Hydrological system time lag responses to meteorological shifts Defasagem temporal de resposta do sistema hidrológico sob mudanças meteorológicas

Hydrological system’s sensibility and resilience to dry periods are crucial for estimating the potential impacts of droughts. Quantifying response times (RT) of this system’s components relative to droughts allows one to develop a predictive understanding of future impacts. In this context, this study proposes the use of non-parametric statistical methods to estimate RT between meteorological shifts, given by the Standardized Precipitation Index (SPI), and the respective changes in the hydrological system, measured by river discharge (Q) and reservoir storage time series. Change point (CP) analyses were applied to time series of (i) SPI and accumulated storage relative to 32 reservoirs within the Paraná basin; and (ii) SPI, Q and reservoir storage relative to Furnas hydroelectric power plant. Based on the responses from CP analyses, RT in case (i) varied from 0 – 6 months, whereas, in case (ii), results indicate that significant changes in Q occurred in the same month of changes in rainfall. Results also suggest a minor role of anthropogenic factors (dam operation) compared to natural forcing in reservoir depletion during the 2014 drought than that in 2000/2001. This study reinforces the importance of an optimized reservoir management, considering the balance between anthropogenic and natural forcing as a strategy to combat droughts impacts.


INTRODUCTION
Climate extremes, commonly reflected in the hydrological system as natural disasters, often bring negative impacts on society.Natural disasters, such as droughts, can cause major impacts on water supply and electricity generation.Between 1970 and 2012, droughts were responsible for ~1/3 of disaster-related deaths and ~US$ 200 billion of economic losses globally (WMO, 2014).In Brazil, two major droughts affected millions of people in the current millennium by jeopardizing (i) hydroelectricity generation in the early 2000s, which caused the implementation of energy-rationing programs and blackouts, and (ii) potable water supply for ~130 cities in the southeast region (ROSA; LOMARDO, 2004;LOBEL et al., 2014).
Droughts can be classified according to the following types: meteorological (abnormal negative precipitation anomaly), agricultural (abnormal low soil moisture), hydrological (reduced streamflow, low water table levels, etc) and socio-economic (failure to supply the demand of economic goods, such as potable water, food grains, hydroelectric generation, etc) (WILHITE; GLANTZ, 1985).
Although this distinction is often neglected in droughtrelated studies, it is necessary for characterizing the impacts on different components of the hydrological system.Ignoring this distinction may lead to some problems, such as propagating misleading information.Wilhite and Glantz (1985) revised some cases worldwide in which droughts were estimated to have had a certain duration but, as meteorologists analysed the precipitation in the region, initial estimates were proved to be inaccurate.Such divergences were caused because a clear distinction between types of droughts was lacking.
Several studies focused on understanding how the meteorological drought propagates to socio-economic drought (VAN LOON; VAN HUIJGEVOORT; VAN LANEN, 2012;BARKER et al., 2015;WANG et al., 2016;FIORILLO;GUADAGNO, 2010;TIGKAS;VANGELIS;TSAKIRIS, 2012).Quantifying linkages between types of droughts requires continuous monitoring of drought indicators and is critical for drought preparedness.Although meteorological droughts cannot be avoided, the society can take measures to mitigate hydrological and agricultural droughts, for example.As reported by Barker et al. (2015), hydrological responses to meteorological droughts occurs after a certain time interval, that is, hydrological and meteorological droughts are lagged events.
As previously mentioned, meteorological drought occurrence is, essentially, human independent; but its effect on the hydrological system depends on the actions taken by society.In this definition we are not considering man induced climate changes, since this issue is out of the scope of our analysis.Additionally, it may be utopic to assume that the end of a meteorological drought is instantaneously followed by the end of a hydrological drought.Leblanc et al. (2009) reported a continuous decline of groundwater storage even 6 years after the onset of the meteorological drought and a persistence of the hydrological drought although rainfall was close to the historic annual average in the sixth year.
Previous estimates of the time lag between the onset of meteorological droughts and the impacts on the hydrological system ranged from few months (BARKER et al., 2015;VICENTE-SERRANO;LÓPEZ-MORENO, 2005) to few years (LEBLANC et al., 2009;VAN DIJK et al., 2013;BARKER et al., 2015).Quantifying such time lags is crucial to anticipate the associated impacts and implement mitigation measures to minimize such impacts.
However, none of the previous studies assessed the proper method to calculate the time lag between meteorological shifts and hydrological responses.Adopted approaches are widely different amongst studies.Van Dijk et al. (2013) compared timing of occurrence of minimum values of average precipitation anomalies and total water storage.Vicente-Serrano and López-Moreno (2005) calculated correlation coefficients (CC) between reservoir storage and the Standardized Precipitation Index (SPI) at different time scales and assuming that the time lag is given as the time scale with higher CC.
In this context, the objective of this study is to quantify the time lag between meteorological shifts, measured by means of SPI, and the hydrological system response in the Paraná basin.To achieve this goal, non-parametric statistics-based approaches (change-point analysis) were applied to rainfall, river discharge and reservoir storage time series.This analysis was carried out considering two cases.First, the time lag between changes in SPI and water storage of 32 reservoirs in the Paraná basin was evaluated.Second, a reservoir within the Paraná basin was selected as a case study with the objective of evaluating the response time lag in river discharge as well.
To the authors' knowledge, the use of change-point analysis with the proposed end is unprecedented and unique; furthermore, it can provide trustful and valuable insights for water resources planning in the context of droughts preparedness.

Study area
The reservoirs within the Paraná basin (PB) (~880,000 km 2 ) were selected as a case study due to the importance of this basin for the country (Figure 1).The PB, southeast Brazil, is the most populated basin in Brazil, accounting for ~55% of national Gross Domestic Product (GDP) in 2012 and ~65% of national population; it produces ~60% of the hydroelectricity in Brazil and provides ~25 km 3 /yr of surface water for several uses (ANA, 2010;IBGE, 2014).
The time lags between meteorological forcing and hydrological responses were evaluated considering the 32 reservoirs as an equivalent system and a typical case within the Paraná basin.Reservoir storage of the equivalent system (RESS) was obtained by accumulating monthly storage data of the selected reservoirs.To calculate SPI, the rainfall in the contributing basins of the 32 reservoirs was averaged.The reservoir of Furnas hydroelectric power plant (HEP) (Figure 1) was selected as a detailed case study in the PB because the monthly storage variation is similar to that of the equivalent system.Further information about the reservoirs is shown in Table 1.
Reservoir storage data from 32 reservoirs (Table 1) and inflow/outflow records from Furnas HEP were downloaded from the Brazilian Water Agency (ANA -Agência Nacional de Águas) web site (http://sar.ana.gov.br/MedicaoSIN),considering the period Jan 1995 -Jun 2015.The data is available at daily scale.Because SPI is given as monthly values, reservoir daily data were averaged to obtain monthly time series.Seasonal signal from the discharge data was removed prior to the change point analysis by subtracting monthly data by the monthly means ( , , ,

Meteorological drought index
The Standardized Precipitation Index (SPI) is a traditional choice for characterizing meteorological droughts as it provides information concerning positive/negative anomalies in rainfall, at different time scales (e. g., VICENTE-SERRANO; LOPEZ-MORENO, 2005; FIORILLO; GUADAGNO, 2009) based on historical records.To calculate SPI, rainfall records are fit to a probability function, usually Gamma, and the cumulative probability of rainfall occurrence over an area is obtained (MCKEE;DOESKEN;KLEIST, 1993;TEODORO et al., 2015).In this study, SPI was obtained at a 12-month scale (SPI-12).

Change-point analysis
There are several approaches available for detecting change point (CP) in time series (PETTITT, 1979;SHARIFZADEH;AZMOODEH;SHAHABI, 2005;RADZIEJEWSKI;BARDOSSY;KUNDZEWICZ, 2000;LAVIELLE, 1999;SHI et al., 2016).However, each approach may result in different results depending on the employed method.A time series may contain change in mean, variance, regression or time-dependency.Here, only the changes in the mean were considered.In this study, various non-parametric methods were used.
One of the selected approaches for such purpose is that proposed by Pettitt (1979), previously used to determine change points in streamflow and sediment discharge time series (GAO et al., 2011).This method is based on the Mann-Whitney test but the calculated statistic ( , t T U ) is given by: ( ) where 1 X , 2 X , …, T X are the values in the time series X, sgn , 1979).After computing the statistic , t T U for all t = 1, 2, …T, the test statistic The significance probability associated with T K is, thus, obtained as: .Here we adopted a significance level of 0.01, hence, lim p 99% = .
The second approach is similar to that applied by Gocic and Trajkovic (2013) to detect changes in meteorological variables; it combines cumulative sums (CUSUM) with data resampling using bootstrap method (EFRON, 1979).Our analysis is based on 1000 bootstrap samples.Given a sample data vector X = { 1 X , 2 X , …, T X }, where T is the vector length, the cumulative sums 0 S , 1 S , …, T S are obtained by and x = average of X.
Bootstrap analysis is applied to determine the confidence level.Given max S (Equation 4) and min S (Equation 5) the magnitude of change ( diff S ) is calculated by Equation 6. max , , , Further, the original vector X is randomly reordered, generating a bootstrap sample , , , … , from which the bootstrap CUSUM ( , , , .This process is repeated T times and the confidence level at which a CP occurred is given as: Finally, a R package (CPM) for multiple change point analysis of non-parametric time series was used (ROSS, 2015).Change point detection with CPM package is achieved by "evaluating a two-sample test statistic at every possible split point" (ROSS, 2015).The selected tests (Mann-Whitney -MW, Mood, Lepage -LP and Kolmogorov-Smirnov -KS) used in this study are described in Ross, Tasoulis and Adams (2011) and Ross and Adams (2012).
Besides the test statistics used by CPM, the user must set two parameters: ARL 0 and 'startup'.ARL 0 is a parameter representing the average number of observations before the occurrence of a false positive, considering that the sequence does not undergo a change (Ross, 2015).ARL 0 can assume the following values: 370, 500, 600, ..., 1000, 2000, …, 10000, 20000, …, 50000.'startup' defines the number of observations after which the algorithm will begin to look for change points (Ross, 2015).In this study, the following values were used: ARL 0 = 1000 and 'startup' = 40.

Equivalent system
The detected changes in SPI and RESS series varied depending on the method used (Table 2).In Figure 2, the change points (CPs) detected by individual methods (dashed lines, PTT -Pettitt, CSBT -CUSUM+Bootstrap, ITR -individual tests from R package) were differentiated from those identified by multiple methods (solid lines).In this second case, CPs detected by all four tests in 'CPM' (MW, Mood, LP and KS) were distinguished from those detected by at least two of the three adopted approaches (PTT, CSBT, CPM).
Not all the changes in SPI resulted in changes in RESS (e.g., Nov/2006, Oct/2007, etc).The horizontal bar in Figure 2 shows the CPs relative to SPI (upper) and RESS (bottom) selected for analysis.In this bar, months are specified as numbers: Jan (1), Feb (2), …, Dec (12).
The change point analysis indicates that a change in SPI between March (3) and July (7) 1999 caused the depletion of the equivalent system starting between July (7) and September (9) 1999.This indicates that the time lag between the meteorological shift and the hydrological response (significant decline) in RESS was 0-6 months.Considering the onset of the meteorological drought  RESS complete recovery (early 2002) was independent of the onset of a wet period (Figure 2).In fact, SPI was mostly negative during the RESS recovery period (Jan/2002 -Feb/2004), indicating that such recovery is related to operational factors, i.e., outflow control.By reducing the outflow, there is a positive balance in the reservoir storage change and that leads to a reduction in hydroelectric generation (HEG).This hypothesis is supported by HEG historical data for the region (Figure 3).According to SPI, the driest period occurred in the early 2000s (~1999-2000) but only in 2001 that a reduction in HEG occurred along with the demand.According to Figures 2 and 3, only after RESS reached its maximum capacity in 2005 the HEG resumed the expected growing that would have followed after 2000 without the drought, i.e., electric generation in 2005 was substantially greater than the previous years since the onset of the early 2000s drought.
The second major change towards the second drought of the analyzed period is detected before the beginning of the 2012/2013 water year (WY).The PTT and CSBT methods detected a CP in Jan(1) 2012 (solid black line, Figure 2) that might explain the decline in RESS that occurred between July(7) and Aug(8) 2012, indicating that the time lag between the meteorological shift and the hydrological response (significant decline in RESS) was 6-7 months.A second drop in both SPI and RESS occurred in Jan( 1

Case study: Furnas reservoir
A detailed analysis is performed only for the Furnas reservoir (FR), which was selected as a representative case within the Paraná basin.The change points (CPs) detected in the time series of SPI, inflow anomaly ( anomaly

Q
) and reservoir storage of Furnas HEP are show in Table 3.
A moderate to severe wet period (1 SPI 2 ≤ < ) occurred in the WY 1996/1997, ending in Dec( 12) 1997 with SPI~0 (Figure 4).The transition from that wet year to a period with rainfall ranging around the long term average reflected a change in the mean inflow (Q) to Furnas reservoir (FR) in the same month (Figure 4), i.e., a time lag of less than 1 month.Such time interval is similar, although slightly shorter, to previous values reported by Vicente-Serrano and López-Moreno (2005) and Barker et al. (2015).Both studies concluded that hydrological droughts, measured by river discharge anomalies, occurred 1-3 months after the onset of a meteorological drought.
As a result of the decrease in Q, a drop in FR levels was observed ~7 months later as a change point was detected between Jun and Aug 1998.Similar results were reported by Szalai, Szinell and Zoboki (2000) and Vicente-Serrano and López-Moreno (2005); both studies found time lag responses between SPI and reservoir storage change ranging from 7 to 10 months.Although no significant changes were observed in SPI or Q between late 1997 and early 2000s, FR storage continued to decline, with another change point in Jul( 7) 2000 (Figure 4).
The early 2000s drought that led to the 2001 energy crisis in Brazil was characterized by moderate to severe dry conditions ( 2 SPI 1 − < ≤ − ) in the contributing basin of FR.CP analysis indicates the onset of a ~1 year-long (pink bar in SPI horizontal bar) meteorological drought in Jan 2001, resulting in low Q for 6-8 months (pink bar in Q bar).Regardless of the CP analysis, the impacts of such rainfall negative anomaly can also be noticed by the low peak of Q in the rainy season (Dec 2000-Feb 2001) (Figure 5), which resulted in the low reservoir levels during the same months.
Recovery of FR (blue bar in RS) began 0-3 months (Dec 2001 -Feb 2002) after rainfall returned to normality (SPI≥-1) (Sep -Dec 2001) (Figure 4) although no substantial increase of Q was observed.CP analysis indicates that a complete recovery of FR occurred after ~2 year (early 2002(early to Feb 2004)).
Prior to the 2014 drought, reservoir storage began to decline between May(5) and August(8) 2012.Similarly to the previous drought, such decline occurred although no significant decrease in rainfall and Q was detected.Additionally, the increasing demand Melo and Wendland  Hydrological system time lag responses to meteorological shifts for electric energy, especially since 2010 (Figure 3), may have demanded more hydroelectric generation in 2012 from Furnas HEP.Significant changes in SPI and Q occurred in Dec 2013, which were followed by another change in reservoir storage after 1-2 months.
In both droughts (early 2000s and 2014), the previous decline of reservoir levels occurred because the hydrological responses in this reservoir are controlled by both natural and anthropogenic forcing factors.However, the balance between these two forcing factors may vary in time.Inflow (Q in ) and outflow (Q out ) time series from Furnas reservoir indicate that, in general, in out Q Q > in the rainy season and out in Q Q > in the dry season (Figure 5).During a drought, the electricity generation balances with the need to maintain the minimum outflow, regulated by the Electric System National Operator (ONS -Operador Nacional do Sistema Elétrico), and to minimize storage loss.
Q out data indicate that HEG was reduced in 2001 (grey bands in Figure 5), with Q in ≅ Q out during the dry season.As a result, the positive and negative residual dQ (Q in -Q out ) converged to zero.In the following drought, dQ was mostly negative between mid-2013 through late 2014 although the absolute values of Q out were similar to that in early 2000: the lowest value of the moving average of Q out between 2000 and 2003 was ~0.5 m 3 /s.On the other hand, the decrease of Q in was more critical during the 2014 dry period than in the early 2000s: the moving average of Q in was ~0.35 m 3 /s in Jan 2015, representing a reduction of ~30% relative to that in Jan 2002 (~0.5 m 3 /s).
Based on that analysis and supported by SPI (Figure 4), it is reasonable to deduce that the hydrological impacts of the 2014 drought in this basin were greater than that in the early 2000s.Why, then, similar depletion of FR is observed during both periods?Note that, between Jan 1998 and late 2000 (~3 years), the accumulated residual (dQ) is negative, as the moving average of Q out > Q in .This is basically the same period during which reservoir storage declined and change points were identified (Figure 4).Conversely, before the severe to extreme dry period (SPI ~-2.5) in 2014, the period with negative accumulated residual last ~1.5 year (Jan 2012 to ~Jun 2013, grey bands in Figure 5).
Additionally, Q out records suggest that the hydroelectric generation in Furnas HEP was reduced throughout the year of 2001.At that same period, a moderate to severe dry condition (SPI ~-1.5) established in the basin (Figures 3 and 4).On the other hand, moving average of Q out experienced a reduction in early 2013, ~1 year before the onset of the 2014 drought.Thus, a lower HEG in 2001 likely resulted in a less critical depletion of Furnas reservoir whereas such "strategy" was not enough in 2013/2014 as the rainfall deficits in this basin were much more critical than in the early 2000s drought (Figure 4).

Sensitivity analysis
The results in the previous section expose the uncertainty of the selected approaches for change point detection as they do not always identify the same CPs.Indeed, there are several methods for detecting change points in time series and is unlikely that the detected changes will be the same in all of them.To illustrate that fact, RESS data were used to perform several runs with the R package 'CPM', varying the parameter ARL 0 and fixing the parameter 'startup' to the minimum value allowed by the package (20).The number of detected points is expected to decrease as ARL 0 increase.
In general, the decrease of detected change points occurs for 1000<ARL 0 <3000 and ARL 0 >10000.Figure 6 shows that the Mann-Whitney (MW) and Kolmogorov-Smirnov (KS) tests are the less sensitive: the number of detected change points drops from 9 to 5 (MW) for the total range of ARL 0 whereas, using Mood, there is a drop from 8 to only 1 change point.
It can also be noted that setting the same value of ARL 0 for all four methods results in different number of CPs.For ARL 0 =19000, six CPs were detected using Mann-Whitney (MW) and Lepage (LP) tests whereas only one CP was detected using Mood test.Conversely, for ARL 0 =2000 the number of detected CPs ranged from five (KS) to eight points.This analysis shows the importance concerning the choice of ARL 0 in reducing the divergence among results from different tests, which makes the user more confident about the detected CPs.

CONCLUSION
In this study, six test statistics were applied to monthly time series of reservoir storage, river discharge and SPI to detect significant change points in the average behavior.
Based on change point (CP) analysis, it can be concluded that the time lag between meteorological shifts and total reservoir storage of 32 reservoirs (RESS) in the Paraná basin varies from 0 to 6 months.There is strong evidence that RESS was more sensitive to meteorological forcing in the 2014 drought than it was in the early 2000s drought.CP analysis using Furnas reservoir (FR) storage and discharge (Q) data, and SPI relative to the contributing basin of FR indicated that the time lag between changes in SPI and Q is less than one month.Similar to the behavior reported regarding RESS, response time between meteorological forcing and changes in FR storage was shorter in the 2014 drought to the early 2000s drought.
Analysis of SPI, FR storage and balance between inflow and outflow to/from FR revealed that, although similar decline in the lake levels were registered, the depletion during the early 2000s drought was most likely caused by anthropogenic forcing, i.e., dam operation; whereas the meteorological forcing had a major role in determining the storage depletion in 2013/2014.
Results from the CP analysis suggested different responses depending on the method and parameter setup.For example, a sensitive analysis of the R package 'CPM' showed that the test statistics Mann-Whitney and Kolmogorov-Smirnoff are less sensitive than the Lepage and Mood methods.Thus, it is recommended that the identification of change points in hydrological time series should be a supervised process and that multiple approaches should be used.That should allow the user to identify limitations of each method.It is worth mentioning that the CP analysis intends to specify the exact point where a change occurred in a time interval whereas visual inspection can only capture the existence of such change.
The presented results show that storage variation in reservoirs is controlled by a balance between meteorological forcing and human controls.Such balance is particularly important for determining the impacts of droughts on hydroelectricity generation and water supply, especially in Brazil, given that ~70% of electricity in the country is from hydroelectric power plants (HEP).Thus, quantifying linkages between meteorological forcing and hydrological responses is critical for water resources management and hydroelectricity generation planning.

Figure 1 .
Figure 1.Study area: the Paraná basin in the national context (a); 32 reservoirs composing the equivalent system (b); and Furnas reservoir, selected as a detailed case study (c).
1999, it persisted for 13-14 months (until Aug-Sep 2000) (pink bar in SPI horizontal bar).The associated consequence to RESS was the continuous decline for ~15 months (pink bar in RESS horizontal bar).
) 2014.The unanimity related to the position of the CP in both SPI and RESS in Jan 2014 poses strong evidence that the response time lag of RESS to SPI decreased compared to the previous drought.The comparison of the values reported here and in previous studies found in the literature reveals a relatively fast response of the hydrologic system in the Paraná basin.For example, Vicente-Serrano and López-Moreno (2005) analyzed reservoir storage

Figure 2 .
Figure 2. Detected change points (CPs) in SPI and reservoir storage of the equivalent system (RESS).The CPs selected for analysis are featured in the horizontal bar in the center; it shows the months when the changes occurred (Jan-1, Feb-2, …, Dec-12).Dashed lines represent the CPs from Pettitt (PTT) and CUSUM+Bootstrap (CSBT) methods; and individual tests from CPM package (ICPM).Solid lines represent the CPs detected by all methods in CPM package (ACPM) or at least two out of the three used approaches (PTT, CSBT or CPM).

Figure 3 .
Figure 3. Electric demand and generation by 13 hydroelectric power plants in southeast and mid-west Brazil from 2000 to 2014.Source: ONS (2015).

Figure 4 .
Figure 4. Detected change points (CPs) in SPI and reservoir storage of the equivalent system (RESS).The CPs selected for analysis are featured in the horizontal bar in the center; it shows the months when the changes occurred (Jan-1, Feb-2, …, Dec-12).Dashed lines represent the CPs from Pettitt (PTT) and CUSUM+Bootstrap (CSBT) methods; and individual tests from CPM package (ICPM).Solid lines represent the CPs detected by all methods in CPM package (ACPM) or at least two out of the three used approaches (PTT, CSBT or CPM).

Figure 5 .
Figure 5.Time series of inflow and outflow at Furnas reservoir; dQ (right axe) is the residual, given by Qin − Qout.The solid and dotted black lines are the moving average of Qin and Qout, respectively.The periods with grey bands are discusses in detail in the text.

Figure 6 .
Figure 6.Sensitivity analysis of the CPM package to changes in the parameter ARL0 for change point detection based on four test statistics: Kolmogorov-Smirnov (KS), Lepage (LP), Mann-Whitney (MW) and Mood.Both figures show the same results but with different ranges in the x-axis.

Table 1 .
General information about the reservoirs considered in this study.

Table 2 .
Position of detected change point (CP) and associated probability (CSBT and PTT) by individual methods in RESS (Reservoir Storage of the equivalent System) and SPI (Standardized Precipitation Index) time series.