Evolution of Rainfall Characteristics in Catalonia, Spain, Using a Moving-Window Approach (1950–2022)

Abstract

A comprehensive analysis of the evolution of rainfall characteristics in Catalonia, NE Spain, was conducted using monthly data from 72 rain gauges over the period 1950–2022. A moving-window approach was applied at annual, seasonal, and monthly scales, calculating mean values, coefficients of variation (CV), and trends across 43 overlapping 31-year periods. To assess trends in these moving statistics, a modified Mann–Kendall test was applied to both the 31-year means and CVs. Results revealed a significant 10% decrease in annual rainfall, with summer showing the most pronounced decline, as nearly 90% of stations exhibited negative trends, while the CV showed negative trends in coastal areas and mostly positive trends inland. At the monthly scale, February, March, June, August, and December exhibited negative trends at more than 50% of stations, with rainfall reductions ranging from 20% to 30%. Additionally, the temporal evolution of Mann–Kendall trend coefficients within each 31-year moving window displayed a fourth-degree polynomial pattern, with a periodicity of 30–35 years at annual and seasonal scales, and for some months. Finally, at the annual scale and in two centennial series, the 80-year oscillations found were inversely correlated with the large-scale climate indices North Atlantic Oscillation (NAO) and Atlantic Multidecadal Oscillation (AMO).

1. Introduction

Analyzing precipitation trends is essential for understanding climate change. According to the findings presented the IPCC Cross-Chapter Paper 4 on the Mediterranean Region (CCP4.1, [1]), the observed trends in annual precipitation in the Mediterranean are significant only in some areas and some periods, and they are stationary in the long term throughout the region. Several authors have reported a decrease in average precipitation since the 1960s [2,3,4]. However, a decreasing trend in annual rainfall amounts was found [5] only in 18% of the Spanish territory for the period 1951–2019. A similar result was reported in [6], which analyzed annual rainfall trends in Spain for the period 1901–2010. Focusing on the Spanish eastern region and for the period 1951–2000, an overall reduction of 12% in annual rainfall across 90% of the studied areas was found by [7]. Regarding total precipitation in Spain for the period 1971–2022, a trend toward a drier climate cannot be confirmed with a significant level of statistical accuracy [8]. In addition, [9] concluded that there is a lack of statistically significant trends in long-term precipitation records in Southwestern Europe, while [10] reported that, although trends in individual Spanish regions may not be statistically significant when analyzed separately, their aggregation reveals a significant decreasing trend in total precipitation across Southwestern Europe, including France, Spain, and Portugal. However, this trend contrasts with other parts of Europe, which exhibit stable or increasing precipitation patterns [11,12].

On the other hand, precipitation extremes have increased in some northern Mediterranean areas and are projected to continue rising, potentially leading to a higher incidence of flash floods, with no change in the southern part [1]. An increasing trend in extreme rainfall events in Mediterranean coastal areas of the Iberian Peninsula was reported by [13,14]. This aligns with studies in other areas, such as those conducted along the Mediterranean coast of France [15,16,17,18] and Morocco [19,20,21]. Nevertheless, a recent study by [22] found no evidence of an increase in the frequency of the monthly RX1 day (the highest daily precipitation amount within a given month) exceeding 100 and 200 mm in the Spanish mainland from 1916 to 2022, which aligns with other works [23,24]. In Catalonia, an increase in rainfall irregularity, based on the temporal evolution of its scaling behavior [25,26], has been reported. Additionally, studies have observed a rise in the time concentration and intensity of convective-type events [27], as well as their contribution, particularly in areas where this type of precipitation is dominant [28]. These shifts in precipitation patterns, linked to an increase in variability, lead to significant implications for water management, agriculture, and urban planning [29,30,31]. The spatial distribution of maximum daily precipitation in Catalonia for several established return periods was found by [32], providing rainfall intensity-frequency values for sub-daily durations. In addition, drought has also been studied in this area. For instance, [33] analyzed patterns of monthly rainfall shortages and excesses, while [34,35] examined trends and statistical distributions of dry spells across the region.

The mentioned studies are some examples of the extensive list of articles that have contributed to a general understanding of precipitation patterns in this region, although they often focused on fixed time periods without accounting for variability across different time scales. The use of moving windows (MW) offers a dynamic and continuous perspective, allowing for the detection of more subtle and temporal changes in the time series, and may help explain the differences in conclusions across studies. In a recent paper, [36] examined the spatial and temporal variations in seasonal precipitation patterns for the period 1916–2015, applying moving windows of 30 and 60 years. In addition, [37] applied MW analysis to the long series with more than two centuries of registers in Barcelona. In [38], the secular series of the Fabra Observatory were analyzed and compared for three reference periods of 30 years. Although the aforementioned articles employed moving windows, their objectives and findings differ from those of the present work.

The present study aims to detect multidecadal oscillations in rainfall amount and coefficient of variation in Catalonia and their trends when 31-year moving windows (MW31) are applied. This 31-year period has been chosen because it closely aligns with the 30-year periods recommended by the World Meteorological Organization (WMO, [39]) for calculating climatological averages. Analyzing the key statistical features of these periods provides further insight into their underlying dynamics. This approach enables the assessment of how trends may vary when the study periods shift, revealing multidecadal periodicities and providing another point of view of the evolution of precipitation, contributing to the development of more effective long-term water resource management and territorial planning strategies.

The paper is organized as follows. Section 2 presents the selected database, the study region, and the methodology used. Section 3 illustrates the results obtained, and Section 4 discusses the results. Finally, Section 5 summarizes the main conclusions.

2. Materials and Methods

2.1. Database

A complete monthly rainfall database corresponding to 72 rain gauges has been obtained from Servei Meteorològic de Catalunya (SMC, [40]) for the period 1950–2022. Most of the rain gauges (70) are located in Catalonia, while the other two are in Ransol (Andorra) and Perpinyà (France), labeled as 20 and 33 in Figure 1, respectively. All these series have been subjected to rigorous quality control and time series homogenization [41,42]. Figure 1 shows the main orographic features of Catalonia, the location of the selected stations, and the annual average rainfall computed from the stations used in this study.

The code number of each station, shown in Figure 1, is also included in

Table 1. Name, code, coordinates UTM X and UTM Y (31T), and altitude (m.a.s.l.) of rain gauges. The names of the gauges with both thermometric and rainfall records are shown in bold.

Code	Name	UTM X (km)	UTM Y (km)	Altitude (m.a.s.l.)	Code	Name	UTM X (km)	UTM Y (km)	Altitude (m.a.s.l.)
1	El Pont de Suert	314.390	4696.649	823	44	Prats de Lluçanès	419.397	4651.026	701
2	Vielha	319.403	4729.904	975	45	Rocafort	356.457	4593.22	560
3	Figueres	496.369	4684.011	31	46	Montblanc	346.606	4582.81	340
4	Moià	424.938	4629.639	735	47	Esparraguera	405.436	4599.078	187
5	Ebro Observatory	288.703	4522.022	49	48	Torroella	516.672	4655.775	2
6	Reus Airport	345.585	4556.658	73	49	Montbrió	333.136	4554.598	132
7	Barcelona Airport	419.544	4572.631	3	50	Organyà	362.27	4675.133	566
8	Fabra Observatory	426.879	4585.783	412	51	La Vall d’en Bas	455.339	4663.113	510
9	Girona	484.094	4648.026	72	52	Castellfollit	462.603	4674.424	296
10	Flix	298.285	4562.288	53	53	Cadaqués	522.557	4681.476	24
11	Tivissa	309.325	4546.042	313	54	El Bruc	398.259	4603.715	489
12	Lleida	299.694	4611.309	192	55	St. Quintí de Mediona	390.919	4593.443	325
13	Tàrrega	347.109	4614.634	380	56	Castellví	384.319	4575.694	198
14	Caldes	430.803	4607.309	176	57	Balsareny	406.601	4635.019	327
16	Malla– Torrellebreta	438.458	4634.027	570	58	Palafrugell	513.318	4640.267	64
17	Vic	437.077	4643.040	499	59	Jafre	505.127	4655.771	15
18	Vilafranca	389.362	4576.479	176	60	Puig-Reig	406.818	4647.462	455
19	Granollers	441.629	4606.726	202	61	Berga	404.203	4661.652	704
20	Ransol	388.463	4715.122	1645	62	Sarral	353.598	4589.634	467
21	Sallent	411.665	4627.476	278	63	Els Omellons	329.778	4596.644	385
22	Valls	354.383	4572.742	230	64	La Granadella	305.008	4580.475	505
23	Igualada	384.760	4603.934	333	65	Cubelles	386.684	4561.776	17
24	Tremp	325.636	4670.183	473	66	Malgrat	479.729	4610.62	2
25	Oliana	360.703	4659.884	490	67	Mas de Barberans	280.386	4510.733	240
26	El Turó de l’Home	453.364	4624.999	1668	68	Amposta	295.436	4508.513	3
27	Manresa	403.719	4619.630	291	69	Torelló	437.113	4657.362	508
29	Vila-seca	344.301	4552.210	53	70	Benissanet	301.215	4547.698	32
33	Perpinyà	489.425	4731.437	44	71	Riba-roja	289.19	4569.44	76
34	Puigcerdà	412.395	4699.199	1214	72	Miravet	298.143	4546.014	43
37	Llinars	449.806	4610.209	198	73	Campdevànol	431.279	4674.834	738
38	Terrassa	418.373	4601.603	290	74	Cervera	356.469	4614.555	554
39	Rocallaura	345.288	4596.651	645	75	Riner	384.044	4644.945	830
40	Agramunt	341.843	4627.918	337	76	Vimbodí	336.933	4585.049	446
41	Vilalba	282.449	4555.323	442	77	L’Ametlla de Mar	312.141	4531.061	93
42	Breda	463.111	4621.813	169	78	La Pobla de Segur	332.041	4678.363	508
43	Cabacers	310.237	4568.904	357	79	Esterri	346.296	4721.003	957

along with the corresponding name, coordinates, and altitude. Furthermore, for comparison with temperature behavior, 23 thermometric series from Catalonia, obtained from the SMC, have also been used; these are highlighted in bold in Table 1.

In addition, two of these rain gauges—Fabra Observatory (Barcelona, 412 m a.s.l.) and Ebro Observatory (Roquetes, Tarragona, 49 m a.s.l.)—have data series extended to longer historical periods to support further analysis and interpretation of the results. The Fabra Observatory series spans from 1914 to 2024 and was obtained from the Reial Acadèmia de Ciències i Arts de Barcelona [43]. The Ebro Observatory record, covering the period from 1905 to 2023, was provided by the Ramon Llull University (URL) and the Spanish National Research Council (CSIC) through the Observatori de l’Ebre [44]. The 31-year running averages of these two centennial stations will be correlated with the corresponding values for the North Atlantic Oscillation index (NAO) and the Atlantic Multidecadal Oscillation index (AMO) obtained from the official website of the National Oceanic and Atmospheric Administration (NOAA, [45]).

2.2. Methodology

2.2.1. Main Characteristics of Each 31-Years Window

A 31-year moving-window approach, MW31, with a 1-year shift, has been applied to annual, seasonal and monthly amounts for the 72 rain gauges from 1950 to 2022 in order to analyze possible temporal oscillations and time trends. Then, two characteristics define every one of the resulting 43 moving windows for each station. These characteristics are the average rainfall amount, $\overline{R}$, and the coefficient of variation, $CV$.

For a first insight into the variation in the main annual characteristics, the comparison between the two reference periods, 1960–1990 and 1990–2020, has been analyzed. For this purpose, a relative difference for the mean annual rainfall, in percentage, has been computed for each rain gauge. These relative differences have also been computed for the $CV$ and summarized in two respective histograms.

In addition, the main characteristics are graphically represented for all 43 windows and 72 stations at annual, seasonal and monthly scales. Seasons were defined as winter (DJF), spring (MAM), summer (JJA) and autumn (SON). The global linear trends of these 43 $\times$ 72 points are obtained by means of the ordinary least squares regression method (OLS). The percentage of these global trends is calculated using Equation (1), where the function $y$ represents the linear trend, and 1965 and 2007 are the central years of the first and last MW, respectively.

$$Global trend\left(\%\right)={\displaystyle \frac{y\left(\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{M}\mathrm{W}\right)-y\left(\mathrm{f}\mathrm{i}\mathrm{r}\mathrm{s}\mathrm{t}\mathrm{M}\mathrm{W}\right)}{y\left(\mathrm{f}\mathrm{i}\mathrm{r}\mathrm{s}\mathrm{t}\mathrm{M}\mathrm{W}\right)}}\times 100={\displaystyle \frac{y\left(2007\right)-y\left(1965\right)}{y\left(1965\right)}}\times 100.$$

(1)

Furthermore, the main values of the principal characteristics at annual, seasonal, and monthly scales, along with some results, will be presented in the following sections.

2.2.2. Trends Within Each 31-Years Window

The linear trend of rainfall amounts, $Tr$, for each window and station, has been computed. These trends have been studied through the ordinary least squares method, OLS, and their significance assessed by means of the Mann–Kendall (MK) trend test [46]. The significance has been evaluated by comparing the standardized test statistic $Z={\displaystyle \frac{S}{\sqrt{V\left(s\right)}}}$ with the standard normal variate at the desired significance level. In this article, the significance level is set to 5%, corresponding to a 95% confidence level (p-value = 0.05). In addition, the 85% confidence level (p-value = 0.15) is also considered. Finally, the time evolution of the MK coefficients will be graphically represented and fitted to a fourth-degree polynomial.

2.2.3. Trends of Moving Window Characteristics

The evolution of the moving average values and coefficient of variation along the 43 moving windows and 72 stations has also been studied. These new trends have also been computed by means of the OLS. These computations correspond to the trends of the moving averages,$Tr\overline{R}$, and of the moving coefficient of variation, $TrCV$.

However, for the significance of these trends, when dealing with autocorrelated series, as is often the case with moving window averages, applying the MK test can lead to erroneous conclusions because the test assumes that the data are independent and randomly ordered. Therefore, this study has utilized the modified Mann–Kendall (mMK) test for autocorrelated data [47] to assess the significance of detected trends in the time series processed using the moving-window technique.

The modified variance is computed as Equation (2), where ${\displaystyle \frac{n}{n_s^{*}}}$ represents a correction due to the autocorrelation in the data, computed using Equation (3).

$$V^{*}\left(S\right)=V\left(S\right){\displaystyle \frac{n}{n_s^{*}}}={\displaystyle \frac{n(n-1)(2n+5)}{18}}{\displaystyle \frac{n}{n_s^{*}}}.$$

(2)

$${\displaystyle \frac{n}{n_s^{*}}}=1+{\displaystyle \frac{2}{n(n-1)(n-2)}}{\sum }_{j=1}^{n-1}(n-j)(n-j-1)(n-j-2){\rho }_s\left(j\right).$$

(3)

In both Equations (2) and (3), $n$ denotes the number of sample elements; in this article, $n=43$, which corresponds to the number of moving windows. In Equation (3), ${\rho }_s\left(j\right)$ is the autocorrelation function of the rainfall amount ranks, at time lag $j$.

Finally, the trends of the 31-year moving averages and the $CV$ will be spatially represented over Catalonia at annual, seasonal and monthly scales. The stations with a confidence level greater than or lower than 95% (p-value = 0.05) are also indicated. Figure 2 summarizes the main steps of this research.

2.2.4. Two Centennial Series and Correlation with NAO and AMO

In order to compare the results for the years 1950–2022 with those obtained over longer periods, for two centennial series (Fabra and Ebro Observatories) and at an annual scale, the 31-year running averages will be represented and the oscillations studied. In addition, the correlations with the MW31 NAO and AMO indices will be analyzed. The significance of the correlation between two autocorrelated series is obtained using the effective number of degrees of freedom, $N_{eff}$, by means of the approximation given in Equation (4) [48,49], where $N$ is the sample size and ${\rho }_{xx}\left(j\right)$ and ${\rho }_{yy}\left(j\right)$ are the autocorrelations of two sampled time series $x$ and $y$ at time lag $j$, respectively.

$${\displaystyle \frac{1}{N_{eff}}}\approx {\displaystyle \frac{1}{N}}+{\displaystyle \frac{2}{N}}{\sum }_{j=1}^N{\displaystyle \frac{N-j}{N}}{\rho }_{xx}(j){\rho }_{yy}(j).$$

(4)

3. Results

3.1. Annual Amounts

3.1.1. First Insight

Figure 3 shows three examples of the evolution of the mean annual rainfall amounts and the corresponding coefficient of variation for the 43 moving windows of 31 years. The three selected stations have different types of climate. Viella (station code 2), with high annual amounts, is located on the north face of the Pyrenees, with a NE orientation and Atlantic influences. Barcelona Airport (code 7) is on the central coast of Catalonia, with typical Mediterranean weather, and Lleida (code 12), with a more continental climate, is located in the Central Basin and experiences lower annual rainfall amounts. Although their climates are quite different, the linear trends of the mean values are negative and statistically significant at the 95% confidence level for the three stations.

For instance, the annual mean in Barcelona Airport has been decreasing, with some oscillations, from an initial value of 616.2 mm for the first window (1950–1980) to 547.1 mm for the last window (1992–2022), which represents a decreasing percentage of 11.2%. On the other hand, for the coefficient of variation, the linear trend is negative in the Barcelona Airport, while in the other two rain gauges it is positive. All three trends are statistically significant at a 95% confidence level.

Figure 4 illustrates the histograms of the relative differences between the two reference periods, 1960–1990 and 1990–2020, for the mean and $CV$ values and each station. For the mean values, the differences are negative for 62 of 72 stations. Furthermore, a diminution between 5% and 10% has been accomplished for 28 locations. However, for $CV$, the number of stations with positive and negative differences are more variably distributed.

3.1.2. Mean Annual Rainfall and $CV$ for Each Window and Station

The averages of the annual rainfall amounts, $\overline{R}$, for the 72 rain gauges and the 43 moving windows are represented in Figure 5. These values range from 339.0 mm to 1111.8 mm (

Table 2. Minimum ($MIN$), maximum ($MAX$), average ($AVG$) and standard deviation ($S$) of the average rainfall ($\overline{R}$) and coefficient of variation ($CV$) for each MW31 and rain gauge.

	${\overline{\mathit{R}}}_{\mathit{M}\mathit{I}\mathit{N}}$ (mm)	${\overline{\mathit{R}}}_{\mathit{M}\mathit{A}\mathit{X}}$ (mm)	${\overline{\mathit{R}}}_{\mathit{A}\mathit{V}\mathit{G}}$ (mm)	${\overline{\mathit{R}}}_{\mathit{S}}$ (mm)	$\mathit{C}{\mathit{V}}_{\mathit{M}\mathit{I}\mathit{N}}$	$\mathit{C}{\mathit{V}}_{\mathit{M}\mathit{A}\mathit{X}}$	$\mathit{C}{\mathit{V}}_{\mathit{A}\mathit{V}\mathit{G}}$	$\mathit{C}{\mathit{V}}_{\mathit{S}}$
Annual	339.0	1111.8	615.7	156.9	0.14	0.41	0.25	0.042
Winter	60.1	289.2	120.5	37.3	0.34	0.81	0.58	0.086
Spring	101.8	320.5	166.0	40.6	0.20	0.81	0.45	0.094
Summer	43.1	364.5	130.2	59.9	0.26	0.84	0.51	0.114
Autumn	101.2	336.0	199.0	39.4	0.30	0.83	0.47	0.091
January	20.5	110.6	40.9	13.2	0.54	1.43	1.05	0.131
February	12.9	77.2	32.1	11.8	0.53	1.41	0.94	0.147
March	21.2	99.6	43.7	12.7	0.48	1.52	0.88	0.158
April	28.1	103.9	55.6	13.6	0.38	1.40	0.70	0.174
May	32.3	133.0	66.7	18.5	0.30	1.24	0.68	0.161
June	17.9	125.8	50.3	20.8	0.34	1.62	0.82	0.235
July	6.4	113.0	30.0	19.3	0.45	1.87	0.97	0.253
August	11.4	133.0	50.0	21.8	0.39	1.30	0.76	0.163
September	34.8	108.5	67.5	14.8	0.40	1.58	0.76	0.194
October	36.0	132.3	74.1	16.9	0.50	1.75	0.83	0.153
November	26.0	119.0	57.5	14.6	0.52	1.86	0.90	0.154
December	20.1	116.6	47.4	14.6	0.46	1.58	0.99	0.129

). The global trend is negative with $-$1.5 mm/year, implying a reduction close to 10% for the MW31 mean annual value. For the moving $CV$, the values of the first window are more dispersed (0.14–0.41) than the $CV$ of the last windows (0.17–0.32), and the mean trend, as in the case of average amounts, is approximately $-$10%.

3.1.3. Trends of Annual Amounts Within Each 31-Years Window

For each window and station, the trends of the annual amounts have also been computed. The MK coefficients corresponding to these MW31 trends and the 72 available stations are represented in Figure 6a, and

Table 3. Minimum ($MIN$), maximum ($MAX$), average ($AVG$) and standard deviation ($S$) of trends ($Tr$) and Mann–Kendall test coefficient (MK). for each MW31 and rain gauge.

	$\mathit{T}{\mathit{r}}_{\mathit{M}\mathit{I}\mathit{N}}$ (mm/y)	$\mathit{T}{\mathit{r}}_{\mathit{M}\mathit{A}\mathit{X}}$ (mm/y)	$\mathit{T}{\mathit{r}}_{\mathit{A}\mathit{V}\mathit{G}}$ (mm/y)	$\mathit{T}{\mathit{r}}_{\mathit{S}}$ (mm/y)	$\mathit{M}{\mathit{K}}_{\mathit{M}\mathit{I}\mathit{N}}$	$\mathit{M}{\mathit{K}}_{\mathit{M}\mathit{A}\mathit{X}}$	$\mathit{M}{\mathit{K}}_{\mathit{A}\mathit{V}\mathit{G}}$	$\mathit{M}{\mathit{K}}_{\mathit{S}}$
Annual	−14.8	8.93	−1.72	2.74	−3.59	2.72	−0.51	0.83
Winter	−6.23	7.68	−0.42	1.27	−3.26	2.89	−0.42	0.86
Spring	−7.59	4.99	−0.10	1.68	−3.43	2.48	−0.09	1.13
Summer	−5.82	3.70	−0.72	1.08	−3.32	2.92	−0.53	0.84
Autumn	−7.97	6.31	−0.47	2.21	−3.60	2.97	−0.16	1.05
January	−3.43	4.28	0.14	0.72	−2.52	2.47	0.08	0.70
February	−2.89	2.77	−0.13	0.60	−3.45	2.77	−0.28	1.03
March	−3.06	2.96	−0.18	0.91	−3.64	3.52	−0.18	1.31
April	−2.53	2.95	0.20	0.72	−2.02	3.28	0.39	0.85
May	−3.75	4.19	−0.12	0.81	−3.16	2.67	−0.14	0.88
June	−2.51	1.82	−0.41	0.62	−3.06	2.37	−0.62	0.90
July	−2.62	2.66	−0.07	0.53	−3.28	3.46	−0.04	1.02
August	−3.23	2.08	−0.24	0.65	−2.84	2.69	−0.33	0.88
September	−5.35	4.28	−0.43	1.37	−3.62	4.28	−0.26	1.31
October	−4.50	4.35	−0.11	1.12	−3.16	2.58	0.08	0.89
November	−4.09	3.26	0.07	1.04	−3.33	3.30	0.01	1.00
December	−4.76	3.42	−0.44	1.04	−3.35	2.74	−0.47	1.05

summarizes some values of the trends and MK coefficients at the annual scale and, in addition, for the analyses in the following sections, at seasonal and monthly scales.

Few stations have values greater than $+2.0$ or less than $-2.0$, corresponding to the 95% confidence level (p-value = 0.05), for $N=31$. On the one hand, only some stations with significant negative trends are detected during the periods centered between 1970 and 1985, with a minimum MK value of −3.59 (99.89% or p-value = 0.00112). The 31-year period with the highest number of significant negative trends, centered in 1974, was 1959–1989, with 26% of stations. However, for the 85% confidence level (p-value = 0.15), 54% of stations show significant negative trends during the same period. For the more recent years, the 31-period centered in 2002 (1987–2017) shows 11% of stations with significant negative trends. On the other hand, very few stations with positive significant trends (coefficients greater than $+2.0$) are observed around 1995, with a maximum MK value of 2.72 (98.94% or p-value = 0.0106). A comparative study with temperatures in this region, based on the 23 available thermometric gauges (Table 1), is shown in Figure 6b,c for maximum and minimum temperatures.

The difference between temperature and rainfall behavior is evident. For both maximum and minimum temperatures, trends have been significant and positive since the MW31 centered in 1975 for maximum temperature and in 1978 for minimum temperature.

3.1.4. Trends in Characteristics of Annual Moving Windows

Figure 7 represents the relative trends, in percentage, and the significance, obtained with the mMK test, at the 95% confidence level of the moving average amounts, $Tr\overline{R}$, and the moving coefficient of variation, $TrCV$. This percentage has been calculated relative to the value of the first MW31 (1950–1980).

Table 4. Number and percentage of rain gauges with significant positive and negative trends (95% confidence level) for the moving average and $CV$. Positive trends are shown in blue, and negative trends in red.

	$\mathit{T}\mathit{r}{\overline{\mathit{R}}}_{\mathit{M}\mathit{W}\mathbf{31}}$				$\mathit{T}\mathit{r}{\mathit{C}\mathit{V}}_{\mathit{M}\mathit{W}\mathbf{31}}$
	Number/%		Number/%		Number/%		Number/%
Annual	0	0.0	63	87.5	19	26.4	21	29.2
Winter	0	0.0	45	62.5	57	79.2	3	4.2
Spring	6	8.3	28	38.9	10	13.9	29	40.3
Summer	1	1.4	64	88.9	32	44.4	3	4.2
Autumn	19	26.4	5	6.9	5	6.9	31	43.1
January	12	16.7	4	5.5	15	20.8	17	23.6
February	0	0.0	47	65.3	41	56.9	4	5.6
March	0	0.0	41	56.9	21	29.2	1	1.4
April	24	33.3	2	2.8	0	0.0	47	65.3
May	0	0.0	27	37.5	21	29.2	15	20.8
June	0	0.0	56	77.7	61	84.7	0	0.0
July	6	8.3	19	26.4	11	15.3	13	18.1
August	3	4.2	46	63.9	18	25.0	16	22.2
September	5	6.9	29	40.3	6	8.3	39	54.2
October	34	47.2	7	9.7	4	5.6	38	52.8
November	16	22.2	0	0.0	7	9.7	25	34.7
December	0	0.0	54	75.0	27	37.5	2	2.8

summarizes the number of stations with significant positive and negative moving trends for the mean values and the $CV$ at annual, seasonal and monthly scales. For the moving annual average, 63 of 72 stations (88%) have significant negative trends with a relative percentage as low as −20%. The minimum MK value is −5.99 (p-value < 0.000001), which corresponds to a station located in the southern corner of Catalonia.

However, for the corresponding $CV$, some inland regions and the Pyrenees show significant positive trends (19 out of 72), while in coastal areas, trends are mostly negative (21 out of 72), especially in the southern and northern corners.

These results indicate that regions, such as the Pyrenees, with high amounts of annual precipitation and a low irregularity, are experiencing a decrease in the total amounts and an increase in irregularity in the recent years.

3.1.5. Two Centennial Series and Correlation with NAO and AMO

In Figure 8, the mean annual rainfall of two long-term series, Fabra Observatory (1914–2024) and Ebro Observatory (1905–2023), is represented. This figure shows that, while the MW31 annual averages are decreasing during the study period of this article, earlier periods also exhibited positive trends. For instance, at the Ebro Observatory, a positive trend is observed from the central year 1920 (period 1905–1935) to 1960 (period 1945–1975), and at the Fabra Observatory, from 1940 (period 1925–1955) to 1985 (period 1970–2000). The MW31 averages at Fabra Observatory range from 586.8 to 660.4 mm, with a mean value of 620.8 mm.

For the Ebro Observatory, the first two reference periods have similar values, both higher than that of the last period. The difference between the minimum (482.9 mm) and the maximum (599.1 mm), for this station, is greater than 100 mm. A periodicity close to 80 years is detected in Figure 8. Although for rainfall amounts, several studies correlate precipitation in Catalonia mainly with Mediterranean indices, such as Mediterranean Oscillation (MO), Western Mediterranean Oscillation (WeMO), or upper-level MO (ULMO) [50,51,52], for MW31 values these oscillations could be explained by the quasi-periodic multidecadal variability of the North Atlantic Oscillation (NAO) or by the Atlantic Multidecadal Oscillation (AMO). To this end, the MW31 averages of the NAO (NAO_MW31) and AMO (AMO_MW31) are calculated to compare them with the mean annual averages, $\overline{R}$_MW31, of Ebro (Ebro_MW31) and Fabra (Fabra_MW31), respectively. While for the NAO a minimum is centered in 1960, a maximum is observed for the Ebro Observatory (Figure 9a), explaining an inverse correlation between the NAO index and rainfall at this station. The coefficient correlation between the reconstructed NAO_MW31 [53,54] and annual $\overline{R}$_MW31 of Ebro, from the central years 1920 to 1986, is equal to −0.79 with a confidence level of 91% (p-value = 0.09), obtained with the effective number, $N_{eff}$, from Equation (4). The coefficient of correlation between NAO_MW31 of NOAA [45] and annual $\overline{R}$_MW31 of Ebro for the period of central years 1920 to 1996 is equal to −0.63 with a confidence level of 86% (p-value = 0.14).

Figure 9b shows the evolution of the Fabra_MW31 annual rainfall and the AMO_MW31 index. The correlation coefficient is equal to −0.92 with a confidence level of 94% obtained by means of Equation (4). The high negative correlation between both magnitudes is noteworthy. Figure 10 shows the correlation between Ebro_MW31 and Fabra_MW31 for different lags. The maximum correlation is equal to 0.88 with a 20-year lag.

3.2. Seasonal Amounts

3.2.1. Mean Seasonal Rainfall and $CV$ for Each Window and Station

Figure 11 represents the moving seasonal means for the MW31 with a one-year shift. Trends are globally negative except for autumn, without a clear trend. The summer season presents the highest global negative trend (−0.76 mm/year), equivalent to a 21.5% decrease. For instance, the station with the highest summer moving values is a pre-Pyrenees station (Campdevànol, code 73) with a first mean value of 363.6 mm and a last value of 292.4 mm and with a monotonic negative trend. The greatest seasonal standard deviation of the moving average and moving $CV$ values corresponds to summer, with 59.9 mm and 0.114 (Table 2), respectively. This season presents at the same time the lowest (43.1 mm) and the highest moving averages (364.5 mm). The second season with the highest negative average trend is winter (−0.43 mm/year) with a global negative trend of −14.6% with some oscillations. Autumn is the season with the highest mean (199.0 mm) of all the moving averages and stations.

The evolution of the moving seasonal $CV$ is represented in Figure 12. While winter and summer have positive trends, indicating an increase in the irregularity since 1950 for these two seasons, spring and autumn show global negative trends. Notably, the $CV$ increase in winter is particularly prominent.

3.2.2. Trends in Seasonal Amounts Within Each 31-Year Window

Figure 13 depicts the evolution of the MK coefficients corresponding to the trends of the seasonal amounts within each MW31 and for each rain gauge. For spring, the period of the central years from 1981 to 1991 shows a non-negligible number of rain gauges with significant negative coefficients. Autumn is the season with the greatest minimum and maximum MK coefficient values, −3.60 and 2.97 (Table 3), which correspond to p-values of 0.00109 and 0.00571, respectively. A fourth-degree polynomial is adequate to fit the average evolution of the MK coefficients for the four seasons, revealing a phase opposition between spring and autumn. For these two seasons, a clear oscillation with a periodicity of 30–35 years is observed.

3.2.3. Trends in the Characteristics of Seasonal Moving Windows

Figure 14 depicts the spatial distribution of the significant and non-significant trends in the moving averages for each rain gauge. For winter and especially summer, trends are negative for a high number of stations: 45 and 64, respectively (Table 4). The red (negative) color is predominant in these two figures. However, for spring and autumn, there are regional differences with positive (blue) and negative (red) trends. For the moving $CV$ (Figure 15) in winter, the positive trends are notable, especially in the inland areas with trends above 90%. In addition, for autumn, these inland regions also present positive trends (over 40%), while coastal regions and the Pyrenees show negative trends (up to −50%).

3.3. Monthly Amounts

3.3.1. Mean Monthly Rainfall and $CV$ for Each Window and Station

Mean monthly values for each MW31 and rain gauge are represented in Figure 16. The solid line represents the global linear trend, considering all 43 $\times$ 72 values. The highest global negative trends are observed in February, March, June, August and December. June shows the highest negative trend with −0.42 mm/year, equivalent to a 30% decrease with respect to the first value of the linear fit. However, January, April, October and November show global positive trends.

The monthly $CV$ values for each MW31 and rain gauge are depicted in Figure 17. Observing the global trends, moving $CV$ shows the highest positive trends in June and February and the most negative in September, April, October and November. June has the highest global positive trend for $CV$ and at the same time the highest negative for the average amounts. Table 2 summarized the main statistics of the MW31. The maximum values of $\overline{R}$ are reached in May, August and October, and the minimum in July. While summer months (June, July and August) show the highest standard deviation of moving averages, February has the lowest. These deviations can also be observed in Figure 16.

For $CV$, the minimum value is reached in May, and the maximum in July and November. In contrast, the highest deviations for $CV$ occur in two summer months (June and July), and the lowest in two winter months (January and December). Four months show the highest positive trends for certain MW31 windows and rain gauges. These months are January, May, September, and October, with values greater than +4.0 mm/year (Table 3). Conversely, the highest negative trends are obtained in autumn months (September, October and November) and in December, all trends with values lower than −4.0 mm/year.

Regarding the average trend considering all 43 × 72 trends, the highest trends are negative and correspond to June, September, and December. The MK coefficients of March and September present high positive and negative values. Other months with high positive MK values are April, July, and November.

3.3.2. Trends of Monthly Amounts Within Each 31-Year Window

Figure 18 depicts the MK coefficients for each MW31 and rain gauge, along with the fourth-degree polynomial fits. Similarities in the evolution of the MK coefficients between September and December can be observed, with a minimum around the central year 1970 and a maximum near 1990. February and March show the opposite behavior, with positive trends during the most recent periods, which aligns with [55]. September has the highest positive MK value, 4.28 (99.98% or p-value = 0.00017, Table 3), which is found in the MW31 centered in 1991. The polynomial fits for January and August show lower oscillations, and January is the month with the fewest significant trends.

3.3.3. Trends in Characteristics of Monthly Moving Windows

Figure 19 and Figure 20 show the spatial distribution of the MW31 relative trends for the mean monthly rainfall and the corresponding $CV$, including their statistical significance at the 95% confidence level. Five months (February, March, June, August, and December) show a high number of significant negative (red) trends (Table 4) for the mean MW31 rainfall. June and December have the highest number of rain gauges with negative trends: 56 and 54 out of 72, respectively, and none with positive trends. Three months, May, July and September, also display predominantly negative trends. Only two months (April and October) have a high number of rain gauges with significant positive (blue) trends.

For $CV$, June is the month with the highest number of positive trends (61 out of 72), and February also shows a large number with 41. On the other hand, significant negative $CV$ trends are observed in April, September and October.

4. Discussion

The comparison between the trend results obtained in the present work (Table 4), using moving windows for Catalonia (1950–2022), and those reported in other studies analyzing total precipitation trends in the region (

Table 5. Rainfall trends in six previous analyses [5,7,36,56,57,58] and in the present work. All columns show the percentages of stations with a significant (positive/negative) trend, except for column [7], which shows the percentage of stations with negative trends and the trend magnitudes in parentheses.

	[56]	[7]	[58]	[57]	[5]	[36]	Present Work
Scale	Monthly	Seasonal	Monthly	Monthly, Annual	Monthly, Seasonal, Annual	Seasonal, Annual	Monthly, Seasonal, Annual MW31
Region	Mediterranean Spanish coast	Mediterranean Spanish coast	Spain	Catalonia	Spain	Spain	Catalonia
Confidence Label	95% (+/−)	95%	90% (+/−)	85% (+/−)	95% (+/−)	90% (+/−)	95% (+/−)
Annual		90 (−12.4)		(4.2/26.0)	(0.74/18.00)	(1.2/22.5)	(0.0/87.5)
Winter		64 (−7.3)			(0.00/15.00)	(0.6/7.0)	(0.0/62.5)
Spring		82 (−19.3)			(0.11/9.60)	(0.8/40.6)	(8.3/38.9)
Summer		85 (−22.5)			(0.01/47.71)	(0.4/20.0)	(1.4/88.9)
Autumn		61 (−5.2)			(0.89/0.19)	(3.9/1.8)	(26.4/6.9)
January	(16.3/7.7)		(0.0/6.1)	(1.0/1.0)	(0.0/1.0)		(16.7/5.5)
February	(18.7/36.1)		(2.4/1.9)	(0.0/30.2)	(0.0/1.0)		(0.0/65.3)
March	(2.8/72.4)		(0.0/68.9)	(0.0/32.3)	(0.0/27.5)		(0.0/56.9)
April	(24.8/20.5)		(5.0/3.6)	(19.8/1.0)	(7.5/2.0)		(33.3/2.8)
May	(12.2/6.2)		(0.0/0.6)	(3.1/8.3)	(0.5/1.0)		(0.0/37.5)
June	(4.4/42.6)		(0.1/31.8)	(0.0/52.1)	(0.0/65.0)		(0.0/77.7)
July	(20.8/25.2)		(6.1/6.2)	(5.2/18.8)	(0.0/12.0)		(8.3/26.4)
August	(19.3/9.0)		(1.6/5.1)	(0.0/15.6)	(1.0/2.5)		(4.2/63.9)
September	(13.7/19.6)		(1.3/0.3)	(3.1/7.3)	(7.5/4.0)		(6.9/40.3)
October	(3.0/34.3)		(33.7/1.4)	(1.0/5.2)	(1.5/2.5)		(47.2/9.7)
November	(5.1/6.2)		(3.3/0.0)	(7.3/1.0)	(0.5/1.0)		(22.2/0.0)
December	(2.9/18.6)		(0.0/0.8)	(2.1/31)	(0.0/4.0)		(0.0/75.0)

) shows that the annual results are consistent with those obtained by [7], who found a decrease in precipitation across more than 90% of the Mediterranean Spanish coast for the period 1951–2000.

For the seasonal study, the results are also aligned with those of [56] for the period 1951–2000. In both cases, summer is the season with the highest number of negative trends, 89% and 85%, respectively, with an average decrease of 22% in both studies. For winter, the proportion of negative trends are similar around 64% in both cases, with an overall decrease between 7% and 9%. The largest differences between the two studies are observed in spring and autumn. In spring, although both studies report negative trends, the percentage is higher for the entire Mediterranean coast than for Catalonia, due to the high number of negative trends along the southern coast of Spain. In autumn, while the present study shows a predominance of positive trends (26%), the broader Mediterranean Spanish coast exhibits negative trends in 61% of the territory.

In Catalonia, June is the month with the highest number of negative trends, which also aligns with [5] for the whole of Spain. In addition, December and February have a high number of stations with negative trends in Catalonia and along the Mediterranean Coast; however, these percentages are very low in the analysis of Spain [5,56]. Regarding positive trends in Catalonia, some discrepancies are observed compared to the different results shown in Table 5. For instance, while, for October, a high percentage of positive trends is obtained in the present work and in [58], the remaining studies report very low percentages for this month. With respect to the MW31 $CV$ trends, winter and summer show increasing values, mainly due to the positive trends in February and June. On the other hand, spring and autumn exhibit a decrease in irregularity, primarily due to April, September, October and November, while August is the month with the highest stability in MW31 $CV$ values.

Although in [57] trends are computed for monthly rainfall amounts and for the entire studied period, some similarities can be observed. Specifically, the number of stations showing statistically significant trends at the 95% confidence level using the MW31 method is comparable to those identified at the 85% confidence level when trends in monthly rainfall amounts are analyzed. Despite the application of a modified Mann–Kendall trend test, the MW31 approach yields a greater number of significant trends than the analysis based on monthly totals over the full period.

The moving-window approach used in this study offers key advantages. It enables the detection of temporal variability in rainfall trends at different time scales and reveals potential oscillatory behaviors that may remain hidden in fixed-period analyses. By applying the method consistently over overlapping 31-year periods, we capture evolving patterns in both trend direction and variability. However, this approach also presents limitations. First, it assumes local stationarity within each window, which may not fully account for abrupt shifts or non-linear changes within those periods. Second, although precautions were taken to reduce the effects of autocorrelation in the overlapping windows, the greater number of statistically significant trends observed, especially in comparison with studies using full-period analyses (e.g., [57]), may reflect residual autocorrelation effects that artificially inflate significance levels. This possibility highlights the need for careful interpretation of trend significance in moving-window analyses. Nevertheless, the consistency of our findings with previous research, along with the ability to detect multi-decadal oscillations, supports the methodological value of this approach.

Concerning the trends in the amounts within each MW31, oscillations and periodicities of approximately 30–35 years, particularly evident in spring and autumn, are consistent with findings from other studies reporting similar cycles in annual rainfall and the North Atlantic Oscillation (NAO). For instance, in [59] a 33.3-year periodicity in annual rainfall in Croatia was identified, while [60] reported several NAO cycles, including one lasting 34 years. From a monthly perspective, some months show periodicity and oscillations, for example, February, March, September, October, November, and December. At the annual scale, however, lower-frequency periodicities are also observed, suggesting the presence of different underlying patterns. The contrast with temperature behavior indicates the existence of two distinct modes of variability. This aspect represents a promising direction for future research, particularly through the analyses of temperature trend variability using moving windows of different lengths. Additionally, the opposing behavior observed between spring and autumn should be further investigated in future studies.

With respect to the oscillations observed in annual MW31 amounts for the two long series, Fabra and Ebro, similar cycles to those shown in Figure 8 were found in [53] for the NAO and AMO, but with opposite phases and based on 21-year running averages. In addition, the inverse correlation found between the NAO index and MW31 annual rainfall in Ebro as represented in Figure 9a is consistent with the findings of [61]. Although Fabra and Ebro have a similar periodicity close to 80 years, both cycles are shifted by 20 years, confirmed by the cross-correlation analysis (Figure 10), indicating a different behavior between these two gauges, which are 180 km apart. These differences are likely caused by the orography, orientation of the coastline, the more southwestern location of the Ebro Observatory, which results in a greater influence from the Ebro Valley, and the different altitudes: 412 m for Fabra and 49 m for Ebro. It is surprising to observe the coincidence of the 20-year lag between Ebro_MW31 and Fabra_MW31 and between NAO_MW31 and AMO_MW31, as found by [53].

In addition to the influences of the NAO and AMO on the MW31 rainfall oscillations, the Gleissberg 80-year solar cycle should also be considered [62,63]. Solar cycles influence the Earth’s climate and, consequently, rainfall regimes. While the 11-year period of the solar cycle is well known for its correlation with climatological variability, the 80-year cycle also appears to have a significant impact on rainfall variability. Several studies have identified periodicities close to 80 years in rainfall, floods, lakes and sea level, droughts, tree rings and temperatures [64,65,66].

Future research should aim to extend these analyses to the widest possible set of long-term datasets available across the Iberian Peninsula, both spatially and across other meteorological variables. In particular, applying this moving-window approach to temperature records in the same region may help reveal potential links between thermal and rainfall variability. Comparing trends in precipitation and temperature over similar time frames could offer a more comprehensive understanding of the climatic dynamics affecting the Mediterranean basin and provide further insights to support long-term water resource planning.

5. Conclusions

This detailed study, conducted using 31-year moving windows of annual, seasonal, and monthly precipitation values from 72 stations in Catalonia over the period 1950–2022, shows that the annual moving average values have decreased in nearly 90% of the stations, with a global reduction close to 10%. Rainfall variability, measured by the coefficient of variation ($CV$), has decreased along the coast but increased in inland areas and the Pyrenees. On a seasonal scale, summer stands out as the season with the most significant negative trend in MW31 averages, while autumn shows an almost overall neutral trend, although some regions in central Catalonia exhibit a positive trend. The winter $CV$ has significantly increased in about 80% of the territory.

On the monthly scale, June, December and February exhibit the highest percentage of stations with negative trends, and for June and February, they also show the greatest reductions in precipitation, reaching up to 80%. At the same time, these two months show a significant increase in variability.

Additionally, the analysis of precipitation trend values within each MW31 shows Mann–Kendall (MK) test coefficients that, although statistically significant only in certain years and stations, reveal a fourth-degree polynomial fit that indicates whether the trend is becoming increasingly positive or negative. A periodicity of 30–35 years is especially evident in spring and autumn, with the completely opposite behavior between these two seasons being particularly striking. Furthermore, at least six months display similar variability patterns. A comparable oscillation of 33–34 years has also been identified in the NAO index and in annual rainfall in previous articles.

Finally, a periodicity of approximately 80 years has been identified in the 31-year moving averages of two centennial stations, Fabra Observatory (Barcelona) and Ebro Observatory (Tarragona). This periodicity may be attributed to the oscillations of the AMO and NAO indices and the 80-year Gleissberg solar activity cycle. This insight can support future projections and contribute to more effective long-term water resources management. However, the study period of this research (1950–2022) falls within a phase of negative trend, but it may suggest that this decline is approaching its end.

Beyond the scientific implications, these findings may also hold relevance for water resource management. The results presented in this study provide valuable insights into the historical evolution of precipitation patterns in the Mediterranean region. Although the analysis is retrospective, identifying when and where significant shifts in rainfall occurred can help water resource managers understand the timing and spatial extent of past changes. This historical perspective is crucial for evaluating long-term variability, benchmarking current conditions, and informing adaptive water planning strategies, especially in regions with increasing climatic and hydrological pressures.