that occupy the same slopes. This is clear
evidence of the influence of topography on local atmospheric dynamics (Figure 2). Daily
ground snow data were used to evaluate agglomerative hierarchical clustering in order to
identify whether there may be clusters of weather stations that show similar trends in
ground snow cover and consequently are exposed to the same atmospheric dynamics.
The first group includes Forca di Gualdo, Monte Bicco, Monte Bove, and Monte Prata,
while the second group includes Colle, La Valletta, Parco Guarnieri, Pintura di Bolognola,
and Sassotetto, while Rifugio Perugia is the only weather station facing the Tyrrhenian
slope in its own group (Figure 2).
Figure 2. Agglomerative hierarchical clustering based on daily snow depth data from 2010 to 2022.
3.2. Trend Test for the Period 1991–2020
Trend analysis is the fundamental tool for answering the question of whether a cli-
mate change is taking place for the snow cover variable, in this case over the 30-year pe-
riod 1991–2020, and whether it is significant. The trend analysis tests were performed
over the 30-year reference period 1991–2020 in both annual and monthly steps; however,
Figure 2. Agglomerative hierarchical clustering based on daily snow depth data from 2010 to 2022.
3.2. Trend Test for the Period 1991–2020
Trend analysis is the fundamental tool for answering the question of whether a climate
change is taking place for the snow cover variable, in this case over the 30-year period
1991–2020, and whether it is significant. The trend analysis tests were performed over
the 30-year reference period 1991–2020 in both annual and monthly steps; however, it
was decided for reasons of practicality to show only the annual analysis, also because
the monthly analysis has similar results. In particular, it was observed that there are no
significant trends in the average snow depths, in the maximums snow depths, or in the

Climate 2023,11, 72 9 of 17
days with persistent snow on the ground. The trend shown in the graphs is decreasing
for some weather stations, while for others it is increasing, although the null hypothesis
cannot be discarded, as it shows a lack of 95% significance in the trend (Figures 3–5). The
trend line was derived through the Sen slope estimator.
Climate 2023, 10, x FOR PEER REVIEW 9 of 18
it was decided for reasons of practicality to show only the annual analysis, also because
the monthly analysis has similar results. In particular, it was observed that there are no
significant trends in the average snow depths, in the maximums snow depths, or in the
days with persistent snow on the ground. The trend shown in the graphs is decreasing
for some weather stations, while for others it is increasing, although the null hypothesis
cannot be discarded, as it shows a lack of 95% significance in the trend.(Figures 3–5). The
trend line was derived through the Sen slope estimator.
(a) (b)
(c) (d)
(e) (f)
0
10
20
30
40
50
60
70
80
90
100
1995 2000 2005 2010 2015 2020
cm
years
LA VALLETTA (1352 m)
0
20
40
60
80
100
120
1995 2000 2005 2010 2015 2020
cm
years
MONTE BICCO (1450 m)
0
10
20
30
40
50
60
70
80
90
1995 2000 2005 2010 2015 2020
cm
years
FORCA DI GUALDO (1496 m)
0
5
10
15
20
25
30
35
40
45
1995 2000 2005 2010 2015 2020
cm
years
PARCO GUARNIERI (980 m)
0
5
10
15
20
25
30
35
40
45
1995 2000 2005 2010 2015 2020
cm
years
COLLE (1036 m)
0
10
20
30
40
50
60
70
80
90
1995 2000 2005 2010 2015 2020
cm
years
RIFUGIO PERUGIA (1500 m)
Figure 3.
Trend of average annual snow depths from 1991 to 2020, in black the trend line, for the
weather stations: (
a
) La Valletta, (
b
) Monte Bicco, (
c
) Forca di Gualdo, (
d
) Parco Guarnieri, (
e
) Colle,
(f) Rifugio Perugia.

Climate 2023,11, 72 10 of 17
Climate 2023, 10, x FOR PEER REVIEW 10 of 18
Figure 3. Trend of average annual snow depths from 1991 to 2020, in black the trend line, for the
weather stations: (a) La Valletta, (b) Monte Bicco, (c) Forca di Gualdo, (d) Parco Guarnieri, (e) Colle,
(f) Rifugio Perugia .
The annual average of snow on the ground in the period from 1 November to 30
April each year shows a decrease for four of the six stations, although Colle and Parco
Guarnieri show an increasing trend. Colle and Parco Guarnieri are two very closely re-
lated stations that show exactly opposite trends to the other weather stations (Figure 3).
(a) (b)
(c) (d)
(e) (f)
0
50
100
150
200
250
1995 2000 2005 2010 2015 2020 2025
cm
years
LA VALLETTA (1352 m)
0
50
100
150
200
250
1995 2000 2005 2010 2015 2020 2025
cm
years
MONTE BICCO (1450 m)
20
40
60
80
100
120
140
160
1995 2000 2005 2010 2015 2020 2025
cm
years
FORCA DI GUALDO (1496 m)
0
20
40
60
80
100
120
140
160
180
200
1995 2000 2005 2010 2015 2020 2025
cm
years
PARCO GUARNIERI (980 m)
0
20
40
60
80
100
120
1995 2000 2005 2010 2015 2020 2025
cm
years
COLLE (1036 m)
20
40
60
80
100
120
140
160
1995 2000 2005 2010 2015 2020 2025
cm
years
RIFUGIO PERUGIA (1500 m)
Figure 4.
Trend of maximum annual snow depths from 1991 to 2020; the trend line is in black, for the
weather stations: (
a
) La Valletta, (
b
) Monte Bicco, (
c
) Forca di Gualdo, (
d
) Parco Guarnieri, (
e
) Colle,
(f) Rifugio Perugia.

Climate 2023,11, 72 11 of 17
Climate 2023, 10, x FOR PEER REVIEW 11 of 18
Figure 4. Trend of maximum annual snow depths from 1991 to 2020; the trend line is in black, for
the weather stations: (a) La Valletta, (b) Monte Bicco, (c) Forca di Gualdo, (d) Parco Guarnieri, (e)
Colle, (f) Rifugio Perugia.
Again, the trend is not significant for any of the weather stations analyzed, but in
this case we have 4 stations where the maximum annual snow depths appear to increase
during the 30-year period 1991–2020 and only for 2 of them do they decrease (Figure 4).
(a) (b)
(c) (d)
(e) (f)
0
20
40
60
80
100
120
1995 2000 2005 2010 2015 2020 2025
days
years
LA VALLETTA (1352 m)
0
20
40
60
80
100
120
140
160
1995 2000 2005 2010 2015 2020 2025
days
years
MONTE BICCO (1450 m)
0
20
40
60
80
100
120
140
1995 2000 2005 2010 2015 2020 2025
days
years
FORCA DI GUALDO (1496 m)
0
10
20
30
40
50
60
70
80
1995 2000 2005 2010 2015 2020 2025
days
years
PARCO GUARNIERI (980 m)
0
10
20
30
40
50
60
70
80
90
1995 2000 2005 2010 2015 2020 2025
days
years
COLLE (1036 m)
0
20
40
60
80
100
120
140
1995 2000 2005 2010 2015 2020 2025
days
years
RIFUGIO PERUGIA (1500 m)
Figure 5.
Trend of days with snow on the ground from 1991 to 2020; the trend line is in black, for the
weather stations: (
a
) La Valletta, (
b
) Monte Bicco, (
c
) Forca di Gualdo, (
d
) Parco Guarnieri, (
e
) Colle,
(f) Rifugio Perugia.

Climate 2023,11, 72 12 of 17
The annual average of snow on the ground in the period from 1 November to 30 April
each year shows a decrease for four of the six stations, although Colle and Parco Guarnieri
show an increasing trend. Colle and Parco Guarnieri are two very closely related stations
that show exactly opposite trends to the other weather stations (Figure 3).
Again, the trend is not significant for any of the weather stations analyzed, but in this
case we have 4 stations where the maximum annual snow depths appear to increase during
the 30-year period 1991–2020 and only for 2 of them do they decrease (Figure 4).
Finally, the trend of days with snow cover on the ground decreased for all the weather
stations, except for Forca di Gualdo, which saw a slight increase (Figure 5).
3.3. Interpolation of Snow Cover Variables for the Period 2010–2022
The final goal of this research is to obtain an annual mapping of the study area from
2010 to 2022 for the average snow depth, maximum snow depth, and days with snow on
the ground. The interpolation of the territory of the Monti Sibillini National Park could help
to quantify snowfall; however, due to the number of weather stations available, it was only
possible to perform the interpolation for the period 2010–2022. Thus, data from
10 weather
stations were used for the three variables of interest, and as far as the average snow cover
was concerned, values from 3 cm up to 36 cm were achieved in the most surveyed parts of
the territory (Figure 6).
Climate 2023, 10, x FOR PEER REVIEW 13 of 18
3.3. Interpolation of Snow Cover Variables for the Period 2010–2022
The final goal of this research is to obtain an annual mapping of the study area from
2010 to 2022 for the average snow depth, maximum snow depth, and days with snow on
the ground. The interpolation of the territory of the Monti Sibillini National Park could
help to quantify snowfall; however, due to the number of weather stations available, it
was only possible to perform the interpolation for the period 2010–2022. Thus, data from
10 weather stations were used for the three variables of interest, and as far as the average
snow cover was concerned, values from 3 cm up to 36 cm were achieved in the most
surveyed parts of the territory (Figure 6).
Figure 6. Average snow depth in the period 2010–2022 measured in cm.
With regard to the maximum annual snow depths, the situation is very similar to
that in Figure 6, although with some differences, for example in the peaks near the Colle
weather station, which in this case show lower values than the peaks in the central area
(Figure 7).
Figure 6. Average snow depth in the period 2010–2022 measured in cm.

Climate 2023,11, 72 13 of 17
With regard to the maximum annual snow depths, the situation is very similar
to that in Figure 6, although with some differences, for example in the peaks near
the Colle weather station, which in this case show lower values than the peaks in the
central area (Figure 7).
Climate 2023, 10, x FOR PEER REVIEW 14 of 18
Figure 7. Maximum snow depth in the period 2010–2022 measured in cm.
Finally, the map of days with snow cover on the ground also shows more persistent
coverage in the case of the major peaks, which gradually decreases as one moves toward
the hilly area (Figure 8).
Figure 7. Maximum snow depth in the period 2010–2022 measured in cm.
Finally, the map of days with snow cover on the ground also shows more persistent
coverage in the case of the major peaks, which gradually decreases as one moves toward
the hilly area (Figure 8).
The interpolations achieved a good quality, as is evident from the statistical indices
calculated following cross-validation (Table 4).
Table 4.
Statistical indices to evaluate the performance of interpolations related to the three variables
under investigation.
Statistical Index Average Snow Cover Maximum Snow Cover Days with Snow Cover on the Ground
ASE (cm) 12.09 24.76 21.46
MSE 0.32 0.25 0.27
RMSE (cm) 8.98 23.17 21.04
RMSSE 0.85 0.98 0.98

Climate 2023,11, 72 14 of 17
Climate 2023, 10, x FOR PEER REVIEW 15 of 18
Figure 8. Days with snow cover in the period 2010–2022 measured in cm.
The interpolations achieved a good quality, as is evident from the statistical indices
calculated following cross-validation (Table 4).
Table 4. Statistical indices to evaluate the performance of interpolations related to the three varia-
bles under investigation.
Statistical Index Average Snow Cover Maximum Snow Cover Days with Snow Cover on the Ground
ASE (cm) 12.09 24.76 21.46
MSE 0.32 0.25 0.27
RMSE (cm) 8.98 23.17 21.04
RMSSE 0.85 0.98 0.98
4. Discussion
The aim of this research was to characterize the area of the Monti Sibillini National
Park in Central Italy from the snow cover point of view, a mountainous area that has
never before been analyzed in in relation to this climatic variable. The purpose of this
research was two-fold: on the one hand, an analysis of the nivometric trend of the 30-year
period 1991–2020 was performed, while on the other hand, a nivometric analysis was
obtained with regard to the maximum and average annual snow depths, as well as an
Figure 8. Days with snow cover in the period 2010–2022 measured in cm.
4. Discussion
The aim of this research was to characterize the area of the Monti Sibillini National
Park in Central Italy from the snow cover point of view, a mountainous area that has
never before been analyzed in in relation to this climatic variable. The purpose of this
research was
two-fold:
on the one hand, an analysis of the nivometric trend of the 30-year
period 1991–2020 was performed, while on the other hand, a nivometric analysis was
obtained with regard to the maximum and average annual snow depths, as well as an
assessment of the ground persistence of snow, over the last period 2010–2022, which would
provide a current and up-to-date basis for future research on afferent fields. In addition, the
similarity between the available weather stations was also characterized by evaluating their
correlation and applying AHC in order to understand the differences, showing weather
stations that are close to each other but with different exposure to prevailing air masses.
This research has a number of innovative features, including the fact that a variable such as
the maximum annual snow depth was investigated, which is uncommon among research
in the field but is of clear interest from the perspective of an in-depth assessment of
climate change [
25
]. Another innovative feature of this study is that it provides a reliable
interpolation of recent snow cover (2010–2022) and also allows the area to be characterized
in terms of both the trends and similarities for the snow variable between the different
areas of the Monti Sibillini National Park. Moreover, there were as many as three clusters
in this restricted area, which was very significant, and is a symptom of a local atmospheric
dynamic that is also very varied due to the position of the Apennine chain. Evaluating

Climate 2023,11, 72 15 of 17
this result in light of other studies on much larger territories, we note much less marked
dissimilarities that are practically non-existent on such limited territories [
9
]. In recent
years, research on snow cover on the ground has turned toward satellite instruments
that can cover the Earth’s surface more evenly and sometimes more accurately, due to
the problems that rain gauges have in terms of counting solid precipitation in certain
environments [
25
,
26
]. In this case, on the other hand, data were obtained from weather
stations equipped with sonar to assess the depth of the snow and from manual weather
stations, where the measurements were taken in the presence of the operator. Data from
heated rain gauges were deliberately discarded because they are very often inaccurate due
to the strong winds in a mountain environment, which generate significant underestimates
when counting the snowpack thickness [
17
,
27
]. Moreover, in this part of the Apennines in
central Italy, detailed snow cover studies had never been carried out, given the fragmentary
and scarce data. The retrieval, homogenization, and validation of data was a long process,
but one that allowed for an important result aimed at climate characterization using
reliable weather stations, which is similar to what has been performed in other mountain
environments where surveys are longer and more comprehensive [
9
]. In terms of the
analysis, results have been reached that are in line with, but also differ from, the scientific
literature on the subject. For example, a trend analysis revealed a slight decreasing trend
and only for some weather stations from 1991 to 2020, an occurrence that is also refuted
by other research, since a definite decrease in snowfall is considered to have occurred in
the 1990s [28–30]. Unfortunately, in this case, it was not possible to assess the trends prior
to the 1990s, due to a lack of reliable nivometric data. Finally, interpolation using GIS
software with geostatistical techniques is the final result of this research; however, it is
quite rare, especially in relation to the scarce availability of the complete snow data, to
conduct a spatial analysis of the ground snow cover data. The use of the altitude-based
co-kriging technique is most common for temperature and precipitation; however, there are
also cases in the literature where it has also been used for snow cover [
31
,
32
]. Furthermore,
it is necessary to specify that in some other pieces of research that are similar to this study, a
strong dependence on the amount of snow cover on altitude could be observed [
33
]. Finally,
it should be highlighted that the excellent correlation result found through geostatistical
analysis, as the values of the statistical indices obtained are very close to the optimal values,
especially when analyzing the values of the standardized statistical indices, is uncommon
when it comes to interpolations for snow cover analysis [
34
,
35
]. This recent mapping
of the territory makes it possible to make this tool an operational tool for many other
environmental analyses, including mappings that are by no means common in the scientific
literature on the subject.
5. Conclusions
Snow characterization is very important for improving the hydrological modeling of
the area, as snow has a great influence on the recharge of the water table, so being able
to model with reliable values is certainly preferable to reconstructing them empirically.
Furthermore, understanding whether there are appreciable differences in the various
months is equally important in order to assess any consequences that may be suffered by
the indigenous vegetation. This research obtained clear results, such as the presence of
a weak decreasing trend in daily snow cover between November and April from 1991 to
2020, which, however, is not significant. In addition, it is possible to identify the presence
of at least three clusters in the study area, a sign that the local atmospheric dynamics are
decisively influenced by the position of the main reliefs. Finally, this study enabled a spatial
mapping of the territory, both in terms of the average and maximum annual snow cover
and in terms of the days with snow cover on the ground. However, this research also has
limitations, such as the number of years available for these weather stations, as only a few
have data from before 1990, which would be important for a trend assessment over a longer
period. In particular, it would be interesting to evaluate the data from this area backwards
with those from the Alps or other Apennine areas, although extensive reconstructions

Climate 2023,11, 72 16 of 17
would have to be carried out, which is why a prior correlation analysis and evaluation of
clusters was also carried out. Finally, this analysis should be considered a starting point to
supplement other available data or to correctly calibrate the available satellite products for
ground snow cover in the study area.
Author Contributions:
Conceptualization. M.G., A.C. and G.P.; methodology. M.G., T.P., S.M. and
Y.H.; software. M.G. and R.M.; validation. M.G. and G.P.; formal analysis. M.G.; investigation. G.P.;
resources. M.G.; data curation. G.P.; writing—original draft preparation. M.G.; writing—review
and editing. G.P.; visualization. M.G.; supervision. A.C. and G.P.; project administration. M.G. All
authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
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