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Citation: Markovi´c, R.; Mudelsee, M.;
Radakovi´c, M.G.; Radivojevi´c, A.R.;
Schaetzl, R.J.; Basarin, B.; Nikoli´c, J.;
Markovi´c, S.B.; Spalevi´c, V.; Anti´c, A.;
et al. An Index for Snowmelt-Induced
Landslide Prediction for Zavoj Lake,
Serbia. Atmosphere 2024,15, 256.
https://doi.org/10.3390/
atmos15030256
Academic Editor: John Walsh
Received: 19 December 2023
Revised: 9 February 2024
Accepted: 17 February 2024
Published: 21 February 2024
Copyright: © 2024 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/).
atmosphere
Article
An Index for Snowmelt-Induced Landslide Prediction for
Zavoj Lake, Serbia
Rastko Markovi´c 1, *, Manfred Mudelsee 2,3,4 , Milica G. Radakovi ´c 5, Aleksandar R. Radivojevi´c 1,
Randall J. Schaetzl 6, Biljana Basarin 5, Jugoslav Nikoli´c 7, Slobodan B. Markovi´c 5,8,9, Velibor Spalevi´c 9,
Aleksandar Anti´c 5, 10, Miloš Marjanovi´c 5and Tin Luki´c 5, *
1Department for Geography, Faculty of Sciences, University of Niš, Višegradska 33, 18000 Niš, Serbia;
aleksandar.radivojevic@pmf.edu.rs
2Climate Risk Analysis, Kreuzstrasse 27, 37581 Bad Gandersheim, Germany;
mudelsee@climate-risk-analysis.com
3Advanced Climate Risk Education gUG, Kreuzstrasse 27, 37581 Bad Gandersheim, Germany
4Institute of Geosciences, University of Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany
5Department of Geography, Tourism and Hotel Management, Faculty of Sciences, University of Novi Sad,
Trg Dositeja Obradovi´ca 3, 21000 Novi Sad, Serbia; milicar@dgt.uns.ac.rs (M.G.R.);
biljana.basarin@dgt.uns.ac.rs (B.B.); slobodan.markovic@dgt.uns.ac.rs (S.B.M.);
aleksandar.antic@dgt.uns.ac.rs (A.A.); milos.marjanovic@mail.com (M.M.)
6Department of Geography, Environment, and Spatial Sciences, Michigan State University,
673 Auditorium Drive, East Lansing, MI 48824, USA; soils@msu.edu
7Republic Hydrometeorological Service of Serbia, Kneza Višeslava 66, 11030 Belgrade, Serbia;
ofce@hidmet.gov.rs
8Serbian Academy of Arts and Sciences, Knez Mihajlova 35, 11000 Belgrade, Serbia
9Biotechnical Faculty, University of Montenegro, Mihaila Lali´ca 15, 81000 Podgorica, Montenegro;
velibor.spalevic@ucg.ac.me
10 Institute of Geography and Sustainability, University of Lausanne, CH-1967 Sion, Switzerland
*Correspondence: rastko.markovic@pmf.edu.rs (R.M.); tin.lukic@dgt.uns.ac.rs (T.L.)
Abstract: In February 1963, a huge landslide (ca. 1,950,000 m
3
) blocked the Visoˇcica River and, thus,
formed Zavoj Lake. The primary objective of this research was to investigate the importance of
snowmelt in relation to landslide occurrence and to dene the critical climatic conditions that may
trigger massive winter landslides. We used monthly precipitation and average monthly maximum
temperature data from meteorological and precipitation stations in the Visoˇcica River basin (Dojkinci)
and in the immediate proximity of Lake Zavoj (Pirot, Dimitrovgrad and Topli Do) as data inputs to
the Snow-Melt Landslide (SML) index. It considers the summed monthly precipitation for previous
months that continuously have an average maximum temperature below 0
◦
C. According to this
method, the event at Zavoj Lake stands out among all other precipitation and snowmelt values
for the past 72 years. After applying the SML index, all stations showed values of >300 mm for
February 1963, which we consider as the threshold value for potential landslides appearance. In
addition to meteorological data, we applied the SML index to data from the Coordinated Regional
Downscaling Experiment (CORDEX) regional climate model outputs for the region from 2022 to
2100. As expected, climate change will have inuenced the temperature values, especially during the
winter. Conversely, the study area is experiencing drastic changes in land use caused by depopulation,
leading to a reduced risk of winter landslides in the Visoˇcica basin. We suggest that future climatic
conditions in the area will make it more likely to experience extreme summer precipitation events,
which might trigger large landslides. The SML method can be implemented for all landscapes that
experience snowy winters, providing information in a timely manner so that local residents can
react properly when the probability of landslide occurrence rises. The SML index, grounded in
essential meteorological principles, provides a tailor-made, data-driven methodology applicable
across varied geographical settings. Its utility extends to mitigating hydro-meteorological hazards on
scales ranging from local to national scales, offering diverse and effective early warning solutions.
Atmosphere 2024,15, 256. https://doi.org/10.3390/atmos15030256 https://www.mdpi.com/journal/atmosphere
Atmosphere 2024,15, 256 2 of 20
Keywords: SML index; Visoˇcica River; climate; Stara Planina (Balkan Mountains); CORDEX regional
climate model; snow accumulation; landslide occurrence
1. Introduction
A landslide is characterized by the swift movement of a mass of rock, residual soil, or
adjacent sediments along a slope [
1
]. The primary triggers for landslide activation encom-
pass uctuations in underground water levels, changes in land use due to deforestation,
heavy rainfall, prolonged periods of drought, snowmelt, inadequate drainage systems, un-
regulated surface water drainage, earthquakes, human activities, and more [
2
–
4
]. Among
these factors, precipitation variability is of paramount importance, as its outcomes are
largely responsible for soil erosion and, often, landslide events [
5
]. Thus, soil erosion can be
regarded as a complex process inuenced by the climatic regime, land cover, and landscape
characteristics, which can be exacerbated by human activities. Landslides are prevalent
in regions with intensive agricultural practices, as well as in areas affected by mining,
construction, and extensive deforestation [6].
Economic losses due to landslides, in some places, are estimated at billions of US
dollars. Besides nancial damage, many landslides caused injury and death [
7
–
10
]. Hence,
the prediction of landslide occurrence can be crucial in preventing major environmental
and human consequences. Information, such as landslide susceptibility mapping [
11
], the
formulation of various modeling techniques [
12
], and the use of indices [
13
,
14
], improves
the chances of predicting landslides. The many papers that have dealt with this topic
typically examine the relationship between climate, topographic, and pedological factors
as triggering agents (e.g., [15,16]).
Effective planning involving soil conservation measures necessitates a deep under-
standing of the factors contributing to these hazardous events, such as sediment yield
production [
17
] and landslides induced by snow melting. Contemporary research has pri-
marily concentrated on examining the intricate interplay between various environmental
factors, such as air temperature, humidity, wind, precipitation, and snowmelt and their
impact on different economic sectors. For example, Habibi et al. (2021) [
18
] enhanced our
understanding of the connections between the decreasing lake level within the Urmia Lake
Basin and the evolving local drought conditions for the period 1981–2018. The authors
employed the Standard Precipitation Index (SPI), the Standard Precipitation Evaporation
Index (SPEI), and the Standardized Snow Melt and Rain Index (SMRI) to characterize
environmental conditions in the catchment. Similarly, Yu et al. (2022) [
19
] assessed a
predictive model for the suitability of ice–snow tourism under climate warming known
as the Ice–Snow Tourism Suitability Index (ISTSI). This comprehensive index considered
environmental factors such as air temperature, humidity, wind, and precipitation, along
with subjective human initiatives. ISTSI effectively quanties the comfort level of ice–snow
tourism. Hultstrand et al. (2022) [
20
] estimated snow depths based on a winter season
index for the West Glacier Lake watershed in Wyoming, US. The authors incorporated
topographical, climatological, and winter season index inputs to gain insights into the
quantity and distribution of snow, particularly for streamow forecasting in mountainous
regions. The prediction of snowmelt-induced landslides was calculated for Ottawa, Canada,
by using the degree-day method. This method is based on multiplying the degree-day
parameter (in units of mm per day and
◦
C) with the mean daily temperature (
◦
C), thus
excluding days when the temperature was positive. The model’s validity was conrmed
by historical landslide maps [21].
Several studies have analyzed landslides that were triggered by snowmelt [
22
–
25
].
Xian et al. (2022) [
26
] delved into the mechanisms governing deformation and failure
processes leading to snowmelt-induced landslides in Yili, Xinjiang, China. The study
revealed that the loess slope in question experienced two signicant sliding failures, with
varying degrees of pre-existing slope deformation observed between these failures. The
Atmosphere 2024,15, 256 3 of 20
early-stage formation and development of surface cracks on the slope were predominantly
inuenced by human grazing activities. The distinctive loess exhibited a strong sensitivity
to water, contributing to the deterioration of soil strength in the slip zone. The research
indicated that with the escalation of regional grazing activities and the heightened impact
of global warming, the potential for resurgence of landslides is likely to increase. Gou et al.
(2023) [
27
] examined the seasonal movement characteristics of the Cheyiping landslide
in western Yunnan Province, China, using time-series InSAR technology. The authors
observed a signicant correlation between the movement of the landslide and seasonal
rainfall. Water level changes in the Lancang River, attributed to the water storage of the
hydropower station and seasonal rainfall, were identied as triggers for landslide defor-
mation [
27
]. Another study from Japan [
28
] successfully produced a snowmelt-induced
landslide susceptibility map by employing a probabilistic model based on multiple logistic
regression analyses of data on hydraulic gradient, relief energy, and geology. In a recent
study [
29
], the shallow landslides of Lombardy, Italy that occurred after snowfall events
and rapid temperature increases were investigated. Applying the model to the Tartano
basin in the Alps, the authors found that 26% of slopes exhibited unstable conditions;
previous models that used only rainfall-based predictions suggested that only 19% of the
slopes were unstable. Snowmelt water was also proposed as a trigger for the Ludoialm
landslide in Tyrol, Austria as the groundwater levels increased [30].
The risk of soil erosion and landslides constitutes a major environmental concern in
Southeastern Europe. Although predictions remain uncertain, changes in precipitation
patterns stemming from future climate changes are anticipated for southeastern parts of
Europe, including the Balkans [
31
,
32
]. The Western Balkans face a signicant risk for
increased erosion [
33
]. In certain regions, erosion has reached a critical, irreversible stage
due to their limited soil cover. In areas with slow soil formation, any soil loss exceeding
1.0 t ha−1yr−1
over 50–100 years is deemed irreversible [
34
]. Indeed, the tolerable soil
erosion rate for southern Europe is ≈0.3 t ha−1yr−1[35].
Landslides in Serbia represent a significant environmental and economic
problem [36–38]
.
In urban areas, many landslides are inuenced by anthropogenic activities [
36
], but they
can also be triggered by extreme climatic events [39]. In our study, we investigated one of
the most catastrophic landslide events in recent Serbian history. This landslide occurred
in February 1963 in the Visoˇcica River valley in Southeastern Serbia. Previous authors
indicated that the main factor responsible for this event was snowmelt [
40
,
41
]. However,
there exists no detailed quantication of the climatic conditions responsible for the landslide.
Therefore, the goal of this paper is to devise an indicator of landslide probability using the
Snow-Melt Landslide (SML) index based on existing climatological data. The index can be
calculated for most areas of the world, requiring only basic meteorological data (monthly
precipitation and average monthly maximum temperatures). In addition to predicting
winter landslides, the SML index helps dene critical points in snow accumulation before
catastrophic landslides occur.
Based on the assessment work by the Intergovernmental Panel on Climate Change
(IPCC) and other publications [42,43], we are witnessing rapid changes in climate all over
the world. These trends are expected to continue in the future and, thus, affect the landslide
incidence around the globe [
26
]. In this study, we also implement the SML index, using data
derived from regional climate prediction models from the CORDEX database (Copernicus
Climate Change Service, Climate Data Store, 2019 [
44
]), thereby providing regional model
projections up to the year 2100. In this way, the SML index data can be considered a
prediction tool to alert us to critical future climate scenarios, thereby helping prevent some
of the negative consequences of landslides.
2. Study Area
The Visoˇcica and Toplodolska River basins in Serbia are also known as the Visok geo-
graphical region [
45
]. This area is one of the geomorphologically and hydrologically most
interesting areas in Serbia. The Visok is located between Stara Planina and Vidliˇc Mountain
Atmosphere 2024,15, 256 4 of 20
in eastern Serbia, although the Visoˇcica basin is also partially in Bulgaria
(Figure 1
). The Vi-
soˇcica River catchment exhibits signicant asymmetry, with the Visoˇcica River demarcating
a substantially larger area of the slopes of Stara Planina (381.8 km
2
) and a comparatively
smaller area on the slopes of Vidliˇc Mountain and in Bulgaria (178.1 km
2
). The Serbian part
of the basin is located within the borders of the municipalities of Pirot and Dimitrovgrad. In
the Visok microregion, there are 26 villages (22 in Serbia), all of which are losing population.
No village has more than 100 inhabitants (Census, 2022 [46]).
Figure 1. Geographical position of the Visok microregion. (A). Position of Serbia in Europe;
(
B). Position
of the study area; (C). Main geographical features of the study area (Meteorological
stations used in this study are represented by red dots on the (C) panel).
The Stara Planina–Poreˇc geological unit, located in Eastern Serbia, is renowned for its
Permian, Triassic, and Jurassic deposits, characterized by their unique paleontology and
sedimentology. These deposits, predominantly on the southern Stara Planina Mountain,
encompass marine sandstones and shallow marine ramp limestones. This geological phe-
nomenon is set against the backdrop of the East Serbian Carpatho–Balkanides, a geological
framework that constitutes a part of the Dacia megaunit [
47
]. According to Dimitrijevi´c
and Karamata (2003) [48] and as presented in Figure 2A, the bedrock geology of the basin
above Zavoj Lake is primarily composed of Mesozoic-age rocks. Among the rock types,
variegated sandstones and conglomerates prevail. Limestone and dolomitic limestone
occupy signicant portions of the Visok region, while siltstones and clays appear as layers
in the Carboniferous rocks. The far northeastern part of the basin is characterized by
Paleozoic-age shales with gabbro inclusions. Many of the rocks are regularly intermixed,
often forming ysch. The geology of the Toplodolska River watershed is much more homo-
geneous than that of the Visoˇcica River basin, characterized by Permian red sandstones with
alternating silt and clay layers. Depending on location, the slope of the terrain changes, but
in general, slopes of >10
◦
dominate (Figure 2B). In the Visoˇcica basin (Zavoj Lake), mostly
red sandstones and limestone–dolomite have developed. The characteristic feature of all
these soils is their shallow, sandy, skeletal nature, with low pH values and organic matter
contents, typical of mountainous soils. Figure 2C illustrates the distribution of soils in the
basin based on permeability. Given the mountainous nature of the terrain, the amount of
Atmosphere 2024,15, 256 5 of 20
forest cover in the basin is insufcient from the perspective of soil erosion protection (in
such conditions, a forestation level above 50% is required). Additionally, it should be noted
that a signicant portion of the areas classied as forest consists of degraded forests and
shrubs, which provide only minimal erosion protection (Figure 2D,E).
Figure 2. Thematic maps of the Visok microregion associated with soil erosion. (On panels (C–E), the
Bulgarian part of the region was not included) (A). Geological map of (the Serbian part was digitalized
using a basic geological map with a resolution of 1:100,000, while the Bulgarian part was digitalized
using the map of the Carpatho–Balkanides with a 1:300,000 resolution [
48
]; (B). Slopes;
(C). Soil
permeability, according to the IntErO model [
49
]; (D). Erosion intensity during 1971 (Manojlovi´c et al.
(2018) [50], modied); (E). Erosion intensity during 2011 (Manojlovi´c et al. (2018) [50], modied).
Evidence of intensive uvial erosion on this landscape is indicated by >60 waterfalls in
the Visok microregion (Figure 3A,B; [
48
]), not all of which have been described. Regardless
of the enormous scientic and tourist potential, only a few papers have been published
about this area [47,51–53].
The Lake Zavoj dam (22.64
◦
E, 43.27
◦
N), at 576 m.a.s.l., lies 18 km away from Pirot
city, in the municipality of the same name. It received its name from the village Zavoj,
which was completely submerged in the catastrophe that occurred in February, 1963, when
it had roughly 1485 inhabitants (Census, 1961 [54]).
The case study for this paper is one of the largest landslides in Serbia’s modern
history—the Zavoj Lake catastrophe of 25 February 1963. The landslide was triggered by
saturated conditions caused by rapid snowmelt. The landslide was triggered at elevations
between 790 and 960 m.a.s.l. The height difference from the landslide origin to the bottom
of the Visoˇcica bed was 426 m, with a horizontal distance of 1550 m. The slope of the terrain
was as high as 17
◦
. Regolith from the landslide blocked the Visoˇcica River on 26 February,
forming a rock–earth dam with a volume of 1,950,000 m
3
and a width of 530 m. The height
of the earthen dam was at maximum 140 m [
40
]. The speed of the landslide was 7 m/h.
The total extent of the landslide measured 1.3 km in length, impacting an area spanning
240,000 m2[41,55].
Atmosphere 2024,15, 256 6 of 20
Figure 3. (A). Waterfall Tupavica; (B). Waterfall Skok; (C). Zavoj Lake from the viewpoint at Koziji
kamen (D,E). The submerged village of Velika Lukanja, during the extremely low water level of Zavoj
Lake. Photo by: Rastko Markovi´c.
Due to the risk of dam failure, proactive measures were undertaken in 1964, when
military authorities constructed a channel and initiated the controlled drainage of the
reservoir. After the construction of the superimposed articial dam, implemented in the
year 1977, a consequence of this infrastructure development submerged two more villages:
Velika Lukanja (Figure 3D) and Mala Lukanja. This articial reservoir, established as a result,
currently serves as a vital component in the operational framework of the Hydropower
Plant “Pirot” [
40
]. The Zavoj accumulation, as of today, spans a length of
17 km,
extending
from the village of Gostuša to the site of the catastrophic event (Figure 3C). The lake serves
as a reservoir for energy exploitation, and during this process, all water from the lake is
occasionally utilized and remains of the villages Zavoj, Velika Lukanja, and Mala Lukanja
can be seen [
56
]. Consequently, the submerged villages can be compared to the mythical
villages of the “Serbian Atlantis” (Figure 3D,E). Furthermore, water extraction consistently
occurs from the bottom of the lake, leading to a lower temperature in the Temštica River
compared to its tributaries, the Toplodolska and Visoˇcica Rivers. This temperature disparity
impacts the stability of the ecosystem in the region.
Atmosphere 2024,15, 256 7 of 20
The intensity of erosion in the Visoˇcica watershed is currently being monitored with
the aim of being better prepared for any future similar disasters. High erosion areas occur
on the right side of the Visoˇcica valley, upstream from the dam prole to the village of
Rsovci. Land in the lower reaches of the Belska and Gostuška Rivers also have areas of
medium and strong erosion [
50
,
57
]. Erosion in the Zavoj Lake basin has decreased in the
last few decades, with the highest erosion occurring on the left bank of Visoˇcica because of
decreases in population and changes in land use [17,58].
3. Material and Methods
Climate data and data derived from regional climate models constitute the main inputs
to our model. We rst determined the weather conditions at the time of the landslide. Next,
we examined modeled data on the future climate of this area (Figure 4).
Figure 4. Aowchart of the methodology used in this study.
3.1. Meteorological Stations
For this study, we used monthly precipitation data from four meteorological (Pirot,
Dimitrovgrad) and precipitation (Topli Do and Dojkinci) stations and average monthly max-
imum temperature data from the two meteorological stations (Table S1 of
Supplementary
Material). Only the Dojkinci station is located in the Visoˇcica River basin, but the other
stations are in immediate proximity to Lake Zavoj (Figure 1). The data were obtained
from the ofcial statistics of the Republic Hydrometeorological Service of Serbia, using
meteorological yearbooks from the year 1949 to 2021. The 32 years of data align with the
standards set by the World Meteorological Organization (WMO).
Since all of these stations are relatively close to each other (Figure 1), we calculated
Pearson’s correlation coefcient, r, with 95% calibrated bootstrap condence intervals
for precipitation and the average monthly maximum temperatures from all four stations
(Table 1). This method is robust against the presence of (1) autocorrelation in the series
and (2) non-normal distributions [
59
,
60
]. All seven combinations of monthly precipitation
Atmosphere 2024,15, 256 8 of 20
(P) and average monthly maximum temperatures (Tmax) showed very high Pearson’s r,
95% condence interval for Tmax, and relatively high for P, indicating a strong correlation
between the stations:
Table 1. Pearson’s r (with 95% condence interval) calculated for all combinations of average monthly
maximum temperature (Tmax) and monthly precipitation (P) data.
Data Relationship Pearson’s r [95% Condence Interval]
Dimitrovgrad (Tmax)–Pirot (Tmax): 0.995 [0.977; 0.999]
Dimitrovgrad (Tmax)–Topli Do (Tmax): 0.997 [0.995; 0.998]
Pirot (Tmax)–Topli Do (Tmax): 0.996 [0.995; 0.997]
Dimitrovgrad (P)–Pirot (P): 0.852 [0.810; 0.885]
Dimitrovgrad (P)–Topli Do (P): 0.765 [0.717; 0.805]
Dimitrovgrad (P)–Dojkinci (P): 0.715 [0.670; 0.754]
Pirot (P)–Topli Do (P): 0.789 [0.749; 0.823]
Pirot (P)–Dojkinci (P): 0.724 [0.678; 0.764]
Topli Do (P)–Dojkinci (P): 0.745 [0.680; 0.798]
Because the Dimitrovgrad and Pirot meteorological stations are situated at signicantly
lower elevations than that of the basin, the meteorological data needed to be interpolated to
align with their altitudes. The high correlation values gave us the condence to interpolate
the Tmax data to the average height of the basin. This number was obtained from open-
source Digital Elevation Model (DEM) data with horizontal resolutions from 1 arc-second
(30 m) (SRTM) to 12.5 m (ALOS PALSAR RT1) [
61
,
62
]. Observations indicated that ALOS-
PALSAR images with optimal baseline parameters produced a high-resolution DEM with
enhanced height accuracy. Subsequently, the validated DEM was employed for topographic
correction of ALOS-PALSAR images within the same region, resulting in superior outcomes
compared with those achieved with ASTER and SRTM-DEM [
61
]. The program used for
this analysis was ArcGIS Pro 2.5.0. The DEM was used to dene percentages of land area
along every 100 m step, except for the lowest area, which is dened as between 588 and
600 m.a.s.l., and the highest (between 2000 and 2003 m.a.s.l.). The average height of the
investigated area then was calculated to be ~1146.47 m.a.s.l. Thus, height correlations to the
hypsometric center of the basin could be performed. Topli Do had an active meteorological
station but lacked continuous measurements from 1954 to 1985. For this reason, Tmax data
for Topli Do are not presented and cannot be used for the calculation of the SML index.
However, its data were used to calculate the temperature gradient. The difference between
the average temperature of Dimitrovgrad and Topli Do is ~1.073
◦
C. The Topli Do station is
located 250 m higher than the Dimitrovgrad station; therefore, the temperature gradient
between these two stations is ~0.43
◦
C per 100 m altitude. The same calculation yielded a
temperature gradient between Topli Do and Pirot station of ~0.57 ◦C per 100 m altitude.
The SML index was developed to determine the likely conditions for landslide ac-
tivation in the Visoˇcica basin by providing a threshold number. Before constructing this
index, we considered historical data from the years 1962 and 1963. For three months prior
to the Zavoj Lake formation, temperatures at the level of the landslide were <0
◦
C, allowing
the accumulation of precipitations in the form of snow. Temperatures increased in the
February of 1963, which triggered the snowmelt and the landslide. Equation (1), used for
the calculation of the SML index, is as follows:
P(SML)n+2 = Pn+2 if (Tmaxn+2 > 0) + (Pn+1 if (Tmaxn+2 > 0) and (Tmaxn+1 < 0)) + (Pnif (Tmaxn+2 > 0) and (Tmaxn+1 < 0) and
(Tmaxn< 0)), (1)
where P is total monthly precipitation (units: mm), Tmax is the average monthly maximum
temperature (units: ◦C), and n is the number of months.
Atmosphere 2024,15, 256 9 of 20
The mathematical explanation of the formula is as follows. Let n + 2 denote the
current month for which the SML index (denoted by P
(SML)n+2
) is to be calculated. If the
current maximum temperature (Tmaxn+2) is positive, then the current precipitation (Pn+2)
contributes to the index. If, additionally, the maximum temperature in the preceding month
(Tmax
n+1
) is negative (i.e., no melting occurred), then the precipitation in the preceding
month (P
n+1
) also contributes to the index (i.e., is added). Finally, if, additionally, the
maximum temperature in the penultimate month (Tmax
n
) is negative, then the precipitation
in the penultimate month (Pn) also contributes to the index.
This formula used data from the above-mentioned meteorological and precipitation
stations (Figure 4), for which we imposed the magnitude classication theme of Table 2.
On all graphs, this threshold represents February of 1963. Table 2shows the proposed
classication of the SML index values, which were obtained by observing the historical
data from meteorological stations and based on the SML value from February 1963 when
the landslide occurred.
Table 2. Classication of Snow-Melt Landslide Index values.
SML Value (Units: mm) Probability of Landslide Occurrence
above 300 High probability of a landslide in the Visoˇcica basin
250 to 300 Medium probability of a landslide in the Visoˇcica basin
below 250
No chance or low probability of a landslide in the Visoˇcica basin
3.2. Regional Climate Models
Global Climate Models (GCMs) provide projections of potential future changes in
climate. The consequences of this changing climate and the required adaptation strategies
tend to manifest on regional and national scales. To address this issue, regional climate
models (RCMs) and Empirical Statistical Downscaling (ESD), applied to specic areas
and driven by GCMs, can provide information for smaller areas. The downscaled data
supports more detailed assessments and planning for impacts and adaptation, especially
crucial in vulnerable regions. Therefore, Regional Climate Downscaling (RCD) data play
a vital role in this context, offering projections with greater detail and more accurate
representations of localized extreme events [
63
]. To determine how likely such events
would occur in the future, we used data from regional climate models (RCMs). Several
RCMs were analyzed (for the model output grid centers, see Table 3), both with and without
corrected bias (Tables 4and 5). The choice of the bias-corrected RCMs was based on a
previous assessment by McSweeney et al. (2015) [
64
] of RCMs in the European area. In their
summary of CMIP5 model performance, the CNRM-CM5, HadGEM2-ES, MPI-ESM-LR,
and MPI-ESM-ES models were viewed as “satisfactory” for the region. Representative
Concentration Pathways (RCP) 2.6, 4.5, and 8.5 were considered for the bias-corrected
models but only RCP 8.5 for non-bias-corrected models. The temporal resolution is monthly,
and the selected variables were the maximum 2 m temperature for the last 24 h, as well
as the mean precipitation ux. The horizontal resolution is 0.11 degrees, meaning that
estimates for the 12 coordinates in the Visoˇcica catchment were derived for the following
RCM grid (Table 3).
Next, the ensemble mean value for the entire basin was calculated as the average value
from these coordinates. The SML, as dened in Equation (1), incorporates precipitation
amounts from the preceding two months. Prior to opting for the inclusion of only two
consecutive months with negative temperatures in Equation (1), we also experimented
with one and three months. However, when employing these alternative approaches, the
1963 landslide catastrophe did not manifest as prominently as it did when using data for
two months (Equation (1)).
Atmosphere 2024,15, 256 10 of 20
Table 3. CORDEX Grid coordinates for the Visoˇcica catchment.
Grid Latitude Longitude
1 23.1076◦E 43.3057◦N
2 23.0971◦E 43.196◦N
3 23.0866◦E 43.0863◦N
4 22.958◦E 43.3132◦N
5 22.9478◦E 43.2034◦N
6 22.9376◦E 43.0937◦N
7 22.8084◦E 43.3204◦N
8 22.7985◦E 43.2107◦N
9 22.7886◦E 43.1009◦N
10 22.6587◦E 43.3275◦N
11 22.6491◦E 43.2177◦N
12 22.6396◦E 43.1079◦N
Table 4. Non-bias-corrected regional climate models used in this study.
RCP Mean Precipitation Flux
Maximum 2 m Temperature in the Last 24 h
8.5
CCCma-CanESM2,
CLMcom-CLM-CCLM4-8-17
CCCma-CanESM2,
CLMcom-CLM-CCLM4-8-17
ICHEC-EC-EARTH,
CLM-comETH-COSMO-crCLIM
ICHEC-EC-EARTH,
CLM-comETH-COSMO-crCLIM
IPSL-CM5A-MR, SMHI-RCA4 IPSL-CM5A-MR, SMHI-RCA4
NCC-NorESM1-M,
MOHC-HadREM3-GA7-05
NCC-NorESM1-M,
MOHC-HadREM3-GA7-05
MPI-M-MPI-ESM-LR,
KNMI-RACMO22E MPI-M-MPI-ESM-LR, KNMI-RACMO22E
Table 5. Bias-corrected regional climate models used in this study.
RCP Mean Precipitation Flux Maximum 2 m Temperature in the Last 24 h
2.6 MPI-M-MPI-ESM-LR_rcp26_r1i1p1_MPI-
CSC-REMO2009_v1-SMHI-DBS45-MESAN
MPI-M-MPI-ESM-LR_rcp26_r1i1p1_MPI-CSC-
REMO2009_v1-SMHI-DBS45-MESAN
4.5
CNRM-CERFACS-CNRM-
CM5_rcp45_r1i1p1_SMHI-RCA4_v1-SMHI-
DBS45-MESAN
CNRM-CERFACS-CNRM-
CM5_rcp45_r1i1p1_SMHI-RCA4_v1-SMHI-
DBS45-MESAN
MPI-M-MPI-ESM-LR_rcp45_r1i1p1_SMHI-
RCA4_v1a-SMHI-DBS45-MESAN
MPI-M-MPI-ESM-LR_rcp45_r1i1p1_SMHI-
RCA4_v1a-SMHI-DBS45-MESAN
MOHC-HadGEM2-
ES_rcp45_r1i1p1_CLMcom-CCLM4-8-
17_v1-SMHI-DBS45-MESAN
MOHC-HadGEM2-ES_rcp45_r1i1p1_CLMcom-
CCLM4-8-17_v1-SMHI-DBS45-MESAN
8.5
CNRM-CERFACS-CNRM-
CM5_rcp85_r1i1p1_CLMcom-CCLM4-8-
17_v1-SMHI-DBS45-MESAN
CNRM-CERFACS-CNRM-
CM5_rcp85_r1i1p1_CLMcom-CCLM4-8-17_v1-
SMHI-DBS45-MESAN
MPI-M-MPI-ESM-LR_rcp85_r1i1p1_MPI-
CSC-REMO2009_v1-SMHI-DBS45-MESAN
MPI-M-MPI-ESM-LR_rcp85_r1i1p1_SMHI-
RCA4_v1a-SMHI-DBS45-MESAN
MOHC-HadGEM2-ES_rcp85_r1i1p1_SMHI-
RCA4_v1-SMHI-DBS45-MESAN
MOHC-HadGEM2-ES_rcp85_r1i1p1_CLMcom-
CCLM4-8-17_v1-SMHI-DBS45-MESAN
Atmosphere 2024,15, 256 11 of 20
4. Results
4.1. Historical Data
The presentation of results for the historical measurement period focuses on the
Dimitrovgrad station because the Pirot station exhibits a considerable number (17) of
missing values. Figure 5shows the average monthly temperature (Tavg), average maximum
monthly temperature (Tmax), precipitation (P), and the constructed SML index series for
Dimitrovgrad from January 1949 to December 2021.
Figure 5. Data from the Dimitrovgrad meteorological station. (A). Precipitation data with the SML
index applied; (B). Tmax data; (C). Tavg data; (D). Monthly precipitation values. Black lines represent
linear trend curves estimated using ordinary least-squares regression.
Atmosphere 2024,15, 256 12 of 20
The SML index was applied to Topli Do and Dojkinci precipitation data, as well as
to historical data on average monthly maximum temperatures from Dimitrovgrad, as
interpolated to the mean elevation of the basin. All graphs clearly indicate that February
1963 had the most precipitation and snowmelt (combined into the SML index) over the
investigated period. Based on Topli Do data, during February 1963, precipitation and
snowmelt totaled
≈
399 mm of water. No other peaks above 300 mm occurred during the
study period, although there are six values of >250 mm. Based on data from the Dojkinci
gauge, the precipitation event peak at Zavoj is represented with SML = 416.3 mm. The
second SML peak exceeds 300 mm, and there are three more peaks greater than 250 mm
(Figure 6). The observed event exceeds a threshold value of SML = 300 mm in all cases, and
for this reason, the critical value for the landslide appears to be 300 mm. The Zavoj Lake
event peak is at least ≈20% higher than all the other values in all three cases.
Figure 6. Precipitation data from the Dimitrovgrad, Topli Do, and Dojkinci gauges, with applied
SML index based on the interpolated Dimitrovgrad Tmax to the average height of the basin. Dened
thresholds of 300 mm (red line) and 250 mm (yellow line) are presented in Table 2. (A). Dimitrovgrad
station precipitation data; (B). Topli Do station precipitation data; (C). Dojkinci station precipitation
data. For the denition of the thresholds (red and yellow horizontal lines), see Table 2.
Atmosphere 2024,15, 256 13 of 20
Because the SML index also includes snowmelt, it is important to analyze regular
summer and winter monthly precipitation values as well. The summer months in hydrology
are from May to October, while the winter months are from November to April. As an
archive with no missing values, we analyzed Dimitrovgrad station data. Based on these
data, the summer months average more precipitation (59.6 mm) than the winter months
(48 mm) (Table 6). Also, the maximum monthly summer precipitation totals are higher on
average (165.9 mm) than during the winter months (148.4 mm). Interestingly, the highest
value during the investigated period appeared in January (Table 6).
Table 6. Monthly precipitation (mm) data for the Dimitrovgrad station. AVG, average;
σ
, standard
deviation; MAX, maximum.
Month January
February
March April May June July August
September
October
November December
MAX
AVG 13.66 12.91 14.62 15.71 21.76 24.82 25.08 19.71 17.58 18.54 17.37 14.01 25.08
σ9.98 7.50 9.02 8.41 11.45 13.00 20.63 12.47 12.68 11.68 10.24 8.52 17.00
MAX 67.9 47.9 52.5 46.4 61.9 71.3 123.3 53.8 84.5 49.1 48 43.9 123.3
We also examined maximum daily precipitation totals by month, as it may be a proxy
for summer landslide appearance. When it comes to maximum values for maximum
daily precipitation per month, summer months (73.98 mm) are larger than winter months
(51.1 mm). July had one extreme precipitation value of 123.3 mm (Table 7).
Table 7. Maximum daily precipitation values at the Dimitrovgrad station by month. AVG, average;
Σ, sum; MAX, maximum.
Month January
February
March April May June July August
September
October
November December
SUM
AVG 43.6 40.1 46.9 53.3 77.3 79.7 58.8 46.6 45.4 49.9 54.5 49.6 645.8
Σ33.2 22.0 28.6 25.4 36.7 43.1 36.8 33.8 35.4 34.2 33.2 30.0
MAX 212.9 101.4 138.4 145.8 169.1 205.4 152.5 168.3 174.3 125.7 148.2 143.9 976.6
These data show that if the SML index is not taken into account, summers will be
more likely to have landslides. However, when the SML index is implemented, it becomes
evident that the three highest peaks occur in the winter months (Figure 7).
Figure 7. SML index values for the Dimitrovgrad station, showing summer (red) and winter (blue)
monthly values. Dened thresholds of 300 mm (red line) and 250 mm (yellow line) are indicated.
Atmosphere 2024,15, 256 14 of 20
For all the variables (Tmax, Tavg, and P), the slope is signicantly positive. Tmax
increases nearly three times as much as Tavg (0.0305 versus 0.0125; see Table 8). Precipitation
(P) increases signicantly as well (Figure 5).
Table 8. Linear ordinary least-squares (OLS) regression results (slope and intercept estimates) with
bootstrap standard errors (se), obtained from 2000 moving-block bootstrap resampling (following the
approach of Mudelsee (2014) [59]).
Dimitrovgrad
Station Slope se_Slope Intercept se_Intercept
Units (Degrees/Year) (Degrees/Year) Degrees Degrees
Tmax 3.047 ×10−21.087 ×10−2−4.403 ×1012.158 ×101
Tavg 1.245 ×10−27.698 ×10−3−1.459 ×1011.527 ×101
P8.605 ×10−26.058 ×10−2−1.168 ×1021.203 ×102
4.2. CORDEX Climate Model Data
In Figure 8, historical data are presented on the left, while bias-corrected CORDEX
climate model data are shown on the right. Among the seven models, all run until the year
2100, only three values exceed an SML value of 300 mm.
Figure 8. SML index data calculated using Dimitrovgrad station data. (A). Predictions based on
bias-corrected RCM; (B). Predictions based on non-bias-corrected RCM. The SML threshold (300 mm)
exceedances are indicated by a red asterisk.
Initially, non-bias-corrected CORDEX climate model data were downloaded, but
values included precipitation values larger than 700 mm in one summer month for one
Atmosphere 2024,15, 256 15 of 20
grid. Due to this, we present this data with caution. When the average values for the
Visoˇcica basin are calculated, the results look more representative. Figure 8shows SML
values applied to historical and RMC data (both bias and non-bias-corrected). Given that
the threshold for landslide occurrence is set to SML = 300 mm, three such peaks indicating
potential events are evident in the model output data (Figure 8).
5. Discussion and Concluding Remarks
Fine-scale meteorological data, particularly pertaining to air temperature and pre-
cipitation, are imperative for comprehending and forecasting climate-induced effects on
landscape structure and function. Nevertheless, the spatial resolution of climate reanalysis
data, as well as outputs from climate models, frequently prove inadequate for investiga-
tions conducted at local or landscape scales [
65
]. When analyzing the historical climate
data for the 72-year interval from January 1949 to December 2021, February 1963 is shown
as the most hazardous month in terms of the SML index value. Based on precipitation data
alone, the likelihood of an extreme landslide might have been missed. However, the SML
index provides new insights into the likelihood of extreme events using a mix of data. The
analysis also demonstrates that the climate variable Tmax in urban and low-elevation areas,
such as Pirot and Dimitrovgrad, is not representative, as evidence by the SML data without
Tmax interpolation (Figure 9).
p
(
g
)
Figure 9. SML with interpolated Tmax (gray) and without interpolated Tmax (blue) for stations
Dimitrovgrad (A), Topli Do (B), and Dojkinci (C). Dened thresholds of 300 mm (red line) and
250 mm (yellow line) are indicated on the panels.
Based on studies by Handwerger et al. (2013) [
66
] and Pfeiffer et al. (2021) [
25
], it
is noticeable that snowmelt yields a more rapid response to potential land sliding than
rainfall precipitation. This observation implies that the observed snowmelt either happens
Atmosphere 2024,15, 256 16 of 20
in closer proximity to the landslide area or inltrates more efciently than rainfall. This phe-
nomenon could be linked to the greater variability in the duration and intensity of rainfall
as compared to the more consistent and prolonged snowmelt event, which also happens
during a season of low vegetative demand for water. Earman et al. (2006) [
67
] found that in
their study sites, 40–70% of groundwater recharge is associated with snowmelt despite only
25–50% of the average annual precipitation falls as snow. Crosta et al. (2014) [
68
] made
similar observations regarding the rapid response of landslides to snowmelt.
Historical data indicate that there is a signicant gap between the Zavoj event and other
SML peaks (by at least 20%, see Section 4.1). The predictive SML values also heavily depend
on different terrain, pedology, geology, and other properties that inuence landslides. Thus,
a value of 300 mm can be considered as a potential threshold for this region but may not
apply elsewhere. Therefore, for the calibration of potential threshold values in other regions,
an intersection between the identied critical points and eld-observed landslide processes
is needed, as shown by Musta´c et al. (2008) [57] and Manojlovi´c et al. (2018) [50].
Loss of population is prevalent across southeastern Serbia, especially in the study
area [
69
,
70
]. Currently, the investigated area has no village with more than 100 inhabitants
(Census, 2022 [
46
]). The population decreased from 13,914 (Census, 1953 [
71
]) to 504
(Census, 2022 [
46
]) inhabitants in the Serbian part of the Visok microregion (22 villages).
The depopulation and the associated decline in agricultural activities have allowed forests
and other types of vegetation to recover, reducing the likelihood of mass movements [
50
,
57
].
This means that for the occurrence of any future event, climatic values would probably
need to exceed those reported here.
Global temperature trends point to worldwide warming [
42
,
72
]. Data from our me-
teorological stations also showed increasing temperatures and signicant increases in
precipitation (Figure 5; Table 7). Our results can be associated with the work of Georgoulias
et al. (2022) [
63
]. Indeed, statistically signicant increases in daily mean, daily minimum,
and daily maximum near-surface air temperatures (
◦
C) are occurring in southeastern Serbia
both for the investigated periods (2021–2050 and 2071–2100) and across all examined RCPs
(2.6, 4.5, and 8.5). By the end of the century, models predict additional increases in precipita-
tion for southeastern Serbia. RCP 8.5 shows a somewhat similar change pattern, with slight
increases in precipitation during winter (December to February) and spring (March to May).
Thus, for future predictions, due to the presence of very high and rapid precipitation values,
non-bias-corrected data should not be used for the implementation of the SML index. Most
of the bias-corrected CORDEX climate models indicate the highest values during summer
months and winter values that are not inuenced by the SML index. In some models, there
is almost no negative Tmax, that means, the SML index is not inuenced at all. We did not
need to interpolate temperature (as in historical data) because CORDEX climate models
calculate grid cell temperature data that have taken into account the elevation. Therefore,
we conclude that, for this region, there is a relatively small chance for a landslide event in
the future that would rival the February 1963 event. However, should one occur, it would
be driven by excessive precipitation episodes rather than rapid snowmelt.
Predicting the weather remains one of the foremost challenges in contemporary sci-
ence, especially as our current forecasting capabilities struggle to extend beyond a 10-day
period [
73
]. Our study employs climate models to assess the likelihood of landslide events
for this area up to the year 2100. Future research should consider applying the SML index
in colder regions, where the anticipated trends of warmer winters and early springs are
expected to accelerate snowmelt, particularly in the high latitudes and in areas of higher
elevation [
25
]. The proposed SML index, rooted in fundamental meteorological properties,
offers a data-driven approach that can be applied across diverse geographical locations and
for mitigation of hydro-meteorological hazards at local to national scale.
The majority of ofcial meteorological stations in Serbia commenced operations in
1949, including those in our study area. However, there are some very sporadic data
points before the year 1949. Nevertheless, meaningful calculation of the SML index, which
necessitates knowledge about consecutive months, would not have been feasible with
Atmosphere 2024,15, 256 17 of 20
such sporadic data (therefore, we opted to avoid using it). Furthermore, missing data
add difculties to the successful implementation of the SML index. In our study, only the
Dimitrovgrad station operated continuously without missing values, while other stations
had missing data. Filling in such a series can be achieved through interpolation, as well
as the application of other statistical-mathematical methods and models. It would also be
benecial for future research to establish a landslide cadaster. Also, the limitation of the
SML index is presented in the variable threshold.
Landslides are a threat for damage to agriculture, water management, and other
economic and social anthropogenic activities [
50
,
57
]. Therefore, studying phenomena of
this magnitude is essential. For this purpose, the SML index primarily serves as an alarm
system after critical snow accumulations, while CORDEX climate data provide information
about the probability of future landslides using data from current trends and physical
models. Future research procedures aimed at improving the SML index should move
toward comparing thresholds in different basins and watersheds as well as correlating SML
values with changes in geographical, demographic, and socioeconomic aspects of the area.
Supplementary Materials: The following supporting information can be downloaded at: https:
//www.mdpi.com/article/10.3390/atmos15030256/s1, Table S1: Data used in this study.
Author Contributions: Conceptualization, R.M., M.M. (Manfred Mudelsee), A.R.R. and T.L.; method-
ology, R.M., M.M. (Manfred Mudelsee), M.G.R. and B.B.; software, R.M. and M.M. (
Manfred Mudelsee
);
validation, A.R.R., M.M. (Miloš Marjanovi´c), S.B.M., V.S. and T.L.; formal analysis, R.M., M.M.
(
Manfred Mudelsee)
and M.G.R.; investigation, R.M.; resources, M.M. (Manfred Mudelsee), J.N., B.B.
and T.L.; data curation, R.M. and J.N.; writing—original draft preparation, R.M.;
writing—review
and editing, M.M. (Manfred Mudelsee), R.J.S., A.A. and T.L.; visualization, R.M., M.G.R., M.M.
(Miloš Marjanovi´c) and A.A.; supervision, M.M. (Manfred Mudelsee), S.B.M., A.R.R., V.S. and T.L.;
project administration, B.B., M.M. (Manfred Mudelsee) and T.L.; funding acquisition, M.M. (Manfred
Mudelsee) and T.L. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Data is contained within the article or Supplementary Materials.
Acknowledgments: This research is supported by the EXtremeClimTwin project funded by the
European Union’s Horizon 2020 research and innovation program under grant agreement No. 952384;
Ministry of Science, Technological Development and Innovation, Republic of Serbia (No. 451-03-
47/2023-01/ 200124); Ministry of Science, Technological Development and Innovation of the Republic
of Serbia (No. 451-03-66/2024-03/ 200125 & 451-03-65/2024-03/200125). The authors are grateful to
the anonymous reviewers whose comments and suggestions greatly improved the manuscript.
Conicts of Interest: Author Aleksandar Anti´c is an employee of MDPI; however, he was not
working for the journal Atmosphere at the time of submission and publication. Author Manfred
Mudelsee is an employee of Climate Risk Analysis and Advanced Climate Risk Education gUG. The
companies played no role in the design of the study, the collection, analysis, or interpretation of data,
the writing of the manuscript, or the decision to publish the articles. The paper reects the views of
the scientists and not those of the company. Other authors declare no conict of interest.
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