Comparative Analysis of SPEI and WEI⁺ Indices: Drought and Water Scarcity in the Umbria Region, Central Italy

Abstract

The purpose of this study is to assess the possibility of relating two phenomena: first, meteorological drought, which is exclusively dependent on climate; second, water scarcity and its uses, which are predominantly anthropogenic in nature. Sometimes these phenomena may overlap, with the former amplifying the latter, but direct correlation is not always highlightable due to the anthropogenic character of water shortage and the variability of water supply sources. In the literature, many papers evaluate these two phenomena separately: in particular, the SPEI (Standardized Precipitation-Evapotranspiration Index) is widely used for detecting meteorological drought, while the link between water shortage and its uses is assessed through an index of water resource exploitation, WEI⁺ (Water Exploitation Index Plus), which is based on the calculation of an anthropogenic factor, withdrawals net of restitutions. Specifically, this study examines the SPEI and WEI⁺, respectively, calculated for the July–August–September quarter (SPEI3 sept) and during the low-flow period (WEI⁺_EF low flow), according to the environmental flow constraint. These periods are considered seasonally overlapping in the study area of the Umbria region. The results analyzed by spatial method show the more critical areas, where SPEI3 sept and WEI⁺_EF overlap their critical values, respectively, <−1.0 and >100%. The proposed methodological approach provides stakeholders in the water sector with essential information to adopt a proactive approach to drought phenomena.

1. Introduction

The management and sustainability of water resources is a very important issue in the world. Issues such as climate change, population growth, pollutants, and man-made disasters have led to a decline in water resources [1]. In this context, countries need to develop knowledge and implement policies to effectively manage water resources [2,3].

Researchers and decision makers involved in operational water management can collaborate to identify critical issues and propose solutions [4]. For example, drought and water scarcity are two phenomena of a very different nature, but they can be closely correlated in water resource management policies.

Drought is a climate-related event and has extensive consequences in many sectors, such as agriculture [5], energy [6], ecosystems [7], and overall socioeconomic impact [8]. Drought is also influenced by global warming, mainly due to greenhouse gas emissions, which have altered the global hydrological cycle and have caused more frequent and persistent natural hazards [9].

Many studies have been conducted on drought, using various standardized drought indices to evaluate and estimate this event. Among the most cited are the Standardized Precipitation Index (SPI) [10,11], Standardized Precipitation Evapotranspiration Index (SPEI) [12,13,14], Palmer Drought Severity Index (PDSI) [15,16], and Reclamation Drought Index (RDI) [17]. The relevance of SPI in drought studies is due to its simplicity and its sole dependence on precipitation data. However, under the global climate warming, air temperature variations are expected to become the new primary driver of droughts. Therefore, using evapotranspiration (ET) together with precipitation (P) in the structure of the SPEI index allows for a more comprehensive drought assessment [18,19].

The water gap between water demand and availability leads to water scarcity, which is therefore closely linked to the use and management of water resources for different uses. A multitude of local and global studies analyzed the drivers and pressures that contribute to water scarcity [20]. Leijnse et al. [21] studied the most important water scarcity hotspots worldwide, combining outputs from a global hydrological model with the extensive literature. For Italy, this study identifies the hydroclimatic change, temperature increase, and agricultural and municipal water use to be the key global drivers and pressures. The most significant impacts on water resources include groundwater and surface water depletion, as well as salinization. The successive impacts on social–environmental systems include reduced agricultural production as the primary impact, while secondary impacts involve ecosystem damage, health deterioration, conflicts and migration, and educed hydroelectricity production. Responses can differ significantly. While some responses have a positive impact on alleviating water scarcity, such as increased water storage capacity, others are ineffective or can even worsen water scarcity problems due to inefficient water use. These results are substantially in agreement with local studies on climate [22,23,24], agricultural water use [25,26], and the importance of reservoirs [27,28].

This paper aims to evaluate the connection between meteorological drought and water scarcity, a topic that has received limited attention in the literature. To date, the only study on this subject is by Fan et al. [29], which focuses on the case study in the Beijing–Tianjin–Hebei Metropolitan Areas. These two events can occur often simultaneously; therefore, identifying the areas where their effects overlap can be highly helpful for water resource management policies.

This evaluation was based on the analysis of the meteorological drought using the SPEI, while water scarcity was assessed by the Water Exploitation Index Plus (WEI⁺) [30]. In particular, the SPEI was used for the July–August–September quarter (hereafter: SPEI 3 sept), and the WEI⁺ was calculated for the low-flow period. The values obtained were spatialized with a geostatistical procedure according to the Kriging method, thus highlighting the areas most affected by meteorological drought phenomena and by different levels of exploitation of the water resource or water scarcity. A quantification procedure of the overlapping of the two phenomena was also proposed. Similarly, in [31], a spatial distribution of two drought indices (SPI and SDI) using the IDW interpolation method was proposed to compare the agreement between the two indices in identifying drought occurrence.

The study area is the Umbria region, in Central Italy, where recent observations of unfavorable climate trends have highlighted the need for careful water resource management [32,33,34].

The remainder of this paper is organized as follows: Section 2 outlines the methodology, including the WEI⁺ index (Section 2.1), SPEI index (Section 2.2), Kriging interpolation method (Section 2.3), and the quantitative approach used to compare the two indices (Section 2.4). A brief description of the case study is provided in Section 3. Section 4 presents the results of the analysis, followed by a discussion in Section 5 explaining the findings. Finally, conclusions are presented in Section 6.

2. Materials and Methods

2.1. Water Exploitation Index (WEI⁺)

The Water Exploitation Index (WEI) is an indicator of water scarcity, updated in its WEI⁺ form by the European Commission’s Committee of Experts. WEI⁺ includes the potential return of water withdrawal resources and how they can be managed [30].

This index has been recognized as relevant to the drought research sector, following the introduction of the SPI (Standardized Precipitation Index) and FAPAR (Fraction of Absorbed Photosynthetically Active Solar Radiation).

The calculation of the index involves the ratio of the withdrawal volumes, net of restitution, to the volume representing the availability of renewable water resources:

$${\mathrm{W}\mathrm{E}\mathrm{I}}^{+}={\displaystyle \frac{\mathrm{a}\mathrm{b}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}-\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{n}\mathrm{s}}{\mathrm{R}\mathrm{W}\mathrm{R}}}$$

(1)

To this end, it is necessary to have a detailed understanding of the withdrawals and their possible restitution, along with the necessary assessment of the renewable water resource (RWR). This assessment can be performed using a hydrological balance model of the basin or through renaturation techniques of the measured flows:

$$\mathrm{R}\mathrm{W}\mathrm{R}=\mathrm{E}{\mathrm{x}}_{\mathrm{i}\mathrm{n}\mathrm{f}}+\mathrm{P}-\mathrm{E}{\mathrm{t}}_{\mathrm{a}}-\Delta {\mathrm{S}}_{\mathrm{n}\mathrm{a}\mathrm{t}}$$

(2)

$$\mathrm{R}\mathrm{W}\mathrm{R}={\mathrm{Q}}_{\mathrm{n}\mathrm{a}\mathrm{t}}={\mathrm{Q}}_{\mathrm{o}\mathrm{b}\mathrm{s}}+\left(\mathrm{a}\mathrm{b}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}-\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{n}\mathrm{s}\right)\pm \Delta {\mathrm{S}}_{\mathrm{a}\mathrm{r}\mathrm{t}}$$

(3)

where:

Ex_inf = total volume of the actual flow of rivers, coming from neighboring territories (e.g., external water inputs from another basin or sub-basin);

P = total volume of atmospheric wet precipitation;

Et_a = total volume of evaporation from the ground, wetlands, and natural water bodies, as well as transpiration of plants;

ΔS_nat = changes in the stored amount of water (>0, if storage is increasing) during the given time period;

Q_nat = volume of natural flow;

Q_obs = volume of observed/measured flow;

abstractions-returns = volume of net water withdrawals;

ΔS_art = volume variation resulting from regulated lakes or artificial reservoirs, if any.

The application of these two methods for estimating the RWR does not appear to be completely independent of each other; in fact, to calibrate and validate the hydrological balance in Equation (2), it is necessary to know the volume of natural flow that can be obtained from Equation (3).

Due to the difficulties in applying Equations (1) and (2), a third approach to evaluate the RWR was studied using the flow duration curves (FDC) tool, specifically by utilizing the estimated natural duration curves [35].

FDCs can be constructed from the available flow data and naturalized as a function of water withdrawals or estimated as natural FDCs using a regionalization procedure studied across the entire Tiber basin. In Figure 1, it can be observed how an example of average duration curve can be used to estimate the average volume and the available low water volume, represented by the areas under the respective graphs. Specifically, the ordinary low flow volume is considered as the part under the FDC between the duration of 274 days and 365 days. This is based on the Hydrographic Service’s definition of ordinary low water, which refers to the flow rate that is exceeded on 75% of the days.

In this study, both volumes (RWR and RWR_lowflow) are evaluated net of the flow assumed as ecological flow, defining a new WEI⁺_EF index:

$${\mathrm{W}\mathrm{E}\mathrm{I}}_{\mathrm{E}\mathrm{F}}^{+}={\displaystyle \frac{\mathrm{a}\mathrm{b}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}-\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{n}\mathrm{s}}{\mathrm{R}\mathrm{W}\mathrm{R}-\mathrm{E}\mathrm{F}\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{e}}}$$

(4)

WEI⁺_EF is strongly conditioned by the flow value assumed as ecological flow (EF) [36], which, in this work, is represented by a set of temporally distributed values, according to the principle of the natural flow paradigm [37]. Therefore, the minimum Ecological Flow (EF_min) is determined according to the microhabitat method [38,39]. Subsequently, its variability is linked to the variability of natural flows through a flow modulation criterion, aiming to ensure a percentage of the naturally occurring flow variations in the hydrological cycle that affect aquatic organisms and bank vegetation. For example, in this study, it was proposed that this variation be obtained using a flow rate equal to 10% of the difference between the natural flow and the EF_min, without modulation [40,41]. This modulation criterion can be applied to the natural duration curves estimated in the duration interval of 1–274 days (EF_var), imposing the EF_min for the entire low-water period beyond the duration of 274 days. In order to avoid possible abrupt changes in EF at the 274 day duration, the results can then be interpolated using a logarithmic function of the following type:

$$Q_{EF}=-a\log \left(d\right)+b$$

(5)

where d represents the various durations from 1 to 274 days, beyond which the low-water conditions require the use of EF_min. Parameters a and b can be derived by imposing the maximum and minimum values of the modulated Q_EF. Specifically, the minimum value corresponds to the duration of 274 days, while, for the maximum value, the first 9 values were excluded, thus corresponding to the duration of 10 days. This exclusion in based on the consideration that modulation on values likely attributable to flood phenomena would be inappropriate.

$$a={\displaystyle \raisebox{1ex}{$\left({EF}_{var274}-{EF}_{var10}\right)$}\!\left/ \!\raisebox{-1ex}{$\left[\log \left(10\right)-\mathrm{l}\mathrm{o}\mathrm{g}\left(274\right)\right]$}\right.}$$

(6)

$$b={EF}_{var10}+a \mathrm{l}\mathrm{o}\mathrm{g}\left(10\right)$$

(7)

An example of the possible modulated trend of the EF is shown in Figure 2.

2.2. Standardized Precipitation-Evapotranspiration Index (SPEI)

Vicente Serrano et al., in 2010 [42], presented the Standardized Precipitation Evapotranspiration Index (SPEI), a multiscale index able to identify an increase in drought severity as a consequence of a higher water demand related to evapotranspiration. SPEI is similar to the Standardized Precipitation Index (SPI) but introduces the calculation of Potential Evapotranspiration (PET). In this way, SPEI preserves the simplicity, scalability, and statistical interpretability of SPI but considers the influence of temperature.

In the literature, it is generally accepted to adopt seven classes for SPEI severity [43] in accordance with WMO’s SPI User Guide [44] (

Table 1. SPEI classes and corresponding value intervals.

SPEI Value Intervals	SPEI Class
SPEI  ≥  2	Extremely wet
2  >  SPEI  ≥  1.5	Severely wet
1.5  >  SPEI  ≥  1	Moderately wet
1  >  SPEI  >  −1	Normal
−1  ≥  SPEI  >  −1.5	Moderately dry
−1.5  ≥  SPEI  >  −2	Severely dry
SPEI  ≤  −2	Extremely dry

).

The SPEI is a standardized variable and follows a normal distribution: a positive value of the index indicates the condition wetter-than-average, whereas a negative value indicates a drier-than-average one. SPEI values can be calculated for different time scales, such as 1, 3, 6, 12, 24 and 48 months. At a given month, a time scale of n months implies that data from the current month and of the past (n − 1) months will be used for computing the SPEI value.

In this study, SPEI values were calculated in the R-environment using the SPEI package https://cran.r-project.org/package=SPEI (accessed on 26 March 2025). The input is the difference $D_i$ (water balance) between the precipitation $P_i$ and potential evapotranspiration ${PET}_i$:

$$D_i=P_i-{PET}_i$$

(8)

where $D_i$ in Equation (7) provides a measure of the water surplus or deficit [36] for the i-month. In particular, the $D_i$ values have been aggregated at the 3-month time scale, in order to consider the quarter (July–August–September). Potential evapotranspiration is calculated using the Hargreaves–Samani formula [45,46]:

$${PET}_i=0.0023·\left(T_{i,mean}+17.8\right)·{\left(T_{i,max}-T_{i,min}\right)}^{0.5}·R_{i,a}·0.408$$

(9)

where ${PET}_i$ is expressed in mm; $T_{i, mean}$, $T_{i,max}$, and $T_{i,min}$ are, respectively, the average, maximum, and minimum temperatures in °C; $R_{i, a}$ is the extra-terrestrial radiation expressed in MJ m⁻².

The three-parameter log–logistic distribution is chosen as fitting distribution. The probability density (PDF) of the variable $x$ is expressed as follows:

$$f\left(x\right)={\displaystyle \frac{\beta }{\alpha }}{\left({\displaystyle \frac{x-\gamma }{\alpha }}\right)}^{\beta -1}{\left[1+{\left({\displaystyle \frac{x-\gamma }{\alpha }}\right)}^{\beta }\right]}^{-2}$$

(10)

The cumulative distribution function (probability of exceeding a determined value of $D_i$) is shown as follows:

$$F\left(x\right)={\left[1+{\left({\displaystyle \frac{\beta }{x-\gamma }}\right)}^{\alpha }\right]}^{-1}$$

(11)

Finally, SPEI can be easily obtained as the standardized values of $F\left(x\right)$ using the following approximated formulas [47]:

$$SPEI=\left\{\begin{array}{c}t-{\displaystyle \frac{c_0+c_{1}t+c_2{t}^2}{1+d_{1}t+d_2{t}^2+d_3{t}^3}} t=\sqrt{-2ln P_r} P_r\le 0.5 \\ -\left(t-{\displaystyle \frac{c_0+c_{1}t+c_2{t}^2}{1+d_{1}t+d_2{t}^2+d_3{t}^3}}\right) t=\sqrt{-2ln\left(1-P_r\right)} P_r>0.5 \end{array}\right.$$

(12)

where $P_r=1-F\left(x\right)$ is the probability of exceeding a certain value of the deficit $D$. The values of the coefficient are shown as follows:

$$c_0=2.515517 ,c_1=0.802853, c_2=0.010328, d_1=1.432788, d_2=0.189269, d_3=0.001308$$

2.3. Spatial Data Interpolation: Kriging Method

In this study, SPEI and WEI⁺_EF indices were spatialized using an interpolation model that optimally assigns weights to the sampled data, on the base of the Kriging method [48,49], employing the empirical Bayesian Kriging (EBK) algorithm.

Kriging is a geostatistical procedure that differs from deterministic approaches like IDW (Inverse Distance Weighting) or Spline interpolation, simply based on a specified mathematical formulation. In fact, it estimates a surface also on the base of the evaluation of the autocorrelation between data at measured points, providing a measure of the accuracy of the prediction values.

However, traditional Kriging models, such as simple, ordinary, and universal, are based on severe assumptions that are often violated by data. The EBK algorithm, a variant of Kriging, addresses several limitations of previous models: the assumption that data are a realization of a stationary process and follow a Gaussian distribution, the expectation that data can be accurately described by a single generating model, and the restriction against coincident data and individual measurement errors. A comprehensive presentation of the EBK algorithm is given in the work of Gribov and Krivoruchko [50]. In [51], the ability of modeling parameters’ uncertainties of approaches based on a Bayesian standpoint is put in evidence. EBK has shown to be more appropriate for interpolating non-stationary data for large areas requiring fewer sample data.

2.4. Spatial Data Quantification

In this analysis, to superimpose the spatialized data of the SPEI and WEI⁺_EF indices, a GIS procedure was carried out in the QGIS environment, based on these steps:

• Both for spatialized values of the WEI⁺_EF and SPEI, within the Umbria region boundary, classes characterized by the same amplitude, with an increasing criticality level, were identified. In particular, five classes were found for the WEI⁺_EF (

  Table 2. WEI⁺ classes.

  Classes	WEI+EF Values Intervals
  1	1 < WEI+EF ≤ 25
  2	25 < WEI+ EF ≤ 50
  3	50 < WEI+EF ≤ 75
  4	75 < WEI+EF ≤ 100
  5	WEI+EF > 100

  ) [52], and four classes were found both for the average and 10th percentile values of SPEI 3 sept (

  Table 3. SPEI 3 sept values intervals.

  Classes	Average	10th Percentile
  1	SPEI ≤ −0.2	SPEI ≤ −1.25
  2	−0.2 < SPEI ≤ 0	−1.25 < SPEI ≤ −1
  3	0 < SPEI ≤ 0.2	−1 < SPEI ≤ −0.75
  4	SPEI > 0.2	SPEI > −0.75

  ). The four SPEI classes were selected to ensure that the intervals were symmetrically distributed around a specific value. For the average, this value was zero, representing the mean of the normal standard distribution. For the 10th percentile, the value was −1, which was considered the threshold separating normal conditions from moderately dry conditions (Table 1).

2.

The QGIS Raster Calculator tool, by means of an algebraic expression, allowed us to identify pixels belonging to the different WEI⁺_EF classes specified in Table 2. In Figure 3, the vector map of WEI⁺_EF classes is shown.

3.

The QGIS Clip raster by mask layer tool allowed us to clip the raster maps of SPEI 3 using, as a mask, the vector WEI⁺ zones in Figure 3. In this way, it was possible to identify how many pixels in the SPEI maps were included in the different classes of WEI⁺_EF. As an example, Figure 4 shows the distribution of SPEI 3 sept values (10th percentile) that belong to the 4th class of WEI⁺_EF.

4.

For each WEI⁺_EF class, a specific expression was set in the QGIS Raster Calculator tool, and the SPEI pixels (for both the average and 10th percentile classes) were classified according to the intervals in Table 3.

The outcomes of the aforementioned procedure are presented in the results section.

3. Study Area and Data

Umbria is a region in central Italy (Figure 5) and covers an area of 8456 km². It is a hilly region, partially dominated by the Apennine reliefs. Urban areas and main arterial roads are placed along the valley of the Tiber River that extends from the North to the South of the region. The Tiber River travels about 409 km through Tuscany, Umbria, and Lazio before draining into the Tyrrhenian Sea, and the Tiber basin covers about 17,375 km². The Tiber’s major tributaries are Chiascio, Topino, and Nera, and they flow in the south of the Umbria region. Trasimeno lake is placed at the west boundary of the region, near Tuscany. The lake covers an area of 128 km², making it the fourth largest lake in Italy.

A temperate climate characterizes the Umbria region, with variations depending on the elevation. Precipitation is more frequent during the spring and autumn. Summers are generally hot and dry, especially in July and August, while winter brings cooler temperatures and rainfall but rarely severe cold or snow, except at high altitudes.

The region experiences an average annual rainfall of approximately 900 mm, ranging from 650 mm to 1450 mm depending on geographic location. The mean monthly temperature varies between 25.5 °C and 6 °C and between 24.41 °C and 5.54 °C, respectively, in the two administrative centers of Umbria, Perugia, and Terni. Typically, the highest temperatures occur in July or August (the daily maximum temperature in July averages 31 °C), while the lowest are recorded in January (the daily minimum averages 1 °C). The highest cumulative precipitation occurs in November (the monthly maximum precipitation averages about 85 mm/month), while the lowest is in July (the monthly minimum precipitation averages about 30 mm/month).

In

Table A1. Statistical parameters of precipitation and temperature: average, minimum, and maximum of the annual total rainfall; minimum and maximum of the monthly temperature, then aver-aged over the study period.

		Annual Cumulative Rainfall (mm)			Temperature (°C)
ID	Name	Mean	Minimum	Maximum	Maximum	Minimum
1	Nocera Umbra	955.9	589.2	1217.6	30.5	−0.3
2	Ponte S.Maria	789.6	308.1	1089.4	32.2	−1.4
3	Montelovesco	823.2	480.0	1270.0	31.5	1.5
4	Citta’di Castello	853.8	559.3	1127.9	33.1	−0.7
5	Petrelle	907.4	599.2	1226.7	32.5	−1.1
6	Todi	773.7	430.4	1078.9	33.1	0.5
7	Compignano	761.6	471.8	1086.7	33.9	−0.7
8	Gubbio	968.3	608.2	1407.6	31.6	−0.3
9	Castiglione del Lago	759.7	468.6	987.6	33.3	0.4
10	Casa Castalda	1019.9	579.2	1463.4	28.8	0.3
11	S.Benedetto Vecchio	834.9	571.8	1149.2	28.3	0.1
12	Bastardo	861.5	530.6	1272.8	31.9	0.3
13	S.Silvestro	885.1	625.6	1202.0	32.1	0.6
14	Orvieto Scalo	754.2	419.0	1217.6	33.4	−0.2
15	Carestello	1026.9	618.2	1593.0	29.9	−0.3
16	Perugia	856.6	547.6	1283.2	32.3	1.7
17	Piediluco	992.3	620.0	1442.4	31.0	−1.5
18	Norcia	786.4	467.4	1144.0	30.8	−2.7
19	Bevagna	751.4	456.0	1084.4	33.3	0.3
20	Terni	822.9	517.0	1177.4	33.3	2.1
21	Cortona	775.1	377.6	1079.2	32.3	1.3
22	Anghiari	848.9	571.8	1165.0	31.2	−1.7
23	Bagnoregio	903.1	541.4	1246.7	29.4	2.2
24	Rieti	1062.0	644.1	1363.9	32.3	−1.9
25	Apecchio	1221.3	838.2	1500.6	29.8	−1.6
26	Campodiegoli	1112.2	442.8	1746.8	30.5	0.6
27	Montemonaco	1139.8	709.5	1470.4	27.1	0.3

(Appendix A), basic statistical parameters of precipitation and temperature were calculated for each station, specifically the average, minimum, and maximum of the annual total rainfall over the study period, which varied depending on the actual availability of precipitation and temperature data. Additionally, the mean of the minimum and maximum monthly temperatures for each year in the same observation period was calculated.

In Figure 6, the precipitation and temperature stations of the Umbria, Tuscany, Marche, and Lazio regions that were considered in this work are shown.

Table A2. List of precipitation and temperature monitoring stations shown in Figure 6. For each station, the following are specified: denomination, basin, region, elevation, latitude and longitude (EPSG: 4326), first recording year for precipitation (P), temperature (T), and the period that the SPEI series actually covers.

ID	Name	Basin	Region	Elevation (m a.s.l.)	Latitude (N)	Longitude (E)	First Recording Year	SPEI Time Series Length
1	Nocera Umbra	Tiber	Umbria	530	43.1189	12.7911	1921 (P) 1988 (T)	2000–2022
2	Ponte S.Maria	Tiber	Umbria	240	42.8958	12.0214	1988 (P) 1989 (T)	2000–2022
3	Montelovesco	Tiber	Umbria	632	43.3069	12.4167	1921 (P) 1995 (T)	2000–2022
4	Citta’di Castello	Tiber	Umbria	304	43.4614	12.2514	1951	2003–2022
5	Petrelle	Tiber	Umbria	346	43.3497	12.16	1921 (P) 1988 (T)	2000–2022
6	Todi	Tiber	Umbria	326	42.7861	12.4092	1921 (P) 1934 (T)	1960–2022
7	Compignano	Tiber	Umbria	238	42.9478	12.2836	1921 (P) 1995 (T)	2000–2022
8	Gubbio	Tiber	Umbria	471	43.3478	12.5667	1947	2000–2022
9	Castiglione del Lago	Tiber	Umbria	259	43.1308	12.0464	1921 (P) 2008 (T)	2009–2022
10	Casa Castalda	Tiber	Umbria	695	43.1775	12.6597	1992 (P) 1994 (T)	2000–2022
11	S.Benedetto Vecchio	Tiber	Umbria	729	43.4367	12.4639	1955 (P) 1994 (T)	2000–2022
12	Bastardo	Tiber	Umbria	331	42.8653	12.5578	1951 (P) 1994 (T)	2004–2022
13	S.Silvestro	Tiber	Umbria	379	42.7558	12.6739	1992 (P) 1994 (T)	2000–2022
14	Orvieto Scalo	Tiber	Umbria	311	42.718	12.1077	1921 (P) 1948 (T)	2000–2022
15	Carestello	Tiber	Umbria	518	43.2861	12.5342	1999 (P) 1994 (T)	2000–2022
16	Perugia	Tiber	Umbria	437	43.1012	12.3959	1924	1960–2022
17	Piediluco	Tiber	Umbria	369	42.5342	12.7672	1996	2000–2022
18	Norcia	Tiber	Umbria	690	42.7986	13.105	1951	2004–2022
19	Bevagna	Tiber	Umbria	211	42.9442	12.6389	1921 (P) 1998 (T)	2004–2022
20	Terni	Tiber	Umbria	122	42.5597	12.6503	1921 (P) 1947 (T)	1960–2022
21	Cortona	Arno	Tuscany	413	43.269	11.996	1991 (P) 2000 (T)	2000–2022
22	Anghiari	Tiber	Tuscany	314	43.559	12.097	2012 (P) 1993 (T)	2000–2022
23	Bagnoregio	Tiber	Lazio	361	42.586	12.1588	1997	2004–2022
24	Rieti	Tiber	Lazio	377	42.4218	12.8118	1986	2007–2022
25	Apecchio	Metauro	Marche	544	43.55	12.4167	2003	2007–2022
26	Campodiegoli	Esino	Marche	559	43.3	12.8167	2001 (P) 2003 (T)	2007–2022
27	Montemonaco	Aso	Marche	987	42.8833	13.3167	2003	2007–2022

in Appendix A contains the complete list of the monitoring stations, where, for each station, the following are specified: ID, denomination, basin, region, elevation, latitude and longitude in WGS 84 reference system (EPSG: 4326), first recording year, and period that the SPEI series covers. Further details on the hydrological data of these station can be found in [32].

In Figure 7, the drainage basin boundaries considered in this study are shown, along with the corresponding centroids where the WEI⁺_EF value of each basin is ideally concentrated to facilitate spatial data interpolation.

Table A3. List of basins in Figure 7. For each basin, the following information is specified: river, basin area, presence of the hydrometric station, name, latitude and longitude (EPSG: 4326), and the time series in the calculation of the FDCs.

Drainage Basin Centroid	River	Basin Area (Km2)	Gauged Station	Name	Latitude (N)	Longitude (E)	FDCs Time Series
1	Tiber	363.55	No
2	Tiber	4145.00	Yes	Ponte Nuovo	43.0103	12.4292	1994–2021
3	Tiber	5748.17	No
4	Tiber	928.92	Yes	Santa Lucia	43.4217	12.2389	1991–2021
5	Tiber	2191.00	No
6	Chiascio	481.00	No
7	Chiascio	538.00	Yes	Pianello	43.1439	12.5653	1998–2021
8	Chiascio	1956.00	Yes	Ponte Rosciano	43.0250	12.4456	1997–2022
9	Topino	191.00	Yes	Valtopina	43.0533	12.7558	1997–2021
10	Topino	446.20	No
11	Topino	1094.33	Yes	Cannara	42.9958	12.5842	1994–2021
12	Topino	1215.00	Yes	Bettona	43.0247	12.5097	1994–2021
13	Marroggia	65.00	Yes	Azzano	42.8125	12.7569	1994–2022
14	Timia	608.40	No
15	Nestore	447.20	Yes	Mercatello	42.9742	12.2664	2005–2022
16	Nestore	705.71	Yes	Marsciano	42.9161	12.3372	1991–2021
17	Paglia	802.60	No
18	Paglia	1285.40	Yes	Orvieto Scalo	42.7244	12.1358	1992–2021
19	Paglia	1357.70	No
20	Corno	438.76	No
21	Nera	144.5	No
22	Nera	1362.11	Yes	Torreorsina	42,5717	12.7403	1997–2021
23	Nera	3881.88	No
24	Nera	4308.80	No

in Appendix A lists all the basins for which the WEI⁺_EF index was calculated, specifying their characteristics. In particular, for the gauged basins, the table includes the name of the hydrometric station, the WGS 84 coordinates, and the data time series used for the calculation of the FDCs. For the ungauged basins, the basin area used in the FDC regionalization method is provided.

Finally, data on water withdrawals for various uses were acquired from the Umbria region. These data were processed in the calculation of the WEI⁺_EF based on the maximum allowable volume of water withdrawal. The degree of restitution (abstraction returns) was determined by the specific use of the water and the withdrawal period. For example, irrigation does not involve any restitution, and the largest withdrawals occur during the drought period, which corresponds to the low flow period of the duration curve [35].

4. Results

To effectively compare the SPEI 3 sept and WEI⁺_EF indices as continuous variables across the Umbria region, the average of SPEI 3 sept (hereafter, avg-SPEI 3 sept), the 10th percentile of the SPEI 3 sept (hereafter, 10th-SPEI 3 sept), and WEI⁺_EF indices were interpolated using the Kriging method (Section 2.3).

4.1. SPEI 3 Sept Analysis

Specifically, SPEI 3 sept values were calculated based on a ten-year span of data, from 2012 to 2022. The values of the SPEI 3 sept time series are displayed in

Table A4. SPEI 3 sept time series values (2012–2022).

Monitoring Station	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022
Nocera Umbra	−0.408	−2.289	1.807	−0.238	0.397	−0.552	−0.768	0.685	0.800	−1.377	1.375
Ponte S.Maria	−1.214	0.079	0.544	−0.927	0.128	−1.693	−0.529	0.323	0.820	−1.277	1.362
Montelovesco	−0.795	1.200	1.313	−1.475	−0.383	−1.071	−0.414	0.667	0.190	−0.677	1.180
Citta’di Castello	−0.298	−0.190	1.537	−0.853	0.038	0.400	−1.351	1.370	0.882	−0.557	1.749
Petrelle	−0.433	0.657	0.868	−2.090	−0.222	−0.931	−0.568	0.834	0.609	−0.494	2.018
Todi	−0.622	−0.128	0.860	−0.270	0.147	0.355	−1.144	−0.211	0.745	−2.122	0.546
Compignano	0.247	−0.850	1.794	−0.378	0.448	−0.653	−0.585	−0.164	0.982	−2.165	0.202
Gubbio	−1.880	1.082	1.542	−0.949	0.310	−0.860	−0.791	0.403	0.543	−0.144	1.484
Castiglione del Lago	−1.371	0.522	1.570	−0.420	0.467	−0.838	−1.140	−0.279	1.100	−0.963	1.357
Casa Castalda	0.056	−0.289	1.532	−1.166	0.553	−0.413	−0.482	0.308	1.902	0.014	1.181
S.Benedetto Vecchio	−0.656	−0.009	1.695	−1.144	0.140	−1.961	−0.938	0.555	0.449	−0.229	1.665
Bastardo	−1.016	−0.016	0.878	−1.211	1.048	−0.416	−1.339	−0.074	1.418	−1.608	1.155
S.Silvestro	−1.422	0.972	1.162	0.536	−0.287	−0.706	−0.604	0.093	0.819	−1.723	1.133
Orvieto Scalo	−1.312	−0.197	1.359	−0.629	0.000	0.205	0.253	−0.123	0.886	−2.141	1.268
Carestello	−1.678	0.939	1.115	−1.142	0.079	−0.454	−0.962	0.438	1.923	−0.760	1.258
Perugia Fontivegge	−1.336	−0.152	0.961	−1.574	−0.461	−1.372	−1.665	−0.108	0.581	−1.072	1.198
Piediluco	−0.675	1.230	1.166	−0.016	−0.164	−0.240	0.195	−0.238	−0.425	−1.568	0.987
Norcia	0.253	0.822	1.486	0.851	0.189	−0.025	−1.151	0.450	−0.619	−1.136	1.145
Bevagna	−0.577	−1.494	1.497	−0.412	−0.165	0.961	−1.692	−0.672	1.083	−0.919	0.729
Terni	−0.612	0.608	0.195	−0.160	0.125	−0.061	−0.288	0.359	−0.057	−1.530	0.544
Cortona	0.233	−0.738	1.388	−0.897	0.919	−0.738	−1.073	0.246	0.630	−1.500	1.011
Anghiari	−0.612	0.337	1.548	−0.910	−0.617	−0.279	−1.529	0.437	0.804	−1.953	1.724
Bagnoregio	0.490	0.800	1.554	1.537	0.912	−0.959	−0.629	0.506	−0.294	−0.284	1.044
Rieti	0.505	0.434	0.312	−0.182	0.732	−0.569	0.871	−0.277	−0.335	0.225	2.100
Apecchio	−0.118	−0.013	1.653	−0.148	0.408	0.055	−1.105	0.641	0.207	−1.239	1.755
Campodiegoli	0.117	−0.119	1.718	0.029	−0.542	−1.051	−1.511	0.401	1.211	−0.020	1.451
Montemonaco	1.637	0.339	0.590	−0.317	1.032	−0.698	1.389	1.290	−1.369	−1.058	−0.967

(Appendix B). For each monitoring station listed in Figure 6, a graphical representation of SPEI series is provided in the supplementary file.

It should be noted that the selected time interval was chosen to ensure a sufficient number of stations across the Umbria region and properly close to its boundaries, with a continuous and homogeneous sequence of rainfall and temperature data. In fact, some stations provide a long and continuous time series (i.e., Todi, Perugia, Terni), while others cover a shorter period (see Table A2) with frequent missing data.

Table 4. SPEI 3 sept average and 10th percentile. Both the minimum and maximum values for the average and the 10th percentile are in bold.

Station	Average	10th Percentile	Station	Average	10th Percentile
Nocera Umbra	−0.052	−1.377	Carestello	0.069	−1.142
Ponte S.Maria	−0.217	−1.277	Perugia	−0.454	−1.574
Montelovesco	−0.024	−1.071	Piediluco	0.023	−0.675
Citta’di Castello	0.248	−0.853	Norcia	0.206	−1.136
Petrelle	0.022	−0.931	Bevagna	−0.151	−1.494
Todi	−0.168	−1.144	Terni	−0.080	−0.612
Compignano	−0.102	−0.850	Cortona	−0.047	−1.073
Gubbio	0.068	−0.949	Anghiari	−0.095	−1.529
Castiglione del Lago	0.000	−1.140	Bagnoregio	0.425	−0.629
Casa Castalda	0.291	−0.482	Rieti	0.347	−0.335
S.Benedetto Vecchio	−0.039	−1.144	Apecchio	0.190	−1.105
Bastardo	−0.107	−1.339	Campodiegoli	0.153	−1.051
S.Silvestro	−0.002	−1.422	Montemonaco	0.170	−1.058
Orvieto Scalo	−0.039	−1.312

displays the avg-SPEI 3 sept and the 10th-SPEI 3 sept of the time-series values in Table A4. The lowest value of the index, for the average, occurs in Perugia (−0.454), while the highest is in Bagnoregio (0.425). For the 10th percentile, the lowest is also in Perugia (−1.574), while the highest is in Rieti (−0.335).

The values of the SPEI 3 sept average and the 10th percentile in Table 4 were used as references for constructing the interpolated maps: Figure 8 and Figure 9 show, respectively, the avg-SPEI 3 sept and the 10th-SPEI 3 sept maps.

The avg-SPEI 3 sept index map varies between a maximum value of 0.158 and a minimum of −0.253; the 10th-SPEI 3 sept index map varies between a maximum value of −0.746 and a minimum of −1.299.

Regarding the SPEI index, it was observed that the minimum and maximum values of the interpolated map were, respectively, higher and lower than the exact values at the stations. This difference was expected and was a result of the smoothing effect of the interpolation process [53].

4.2. WEI⁺_EF Low Flow Analysis

Table 5. WEI⁺_EF values at the basin centroid.

ID Drainage Basin	WEI+EF [%]	ID Drainage Basin	WEI+EF [%]	ID Drainage Basin	WEI+EF [%]
1	2353	9	59	17	32
2	62	10	121	18	33
3	61	11	77	19	36
4	25	12	81	20	1
5	111	13	58	21	14
6	65	14	60	22	65
7	68	15	112	23	261
8	64	16	78	24	40

displays the WEI⁺_EF index values evaluated under low flow conditions. The most critical values of the WEI⁺_EF (higher than 100) correspond to basins 1, 5, 10, 15, and 23. It should be noted that the WEI⁺_EF was the calculated net of the flow assumed as ecological flow; therefore, a value greater than 100 indicates a high risk of the water resource use that is incompatible with ecological flow [52].

The WEI⁺_EF values are located at the centroids of the different basins and are interpolated as shown in Figure 10. The WEI⁺_EF index varies between a minimum value of 1% and a maximum of 120%, with the smoothing of the extreme values (compared to the exact values of centroids) resulting from the interpolation process [53].

All the maps (both WEI⁺_EF and SPEI) use a pixel size of 250 m, providing a sufficient resolution for the purposes of the study.

4.3. Results Overlap of SPEI 3 Sept and WEI^+EF Low Flow

In

Table 6. Comparison of SPEI 3 sept average classes and WEI⁺_EF low flow classes.

	Class	1 < WEI+EF ≤ 25 (%)	25 < WEI+EF ≤ 50 (%)	50 < WEI+EF ≤ 75 (%)	75 < WEI+EF ≤ 100 (%)	WEI+EF ≥ 100 (%)
1	avg-SPEI 3 sept ≤ −0.2	0.00	0.00	0.00	0.30	0.00
2	−0.2 < avg-SPEI 3 sept ≤ 0	0.00	28.03	42.54	63.94	89.19
3	0 < avg-SPEI 3 sept ≤ 0.2	100.00	71.97	57.46	35.76	10.81
4	avg-SPEI 3 sept > 0.2	0.00	0.00	0.00	0.00	0.00

and

Table 7. Comparison of SPEI 3 sept 10th percentile classes and WEI⁺_EF low flow classes.

	Class	1 < WEI+EF ≤ 25 (%)	25 < WEI+EF ≤ 50 (%)	50 < WEI+EF ≤ 75 (%)	75 < WEI+EF ≤ 100 (%)	WEI+EF ≥ 100 (%)
1	SPEI 3 sept ≤ −1.25	0.00	0.00	0.00	0.57	0.00
2	−1.25 < SPEI 3 sept ≤ −1	11.22	64.47	88.62	95.87	100.00
3	−1 < SPEI 3 sept ≤ −0.75	88.78	35.53	11.38	3.47	0.00
4	SPEI 3 sept > −0.75	0.00	0.00	0.00	0.09	0.00

, the results of the quantification procedure described in Section 2.4 are displayed. In particular, Table 6 shows, for each WEI⁺_EF class, the percentage of pixels corresponding to the different avg-SPEI 3 sept classes.

To effectively visualize the comparison between SPEI and WEI classes, in Figure 11, the graph of pixel percentages displayed in Table 6 is presented; it is possible to observe that the histogram values were interpolated by a linear trendline that well reproduces the data trend.

Similarly, Table 7 shows, for each WEI⁺_EF class, the percentages of pixels corresponding to the different 10th-SPEI 3 sept classes.

Figure 12 shows the graph of the results from Table 7. This time, the histogram values were accurately interpolated using a third-order polynomial trendline.

Finally, an overlay map (Figure 13) was created to visually highlight areas where both WEI⁺_EF and 10th-SPEI 3 sept reached critical values. As shown in the legend, the colored areas in the map represent the different combinations of WEI and SPEI classes across the Umbrian territory, where the first number represents the SPEI class, and the second represents the WEI class. It is noted that we adopted the class subdivision specified in Table 2 and in Table 3. Consequently, the combinations of WEI and SPEI classes shown in the legend of the overlay map match exactly with those previously found in Table 7.

5. Discussion

A preliminary comparison of the SPEI and WEI⁺_EF indices can be conducted qualitatively by simply observing their respective interpolated maps.

In Figure 8, the negative values of the avg-SPEI 3 sept index are between −0.253 and 0 and are concentrated in the central area of the Umbria region, bounded between Perugia at the north (monitoring station st.16) and Terni at the south (station n.20). The WEI⁺_EF map in Figure 10 presents two areas with values indicating extreme water stress (WEI⁺_EF >100), signifying a high risk of the water resource use that is incompatible with ecological flow, as well as a possible unverified water balance. Only one area (basins 5 and 15) partially overlaps with the critical values of the avg-SPEI 3 sept; in particular, both Terni and Perugia stations are located within the area where WEI⁺_EF is near or exceeds 100. However, a significant difference between the avg-SPEI 3 sept map and WEI⁺_EF map can be observed in the southeastern part of the region, specifically in the Umbrian Valley (st. 12, 13, and 19). In this area, the WEI⁺_EF index presents values above 100, while the avg-SPEI 3 sept indicates positive and non-critical values, likely due to the smoothing effect of the average. In fact, the difference between SPEI and WEI⁺_EF maps decreases when the 10th-SPEI 3 sept, which represents values at the lower extreme of the Gaussian distribution, is considered (Figure 9). In this case, the area between Nocera Umbra (st.1), Bevagna (st.19), and Norcia (st.18) is characterized by SPEI 3 values that indicate moderate drought, which can then be superimposed onto the WEI⁺_EF critical area.

Next, the SPEI and WEI⁺_EF indices are compared quantitatively, following the procedure described in Section 2.4. It is important to note that the selection of the four SPEI 3 classes in Table 3 (for both the average and 10th percentile) is based on the chosen resolution (250 m × 250 m square pixels). In fact, a higher number of classes would result in an insufficient number of pixels per class, leading to difficulties in identifying trends.

First, let us examine how the avg-SPEI 3 sept index changes in relation to the WEI⁺_EF. Table 6 displays the percentage of pixels in each avg-SPEI 3 sept class that belong to the different WEI⁺_EF classes, and Figure 12 presents data in a histogram format. Referring primarily to the second and third classes, as they are the only ones containing a significant number of pixels, we observe that, as the WEI⁺_EF value increases, the number of pixels in the second class rises, while the pixel number in the third class decreases. Since the second class is more critical than the third (due to having more negative values), this result proves that, as the SPEI reaches more critical (lower) values, the WEI⁺_EF too reaches more critical (higher) values.

Similar observations can be made about the relationship between the 10th-SPEI 3 sept and the WEI⁺_EF (Table 7 and Figure 13). Referring always to the second and third classes, results demonstrate that, as the SPEI moves toward more crucial values, the WEI⁺_EF also tends toward more crucial values.

Thus, both the average and the 10th percentile of the SPEI 3 sept exhibit a tendency to reach critical values alongside the WEI⁺_EF low-flow index, indicating the risk of the overlapping of meteorological drought and water scarcity in significant areas of the Umbria region.

However, it is also possible to observe differences in the trendline of the SPEI 3 sept average and the 10th percentile. Specifically, the SPEI average (Figure 12) increases linearly along with the WEI⁺_EF. Differently, the growth of the 10th percentile trendline (Figure 13) is significantly faster and follows a third order polynomial pattern. This is because the average tends to smooth out annual SPEI values (see Table A4), while the 10th percentile, which captures the negative extremes of the distribution, seems more suitable at highlighting the critical trend of the index.

The map in Figure 13 visualizes the overlap between critical values of WEI⁺_EF and 10th-SPEI 3 sept. We chose to focus on the 10th percentile of SPEI 3 sept because its map (Figure 9) aligns more closely with WEI⁺_EF low-flow values (Figure 10). The most critical areas for both SPEI and WEI can be identified by the combination of classes 1–4 and 2–5. The class 1–4, primarily influenced by SPEI, is concentrated in small areas around monitoring stations 16 and 19, where SPEI values drop below −1.25. Meanwhile, class 2–5, mainly driven from WEI values, reaches high critical levels in the area between basin centroids 5 and 15, as well as around centroid 10 in Figure 10. Finally, Figure 13 shows an overlap of critical conditions in both meteorological drought and water scarcity. This overlap is highly significant for the combination of classes 2–5 and 2–4, covering approximately 3300 km², and is moderately significant for the combination class 2–3, which spans around 2150 km².

Previous considerations about SPEI 3 sept and WEI⁺_EF suggest that, in areas where there is an overlap of critical SPEI (particularly the 10th percentile) and WEI⁺_EF values, and given that SPEI is largely influenced by climate and cannot be controlled, water resource management policies aimed at optimizing water use should be a priority, including the use of unconventional or harvested water resources.

6. Conclusions

To address the growing frequency of droughts [54], it is crucial to understand how this natural phenomenon interacts with varying levels of water resource usage.

This study analyzed this issue using two indicators: the SPEI to represent meteorological drought and the WEI⁺_EF to analyze situations of water scarcity resulting from the use of water resources. In particular, the focus was on the SPEI 3 sept and the WEI⁺_EF calculated during low flow periods, which, in the study area, overlaps with the calculation period of the SPEI 3 sept.

The more detailed local approach can help highlight critical issues that may escape notice at a larger scale, such as that of the hydrographic district [55]. Furthermore, this study incorporated environmental aspects by introducing the WEI⁺_EF, a factor that is not always considered in the assessment of water scarcity.

Two indicators were defined differently throughout the study area. The SPEI was calculated based on rainfall and temperature data from hydrological monitoring stations, while the WEI⁺_EF calculation method assigned the indicator values to a basin, where the available natural water resource and water withdrawals net of returns were evaluated.

The results obtained in the study area (Umbria region in Central Italy) were analyzed both qualitatively and quantitatively by classifying the indices and analyzing their overlap in terms of pixels percentages.

The qualitative analysis immediately revealed that the average of the SPEI 3-months, calculated from the studied time series data, did not fully capture the critical issues related to drought in the study area. Specifically, the entire southeast area was not identified, whereas it was clearly identified using the 10th percentile of the SPEI 3 sept. This latter scenario closely resembled the low-flow WEI⁺_EF map, highlighting a potentially dangerous overlap between the two phenomena: extreme meteorological drought and water scarcity.

The quantitative analysis confirmed this finding. In fact, the overlay between classes of the average SPEI 3 sept classes and the low flow WEI⁺_EF showed a linear growth trend of higher WEI⁺_EF values with more critical SPEI 3 sept classes (−0.2 < avg-SPEI 3 sept ≤ 0). However, using values from the 10th percentile of the SPEI 3 sept, the overlap showed a much more pronounced growth, particularly with more critical SPEI 3 sept classes (−1.25 < SPEI 3 sept ≤ −1). This suggests that the 10th percentile may be better suited for representing ongoing unfavorable climatic trends.

The methodological approach proposed enables the identification of well-localized areas at a higher risk of water drought and, at the same time, highlights where there is excessive exploitation of water resources during the low-flow periods. This provides stakeholders in the water sector with essential information to adopt a proactive approach, either by reducing water consumption or by preparing alternative water supply sources to the current ones.

For future research, we will focus on evaluating two aspects of this topic: (1) the possibility of combining the SPEI and WEI⁺ indices, expressing them concisely using a formula that can be applied on a cell-by-cell basis to ensure that the resulting map accurately represents critical areas while preserving the integrity of the underlying data; and (2) a better understanding of the location and characteristics of water withdrawals for the calculation of the WEI⁺, along with an analysis of the respective databases using techniques that incorporate artificial intelligence.