Simulating hourly rainfall occurrence within an equatorial rainforest,Borneo Island / Simulation de l'occurrence de pluie horaire au sein de la forêt équatoriale,Ile de Bornéo

Abstract

The ability to simulate characteristics of the diurnal cycle of rainfall occurrence, and its evolution over the seasons is important to the forecasting of hydrological impacts resulting from land-use and climate changes within the humid tropics. This stochastic modelling study uses a generalized linear model (GLM) solution to second-order Markov chain models, as these discrete models are better at describing binary occurrence processes on an hourly time-scale than continuous-time approaches such as stochastic state-space models. We show that transition probabilities derived by the Markov chain method need to be time-varying rather than stationary to simulate the evolution of the diurnal cycle of rainfall occurrence over a Southeast Asian monsoon sequence. The conceptual and pragmatic links between discrete diurnal processes and continuous processes occurring over seasonal periods are thereby simulated within the same model.     

Doubly stochastic Poisson pulse model for fine-scale rainfall

Stochastic rainfall models are widely used in hydrological studies because they provide a framework not only for deriving information about the characteristics of rainfall but also for generating precipitation inputs to simulation models whenever data are not available. A stochastic point process model based on a class of doubly stochastic Poisson processes is proposed to analyse fine-scale point rainfall time series. In this model, rain cells arrive according to a doubly stochastic Poisson process whose arrival rate is determined by a finite-state Markov chain. Each rain cell has a random lifetime. During the lifetime of each rain cell, instantaneous random depths of rainfall bursts (pulses) occur according to a Poisson process. The covariance structure of the point process of pulse occurrences is studied. Moment properties of the time series of accumulated rainfall in discrete time intervals are derived to model 5-min rainfall data, over a period of 69 years, from Germany. Second-moment as well as third-moment properties of the rainfall are considered. The results show that the proposed model is capable of reproducing rainfall properties well at various sub-hourly resolutions. Incorporation of third-order moment properties in estimation showed a clear improvement in fitting. A good fit to the extremes is found at larger resolutions, both at 12-h and 24-h levels, despite underestimation at 5-min aggregation. The proportion of dry intervals is studied by comparing the proportion of time intervals, from the observed and simulated data, with rainfall depth below small thresholds. A good agreement was found at 5-min aggregation and for larger aggregation levels a closer fit was obtained when the threshold was increased. A simulation study is presented to assess the performance of the estimation method.     

Stochastic modelling of seasonal and yearly rainfalls with low-frequency variability

Stochastic rainfall models are important for many hydrological applications due to their appealing ability to simulate synthetic series that resemble the statistical characteristics of the observed series for a location of interest. However, an important limitation of stochastic rainfall models is their inability to preserve the low-frequency variability of rainfall. Accordingly, this study presents a simple yet efficient stochastic rainfall model for a tropical area that attempts to incorporate seasonal and inter-annual variabilities in simulations. The performance of the proposed stochastic rainfall model, the tropical climate rainfall generator (TCRG), was compared with a stochastic multivariable weather generator (MV-WG) in various aspects. Both models were applied on 17 rainfall stations at the Kelantan River Basin, Malaysia, with tropical climate. The validations were carried out on seasonal (monsoon and inter-monsoon) and annual basis. The third-order Markov chain of the TCRG was found to perform better in simulating the rainfall occurrence and preserving the low-frequency variability of the wet spells. The log-normal distribution of the TCRG was consistently better in modelling the rainfall amounts. Both models tend to underestimate the skewness and kurtosis coefficient of the rainfall. The spectral correction approach adopted in the TCRG successfully preserved the seasonal and inter-annual variabilities of rainfall amounts, whereas the MV-WG tends to underestimate the variability bias of rainfall amounts. Overall, the TCRG performed reasonably well in the Kelantan River Basin, as it can represent the key statistics of rainfall occurrence and amounts successfully, as well as the low-frequency variability.     

A doubly stochastic rainfall model with exponentially decaying pulses

We develop a doubly stochastic point process model with exponentially decaying pulses to describe the statistical properties of the rainfall intensity process. Mathematical formulation of the point process model is described along with second-order moment characteristics of the rainfall depth and aggregated processes. The derived second-order properties of the accumulated rainfall at different aggregation levels are used in model assessment. A data analysis using 15 years of sub-hourly rainfall data from England is presented. Models with fixed and variable pulse lifetime are explored. The performance of the model is compared with that of a doubly stochastic rectangular pulse model. The proposed model fits most of the empirical rainfall properties well at sub-hourly, hourly and daily aggregation levels.     

Significance of AIC differences for precipitation intensity distributions

Chain dependent models for daily precipitation typically model the occurrence process as a Markov chain and the precipitation intensity process using one of several probability distributions. It has been argued that the mixed exponential distribution is a superior model for the rainfall intensity process, since the value of its information criterion (Akaike information criterion or Bayesian information criterion) when fit to precipitation data is usually less than the more commonly used gamma distribution. The differences between the criterion values of the best and lesser models are generally small relative to the magnitude of the criterion value, which raises the question of whether these differences are statistically significant. Using a likelihood ratio statistic and nesting the gamma and mixed exponential distributions in a parent distribution, we show indirectly that generally the superiority of the mixed exponential distribution over the gamma distribution for modeling precipitation intensity is statistically significant. Comparisons are also made with a common-a gamma model, which are less informative.     

A class of hidden Markov models for regional average rainfall

Abstract

Basic hidden Markov models are very useful in stochastic environmental research but their ability to accommodate sufficient dependence between observations is somewhat limited. However, they can be modified in several ways to form a rich class of flexible models that are useful in many environmental applications. We consider a class of hidden Markov models that incorporate additional dependence among observations to model average regional rainfall time series. The focus of the study is on models that introduce additional dependence between the state level and the observation level of the process and also on models that incorporate dependence at observation level. Construction of the likelihood function of the models is described along with the usual second-order properties of the process. The maximum likelihood method is used to estimate the parameters of the models. Application of the proposed class of models is illustrated in an analysis of daily regional average rainfall time series from southeast and southwest England for the winter season during 1931 to 2010. Models incorporating additional dependence between the state level and the observation level of the process captured the distributional properties of the daily rainfall well, while the models that incorporate dependence at the observation level showed their ability to reproduce the autocorrelation structure. Changes in some of the regional rainfall properties during the time period are also studied.

Editor D. Koutsoyiannis     

Pulse generation models for daily intermittent streamflows / Modèles de génération d’impulsions pour des débits journaliers intermittents

Abstract

Abstract Generating pulses and then converting them into flow are two main steps of daily streamflow generation. Three pulse generation models have been proposed on the basis of Markov chains for the purpose of generating daily intermittent streamflow time series in this study. The first one is based on two two-state Markov chains, whereas the second uses a three-state Markov chain. The third model uses harmonic analysis and fits Fourier series to the three-state Markov chain. Results for a daily intermittent streamflow data series show a good performance of the proposed models.     

A stochastic model describing the impact of daily rainfall depth distribution on the soil water balance

Simplified, vertically-averaged soil moisture models have been widely used to describe and study eco-hydrological processes in water-limited ecosystems. The principal aim of these models is to understand how the main physical and biological processes linking soil, vegetation, and climate impact on the statistical properties of soil moisture. A key component of these models is the stochastic nature of daily rainfall, which is mathematically described as a compound Poisson process with daily rainfall amounts drawn from an exponential distribution. Since measurements show that the exponential distribution is often not the best candidate to fit daily rainfall, we compare the soil moisture probability density functions obtained from a soil water balance model with daily rainfall depths assumed to be distributed as exponential, mixed-exponential, and gamma. This model with different daily rainfall distributions is applied to a catchment in New South Wales, Australia, in order to show that the estimation of the seasonal statistics of soil moisture might be improved when using the distribution that better fits daily rainfall data. This study also shows that the choice of the daily rainfall distributions might considerably affect the estimation of vegetation water-stress, leakage and runoff occurrence, and the whole water balance.     

A two steps disaggregation method for highly seasonal monthly rainfall

 The need for high resolution rainfall data at temporal scales varying from daily to hourly or even minutes is a very important problem in hydrology. For many locations of the world, rainfall data quality is very poor and reliable measurements are only available at a coarse time resolution such as monthly. The purpose of this work is to apply a stochastic disaggregation method of monthly to daily precipitation in two steps: 1. Initialization of the daily rainfall series by using the truncated normal model as a reference distribution. 2.␣Restructuring of the series according to various time series statistics (autocorrelation function, scaling properties, seasonality) by using a Markov chain Monte Carlo based algorithm. The method was applied to a data set from a rainfall network of the central plains of Venezuela, in where rainfall is highly seasonal and data availability at a daily time scale or even higher temporal resolution is very limited. A detailed analysis was carried out to study the seasonal and spatial variability of many properties of the daily rainfall as scaling properties and autocorrelation function in order to incorporate the selected statistics and their annual cycle into an objective function to be minimized in the simulation procedure. Comparisons between the observed and simulated data suggest the adequacy of the technique in providing rainfall sequences with consistent statistical properties at a daily time scale given the monthly totals. The methodology, although highly computationally intensive, needs a moderate number of statistical properties of the daily rainfall. Regionalization of these statistical properties is an important next step for the application of this technique to regions in where daily data is not available.     

Further developments of a transient Poisson-cluster model for rainfall

Stochastic point processes for rainfall are known to be able to preserve the temporal variability of rainfall on several levels of aggregation (e.g. hourly, daily), especially when the cluster approach is used. One major assumption in most of the applications todate is the stationarity of the rainfall properties in time, which must be reconsidered under a climate change hypothesis. Here, we propose new theoretical developments of a Poisson-based model with cluster, namely the Neyman–Scott Rectangular Pulses Model, which treats storm frequency as a nonstationary function. In this paper, storm frequency is modelled as a linear function of time in order to reproduce an increase (or decrease) of the mean annual precipitation. The basic theory is reconsidered and the moments are derived up to the third order. Then, a calibration method based on the generalized method of moments is proposed and discussed. An application to a rainfall time series from Uccle illustrates how this model can reproduce a trend for the average rainfall. This work opens new avenues for future developments on transient stochastic rainfall models and highlights the major challenges linked to this approach.     

Reproduction of temporal scaling by a rectangular pulses rainfall model

The presence of scaling statistical properties in temporal rainfall has been well established in many empirical investigations during the latest decade. These properties have more and more come to be regarded as a fundamental feature of the rainfall process. How to best use the scaling properties for applied modelling remains to be assessed, however, particularly in the case of continuous rainfall time‐series. One therefore is forced to use conventional time‐series modelling, e.g. based on point process theory, which does not explicitly take scaling into account. In light of this, there is a need to investigate the degree to which point‐process models are able to ‘unintentionally’ reproduce the empirical scaling properties. In the present study, four 25‐year series of 20‐min rainfall intensities observed in Arno River basin, Italy, were investigated. A Neyman–Scott rectangular pulses (NSRP) model was fitted to these series, so enabling the generation of synthetic time‐series suitable for investigation. A multifractal scaling behaviour was found to characterize the raw data within a range of time‐scales between approximately 20 min and 1 week. The main features of this behaviour were surprisingly well reproduced in the simulated data, although some differences were observed, particularly at small scales below the typical duration of a rain cell. This suggests the possibility of a combined use of the NSRP model and a scaling approach, in order to extend the NSRP range of applicability for simulation purposes. Copyright © 2002 John Wiley & Sons, Ltd.     

Rainfall data simulation by hidden Markov model and discrete wavelet transformation

In many regions, monthly (or bimonthly) rainfall data can be considered as deterministic while daily rainfall data may be treated as random. As a result, deterministic models may not sufficiently fit the daily data because of the strong stochastic nature, while stochastic models may also not reliably fit into daily rainfall time series because of the deterministic nature at the large scale (i.e. coarse scale). Although there are different approaches for simulating daily rainfall, mixing of deterministic and stochastic models (towards possible representation of both deterministic and stochastic properties) has not hitherto been proposed. An attempt is made in this study to simulate daily rainfall data by utilizing discrete wavelet transformation and hidden Markov model. We use a deterministic model to obtain large-scale data, and a stochastic model to simulate the wavelet tree coefficients. The simulated daily rainfall is obtained by inverse transformation. We then compare the accumulated simulated and accumulated observed data from the Chao Phraya Basin in Thailand. Because of the stochastic nature at the small scale, the simulated daily rainfall on a point to point comparison show deviations with the observed data. However the accumulated simulated data do show some level of agreement with the observed data.     

TRMM多卫星降水分析资料揭示的青藏高原及其周边地区夏季降水日变化

本文在对比了TRMM多卫星降水分析TMPA(TRMM Multi-satellite Precipitation Analysis)资料和中国643个气象站观测降水量时空分布的基础上,采用2002~2006年夏季TMPA每小时降水量资料,用合成分析和谐波分析的方法研究了青藏高原及其周边地区夏季降水量和降水频率的日变化特征.分析结果表明,平均降水量和降水频率日变化谐波分析的标准振幅显示出青藏高原地区夏季降水具有显著的日变化特征,高原中部地区对流活动日变化最强,其次是高原西南方向的印度半岛地区.谐波分析的位相表明降水量和降水频率最大值出现的时间具有选择性,高原中部降水量最大值多集中在傍晚前后,高原以东的四川盆地通常在夜晚,尤其是在后半夜达到最大值,而长江上游和中下游地区对流活动则分别在上午和下午最为活跃.青藏高原以东地区降水量日变化的位相明显不同于其他陆地地区,也不同于高原中部,具有自西向东传播的信号,四川盆地的夜雨现象可能是高原地区对流活动日变化自西向东传播的结果.     

Linking space–time variability of river runoff and rainfall fields: a dynamic approach

Statistical self-similarity in the spatial and temporal variability of rainfall, river networks, and runoff processes has been observed in many empirical studies. To theoretically investigate the relationships between the various time and space scales of variability in rainfall and runoff process we propose a simplified, yet physically based model of a catchment–rainfall interaction. The channel network is presented as a random binary tree, having topological and hydraulic geometry properties typically observed in real river networks. The continuous rainfall model consists of individual storms separated by dry periods. Each given storm is disaggregated in space and time using the random cascade model. The flow routing is modelled by the network of topologically connected nonlinear reservoirs, each representing a link in the channel network. Running the model for many years of synthetic rainfall time series and a continuous water balance model we generate an output, in the form of continuous time series of water discharge in all links in the channel network. The main subject of study is the annual peak flow as a function of catchment area and various characteristics of rainfall. The model enables us to identify different physical processes responsible for the empirically observed scaling properties of peak flows.     

Analysis and modelling of rainfall fields at different resolutions in southern Italy

Abstract

The spatial and temporal variability of the scaling properties and correlation structure of a data set of rainfall time series, aggregated over different temporal resolutions, and observed in 70 raingauges across the Basilicata and Calabria regions of southern Italy, is investigated. Two types of random cascade model, namely canonical and microcanonical models, were used for each raingauge and selected season. For both models, different hypotheses concerning dependency of parameters on time scale and rainfall height can be adopted. In particular, a new approach is proposed which consists of several combinations of models with a different scale dependence of parameters for different temporal resolutions. The goal is to improve the modelling of the main features of rainfall time series, especially for cases where the variability of rainfall changes irregularly with temporal aggregation. The results obtained with the new methodology showed good agreement with the observed data, in particular, for the summer months. In fact, during this season, rainfall heights aggregated at fine temporal resolutions (from 5 to 20 min) are more similar (relative to the winter season) to the values cumulated on 1 or 3 h (due to convective phenomena) and, consequently, the process of rainfall breakdown is nearly stationary for a range of finer temporal resolutions.

Editor D. Koutsoyiannis; Associate editor A. Montanari     

A hybrid stochastic-weather-generation method for temporal disaggregation of precipitation with consideration of seasonality and within-month variations

Linking atmospheric and hydrological models is challenging because of a mismatch of spatial and temporal resolutions in which the models operate: dynamic hydrological models need input at relatively fine temporal (daily) scale, but the outputs from general circulation models are usually not realistic at the same scale, even though fine scale outputs are available. Temporal dimension downscaling methods called disaggregation are designed to produce finer temporal-scale data from reliable larger temporal-scale data. Here, we investigate a hybrid stochastic weather-generation method to simulate a high-frequency (daily) precipitation sequence based on lower frequency (monthly) amounts. To deal with many small precipitation amounts and capture large amounts, we divide the precipitation amounts on rainy days (with non-zero precipitation amounts) into two states (named moist and wet states, respectively) by a pre-defined threshold and propose a multi-state Markov chain model for the occurrences of different states (also including non-rain days called dry state). The truncated Gamma and censored extended Burr XII distributions are then employed to model the precipitation amounts in the moist and wet states, respectively. This approach avoids the need to deal with discontinuity in the distribution, and ensures that the states (dry, moist and wet) and corresponding amounts in rainy days are well matched. The method also considers seasonality by constructing individual models for different months, and monthly variation by incorporating the low-frequency amounts as a model predictor. The proposed method is compared with existing models using typical catchment data in Australia with different climate conditions (non-seasonal rainfall, summer rainfall and winter rainfall patterns) and demonstrates better performances under several evaluation criteria which are important in hydrological studies.     

Evaluation of multiple stochastic rainfall generators in diverse climatic regions

Long term synthetic precipitation data are useful for water resources planning and management. Commonly stochastic weather generator (SWG) models are useful to produce synthetic time series of unlimited length of weather data based on the statistical characteristics of observed weather at a given location. However, it is difficult to find a single model which works best for all weather (climate) patterns. The objective of this study is to evaluate five different SWG models namely CLIGEN, ClimGen, LARS-WG, RainSim and WeatherMan to generate precipitation at three diverse climatic regions: a Mediterranean climate of western USA, temperate climate of eastern Australia and tropical monsoon region in northern Vietnam. The performance of SWG models to generate precipitation characteristics (i.e., precipitation occurrence; wet and dry spell; and precipitation intensity on wet days) varies between three selected climatic regimes. It was observed that the second order Markov chain (ClimGen and WeatherMan) performed well for all three selected regions in generating precipitation occurrence statistics. All models are able to simulate the ratio of wet/dry spell lengths with respect to observed precipitation. The RainSim performed well in reproducing wet/dry spell lengths in comparison to other models for wetter regions in Australia and Vietnam. ClimGen and WeatherMan are the two best models in simulating precipitation in the western USA, followed by CLIGEN and LARS. Similarly, ClimGen and WMAN are the two best models for synthetic precipitation generation for eastern Australian and northern Vietnam stations, but CLIGEN performs poorly over these regions. All SWG model performed differently with respect to climatic regimes, therefore careful validation is required depending on the weather pattern as well as its application in different water resources sectors. Although our findings are preliminary in nature, however, in order to generalize the performance of SWG’s in a given climate type, it is recommended that more number of stations needs to be evaluated in future studies.     

Discrete cosine transform for parameter space reduction in Bayesian electrical resistivity tomography

Electrical resistivity tomography is a non-linear and ill-posed geophysical inverse problem that is usually solved through gradient-descent methods. This strategy is computationally fast and easy to implement but impedes accurate uncertainty appraisals. We present a probabilistic approach to two-dimensional electrical resistivity tomography in which a Markov chain Monte Carlo algorithm is used to numerically evaluate the posterior probability density function that fully quantifies the uncertainty affecting the recovered solution. The main drawback of Markov chain Monte Carlo approaches is related to the considerable number of sampled models needed to achieve accurate posterior assessments in high-dimensional parameter spaces. Therefore, to reduce the computational burden of the inversion process, we employ the differential evolution Markov chain, a hybrid method between non-linear optimization and Markov chain Monte Carlo sampling, which exploits multiple and interactive chains to speed up the probabilistic sampling. Moreover, the discrete cosine transform reparameterization is employed to reduce the dimensionality of the parameter space removing the high-frequency components of the resistivity model which are not sensitive to data. In this framework, the unknown parameters become the series of coefficients associated with the retained discrete cosine transform basis functions. First, synthetic data inversions are used to validate the proposed method and to demonstrate the benefits provided by the discrete cosine transform compression. To this end, we compare the outcomes of the implemented approach with those provided by a differential evolution Markov chain algorithm running in the full, un-reduced model space. Then, we apply the method to invert field data acquired along a river embankment. The results yielded by the implemented approach are also benchmarked against a standard local inversion algorithm. The proposed Bayesian inversion provides posterior mean models in agreement with the predictions achieved by the gradient-based inversion, but it also provides model uncertainties, which can be used for penetration depth and resolution limit identification.