The Comahue region is located in the Central Andes Mountains in Argentina, between 36°S and 42°S. The region is crossed by three rivers: the Limay, Neuquén and Negro. With regard to energy, it is one of the major river systems because the hydro-electric energy used in the country is mainly generated there, by operating dams such as El Chocón, Alicurá and Piedra del Aguila in the Limay river basin and Portezuelo, Los Barreales and El Chañar in the Neuquén river basin. It drains an area of 140,000 km2 and covers almost the whole of the province of Neuquén and part of the provinces of Buenos Aires and Rio Negro. The various uses of this water include hydroelectric generation for the national grid and water supply for the development of local subsistence economies. The operation of dams is highly dependent on rainfall, as it is the main variable that regulates the flow of rivers. In this area the annual cycle of rainfall is characterized by a maximum in winter (April–September) but the interannual rainfall variability is high. Therefore, in order to efficiently operate the dams, it is relevant to forecast the seasonal rainfall. For example, in the Limay and Neuquén river basins, rainfall above average has been recorded in only 4 out of the 13 years during the period 2000–2012. These values are indicative that the region is going through a period of below-normal rainfall which affects the optimal operation of dams. In this context, it becomes relevant to study the relationship between precipitation and flow, as well as the ability to predict these events.
Current forecasts of seasonal rainfall using dynamic modeling have serious shortcomings because of, among other things, the low spatial resolution. That is why the development of statistical rainfall forecasting techniques, specially adapted to the study region, is addressed in this paper. The scientific basis of seasonal climate predictability lies in the fact that slow variations in the earth boundary conditions (i.e.
, sea surface temperature or soil wetness) can influence global atmospheric circulation, and thus precipitation. Some authors have analyzed these relationships in the southern hemisphere, for example Gissila et al.
] in Ethiopia; Reason [2
] in South Africa and Zheng and Frederiksen [3
] in Australia. In Argentina, Gonzalez and Vera [4
] detected rainfall patterns by analyzing interannual rainfall variability in the Comahue region using a principal component analysis. Gonzalez et al.
] derived rainfall prediction schemes, using multiple linear regressions which explained 51% of the winter rainfall variance in the Limay River basin and 44% in the Neuquén River basin. Gonzalez and Herrera [6
] discussed several different statistical models: an autoregressive integrated moving average model (ARIMA), Holt Winter (HW), the Climate Prediction Tool (CPT) and a combination of all three to predict rainfall in southern Argentina (Patagonia). Scarpati et al.
] and Gonzalez [8
] studied rainfall and flow characteristics in this region of Argentina. Gonzalez and Dominguez [9
] applied a prediction scheme using multiple linear regression and showed that 46% of the standardized precipitation index (SPI) variance could be explained by this model in the Limay river basin. In general, the SPI was used to quantify the conditions of deficit or excess of precipitation for a several-month interval, and it is usually used in hydrological studies (Mckee et al.
]), especially for improving the operation of dams. The aim of this paper is to develop a technique to predict seasonal rainfall in the Neuquén River basin using statistical methods applied to SPI. This basin is located in the northern part of the Comahue region. The Neuquén River is the boundary of the Neuquén and Mendoza provinces. The river runs from the high Los Andes Mountain in the west towards the Patagonian plateau in the east and drains an area of 30,000 km2
. Between 80%–90% of the total rainfall occurs in winter, and this is the most important factor that contributes to river flow. Snowfall accumulates until late spring in high mountains in the west and generates a secondary peak in river flow. The paper is organized as follows: Section 2
describes the dataset and the methodology. Section 3.1
presents the SPI low frequency features in Neuquén river basin. Section 3.2
shows the difference in the behavior of sea surface temperature and atmospheric circulation when extreme SPI is registered. Section 3.3
presents some regression models to estimate wet and dry events and discusses their efficiency. Section 4
presents the main conclusions.
2. Data and Methodology
Rainfall data from different sources (National Meteorological Service, the Secretary of Hydrology of Argentina and the Territory Authority of the Limay, Neuquén and Negro river basins) in 12 stations of the Neuquén River basin (NRB) over the period 1980–2007 were used in this study (Figure 1
). In this period, all the stations have less than 20% missing monthly rainfall data and their quality has been carefully ascertained. A number of techniques were applied as part of the quality control process. First we discriminated cases with no precipitation in one month due to missing data. No stations have records affected by changes of location and instrumentation. Rainfall greater than the 95th percentile was evaluated in order to detect outliers. In a consistency check, the observation was compared with a nearby station value to see if it was physically or climatologically consistent. Suspicious observations due to inconsistencies were removed. Precipitation was homogeneous all over the basin as proven by applying the Lund method using a 0.6 correlation coefficient (Garbarini and González [12
]). In order for the average of monthly precipitation to be representative of the precipitation over the basin, a mean rainfall series was calculated in NRB.
Area of study and location of the stations used.
Area of study and location of the stations used.
The SPI was defined by Mckee [10
] with the aim of detecting wet and dry periods. The basic approach is to use standardized precipitation for a set of time scales which together represent water sources of several types. The accumulated precipitation in different time scales is fitted using a gamma distribution. After fitting the gamma probability distribution to precipitation data, the cumulative distribution is transformed through an equal-probability transformation into a normal distribution so that the mean SPI is set to zero. It represents the number of standard deviations that the precipitation is away from its historical average. Negative (positive) values of SPI represent deficits (excess) of rainfall compared with the expected normal value. The period used to calculate SPI depends on the use. For example, SPI calculated at a 6-month scale is useful for evaluating dry and wet periods and is useful for hydrological droughts. The one-month SPI has been useful for evaluating agronomical droughts (Mckee [10
]). The main advantages of using SPI are the simplicity of calculation because it only uses rainfall data, the possibility of calculating the index at different time scales, and the consistent frequency of extreme and severe cases for any location and any timescale because of the normal distribution. Mckee [10
] suggests a classification of excess and dry cases using SPI (see Table 1
). Hayes et al.
] explained the advantages and limitations of SPI use and Heim [14
] did a detailed comparison of different drought indexes used including SPI.
Years classified using the value of SPI9. Percentage frequency is detailed.
Years classified using the value of SPI9. Percentage frequency is detailed.
| ||Category||Definition||Frequency (%)||Years|
| ||Extreme drought||SPI9 < −2||3.5||1998|
| ||Severe drought||−2 < SPI9 < −1.5||3.5||1996|
|DRY||Moderate drought||−1.5 < SPI9 < −1||10.7||1989, 1990, 2007|
|CASES||Slight drought||−1 < SPI9 < −0.5||7.1||1985, 2003|
| ||Normal||−0.5 < SPI9 < 0.5||39.3||1981, 1983, 1984, 1987, 1988, 1991, 1992, 1994, 1995, 1999, 2004|
| ||Slight excess||0.5 < SPI9 < 1||21.4||1986, 1993, 1997, 2000, 2002, 2005|
| ||Moderate excess||1 < SPI9 < 1.5||10.7||1980, 2001, 2006|
|WET||Severe excess||1.5 < SPI9 < 2||3.5||1982|
|CASES||Extreme excess||SPI9 > 2||0||-|
In this work, SPI was calculated using monthly rainfall data at a time scale of six months for the period 1980–2007. That means that SPI was calculated for every month using the accumulated precipitation in the six-month period previous to that month. A gamma probability density function is fitted to calculate SPI. SPI greater than zero indicates water excess, while a value lower than zero indicates a deficit. The magnitude of the index allows the six-month accumulated rainfall to be classified into categories that go from extreme drought to extreme excess (extremely dry SPI less than −2; severe dry, SPI between −2 and −1.5; moderate dry, SPI between −1.5 and −1; slight dry, SPI between −1 and −0.5; normal, SPI between −0.5 and 0.5; slight wet, SPI between 0.5 and 1; moderate wet, SPI between 1 and 1.5; severe wet, SPI between 1.5 and 2 and extremely wet, SPI greater than 2).
Some characteristics of the SPI series were detailed with the aim of describing its behavior: the possible long term trend, the cycles greater than a year and the probability that an extreme value occurred. All these factors are important when the interannual variability is studied because they influence the amount of precipitation in a particular year and they must all be considered together.
SPI series was analyzed for low frequency variability using a linear trend method of minimum squares, and statistical significance was tested using a Student T test. The dominant periodicities associated with periods greater than one year were identified through spectral analysis. The technique used was the Blackman-Tukey method (Mitchell et al.
], Blackman and Tukey [16
]), which consists of applying a harmonic analysis to the autocorrelation function in order to detect cycles present in the original series. The spectral analysis was applied to the series after filtering the annual cycle. The aim is to find the cycles with the greatest spectral densities, that is, the frequency regions, consisting of many adjacent frequencies that mostly contribute to the overall periodic behaviour of the series. Therefore, a smoothing of spectral values using a weighed moving average transformation was done using a Tukey window. Its significance, depending on whether the spectrum fits a white or a red noise model, was also tested using the Blackman-Tukey method, and a confidence level of 95% was used to detect significant peaks. According to Blackman and Tuckey [16
] each spectral estimate is distributed as a chi-square divided by degree of freedom. This fact allows the confidence interval of each estimate of a computed spectrum to be easily determined by reference to a chi-square table.
Sometimes return periods are used to express the expected frequency of a flood or droughts of a certain magnitude in order to evaluate the actual risk in a basin. To calculate the return period of extreme SPI, a Gumbel function was fitted to the maximum and minimum monthly SPI.
As SPI was calculated for every month of the six-month period from 1980 to 2007, the value of SPI in September (SPI9) represents the accumulated rainfall from April to September. SPI9 is used in this study because rainfall season takes place over this period in the Neuquén River basin. Years were classified as wet or dry––as well as their different categories––using the value of SPI9, and represent the accumulated rainfall from April to September. Composite fields in April (when the rainfall period begins) of several variables for wet and dry years and the difference between them were plotted. Variables used were monthly sea surface temperatures (SST), 500 hPa (G500), 1000 hPa (G1000) and 200 hPa (G200) geopotential heights, zonal (U) and meridional (V) winds at 850 hPa and precipitable water (PW) from National Center of Environmental Prediction (NCEP) reanalysis (Kalnay et al.
]). Monthly anomalies were determined by removing the climatologically monthly means from the original values.
SPI9 predictors were defined using the difference between meteorological variables behavior in wet and dry years. Different sets of predictors, carefully selected based on statistical significance and physical reasoning, were proved to design statistical forecast models using the forward stepwise regression method (Wilks [18
]) which retained only the variables correlated with a 95% confidence level. Forward stepwise regression is a model-building technique that finds subsets of predictor variables that most adequately predict responses on a dependent variable by linear regression, considering the specified criteria for adequacy of model fit (Darlington [19
]). A common approach to better estimate predicting skills is a cross-validation (Wilks [18
]), where n − 1 years were used for calibration and the remaining year was used to validate the model. This process was repeated several times with different years. This method is generally strong in the presence of long-term climate variability and it is used especially when the amount of data is not so large. In the process of cross-validation, the exclusion of a single year from the data might not cause important changes in the model when detecting any evidence of numerical instability. With the aim of evaluating forecast effectivness, two indices (Wilks [18
]) were also calculated for wet and dry cases. The probability of detection (POD) is defined as the fraction of those occasions when the forecast event occurred in which it was also forecast. The false alarm relation (FAR) is the proportion of forecast events that fail to happen.