Servicios Personalizados
Revista
Articulo
Indicadores
- Citado por SciELO
- Accesos
Links relacionados
- Similares en SciELO
Compartir
Tecnología y ciencias del agua
versión On-line ISSN 2007-2422
Tecnol. cienc. agua vol.11 no.3 Jiutepec may./jun. 2020 Epub 10-Jun-2024
https://doi.org/10.24850/j-tyca-2020-03-02
Articles
Non-stationary modeling of the magnitude and frequency of floods in Alto Cauca through climatic and reservoir operation indexes
1Universidad del Valle, Cali, Valle del Cauca, Colombia, karimesedano@gmail.com
2Universidad del Valle, Cali, Valle del Cauca, Colombia, yesid.carvajal@correounivalle.edu.co
3Universidad de Colima, Facultad de Ingeniería Civil, Colima, México, jlopez71@ucol.mx
4Universitat Politècnica de València, Valencia, España, ffrances@upv.es
In this study, changes in the frequency and magnitude of annual floods in the Cauca River (Southwest Colombia) are modeled using a non-stationary framework by means of the Generalized Additive Models of Localization, Scale and Shape. Non-stationary flood frequency analysis incorporates two climatic indices and an anthropic index that allows us to assume that changes in the water reservoir and the percentage of regulated tributary area are factors which disturb the capacity of the dam to withhold the flood. The results highlight the role of the El Niño Southern Oscillation (ENSO) phenomenon and the proposed Reservoir Index, as significant covariates in the parameters of the selected distributions. The dependence of model parameters on covariates improves the model’s capacity for representing temporal variability of the flood regime. Non-stationary models indicate significant differences in the flow associated with a specific return period, and in the failure risk of flow design, depending on the working life, in contrast to classical stationary models. The main conclusion is that since 1986 in the gauging station Juanchito, flooding has shown a gradual increase in magnitude, which is unambiguously associated with the cold phase of the ENSO phenomenon. Therefore, the non-stationary models provide valuable information on the reservoir, its regulation strategy for high flow, and for flood risk management in the Cauca river basin.
Keywords: Floods frequency analysis; non-stationary; El Niño South Oscillation Phenomenon; Colombia; anthropogenic interference
A través de los modelos aditivos generalizados de localización, escala y forma se estudian los cambios en la frecuencia y magnitud de las crecidas anuales en el río Cauca, localizado en el suroccidente de Colombia. El análisis de frecuencias de crecidas no estacionario incorpora dos índices macroclimáticos y un índice antrópico, que permite asumir los cambios en el almacenamiento de agua en el embalse y el porcentaje de área tributaria regulada, como factores que inciden en la capacidad de la represa para laminar las crecidas. Los resultados muestran que forzamientos que dependen del Índice Multivariado del Fenómeno El Niño Oscilación del Sur (ENSO, por sus siglas en inglés) y del índice de embalse propuesto, cuando son aplicados a los parámetros de la función de distribución, mejoran la calidad de ajuste y la descripción de la variabilidad temporal de la serie de tiempo de crecidas. Frente al análisis convencional, los modelos no estacionarios indican diferencias significativas en los caudales asociados con cierto periodo de retorno y en el riesgo de fallo de un caudal de diseño en función de la vida útil. La principal conclusión es que desde 1986, en la estación de aforo Juanchito, los caudales exhiben un incremento en magnitud que está asociada inequívocamente con eventos de la fase fría del fenómeno ENSO. Por lo tanto, los modelos no estacionarios proveen información de interés para el embalse, su estrategia de regulación de caudales altos y en la gestión del riesgo de inundaciones.
Palabras clave: análisis de frecuencias de crecidas; no estacionariedad; fenómeno ENSO; Colombia; alteración antrópica
Introduction
The climatic variability associated with ENSO is of profound environmental and socioeconomic impact in Colombia. The cold phase of ENSO generates emergencies due to flooding and landslides, potentially affecting more than 500,000 people with a 2- to 4-year frequency. During the period 1950-2018, 177 natural disasters were reported in the country, with 45% of cases corresponding to floods (EM-DAT, 2018). Furthermore, in relation to Latin America, Colombia has the highest rate of recurrent emergencies caused by natural phenomena (more than 600 reports per year); due not only to natural environmental conditions, but to the fact that 84.7% of the population are located in areas exposed to two or more natural hazards (Banco Mundial, 2014).
Flood Frequency Analysis (FFC) is the statistical model most frequently used to estimate the flooding flow rate and / or its frequency of occurrence, in order to determine the size of hydraulic structures and manage water resources in a basin. The analysis makes inferences about a hydrological variable, assuming the hypothesis that the observations are independent and identically distributed (i.i.d. hypothesis); therefore, there are no systematic changes in the mean or variance that determine the appearance of trends during the observation period, nor in the extrapolations made on said data. However, there is evidence of the effects of global environmental changes and climate variability in relation to the alteration of the behavior of hydrological variables in both space and time, which explains why statistical methodologies that address non-stationary FFC have been under development for more than a decade.
Previous studies on the effects of climate variability on the hydrological regime of Colombia have found: 1) Strong correlations between ENSO and hydrological variables, e.g.: greater variability in the monthly flow rate of the Cauca and Magdalena rivers; 2) Trends of increase / decrease in time of: air temperature, precipitation and monthly flow rate especially in the Andean region; and 3) that the probability distribution function of the maximum flow rate series is affected by both phases of ENSO (Ávila, Guerrero, Escobar, & Justino, 2019; Carvajal, Jiménez, & Materon, 1998; Gutiérrez & Dracup, 2001; Jiménez-Cisneros et al., 2014; Poveda, 2004; Poveda & Álvarez, 2012; Poveda et al., 2002; Poveda, Waylen, & Pulwarty, 2006; Puertas & Carvajal, 2008). Prior evidence has shown that the analysis of the hydrological risk associated with the ENSO phenomenon is key for flood management in Colombia, particularly in the Andean region where 80% of the population is concentrated.
At present, the debate on whether or not to adopt the assumption of stationarity required in hydrological statistics still continues (Matalas, 1997; Milly et al., 2015; Milly et al., 2008; Montanari & Koutsoyiannis, 2014). The discourse is antagonistic. On one hand, there is a call to incorporate non-stationarity in hydrological modeling to better represent reality; whereas others argue that multiple sources of uncertainty must be considered in order to ensure the stochastic approach remains robust. Although there is no consensus on the best analysis methodology, there are common points, such as: the need to increase the understanding of the climate-water-society system, reduce sources of uncertainty in the models, and above all, develop more robust analysis methodologies in order to propose effective, adaptive solutions to trends in hydrological risk change.
Many investigations have addressed non-stationarity in hydrological variables, via the development of non-stationary methodologies for the Frequency Analysis of extreme events, and propose adaptations to the concepts of return period and risk in hydrological design (Khaliq, Ouarda, Ondo, Gachon, & Bobée, 2006; Salas & Obeyskera, 2014). The most studied non-stationary models incorporate the forcing of trends using external covariates such as: climate variability indices, precipitation and temperature data; global change signals on a reduced scale, urbanization rates, reservoir rates, etc. This type of analysis aims to establish links between physical processes in the environment and changes in the distribution of probabilities associated with annual records of maximum flow rates. There are abundant references for the use of generalized additive models with the parameters of location, scale and form (GAMLSS), as a flexible alternative, both in the selection of the distribution function and the type of parameter trends (Ahn & Palmer, 2016; Córdoba, Palomino, Gámiz, Castro, & Esteban, 2015; Vasiliades, Galiatsatou, & Loukas, 2015; Villarini & Strong, 2014). Other works use Bayesian models and Singular Spectral Analysis (Escalante-Sandoval, & Garcia-Espinoza, 2014; Lima & Lall, 2011; Poveda & Álvarez, 2012).
All of the aforementioned, motivates the non-stationary statistical modeling of floods in Colombia. The evaluation of maximum annual flow rate in the Cauca River - located in the High Cauca Valley basin within the Andean region - was chosen as the case study. The region has a bimodal regime with rainfall between 1300 mm and 3000 mm, and has a floodplain of 840 km2 susceptible to periodic flooding. Since 1985, flow rates in the river basin have been regulated by a reservoir. The Cauca River is of interest since it is one of the most urbanized regions of Colombia. In addition, between 1950 and 2015, 14 historical flood events in the Cauca River were recorded (Enciso, Carvajal, & Sandoval, 2016); six of these occurred after the construction of the reservoir (in 1988, 1997, 1999, 2008, 2010 and 2011) and coincided with La Niña phenomenon. The data corresponds to two hydrometric stations of interest, and was analyzed using the GAMLSS model proposed by Rigby and Stasinopulos (2005).
The hypothesis considers whether the use of non-stationary models present significant differences compared to stationary analysis, and aims to demonstrate that the incorporation of climatic forcing (through several macroclimatic indices associated with the South American tropics) and human activity (using a specific reservoir operation index) are suitable as additive terms that describe changes in the frequency and magnitude of maximum annual flow rate. The statistical models evaluated may be of interest to demonstrate opportunities for water resources management, especially the rules of operation for the reservoir to guard against flooding events, to the benefit of the city of Cali (the third most populous city in Colombia). Next, a characterization of the study area is presented, as well as the methodology used in the non-stationary frequency analysis. The results obtained are analyzed and some conclusions are summarized.
Study área
The high Cauca basin is located in southwestern Colombia. The Cauca river follows a south-north direction in an inter-andean valley (Figure 1). In the first 153 km, the channel descends 2.8 km to reach Salvajina reservoir, whose drainage area is 3,652 km2. Downstream, the basin reaches 5,111 km2 at La Balsa station and finally the area of interest closes at the Juanchito hydrometric station, covering a total of 8,556 km2. Both stations were selected considering: 1) the proximity to the reservoir outlet, 2) Juanchito station is the control point for the volume operation in the Salvajina dam and 3) Juanchito is located on the outskirts of the city of Cali, which is the third most populous city in Colombia with 2.4 million inhabitants.
The Salvajina reservoir has a maximum storage capacity of 848 hm3, its operation objectives are flood and estuarine control, guaranteeing flow rates between 900 m3 / s and 130 m3 / s for 95% of the time at Juanchito station (Sandoval, Ramirez, & Santacruz, 2011).
The hydrological regime in the region is strongly affected by the climatic variability associated with the double passage of the Intertropical Convergence Zone (ITCZ), orography, the processes that occur in the Atlantic ocean, the Caribbean sea, the Pacific and the Amazon, but above all, by the influence of the ENSO phenomenon in its extreme phases (García, Botero, Bernal, Ardila, & Piñeros, 2012; Puertas & Carvajal, 2008; Rueda & Poveda, 2006).
Mean annual rainfall in the upper Cauca river basin is 1900 mm, and a bimodal cycle with greater rainfall predominates in the periods: March-April-May (MAM) and September-October-November (SON) (Figure 1, right) (Sandoval & Ramirez, 2007). Strong connections have been reported between mean monthly flow rates of various rivers in western Colombia with the El Niño Oceanic Index - 𝑂𝑁𝐼, and other signs of change in the surface temperature of the Pacific ocean, the Pacific Decadal Oscillation - PDO, with composite climatic signals for atmospheric and oceanic variables such as the ENSO - MEI Multivariate Index and exclusively atmospheric variables such as the Chorro del Chocó - CCC and the SOI Southern Oscillation Index, among others (Jiménez-Cisneros et al., 2014; Poveda, Jaramillo, & Vallejo, 2014; Poveda et al., 2006).
Materials
All the hydrological and climatic variables were constructed considering that the
hydrological year in Colombia begins on June 1 of year 𝑖 and ends on May 31 of
year
Reservoir index
López and Francés (2013) propose an IE reservoir index (Equation 1), which establishes the degree of alteration of the hydrological regime based on the percentage of unregulated area, and the percentage of average runoff that cannot be retained in the reservoir.
Where,
The impacts of a reservoir on the rolling of floods depends upon: the
available capacity of the reservoir, the size of the works in relation to
basin water supply, the uses of stored water and water levels in the
reservoir before the channel, etc. (Moreno,
Begueria, Garcés, & García, 2003). Available capacity means
the free volume or difference between the maximum storage capacity and the
volume of water at any given time. Changes in available capacity may limit /
favor the management of maximum annual flow rates at the target station.
Therefore, in this paper it is proposed to adjust equation 1, replacing the
relationship between reservoir capacity and average runoff, by the annual
reserve volume coefficient
Where
Indices of climatic variability
Bearing in mind that the ENSO phases are defined by the US National Ocean and
Atmosphere Agency (NOAA) based on the El Niño Oceanic Index (ONI), in this
work the mean annual value of ONI is adopted as a criterion to classify each
hydrological year, as follows: one year is considered La Niña if the ONI
mean annual value
Generalized Additive Models of Location, Scale and Shape parameters-GAMLSS
GAMLSS models assume that the response variable
Where
As a smoothing function, the B-splines,
Non-stationary return period
The return period
Where
The values of the probability of exceedance 𝑝 𝑡 are obtained from
Where the values
Serinaldi (2015) argues that one of
the most important indicators in the planning and design of hydraulic works
is the Risk of Failure 𝑅 or probability 𝑅 that an extreme event will be
observed at least once
Where
Methodology
Statistical modeling of the frequency and magnitude of hydrological extremes is based on the generalized additive models of location, scale and the GAMLSS form. All calculations can be executed in the R program, using the available free GAMLSS packages. The analysis has the stages of Figure 2.
Identification of changes and trends in the flood regime
The non-parametric statistical tests of Mann-Kendall (Mann, 1945; Yue & Wang, 2002) and Pettitt (1979) are applied to the time series to analyze the stationarity. Additionally, in order to address the effects of reservoir operation, the maximum annual flood series were divided into the periods: 1965-1984 and 1986-2015, thereby representing the unregulated regime and the altered regime, respectively.
Adjustment and selection of non-stationary statistical models
GAMLSS models are used to force gradual changes in the location parameter
Two types of statistical models are analyzed: Stationary models (M0), where
both distribution parameters are independent; and the models of external
covariates (M1), in which the location parameter
Where
In the absence of a statistic to determine the goodness of fit of the GAMLSS models, Stasinopoulos et al. (2015) propose to verify the normality of the residuals, for this the Filliben correlation coefficient and the behavior of the graphs without the residuals trend (worm-plot) are evaluated. This ensures that the selected model represents the systematic part and that the remaining (residual) information is white noise.
The return period in non-stationary models
To compare the results obtained in the M0 and M1 models, the EWT and AAR
formulations are used. The calculation starts by defining a flow rate
Results and discussion
Altered flood regime
Next, the changes in the flood regime in La Balsa and Juanchito are analyzed.
Table 1 confirms that the flow rate
at La Balsa decreases during the registration period and this trend is
significant at
Station | La Balsa | Juanchito | ||||||
---|---|---|---|---|---|---|---|---|
Series | Test | Period | 65-15 | RN | RA | 65-15 | RN | RA |
Qmax | M-K |
|
-0.33* | -0.38 | -0.04 | -0.06 | -0.02 | 0.22* |
Sig. | P1 | P5 | NS | NS | NS | P10 | ||
Pet | Year | 1984 | 1975 | 1991 | 1984 | 1975 | 1994 | |
Sig. | P1 | P5 | NS | NS | NS | P5 |
RN: 1965-1984, RA: 1986-2015. M-K: The Mann-Kendall test;
The following physical processes that may be related to the trends of increase in the flood regime of Juanchito station between 1986 and 2015 are:
Changes in land use in the last 30 years that affect the runoff of tributary rivers downstream of the reservoir. Given that 43% of the total drainage area to Juanchito corresponds to the reservoir basin, it is consistent to consider that important tributary rivers that are not currently regulated make a strong contribution to runoff in the area. Also, there is evidence of increased precipitation in that region. Ávila et al. (2019) analyzed the time series of extreme climatic precipitation indexes in 39 meteorological stations of the Alto Cauca Valley in the period 1970-2013. They recognized that for a statistical significance 𝛼=0.10: the accumulated precipitation in one and five consecutive days increases between 40 - 80 mm in the south region of the western Andes mountain range (between the reservoir and Juanchito). This coincides with the Climate Change projections that foresee a 6% increase in total rainfall in the climatic models of Valle del Cauca, from the periods 2011-2040, 2041-2070 and 2071-2100 (IDEAM et. al, 2015). If, in addition, it is considered that the La Niña phenomenon increases and prolongs high flow rates, it is to be expected that the effect of the reservoir on the control of floods is limited and that the floods are largely due to the contribution of the unregulated tributary rivers.
Between 1986 and 2015, seven historical floods have been recorded in La Niña years (Enciso et al., 2016). Of these floods, four occured simultaneously with the cold phase of the PDO. Of all recent floods, those occurring in 2010-2011, are recorded during one of the most severe La Niña events in recent history (NOAA-ESRL-PSD, 2017).
Until 1975, and then between 1999 and 2014, cold phases of the Pacific Decadal Oscillation (PDO) prevailed (JMA & WMO, 2017; Herzog, Martinez, Jorgensen, & Tiessen, 2012; NOAA, 2017). There are several references on the simultaneous action of ENSO and the PDO on the hydrological regime in various regions of the world that establish that the effects of El Niño / La Niña events are stronger and occupy a larger global space area when they occur in phase with hot / cold periods of the PDO (Garreaud, Vuille, Compagnucci, & Marengo, 2009; Méndez, Ramírez, Cornejo, Zárate, & Cavazos, 2011; Wang, Huang, He, & Guan, 2015). This shows the need for more research on the joint action of different signs of climate variability and the hydrology of the Colombian southwest.
Changes in the hydrometric stations and / or in the way of processing the data could also be another explanation for the abrupt changes observed (Villarini et al., 2009a).
The results obtained in Table 1 highlight the difficulty in accepting / rejecting the i.i.d. hypothesis for the 1965-2015 period at Juanchito station, since the non-parametric tests applied indicate stationarity. However, changes in the slope of the trend lines in the RN and RA periods mask the continuous increase in annual flooding in the last 30 years of the analysis period and therefore, the RA sample requires the non-stationary Flooding Frequency Analysis.
Figure 3 shows the behavior of maximum
annual floods as a function of time and reservoir and climate indices, which
suggest that although there is a moderate linear correlation
River
The results of the statistical modeling of the annual maximum daily flow rates for La Balsa (1965-2015) and Juanchito (1986-2015) are presented below.
Table 2 shows that the stationary model (M0) in La Balsa follows the Lognormal distribution (LN2). The Log transformation helps reducing the positive asymmetry of the observations. Then, the floods in Juanchito conform to the Gamma distribution, which is a function that has a smooth form and does not require the Log function to counteract the asymmetry; This last result is similar to that obtained by Enciso et al. (2016), who finds that Juanchito's annual maximum daily flow rates in the 1986-2015 period are adequately adjusted to a Log Pearson III distribution, which is a generalization of the Gamma distribution. Next, it can be seen that the GAIC statistic suggests that the M1 models have lower loss of information. Regarding the quality of fit, in all cases, the Filliben correlation coefficients are higher than the critical values, therefore, the hypothesis of normality in the residuals is accepted and the models are adequately adjusted to the observations.
Variable Station Period Distribution | Model | Parameters (Error St.) | CIAG | C.F. |
---|---|---|---|---|
Qmax La Balsa 1965-2015 LN2, n=50 | M0 |
|
664.01 | 0.991 |
M1 |
|
631.05 | 0.996 | |
Qmax Juanchito 1986-2015 GA, n=30 | M0 |
|
405.85 | 0.988 |
M1 |
|
385.68 | 0.993 |
The non-stationary model of the LN2 and GA distributions have
as linking function the localization parameter:
Debele, Bogdanowicz and Strupczewski (2017) suggest that the selection of the distribution function (fdp) is one of the most important decisions for the proper analysis of the models. We consider that the hypothesis tests establish an adequate fitting, but do not necessarily lead to the selection of the best fdp. For this, GAMLSS models provide a broad range of comparison options between different families of fdp and also the consideration of non-stationarity. However, it is necessary to use the expert’s criterion to select a pfd that controls the effect of the positive asymmetry characteristic of the hydrological series and a model without over-parameterization.
Among non-stationary models with the best fit we have:
The temporal variability of the floods at La Balsa station is explained through the IE2 reservoir index. This is due to the fact that La Balsa has the smallest area of total contribution and since it is located near the reservoir output, the anthropic regulation predominates over the change patterns of the series
The maximum flow rates at Juanchito for 1986-2015 have a non-linear dependence on the MEI index through 𝑝𝑏() smoothing and linear to IE2. Different publications indicate that GAMLSS with climatic forcing are significant to represent changes in the frequency and magnitude of floods in different regions of the planet (Machado et al., 2015; Obeyskera & Salas, 2016; Villarini, Smith, Serinaldi, Ntelekos, & Schwarz, 2012). In this work, the ENSO signals and the proposed reservoir index are adequate to link anthropic and climatic effects to patterns of the annual flood series for the southwest of Colombia. In addition, it is possible that as the station moves away from the reservoir, the effect of climate variability becomes more significant as an explanatory variable
It is important to highlight that based on the evidence of non-stationarity, it is necessary to adopt methodologies that incorporate change patterns and allow a comparative analysis of results. In this work, the non-stationary models based on co-variables (M1) show a better representation of the variability of the time series, considering that the majority of the observations are within the band of quantiles 1% to 99% of the models (Figure 4a and Figure 4b). Villarini, Serinaldi, Smith, & Krajewski (2009b) obtained similar results using GAMLSS for the analysis of floods in a US basin, mentioning that the models manage to capture the wide dispersion and nonlinearity of data for percentiles between 5 and 95%.
The non-stationary M1 models show - for all the percentiles plotted - that at certain times the magnitude of the variables obtained is different from that estimated under stationary conditions, e.g. during La Niña years, and that increases in the magnitude of flow rates that can affect flood risk indicators such as the return period and the risk of failure for a particular project life can be identified. Regarding this result, López and Francés (2014), when evaluating floods in the Northwest of Mexico, also find a significant influence of the ENSO phenomenon in the inter-annual variability of the flood regime, highlighting increases in magnitude during La Niña. In addition to the above, it is necessary to recognize that a limitation of the results of the co-variable models is the uncertainty associated with ignorance about the future, e.g. the behavior of the explanatory variables beyond the registration period (there are no long-term projections for the ENSO indices that may be incorporated into the predictive power of the models) and that other physical processes (not considered in the present study) may be more significant to describe the variability of floods.
Figures 4c-4f evaluate the normality of the residuals of the different models based on their configuration. In a Q-Q graph with no tendencies, which is usually shaped like a worm, one seeks for the continuous red line (trend) to be similar to a straight line, parallel and close to the horizontal axis. On the contrary, when the residuals show accentuated configurations either in S or U, they indicate high asymmetry and / or kurtosis (Buuren & Fredriks, 2001). In both stations, it is evident that the models meet the normality condition. However, of all of them, the M1 model of La Balsa has fewer deviations from that assumption.
Analysis of changes in the return period
Figure 5 and Table 3 show the variations obtained when estimating the
period of return
Station | La Balsa | |||||||
Qmax (m3/s) | 212 | 445 | 735 | 883 | 995 | 1107 | 1221 | 1494 |
T (years) | 1 | 2 | 10 | 25 | 50 | 100 | 200 | 1000 |
T(EWT)(years) | 1 | 1 | 24 | 1363 | 4410 | 7227 | 8829 | 9881 |
T(AAR)(years) | 1 | 2 | 9 | 26 | 62 | 155 | 402 | 4143 |
Station | Juanchito | |||||||
Qmax (m3/s) | 397 | 700 | 975 | 1091 | 1171 | 1246 | 1316 | 1470 |
T (years) | 1 | 2 | 10 | 25 | 50 | 100 | 200 | 1000 |
T(EWT)(years) | 1 | 3 | 9 | 19 | 34 | 61 | 116 | 497 |
T(AAR)(years) | 1 | 2 | 9 | 20 | 40 | 82 | 178 | 1194 |
In the case of annual floods at Juanchito between 1986 and 2015, an
increasing trend has been described (Figure
3b). When comparing the non-stationary return period, Figure 5b shows: 1) When
All the changes in the hydrological risk indicators (
Conclusions
In this work, the effects of reservoir operation and climate variability as patterns of alteration of the annual flood regime are analyzed with the Non-Stationary Flood Frequency Analysis, using GAMLSS models. The main conclusions are.
Daily flow rate records between 1965 and 2015 at La Balsa station point to a
significant decrease (
Maximum annual floods at the Juanchito station between 1965 and 2015, show a
pattern of significant increase (
The increase in the magnitude of maximum annual flow rate at Juanchito may be associated with the close connection between the prolonged and strong floods and climatic events, which in conjunction with the cold phase of the PDO strengthens the nuclei of maximum rainfall in the study area. This information shows the need for more research to establish the type of connection and the effects that the joint action of the PDO and ENSO have on the hydrology of the Colombian southwest. Additionally, it is likely that land use changes in the area tributary to Juanchito that are not regulated by the reservoir (57% of the total area), also affect the trends of increased runoff.
For all the stations evaluated, the study demonstrates that the use of additive terms improves the description of changes to the frequency and magnitude of floods, accepting the hypothesis of significant differences between stationary and non-stationary models.
The non-stationary statistical modeling of the annual maximum daily flow rates uses the IE2 covariate to describe the changes at La Balsa station, and the set of MEI and IE2 indices to explain the behavior over time of the floods at Juanchito, achieving the objective of the study. The proposed new reservoir index helps improve the representation of flood variability. Despite the uncertainty of the results, the new information can contribute to a more robust selection of flow rates design and the acceptable threat and risk ranges.
This article manages to assess the EWT Expected Waiting Time and AAR Medium Risk
Analysis methods to determine the non-stationary return period and risk of
failure, both indicators are able to adequately capture the changes in the
probability of exceedance and therefore work as new flood risk indicators.
Regardless of the method of determination, the less frequent or rarer floods are
identified: i) a higher
Finally, all the above information is of interest in flood risk management in the Cauca River High Valley, for example, it can influence the sizing of flood protection works, the design of storm drain discharge works of Cali, lead to changes in the zoning of the degree of threat and flooding risk, and may have implications for land use; but above all, it shows the need to incorporate both the effects of ENSO, and non-stationarity, in the operating rules of Salvajina reservoir. However, it is important to mention that flood management must have a comprehensive framework of available measures, natural resources management, future visions and environmental constraints.
Acknowledgements
To Colciencias - Francisco José de Caldas Scholarships; to the Ministry of Economy and Competitiveness of Spain, research project TETISMED (CGL2014-58127-C3-3-R); to Universidad del Valle, IREHISA research group; to Universitat Politècnica de València, Spain and the Universidad de Colima, Mexico. For the supply of information from the Regional Autonomous Corporation of Valle del Cauca- CVC
REFERENCES
Ahn, K., & Palmer, R. (2016). Use of a nonstationary copula to predict future bivariate low flow frequency in the Connecticut River basin. Hydrological Processes, 30(19), 3518-3532. Recuperado de https://doi.org/10.1002/hyp.10876 [ Links ]
Ávila, Á., Guerrero, F., Escobar, Y., & Justino, F. (2019). Recent precipitation trends and floods in the Colombian Andes. Water, 11(2), 379. Recuperado de https://doi.org/10.3390/w11020379 [ Links ]
Banco Mundial. (2014). Notas de política Colombia: hacia la paz sostenible, la erradicación de la pobreza y la prosperidad compartida. Washington, DC, EUA: Banco Mundial. Recuperado de http://www.bancomundial.org/content/dam/Worldbank/Feature Story/lac/Colombia Policy Notes pub SPA 11-7-14web.pdf [ Links ]
Buuren, S. V., & Fredriks, M. (2001). Worm plot: A simple diagnostic device for modelling growth reference curves. Statistics in Medicine, 20(8), 1259-1277. Recuperado de https://doi.org/10.1002/sim.746 [ Links ]
Carvajal, Y., Jiménez, H., & Materon, H. (1998). Incidencia del fenómeno ENSO en la hidroclimatología del valle del río Cauca-Colombia. Bull. l'Institut Français d'Études Andines, 27(3). Recuperado de http://www.redalyc.org/resumen.oa?id=12627336 [ Links ]
Chow, V. T., Maidment, D. R., & Mays, L. W. (1994). En: Suarez, M. (ed.). Hidrología aplicada, 2ª ed. Bogotá, Colombia: McGraw-Hill. [ Links ]
Córdoba, S., Palomino, R., Gámiz, S., Castro, Y., & Esteban, M. (2015). Influence of tropical Pacific SST on seasonal precipitation in Colombia: Prediction using El Niño and El Niño Modoki. Climate Dynamics, 44(5-6), 1293-1310. Recuperado de https://doi.org/10.1007/s00382-014-2232-3 [ Links ]
Debele, S. E., Bogdanowicz, E., & Strupczewski, W. G. (2017). Around and about an application of the GAMLSS package to non-stationary flood frequency analysis. Acta Geophysica, 65(4), 885-892. Recuperado de https://doi.org/10.1007/s11600-017-0072-3 [ Links ]
El País. (2011). Conozca el drama de los habitantes de Juanchito causado por las inundaciones. El País. Recuperado de https://www.elpais.com.co/cali/conozca-el-drama-de-los-habitantes-de-juanchito-causado-por-las-inundaciones.html [ Links ]
EM-DAT. (2018). The emergency events database - Universite Catholique de Louvain (UCL)-. Brussels, Belgium: CRED, D. Guha-Sapir. Recuperado de www.emdat.be [ Links ]
Enciso, A., Carvajal, Y., & Sandoval, M. (2016). Hydrological analysis of historical floods in the upper valley of Cauca River. Ingeniería y Competitividad, 57(1), 46-57. [ Links ]
Escalante-Sandoval, C., & Garcia-Espinoza, E. (2014). Analysis of annual flood peak records in Mexico. WIT Transactions on Information and Communication Technologies, 47, 49-60. Recuperado de https://doi.org/10.2495/RISK140051 [ Links ]
García, M., Botero, A., Bernal, F., Ardila, E., & Piñeros, A. (2012). Variabilidad climática, cambio climático y el recurso hídrico en Colombia. Revista de Ingeniería. Universidad de los Andes, 36(0121-4993), 60-64. Recuperado de http://ojsrevistaing.uniandes.edu.co/ojs/index.php/revista/article/view/136 [ Links ]
Garreaud, R., Vuille, M., Compagnucci, R., & Marengo, J. (2009). Present-day South American climate. Palaeogeography, Palaeoclimatology, Palaeoecology, 281(3-4), 180-195. Recuperado de https://doi.org/10.1016/j.palaeo.2007.10.032 [ Links ]
Gutiérrez, F., & Dracup, J. (2001). The use of ENSO based streamflow forecasts for reservoir operations in Colombia. In: Bridging the gap (pp. 1-7). Reston, USA: American Society of Civil Engineers. Recuperado de https://doi.org/10.1061/40569(2001)164 [ Links ]
Herzog, S. K., Martinez, R., Jorgensen, P., & Tiessen, H. (eds.). (2012). Cambio climático y biodiversidad en los Andes tropicales. París, Francia: Instituto Interamericano para la Investigación del Cambio Global (IAI), São José dos Campos, y Comité Científico sobre los Problemas del Medio Ambiente (SCOPE). [ Links ]
IDEAM-PNUD-MADS-DNP-Cancillería, Instituto de Hidrología, Meteorología y Estudios Ambientales, Programa de las Naciones Unidas para el Desarrollo, Ministerio de Ambiente y Desarrollo Sostenible, Departamento Nacional de Planeación, & Cancillería. (2015). Nuevos escenarios de cambio climático para Colombia 2011-2100: tercera comunicación nacional de cambio climático. Recuperado de http://modelos.ideam.gov.co/media/dynamic/escenarios/documento-nacional-departamental-2015.pdf [ Links ]
Jiménez-Cisneros, B. E., Oki, T., Arnell, N. W., Benito, G., Cogley, J. G., Döll, P., Jiang, T., & Mwakalila, S. S. (2014). Freshwater resources. In: Field, C. B., Barros, V. R., Dokken, D. J., Mach, K. J., Mastrandrea, M. D., Bilir, T. E., Chatterjee, M., Ebi, K. L., Estrada, Y. O., Genova, R. C., Girma, B., Kissel, E. S., Levy, A. N., MacCracken, S., Mastrandrea, P. R., & White, L. L. (eds.). Climate change 2014: Impacts, adaptation, and vulnerability. Part A: Global and sectoral aspects (pp. 229-269). Cambridge, UK, New York, USA: Cambridge University Press, Working Group II to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. [ Links ]
JMA & WMO, Japan Meteorological Agency & World Meteorological Organization. (2017). El Nino monitoring and outlook/TCC. Recuperado de http://ds.data.jma.go.jp/tcc/tcc/products/elnino/decadal/pdo.html [ Links ]
Khaliq, M. N., Ouarda, T. B. M. J., Ondo, J. C., Gachon, P., & Bobée, B. (2006). Frequency analysis of a sequence of dependent and/or non-stationary hydro-meteorological observations: A review. Journal of Hydrology, 329(3-4), 534-552. Recuperado de https://doi.org/10.1016/j.jhydrol.2006.03.004 [ Links ]
Liang, Z., Jing, H. Y., Wang, Y., Binquan, L., & Zhao, J. (2017). A sample reconstruction method based on a modified reservoir index for flood frequency analysis of non-stationary hydrological series. Stochastic Environmental Research and Risk Assessment, 32. Recuperado de https://doi.org/10.1007/s00477-017-1465-1 [ Links ]
Lima, C., & Lall, U. (2011). Spatio-temporal non-stationary flood frequency modeling: seasonal peak floods in southern Brazil modeled using pre- and concurrent Pacific and Atlantic Ocean conditions. AGU Fall Meeting Abstracts, 1, 06. Recuperado de http://adsabs.harvard.edu/abs/2011AGUFM.H24C.06L [ Links ]
López de la, J., & Francés, F. (2013). Non-stationary flood frequency analysis in continental Spanish rivers, using climate and reservoir indices as external covariates. Hydrology and Earth System Sciences, 17(8), 3189-3203. Recuperado de https://doi.org/10.5194/hess-17-3189-2013 [ Links ]
López de la, J., & Francés, F. (2014). La variabilidad climática de baja frecuencia en la modelación no estacionaria de los regímenes de las crecidas en las regiones hidrológicas Sinaloa y Presidio San Pedro. Tecnología y ciencias del agua, 5(4), 79-101. Recuperado de http://www.redalyc.org/pdf/3535/353532522005.pdf [ Links ]
Machado, M., Botero, B., López de la, J., Francés, F., Díez, A., & Benito, G. (2015). Flood frequency analysis of historical flood data under stationary and non-stationary modelling. Hydrology and Earth System Sciences, 19(6), 2561-2576. Recuperado de https://doi.org/10.5194/hess-19-2561-2015 [ Links ]
Mann, H. (1945). Non-parametric tests against trend. Econométrica, 13(3), 163-171. Recuperado de https://doi.org/10.2307/1907187 [ Links ]
Matalas, N. C. (1997). Stochastic hydrology in the context of climate change. Climatic Change, 37, 89-101. [ Links ]
Méndez, J., Ramírez, A., Cornejo, E., Zárate, A., & Cavazos, T. (2011). Teleconexiones de la oscilación decadal del Pacífico (PDO) a la precipitación y temperatura en México. Investigaciones Geográficas, (73). Recuperado de http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S0188-46112010000300005 [ Links ]
Milly, P. C. D., Betancourt, J., Falkenmark, M., Hirsch, R. M., Kundzewicz, Z. W., Lettenmaier, D. P., Stouffer, R. J., Dettinger, M. D., & Krysanova, V. (2015). On critiques of “Stationarity is dead: Whither water management?” Water Resources Research, 51(9), 7785-7789. Recuperado de https://doi.org/10.1002/2015WR017408 [ Links ]
Milly, P., Betancourt, J., Falkenmark, M., Hirsch, R., Kundzewicz, Z., Lettenmaier, D., & Stouffer, R. (2008). Stationarity is dead: Whither water management ? Science, 319(February), 573-574. [ Links ]
Montanari, A., & Koutsoyiannis, D. (2014). Modeling and mitigating natural hazards: Stationarity is immortal! Water Resources Research, 50(12), 9748-9756. Recuperado de https://doi.org/10.1002/2014WR016092. [ Links ]
Moreno, J., Begueria, S., Garcés, L., & García, J. (2003). Intensidad de las avenidas y aterramiento de embalses en el Pirineo Central español. Ería, (61), 159-167. Recuperado de https://doi.org/10.17811/ER.0.2003.159-167 [ Links ]
NOAA-ESRL-PSD, National Oceanic and Atmospheric Administration, Earth System Research Laboratory, & Physical Sciences Division. (2017). Climate indices: monthly atmospheric and ocean time series. Recuperado de https://www.esrl.noaa.gov/psd/data/climateindices/list/ [ Links ]
NOAA, National Oceanic and Atmospheric Administration. (2017). Pacific Decadal Oscillation (PDO)-Northwest Fisheries Science Center. Recuperado de https://www.nwfsc.noaa.gov/research/divisions/fe/estuarine/oeip/ca-pdo.cfm [ Links ]
Obeyskera, J., & Salas, J. D. (2016). Frequency of recurrent extremes under non-stationarity. Journal of Hydrologic Engineering, 21(5), 04016005. Recuperado de https://doi.org/10.1061/(ASCE)HE.1943-5584.0001339 [ Links ]
Pettitt, A. N. N. (1979). A non-parametric approach to the change-point problem. Applied Statistics, 28(2), 126-135. Recuperado de https://doi.org/10.2307/2346729 [ Links ]
Poveda, G. (2004). La hidroclimatología de Colombia: Una síntesis desde la escala interdecadal. Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales, 28-107, 201-222. Recuperado de http://www.clas.ufl.edu/users/prwaylen/geo3280articles/Synthesis of Colombian hydrology.pdf [ Links ]
Poveda, G., & Álvarez, D. (2012). El colapso de la hipótesis de estacionariedad por cambio y variabilidad climática: implicaciones para el diseño hidrológico en ingeniería. Revista de Ingeniería. Universidad de los Andes, 36(0121-4993), 65-76. [ Links ]
Poveda, G., Jaramillo, L., & Vallejo, L. (2014). Seasonal precipitation patterns along pathways of South American low-level jets and aerial rivers. Water Resources Research, 50(1), 98-118. Recuperado de https://doi.org/10.1002/2013WR014087 [ Links ]
Poveda, G., Velez, J., Mesa, O., Hoyos, C., Mejía, F., Barco, O., & Correa, P. (2002). Influencia de fenómenos macroclimáticos sobre el ciclo anual de la hidrología colombiana: cuantificación lineal, no lineal y percentiles probabilísticos. Meteorología Colombiana, (6), 121-130. Recuperado de http://www.geociencias.unal.edu.co/unciencias/data-file/user_23/file/METEOROLOGIA/13Poveda Clima Nuevo.pdf [ Links ]
Poveda, G., Waylen, P., & Pulwarty, R. (2006). Annual and inter-annual variability of the present climate in northern South America and southern Mesoamerica. Palaeogeography, Palaeoclimatology, Palaeoecology, 234(1), 3-27. Recuperado de https://doi.org/10.1016/j.palaeo.2005.10.031 [ Links ]
Puertas, O., & Carvajal, Y. (2008). Incidencia de El Niño-Oscilación del Sur en la precipitación y la temperatura del aire en Colombia, utilizando el Climate Explorer. Revista Científica Ingeniería y Desarrollo, (23), 104-118. Recuperado de http://rcientificas.uninorte.edu.co/index.php/ingenieria/article/view/2097/1346 [ Links ]
Rigby, R. A., & Stasinopoulos, M. (2005). Generalized additive models for location, scale and shape. Journal of the Royal Statistical, 54, Part3(3), 507-554. Recuperado de https://doi.org/10.1111/j.1467-9876.2005.00510.x [ Links ]
Rueda, O., & Poveda, G. (2006). Variabilidad espacial y temporal del Chorro del Chocó y su efecto en la hidroclimatología de la región del Pacífico colombiano. Meteorología Colombiana, (501), 132-145. [ Links ]
Salas, J. D., Obeysekera, J., & Vogel, R. M. (2018). Techniques for assessing water infrastructure for nonstationary extreme events: A review. Hydrological Sciences Journal, 63(3), 325-352. Recuperado de https://doi.org/10.1080/02626667.2018.1426858 [ Links ]
Salas, J. D., & Obeyskera, J. (2014). Revisiting the concepts of return period and risk for nonstationary hydrologic extreme events. Journal of Hydrologic Engineering, 19(3), 554-568. Recuperado de https://doi.org/10.1061/(ASCE)HE.1943-5584.0000820 [ Links ]
Sandoval, M., & Ramirez, C. (eds.). (2007). El río Cauca en su valle alto: un aporte al conocimiento de uno de los ríos más importantes de Colombia. Cali, Colombia: CVC, Corporación Autónoma Regional del Valle del Cauca. Recuperado de http://www.cvc.gov.co/index.php/servicio-al-ciudadano/inscriba-departamento-de-gestion-ambiental/77-recurso-hidrico/1386-libro-rio-cauca [ Links ]
Sandoval, M., Ramirez, C., & Santacruz, S. (2011). Optimización de la regla mensual de operación del embalse de Salvajina. Ingeniería de Recursos Naturales y del Ambiente, (6), 93-104. Recuperado de http://bibliotecadigital.univalle.edu.co/handle/10893/2596 [ Links ]
Serinaldi, F. (2015). Dismissing return periods! Stochastic Environmental Research and Risk Assessment, 29(4), 1179-1189. Recuperado de https://doi.org/10.1007/s00477-014-0916-1 [ Links ]
Stasinopoulos, M., Rigby, R. A., Vlasios, V., Heler, G., & Bastiani De, F. (2015). Flexible regression and smoothing the GAMLSS packages in R. Recuperado de http://www.gamlss.org/wp-content/uploads/2015/07/FlexibleRegressionAndSmoothingDraft-1.pdf [ Links ]
Vasiliades, L., Galiatsatou, P., & Loukas, A. (2015). Nonstationary frequency analysis of annual maximum rainfall using climate covariates. Water Resources Management, 29(2), 339-358. Recuperado de https://doi.org/10.1007/s11269-014-0761-5 [ Links ]
Villarini, G., Smith, J., Serinaldi, F., Ntelekos, A., & Schwarz, U. (2012). Analyses of extreme flooding in Austria over the period 1951-2006. International Journal of Climatology, 32(8), 1178-1192. Recuperado de https://doi.org/10.1002/joc.2331 [ Links ]
Villarini, G., & Strong, A. (2014). Roles of climate and agricultural practices in discharge changes in an agricultural watershed in Iowa. Agriculture, Ecosystems & Environment, 188, 204-211. Recuperado de https://doi.org/10.1016/j.agee.2014.02.036 [ Links ]
Villarini, G, Smith, J. A., Serinaldi, F., Bales, J., Bates, P. D., & Krajewski, W. F. (2009a). Flood frequency analysis for nonstationary annual peak records in an urban drainage basin. Advances in Water Resources, 32(8), 1255-1266. Recuperado de https://doi.org/10.1016/j.advwatres.2009.05.003 [ Links ]
Villarini, G., Serinaldi, F., Smith, J. A., & Krajewski, W. F. (2009b). On the stationarity of annual flood peaks in the continental United States during the 20th century. Water Resources Research, 45(8), 1-17. Recuperado de https://doi.org/10.1029/2008WR007645 [ Links ]
Wang, S., Huang, J., He, Y., & Guan, Y. (2015). Combined effects of the Pacific decadal oscillation and El Niño-Southern Oscillation on global land dry-wet changes. Scientific Reports, 4(6651). Recuperado de https://doi.org/10.1038/srep06651 [ Links ]
Wolter, K., & Timlin, M. (1998). Measuring the strength of ENSO events: How does 1997/98 rank? Weather, 53(9), 315-324. Recuperado de https://doi.org/10.1002/j.1477-8696.1998.tb06408.x [ Links ]
Yue, S., & Wang, C. Y. (2002). Applicability of prewhitening to eliminate the influence of serial correlation on the Mann-Kendall test. Water Resources Research, 38(6), 4-1. Recuperado de https://doi.org/10.1029/2001WR000861 [ Links ]
Received: September 26, 2018; Accepted: August 23, 2019