SPI Modes of Drought Spatial and Temporal Variabilityin Portugal: Comparing Observations, PT02 and GPCCGridded Datasets

Tayeb Raziei & Diogo S. Martins & Isabella Bordi &João F. Santos & Maria Manuela Portela &

Luis S. Pereira & Alfonso Sutera

Received: 23 December 2013 /Accepted: 22 May 2014# Springer Science+Business Media Dordrecht 2014

Abstract Regional drought modes in Portugal are identified applying the PrincipalComponent Analysis (PCA) and Varimax rotation to the Standardized Precipitation Index(SPI) computed on various time scales using the three precipitation datasets covering theperiod 1950–2003: (i) The observation dataset composed of 193 rain-gauges distributed almostuniformly over the country, (ii) the PT02 high-resolution gridded dataset provided by thePortuguese Meteorological Institute, and (iii) the GPCC dataset with 0.5° spatial resolution.Results suggest that the three datasets well agree in identifying the principal drought modes,i.e. two sub-regions in northern and southern Portugal with independent climate variability.The two sub-regions appear stable when the SPI time scale is varied from 3- to 24-month, andthe associated rotated principal component scores (RPCs) do not show any statisticallysignificant linear trend. The degree of similarity between the rotated loadings or REOFs ofdifferent SPI time scales for the three used datasets was examined through the congruencecoefficients, whose results show a good agreement between the three datasets in capturing themain Portuguese sub-regions. A third spatial mode in central-eastern Portugal was identifiedfor SPI-24 in PT02, with the associated RPC characterized by a statistically significantdownward trend. The stability of the identified sub-regions as a function of studied timeperiod was also evaluated applying the same methodologies to a set of three different time

Water Resour ManageDOI 10.1007/s11269-014-0690-3

T. Raziei : D. S. Martins : L. S. Pereira (*)CEER-Biosystems Engineering, Institute of Agronomy, University of Lisbon, Tapada da Ajuda,81349-017 Lisboa, Portugale-mail: lspereira@isa.ulisboa.pt

I. Bordi : A. SuteraDepartment of Physics, Sapienza University of Rome, Rome, Italy

T. RazieiSoil Conservation and Watershed Management Research Institute (SCWMRI), Tehran, Iran

J. F. SantosDepartment of Engineering, Polytechnic Institute of Beja, Lisbon, Portugal

M. M. PortelaDepartment of Civil Engineering, SHRH, Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

windows and it was found that the southern sub-region is very stable but the northern andcentral-eastern sub-regions are very sensitive to the selected time window.

Key words Regional drought patterns . SPI . Gridded dataset . Principal component analysis .

Trend analysis

1 Introduction

Drought originates from a deficiency of precipitation (less than normal) over an extendedperiod of time. It may occur in all climatic zones and is triggered by large-scale features of theatmospheric circulation, such as high-pressure systems, winds carrying continental rather thanoceanic air masses, or high temperatures. However, drought characteristics vary significantlyfrom one region to another due to local effects and its impact on local water resourcesavailability compared to needs (Pereira et al. 2009). Thus, the identification of homogeneousregions within a country with distinct drought behaviors is of particular interest for droughtrisk assessment and for a more efficient water resources management at regional level.

Being drought a creeping phenomenon, it slowly sneaks up and impacts many sectors of theeconomy, the environment, and operates on many different time scales (Rossi 2000; Wilhiteet al. 2007). Droughts can be grouped into various categories as meteorological, agricultural,hydrological, water supply and groundwater drought which refer to both the time when aprecipitation deficit is observed and the lag time for perception of effects of the precipitationdeficit by different sectors (Pereira et al. 2009). For example, soil moisture responds toprecipitation deficits occurring on a relatively short time scale, whereas streamflow, reservoirstorage and groundwater respond to precipitation deficits arising over many months. Amongseveral available indices the Standardized Precipitation Index (SPI, McKee et al. 1993) issuited to monitor those kinds of drought (Heim 2002; Keyantash and Dracup 2002) since it is astandardized and multi-scale index and allows objectively comparing dry/wet conditions ofregions with different hydrological regimes.

Using the SPI and/or other indices, many authors have analyzed spatial modes and timevariability of drought in different areas (see for example Bordi and Sutera 2002; Bonaccorsoet al. 2003, 2013; Bordi et al. 2004; Vicente-Serrano 2006; Santos et al. 2010; Raziei et al.2013). However, spatial modes of drought over a region might change as a function of the timescale considered, i.e. the type of drought analyzed. Vicente-Serrano (2006) showed that usingrain-gauge data over the Iberian Peninsula the spatial modes of droughts are conditioned to theSPI time scale, pointing out the increasing spatial complexity of drought modes as the timescale of the index is increased. Raziei et al. (2011) identified four sub-regions for Iran applyingthe Principal Component Analysis (PCA) and Varimax rotation to the SPI on 12-month timescale computed using observations, gridded (Global Precipitation Climatology Centre, GPCC)and reanalysis (National Center for Environmental Prediction/National Center for AtmosphericResearch, NCEP/NCAR) datasets. The stability of drought spatial modes as a function of SPItime scale and spatial resolution was also investigated for Iran applying PCA to SPI indexcomputed for different time scales using the GPCC precipitation dataset with 2.5-, 1- and 0.5°resolution (Raziei et al. 2013). Results showed that the identified drought modes are quitestable when a coarse spatial resolution is used, whereas at finer resolutions drought modesappear more sensitive to the index time scale, becoming less spatially homogeneous as thetime scale is increased.

Time variability of drought has been investigated for Portugal at regional level by Pauloet al. (2005) and Moreira et al. (2006) based on the stochastic properties of the SPI drought

T. Raziei et al.

index time series using Markov chains and log-linear models. Moreira et al. (2012) assessedthe possible cyclic behavior of droughts aiming at inferring if they are aggravating due toimpacts of climate change. Drought trends in mainland Portugal were investigated by Pauloet al. (2012) using the Mann-Kendall trend test (Mann 1945; Kendall 1975) and the Sen’sslope estimator (Sen 1968). The spatial and temporal patterns of drought in mainland Portugalhave been also investigated by Santos et al. (2010) and Martins et al. (2012) through theapplication of spatial classification methods to the SPI field on given time scales, identifying 3and 2 sub-regions, respectively. However, the stability of the identified sub-regions withrespect to different SPI time scales and precipitation dataset was not taken into account.Therefore, the present paper aims to complement those studies by investigating that issue.For this purpose in the present paper we consider various SPI time scales (3-, 6-, 12- and 24-month) commonly used for monitoring the different kinds of drought and three precipitationdatasets: observations, the newly developed high-resolution gridded precipitation dataset formainland Portugal referred as PT02 (Belo-Pereira et al. 2011), and GPCC dataset at 0.5°resolution. In addition, due to the influence of the length of time series on drought trends, theimpact of these time lengths using observation data are also investigated.

2 Data and Methods

2.1 Precipitation Data Sets

To study the spatial and temporal variability of drought over Portugal, observations, PT02 andGPCC gridded precipitation datasets for the common period 1950–2003 are used. The selectedperiod was set to coincide with the time period of the Portuguese PT02 high-resolution dailyprecipitation dataset developed by Belo-Pereira et al. (2011).

The observation dataset consists of 193 stations uniformly distributed over mainlandPortugal (Fig. 1a). Most of the stations are provided by the Portuguese Water Institute thatis responsible for the hydrologic data collection and validation, whereas 27 of the used stationsbelong to the Meteorological Service of Portugal.

The PT02 dataset has 250 grid points distributed over mainland Portugal (Fig. 1b) with 0.2°resolution and covers the period 1950–2003. To develop PT02 dataset a dense network of raingauges distributed over Portugal (more than 400 stations) was used. The ordinary krigingmethod with the exponential variogram was used to interpolate the dataset into the 0.2°×0.2°mesh grid. The performance of the gridded output was compared with observations at selectedstations through the country using cross-validation method coupled with some statistic tools(Belo-Pereira et al. 2011). The PT02 was also compared with the outputs of some availablegridded and reanalysis datasets and it was found that the PT02 well spatially represent thegeographical variation of precipitation field over main land Portugal (Belo-Pereira et al. 2011).For the present study, monthly accumulations of PT02 daily precipitation data were used forthe SPI computation at each grid point.

The GPCC Full Data Product Version 5, updated in December 2010, is a gauge-basedgridded monthly precipitation dataset for the global land surface, available in 2.5º, 1º and 0.5°spatial resolutions. The dataset covers the period 1901–2009 and is based on both non real-time and real-time stations (Schneider et al. 2010). GPCC monthly precipitation analysisproducts are based on anomalies from climatological normals at the stations, or from GPCChigh-resolution gridded climatology where no station normal is available. The GPCC precip-itation climatology (reference period 1951–2000) consists of normals collected by WMO,delivered by the countries to GPCC, or calculated from time series of monthly data (with at

SPI Modes of Drought Spatial and Temporal Variability in Portugal

least 10 complete years of data) available in the GPCC data base (for details see the GPCCannual reports at http://gpcc.dwd.de). Raziei et al. (2011) assessed the spatial and temporalvariability of drought over Iran using the GPCC dataset and found satisfactory agreement withobservations. For the present study the 0.5° spatial resolution (i.e., the finest resolutionprovided by GPCC) is used. This dataset has 49 grid points over mainland Portugal (Fig. 1c).

2.2 Methods

Drought conditions are assessed through the SPI computed on 3-, 6-, 12- and 24-month timescales following the original definition by McKee et al. (1993), thus representing various kindsof drought. The SPI computation for a given location and month of the year is based on thelong-term precipitation records accumulated over the selected time scale. A probabilitydistribution is fitted to the cumulated precipitation records. Originally McKee et al. (1993)used the two-parameter Gamma distribution for fitting the observed precipitation distribution,which has become the most usual for computing SPI, although, for some regions otherdistributions may be more suitable (Guttman 1999). In the present study the original definitionof the SPI is applied. The cumulative theoretical distribution is then transformed through anequal-probability transformation into a normal distribution. Thus, the SPI represents a Z-score,or the number of standard deviations above or below that a precipitation event is from themean. Positive SPI values indicate greater than median precipitation, and negative valuesindicate less than median precipitation.

For each time scale considered, the S-mode PCA (Rencher 1998) and Varimax rotation areapplied to the SPI field to search for aggregation of climate sub-regions that experiencedsimilar drought (wetness) conditions during the study period. The PCA consists in computingthe covariance matrix of the SPI data with the corresponding eigenvalues and eigenvectors(Rencher 1998). The projection of the SPI fields onto the orthonormal eigenfunctions providesthe principal components or PC score time series, whereas the spatial patterns of eigenvectors

Fig. 1 Spatial distribution of stations/grid points over Portugal for: a observations, b PT02, and c GPCC datasets

T. Raziei et al.

(loadings) represent the correlation between the original data (SPI time series at single station/grid points) and the corresponding principal component time series. More localized patternsare obtained by applying the Varimax rotation to selected loadings (rotated loadings or REOFsin the text). Since such orthogonal rotation preserves the orthogonality in time, i.e. the rotatedprincipal components are not correlated (Rencher 1998; Mestas-Nuñez 2000), the methodallows finding sub-regions within the country that have rather independent drought behaviors.Following the rule by North et al. (1982), the sampling errors at 95 % confidence level of theeigenvalues associated with the principal components have been estimated, allowing toestablish how many loadings to retain for rotation.

To assess the degree of similarity between rotated loadings of the SPI on different timescales for a given dataset and/or inter-comparisons of the loadings configurations relative tothe three used datasets, the vectors of the loadings matrices are compared using the congruencecoefficient (Harman 1976):

gAB ¼

X

j¼1

n

bjA � bjB� �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX

j¼1

n

b2jA

!�

X

j¼1

n

b2jB

!vuutð1Þ

where bjA is a loading from the rotated loading vector A from one solution, bjB is a loadingfrom the rotated loading vector B from another solution, and n is the number of variables ineach eigenvector, which for the S-mode PCA corresponds to the number of the grid points.The coefficient ranges in value from +1 for perfect agreement (or −1 for perfect inverseagreement) to 0 for no agreement. The congruence coefficient is preferred to the correlationcoefficient for measuring pattern similarity because it preserves the mean (whereas thecorrelation coefficient measures deviations from the mean), which is an important feature ofa PC loading vector (Richman 1986). Following Richman (1986) and the references therein,the guidelines listed below are adopted as an indicator of the degree of likeness betweenpatterns: excellent≥0.98, 0.98>good≥0.92, 0.92>borderline≥0.82, 0.82>poor≥0.68, verypoor<0.68. To do so, all loadings vectors relative to the different SPI time scales obtainedfor observations and GPCC datasets were re-gridded to the same mesh grid as for PT02 (i.e.,0.2° spatial resolution) to achieve similar spatial dimensions which is prerequisite for thecomputation of the congruence coefficient. For the re-gridding of the loading vectors ordinarykriging was used with the isotropic model that best fitted the underlying experimentalvariogram of a given loading vector and resulted in the lowest estimation bias when comparedto the original loadings using the cross-validation approach.

Finally, the time variability of the selected RPC scores were examined for possible trends todrought aggravation or attenuation in the identified sub-regions using linear regression and theMann-Kendall trend test (Mann 1945; Kendall 1975) and the magnitude of the trends wereestimated using the Sen slope estimator (Sen 1968).

3 Results

3.1 PCA

For each SPI time scale, the number of principal components retained for Varimax rotation wasselected based on the scree plot and the North’s rule of thumb criterion (Fig. 2). Based on

SPI Modes of Drought Spatial and Temporal Variability in Portugal

Fig. 2, the first leading components relative to the eigenvalues whose 95 % confidenceintervals do not overlap are retained for Varimax rotation. The first four components areretained for SPI-3, SPI-12 and SPI-24 when using observations dataset. The same number ofcomponents are retained for SPI-12 and SPI-24 associated with PT02 dataset. For the SPI-6relative to the observations dataset the first three components are selected for rotation, whereasonly the first two components are retained for SPI-3 and SPI-6 of PT02 dataset. Differently,results for the GPCC dataset suggested retaining only the first two leading components for allSPI time scales.

Table 1 presents the explained variances of un-rotated and Varimax rotated componentsrelative to the considered SPI time scales and datasets. The table shows that the first un-rotatedcomponent relative to observation dataset explains from 66 % to 69.9 % of the total variancedepending on the time scale, with the minimum and maximum variances observed for SPI-24and SPI-12, respectively. The second un-rotated component explains about 10 % of the totalvariance, while the third component explains very small variances from SPI-3 to SPI-6 (1.7 %–1.8 %) and it accounts for 2.4 % and 3.9 % for SPI-12 and SPI-24, respectively. Similarly, thefourth component accounts for a very small percentage of variance. For the case of PT02(Table 1) the first un-rotated component explains 77.8 %–78.3 % of the total variance for SPI-3to SPI-12, but it decreases to 74.5 % for SPI-24 due to an increase in the explained variances ofthe second and third components. Similar results are observed relative to the variances of thefirst GPCC un-rotated components, ranging between 80.9 % and 83.9 % (Table 1). It can benoted that the variance explained by the first un-rotated component is higher in GPCC than inPT02, and lower than both in the observation dataset; this can be attributed to the effect of thecoarse spatial resolution of GPCC compared to those for PT02 and observations. This featureis in agreement with the results found by Raziei et al. (2013) who compared the spatial modesof drought variability in Iran using GPCC datasets having different spatial resolutions.

3.2 Drought Spatial Variability

The rotated loadings (REOFs) for the different SPI time scales and datasets are shown inFig. 3. For the SPI on 3-month time scale, the three datasets identify two sub-regions ofdrought variability in southern and northern Portugal that are characterized by high positiverotated loading values greater than 0.6 (Fig. 3a). A similar drought spatial pattern is obtainedfor SPI-6 and SPI-12 (Fig. 3b and Fig. 3c). When the longer time scale is considered (24-month), a hint of a third sub-region in central-eastern Portugal appears for the PT02 datasetwith rotated loading values between 0.6 and 0.8 (Fig. 3d). This feature is also visible at 12-month time scale for PT02 dataset (Fig. 3c, yellow area in the third rotated loading). Theidentified northern sub-region is a mountainous area and is heavily influenced by the Atlanticair masses that favour in this area the highest precipitation amount of the continentalPortugal, whereas the southern sub-region has a much smoother and flatter relief andis characterized by a sub-humid climate. The relatively high elevation of the thirdsub-region and its distance from the Atlantic Ocean mitigate the direct influence ofthe maritime air masses, resulting in a different precipitation regime in that area.However, despite that the identified spatial mode of the third sub-region explains arelatively small percentage of the total variance (14 %) and the loadings are not highenough, it could be considered of particular relevance for the spatialization ofhydrological droughts. The same spatial patterns of the loadings were identified inprevious studies by Santos et al. (2010) and Martins et al. (2012) but, becausedifferent critical values of the loadings were used (0.7 and 0.8, respectively), theseauthors achieved smaller sub-regions than in the present study.

T. Raziei et al.

Thus, results suggest that the northern and southern sub-regions are the leading droughtmodes for Portugal, that are well captured by the three datasets with high loading values at allselected time scales. Differently, the central-eastern sub-region is less stable with respect totime scales and the dataset considered. The absence of the third sub-region in the rotatedloadings of GPCC dataset could be related to the fact that limited Portuguese stations wereincluded in the GPCC gridding procedure, whereas a much denser network of stations wereused in developing the PT02 dataset. Also, the number of stations considered for griddingPT02 dataset is larger than the number of stations of the observation dataset in the centraleastern region. Moreover, the GPCC rotated loadings show to be spatially more homogeneouswhen compared with those of observations and PT02 datasets (Fig. 3). This is in agreement

Fig. 2 First twenty eigenvalues with the corresponding errorbars at 95 % confidence level resulting from thePCA applied to the SPI computed on different time scales (rows) using observations (193 stations) and PT02 andGPCC datasets (columns)

SPI Modes of Drought Spatial and Temporal Variability in Portugal

with the results found for Iran by Raziei et al. (2013), indicating that drought modes obtainedusing a dataset with the finer spatial resolution have more spatial inhomogeneity.

The degree of similarity between rotated PC solutions for different datasets and SPI time scaleswere quantitatively assessed by comparing their respective loadingmatrices through the congruencecoefficients (Harman 1976; White et al. 1991). Table 2 shows the congruence coefficients relatingthe rotated loadings of different SPI time scales associated with different datasets. It should be notedthat only the REOF-1 and REOF-2 of each SPI time scale were considered for assessing the degreeof agreement between the datasets in capturing themain country sub-regions (northern and southernsub-regions). The congruence coefficient was not computed for REOF-3 of PT02 since it has nocounterpart in other datasets and/or time scales. Results in Table 2 suggest that the congruencecoefficients between the REOFs associated with the same sub-regions shown in Fig. 3 are greaterthan the critical value of 0.98, which indicates an excellent spatial congruence for all the SPI timescales. These results also indicate a perfect agreement between the three datasets in capturing themain Portuguese sub-regions at all considered SPI time scales.

The congruence coefficients between the REOFs of different SPI time scales relative to agiven dataset were also computed and analyzed. Almost all congruence coefficients wereabove 0.99 for all sub-regions and the considered datasets, thus indicating a very strongagreement between loading patterns of different SPI time scales identified for each dataset.Though the congruence coefficients slightly decrease when comparing the REOFs of shorterSPI time scales with those of longer time scales, they were still high (>0.99), which indicatesan excellent agreement between the REOFs of different SPI time scales for the same sub-region. This fact also reflects a strong spatial consistency between the loading patterns ofdifferent SPI time scales captured by a given dataset. Thus, results suggest that the spatialpatterns of rotated loadings identified by each dataset are stable throughout all the considered

Table 1 Percentage of the total variance explained by the un-rotated (UR) and Varimax rotated (VR) loadings ofthe SPI on different time scales computed using observations and gridded PT02 and GPCC datasets. Units are %

SPI-3 SPI-6 SPI-12 SPI-24

Dataset PC UR VR UR VR UR VR UR VR

Observations 1 68.9 36.9 67.4 38.1 69.9 39.1 66.0 37.7

2 10.3 36.5 11.4 35.9 10.1 38.8 11.2 36.3

3 1.7 4.4 1.8 6.6 2.4 4.1 3.9 6.4

4 1.3 4.2 1.7 2.0 2.7 3.3

Total 82.1 82.1 80.6 80.6 84.1 84.1 83.7 83.7

SPI-3 SPI-6 SPI-12 SPI-24

Dataset PC UR VR UR VR UR VR UR VR

PT02 1 77.8 44.3 76.5 45.0 78.3 41.5 74.5 38.4

2 9.1 42.5 10.0 41.15 8.9 41.1 9.6 34.6

3 2.1 5.1 3.7 14

4 1.5 3.1 2.1 3

Total 86.8 86.8 86.5 86.5 90.7 90.7 90.0 90.0

SPI–3 SPI–6 SPI–12 SPI–24

Dataset PC UR VR UR VR UR VR UR VR

GPCC 1 81.1 46.6 80.9 48.6 83.9 49.5 82.1 47.9

2 9.9 44.3 10.7 43.0 9.5 43.9 10.8 45.5

Total 90.9 90.9 91.6 91.6 93.4 93.4 93.0 93.0

T. Raziei et al.

Fig. 3 Varimax rotated loadings (REOFs) relative to the SPI on a 3-, b 6-, c 12- and d 24-month time scale,computed using observations (193 stations), and PT02 and GPCC precipitation datasets

SPI Modes of Drought Spatial and Temporal Variability in Portugal

Tab

le2

Inter-comparisonof

thethreeused

datasetsby

relatingtheirrotatedloadings

associated

with

differentS

PItim

escales

throughcongruence

coefficients.T

obetterhighlightthe

differencesam

ongthecoefficientsthey

arelistedin

threedecimalplaces

SPI-3

NorthernSu

b-region

Southern

Sub-region

Obs.R

EOF–

1PT

02REOF–

1GPC

CREOF–

1Obs.R

EOF–

2PT

02REOF–

2GPC

CREOF–

2

Obs.R

EOF–

11

0.996

0.996

Obs.R

EOF-2

10.998

0.998

PT02

REOF-1

10.999

PT02

REOF-2

10.999

GPC

CREOF-1

1GPC

CREOF-2

1

SPI-6

NorthernSu

b-region

Southern

Sub-region

Obs.R

EOF–

1PT

02REOF–

1GPC

CREOF–

1Obs.R

EOF–

2PT

02REOF–

2GPC

CREOF–

2

Obs.R

EOF–

11

0.995

0.994

Obs.R

EOF–

21

0.997

0.998

PT02

REOF–1

10.999

PT02

REOF–

21

0.999

GPC

CREOF–1

1GPC

CREOF–

21

SPI–12

NorthernSu

b-region

Southern

Sub-region

Obs.R

EOF–

1PT

02REOF–

1GPC

CREOF–

1Obs.R

EOF–

2PT

02REOF–

2GPC

CREOF–

2

Obs.R

EOF–

11

0.995

0.994

Obs.R

EOF–

21

0.997

0.997

PT02

REOF–1

10.997

PT02

REOF–

21

0.998

GPC

CREOF–1

1GPC

CREOF–

21

SPI–24

NorthernSu

b-region

Southern

Sub-region

Obs.R

EOF–

2PT

02REOF–

2GPC

CREOF–

1Obs.R

EOF–

1PT

02REOF–

1GPC

CREOF–

2

Obs.R

EOF–

21

0.988

0.989

Obs.R

EOF–

11

0.993

0.995

PT02

REOF–2

10.988

PT02

REOF–

11

0.996

GPC

CREOF–1

1GPC

CREOF–

21

T. Raziei et al.

SPI time scales, i.e., when the SPI time scale changes the identified sub-regions remain aboutidentical. This is evident when visually comparing the identified sub-regions captured by thethree used datasets and for all the SPI time scales (Fig. 3).

3.3 Stability of Drought Modes

Previous results suggest that the northern and southern sub-regions identified in the present study arestable with respect to the different datasets as well as to the different types of drought defined by theSPI, from shorter to longer time-scales. However, the identification of the third sub-region, when thePCAwas applied to SPI-12 and SPI-24 of PT02 dataset, seems to depend on the spatial resolution ofthe used dataset and/or upon the considered time period. The effects of stations density could also bequite relevant as it is somewhat evident when comparing the numbers of grids/stations of the threedatasets in the central-eastern Portugal, which is identified as the third mode in the PCA results ofSPI-24 of PT02: the PT02 has 52 grid points in this area whereas the observation dataset has 29irregularly distributed stations andGPCConly has 4 grid points in the same area. Therefore, the thirdmode captured by PT02 could possibly relate to the higher numbers of grid points of PT02 in thatarea when compared with those of GPCC and observations datasets.

The selected time window for drought analysis might possibly affect the regional droughtpatterns through changes in the number of identified sub-regions or their areal coverage. Toassess this, a longer observation dataset consisting in 144 stations and covering the period1910–2003 (Santos et al. 2010) was considered for further analysis. This set of stations issparser than the main observation dataset used in this study (193 stations, Fig.1a). Therefore,the PCA was applied to the matrix of 144 stations corresponding to the longer (1910–2003)and two shorter (1910–1949; 1950–2003) time windows in order to examine if the identifiedsub-regions remain stable when the time window changes. Table 3 shows the percentages of

Table 3 Percentage of the total variance explained by the un-rotated (UR) and Varimax rotated (VR) loadings ofthe SPI–3, SPI-12 and SPI-24 computed using observations from 144 stations for three different time sections.Units are %

1910-1949 1950-2003 1910-2003

SPI Time scale PC UR VR UR VR UR VR

SPI–3 1 59.1 31.9 68.4 36.0 64.2 33.1

2 8.2 25.4 10.6 35.4 9.5 31.7

3 2.7 12.7 1.9 9.4 2.2 10.8

4 1.3 1.5

Total 70.0 70.0 80.9 80.9 77.1 77.1

SPI–12 1 59.5 30.2 69.1 40.9 63.1 32.4

2 8.1 28.5 10.2 36.5 8.8 21.1

3 5.8 14.6 2.6 4.5 3.9 20.9

4 2.3 3.7

Total 73.4 73.4 82.0 82.0 78.1 78.1

SPI–24 1 55.2 29.9 64.8 39.2 57.2 27.3

2 9.8 27.3 11.4 33.6 8.9 18.2

3 7.8 15.6 4.2 7.1 6.2 16.3

4 3.0 3.5 3.7 14.3

Total 72.8 72.8 83.3 83.3 76.1 76.1

SPI Modes of Drought Spatial and Temporal Variability in Portugal

the total variances explained by un-rotated and Varimax rotated loadings of SPI-3, SPI-12 andSPI-24 computed using 144 observations for these three time windows. Results show that thenumbers of significant components retained for rotation are three for almost all SPI time scaleswhen shorter time windows are considered, but they increased to four components for thelonger time window. The total explained variance is noticeably higher for the 1950–2003 thanfor the 1910–1949 time window for all SPI time scales. However, the explained variance of thethird component is much pronounced for the 1910–1949 time window. Differently, when thelonger time window is considered, the first four components were retained for rotation for allSPI time scales, accounting for 77.1 %, 78.1 % and 76.1 % of total variance for SPI-3, SPI-12and SPI-24, respectively. The explained variance of the third rotated component considerablyincreased, being comparable to the second rotated component of SPI-12 and SPI-24 when thelonger time scale is considered. This may indicate a higher importance of the third mode in thelonger time window.

The observed differences shown in Table 3 suggest that the eigenvector solution maydepend to the sampling data both in space (space resolution) and time (time window). This issupported by Fig. 4 illustrating the spatial patterns of the rotated loadings of SPI-3, SPI-12 andSPI-24 associated with the three different time windows. The spatial patterns of the rotatedloadings corresponding to 1910–1949 (Fig. 4) are almost identical to those obtained by Santoset al. (2010) who applied PCA to the SPI-12 matrix relative to a longer time window (1910–2004) using the same dataset. The spatial configurations of the REOFs associated with the1910–1949 period are far different from those of 1950–2003 time window (Fig. 3) when usinga more dense network of observations. Differently, the REOFs associated with 1951–2003time window are almost identical to those shown in Fig. 3 although the number and density ofstations used are different. However, comparing the loading patterns shown in Fig. 4 it appearsthat the PCA solution for the longer time window mostly reflects the spatial configurations ofrotated loadings associated with the 1910–1949 time window. This is particularly clear in theloading patterns of SPI-12 and SPI-24. Results depicted in Fig. 4 suggest that the northern sub-region is more localized and restricted to a small area in far north-western Portugal, whichcorresponds to the region in the country with the larger amount of annual precipitation, whileby its westward expansion the third sub-region covers the entire north-central Portugal whenthe 1910–1949 and 1910–2003 time windows are considered. This suggests that the northernsub-region, that is clearly identified by the three used datasets at all considered SPI time scales(Fig. 3), is also sensitive to the time period used (Fig. 4). The instability of the third sub-regionis clearly evident in Fig. 4 as its areal extent changes noticeably with respect to the SPI timescale and data time period. Differently, it was found that the southern sub-region is the moststable sub-region that clearly emerged in the PCA results relative to all considered datasets andtime windows here analyzed.

3.4 Temporal Variability of Drought

The time series of the rotated PC scores relative to observations (193 stations), PT02 andGPCC datasets are displayed and compared in Fig. 5. The correlation coefficients between theRPC time series for the three datasets are listed in Table 4, where those associated with thesame sub-region are denoted in bold. According to Fig. 5 and Table 4 it appears that the RPCscores of the different datasets associated with the same sub-region are strongly correlated forall SPI time scales.

The RPC1 and RPC2 time series are characterized by multi-year variability and there are nostatistically significant long-term linear trends for the time window here considered. The RPC3that is associated with the third mode captured by PT02 at longer time scales (12- and 24-

T. Raziei et al.

Fig. 4 Varimax rotated loadings (REOFs) relative to the SPI on a 3-, b 12-, and c 24-month time scale,computed using observations from 144 stations for 1910–1949, 1950–2003 and 1910–2003 time windows

SPI Modes of Drought Spatial and Temporal Variability in Portugal

month) shows a downward linear trend towards negative values accounting for 0.58 % and0.69 % of the variance of the time series for SPI-12 and SPI-24, respectively. Due to verystrong co-variability between the RPCs of the three used datasets (Fig. 5 and Table 4) only thePT02 RPC scores were considered herein for trend analysis, computing the Mann-Kendalltrend test and the Sen slope estimator for the annual average of the RPC scores relative to SPI-12 and SPI-24 of PT02 (Table 5). Table 5 shows no statistically significant trends in the annualaverage of RPC1 and RPC2 for both time scales.

The PC scores corresponding to different individual months and seasons were also exam-ined using the test statistics to reveal if the trend is more evident in any given month andseason; however, no differences were found. Considering that the RPC1 and RPC2 arerepresentative time series for the two main Portuguese sub-regions, northern and southernareas, it can be concluded that present results agree with those of previous studies on trendanalysis for main land Portugal using either precipitation (Santos and Portela 2007; de Limaet al. 2010) or drought indices time series (Moreira et al. 2006; Paulo et al. 2012) that detectedno trend for the majority of Portuguese stations. The results are particularly in agreement withthe findings of Moreira et al. (2012) who found no evidence for aggravation or attenuation ofdrought severity and frequency for most of the stations situated in either northern or southernsub-regions identified in the present study. Differently, the RPC3 associated with PT02 showsa statistically significant downward trend for both SPI-12 and SPI-24 time scales with −0.054

Fig. 5 Rotated principal component score time series (RPCs) associated with the REOFs illustrated in Fig. 3.Rows from top to bottom refer to the SPI-3, SPI-6, SPI-12 and SPI-24, respectively. Horizontal dotted line is thezero-line

T. Raziei et al.

Tab

le4

Correlatio

ncoefficientsbetweentheRPC

sforobservations

andPT

02andGPC

Cgriddeddatasets.CorrelationcoefficientsbetweenRPC

sassociated

with

thesamesub-

regionsareunderlined

OBS

PT02

SPI–3

PT02

RPC

RPC

1RPC

2RPC

3RPC

4RPC

1RPC

2

RPC

10.96

0.00

0.18

0.19

RPC

2–0.05

0.97

0.15

0.12

SPI–6

GPC

CRPC

10.95

0.01

0.14

0.19

0.98

0.01

RPC

2–0.04

0.96

0.13

0.12

0.01

0.97

RPC

RPC1

RPC2

RPC

3RPC

4RPC1

RPC2

PT02

RPC

10.97

0.00

0.21

RPC

2–0.04

0.98

0.20

GPC

CRPC

10.97

0.01

0.19

0.99

0.01

RPC

2–0.03

0.97

0.17

0.00

0.99

RPC

RPC1

RPC2

RPC

3RPC

4RPC1

RPC2

RPC

3RPC

4

PT02

RPC

10.96

0.01

0.10

0.14

SPI–12

GPC

CRPC

2–0.03

0.99

0.06

0.05

RPC

30.11

0.04

0.58

–0.59

RPC

40.17

0.09

–0.38

0.15

RPC

10.98

0.03

0.13

0.09

0.97

0.00

0.17

0.17

PT02

RPC

2–0.02

0.99

0.08

–0.01

–0.02

0.99

0.11

0.07

RPC

RPC1

RPC2

RPC

3RPC

4RPC1

RPC2

RPC

3RPC

4

RPC

10.99

–0.05

0.02

0.10

SPI–24

GPC

CRPC

20.01

0.94

–0.01

0.26

RPC

30.08

0.25

0.65

–0.62

RPC

40.06

0.19

–0.41

–0.13

RPC

10.02

0.97

0.18

0.04

–0.03

0.93

0.36

0.11

RPC

20.98

–0.03

0.12

–0.02

0.98

–0.03

0.17

0.05

SPI Modes of Drought Spatial and Temporal Variability in Portugal

and −0.061 units per year, respectively. Regarding the observed significant downward trendfor the RPC3 of PT02 it is worth noticing that such a negative trend towards dryer periods hasbeen already reported by Paulo et al. (2012) and Santos and Portela (2007), both analyzingmonthly precipitation for 1941–2006 and 1910–2004 time periods, respectively, and byMoreira et al. (2012) that highlighted a possible drought aggravation for some stations inthe central sub-region.

4 Discussion and Conclusions

The present study provided an analysis of regional drought patterns in Portugal using rainfallobservations and PT02 and GPCC rainfall gridded datasets. The S-mode PCA and Varimaxrotation were applied to the SPI on different time scales computed using the three precipitationdatasets for the period 1950–2003. Results identified the northern and southern Portugal as thetwo main sub-regions of drought variability. In addition, a small sub-region in the mountainousinland of central-eastern Portugal was found for the 24-month time scale using the PT02dataset. The agreement between the identified sub-regions represented by different datasetsand SPI time scales were evaluated by computing a congruence coefficient. Moreover, a longerobservations dataset was used, which allowed to consider three time windows to examine thestability of the identified sub-regions.

The northern and southern sub-regions were identified with high positive rotated loadingvalues. Similar spatial patterns were found using the three datasets and all considered SPI timescales, suggesting that the sub-regions are quite stable with respect to the changes in the SPItime scale. Differently, a third sub-region is observed for the PT02 dataset referring to central-eastern Portugal, which is sensitive to the SPI time scale and spatial resolution of the dataset.Despite the third spatial mode explains a smaller percentage of the total variance, its position inthe mountainous area of central Portugal and the statistically significant downward trendcharacterizing the associated RPC, suggest the need for further studies relative to that regionusing a dense network of observations. Results also indicate a slight increasing in thecomplexity of drought spatial variability for longer SPI time scales as was argued for Spain(Vicente-Serrano 2006) and Iran (Raziei et al. 2013).

The congruence coefficients between the REOFs associated with the same sub-regions haveshown an excellent spatial congruence for all datasets and SPI time scales, thus suggesting avery good agreement between the three datasets in capturing the main Portuguese sub-regionsat all considered SPI time scales. The results also revealed a strong agreement between theREOFs of different SPI time scales within a given dataset. It was also found that thecongruence coefficient slightly decreases when comparing the REOFs of shorter SPI timescales with those of longer time scales, which could be related to the inherent complexity ofloading patterns of longer SPI time scales.

Table 5 Results of the Sen Slope estimates and the Mann-Kendall trend test (in parenthesis) applied to theannual average of RPC scores relative to SPI–12 and SPI-24 of PT02. The statistically significant values at 0.05significant level are underlined

SPI-12 SPI-24

Dataset RPC-1 RPC-2 RPC-3 RPC-1 RPC-2 RPC-3

PT02 0.002 (0.16) −0.003 (−0.33) −0.054 (−6.30) −0.001 (−0.13) 0.013 (1.38) −0.061 (−6.51)

T. Raziei et al.

The two main sub-regions here identified appear consistent with the results obtained bySantos et al. (2010) and Martins et al. (2012) pointing to the northern and southern Portugal asdistinct areas of drought variability, whereas the central sub-region was observed by Santoset al. (2010) using rain gauge data from 144 stations covering the period 1910–2004. In thepresent study, the same dataset was used to create three different time windows in order toexamine if the identified sub-regions are conditioned to the considered time window. Theresults showed that the southern sub-region is the most stable one while the northern andcentral-eastern sub-regions are very sensitive to the selected time window.

The identification of these sub-regions with similar drought variability and characteristicscan be useful for drought risk management at a regional scale. Two of the most important riverbasins in Portugal (Tagus and Guadiana) are both in the Southern sub-region and the Dourobasin is inside the Northern sub-region. This means that the drought sub-regions here identifiedwell represent the distinct drought variability characterizing the three main river basins. Thus,these regional drought patterns may be taken into account when implementing the EU WaterFramework Directive, possibly with similar water resources management strategies expectedfor Tagus and Guadiana and different drought management plans for Douro.

Further applications using different gridded datasets are suggested to verify the role playedby the spatial resolution of the input data on regional drought patterns with different SPI timescales, particularly relative to the identification of a possible third region.

Acknowledgments This study was partially funded by a research contract with FCT, Portugal, nr. PTDC/GEO-MET/3476/2012. The first author thanks the fellowship awarded by the Portuguese Science Foundation (FCT).PT02 gridded precipitation dataset was freely provided by Margarida Belo-Pereira, Instituto de Meteorologia,Portugal and the GPCC gridded precipitation data (Full Data Product Version 5) was also freely acquired fromthe Deutscher Wetterdienst through their web site http://www.dwd.de. The observations dataset are composed ofSNIRH rain gauges and synoptic and climatological stations of the Portuguese Meteorological Service (IPMA).

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