Application of Copula theory for IHACRES hydrologic model evaluation (Case study: Taleghan watershed)

Authors

1 Ph.D. Student, Department of Watershed Science Engineering, Sari University of Agriculture and Natural Resources, Sari, Iran

2 Associate Professor, Department of Watershed Science Engineering, Sari University of Agriculture and Natural Resources, Sari, Iran

3 Professor, Department of Watershed Science Engineering, Sari University of Agriculture and Natural Resources, Sari, Iran

Abstract

Hydrologic modeling plays an important role in hydrologic response prediction for water resources managements, flood control and soil and water conservation. Performance evaluation is necessary before using a hydrologic model in a watershed. Various traditional evaluation criteria such as Nash-Sutcliff (E), correlation coefficient (R), Root Mean Square Error (RMSE) and index of agreement (d) are commonly used for the performance evaluation of hydrologic models. All these criteria compare the model output with observed data, however they cannot capture all the features reproduced by the hydrologic models such as information content of data and stochastic relationship between rainfall and run-off. This is doubly important when carrying out frequency analysis on the model output. This study aims at introducing a new application of copulas for the performance evaluation of hydrologic models in accurate simulation of stochastic relationship between rainfall and runoff. To this end, IHACRES hydrologic model was selected for daily flow simulation in the Taleghan watershed. The selected model was calibrated for the 5-year period of 1995-2000 and evaluated for 5-year period of 2000-2005. The non-linear module calibration optimized the parameters C, τw and F as 0.002 mm, 22 days and 4 degree Celsius respectively. The linear module parameters was also optimized as τq = 0.02 days, τs = 41.25 days and vs = 1. Performance evaluation of the model via Nash-Sutcliff (E=0.75), Pearson correlation coefficient (R= 0.87), root mean square error (RMSE=7.2) and index of agreement (d=0.93) indicated a good performance of the model for the evaluation period. Although the numerical performance evaluation criteria show satisfying results, however visual inspection of the scatter plot of observed and simulated flow showed that the model significantly underestimated the peak flows in spring. In contrast, the winter flow rate is noticeably overestimated. Regarding the Mediterranean climate of the study area, the greater portion of the winter precipitation falls as snow which piles up in mountains without draining into the river network. With the onset of spring and warming weather, the snow pack melting accompanied with spring precipitations lead to the peak flow generation in spring. As the snowmelt simulation module is not included in the model, the model considered all precipitation as rain in January, February and March. This lead to the overestimation of winter flow rate. On the other hand, the spring peak flows is underestimated because of neglecting the snowmelt runoff. In the next step various copula functions with different tail dependence structure in the upper and lower tail including Archimedean copulas (Clayton, rotated Clayton, Gumbel, rotated Gumbel, Frank) and elliptical copulas (Gaussian, t-copulas) were fitted on observed and simulated rainfall-runoff time series. Various goodness-of-fit test criteria AIC, BIC and Log likelihood (LL) were employed to choose the best fit copula functions for the observed and modeled time series. Results showed that the Clayton copula with the lowest AIC, BIC and LL values (AIC = –236.28, BIC = –236.28 and LL = –118.13) best fitted observed rainfall-runoff time series. Gaussian copula with lowest AIC, BIC and LL values (AIC = –217.08 BIC = –217.08 and LL = –108.54) was also selected as the best fitted copula for modeled rainfall-runoff time series. Nevertheless, the poor performance of the model in simulating the spring peak flows due to snowmelt runoff, the model has been approved by traditional performance evaluation criteria. However fitting the observed and simulated rainfall-runoff time series with Clayton and Gaussian copulas with different tail dependencies indicated inability of the model to properly simulate stochastic relationship between rainfall and runoff.

Keywords

Main Subjects

References

آشفته، پ. و مساح بوانی، ع.، 1388، تاثیر تغییر اقلیم بر روی دبی­های پیک( مطالعه موردی حوضه آیدوغموش، آذربایجان شرقی)، مجله علوم و فنون کشاورزی و منابع طبیعی، 53، 25-39.
دوستی، م.، شاهدی، ک.، حبیب نژاد روشن، م. و میریعقوب‌زاده، م.، 1393، استفاده از مدل نیمه مفهومی IHACRES در شبیه‌سازی جریان روزانه، پژوهشهای حفاظت آب و خاک، 21 (2)، 277-292.
رضوی‌زاده، س.، سلاجقه، ع.، خلیقی سیگارودی، ش. و جعفری، م.، 1390، بررسی تاثیر تغییر کاربری اراضی بر خصوصیات سیلاب با استفاده از مدل HEC-HMS . مرتع و آبخیزداری. 66 (3)، 373-386.
عبدالحسینی، م.، 1391، کاربرد کوپلا در تحلیل فراوانی چند متغیره جریانهای کم و ارزیابی رگرسیون کوپلایی به منظور استفاده در تحلیل متغیرهای غیر مستقل، پایان نامه دکتری، دانشکده کشاورزی، دانشگاه صنعتی اصفهان.
زارعی، م.، قنبرپور، م. ر.، حبیب نژاد روشن، م. و شاهدی، ک.، 1388، شبیه‌سازی جریان رودخانه با استفاده از مدل بارش-رواناب IHACRES (مطالعه موردی: حوضۀ آبخیز کسیلیان)، علوم و مهندسی آبخیزداری ایران، 3(8)، 11-20.
صادقی، ه.، قاسمیه، ه. و ساداتی نژاد، ج.، 1394، ارزیابی کارایی مدل هیدرولوژیکی IHACRES در مناطق مرطوب (مطالعه موردی، حوضه ناورود، گیلان)، نشریه علوم آب و خاک (علوم و فنون کشاورزی و منابع طبیعی)، 19(73)، 73-82.
میراکبری، م. و گنجی، آ.، 1391، تحلیل دو متغیره مشخصه‌های شدت و مدت خشک‌سالی هواشناسی (مطالعه موردی : استان کرمانشاه)، مجله پژوهش آب ایران، 11، 17-25.
نظری پویا، ه.، کردوانی، پ. و فرجی راد، ع.، 1394، واسنجی و ارزیابی عملکرد مدلهای هیدرولوژی IHACRES و SWAT در شبیه‌سازی رواناب، نشریه تحلیل فضایی مخاطرات محیطی، 2(2)، 99-112.
یعقوبی، م. و مساح بوانی، ع.، 1393، تحلیل حساسیت و مقایسه عملکرد سه مدل مفهومی HBV، IHACRES و HEC-HMS در شبیه‌سازی بارش رواناب پیوسته در حوضه‌های نیمه خشک (بررسی موردی: حوضه اعظم هرات-یزد)، مجله فیزیک زمین و فضا، 40(2)، 153-172.
Abdi, A., Hasanzadeh, Y., Talatahari, S., Fakheri-Fard, A. and Mirabbasi, R., 2016, Regional bivariate modeling of droughts using L-comoments and copulas, Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-016-1222-x.
Akaike, H., 1974, A new look at the statistical model identification. Journal of IEEE Transactions on Automatic Control, 19(6), 716–723.
Be´nard, B. and Lang, M., 2007, Use of a Gaussian copula for multivariate extreme value analysis: some case studies in hydrology, Advances in Water Resources 30,897–912.
Bozdogan, H., 2000, Akaike’s Information Criterion and recent developments in information complexity, Journal of Mathematical Psychology, 44(1), 62–91.
Box, G. E. P. and Jenkins, G. M., 1970, Time Series Analysis: Forecasting and Control. Holden- Day, San Francisco. 230p.
Crochemore, L., 2010, Evaluation of hydrological models: Expert judgments vs numerical criteria, Poly technique  Paris-UPMC Science de la terre.
Croke, B. F. W. and Littlewood, I. G., 2005, Comparison of Alternative Loss Modules In The IHACRES Model: An Application To 7 Catchments In Wales. International Congress on Modelling and Simulation (MODSIM 2005), 7p.
Croke, B. F. W., Andrews, F., Jakeman, A. J., Cuddy, S. M. and Luddy, A., 2005a, Redesign of the IHACRES rainfall runoff model. In: Proceedings of the 29th Hydrology and Water Resources Symposium. Engineers Australia.
Croke, B. F. W., Andrews, F., Spate, J. and Cuddy, S. M., 2005b, IHACRES User Guide. Technical Report 2005/19, second ed. ICAM, School of Resources, Environment and Society, The Australian National University, Canberra. http://www.toolkit.net.au/ihacres. 39 pp.
Day, P. J. and Croke, B. F. W., 2003, Evaluation of streamflow predictions by the IHACRES rainfall-runoff model in two South African catchments. Journal of Environmental Modeling and Software, 18, 705-712.
De Michele, C. and Salvadori, G., 2003, A generalized Pareto intensity duration model of storm rainfall exploiting 2-copulas, Journal of Geophysical Research, 108(15), 1-11.
Dung, N. V., Merz, B., Bardossy, A. and Apel, A., 2015, Handling uncertainty in bivariate quamtile estimation-An application to flood hazard analysis in the Mekong Delta. Journal of Hydrology, 527, 704-717.
Dupuis, D. J., 2007, Using copulas in hydrology: benefits, cautions, and issues, Journal of Hydrological Engineering, 12(4), 381–393.
Favre, A-C., El Adlouni, S., Perreault, L., Thiemonge, N. and Bobee, B., 2004, Multivariate hydrological frequency analysis using copulas. Water Resources Research, 40(1), 1-12.
Gartsman, B., van Nooyen, R. and Kolechkina, A., 2009, Implementation issues for total risk calculation for groups of sites, Physics and Chemistry of the Earth, 34, 619–625.
Genest, C. and Rivest, L. P., 1993, Statistical inference procedures for bivariate Archimedean copulas, Journal of the American Statistical Association, 88(423), 1034–1043.
Genest, C. and Favre, A-C., 2007, Everything you always wanted to know about copula modelling but were afraid to ask, Journal of Hydrological Engineering, 12(4), 347–368.
Grubbs, F. E. and Beck, G., 1972, Extension of sample sizes and percentage points for significant tests of outlying observations, Technometrics, 14, 847-854.
Gupta, H. V., Sorooshian, S. and Yapo, P. O., 1998, Toward improved calibration of hydrologic models: Multiple and no commensurable measures of information, Water Resources Research, 34(4), 751-763.
Javid, Y. and Apoorva, K. V., 2015, Flow regionalization under limited data availability-Application of IHACRES in the western Ghats, Aquatic Procedia, 4, 933-941.
Karmakar, S. and Simonovic, S. P., 2009, Bivariate flood frequency analysis. Part 2: a copula-based approach with mixed marginal distributions, Journal of Flood Risk Management, 2, 32–44.
Khosravi, M., 2008, Flood Forecasting Using Artificial Neural Network and Empirical Equations, Watershed management MSc thesis, Faculty of Natural Resources, Tehran University.
Kim, H. S., 2015, Application of a baseflow filter for evaluating model structure suitability of the IHACRES CMD, Journal of Hydrology, 521, 543-555.
Klein, B., Pahlow, M., Hundecha, Y. and Schumann, A., 2008, Probability analysis of hydrological loads for the design of flood control systems using copulas, Journal of Hydrological Engineering, 10, 360-369.
Krause, P., Boyle, D. P. and Base, F., 2005, Comparison of different efficiency criteria for hydrological model assessment, Advances in Geoscience, 5, 89-97.
Masufa, C. K., Trigg, M. A., Carter, A. and Howden, N. J. K., 2016, Water availability and agricultural demand: An assessment framework using global datasets in a data scarce catchment, Rokel-Seli River, Sierra Leone, Journal of Hydrology: regional studies, 8, 222-234.
Mirabbasi, R., Fakheri-Fard, A. and Dinpashoh, Y., 2012, Bivariate drought frequency analysis using the copula method, Theoretical and applied climatology, 108(1), 191-206.
Muhaisen, O. S., Osorio, F. and Garc´a, P. A., 2009, Two-copula based simulation for detention basin design, Civil Engineering Environmental Systems, 26(4), 355–366.
Nash, J. E. and Sutcliffe, J. V., 1970, River flow forecasting through conceptual model. Journal of Hydrology, 10 (3), 282-290.
Osorio, F., Muhaisen, O. and Garcı´a, P. A., 2009, Copula-based simulation for the estimation of optimal volume for a detention basin, Journal of Hydrological Engineering, 10, 1378-1382.
Pachepsky, Y., Guber, A., Jacques, D., Simunek, J., Van Genuchten, M. T., Nicholson, T. and Cady, R., 2006, Information 20 content and complexity of simulated soil water fluxes, Geoderma, 134, 253–266.
Reusser, D. E., Blume, T., Schaefli, B. and Zehe, E., 2009, Analyzing the temporal dynamics of model performance for 10 hydrological models. Hydrological Earth System Science, 13, 999-1018.
Serinaldi, F., Bonaccorso, B., Cancelliere, A. and Grimaldi, S., 2009, Probabilistic characterization of drought properties through copulas, Physics and Chemistry of the Earth, 34, 596–605.
Shiau, J-T., 2006, Fitting drought duration and severity with two dimensional copulas. Water Resources Management 20, 795–815.
Shiau, J-T., Feng, S. and Nadarajah, S., 2007, Assessment of hydrological droughts for the Yellow River, China, using copulas, Hydrological Process, 21, 2157–2163.
Shiau, J. T. and Modarres, R., 2009, Copula-based drought severity-duration frequency analysis in Iran, Journal of Applied Meteorology, 16(4), 481–489.
Sklar, M., 1959, Fonctions de r´epartition `a n dimensions et leursmarges. Paris, Publications institute statistique university.
Wang, C., Ni-Bin Chang, N-B. and Yeh, G-T., 2009, Copula-based flood frequency (COFF) analysis at the confluences of river systems, Hydrological Process 23, 1471–1486.
Weijs, S. V., Schoups, G. and van de Giesen, N., 2010, Why hydrological predictions should be evaluated using information theory. Hydrological Earth System Science, 14, 2545-2558.
Zhang, L. and Singh, V. P., 2006, Bivariate flood frequency analysis using the copula method. Journal of Hydrological Engineering, 11(2), 150–164.
Journal of the Earth and Space Physics
Volume 44, Issue 1
April 2018
Pages 71-88

Files

Share

How to cite

Statistics