The results were divided into two parts. First, an analysis of drought events and index values was carried out, taking into consideration the Target Levels, for the period from 2002 to 2020. The second part involved assigning values for the weights of the criteria (robustness, treatability, transparency, sophistication, extensibility, and dimensionality), which were defined according to their relative importance to the drought indices. Scores were also established for the main characteristics of the indexes, which were defined based on the analysis and performance of each tool. As a result, it was possible to list the best indices to be used in the hydrological monitoring of the study area.
3.1. Indices Analysis in Relation to the Target Levels
From the comparison of the values of the annual volumes of the Castanhão, Orós, and Banabuiú reservoirs with the Target Levels, it was possible to quantify and categorize the drought events that occurred in the period from 2002 to 2020 in each system. Based on this identification, a detailed analysis of the index values and the drought events they are able to identify was carried out in order to represent the hydric state of the reservoirs analyzed.
3.1.1. Index Analysis
The analysis of the indices, in relation to droughts, aimed to capture the sensitivity of each index in representing—or not—the drought state of the reservoirs. To this end, all index values were compared with the ratings of the Target Levels in order to quantify the events that each one was able to capture.
, Table 11
and Table 12
show the reference dates for the index calculation, as well as the volumes of the reservoirs in that period. In addition, the ratings of the Target Levels and the index values with the colors corresponding to the Target Levels are presented.
For the Banabuiú reservoir (Table 10
), Target Level 1 corresponded to the years 2004 to 2006 and 2008 to 2012, having been well captured by SWSI—12 and RDI. The other indexes had difficulties in representing this event. Target Level 2 was portrayed by the years 2007 and 2013, and only SPI—12, SPI—36, SDI—12, and SDI—36 were able to capture this event. Target Levels 3 and 4 were evidenced in 2002 to 2003 and 2020, respectively, where no index was able to identify them. Target Level 5 is equivalent to the period from 2014 to 2019, being captured at times by the SWSI—12, RDI, and SPI—36.
The Castanhão reservoir (Table 11
) presented Target Level 1 in the years 2004 to 2006 and 2008 to 2012. These years were identified by SWSI—12 and RDI; the other indexes presented limitations to capture these events. Target Level 2 was displayed in the years 2007 and 2013, and only SPI—12, SPI—36, SDI—12, SDI—36, and EDDI—12 were able to identify these events. Target Level 3 was observed in 2014, being captured only by EDDI—12. Target Level 4 corresponded to the years 2015 and 2020 and was identified by SWSI—12, SDI—12, SDI—36, SPI—12, and EDDI—12. Target Level 5 appeared in the period from 2002 to 2003 and 2016 to 2019 and was captured by SWSI—12, RDI, and SPI—36.
The Orós reservoir (Table 12
) presented the Target Level 1 in the years 2004, 2006, and 2008 to 2012, being identified by SWSI—12 and RDI; the other indexes captured few events of hydric normality. Target Level 2 was observed in the years 2005, 2007, 2013, and 2014, being captured at times by SDI—12, SDI—36, SPI—12, SPI—36, and EDDI—12. Target Level 3 appeared only in 2015 and was identified only by SPI—12. Target Level 4, on the other hand, appeared in the years 2002, 2003, 2016, and 2020, being picked up by SWSI—12, RDI, SPI—36, and EDDI—12. The period from 2017 to 2019 was marked by Target Level 5, being identified by SWSI—12, RDI, SPI—36, and EDDI—12.
3.1.2. Quantification of Drought Events according to Their Severity
includes the drought events quantification that each index was able to identify, according to severity. SWSI—12 and RDI were able to detect all the normality events that occurred in the three reservoirs (as specified in Table 8
). Regarding Target Level 2, SPI—36 was the index that presented a greater capture of these episodes. The events occurring at Target Level 3 were identified only by SPI—12 and EDDI—12. Target Level 4 was captured, at times, by all the indices. However, SWSI—12 performed better in this distinction. Target Level 5 was identified by SWSI—12, RDI, SPI—36, and EDDI—12.
Consequently, out of the total 11 drought events for Bananabuiú, SPI—36 was able to record 3, followed by SWSI—12 and RDI, which were able to identify 2, and lastly, SDI—12, SDI—36, and SPI—12, which were only able to capture 1. In this same context, Castanhão also exhibited 11 years of drought, of which 4 years were identified by RDI, 3 years by SWSI—12, SPI—12, SPI—36, and EDDI—12, and 2 years by SDI—12 and SDI—36.
The Orós reservoir exhibited a 12-year drought and the index that had the greatest ability to identify these events was SPI—36, which captured five episodes. The SWSI—12 and SPI—12 were able to register four events, followed by RDI and EDDI—12 with three events, and finally, SDI—12 and SDI—36 with only two events.
3.1.3. Quantification of Drought Events Regardless of the Severity
A survey was carried out on the ability of each index to identify drought, regardless of severity (Table 14
), i.e., at how many times did the index indicate that it was or was not in drought, even if this did not correspond to magnitude of the Target Levels.
Of the 11 drought events registered for Banabuiú reservoir, the indexes that managed to identify the most episodes was the SPI—12 and the SPI—36 (11 events), followed by the SDI—12 and SDI—36 (7 events), RDI (7 events), SWSI—12 (5 events), and EDDI—12 (2 events).
As for the Castanhão reservoir, there is the SPI—36 and EDDI—12 with the identification of 11 events, followed by SPI—12 with 10 events and SWSI—12, RDI, SDI—12, and SDI—36 with 7 episodes each.
For the Orós reservoir, the SPI—36 and EDDI—12 indices were able to identify the 12 drought episodes. While the SPI—12 captured 11 events, the SDI—12 and SDI—36 identified 9 events each, and the SWSI—12 7 and the RDI identified 6 events each.
3.2. Comparative Evaluation of Drought Indices
Robustness was chosen as the most important criterion and received the maximum score regarding the weights, i.e., value of 8 and relative importance of 27%. SPI and EDDI were quite responsive in detecting drought conditions in the study region, where the former was very sensitive to precipitation variations and the latter to potential evapotranspiration variations. However, these indices do not take into account the variability of water resources within the basin. Therefore, for the robustness criterion, SPI and EDDI received a value of 4.
The SWSI and RDI are hydro-meteorological indexes, in which the former uses three input variables (precipitation, affluent streamflow, and reservoir volume) in its composition and the latter uses four (precipitation, affluent streamflow, volume, and temperature). This range of variables allows the indexes to analyze not only factors related to precipitation but also to water availability in the reservoirs. Thus, the SWSI and the RDI showed good capture of drought according to its severity, managing to identify, at some times, more drought episodes than the SPI. However, regardless of severity, these indices tend to capture less than 65% of the occurred episodes when analyzing the occurrence of drought events. For this reason, the score assigned to the two indices for the robustness criterion was 3. The SDI, on the other hand, presented a lower identification of drought in relation to its magnitude but exhibited a good capture of the events regardless of severity, so the robustness score for it was 3.
The treatability received the weight of 6 (20% of relative importance), because the institutions responsible for monitoring droughts in Brazil, such as FUNCEME, tend to opt for more treatable indices, as these are easier to be implemented and generated. Regarding the treatability criterion, the indices were evaluated in relation to the ease of calculation (number of steps) and the required input variables.
Thus, SPI obtained the highest score (4) in relation to the other indexes since it uses precipitation data only in its formulation (easily accessible data) and it presents three calculation steps.
Although the EDDI requires only PET data and displays, like the SPI, three calculation steps, the data available for calculating the index have a more restricted access and often flaws in its construction. For these reasons, a rating of 3 has been assigned to the EDDI.
SDI, like SPI and EDDI, requires only one input variable, which in this case is the streamflow. SDI calculation is more complex and covers five steps, so SDI was given a score of 3.
SWSI and RDI are more complex to calculate and have more input variables involved. However, RDI needs one more variable (air temperature near to surface) and its calculation has more steps when compared to SWSI. Thus, SWSI received a score of 3 and RDI a score of 2 for the treatability criterion.
Transparency was given a weight of 5 (17% of relative importance), as the indices used in drought monitoring are expected to be easily understood by the general public. In this way, the indexes can help, for example, farmers to define the best time to plant, or the managers of water resources to determine the moment of release or storage of water in reservoirs.
Essentially, the indexes presented in this paper are easy to understand by researchers and professionals in the area but are not well understood by the general public. Therefore, SPI and SDI received a score of 3, and the other indexes (SWSI, RDI, and EDDI), for being more complex, received a score of 2.
Since the goal of this work is to identify the indices that can be used for hydrological monitoring of the Castanhão, Banabuiú, and Orós reservoirs, and this identification is related to a series of hydro-meteorological factors, the use of more sophisticated tools is necessary. However, one of the disadvantages of more complex approaches to identify droughts is that they usually require greater availability and quality of data, which makes them less transparent and less tractable. In addition, indices that have a greater number of input parameters tend to be more sophisticated, so this variety of parameters allows the index to better assess the conditions that influence drought events.
Thus, the weight of 6 was assigned to the sophistication criterion, which has a relative importance of 20%. The SWSI and RDI indices received the highest scores (5) because they require a greater number of input data. Their calculations are based on hydro-meteorological variables, and both exhibit the ability to identify drought events according to their magnitude. As for the other indices, SPI, SDI, and EDDI, a score of 3 was given, as they are less sophisticated indices when compared to SWSI and RDI.
Extensible indices present greater importance for decision makers, as they devise action plans based on previous droughts. In this case, extensibility received a weight of 3 (10% relative importance), because its relevance is lower when compared to the previously mentioned criteria. So, it was considered more important the index’s ability to identify droughts, its degree of sophistication, than if it were easy to understand and with a simpler calculation.
Precipitation data series is long (more than 40 years), which allows the indexes that depend on this variable to analyze the behavior of droughts in the past and identify behavior trends for these events. On the other hand, the affluent streamflow can be estimated by rainfall/flow hydrological models [56
], which are calibrated by means of variables such as precipitation, so that the series obtained are simulated and not observed. In this case, one can have a generation of very extensive hydrological series, thus allowing the index expansion.
The reservoir volume (water level) data are limited to the beginning of reservoir operation, which hinders the extensibility of the index, since many reservoirs were built recently, as is the case of the Castanhão (2002). As an alternative for the extension of these data, there is an equivalent reservoir approach, which aims to reproduce the characteristics of that body of water in order to simulate volume and level data. However, this is not a widespread technique among data provider institutions, so they end up providing only the series of volumes collected after the beginning of reservoir activities. Thus, even if it is possible to obtain extensive precipitation and streamflow series, the volume data would end up limiting the period for calculating the indices.
The same analysis can be performed for potential evapotranspiration data, since they need the temperature to be calculated, as in the method from [57
], or other components (wind speed, insolation, and relative humidity) to use the Penman–Monteith estimation. This need for other variables ends up limiting the size of the potential evapotranspiration series because not all rainfall stations have sensors to detect local temperature or collect the other necessary data.
Based on the aforesaid, the SPI received the highest extensibility score (5), for being an index that uses only precipitation as an input variable, which enables expansion and, consequently, a better analysis of past droughts. The SDI was assigned a score of 3 because it uses streamflow in its equation and presents limitations regarding these data since they come from hydrological models.
SWSI and EDDI received the same scores (3), which are justified by the fact that SWSI presents more input variables, which can directly impact the expansion of its values since the reservoir volume is a limiting data. Concerning EDDI, the evapotranspiration data may present flaws or even be absent, thus making it impossible to expand the index.
RDI was the index that received the lowest score (2) because besides using the same data as the SWSI, it also incorporates temperature, which can be limiting data for the expansion of this index to the regions.
For the dimensionality criterion, it is desirable that the index has a simple unit with physical meaning, such as m3
of water volume and percentage of rainfall, rather than dimensionless or complex units [8
], to allow the index to connect clearly with the physical conditions of the environment. Thus, simpler indices such as standardized anomalies and percentiles are advantageous for comparing resources across locations and time periods.
In this case, weight of 2 (6% relative importance) was assigned to this criterion, since part of the drought indices discussed in this paper exhibit more complex or dimensionless units. Regarding the scores, the indices SPI, SDI, and EDDI received the highest values (4), which are justified by their simplicity and the fundamental units they represent. Meanwhile, the SWSI and RDI received a score of 3, as they are more complex indices that display dimensionless information.
3.2.7. Analysis of the Results between the Indexes and the Decision Criteria
Based on the qualitative and quantitative evaluations, this study points out that SPI is better than SWSI, EDDI, SDI, and RDI for quantifying drought conditions in the Banabuiú, Castanhão, and Orós reservoirs. Thus, the total scores assigned to the indices were 118 for SPI, 97 for SWSI, 95 for EDDI and SDI, and 88 for RDI (Table 15
The result regarding SPI has already been pointed out in previous works, such as those from [8
], which determined that this index was one of the most suitable to be used in the monitoring of meteorological drought.
Within this context, the SPI ranked well on all six decision criteria because it has a good ability to measure drought over a wide range of conditions and can be calculated for various scales of interest (monthly, quarterly, semiannual, annual, biennial, and triennial), is spatially and temporally comparable, and has a simple calculation. Moreover, it uses only one input variable (precipitation), its values are easily understood by the scientific community (positive values indicate wetter than normal conditions and negative values indicate drier than normal conditions), its time series can be extended, and the index values can be compared to fundamental units. However, Quirind (2009) points out in his paper that SPI has limitations in arid locations, which exhibit seasons with no precipitation.
The SWSI has also been evaluated in relation to the criteria by the researchers [17
], where the former attributed a higher score to the SWSI in relation to the SPI because it was considered more robust and sophisticated. On the other hand, the second study pointed out that the SPI is superior to the SWSI in the six criteria used, and therefore attributed a lower score to the SWSI.
Thus, when compared to the other indexes, the SWSI was identified as the second best to identify droughts in the reservoirs under study. It showed a good capacity to identify drought episodes according to magnitude, however, it showed limitations to capture these events despite the severity. The SWSI can also be calculated for various time spaces, being spatially and temporally comparable, but it presents a greater complexity of calculation, with more variables involved, which makes it difficult for users to understand. Its series can be extended; however, the volume data are a limiting factor, and its values are dimensionless.
EDDI and SDI ranked third, and both received the same score, differing in the criteria of robustness, transparency, and extensibility. First of all, EDDI proved to be more robust than SDI, as it was able to better capture the drought conditions of the reservoirs. Regarding transparency, EDDI obtained a lower evaluation than SDI, because it presents a more complex calculation methodology, and more difficult to understand by final users. In the extensibility criterion, EDDI also obtained a lower score, because the calculation of potential evapotranspiration needs other variables, which may limit the index expansion.
RDI obtained the same scores for robustness, transparency, sophistication, and dimensionality as SWSI, because they are similar indexes in construction and input variables. The criteria for differentiation between them were treatability and extensibility, as the RDI presents one more variable than the SWSI and a more complex calculation methodology. In addition, the RDI presents more restrictions to be extended, considering that it uses two variables (volume and temperature), which present limitations in obtaining and extending.