1. Introduction
Drought is one of the most serious and complex threats that humankind must deal with. According to the Food and Agriculture Organizatio (FAO) (2018) [
1], for the 2005–2015 period, drought was the most expensive disaster in Latin America and the Caribbean. The associated losses for that lapse of time reached US
$13 billion and were related with crop and livestock affectations. South and Central American economies rely significantly on rain-dependent crops, i.e., about 80% of total regional agricultural yield production is related to rain-fed crops [
2]. Moreover, a large percentage of the GDP of these countries is associated with agriculture [
2], and the zone produces and exports almost 11% of the global food supply [
3]. Particularly vulnerable areas include north and central regions of Chile, the northern region of Mexico, and the northeast region of Brazil [
4]. In the first case, the 1968 drought event caused an approximated loss of 1 billion dollars, as well as a national decrease of 45% in cattle mass and 40% in irrigated surface, apart from an increase of 250,000 unemployed people [
4]. Specifically, in Colombia, the 2015–2016 drought episode, related to El Niño South Oscillation (ENSO) large-scale climate anomalies, generated reductions of 50%, 44%, and 27% in barley, corn, and wheat yields, respectively. In addition, the energy spot price increased by about 900%, 38,000 animals died in the husbandry industry, and there was drinking water rationing in Medellin and Cali, the two larger cities of the country after the capital Bogotá [
5].
Despite the significant socioeconomic effects of drought, its characterization is challenging for two key reasons. First, each drought event has an important and independent spatial and temporal variability [
6,
7,
8,
9,
10,
11]; hence, it is possible to consider that every occurrence is different from others, and it is challenging to determine its starting and ending dates, and its spatial extension. Second, there is no unique technical definition of drought, and therefore it is easier to describe it in terms of its associated impacts [
12,
13]. Drought monitoring is also challenging because there are diverse methods to characterize, track, and enclose the spatial expansion of these events.
Frequently, drought is defined in terms of its influence on different hydrological and socioeconomic parameters. The most usual classification divides droughts into four types: (i) Meteorological drought [
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24], (ii) Hydrological drought [
13,
14,
25,
26,
27,
28,
29,
30,
31], (iii) Agricultural drought [
7,
13,
25,
32,
33,
34,
35,
36,
37,
38], and (iv) Socio-economic drought [
13].
Typically, drought is quantified and studied using drought indices. These are simply indirect indicators based on climatic data (usually rainfall and temperature), which allow the objective and quantitative evaluation of drought gravity [
39], as well as the definition of different drought parameters like severity, duration, and intensity [
13]. The most common indices include the Percent of Normal Precipitation Index (PN) [
40], the Standardized Precipitation Index (SPI) [
41], the Palmer Drought Severity Index (PDSI), the Moisture Anomaly Index (Z), the Palmer Hydrological Drought Index (PHDI) [
42], the Reconnaissance Drought Index (RDI) [
43,
44], the Standardized Precipitation-Evapotranspiration Index (SPEI) [
45], and the Streamflow Drought Index (SDI) [
46], among others. To rigorously assess droughts, a new set of Non-Parametric Indices (NPI), which account for non-stationarity of hydrological series and are calculated using daily information, were developed by Onyutha [
47].
Hydrologic frequency analysis aims to study historic data to estimate future probabilities of occurrence [
48,
49]. However, frequency of occurrence alone, when analyzing droughts, may be inadequate unless it is quantitatively related to other specific characteristics, such as duration, severity, intensity, or areal extent [
50,
51]. In other words, droughts are dynamic and have different characteristics that should be simultaneously considered when evaluating their associated risk [
51]. In view of this, numerous multivariate tools for drought research have been developed and applied extensively. These analysis methods include Severity-Area-Frequency (SAF) curves, Severity-Duration-Frequency (SDF) curves, and Severity-Area-Duration (SAD) curves [
50,
51,
52,
53,
54]. For a particular drought index, SDF curves indicate the severity value for a specific drought duration and a given return period [
50,
51,
55,
56].
In the application of SDF curves on a regional basis, various studies have mapped drought iso-severity contours, using point SDF information. These studies include maps for Greece [
50], Iran [
55], Italy [
51], and climatologic homogenous regions of the U.S. [
19]. Additionally, other spatially distributed applications of drought indices are studies from Bonaccorso et al. (2003) [
26], Vicente-Serrano (2006) [
57], Raziei et al. (2009) [
8], Santos et al. (2010) [
9], Martins et al. (2012) [
10], Paparrizos et al. (2016) [
15], Wang et al. (2015) [
11], Zhu et al. (2016) [
58], Ayantobo et al. (2017) [
59], Dabanlı et al. (2017) [
16], and Kaluba et al. (2017) [
17].
However, the aforementioned cases do not end up in specific values of drought severity associated to a given duration and return period for the entire study area. There is a strong chance that, if regional values among catchments are compared and results for indices that identify same type of drought are contrasted, it allows the setting up of a stronger study case-comparison for same type-droughts. Regional SDF curves could help to classify historic regional drought events according to their frequency, being more accurate than using arbitrary intensity-based classification for different drought indexes [
41,
42].
To achieve the above aims, this study compares two basins in Colombia. Monthly historic data from available hydro-meteorological stations was used to calculate the selected drought indices time series and construct point SDF curves, for subsequent regionalization and comparison between the two basins. Consistency among indices was evaluated for the same types of drought (meteorological, agricultural, and hydrological). For both basins, historical regional drought occurrences were selected and identified in the corresponding SDF curves to determine their gravity. Results of this study could contribute to regional monitoring and assessment of different types of droughts.
3. Results and Discussion
3.1. Regional SDF Curves
The regional SDF curves for the two case studies were compared to assess the consistency of different drought-index methods to classify the seriousness of the drought events, according to their type. As mentioned before, for the majority of DI, regionalization process was carried out by spatial interpolation of severity values obtained from point frequency analyses. In this sense, iso-severity maps constructed for maximum possible durations and return period (50 years) are displayed in
Figure 5. It is notable that the location of more severe areas varies between DI methodologies. This feature is related to two relevant factors of the stations and datasets employed: (i) Variability in the length of climatic-parameters series between catchments, and between same-catchment-stations; and (ii) Differences in the spatial distribution of measuring-stations density in both case studies. The first consideration is associated with the available data for event identification and the reliability of performed frequency analysis, as well as with the regionalization of useful stations, given that each presents a diverse group of durations (according to the number of recognized drought events), and the spatial interpolation process requires a majority of stations to have a certain common duration value. The second issue is linked to the quality of the spatial interpolation procedure, which is clearly influenced by stations-proximity and catchment extent.
Additionally, it is important to mention that, as can be seen in
Figure 5a, the most severe drought occurrences are concentrated on the southern and eastern regions of the LRB, except for SPI3 and SPI6, which showed higher magnitudes for stations located on the western zone of the catchment. In the SRB case study (see
Figure 5b), severity spatial distribution showed lower consistency among the DI than in the LRB. Therefore, it was impossible to define a specific basin zone for which severities were shown to be larger in the SRB case study. The discrepancies described above could be fundamentally attributed to the fact that the analyzed basins were located in different hydrological zones, which implied that the particular features of the dry spells that affected them also varied. In addition, the previously-described stations and dataset characteristics, strongly influenced the spatial interpolation results.
Regional SDF curves for the two study areas are depicted in
Figure 6, showing that for any drought index, the regional SDF curves show similar behavior for both catchments. This fact supports the conclusion that frequency analyses maintained a distinctive relationship between severity and duration, for all drought indices. As expected, magnitudes of severities and durations for a given return period differed between catchments, which could be acceptable given that the specific hydrological attributes of both case studies (i.e., spatial distribution of stations, rainfall and temperature magnitudes, regularity of extreme event occurrences, etc.) affected the results, as mentioned before.
Specifically it was found that, for the same return period, PN, Z, and PHDI exhibited duration dependency. The first two methodologies consistently identified that the LRB presented larger gravities than the SRB for short durations (i.e., 1 to 4 months), whilst this behavior was reversed for higher durations (i.e., 5 months onward). PHDI showed that for durations between 1 and 4 months, the LRB presented larger severity values, whilst for durations of 5 months or more, the SRB surpassed it. Additionally, the LRB presented more serious occurrences identified through SPI6, SPI9, PDSI, RDI, and SDI. Remaining methodologies (SPI1 and SPI3) showed that the SRB drought events displayed larger magnitudes.
The results shown revealed the existence of a certain degree of consistency in regional-SDF curves. In this regard, PN and Z showed agreement on the identification of the study-area that displayed the most serious drought-events. Furthermore, in that particular case, concordance was reached even when differentiating outcomes depended on duration. Concurrence on the detection of the zone with the most severe same-type droughts was achieved for three more cases: (i) SPI1 and SPI3 (meteorological drought); (ii) SPI6, PDSI, and RDI (agricultural drought); and (iii) SPI9 and SDI (hydrological drought). Finally, the PHDI comparison was ambiguous given that it derived from duration–reliance results that showed no coherence with any other methodology.
According with specific DI outcomes, it was possible to define four groups of indices in terms of their compatibility between catchments: (i) PN and Z; (ii) SPI1 and SPI3; (iii) SPI6, PDSI, and RDI; and (iv) SPI9 and SDI. PHDI could not be included in any of the categories because of its lack of complete agreement with other indices that identify hydrological droughts. This grouping was useful because it facilitated the identification of DI methodologies that led to consistent results, and thus, in terms of regional planning and operation, allowed those indices with simpler calculation procedures and fewer information requirements to be selected as monitoring tools, optimizing work and resources. With this in mind, for each of the defined categories, the most appropriate operational DI would be: (i) PN; (ii) the calculation method that remains the same, so that any of the indices might be used; (iii) given that calculation methodology remains the same, data requirements were lower in SPI6 than they were in PDSI; and (iv) depending on available data (rainfall or streamflow), any of the options could be adopted.
3.2. Location of Regional Drought-Events on Regional SDF Curves
Once regional SDF curves were constructed and interactions between them were explored, the next step consisted of locating historical drought-regional events, derived from datasets built from drought-indices. To identify time periods for which a significant number of stations showed drought, these occurrences were pinpointed. Once identified, spatial interpolation of drought-severities and durations was carried out, employing the same methods as SDF curves regionalization. In this way, the specific location of events over regional SDF curves were defined and their associated return period determined.
Table 4 summarizes some important statistics for identified regional drought events, which were later located over constructed SDF curves. Apart from including statistics for severity and duration parameters, regional intensity measures were also included.
The results of event-location on SDF curves are presented in
Figure 7a (LRB) and
Figure 7b (SRB).
Table 5 contains a summary of Pearson linear correlation coefficients, computed to compare the consistency of different DI methodologies to identify regional occurrences. In this respect, the SPI3 case was notable given that it could be considered as transitional between the meteorological and agricultural drought types, and for that reason, it was compared to the DI of both categories.
Figure 6 displays the box-whisker diagrams constructed to compare the behavior of regional event durations and return periods among different DI, for the same drought type.
Table 4 and
Figure 7 identify the drought-type that displayed the highest number of regional occurrences. It was observed that meteorological drought was the most common type for both case studies (28 to 73 events in the SRB and 34 to 81 events in the LRB); agricultural drought was the second most frequent type, varying from 12 to 16 events in the SRB and from 13 to 20 events in the LRB, and the most infrequent drought type was the hydrological, with 13 to 22 episodes in the SRB and 10 to 12 in the LRB. These results were expected given the longer duration of hydrological droughts, which make them less likely to occur than the agricultural or meteorological droughts. Additionally, as will be reinforced with the results outlined below, it was found that the majority of analyzed regional events displayed return periods between 2 and 5 years, which in general terms can be considered as low.
Table 5 presents computed results after comparing duration and return period series obtained through studied DI methodologies. The main goal of this analysis was to assess the consistency of the results for different calculation procedures, with respect to the specific parameters of duration and return period series. In this sense, high values of correlation would indicate that DI methodologies could single out similar drought events, at least for duration and occurrence frequency.
Firstly, correlation values concluded that among methodologies, for both study catchments, duration series tended to be more consistent than return period series. This conclusion arose from the fact that a higher number of significant correlations were found on the duration side of
Table 5 (13 of 30 evaluated correlations), than on return period side (7 of 30 evaluated correlations). Significant values were defined as those higher than 0.5, and they are shown in bold on
Table 5. Secondly, it was found that higher correlations were present for the SRB than for the LRB. In the case of duration series, the SRB displayed 8 of the 13 significant correlations, whilst for frequency series, it had 5 of 7. Thirdly, it was observed that correlation coefficients for durations were significantly higher than those obtained for return periods. These results supported the conclusion that frequencies obtained through SDF regional curves, unlike durations, were highly influenced by the regionalization process. Fourthly, when analyzing relationships connected to drought type (see
Table 6), the analysis found that correlations among durations tended to be higher for meteorological and hydrological droughts, than they were for agricultural droughts. In the case of frequency, the behavior was less clear, with SRB reacting in the same way as duration. Meanwhile, LRB showed larger coefficients for hydrological drought, followed by agricultural, and then meteorological. Finally, almost all of the correlation coefficients displayed a positive figure (50 of 60 evaluated correlations), which implied that for both studied parameters, correlations tended to be direct among different DI methodologies.
An analysis of the distribution of duration and return period data, obtained through different DI methodologies was carried out by means of box-and-whisker diagrams. These were constructed independently for LRB (
Figure 8a) and SRB (
Figure 8b). This procedure sought to evaluate consistency in duration and return period results for regional events, after characterizing both of these using regional SDF curves. For that reason, DI were grouped by drought type and each group was compared independently.
Firstly, as was previously mentioned, Box plots (
Figure 8) showed that most of the identified regional events, through all the studied methodologies, displayed low return periods (between 0 and 10 years for all the DI). This could be related to the length of record employed to build the point DI series, as well as with the consistency of the identification of occurrences between stations, which classified an event as regional or not. Therefore, the importance of using datasets with a relatively long length emerged as one of the key conditions for obtaining more accurate regional analysis and identifying more high-frequency occurrences, which may be useful in the study of convenience for generated SDF areal curves.
Secondly, contrasting with the results from the Pearson correlation coefficients (
Table 6), the same regional events displayed as notched box plots allowed different DI calculation procedures that were consistent with each other to be observed, with regards to duration and frequency data distribution. The box notch shows the confidence interval around the data median. Although not a formal test, if two box notches do not overlap, it is possible to consider that there is strong evidence with a 95% confidence level, that the medians of the two datasets are different. In this case, it was found that the notches corresponding to boxes of DI methodologies that identified the same type of drought tended to overlap, except for the SPI3 case which showed its transitional nature by not adjusting to the behavior of either meteorological or agricultural droughts. Moreover, it was observed that duration data distribution was more compact than frequency grouping; in other words, duration data displayed lower variability than the return period. Higher differences among DI arose from whisker length, box width, and the number and magnitude of observations outside of the whisker (i.e., possible outliers). All the mentioned discrepancies could be related with individual procedure features which determine particular data distribution, as well as with the sensitivity that durations and frequencies displayed to the regionalization process.
Finally, a relative consistency for the identification of serious events was found for both case studies using different methodologies, i.e., occurrences identified as ‘outliers’ tended to be persistent amongst calculation procedures, for both duration and frequency. Furthermore, it was found that the most severe occurrences tended to greatly impact socio-economic regional issues. For example, the previously described late 2015 and early 2016 dry period in the SRB was identified as an event with a significantly high return period by SPI3, SPI6, PDSI, and PHDI. This was not exactly an atypical value for all DI distributions, but certainly one of the higher return period values found. These results allowed this occurrence to be considered an agricultural drought for this catchment, due to the majority of methodologies that recognized it, and so it led to this conclusion. However, this drought-classification may not be taken as absolute since it also could be considered as a meteorological or hydrological-type drought, because of the SPI3 and PHDI results. The same drought episode in the LRB case study was cataloged as severe by PN, SPI3, SPI6, SPI9, and RDI. Therefore, in that case, the analyzed event could be considered transitional between a meteorological and an agricultural drought, and it also could be concluded that the occurrence was more serious than the one in the SRB, because of the number of indices that identified it. These results reaffirmed the spatial differences that the droughts exhibited when comparing distant catchments, and it confirmed that the particular characteristics of study areas defined the presence and impacts of a dry spell.