پديد آورندگان :
فتح آبادي، ابوالحسن داﻧﺸﮕﺎه ﮔﻨﺒﺪﮐﺎووس، ﮔﻠﺴﺘﺎن - ﮔﺮوه ﻣﺮﺗﻊ و آﺑﺨﯿﺰداري , روحاني، حامد داﻧﺸﮕﺎه ﮔﻨﺒﺪﮐﺎووس، ﮔﻠﺴﺘﺎن - ﮔﺮوه ﻣﺮﺗﻊ و آﺑﺨﯿﺰداري , سيديان، مرتضي داﻧﺸﮕﺎه ﮔﻨﺒﺪﮐﺎووس، ﮔﻠﺴﺘﺎن - ﮔﺮوه ﻣﺮﺗﻊ و آﺑﺨﯿﺰداري
كليدواژه :
آﻧﺎﻟﯿﺰ ﺣﺴﺎﺳﯿﺖ , آﻧﺘﺮوﭘﯽ , ﺳﻮﺑﻮل , ﻣﻮرﯾﺲ , ﻣﺪل ﻫﯿﺪروﻟﻮژﯾﮑﯽ
چكيده فارسي :
ﺳﺎﺑﻘﻪ و ﻫﺪف: در ﻃﯽ دﻫﻪ ﻫﺎي اﺧﯿﺮ ﺑﺎ اﻓﺰاﯾﺶ ﻗﺎﺑﻠﯿﺖ ﻣﺪل ﺳﺎزي ﺑﺎ ﮐﺎﻣﭙﯿﻮﺗﺮ ﺷﺎﻫﺪ اﻓﺰاﯾﺶ ﭘﯿﭽﯿﺪﮔﯽ و ﺗﻨﻮع ﻣﺪل ﻫﺎي ﻫﯿﺪروﻟﻮژﯾﮑﯽ ﺑﻮده اﯾﻢ. ﺑﺎ اﻓﺰاﯾﺶ ﭘﯿﭽﯿﺪﮔﯽ ﻣﺪل، ﺗﻌﺪاد ﭘﺎراﻣﺘﺮﻫﺎي ﻣﺪل زﯾﺎد ﺷﺪه ﮐﻪ اﯾﻦ ﻣﺴﺄﻟﻪ ﺑﺎﻋﺚ اﻓﺰاﯾﺶ اﺣﺘﻤﺎل ﺑﯿﺶ ﺑﺮازﺷﯽ و ﺳﺨﺖ ﺷﺪن ﺷﻨﺎﺳﺎﯾﯽ ﭘﺎراﻣﺘﺮﻫﺎ و ﺳﺎﺧﺘﺎر ﻣﺪل ﻣﯽ ﺷﻮد. ﺑﺪﯾﻦ ﻣﻨﻈﻮر ﺑﺎ اﺳﺘﻔﺎده از آﻧﺎﻟﯿﺰ ﺣﺴﺎﺳﯿﺖ ﭘﺎراﻣﺘﺮﻫﺎي ﻣﻬﻢ ﮐﻪ ﺑﻪ ﻧﻮﻋﯽ رﻓﺘﺎر ﻣﺪل را ﮐﻨﺘﺮل ﻣﯽ ﮐﻨﻨﺪ ﺷﻨﺎﺳﺎﯾﯽ ﺷﺪه و ﺳﻬﻢ ﻫﺮ ﯾﮏ از ﭘﺎراﻣﺘﺮﻫﺎ در ﻋﺪم ﻗﻄﻌﯿﺖ ﺧﺮوﺟﯽ ﻣﺪل ﺗﻌﯿﯿﻦ ﻣﯽ ﺷﻮد. روش ﻫﺎي ﻣﺨﺘﻠﻔﯽ ﺑﺮاي آﻧﺎﻟﯿﺰ ﺣﺴﺎﺳﯿﺖ ﭘﺎراﻣﺘﺮﻫﺎ و ورودي ﻫﺎي ﻣﺪل ﻫﺎي ﻣﺨﺘﻠﻒ وﺟﻮد دارد ﮐﻪ آن ﻫﺎ را ﺑﻪ دو دﺳﺘﻪ ﻣﻮﺿﻌﯽ و ﺳﺮاﺳﺮي ﺗﻘﺴﯿﻢ ﺑﻨﺪي ﻣﯽ ﮐﻨﻨﺪ. در ﺣﺎﻟﯽ ﮐﻪ در روش ﻫﺎي ﻣﻮﺿﻌﯽ ﺗﻐﯿﯿﺮات ﺧﺮوﺟﯽ ﻣﺪل در ﺣﺎﻟﺘﯽ ﮐﻪ ﺳﺎﯾﺮ ﭘﺎراﻣﺘﺮﻫﺎ ﺛﺎﺑﺖ ﺑﻮده و ﻓﻘﻂ ﯾﮑﯽ از ﭘﺎراﻣﺘﺮﻫﺎ ﺗﻐﯿﯿﺮ ﻣﯽ ﮐﻨﺪ ﺑﺮرﺳﯽ ﻣﯽ ﺷﻮد. روش ﻫﺎي ﺳﺮاﺳﺮي ﻗﺎدر ﺑﻮده آﻧﺎﻟﯿﺰ ﺣﺴﺎﺳﯿﺖ را ﺑﺮاي ﮐﻞ داﻣﻨﻪ ﭘﺎراﻣﺘﺮﻫﺎي ﻣﺪل اﺟﺮا ﮐﺮده و ﻫﻤﭽﻨﯿﻦ ﻣﯽ ﺗﻮاﻧﻨﺪ اﺛﺮات ﻣﺘﻘﺎﺑﻞ ﺑﯿﻦ ﭘﺎراﻣﺘﺮﻫﺎ و ﻏﯿﺮ ﺧﻄﯽ ﺑﻮدن را ﻧﯿﺰ در ﻧﻈﺮ ﺑﮕﯿﺮﻧﺪ. در اﯾﻦ ﭘﮋوﻫﺶ ﮐﺎراﯾﯽ ﺳﻪ روش آﻧﺎﻟﯿﺰ ﺣﺴﺎﺳﯿﺖ ﺷﺎﻣﻞ روش ﻫﺎي ﻣﻮرﯾﺲ، ﺳﻮﺑﻮل و ﺷﺎﺧﺺ آﻧﺘﺮوﭘﯽ در آﻧﺎﻟﯿﺰ ﺣﺴﺎﺳﯿﺖ ﭘﺎراﻣﺘﺮﻫﺎ و ورودي ﻫﺎي ﻣﺪل ﻫﺎي ﻫﯿﺪرﻟﻮژﯾﮑﯽ ﺑﺮرﺳﯽ ﺷﺪ. در ﻫﺮ دو ﻣﺪل ﻣﻬﻢ HBV و TOPMODEL ﺗﺮﯾﻦ ﭘﺎراﻣﺘﺮﻫﺎ ﺷﻨﺎﺳﺎﯾﯽ ﺷﺪه و ﺑﺮ اﺳﺎس اﻫﻤﯿﺖ آن ﻫﺎ در ﺧﺮوﺟﯽ ﻣﺪل رﺗﺒﻪ ﺑﻨﺪي ﺷﺪﻧﺪ. اﯾﻦ ﭘﮋوﻫﺶ در ﺑﺨﺸﯽ از ﺣﻮزه ﮔﺮﮔﺎﻧﺮود (ﺣﻮزه آﺑﺨﯿﺰ ﭼﻬﻞ ﭼﺎي) اﻧﺠﺎم ﺷﺪ.
ﻣﻮاد و روش ﻫﺎ: ﺳﻪ روش آﻧﺎﻟﯿﺰ ﺣﺴﺎﺳﯿﺖ ﻣﻮرﯾﺲ، ﺳﻮﺑﻮل و آﻧﺘﺮوﭘﯽ در اﯾﻦ ﭘﮋوﻫﺶ ﺑﺮرﺳﯽ ﺷﺪﻧﺪ. روش ﻣﻮرﯾﺲ ﺟﻬﺖ آﻧﺎﻟﯿﺰ ﺣﺴﺎﺳﯿﺖ و ﻏﺮﺑﺎل ﮔﺮي و ﺗﺸﺨﯿﺺ ﭘﺎراﻣﺘﺮﻫﺎ و ورودي ﻫﺎي ﻣﻬﻢ اراﺋﻪ ﺷﺪه اﺳﺖ. اﯾﻦ روش ﺑﺮ اﺳﺎس روش ﻧﻤﻮﻧﻪ ﻫﺎي ﺗﺼﺎدﻓﯽ و ﺗﮑﺮاري ﯾﮏ ﭘﺎراﻣﺘﺮ در ﻫﺮ اﺟﺮا ﭘﺎﯾﻪ ﮔﺬاري ﺷﺪه اﺳﺖ. روش ﺳﻮﺑﻮل ﯾﮑﯽ از ﻣﺘﺪاول ﺗﺮﯾﻦ روش ﻫﺎي آﻧﺎﻟﯿﺰ ﺣﺴﺎﺳﯿﺖ ﺳﺮاﺳﺮي اﺳﺖ ﮐﻪ ﺑﺮ ﻣﺒﻨﺎي ﺗﺠﺰﯾﻪ وارﯾﺎﻧﺲ ﻣﯽ ﺑﺎﺷﺪ. روش آﻧﺘﺮوﭘﯽ ﺑﺮاي آﻧﺎﻟﯿﺰ ﺣﺴﺎﺳﯿﺖ ﺑﺮاي TOPMODEL و HBV ﻣﺒﺘﻨﯽ ﺑﺮ اﻃﻼﻋﺎت ﻣﺘﻘﺎﺑﻞ ﺑﺎ ﺟﺪول ﻣﻘﺎﯾﺴﺎت اراﺋﻪ ﺷﺪه اﺳﺖ. دو ﻣﺪل ﻫﯿﺪروﻟﻮژﯾﮑﯽ ﻣﻘﺎﯾﺴﻪ ﺳﻪ روش آﻧﺎﻟﯿﺰ ﺣﺴﺎﺳﯿﺖ اﺳﺘﻔﺎده ﺷﺪ، ﮐﻪ ﺑﻪ ﺗﺮﺗﯿﺐ داراي 13و9 ﭘﺎراﻣﺘﺮ ﻫﺴﺘﻨﺪ. در اﯾﻦ ﭘﮋوﻫﺶ از روش ﻧﻤﻮﻧﻪ ﺑﺮداري ﻣﺮﺑﻊ ﻻﺗﯿﻦ ﺑﺮاي ﻧﻤﻮﻧﻪ ﺑﺮداري ﺗﺼﺎدﻓﯽ از ﻣﺠﻤﻮﻋﻪ ﭘﺎراﻣﺘﺮﻫﺎ ﺑﻪ ﻋﻠﺖ ﮐﺎراﯾﯽ آن اﺳﺘﻔﺎده ﮔﺮدﯾﺪ. ﻋﻼوه ﺑﺮ آن ﺳﻪ روش آﻧﺎﻟﯿﺰ ﺣﺴﺎﺳﯿﺖ از ﻟﺤﺎظ ﻫﻤﮕﺮاﯾﯽ، رﺗﺒﻪ ﺑﻨﺪي ﭘﺎراﻣﺘﺮﻫﺎ و ﺗﻌﺪاد ﻣﺤﺎﺳﺒﺎت ﻣﻮرد ﻧﯿﺎز ارزﯾﺎﺑﯽ ﺷﺪﻧﺪ.
در روش ﻣﻮرﯾﺲ ﺗﻌﺪاد ﻧﻤﻮﻧﻪ ﺑﺮداري ﺑﺮاي اﯾﻨﮑﻪ ﺗﻌﺪاد ﺗﮑﺮار ﻣﺪل ﺑﻪ ﻫﻤﮕﺮاﯾﯽ ﺑﺮﺳﺪ ﺑﻪ 1000 و 700 ﺗﺮﺗﯿﺐ T ﺗﮑﺮار در دو ﻣﺪل ﺑﻮد. در روش ﺳﻮﺑﻮل ﻫﻤﮕﺮاﯾﯽ ﻧﻤﻮﻧﻪ HBV و OPMODEL ﺑﺮداي ﭘﺎراﻣﺘﺮﻫﺎ ﺑﺮاي دو ﻣﺪل ﺑﻪHBV و TOPMODEL ﺗﺮﺗﯿﺐ در ﺗﻌﺪاد ﻧﻤﻮﻧﻪ ﺑﻪ 28000 و 22000 ﺑﺮداري ﺑﺮاﺑﺮ ﺑﺎ دﺳﺖ آﻣﺪ. در روش آﻧﺘﺮوﭘﯽ در و ﺿﺮﯾﺐ ﻋﺪم ﻗﻄﻌﯿﺖ ﮐﺎﻫﺶ ﯾﺎﻓﺘﻪ و ﺑﻪ R ﺑﻪ ﺑﻌﺪ ﺗﻐﯿﯿﺮات آﻣﺎره 6000ﻫﺮ دو ﻣﺪل ﻫﯿﺪروﻟﻮژﯾﮑﯽ در ﺗﻌﺪاد ﺗﮑﺮار ﻧﻮﻋﯽ در اﯾﻦ ﺗﻌﺪاد ﺗﮑﺮار ﻣﺪل روشTOPMODEL ﻫﺎ ﺑﻪ ﻫﻤﮕﺮاﯾﯽ رﺳﯿﺪﻧﺪ. در ﻣﺪل ﻫﺎي ﺳﻮﺑﻮل و ﻣﻮرﯾﺲ رﺗﺒﻪ ﺑﻨﺪي و M ﯾﮑﺴﺎﻧﯽ اراﺋﻪ دادﻧﺪ. روش آﻧﺘﺮوﭘﯽ ﻧﯿﺰ ﻣﺸﺎﺑﻪ اﯾﻦ دو روش ﻋﻤﻞ ﮐﺮده ﺑﺎ اﯾﻦ ﺗﻔﺎوت ﮐﻪ در اﯾﻦ روش ﭘﺎراﻣﺘﺮﻫﺎي ﺑﻪ Srmax ﺗﺮﺗﯿﺐ رﺗﺒﻪ را دارﻧﺪ در ﺣﺎﻟﯽ4 و 3 ﻫﺎي ﮐﻪ در دو روش دﯾﮕﺮ اﯾﻦ ﭘﺎراﻣﺘﺮﻫﺎ ﺑﻪ ﺗﺮﺗﯿﺐ رﺗﺒﻪ را ﺑﻪ 3 و 4 ﻫﺎي دو روش ﺳﻮﺑﻮل و ﻣﻮرﯾﺲ ﻋﻤﻠﮑﺮد ﯾﮑﺴﺎﻧﯽ داﺷﺘﻨﺪ. در 5 ﺗﺎ ﭘﺎراﻣﺘﺮﻫﺎي ﻣﺮﺗﺒﻪ HBV ﺧﻮد اﺧﺘﺼﺎص دادﻧﺪ. در ﻣﺪل ﻣﻬﻢ HBVﻣﺪل ﺗﺮﯾﻦ ﺗﻔﺎوت ﺣﺴﺎﺳﯿﺖ ﭘﺎراﻣﺘﺮﻫﺎ ﺑﺎ روش آﻧﺘﺮوﭘﯽ ﻣﺤﺎﺳﺒﻪ ﺷﺪ، ﺑﻪ ﻃﻮري FC ﮐﻪ در اﯾﻦ روش ﭘﺎراﻣﺘﺮ ﺑﻪ ﻋﻨﻮان ﺣﺴﺎﺳﯿﺖ ﺗﺮﯾﻦ ﭘﺎراﻣﺘﺮ ﺗﺸﺨﯿﺺ داده ﺷﺪ؛ اﯾﻦ در ﺣﺎﻟﯽ اﺳﺖ ﮐﻪ در دو روش دﯾﮕﺮ ﭘﺎراﻣﺘﺮ BETA ﺣﺴﺎس ترين پارامتربود.
ﻧﺘﯿﺠﻪ ﮔﯿﺮي: ﯾﮏ روﯾﮑﺮد واﺣﺪ ﺑﺮاي ﺣﻞ ﺗﻤﺎم ﻣﺴﺎﺋﻞ وﺟﻮد ﻧﺪارد. ﺑﻨﺎﺑﺮاﯾﻦ ﺑﻪ ﻃﻮر ﻣﻌﻤﻮل دو ﯾﺎ ﭼﻨﺪ روش ﺑﯿﺶ ﺗﺮ ﮐﻪ ﺟﻬﺖ اﻓﺰاﯾﺶ اﻃﻤﯿﻨﺎن در رﺗﺒﻪ، ﺗﺮﺟﯿﺤﺎً اﺳﺎس ﺗﺌﻮري ﯾﮑﺴﺎﻧﯽ را ﻧﺪارﻧﺪ ﺑﻨﺪي ﺣﺴﺎﺳﯿﺖ ﭘﺎراﻣﺘﺮﻫﺎ اﺳﺘﻔﺎده ﻣﯽ ﺷﻮد. در اﯾﻦ ﻣﻄﺎﻟﻌﻪ ارزﯾﺎﺑﯽ ﺟﺎﻣﻊ ﺑﺮاي اﺛﺮﺑﺨﺸﯽ و ﮐﺎراﯾﯽ ﺳﻪ روش آﻧﺎﻟﯿﺰ ﺣﺴﺎﺳﯿﺖ ﺑﺮ روي ﭘﺎراﻣﺘﺮﻫﺎي دو ﻣﺪل ﻫﯿﺪروﻟﻮژﯾﮑﯽ HBV و TOPMODEL
اجراشد.نقاط قوت و ضعف هاي سه روش مورد بحث بررسي شد.درروش سويول ﻫﻤﮕﺮاﯾﯽ ﻧﻤﻮﻧﻪ در دو ﻣﺪل ﻫﯿﺪروﻟﻮژﯾﮑﯽ ﻧﯿﺎز داﺷﺖ. ﺑﻨﺎﺑﺮاﯾﻦ اﺟﺮاي آن (>20000) ﺑﺮداري ﭘﺎراﻣﺘﺮﻫﺎ ﺑﻪ ﺗﻌﺪاد زﯾﺎدي اﺟﺮا در ﻣﺪل ﻫﺎي ﭘﯿﭽﯿﺪه ﺑﺴﯿﺎر وﻗﺖ ﮔﯿﺮ اﺳﺖ. در ﻣﻘﺎﺑﻞ روش ﻣﻮرﯾﺲ ﻓﻘﻂ ﻧﯿﺎز ﺑﻪ اﺟﺮاي ﮐﻢ ﺷﺒﯿﻪ1000 ﺗﺮ از ﺳﺎزي داﺷﺖ.
چكيده لاتين :
Background and Objectives: In recent decades following the massive increase in computational power, considerable progress has been made in hydrological models. As the complexity of the model increases, model parameters increases and this lead to increasing the chances of overfitting and difficulty in identifying both model parameter values and model structure. One possible way to mitigate over-parameterization/non-identifiability is reducing the number of parameters to a small number that can be sufficiently calibrated with limited data. Sensitivity analysis (SA) is a commonly used approach for identifying important parameters that dominate model behaviors. Overall, they can be categorized into two groups: local SA and global SA. The local SA explores the changes of model response by varying one parameter while keeping other parameters constant . On the other hand, the global SA examines the changes of model response by varying all parameters at the same time. No general rule has yet been defined for verifying the convergence of the General SA methods. In order to fill this gap this paper presents a convergence analysis of three widely used SA methods (Morris screening, Sobol and Entropy index) for two rainfall-runoff models, TOPMODEL and HBV. The simulations are carried out over ChehlChay watershed within Gorganrood River Basin. Materials and Methods: The sensitivity and interaction analysis based onSobol, Morris screen and Entropy methods were applied. The Morris method has been proposed as a screening method to identify a subset of inputs that have the greatest influence on the outputs.Sobol SA is a global, variance-based method that attributes variance in the model output to individual parameters and their interactions.Mutual entropy analysis is a sensitivity analysis method in which the mutual entropy of two variables is regarded as the correlative extent between these two variables. The distribution character of data (X, Y) can be expressed by contingency tables. The HBV model and TOPMODEL are used as a test problem. There are thirteen and nine parameters in the HBV model and TOPMODEL models, respectively. In each model, samples of the model parameter space are obtained using a latin-hypercube. The convergence analysis has been performed by increasing the number of simulations until there was no significant change of the sensitivity measure. In addition, the three SA methods are evaluated and compared in terms of convergence, the related evolution of the parameter ranking results and required computation cost. Results: Results of the quantitative convergence analysis for Morris screen was achieved at 700 and 1000 number of simulations for HBV and TOPMODEL models, respectively. Results for the Sobol method deviated considerably from the other methods by 22000 and 28000 for the TOPMODEL and HBV models, respectively. In Entropy method need about 6000 samples for the same purpose in both hydrological models. The ranking of parameters sensitivity indices in TOPMODEL for the first two most sensitive parameters for the three methods are similar. In general, the ranks of sensitive parameters are the same for all methods. Meanwhile for Entropy method, M and Srmax as the third and fourth ranking are vice versa than other two methods. In HBV model, Sobol and Morris screen methods provide similar results for those model parameters having the highest influence. For the parameter P, the sensitivity obtained from Entropy method was 3rd rank but in two other methods the parameter ranking varies from 3rd to sixth. In Entropy parameter FC becomes the most important parameter but in Morris screen and Sobol methods, the model parameter BETA selected as the parameter with the highest importance. Conclusion: There is no single best strategy for all problems. Therefore in general use of two or more methods, preferably with dissimilar theoretical foundations, may be needed to increase confidence in the ranking of the key inputs.This study conducted a comprehensive evaluation of the effectiveness and efficiency of three SA methods by using the HBV and TOPMODEL models as test problem. The strengths and limitations of qualitative and quantitative SA methods are explored.For the Sobol method, a comparatively large number of simulations (>20 000) were required to sufficiently cover the parameter space. Hence, performing Sobol method for complex models is often becoming problematic. The Morris method, instead, is computationally cheap and needed only <1000 simulations to obtain stable results.
