A key component for landslide early warning systems
(LEWSs) is constituted by thresholds providing the conditions above which a
landslide can be triggered. Traditionally, thresholds based on rainfall
characteristics have been proposed, but recently, the hydrometeorological
approach, combining rainfall with soil moisture or catchment storage
information, is becoming widespread. Most of the hydrometeorological
thresholds proposed in the literature use the soil moisture from a single
layer (i.e., depth or depth range). On the other hand, multi-layered soil
moisture information can be measured or can be available from reanalysis
projects as well as from hydrological models. Approaches using this
multi-layered information are lacking, perhaps because of the need to
keep the thresholds simple and two-dimensional. In this paper, we propose
principal component analysis (PCA) as an approach for deriving
two-dimensional hydrometeorological thresholds that use multi-layered soil
moisture information. To perform a more objective assessment we also propose
a piecewise linear equation for the identification of the threshold's
shape, which is more flexible than traditional choices (e.g., power law or
bilinear). Comparison of the receiver operating characteristic (ROC) (true skill statistic, TSS) of
thresholds based on single- and multi-layered soil moisture information also
provides a novel tool for identifying the significance of multi-layered
information on landslide triggering in a given region. Results for Sicily
island, considering the ERA5-Land reanalysis soil moisture data (available
at four different depth layers), corroborate the advantages of the
hydrometeorological approach gained in spite of the coarse spatial
resolution and the limited accuracy of reanalysis data. Specifically, the
TSS of traditional precipitation intensity–duration thresholds is equal to
0.5, while those of the proposed hydrometeorological thresholds is
significantly higher (TSS=0.71). For the analyzed region, however,
multi-layered information seems not to be relevant, as performances in terms
of TSS are similar to those obtained with single-layer soil moisture at the
upper depths, namely 0–7 and 7–28 cm, which can imply that in Sicily
landslide phenomena are mainly influenced by soil moisture in most shallow
soil layers.
Introduction
The impact of landslides triggered by rainfall is constantly increasing due
to landscape modifications, i.e., urbanization, deforestation, land changes,
and the abandonment of rural areas (Roccati et
al., 2019). Landslides can cause serious damage to man-made structures and
land, as well as loss of natural resources and lives. The role of landslide
risk in human well-being is highlighted by the fact that more than 4800
landslide occurrences were documented from 2004 to 2016, with over
55 000 reported fatalities at a global scale (Froude and Petley, 2018).
Furthermore, landslides triggered by rainfall have been identified as the
cause of approximately 90 % of fatalities globally (Haque et al., 2016;
Sultana, 2020), and, from an economic point of view, annual losses were
estimated to total USD 20 billion (Sim et al.,
2022).
Over the last decades, an increasing number of studies also focused on the
potential effects of climate change on landslide phenomena
(McInnes
et al., 2007; Dijkstra and Dixon, 2010; Crozier, 2010), pointing out that there
are some unresolved issues, such as the abundance, activity, frequency, and
return period of landslides in response to the projected climate change
(Gariano and
Guzzetti, 2016; Peres and Cancelliere, 2018). In light of these
considerations and, after recent catastrophic landslides worldwide, there is
high interest from scholars and civil protection agencies in the development
of landslide early warning systems (LEWSs), which can serve as an aid in
predicting possible slope movements and thus as a risk mitigation tool
(Roccati et al., 2020; Highland
and Bobrowsky, 2008; Chae et al., 2017).
Landslide-triggering thresholds are a key component of LEWSs. In general,
empirical rainfall thresholds, which relate the occurrence of landslides to
rainfall event characteristics such as intensity, duration, total amounts,
or a combination thereof, are commonly applied for the majority of regional
LEWSs
(Guzzetti
et al., 2007, 2008; Segoni et al., 2018a; Aleotti, 2004). When information
on non-triggering rainfall is also available, thresholds can be determined
as the best classifiers based on the confusion matrix
(Berti et al., 2012; Staley et al., 2013; Peres and Cancelliere, 2014, 2021; Postance et
al., 2018). In the last decade, there has been
an increasing interest in the development of hydrometeorological thresholds
that consider rainfall characteristics and subsurface hydrological
variables, such as soil moisture content and catchment storage information
(Uwihirwe et al., 2022; Mirus et al.,
2018a, b; Thomas et al., 2018; Segoni et al., 2018b; Wicki et al., 2020, 2021; Bogaard and Greco, 2018, 2016; Reder and Rianna, 2021;
Marino et al., 2020; Palau et al., 2021; Conrad et al., 2021). These studies
demonstrate improvements of the prediction performances with the
hydrometeorological approach, with respect to the traditional precipitation-based
thresholds, even if not all climatic areas have been explored, so further
applications are still useful. Furthermore, none of the previous studies
take into account the possibility to exploit the information from a soil
moisture profile or multi-layered soil moisture information, corresponding
to several depths or depth ranges. This is most likely because thresholds
have to be kept simple, i.e., two-dimensional, for being effectively
communicated to decision makers.
In the present work, we propose an approach that allows taking into account
the multi-layer soil moisture information within hydrometeorological
thresholds while keeping these two-dimensional thanks to a statistical
technique named principal component analysis (PCA)
(Jolliffe, 2002). This technique allows us to find the linear
combination between soil moisture at different depth layers which retains as
much as possible the information content of the multiple layers together,
capitalizing on the presence of correlation between the soil moisture at
different depths. The proposed approach is also intended to test whether
multi-layer soil moisture information may provide better predictive
performance than the single-layer one by comparing the relative prediction
performances in terms of receiver operating characteristic (ROC) indices,
such as the well-known true skill statistic (TSS). We carry out our
investigation using observed precipitation in combination with ERA5-Land
reanalysis soil moisture data, available at four different depth layers with
a 0.1∘×0.1∘ (≅9 km) resolution
(Hersbach et al., 2020). Recent studies
proved that the main climate variables (i.e., soil moisture, temperature,
precipitation) obtained from third-generation atmospheric and reanalysis
datasets (i.e., ERA5 project) have a reasonable accuracy in reproducing in
situ measurements
(Dorigo et al., 2011; Li et al., 2020; Beck et al., 2021), though accuracy issues still
remain significant. The case study of the Sicily region is used to test
the proposed methodology.
The paper is organized as follows. First, the procedure for the dataset
creation and description of the methodology leading to the proposed approach
to implement multi-layer soil moisture data in hydrometeorological
thresholds are presented in the “Material and methods” section. Then, the
“Study area” section describes the relevant features of the study area,
namely the Sicily island (southern Italy). Next, the results and discussion
concerning the performance obtained in correspondence with all identified
rainfall-triggering thresholds are presented in the “Results and
discussion” section. Finally, conclusions are drawn in the last section.
Materials and methodsDataset construction
The construction of the rainfall and landslide events dataset is a key step that
involves different types of data (i.e., observed landslides, rainfall events,
and reanalysis data of soil moisture). As schematically illustrated in Fig. 1, in the first step the FraneItalia project
(Calvello and Pecoraro, 2018) is
employed to collect information regarding the observed landslides, as it is
a thorough spatiotemporal inventory of historical landslides that have
impacted the Italian territory since 2010, including both occurrences that
resulted in fatalities and occurrences that did not.
Schematization of the procedure followed for dataset construction.
The first classification criterion by the FraneItalia catalog is based on
the number of landslides triggered by the same rainfall event in a given
geographic area. Specifically, single landslide events (SLEs) and areal
landslide events (ALEs) are distinguished for records referring to single or
multiple landslides, respectively. Both SLEs and ALEs are then categorized
into one of three classes in relation to their impacts, in order to track
whether a landslide occurrence resulted in casualties or missing people (C1,
very severe), injured people and evacuations (C2, severe), or no one was
physically harmed (C3, minor). The data on occurrence location, the date the
landslide occurred, the source of information, and the number of landslides
for ALEs are further details that have also been included in the catalog,
together with the onset and duration of the landslide occurrence and its
consequences.
Thanks to this accurate level of detail, it is possible to filter only the
landslide events triggered by rainfall, which are precisely those to take
into consideration in our study.
The CTRL-T (Calculation of Thresholds for Rainfall-induced Landslides-Tool)
code (Melillo et al., 2018) is subsequently
used for the identification of the rainfall events that were more likely to
be responsible for the observed slope failures. Specifically, CTRL-T
automatically and objectively reconstructs rainfall events and the
triggering conditions responsible for the failure using a set of adjustable
parameters to account for different morphological and climatic settings.
Briefly, the tool consists of distinct modules with specific purposes. Among
these, one module operates the reconstruction of rainfall events in term of
duration (D, in h) and cumulated event rainfall (E, in mm) using a
continuous hourly rainfall time series and setting several climate and
spatial parameters such as the warm period in a year (CW), the cold
period in a year (CC), the resolution of the rain gauge (GS), the
instrumental sensitivity of the rain gauge and the minimum value exceeding
which the isolated hourly measurements are considered relevant (ER), and
the radius of the buffer to assign each landslide to the closest rain gauge
(RB). Furthermore, in order to account for seasonality (i.e., different
evapotranspiration rates in different periods of the year), additional
rainfall parameters can be set by the user, namely the dry interval
separating isolated rainfall measurements (P1); the time periods used to
remove irrelevant amounts of rainfall, (P2), and (P3); and the
minimum dry period separating two rainfall events (P4). The readers are
referred to Melillo et al. (2018) for more detailed information on these
parameters. A further module instead performs the selection of the rain gauge
representative for the landslide. Once the maximum allowed distance between a landslide and a rain gauge is defined as a circle of radius RB specified by the user, if more than one rain gauge is located within the circle, then the rainfall events from each rain gauge are weighted based on the rain gauge–landslide distance and the rainfall event characteristics (cumulated
rainfall and duration). More specifically, given the multiple rainfall
conditions (MRCs) that are most likely responsible for the slope failures as
pair of rainfall event duration (DL) and cumulated event rainfall
(EL), or a set of two or more pairs, each MRC is assigned a weight to
select the representative rain gauge and the rainfall conditions associated
with the landslide. The weight is proportional to the inverse square
distance between the rain gauge and the landslide (d-2), the cumulated rainfall (EL), and the rainfall mean intensity (ELDL-1):
w=f(d,EL,DL)=d-2EL2DL-1.
Thus, among all the identified MRCs, those with the highest weights w are
defined as the maximum probability rainfall conditions (MPRCs), and these
reconstructed rainfall conditions were assumed as the triggering rainfall
events. Lastly, Fig. 2, depicts how the duration of a triggering rainfall
event is defined. Specifically, when a landslide occurs during a dry period
the whole event that preceded it is considered as a triggering rainfall event;
otherwise, just the rainfall that occurred before the landslide occurrence
is taken into account.
Sketch illustrating how the duration of a triggering rainfall
event is defined (adapted from Peres et al., 2018).
As shown in Fig. 1, the last step for the dataset set-up consists of the
association of soil moisture data to the beginning of each rainfall event,
both triggering and non-triggering ones. In this regard, the ERA5-Land
reanalysis dataset is used. It provides the volume of water
ϑ [m3m-3] at
four distinct soil depths levels (i.e., 0–7, 7–28, 28–100, and
100–289 cm). The ERA5-Land soil moisture data are provided at the hourly
scale as grid data with a horizontal resolution of 0.1∘×0.1∘. Thus, being at the same temporal resolution of rainfall
time series, the soil moisture values representative of the closest cell to
the rain gauge that recorded the rainfall event are associated, without
delay, to the considered event.
Principal component analysis
Principal component analysis (Jolliffe, 2002) is a
multivariate technique that analyzes a data table in which observations are
described by several intercorrelated quantitative dependent variables to
extract the important information from the table and to represent it as a
set of new orthogonal variables called principal components
(Abdi and Williams, 2010).
Precisely, the data are transformed according to a new coordinate system
having the x axis, known as the first principal axis, characterized by the
highest data variation. Along the successive axes (e.g., the second
principal axis, the third principal axis, and so on), the data are
characterized by increasingly lower variation. Each succeeding principal
component explains the maximum amount of variance feasible with the
requirement that it is orthogonal to the previous principal components. In
practice, identifying the eigenvalues and eigenvectors of the covariance
matrix is the formal mathematical equivalent of solving the PCA problem. The
direction along which the data have the highest variance is the eigenvector,
while the related eigenvalue is a quantification of the variance in the data
along the corresponding eigenvector. Accordingly, the first principal
component is the eigenvector with the greatest eigenvalue, followed by the
eigenvector with the second-highest eigenvalue, and so on. Thus, the so
computed principal components are employed for the projection of the data
into the new coordinate space (Kherif and
Latypova, 2019).
Practically, in our study, θ (Eq. 2) represents the soil
moisture data table for which to compute the principal components, specified
as an n-by-p matrix. Rows correspond the total number n of the considered
rainfall events (i.e., observations), and the number of columns to the four
depths levels at which the initial soil moisture data are provided (i.e.,
variables).
θ=ϑ11ϑ12ϑ13ϑ14ϑ21ϑ22ϑ23ϑ24⋮⋮⋮⋮ϑn1ϑn2ϑn3ϑn4A instead represents the principal component loadings (i.e.,
coefficients) table, specified as a p-by-p matrix. The rows of matrix A are
called the eigenvectors, and these specify the orientation of the principal
components relative to the original variables.
A=a11a12a13a14a21a22a23a24a31a32a33a34a41a42a43a44
Thus, the principal components (Si) for the generic ith row are
given by a linear combination of the variables θ and
A, namely
4Si1=a11ϑi1+a12ϑi2+a13ϑi3+a14ϑi4,5Si2=a21ϑi1+a22ϑi2+a23ϑi3+a24ϑi4,6Si3=a31ϑi1+a32ϑi2+a33ϑi3+a34ϑi4,7Si4=a41ϑi1+a42ϑi2+a43ϑi3+a44ϑi4,
with i=1,…,n.
In matrix notation, the transformation of the original variables to the
principal components is written as
S=θA.
Thresholds' identification
First, we identify the traditional rainfall intensity–duration power-law
thresholds. The ID threshold has the form of a power law I=αD-β, where I [mmh-1]
represents the rainfall intensity, i.e., the average precipitation rate over
the considered period; D [h] represents the duration of the
rainfall event; α is the intercept parameter; and β is the
slope parameter. After reconstructing the rainfall events with the
methodology explained for the dataset creation, and after calculating the
main variables (i.e., mean rainfall intensity and duration), an optimization
tool (i.e., the MATLAB® particle swarm
optimization toolbox) is used with the aim to search for the best possible
α and β curve parameters able to maximize the true skill
statistic (TSS) index objective function (Eq. 11), which is based on the
confusion matrix or the receiver operating characteristics (ROCs). The
confusion matrix is expressed in terms of the count of true positives (TPs),
true negatives (TNs), false positives (FPs), and false negatives (FNs)
(Peirce, 1884) (Table 1).
As a function of the variables reported in Table 1, the three reference
standard ROC indices – namely, true positive rate, false positive rate, and
true skill statistic – are listed below (Eqs. 9–11):
9TPR=TP(TP+FN),10FPR=FP(TN+FP),11TSS=TPR-FPR.
The highest performances correspond to TSS=1 when the model
produces no false or missing predictions.
Afterwards, the analysis is focused on the identification of the
hydrometeorological threshold trough a novel parametric equation that
represents the lower boundary between triggering and non-triggering rainfall
events on the basis of the mean rainfall intensity and the reanalysis of
soil moisture values. In this context, we propose a piecewise linear
equation as a reliable relationship able to well classify the events on the
semi-log plane:
I=y0,ϑ<x0y1-y0x1-x0(ϑ-x0)+y0,x0≤ϑ≤x1y1,ϑ>x1,
where I and ϑ correspond to rainfall intensity and to soil
moisture values, respectively. This parametric form of the threshold has
been devised based on the visual inspection of the scatter plot of
triggering and non-triggering events (i.e., heuristically) and corroborated
by comparison with other relationships proposed in the literature –
specifically, the power law and the simple bilinear (as opposed to a linear
or more complex power or high-degree polynomial)
(Uwihirwe et al., 2022;
Thomas et al., 2019; Mirus et al., 2018b). x0, x1, y0, and
y1 are the threshold's parameters that must be estimated. In this
regard, these parameters are computed by adopting the same objective
function and optimization procedure as those used for the identification of
the parameters of the power-law ID threshold, i.e., the TSS objective
function (Eq. 11) and the MATLAB® particle
swarm global optimization toolbox. Therefore, Eq. (12) is used to derive the
hydrometeorological thresholds employing single- and multi-layer soil
moisture data, respectively. Specifically, the mean rainfall intensity (I)
and the soil moisture at each of the four depth levels (ϑ1,
ϑ2, ϑ3, ϑ4) available from the
ERA5-Land reanalysis data are used for the single-layer approach, while the
mean rainfall intensity (I) together with the first principal component of
soil moisture, i.e., the linear combination of soil moisture at the four
depths corresponding to the minimum information loss (highest explained
variance), are used for the multi-layer approach. The TSS values obtained in
the applications considering soil moisture, both single- and multi-layered,
(hereinafter indicated as TSSpar) are being compared to one another,
as well as to the TSS value obtained for the power-law ID threshold
(hereinafter TSSpl).
Study area
The study area selected for our study is the island of Sicily (southern
Italy, 37.75∘ N, 14.25∘ E) which, with an area of ∼25700km2, is the largest island of the Mediterranean Sea. A hilly
morphology (62 %) dominates the landscape in the island, while the rest is
characterized by a mountainous and flat morphology, especially in the
eastern part of the island around Catania. The terrain average elevation is
about 400 m above sea level, ranging from 0 to 3320 m on the peak
of the Etna volcano. Geologically, the Sicily island arose during the
Neogene, when the European and African plates converged. Thus, Sicily stands
out for its complex geological and lithological features which,
cooperatively with anthropic activities (e.g., changes in land use,
management of forest), have generated a wide range of different types
of soil (Venturella, 2004).
The climate is warm-temperate, with hot and dry summers, especially on the
southern coasts, and higher and more frequent precipitation during the
colder winter months, in the mountainous internal areas
(Pumo et al., 2019). Mean annual
precipitation ranges between 700 and 800 mm, and autumn and winter are the
rainiest seasons. The most severe rainfall events frequently hit the eastern
side of the island and, specifically, the eastern side of the Etna volcano
and the flanks of the Peloritani mountains, with the greatest precipitation
peaks on the Ionian side
(Gariano et al., 2015). On the
other hand, south Sicily is distinguished by lower precipitation than the
mean values recorded in the rest of the region, since it is located at a
lower height and is exposed to the hot and dry African winds
(Alecci and Rossi, 2007).
Figure 3 shows the geographical context of Sicily, the rain gauge locations
for the period 2009–2018 (Distefano et al.,
2022), and the observed landslide locations. In more detail, 207 landslide
events were retrieved by the FraneItalia database from 2010 to 2018 and, for
each of them, longitude–latitude coordinates (WGS84 datum), together with
the initiation time, were retrieved.
Elevation map of the study area (Sicily region), showing the
location of the rain gauges and landslide occurrences (credit to
http://www.sinanet.isprambiente.it/it/sia-ispra/download-mais, last access: 13 January 2023,
and ESRI, 2020).
Concerning the observed rainfall measurements, we consulted the data
provided by the regional water observatory (Osservatorio delle Acque, OdA),
the SIAS (Sicilian Agro-meteorological Information Service), and the
Regional Civil Protection Department (DRPC), namely the three main gauging
networks installed in Sicily.
This enabled an hourly time series to be reconstructed for the precipitation
over the period 2009–2018. As previously explained in Sect. 2.1, using
these continuous rainfall time series, the rainfall events were identified
using the CTRL-T research code. For the calibration of these regional
parameters required by CTRL-T, we referred to a previous application of the
algorithm to the Sicily island (Melillo et al., 2015). Specifically,
according to this approach, the dry period (no rain) has been set equal to
48 h (P4,warm) between April and October (warm season,
Cw), while it has been set equal to 96 h (P4,cold) from
November to March (cold season, Cc). Indeed, in line with Köppen (1936) and Trewartha (1968), it is reasonable to assume that in Sicily, due
to the Mediterranean climate, the warm period is longer than the cold one.
The rain gauge sensitivity GS has been set equal to 0.2 mm, while the rain
gauge search radius RB has been established equal to 16 km. Table 2
summarizes adopted values for mentioned CTRL-T parameters.
CTRL-T parameters for the reconstruction of the rainfall events
used in the present study.
An explorative analysis was carried out, to investigate the correlation
between the four soil moisture depths (ϑ1, ϑ2,
ϑ3, ϑ4). The plot shown in Fig. 4 represents the
correlation matrix between all pairs of variables, together with the
Pearson's correlation coefficients.
Correlation matrix between the four soil moisture level depths
(ϑ1, ϑ2, ϑ3, ϑ4). Each off-diagonal subplot
contains a scatterplot of a pair of variables with a least-squares reference
line, the slope of which is equal to the displayed Pearson correlation
coefficient. Each diagonal subplot contains the distribution of a variable
as a histogram.
Overall, all the four soil moisture depths are related to each other.
Specifically, the diagonal subplot between the upper two depth levels
ϑ1 and ϑ2 has the highest correlation, with a
Pearson correlation coefficient equal to 0.85. This suggests that PCA can be
adopted in order to find out the linear combination expressing the
correlation between the involved soil moisture variables.
The preliminary step, required when PCA is performed, is to center the data
on the mean values of each variable, namely by subtracting the mean. This
step allows the cloud of data to be centered on the origin of the principal
components, but it affects neither the spatial relationships of the data,
nor the explained variance along the variables. At this stage, it was
possible to proceed with PCA and, according to Eqs. (4)–(7), the four
principal components of soil moisture were defined as follows:
13Si1=0.65ϑi1+0.58ϑi2+0.47ϑi3+0.15ϑi4,14Si2=-0.54ϑi1-0.04ϑi2+0.63ϑi3+0.55ϑi4,15Si3=0.37ϑi1-0.29ϑi2-0.39ϑi3+0.79ϑi4,16Si4=-0.38ϑi1+0.76ϑi2-0.48ϑi3+0.23ϑi4.
The loading values of each principal component are intended as the weights
aij (Eq. 3); therefore, the higher the value of the weight, the larger
the contribution of a variable to the component associated with the weight.
The sign of a loading indicates whether a variable and a principal component
are positively or negatively correlated. Here, although overall slightly
large loadings correspond to the first principal component, none of the four
variables has a strong relationship with a particular principal component.
(a) Total variance explained by each principal component; (b)
estimated loadings for each principal component Si.
Figure 5a shows the scree plot representing the total percentage of variance
explained by each of the four principal components. The chart reveals the
decreasing rate at which variance is explained by additional principal
components. Figure 5b represents a grouped bar plot indicating the estimated
loadings corresponding to each of four principal components as reported at
Eqs. (13)–(16).
Panel showing four different triggering rainfall events. For each
of them the precipitation time series together with the soil moisture time
series (ϑ1, ϑ2, ϑ3, ϑ4) are reported, as well as the first principal component of
soil moisture S1 and the timing of each
landslide.
Because dimensionality reduction is a goal of PCA, several criteria can be
considered for determining how many principal components should be examined
and how many should be ignored (Rencher, 1998). A few of the criteria that can be considered include the following: (i) ignore principal components at the point at which the next principal
component offers little increase in the total explained variation; (ii) ignore
the last principal component whose explained variations are all roughly
equal; (iii) include all principal components up to a predetermined total
explained variation. In our study, the third criterion was applied
considering a threshold value of 75 %. Therefore, only the first principal
component was considered as it guaranteed the desired explained variation of
about 75 %.
Threshold identification
CTRL-T tool reconstructed 144 landslide events out of the 207 landslides
retrieved by the FraneItalia database. Four different triggering rainfall
events, representing a range of triggering conditions, were selected within
the database, and the precipitation time series together with the soil
moisture time series are plotted in Fig. 6.
As expected, the upper two soil moisture layers are those that are most
similar to precipitation trends, as well as the first principal component of
soil moisture S1, computed using Eq. (13). Overall, a greater variability
in soil moisture values can be observed in correspondence with ϑ1 and ϑ2, which assume maximum values about equal to 0.4
in correspondence with all the analyzed triggering rainfall events.
First, the power-law ID threshold maximizing TSS was identified (Fig. 7).
In particular, the plot shows the triggering events as red points, while the
non-triggering events, since there are a very large number, are better
represented by a color map indicating the relative frequency of
non-triggering rainfall events, following a plotting technique inspired by
Leonarduzzi et al. (2017).
Traditional power-law threshold on the log–log plane between
observed mean rainfall intensity (I) and duration (D).
Parametric thresholds on the semi-log plane between mean rainfall
intensity and soil moisture at the four distinct depths: (a)ϑ1 0–7 cm; (b)ϑ2 7–28 cm; (c)ϑ3 28–100 cm;
(d)ϑ4 100–289 cm.
For this threshold a TSSpl=0.50, corresponding to a TPRpl=0.76
and FPRpl=0.26, is obtained. Figure 8 shows the obtained thresholds
when the mean rainfall intensity and the soil moisture at each of the four
depth levels are considered. As can be seen, especially in correspondence with
the upper two depths (i.e., 0–7, 7–28 cm), the triggering rainfall events
are located, for the most part, on the upper right side of the graph, suggesting
that the equation proposed for the identification of the thresholds (Eq. 12)
well fits this trend. Furthermore, at all depths taken into consideration,
there is a noticeable clustering of the highest relative frequency values of
non-triggering rainfall events below the related parametric threshold. All
four identified thresholds have better performance than the ID threshold.
Specifically, higher TSS values were obtained for the first two depths, with
a TSSpar equal to 0.71, while significantly lower values of
TSSpar (0.61 and 0.54) are obtained with the third and fourth soil
moisture level, respectively.
TSS values in correspondence with each analyzed scenario and
parameters (x0, y0, x1, y1) estimated for the parametric thresholds.
Moving to the multi-layer approach, the optimal parametric threshold
identified using the mean rainfall intensity and first principal component
of soil moisture is presented in Fig. 9. In this case, a TSSpar=0.71
was obtained.
Parametric threshold on the semi-log plane between observed mean
rainfall intensity (I) and first principal component of soil moisture
(S1).
Table 3 summarizes the TSS values in correspondence with the analyzed
thresholds, together with the values of parameters (Eq. 12) estimated for
the parametric thresholds.
Overall, the results relative to the hydrometeorological thresholds
corroborate other studies showing their better predictive performance when
compared to the traditional ID threshold. For the specific case study of
Sicily, thresholds based on multi-layered soil moisture information have
similar predictive performances to thresholds based on single-layered
information. This points out that the two shallowest depth layers are of the
greatest relevance for landslide triggering in Sicily. This may not be the
case for other case study areas, and the proposed approach of comparing
multi- vs. single-layer information allows us to define which layers of soil are
most relevant in controlling landslide triggering in a given region.
Conclusions
In this study, a framework based on PCA aimed at introducing multi-layer
soil moisture information within hydrometeorological threshold
identification has been proposed. Our investigation, relative to Sicily,
corroborates previous studies showing higher performances for
hydrometeorological thresholds compared to the traditional ID
power-law thresholds. Specifically, a significant improvement of
performances was found with hydrometeorological thresholds, leading to TSS
values of up to 0.71, which were much higher than those obtained with the
traditional approach (TSS=0.50). The application of PCA to soil
moisture data at various depths turned out to be a valuable approach to
include multi-layer soil moisture information while keeping the thresholds
two-dimensional, though for the case study region, multi-layer information
seemed not so relevant, as performances corresponding to the two uppermost
layers are similar to those corresponding to the PCA combination of all four
layers. Comparison of prediction performances relative to thresholds based
on multi- versus single-layer soil moisture information provides a mean to
assess which soil depth intervals retain the most relevant information for
improving thresholds' predictive performances. This represents a strategic
tool supporting decision-making in LEWSs development. Finally, it is worth mentioning that our investigation considered ERA5-Land soil moisture data, whose actual use for landslide prediction is limited by the fact that they are made available with a delay of some weeks from real time. However, this delay is expected to be significantly reduced in the near future in light of the increasing computational capabilities. In this regard, the valuable improvements,
gained despite the inherent uncertainty of reanalysis data, further
encourage the installation of monitoring networks for direct in situ soil
moisture measurements with enhanced spatial and temporal resolutions, as
with these observations even higher improvements are to be expected. Future
developments of this research will consider other geographical regions in
order to further explore the role of multi-layer soil moisture.
Data availability
The FraneItalia landslides catalog is available at 10.17632/zygb8jygrw.2 (Calvello and
Pecoraro, 2018). Rainfall measurements are available at the
website of the Servizio Informativo Agrometeorologico Siciliano (SIAS)
(http://www.sias.regione.sicilia.it/, SIAS, 2023) and at
the Osservatorio delle Acque
(http://www.bio.isprambiente.it/annalipdf/,
ISPRA, 2023). Reanalysis soil
moisture data are available from
10.24381/cds.e2161bac
(Muñoz Sabater, 2021).
Author contributions
Conceptualization was done by NP, DJP, EC, and AC; formal analysis by NP and DJP; investigation by NP and DJP; methodology by NP and DJP; coding by NP and DJP; supervision by DJP, EC, and AC; writing the original draft by NP and DJP; and the writing, review, and editing by NP, DJP, EC, and AC. All authors have read and agreed to the published version of the paper.
Competing interests
At least one of the (co-)authors is a member of the editorial board of Natural Hazards and Earth System Sciences. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Special issue statement
This article is part of the special issue “Hydro-meteorological extremes and hazards: vulnerability, risk, impacts, and mitigation”. It is a result of the European Geosciences Union General Assembly 2022, Vienna, Austria, 23–27 May 2022.
Acknowledgements
The authors acknowledge Francesco Marra (handling editor) and the anonymous referees for their valuable comments. Support from the Italian MIUR and the University of Pavia is acknowledged within the program Dipartimenti di Eccellenza 2023–2027. Nunziarita Palazzolo's doctoral program was offered by the University of Pavia.
Financial support
Nunziarita Palazzolo is supported by post-doctoral contract “Eventi idrologici estremi e resilienza ai cambiamenti climatici”, funded within the activities of the research project “LIFE SimetoRES – Urban adaption and community learning for a RESilient Simeto Valley” – grant agreement no. LIFE17CCA/IT/000115 – CUP C65H18000550006. This research was partially carried out within the project HydrEx – Hydrological extremes in a changing climate – Piano di incentivi per la ricerca di Ateneo (Pia.ce.ri.), 2020–2022, Università di Catania, and the Ministero dell’Università e della Ricerca (Programma Operativo Nazionale Ricerca e Innovazione 2014–2020 – Progetto “reCITY – Resilient City Everyday Revolution” – grant agreement no. ARS01_00592 – CUP B69C21000390005). APCs were funded by “Fondi di Ateneo 2020–2022, Università di Catania, linea Open Access”.
Review statement
This paper was edited by Francesco Marra and reviewed by two anonymous referees.
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