In today’s world, using the statistical modeling process, natural phenomena can be used to analyze and predict the events under study. Many hydrological modeling methods do not make the best use of available information because hydrological models show a wide range of environmental processes that complex the model. In particular, when predicting, parameters affect the performance of statistical models. In many risk assessment issues, the presence of uncertainty in the parameters leads to uncertainty in predicting the model. Global sensitivity analysis is a tool used to show uncertainty and
is used in decision making, risk assessment, model simplifcation and so on. Minkowski distance sensitivity analysis and regional sensitivity analysis are two broad methods that can work with a given sample set of model input-output pair. One signifcant difference between them is that minkowski distance sensitivity analysis analyzes output distributions conditional on input values (forward), while regional sensitivity analysis analyzes input distributions conditional on output values (reverse). In this dissertation, we study the relationship between these two approaches and show that regional sensitivity analysis (reverse), when focusing on probability density functions of input, converges towards minkowski distance sensitivity analysis (forward) as the number of classes for conditioning model outputs in the reverse method increases. Similar to the existing general form of forward sensitivity indices, we derive a general form of the reverse sensitivity indices and provide the corresponding reverse given-data method. Finally, the sensitivity analysis of a water storage design with high dimensions of the model outputs is performed.
Type of Study: Applicable |
Subject: General Received: 2022/03/16 | Accepted: 2022/03/30 | Published: 2022/09/8
References
1. [1] Bergstroem, S. (1975), The development of a snow routine for the HBV-2 model, Hydrology Research, 6, 73. [DOI:10.2166/nh.1975.0006]
2. [2] Beven, K. J. (2011), Rainfall-runoff modelling: the primer, John Wiley & Sons, West Sussex. [DOI:10.1002/9781119951001]
3. [3] Borgonovo, E. (2007), A new uncertainty importance measure, Reliability Engineering & System Safety, 92, 771-784. [DOI:10.1016/j.ress.2006.04.015]
4. [4] Borgonovo, E., Hazen, G. B., and Plischke, E. (2016), A common rationale for global sensitivity measures and their estimation, Risk Analysis, 36, 1871-1895. [DOI:10.1111/risa.12555]
5. [5] Botev, Z. I., Grotowski, J. F., Kroese, D. P., et al. (2010), Kernel density estimation via diffusion, The annals of Statistics, 38, 2916-2957. [DOI:10.1214/10-AOS799]
6. [6] Da Veiga, S. (2015), Global sensitivity analysis with dependence measures, Journal of Statistical Computation and Simulation, 85, 1283-1305. [DOI:10.1080/00949655.2014.945932]
7. [7] Freedman, D. and Diaconis, P. (1981), On the histogram as a density estimator: L 2 theory, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 57, 453-476. [DOI:10.1007/BF01025868]
8. [8] Kollat, J., Reed, P., and Wagener, T. (2012), When are multiobjective calibration trade-offs in hydrologic models meaningful?, Water Resources Research, 48(3). [DOI:10.1029/2011WR011534]
9. [9] Oreskes, N., Shrader-Frechette, K., and Belitz, K. (1994), Verifcation, validation, and confrmation of numerical models in the earth sciences, Science, 263, 641-646. [DOI:10.1126/science.263.5147.641]
10. [10] Plischke, E., Borgonovo, E., and Smith, C. L. (2013), Global sensitivity measures from given data, European Journal of Operational Research, 226, 536-550. [DOI:10.1016/j.ejor.2012.11.047]
11. [11] Saltelli, A., Annoni, P., Azzini, I., Campolongo, F., Ratto, M., and Tarantola, S. (2010), Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index, Computer physics communications, 181, 259-270. [DOI:10.1016/j.cpc.2009.09.018]
12. [12] Sobol, I. M. (1993), Sensitivity analysis for non-linear mathematical models, Mathematical modelling and computational experiment, 1, 407-414.
13. [13] Spear, R. C., Grieb, T. M., and Shang, N. (1994), Parameter uncertainty and interaction in complex environmental models, Water Resources Research, 30, 3159-3169. [DOI:10.1029/94WR01732]
14. [14] Wagener, T., Boyle, D. P., Lees, M. J., Wheater, H. S., Gupta, H. V., and Sorooshian, S. (2001), A framework for development and application of hydrological models, Hydrology and Earth System Sciences, 5, 13-26. [DOI:10.5194/hess-5-13-2001]
15. [15] Zhai, Q., Yang, J., Xie, M., Zhao, Y. (2014). Generalized moment-independent importance measures based on Minkowski distance. European Journal of Operational Research, 239(2), 449-455. [DOI:10.1016/j.ejor.2014.05.021]