Articles | Volume 25, issue 7
https://doi.org/10.5194/hess-25-3819-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-25-3819-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Conditional simulation of spatial rainfall fields using random mixing: a study that implements full control over the stochastic process
Jieru Yan
College of Environmental Science and Engineering, Tongji University, Shanghai, China
Fei Li
College of Environmental Science and Engineering, Tongji University, Shanghai, China
András Bárdossy
Institute for Modelling Hydraulic and Environmental Systems, Department of Hydrology and Geohydrology, University of Stuttgart, Stuttgart, Germany
Tao Tao
CORRESPONDING AUTHOR
College of Environmental Science and Engineering, Tongji University, Shanghai, China
Related authors
No articles found.
Abbas El Hachem, Jochen Seidel, and András Bárdossy
Hydrol. Earth Syst. Sci., 29, 1335–1357, https://doi.org/10.5194/hess-29-1335-2025, https://doi.org/10.5194/hess-29-1335-2025, 2025
Short summary
Short summary
The influence of climate change on areal precipitation extremes is examined. After an upscaling of reference observations, the climate model data are corrected, and a downscaling to a finer spatial scale is done. For different temporal durations and spatial scales, areal precipitation extremes are derived. The final result indicates an increase in the expected rainfall depth compared to reference values. However, the increase varied with the duration and area size.
Sanika Baste, Daniel Klotz, Eduardo Acuña Espinoza, Andras Bardossy, and Ralf Loritz
EGUsphere, https://doi.org/10.5194/egusphere-2025-425, https://doi.org/10.5194/egusphere-2025-425, 2025
Short summary
Short summary
This study evaluates the extrapolation performance of Long Short-Term Memory (LSTM) networks in rainfall-runoff modeling, specifically under extreme conditions. The findings reveal that the LSTM cannot predict discharge values beyond a theoretical limit, which is well below the extremity of its training data. This behavior results from the LSTM's gating structures rather than saturation of cell states alone.
Abbas El Hachem, Jochen Seidel, Tess O'Hara, Roberto Villalobos Herrera, Aart Overeem, Remko Uijlenhoet, András Bárdossy, and Lotte de Vos
Hydrol. Earth Syst. Sci., 28, 4715–4731, https://doi.org/10.5194/hess-28-4715-2024, https://doi.org/10.5194/hess-28-4715-2024, 2024
Short summary
Short summary
This study presents an overview of open-source quality control (QC) algorithms for rainfall data from personal weather stations (PWSs). The methodology and usability along technical and operational guidelines for using every QC algorithm are presented. All three QC algorithms are available for users to explore in the OpenSense sandbox. They were applied in a case study using PWS data from the Amsterdam region in the Netherlands. The results highlight the necessity for data quality control.
Amy C. Green, Chris Kilsby, and András Bárdossy
Hydrol. Earth Syst. Sci., 28, 4539–4558, https://doi.org/10.5194/hess-28-4539-2024, https://doi.org/10.5194/hess-28-4539-2024, 2024
Short summary
Short summary
Weather radar is a crucial tool in rainfall estimation, but radar rainfall estimates are subject to many error sources, with the true rainfall field unknown. A flexible model for simulating errors relating to the radar rainfall estimation process is implemented, inverting standard processing methods. This flexible and efficient model performs well in generating realistic weather radar images visually for a large range of event types.
Wen Zhu, Tao Tao, Hexiang Yan, Jieru Yan, Jiaying Wang, Shuping Li, and Kunlun Xin
Hydrol. Earth Syst. Sci., 27, 2035–2050, https://doi.org/10.5194/hess-27-2035-2023, https://doi.org/10.5194/hess-27-2035-2023, 2023
Short summary
Short summary
To provide a possibility for early warning and forecasting of ponding in the urban drainage system, an optimized long short-term memory (LSTM)-based model is proposed in this paper. It has a remarkable improvement compared to the models based on LSTM and convolutional neural network (CNN) structures. The performance of the corrected model is reliable if the number of monitoring sites is over one per hectare. Increasing the number of monitoring points further has little impact on the performance.
András Bárdossy and Faizan Anwar
Hydrol. Earth Syst. Sci., 27, 1987–2000, https://doi.org/10.5194/hess-27-1987-2023, https://doi.org/10.5194/hess-27-1987-2023, 2023
Short summary
Short summary
This study demonstrates the fact that the large river flows forecasted by the models show an underestimation that is inversely related to the number of locations where precipitation is recorded, which is independent of the model. The higher the number of points where the amount of precipitation is recorded, the better the estimate of the river flows.
Abbas El Hachem, Jochen Seidel, Florian Imbery, Thomas Junghänel, and András Bárdossy
Hydrol. Earth Syst. Sci., 26, 6137–6146, https://doi.org/10.5194/hess-26-6137-2022, https://doi.org/10.5194/hess-26-6137-2022, 2022
Short summary
Short summary
Through this work, a methodology to identify outliers in intense precipitation data was presented. The results show the presence of several suspicious observations that strongly differ from their surroundings. Many identified outliers did not have unusually high values but disagreed with their neighboring values at the corresponding time steps. Weather radar and discharge data were used to distinguish between single events and false observations.
Dhiraj Raj Gyawali and András Bárdossy
Hydrol. Earth Syst. Sci., 26, 3055–3077, https://doi.org/10.5194/hess-26-3055-2022, https://doi.org/10.5194/hess-26-3055-2022, 2022
Short summary
Short summary
In this study, different extensions of the degree-day model were calibrated on snow-cover distribution against freely available satellite snow-cover images. The calibrated models simulated the distribution very well in Baden-Württemberg (Germany) and Switzerland. In addition to reliable identification of snow cover, the melt outputs from the calibrated models were able to improve the flow simulations in different catchments in the study region.
András Bárdossy, Jochen Seidel, and Abbas El Hachem
Hydrol. Earth Syst. Sci., 25, 583–601, https://doi.org/10.5194/hess-25-583-2021, https://doi.org/10.5194/hess-25-583-2021, 2021
Short summary
Short summary
In this study, the applicability of data from private weather stations (PWS) for precipitation interpolation was investigated. Due to unknown errors and biases in these observations, a two-step filter was developed that uses indicator correlations and event-based spatial precipitation patterns. The procedure was tested and cross validated for the state of Baden-Württemberg (Germany). The biggest improvement is achieved for the shortest time aggregations.
Cited articles
Adams, T.: Chapter 10 – Flood Forecasting in the United States NOAA/National
Weather Service, in: Flood Forecasting, edited by: Adams, T. E. and Pagano,
T. C., Academic Press, Boston, 249–310, https://doi.org/10.1016/B978-0-12-801884-2.00010-4, 2016. a
Bárdossy, A. and Hörning, S.: Random Mixing: An Approach to Inverse
Modeling for Groundwater Flow and Transport Problems, Trans. Porous Media, 114, 241–259, https://doi.org/10.1007/s11242-015-0608-4, 2016. a, b
Bell, T. L.: A space-time stochastic model of rainfall for satellite
remote-sensing studies, J. Geophys. Res.-Atmos., 92, 9631–9643, https://doi.org/10.1029/JD092iD08p09631, 1987. a
Berenguer, M., Sempere-Torres, D., and Pegram, G.: SBMcast – An ensemble
nowcasting technique to assess the uncertainty in rainfall forecasts by
Lagrangian extrapolation, J. Hydrol., 404, 226–240, 2011. a
Berne, A. and Krajewski, W. F.: Radar for hydrology: Unfulfilled promise or
unrecognized potential?, Adv. Water Resour., 51, 357–366, 2013. a
Bowler, N. E., Pierce, C. E., and Seed, A. W.: STEPS: A probabilistic
precipitation forecasting scheme which merges an extrapolation nowcast with
downscaled NWP, Q. J. Roy. Meteorol. Soc., 132, 2127–2155, https://doi.org/10.1256/qj.04.100, 2006. a
Brandes, E. A.: Optimizing Rainfall Estimates with the Aid of Radar, J. Appl. Meteorol., 14, 1339–1345, 1975. a
Calder, C. and Cressie, N.: Kriging and Variogram Models, in: International
Encyclopedia of Human Geography, edited by: Kitchin, R. and Thrift, N., Elsevier, Oxford, 49–55, https://doi.org/10.1016/B978-008044910-4.00461-2, 2009. a
Chilès, J.-P. and Delfiner, P.: Geostatistics: Modeling Spatial Uncertainty, J. Am. Stat. Assoc., 95, 695, https://doi.org/10.1002/9781118136188, 2000. a
Collier, C.: The impact of wind drift on the utility of very high spatial
resolution radar data over urban areas, Phys. Chem. Earth Pt. B, 24, 889–893, https://doi.org/10.1016/S1464-1909(99)00099-4, 1999. a
Crane, R. K.: Space-time structure of rain rate fields, J. Geophys. Res.-Atmos., 95, 2011–2020, 1990. a
Cristiano, E., ten Veldhuis, M.-C., and van de Giesen, N.: Spatial and temporal variability of rainfall and their effects on hydrological response in urban areas – a review, Hydrol. Earth Syst. Sci., 21, 3859–3878, https://doi.org/10.5194/hess-21-3859-2017, 2017. a
Curry, G. R.: Radar Essentials: A Concise Handbook for Radar Design and
Performance Analysis, IET Digital Library, SciTech Publishing, https://doi.org/10.1049/SBRA029E, 2012. a
Deutsch, C. V. and Journel, A.: GSLIB – Geostatistical Software Library and
User's Guide (Second edition), in: Applied Geostatistics Series, Oxford
University Press, Oxford, https://doi.org/10.2307/1270548, 1998. a
Doviak, R. J. and Zrnić, D. S.: Doppler radar and weather observations, in: 2nd Edn., Academic Press, San Diego, 523–545, 1993. a
Emmanuel, I., Andrieu, H., Leblois, E., and Flahaut, B.: Temporal and spatial
variability of rainfall at the urban hydrological scale, J. Hydrol., 430, 162–172, 2012. a
Foresti, L., Reyniers, M., Seed, A., and Delobbe, L.: Development and verification of a real-time stochastic precipitation nowcasting system for urban hydrology in Belgium, Hydrol. Earth Syst. Sci., 20, 505–527, https://doi.org/10.5194/hess-20-505-2016, 2016. a
Haberlandt, U.: Geostatistical interpolation of hourly precipitation from rain gauges and radar for a large-scale extreme rainfall event, J. Hydrol., 332, 144–157, https://doi.org/10.1016/j.jhydrol.2006.06.028, 2007. a
Hengl, T., Heuvelink, G., and Stein, A.: Comparison of kriging with external
drift and regression-kriging, Technical Note, ITC, available at: https://webapps.itc.utwente.nl/librarywww/papers_2003/misca/hengl_comparison.pdf (last access: June 2021), 2003. a
Hörning, S. and Haese, B.: RMWSPy (v 1.1): A Python code for spatial
simulation and inversion for environmental applications, Environ. Model. Softw., 138, 104970, https://doi.org/10.1016/j.envsoft.2021.104970, 2021. a
Hu, L. Y.: Combination of Dependent Realizations Within the Gradual Deformation Method, Math. Geol., 34, 953–963, https://doi.org/10.1023/A:1021316707087,
2002. a
Hu, L. Y., Blanc, G., and Noetinger, B.: Gradual Deformation and Iterative
Calibration of Sequential Stochastic Simulations, Math. Geol., 33, 475–489, https://doi.org/10.1023/A:1011088913233, 2001. a
James, W. P., Robinson, C. G., and Bell, J. F.: Radar‐Assisted Real‐Time Flood Forecasting, J. Water Resour. Plan. Manage., 119, 32–44, 1993. a
Jiang, S., Ren, L., Hong, Y., Yong, B., Yang, X., Yuan, F., and Ma, M.:
Comprehensive evaluation of multi-satellite precipitation products with a
dense rain gauge network and optimally merging their simulated hydrological
flows using the Bayesian model averaging method, J. Hydrol., 452–453, 213–225, https://doi.org/10.1016/j.jhydrol.2012.05.055, 2012. a
Kumar, P. and Foufoula-Georgiou, E.: Characterizing multiscale variability of
zero intermittency in spatial rainfall, J. Appl. Meteorol., 33, 1516–1525, 1994. a
Lantuéjoul, C.: Geostatistical Simulation, J. Roy. Stat. Soc., 52, 699–700, 2002. a
Liguori, S. and Rico-Ramirez, M. A.: A review of current approaches to
radar-based quantitative precipitation forecasts, Int. J. River Basin Manage., 12, 391–402, 2014. a
Liu, X., Yang, T., Hsu, K., Liu, C., and Sorooshian, S.: Evaluating the
streamflow simulation capability of PERSIANN-CDR daily rainfall products in
two river basins on the Tibetan Plateau, Hydrol. Earth Syst. Sci., 21, 169–181, https://doi.org/10.5194/hess-21-169-2017, 2017. a
Mantoglou, A. and Wilson, J. L.: The Turning Bands Method for simulation of
random fields using line generation by a spectral method, Water Resour. Res., 18, 1379–1394, https://doi.org/10.1029/WR018i005p01379, 1982. a
Marshall, J. and Palmer, W.: The distribution of raindrops with size, J. Appl. Meteorol., 5, 165–166, https://doi.org/10.1175/1520-0469(1948)005<0165:TDORWS>2.0.CO;2, 1948. a
Méndez Antonio, B., Magaña, V., Caetano, E., da silveira, R., and
Domínguez, R.: Analysis of daily precipitation based on weather radar
information in México City, Atmosfera, 22, 299–313, 2009. a
Michaelides, S., Tymvios, F., and Michaelidou, T.: Spatial and temporal
characteristics of the annual rainfall frequency distribution in Cyprus, Atmos. Res., 94, 606–615, https://doi.org/10.1016/j.atmosres.2009.04.008, 2009. a
Michelson, D. B. and Koistinen, J.: Gauge-radar network adjustment for the
Baltic Sea Experiment, Phys. Chem. Earth Pt. B, 25, 915–920, 2000. a
Pegram, G. G. and Clothier, A. N.: High resolution space-time modelling of rainfall: the “String of Beads” model, J. Hydrol., 241, 26–41, https://doi.org/10.1016/S0022-1694(00)00373-5, 2001. a
Pierce, C., Seed, A., Ballard, S., Simonin, D., and Li, Z.: Nowcasting, in:
Doppler Radar Observations – Weather Radar, Wind Profiler, Ionospheric
Radar, and Other Advanced Applications, edited by: Bech, J. and Chau, J. L., InTech, 97–142, https://doi.org/10.5772/39054, 2012. a
Pulkkinen, S., Nerini, D., Pérez Hortal, A. A., Velasco-Forero, C., Seed, A., Germann, U., and Foresti, L.: Pysteps: an open-source Python library for probabilistic precipitation nowcasting (v1.0), Geosci. Model Dev., 12, 4185–4219, https://doi.org/10.5194/gmd-12-4185-2019, 2019. a, b
Ravalec, M. L., Noetinger, B., and Hu, L. Y.: The FFT Moving Average (FFT-MA)
Generator: An Efficient Numerical Method for Generating and Conditioning
Gaussian Simulations, Math. Geol., 32, 701–723, https://doi.org/10.1023/A:1007542406333, 2000. a
Schuurmans, J. M., Bierkens, M. F. P., Pebesma, E. J., and Uijlenhoet, R.:
Automatic Prediction of High-Resolution Daily Rainfall Fields for Multiple
Extents: The Potential of Operational Radar, J. Hydrometeorol., 8, 1204–1224, https://doi.org/10.1175/2007JHM792.1, 2007. a
Shehu, B. and Haberlandt, U.: Relevance Of Merging Radar And Rainfall Gauge
Data For Rainfall Nowcasting In Urban Hydrology, J. Hydrol., 594, 125931, https://doi.org/10.1016/j.jhydrol.2020.125931, 2020. a, b, c
Sideris, I., Gabella, M., Erdin, R., and Germann, U.: Real-time
radar–raingauge merging using spatio-temporal co-kriging with external drift
in the Alpine terrain of Switzerland, Q. J. Roy. Meteorol. Soc., 140, 1097–1111, https://doi.org/10.1002/qj.2188, 2014. a
Sinclair, S. and Pegram, G.: Combining radar and rain gauge rainfall estimates using conditional merging, Atmos. Sci. Lett., 6, 19–22,
https://doi.org/10.1002/asl.85, 2005. a, b
Todini, E.: A Bayesian technique for conditioning radar precipitation estimates to rain-gauge measurements, Hydrol. Earth Syst. Sci., 5, 187–199, https://doi.org/10.5194/hess-5-187-2001, 2001. a
Uijlenhoet, R.: Raindrop size distributions and radar reflectivity–rain rate
relationships for radar hydrology, Hydrol. Earth Syst. Sci., 5, 615–628, https://doi.org/10.5194/hess-5-615-2001, 2001. a
Velasco-Forero, C. A., Sempere-Torres, D., Cassiraga, E. F., and
Gómez-Hernández, J. J.: A non-parametric automatic blending
methodology to estimate rainfall fields from rain gauge and radar data, Adv. Water Resour., 32, 986–1002, https://doi.org/10.1016/j.advwatres.2008.10.004, 2009. a
Verworn, A. and Haberlandt, U.: 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, 2011. a
Wang, L. P., Ochoa-Rodriguez, S., Simões, N., Onof, C., and Maksimovic, Č.: Radar-raingauge data combination techniques: A revision and analysis of their suitability for urban hydrology, Water Sci. Technol., 68, 737–47, 2013. a
Wilson, J. W.: Integration of Radar and Raingage Data for Improved Rainfall
Measurement, J. Appl. Meteorol., 9, 489–497,
https://doi.org/10.1175/1520-0450(1970)009<0489:IORARD>2.0.CO;2, 1970. a
Wood, A. T.: When is a truncated covariance function on the line a covariance
function on the circle?, Stat. Probab. Lett. 24, 157–164,
https://doi.org/10.1016/0167-7152(94)00162-2, 1995. a
Wood, A. T. and Chan, G.: Simulation of stationary Gaussian processes in [0, 1] d, J. Comput. Graph. Stat., 3, 409–432, 1994. a
Yan, J.: Supplementary material for the paper “Conditional simulation of spatial rainfall fields using random mixing: a study that implements full control over the stochastic process”, Figshare, https://doi.org/10.6084/m9.figshare.14864910.v1, 2021. a
Yan, J. and Bárdossy, A.: Short time precipitation estimation using weather radar and surface observations: With rainfall displacement information integrated in a stochastic manner, J. Hydrol., 574, 672–682,
https://doi.org/10.1016/j.jhydrol.2019.04.061, 2019. a
Yan, J., Bárdossy, A., Hörning, S., and Tao, T.: Conditional simulation of surface rainfall fields using modified phase annealing, Hydrol. Earth Syst. Sci., 24, 2287–2301, https://doi.org/10.5194/hess-24-2287-2020, 2020. a, b
Yilmaz, K. K., Hogue, T. S., Hsu, K.-L., Sorooshian, S., Gupta, H. V., and
Wagener, T.: Intercomparison of Rain Gauge, Radar, and Satellite-Based
Precipitation Estimates with Emphasis on Hydrologic Forecasting, J.
Hydrometeorol., 6, 497–517, https://doi.org/10.1175/JHM431.1, 2005. a
Short summary
Accurate spatial precipitation estimates are important in various fields. An approach to simulate spatial rainfall fields conditioned on radar and rain gauge data is proposed. Unlike the commonly used Kriging methods, which provide a Kriged mean field, the output of the proposed approach is an ensemble of estimates that represents the estimation uncertainty. The approach is robust to nonlinear error in radar estimates and is shown to have some advantages, especially when estimating the extremes.
Accurate spatial precipitation estimates are important in various fields. An approach to...