### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methodology
- 4. Results and Discussion
- 5. Conclusions
- Acknowledgements
- References
- Supporting Information

An analysis of recent-past changes in rainfall records from the three major transnational basins in Iberia was performed, using data from Spain and Portugal which are generally considered separately. Change point (to detect abrupt changes in rainfall) and trend analysis were performed in the basins of rivers Douro, Tagus and Guadiana for the period 1961 to 2009. Nonparametric tests (Pettitt, cusum and Mann–Kendall) were used in order not to assume a specific distribution for the data. Field significance was taken into account when applying the tests for trends and change points. The importance of spatial correlation when calculating field significance was demonstrated. As well as finding changes in rainfall which have great significance for water resources, some important issues are raised as to the nature of changes in rainfall to be expected. Significant decreases in rainfall were found for the month of February and, to a lesser extent, March. Significant increases in rainfall were found for October in the Spanish side of Douro and Tagus catchments. The variability of the NAO index was considered a likely explanation for the changes detected. It was also demonstrated that changes in rainfall cannot be interpreted as trends or change points always because the pattern of change can be more complex than these two simplistic ways of describing change. Furthermore, the magnitude of the change can be completely different depending on the type of change assumed. Therefore the quantification of the change must be made with care, as the widely used linear trend can result in an overestimation of the change and, in principle, is not coherent with the multiple alternative hypotheses (different admissible monotonic patterns) implied by the Mann–Kendall test. Copyright © 2013 Royal Meteorological Society

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methodology
- 4. Results and Discussion
- 5. Conclusions
- Acknowledgements
- References
- Supporting Information

The spatial and seasonal distribution of rainfall and its big interannual variability in the Iberian Peninsula makes water scarcity an important issue both in Spain and Portugal. Santos *et al*. (2010) have recently concluded that the frequency of moderate to extreme droughts in the south of Portugal is approximately 3.6 years. Droughts in Iberia are responsible for losses in crop yields, especially in non-irrigated agriculture, and soil degradation in semiarid areas due to loss of vegetation cover, among other problems. More severe droughts, like the one in 2004/2005 cause major socioeconomic impacts (Santos *et al*., 2007). Water restrictions (impacting quality of life and tourism), complete destruction of crops in some areas, numerous livestock deaths and widespread forest fires have all been felt in Iberia in recent years. There is an apparent increase in the frequency and the area affected by droughts, and studying climate variability may contribute to a better management of these extreme climatic occurrences (Santos *et al*., 2010).

The location of the Iberian Peninsula at the subtropical fringe and between the Atlantic Ocean and the Mediterranean Sea makes its climate a complex system, which is amplified by the effect of different mountain ranges and a high mean altitude (González-Hidalgo *et al*., 2010a, 2010b). The rainfall regime in Iberia is highly variable in space; in the mountainous northwest the average annual rainfall is higher than 2200 mm year^{−1}, being one of the highest in Europe (Trigo and DaCamara, 2000). Contrastingly, some areas of the southeast coast of the peninsula have less than 300 mm year^{−1} of rain (Trigo *et al*., 2004). This spatial variability can be explained by different origins of rainfall:

- On the northern coast of Iberia, rainfall is mostly due to meridional fluxes that the local orography forces to ascend and consequently produce rainfall;
- In the centre and west of Iberia, rainfall is mainly produced by westerly air flows coming from the Atlantic and is clearly influenced by the North Atlantic Oscillation (NAO);
- The Mediterranean coast is protected from the Atlantic influence by mountain ranges, in this region precipitation is mainly produced by easterly air flows and by convection (Rodrigo and Trigo, 2007).

The wet season in Iberia, when almost all the rainfall occurs, is between October and May (Trigo *et al*., 2004). In the central and western regions of Iberia the maximum rainfall occurs from November to February and in the eastern parts there is an absolute maximum in autumn and a secondary maximum in spring (Paredes *et al*., 2006). In small parts of central Spain the maximum rainfall is in the summer (Río *et al*., 2010).

In the winter, the rainfall is controlled by the position and intensity of the Icelandic Low and associated westerlies. This rainfall is increased by the passage of cold fronts associated with families of transient depressions, especially when the Icelandic Low is strong and shifted south. However, in the winter, most of the Iberian Peninsula can also be affected by northward extensions of the Azores anticyclone which steers a polar continental mild and dry airflow (of tropical maritime origin) into Portugal (Trigo *et al*., 2004).

The Azores anticyclone dominates the large-scale atmospheric circulation in Iberia during the summer. In its north-westerly position, it produces northerly or north-easterly winds that bring warm and dry air into Portugal (continental or maritime modified by continental influence origins). Regionally reinforcing this circulation pattern is the normal development of a thermal low, centred over the Iberian Peninsula (Trigo and DaCamara, 2000). The few rainfall episodes that occur in summer are normally explained by convective mesoscale systems (Rodrigo and Trigo, 2007). Due to the scarce summer rainfall in the Iberian Peninsula, trends and their significance are difficult to calculate and to assess. Therefore, the majority of papers dealing with Iberian rainfall do not present analysis for the summer season (Rodrigo and Trigo, 2007).

The marked seasonal character of the rainfall regime in Iberia makes spring and autumn transition periods between winter and summer. Early autumn is influenced by convective and local storms, from October onwards the westerly circulation types prevail (Rodrigo and Trigo, 2007).

In Iberia a few daily events can significantly change monthly, seasonal and annual rainfall making the interannual variability very high (González-Hidalgo *et al*., 2010a). This strong interannual variability, with very wet and very dry years occurring frequently, represents a major problem in some areas where demands on water supply are higher than water availability (Paredes *et al*., 2006).

The interannual variability cannot be explained by regional climate factors, such as the latitude, orography or oceanic and continental influences (Trigo and DaCamara, 2000). Most of the rainfall occurring in Iberia during the wet winter season can be explained by a small number of large-scale atmospheric modes and in particular by the NAO (Trigo *et al*., 2004). The negative correlation between the NAO index and daily rainfall is only significant in winter and in the central and western areas of Iberia. The NAO index appears to determine rainfall fluctuations (number of wet days and intensity) over a large part of the Iberian Peninsula, but it only seems to influence the extreme episodes significantly in the southern areas (Rodrigo and Trigo, 2007).

Several studies show a decline in March rainfall in Iberia, when water is needed for spring crop growth. Paredes *et al*. (2006), using daily rainfall in Iberia, concluded that the trend is roughly confined to the month of March and that the region affected by significant changes was the central and western sectors of the Iberian Peninsula. When analysing rainfall trends for March in Europe from 1960 to 2000, Paredes *et al*. (2006) found that the Iberian Peninsula showed a large continuous negative trend of about 50% (40 mm) while Northern Europe showed significant positive trends, which extend from Ireland and Scotland to the Scandinavian Peninsula. The NAO index for March presented a significant positive trend which explained the storm track behaviour and the declining (increasing) frequency of wet weather types over Iberia (British Isles). Furthermore, in Iberia, the region displaying the maximum correlation values between NAO and March rainfall was roughly the same that presented the largest changes in rainfall.

González-Hidalgo *et al*. (2010a, 2010b) performed trend analysis on 2670 spanish monthly rainfall series from 1964 to 2005 and showed a high spatial and temporal variability on a monthly scale with consecutive months exhibiting different trends and the spatial distribution of signals varying significantly from month to month. Therefore caution must be exercised when interpreting seasonal or annual trend analyses for Iberia. The trends detected were only significant (0.10 significance level) for 3 months: a decrease in March for 69% of Spain (a rainfall change of up to −22% per decade), a decrease in June affecting 32% of Spain (−5% to −15% per decade) and an increase in October for 34% of the Spain, with increases between +15% and +10% per decade (González-Hidalgo *et al*., 2010a).

Río *et al*. (2010) analysed 553 monthly series of Spanish data for the period 1961–2006 and found that rainfall is significantly decreasing in February (in more than 60% of Spain), March (>10% of Spain) and June (>40%). Positive trends are mainly detected in August (>5% of Spain) and October (>20%). At the annual scale the rainfall is significantly decreasing in more than 10% of the country.

The magnitude of the trends was not presented in Río *et al*. (2010) which hinders the comparison of these two studies. It is however interesting that they analyse almost the same period of data (1961–2006 and 1964–2005) from the Spanish Meteorological Institute (AEMET) and arrived at significantly different conclusions, especially considering the month where the decrease in rainfall is more widespread (February or March) and different geographic location of June's rainfall significant decrease.

Costa and Soares (2009) analysed 107 daily rainfall series of stations located in the South of Portugal and selected 15 stations with homogeneous daily records in the period 1955 to 1999. They came to the conclusion that the aridity increased over most of the study region and that an analysis of the standard deviations showed that extreme rainfall variability and climate uncertainty are greater in recent times.

The detection of changes in rainfall time series is of great importance for establishing the validity of the dataset for frequency analysis or use in other water resource and hydrologic modelling studies. Rainfall time series often show complex variability and the effects of autocorrelation and seasonality can be easily confused with changes in the mean or variance. Such changes may be in the form of trends over some period in time or of a more abrupt nature (a change point) and a detection methodology must be carefully designed to take account of both of these mechanisms. In order to reliably interpret such variability and/or changes, knowledge of the underlying processes and potential causes of variability are invaluable.

The motivation for this study was to understand the nature of spatiotemporal variation in rainfall over Iberian basins over the historical period (1961 to 2009) with a view to characterizing the rainfall regime to allow further modelling and provide a context for study of future climate change. Our objectives were as follows:

- To investigate the nature of time variations in rainfall in Iberia, distinguishing between abrupt changes (change points) and trends if present;
- To demonstrate the use of a range of statistical tests for change points and trends, identifying instances of agreement and discrepancy;
- And to demonstrate the effects of space and time correlation in limiting the detection of change points and trends.

A full geographic context is used across three important transnational basins: Douro, Tagus and Guadiana. Both changes in the mean and in the variance will be analysed because changes in the variance are important for extreme events. The impact of the changes' shape on the quantification of the magnitude of the change is studied due to its importance to water resources management. Comparisons with a large-scale circulation index are carried out in order to give a climatological context.

Fatichi *et al*. (2009) point out that stochastic behaviour of a time series can sometimes be interpreted as an apparent deterministic trend due to long-range dependence (also refered to as long memory or long-term persistence). However, due to the short time-series available and the motivation for this analysis, long-range dependence will not be analysed in this study.

This paper is organized as follows. In Section 'Data', we present the study area, the rainfall dataset used and the summary of the atmospheric circulation using the NAO index. Section 'Methodology' describes the applied testing strategy, which accounts for changes (at a point or trend) as well as autocorrelation and spatial correlation and the correlation and synchrony of changes between rainfall and the NAO index. Significant results for autocorrelation, change points and trends (in the mean and variance), correlations with the NAO Index and a detailed analysis of the changes occurring in the months of February, March and October are discussed in Section 'Results and Discussion'. We conclude with the identification and interpretation of the important results and their implications for water resources management.

### 3. Methodology

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methodology
- 4. Results and Discussion
- 5. Conclusions
- Acknowledgements
- References
- Supporting Information

First a change point analysis was performed in order to detect abrupt changes in the rainfall series. Contrary to the slow changes that translate into trends, change points in rainfall are related with climate regime shifts or changes in the monitoring procedure or equipment. To detect change points both the Pettitt and the cusum tests were used because different tests can give different results and there is not a unique widely accepted test for change point detection.

Secondly a trend analysis was performed to detect slow changes or tendencies in the data, using the Mann–Kendall test. This is the most popular test for trend detection (Fatichi *et al*., 2009). Also, it has a similar power for trend detection to the widely used Spearman's test, being practically indistinguishable (Yue *et al*., 2002). Therefore only the Mann–Kendall test was used.

All these tests are nonparametric, which means that there are no assumptions on the distribution of the populations. However, they all assume temporal/serial independence of the data, which was checked using the autocorrelation function (ACF).

Owing to the statistical nature of these tests, the results are never free of error, and the probability of wrongly rejecting the null hypotheses (which is no changes in rainfall) is given by the significance level chosen for the test (0.05 in this study). In other words, when performing one of these tests in the time series from one gauge there is a 5% chance of detecting a change that does not exist. However, these tests were not performed just one time; there are 81 gauges, so each test was performed 81 times. Therefore the probability of detecting one false change (in any of the 81 gauges) is higher than 5% and is given by what is called ‘field significance’. Because our gauges are spatially correlated, field significance had to be calculated using bootstrap resampling.

Correlations, change point and trend tests were also used to study the relationship of the rainfall series to the NAO. All these tests and techniques are described in the following subsections.

#### 3.1. Change point analysis

Both the Pettitt and the cusum test are nonparametric/distribution-free tests used to detect change in the median or mean at an unknown point in time (WMO, 2000). The method adopted for the cusum test analysis was based in Smadi and Zghoul (2006) where the cusum test is used to identify the time of change and a bootstrap procedure is used to find the critical values under the null hypothesis (no abrupt changes).

First, a step change analysis was performed on the means, by applying the cusum and the Pettitt test to all stations and all months. It was assumed that only one change point could be present in a series, to avoid fragmentation of the time series into small segments where a trend analysis would not be meaningful. The same tests were used to check for change points in the variance, which was done applying the tests to the squared residuals calculated by fitting the time series with a locally weighted scatterplot smoothing (LOESS) function (Villarini *et al*., 2009; Villarini *et al*., 2011).

#### 3.2. Trend analysis

The Mann–Kendall test was used to assess the existence of statistical significant trends in the data. This is a nonparametric test widely used for trend detection. Initially the test was applied to all data. Later for the gauges that presented change points, the Mann–Kendall test was applied before and after the change point. This was done in order to see how the existence of a change point in the time series affected the existence of a trend.

Linear regression was used in order to calculate the magnitude of the significant trends. Fitting a linear model implies the assumption of a linear trend, while the Mann–Kendall test is devised for detecting a monotonic trend that is not necessarily linear. However, some lenience has to be exercised in order to be able to calculate the magnitude of trends. The implications of this assumption will be discussed in Section 'Results and Discussion'.

The trend analysis for the variance was done by applying the Mann–Kendall test to the squared residuals calculated by fitting the time series with a LOESS function (similar to the change point analysis for variance).

#### 3.3. Autocorrelation function

All the statistical tests chosen assume the independence of the data. Therefore the serial independence of the monthly rainfall data was checked using the lag-1 of the ACF (denoted as ACF1). For each month, the ACF1 coefficients for all the gauges were plotted along with the 95% CI (figures not shown), and the number of gauges outside the CIs was counted for each month.

#### 3.4. Field significance

When analysing a number of gauges, a simultaneous evaluation of multiple hypothesis tests is performed and therefore the problem of test multiplicity or field significance arises (Wilks, 2006). The significance level (*α*) chosen for this study is 0.05, so for any specific gauge, there is a 5% probability that the null hypothesis is falsely rejected. However, because the analysis is being performed multiple times, even if the null hypothesis is true in all gauges (*K* gauges), on average *Kα* of them will be erroneously rejected. It is therefore necessary to account for a global significance level (in order to be able to accept or reject the null hypothesis that all *K* local null hypotheses are true), or in other words, the field significance (Wilks, 2006).

Field significance is usually calculated using a binomial probability distribution. If each test is independent and *X* is the number of times we accept the null hypothesis using *K* individual *α* level hypothesis tests, then *X* follows a binomial probability distribution with parameters *K* and *α* (Douglas *et al*., 2000). A bootstrap approach must be used when there is a need to account for spatial correlations (Yue *et al*., 2003; Kenawy *et al*., 2011).

Field significance was calculated for the ACF1 values and for the test statistics of the Pettitt test, the cusum test and the Mann–Kendall test.

#### 3.5. Bootstrap

As previously mentioned the bootstrap resampling has been applied to assess the field significance for spatially correlated time series. When bootstrap was used, the data were sampled simultaneously across the gauges to preserve the spatial correlation while removing the temporal correlation and any possible trend. For each bootstrap replication, the significance of the ACF1 was tested and the Pettitt, cusum and Mann–Kendall tests were applied to each series. The number of series failing to pass the tests at 5% nominal level was recorded. Repeating the resampling procedure 10 000 times allowed defining the sampling distribution of the number of successes (rejections of the null hypothesis) in a multiple testing exercise under spatial dependence. The sampling distribution was then used to define the critical values (95th percentile for the 5% field significance level) for testing the significance of the number of successes recognized in the set of the observed time series. A more detailed explanation of the procedure can be found in Douglas *et al*. (2000).

#### 3.6. Rainfall–NAO relationship

The relationship of the rainfall series to the NAO was also investigated by (a) using monthly mean correlation between the rainfall of each gauge and the NAO index; (b) performing the change point and trend analysis for the monthly NAO index using the Pettitt, cusum and Mann–Kendall tests (as done for the rainfall data) to check for the synchrony between changes in the NAO index and changes in the rainfall data.

### 5. Conclusions

- Top of page
- Abstract
- 1. Introduction
- 2. Data
- 3. Methodology
- 4. Results and Discussion
- 5. Conclusions
- Acknowledgements
- References
- Supporting Information

In this study, we addressed the problem of quantifying the spatiotemporal variation of rainfall in Iberian basins for the period 1961–2009. The analysis allowed highlighting both methodological aspects related to the statistical inference and empirical results concerning the analysed data. From a methodological point of view, an attempt to distinguish between abrupt changes (change points) and trends was made. However this differenciation was not always posible in the short, noisy series analysed because the pattern of change can be more complex than these two simplistic ways of describing change. Performing the Mann–Kendall test before and after the change points did not help this differentiation because it was not possible to separate the effect that the change point might have on the trend from the effect of reducing the length of the record.

The danger of overestimating changes in rainfall by assuming that they take the form of linear trends was demonstrated. The analysis points out that Mann–Kendall test is devised to detect a monotonic change which in the limit case can be abrupt and is hardly ever linear. Moreover, it is well known that the progressive Mann–Kendall can be used to detect a change point (thanks to the similarity between the Mann–Kendall and Pettitt test statistics). Therefore, possible regime shifts that evolve in some steps can be recognized as monotonic S-shaped trend. When both trend tests and change-point tests recognize a possible change, its quantification must be made with care, as the widely used linear trend could provide a poor and rough assessment and, in principle, is not coherent with the multiple alternative hypotheses (different admissible monotonic patterns) implied by nonparametric tests.

The effects of space and time correlation were also studied. The problem of performing multiple tests on data that ehxibit spatial correlation is well known in the literature, but is often overlooked in empirical studies. In agreement with previous studies, our analyses show that the impact of the spatial correlation can dramatically influences the results, thus leading to very different conclusions about the presence of time correlation, trends, and change points. As an example, when calculating the critical number of gauges whose ACF1 could be significant at 5% nominal significance level in February the result was seven gauges using the binomial approach (which does not account for spatial correlation). When this calculation was done using a bootstrap approach (which accounts for spatial correlation) the result was 17. This huge difference can lead to opposite conclusions on the overall significance of the ACF1 values. Also, plotting the data on maps to assess the existence of spatial clusters across physically coherent areas that were not accounted for in the field significance analysis proved to be important. The possible shortcomings of a *post hoc* domain selection were recognized as well.

Focusing on the empirical findings, the results of two statistical tests for change points analysis were used. Althought they presented some discrepancy, significant change points in the mean were identified in February, March and June – all of them negative. February also shows negative change points in the variance.

Significant trends in the mean were identified in February (negative), June (negative) and also March for the Guadiana basin (negative) and October for the Spanish side of the Douro and Tagus basins (positive). Significant trends in the variance were identified in February (negative).

Correlations between rainfall and the NAO index did not vary much from basin to basin. However, they showed a very strong seasonal pattern, with the months of December, January, February and March showing relatively strong negative correlations (correlation coefficients around −0.6) and zero or weak positive correlations for the months of June to September.

By months, those presenting the most interesting changes are February, March and October. February is the month where more changes are present, either as a trend or as a change point (with the Pettitt test identifying the change more often as a change in the variance and the cusum test identifying it more often as a change in the mean). The changes in the mean for February range from a 39% decrease to a 149% decrease in the rainfall over the period 1961 to 2009 (depending on the gauge and on the type of change considered). Most change points in February occur in the year 1978, which corresponds to the year where the NAO index was more negative, and in the years 1985/1986 which is adjacent to the change point in the February NAO index (1987).

For March, if the trend analysis is done for the period 1961 to 2000 (which was done to compare our results with previous studies), almost all gauges show significant negative trends. However, those trends are no longer significant for the majority of gauges when the analysis is done for 1961 to 2009. When analysing the entire record, the changes in the mean for March range from a 45% decrease to a 123% decrease. The NAO index for March shows a significant increasing trend (Mann–Kendall test at 0.05 significant level) for the period 1961 to 2000 that loses its significance for the period 1961 to 2009. This might explain the behaviour of the rainfall trends for March.

October showed positive significant trends in the Spanish side of Douro and Tagus catchments that ranged from 63% to 119%. This might be explained by a monotonic decreasing trend (with a *p*-value of 0.016 for the Mann–Kendall test) in the NAO index for the month of October. As the number of change points in the rainfall data was below the limit of field significance (and the NAO did not present any change points), in this case, interpreting the change as a slowly varying trend might be reasonable.

Therefore, this work has extended previous studies on Iberian rainfall (Paredes *et al*., 2006; Rodrigo and Trigo, 2007; Costa and Soares, 2009; González-Hidalgo *et al*., 2010a, 2010b; Río *et al*., 2010) in several important respects: by updating rainfall data to 2009, by covering three major transnational basins, entailing data from Spain and Portugal which are normally considered separately, by using a portfolio of statistical tests, allowing for detecting change points as well as trends, by considering the effects of field significance and by showing the overestimation of changes in rainfall that can come from assuming the change is happening as a linear trend.