INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 23: 103–115 (2003) Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/joc.853
INTERANNUAL VARIABILITY IN THE URUGUAY RIVER BASIN a
C. M. KREPPER,a N. O. GARC´IAb, * and P. D. JONESc Centro de Recursos Naturales Renovables de la Zona Semi´arida (CERZOS), Universidad Nacional del Sur, Bah´ıa Blanca, Argentina b Facultad de Ingenier´ıa y Ciencias H´ıdricas, Universidad Nacional del Litoral, Santa Fe, Argentina c Climatic Research Unit, University of East Anglia, Norwich NR4 7TJ, UK Received 13 June 2001 Revised 22 July 2002 Accepted 22 July 2002
ABSTRACT Both (El Ni˜no–southern oscillation ENSO)-scale and near-decadal variations in precipitation and river flow have been noted in southeastern South America. Here we focus on the Uruguay river basin and its subcatchments. Both river flow and precipitation are analysed with singular spectrum analysis in an examination of how the signals of the subcatchments are related to the overall basin signal. The approximate 6 year signal and the 3.5 year ENSO signal are the two statistically significant peaks for the river flow. Both signals are present in all the available river flows, but only in the precipitation of the upper two-thirds of the basin. Precipitation in the lower part of the basin shows positive trends. The ENSO signal is strongly modulated at the secular time scale; we construct a simple sinusoidal model for this modulation. Copyright 2003 Royal Meteorological Society. KEY WORDS:
southeastern South America; climatic variability; precipitation; river discharge; singular spectrum analysis
1. INTRODUCTION The relationship between the climatic regimes over a river basin and its hydrologic response, through its streamflow, presents different degrees of complexity according to the physical characteristics of the basin. Chiew et al. (1995) have mentioned that the variations in precipitation are amplified in streamflow, and that, in general, it is easier to detect a change in discharge than directly in the basic climatic variables (e.g. precipitation or temperature). Streamflow is a synthesis of precipitation, evapotranspiration and the rest of the hydrologic cycle components, together with possible anthropogenic influences. The Uruguay river is the second tributary in importance of the R´ıo de la Plata basin with a length of approximately 1600 km, with its own basin covering an area of around 365 000 km2 (Figure 1). The source of the river is located in Brazil, in Serra Geral at 28° 10 S, where it takes the name Pelotas river at a height of approximately 1800 m above sea level (Bischoff et al., 2000). The whole upper part of the Uruguay river basin is located in Brazil, and downstream of the confluence with the Pepir´ı Guaz´u river it forms the border with Argentina, up to the confluence with the Cuareim at 30° 15 S. From that point on the river forms the border between Argentina and Uruguay as far as the R´ıo de la Plata. The main tributaries of the Uruguay river come from the east of the basin. The Iju´ı, Ibicu´ı and Cuareim rivers have relatively small basins but they contribute considerable streamflow. For example, calculation of the specific discharge of the Ibicu´ı basin, for the 1931–95 period shows a value of 20.1 l km−2 s−1 , whereas for the Cuareim it is 18.3 l km−2 s−1 . The largest tributary of the Uruguay river is the Negro, with a mean annual discharge of 500 m3 s−1 and an approximate length of 560 km. This river basin is located almost completely in Uruguay (Figure 1). Several studies performed on southeastern South America have used river flows as indicators of climatic variability from the interannual to * Correspondence to: N. O. Garc´ıa, Hydroclimatic Research Unit, Department of Hydrologic Sciences, National University of Littoral, CC 217, (3000) Santa Fe, Argentina; e-mail:
[email protected]
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Figure 1. The study area
the secular scale (Aceituno, 1998; Rickey et al., 1989; Hastenrath, 1990; Mechoso and P´erez Iribarren, 1992; Marengo, 1995; Garc´ıa and Vargas, 1996, 1998; Genta et al., 1998; Robertson and Mechoso, 1998). Garc´ıa and Vargas (1998), in particular, analysed the R´ıo de la Plata basin and found positive trends in the runoff since 1970, and changes in the series around the years 1917–18 and 1943. Genta et al. (1998) examined long discharge series of the major rivers in southeastern South America looking for long-term changes. Robertson and Mechoso (1998) examined the power spectrum of the combined Uruguay, Negro and Parana–Paraguay river discharges, with the purpose of determining the existence of oscillatory components and their possible relationship with sea surface temperature (SST) variations. These authors have found evidence of the existence of nonlinear trends in the combined river discharges and oscillatory components with periods of around 3.5 and 6 years. The different basins of the region have been affected by anthropogenic change, such as deforestation and changes in land use, which may have influenced the river flow characteristics, as was shown by Garc´ıa (2000) for the R´ıo de la Plata basin. The main purpose of this work consists of studying the interannual variability of the Uruguay river basin, particularly the quasi-oscillatory variability that is present in the series. It is also of interest to be able to determine the presence of possible interaction among the different signals, generally of nonlinear signals in the oscillatory components. A second objective consists of determining probable relations between the oscillatory modes of the river flow and those of precipitation on different subcatchments of the basin. A simple procedure, filtering the series by means of moving averages over different periods, is used to study the low-frequency variability in both the river flow and in the precipitation. A singular spectrum analysis (SSA) is used to isolate the interannual oscillation modes in the series and to reconstruct the oscillatory components. This technique has several advantages over other types of spectral analysis (Ghill and Mo, 1991; Vautard et al., 1992); in particular, the temporal empirical orthogonal function need not be sinusoidal, which implies that the method does not need to decompose a single nonlinear oscillation into a large number of sine waves. SSA assumes only stationarity; however, even this assumption seems to be weak in practice. In Copyright 2003 Royal Meteorological Society
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fact, one of the remarkable results of Vautard and Ghill (1989) and Ghill and Vautard (1991) is that, although the assumption of stationarity is usually implicit in SSA, the analysis performs very well in the presence of long-term nonstationarities, like trends.
2. DATA AND METHODS OF ANALYSIS 2.1. Data used Four gauging stations on the Uruguay river with at least 60 years of discharge data were used in the present study. The names and location of the stations, as well as the periods of the record and the annual mean discharge for a common period (1931–92), are shown in Table I. Precipitation data for the catchment come from the 0.5° × 0.5° gridded data of New et al. (1999, 2000). These data cover the 1901–95 period. This database uses, among others, data coming from the 1192 stations collected in the ‘Assessing the impact of future climatic change on water resources and hydrology of the R´ıo de la Plata basin’ project (Jones et al., 1999). 2.2. Methodology SSA is a statistical method related to principal components analysis (PCA) but it is applied in the time domain. The objective is to describe the variability of a discrete and finite time series Xi = X(it)(i = 1, 2, . . . , N ), where t is the sampling interval, in terms of its lagged autocovariance structure (Vautard and Ghill, 1989). The eigenvalue decomposition of the lagged autocovariance matrix C(M × M), up to lag Mt, produces temporal-empirical orthogonal functions T-EOFs (s = 1, . . . , M) and statistically independent temporalprincipal components T-PCs , with no presumption as to their functional form. M is the maximum number of lags and is also called the window length. Each T-PCs has a variance λs [(eigenvalue) and represents a filtered version of the original series Xi . The SSA develops a set of data adaptive filters, in such a way that the original series Xi is decomposed in the following way: X(k) = A
M
[T-PCs (i)][T-EOFs (j )]
(1)
s=1 i+j =k
where X(k) is the (i + j )th value of the time series. The index i denotes a moment in time, and the index j denotes a lag from time i. T-EOFs (j ) is the j th element of the sth filter, and T-PCs (i) is the amplitude of the signal captured by the sth filter. The value of A is generally 1/M, except near the beginning and end of the time series (Vautard et al., 1992; Plaut and Vautard, 1994). In the SSA context, a quasi-oscillatory structure will be present in X(k) when the following criteria are met: (a) two consecutive eigenvalues, λs and λs+1 , are nearly equal (degenerate pair); (b) the two corresponding T-EOFs and T-EOFs+1 are nearly periodic, with the same period, and in quadrature; (c) the associated T-PCs and T-PCs+1 are also in quadrature. SSA has the interesting property that oscillations with small frequency variation (within some small frequency range) Table I. Names and location of the stations used Gauging station
Latitude
Longitude
It´a Santo Tom´e Paso de los Libres Concordia
27.26 ° S 28.53 ° S 29.45 ° S 31.23 ° S
52.31 ° W 56.01 ° W 57.04 ° W 58.02 ° W
Copyright 2003 Royal Meteorological Society
Data period
1931–92 1908–97 1909–97 1898–1997
Mean annual discharges (1931–92) (m3 s−1 ) 1022 2522 4028 4592 Int. J. Climatol. 23: 103–115 (2003)
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are identified and reconstructed as a single oscillation, rather than as several separate signals as in most other spectral analysis methods. However, SSA can only distinguish between neighbouring spectral peaks, with frequencies fk and fk+1 , if |fk − fk+1 > 1/M. The choice of the window length M is a sensitive issue. The choice represents a compromise between information content (large M) and statistical confidence (small M) (Plaut and Vautard, 1994). Within the context of this work, in order to avoid confusions with other definitions found in the literature, we can divide the broad interannual band into two. The interannual band (IAB) itself, with periods between 1 and 10 years, and the low-frequency band (LFB), with periods over 10 years.
3. VARIABILITY OF THE URUGUAY RIVER FLOWS Monthly mean river flow series from It´a, Santo Tom´e, Paso de los Libres and Concordia on the Uruguay river were analysed. The series corresponding to It´a was not used for the analysis of long-period fluctuations owing to its shorter length (62 years). To observe possible long-period changes in LFB, the annual average flows were examined over the different running average periods (centred on 11, 21 and 31 years). Figure 2 shows the results obtained for a smoothing of 11 and 31 years, where the resulting flows have been normalized ((X − Xmean )/σ ) so as to make comparison easier. Similar behaviour shown by the Santo Tom´e, Paso de los Libres and Concordia series can also be observed. Despite the river flow increasing about 59.8% (Table I) between Santo Tom´e and Paso de los Libres, the smoothed flow behaviour does not show any differences. Figure 2(a) shows a period of absolute minima between 1940 and 1950, coinciding with several important droughts that developed in the river basin during 1943, 1944 and 1945 (Genta et al., 1998). Such an extreme drought period separates the Uruguay river flows into two contrasting periods. First, there is the period before 1940, which is characterized by oscillations with periods over 10 years; second, after 1950 an appreciable positive trend occurs. The same type of behaviour is maintained in the smoothed flows series (Figure 2(b)). This shows that the characteristics of variability in the LFB are given by very long-period signals (T > 30 years). The period after 1950 shows a change in the trend around 1970, as has been discussed by Garc´ıa and Vargas (1998). When a spectral analysis (SA) of the mean annual river flow series (Santo Tom´e, Paso de los Libres and Concordia) is performed (Figure 3), the only significant peaks at the 95% confidence level (WMO, 1966) occur within the IAB with periods around 3 and 6 years, in agreement with those found by Robertson and Mechoso (1998). The general spectral shape does not change from one station to another, only the relative magnitude of the peaks. In order to analyse the oscillatory structures within the IAB, an SSA was applied to the series of flows corresponding to It´a, Santo Tom´e, Paso de los Libres and Concordia, using, in each case, all the data available. Table II summarizes the results obtained with the most suitable window length possible for each case. It is possible to appreciate the relative importance of each oscillatory mode, in accordance with the percentage of explained variance. The series of mean annual river flows at It´a presents only one oscillation mode, with a dominant period of around T ≈ 3 years, formed by the T-EOF3 and T-EOF4 pair; however, in the remaining series, an oscillation mode of around T ≈ 6 years, formed by T-EOF1 and T-EOF2 , and a secondary one with T ≈ 3 years (T-EOF3 and T-EOF4 ), are evident. For all these gauging stations, the oscillatory components with a period close to 6 years represent a quasiharmonic oscillation, whereas the components with T ≈ 3 years, especially downstream at Santo Tom´e, show nonlinear interactions between frequencies of different ranges. In particular, Figure 4 shows the T-PCs for Paso de los Libres associated with such oscillation modes. Figure 4(a) shows the series reconstructed by T-PC3 and T-PC4 , RC(3–4), computed by Equation (1) when s = 3 and 4, which accounts for 13.1% of the variance and the reconstruction using the first four T-PCs , RC(1–2–3–4) (Figure 4(b)). The oscillatory pairs with dominant periods of 3 and 6 years, together, explain 35.8% of the variance in the river flow series. Figure 4(a) gives evidence of an amplitude modulation of RC(3–4), which must be a reflection of what occurred in T-PC3 and T-PC4 . The RC(3–4) presents a very distinct attenuation between 1940 and 1960, which would be associated with a modulation by a long wave belonging to the LFB. With the objective of Copyright 2003 Royal Meteorological Society
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3
Standardized values
2 1 0 -1 -2 -3 1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Years Concordia
Santo Tomé
Paso de los Libres
3
Standardized values
2 1 0 -1 -2 -3 1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
Years Concordia
Paso de los Libres
Santo Tomé
Figure 2. (a) The 11 year centred moving averages of the streamflow series: Santo Tom´e (mean = 2506 m3 s−1 , σ = 291 m3 s−1 ); Paso de los Libres (mean = 4010 m3 s−1 , σ = 499 m3 s−1 ; Concordia (mean = 4487 m3 s−1 , σ = 365 m3 s−1 ). (b) The 31 year centred moving averages of the streamflow series: Santo Tom´e (mean = 2451 m3 s−1 , σ = 167 m3 s−1 ); Paso de los Libres (mean = 3913 m3 s−1 , σ = 304 m3 s−1 ; Concordia (mean = 4386 m3 s−1 , σ = 365 m3 s−1 )
fitting the T-PC3 and T-PC4 signals, the following simple nonlinear model is proposed: Y (t) = F (t){[sin(2πf0 t + φ) + C]} + B sin(2πf0 t + φ)
(2)
where 1/f0 corresponds to the dominant period of the oscillation mode and F (t) is another sine wave with frequency f1 , assuming that f1
