**1. Introduction**

Landslides are one of the most common hazardous natural phenomena in Slovenia and worldwide, threatening the safety of local residents and damaging infrastructure. The main triggering factor of shallow landslides in Slovenia is rainfall, especially short and intense rainstorms, combined with

local geological, geomorphological and climatic conditions [1]. In recent decades, intensive rainfall events have become much more frequent. This is also due to global climate change, which leads to a high number of shallow slope failures [2]. Every year dozens to hundreds of new shallow landslides are recorded in Slovenia. Many of them cause damage to infrastructure and properties, including residential buildings and agricultural land. To mitigate possible serious consequences and damage, the use of a landslide early warning system (LEWS) is fundamental. To operate a successful LEWS, it is essential to understand the relationship between rainfall and landslide occurrence. This relationship is commonly defined by means of empirical rainfall thresholds. The calculation of rainfall thresholds for landslide triggering has been a major challenge over the last few decades. Campbell [3] was the first to demonstrate the connection between antecedent rainfall and its infiltration into low-permeable rocks with the triggering of landslides. Nilsen and Turner [4] also proved the impact of rainstorms and antecedent rainfall on the occurrence of slope mass movements and calculated threshold values for the investigated area. Caine [5] proposed a power law equation linking mean rainfall intensity (*I*) and duration of the rainfall event (*D*) based on data from different geological, morphological and climatic settings. Since then many different methods and algorithms have been developed for calculating rainfall thresholds [6–8]. LEWSs based on thresholds of different types have been implemented in many countries and regions [9,10], e.g., for the coastal areas of San Francisco [11,12], the metropolitan areas of Rio de Janeiro [13,14] and Vancouver [15], southern Taiwan [16], Italy [17] and regions in Italy such as Emilia-Romagna [18], Piedmont [19], Tuscany [20–22] and Sicily [23].

In Slovenia, Komac [1] calculated rainfall thresholds for individual lithological units on the entire Slovenian territory using the statistical chi-square method. Jemec Aufliˇc and Komac [24] analyzed rainfall patterns for shallow landslides in the Škofjeloško-Cerkljansko hills during six major rainfall events between 1991 and 2010, while Rosi et al. [25] used the MaCumBA (MAssive CUMulative Brisk Analyzer) algorithm by Segoni et al. [26] to determine the first mean intensity-duration *ID* thresholds on a regional scale and for four major river zones in Slovenia. Bezak et al. [27] determined empirical thresholds for flash floods and landslides in Slovenia using a copula-based method. Bezak et al. [28] also worked on the application of hydrological modelling for temporal prediction of shallow landslides, while Jordanova et al. [29] focused on the determination of empirical thresholds for shallow landslides in the Posavsko hills, Eastern Slovenia, with an analysis of antecedent rainfall and the intensity of seven major rainfall events between 2013 and 2017.

With the aim of improving prevention measures, the prototype of a LEWS for Slovenia was developed in 2013 [30]. The system is based on the comparison between the forecasted precipitation for the next 24 h and rainfall thresholds, determined using the chi-square method and 40 years of average rainfall correlated to the lithological unit [1]. Recently, a validation of this LEWS was carried out [29,31] and demonstrated the need for new thresholds.

The definition of empirical rainfall thresholds is often affected by subjective criteria, such as the definition of the rainfall events responsible for landslide triggering, and by uncertainties, such as the quality of rainfall data and the accuracy of the location and timing of landslide occurrences [32,33]. To avoid any subjective bias in the results, Melillo et al. [34,35] proposed an algorithm for the automatic calculation of thresholds for rainfall-induced landslides, which was improved and implemented in a software tool (CTRL-T, Calculation of Thresholds for Rainfall-induced Landslides Tool) [32]. The tool uses objective, standardized criteria for the automatic reconstruction of landslide-triggering rainfall conditions, based on historical rainfall records and landslide occurrence dates. It was applied by several authors in diverse environments in Italy [32,36], India [37] and Bhutan [38].

According to the determination of the amount of rainfall responsible for the landslide occurrence, we propose new rainfall thresholds, calculated using CTRL-T, for the entire national territory of Slovenia and for climatic and geological subdivisions. The new national rainfall thresholds are compared with the global and regional thresholds proposed by Caine [5], Guzzetti et al. [6,7], Rosi et al. [24], Peruccacci et al. [39] and Palladino et al. [40].

#### **2. Study Area**

Slovenia (20,273 km2) lies in Central Europe in the southeastern part of the Alps (Figure 1). The sparse landscape and the diverse geological conditions range from the Pannonian plains and hills and their sediments in the northeast through the Alpine foothills in the Prealpine region (East to Western Slovenia) to the Alpine region in the northwest and the Eocene flysch in the southwestern Mediterranean plateau. The tectonic and structural elements, intersecting the area, have led to unstable rock masses and landslide-prone conditions [41].

The rainfall is unevenly distributed over the country due to its location between the Alps, the Dinarides, the Pannonian Basin and the Adriatic Sea, which contributes to the Mediterranean climate conditions (Figure 1). According to the Slovenian Environment Agency (ARSO), the annual average precipitation between 1981 and 2010 shows that the western part of Slovenia (excluding the southwestern coastal area) and especially the northwestern Alpine region is the rainiest part [42]. The average annual rainfall ranges from 1600 mm to over 3200 mm in the Julian Alps. Rain clouds usually move north and east towards the Alps and Dinarides, which serve as an orographic barrier. Many deep-seated landslides and debris flows (e.g., Stože, Slano Blato, Potoška Planina) are present in the western and northwestern parts of Slovenia, while the east is more prone to shallow landslides. The less rainy area in the northeast accumulates on average almost 1000 mm per year.

**Figure 1.** Location of Slovenia, with indication of the rain gauges used to reconstruct the rainfall events responsible for the failures, classified into four geographical areas related to rainfall characteristics, and of the landslides included in the analyzed catalogue. The landslides used for threshold calculations are indicated with orange dots.

## **3. Methods and Data**

## *3.1. CTRL-T Tool and Threshold Equation*

CTRL-T is a tool for the automatic calculation of rainfall thresholds for their use in operative prediction of shallow landslides [32]. The calculation of thresholds is based on continuous sets of hourly rainfall data gathered from rain gauges, and on a landslide database, consisting of known locations (geographic coordinates) and times (accurate dates and, when available, hour) of landslide occurrences. The tool reconstructs rainfall events and determines the events that are more likely to be responsible for the observed slope failures. Two important input parameters were defined prior to the identification of rainfall events, i.e., (i) the maximum permissible distance between the representative rain gauge and the landslide (15 km) and (ii) the maximum acceptable delay between the end of a rainfall event and the occurrence of a landslide (48 h).

The calculations are performed by three separate segments, each of which performs specific tasks [32]. The first segment performs the reconstruction of the individual rainfall events from the continuous rainfall series and calculates the duration (*D*, in hours) and the cumulated rainfall (*E*, in mm) of the rainfall events. The separation of consecutive rainfall events is based on climatic and seasonal settings: two "no rain" time intervals are distinguished for a warm/dry and cold/rainy season, respectively. The determination of the two seasons is based on monthly soil–water balance (MSWB) model [43–45]. In more detail, the MSWB model exploits monthly rainfall and temperature data and allows estimating the average monthly potential and real evapotranspiration utilizing a water balance over the mean hydrological year. Furthermore, the aridity index (AI), i.e., the ratio between the average monthly rainfall and the average monthly potential evapotranspiration, is used to define the length of the two seasons for each of the four regions. The warm/dry season has AI < 1, while in the cold/rainy season AI ≥ 1. Once the length of the two seasons in each region has been defined, the ratio between the total amount of real evapotranspiration in the warm and the cold seasons is used to define the ratio between the "no rain" time intervals in each season.

The task of the second segment is to select the nearest rain gauge for each landslide. The maximum allowed distance between a landslide and a rain gauge is within a circular area of a given radius. This task is followed by the selection of single or multiple rainfall conditions (MRC) that are most likely responsible for the slope failures. Each MRC is assigned a weight to select the representative rain gauge and the rainfall conditions associated with the landslide. The weight is equal to the ratio between the cumulated rainfall (*E*) times the mean rainfall intensity (*I*) divided by the square of the distance between the rain gauge and the landslide.

The third segment is the calculation of cumulated event rainfall–rainfall duration—*ED*—thresholds at different non-exceedance probabilities (NEPs), and the associated uncertainties, where the MRC with the maximum weight for each failure (MPRC, Maximum Probability Rainfall Condition) are selected. The thresholds are defined using a frequentist approach [46,47] and have a power law form linking *E* to *D*:

$$E = \left(\alpha \pm \Delta\alpha\right) \cdot D^{\left(\gamma \pm \Delta\gamma\right)}\tag{1}$$

where α is the scaling parameter and γ is the shape parameter, i.e., the intercept and slope of the power law curve respectively; Δα and Δγ represent the relative uncertainties of the two parameters [46,47]. A more detailed description of CTRL-T can be found in Melillo et al. [32,34,35].

## *3.2. Landslide Data*

Initially, the landslide database consisted of 2179 landslides that occurred between 18 September 2007 and 5 May 2018. We classified all landslides in the database as shallow landslides. The failures, probably caused by snowmelt during the winter and the first months of spring (i.e., from early December to early April), were discarded. Landslides with unknown dates of occurrence or location and double entries (e.g., two landslides in the same place and time) were also excluded from the analysis. In total, we manually removed 583 landslides from the database, leaving 1596 landslides for further analysis.

The exact time of the failures was not known; therefore, all landslides were recorded as they had occurred at the end of the day. This could introduce uncertainties in the amount of rainfall responsible for the landslides (see e.g., [48]), which however were not evaluated. In particular, all rainfall up to the end of the day of the recorded dates was considered, although the landslides probably occurred earlier and could have consisted of lower amounts of rainfall.
