ﮐﺎرﺑﺮد آﻧﺎﻟﯿﺰ ﺑﯿﺰ و ﻓﯿﻠﺘﺮ ذره اي در ﻣﺪل ﻫﺎي ﺑﺎرش - رواﻧﺎب و ﺗﺤﻠﯿﻞ ﻋﺪم ﻗﻄﻌﯿﺖ

Bayesian analysis and particle filter application in rainfall-runoff models and quantification of uncertainty

ﺳﺎﺑﻘﻪ و ﻫﺪف :اﺳﺘﻔﺎده از ﻣﺪل ﻫﺎي ﻫﯿﺪروﻟﻮژﯾﮑﯽ و اﻧﺠﺎم ﭘﯿﺶ ﺑﯿﻨﯽ در ﻣﻄﺎﻟﻌﺎت ﻣﺨﺘﻠﻒ ﻣﻨﺎﺑﻊ آب ﯾﮏ ﺿﺮورت ﻣﯽ ﺑﺎﺷﺪ .ﭘﯿﺶ ﺑﯿﻨﯽ ﺟﺮﯾﺎن ﺧﺮوﺟﯽ از ﺣﻮﺿﻪ ﻫﺎي آﺑﺮﯾﺰ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﭘﯿﭽﯿﺪﮔﯽ ﻫﺎي ﻣﻮﺟﻮد در ﭼﺮﺧﻪ ﻫﯿﺪروﻟﻮژﯾﮑﯽ ﻫﻤﻮاره ﺑﺎ اﻧﺠﺎم ﻓﺮض ﻫﺎﯾﯽ ﻫﻤﺮاه اﺳﺖ .ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺳﺎدهﺳﺎزي در رواﺑﻂ ﺗﻮﺳﻌﻪ داده ﺷﺪه در ﺳﺎﺧﺘﺎر ﻣﺪل ﻫﺎي ﺑﺎرش- رواﻧﺎب و ﻓﺮﺿﯿﺎت ﺑﻪ ﮐﺎر رﻓﺘﻪ در آنﻫﺎ، ﭘﯿﺶ ﺑﯿﻨﯽ ﻫﺎ ﻫﻤﻮاره ﺑﺎ ﻋﺪم ﻗﻄﻌﯿﺖ ﻫﻤﺮاه ﻣﯽ ﺑﺎﺷﻨﺪ .ﻣﻨﺎﺑﻊ ﻋﺪم ﻗﻄﻌﯿﺖ در اﯾﻦ ﻣﺪل ﻫﺎ را ﻣﯽ ﺗﻮان در ﺳﻪ دﺳﺘﻪ ﮐﻪ ﻧﺎﺷﯽ از ﺑﻪ ﮐﺎرﮔﯿﺮي ﭘﺎراﻣﺘﺮﻫﺎ، ﺳﺎﺧﺘﺎر ﻣﺪل و داده ﻫﺎي ﻣﻮرد اﺳﺘﻔﺎده ﻣﯽ ﺑﺎﺷﻨﺪ، دﺳﺘﻪ ﺑﻨﺪي ﻧﻤﻮد .ﻟﺰوم ﺗﺪﻗﯿﻖ ﭘﯿﺶ ﺑﯿﻨﯽ ﻫﺎ و اراﺋﻪ ﻋﺪم ﻗﻄﻌﯿﺖ ﻣﺪل ﻫﺎ ﺑﺎﯾﺪ ﻣﻮرد ﺗﻮﺟﻪ ﻗﺮار ﮔﺮﻓﺘﻪ و ﺑﺮاي ﺗﺤﻠﯿﻞ اﯾﻦ ﻣﻮﺿﻮع روش ﻫﺎي ﻣﺨﺘﻠﻔﯽ اراﺋﻪ ﺷﺪه اﺳﺖ .از ﺟﻤﻠﻪ روش ﻫﺎي ﭘﯿﺸﻨﻬﺎدي ﺷﯿﻮه ﺑﺮوزرﺳﺎﻧﯽ داده ﻫﺎ ﻣﯽ ﺑﺎﺷﺪ و ﻓﯿﻠﺘﺮ ذره اي از روش ﻫﺎي ﺗﻮﺳﻌﻪ داده ﺷﺪه در اﯾﻦ ﺧﺼﻮص ﻣﯽ ﺑﺎﺷﺪ. ﻫﺪف از اﯾﻦ ﭘﮋوﻫﺶ اﺳﺘﻔﺎده از روش ﻓﯿﻠﺘﺮ ذره اي در ﺑﺮوزرﺳﺎﻧﯽ و ﺑﻬﺒﻮد ﭘﯿﺶ ﺑﯿﻨﯽ ﺟﺮﯾﺎن آب ﺷﺒﯿﻪ ﺳﺎزي شده توسط مدل بارش - رواناب HYMOD با لحاظ جريان ﻣﺸﺎﻫﺪاﺗﯽ ﻣﯽ ﺑﺎﺷﺪ. ﻫﻤﭽﻨﯿﻦ ﺑﺎ ﮐﺎرﺑﺮد اﯾﻦ روش ﮐﻤﯽ ﺳﺎزي ﻋﺪم ﻗﻄﻌﯿﺖ و ﮐﺎﻫﺶ آن ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﻨﺎﺑﻊ ﻣﺨﺘﻠﻒ ﺧﻄﺎ ﻣﻮرد ارزﯾﺎﺑﯽ ﻗﺮار ﮔﺮﻓﺖ. ﻣﻮاد و روش ﻫﺎ: در اﯾﻦ ﻣﻄﺎﻟﻌﻪ، ﺑﺮاي ﺗﺪﻗﯿﻖ ﭘﯿﺶ ﺑﯿﻨﯽ ﻫﺎ از ﺷﯿﻮه ﺑﺮوزرﺳﺎﻧﯽ داده ﻫﺎ اﺳﺘﻔﺎده ﮔﺮدﯾﺪ . .اﯾﻦ روش ﺑﺎ به كارگيري فيلتر ذره اي ، تخمين متوالي بيز و تابع توزيع پسين مقدار رطوبت مدل Hymod و پارامترهاي آن را در حوضه آبريز كسيليان با مساحت حدود 67 كيلومتر مربع در مقياس روزانه محاسبه شد. فيلتر ذره اي بر پايه معادله بيز و ﺗﺎﺑﻊ ﺣﺪاﮐﺜﺮ درﺳﺘﻨﻤﺎﯾﯽ ﺧﻄﺎﻫﺎ در ﺑﺎزه زﻣﺎﻧﯽ ﻣﻮرد ﻧﻈﺮ ﻣﯽ ﺑﺎﺷﺪ .در ﺿﻤﻦ در ﺑﻪ ﮐﺎرﮔﯿﺮي اﯾﻦ ﺷﯿﻮه ﺑﺎﯾﺪ از روش ﺗﺮﮐﯿﺒﯽ ﺑﺎزﻧﻤﻮﻧﻪ ﮔﯿﺮي اﺣﺘﻤﺎﻻﺗﯽ ﻧﯿﺰ اﺳﺘﻔﺎده ﮐﺮد .اﯾﻦ روش از واﮔﺮاﯾﯽ ﺗﺤﻠﯿﻞ ﻫﺎ ﺟﻠﻮﮔﯿﺮي ﮐﺮده و ﻫﻤﭽﻨﯿﻦ ﻣﺸﮑﻼﺗﯽ ﻣﺎﻧﻨﺪ ﺗﺒﻬﮕﻨﯽ و ﭘﺪﯾﺪه ﻏﻨﯽ ﺳﺎزي دﺳﺘﻪ ذرات و ﻣﯿﻞ ﻧﻤﻮدن وزن دﺳﺘﻪ ذرات ﺑﻪ ﻋﺪد واﺣﺪ را ﺗﺼﺤﯿﺢ ﻣﯽ ﻧﻤﺎﯾﺪ. ﯾﺎﻓﺘﻪ ﻫﺎ: روش ﻓﯿﻠﺘﺮ ذره اي اﺳﺘﻔﺎده از ﭘﺎراﻣﺘﺮﻫﺎي ﻣﺪل در ﺷﺒﯿﻪ ﺳﺎزي و ﭘﯿﺶ ﺑﯿﻨﯽ ﺟﺮﯾﺎن ﺑﺎ ﺗﻮﻟﯿﺪ دﺳﺘﻪ ﭘﺎراﻣﺘﺮﻫﺎي ﺗﺼﺎدﻓﯽ و اﯾﺠﺎد ﺗﻮزﯾﻊ ﭘﯿﺸﯿﻦ را اﻣﮑﺎن ﭘﺬﯾﺮ ﻣﯽ ﻧﻤﺎﯾﺪ. اﯾﻦ ﺷﯿﻮه در ﺗﺪﻗﯿﻖ ﭘﯿﺶ ﺑﯿﻨﯽ ﻫﺎ و اﺳﺘﻔﺎده ﻫﻢ زﻣﺎن از ﻣﺘﻐﯿﺮ رﻃﻮﺑﺖ ﺧﺎك و ﭘﺎراﻣﺘﺮﻫﺎ در ﺗﺤﻠﯿﻞ ﻫﺎ ﻣﺆﺛﺮ اﺳﺖ .ﻫﻤﭽﻨﯿﻦ ﺑﺎ ﺗﻌﺮﯾﻒ ﺗﺎﺑﻊ درﺳﺘﻨﻤﺎﯾﯽ ﺧﻄﺎي اوﻟﯿﻪ و ﺑﻪ ﮐﺎر ﺑﺮدن ﺗﺌﻮري ﺑﯿﺰ ﻧﺴﺒﺖ ﺑﻪ اﺻﻼح ﭘﯿﺶ ﺑﯿﻨﯽ ﻫﺎ ﮐﻤﮏ ﻣﯽ ﻧﻤﺎﯾﺪ .ﺑﻪ ﻋﻼوه اﯾﻦ روش ﺗﺎﺑﻊ ﭼﮕﺎﻟﯽ اﺣﺘﻤﺎل ﭘﺴﯿﻦ ﭘﺎراﻣﺘﺮﻫﺎ را ﻧﯿﺰ اراﺋﻪ ﻧﻤﻮده و ﺗﺎﺑﻊ ﭼﮕﺎﻟﯽ اوﻟﯿﻪ را اﺻﻼح ﻣﯽ ﮐﻨﺪ . ﻧﺘﯿﺠﻪ ﮔﯿﺮي :ﻧﺘﺎﯾﺞ ﻧﺸﺎن داد ﮐﻪ اﺳﺘﻔﺎده از روش ﻓﯿﻠﺘﺮ ذره اي در ﺗﺮﮐﯿﺐ ﺑﺎ ﺷﯿﻮه ﺑﺎزﻧﻤﻮﻧﻪ ﮔﯿﺮي آﻣﺎري در ﺑﺮوزرﺳﺎﻧﯽ ﻫﯿﺪروﻟﻮژﯾﮑﯽ ﺳﺒﺐ ﺗﺪﻗﯿﻖ ﭘﯿﺶ ﺑﯿﻨﯽ ﻫﺎ در ﺣﻮﺿﻪ آﺑﺮﯾﺰ ﮐﺴﯿﻠﯿﺎن ﻣﯽ ﮔﺮدد .ﻫﻤﭽﻨﯿﻦ روش ﻓﯿﻠﺘﺮ ذره اي ﺳﺒﺐ ﻣﯽ ﮔﺮدد ﮐﻪ ﺷﺎﺧﺺ ﻧﺶ- ﺳﺎﺗﮑﻠﯿﻒ در ﻣﻘﺎﯾﺴﻪ ﺑﺎ ﺷﯿﻮه ﻣﺘﺪاول در ﺷﺒﯿﻪ ﺳﺎزي و پيش بيني جريان ، 22 درصد افزايش داشته و مقدار آن از 0/55 به 0/67 برسد .

Background and Objectives: Applying hydrologic models and forecast is a necessity in different studies in water resources. There should be multiple assumptions in forecasting the outflow of watersheds due to different complex relations in hydrologic cycle. Because of assumptions and simplifications those applied in the structure of models and developed relations, forecasts made by rainfall runoff models are always subject to uncertainties. Different sources of uncertainty are categorized into three parts: first, the uncertainty attributed to the applied data, second, the structure of model and third and the parameters. It is also necessary to address uncertainties and improve the precision of the forecasts. Therefore, there are multiple methods developed to analyze uncertainties. For this aim, data assimilation is a recommended approach and particle filter method is one of the developed models in this regard. The main goal of this research is to apply particle filter to update and improve the HYMOD rainfall runoff model forecasts based on observed stream flow. In addition, by the use of this approach, quantification and decreasing the uncertainty is evaluated based on different sources of error. Materials and Methods: In this study, improving the forecasts is implemented by data assimilation approach. To this aim, particle filter method, successive Bayesian estimation and posterior probability density function are applied for obtaining the soil moisture and Hymod parameters in daily scale in Kassilian river basin with approximately 67 square kilometers area. Particle filter is based on Bayes equation and maximum likelihood function of errors for the given time period. Moreover, this method should be combined with statistical resampling that prevents divergence of the analysis and corrects degeneracy, sample impoverishment of particles and tendency of the state variables particle weights to unit value (1). Results: Applying particle filter method makes it possible to use the intended model parameters for simulating and forecasting by random ensemble parameters generation and calculating prior probability density function. This method is also effective for precising forecasts and simultaneous application of parameters and soil moisture variable in analysis. Also this method helps to modify the forecasts using Baysian theory and definition of primary errors maximum likelihood function. In addition, this method also represents the posterior probability density function and corrects the prior density function. Conclusion: The results show applicability of particle filter method in combination with statistical resampling for hydrological data assimilation and improvement of the precision of forecasts of outflow from Kassilian river basin. It is shown that, the applied method improved the Nash-Sutcliffe statistic in comparison with open loop procedure. As the Nash-Sutcliffe statistic improved by 22%, rising from 0.55 to 0.67.