تخمین طول منطقه اشباع و زمان پیمایش زیر سطحی دامنه ها بر اساس سه شبیه اشباع پذیری دامنه های مرکب

نوع مقاله : مقاله پژوهشی

نویسندگان

• تورج سبزواری ¹
• رامتین کریمی ²
• مهدی کرمی مقدم ³

¹ دانشیار گروه مهندسی عمران دانشگاه آزاد اسلامی واحد استهبان، استهبان، ایران

² دانش اموخته کارشناسی ارشد مهندسی عمران دانشگاه آزاد اسلامی واحد استهبان، استهبان، ایران

³ استادیار، گروه کشاورزی، دانشگاه پیام نور، ایران

چکیده

دامنه های حوزه های آبخیز در طبیعت دارای هندسه مرکب هستند. شکل پلان (همگرایی، واگرایی و موازی) و میزان انحنای دامنه(مقعر، صاف و محدب)، نه شکل مختلف دامنه های مرکب را تشکیل می دهند. جهت بررسی میزان رواناب سطحی و زیر سطحی دامنه ها، طبق مکانیسم دانی بلاک نیازمند جداسازی منطقه اشباع از منطقه غیر اشباع می باشد. زمان پیمایش جریان زیر سطحی و سطحی دامنه ها یک پارامتر کلیدی در تخمین رواناب دامنه هادر بسیاری از مدل های بارندگی-رواناب مانند مدل های هیدروگراف واحد لحظه ای می باشند. در این تحقیق یک مدل جدید به نام گاما با هندسه و معادلات ساده تر به کار گرفته شد. در این مدل معادلاتی تحلیلی جهت محاسبه طول منطقه اشباع(SZL) و زمان پیمایش دامنه های مرکب(STT) ارایه شد. نتایج مدل اشباع پذیری و زمان پیمایش مدل پیشنهادی گاما با مدل زیگما و w که در تحقیقات گذشته ارایه شده بود مورد مقایسه قرار گرفت. برای ارزیابی دو مدل گاما و زیگما، مدل W به عنوان مبنا قرار گرفت و از دو معیار ریشه میانگین مربع خطاها(RMSE) و ضریب کارایی ناش(CE) استفاده گردید. متوسط مقدار RMSE برای تخمین SZL طبق مدل گاما و زیگما به ترتیب 0.84و 0.82 متر می باشند. متوسط مقادیر CE برای محاسبه پارامتر STT برای مدل گاما و زیگما به ترتیب 0.79 و 0.72 است که ارزیابی از نوع خوب می باشد. مدل گاما نتایج بسیار نزدیکی به مدل زیگما دارد ولی برای دامنه های واگرا صاف و محدب پیشنهاد نمی گردد.

کلیدواژه‌ها

• دامنه های مرکب
• زمان پیمایش زیر سطحی
• طول منطقه اشباع

20.1001.1.20086377.1398.12.43.5.7

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عنوان مقاله [English]

Prediction of saturated zone length and subsurface travel time of hillslopes based on three saturation models of complex hillslopes

نویسندگان [English]

• t. s ¹
• R. K ²
• M. K.M ³

¹ Associate Professor, Department of Civil Engineering, Islamic Azad University, Estahban Branch, Estahban, Iran

² Master of Science in Civil Engineering, Islamic Azad University, Estahban Branch, Estahban, Iran

³ Assistant Professor, Department of Agriculture, Payame Noor University, Iran

چکیده [English]

Hillslopes of natural catchments have a complex geometry. In complex hillslopes, the plan shape (convergence, parallelity and the amount of profile curvature (concave, straight and convex) create nine different shapes of complex hillslopes. To examine the amount of surface and subsurface runoff of hillslopes based on Dunne-Black mechanism, the saturated and unsaturated zones of hillslopes must be first separated. Travel time of surface and subsurface flow is a key parameter in runoff prediction of most rainfall-runoff models like time-dependent hydrograph models. In this research, a new simple saturation model, called Gamma, was employed with simpler geometry and equations. In this model, analytical equations were introduced to calculate saturation zone length (SZL) and subsurface travel time (STT). Results of Gamma saturation model and travel time of the proposed model were compared with other complex saturation models like W model and Sigma model by using two criteria of root mean square error (RMSE) and Nash efficiency factor (CE). The mean of RMSE for SZL prediction according to Gamma and Sigma models are 0.84 and 0.82 respectively. The mean CE for STT prediction according to Gamma and Sigma models are 0.79 and 0.72 respectively that were evaluated well. The main goal of this study is the examination of the efficiency of three models in estimation of saturated zone length and subsurface travel time. According to the results, Gamma model results were very close to those of Sigma model but for the straight divergent and convex divergent hillslopes, the Gamma model is not recommended.

کلیدواژه‌ها [English]

• Saturation
• Complex hillslope
• Subsurface Travel time

مراجع

1)       Anderson MG, Burt TP. 1978. Towards more detailed field monitoring of variable source area. Water Resources Research 14: 1123–1131.

2)       Aryal, S.K., O’Loughlin, E.M., and Mein, R.G. 2005. A similarity approach to determine response times to      steady-state saturation in landscapes. Adv. Water Resour., 28, 99–115.

3)       Berne, A., R. Uijlenhoet and P. A. Troch, 2005. Similarity analysis of subsurface flow response of hillslopes with complex geometry, Water Resour. Res., 41, W09410. 

4)       Beven, K. 1982. On subsurface stormflow: prediction with simple kinematic theory for saturated and unsaturated flows, Water Resour. Res., 18 (6), 1627–1633.

5)       Dunne T, Black RD. 1970a. Partial-area contributions to storm runoff in a small New England watershed. Water Resources Research 6: 1296–1311.

6)       Dunne T, Black RD. 1970b. An experimental investigation of runoff production in permeable soil. Water Resources Research 6: 478–490.

7)       Evans  I. S ,1980. An integrated system of terrain analysis and slope mapping. Zeitschrift fur Geomorphologie, Supplementband. 36: 274-295.

8)       Fan, Y., Bras, R., 1998. Analytical solutions to hillslope subsurface storm flow and saturation overland flow. Water Resour. Res. 34 (4), 921–927.

9)       Freeze, R.A. 1971. Three-dimensional, transient, saturated-unsaturated flow in a groundwater basin. Water Resour. Res., 7, 929–941.

10)   Freeze, R.A. 1972a. Role of subsurface flow in generating surface runoff: 1. Baseflow contributions to channel flow. Water Resour. Res., 8, 609–623.

11)   Freeze, R.A. 1972b. Role of subsurface flow in generating surface runoff: 2. Upstream source areas. Water Resour. Res., 8, 1272–1283.

12)   Freeze, R.A., and Harlan, R.L. 1969. Blueprint for a physically-based digitally simulated hydrologic response model. J. Hydrol., 9, 237–258.

13)   Hewlett JD, Hibbert AR. 1963. Moisture and energy conditions within a sloping soil mass during drainage. Journal of Geophysical Research 68: 1080–1087.

14)   Hewlett JD, Hibbert AR. 1967. Factors affecting the response of small watersheds to precipitation in humid areas. In International Symposium on Forest Hydrology, Sopper WE, Lull HW (eds). Pergamon Press: Oxford; 275–290.

15)   Hilberts, A., E. Van Loon, P. A. Troch and C. Paniconi,2004. The hillslope-storage Boussinesq model for non-constant bedrock slope, J. Hydrol., 291, 160-173.

16)   Hilberts, A., P. A. Troch, C. Paniconi and J. Boll ,2007. Low-dimensional modeling of hillslope subsurface flow: the relationship between rainfall, recharge, and unsaturated storage, Water Resour. Res., 43, W03445.

17)   Norbiato D., Borga. M, 2008. Analysis of hysteretic behaviour of a hillslope-storage kinematic wave model for subsurface flow , Advances in Water Resources journal, 31 , 118–131

18)   Noroozpour S, Saghafian B, Akhondali AM, Radmanesh F ,2014. Travel time of curved parallel hillslopes. Hydrol Res J 145(4), 190–199. doi:10.2166/nh.2013.171.

19)   Lee, K.T., and Chang, C.H., 2005. Incorporating subsurface-flow mechanism into geomorphology-based IUH modeling. Journal of Hydrology 311:91–105.

20)   O'Loughlin EM. 1981. Saturation regions in catchments and their relations to soil and topographic properties. J Hydrol;53:229–46.

21)   Sabzevari T, Talebi A, Ardakanian R and Shamsai A, 2010. A steady-state saturation model to determine the subsurface travel time (STT) in complex hillslopes, Hydrol. Earth Syst. Sci.14: 891–900.

22)   Sabzevari T. Noroozpour.S,2014 .Effects of hillslope geometry on surface and subsurface flows, Hydrogeology Journal 22: 1593–1604, DOI 10.1007/s10040-014-1149-6

23)   Singh VP, Agiralioglu N ,1981a. Diverging overland flow: analytical solutions. Nord Hydrol 12(2):81–89

24)   Singh VP, Agiralioglu N, 1981b. Diverging overland flow, application to natural watersheds. Nord Hydrol 12(2):99–110

25)   Singh VP, Agiralioglu N (1982) Lag time for diverging overland flow. Nordic Hydrol 13:39–48.

26)   Troch, P., van Loon, E., Hilberts, A., 2002. Analytical solutions to a hillslope-storage kinematic wave equation for subsurface flow. Adv. Water Resour. 25, 637–649.

27)   Troch, P., A. van Loon, and A. Hilberts .,2004, Analytical solution of the linearized hillslope-strorage Boussinesq equation for exponential hill- slope width functions, Water Resour. Res., 40, W08601.

28)   Talebi  A, Troch P. A and Uijlenhoet R ,2008. A steady-state analytical hillslope stability model for complex hillslopes. Hydrol. Process, 22:546-553.

29)   Zaslavsky, D., and Rogowski, AS. , 1969. Hydrologic and morphologic implications of anisotropy and infiltration in soil profile development. Soil Sci Soc Am Proc; 33(4):594–599.