Dự đoán lưu lượng dòng chảy đa mô hình sử dụng hồi quy tuyến tính bội phần với điều chỉnh thiên lệch có điều kiện

Ali Jozaghi1, Haojing Shen1, Mohammadvaghef Ghazvinian1, Dong-Jun Seo1, Yu Zhang1, Edwin Welles2, Seann Reed3
1Department of Civil Engineering, The University of Texas at Arlington, Arlington, USA
2Deltares USA, Silver Spring, USA
3NWS Middle Atlantic River Forecast Center, State College, USA

Tóm tắt

Mục tiêu hợp nhất nhiều dự báo để cải thiện độ chính xác của dự báo là mối quan tâm lớn trong nhiều lĩnh vực. Hồi quy tuyến tính bội phần (MLR) là một kỹ thuật cực kỳ hấp dẫn cho mục đích này vì tính đơn giản và khả năng giải thích của nó. Tuy nhiên, để mô hình hóa và dự đoán các cực trị như lũ lụt bằng cách sử dụng MLR, độ thiên lệch suy giảm là một vấn đề rất nghiêm trọng, vì nó dẫn đến sự dự đoán thiếu và dư có hệ thống ở các đuôi trên và dưới của biến mục tiêu, tương ứng. Trong công trình này, chúng tôi giới thiệu hồi quy tuyến tính bội phần điều chỉnh thiên lệch có điều kiện (CBP-MLR) nhằm giảm bớt độ thiên lệch suy giảm bằng cách đồng thời tối thiểu hóa sai số bình phương trung bình (MSE) và sai số loại II bình phương. Trong khi CBP-MLR cải thiện độ chính xác dự đoán ở các đuôi, nó làm suy giảm hiệu suất gần hàng trung bình. Để giữ hiệu suất giống như MLR gần hàng trung bình trong khi tận dụng khả năng của CBP-MLR để cải thiện độ chính xác ở các đuôi, chúng tôi áp dụng hồi quy tuyến tính bội phần tổ hợp (CompMLR), mà trung bình trọng số tuyến tính các ước lượng của MLR và CBP-MLR. Để đánh giá so sánh, chúng tôi áp dụng kỹ thuật đề xuất vào dự đoán lưu lượng dòng chảy đa mô hình bằng cách sử dụng một số dự báo lưu lượng dòng chảy được sản xuất trong hoạt động như các biến dự đoán. Các kết quả cho các nhóm dự báo khác nhau trong khu vực dịch vụ của Trung tâm Dự báo Dòng nước Quốc gia Mỹ cho thấy rằng hiệu suất tương đối giữa các dự báo đầu vào khác nhau thay đổi đáng kể với phạm vi của lưu lượng dòng chảy quan sát được xác thực, và rằng CompMLR thường vượt trội hơn so với các dự báo có hiệu suất tốt nhất theo nghĩa sai số bình phương trung bình ở các điều kiện dễ đoán và kỹ năng dự đoán rất khác nhau.

Từ khóa

#hồi quy tuyến tính bội phần; thiên lệch; lưu lượng dòng chảy; dự đoán khí tượng thủy văn; sai số bình phương trung bình

Tài liệu tham khảo

Abel AB (2017) Classical measurement error with several regressors. Wharton School of the University of Pennsylvania, National Bureau of Economic Research Adams T (2015) Verification of the NOAA/NWS MMEFS operational hydrologic ensemble forecasting system in the Ohio River Valley. World Environmental and Water Resources Congress, Austin Adams TE (2016) Flood Forecasting in the United States NOAA/National Weather Service. In: Flood Forecasting. Elsevier, pp 249–310 Adnan RM, Liang Z, El-Shafie A, Zounemat-Kermani M, Kisi O (2019) Prediction of suspended sediment load using data-driven models. Water 11:2060. https://doi.org/10.3390/w11102060 Alizadeh B, Limon RA, Seo D-J et al (2020) Multiscale postprocessor for ensemble streamflow prediction for short to long ranges. J Hydrometeorol 21:265–285. https://doi.org/10.1175/JHM-D-19-0164.1 Anderson EA (1973) National Weather Service river forecast system: snow accumulation and ablation model. Silver Springs. https://www.wcc.nrcs.usda.gov/ftpref/wntsc/H&H/snow/AndersonHYDRO17.pdf Anderson E (2006) Snow accumulation and ablation model—SNOW-17. https://www.wcc.nrcs.usda.gov/ftpref/wntsc/H&H/snow/AndersonSnow17.pdf Baharvand S, Lashkar-Ara B (2021) Hydraulic design criteria of the modified meander C-type fishway using the combined experimental and CFD models. Ecol Eng 164:106207. https://doi.org/10.1016/j.ecoleng.2021.106207 Baharvand S, Jozaghi A, Fatahi-Alkouhi R et al (2020) Comparative study on the machine learning and regression-based approaches to predict the hydraulic jump sequent depth ratio. Iran J Sci Technol Trans Civ Eng. https://doi.org/10.1007/s40996-020-00526-2 Brown JD, Seo D-J (2013) Evaluation of a nonparametric post-processor for bias correction and uncertainty estimation of hydrologic predictions. Hydrol Process 27:83–105. https://doi.org/10.1002/hyp.9263 Brown JD, He M, Regonda S et al (2014a) Verification of temperature, precipitation, and streamflow forecasts from the NOAA/NWS Hydrologic Ensemble Forecast Service (HEFS): 2. Streamflow verification. J Hydrol 519:2847–2868. https://doi.org/10.1016/j.jhydrol.2014.05.030 Brown JD, Wu L, He M et al (2014b) Verification of temperature, precipitation, and streamflow forecasts from the NOAA/NWS Hydrologic Ensemble Forecast Service (HEFS): 1. Experimental design and forcing verification. J Hydrol 519:2869–2889. https://doi.org/10.1016/j.jhydrol.2014.05.028 Carl G, Kühn I (2008) Analyzing spatial ecological data using linear regression and wavelet analysis. Stoch Environ Res Risk Assess 22:315–324. https://doi.org/10.1007/s00477-007-0117-2 Chow VT, Maidment DR, Mays LW (1988) Applied hydrology. McGraw-Hill, New York Conway DA, Roberts HV (1983) Reverse regression, fairness, and employment discrimination. J Bus Econ Stat 1:75. https://doi.org/10.2307/1391775 Cui B, Toth Z, Zhu Y, Hou D (2012) Bias correction for global ensemble forecast. Weather Forecast 27:396–410. https://doi.org/10.1175/WAF-D-11-00011.1 Danandeh Mehr A, Kahya E, Şahin A, Nazemosadat MJ (2015) Successive-station monthly streamflow prediction using different artificial neural network algorithms. Int J Environ Sci Technol. https://doi.org/10.1007/s13762-014-0613-0 Demargne J, Wu L, Regonda SK et al (2014) The science of NOAA’s operational hydrologic ensemble forecast service. Bull Am Meteorol Soc 95:79–98. https://doi.org/10.1175/BAMS-D-12-00081.1 Deutsch R (1965) Estimation theory. Prentice-Hall, Englewood Cliffs Diks CGH, Vrugt JA (2010) Comparison of point forecast accuracy of model averaging methods in hydrologic applications. Stoch Environ Res Risk Assess 24:809–820. https://doi.org/10.1007/s00477-010-0378-z Du J, McQueen J, DiMego G et al (2004) 21.3 The NOAA/NWS/NCEP short range ensemble forecast (SREF) system: evaluation of an initial condition vs multiple model physics ensemble approach. Bull Am Meteorol Soc 2329–2338 Duan Q, Ajami NK, Gao X, Sorooshian S (2007) Multi-model ensemble hydrologic prediction using Bayesian model averaging. Adv Water Resour 30:1371–1386. https://doi.org/10.1016/j.advwatres.2006.11.014 Fedora MA, Beschta RL (1989) Storm runoff simulation using an antecedent precipitation index (API) model. J Hydrol 112:121–133. https://doi.org/10.1016/0022-1694(89)90184-4 Frost C, Thompson SG (2000) Correcting for regression dilution bias: comparison of methods for a single predictor variable. J R Stat Soc Ser A Stat Soc 163:173–189. https://doi.org/10.1111/1467-985X.00164 Fuller W (1987) Measurement error models. Wiley, Chichester Georgakakos KP, Seo D-J, Gupta H et al (2004) Towards the characterization of streamflow simulation uncertainty through multimodel ensembles. J Hydrol 298:222–241. https://doi.org/10.1016/j.jhydrol.2004.03.037 Gochis DJ, Barlage M, Dugger A et al (2018) The WRF-hydro modeling system technical description, (Version 5.0). NCAR technical note. https://ral.ucar.edu/sites/default/files/public/WRFHydroV5TechnicalDescription.pdf Goldberger AS (1984) Reverse regression and salary discrimination. J Hum Resour 19:293–318. https://doi.org/10.2307/145875 Goodarzi E, Ziaei M, Hosseinipour EZ (2014) Introduction to optimization analysis in hydrosystem engineering. Springer, Cham Graziano T, Clark E, Cosgrove B, Gochis D (2017) Transforming National Oceanic and Atmospheric Administration (NOAA) water resources prediction. In: 31st conference on hydrology, Seattle, WA, Amer. Meteor. Soc., 2A.2, https://ams.confex.com/ams/97Annual/webprogram/Paper314016.html Green CA, Ferber MA (1984) Employment discrimination: an empirical test of forward versus reverse regression. J Hum Resour 19:557. https://doi.org/10.2307/145948 Hamill TM, Bates GT, Whitaker JS et al (2013) NOAA’s second-generation global medium-range ensemble reforecast dataset. Bull Am Meteorol Soc 94:1553–1565. https://doi.org/10.1175/BAMS-D-12-00014.1 Hassanzadeh Y, Ghazvinian M, Abdi A, Baharvand S, Jozaghi A (2020) Prediction of short and long-term droughts using artificial neural networks and hydro-meteorological variables. arXiv:2006.02581 [physics.ao-ph] Hausman J (2001) Mismeasured variables in econometric analysis: problems from the right and problems from the left. J Econ Perspect 15:57–67. https://doi.org/10.1257/jep.15.4.57 Hoerl AE (1962) Application of ridge analysis to regression problems. Chem Eng Prog 58:54–59 Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics. https://doi.org/10.1080/00401706.1970.10488634 Hoeting JA, Madigan D, Raftery AE et al (1999) Bayesian model averaging: a tutorial (with discussion). Stat Sci 14:382 Hughes MD (1993) Regression dilution in the proportional hazards model. Biometrics 49:1056. https://doi.org/10.2307/2532247 Jahan A, Edwards KL, Bahraminasab M (2016) Multi-criteria decision analysis for supporting the selection of engineering materials in product design. Butterworth-Heinemann Elsevier Ltd, Oxford Jolliffe IT, Stephenson DB (eds) (2011) Forecast verification. Wiley, Chichester Jozaghi A, Shamsai A (2017) Application of geospatial information system and technique for order preference by similarity to ideal solution for sitting water reservoirs case study: south of Sistan&Balouchestan Province. Sci Res Q Geogr Data 25(100):5–15. https://doi.org/10.22131/sepehr.2017.24802 Jozaghi A, Alizadeh B, Hatami M, Flood I, Khorrami M, Khodaei N, Ghasemi Tousi E (2018) A comparative study of the AHP and TOPSIS techniques for dam site selection using GIS: a case study of Sistan and Baluchestan Province. Iran Geosci 8:494. https://doi.org/10.3390/geosciences8120494 Jozaghi A, Nabatian M, Noh S et al (2019) Improving multisensor precipitation estimation via adaptive conditional bias-penalized merging of rain gauge data and remotely sensed quantitative precipitation estimates. J Hydrometeorol 20:2347–2365. https://doi.org/10.1175/JHM-D-19-0129.1 Jozaghi A, Ghazvinian M, Seo D et al (2020) Improving water forecasting with Bayesian averaging of multiple forecasts. In: 34th conference on hydrology, Boston, MA, Amer. Meteor. Soc., J26.3. https://ams.confex.com/ams/2020Annual/meetingapp.cgi/Paper/369034 Jozaghi A, Shen H, Seo D et al (2021) Improving flood forecasting via conditional bias-penalized bayesian model averaging. In: Amer. Meteor. Soc., 35th conference on hydrology, New Orleans, LA Khan UT, Valeo C, He J (2013) Non-linear fuzzy-set based uncertainty propagation for improved DO prediction using multiple-linear regression. Stoch Environ Res Risk Assess 27:599–616. https://doi.org/10.1007/s00477-012-0626-5 Khanmohammadi N, Rezaie H, Montaseri M, Behmanesh J (2018) The application of multiple linear regression method in reference evapotranspiration trend calculation. Stoch Environ Res Risk Assess 32:661–673. https://doi.org/10.1007/s00477-017-1378-z Kim B, Seo D-J, Noh SJ et al (2018) Improving multisensor estimation of heavy-to-extreme precipitation via conditional bias-penalized optimal estimation. J Hydrol 556:1096–1109. https://doi.org/10.1016/j.jhydrol.2016.10.052 Krzysztofowicz R (1999) Bayesian theory of probabilistic forecasting via deterministic hydrologic model. Water Resour Res. https://doi.org/10.1029/1999WR900099 Lashkar-Ara B, Baharvand S, Najafi L (2021) Study the performance of data-driven models to predict the scour depth caused by the aerated vertical jet. Irrig Sci Eng 43(4):79–89 Lee H, Shen H, Noh SJ et al (2019) Improving flood forecasting using conditional bias-penalized ensemble Kalman filter. J Hydrol 575:596–611. https://doi.org/10.1016/j.jhydrol.2019.05.072 Levi MD (1973) Errors in the variables bias in the presence of correctly measured variables. Econometrica. https://doi.org/10.2307/1913819 Liu Y, Ye L, Qin H, Hong X, Ye J, Yin X (2018) Monthly streamflow forecasting based on hidden Markov model and Gaussian Mixture Regression. J Hydrol. https://doi.org/10.1016/j.jhydrol.2018.03.057 Luo X, Yuan X, Zhu S, Xu Z, Meng L, Peng J (2019) A hybrid support vector regression framework for streamflow forecast. J Hydrol. https://doi.org/10.1016/j.jhydrol.2018.10.064 Madigan D, Raftery AE (1994) Model selection and accounting for model uncertainty in graphical models using occam’s window. J Am Stat Assoc. https://doi.org/10.1080/01621459.1994.10476894 Makkonen L (2006) Plotting positions in extreme value analysis. J Appl Meteorol Climatol. https://doi.org/10.1175/JAM2349.1 MARFC (2010) Understanding the River Forecast Process, NWS Middle Atlantic River Forecast Center, State College, PA. https://www.weather.gov/media/marfc/FactSheets/Fact_Sheet_Understanding_River_Forecast_Process_FINAL_singlepgs.pdf, Accessed 02 June 2021 Muhammad A, Stadnyk TA, Unduche F, Coulibaly P (2018) Multi-model approaches for improving seasonal ensemble streamflow prediction scheme with various statistical post-processing techniques in the Canadian Prairie Region. Water (Switzerland). https://doi.org/10.3390/w10111604 Murphy AH, Winkler RL (1987) A general framework for forecast verification. Mon Weather Rev. https://doi.org/10.1175/1520-0493(1987)115%3c1330:AGFFFV%3e2.0.CO;2 National Weather Service (2006) NWSRFS User Manual Documentation. Office of Hydrologic Development, Silver Spring, MD. https://www.nws.noaa.gov/oh/hrl/nwsrfs/users_manual/htm/warnpdf.php National Weather Service (2008a) Single reservoir regulation (RES-SNGL) model. In: Office of Water Prediction (NWS OWP/NOAA). https://www.nws.noaa.gov/oh/hrl/general/chps/Models/Single_Reservoir_Regulation.pdf. Accessed 30 Jan 2017 National Weather Service (2008b) Joint reservoir regulation (RES-J) model. In: Office of Water Prediction (NWS OWP/NOAA). http://www.nws.noaa.gov/oh/hrl/general/chps/Models/Joint_Reservoir_Regulation.pdf. Accessed 30 Jan 2017 National Weather Service (2015) ensemble postprocessor (EnsPost) user’s manual. Office of Hydrologic Development, Silver Spring. https://www.nws.noaa.gov/oh/hrl/general/HEFS_doc/EnsPost_Users_Manual.pdf. Accessed 04 Apr 2015 National Weather Service (2016) meteorological ensemble forecast processor (MEFP) user’s manual. Office of Hydrologic Development, Silver Spring. https://www.nws.noaa.gov/oh/hrl/general/HEFS_doc/MEFP_Users_Manual.pdf Nelson BR, Seo D-J, Kim D (2010) Multisensor precipitation reanalysis. J Hydrometeorol 11:666–682. https://doi.org/10.1175/2010JHM1210.1 Raftery AE, Gneiting T, Balabdaoui F, Polakowski M (2005) Using Bayesian model averaging to calibrate forecast ensembles. Mon Weather Rev. https://doi.org/10.1175/MWR2906.1 Raftery AE, Hoeting J, Volinsky CT et al (2015) BMA: Bayesina model averaging. http://cran.r-project.org/package=BMA Raiffa H, Schlaifer R (1961) Applied statistical decision theory. Harvard University Press, Boston Regonda SK, Seo DJ, Lawrence B et al (2013) Short-term ensemble streamflow forecasting using operationally-produced single-valued streamflow forecasts: a Hydrologic Model Output Statistics (HMOS) approach. J Hydrol. https://doi.org/10.1016/j.jhydrol.2013.05.028 Roe J, Dietz C, Restrepo P et al (2010) NOAA’s community hydrologic prediction system. In: 2th federal interagency hydrologic modeling conference, Las Vegas, NV. https://acwi.gov/sos/pubs/2ndJFIC/Contents/7E_Roe_12_28_09.pdf Schaake J, Demargne J, Hartman R et al (2007) Precipitation and temperature ensemble forecasts from single-value forecasts. Hydrol Earth Syst Sci Discuss. https://doi.org/10.5194/hessd-4-655-2007 Schweppe FC (1973) Uncertain dynamic systems. Prentice Hall, Englewood Cliffs Seber GAF, Wild CJ (1989) Nonlinear regression. Wiley, Hoboken Seo DJ (2013) Conditional bias-penalized kriging (CBPK). Stoch Environ Res Risk Assess. https://doi.org/10.1007/s00477-012-0567-z Seo D-J, Herr HD, Schaake JC (2006) A statistical post-processor for accounting of hydrologic uncertainty in short-range ensemble streamflow prediction. Hydrol Earth Syst Sci Discuss. https://doi.org/10.5194/hessd-3-1987-2006 Seo DJ, Siddique R, Zhang Y, Kim D (2014) Improving real-time estimation of heavy-to-extreme precipitation using rain gauge data via conditional bias-penalized optimal estimation. J Hydrol. https://doi.org/10.1016/j.jhydrol.2014.09.055 Seo D-J, Saifuddin MM, Lee H (2018a) Conditional bias-penalized Kalman filter for improved estimation and prediction of extremes. Stoch Environ Res Risk Assess 32:183–201. https://doi.org/10.1007/s00477-017-1442-8 Seo D-J, Saifuddin MM, Lee H (2018b) Correction to: Conditional bias-penalized Kalman filter for improved estimation and prediction of extremes. Stoch Environ Res Risk Assess. https://doi.org/10.1007/s00477-018-1626-x Shen H, Lee H, Seo D-J (2019) Adaptive conditional bias-penalized kalman filter for improved estimation of extremes and its approximation for reduced computation. arXiv:1908.00482 Siddique R, Mejia A, Brown J et al (2015) Verification of precipitation forecasts from two numerical weather prediction models in the Middle Atlantic Region of the USA: a precursory analysis to hydrologic forecasting. J Hydrol. https://doi.org/10.1016/j.jhydrol.2015.08.042 Sittner WT, Schauss CE, Monro JC (1969) Continuous hydrograph synthesis with an API-type hydrologic model. Water Resour Res. https://doi.org/10.1029/WR005i005p01007 Theil H (1961) Economic forecasts and policy. North-Holland Pub. Co., Amsterdam Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc Ser B. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x Tibshirani R (1997) The lasso method for variable selection in the cox model. Stat Med. https://doi.org/10.1002/(SICI)1097-0258(19970228)16:4%3c385::AID-SIM380%3e3.0.CO;2-3 Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems. Winston and Sons, Washington Tikhonov AN, Goncharsky AV, Stepanov VV, Yagola AG (1995) Numerical methods for the solution of ill-posed problems Toth Z, Kalnay E (1997) Ensemble forecasting at NCEP and the breeding method. Mon Weather Rev. https://doi.org/10.1175/1520-0493(1997)125%3c3297:EFANAT%3e2.0.CO;2 Wilks DS (2005) Statistical methods in the atmospheric sciences, 2nd edn. Academic Press, London Wu L, Seo DJ, Demargne J et al (2011) Generation of ensemble precipitation forecast from single-valued quantitative precipitation forecast for hydrologic ensemble prediction. J Hydrol. https://doi.org/10.1016/j.jhydrol.2011.01.013 Zeugner S (2011) Bayesian model averaging with BMS. WwwCranR-ProductOrg Zhu Y, Toth Z (2008) NAEFS and NCEP global ensemble. Presentation for National DOH Workshop. https://www.nws.noaa.gov/oh/hrl/hsmb/docs/hep/events_announce/NAEFS_Yuejian_Zhu.pdf