# Grid-Point Rainfall Trends, Teleconnection Patterns, and Regionalised Droughts in Portugal (1919–2019)

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## Abstract

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## 1. Introduction

## 2. Material and Models

#### 2.1. Grid-Point Rainfall and North Atlantic Oscillation Index Data Set

**Figure 1.**Schematic location of (

**a**) the 532 rain gauges, i.e., original rainfall series—from Portela et al. [13]—and (

**b**) the constructed mesh with the 126 centroids used for the rainfall trend analysis and teleconnection. Centroids’ coordinate referencing system: WGSM84, UTM zone 29 N; for instance, in metres C1 (527908 and 4652269) and F20 (617908 and 4082269).

#### 2.2. Monotonic and Sequential Trend Models

- The values of the original series ${X}_{i}$ were replaced by their ranks ${r}_{i}$, arranged in ascending order.
- The magnitudes of ${r}_{i}$, $(i=1,2,\dots ,n)$, were compared with ${r}_{j}$, $(j=1,2,\dots ,i-1)$, and at each of the comparisons, the number of cases ${r}_{i}>{r}_{j}$ were counted and denoted by ${n}_{i}$.
- A statistic ${t}_{i}$ was defined as follows:$${t}_{i}=\sum _{k=1}^{i}{n}_{k}$$
- The mean and variance of the test statistic were computed as:$$E\left({t}_{i}\right)=\frac{i(i-1)}{4}\phantom{\rule{4.pt}{0ex}}\mathrm{and}\phantom{\rule{4.pt}{0ex}}\mathrm{Var}\left({t}_{i}\right)=\frac{i(i-1)(2i+5)}{72}$$
- The sequential values of the statistic u(${t}_{i}$) were then calculated as:$$u\left({t}_{i}\right)=\frac{[{t}_{i}-E\left({t}_{i}\right)]}{\sqrt{\mathrm{Var}\left({t}_{i}\right)}}$$

## 3. Results

#### 3.1. Spatial Distribution of the Grid-Point Rainfall and Their Trends

#### 3.2. Sequential Observed Trends in Rainfall and in the North Atlantic Oscillation

#### 3.3. Teleconnection between the Grid-Point Rainfall Trends and the NAOI Trends

## 4. Discussion

#### 4.1. Persistent Influence of the North Atlantic Oscillation on Rainfall Trends

#### 4.2. Regionalised Droughts in Portugal during 1919–2019

**X**${}_{100\times 126}$. Additionally, when analysing droughts based on spatiotemportal data only, it is necessary to identify regions or centroids, in this case, with similar temporal patterns and put them together in space [49]. Thus, a two-step process was applied based on the FA (i) to group the centroids, and then (ii) to spatially average the gridded rainfall series of the centroids in the identified homogeneous region. The first two unrotated principal components suggested non-random signals when the scree test [50] was applied to the eigenvalue series (not shown here). The number of principal components was two, explaining 91.9% of the total variance of the original problem. This helped to obtain the factor loadings, in this application, with two factors retained (Factor 1, F1 and Factor 2, F2; explaining 47.1% and 44.8% of total variance, respectively), using Varimax raw for factor rotation, and PCA as an extraction method [51]—the retention of more factors was also tested but is meaningless in this application due to a probable overfactoring.

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Average rainfall and Sen’s slope estimates (right and left side of each combo, respectively) for Portugal, based on the grid-point rainfall, for the 100 hydrological year period from 1919–2019 (IDW2 interpolation method used for mapping).

**Figure 3.**Progressive-trend series u(t in grey scales, unitless, of the quarterly OND, JFM; four-monthly DJFM, and annual ANN grid-point rainfall series for Portugal (based on the 126 centroids of Figure 1b).

**Figure 4.**Progressive-trend series u(t, unitless, of the quarterly nOND, nJFM; four-monthly nDJFM, and annual nANN NAO indices, NAOI; station-based indices based on the difference of SLP between Lisbon, Portugal and Reykjavik, Iceland—based on the data from Hurrell and NCAR [22].

**Figure 5.**Teleconnection between the grid-point rainfall trends and NAOI trends from 1919–2019. Spatial distribution of the Pearson correlation coefficient, r, between the progressive-trend series, u(t, of OND, JFM, DJFM and ANN rainfall; and nOND, nJFM, nDJFM and nANN NAOI, respectively (IDW2 interpolation method used for mapping).

**Figure 6.**Teleconnection between the grid-point rainfall trends and NAOI trends from 1919–2019. Spatial distribution of the Pearson correlation coefficient, r, between the progressive-trend series, u(t), of JFM-nDJF, DJFM-nDJF, ANN-nDJF, and ANN-nDJFM (IDW2 interpolation method used for mapping).

**Figure 7.**Factor loadings (correlation between observed variables and latent common factors) for the annual 126 gridded rainfall series (1919–2019) in (

**a**) Factor 1 and (

**b**) Factor 2. (

**c**) Regionalisation of three identified climatic regions based on factor analysis, namely, north, transition, and south—coordinates WGS84 (UTM zone 29N), IDW2 interpolation method used for mapping the factor loadings.

**Figure 8.**Annual rainfall from 1919–2019 at each of the climatic regions averaged out of the total 126 grid-point rainfall series clustered from the factor analysis, i.e., at the north (54 centroids), transition (20 centroids) and south (52 centroids).

**Figure 9.**Northern region. Time dependent occurrence rates, λ(t) (year

^{−1}), in red, and confidence band in grey of (

**a**) moderate and (

**b**) severe droughts for SPI6 and SPI12 in blue. The horizontal-dashed lines different to zero represent the drought thresholds and vertical ticks, with SPI below them.

**Figure 10.**Transitional region. Time dependent occurrence rates, λ(t) (year

^{−1}), in red, and confidence band in grey of (

**a**) moderate and (

**b**) severe droughts for SPI6 and SPI12 in blue. The horizontal-dashed lines different to zero represent the drought thresholds and vertical ticks, with SPI below them.

**Figure 11.**Southern region. Time dependent occurrence rates, λ(t) (year

^{−1}), in red, and confidence band in grey of (

**a**) moderate and (

**b**) severe droughts for SPI6 and SPI12 in blue. The horizontal-dashed lines different to zero represent the drought thresholds and vertical ticks, with SPI below them.

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**MDPI and ACS Style**

Espinosa, L.A.; Portela, M.M.
Grid-Point Rainfall Trends, Teleconnection Patterns, and Regionalised Droughts in Portugal (1919–2019). *Water* **2022**, *14*, 1863.
https://doi.org/10.3390/w14121863

**AMA Style**

Espinosa LA, Portela MM.
Grid-Point Rainfall Trends, Teleconnection Patterns, and Regionalised Droughts in Portugal (1919–2019). *Water*. 2022; 14(12):1863.
https://doi.org/10.3390/w14121863

**Chicago/Turabian Style**

Espinosa, Luis Angel, and Maria Manuela Portela.
2022. "Grid-Point Rainfall Trends, Teleconnection Patterns, and Regionalised Droughts in Portugal (1919–2019)" *Water* 14, no. 12: 1863.
https://doi.org/10.3390/w14121863