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

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

Stochastic generation of annual, monthly and daily climate data: A review

International audienceThe generation of rainfall and other climate data needs a range of models depending on the time and spatial scales involved. Most of the models used previously do not take into account year to year variations in the model parameters. Long periods of wet and dry years were observed in the past but were not taken into account. Recently, Thyer and Kuczera (1999) developed a hidden state Markov model to account for the wet and dry spells explicitly in annual rainfall. This review looks firstly at traditional time series models and then at the more complex models which take account of the pseudo-cycles in the data. Monthly rainfall data have been generated successfully by using the method of fragments. The main criticism of this approach is the repetitions of the same yearly pattern when only a limited number of years of historical data are available. This deficiency has been overcome by using synthetic fragments but this brings an additional problem of generating the right number of months with zero rainfall. Disaggregation schemes are effective in obtaining monthly data but the main problem is the large number of parameters to be estimated when dealing with many sites. Several simplifications have been proposed to overcome this problem. Models for generating daily rainfall are well developed. The transition probability matrix method preserves most of the characteristics of daily, monthly and annual characteristics and is shown to be the best performing model. The two-part model has been shown by many researchers to perform well across a range of climates at the daily level but has not been tested adequately at monthly or annual levels. A shortcoming of the existing models is the consistent underestimation of the variances of the simulated monthly and annual totals. As an alternative, conditioning model parameters on monthly amounts or perturbing the model parameters with the Southern Oscillation Index (SOI) result in better agreement between the variance of the simulated and observed annual rainfall and these approaches should be investigated further. As climate data are less variable than rainfall, but are correlated among themselves and with rainfall, multisite-type models have been used successfully to generate annual data. The monthly climate data can be obtained by disaggregating these annual data. On a daily time step at a site, climate data have been generated using a multisite type model conditional on the state of the present and previous days. The generation of daily climate data at a number of sites remains a challenging problem. If daily rainfall can be modelled successfully by a censored power of normal distribution then the model can be extended easily to generate daily climate data at several sites simultaneously. Most of the early work on the impacts of climate change used historical data adjusted for the climate change. In recent studies, stochastic daily weather generation models are used to compute climate data by adjusting the parameters appropriately for the future climates assumed

Multiscale climate emulator of multimodal wave spectra: MUSCLE-spectra

Characterization of multimodal directional wave spectra is important for many offshore and coastal applications, such as marine forecasting, coastal hazard assessment, and design of offshore wave energy farms and coastal structures. However, the multivariate and multiscale nature of wave climate variability makes this complex problem tractable using computationally expensive numerical models. So far, the skill of statistical-downscaling model-based parametric (unimodal) wave conditions is limited in large ocean basins such as the Pacific. The recent availability of long-term directional spectral data from buoys and wave hindcast models allows for development of stochastic models that include multimodal sea-state parameters. This work introduces a statistical downscaling framework based on weather types to predict multimodal wave spectra (e.g., significant wave height, mean wave period, and mean wave direction from different storm systems, including sea and swells) from large-scale atmospheric pressure fields. For each weather type, variables of interest are modeled using the categorical distribution for the sea-state type, the Generalized Extreme Value (GEV) distribution for wave height and wave period, a multivariate Gaussian copula for the interdependence between variables, and a Markov chain model for the chronology of daily weather types. We apply the model to the southern California coast, where local seas and swells from both the Northern and Southern Hemispheres contribute to the multimodal wave spectrum. This work allows attribution of particular extreme multimodal wave events to specific atmospheric conditions, expanding knowledge of time-dependent, climate-driven offshore and coastal sea-state conditions that have a significant influence on local nearshore processes, coastal morphology, and flood hazards.We thank Jorge Perez for the ESTELA code. A.R., J.A.A.A., and F.J.M. acknowledge the support of the Spanish ‘‘Ministerio de Economia y Competitividad’’ under grant BIA2014-59643-R. P.C. acknowledges the support of the Spanish ‘‘Ministerio de Economia y Competitividad’’ under grant BIA2015-70644-R. J.A.A.A. is indebted to the MEC (Ministerio de Educacion, Cultura y Deporte, Spain) for the funding provided in the FPU (Formacion del ProfesoradoUniversitario) studentship (BOE-A-2013-12235). This material is based upon work supported by the U.S. Geological Survey under grant/cooperative agreement G15AC00426. P.R. acknowledges the support of the National Oceanic and Atmospheric Administration Climate Program Office via award NA15OAR4310145. Support was provided from the US DOD Strategic Environmental Research and Development Program (SERDP Project RC-2644) through the NOAA National Centers for Environmental Information (NCEI). Atmospheric data from CFSR are available online at https://climatedataguide.ucar.edu/climatedata/climate-forecast-system-reanalysis-cfsr. Marine data from global reanalysis are lodge with the IHData center from IHCantabria and are available for research purposes upon request (contact: [email protected])

A frailty-contagion model for multi-site hourly precipitation driven by atmospheric covariates

Accurate stochastic simulations of hourly precipitation are needed for impact studies at local spatial scales. Statistically, hourly precipitation data represent a difficult challenge. They are non-negative, skewed, heavy tailed, contain a lot of zeros (dry hours) and they have complex temporal structures (e.g., long persistence of dry episodes). Inspired by frailty-contagion approaches used in finance and insurance, we propose a multi-site precipitation simulator that, given appropriate regional atmospheric variables, can simultaneously handle dry events and heavy rainfall periods. One advantage of our model is its conceptual simplicity in its dynamical structure. In particular, the temporal variability is represented by a common factor based on a few classical atmospheric covariates like temperatures, pressures and others. Our inference approach is tested on simulated data and applied on measurements made in the northern part of French Brittany.Comment: Presented by Erwan Koch at the conferences: - 12th IMSC, Jeju (Korea), June 2013 - ISI WSC 2013, Hong Kong, Aug.2013. Invited speaker in the session "Probabilistic and statistical contributions in climate research

Modeling long-term persistence in hydroclimatic time series using a hidden state Markov model

A hidden state Markov (HSM) model is developed as a new approach for generating hydroclimatic time series with long-term persistence. The two-state HSM model is motivated by the fact that the interaction of global climatic mechanisms produces alternating wet and dry regimes in Australian hydroclimatic time series. The HSM model provides an explicit mechanism to stochastically simulate these quasi-cyclic wet and dry periods. This is conceptually sounder than the current stochastic models used for hydroclimatic time series simulation. Models such as the lag-one autoregressive (AR(1)) model have no explicit mechanism for simulating the wet and dry regimes. In this study the HSM model was calibrated to four long-term Australian hydroclimatic data sets. A Markov Chain Monte Carlo method known as the Gibbs sampler was used for model calibration. The results showed that the locations significantly influenced by tropical weather systems supported the assumptions of the HSM modeling framework and indicated a strong persistence structure. In contrast, the calibration of the AR(1) model to these data sets produced no statistically significant evidence of persistence.Mark Thyer and George Kucze

Multivariate and multi-scale generator based on non-parametric stochastic algorithms

A method for generating combined multivariate time series at multiple locations and at different time scales is presented. The procedure is based on three steps: first, the Monte Carlo method generation of data with statistical properties as close as possible to the observed series; second, the rearrangement of the order of simulated data in the series to achieve target correlations; and third, the permutation of series for correlation adjustment between consecutive years. The method is non-parametric and retains, to a satisfactory degree, the properties of the observed time series at the selected simulation time scale and at coarser time scales. The new approach is tested on two case studies, where it is applied to the log-transformed streamflow and precipitation at weekly and monthly time scales. Special attention is given to the extrapolation of non-parametric cumulative frequency distributions in their tail zones. The results show a good agreement of stochastic properties between the simulated and observed data. For example, for one of the case studies, the average relative errors of the observed and simulated weekly precipitation and streamflow statistics (up to skewness coefficient) are in the range of 0.1–9.2% and 0–5.4%, respectively.This is the submitted version of the article: Đ. Marković, S. Ilić, D. Pavlović, J. Plavšić, and N. Ilich, ‘Multivariate and multi-scale generator based on non-parametric stochastic algorithms’, Journal of Hydroinformatics, vol. 21, no. 6, pp. 1102–1117, Nov. 2019, [https://doi.org/10.2166/hydro.2019.071