1. Introduction
Precipitation, occurring at various spatial scales, has a significant influence on ecological processes [
1,
2], driving the exchange of water storage and energy release during climate fluctuations [
3]. However, converting point precipitation measurements from ground gauges to areal precipitation poses a challenge in climatic studies [
4,
5,
6] and broader ecological implications [
1,
7,
8], including water cycle and hydrological modelling [
9,
10,
11,
12]. Thus, addressing climate and hydrological issues at the areal scale often requires homogeneous spatially and temporally consistent datasets [
13,
14,
15]. However, while ecological research routinely relies on in situ precipitation observations, hydrological models operating at the basin scale often face challenges due to the lack of homogeneous pluviometric data [
16]. The lack of homogeneity in extended time-series of climate data may arise from the combined effects of station relocations and changes in local features [
17]. In fact, over extended periods (e.g., 50–100 years), observing stations may have been moved, sometimes to positions with slight elevation differences. Furthermore, the surrounding vegetation and land-use might have experienced modifications.
In response to the increasing development of models that consider spatio-temporal variations in climate, there is a growing need for techniques that can accurately assess changes in homogeneous areal precipitation [
18,
19]. The study of mean areal precipitation (MAP) changes focuses on the establishing relationships applicable at the grid-cell or basin scales of models, enabling their implementation in environmental change processes [
20]. A major challenge in predicting MAP changes at scales meaningful for hydrological modelling lies in effectively representing the effects exerted by orographic surfaces and other weather features on an annual time-scale [
21].
In recent decades, satellite and remote sensing technology has allowed for high-spatial resolution estimates of precipitation over specific areas, specifically for hydrological and climate studies [
22]. However, these data are generally available only after 1990. While global data derived from Global Hydrological Models (GHMs; [
23]) have become more accessible, they are not ideal for basin-scale applications due to the coarser resolution [
24]. To address the challenge of coarser spatial resolution, Karger et al. [
25] used a Model Output Statistics algorithm to correct data from ERA-Interim reanalysis using gauge-derived products from the GPCC and GHCN datasets. However, this approach requires greater computational resources and expertise. Alternatively, stochastic weather generators can generate very long time-series of weather patterns, but they have limited capability in reproducing the interannual variability of MAP [
26] (Breinl et al., 2017). For small basins, groups of ground stations remain crucial for understanding the climatic variability of MAP. However, their configurations can change over time, and reliable consistency is not always available for historical periods. Evaluating the spatial variability and trends of MAP in these basins can be approached in two ways [
6]. The first involves independently interpolating current rainfall grid surfaces, creating gridded precipitation data to fill gaps in climatic data. This method also facilitates assessing the consequences of precipitation change in unsurveyed regions by generating successive precipitation surfaces [
27]. However, this strategy can be time-consuming and may not always be appropriate, especially when there are too few stations to perform interpolation. The second method involves directly interpolating station indices and precipitation, followed by calculating indicators for each grid. However, this technique may struggle to accurately represent the distribution of these indices.
In cases where the number of weather stations varies significantly over time and none of the previously mentioned strategies are suitable, an Empirical Modelling Approach (EMA) can offer a potential solution. The EMA combines human expertise with statistical techniques to capture the historical information contained in available station time series, enabling the transfer of point-scale data to larger-scale MAP predictions. EMA can involve two main modes: one focuses on understanding how equations and parameters of dynamic models change with scale [
28,
29], while the other emphasises the best statistical representation and uncertainty representation [
30], which is the main focus of this article.
In this study, we employed the EMA approach using a statistical Multivariate-Regression Process Model (hereafter MRPM) to analyse the entire spatial domain of the Calore River Basin (CRB), in Southern Italy. At the transition between the central and southern Italian Apennines, the CRB presents a notable division between two distinct areas with contrasting characteristics [
31]. To the east, rainfall exhibits a relatively uniform distribution, while to the west, there is a notable rainfall gradient leading to higher precipitation values. Recognising the spatial heterogeneity inherent in the precipitation data, two observing stations were selected to represent the pluviometric conditions within the CRB: Benevento (BNOBS) for the flat areas and Montevergine (MVOBS) for the mountainous areas (
Figure 1c). The orography of the CRB plays a crucial role in influencing the spatial pattern and amount of precipitation through various processes. As a result, precipitation increases with elevation, particularly on windward slopes, while the leeward side of mountain ranges experiences lower precipitation levels. By considering these factors, we aimed to capture the complex interplay between topography and precipitation in the CRB, allowing for a more comprehensive analysis of the region’s hydrological dynamics.
This article is organised as follows.
Section 2 introduces the data and methods used in this study:
Section 2.1 provides an overview of the environmental setting, while
Section 2.2 addresses the upscaling issue and outlines the solutions that have been applied to the CRB.
Section 3 evaluates the model and presents the reconstructed annual MAP across the CRB for the period 1869–2020. Finally, in
Section 4, we conclude on research needs and the practical implications of spatio-temporal scaling.
2. Data and Methods
2.1. Pluviometric Network and Reference Stations
The study area focuses on the Calore River Basin (CRB), located in Northern Campania, Southern Italy, covering an approximate area of 3000 km
2 (
Figure 1a,b). The CRB is situated between 41°11′ North and 14°27′ East, representing the transition zone between the central and southern Italian Apennines. The elevation within the basin ranges from about 50 to 1800 m a.s.l. Due to its topographic variability, a pluviometric network was established in the CRB. The initial stations were set up around 1920, and, over time, additional stations were added. By the 1940s, the pluviometric network had reached its maximum consistency with 56 sites (
Figure 1c). This network remained relatively stable until the 1980s, albeit with occasional gaps in data, such as between 1947 and 1954 and during other shorter periods. Among these stations, only two have the longest and most continuous data series to date. These are the Benevento Meteorological Observatory of Benevento (hereafter BNOBS), which commenced operations on 1 March 1869, under the guidance of Nicola Orazio Albino, and the Montevergine Sanctuary Meteorological Observatory, established a few years later in 1884 (marked as numbers 1 and 2 in
Figure 1c).
The CRB features predominantly mountainous terrain in the western part, with peaks reaching elevations of 1400 m a.s.l. (in the Taburno massif) and 1700 m a.s.l. (in the Picentini mountain range). In contrast, the eastern region consists of lower relief, with some elevations reaching around 1000 m a.s.l. The topography of the area exhibits a diverse range of elevations. Approximately 27% of the land is situated below 300 m a.s.l., while 36% consists of hills ranging between 300 and 600 m a.s.l. Another 23% is characterized by elevations between 600 and 900 m a.s.l., and the remaining 13% comprises mountainous areas exceeding 900 m a.s.l. These natural landscapes, already exhibiting a variety of forms, colours and textures, are further shaped by the presence of hills, mountains and villages that dot the landscape around the Calore River and its tributaries.
The instrumental precipitation data series of Benevento includes four distinct periods that follow the precipitation anomalies recorded since 1675 [
32]. The first period covers 1 March 1869 to 31 December 1906, during which observations were conducted by Ambrogio Di Renzo. The second period encompasses the years from 1907 to 1947 and includes observations by Venanzio Vari, with the addition of Panfilo Boccabella. The third period encompasses the years from 1948 and 1968 and corresponds to the observations made by Nazario Doretti. The fourth period spans from 1969 to 2020 and consists of pluviometric surveys managed initially by the National Hydrographic and Mareographic Service until 1999, and later continued by the Meteorological Forecasting Functional Center of the Campania Region [
32]. The Montevergine observatory (hereafter MVOBS) is the oldest among the high-altitude meteorological observatories located in Central and Southern Italy. It was established at the initiative of Barnabite Father Francesco Denza and has been managed by the Benedectine Community of Montevergine’s Abbey. The first meteorological observations began under the guidance of Father Giuseppe Llobet, who served as the observer from 1884 to 1919. From 1920 to 1938, the directors of the observatory included Fathers Ildebrando Mancini, Ilario Mauro, Ugo Inzan and Giulio Corvino. In 1939, Father Virginio Cinella assumed responsibility for the observatory’s services. The period of activity continued until 1961 [
33]. Systematic observations resumed at the end of 1960 under the new direction of Father Amato Gubitosa and continued until 2006. Under the guidance of Father Andrea Komar and with the support of Dr. Vincenzo Capozzi, the Montevergine Observatory underwent significant renovations and modernisation after 2006. This included the installation of new equipment, including digital instruments, to enhance its capabilities. Since then, the updated data from the observatory have been based on the work of Capozzi and Budillon [
34], as well as the Montevergine Observatory’s official website (
http://www.mvobsv.org) (accessed on 28 June 2023), which provides annual updates.
The variables used for model development include precipitation at BNOBS, the corresponding monthly standard deviation for each year, and precipitation at MVOBS. The years selected for model calibration (
Figure 2, grey bands) were 1935–1942 and 1951–1977, during which the number of stations across the CRB varied slightly from year to year (mean: 37 ± 6 standard deviation). For model validation, the years chosen were 1978–1993, which exhibited greater variability in the number of stations (mean: 43 ± 11 standard deviation). The years between 1943 and 1950 were not included in the calibration stage due to many stations temporally ceasing their activity during the World War II. It should be noted that for the validation process, we have also intentionally excluded a group of years that may be less reliable and not fully representative of the CRB. This is due to the varying number of stations used annually to calculate the Actual Mean Areal Precipitation across the Calore River Basin, AMAP(CRB). Furthermore, after 1993, the pluviometric network in Campania experiences a significant and gradual decrease in the number of stations. For this reason, we did not extend the validation time series beyond this date.
2.2. Climate and Seasonal Regime Patterns
The activity of precipitation systems in the CRB is influenced by the convergence of moist air masses associated with different cyclonic situations, which occur when air masses with varying thermal characteristics meet in the central Mediterranean basin. The climate in this part of southern Italy is influenced by the complex interactions between cold air masses of northern Europe and tropical air masses, which give rise to Mediterranean cyclogenesis [
35]. These depressions have the greatest impact on northern Italy and the Tyrrhenian coast, resulting in significant rainfall variability (
Figure 3a).
By adjusting the spatial scale to focus on the area under study, we can appreciate a more detailed representation of precipitation variability across the CRB (
Figure 3b). Consequently, the CRB exhibits a distinct divide between two contrasting areas. The eastern region experiences relative uniform precipitation patterns (
Figure 3b, blue shape), with slightly higher amounts near the Apennine watershed (up to 900–1000 mm yr
−1). In contrast, the western region displays a significant pluviometric gradient, resulting in higher rainfall values (
Figure 3b, violet band). These differences can be attributed to variations in altitude, geographic positioning, and the direction of the moist air flows. When precipitation systems encounter the sub-Apennine chain, they undergo enhanced water vapour condensation, leading to greater rainfall amounts before progressing eastwards into the basin’s interior.
Considerable rainfall occurs throughout the summer in continental Campania, particularly from May to September, often in the form of showers and thunderstorms. It is worth mentioning that in Benevento, and on the central-eastern slopes in general, heavy rainfall (>20 mm d
−1) can occur due to both cold occlusions originating from the east and the passage of storms from the west. The south-western perturbed flows, which occur more frequently in the extreme western sectors of the CRB (such as Claudina valley, Partenio mountains, valley Teleseina and areas of Matese-Titerno), release their higher moisture content. As these flows progress towards the innermost areas of the CRB, they bring modest quantities of rainfall, generally ranging from 10 to 20 mm d
−1 [
36].
The CRB exhibits four distinct seasons from a bioclimatic perspective (
Figure 4). The first is the humid and cold season, which spans from January to April. This is followed by the growth season, occurring from April to July. The dry season dominates from July to September. It is only after mid-September that the humid season begins, and from October to December, the Atlantic perturbations bring rains back with maximum abundance in a more consistent manner.
2.3. Mean Areal Annual Precipitation (AMAP) Data
To determine the actual mean areal precipitation for the years when a sufficient number of stations (up to 56) were available across the CRB, we derived the corresponding AMAP values using the Thiessen approach, which is a direct weighted average method that involves dividing a region into sub-regions centred on each monitoring site [
37]. Although the sub-basins do not align perfectly with the Thiessen sub-regions, it is possible to calculate the fraction of each Thiessen sub-region that contributes to each sub-basin. This allows for the computation of weighted averages to estimate the AMAP for each sub-basin. The equations used to compute the spatial average are as follows [
38]:
where AMAP is the actual mean areal precipitation for
G gauges, denoted as
g = 1, …,
G;
Pg (mm yr
−1) is the precipitation measured at each gauge;
ag (km
2) is the area of each sub-region, whose sum is the total area of the basin (A = 3058 km
2).
2.4. Model Development
The varied topography of the basin can modify local precipitation patterns. The influence of precipitation change on a larger scale is determined by the spatial and temporal scale of disturbances, as well as the interplay between disturbances and the small-scale landscape variability [
20].
Orographic precipitation, which is prominent in mountainous river basins, exhibits a substantial spatial variability. Consequently, mean areal precipitation is scale-dependent and statistically non-homogeneous in space [
39]. To minimise uncertainty in estimating the annual MAP across the CRB, MAP(CRB), we have employed a multivariate linear regression approach with three variables and four parameters. This enables us to examine the relationship between a response variable (AMAP) and one or more predictor variables, e.g., P(BNOBS) and P(MVOBS). By understanding how changes in predictor variables are associated with changes in the response variable, we can estimate the value of the response variable based on the known values of the predictor variables [
40].
From this sample, our initial focus was on gaining a comprehensive understanding of the factors that potentially influence the amount and spatial-temporal distribution of precipitation in each year. We engaged an iterative process, employing a trial-and-error approach to identify the relevant drivers and develop an explanation for the long-term dynamics of areal precipitation in a relatively simplified manner. This involved a stepwise approach, systematically adding and removing terms as needed. As we progressed, we incorporated more complex terms while adhering to the principle of parsimony, ensuring that the model included only a limited number of factors for a MRPM. The following approach was thus formulated for estimating MAP(CRB):
The parameters of Equation (3), α, β, ϑ (scale factors), γ (position factor) and C (linearisation factor), were optimised through a co-iterative calibration process against AMAP(CRB) values derived from the Thiessen method. The monthly standard precipitation (SDP) calculated for Benevento station, SDP(BNOBS), served as a determinant factor. A higher SDP(BNOBS) indicates not only deficient rainfall at BNOBS but also a higher likelihood of drought across the CRB. The precipitation ratio, represented in the third term, provides insights into the precipitation pattern across the CRB. A ratio close to 1 suggests attenuated precipitation over the CRB, while a ratio significantly greater than 1 indicates increased precipitation. This ratio captures the extent of the precipitation system over the basin, with a higher ratio indicating a larger coverage area. The factors contributing to this ratio can be explained as follows: (1) the sub-Apennine chain is situated to the west of the CRB, which is typically the direction from which precipitation systems originate. If there is a substantial difference in rainfall between Montevergine and Benevento, it indicates the recurrence of disturbances during that particular year; (2) Montevergine represents meteorological conditions at higher altitudes, while Benevento represents conditions in a flat area. Thus, the ratio aims to consider the overall frequency, duration and quantity of precipitation systems affecting the CRB, taking into account both altitude-related meteorological conditions and disturbances originating from the sub-Apennine chain.
The calibration process focused on maximising the goodness-of-fit (R
2) of the linear regression between the actual and estimated MAP data (and the linear correlation coefficient r = √(R
2). The optimum value for R
2 is 1. Additionally, the Nash-Sutcliffe (NSI) efficiency index [
41] was maximised. The NSI, with an optimum value of 1, extends the R
2 statistics to assess the relative accuracy of predictions from any class of models, where values below zero indicate worse performance than a simple mean estimation and values above zero indicate better performance. The mean absolute error (MAE) was also calculated to quantify the amount of error. Skewness and kurtosis metrics were examined to evaluate the distribution of the data and assess the departure from normality. In addition, a range of statistical tests were conducted to provide a comprehensive analysis of the model’s performance. The two-sided Kolmogorov–Smirnov test [
42] was used to compare the distribution of observed and predicted values. The Durbin–Watson test [
43] was employed to examine residual autocorrelation. Student’s
t-test [
44] and Wilcoxon (1945) test [
45] were utilised for comparing means between different groups. Lastly, the Kendall [
46] test was employed for trend analysis together with Buishand [
47] test to assess the presence of any systematic changes over time.
The data processing, interpretation, and exploration of patterns and relationships were conducted by leveraging the capabilities of spreadsheet-based tools and statistical software. Various statistical test and analysis were conducted, using the online software STATGRAPHICS (
http://www.statpoint.net/default.aspx) (accessed on 28 June 2023) and VassarStats (
http://vassarstats.net) (accessed on 28 June 2023). Additionally, graphical support for data visualisation and analysis was obtained from AnClim (
http://www.climahom.eu/software-solution/anclim; [
48]) (accessed on 28 June 2023) and CurveExpert Professional 1.6 (
https://www.curveexpert.net) (accessed on 28 June 2023).
4. Conclusions and Perspectives
In this study, we successfully applied the Multivariate-Regression Process Model (MRPM) to capture and replicate precipitation patterns in the Mediterranean basin of the Calore River. Our analysis revealed a significant climatic shift around 1951, indicating that the recent period exhibits a greater diversity of precipitation patterns compared to the earlier period. This finding emphasizes the need to consider the complexity of precipitation processes and their impacts on the local environment. Understanding these dynamics is crucial for effective water resource management, agriculture, and ecosystem conservation in the Calore River Basin.
The observed climate shifts and changes in precipitation patterns have important implications for adaptation in the face of evolving climate conditions. Future research should focus on refining the MRPM by optimising model parameters and incorporating additional variables or data sources. This would enhance the model’s performance and provide a more comprehensive understanding of precipitation patterns across various regions. Furthermore, investigating the drivers behind the identified climatic shift and its implications for local ecosystems and communities is essential. This knowledge would facilitate climate adaptation and resilience planning, ensuring the sustainability of natural resources and human well-being.
To improve the accuracy and reliability of precipitation modelling, efforts should be made to expand the pluviometric network and enhance data collection and monitoring systems. The observed lower accuracy in the validation stage, attributed to the reduced number of stations in the dataset, underscores the importance of maintaining and expanding observational networks. Increasing the spatial and temporal coverage of precipitation data will enable more accurate assessments and modelling at different scales.
Overall, this study contributes valuable insights into geographically referenced precipitation variables and their implications in the Calore River Basin. The findings inform decision-making processes and support the development of sustainable water resource management strategies in response to changing precipitation patterns and climate conditions. By continually advancing our understanding of precipitation dynamics, we can foster resilience and ensure the long-term viability of ecosystems and communities in the face of a changing climate.