Figura 1 - uploaded by Fernando González-Leiva
Content may be subject to copyright.
Source publication
This paper proposes the use of the discreet Kalman filter (DKF) along with an autoregressive model with exogenous inputs (ARX) for short-term streamflow forecasting with lead times of 24, 48, 72 and 96 hours. This model was applied to the Turbio River basin, located in the state of Guanajuato and a portion of the state of Jalisco, Mexico. This area...
Similar publications
We built an easy-to-interpret individual vulnerability index to floods that is amenable for empirical testing and may be adapted to any perceived hazard or ecological setting. An individual’s vulnerability value (Vi) was estimated from characteristics unique to him/her, added to those he or she shared with people sleeping in the same building, then...
Flood is one of the conditions when overflowing water inundated the lower areas. The occurrence of floods always has both positive and negative impacts. If the flood occurs in residential areas, it will have a more negative impact. Therefore, people should have preparedness to prevent the effects of the flood. In 2022, a flood occurred in the Jampe...
Citations
... Having advance information on streamflow behavior becomes an indispensable tool for the administration of dams and disaster risk management (IPCC, 2012;Singh and Zommers, 2014). Different methods have been used for streamflow forecasting, such as autoregressive methods, neural networks (Box et al., 2016;Shmueli and Lichtendahl, 2016), and, more recently, data assimilation methods such as Kalman filters (Abaza et al., 2015;Alvarado-Hernández et al., 2020;González-Leiva et al., 2015;Morales-Velázquez et al., 2014). In hydrological studies, the Ensemble Kalman Filter (EnKF) (Evensen, 1994(Evensen, , 2009Gillijns et al., 2006) has been widely used as a method of assimilation (Liu and Gupta, 2007;Maxwell et al., 2018;Sun et al., 2016), with little evaluation in forecasting flows. ...
... The fit reached by each algorithm was evaluated using the Nash-Sutcliffe coefficient (NS) (Nash and Sutcliffe, 1970) and the RMSE (Morales-Velázquez et al., 2014), as expressed by Equations (1) and (2). The assumed normality of errors was verified using graphs (González-Leiva et al., 2015). ...
Hydrological phenomena are characterized by the formation of a non-linear dynamic system, and streamflows are not unrelated to this premise. Data assimilation offers an alternative for flow forecasting using the Ensemble Kalman Filter, given its relative ease of implementation and lower computational effort in comparison with other techniques. The hourly streamflow of the Chapalagana station was forecasted based on that of the Platanitos station in northwestern México. The forecasts were made from one to six steps forward, combined with set sizes of 5, 10, 20, 30, 50, and 100 members. The Nash-Sutcliffe coefficients of the Discrete Kalman filter were 0.99 and 0.85 for steps one and six, respectively, achieving the best fit with a tendency to shift the predicted series, similar to the persistent forecast. The Ensemble Kalman Filter (EnKF) obtained 0.99 and 0.05 in steps one and six. However, it converges on the observed series with the limitation of considerable overestimation in higher steps. All three algorithms have equal statistical adjustment values in step one, and there are progressive differences in further steps, where ARX and DKF remain similar and EnKF is differentiated by the overestimation. EnKF enables capturing non-linearity in sudden streamflow changes but generates overestimation at the peaks.
... El ajuste de las series pronosticadas se evaluó mediante el coeficiente de Nash-Sutcliffe (Nash & Sutcliffe, 1970) supuestos de normalidad de errores del filtro de Kalman se verificaron mediante gráficos comparados con la curva normal estandarizada (González-Leiva, Ibáñez-Castillo, Valdés, Vázquez-Peña, & Ruiz-García, 2015). Los valores atípicos y su ubicación se determinó con base en los residuales estandarizados (Cryer & Chan, 2008). ...
... Asimismo, dado que los caudales que se miden en la parte alta de la cuenca son proporcionalmente menores debido a la menor área de captación disponible, es conveniente incluir en el modelo parámetros que ayuden a equiparar las magnitudes de los caudales. Además, es determinante tener registros de estaciones meteorológicas distribuidas en el área de la cuenca para definir y actualizar la función de respuesta de la cuenca (HUI) (González-Leiva et al., 2015). ...
La asimilación de datos integrada para el pronóstico de caudales puede brindar flexibilidad y reducción de errores sistemáticos en los modelos. En este trabajo se evalúan la capacidad predictiva del filtro de Kalman discreto, filtro de Kalman de conjuntos y su integración, utilizando registros horarios de caudal de las estaciones Chapalagana y Platanitos ubicadas sobre el río Huaynamota, región hidrológica 12. La cuenca se ubica al noroeste de la república mexicana, y se comparte entre los estados de Durango, Nayarit, Zacatecas y Jalisco. Para el análisis se utilizaron series con 1 360 registros horarios del año 2017 comprendidos entre el 2 de agosto a las 9:00 horas hasta el 28 de septiembre a las 0:00 horas. Se realizaron pronósticos a 1, 2, 3, 4, 5 y 6 pasos hacia adelante, combinados con tamaños de conjunto de 5, 8, 10, 20, 50 y 100 miembros utilizando caudales de la estación Platanitos como variable exógena. El ajuste entre la serie observada y las pronosticadas se estimó mediante el coeficiente de Nash-Sutcliffe y la raíz del cuadrado medio del error para determinar que el filtro de Kalman discreto alcanza mejor ajuste y actualización con base en el tiempo de retraso entre series. El filtro de Kalman de conjuntos genera un suavizado de la serie pronosticada, y al igual que la integración de filtros aumenta el efecto de desplazamiento de la serie pronosticada. El filtro de Kalman discreto alcanza ajuste superior a ARX y a la combinación ARX-DKF.
... The Root Mean Square Root (RMSE) measures the mean magnitude of the error. Corresponds to the square root of the average of the squared differences between the prediction and the observation, therefore this measure has been used in the evaluation of forecasting models [18,19]. Amplifies and penalizes with greater force those errors of greater magnitude (Eq. ...
In this work, supervised machine learning was applied, using regression trees, to develop a predictive model of the monthly phase of the Pacific De-cadal Oscillation. This oscillation is associated with the alteration of weather patterns , mainly in the North Pacific and southwestern North America. As characteristics , the records of the PDO phase of the 24 months prior to the forecast target month were used. The predictive model developed presented an acceptable capacity to estimate the monthly phase of the PDO. This according to the performance evaluation statistics corresponding to the Mean Absolute Error, Maximum Error, Mean Quadratic Error and Pearson's Correlation, which obtained ranges of [0.55,1.07], [1.58,3.29], [0.55,1.82] and [0.30,0.74] respectively for 20% of test data for the period 1854-2020.
... The model was evaluated using the flows obtained from the modified inverse routing reservoir, measured at the Sayula hydrometric station and obtained Nash-Sutcliffe efficiency indexes of 0.98 for hourly flow forecast. González-Leiva et al. (2015) implemented a discrete Kalman Filter model, autoregressive exogenous input (DKF-ARX) to predict daily mean streamflow in the Turbio River basin, Guanajuato; Morales-Velázquez et al. (2014) aplicaron el filtro de Kalman discreto para predecir caudales horarios en la cuenca de la presa Ángel Albino Corso (Peñitas); el modelo se evaluó a partir de caudales obtenidos del tránsito inverso modificado en vasos o antitránsito medidos en la estación hidrométrica Sayula, y tuvo valores del índice de eficiencia de Nash-Sutcliffe para pronóstico de caudal a cada hora de 0.98. González-Leiva et al. (2015) implementaron un modelo de Filtro de Kalman discreto, autorregresivo y entrada exógena (DKF-ARX) para predicción de caudal medio diario en la cuenca del río Turbio, Guanajuato; no se implementó una predicción horaria, porque en la estación de aforo trabajada, Las Adjuntas, no existen datos medidos horarios; la cuenca del río Turbio no es de interés hidroeléctrico para la CFE, por lo que no hay medición continúa de caudales. ...
... González-Leiva et al. (2015) implemented a discrete Kalman Filter model, autoregressive exogenous input (DKF-ARX) to predict daily mean streamflow in the Turbio River basin, Guanajuato; Morales-Velázquez et al. (2014) aplicaron el filtro de Kalman discreto para predecir caudales horarios en la cuenca de la presa Ángel Albino Corso (Peñitas); el modelo se evaluó a partir de caudales obtenidos del tránsito inverso modificado en vasos o antitránsito medidos en la estación hidrométrica Sayula, y tuvo valores del índice de eficiencia de Nash-Sutcliffe para pronóstico de caudal a cada hora de 0.98. González-Leiva et al. (2015) implementaron un modelo de Filtro de Kalman discreto, autorregresivo y entrada exógena (DKF-ARX) para predicción de caudal medio diario en la cuenca del río Turbio, Guanajuato; no se implementó una predicción horaria, porque en la estación de aforo trabajada, Las Adjuntas, no existen datos medidos horarios; la cuenca del río Turbio no es de interés hidroeléctrico para la CFE, por lo que no hay medición continúa de caudales. González-Leiva et al. (2015) consideraron cuatro pasos de tiempo de anticipación (L1, L2, L3 y L4), es decir los tiempos en que no se ejecutó la fase de corrección del modelo DKF; de los dos periodos analizados el del año 2003 presenta valores del índice de eficiencia de Nash-Sutcliffe de 0.95, 0.87, 0.76 y 0.63 para los distintos pasos de anticipación, y análogamente para la serie de datos de 2004 los valores de Nash-Sutcliffe fueron 0.93, 0.82, 0.72 y 0.62. ...
... González-Leiva et al. (2015) implementaron un modelo de Filtro de Kalman discreto, autorregresivo y entrada exógena (DKF-ARX) para predicción de caudal medio diario en la cuenca del río Turbio, Guanajuato; no se implementó una predicción horaria, porque en la estación de aforo trabajada, Las Adjuntas, no existen datos medidos horarios; la cuenca del río Turbio no es de interés hidroeléctrico para la CFE, por lo que no hay medición continúa de caudales. González-Leiva et al. (2015) consideraron cuatro pasos de tiempo de anticipación (L1, L2, L3 y L4), es decir los tiempos en que no se ejecutó la fase de corrección del modelo DKF; de los dos periodos analizados el del año 2003 presenta valores del índice de eficiencia de Nash-Sutcliffe de 0.95, 0.87, 0.76 y 0.63 para los distintos pasos de anticipación, y análogamente para la serie de datos de 2004 los valores de Nash-Sutcliffe fueron 0.93, 0.82, 0.72 y 0.62. ...
Debido a los eventos de precipitación extrema provocada por el cambio climático y a la alteración acelerada de las cuencas por el crecimiento poblacional, es importante pronosticar los caudales que generan las cuencas por los eventos de precipitación. El objetivo de este estudio fue predecir caudales horarios en la cuenca del río Huaynamota usando el Filtro de Kalman Discreto (DKF) junto con un modelo autorregresivo con entrada exógena (ARX). Al inicio los parámetros del filtro de Kalman se definen y después se recalculan por periodos definidos, es decir los valores de los parámetros del modelo se actualizan constantemente. El pronóstico de caudales se realizó en seis pasos hacia adelante (L=1, 2, 3, 4, 5 y 6 horas). La cuenca de estudio es parte del río Huaynamota, delimitada por la estación hidrométrica Chapalagana, aguas arriba de la presa Aguamilpa, en Nayarit, México. La cuenca del río Huaynamota es un tributario del río Santiago. Series de datos horarias se emplearon para precipitación y caudal, de agosto a septiembre del 2017. El modelo de pronóstico DKF-ARX mostró índices de eficiencia de Nash-Sutcliffe entre 0.99 y 0.85 con L=1 y L=6, respectivamente. Se concluye que es factible obtener un buen pronóstico de caudales horarios con filtro de Kalman discreto.
... The model was evaluated using the flows obtained from the modified inverse routing reservoir, measured at the Sayula hydrometric station and obtained Nash-Sutcliffe efficiency indexes of 0.98 for hourly flow forecast. González-Leiva et al. (2015) implemented a discrete Kalman Filter model, autoregressive exogenous input (DKF-ARX) to predict daily mean streamflow in the Turbio River basin, Guanajuato; Morales-Velázquez et al. (2014) aplicaron el filtro de Kalman discreto para predecir caudales horarios en la cuenca de la presa Ángel Albino Corso (Peñitas); el modelo se evaluó a partir de caudales obtenidos del tránsito inverso modificado en vasos o antitránsito medidos en la estación hidrométrica Sayula, y tuvo valores del índice de eficiencia de Nash-Sutcliffe para pronóstico de caudal a cada hora de 0.98. González-Leiva et al. (2015) implementaron un modelo de Filtro de Kalman discreto, autorregresivo y entrada exógena (DKF-ARX) para predicción de caudal medio diario en la cuenca del río Turbio, Guanajuato; no se implementó una predicción horaria, porque en la estación de aforo trabajada, Las Adjuntas, no existen datos medidos horarios; la cuenca del río Turbio no es de interés hidroeléctrico para la CFE, por lo que no hay medición continúa de caudales. ...
... González-Leiva et al. (2015) implemented a discrete Kalman Filter model, autoregressive exogenous input (DKF-ARX) to predict daily mean streamflow in the Turbio River basin, Guanajuato; Morales-Velázquez et al. (2014) aplicaron el filtro de Kalman discreto para predecir caudales horarios en la cuenca de la presa Ángel Albino Corso (Peñitas); el modelo se evaluó a partir de caudales obtenidos del tránsito inverso modificado en vasos o antitránsito medidos en la estación hidrométrica Sayula, y tuvo valores del índice de eficiencia de Nash-Sutcliffe para pronóstico de caudal a cada hora de 0.98. González-Leiva et al. (2015) implementaron un modelo de Filtro de Kalman discreto, autorregresivo y entrada exógena (DKF-ARX) para predicción de caudal medio diario en la cuenca del río Turbio, Guanajuato; no se implementó una predicción horaria, porque en la estación de aforo trabajada, Las Adjuntas, no existen datos medidos horarios; la cuenca del río Turbio no es de interés hidroeléctrico para la CFE, por lo que no hay medición continúa de caudales. González-Leiva et al. (2015) consideraron cuatro pasos de tiempo de anticipación (L1, L2, L3 y L4), es decir los tiempos en que no se ejecutó la fase de corrección del modelo DKF; de los dos periodos analizados el del año 2003 presenta valores del índice de eficiencia de Nash-Sutcliffe de 0.95, 0.87, 0.76 y 0.63 para los distintos pasos de anticipación, y análogamente para la serie de datos de 2004 los valores de Nash-Sutcliffe fueron 0.93, 0.82, 0.72 y 0.62. ...
... González-Leiva et al. (2015) implementaron un modelo de Filtro de Kalman discreto, autorregresivo y entrada exógena (DKF-ARX) para predicción de caudal medio diario en la cuenca del río Turbio, Guanajuato; no se implementó una predicción horaria, porque en la estación de aforo trabajada, Las Adjuntas, no existen datos medidos horarios; la cuenca del río Turbio no es de interés hidroeléctrico para la CFE, por lo que no hay medición continúa de caudales. González-Leiva et al. (2015) consideraron cuatro pasos de tiempo de anticipación (L1, L2, L3 y L4), es decir los tiempos en que no se ejecutó la fase de corrección del modelo DKF; de los dos periodos analizados el del año 2003 presenta valores del índice de eficiencia de Nash-Sutcliffe de 0.95, 0.87, 0.76 y 0.63 para los distintos pasos de anticipación, y análogamente para la serie de datos de 2004 los valores de Nash-Sutcliffe fueron 0.93, 0.82, 0.72 y 0.62. ...
Because of extreme rainfall events caused by climate change and of accelerated alteration of basins by population growth, it is important to forecast streamflow generated by precipitation events. The objective of this study was to predict hourly flows in the Huaynamota River basin using the Discrete Kalman Filter (DKF), together with the autoregressive exogenous input model (ARX). Initially, the Kalman filter parameters are defined then recalculated for defined periods; that is, the model parameter values are constantly updated. Flows were forecasted six steps ahead (L=1, 2, 3, 4, 5 and 6 hours). The basin studied is part of the Huynamota River, delimited by the Chapalangana hydrometric station, upstream from the Aguamilpa reservoir, Nayarit, Mexico. The Huaynamota River is a tributary of the Santiago River. Hourly data series were used for precipitation and flow from August to September 2017. The DKF-ARX forecasting model showed Nash-Sutcliffe efficiency indexes between 0.99 and 0.85, with L=1 and L=6, respectively. It is concluded that it is feasible to obtain a good forecast of hourly streamflow with the discrete Kalman filter
... Ravelo et al. (2014) estudiaron detección, evaluación y pronóstico de sequías en la región Organismo de Cuenca Pacífico Norte mediante redes neuronales, y concluyeron que en 2011 y 2012 se presentaron las sequías más severas. También hay estudios de pronóstico de caudales con el filtro de Kalman discreto en cuencas mexicanas (Morales et al., 2014;González et al., 2015). Además, Kim et al. (2002) analizaron sequías en la cuenca del río Conchos, pero no abordaron el pronóstico de sequías. ...
... Ravelo et al. (2014) studied drought detection, evaluation and forecasting in the North Pacific Basin Agency region through neural networks and concluded that the most severe droughts occurred in 2011 and 2012. There are also flow forecast studies with the Discrete Kalman filter in Mexican watersheds (Morales et al., 2014, González et al., 2015. In addition, Kim et al. (2002) analyzed droughts in the Conchos river watershed but did not address the forecast of droughts. ...
The monitoring and forecasting of droughts are important to evaluate risks, take decisions, as well as undertake effective and timely actions to avoid and reduce their negative effects. Therefore, the objective of this study was to forecast the SPI (Standard Precipitation Index) and SPEI (Standard Precipitation Evapotranspiration Index) drought indices for 14 meteorological stations in the Fuerte River watershed in northwest Mexico. Our hypothesis was that it is possible to achieve such objective through the implementation of the Discrete Kalman filter algorithm (DKF). The Fuerte River watershed, Sinaloa, Mexico, is important for its agricultural production and generation of hydroelectric power. We did the forecast of the SPI and SPEI drought indices for time scales (drought durations) of 3, 6, 12 and 24 months, during the period 1961-2011, and with 1, 2, 3 and 4 months in advance. Two models were implemented using the Discrete Kalman filter: a second-order autoregressive (DKF-AR2), and a second-order autoregressive with exogenous input (DKF-ARX). The climatic variables tested as exogenous were precipitation (Pt), maximum and minimum temperatures (Tmax and Tmin) and reference evapotranspiration (ET0); the exogenous variable precipitation, Pt, recorded better results. The DKF-AR2 methodology presented the best result in the forecast of the indices for six stations located in the upper part of the watershed, with predominance of temperate and semi-cold climates. The DKF-ARX-Pt methodology proved better in the remaining eight stations of the middle and lower parts, located in warm climates. The best forecasts were obtained for scales (drought durations) of 12 and 24 months, and the SPEI forecast was better than that of SPI. The Nash-Sutcliffe indices (E) for 12 and 24 months reached up to 0.92 and 0.96; in the case of 3 and 6 months, the Nash-Sutcliffe indices were approximately 0.5. The anticipation of the prognosis was better for 1 and 2 months.
... Ravelo et al. (2014) estudiaron detección, evaluación y pronóstico de sequías en la región Organismo de Cuenca Pacífico Norte mediante redes neuronales, y concluyeron que en 2011 y 2012 se presentaron las sequías más severas. También hay estudios de pronóstico de caudales con el filtro de Kalman discreto en cuencas mexicanas (Morales et al., 2014;González et al., 2015). Además, Kim et al. (2002) analizaron sequías en la cuenca del río Conchos, pero no abordaron el pronóstico de sequías. ...
... Ravelo et al. (2014) studied drought detection, evaluation and forecasting in the North Pacific Basin Agency region through neural networks and concluded that the most severe droughts occurred in 2011 and 2012. There are also flow forecast studies with the Discrete Kalman filter in Mexican watersheds (Morales et al., 2014, González et al., 2015. In addition, Kim et al. (2002) analyzed droughts in the Conchos river watershed but did not address the forecast of droughts. ...
The monitoring and forecasting of droughts are important to evaluate risks, take decisions, as well as undertake effective and timely actions to avoid and reduce their negative effects. Therefore, the objective of this study was to forecast the SPI (Standard Precipitation Index) and SPEI (Standard Precipitation Evapotranspiration Index) drought indices for 14 meteorological stations in the Fuerte River watershed in northwest Mexico. Our hypothesis was that it is possible to achieve such objective through the implementation of the Discrete Kalman filter algorithm (DKF). The Fuerte River watershed, Sinaloa, Mexico, is important for its agricultural production and generation of hydroelectric power. We did the forecast of the SPI and SPEI drought indices for time scales (drought durations) of 3, 6, 12 and 24 months, during the period 1961-2011, and with 1, 2, 3 and 4 months in advance. Two models were implemented using the Discrete Kalman filter: a second-order autoregressive (DKF-AR2), and a second-order autoregressive with exogenous input (DKF-ARX). The climatic variables tested as exogenous were precipitation (Pt), maximum and minimum temperatures (Tmax and Tmin) and reference evapotranspiration (ET0); the exogenous variable precipitation, Pt, recorded better results. The DKF-AR2 methodology presented the best result in the forecast of the indices for six stations located in the upper part of the watershed, with predominance of temperate and semi-cold climates. The DKF-ARX-Pt methodology proved better in the remaining eight stations of the middle and lower parts, located in warm climates. The best forecasts were obtained for scales (drought durations) of 12 and 24 months, and the SPEI forecast was better than that of SPI. The Nash-Sutcliffe indices (E) for 12 and 24 months reached up to 0.92 and 0.96; in the case of 3 and 6 months, the Nash-Sutcliffe indices were approximately 0.5. The anticipation of the prognosis was better for 1 and 2 months.
... On the other hand, physical conditions are not considered in the formulation of the ARX-DKF model, which is intended to find the best mathematical or causal relation(s) between the input and the output of the hydrological system [46] [53]- [55]. This coupled model is based on an autoregressive component (ARX) for the streamflow, in which rainfall is considered the exogenous input. ...
... The ARX-DKF model contains timevarying parameters (i.e., they evolve over time) obtained from the autoregressive component, which are then used in the Kalman implementation ( Table 2). The autoregressive characteristics of the streamflow records allow for the development of a matrix of parameters that are used to forecast streamflow [55]. A and B are matrices containing α and β parameters from the series of streamflow and rainfall data in the ARX model. ...
Floods have caused significant human and economic losses in the Cazones River Basin, located on the Gulf of Mexico. Despite this knowledge, steps towards the design and implementation of an early warning system for the Cazones are still a pending task. In this study we contributed by establishing a hydrological scheme for forecasting mean daily discharges in the Cazones Basin. For these purposes, we calibrated, validated and compared the HyMod model (HM) which is physics-based, and an autoregressive-based model coupled with the Discrete Kalman Filter (ARX-DKF). The ability of both models to accurately predict discharges proved satisfactory results during the validation period with RMSEHYMOD = 2.77 [mm/day]; and RMSEARX-DKF = [2.38 mm/day]. Further analysis based on a Streamflow Assimilation Ratio (SAR) revealed that both models underestimate the discharges in a similar proportion. This evaluation also showed that, under the most common conditions, the simpler stochastic model (ARX-DKF) performs better; however, under extreme hydrological conditions the deterministic HM model reveals a better performance. These results are discussed under the context of future applications and additional requirements needed to implement an early warning hydrologic system for the Cazones Basin.
This paper proposes the use of the discreet Kalman filter (DKF) along with an autoregressive model with exogenous inputs (ARX) for short-term streamflow forecasting with lead times of 24, 48, 72 and 96 hours. This model was applied to the Turbio River basin, located in the state of Guanajuato and a portion of the state of Jalisco, Mexico. This area is vulnerable to flooding during rainy periods which normally occur in the region. The forecasting was based on available precipitation and streamflow data from the years 2003 and 2004. The results indicate that the forecasts performed with one-step ahead, that is with a 24-hour lead time, present better fits than 48,72 and 96-hour lead times in terms of Nash-Sutcliffe, MSE and RMSE.
