Abstract
Over the past several decades, weather radar has become an indispensable tool in flood forecasting studies, especially in ungauged regions. However, the rainfall extremes with radar data may contain biases, and this can be removed by using the information provided by rain gauges. For this purpose, a procedure that covers additive and multiplicative error correction methods with three vector norms, taxicab norm (L1), Euclidean norm (L2), and maximum norm (L∞), is proposed for adjusting radar data. The top 26 flood events with 20 stations in a 5-year database of radar data are used to quantify the overall agreement between radar and gauge datasets. After finding the best model and norm for adjusting the error in radar data, the correction factor in the model is analyzed with the aspects of the season, station height, rainfall amount, and distance between radar location and rain gauge station. Results show that the multiplicative error model with L1 norm minimization is the best choice given all criteria. It is noted that as the systematic error in the radar data is nonlinear, the additive factors are inconclusive in rainfall variability. Moreover, it is found out that the values in multiplicative constant evaluation are more apparent with grouping done for the season, rainfall amount, and distance, but a consistent result is not found for the grouping done for the station height.
This is a preview of subscription content, log in via an institution to check access.
taken from the flood area after the 16 November 2018 (in Bodrum) and 28 December 2017 (in Fethiye) flood events, respectively. (Sources: for a, https://www.bodrumgundem.com/2018/11/18/bodrumda-yine-sel-felaketi-yurttas-artik-laf-degil-cozum-istiyor-foto-galeri/; for b, https://www.milliyet.com.tr/galeri/fethiyeyi-sel-aldi-443398/1)
Similar content being viewed by others
Data availability
The data can be purchased from the Turkish State Meteorological Service (TSMS).
Code availability
The authors used different software such as MATLAB, ArcGIS, and Microsoft Excel for preparation or analyzing data and producing map.
References
Aksoy M (2020) Evaluation of numerical weather prediction models for flash flood warnings in Turkey. Master’s Thesis, Middle East Technical University, Çankaya/Ankara, Turkey, 2020
Alfieri L, Claps P, Laio F (2010) Time-dependent <i>Z-R</i> relationships for estimating rainfall fields from radar measurements. Nat Hazards Earth Syst Sci 10:149–158. https://doi.org/10.5194/nhess-10-149-2010
Anagnostou MN, Kalogiros J, Anagnostou EN et al (2010) Performance evaluation of high-resolution rainfall estimation by X-band dual-polarization radar for flash flood applications in mountainous basins. J Hydrol 394:4–16. https://doi.org/10.1016/j.jhydrol.2010.06.026
Anagnostou EN, Morales CA (2002) Rainfall estimation from TOGA radar observations during LBA field campaign. J Geophys Res: Atmos 107:LBA 35–1-LBA 35–14. https://doi.org/10.1029/2001JD000377
Baeck ML, Smith JA (1998) Rainfall estimation by the WSR-88D for heavy rainfall events. Weather Forecast 13:416–436. https://doi.org/10.1175/1520-0434(1998)013%3c0416:REBTWF%3e2.0.CO;2
Bayazıt Y, Koç C, Bakış R (2021) Urbanization impacts on flash urban floods in Bodrum Province, Turkey. Hydrol Sci J 66:118–133. https://doi.org/10.1080/02626667.2020.1851031
Bech J, Codina B, Lorente J, Bebbington D (2003) The sensitivity of single polarization weather radar beam blockage correction to variability in the vertical refractivity gradient. J Atmos Oceanic Technol 20:845–855. https://doi.org/10.1175/1520-0426(2003)020%3c0845:TSOSPW%3e2.0.CO;2
Bektaş S, Şişman Y (2010) The comparison of L1 and L2-norm minimization methods. IJPS 5:1721–1727.10.1.1.876.4314
Brandes EA (1975) Optimizing rainfall estimates with the aid of radar. J Appl Meteorol Climatol 14:1339–1345. https://doi.org/10.1175/1520-0450(1975)014%3c1339:OREWTA%3e2.0.CO;2
Briggs NE, MacCallum RC (2003) Recovery of weak common factors by maximum likelihood and ordinary least squares estimation. Multivar Behav Res 38:25–56. https://doi.org/10.1207/S15327906MBR3801_2
Brooks JP, Dulá JH, Boone EL (2013) A pure L1-norm principal component analysis. Comput Stat Data Anal 61:83–98. https://doi.org/10.1016/j.csda.2012.11.007
Cecinati F, Rico-Ramirez MA, Heuvelink GBM, Han D (2017) Representing radar rainfall uncertainty with ensembles based on a time-variant geostatistical error modelling approach. J Hydrol 548:391–405. https://doi.org/10.1016/j.jhydrol.2017.02.053
Chen S-T, Yu P-S, Liu B-W (2011) Comparison of neural network architectures and inputs for radar rainfall adjustment for typhoon events. J Hydrol 405:150–160. https://doi.org/10.1016/j.jhydrol.2011.05.017
Chumchean S, Seed A, Sharma A (2004) Application of scaling in radar reflectivity for correcting range-dependent bias in climatological radar rainfall estimates. J Atmos Oceanic Technol 21:1545–1556. https://doi.org/10.1175/1520-0426(2004)021%3c1545:AOSIRR%3e2.0.CO;2
Ciach GJ, Morrissey ML, Krajewski WF (2000) Conditional bias in radar rainfall estimation. J Appl Meteorol 39:1941–1946. https://doi.org/10.1175/1520-0450(2000)039%3c1941:CBIRRE%3e2.0.CO;2
Conde F, Barros MT, Filho KR, Pion SM, Sosnoski A (2019) Improving Flooding Forecast in Real Time Using the Integration between Weather Radar and Raingages: Case Study; Megacity São Paulo. In World Environmental and Water Resources Congress 2019: Watershed Management, Irrigation and Drainage, and Water Resources Planning and Management (pp. 166-176). Reston, VA: American Society of Civil Engineers. https://doi.org/10.1061/9780784482339.018
Delrieu G, Wijbrans A, Boudevillain B et al (2014) Geostatistical radar–raingauge merging: a novel method for the quantification of rain estimation accuracy. Adv Water Resour 71:110–124. https://doi.org/10.1016/j.advwatres.2014.06.005
Ding B, Yang K, Qin J et al (2014) The dependence of precipitation types on surface elevation and meteorological conditions and its parameterization. J Hydrol 513:154–163. https://doi.org/10.1016/j.jhydrol.2014.03.038
Drucker H, Burges CJ, Kaufman L, Smola A, Vapnik V (1996) Support vector regression machines. Advances in neural information processing systems, 9
Durdu ÖF (2010) Application of linear stochastic models for drought forecasting in the Büyük Menderes river basin, western Turkey. Stoch Environ Res Risk Assess 24:1145–1162. https://doi.org/10.1007/s00477-010-0366-3
Einfalt T, Arnbjerg-Nielsen K, Golz C et al (2004) Towards a roadmap for use of radar rainfall data in urban drainage. J Hydrol 299:186–202. https://doi.org/10.1016/j.jhydrol.2004.08.004
Fo AJP, Crawford KC, Hartzell CL (1998) Improving WSR-88D hourly rainfall estimates. Weather Forecast 13:1016–1028. https://doi.org/10.1175/1520-0434(1998)013%3c1016:IWHRE%3e2.0.CO;2
Friedman JH (1991) Multivariate adaptive regression splines. Ann Stat 19:1–67. https://doi.org/10.1214/aos/1176347963
Gabella M, Perona G (1998) Simulation of the orographic influence on weather radar using a geometric–optics approach. J Atmos Oceanic Tech 15:1485–1494. https://doi.org/10.1175/1520-0426(1998)015%3c1485:SOTOIO%3e2.0.CO;2
Ganguli P, Nandamuri YR, Chatterjee C (2020) Analysis of persistence in the flood timing and the role of catchment wetness on flood generation in a large river basin in India. Theor Appl Climatol 139:373–388. https://doi.org/10.1007/s00704-019-02964-z
Gou Y, Chen H (2020) Combining radar attenuation and partial beam blockage corrections for improved quantitative application. J Hydrometeorol 22:139–153. https://doi.org/10.1175/JHM-D-20-0121.1
Gou Y, Chen H, Zheng J (2019) An improved self-consistent approach to attenuation correction for C-band polarimetric radar measurements and its impact on quantitative precipitation estimation. Atmos Res 226:32–48. https://doi.org/10.1016/j.atmosres.2019.03.006
Hildebrand PH (1978) Iterative correction for attenuation of 5 cm radar in rain. J Appl Meteorol Climatol 17:508–514. https://doi.org/10.1175/1520-0450(1978)017%3c0508:ICFAOC%3e2.0.CO;2
Kitchen M, Brown R, Davies AG (1994) Real-time correction of weather radar data for the effects of bright band, range and orographic growth in widespread precipitation. Q J R Meteorol Soc 120:1231–1254. https://doi.org/10.1002/qj.49712051906
Kundzewicz ZW, Ulbrich U, Brücher T et al (2005) Summer floods in Central Europe – climate change track? Nat Hazards 36:165–189. https://doi.org/10.1007/s11069-004-4547-6
Lau CL, Smythe LD, Craig SB, Weinstein P (2010) Climate change, flooding, urbanisation and leptospirosis: fuelling the fire? Trans R Soc Trop Med Hyg 104:631–638. https://doi.org/10.1016/j.trstmh.2010.07.002
Marshall JS, Palmer WMK (1948) The distribution of raindrops with size. J Meteorol 5:165–166
Özmen A, Weber GW (2014) RMARS: robustification of multivariate adaptive regression spline under polyhedral uncertainty. J Comput Appl Math 259:914–924. https://doi.org/10.1016/j.cam.2013.09.055
Özmen A, Batmaz İ, Weber G-W (2014) Precipitation modeling by polyhedral RCMARS and comparison with MARS and CMARS. Environ Model Assess 19:425–435. https://doi.org/10.1007/s10666-014-9404-8
Öztürk K, Yılmazer AU (2007) Improving the accuracy of the radar rainfall estimates using gage adjustment techniques: case study for west Anatolia, Turkey. Atmos Res 86:139–148. https://doi.org/10.1016/j.atmosres.2007.03.009
Prudden R, Adams S, Kangin D, Robinson N, Ravuri S, Mohamed S, Arribas A (2020) A review of radar-based nowcasting of precipitation and applicable machine learning techniques. arXiv preprint arXiv:2005.04988
Ramsey EW (1995) Monitoring flooding in coastal wetlands by using radar imagery and ground-based measurements. Int J Remote Sens 16:2495–2502. https://doi.org/10.1080/01431169508954571
Rapant P, Kolejka J (2021) Dynamic pluvial flash flooding hazard forecast using weather radar data. Remote Sensing 13:2943. https://doi.org/10.3390/rs13152943
Schleiss M, Olsson J, Berg P et al (2020) The accuracy of weather radar in heavy rain: a comparative study for Denmark, the Netherlands, Finland and Sweden. Hydrol Earth Syst Sci 24:3157–3188. https://doi.org/10.5194/hess-24-3157-2020
Shao Y, Fu A, Zhao J et al (2021) Improving quantitative precipitation estimates by radar-rain gauge merging and an integration algorithm in the Yishu River catchment, China. Theor Appl Climatol 144:611–623. https://doi.org/10.1007/s00704-021-03526-y
Sideris IV, Gabella M, Erdin R, Germann U (2014) Real-time radar–rain-gauge merging using spatio-temporal co-kriging with external drift in the alpine terrain of Switzerland. Q J R Meteorol Soc 140:1097–1111. https://doi.org/10.1002/qj.2188
Sim K, Hartley R. Removing outliers using the L\infty norm. In 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06), vol. 1, pp. 485-494. IEEE, 2006
Sun X, Mein RG, Keenan TD, Elliott JF (2000) Flood estimation using radar and raingauge data. J Hydrol 239:4–18. https://doi.org/10.1016/S0022-1694(00)00350-4
Tian Y, Huffman GJ, Adler RF et al (2013) Modeling errors in daily precipitation measurements: additive or multiplicative? Geophys Res Lett 40:2060–2065. https://doi.org/10.1002/grl.50320
Uijlenhoet R (1999) Parameterization of rainfall microstructure for radar meteorology and hydrology. Ph.D. thesis, Wageningen University, 279 pp
Uysal G, Şorman AÜ (2021) Evaluation of PERSIANN family remote sensing precipitation products for snowmelt runoff estimation in a mountainous basin. Hydrol Sci J 0:1–18. https://doi.org/10.1080/02626667.2021.1954651
Verworn A, Haberlandt U (2011) Spatial interpolation of hourly rainfall – effect of additional information, variogram inference and storm properties. Hydrol Earth Syst Sci 15:569–584. https://doi.org/10.5194/hess-15-569-2011
Villarini G, Mandapaka PV, Krajewski WF, Moore RJ (2008) Rainfall and sampling uncertainties: a rain gauge perspective. J Geophys Res: Atmos 113https://doi.org/10.1029/2007JD009214
Villarini G, Krajewski WF (2010) Sensitivity studies of the models of radar-rainfall uncertainties. J Appl Meteorol Climatol 49:288–309. https://doi.org/10.1175/2009JAMC2188.1
Villarini G, Krajewski WF (2010) Review of the different sources of uncertainty in single polarization radar-based estimates of rainfall. Surv Geophys 31:107–129. https://doi.org/10.1007/s10712-009-9079-x
Wang J, Cheng M, Gao Y, Xiong Y, Zhu S (2008) Classification of precipitation radar reflectivity echo with back-propagation ANN. In 2008 IEEE Pacific-Asia Workshop on Computational Intelligence and Industrial Application (Vol. 2, pp. 630-633). IEEE
Wright DB, Smith JA, Villarini G, Baeck ML (2012) Hydroclimatology of flash flooding in Atlanta. Water Resources Research, 48(4).https://doi.org/10.1029/2011WR011371
Yilmaz AG (2015) The effects of climate change on historical and future extreme rainfall in Antalya, Turkey. Hydrol Sci J 60:2148–2162. https://doi.org/10.1080/02626667.2014.945455
Yo T-S, Su S-H, Chu J-L et al (2021) A deep learning approach to radar-based QPE. Earth Space Sci 8:e2020EA001340. https://doi.org/10.1029/2020EA001340
Yoon S-S (2019) Adaptive blending method of radar-based and numerical weather prediction QPFs for urban flood forecasting. Remote Sens 11:642. https://doi.org/10.3390/rs11060642
Zhang P, Zrnić D, Ryzhkov A (2013) Partial beam blockage correction using polarimetric radar measurements. J Atmos Oceanic Tech 30:861–872. https://doi.org/10.1175/JTECH-D-12-00075.1
Zhu D, Peng DZ, Cluckie ID (2013) Statistical analysis of error propagation from radar rainfall to hydrological models. Hydrol Earth Syst Sci 17:1445–1453. https://doi.org/10.5194/hess-17-1445-2013
Acknowledgements
The radar and gauge rainfall data were provided by the Turkish State Meteorological Service (TSMS).
Author information
Authors and Affiliations
Contributions
AO, conceptualization, writing—original draft, software, formal analysis, and visualization. AEY, conceptualization, software, review, and editing. All authors reviewed the final manuscript.
Corresponding author
Ethics declarations
Ethics approval
Not applicable.
Consent to participate
All authors consent to participate of the present study.
Consent for publication
All authors read the manuscript and agree for the publication.
Conflict of interest
Not applicable.
Additional information
Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ozkaya, A., Yilmaz, A.E. Analyzing radar rainfall estimate errors with three vector norms: application to weather radar rainfall data in Muğla, Turkey. Theor Appl Climatol 149, 103–117 (2022). https://doi.org/10.1007/s00704-022-04034-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00704-022-04034-3