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Keywords:

  • rainfall;
  • Douro;
  • Tagus;
  • Guadiana;
  • transnational basins;
  • change points;
  • trends;
  • field significance

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methodology
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References
  10. 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

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methodology
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References
  10. 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.

2. Data

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methodology
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

2.1. Rainfall data

The study area comprises the transnational catchments of rivers Douro, Tagus and Guadiana in the Iberian Peninsula, in Southwest Europe (Figure 1). These rivers start in Spain and flow to Portugal and are vital sources of water for both countries.

image

Figure 1. Map of Western Europe with the three river basins of this study highlighted.

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Defining the study area by basins instead of countries is more coherent from a water resources point of view. The Douro River is 927-km long and its basin is 97 603 km2 (INAG, 1999a). Tagus is the longest river in Iberia with 1100 km. Its river basin has an area of 80 629 km2. In Portugal the Tagus Basin area corresponds to one third of the country (INAG, 1999b). The Guadiana River is 810-km long and its basin is 66 800km2 (INAG, 2001).

The dataset used consists of daily rainfall series from 81 gauges, 25 in Portugal and 56 in Spain, evenly distributed over the Douro, Tagus and Guadiana basins. The Spanish rainfall data were supplied by the Spanish Meteorological Institute (AEMET) and the Portuguese rainfall data were downloaded from the Portuguese Water Institute (INAG) Web site: http://snirh.pt/

The analysed period was 1961 to 2009. This period was chosen to get the maximum amount of gauges with complete records. Many Spanish gauges have gaps in the 1930s, 1940s and 1950s (possibly due to disruptions caused by the Spanish civil war) and most Portuguese gauges do not have complete records after 2009 due to budget cuts that prompted the lack of regular maintenance of the monitoring network.

The 81 gauges were chosen considering both the need for a homogenous spatial coverage and the percentage of missing data of each record. Most chosen gauges had less than 6% of missing data (Figure 2). In terms of quality control, the following procedures were performed:

  • Histograms with the distribution of daily rainfall were plotted. Annual maxima of daily rainfall were plotted for every station. All were within plausible bounds.
  • Bar plots of the mean rainfall per day of the month were plotted, to check for reporting of possible multi-day accumulations. Mean rainfall and a 99% CI (using Student-t distribution) were also plotted. No abnormal behaviour was found.
image

Figure 2. Map of Portugal and Spain with the percentage of missing data of the gauges used in this study. The three basins studied are delimitated in grey.

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Finally, the daily data were aggregated to monthly values and the series were split by months. The mean rainfall of each gauge, for each month, is shown in Figure 3.

image

Figure 3. Mean monthly rainfall from 1961 to 2009 for all gauges used in this study.

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2.2. NAO index

The NAO is a shift of atmospheric mass between the Icelandic Low and the Azores High. Therefore the sea level pressures (SLPs) of these two places are negatively correlated (r = −0.63) and the difference between them can be used as an index of the NAO (Osborn et al., 1999). Alternatively, the SLP of Lisbon or Gibraltar can be used instead of the Azores, or a principal component analysis (PCA) can be used to define the NAO. A number of different NAO series are available; however Osborn et al. (1999) showed that they are highly correlated, with inter-series correlations being typically around 0.9.

The NAO indices based on PCA are calculated using gridded SLP data. This means they can represent the full NAO spatial pattern better than the difference between two points (because the NAO centres of action move during the annual cycle) but it also means that their time-series cannot be extended long into the past. Besides having less information, another disadvantage of using the difference between two stations is that the Iceland and the Azores, Lisbon or Gibraltar stations are affected by local weather that is not related to the NAO (Osborn, 2006; Hurrell and Deser, 2009).

The length of record is not an issue in considering which NAO index to use for the period of 1961 to 2009. Therefore the NOAA's PCA NAO index (ftp://ftp.cpc.ncep.noaa.gov/wd52dg/data/indices/tele_index.nh) was used in this study.

3. Methodology

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methodology
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References
  10. 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.

4. Results and Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methodology
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

4.1. Autocorrelation

The binomial distribution approach was initially used to calculate field significance of the ACF1. In a repeated testing procedure, the test results can be interpreted as the outcomes of a sequence of Bernoulli trials, where the outcome 1 (success) is the rejection of the null hypothesis and 0 (failure) is the lack of rejection. With 81 trials, the minimum number of locally significant results to ensure 5% field significance is seven successes. Since 0 or 1 gauge exhibit significant ACF1 values for most of the months, the series could be considered temporally independent when field significance is accounted for.

However, February had 21 gauges showing significant ACF1, April had 11 and May had 9. One possible explanation was the effect of spatial correlation or cross correlation. If spatial correlation exists, then each test is not independent and the binomial approach cannot be applied to calculate field significance (Douglas et al., 2000). Cross correlations for each pair of gauges and for each month were calculated to understand its variability and the possible impact on the field significance. The spatial correlations, quantified by Pearson correlation coefficient, were very high reaching the value 0.8 for the wet winter months.

When correlation is present, the null hypotheses are rejected too often because the effective sample size of a dataset is reduced. For example, if a trend is found at one gauge it is more likely to find trends at nearby gauges (Douglas et al., 2000). Therefore, spatial correlation would easily explain 11 (9) gauges exhibiting significant ACF1 in April (May). However, more analysis was required to confirm February's data serial independence.

For the month of February, the bootstrap resampling was applied to obtain the sampling null distribution of the number of successes (failures to reject the hypothesis ACF1 = 0) under spatial dependence. The 95th (99th) percentile of the resulting bootstrap distribution was 17 (37). The February exceedance number (19) is only marginally above the 95th percentile and well below the 99th percentile. Therefore, we concluded that when accounting for spatial correlations, the hypothesis of temporal independence cannot be rejected for the February data.

The value of the exceedance number calculated using the bootstrap approach (17) was more than double the one calculated using the binomial test (7), which shows the importance of considering the spatial correlations between the gauges. The differences between the bootstrap and the binomial distributions used to calculate the critical number of exceedances are highlighted by the probability density functions (PDFs) and cumulative distribution functions (CDFs) plotted in Figure 4.

image

Figure 4. PDFs (with the x-axis limited between 0 and 30 to make it more readable) and CDFs of the bootstrap and binomial distributions used to calculate the critical value (CV) corresponding to the null hypothesis ACF1 = 0.

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4.2. Change point analysis

Regarding the analysis of the change points in the mean, February, March and June presented significant change points when accounting for field significance using the Pettitt test. However, for the cusum test only February presented significant change points when accounting for field significance (Figure S1).

In terms of the variance analysis, using the Pettitt test, February presented significant change points when accounting for field significance. Using the cusum test there were no significant change points, although February is very close to the limit of field significance (Figure S2).

As explained before, for the cusum test the p-values are calculated using the bootstrap approach. For the cusum test, for variance, another methodology was also tested, using the R package ‘change point’ (available at http://cran.r-project.org/), where an asymptotic distribution is used for the calculation of the p-values. The results obtained with this methodology were identical to the Pettitt test results. Therefore the differences in results of these two tests (Pettitt and cusum) should not be ascribed to the tests per se but in the methods used for the calculation of their p-values. Further analysis on the behaviour of the different tests/procedures applied was considered to be outside the scope of this study, therefore the results of both tests will be considered.

As the Pettitt test showed more months with significant changes than the cusum test, maps were plotted for all months to check the existence of spatial clusters that might be significant. Regarding the result of the Pettitt test applied to the mean (Figure 5), only February, March and June had enough significant change points to check for spatial patterns. In these months all the change points detected were negative. In February and March no clustering is visible, but in June most of the gauges with change points are located in the Tagus and Guadiana basin. The northeast of the Douro basin seems to have a cluster of positive change points in October, but the number of gauges (five) is too small to be considered.

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Figure 5. Change points in the mean calculated using the Pettitt test, for all months and for all gauges (the significance level is 0.05). Months for which the number of gauges showing significant change points is above the field significance are highlighted in green.

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Regarding the result of the Pettitt test applied to the variance (Figure 6), almost all the study area is affected by negative change points in February. This decrease in the variance in February is noticeable just by looking at most of the time series from the 81 gauges (Figure S5). In July and August, and to a lesser extent in September, there are numerous gauges with significant change points spread throughout the entire study area, but some correspond to an increase in variance while others correspond to a decrease.

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Figure 6. Change points in the variance calculated using the Pettitt test, for all months and for all gauges (the significance level is 0.05). The month for which the number of gauges showing significant change points is above the field significance is highlighted in green.

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4.3. Trend analysis for the mean

The results for the significant (0.05 significance level) and non-significant trends detected using the Mann–Kendall test are shown in Figure 7. It is interesting to note that all gauges present negative trends (whether significant or not) in the months of February and March, and almost all gauges in the months of January, June and November. In October all gauges presented a positive trend.

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Figure 7. Number of gauges with significant and non-significant trends for the mean (significance level of 0.05) calculated per month, using the Mann–Kendall test. Negative trends are shown on the graph on the left and positive trends are shown on the right.

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The months of February and June (and to a lesser extent, January, March, July, September and November) presented negative trends that are statistically significant at a 0.05 significance level. Statistically significant positive trends were found mainly in August and October, but also a few in May, July, September and December.

These results agree with the results of Río et al. (2010), who found significant (0.05 significance level) negative trends in Spain mainly in February and June but also in March and January. Positive trends were found in August and October and to a lesser degree in April, May, July and September.

González-Hidalgo et al. (2010a) found significant (0.1 significance level) negative trends in the Spanish side of Douro, Tagus and Guadiana catchments mainly in March and June, with small areas also occurring in January, February, April, July, August, September and December. Positive significant trends were found in October with small areas also occurring in April, June, July and August. The main difference with this study is that the large negative trend is found in March, instead of February like it is in Río et al. (2010) and in the present analysis.

The comparisons of results are hindered by the fact that these studies only considered the Spanish side of the catchments and the period of analysis is also not exactly the same: 1961 to 2006 for the first study, 1964 to 2005 in the second and 1961 to 2009 in the present analysis.

However, when field significance is considered (Figure S3) only February and June have trends above the limit of field significance. Trends detected in other months are therefore supposed to be coherent with random fluctuations rather than systematic trends. Nonetheless maps were plotted for all months to check for the existence of spatial clusters that might be significant (Figure 8).

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Figure 8. Trends for the mean calculated for all months and for all gauges (significant trends are significant at a 0.05 significance level). Months for which the number of gauges showing significant trends is above the field significance are highlighted in green.

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In February no clustering is visible, but in June most of the gauges with trends are located in the western Douro, western Tagus and in the Guadiana basin. Although the number of gauges with significant trends for all the other months is below the limit of field significance, spatial clusters seems to be present in the months of March (Guadiana basin) and October (Spanish side of Douro and Tagus basins). Therefore, it seems logical to perform a field significance test on smaller regions containing large number of stations that exhibit significant trends. However, it should be noted that the clustering is an inherent property of spatially correlated data, and sub-regions should be determined with a physically based justification before performing the local analysis, as a post hoc domain selection could give biased results (Daniel et al., 2012). In the present analysis, the sub-regions correspond to the drainage basins, which are hydrologically coherent physical units. When the field significance analysis is performed just for the Guadiana, the limit of field significance for March is nine gauges. This area presented 11 gauges with significant positive trends, therefore being above the field significance limit. When the field significance analysis is performed in the month of October in the Spanish side of Douro and Tagus basins, the limit of field significance is 10 gauges. This area presented 13 gauges with significant positive trends, therefore being above the field significance limit. These results show the importance of plotting the data on a map to check for spatial clusters on physically coherent units before discarding results based on field significance analysis, even though the possible shortcomings of a post hoc selection must be kept in mind always.

For the gauges that presented change points, the Mann–Kendall test was applied to the record before and after the change point, following the method applied by Villarini et al. (2011). This was done in order to see how the existence of a change point in the time series affected the existence of a trend. When testing for trends before and after the change points in the mean identified by the Pettitt test, no significant trends were found. Therefore, one might assume that for the gauges with change points, changes in rainfall in Douro, Tagus and Guadiana, from 1961 to 2009 occurred in the form of step changes instead of slow changes that could be perceived as trends. However, if we analyse the gauges that have significant trends but no significant change points (for example for February) and apply the Mann–Kendall test before and after 1985 (because in February the change points in the mean using the Pettitt test are all between 1978 and 1991) the result is also zero significant trends. So, although no change point has been detected for these gauges, just by reducing the length of the records, the trends are no longer significant. As this is a shortcoming of this method, further development is warranted and discussed later.

Considering that the results of the Pettitt and cusum tests can be affected by the presence of a trend and that the Mann–Kendall results can be affected by the presence of a change point, it is not possible to draw any definite conclusion about the type of change occurring just by performing these tests. Moreover, it should be noted that the abrupt change is a limit type of a generic monotonic trend, and Mann–Kendall and Pettitt test statistics are strictly related, so that the results can be ambiguous especially for short and noisy series (Rougé et al., 2013). We cannot also exclude regime shifts evolving in few years, which can be recognized as abrupt changes only on long time series. This difficulty of defining the type of change that is occurring is not only due to the power of the statistical tests that were applied but also to the possible presence of temporal patterns that can be more complex than those described by a single change point or a monotonic trend.

In Figure 9 the changes in the rainfall record of a gauge in the Spanish Guadiana (AEMET gauge X4016) for February are showed as an example. It can be seen that both the change point interpretation and the linear trend interpretation seem to be reasonable but a more flexible LOESS curve points out that the behaviour might not be that simple, as the underlying pattern can be non-monotonic. The result in terms of magnitude of the change can be completely different depending of the type of change assumed. Using the example shown in Figure 9 if the change is perceived as a change point, its magnitude (computed as the difference in means before and after the change point) is −26.3 mm. If the change is perceived as a linear trend, its magnitude (computed as the difference between the last and first prediction value when a linear regression is fitted) is −47.3 mm. This analysis also reinforces the notion that extrapolation of the results of linear regression analysis for the future is without justification as the change might be occurring as a result of a regime shift that can evolve in some years, producing mixed non-monotonic patterns further complicated by the intrinsic fluctuations of the rainfall process.

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Figure 9. Rainfall series for February, gauge X4016 (top left). In the top right corner the change is interpreted as a change point in the mean (with a significant p-value of 0.003 calculated using the Pettitt test). In the bottom left corner the change is interpreted as a trend (with a significant p-value of 0.001 calculated using the Mann–Kendall test) and a linear trend has been plotted. In the bottom right corner the change is shown using a local polynomial regression fitting (loess). This gauge did not present a significant change point in the variance.

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4.4. Trend analysis for the variance

The results for the significant (0.05 significance level) and non-significant trends in the variance detected using the Mann–Kendall test are shown in Figure 10. It is interesting to note that, in February, all gauges present negative trends (whether significant or not), and almost all gauges in the months of January, March, June, July and September. In December almost all gauges show a positive trend.

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Figure 10. Number of gauges with significant and non-significant trends for variance (significance level of 0.05) calculated per month, using the Mann–Kendall test. Negative trends are shown on the graph on the left and positive trends are shown on the right.

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However, when field significance is considered only February has trends above the limit of field significance. The summer months (and specially July and August) present a high number of gauges showing a significant trend; however, they also have a high limit of field significance (Figure S4). These months are very dry throughout the basins with a baseline of low (sometimes zero) rainfall punctuated by a few high rainfall years. When LOESS is fitted to these datasets sequences of identical values are transformed into increasing/decreasing patterns and therefore (artificial) trends are detected.

Maps were plotted for all months to check for the existence of spatial clusters that might be significant (Figure 11). No spatial clusters were found for months below the limit of field significant, with the possible exception of negative trends in the Spanish side of the Guadiana in July. However, for the reasons explained in the previous paragraph, this apparent cluster was not taken into account.

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Figure 11. Trends for the variance calculated for all months and for all gauges (significant trends are significant at a 0.05 significance level). The month for which the number of gauges showing significant trends is above the field significance is highlighted in green.

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4.5. Analysis of individual months

From a water resource point of view the months of October to May are the most important for Iberia. They are the months with higher rainfall (Figure 3), and although evapotranspiration is high in the spring and autumn, which translates into lower discharges, the rain in these seasons is very important for agriculture. Also, problems of water scarcity occur regularly in years with dry springs and autumns, and dams which have flood defence purposes are not allowed to fill their reservoirs before May.

As can be seen in Table 1, when accounting for field significance, February is the only month that shows a change with all the tests used, except for the cusum applied to the variance (where it is very close to the field significance limit).

Table 1. Months with change points detected by Pettitt and cusum test applied to the mean and the variance, when accounting for field significance
Test usedMonths with significant changes
  1. a

    The number of gauges in February was very close to the limit of field significance.

  2. b

    For the Guadiana basin.

  3. c

    For the Spanish side of Douro and Tagus.

Pettitt: MeanFebruary, March, June
Cusum: MeanFebruary
Pettitt: VarianceFebruary
Cusum: Variancea
Mann–Kendall: MeanFebruary, Marchb, June, Octoberc
Mann–Kendall: VarianceFebruary

Several authors have identified March as a month with decreasing trends in the mean in Iberia. In this study, the number of gauges with significant trends in March is below, but close, to the limit of field significance and when the trends are calculated for the Guadiana basin they become significant. March also showed significant change points in the mean when using the Pettitt test.

October will also be considered for further analysis because it shows positive trends in the mean in the Douro and Tagus basins that might be important.

June shows significant changes in the mean (Pettitt) and shows significant trends for mean; however, these are negative trends/change points in a month that is already relatively dry especially in the Tagus/Guadiana region where these changes are taking place.

Therefore a closer analysis will be performed for the months of February, March and October in order to find a possible physical explanation for the change points and trends. As pointed out in Section 'Introduction', several authors have identified the NAO as the main large-scale atmospheric mode that explains the rainfall in the winter months in Iberia. Therefore the correlations between the rainfall data and the NAO index were calculated. Figure 12 shows the monthly variation of the temporal correlation between the monthly series of the NAO index and the rainfall amount for the three basins. The months December, January, February and March have the higher negative correlations, with February being the highest (between −0.6 and −0.7). This is consistent with the links identified between NAO index and Iberian rainfall in the winter by Trigo et al. (2004).

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Figure 12. Correlation coefficients between the rainfall series and the NAO index, per month, averaged per basin.

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4.5.1. The case of February

The overwhelming majority of gauges showed a change in the month of February, in the mean or the variance, either as a change point or as a trend (plots of rainfall series for February are presented in Figure S5). Regarding change points, the Pettitt test identifies the change more often as a change in the variance than in the mean, while the cusum test does the opposite.

The changes in the mean, as trends or change points, are very relevant as they range from 39% decrease to 149% decrease (relative to the mean) in the rainfall over the period 1961 to 2009 (Figure 13). This decrease in rainfall ranges from 13.9 to 240.0 mm in absolute values. The Guadiana basin and the Portuguese side of the Douro and Tagus basins are the most affected by decreasing trends, while change points cover almost all gauges. Considering that the data come from two different countries (and in Spain from different autonomous regions), an undocumented change in monitoring procedures/equipment would not explain the change points that occurs both in the Portuguese and the Spanish datasets in the same month.

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Figure 13. Magnitude of the changes (in percentage relative to the mean) for each gauge, for the period 1961 to 2009, when interpreting the change as a linear trend detected by the Mann–Kendall test (left), a change point in the mean detected with Pettitt test (middle) or a change point in the mean detected with cusum test (right). The significance level is 0.05 for all tests.

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A graph was plotted showing the years when the significant (0.05 significance level) change points occurred, both in the mean and in the variance for both statistical tests (Figure 14). When accounting for the result of both tests, there seem to be two years that concentrate the majority of the significant change points in the mean: 1978 (mainly the cusum test) and 1986 (both tests). In the variance these years seem to be 1978 (cusum test) and 1985 (Pettitt test).

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Figure 14. Years when the significant change points occurred in the mean (left) and in the variance (right) in February. The significance level is 0.05 for the Pettitt test (red) and for the cusum test (blue).

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According to NOAA's Climate Prediction Center (2011), in the winter of 1978/1979 the NAO changed from a predominantly negative phase (that lasted since the mid 1950s) to a positive phase that lasted until the winter of 1994/1995 which was only interrupted by two predominately negative winters: 1984/1985 and 1985/1986. This could represent a physical explanation for the change points in rainfall data detected by the Pettitt and cusum tests.

When analysing the NAO index for the month of February, the Mann–Kendall test shows a significant increasing trend (with a p value of 0.02), which might be the cause of the decreasing trends present in the rainfall records. Both Pettitt and cusum tests show a significant change point in the NAO for the year 1987 (Figure 15) with a p value of 0.01 for both tests. By performing a one-tailed Pettitt test one can conclude that the change point corresponds to an increasing change. The 1978 change points in the rainfall records correspond to an extremely negative NAO (Figure 15), while the 1985/1986 change points in rainfall are adjacent to the change point in the NAO index (1987).

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Figure 15. NAO index for the month of February (from 1961 to 2009) with its change point highlighted with a solid line (p value of 0.01 for both Pettitt and cusum tests). Dotted lines denote the years where most gauges show a significant change point in the rainfall record for the month of February.

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A positive NAO index induces a northern movement of the eddy driven jet (Woollings, 2010), therefore steering the Atlantic storm track towards the North of Europe. Consequently a positive trend in the NAO index could perhaps explain the negative trend in the rainfall variance since the stronger systems associated with the storm track are no longer present in Iberia, leaving only the weaker systems (instead of a combination of strong and weak systems) to influence the amount of rainfall.

4.5.2. The case of March

For the month of March, if the trend analysis is done just for the period 1961 to 2000, almost all gauges show significant negative trends (Figure 16). This concurs with various papers that described a decreasing trend in Iberia in March. However that trend, although still present, is no longer significant for the majority of gauges when the analysis is performed from 1961 to 2009.

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Figure 16. Maps of significant and non-significant (0.05 significance level) trends (in the mean) for the month of March in the study area. On the left the trends were calculated for the period 1961 to 2000 and on the right the trends were calculated for the entire record (1961 to 2009).

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When analysing the entire record, the changes in the mean for March, although not as widespread as the changes in February, are relevant as they range from 45% decrease to 123% decrease in the rainfall over the period 1961 to 2009 (Figure 17). This decrease in rainfall ranges from 17.7mm to 90.1mm in absolute values. The Guadiana basin and the southern gauges of Douro are the most affected by change points. In terms of trends the same area plus the Portuguese side of Tagus is affected. Although the results of the cusum test were not above the limit of field significance, they are in agreement with those from the Pettitt test which do exceed the limit of field significance (Figure 17).

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Figure 17. Magnitude of the changes (in percentage relative to the mean) for each gauge, for the period 1961 to 2009, when interpreting the change as a linear trend detected by the Mann–Kendall test (left), a change point in the mean detected with Pettitt test (middle) or a change point in the mean detected with cusum test (right). The significance level is 0.05 for all tests.

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Looking at the behaviour of the NAO index for the month of March (Figure 18) there is an apparent monotonic trend from the beginning of the study period until the nineties that is no longer visible after the year 2000. If a Mann–Kendall test is performed at a 0.05 significance level, there is a significant trend for the NAO in the period 1961–2000 (with a p value of 0.002) but not for the period 1961–2009 (p value of 0.055). This might explain the trend in the rainfall record for the 1961–2000 period. No change points were found in the NAO index for March, either using the cusum or the Pettitt tests, at 0.05 significance level.

image

Figure 18. NAO index for the month of March with the year 2000 highlighted with a vertical line.

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4.5.3. The case of October

When performing the trend analysis for the mean, a spatial cluster of significant positive trends in the month of October in the Spanish side of Douro and Tagus catchments was identified. The magnitude of the linear trends identified ranges from 63% to 119% (Figure 19). This increase in rainfall ranges from 22.2 to 111.5 mm in absolute values. The number of gauges with significant change points was much smaller than the number of gauges with significant trends. Therefore for the case of rainfall in October, interpreting the change as a trend might be reasonable.

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Figure 19. Magnitude of the changes (in percentage relative to the mean) for each gauge, for the period 1961 to 2009, when interpreting the change as a linear trend detected by the Mann–Kendall test (left), a change point in the mean detected with Pettitt test (middle) or a change point in the mean detected with cusum test (right). The significance level is 0.05 for all tests.

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The NAO index for the month of October (Figure 20) shows a monotonic decreasing trend (with a p value of 0.016 for the Mann–Kendall test), which could explain the increasing trend in the rainfall in the Spanish side of Douro and Tagus catchments. As expected, no change points were found for the NAO, either using the cusum or the Pettitt tests at 0.05 significance level.

image

Figure 20. NAO index for the month of October.

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5. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methodology
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References
  10. 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.

Acknowledgements

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methodology
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

The Spanish rainfall data were kindly supplied by the Spanish Meteorological Institute (AEMET). This work is being financed by the Portuguese Foundation for Science and Technology (FCT). We gratefully acknowledge the constructive and insightful comments of the anonymous referees which have substantially improved the paper.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methodology
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Methodology
  6. 4. Results and Discussion
  7. 5. Conclusions
  8. Acknowledgements
  9. References
  10. Supporting Information
FilenameFormatSizeDescription
joc3669-sup-0001-FigureS1.pdfPDF document18KNumber of gauges with significant change points (with a significance level of 0.05) in the mean calculated using the Pettitt test (left) and the cusum test (right). Limits of field significance were calculated by resampling 10 000 times.
joc3669-sup-0002-FigureS2.pdfPDF document18KNumber of gauges with significant change points (with a significance level of 0.05) in the variance calculated using the Pettitt test (left) and the cusum test (right). Limits of field significance were calculated by resampling 10 000 times.
joc3669-sup-0003-FigureS3.pdfPDF document15KSignificant trends for the mean (positive and negative), with a significance level of 0.05, calculated using the Mann–Kendall test. Limits of field significance were calculated by resampling 10 000 times.
joc3669-sup-0004-FigureS4.pdfPDF document15KSignificant trends for the variance (positive and negative), with a significance level of 0.05, calculated using the Mann–Kendall test. Limits of field significance were calculated by resampling 10 000 times.
joc3669-sup-0005-FigureS5.pdfPDF document16KFebruary rainfall time-series for randomly selected gauges (1961–2009).

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