Important features of extreme precipitation in the La Plata Basin are studied on daily, seasonal, and annual time scales, using information from 1861 to 2005 and a common period from 1959 to 1998. A relation between the daily precipitation annual maximum and different time scales is developed. The points that make up part of the association field, the location of the maximum annual frequencies, the maximum annual precipitation totals, and the years in which they occur in the basin region are also presented.
Owing to the increase in precipitation documented in the region during the last decades of the twentieth century, this work will attempt to estimate the trends during the time periods studied in each of the basin stations prior to analysing the trend estimators calculated for different periods. Conditioning over the physical inference of the trends is related to the previous estimation results. Indeed, trend estimators may identify a long wavelength with a small amplitude at a physical level or the presence of waves during the calculation period with wavelengths longer than the period itself.
Precipitation extremes, their duration, and their intensity (due to excess amounts of water) are of interest in the field of hydrology. The planning of flood impact-curbing strategies, especially in highly populated areas, as well as the development of hydroelectric structures, is closely linked to the analysis and modelling of this type of extreme event. The development of this kind of analysis requires precipitation information obtained on a daily, or even hourly, timescale.
However, the majority of precipitation studies are done on monthly and yearly timescales. To a lesser extent, some precipitation phenomena are studied on a daily or shorter scale. This is mainly due to the lack of information on shorter timescales. However, Marchetti (1952) studied the precipitation intensities in the La Plata Basin in Argentina, focusing on extremes. Likewise, Marino (2007) detailed the daily extremes of the Buenos Aires region, highlighting the trends of daily precipitation values. Naumann et al. (2008) and Vargas et al. (2010) characterised dry spells and, in particular, extreme occurrences or meteorological droughts (on a daily basis) in the La Plata Basin.
It would be useful to enhance the description and diagnosis of extremes in the La Plata Basin, a region that has been poorly studied, despite its importance. However, it must be noted that several studies related to precipitation variations in the region have been performed. Several authors have reported trends and/or increases in precipitation accompanied by a strong impact on the cultural and productive systems of this region (Castañeda and Barros, 1994; Hoffmann et al., 1997; Liebmann et al., 2004; Boulanger et al., 2005; and Barros et al., 2008). The effects, or unusual patterns displayed by past data, especially extreme patterns, may be studied with more clarity by using daily data-gathering sequences. Using a greater time resolution, Liebmann et al. (2001); Liebmann et al. (2004); Re and Barros (2009); and Penalba and Robledo (2010) analysed spatial and low-frequency variations of precipitation extremes on a daily timescale.
This work studies the behaviour of precipitation maxima on three different timescales: daily, seasonal, and annual, and it investigates the correlation between different timescales. Regarding the temporal variability in the region, the trends or low-frequency phenomena that affect the precipitation series are studied as well. Furthermore, a brief discussion on methods for the estimation of trends is presented.
On the other hand, the statistical meaning of the absolute and secondary daily maxima per year, and their time stability, are also discussed. Finally, the theoretical distributions that best fit the regional maxima are surveyed. These results yield an objective inference about the impact and risk of floods.
In Section 2, this work details the materials and methods used. Section 3 describes the trends of regional precipitation on yearly and seasonal timescales. The methods used for the detection of annual precipitation maxima on a daily timescale and their regional and time correlations are described in Section 4. Section 5 details the relation between daily maxima and monthly/yearly precipitation totals. A discussion on the adjustments made to theoretical distributions that describe precipitation extremes is found in Section 6. Finally, the main results are detailed in Section 7.
2. Materials and methods
Daily precipitation data from 94 sampling stations located in the La Plata Basin were used in this study. The stations are located in Argentina, Brazil, Paraguay, and Uruguay, as shown in Figure 1 and Table I. The data were provided by the weather services of these countries and by the Proyecto Prosur database, (Aneel, 2000).
Table I. List of sampling stations used in this study
Stgo. Estero Aero
Conceiçao da Barra
Itau de Minas
La Rioja Aero
Paso de los Libres
V. María R. Seco
Fazenda J. Casimiro
Conceiçao Rio Verde
Usina do Chicao
Ponte do Posta
Conceiçao dos Ouros
Fazenda da Guarda
San Luis Aero
Sao Bento do S.
Punta del Este
Quedas do Iguaçu
Nueve de Julio
R. S. Peña
Mar del Plata
Reference stations were selected for specific and detailed analyses. These stations have daily records of precipitation spanning at least 50 years, with the exception of the Paraná (Brazil) region, which only has records that date back 20 years.
The linear trends were estimated by calculating the regression of the variable time. The significance level of the correlation coefficient r is representative of the slope, and the confidence level was 95%.
The aforementioned analysis was performed, highlighting the effects of the recorded data used on the estimation of trends and the processes involved. To this end, the correlation coefficient between time, yearly precipitation series, and the yearly frequency of rainy days was estimated. It was first estimated for the total period and then for gradually decreasing lengths of periods. The corresponding reference series is from the Observatorio Central Buenos Aires (OCBA) station for the period of 1908–2002.
Owing to the large impact of precipitation extremes, this work estimated the three absolute precipitation maxima per year. The maxima for each of the N years are represented by the day in each year that recorded the greatest precipitation. The subset that contains the N days that were most rainy represents the dataset of extreme values analysed. Likewise, the second and third daily annual maxima were defined. To determine the distribution that best represents daily precipitation extremes in the region, GEV, Gumbel, Gamma, lognormal, and Weibull models were used.
3. Annual precipitation totals
The characteristics of the annual accumulated precipitation maxima in the La Plata Basin will be studied, given that they are shown to be related to the recorded daily precipitation maxima. Figure 2 shows the reference stations (Campinas, Corrientes, Rivera, and OCBA), the total precipitation series, and the trend estimations. The figure shows that the trend is significant for the stations in Argentina, but not for the ones in Uruguay or Brazil, which is in partial agreement with Alexander et al., 2006, although in this case, the estimation is done for substantially shorter periods of time. This work will estimate the trends to infer the presence of low-frequency trends.
On one hand, it is shown that the increases in precipitation observed over the past decades mainly come from Mesopotamia and the Argentine Pampas. On the other hand, the interannual variation in Rivera is lower than in other stations, particularly during the years of 1958–1963. These effects show a correlation between the frequencies and annual totals.
In general, the results in Figure 3 (right) show the estimation of the range of total annual trends in the study region, measured by the coefficient r with a statistical significance of 5% during the period of 1959–1998. It can be seen that the significant trends are clustered in southern Brazil and Argentine Mesopotamia. This occurs because the commonly used period of 1959–2000 does not yield significant estimations of positive trends. Significant estimations are obtained, however, when the total records of the stations are used (Figure 3, left). This study implies that the estimated trend is dependent on the period of analysis, which implies the presence of patterns with long wavelengths that are numerically represented by the trends.
However, the presence of different effects on trends can be distinguished if the annual series are divided by the seasons of the year. Figure 4 shows the trends of seasonal contributions to precipitation. It can be seen that precipitation increases locally in the aforementioned region during summer and spring. During fall, Mesopotamia also shows significant positive trends. In the Brazilian state of Río de Janeiro, the process is not the same because a dense network (which will be detailed later) shows increases, especially during fall and winter, as well as a decrease during summer. These phenomena may be connected with a perturbation in the movements in the South Atlantic Convergence Zone (SACZ), as shown in Liebmann et al., 2004.
As previously analysed, Figure 5 shows different trend types along with the significance at the network stations in the Río de Janeiro region for the four seasons of the year. It can be seen that there is an increase in precipitation for all seasons of the year, except during summer, when a decrease in precipitation is observed. Owing to the density of sampling stations and the consistent behaviour of these estimations, the information from this network is reliable.
As previously inferred, the appearance of trends and, therefore, low frequencies, depends on the sampling period (Vargas et al., 2006), as shown by the annual precipitation series at OCBA station for the period of 1908–2002. To demonstrate this period effect, the trends for the total period and progressively decreasing periods are estimated. Table II shows that for the annual total, the trend is significant for the total period until the years 1948–2002, and from then on, all the periods have non-significant positive trends. The annual frequencies of rainy days display a similar pattern, except for the period of 1928–2002. The trends are not significant from then on, which shows that the estimation results greatly depend on the time length of the sampled period. On the other hand, the variability of the correlation coefficient of the annual frequencies of rainy days in the last periods clearly shows that long-wavelength trends that determine the observed fluctuations may be present in the series.
Table II. Trend variations for the annual precipitation series and the annual frequency of rainy days for OCBA during the period 1908–2002, represented by the correlation coefficients calculated for different time length periods. Significant values at 5% confidence are highlighted in bold
Annual precipitation series
Annual frequency of rainy days
An important aspect of the spatial study of the occurrence of absolute precipitation maxima and the annual rain frequencies is that it allows for verification or inference if the former and the latter are present in defined time periods. This is of greater importance when considering the conditioning exerted by global warming. Maximum precipitation values, annual frequencies, and their years of occurrence in each station are identified. Figure 6 (top) shows the ranges of maximum annual frequency and the year of occurrence, highlighting the period of 1981–1985, especially in Mesopotamia and in the basin. In Uruguay and in the Pampas, in addition to the previously mentioned period, the occurrence of precipitation extremes is predominant in the 1959–1965 period.
The precipitation (Figure 6, bottom) shows a similar trend, highlighting Uruguay, the Pampas, and central Argentina, during 1971–1975. Data from all of the stations were analysed for the common period of 1959–1998. If the same analysis is performed by taking each station with its complete period, the locations of the precipitation maxima and annual frequency do not show any significant changes. To some extent, these results show that in this timescale, the estimated trend is essentially the presence of long waves. These waves produced maxima in periods near the beginning of the twentieth century and during the 1980s (Minetti and Vargas, 1998; Vargas and Naumann 2008). These waves also produced a decrease during the last years, weakening the inference of a generalised precipitation increase in the basin during the last decades.
4. Daily precipitation maxima
Daily precipitation maxima have been identified as fundamentally important by several diagnostic and application approaches, and in some cases, it is believed that their increase is due to the effects of global warming (Groisman et al.1999). Figure 7 shows the series of the three absolute maxima per year and their mean values from reference stations as indicators of daily extreme rainy conditions and also this results are representative of this properties at all stations in the basin. It is important to notice that the three maxima show a certain correlation determined by the phase of the series. In other words, if during one year, the daily maximum tends to be higher than in other years, the second and third highest values also tend to show that same behaviour. This is also true for the opposite trend (Vargas et al.2010).
The coefficient r was estimated for all the stations to determine the behaviour of the absolute daily maxima per year during the long period (Figure 8). Significant positive tendencies in southeast Brazil, parts of Uruguay, and the northern basin region were observed, as well as in northwest Argentina. No other peculiar patterns were seen in eastern Paraguay, Mesopotamia, or the Pampas in Argentina, at least until 2002.
To stabilise the randomness of this variable, the problem was analysed in the same way using the three absolute maxima as well as their mean values. No other modifications were observed in the previous analysis, except in northern Uruguay, so it can be concluded that the maximum range is well represented by the mean values of the three maxima.
The analysis of daily precipitation extremes in the basin and surrounding areas shows that the limiting values must be between 50 and 70 mm for the series to be continuous and for no information gaps to exist in a single year. These limits establish the values for which time series or partial series theory can be applied (Hydrometeorological Practices Guide; WMO, 1994).
To analyse the regional correlation of the precipitation maxima, ten absolute maxima were selected per region. Table III shows the years of occurrence for each maximum and the number of stations that recorded maxima per year during the period of 1930–1998. It is shown that there is no regional trend in the number of maxima per year when the longest sampling period is applied. However, stations such as Pergamino INTA and Pilar Observatory display a greater occurrence during 1930–1950. The stations located in Brazil display two distinct examples of premature (Nova Palmira and Cangucu) and late onset (1990s, Terra Roxa, Carandai, Conceiçao da Barra) occurrences. These results show that despite the high timescale variability and the insufficient network coverage, there is a certain correlation in the occurrence of maxima given by the number of stations that record maxima in a year. This is corroborated by the occurrence of maxima for the years 1963, 1971, and 1985, during which approximately 50% of the stations simultaneously show extremes.
Table III. Years of occurrence of the ten most extreme rainfall events for twenty sampling stations. The numbers indicate the years in which there was more than one extreme event
5. Relation between daily maxima and monthly/ yearly totals
To examine the relations that can link absolute daily maxima with monthly totals, an approximation through correlations was carried out. Daily maxima for each month were correlated with monthly precipitation totals for Brazilian and Argentinean stations. For all the stations, the correlations were significant at 5% with values that generally surpass the critical value of r (0.23). Indeed, the coefficients range from 0.6 to 0.9 (results not shown). While this depends on the number of precipitation days in each month, a robust linear relationship between the totals and daily maxima is inferred to be an acceptable approximation. Generally, daily data in the available archives or databases are less frequently found than monthly and yearly totals. Therefore, this approximation would allow for some estimation of the daily maxima per month.
If the procedure is repeated for the daily maximum series for each year and the annual precipitation totals, the results are also significant. Because the r values are significant for all the stations, we can describe the variance explained by the relation as shown in Figure 9. The explained variance varies regionally between 20 and 60%, with a maximum in northeast Argentina, near the southeast coast of Brazil and Uruguay. The maxima observed in the vicinity of the basin, in west Argentina, are somewhat obvious because the area is semi-arid, and high daily precipitation values are related to the annual range because the maximum can accumulate in a few days of precipitation.
6. Distribution adjustments to daily precipitation maxima
Although the occurrence of extreme daily precipitation events has a low probability in this region, its impact on socio-cultural systems is far reaching. Therefore, the study and development of probability approximations for the extreme values associated with hydrologic processes allow for increased knowledge that can be used in decision making and in the assessment of risks associated with these extreme events. For example, in the design and construction of large water works, flood studies are carried out through probability models. Extreme precipitation events are diagnosed with the same methods (Nash and Sutcliffe, 1970; Sutcliffe, 1978; Sutherland, 1983).
The literature generally shows that Gumbel's distribution is the most commonly used model dealing with hydrologic extremes. However, some studies have shown that in most cases, this distribution underestimates large extreme precipitation values (Wilks, 1993; Koutsoyiannis & Baloutsos, 2000; Coles et al.2003). Regarding this, Koutsoyiannis (2004) performed research with extreme precipitation series and found that the type II general extreme value (GEV) distribution is a better fit, even in series for which records are available for only a few years.
This section will study the fitting of different distributions generally associated with extreme precipitation in the La Plata Basin and surrounding areas. Five distributions associated with extreme values from all the basin stations are fitted (GEV, Gumbel, Gamma, lognormal, and Weibull) to the daily precipitation maxima for one year. To estimate the degree of fitting, the statistical chi-squared test is carried out, taking as a null hypothesis that the dataset used corresponds to each of the theoretical distributions analysed.
It is shown that the GEV distribution best represents the daily precipitation maxima per year in all the regions, where 92% of the stations fit the 5% significance level. On the other hand, 89% of the stations fit a lognormal distribution, while 84% fit a Gamma distribution. Finally, 72% fit to a Weibull distribution, and 67% of the stations fit Gumbel's distribution.
These results show that the GEV distribution defined by three parameters best represents precipitation extremes in the La Plata Basin. The probability distribution function (PDF) is defined by:
where ξ is the location parameter, β is the scale parameter, and κ is the form parameter.
Three special cases of GEV depend on the form parameter κ. If the parameter κ approaches zero in Equation 1, the resulting PDF is:
This PDF is known as a type I Gumbel or Fisher-Tippett distribution.
When κ> 0, Equation 1 is a denominated type II Frechet or Fisher-Tippett distribution. This family of distributions is characterised by the slow decrease of the PDF for large values of the variable x. The third special case occurs when κ< 0 (type III Weibull or Fisher-Tippett distribution). More details about this family of distributions can be found in Wilks (2002).
Given the vastness of the La Plata Basin and the number of climatic regions within it, a classification of the PDF with the best fit (GEV) is made. An objective classification of the PDF from each station was made using the k-means cluster method (MacQueen (1967); Hartigan and Wong (1979)) over the daily precipitation maximum per year. To define the climatic regions (groups), the PDF for each region obtained from cluster analysis must be different from the others. To evaluate the similarity between the distributions, a chi-squared test was performed with a 5% confidence level.
This analysis revealed that the region is characterised by three different models of extreme precipitation. The map on Figure 10 shows how each station belongs to each of the three theoretical models obtained and is characterised by the mean values of each group. This result relates to the findings of Garcia and Vargas (1996), who analysed the annual median and total precipitation values and, based on these, identified three main hydro-climatic regions in the basin.
Model 1 is characterised by a value of (ξ = 67.2, β = 19.6, and κ = − 0.008) and has the lowest variance. This model represents the greatest number of sampling stations and is associated with locations in the northern region of the basin, mainly stations in Brazil, northwest Argentina, southern Córdoba, Santa Fe, and central Buenos Aires. Model 2 (ξ = 85.6, β = 26.1, and κ = − 0.018) has the greatest dispersion and contains the maximum extreme values of the region. This category includes the Rivera station (Uruguay), which recorded the absolute daily maximum of the entire region—in April 1959, a daily maximum of 246 mm was recorded (Vargas, 1987).
Model 3 (ξ = 48.1, β = 21.31, and κ = 0.04) is associated with stations located in the semi-arid region of Argentina (in the west-southwest borders of the basin). Here, the maxima are the result of exceptional surges of moist air from the north-northwest, not the result of the general climate regime (Hoffmann, 1975).
Analysing these models, the region with greatest hydrologic risk is represented by Model 2. This region displays the greatest ENSO impact (Vargas et al.1999; Barros and Silvestre 2002; Penalba and Vargas, 2004; Re and Barros, 2009) where the greatest floods resulting from extreme precipitation during El Niño events were recorded.
On the other hand, Section 4 showed how extreme precipitation events tend to be grouped in consecutive periods of time; in other words, if one year recorded an extreme precipitation event, it is highly probable that the second and third maxima of that year will be extremes as well. Therefore, in considering the risk of floods, modelling of distributions with the first three daily precipitation maxima is needed in the decision-making process.
Figure 11 shows the empirical and theoretical distributions (GEV) for the first three annual maxima of daily precipitation calculated using four reference stations. Table IV also shows the parameters that define each distribution. It is shown that the GEV distribution fits all of the maxima, except for the distribution associated with the third maximum in the Rivera station. This implies that the theoretical model that describes the distributions (GEV) is not modified, even though the parameters that define the distribution are.
Table IV. Parameters associated with the fitting to the GEV distributions for the three maxima at Campinas, Corrientes, Rivera, and OCBA
Several applications require models to be fit to maximum conditions with probability values greater than the absolute maximum. This is necessary when evaluating risks for maximum conditions that are more probable than the absolute ones. Questions regarding the stability of the models arise when the secondary maxima are fitted. Generally, the form parameter (κ) values are greater than 0.1 for the first maximum and decrease to values near zero if secondary maxima are considered. Only the Corrientes station data showed a κ value near zero for all the maxima. On the other hand, it is shown that the third maximum tends to fit a type III GEV distribution, mainly in Campinas (κ = − 0.21). This is reasonable, as the values that define the secondary maxima tend to be controlled by the absolute maximum. Jenkinson (1955) suggested that it is generally reasonable to expect that in nature, maximum values are capped by an upper limit (thus, better fitting to a GEV III distribution). However, this is not the case for maximum precipitation because a considerable precipitation can be recorded and its maximum level is uncontrolled to a certain extent.
The La Plata Basin is a region of significance due to its water resources and the value that the hydrologic cycle variables have on any scale. To manage the use of water and soil resources and to plan their future management, the study of rainfall, and especially its maxima, is of great importance. Global warming plays an important role in the expected scenarios due to long-term climate changes and trends. To avoid the establishment of initial restrictions, daily precipitation data are used, although they are not as common in the available databases.
The results obtained show that the estimation of trends for the period of 1959–1998, i.e. the annual totals that show increases in precipitation, are mainly found in the Argentinean Mesopotamia and Pampas regions. A parallel analysis using all the information available from al the stations shows no substantial change in the results, although the areas that undergo positive changes with time are modified.
Analysis of the seasonal totals shows that precipitation in spring and summer causes positive trends in the Mesopotamia and Pampas regions, while no decrease in precipitation is observed, except for the north basin region (Río de Janeiro), where a decrease occurs during the summer. The latter effect is corroborated by a dense network of sampling stations in the same area that show the same trends.
On a daily timescale, regarding absolute maxima per year, significant positive trends are observed in southeast Brazil, parts of Uruguay, and the north region of the basin, as well as in northwest Argentina. Trend estimators could be identified as a long wave with low amplitude or the presence in the calculation periods of wavelengths longer than the period itself.
To assure consistency in the daily maxima per year, the three main maxima and their mean values were analysed. This analysis reveals that the values of the trends are similar, which suggests that there is a correlation between the value of the first maximum and the second and third ones. In other words, the value of the absolute maximum of a series is generally followed by the second and third maxima in the series, and vice versa.
The regional correlation of the range of daily maxima in each station represented by the ten absolute maxima does not define any significant trends in the variable that represents the amount of stations in the region with a maximum in the year. This allows us to infer that the absolute maxima are caused by mesoscale processes. On the other hand, there are few sampling stations with consistent singular behaviour producing maxima in the period from 1930–1950.
The study of trend values shows that they are strongly dependent on the timescale of the recorded data used. This allows us to conclude that trends obtained with records determined for equal periods for all sampling stations imply an approximation. This is a condition that must be accounted for in the majority of research works related to this topic that are based on previously recorded data.
There is a significantly high correlation between monthly precipitation values and monthly absolute extremes. This also occurs when the annual totals are related to the daily maximum of each year. Therefore, this could offer the possibility of a first estimation of the daily maxima per year and month, remembering that the records most commonly found in databases are monthly totals.
Finally, it is shown that the generalised extreme value (GEV) distribution defined by three parameters best describes the behaviour of rainfall extremes in the basin region. It was also found that the probability of occurrence associated with daily maxima in the basin region is well represented by three variations of the GEV model.
This research was sponsored by projects UBA X-228, CONICET PIP 112-200801-00762 and FONCyT PICT 2008-1820.