Evaluation of Spatial Rainfall Products in Sparsely Gauged Region Using Copula Uncertainty Modeling with Triple Collocation
Publication: Journal of Hydrologic Engineering
Volume 26, Issue 4
Abstract
This study presents a topography-dependent error adjustment technique for observed spatial rainfall estimate (OSRE) with the application of a multivariate t-copula model in a sparsely gauged region in Bangladesh. Multiple satellite precipitation products, including TRMM-3B42v7, TRMM-3B42RT, IMERG-Daily (Final run), PERSIANN-CCS, and PERSIANN-CDR, and reanalysis products, including MERRA-2, ERA-Interim, and JRA55, were tested to remove the topography-dependent errors in OSREs. The Triple Collocation (TC) method was employed as an alternative evaluation method of OSRE in the absence of adequate rain gauges. To address topography-dependent errors, the error adjustment model was separately run over the mountainous and plain zones. After bias correction, the correlation coefficient (CC) values were improved by 17.39%–38.6% for the mountainous region and 23.69%–47.83% for the plain basin. Based on categorical and volumetric performance evaluation matrices, the satellite product IMERG-Daily performed more reasonably than any other OSREs in both the plain and mountainous zones. CC values obtained for IMERG-Daily were high, whereas PERSIANN products exhibited low CC values within the observed datasets. Among the reanalysis products, JRA55 performed poorly, whereas ERA-Interim showed satisfactory results. All reanalysis and precipitation products except for TRMM-3B42v7 provided significant random errors in the coastal area and mountainous basin relative to the plain zone. The TC method provides a similar performance ranking to traditional methods, that is, comparing OSRE with rain gauges. This study works to fill the existing knowledge gap by developing a zone-wise copula uncertainty model for multisource satellite and reanalysis precipitation products. An evaluation technique in a sparsely gauged region using the TC method was adopted to measure OSREs’ performance in the absence of gauge rainfall data.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
The observed satellite precipitation products and reanalysis products are publicly available.
Acknowledgments
The authors gratefully acknowledge the Directorate of Research and Extension of Chittagong University of Engineering and Technology (Project No. CUET/DRE/2017-18/CRHLSR/002) for providing the necessary funding to conduct the research.
References
Aghakouchak, A. 2014. “A baseline probabilistic drought forecasting framework using standardized soil moisture index: Application to the 2012 United States drought.” Hydrol. Earth Syst. Sci. 18 (7): 2485–2492. https://doi.org/10.5194/hess-18-2485-2014.
AghaKouchak, A., A. Bárdossy, and E. Habib. 2010a. “Conditional simulation of remotely sensed rainfall data using a non-Gaussian v-transformed copula.” Adv. Water Resour. 33 (6): 624–634. https://doi.org/10.1016/j.advwatres.2010.02.010.
AghaKouchak, A., A. Bárdossy, and E. Habib. 2010b. “Copula-based uncertainty modelling: Application to multisensor precipitation estimates.” Hydrol. Processes 24 (15): 2111–2124. https://doi.org/10.1002/hyp.7632.
Aghakouchak, A., E. Habib, and A. Bárdossy. 2010c. “A comparison of three remotely sensed rainfall ensemble generators.” Atmos. Res. 98 (2–4): 387–399. https://doi.org/10.1016/j.atmosres.2010.07.016.
Ahmed, A. U. 2006. Bangladesh climate change impacts and vulnerability a synthesis. Dhaka, Bangladesh: Climate Change Cell, Dept. of Environment.
Ahmed, B. 2015. Rainfall pattern modeling of Chittagong District, Bangladesh. Dhaka, Bangladesh: BUET-Japan Institute of Disaster Prevention and Urban Safety.
Alemohammad, S. H., K. A. McColl, A. G. Konings, D. Entekhabi, and A. Stoffelen. 2015. “Characterization of precipitation product errors across the United States using multiplicative triple collocation.” Hydrol. Earth Syst. Sci. 19 (8): 3489–3503. https://doi.org/10.5194/hess-19-3489-2015.
Behrangi, A., K. Andreadis, J. B. Fisher, F. J. Turk, S. Granger, T. Painter, and N. Das. 2014. “Satellite-based precipitation estimation and its application for streamflow prediction over mountainous Western U.S. Basins.” J. Appl. Meteorol. Climatol. 53 (12): 2823–2842. https://doi.org/10.1175/JAMC-D-14-0056.1.
Ben-Gal, I. 2010. “Outlier detection.” In Data mining and knowledge discovery handbook, 63–73. New York: Springer.
Bosilovich, M., et al. 2015. MERRA-2: Initial evaluation of the climate. Greenbelt, MD: National Aeronautics and Space Administration, Goddard Space Flight Center.
Caracciolo, D., A. Francipane, F. Viola, L. V. Noto, and R. Deidda. 2018. “Performances of GPM satellite precipitation over the two major Mediterranean islands.” Atmos. Res. 213 (Nov): 309–322. https://doi.org/10.1016/j.atmosres.2018.06.010.
Chan, Y., and H. Li. 2008. “Tail dependence for multivariate -copulas and its monotonicity.” Insur. Math. Econ. 42 (2): 763–770. https://doi.org/10.1016/j.insmatheco.2007.08.008.
Cong, R.-G., and M. Brady. 2012. “The interdependence between rainfall and temperature: Copula analyses.” Sci. World J. 2012: 405675. https://doi.org/10.1100/2012/405675.
Daneshkhah, A., R. Remesan, O. Chatrabgoun, and I. P. Holman. 2016. “Probabilistic modeling of flood characterizations with parametric and minimum information pair-copula model.” J. Hydrol. 540 (Sep): 469–487. https://doi.org/10.1016/j.jhydrol.2016.06.044.
De Maesschalck, R., D. Jouan-Rimbaud, and D. L. Massart. 2000. “The mahalanobis distance.” Chemom. Intell. Lab. Syst. 50 (1): 1–18.
Demarta, S., and A. J. Mcneil. 2004. “The t copula and related copulas.” Int. Stat. Rev. 73 (1): 111–129. https://doi.org/10.1111/j.1751-5823.2005.tb00254.x.
Derin, Y., and K. K. Yilmaz. 2014. “Evaluation of multiple satellite-based precipitation products over complex topography.” J. Hydrometeorol. 15 (4): 1498–1516. https://doi.org/10.1175/JHM-D-13-0191.1.
Di Bernardino, E., and D. Rullière. 2016. “On tail dependence coefficients of transformed multivariate Archimedean copulas.” Fuzzy Sets Syst. 284 (Feb): 89–112. https://doi.org/10.1016/j.fss.2015.08.030.
Draper, C., R. Reichle, R. De Jeu, V. Naeimi, R. Parinussa, and W. Wagner. 2013. “Estimating root mean square errors in remotely sensed soil moisture over continental scale domains.” Remote Sens. Environ. 137 (Oct): 288–298. https://doi.org/10.1016/j.rse.2013.06.013.
ERA (ECMWF Re-Analysis). 2019. “ERA-Interim a global atmospheric reanalysis product of earth weather system.” Accessed August 21, 2019. https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era-interim.
Favre, A., S. El Adlouni, L. Perreault, N. Thie, and B. Bobe. 2004. “Multivariate hydrological frequency analysis using copulas.” Water Resour. Res. 40 (1): 1–12. https://doi.org/10.1029/2003WR002456.
Gao, C., Y. P. Xu, Q. Zhu, Z. Bai, and L. Liu. 2018. “Stochastic generation of daily rainfall events: A single-site rainfall model with copula-based joint simulation of rainfall characteristics and classification and simulation of rainfall patterns.” J. Hydrol. 564 (Sep): 41–58. https://doi.org/10.1016/j.jhydrol.2018.06.073.
Gelaro, R., et al. 2017. “The modern-era retrospective analysis for research and applications, version 2 (MERRA-2).” J. Clim. 30 (14): 5419–5454. https://doi.org/10.1175/JCLI-D-16-0758.1.
Ghodichore, N., R. Vinnarasi, C. T. Dhanya, and S. B. Roy. 2018. “Reliability of reanalyses products in simulating precipitation and temperature characteristics over India.” J. Earth Syst. Sci. 127 (8): 1–21. https://doi.org/10.1007/s12040-018-1024-2.
Goodison, B. E. 1981. “Compatibility of Canadian snowfall and snow cover data.” Water Resour. Res. 17 (4): 893–900.
GPM (Global Precipitation Measurement). 2019. “Goddard earth sciences data and information services center (GES DISC).” Accessed August 21, 2019. https://disc.gsfc.nasa.gov/datasets/GPM_3IMERGDF_V05.
Habib, E., A. Aduvala, and E. Meselhe. 2008. “Analysis of radar rainfall error characteristics and implications for streamflow simulations uncertainty.” Hydrol. Sci. J. 53 (3): 568–587. https://doi.org/10.1623/hysj.53.3.568.
Haerter, J. O., B. Eggert, C. Moseley, C. Piani, and P. Berg. 2015. “Statistical precipitation bias correction of gridded model data using point measurements.” Geophys. Res. Lett. 42 (6): 1919–1929. https://doi.org/10.1002/2015GL063188.
Hain, C. R., W. T. Crow, J. R. Mecikalski, M. C. Anderson, and T. Holmes. 2011. “An intercomparison of available soil moisture estimates from thermal infrared and passive microwave remote sensing and land surface modeling.” J. Geophys. Res. Atmos. 116 (D15). https://doi.org/10.1029/2011JD015633.
Hillel, D., and J. L. Hatfield. 2015. Encyclopedia of soils in the environment. Amsterdam, Netherlands: Elsevier.
Hodge, V. J., and J. Austin. 2004. “A survey of outlier detection methodologies.” Artif. Intell. Rev. 22 (2): 85–126. https://doi.org/10.1023/B:AIRE.0000045502.10941.a9.
Hong, Y., K. L. Hsu, H. Moradkhani, and S. Sorooshian. 2006. “Uncertainty quantification of satellite precipitation estimation and Monte Carlo assessment of the error propagation into hydrologic response.” Water Resour. Res. 42 (8): 1–15. https://doi.org/10.1029/2005WR004398.
Hossain, F., and E. N. Anagnostou. 2006. “A two-dimensional satellite rainfall error model.” IEEE Trans. Geosci. Remote Sens. 44 (6): 1511–1522. https://doi.org/10.1109/TGRS.2005.863866.
Hou, A. Y., R. K. Kakar, S. Neeck, A. A. Azarbaizan, C. D. Kummerow, M. Komija, R. Oki, K. Nakamura, and T. Iguchi. 2014. “The global precipitation measurement mission.” Bull. Am. Meteorol. Soc. 95 (5): 701–722. https://doi.org/10.1175/BAMS-D-13-00164.1.
Hua, L., and H. Joe. 2014. “Strength of tail dependence based on conditional tail expectation.” J. Multivar. Anal. 123 (Jan): 143–159. https://doi.org/10.1016/j.jmva.2013.09.001.
Huang, W., and A. Prokhorov. 2014. “A goodness-of-fit test for copulas.” Econom. Rev. 33 (7): 751–771. https://doi.org/10.1080/07474938.2012.690692.
Huffman, G. J., D. T. Bolvin, E. J. Nelkin, D. B. Wolff, R. F. Adler, G. Gu, Y. Hong, K. P. Bowman, and E. F. Stocker. 2006. “The TRMM multisatellite precipitation analysis (TMPA): Quasi-global, multiyear, combined-sensor precipitation estimates at fine scales.” J. Hydrometeorol. 8 (1): 38–55. https://doi.org/10.1175/JHM560.1.
Joe, H. 1997. Multivariate models and dependence concepts. London: Chapman and Hall.
Johnston, K., 2004. ArcGIS 9: Using ArcGIS geostatistical analyst. Redlands, CA: Esri Press.
Joyce, R. J., J. E. Janowiak, P. A. Arkin, and P. Xie. 2004. “CMORPH: A method that produces global precipitation estimates from passive microwave and infrared data at high spatial and temporal resolution.” J. Hydrometeorol. 5 (3): 487–503. https://doi.org/10.1175/1525-7541(2004)005%3C0487:CAMTPG%3E2.0.CO;2.
JRA (Japanese Meteorological Agency Reanalysis). 2019. “JRA-55: Japanese 55-year reanalysis, daily 3-hourly and 6-hourly data.” Accessed May 16, 2019. https://rda.ucar.edu/datasets/ds628.0/.
Kelly, K. S., and R. Krzysztofowicz. 1997. “A bivariate meta-Gaussian density for use in hydrology.” Stochastic Hydrol. Hydraul. 11 (1): 17–31. https://doi.org/10.1007/BF02428423.
Khatun, M. A., M. B. Rashid, and H. O. Hygen. 2016. Climate of Bangladesh. Dhaka, Bangladesh: BMD and Norwegian Meteorological Institute.
Khodadoust Siuki, S., B. Saghafian, and S. Moazami. 2017. “Comprehensive evaluation of 3-hourly TRMM and half-hourly GPM-IMERG satellite precipitation products.” Int. J. Remote Sens. 38 (2): 558–571. https://doi.org/10.1080/01431161.2016.1268735.
Kidd, C., and G. Huffman. 2011. “Global precipitation measurement.” Meteorol. Appl. 18 (3): 334–353. https://doi.org/10.1002/met.284.
Kimani, M. W., J. C. B. Hoedjes, and Z. Su. 2018. “Bayesian bias correction of satellite rainfall estimates for climate studies.” Remote Sens. 10 (7): 1074.
Kubota, T., H. Hashizume, S. Shige, K. Okamoto, K. Aonashi, N. Takahashi, T. Ushio, and M. Kachi. 2006. “Global precipitation map using satellite-borne microwave radiometers by the GSMaP project: Production and validation.” Int. Geosci. Remote Sens. Symp. 45 (7): 2584–2587. https://doi.org/10.1109/IGARSS.2006.668.
Lazoglou, G., C. Anagnostopoulou, C. Skoulikaris, and K. Tolika. 2019. “Bias correction of climate model’s precipitation using the copula method and its application in river basin simulation.” Water 11 (3): 600. https://doi.org/10.3390/w11030600.
Li, C., G. Tang, and Y. Hong. 2018. “Cross-evaluation of ground-based, multi-satellite and reanalysis precipitation products: Applicability of the triple collocation method across Mainland China.” J. Hydrol. 562 (Jul): 71–83. https://doi.org/10.1016/j.jhydrol.2018.04.039.
Ma, Y., G. Tang, D. Long, B. Yong, L. Zhong, W. Wan, and Y. Hong. 2016. “Similarity and error intercomparison of the GPM and its predecessor-TRMM multisatellite precipitation analysis using the best available hourly gauge network over the Tibetan Plateau.” Remote Sens. 8 (7): 569. https://doi.org/10.3390/rs8070569.
Maity, R., M. Suman, P. Laux, and H. Kunstmann. 2019. “Bias correction of zero-inflated RCM precipitation fields: A copula-based scheme for both mean and extreme.” J. Hydrometeorol. 20 (4): 595–611. https://doi.org/10.1175/JHM-D-18-0126.1.
McColl, K. A., J. Vogelzang, A. G. Konings, D. Entekhabi, M. Piles, and A. Stoffelen, 2014. “Extended triple collocation: Estimating errors and correlation coefficients with respect to an unknown target.” Geophys. Res. Lett. 41 (17): 6229–6236. https://doi.org/10.1002/2014GL061322.
MERRA (Modern-Era Retrospective Analysis for Research and Applications) 2019. “The modern-era retrospective analysis for research and applications (MERRA).” Accessed April 19, 2019. https://gmao.gsfc.nasa.gov/reanalysis/MERRA/.
Miralles, D. G., W. T. Crow, and M. H. Cosh. 2010. “Estimating spatial sampling errors in coarse-scale soil moisture estimates derived from point-scale observations.” J. Hydrometeorol. 11 (6): 1423–1429. https://doi.org/10.1175/2010JHM1285.1.
Moazami, S., S. Golian, M. R. Kavianpour, and Y. Hong. 2014. “Uncertainty analysis of bias from satellite rainfall estimates using copula method.” Atmos. Res. 137 (Feb): 145–166. https://doi.org/10.1016/j.atmosres.2013.08.016.
Mullick, M. R. A., M. N. Ridwan, M. J. Alam, and K. M. A. Islam. 2019. “Observed trends in temperature and rainfall in Bangladesh using pre-whitening approach.” Global Planet. Change 172: 104–113. https://doi.org/https://doi.org/10.1016/j.gloplacha.2018.10.001.
Nelsen, R. 2006. An introduction to copulas. New York: Springer.
Nkiaka, E., N. R. Nawaz, and J. C. Lovett. 2017. “Evaluating global reanalysis datasets as input for hydrological modelling in the Sudano-Sahel region.” Hydrology 4 (1): 13.
Pandey, P. K., L. Das, D. Jhajharia, and V. Pandey. 2018. “Modelling of interdependence between rainfall and temperature using copula.” Model. Earth Syst. Environ. 4 (2): 867–879. https://doi.org/10.1007/s40808-018-0454-9.
PERSIANN (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks). 2019. “Center for hydrometeorology and remote sensing global precipitation products PERSIANN-CCS and PERSIANN-CDR.” Accessed August 21, 2019. http://chrsdata.eng.uci.edu/.
Porcù, F., L. Milani, and M. Petracca. 2014. “On the uncertainties in validating satellite instantaneous rainfall estimates with raingauge operational network.” Atmos. Res. 144: 73–81. https://doi.org/https://doi.org/10.1016/j.atmosres.2013.12.007.
Rahmawati, N., and M. W. Lubczynsk. 2018. “Validation of satellite daily rainfall estimates in complex terrain of Bali Island, Indonesia.” Theor. Appl. Climatol. 134 (1–2): 513–532. https://doi.org/10.1007/s00704-017-2290-7.
Rashid, H. E. 1991. Geography of Bangladesh. London, UK: Routledge.
Renard, B., and M. Lang. 2007. “Use of a Gaussian copula for multivariate extreme value analysis: Some case studies in hydrology.” Adv. Water Resour. 30 (4): 897–912. https://doi.org/10.1016/j.advwatres.2006.08.001.
Roebeling, R. A., E. L. A. Wolters, J. F. Meirink, and H. Leijnse. 2012. “Triple collocation of summer precipitation retrievals from Seviri over Europe with gridded rain gauge and weather radar data.” J. Hydrometeorol. 13 (5): 1552–1566. https://doi.org/10.1175/JHM-D-11-089.1.
Sadegh, M., E. Ragno, and A. AghaKouchak. 2017. “Multivariate copula analysis toolbox (MvCAT): Describing dependence and underlying uncertainty using a Bayesian framework.” Water Resour. Res. 53 (6): 5166–5183. https://doi.org/10.1002/2016WR020242.
Sahlu, D., S. A. Moges, E. I. Nikolopoulos, E. N. Anagnostou, and D. Hailu. 2017. “Evaluation of high-resolution multisatellite and reanalysis rainfall products over East Africa.” Adv. Meteorol. 2017: 4957960. https://doi.org/10.1155/2017/4957960.
Salvadori, G., C. D. Michele, N. Kottegoda, and R. Rosso. 2007. Extremes in nature. An approach using copulas. New York: Springer.
Schölzel, C., and P. Friederichs. 2008. “Nonlinear processes in geophysics multivariate non-normally distributed random variables in climate research—Introduction to the copula approach.” Nonlinear Processes Geophys. 15: 761–772.
Scott, K. A., M. Buehner, and T. Carrieres. 2014. “An assessment of sea-ice thickness along the Labrador coast from AMSR-E and MODIS data for operational data assimilation.” IEEE Trans. Geosci. Remote Sens. 52 (5): 2726–2737. https://doi.org/10.1109/TGRS.2013.2265091.
Shahid, S. 2011. “Trends in extreme rainfall events of Bangladesh.” Theor. Appl. Climatol. 104 (3–4): 489–499. https://doi.org/10.1007/s00704-010-0363-y.
Sharifi, E., B. Saghafian, and R. Steinacker. 2019. “Copula-based stochastic uncertainty analysis of satellite precipitation products.” J. Hydrol. 570 (Mar): 739–754. https://doi.org/10.1016/j.jhydrol.2019.01.035.
Sharifi, E., R. Steinacker, and B. Saghafian. 2016. “Assessment of GPM-IMERG and other precipitation products against gauge data under different topographic and climatic conditions in Iran: Preliminary results.” Remote Sens. 8 (2): 135. https://doi.org/10.3390/rs8020135.
Sklar, A. 1959. “Fonctions de répartition à n dimensions et leurs marges.” Publ. Inst. Stat. Paris 8: 229–231.
Sorooshian, S., K. Hsu, X. Gao, H. V. Gupta, B. Imam, and D. Braithwaite. 1998. “Evaluation of PERSIANN system satellite-based estimates of tropical rainfall.” Bull. Am. Meteorol. Soc. 81 (9): 2035–2046. https://doi.org/10.1175/1520-0477(2000)081%3C2035:EOPSSE%3E2.3.CO;2.
Subyani, A. M., A. A. Al-Modayan, and F. S. Al-Ahmadi. 2010. “Topographic, seasonal and aridity influences on rainfall variability in western Saudi Arabia.” J. Environ. Hydrol. 18 (2): 1–11.
Tang, G., Z. Zeng, D. Long, X. Guo, B. Yong, W. Zhang, and Y. Hong. 2015. “Statistical and hydrological comparisons between TRMM and GPM level-3 products over a midlatitude basin: Is day-1 IMERG a good successor for TMPA 3B42V7?” J. Hydrometeorol. 17 (1): 121–137. https://doi.org/10.1175/JHM-D-15-0059.1.
Tang, X., J. Zhang, C. Gao, G. B. Ruben, and G. Wang. 2019. “Assessing the uncertainties of four precipitation products for SWAT modeling in Mekong River Basin.” Remote Sens. 11 (3): 304. https://doi.org/10.3390/rs11030304.
Tanim, A. H., and E. Goharian. 2020. “Developing a hybrid modeling and multivariate analysis framework for storm surge and runoff interactions in urban coastal flooding.” J. Hydrol. 125670. https://doi.org/10.1016/j.jhydrol.2020.125670.
Teo, C., and D. I. F. Grimes. 2007. “Stochastic modelling of rainfall from satellite data.” J. Hydrol. 346 (1–2): 33–50. https://doi.org/10.1016/j.jhydrol.2007.08.014.
Thiemig, V., R. Rojas, M. Z. Bigiarini, V. Levizzani, and A. De Roo. 2012. “Validation of satellite-based precipitation products over sparsely-gauged African River basins.” J. Hydrometeorol. 13 (6): 1760–1783. https://doi.org/10.1175/JHM-D-12-032.1.
Tian, Y., G. J. Huffman, R. F. Adler, L. Tang, M. Sapiano, V. Maggioni, and H. Wu. 2013. “Modeling errors in daily precipitation measurements: Additive or multiplicative?” Geophys. Res. Lett. 40 (10): 2060–2065. https://doi.org/10.1002/grl.50320.
Tian, Y., and C. D. Peters-Lidard. 2010. “A global map of uncertainties in satellite-based precipitation measurements.” Geophys. Res. Lett. 37 (24). https://doi.org/10.1029/2010GL046008.
Tian, Y., C. D. Peters-Lidard, J. B. Eylander, R. J. Joyce, G. J. Huffman, R. F. Adler, K. Hsu, F. J. Turk, M. Garcia, and J. Zeng. 2009. “Component analysis of errors in satellite-based precipitation estimates.” J. Geophys. Res. Atmos. 114 (D24). https://doi.org/10.1029/2009JD011949.
Tong, K., F. Su, D. Yang, and Z. Hao. 2014. “Evaluation of satellite precipitation retrievals and their potential utilities in hydrologic modeling over the Tibetan Plateau.” J. Hydrol. 519 (Part A): 423–437. https://doi.org/10.1016/j.jhydrol.2014.07.044.
Tootoonchi, F., J. O. Haerter, O. Räty, T. Grabs, M. Sadegh, and C. Teutschbein. 2020. “Copulas for hydroclimatic applications—A practical note on common misconceptions and pitfalls.” Preprint, submitted July 21, 2020. Hydrol. Earth Syst. Sci. https://doi.org/10.5194/hess-2020-306.
Toté, C., D. Patricio, H. Boogaard, R. Van Der Wijngaart, E. Tarnavsky, and C. Funk. 2015. “Evaluation of satellite rainfall estimates for drought and flood monitoring in Mozambique.” J. Remote Sens. 7 (2): 1758–1776. https://doi.org/10.3390/rs70201758.
TRMM (Tropical Rainfall Measuring Mission). 2019. “Goddard earth sciences data and information services center (GESDISC) Tropical Rainfall Measuring Mission (TRMM) data archive.” Accessed July 11, 2019. https://disc.gsfc.nasa.gov/datasets/TRMM_3B42_7.
Waltz, R. A., J. L. Morales, J. Nocedal, and D. Orban. 2006. “An interior algorithm for nonlinear optimization that combines line search and trust region steps.” Math. Program. 107 (3): 391–408.
Weiß, G. 2011. “Copula parameter estimation by maximum-likelihood and minimum-distance estimators: A simulation study.” Comput. Stat. 26 (1): 31–54. https://doi.org/10.1007/s00180-010-0203-7.
Wu, E., W. Liu, and S. Chawla. 2010. “Spatio-temporal outlier detection in precipitation data.” In Proc., Int. Workshop on Knowledge Discovery from Sensor Data, 115–133. Berlin: Springer.
Xu, X., S. K. Frey, A. Boluwade, A. R. Erler, O. Khader, D. R. Lapen, and E. Sudicky. 2019. “Evaluation of variability among different precipitation products in the Northern Great Plains.” J. Hydrol. 24 (Aug): 100608. https://doi.org/10.1016/j.ejrh.2019.100608.
Yee, K. C., J. Suhaila, F. Yusof and F. H. Mean. 2016. Bivariate copula in fitting rainfall data bivariate copula in fitting rainfall data.” In Proc., AIP Conf. 986. College Park, MD: American Institute of Physics. https://doi.org/10.1063/1.4887724.
Yilmaz, K. K., T. S. Hogue, K. L. Hsu, S. Sorooshian, H. V. Gupta, and T. Wagener. 2005. “Intercomparison of rain gauge, radar, and satellite-based precipitation estimates with emphasis on hydrologic forecasting.” J. Hydrometeorol. 6 (4): 497–517. https://doi.org/10.1175/JHM431.1.
Yuan, F., L. Zhang, K. M. W. Soe, L. Ren, C. Zhao, Y. Zhu, S. Jiang, and Y. Liu. 2019. “Applications of TRMM-and GPM-Era multiple-satellite precipitation products for flood simulations at sub-daily scales in a sparsely gauged watershed in Myanmar.” Remote Sens. 11 (2): 140.
Zhang, W., and G. Villarini. 2017. “Heavy precipitation is highly sensitive to the magnitude of future warming.” Clim. Change 145 (1–2): 249–257. https://doi.org/10.1007/s10584-017-2079-9.
Zhang, Z., Q. Jin, X. Chen, C. Y. Xu, S. Chen, E. M. Moss, and Y. Huang. 2016. “Evaluation of TRMM Multisatellite precipitation analysis in the Yangtze River basin with a typical monsoon climate.” Adv. Meteorol. 2016: 10–13. https://doi.org/10.1155/2016/7329765.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 26 • Issue 4 • April 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: May 28, 2020
Accepted: Nov 30, 2020
Published online: Jan 20, 2021
Published in print: Apr 1, 2021
Discussion open until: Jun 20, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.