A rainfall disaggregation scheme for sub-hourly time scales: Coupling a Bartlett-Lewis based model with adjusting procedures

Abstract Many hydrological applications, such as flood studies, require the use of long rainfall data at fine time scales varying from daily down to 1 min time step. However, in the real world there is limited availability of data at sub-hourly scales. To cope with this issue, stochastic disaggregation techniques are typically employed to produce possible, statistically consistent, rainfall events that aggregate up to the field data collected at coarser scales. A methodology for the stochastic disaggregation of rainfall at fine time scales was recently introduced, combining the Bartlett-Lewis process to generate rainfall events along with adjusting procedures to modify the lower-level variables (i.e., hourly) so as to be consistent with the higher-level one (i.e., daily). In the present paper, we extend the aforementioned scheme, initially designed and tested for the disaggregation of daily rainfall into hourly depths, for any sub-hourly time scale. In addition, we take advantage of the recent developments in Poisson-cluster processes incorporating in the methodology a Bartlett-Lewis model variant that introduces dependence between cell intensity and duration in order to capture the variability of rainfall at sub-hourly time scales. The disaggregation scheme is implemented in an R package, named HyetosMinute, to support disaggregation from daily down to 1-min time scale. The applicability of the methodology was assessed on a 5-min rainfall records collected in Bochum, Germany, comparing the performance of the above mentioned model variant against the original Bartlett-Lewis process (non-random with 5 parameters). The analysis shows that the disaggregation process reproduces adequately the most important statistical characteristics of rainfall at wide range of time scales, while the introduction of the model with dependent intensity-duration results in a better performance in terms of skewness, rainfall extremes and dry proportions.

[1]  Richard E Chandler,et al.  Estimating functions and the generalized method of moments , 2011, Interface Focus.

[2]  Mixed rectangular pulses models of rainfall , 2004 .

[3]  H. Wheater,et al.  Spatial–temporal disaggregation of daily rainfall from a generalized linear model , 2006 .

[4]  Geoffrey G. S. Pegram,et al.  Design rainfall estimation in South Africa using Bartlett–Lewis rectangular pulse rainfall models , 2002 .

[5]  Christian Onof,et al.  Point process models for fine-resolution rainfall , 2013, 1309.4632.

[6]  Keith Beven,et al.  An evaluation of three stochastic rainfall models. , 2000 .

[7]  Niko E. C. Verhoest,et al.  Are stochastic point rainfall models able to preserve extreme flood statistics? , 2010 .

[8]  J. Parlange,et al.  Accuracy evaluation of weather data generation and disaggregation methods at finer timescales , 2007 .

[9]  Christian Onof,et al.  Rainfall disaggregation using adjusting procedures on a Poisson cluster model , 2001 .

[10]  Christian Onof,et al.  Comparison of two hourly to 5-min rainfall disaggregators , 2005 .

[11]  Bellie Sivakumar,et al.  A comparison of alternatives for daily to sub-daily rainfall disaggregation , 2012 .

[12]  Paul S. P. Cowpertwait,et al.  Further developments of the neyman‐scott clustered point process for modeling rainfall , 1991 .

[13]  Ashish Sharma,et al.  Representing low‐frequency variability in continuous rainfall simulations: A hierarchical random Bartlett Lewis continuous rainfall generation model , 2015 .

[14]  Chris Kilsby,et al.  A space‐time Neyman‐Scott model of rainfall: Empirical analysis of extremes , 2002 .

[15]  Garry R. Willgoose,et al.  A HYBRID MODEL FOR POINT RAINFALL MODELING , 1997 .

[16]  Christos Makropoulos,et al.  Surrogate-enhanced evolutionary annealing simplex algorithm for effective and efficient optimization of water resources problems on a budget , 2016, Environ. Model. Softw..

[17]  Conleth Cunnane,et al.  Modelling point rainfall occurrences with the modified Bartlett-Lewis rectangular pulses model , 1996 .

[18]  Juan B. Valdés,et al.  Rectangular pulses point process models for rainfall: Analysis of empirical data , 1987 .

[19]  Demetris Koutsoyiannis,et al.  Coupling stochastic models of different timescales , 2001 .

[20]  Using SWAP to quantify space and time related uncertainty in deep drainage model estimates: A case study from northern NSW, Australia , 2013 .

[21]  Demetris Koutsoyiannis,et al.  A multivariate stochastic model for the generation of synthetic time series at multiple time scales reproducing long-term persistence , 2014, Environ. Model. Softw..

[22]  H. Wheater,et al.  Modelling of British rainfall using a random parameter Bartlett-Lewis Rectangular Pulse Model , 1993 .

[23]  Valerie Isham,et al.  Some models for rainfall based on stochastic point processes , 1987, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[24]  Niko E. C. Verhoest,et al.  On the applicability of Bartlett–Lewis rectangular pulses models in the modeling of design storms at a point , 1997 .

[25]  A. Favre,et al.  Stochastic generation and disaggregation of hourly rainfall series for continuous hydrological modelling and flood control reservoir design. , 2002, Water science and technology : a journal of the International Association on Water Pollution Research.

[26]  Dara Entekhabi,et al.  Probabilistic representation of the temporal rainfall process by a modified Neyman‐Scott Rectangular Pulses Model: Parameter estimation and validation , 1989 .

[27]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[28]  P. Troch,et al.  Evaluation of cluster-based rectangular pulses point process models for rainfall , 1994 .

[29]  H. Wheater,et al.  Improvements to the modelling of British rainfall using a modified Random Parameter Bartlett-Lewis Rectangular Pulse Model , 1994 .

[30]  Demetris Koutsoyiannis,et al.  A scaling model of a storm hyetograph , 1993 .

[31]  Demetris Koutsoyiannis,et al.  Simple Disaggregation by Accurate Adjusting Procedures , 1996 .

[32]  Christian Onof,et al.  Rainfall modelling using Poisson-cluster processes: a review of developments , 2000 .

[33]  Minha Choi,et al.  Let-It-Rain: a web application for stochastic point rainfall generation at ungaged basins and its applicability in runoff and flood modeling , 2017, Stochastic Environmental Research and Risk Assessment.

[34]  Peter Molnar,et al.  On temporal stochastic modeling of precipitation, nesting models across scales , 2014 .

[35]  Demetris Koutsoyiannis,et al.  Climate change, the Hurst phenomenon, and hydrological statistics , 2003 .

[36]  Yeboah Gyasi-Agyei,et al.  Identification of regional parameters of a stochastic model for rainfall disaggregation , 1999 .

[37]  M. B. McGechan,et al.  Disaggregation of daily rainfall by conditional simulation from a point-process model , 1995 .

[38]  Demetris Koutsoyiannis,et al.  Hydrological modelling of temporally-varying catchments: facets of change and the value of information , 2015 .

[39]  David R. Cox,et al.  A simple spatial-temporal model of rainfall , 1988, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[40]  M. R. Anis,et al.  A new magnitude category disaggregation approach for temporal high‐resolution rainfall intensities , 2015 .

[41]  Paul S. P. Cowpertwait,et al.  A spatial‐temporal point process model with a continuous distribution of storm types , 2010 .

[42]  Demetris Koutsoyiannis.  A stochastic disaggregation method for design storm and flood synthesis , 1994 .

[43]  Demetris Koutsoyiannis,et al.  Stochastic analysis and simulation of hydrometeorological processes associated with wind and solar energy , 2014 .

[44]  Yeboah Gyasi-Agyei,et al.  A stochastic model for daily rainfall disaggregation into fine time scale for a large region , 2007 .

[45]  P. E. O'Connell,et al.  Stochastic point process modelling of rainfall. I. Single-site fitting and validation , 1996 .

[46]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[47]  Demetris Koutsoyiannis,et al.  An evolutionary annealing-simplex algorithm for global optimisation of water resource systems , 2002 .

[48]  Hyun-Han Kwon,et al.  Regionalization of the Modified Bartlett–Lewis rectangular pulse stochastic rainfall model across the Korean Peninsula , 2016 .

[49]  Ashish Sharma,et al.  A cascade approach to continuous rainfall data generation at point locations , 2008 .

[50]  V. Isham,et al.  A point process model for rainfall: further developments , 1988, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[51]  Jery R. Stedinger,et al.  Disaggregation Procedures for Generating Serially Correlated Flow Vectors , 1984 .

[52]  Dongkyun Kim,et al.  Regionalization of the Modified Bartlett-Lewis Rectangular Pulse Stochastic Rainfall Model , 2013 .

[53]  Edward C. Waymire,et al.  Scale considerations in the modeling of temporal rainfall , 1984 .

[54]  Demetris Koutsoyiannis,et al.  Multivariate rainfall disaggregation at a fine timescale , 2003 .

[55]  Demetris Koutsoyiannis,et al.  Assessing the performance of Bartlett-Lewis model on the simulation of Athens rainfall , 2015 .

[56]  Eric Laloy,et al.  Modelling intercrop management impact on runoff and erosion in a continuous maize cropping system: Part II. Model Pareto multi‐objective calibration and long‐term scenario analysis using disaggregated rainfall , 2009 .

[57]  Shafiqul Islam,et al.  Aggregation‐disaggregation properties of a stochastic rainfall model , 1994 .

[58]  Christos Makropoulos,et al.  Multiobjective optimisation on a budget: Exploring surrogate modelling for robust multi-reservoir rules generation under hydrological uncertainty , 2015, Environ. Model. Softw..

[59]  Christos Makropoulos,et al.  Simulation and spatio-temporal disaggregation of multi-site rainfall data for urban drainage applications , 2007 .

[60]  Demetris Koutsoyiannis.  A generalized mathematical framework for stochastic simulation and forecast of hydrologic time series , 2000 .

[61]  Hayley J. Fowler,et al.  RainSim: A spatial-temporal stochastic rainfall modelling system , 2008, Environ. Model. Softw..

[62]  Demetris Koutsoyiannis.  “Hurst-Kolomogorov Dynamics and Uncertainty” , 2010 .

[63]  Dara Entekhabi,et al.  Parameter estimation and sensitivity analysis for the modified Bartlett‐Lewis rectangular pulses model of rainfall , 1990 .

[64]  Christian Onof,et al.  Point process models of rainfall: developments for fine-scale structure , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[65]  Y. Gyasi‐Agyei.  Stochastic disaggregation of daily rainfall into one-hour time scale , 2005 .

[66]  Jery R. Stedinger,et al.  Condensed disaggregation procedures and conservation corrections for stochastic hydrology , 1988 .

[67]  Demetris Koutsoyiannis.  RAINFALL DISAGGREGATION METHODS: THEORY AND APPLICATIONS , 2003 .

[68]  Paul S. P. Cowpertwait,et al.  A Poisson-cluster model of rainfall: some high-order moments and extreme values , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[69]  R. Valencia,et al.  Disaggregation processes in stochastic hydrology , 1973 .

[70]  H. Wheater,et al.  Improved fitting of the Bartlett-Lewis Rectangular Pulse Model for hourly rainfall , 1994 .

[71]  Davis,et al.  A Stochastic Spatial-temporal Disaggregation Model for Rainfall , 2006 .

[72]  Andrew Metcalfe,et al.  Stochastic point process modelling of rainfall. II. Regionalisation and disaggregation , 1996 .

[73]  Jery R. Stedinger,et al.  A condensed disaggregation model for incorporating parameter uncertainty into monthly reservoir simulations , 1985 .

[74]  M. Esteves,et al.  Characterization and disaggregation of daily rainfall in the Upper Blue Nile Basin in Ethiopia , 2011 .

[75]  Seung Oh Lee,et al.  Effect of the inter-annual variability of rainfall statistics on stochastically generated rainfall time series: part 2. Impact on watershed response variables , 2013, Stochastic Environmental Research and Risk Assessment.

[76]  Peter Molnar,et al.  A stochastic model for high‐resolution space‐time precipitation simulation , 2013 .

[77]  Demetris Koutsoyiannis,et al.  Holistic versus monomeric strategies for hydrological modelling of human-modified hydrosystems , 2010 .

[78]  Demetris Koutsoyiannis,et al.  Hurst‐Kolmogorov Dynamics and Uncertainty 1 , 2011 .

[79]  V. Isham,et al.  Spatial-temporal rainfall modelling for flood risk estimation , 2005 .

[80]  V. Isham,et al.  Note on the analytical expression of the inter-event time characteristics for Bartlett-Lewis type rainfall models , 1994 .

[81]  W. Atherton,et al.  Application of the stochastic model for temporal rainfall disaggregation for hydrological studies in north western England , 2013 .