Figure 6 - available via license: Creative Commons Attribution 4.0 International
Content may be subject to copyright.
Schematic flow diagram of the TripleM precipitation generator. TripleM can be used as a bootstrap model (Output 1) and a parametric precipitation model (Output 2). Parallelograms represent time series or variables, boxes represent methods. Blue parallelograms represent input and output data. Cholesky matrices and transition matrices are either derived monthly (12) or seasonally (4). The parametric distribution parameters are either derived monthly (12) or seasonally (4) for the number of gauges simulated (n).
Source publication
Stochastic weather generators can generate very long time series of weather patterns, which are indispensable in earth sciences, ecology and climate research. Yet, both their potential and limitations remain largely unclear because past research has typically focused on eclectic case studies at small spatial scales in temperate climates. In additio...
Context in source publication
Context 1
... entire simulation process can be depicted from Fig. 6. In its most simplistic setup (resampling i.e. bootstrap without parametric sampling of precipitation amounts as applied in this study), TripleM has two key parameters the user has to define: the duplication rate and the order of the Markov chain. As for the duplication rate, an inherent characteristic of TripleM is that the clustering ...
Similar publications
Article Info Stochastic weather generators used in meteorological and hydrological studies are mostly statistical models that produce random numbers resembling the observed data on which they have been fitted. They can generate weather sequences that statistically resemble the real observed data. In this study we developed a single-site daily rainf...
An increasing focus of climate change studies is the projection of storm events characterized by heavy, very heavy, extreme, and/or intense precipitation. Projected changes in the spatiotemporal distributions of such intense precipitation events remain uncertain due to large measures of variability in both the definition and evidence of increased i...
Disruptions in harbor operations have significant implications for local, regional and global economies due to ports strategic role as part of the supply chain. A probabilistic evaluation of port operations considering the influence of climate change is required in order to secure optimal exploitation during their useful life. Here, we propose a hy...
A robust hydrological impact assessment is indispensable for mitigation and adaptation planning. This study presents an integrated modelling methodology for evaluating climate change impacts on water availability, sediment yield and extreme events at the catchment scale. We propose the use of the Spatial‐Temporal Neyman‐Scott Rectangular Pulses (ST...
Citations
... Moreover, distribution functions with more parameters performed better than those with fewer parameters [10]. Breinl et al. [11] used the stochastic multi-site precipitation generator TripleM (Multisite Markov Model) to simulate precipitation patterns and conducted a review of applications related to the SPG approaches. The statistical analysis of such large-scale datasets requires parameter estimation techniques that are computationally effective and adequately capture the dynamism of the underlying processes. ...
Precipitation modeling holds significant importance in various fields such as agriculture, animal husbandry, weather derivatives, hydrology, and risk and disaster preparedness. Stochastic precipitation generators (SPGs) represent a class of statistical models designed to generate synthetic data capable of simulating dry and wet precipitation stretches for a long duration. The construction of Hidden Markov Models (HMMs), which treat latent meteorological circumstances as hidden states, is an efficient technique for simulating precipitation. Considering that there are many choices of emission distributions used to generate positive precipitation, the characteristics of different distributions for simulating positive precipitation have not been fully explored. The paper includes a simulation study that demonstrates how the Pareto distribution, when used as the distribution for generating positive precipitation, addresses the limitations of the exponential and gamma distributions in predicting heavy precipitation events. Additionally, the Pareto distribution offers flexibility through adjustable parameters, making it a promising option for precipitation modeling. We can estimate parameters in HMMs using forward–backward algorithms, Variational Bayes Expectation-Maximization (VBEM), and Stochastic Variational Bayes (SVB). In the Xilingol League, located in the central part of the Inner Mongolia Autonomous Region, China, our study involved data analysis to identify crucial locations demonstrating a robust correlation and notable partial correlation between the Normalized Difference Vegetation Index (NDVI) and annual precipitation. We performed fitting of monthly dry days ratios and monthly precipitation using seasonal precipitation and year-round precipitation data at these crucial locations. Subsequently, we conducted precipitation predictions for the daily, monthly, and annual time frames using the new test dataset observations. The study concludes that the SPG fits the monthly dry-day ratio better for annual daily precipitation data than for seasonal daily precipitation data. The fitting error for the monthly dry day ratio corresponding to annual daily precipitation data is 0.053 (exponential distribution) and 0.066 (Pareto distribution), while for seasonal daily precipitation data, the fitting error is 0.14 (exponential distribution) and 0.15 (Pareto distribution). The exponential distribution exhibits the poorest performance as a model for predicting future precipitation, with average errors of 2.49 (daily precipitation), 40.62 (monthly precipitation), and 130.40 (annual precipitation). On the other hand, the Pareto distribution demonstrates the best overall predictive performance, with average errors of 0.69 (daily precipitation), 34.69 (monthly precipitation), and 66.42 (annual precipitation). The results of this paper can provide decision support for future grazing strategies in the Xilingol League.
... While the output provided from these models are statistical estimates and therefore have uncertainty built in, ensemble datasets generated from these models can improve other climate and weather models. Breinl et al. (2017) provides a review of current SPG approaches and applications. ...
Stochastic precipitation generators (SPGs) are a class of statistical models which generate synthetic data that can simulate dry and wet rainfall stretches for long durations. Generated precipitation time series data are used in climate projections, impact assessment of extreme weather events, and water resource and agricultural management. We construct an SPG for daily precipitation data that is specified as a semi-continuous distribution at every location, with a point mass at zero for no precipitation and a mixture of two exponential distributions for positive precipitation. Our generators are obtained as hidden Markov models (HMMs) where the underlying climate conditions form the states. We fit a 3-state HMM to daily precipitation data for the Chesapeake Bay watershed in the Eastern coast of the USA for the wet season months of July to September from 2000--2019. Data is obtained from the GPM-IMERG remote sensing dataset, and existing work on variational HMMs is extended to incorporate semi-continuous emission distributions. In light of the high spatial dimension of the data, a stochastic optimization implementation allows for computational speedup. The most likely sequence of underlying states is estimated using the Viterbi algorithm, and we are able to identify differences in the weather regimes associated with the states of the proposed model. Synthetic data generated from the HMM can reproduce monthly precipitation statistics as well as spatial dependency present in the historical GPM-IMERG data.
... To avoid the pitfall of physically unrealistic simulations, stochastic rainfall models embed a significant part of our conceptual knowledge about rainfall behavior in their parameterization (i.e., they implement statistical relationships that reflect as closely as possible the physical processes at work). However, rainfall properties (Krajewski et al., 2003) and, in turn, the performance of stochastic rainfall generators (Breinl et al., 2017;Vu et al., 2018) strongly depend on the climate of the area of interest. Hence, different models have been proposed for different climates, with each model focusing on a specific aspect of rainfall, for instance, rainfall seasonality in monsoonal climates (Greene et al., 2011), rainfall spatial-temporal correlation in temperate climates (Paschalis et al., 2013), or rainfall occurrence and extreme intensities in arid regions (Wilcox et al., 2021). ...
Stochastic rainfall generators are probabilistic models of rainfall space–time behavior. During parameterization and calibration, they allow the identification and quantification of the main modes of rainfall variability. Hence, stochastic rainfall models can be regarded as probabilistic conceptual models of rainfall dynamics.
As with most conceptual models in earth sciences, the performance of stochastic rainfall models strongly relies on their adequacy in representing the rain process at hand. On tropical islands with high elevation topography, orographic rain enhancement challenges most existing stochastic models because it creates localized precipitations with strong spatial gradients, which break down the stationarity of rain statistics.
To allow for stochastic rainfall modeling on tropical islands, despite
non-stationarity of rain statistics, we propose a new stochastic daily
multi-site rainfall generator specifically for areas with significant
orographic effects. Our model relies on a preliminary classification of
daily rain patterns into rain types based on rainfall space and intensity
statistics, and sheds new light on rainfall variability at the island scale. Within each rain type, the distribution of rainfall through the island is modeled by combining a non-parametric resampling of past analogs of a latent field describing the spatial distribution of rainfall, and a parametric gamma transform function describing rain intensity.
When applied to the stochastic simulation of rainfall on the islands of
O`ahu (Hawai`i, United States of America) and Tahiti (French Polynesia) in
the tropical Pacific, the proposed model demonstrates good skills in jointly simulating site-specific and island-scale rain statistics. Hence, it provides a new tool for stochastic impact studies in tropical islands, in particular for watershed water resource management.
... Some significant fluctuations in the atmospheric patterns such as the frequency and rotational changes of large-scale atmospheric circulations, increasing sea surface temperatures and instability conditions between surface and upper levels change the precipitation amount, duration and intensity, which significantly affects the water cycle of a region (Mishra and Singh, 2010;Trenberth, 2011;Li et al., 2016;Caloiero and Coscarelli, 2020;Dong et al., 2020). Additionally, prolonged wet and/or dry spells negatively affect the natural resources by causing extreme weather events such as floods, droughts and heat waves (Houghton et al., 2001;Li et al., 2010;Breinl et al., 2017;Li et al., 2017;Li et al., 2018;Nabeel and Athar, 2018;Breinl et al., 2020). From natural meteorological disasters, droughts occur in certain places of the earth during dry spells with insufficient precipitation and can be intensified by long continued successive dry days. ...
Understanding the variations and leading atmospheric mechanisms causing wet and dry episodes are very important for the water management strategies. For this purpose, this study investigates the spatiotemporal variation and background environmental conditions for wet and dry spell lengths in Turkey. With this aim, Mann-Kendall rank statistic test and fitted ordinary least squares regression method are implemented to the 92 meteorology stations, which are homogenously distributed over Turkey, for the period 1966–2018. In terms of atmospheric circulation mechanisms, synoptic composites of NCEP/NCAR Reanalysis data (sea level pressure, air temperature at 850-hPa level, geopotential height at 500-hPa level) and sea surface temperature from NOAA High Resolution data are applied to the five years of highest frequency long dry/wet spells. According to the results, both the increasing frequencies of wet spells and their highest contribution to the precipitation are mainly found in the eastern Black Sea Region (BSR) of Turkey during all seasons, especially in spring. In this sub-region, statistically significant increasing (decreasing) springtime wet (dry) spell lengths in the neighboring five stations (i.e. Ardahan, Artvin, Bayburt, Hopa, Rize) indicated that the majority of wet spells (almost 30%) appear to occur between 3 and 5 days and the maximum number of the wet spell days are shown in the last two decades of the eastern BSR. Local quasi-stationary surface high located over eastern Black Sea (1016-hPa core) and associated weak northerly winds transfer relatively warm moist air from the sea surface (11.8 °C in average). This air mass meets with cold- land and low level (6 °C at 850 hPa) air masses, developing instability conditions and resulting in low precipitation rates in wet spells for the eastern BSR. On the other hand, by the extension of the south-west Asian Monsoon to the inner parts of Turkey, relatively hot dry air is transferred to the eastern BSR via southerly winds. As a result of this long-staying Asiatic monsoon characteristics, more dry days are shown in the region due to insufficient moisture and associated lack of precipitation.
... Precipitation is a crucial component of the water cycle, directly or indirectly related to many domains (Breinl et al., 2017;Ye et al., 2018). As the critical factor, rainfall data is vital to the reliability of water resources planning, hydraulic infrastructure design, and flood and drought risk assessment (Kim et al., 2017). ...
As an essential part of the hydrological cycle, precipitation directly contributes to surface runoff and river runoff formation. Simulation on precipitation variables can effectively solve the adverse effects on hydrological assessment in some areas with insufficient or even no runoff observation. With the widespread use of various weather generators, the traditional stochastic hydrological simulation methods tend to be gradually replaced. To compare these two approaches mentioned above, this paper utilizes the precipitation records from 1958 to 2011 at nine meteorological stations within Huaihe River System in Henan Province to evaluate a stochastic hydrological simulation method, SARIMA model, and two types of weather generators, WeaGETS and LARS-WG, through the comparison of statistical characteristics regarding precipitation variables, such as mean, mean square error, extreme value and coefficient of variation. The results show that (1) on the annual scale, SARIMA has a better performance to reproduce the mean and mean square error as well as the extreme precipitation events than weather generators; (2) regarding the monthly-scale precipitation simulation, SARIMA is good at reproducing the statistical properties of monthly precipitation at the average level, while WeaGETS and LARS-WG work better in simulating monthly precipitation extremes; (3) compared with weather generators, SARIMA is highly constrained by the observed records, and among these two weather generators, WeaGETS scores higher on monthly precipitation simulation under the same sample length conditions. In conclusion, the traditional hydrological simulation method, SARIMA, and weather generators, WeaGETS and LARS-WG, have both benefits and drawbacks. The appropriate choice depends on different research backgrounds and purposes.
... Rainfall data is a major meteorological input for water resources management and hydrological, agricultural and ecological applications (Guan et al., 2015;Hettiarachchi et al., 2018). In view that the observed records provide a single realization of the underlying climate and they are short or even unavailable in some cases (Breinl et al., 2017), rainfall weather generators (WGs) or stochastic rainfall models (SRMs) have been widely developed to generate multiple plausible realizations of rainfall sequences with arbitrary length to compensate the above deficiencies and simultaneously preserve the statistical properties of observed data (Gao et al., 2018(Gao et al., , 2020bLi and Babovic, 2018a). Additionally, they are also used as downscaling tools in climate change analysis to downscale projections of global climate models (GCMs) or regional climate models (RCMs) from coarse spatial scales to regional scales (Li et al., 2011(Li et al., , 2017. ...
Multi-site rainfall models are useful tools to provide synthetic realizations of spatially-correlated rainfall at multiple stations, which are of great importance for flood and drought risk assessment and climate change impact analysis. Therefore, a good preservation of various observed rainfall characteristics including rainfall time-series statistics and rainfall event characteristics at individual stations and the inter-site correlations of these rainfall characteristics is very crucial. To achieve this purpose, this study aims to develop a multi-site stochastic daily rainfall model by coupling a univariate Markov chain with a multi-site rainfall event model (MSDRM-MCREM), based on our previously-developed single-site SDRM-MCREM. The univariate Markov chain model in MSDRM-MCREM is used to generate spatially-correlated multi-site rainfall occurrence time series and extract simulated rainfall events for individual stations based on continuous wet days. The multi-site rainfall event model is then constructed using Vine copulas to simulate spatially-correlated rainfall event characteristics of those simulated rainfall events that occur simultaneously at multiple stations, including rainfall durations, rainfall depths and temporal patterns. Subsequently, this model was applied to the Changshangang River basin in Zhejiang Province, East China and its performance in reproducing rainfall characteristics and spatial correlations was evaluated for three cases, i.e. simulations for two, three and four stations. Results show that except for overestimation of light rainfall, MSDRM-MCREM can simultaneously well preserve rainfall time-series statistics (i.e. different rainfall percentiles, mean monthly rainfall, standard deviations and probabilities and mean values of wet days), extreme rainfall (i.e. exceedance probabilities of annual maximum 1-day, 3-day and 5-day rainfall) and rainfall event characteristics (i.e. cumulative probabilities of wet spell, dry spell and rainfall depth, temporal patterns and occurrence probabilities of rainfall types for different depth-based event classes) at individual stations. In addition, the spatial correlations of rainfall characteristics have also been well maintained, including rainfall occurrence time series and rainfall event characteristics in different groups, with the inter-site correlations of rainfall time series being slightly underestimated.
... Of which temperature and precipitation are associated with the pattern of regional and local atmospheric circulations (Kidd & Huffman, 2011;Mockler, OʼLoughlin, et al., 2016). In recent decades, various advanced statistical and stochastic approaches have been developed for climate predictions by incorporating the seasonal and annual fluctuations (Breinl et al., 2017;Khazaei & Ahmadi, 2013;Wu et al., 2011). These studies were highly exposed to uncertainty due to the complex stochastic approach (Vesely et al., 2019) and a number of parameters (Breinl et al., 2017;Okoli et al., 2019). ...
... In recent decades, various advanced statistical and stochastic approaches have been developed for climate predictions by incorporating the seasonal and annual fluctuations (Breinl et al., 2017;Khazaei & Ahmadi, 2013;Wu et al., 2011). These studies were highly exposed to uncertainty due to the complex stochastic approach (Vesely et al., 2019) and a number of parameters (Breinl et al., 2017;Okoli et al., 2019). The ensemble realization of precipitation and temperature were generated using a statistical approach (Equations 1 and 2) for assessing the input data uncertainty. ...
Quantifying possible sources of uncertainty in simulations of hydrological extreme events is very important for better risk management in extreme situations and water resource planning. The main objective of this research work is to identify and address the role of input data quality and hydrological parameter sets, and uncertainty propagation in hydrological extremes estimation. This includes identifying and estimating their contribution to flood and low flow magnitude using two objective functions (NSE for flood and LogNSE for low flow), 20,000 Hydrologiska Byråns Vattenbalansavdelning (HBV) hydrological parameter sets, and three frequency distribution models (Log-Normal, Pearson-III, and Generalized Extreme Value). The influence of uncertainty on the simulated flow is not uniform across all the selected three catchments due to different flow regimes and runoff generation mechanisms. The result shows that the uncertainty in high flow frequency modeling mainly comes from the input data quality. In the modeling of low flow frequency, the main contributor to the total uncertainty is model parameterization. The total uncertainty of QT90 (extreme peak flow quantile at 90-year return period) quantile shows that the interaction of input data and hydrological parameter sets have a significant role in the total uncertainty. In contrast, in the QT10 (extreme low flow quantile at 10-year return period) estimation, the input data quality and hydrological parameters significantly impact the total uncertainty. This implies that the primary factors and their interactions may cause considerable risk in water resources management and flood and drought risk management. Therefore, neglecting these factors and their interaction in disaster risk management, water resource planning, and evaluation of environmental impact assessment is not feasible and may lead to considerable risk.
Recommendations for Water Resource Managers
• The role of hydrological parameters and climate input data is significant in flood and low flow estimations and significantly impacts water resources and extremes management.
• Input data dominantly controlled flood magnitude and frequency, whilst the low flow magnitude and frequency were dominantly affected by both input data quality and hydrological parameters.
• It is crucial to consider the main features that cause considerable risk in water resource management and extreme risk management.
• Neglecting the primary factors and their interaction in disaster risk management, water resource planning, and evaluation of environmental impact assessment is not feasible and may lead to considerable risk.
• Improved extreme water management through a complex modeling approach to better prepare for the impact of extreme high and low flow changes are the best long- and short-term plans and strategies to combat and minimize the risk in water-related sectors of the local economy.
... Instead of the statistical downscaling by a regression relation between precipitation (predictand) and predictors (precipitation outputs by the stochastic weather generator, that is, SDSM; Wilby and Dawson, 2013;Tang et al., 2016), this study took into account the spatial correlation of the grid precipitation data of the GCM outputs and in-situ precipitation observations in the development of a regression model. Hence, the uncertainty introduced by the stochastic weather generator was greatly avoided (Breinl et al., 2017). Meanwhile, the nonlinearity in the relation between GCM-based precipitation and in-situ precipitation observations was also considered: ...
Statistical downscaling is an effective way to downscale General Circulation Model (GCM) outputs to a finer temporal and spatial scale. Here, we proposed and trained a new station‐based non‐linear regression downscaling (SNRD) approach, and quantitatively demonstrated its better performance than linear regression model. In addition, we also compared the SNRD method with the Bias Correction Spatial Disaggregation (BCSD) method, which has been widely applied on downscaling precipitation. Results indicated that RMSEs and residuals of the Bias Correction Spatial Disaggregation (BCSD) method are 4.6~31 times as ones of SNRD in each region of China during validation period (2004‐2015). Besides, with historical in‐situ observed monthly mean precipitation as the benchmark, SNRD downscaled model modified the over‐estimation (1.25~2 times as observed precipitation) flaw of BCSD model in rainy season (June to August) of China, which could provide assistance on the further researches on drought events in rainy season in future. Further, we also surprisingly found that the 2500m was the threshold height for statistical downscaling models. Both BCSD and SNRD downscaled precipitation displayed more steadily and accurately above 2500m, since there are less intense human activities in China. Thus, we recommend further studies should fully consider the height element in downscaling models to improve the accuracies. This article is protected by copyright. All rights reserved.
... Of which, temperature and precipitation are associated with the pattern of regional and local atmospheric circulations (Kidd and Huffman 2011). In recent decades, various advanced statistical and stochastic approaches have been developed for climate predictions by incorporating the seasonal and annual fluctuations (Breinl et al. 2017). These studies were highly exposed to uncertainty due to the complex stochastic approach (Vesely et al. 2019) and the number of parameters ( (Breinl et al. 2017;Okoli et al. 2019). ...
... In recent decades, various advanced statistical and stochastic approaches have been developed for climate predictions by incorporating the seasonal and annual fluctuations (Breinl et al. 2017). These studies were highly exposed to uncertainty due to the complex stochastic approach (Vesely et al. 2019) and the number of parameters ( (Breinl et al. 2017;Okoli et al. 2019). Therefore, in this study, for the input uncertainty analysis, ensemble realization of precipitation and temperature were generated using a statistical approach (Eq. ...
Evaluation of possible sources of uncertainty and their influence on water resource planning and extreme hydrological characteristics are very important for extreme risk reduction and management. The main objective is to identify and holistically address the uncertainty propagation from the input data to the frequency of hydrological extremes. This novel uncertainty estimation framework has four stages that comprise hydrological models, hydrological parameter sets, and frequency distribution types. The influence of uncertainty on the simulated flow is not uniform across all the selected eight catchments due to different flow regimes and runoff generation mechanisms. The result shows that uncertainty in peak flow frequency simulation mainly comes from the input data quality. Whereas, in the low flow frequency, the main contributor to the total uncertainty is model parameterization. The total uncertainty in the estimation of QT90 (extreme peak flow quantile at 90-year return period) quantile shows the interaction of input data and extreme frequency models has significant influence. In contrast, the hydrological models and hydrological parameters have a substantial impact on the QT10 (extreme low flow quantile at 10-year return period) estimation. This implies that the four factors and their interactions may cause significant risk in water resource management and flood and drought risk management. Therefore, neglecting these factors in disaster risk management, water resource planning, and evaluation of environmental impact assessment is not feasible and may lead to significant impact.
... It performs generally well but often fails at generating extreme precipitation that follows a distribution with a heavier tail, such as the generalized extreme value distribution (GEV) or Generalized Pareto distributions. Accordingly, several studies have compared various distribution functions to be used in WGs (Li et al. 2013, Breinl 2016, Breinl et al. 2017, Li and Shi 2019. These studies typically find that the more complex distribution functions, with three or more parameters, outperform the simpler ones, especially for larger quantiles of the observed distributions. ...
Resampling historical time series remains one of the main approaches used to generate long-term probabilistic streamflow forecasts, while there is a need to develop more flexible approaches taking into account non-stationarities. One possible approach is to use a modelling chain consisting of a stochastic weather generator and a hydrological model. However, the ability of this modelling chain to generate adequate probabilistic streamflows must first be evaluated. The aim of this paper is to compare the performance of a stochastic weather generator against resampling historical meteorological time series in order to produce ensemble streamflow forecasts. The comparison framework is based on 30 years of forecasts for a single Canadian watershed. Forecasts resulting from the two methods are evaluated using the continuous ranked probability score (CRPS) and rank histograms. Results indicate that while there are differences between the methods, they nevertheless perform similarly, thus showing that weather generators can be used as substitutes for resampling the historical past.
