Assessing the use of SPI in detecting agricultural and hydrological droughts and their temporal cyclicity: Some Slovakian case studies

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1 European Water 60: , E.W. Publications Assessing the use of SPI in detecting agricultural and hydrological droughts and their temporal cyclicity: Some Slovakian case studies M.M. Portela 1*, A.T. Silva 1, J.F. Santos 2, M. Zeleňáková 3 and H. Hlavatá 4 1 Instituto Superior Técnico, Universidade de Lisboa, CERIS, Portugal 2 Instituto Politécnico de Beja, Beja, Portugal 3 Technical University of Košice, Košice, Slovakia 4 Slovak Hydrometeorological, Košice, Slovakia * maria.manuela.portela@tecnico.ulisboa.pt Abstract: Key words: One of the most common drought indices used to characterize the droughts is the Standardized Precipitation Index, SPI. This index that can be computed at different time scales uses only rainfall records and aims at detecting meteorological drought triggered by rainfall shortfall. If this deficit is combined with higher than normal evapotranspiration, an agricultural drought may occur. If the period with below average precipitation/above average evapotranspiration persists, the streamflows are affected resulting in a hydrological drought. This paper addresses the capability of the SPI to detect agricultural and hydrological droughts in Eastern Slovakia by comparing its values with those of other indices. Regarding agricultural drought, the comparison considered the Standardized Precipitation Evapotranspiration Index, SPEI. Results show that SPI and SPEI have almost identical performance in agricultural drought detection across the analysed rain gauges. Furthermore, to evaluate the capability of SPI to detect hydrological droughts, the Standardized Streamflow Index, SSI, developed using monthly streamflows and the methods of normalization within the computation of SPI, was applied to a small catchment and compared to the SPI at a rain gauge inside the catchment. This comparison revealed that SPI had a poor performance in detecting hydrological drought. Spectral analysis of the seasonal patterns of the SPI index, using the fast Fourier transform algorithm (FFT), showed that there is a generalized 5-6 year cycle in the agricultural pattern for Autumn and Spring. Slovakia, droughts, SPI, SPEI, SSI, spectral analysis 1. INTRODUCTION Previous works of the authors analysed the drought occurrences in Slovakia, including: (i) an extensive characterization of the events over the whole country; (ii) their spatial regionalization and (iii) temporal evolution; (iv) the analysis of the pattern of their annual rates of occurrence, as a way to look for links among those events and the climate change issue; and, finally, (v) the development of a very practical tool aiming at the early detection of the drought occurrences, based only on rainfall data, as synthesized in Portela et al. (2015). Those studies utilized the Standardized Precipitation Index, SPI (McKee et al., 1993), which is perhaps the most common drought index, due to its few data requirements, the simplicity of its computation when compared to other indices and its comparability because it is a dimensionless index (Santos et al., 2010). The SPI can be computed at different time scales and uses only rainfall data because. It aims at detecting meteorological drought triggered by rainfall shortfall. If this deficit is combined with higher than normal evapotranspiration, an agricultural drought may occur. If the period with below average precipitation/above average evapotranspiration persists, the streamflows are affected resulting in a hydrological drought. The analysis of the droughts based on the SPI only requires the adjustment to monthly rainfall series or to cumulative rainfall series of a given statistical distribution. A drought event is considered to occur in a certain location/rain gauge when the SPI falls below a predetermined threshold level, defined according to the drought severity, from moderate to severe and to extreme drought.

2 234 Author(s) Another multiscalar drought index is the Standardized Precipitation-Evapotranspiration Index SPEI. This index was designed to take into account both precipitation and potential evapotranspiration (PET) in identifying droughts, thus capturing the cumulated impact of increased temperature and low water availability. According to Vicente-Serrano et al. (2010), the method used to calculate the PET is not a critical issue when applying SPEI and the simpler method of Thornthwaite (1948), which only requires monthly temperature data, can be applied. This paper addresses the capability of the SPI to detect agricultural and hydrological droughts in Eastern Slovakia by comparing its values with those of other indices. Regarding agricultural drought, the comparison considered the Standardized Precipitation Evapotranspiration Index, SPEI. Results show that SPI and SPEI have almost identical performance in agricultural drought detection across the analysed rain gauges. Furthermore, to evaluate the capability of SPI to detect hydrological droughts, the Standardized Streamflow Index, SSI, was applied to a small catchment and compared to the SPI at a rain gauge inside the catchment. The SSI uses only monthly streamflows or cumulative monthly and the same methods of normalization and computation as the SPI. This comparison revealed that SPI had a poor performance in detecting hydrological drought. The study ends with a brief and simple example on the cyclicity of the SPI index based on spectral analysis. 2. STUDY AREA AND DATA The comparison of drought indices in Eastern Slovakia utilized monthly precipitation and temperature data from 6 rain gauges, which were kindly provided by the Slovakian Meteorological Institute. Table 1 shows the code and name, period of records and coordinates of the rain gauges. Monthly streamflow data from the Medzev river gauge (January 1961 December 2014, catchment area of ca. 90 km 2 ) was also utilized to compute SSI and to compare this index with the SPI. Figure 1 shows the schematic location of the 6 rain gauges, as well as that of the Medzev stream gauge and corresponding catchment drainage divides. Table 1. Utilized rain gauges, period of records of monthly precipitation and temperature, and geographic coordinates. Code Name Period of records Latitude (º) Longitude (º) P1 Červený Kláštor January 1961 December P2 Štós January 1961 December P3 Skalnaté Pleso January 1961 December P4 Kamenica nad Cirochou January 1951 December P5 Bardejov January 1961 December P6 Tisinec January 1963 December METHODS 3.1 Drought indices The SPI index was computed at a 3-month time scale in order to reflect short- and medium-term water deficit conditions whose awareness is important in primary agricultural regions such as Slovakia (Portela et al., 2015). To be comparable, the same time scale was adopted for SPEI and SSI. The computation of the SPI series followed the detailed formulation provided by Edwards & McKee (1997) and Vicente-Serrano (2005), among others. The Gamma distribution was applied to the series of cumulative precipitation in consecutive periods of 3 months (SPI3) in each rain gauge. The SPEI uses the same formulation, but applied to cumulative climatic water balance, i.e., the difference between precipitation and potential evapotranspiration (P PET) (Beguería et al., 2014), in consecutive periods of 3 months (SPEI3). As suggested by Vicente-Serrano et al. (2010), the

3 European Water 60 (2017) 235 monthly potential evapotranspiration was computed by applying the Thornthwaite method which has the advantage of only requiring monthly temperature series. The temperature data were acquired at the same monitoring stations as the rainfall data, as previously mentioned. The SSI computation utilized exactly the same approach as for SPI but applied to monthly streamflows in consecutive periods of three months (SSI3). Figure 1. Map of Eastern Slovakia. Location of the 6 rain gauges and of the Medzev river gauge and corresponding catchment s drainage divide. 3.2 Spectral analysis Spectral analysis methods were used to investigate structured temporal variations (periodicity) embedded in the drought indices in different time seasons. Spectral methods are also known as Fourier transform methods (Bloomfield, 2000) and have been widely used in the hydro-climatological field (e.g. Rajagopalan and Lall, 1998; Golyandina and Zhigljavsky, 2013; or more recently, Moreira et al., 2015). The Fourier transform can describe a physical process either in time domain (function of time) or in the frequency domain were the physical process could be specified by giving its amplitude as a function of frequency, providing interesting features such as long memory, presence of high frequency variation and cyclical behaviour (e.g. McLeod and Hipel, 1995). The input data is generally a simple or multivariate time series, but some authors such as Hijmans (2013) or Golyandina and Usevich (2010), have been successfully testing the use of spectral analysis in multidimensional data like digital images. The related periodogram, which is also a sample estimate of a population function called the spectral density, is a function that provides information about the periodic components of a time series, allowing identifying the dominant cyclical behaviour in a series. Any time series can be expressed as a sum of cosine and sine waves oscillating at the fundamental (harmonic) frequencies. The periodogram gives information about the relative strengths of the various frequencies when explaining the variation in the time series. These strengths are also known as power spectrum, which can be defined as the distribution of variance across frequency (i.e. the spectrum is related to the Fourier transform of the autocorrelation function). Mathematically, the spectral density is defined for both negative and positive frequencies. However, due to symmetry of the function and its repeating pattern for frequencies outside the range -1/2 to +1/2, we only need to be concerned with frequencies between 0 and +1/2. The Spectral Analysis package was used in R (R Development Core Team, 2013) to estimate the

4 236 Author(s) spectral density of seasonal SPI and SSI time series for agricultural drought recognition by using a smoothed periodogram, which calculates the periodogram and smoothed the result with a series of modified Daniell smoothers to achieve consistency (Venables and Ripley, 2002). 4. RESULTS 4.1 Comparison between drought indices The comparison between SPI3 (horizontal axes) and SPEI3 (vertical axes) in rain gauges P1 to P6 is shown in Figure 2. The results are very similar in all rain gauges: the scatter plot is slightly S-shaped, thus suggesting that the SPI index is more sensitive to water shortages and surpluses. These results are similar to those found in a humid region in Portugal by Paulo et al. (2012), who contend that the S shape of the relationship is related to the different behaviour of the variable of interest in SPEI (P PET) from the variable of interest in SPI (P). Figure 2. Comparison of SPI3 and SPEI3 values in the 6 analysed rain gauges (from P1 to P6). Figure 3 shows the comparison between SPI3 at rain gauge P2 and SSI3 at the Medzev river gauge (Figure 1). To account for the delay between precipitation and surface runoff, the SSI series were lagged comparatively to the SPI series from δ = 1 to 3 months meaning that each SPI3 is compared to a SSI3 for a three month period starting δ months after, as proposed by Portela and Santos (2010). Additionally, to account for the minor and mutually dependent droughts with little hydrological importance and that may disturb the analysis, some authors recommend combining those droughts into a single large event which allows capturing the true severity of the events (Moreno et al., 2009). Among the various procedures proposed to do that (Tallaksen et al., 1997), a low-pass filter, namely, the moving average technique, was adopted to smooth the original drought index series.

5 European Water 60 (2017) 237 This procedure combines mutually dependent droughts into a single drought event; it also filters out the minor droughts, providing better results than other methods (Fleig et al., 2006). The time step adopted was n = 10 as done before by Portela and Santos (2010), exactly in the same scope and purpose. Figure 3. Comparison of moving averages (for n=10) of SPI3 at the Stós rain gauge and of SSI3 at the Medzev river gauge with different monthly lags between SPI3 series and SSI3 series and corresponding correlation coefficients. Figure 3 shows that the relationship between SSI3 and SPI3 is not well-defined, even despite the applied smoothing of the moving average, which suggests that SPI is not a worthwhile descriptor of surface water availability. Furthermore, the correlation between the two indices improves when a 1-, 2- or 3-month lag between precipitation and streamflow is introduced, thus suggesting that, given the small size of the catchment, groundwater may provide a significant contribution to surface flow. 3.2 Temporal cyclicity of the SPI3 series The spectral analysis was applied to the SPI3 series at the 6 rain gauges. The spectral density estimates obtained by the periodograms are shown in Figure 4. Representations as the one of this figure allow to detect the existence of relevant periodic components in the time series, as well as to conclude about their relative importance. The main four seasonal SPI series (Winter Jan to Mar; Spring Apr to Jun; Summer Jul to Sep and Autumn Oct to Dec) were chosen for the spectral analysis as they reflect the main weather periods in Slovakia. The method was applied only to SPI3 since the SPEI3 and the SPI3 time series have a similar temporal behaviour.

6 238 Author(s) Winter Spring m= 5-6 years P1 P2 P3 P4 P5 P Summer Autumn m= 5-6 years P1 P2 P3 P4 P5 P6 Figure 4. Spectral density for SPI3 in the 6 analysed rain gauges (from P1 to P6), where m is the period in years. The raw periodogram is a rough sample estimate of the population spectral density, since normally it uses only the discrete fundamental harmonic frequencies for the periodogram whereas the spectral density is defined over a continuum of frequencies. In order to deal with this problem and to provide more consistency to the results the periodograms have been smoothed. Bloomfield (2000) recommends the Daniell window (Daniell, 1946) as a smoothing filter for generating an estimated spectrum from the periodogram (moving averages giving half weight to the end values). The periodograms obtained used coef [-2, -1, 0, 1, 2] = [0.125, , 0.250, 0.125]. Since each value of the SPI3 is computed in an annual basis, the results obtained by the periodogram plots (spectral density) for the agricultural drought temporal patterns manifest a clear peak of m = 5-6 years in Spring and Autumn (Figure 4), where n is the period in years such that m = 1/. Winter and Summer seasons show several high peaks which indicates the existence of several periodic components with different periods, without any clear individualized strong peak. In general, few of those peaks represent a strong periodical signal that cannot be assigned to statistical fluctuations, nevertheless the peaks obtained by the smoothed periodograms were not tested for statistical significance in this paper. 5. CONCLUSIONS Regarding the drought assessment, namely in a region prone to agricultural droughts as Slovakia, the results achieved showed that the Standardized Precipitation Index, SPI, is as good an indicator as the Standardized Precipitation Evapotranspiration Index, SPEI, since it provides almost the same information. Besides allowing identifying the same occurrences, SPI has the advantage of being more sensitive to water shortages and surpluses. In what concerns the hydrological droughts that affect the river streamflows, SPI proved not to be able to detect those identified by the SSI3 index. Because this conclusion was based on a single case study it cannot be generalized. It should be mentioned that other authors find a relationship between SPI and SSI although in a different hydrological framework (Portela and Santos, 2010). In respect to spectral analysis, only a few rain gages in a very small region were analysed which also points towards the need for further research. Despite its preliminary nature, the results showed that the cyclicity of the indices can provide some information about the temporal variability of the agricultural droughts in Slovakia.

7 European Water 60 (2017) 239 Other authors such as Halmova et al. (2015) have also found wet and dry periods in multiannual precipitation series in a southwestern station in Slovakia. From several significant cycles the authors found one that had a duration of 5 years, which statistical relationship with the cycles of Figure 4 derived from SPI3 series should be further investigated. The multi-year fluctuations here obtained by spectral analysis could also be linked to the energy bands that characterize some climate indices affecting the European climate, such as the North Atlantic Oscillation (NAO), a teleconnection pattern which is recognized as a major climatic factor on the European hydrological variables as seen in Rimbu et al. (2004) and Trigo et al. (2004). REFERENCES Beguería, S., Vicente-Serrano, S.M., Reig, F., Latorre, B., Standardized precipitation evapotranspiration index (SPEI) revisited: parameter fitting, evapotranspiration models, tools, datasets and drought monitoring. International Journal of Climatology, 34(10): Bloomfield, P., Fourier analysis of time series: an introduction, 2nd edition. New York, John Wiley & Sons, Inc., 261 p. Daniell, P.J., Discussion on the symposium on autocorrelation in time series. Journal of the Royal Statistical Society (Suppl.), 8: Edwards, D.C., McKee, T.B., Characteristics of 20th century drought in the United States at multiple time scales. Climatology Report 97 2, Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado. Fleig, A. K., Tallaksen, M., Hisdal, H., Demuth, S., A global evaluation of streamflow drought characteristics, Hydrology and Earth System Sciences, 10: Golyandina. N., Usevich, K., D-extension of Singular Analysis: algorithm and elements of theory. In: Matrix methods: Theory, algorithms and applications, V. Olshevsky, E. Tyrtyshnikov (eds.), World Scientific Publishing, pp Golyandina, N., Zhigljavsky, A., Singular spectrum analysis for time series. Springer, doi: / Halmova D., Pekarova P., Olbrimek J., Miklanek P., Pekar J., Precipitation Regime and Temporal Changes in the Central Danubian Lowland Region. Advances in Meteorology, doi: /2015/ Hijmans, R.J., raster: Geographic Data Analysis and Modeling. R package version , McKee, T.B., Doesken, N.J., Kleist, J., The relationship of drought frequency and duration to time scales. In: Proceedings of the 8th Conference on Applied Climatology, American Meteorological Society, Boston, MA, 17(22): McLeod, A.I., Hipel, K.W., Exploratory spectral analysis of hydrological times series. Stochastic Hydrology and Hydraulics, 9: Moreira, E.E., Martins, D.S., Pereira, L.S., Assessing drought cycles in SPI time series using a Fourier analysis. Natural Hazards and Earth System Sciences, 15: López-Moreno, J.I., Vicente-Serrano, S.M., Beguería, S., García-Ruiz, J.M., Portela, M.M., Almeida, A.B., Dam effects on droughts magnitude and duration in a transboundary basin: The Lower River Tagus, Spain and Portugal. Water Resources Research, 45:W02405, doi: /2008wr Paulo, A.A., Rosa, R.D., Pereira, L.S., Climate trends and behaviour of drought indices based on precipitation and evapotranspiration in Portugal. Natural Hazards and Earth System Sciences, 12: Portela, M.M., Zelenáková, M., Santos, J.F., Purcz, P., Silva, A.T., Hlavatá, H., A comprehensive drought analysis in Slovakia using SPI. European Water, 51: Portela, M.M., Santos, J.F., Caracterização de secas por aplicação do índice de precipitação padronizada, SPI, a séries de precipitação e de escoamento: casos de estudo em Portugal Continental. XXIV Congresso LatinoAmericano de Hidráulica, Punta del Este, Uruguay (in Portuguese). R Development Core Team (2013). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, available at: Rajagopalan, B., Lall, U., Interannual variability in Western US precipitation. Journal of Hydrology, 210: Rimbu, N., Dima, M., Lohmann, G., Stefan, S Impacts on the North Atlantic Oscillation and the El Niño-Southern Oscillation on Danube river flow variability. Geophys. Res. Lett., 31:L23203, doi: /2004gl Santos, J.F., Pulido-Calvo, I., Portela, M.M., Spatial and temporal variability of droughts in Portugal, Water Resources Research, 46:W03503, doi: /2009wr Thornthwaite, C.W., An approach toward a rational classification of climate. Geographical review, 38(1): Tallaksen, L.M., Madsen, H., Clausen, B., On the definition and modelling of streamflow drought duration and deficit volume. Hydrological Sciences Journal, 42: Trigo, R.M., D. Pozo-Vázquez, T.J. Osborn, Y. Castro-Diez, S. Gamiz-Fortis, M.J. Esteban-Parra, North Atlantic Oscillation influence on precipitation, river flow and water resources in the Iberian Peninsula. Int. J. Climatol., 24: Venables, W.N., Ripley, B.D., Modern Applied Statistics with S. Fourth edition, Springer. Vicente-Serrano, S.M., Las sequías climáticas en el calle medio del Ebro: factores atmosféricos, evolución temporal y variabilidad espacial. Ser. Invest., vol. 49, Publ. Cons. de Prot. de la Nat. de Aragón, Zaragoza, Spain (in Spanish). Vicente-Serrano, S.M., Beguería, S., López-Moreno, J.I., A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index. Journal of Climate, 23(7):