Comparing SPI and RDI Applied at Local Scale as

Water Resour Manage https://doi.org/10.1007/s11269-017-1855-7

Comparing SPI and RDI Applied at Local Scale as Influenced by Climate Abdelaaziz Merabti 1 & Mohamed Meddi 1 & Diogo S. Martins 2 & Luis S. Pereira 3

Received: 12 June 2017 / Accepted: 2 November 2017 # Springer Science+Business Media B.V., part of Springer Nature 2017

Abstract Drought and wetness events were studied in the Northeast Algeria with SPI and RDI. The study area includes a variety of climatic conditions, ranging from humid in the North, close to the Mediterranean Sea, to arid in the South, near the Sahara Desert. SPI only uses precipitation data while RDI uses a ratio between precipitation and potential evapotranspiration (PET). The latter was computed with the Thornthwaite equation, thus using temperature data only. Monthly precipitation data were obtained from 123 rainfall stations and monthly temperature data were obtained from CFSR reanalysis gridded temperature data. Both data sets cover the period 1979–80 to 2013– 14. Using ordinary kriging, the gridded temperature data was interpolated to all the locations having precipitation data, thus providing to compute SPI and RDI with the same observed rainfall data for the 3-, 6- and 12-month time scales. SPI and RDI were therefore compared at station level and results and have shown that both indices revealed more sensitive to drought when applied in the semi-arid and arid zones. Differently, more wetness events were detected by RDI in the more humid locations. Comparing both indices, they show a coherent and similar behavior, however RDI shows smaller differences among climate zones and time-scales, which is an advantage relative to the SPI and is likely due to including PET in RDI. Keywords Drought indices . Potential evapotranspiration . CFSR reanalysis products . Northeastern Algeria . Climate variability . Global warming

* Luis S. Pereira [email protected]; [email protected]

1

Ecole Nationale Supérieure d’Hydraulique de Blida, Laboratoire GEE, Blida, Algeria

2

Instituto Dom Luiz (IDL), Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal

3

LEAF - Linking Landscape, Environment, Agriculture and Food, Instituto Superior de Agronomia, Universidade de Lisboa, Lisboa, Portugal

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1 Introduction Drought is a natural phenomenon with harmful effects to ecosystems and human related activities, mainly agriculture. Considering an increased water demand by various economic sectors and that climate change impacts exacerbate water scarcity, understanding drought spatial and temporal variability is of great importance for drought prone countries (Tsakiris 2017) such as Algeria. Drought can be defined as a natural but temporary imbalance of water availability, consisting of persistent lower-than-average precipitation of uncertain frequency, duration and severity, of unpredictable or difficult to predict occurrence, resulting in diminished water resources availability and carrying capacity of the ecosystems (Pereira et al. 2009). Various studies focused on droughts at the Mediterranean scale. Spinoni et al. (2014) reported a significant increase in drought frequency, duration, and severity in Mediterranean region. Giorgi and Lionello (2008), in a previous study on climate change impacts in the Mediterranean basin, reported on a pronounced decrease in precipitation associated with noticeable warming, mainly in the summer season. This drying condition is reported to be due to Bincreased anti-cyclonic circulation that yields increasingly stable conditions and is associated with a northward shift of the Atlantic storm track^. Moreover, Giorgi and Lionello (2008) suggested that the Mediterranean might be a highly vulnerable region to global change. Therefore, it is likely that droughts will affect this region as influenced by the referred increased dryness as reported by studies referred hereafter. Sousa et al. (2011) computed the Palmer Drought Severity Index (PDSI) and the Self Calibrated PDSI (scPDSI) with data for the twentieth century in a number of Mediterranean locations. A trend towards drier conditions during the twentieth century in most western and central Mediterranean regions was identified. Despite the wide scale of the analysis, that study allowed to detect a trend for increased dryness in NW Algeria but not in the northeastern region. These authors identified the North Atlantic Oscillation (NAO) as the main driver of the scPDSI pattern in western and central Mediterranean areas, highly relevant in winter and important during the following spring and summer. The Scandinavian Pattern was also significant over central Mediterranean. Weiß et al. (2007) reported that drought severity is expected to increase much more in the northern Mediterranean relative to the southern areas. Hoerling et al. (2012), using climate change model predictions for the Mediterranean basin, also identified an increased drying, mainly in NW, as influenced by NAO. Using tree-ring data, Nicault et al. (2008) reconstructed the PDSI values for 500 years in the Mediterranean basin. Results highlighted multi-decadal PDSI variations in the central and western parts of the Mediterranean but less clear low frequency changes in the east. The 16th and the first part of the 17th centuries were marked by dry episodes in the west similar to those observed by the end of the twentieth century. Relative to the eastern part of the Mediterranean, the heavy drought period observed by the end of last century was considered the strongest of the last 500 years. Touchan et al. (2008) also reconstructed a long series of PDSI (1456–2002) focusing on northwestern Africa with results in agreement with those reported before. Moreover, those authors considered that a transition to more arid mid-latitude conditions is developing, also in agreement with predictions by general circulation models. Their results were confirmed by a second study (Touchan et al. 2011) where the reconstruction went to 1179 over the Maghreb countries, which shows a shift toward dryer conditions. In line with studies referred above, Saadi et al. (2015) reported about predicted changes in precipitation, temperature and grass reference evapotranspiration, ETo, in the Mediterranean basin and predicted important impacts on wheat cropping patterns, a typical rain-fed crop that likely needs

Comparing SPI and RDI Applied at Local Scale as Influenced by Climate

irrigation in future. Similarly, Tanasijevic et al. (2014) identified impacts on the olive crop, that should become irrigated while today it still is often rain-fed. Therefore, it is important to recognize how droughts behave in order to detect main impacts, namely affecting water scarcity in the Mediterranean basin, particularly in the less studied northeastern Algeria. Northern Algeria has been focused on various rainfall and drought studies, however mostly dedicated to the northwestern areas and rarely to NE Algeria. Various authors (Meddi et al. 2010; Hamlaoui-Moulai et al. 2013; Taibi et al. 2017; Zeroual et al. 2017) have reported on a decrease in precipitation totals in NW Algeria. Zeroual et al. (2017) also reported on an increased warming. A marked decrease in average monthly streamflows in northern Algeria was referred by Zeroual et al. (2013) as a consequence of decreased rainfall. Spatial analysis studies have identified the longitude, the distance from the Mediterranean Sea and the topography as important factors influencing rainfall variability (Meddi et al. 2013), and also identified NAO and the Mediterranean Oscillation (MO) as the main driving patterns influencing that variability. Both NAO and MO were also identified by Tramblay et al. (2013) as causing an increase of duration and magnitude of dry episodes, with a decrease of annual precipitation and in the number of wet days. Several indices have been proposed and used to appropriately identify and analyze droughts, namely relative to severity, intensity, duration and spatial extent (Keyantash and Dracup 2002; Paulo and Pereira 2006; Mishra and Singh 2010; Zargar et al. 2011;Tsakiris 2017), as well as for drought prediction and/or to assess impacts of climate change. The most commonly used drought index is the Standardized Precipitation Index (SPI; McKee et al. 1993), which is a normalized index for calculating the deviation from the normal precipitation conditions. The SPI only requires monthly precipitation data is easy to compute and because it is standardized, can be easily compared among periods or regions. Moreover, it can be computed for different time scales, which represent various types of drought: shorter time scales are used to assess meteorological droughts, SPI3- and 6-month time scales are often used for agricultural droughts, while larger time scales, such as 12- or 24-month, are more suitable to describe hydrological and water resources droughts (Mishra and Singh 2010). The SPI is based on the probability of precipitation cumulated for any time scale. The probability of the observed precipitation is then transformed into an index that supports assessing drought severity and may provide for early warning of drought or for assessing climate changes influences (Bordi et al. 2004, 2009; Paulo and Pereira 2007; Moreira et al. 2008, 2016). However, SPI has limitations, namely because evapotranspiration is not considered and the selected calibration period may play an important role when dealing with non-stationary precipitation time-series, likely influenced by climate change (Paulo et al. 2016). Other indices include the effect of potential evapotranspiration (PET) in addition to precipitation: the Palmer Drought Severity Index (PDSI; Palmer 1965), which is computed through a soil water balance approach, and the Reconnaissance Drought Index (RDI; Tsakiris et al. 2007) and the Standardized Precipitation Evapotranspiration Index (SPEI, Vicente-Serrano et al. 2010), which use PET without performing the soil water balance. Both indices use a probabilistic computational procedure similar to the SPI, are normalized in terms of drought severity and may be computed with various time scales as the SPI. More recently, Tsakiris et al. (2016) developed a new approach with RDI for coupling the drought severity and areal extend using a 2D Archimedean Copulas approach. Considering climate change effects, studies show that PET should not be ignored in drought assessment, which supports the use of indices that include both rainfall and evapotranspiration.

Merabti A. et al.

Several recent studies refer to the use of RDI. Banimahd and Khalili (2013) found that the RDI behaved quite uniformly for areas having different climates and for various time scales. Differently, Zarei et al. (2016) reported that using the RDI for short time scales a trend to increase of drought occurrence and severity in arid and semi-arid regions of Iran was identified. Zarch et al. (2011) reported on the good correlation between SPI and RDI, particularly when using the time scales of 3, 6 and 9 months rather than longer ones, and that SPI and RDI compared well for all areas where applied. Shokoohi and Morovati (2015) found that both SPI and RDI performance in drought recognition matched in many cases but RDI was more sensitive to severe drought. Zarch et al. (2015) used RDI in a worldwide scale, covering a variety of climates, and found that the agreement between SPI and RDI reduced from the hyper-arid climates toward the humid ones. They reported that in semi-arid, sub-humid and humid zones the indices showed different trends, with RDI exhibiting more decreasing ones. Zarch et al. (2015) also concluded that different trends but coherent results of SPI and RDI favours adopting both indices in drought studies. Nevertheless, studies on RDI are lacking for central and western Mediterranean areas. The RDI computation follows a procedure similar to SPI but applied to the time series of the monthly ratio of P/PET instead of solely monthly precipitation. The RDI adopts the same drought classification as SPI. The PET Thornthwaite’s equation (Thornthwaite 1948) is often used because it is a purely climatic equation depending only from temperature; the FAO56 grass reference evapotranspiration (ETo, Allen et al. 1998), that represents the evaporative demand of the atmosphere, is also often adopted. However, the selected equation has minor impacts on the index values (Vangelis et al. 2013; Mohammed and Scholz 2017) that, instead, may be influenced by the type and quality of available data as analyzed by Allen et al. (1998). Khalili et al. (2011) reported that when PET was computed with the FAO ETo equation (Allen et al. 1998) the RDI was very sensitive to climatic variability, which authors considered useful in drought analyses focusing on agricultural applications. Tigkas et al. (2012) successfully analyzed streamflow variation with RDI in Greece. The above reviewed current knowledge on drought and climate change in the Mediterranean basin and northern Algeria in particular clearly shows that drought studies relative to NE Algeria are lacking and applications of RDI to Central and western Mediterranean regions are not yet reported in literature. It may therefore be considered that the study of droughts in NE Algeria using RDI is innovative. Hence the main objectives of this paper consist of comparing SPI and RDI when characterizing drought in northeastern Algeria taking into consideration the quite diverse climates of the region and using the 3-, 6- and 12-month time scales. The spatial and time variability of droughts using the same indices and data are presented in a companion paper (Merabti et al. 2017).

2 Material and Methods 2.1 Study Area The northeastern Algeria extends between the longitudes of 3°15′6″E to 8°40′10″E and the latitudes of 37°5′00″N and 34°32′30″N, covering about 109,000 km2 (Fig. 1). It develops from the Mediterranean coast and the highlands of the Tellian Atlas in the north to the Saharian Atlas and the southern plains bordering the Sahara desert in the south. Consequently, precipitation is highly variable in the region, from above 1700 mm year−1 in the coastal area to about 150 mm year−1 in the southern plains (Fig. 2a). It varies with the proximity to the Mediterranean Sea, the site elevation and the exposure to the NW winds, which carry most of rainfall.

Comparing SPI and RDI Applied at Local Scale as Influenced by Climate

Fig. 1 Relief map of the study area with location of rainfall stations used and isolines of the aridity index that separate main climatic areas

Monthly precipitation data from 123 rainfall stations were derived from records of the National Hydraulic Resources Agency (NHRA, www.anrh.dz/) for the hydrological years of

Fig. 2 Spatial distribution of (a) the mean annual precipitation and (b) the Aridity Index

Merabti A. et al.

1960–61 to 2013–14. The precipitation records with missing values were filled using the Hydrolab software (Laborde and Mouhous 2006), which is based on principal component analysis to categorize stations with similar precipitation patterns and thus to be used for filling the gaps and maintaining the series statistical characteristics. Records had less than 10% of missing monthly values in the selected study period. The precipitation data were tested for homogeneity using the Wilcoxon sequential test (Karl and Williams 1987). 22 out of the 123 stations were not considered homogenous, hence the precipitation series were corrected using the double and the cumulative residuals methods (Allen et al. 1998) using the neighboring stations with homogenous data identified as referred above. The representation of the spatial distribution of the annual precipitation is shown in Fig. 2a. The Thornthwaite equation (Thornthwaite 1948) was used to compute PET, hence using temperature data only. Thus, 84 grid-points with monthly temperature data of the Climate Forecast System Reanalysis (CFSR; Saha et al. 2010) were used with data of the hydrological years of 1979–80 to 2013–14. The CFSR reanalysis data is based on both historical and operational archives of observations and newly reprocessed sets of observations produced at meteorological research centers around the world. CFSR assimilates observations from upper air balloon, aircraft and satellite observations and has a spatial resolution of approximately 38 km. Various studies compared CFSR against observations (Fuka et al. 2014; Dile and Srinivasan 2014; Mohammed and Scholz 2017; Worqlul et al. 2017), which support further uses of this reanalysis dataset as for the current study. The 84 grid-points of monthly temperature were interpolated to the 123 sites where precipitation was observed, hence SPI and RDI used the same sets of precipitation data referring to the same locations. Considering that kriging is likely the most accurate method for interpolation of drought indices (Akhtari et al. 2009), Ordinary Kriging was used for that interpolation with consideration of altitude effects. To further understand climate variability in NE Algeria, the UNEP aridity index (AI; UNEP 1997) was used to characterize the climate at every weather station. This index is the ratio between the mean annual precipitation and the mean annual Thornthwaite’s PET relative to the 34 years of data. The AI index shows a pattern with aridity increasing from north to south (Fig. 2b), i.e., from the coastal area to the border of Sahara Desert. Using the Köppen-Geiger climate classification (Kottek et al. 2006), the NE Algeria zone comprises three different climates: warm temperate with a warm and dry summer (Csb) in the northern part, including the mountainous area; arid of steppe type and cold arid (BSk) in the southern mountainous area; and arid of desert type and hot arid (Bwh) in the southern plains. This classification agrees with that of aridity using AI (Fig. 2b).

2.2 Drought Indices Two drought indices, SPI and RDI, were considered to characterize droughts in the NE Algeria and to detect the main spatial and temporal patterns of drought variability in the region. Both indices were briefly reviewed in the Introduction. They are multiscalar indices, thus can be computed for different time scales, and are normalized, so allowing to be compared for different regions and periods. The classification of the severity of drought/wetness events is mild, moderate, severe and extreme with SPI taking, respectively, the values 0 to −0.99/0 to 0.99, −1.00 to −1.49/1.0 to 1.49, −1.50 to −1.99/1.50 to 1.99, and ≤ –2.00/≥ 2.00 (McKee et al. 1993). The calculation of the SPI for any time scale k (3-, 6- and 12-month in the current study) requires the following steps (McKee et al. 1993; Guttman 1999):

Comparing SPI and RDI Applied at Local Scale as Influenced by Climate


 ^ where λ ^ is the vector of estimated parameters. The 1) Estimation of the distribution F x; λ two parameter gamma distribution was adopted with the probability density function (pdf) defined by f ðxÞ ¼

x 1 xα−1 e− β ; x > 0 β α Γ ðαÞ

ð1Þ

where Γ is the gamma function, and α and β are the shape and scale parameters. These parameters were estimated by the maximum likelihood method: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! 1 4A α¼ ð2aÞ 1þ 1þ 4A 3

β¼

X α

ð2bÞ

where x represents the sample statistic, i.e., the rainfall average, and A is given as
 ∑ lnðxÞ A ¼ ln X − n

ð3Þ

and n is the number of observations.
 ^ ^; β 2) Calculation of the probability for each precipitation event p ¼ F x; α 3) Calculation of the standard normal quantile SPI = ϕ−1(p) where ϕ (x; 0, 1) is the standard normal distribution. Any SPI value can be back-transformed into precipitation by the inversion of the statistical and computational methods. The SPI value is transformed into non-exceedance probability through the normal distribution p = ϕ (SPI) and the probability is transformed into a precipi
 ^ . This back^; β tation x by the inversion of the gamma distribution, x ¼ F −1 p; α transformation assumes a perfect fit between the adjusted pdf and the empirical distribution of precipitation (Paulo et al. 2016). The RDI is computed in three steps (Vangelis et al. 2011; Tigkas et al. 2015) like for the SPI computation. First, the monthly time-series of the ratio αk between precipitation and PET cumulated to the selected time scale k is computed as αik ¼

∑kj¼1 Pij ∑kj¼1 PETij

; i ¼ 1 to N

ð4Þ

in which Pij and PETi j are the precipitation and PET relative to the month Bj^ of the hydrological year Bi^, developing from September to August, and N is the length of the time-series. Then RDI is normalized (RDIn) relative to the average ak as

RDI ðniÞ ¼

ðiÞ

ak

ak

−1

ð5Þ

Merabti A. et al.

In this study, the Standardized RDI (RDIst) was computed by fitting the gamma pdf defined in Eq. (1) to the frequency distribution of ak (Tigkas et al. 2015). However, other pdf may be successfully used, e.g., the log-normal pdf (Mosaedi et al. 2015). The RDI time-series were computed using the DrinC (Drought Indices Calculator) software (Tigkas et al. 2015), which also includes a SPI computational tool, successfully used by Surendran et al. (2017) for India.

3 Results and Discussion 3.1 Application and Comparison of SPI and RDI at Local Scale The application of both SPI and RDI is exemplified in Fig. 3 for five weather stations located in different climate zones (Fig. 1): Zitouna (6° 27′ 31″ E, 36° 59′ 28″ N, 564 m altitude) in the northern coastal humid climate zone; Ain Berda (7° 35′ 38″ E, 36° 41′ 28″ N, 114 m alt.) in the northern moist sub-humid zone; Bordj Zemmorah (4° 50′ 02″ E, 36° 16′ 07″ N, 950 m alt.) in the central and mountainous dry sub-humid climatic zone; Batna (6° 10′ 14″ E, 35° 33′ 51″ N, 1040 m alt.) in the central semi-arid mountainous zone; and Biskra (5° 43′ 04″ E, 34° 51′ 45″ N, 124 m alt.) in the southern arid plains. The applications refer to the period consisting of the hydrological years from 1979/80 to 2013/14. The time variation of RDI and SPI computed with the time scales of 3-, 6- and 12-month is represented in Fig. 3. It shows that the behavior of both indices is very similar, with only slight different for the five chosen locations, i.e., for the five considered climates. Drought and wetness identified in one climatic zone are often not identified in another climatic region or are identified with different severity. This is particularly evident for the 3- and 6-month time scales. Differences are likely due to the influence of both very large mountains, the Tellian Atlas and the Saharian Atlas (Fig. 1), which impact the atmospheric circulation at the scale of NE Algeria. Moreover, differences also reflect the influence of local climate due to varied altitude and exposure to the winds that drive moist air masses and latter impact precipitation, temperature and PET. Comparing results for the selected stations, it may be observed that SPI identifies more peak values of both drought and wetness in the humid and moist sub-humid locations, Zitouna and Ain Berda. This behavior is particularly evident for the 6- and 12-month time scales. That behavior apparently changes for the dry sub-humid Bordj Zemmorah where RDI seems to identify more severe wet events than SPI. Relative to semi-arid Batna, differences between indices are quite small. However, for the 3-month time scale RDI identified the more extreme dry and wetness events, which were also identified with SPI but with lower index values. For the 6- and 12-month time scales differences between indices are very small. Regarding Biskra, in the arid zone, differences between indices are larger, with RDI-6 and RDI-12 identifying more severe peak values of drought events. Summarizing, differences between indices are only slightly evident for the shorter time scale and for dry sub-humid and semi-arid climates where PET plays a less important role relative to precipitation; in the humid and moist sub-humid climates the importance of the anomalies of precipitation are better noticed by SPI. Differently, in the arid zone RDI detects larger drought peaks likely because PET plays a major role in areas where rainfall is low. To better identify the differences between drought indices under different time scales, a regression analysis was performed for the above identified five locations relating the SPI and the RDI values for the three time scales (Fig. 4). Results show that the coefficient of

Comparing SPI and RDI Applied at Local Scale as Influenced by Climate

Fig. 3 Time variability of the SPI ( ) and RDI ( ) for the 3 time scales (3-, 6- and 12-month) at Zitouna, humid climate, Ain Berda, moist sub-humid climate, Bordj Zemmorah, dry sub-humid climate, Batna, semi-arid climate, and Biskra, arid climate, for 1979–80 to 2013–14

determination R2 is for all cases greater than 0.90, which indicates that the variances of RDI and SPI are quite similar; however, R2 increases with the time scale, i.e., from the 3-month to the 12-month, thus indicating that variances of RDI-12 and SPI-12 are more similar for the larger time scales. Of interest to note that R2 for the arid location of Biskra equals 0.97 for all time scales, which may be related to the fact that for an arid climate, PET, which is there always much above precipitation, plays a more important role for all time scales. The coefficient of regression b0 decreases when the time scale increases in case of the humid Zitouna and the moist sub-humid Ain Berda, thus contrarily to the other stations, where b0 increases when the time scale increases (Fig. 4). This behavior indicates that when the time scale increases differences between RDI and SPI are larger when the climate is more humid, with a tendency for RDI to underestimate the wetter events. This behavior also indicates that RDI may tend to very slightly overestimate dry events. When aridity increases, and for larger time scales, b0 tends to be larger, so indicating that RDI tends to slightly overestimate wet events.

3.2 Identified Frequencies of Drought and Wetness Events for Diverse Climates To better compare RDI and SPI, the frequency of cases when both indices identify drought and wetness events were computed for all locations and all three time scales (Table 1). For humid and

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Fig. 4 Scatter plots of SPI vs. RDI for the 3 time scales (3-, 6- and 12-month) at Zitouna, humid climate, Ain Berda, moist sub-humid climate, Bordj Zemmorah, dry sub-humid climate, Batna, semi-arid climate, and Biskra, arid climate, for 1979–80 to 2013–14

moist sub-humid climates, with exception of the 3-month time scale, RDI identifies more wet than dry events; similarly, SPI also identifies more wetness events, particularly those classified as moderate or severe and extreme. Differences between indices are quite small. For the dry subhumid climate, results are similar to the previously analyzed more humid climates. However, there are a larger percentage of severe and extreme drought events identified with SPI for all time scales. Relative to the semi-arid zone, the SPI identifies more drought than wetness events, while RDI tends to identify a larger percentage of wet events. Regarding the arid area, the SPI identifies

Number of stations

18

36

19

40

10

Climate

Humid

Moist sub-humid

Dry sub- humid

Semi-arid

Arid

RDI-3 RDI-6 RDI-12 SPI-3 SPI-6 SPI-12 RDI-3 RDI-6 RDI-12 SPI-3 SPI-6 SPI-12 RDI-3 RDI-6 RDI-12 SPI-3 SPI-6 SPI-12 RDI-3 RDI-6 RDI-12 SPI-3 SPI-6 SPI-12 RDI-3 RDI-6 RDI-12 SPI-3 SPI-6 SPI-12

Drought indices

Total droughts

6.8 7.8 8.1 6.7 8.0 8.2 6.3 6.9 6.9 6.2 6.7 6.7 6.5 7.2 7.5 7.0 7.3 7.7 6.6 7.1 7.2 8.0 8.3 8.2 5.9 6.3 6.3 6.9 7.5 7.9

9.4 8.1 8.6 9.8 8.4 8.2 9.9 9.0 9.3 9.1 8.6 8.1 10.2 9.1 9.3 9.0 8.9 9.0 9.2 9.4 9.8 9.4 9.6 10.2 9.3 9.7 11.0 10.4 9.9 11.7

33.8 33.1 31.1 32.6 31.1 29.4 34.5 34.6 33.5 33.5 33.3 32.5 33.3 33.0 31.2 33.7 33.2 31.6 34.2 33.3 31.9 33.9 34.2 33.6 35.9 34.1 33.3 35.7 36.0 33.5

50.1 49.0 47.9 49.1 47.5 45.8 50.6 50.5 49.6 48.8 48.7 47.3 50.0 49.2 47.9 49.6 49.4 48.3 50.0 49.8 48.9 51.3 52.0 52.0 51.1 50.1 50.6 53.1 53.3 53.1

33.8 35.2 36.3 34.3 35.3 36.3 32.8 32.8 34.0 34.4 33.3 33.7 33.4 34.4 36.5 34.6 34.2 35.5 33.4 33.3 34.9 33.8 33.3 34.6 32.1 33.3 33.0 31.8 32.6 33.3

9.4 9.3 10.0 9.8 9.9 10.0 9.7 9.8 9.9 9.7 10.2 10.1 9.8 9.8 9.7 9.7 10.2 9.2 10.0 10.2 10.0 9.5 9.6 8.4 9.4 9.5 9.1 9.5 8.4 9.0

Moderate

Mild

Mild

Severe & extreme

Moderate

Wetness events

Drought events

Percentage of drought and wetness events

6.8 6.6 5.8 6.9 7.4 7.9 7.0 6.9 6.5 7.0 7.9 8.9 6.7 6.5 5.9 6.2 6.2 7.1 6.7 6.7 6.3 5.3 5.1 4.9 7.4 7.1 7.3 5.6 5.7 4.5

Severe & extreme

49.9 51.0 52.1 50.9 52.5 54.2 49.4 49.5 50.4 51.2 51.3 52.7 50.0 50.8 52.1 50.4 50.6 51.7 50.0 50.2 51.1 48.7 48.0 48.0 48.9 49.9 49.4 46.9 46.7 46.9

Total wet events

Table 1 Percentage of drought and wetness events identified with the RDI and SPI for 3 time scales (3-, 6- and 12-month) and the five climate zones, for the period 1979–80 to 2013–14

Comparing SPI and RDI Applied at Local Scale as Influenced by Climate

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a much larger number of drought events than RDI, with both indices identifying more drought than wet events. The results analyzed above are slightly contradictory with those relative to individual locations but essentially they allow to perceive the high coherence of results of both RDI and SPI, and that both indices are well usable with the advantage of considering PET in case of RDI. However, RDI shows smaller differences among climate zones and time-scales, which is an advantage relative to SPI, and was also observed by Banimahd and Khalili (2013). Results from Table 1 showed similar results between SPI and RDI for all time-scales, with both indices being able to identify nearly the same events with approximated severity. Nevertheless, the frequency of severe and extreme drought events is higher with SPI for dry sub-humid, semi-arid and arid climates and is larger with RDI for the humid and moist subhumid climates (Table 1). These results do not contradict previous referred studies (Khalili et al. 2011; Shokoohi and Morovati 2015; Zarch et al. 2015), even considering that differences in data sources and time and spatial scales of these studies is notable, e.g., Zarch et al. (2015) used very long gridded datasets and data from climate model predictions at the worldwide scale, while Shokoohi and Morovati (2015) used reanalysis temperature and observed gridded precipitation for a lake basin in Iran. More importantly, results in Table 1 largely agree with those reported in the companion paper (Merabti et al. 2017) relative to rotated principal components where the first one refers to the more humid zone of the region and the second to the southern more arid areas. Results of both approaches show that RDI, differently of SPI, responds quite uniformly in different climates likely due to the inclusion of PET, which incorporates global warming effects into the RDI.

4 Conclusions Two drought indices, the SPI and RDI, with the time-scales of 3-, 6- and 12-month, were compared at local scale, in northeastern Algeria. Both indices have shown quite similar and coherent results through their application to five locations located in the various climate zones having humid, moist sub-humid, dry sub-humid, semi-arid and arid climates. Only slight differences between indices were identified, with regression coefficients generally larger, and closer to 1.0 for the 3-month time-scale. For the arid and semi-arid zones, SPI identifies a larger number of drought events while for more humid climates, both SPI and RDI identify more wetness events. This behavior may indicate that for sub-humid climates drought and wetness events essentially relate with rainfall, thus making PET to play a minor role in differentiating RDI from SPI. Differences among locations relative to the time variation of both RDI and SPI computed with all time-scales show to depend upon the aridity or wetness of the climate. These conditions are influenced by the local climate, which varies enormously in NE Algeria due to distance to the Mediterranean Sea, and the great mountains of the Tellian Atlas and the Saharan Atlas that impact precipitation and climate in relation to sites elevation and exposure to the air masses flowing above the region. Small but notable differences between RDI and SPI were identified through computing the frequency of various drought and wetness classes. For the humid and sub-humid locations, both RDI and SPI generally identified more wetness events, with SPI finding more events than RDI classified as moderate or severe/extreme wetness. Relative to the semi-arid and arid zones, the SPI identified more drought than wetness events, while RDI identifies about the same frequency for both type of events, although RDI identified slightly more drought events in the arid zone. The

Comparing SPI and RDI Applied at Local Scale as Influenced by Climate

results analyzed above allow to perceive the high coherence of results of both RDI and SPI and the possible advantage of using PET, as for RDI, mainly in dry sub-humid and semiarid areas. These conclusions are compatible with those of the quoted literature but are necessarily different considering the nature of data used in other studies, as well as their spatial and time extents. It may be concluded that more studies are required to better assess the differences of the drought indices for various climates. An in-depth comparison of drought and wetness behavior in the northwestern and the northeastern Algeria is also necessary, likely using other indices that include PET and considering influences of indices of atmospheric circulation such as NAO and MO, which could be not only useful for water resources management but also for improving the knowledge about drought indices and their use in prediction. Acknowledgements The authors wish to thank the National Agency of Water Resources for providing the data of rainfall stations. Authors acknowledge FCT for the PhD research grant SFRH/BD/92880/2013 attributed to the third author, and thank Dr. Ana Paulo and Dr. Paula Paredes for their comments and support. Authors also acknowledge funding of LEAF Research Unit by FCT through the contract UID/AGR/04129/2013.

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