Farshad Fathian; Ahmad Fakheri-Fard; Yagob Dinpashoh; Seyed Saeid Mousavi Nadoushani
Abstract
Introduction: Time series models are generally categorized as a data-driven method or mathematically-based method. These models are known as one of the most important tools in modeling and forecasting of hydrological processes, which are used to design and scientific management of water resources projects. ...
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Introduction: Time series models are generally categorized as a data-driven method or mathematically-based method. These models are known as one of the most important tools in modeling and forecasting of hydrological processes, which are used to design and scientific management of water resources projects. On the other hand, a better understanding of the river flow process is vital for appropriate streamflow modeling and forecasting. One of the main concerns of hydrological time series modeling is whether the hydrologic variable is governed by the linear or nonlinear models through time. Although the linear time series models have been widely applied in hydrology research, there has been some recent increasing interest in the application of nonlinear time series approaches. The threshold autoregressive (TAR) method is frequently applied in modeling the mean (first order moment) of financial and economic time series. Thise type of the model has not received considerable attention yet from the hydrological community. The main purposes of this paper are to analyze and to discuss stochastic modeling of daily river flow time series of the study area using linear (such as ARMA: autoregressive integrated moving average) and non-linear (such as two- and three- regime TAR) models.
Material and Methods: The study area has constituted itself of four sub-basins namely, Saghez Chai, Jighato Chai, Khorkhoreh Chai and Sarogh Chai from west to east, respectively, which discharge water into the Zarrineh Roud dam reservoir. River flow time series of 6 hydro-gauge stations located on upstream basin rivers of Zarrineh Roud dam (located in the southern part of Urmia Lake basin) were considered to model purposes. All the data series used here to start from January 1, 1997, and ends until December 31, 2011. In this study, the daily river flow data from January 01 1997 to December 31 2009 (13 years) were chosen for calibration and data for January 01 2010 to December 31 2011 (2 years) were chosen for validation, subjectively. As data have seasonal cycles, statistical indices (such as mean and standard deviation) of daily discharge were estimated using Fourier series. Then ARMA and two- and three-regime SETAR models applied to the standardized daily river flow time series. Some performance criteria were used to evaluate the models accuracy. In other words, in this paper, linear and non-linear models such as ARMA and two- and three-regime SETAR models were fitted to observed river flows. The parameters associated to the models, e.g. the threshold value for the SETAR model was estimated. Finally, the fitted linear and non-linear models were selected using the Akaike Information Criterion (AIC), Root Mean Square (RMSE) and Sum of Squared Residuals (SSR) criteria. In order to check the adequacy of the fitted models the Ljung-Box test was used.
Results and Discussion: To a certain degree the result of the river flow data of study area indicates that the threshold models may be appropriate for modeling and forecasting the streamflows of rivers located in the upstream part of Zarrineh Roud dam. According to the obtained evaluation criteria of fitted models, it can be concluded the performance of two- and three- regime SETAR models are slightly better than the ARMA model in all selected stations. As well as, modeling and comparison of SETAR models showed that the three-regime SETAR model have evaluation criteria better than two-regime SETAR model in all stations except Ghabghablou station.
Conclusion: In the present study, we attempted to model daily streamflows of Zarrineh Rood Basin Rivers located in the south of Urmia Lake by applying ARMA and two- and three-regime SETAR models. This is mainly because very few efforts and rather less attention have been paid to this non-linear approach in hydrology and water resources engineering generally.
Therefore, two types of data-driven models were used for modeling and forecasting daily streamflow: (i) deseasonalized ARMA-type model, and (ii) Threshold Autoregressive model, including Self-Existing TAR (SETAR) model. Each ARMA and SETAR models were fitted to daily streamflow time series of the rivers located in the study area. In general, it can be concluded that the overall performance of SETAR model is slightly better than ARMA model. Furthermore, SETAR model is very similar AR model, therefor, it can be easily used in water resources engineering field. On the other hand, due to apply these non-linear models, the number of estimated parameters in comparison with linear models has decreased.
Farshad Fathian; Ahmad Fakheri Fard; Yagob Dinpashoh; Seyed Saeid Mousavi Nadoshani
Abstract
Introduction: Time series models are one of the most important tools for investigating and modeling hydrological processes in order to solve problems related to water resources management. Many hydrological time series shows nonstationary and nonlinear behaviors. One of the important hydrological modeling ...
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Introduction: Time series models are one of the most important tools for investigating and modeling hydrological processes in order to solve problems related to water resources management. Many hydrological time series shows nonstationary and nonlinear behaviors. One of the important hydrological modeling tasks is determining the existence of nonstationarity and the way through which we can access the stationarity accordingly. On the other hand, streamflow processes are usually considered as nonlinear mechanisms while in many studies linear time series models are used to model streamflow time series. However, it is not clear what kind of nonlinearity is acting underlying the streamflowprocesses and how intensive it is.
Materials and Methods: Streamflow time series of 6 hydro-gauge stations located in the upstream basin rivers of ZarrinehRoud dam (located in the southern part of Urmia Lake basin) have been considered to investigate stationarity and nonlinearity. All data series used here to startfrom January 1, 1997, and end on December 31, 2011. In this study, stationarity is tested by ADF and KPSS tests and nonlinearity is tested by BDS, Keenan and TLRT tests. The stationarity test is carried out with two methods. Thefirst one method is the augmented Dickey-Fuller (ADF) unit root test first proposed by Dickey and Fuller (1979) and modified by Said and Dickey (1984), which examinsthe presence of unit roots in time series.The second onemethod is KPSS test, proposed by Kwiatkowski et al. (1992), which examinesthestationarity around a deterministic trend (trend stationarity) and the stationarity around a fixed level (level stationarity). The BDS test (Brock et al., 1996) is a nonparametric method for testing the serial independence and nonlinear structure in time series based on the correlation integral of the series. The null hypothesis is the time series sample comes from an independent identically distributed (i.i.d.) process. The alternative hypothesis arenot specified. Keenan test has also been proposed for assessing the linearity or nonlinearitybehavior of a time series in time series analysis. Keenan (1985) derived a test for nonlinearity analogous to Tukey’s degree of freedom for nonadditivity test. Keenan’s test is motivated by approximation a nonlinear stationary time series by a second-order Volterra expansion. While Keenan’s test for nonlinearity is designed for detecting quadratic nonlinearity, it may not be sensitive to threshold nonlinearity. Here, we applied the likelihood ratio test (TLRT) with the threshold model as the specific alternative.The null hypothesis of the TLRT approach for threshold nonlinearity is the fitted model to the series is an AR (p) model, and the alternative hypothesis is the fitted model to the series is a threshold autoregressive (TAR) model with autoregressive order p in each regime.
Results and Discussion: Because both the ADF and KPSS tests are based on linear regression, which has the normal distribution assumption, logarithmization can convert exponential trend possibly present in the data into a linear trend. In the case of stationary analysis, the results showed the standardized daily streamflow time series of all stations are significantly stationary. According to KPSS stationary test, the daily standardized streamflow time series are stationary around a fixed level, but they are not stationary around a trend stationaryin low lag values. Based on the BDS test, the results showed the daily streamflowseries have strong nonlinear structure, but based on the Keenan test, it can be seen the linear structure in thembyusing logarithmization and deseasonalization operators, and it means the coefficients of the double sum part are zero. It should be considered the Keenan test is used to detect quadratic nonlinearity, and it cannot be adequatelyfor threshold autoregressive models since they are linear in each regime.
Conclusion: Streamflow processes of main rivers at 6 stations located in the southern partof Urmia Lake basin were investigated for testingthenonstationarity and nonlinearity behaviors. In general, streamflowprocesses have been considered as nonlinear behaviors. But, the type and intensity of nonlinearity have not been detected at different time scale due to the existence of several evaluation tests. In this study, all daily streamflow series appear to be significantly stationary and have the nonlinearity behavior. Therefore, to model the daily streamflow time series, linear and nonlinear models can be used and their results can be evaluated.
Ahmad Fakheri Fard; Vahid Nourani; Faegheh Niazi
Abstract
Introduction: The influence of urbanization, as one important form of land use, on runoff and floods within watersheds has been a major topic of research during the past few decades. Urbanization affects the hydrology processes of a watershed by replacing the vegetated land cover with impervious surfaces. ...
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Introduction: The influence of urbanization, as one important form of land use, on runoff and floods within watersheds has been a major topic of research during the past few decades. Urbanization affects the hydrology processes of a watershed by replacing the vegetated land cover with impervious surfaces. This can have a substantial effect on the hydrological response of a watershed to rainfall, potentially resulting in faster response, greater magnitude of river flow, higher recurrence of small floods and reduced base-flow, and groundwater recharge. The direct runoff hydrograph generated by rain falling on a watershed reflects the characteristics of both the effective rain hyetograph and the relevant surface features that control the runoff generation and surface-water flow processes.
Materials and Methods: In this study, the effect of land use investigated using GUHCR model and adjusted GUHRLU model is presented. These models and Nash’s conceptual model used to investigate land use impacts for a small, well instrumented watershed consisting of two different land uses sub-watershed in the city of Sierra Vista, Cochise County, Southeastern Arizona. Geomorphological factors for the sub-watersheds extracted by GIS. In this study 13 storm events occurring on both sub-watersheds were selected to examine the proposed model’s performance. Nine events were selected for model calibration. The remaining four events were used to examine the simulated hydrographs for the outlet and the interior natural sub-watershed. The model parameter ( ) was estimated for each event using the moment method and the average of the calibrated values was used for evaluation of the model. The model's performance demonstrated through four popular criteria (i.e. The Nash–Sutcliffe efficiency (NE), the Correlation Coefficient (R), the ratio of the absolute error of peak flow (EP) and the ratio of the absolute error of hydrograph’s volume (Ev)) using available hydro-geomorphological data.
Results and Discussion: The results show that although all studied models forecast the outlet hydrographs with acceptable accuracy, only the presented GUHRLU model shows appropriate results at sub-watershed outlet considering the effect of land use. Clearly, accounting for land use properties in the model formulation leads to improved efficiency at the internal sub-watershed. The Nash model as a lumped model, calculates the hydrography just at the watershed outlet without any information about the hydrological behavior of the interior watershed. Therefore, internal hydrography estimation is impossible via this model. In general, urban runoff tends to have a sharper rising limb and higher peak values while runoffs in natural watersheds have smaller peak values and the rising limb climbs more slowly. The hydrographs show that the overall shapes of the urban sub-watershed hydrographs are similar to each other, while those in the natural sub-watershed tend to be more different, as expected. Simultaneous consideration of geomorphological and land use parameters in the formulation of the proposed model (GUHRLU) provides this capability. As indicated by Ep and Ev, the error of peak flow and the volume of hydrographs show acceptable accuracy. It can be noted that some events show high values of error of peak flows (Ep), however, the model results in small values of Ev that is of great importance in water resource management. Note that, the performance values obtained for the watershed outlet were, for most events, higher than those of the internal sub-watershed outlet in both formulations, which may be due to the use of outlet hydrographs for calculating the model parameter ( )., This might also be due to less uncertainty in urban watersheds where runoff to rainfall ratios is much larger than in the natural sub-watershed. The GUHCR model has slightly better performance at watershed outlet, but it is unable to detect land use variability in its model formulation and so to estimate the internal watershed hydrographs appropriately. Overall, peak discharge and runoff volume for the natural sub-watershed was over-estimated via GUHCR model. The average values for Nash-Sutcliffe criteria at the internal watershed outlet for GUHCR and GUHRLU models are 0.47 and 0.78 respectively. Over 40% improvement is achieved in simulated peak discharge and runoff volume at interior watershed outlet using GUHRLU in compared with GUHCR model.
Conclusion: GUHRLU model considers not only the geomorphologic properties of the watershed, but also the land use variation of the sub-watershed in parameter formulation. This model can also reflect the hydrological conditions of the internal parts of the watershed with divergent land uses. The GUHRLU model is able to improve the efficiency of geomorphological rainfall-runoff simulations at the interior part of the study watershed, located in southeastern Arizona, by taking into account land use. Consideration of land use in the model leads to acceptable results at both watershed and interior sub-watershed outlets, particularly for watersheds like the studied watershed where different land uses sub-watersheds have. The overall efficiency of prediction was slightly poorer for the internal sub-watershed than for the outlet. Application of three models reveals that only the presented GUHRLU model shows appropriate results at sub-watershed outlet in which the land use variation is considered in the model formulation.
A. Fakheri Fard; yaghoub dinpazhoh; F. Ahmadi; J. Behmanesh
Abstract
One of the applicable ways for simulation and forecasting hydrological processes is time series modeling. An important problem in forecasting hydrological data using time series is generating stochastic data. Any changes in stochastic series will change generating data. In this study nonlinear ARCH model ...
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One of the applicable ways for simulation and forecasting hydrological processes is time series modeling. An important problem in forecasting hydrological data using time series is generating stochastic data. Any changes in stochastic series will change generating data. In this study nonlinear ARCH model presented in order to modeling and generating stochastic component of time series. After combing ARCH model with nonlinear bilinear model, BL-ARCH model suggested to forecasting river flow discharge. Daily river flow of Shahar-Chai River located in the west of Urmia Lake and West Azarbaijan province have been used for data analysis and 11 years forecasting. As results shown suggested model with 4.52 error has better than bilinear model with 6.77 error. So this model can be used for short-time river flow forecasting specially daily series.
M. Ghorbani Aghdam; yaghoub dinpazhoh; A. Fakheri Fard; S. Darbandi
Abstract
Having a correct view of the effective factors on climatic changes by explanation of a considerable part of the total variance in data with limited number of principal components the analytical methods of decreasing data dimensions, such as PCA are important tools in water resources planning. In this ...
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Having a correct view of the effective factors on climatic changes by explanation of a considerable part of the total variance in data with limited number of principal components the analytical methods of decreasing data dimensions, such as PCA are important tools in water resources planning. In this study factor analysis method as a tool for projecting the information space on the limited and specific axes, has been applied. The main aim of this study is regionalization of Urmia Lake basin from the view of drought using factor analysis. For this purpose monthly precipitation data of 30 weather stations in the period 1972-2009 were used. For each of the selected stations three and twelve months SPI value were calculated. Factor analysis conducted on SPI values to delineate the study area with respect to drought characteristics. Homogeneity of obtained regions tested using the S-statistics proposed by Wiltshire. Resultes of factor analysis of 3 (12) months SPI values showed that 5 (6) factors having eigen values greater than 1 acounted for 68.08 (78.88) percent of total variance. Urmia Lake basin delineated to 5 (6) distinct regions considering the eigenvectors following rotation using the 3 (12) month time scale. Results of homogeneity test indicated that all of the obtained regions were homogeneous.
B. Fallahi; A. Fakheri Fard; yaghoub dinpazhoh; S. Darbandi
Abstract
Having a correct view of the effective factors on climatic changes by explanation of a considerable part of the total variance in data with limited number of principal components the analytical methods of decreasing data dimensions, such as PCA are important tools in water resources planning. In this ...
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Having a correct view of the effective factors on climatic changes by explanation of a considerable part of the total variance in data with limited number of principal components the analytical methods of decreasing data dimensions, such as PCA are important tools in water resources planning. In this study PCA method as a projection tool for projecting the information space on the limited and specific axes, ward’s method as a hierarchical clustering and k-mean as partitioning clustering method has been applied in this research. Using this methods and application of daily precipitation data of 60 meteorological stations during a 35 years period (1970-2004), 4 types of delineated regions were come out on the basis of daily precipitations, distance-quantity index, time intervals and rainy days series. S statistic test algorithm was used for homogeneity test of the regions. Results showed the nature of the PCA method is such that projects the data space on the main axes and shows the real space. But in the hierarchical methods, clusters do not describe the real structure. Therefore we do expect that the resulting clusters of PCA would be more realistic than that of methods. But hierarchical methods have the advantage of containing the wider clustering information on the basis of homogeneity than the others.
P. Toufani; A. Mosaedi; A. Fakheri Fard
Abstract
Abstract
Obligatory modelling of precipitations in various periods, have a lot of problems and weakness because of their casual nature in time and space. Moreover, their uncertainty in predictions, reduce credibility of estimations which have done via these models. Wavelet is one of the novel and very ...
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Abstract
Obligatory modelling of precipitations in various periods, have a lot of problems and weakness because of their casual nature in time and space. Moreover, their uncertainty in predictions, reduce credibility of estimations which have done via these models. Wavelet is one of the novel and very effective methods in analyzing of time series and signals considered in the hydrology in recent years. In this research, precipitation signal has been decomposed via selected mother wavelet, and then the resulted data are used by fitting direct equations to anticipate the precipitation. These mentioned methods are applied in Zarringol station in Golestan province (Iran) for 33 years predict monthly precipitation with 808 mm annually during 1975-76 until 2007-2008. As a result, decomposed signal via wavelet, correlation among observed and calculated data is 84% and the precipitation prediction can be done with more precise. Meaningless of F test in 90% and above verifies this phenomenon.
Keywords: Precipitation, Modeling, Signal, Wavelet theory, Zarringol