Multiplicative Cascade Model Research Articles

Detection and characterization of scale-invariant behaviour and stochastic downscaling of terrestrial water storage anomalies from GRACE and GPS

ABSTRACT Gravity Recovery and Climate Experiments (GRACE) based terrestrial water storage anomalies (TWSA) are used to characterize large-scale hydrology and to estimate regional groundwater depletion around the globe. Due to their 0.25° resolution, GRACE TWSA do not capture fine-resolution variations in TWSA and can miss the extreme TWSA values within a region. This study aims to develop a stochastic downscaling method that relies only on TWSA data and generates realistic statistical properties of fine resolution (0.0625°) TWSA patterns. It is hypothesized that TWSA are scale invariant, which allows the statistical properties of fine scale variations to be inferred from those of coarse scale variations. Three study regions are considered including the Central Amazon in Brazil, the Sindh province in Pakistan, and a region around California, U.S.A. For each region, the relationships between the TWSA moments and the spatial resolution are examined for resolutions between 0.25° and 4°. Nonlinear relationships between scaling exponents and the moment orders indicate that multifractality occurs for the three regions, but the multifractality differs between the three regions and between wet and dry conditions. Based on these results, a multiplicative random cascade model is developed to downscale the TWSA. When the model is used to downscale to 0.0625°, it can produce wider ranges of TWSA within the region than the coarse resolution input.

Development of an inclusive, scalable, and flexible hydrologic modeling system: Establishing integrated flood simulation system at agricultural watersheds

In this study, we developed a comprehensive hydrological modeling system to address the diverse needs of hydrologists and researchers. The system comprised nine modules, each serving a specific purpose. These modules include a multiplicative random cascade model, frequency analysis, inflow simulation, Hydrologic Engineering Center – 5, Hydrologic Engineering Center – River Analysis System, and farmland drainage simulations. The system follows a structured sequence within a large framework, beginning with user inputs for the initial condition information and period specifications for frequency analysis. It then calculates the time-disaggregated precipitation data utilizing the Dask distributed server for efficient computation. Subsequent module computations were conducted on dedicated mask workers. The Integrated Database serves as a comprehensive repository for simulation studies, encompassing historical precipitation data, shared socioeconomic pathways, climate change scenario data, and reservoir and farmland survey data. This system has been used in several studies and has provided cohesive and reliable results for flood simulations.

Evaluation of future flood probability in agricultural reservoir watersheds using an integrated flood simulation system

In agricultural reservoir watersheds, the presence of various agricultural hydraulic structures combined with the influence of climate change necessitates effective flood risk analysis. This study aims to develop a flood risk evaluation technique for agricultural basins by incorporating the low temporal resolution of climate change scenarios. The approach utilizes flood probability as a key component and incorporates the Multiplicative Random Cascade model as a probability-based rainfall time decomposition model to capture the inherent uncertainty in climate change data. Reliability analysis with the limit state equation is employed for probability-based risk evaluation. Given that agricultural watersheds typically consist of agricultural reservoirs and farmland, the study develops a hydraulic and hydrological linkage model to comprehensively calculate flood probability, simulating from the agricultural reservoir in the upper side to the farmland located at the bottom edge of the watershed. The flood risk assessment is applied to the Yedang Reservoir watershed in Korea, using the Shared Socio-economic Pathways climate change scenario. Results indicate that flood probability is the highest in river levees during future precipitation events, converging to nearly 100% under 24-hour duration rainfall, irrespective of the rain frequency. Despite the hydraulic structures at the farmland being designed for a lower frequency of rain events, the average probability of flooding in the farmland have reached 50%. The agricultural reservoir exhibits a low risk of flooding even under climate change conditions. The proposed method not only enables the establishment of flood countermeasures but also facilitates the evaluation and prediction of future flood risk for each hydraulic structure located in rural areas affected by climate change.

Introduction of k-means clustering into random cascade model for disaggregation of rainfall from daily to 1-hour resolution with improved preservation of extreme rainfall

Temporal disaggregation of rainfall has been of particular focus because of the non-availability of higher-resolution rainfall data for a long-duration period. Fine temporal resolution rainfall is used in a multitude of hydrological applications. Researchers have proposed various disaggregation models to disaggregate coarse temporal resolution rainfall. In this paper, firstly, the microcanonical multiplicative random cascade (MMRC) model is applied for disaggregation from daily rainfall to a one-hour scale. The model is applied in four different rainfall stations for disaggregation having varying rainfall patterns and characteristics. It is observed that the MMRC model can generate statistically reliable rainfall time series; however, the extreme rainfall characteristics are not well conserved by the model for all the stations.This paper describes a new model based on a random multiplicative cascade process where classification and parameter generation is done by k-means clustering such that it can better conserve extreme rainfall conditions and generate a reliable rainfall time series (MMRC-K). K-means clustering is a vector quantization method that divides the observations into a particular number of clusters based on the nearest mean called cluster centroid. The novel approach is tested with the same four Indian cities. The use of k-means clustering has made the classification and parameter generation of the model robust such that it can work with data sets of varying characteristics. It is found that MMRC-K provides improved conservation of extreme rainfall characteristics compared to the MMRC model for all four stations. The MMRC-K model reproduces the IDF curves of Delhi and Mumbai stations quite well; however, a little discrepancy was observed at higher resolution and larger return periods in Kolkata and Chennai stations. Extreme rainfall at finer resolution is used in various hydrological analyses and design problems like urban drainage design, stormwater management, etc. The overall superior conservation of the extreme rainfall characteristics in the model-generated rainfall time series by the MMRC-K model compared to the MMRC model supports the potential applicability of the model for temporal disaggregation.

Assessing the performance of daily to subdaily temporal disaggregation methods for the IDF curve generation under climate change

AbstractGiven the short concentration time in urban watersheds, the design of municipal water infrastructures often requires knowledge of sub-daily precipitation intensity. Sub-daily time series can be directly used in a rainfall–runoff model or to derive intensity–duration–frequency (IDF) curves and calculate the design precipitation. Given that precipitation projections are typically at a daily time scale, temporal disaggregation using techniques of variable complexity is often needed to evaluate the risk/performance of urban infrastructure in the future. This paper proposes a simple steady-state stochastic disaggregation model that generates wet/dry day occurrence using a binomial distribution and precipitation intensity using an exponential distribution. Daily precipitation data from four regional climate models (RCMs) forced with the high-emission scenario representative concentration pathway (RCP 8.5) were downscaled using the quantile mapping (QM) method. The performance of the developed method is compared to widely used temporal disaggregation methods, namely, the multiplicative random cascade model (MRC), the Hurst–Kolmogorov process (HKP), and three versions of the K-nearest neighbour (KNN) model, using the Kolmogorov–Smirnov (KS) test. The six disaggregation techniques were assessed at four stations in the South Nation River Watershed in Eastern Ontario, Canada. Results indicate that, despite its simplicity, the proposed method performed well compared to other temporal disaggregation methods when resampling the observed extreme precipitation.

A User Centric Blockage Model for Wireless Networks

This paper proposes a cascade blockage model for analyzing the vision that a user has of a wireless network. This model, inspired by the classical multiplicative cascade models, has a radial structure meant to analyze blockages seen by the receiver at the origin in different angular sectors. The main novelty is that it is based on the geometry of obstacles and takes the joint blockage phenomenon into account. We show on a couple of simple instances that the Laplace transforms of total interference satisfies a functional equation that can be solved efficiently by an iterative scheme. This is used to analyze the coverage probability of the receiver and the effect of blockage correlation and penetration loss in both dense and sparse blockage environments. Furthermore, this model is used to investigate the effect of blockage correlation on user beamforming techniques. Another functional equation and its associated iterative algorithm are proposed to derive the coverage performance of the best beam selection in this context. In addition, the conditional coverage probability is also derived to evaluate the effect of beam switching. The results not only show that beam selection is quite efficient for multi-beam terminals, but also show how the correlation brought by blockages can be leveraged to accelerate beam sweeping and pairing.

Comparison of rainfall generators with regionalisation for the estimation of rainfall erosivity at ungauged sites

Abstract. Rainfall erosivity values are required for soil erosion prediction. To calculate the mean annual rainfall erosivity (R), long-term high-resolution observed rainfall data are required, which are often not available. To overcome the issue of limited data availability in space and time, four methods were employed and evaluated: direct regionalisation of R, regionalisation of 5 min rainfall, disaggregation of daily rainfall into 5 min time steps, and a regionalised stochastic rainfall model. The impact of station density is considered for each of the methods. The study is carried out using 159 recording and 150 non-recording (daily) rainfall stations in and around the federal state of Lower Saxony, Germany. In addition, the minimum record length necessary to adequately estimate R was investigated. Results show that the direct regionalisation of mean annual erosivity is best in terms of both relative bias and relative root mean square error (RMSE), followed by the regionalisation of the 5 min rainfall data, which yields better results than the rainfall generation models, namely an alternating renewal model (ARM) and a multiplicative cascade model. However, a key advantage of using regionalised rainfall models is the ability to generate time series that can be used for the estimation of the erosive event characteristics. This is not possible if regionalising only R. Using the stochastic ARM, it was assessed that more than 60 years of data are needed in most cases to reach a stable estimate of annual rainfall erosivity. Moreover, the temporal resolution of measuring devices was found to have a significant effect on R, with coarser temporal resolution leading to a higher relative bias.

Wind speed forecasting using a hybrid model considering the turbulence of the airflow

This work presents the conformation of a hybrid model aimed at forecasting the wind speed one step ahead. The model comprises the Multiplicative Cascade and Persistence. To couple both techniques, a transition point was used, in this case, 6.6 m/s, defined from the spectrum of wind speed near the ground. The Multiplicative Cascade was used when speeds were higher than the transition point, while Persistence was used when lower. Two time series measured in Tamaulipas and Veracruz, Mexico, were used to build the hybrid model. The performance of the individual models concerning the hybrid model was compared, finding that the adjustment of the hybrid model exceeds that of the Multiplicative Cascade and Persistence models for both series. Different error metrics were used in the quantitative analysis, where the hybrid model was the most competitive. For example, in Mean Absolute Percentage Error, the difference in performance between the hybrid model and Persistence is 2.72% points for the 10-min time series. In contrast, this difference is 27.89% points for the hourly time series. Finally, this work shows that for the cases analyzed, differentiating the effects of turbulent from non-turbulent flows and modeling with the proper techniques improves forecasting accuracy.

Multiplicative random cascade models of multifractal urban structures

Spatial structures of urban systems are best described as multifractals. To provide insight on a hidden mechanism responsible for such scaling we investigate the multiplicative random cascade (MRC) model of urban spatial structure. MRC is a multiplicative process capable of producing multifractal 2D patterns, which is expressed in a closed analytical form. We use street intersection points pattern (SIPP) data as a proxy of urban structure. Renyi’s generalized dimensions (RGD) spectra, probability distributions of intersections densities, and urban layouts generated by the MRC model are compared to the same descriptors extracted from SIPP data for six U.S. metropolitan statistical areas (MSAs). We found that the RGD spectrum of the best-fit MRC model closely matches the observed spectrum in all cases. We also found that CDF of models’ density distributions do not match closely observed density distributions, although, in some cases, differences are not large. Observed density distributions have forms that are close to the log-normal distribution which suggests that a hidden process is multiplicative. Finally, we found that the MRC model is broadly compatible with the observed urban layouts. Given our findings, we suggest that the hidden process of urban scaling is the preferential attachment dynamics — development is attracted to areas in proportion to the degree of their existing development.

Wind speed forecasting by the extraction of the multifractal patterns of time series through the multiplicative cascade technique

In this work, the forecasting errors produced by the Autoregressive Integrated Moving Average, Deep Learning, and Persistence models were analyzed when these models were applied to two time series for predicting the wind speed one-step-ahead. The analysis consisted of verified, with the aid of the Multifractal Detrended Fluctuation Analysis, whether there were multifractal patterns in the forecasting errors. Then, the multifractal patterns of the errors were extracted by a Multiplicative Cascade model. The sum of the patterns extracted from the models generated new hybrid models such as Autoregressive Integrated Moving Average-Multiplicative Cascade, Deep Learning-Multiplicative Cascade, and Persistence-Multiplicative Cascade. Those new models showed a diminution of the final forecasting error. The wind speed time series used for this study were measured at two wind farms of the State of Oaxaca, Mexico, namely La Mata and La Venta. The first time series has five years of ten-minutes averaged data, while the second one has six years and eleven months of hourly data. Both time series were provided by Mexico’s Federal Electricity Commission. The typical performance metrics tools were used for the quantitative analysis of the forecasting results, where the simple models were compared against the hybrid models by using the Mean Squared Error, the Mean Absolute Error, the Root Mean Squared Error, the Mean Absolute Percentage Error, and the Inter-rater Agreement. The latter was done to find out the actual input in a one-step-ahead forecast. The obtained results showed a gain between 0.331% and 5.285% in the fit of hybrid models in the metrics, which demonstrates the convenience of analyzing the forecasting errors generated by the models aforementioned to improve forecasts and therefore help in planning and dispatching energy flow.

A new discrete multiplicative random cascade model for downscaling intermittent rainfall fields

Abstract. Spatial downscaling of rainfall fields is a challenging mathematical problem for which many different types of methods have been proposed. One popular solution consists of redistributing rainfall amounts over smaller and smaller scales by means of a discrete multiplicative random cascade (DMRCs). This works well for slowly varying homogeneous rainfall fields but often fails in the presence of intermittency (i.e., large amounts of zero rainfall values). The most common workaround in this case is to use two separate cascade models, namely one for the occurrence and another for the intensity. In this paper, a new and simpler approach based on the notion of equal-volume areas (EVAs) is proposed. Unlike classical cascades where rainfall amounts are redistributed over grid cells of equal size, the EVA cascade splits grid cells into areas of different sizes, with each of them containing exactly half of the original amount of water. The relative areas of the subgrid cells are determined by drawing random values from a logit-normal cascade generator model with scale and intensity-dependent standard deviation (SD). The process ends when the amount of water in each subgrid cell is smaller than a fixed-bucket capacity, at which point the output of the cascade can be resampled over a regular Cartesian mesh. The present paper describes the implementation of the EVA cascade model and gives some first results for 100 selected events in the Netherlands. Performance is assessed by comparing the outputs of the EVA model to bilinear interpolation and to a classical DMRC model based on fixed grid cell sizes. Results show that, on average, the EVA cascade outperforms the classical method, producing fields with more realistic distributions, small-scale extremes and spatial structures. Improvements are mostly credited to the higher robustness of the EVA model in the presence of intermittency and to the lower variance of its generator. However, both approaches have their advantages and weaknesses. For example, while the classical cascade tends to overestimate small-scale variability and extremes, the EVA model tends to produce fields that are slightly too smooth and block shaped compared to the observations. The complementary nature of the two approaches, and the fact that they produce errors of opposite signs, opens up new possibilities for quality control and bias corrections of downscaled fields.

A Typical Foreshock and Aftershock Anomaly: Observations, Interpretation, and Applications

Previous publications by this author (Rodkin, 2008a, 2008b, 2012; Rodkin and Tikhonov, 2016; Rodkin and Rundkvist, 2017) proposed and actually used a method for constructing and analyzing the generalized vicinity of large earthquakes (GVLE). The GVLE method provides an enormous increase in the amount of data that is used and, hence, a much more detailed description of the typical features in the foreshock–aftershock process. The GVLE clearly detects the power-law foreshock seismicity increase and the aftershock process obeying the Omori–Utsu law. In addition, many parameters (the slope of the recurrence plot and the average depths of focus, apparent stresses, the duration of the seismic process, and several other quantities) show, when treated in the GVLE framework, similar anomalies whose amplitudes are increasing toward the time of the generalized large earthquake minus the logarithm of the time remaining until the occurrence. Similar anomalies (more frequently with different parameters) are observed both in the foreshock area and in the aftershock area. Because the anomalies are so similar we are entitled to treat them as a seismicity pattern. Precursory anomalies are of special interest. We discuss the question of which of these are primary and which are secondary. The anomaly is interpreted in terms of the multiplicative cascade model. An analogy in the character of this anomaly with Zhurkov’s concept of kinetic failure exists. We discuss the approaches to the use of the anomaly in earthquake prediction.

Temperature-Driven Rise in Extreme Sub-Hourly Rainfall

AbstractEstimates of present and future extreme sub-hourly rainfall are derived from a daily spatial followed by a sub-daily temporal downscaling, the latter of which incorporates a novel, and crucial, temperature sensitivity. Specifically, daily global climate fields are spatially downscaled to local temperature T and precipitation P, which are then disaggregated to a temporal resolution of 10 min using a multiplicative random cascade model. The scheme is calibrated and validated with a group of 21 station records of 10-min resolution in Germany. The cascade model is used in the classical (denoted as MC) and in the new T-sensitive (MC+) version, which respects local Clausius–Clapeyron (CC) effects such as CC scaling. Extreme P is positively biased in both MC versions. Observed T sensitivity is absent in MC but well reproduced by MC+. Long-term positive trends in extreme sub-hourly P are generally more pronounced and more significant in MC+ than in MC. In units of 10-min rainfall, observed centennial trends in annual exceedance counts (EC) of P > 5 mm are +29% and in 3-yr return levels (RL) +27%. For the RCP4.5-simulated future, higher extremes are projected in both versions MC and MC+: per century, EC increases by 30% for MC and by 83% for MC+; the RL rises by 14% for MC and by 33% for MC+. Because the projected daily P trends are negligible, the sub-daily signal is mainly driven by local temperature.

Does the complexity in temporal precipitation disaggregation matter for a lumped hydrological model?

ABSTRACT Flood peaks and volumes are essential design variables and can be simulated by precipitation–runoff (P–R) modelling. The high-resolution precipitation time series that are often required for this purpose can be generated by various temporal disaggregation methods. Here, we compare a simple method (M1, one parameter), focusing on the effective precipitation duration for flood simulations, with a multiplicative cascade model (M2, 32/36 parameters). While M2 aims at generating realistic characteristics of precipitation time series, M1 aims only at accurately reproducing flood variables by P–R modelling. Both disaggregation methods were tested on precipitation time series of nine Swiss mesoscale catchments. The generated high-resolution time series served as input for P–R modelling using a lumped HBV model. The results indicate that differences identified in precipitation characteristics of disaggregated time series vanish when introduced into the lumped hydrological model. Moreover, flood peaks were more sensitive than flood volumes to the choice of disaggregation method.

Application of the multiplicative cascade model for the description of the seismic regime and for the seismic hazard assessment

Seismic process is usually considered as a realization of the regime of self-organizing criticality (SOC-model). This model meets, however, definite problems, besides it gives only a statistical description of the seismic regime. The multiplicative cascade model (MCM) treats the seismic regime as an assemblage of randomly developing episodes of avalanche-like relaxation, occurring in a set of similar metastable sub-systems. In the simplest linear variant without memory the MCM is defined by the flow of events and by two parameters characterizing the hierarchical structure and the level of metastability of a geophysical medium. An advantage of such approach consists in a clear physical sense of character of the model. The MCM model b-value behavior is compared with the complex of typical anomalies revealed in result of examination of a large earthquake generalized vicinity (LEGV). The LEGV vicinity is constructed of earthquakes falling into the zones of influence of a large number (300, 500, or 1000) of largest earthquakes. The construction and examination of LEGV gives possibility to increase radically the available statistics, crucially diminish a random component of the seismic regime, and in result to reveal the typical features of pre- and post-shock seismic activity in details. The combined use of MCM and LEGV methods gives possibility to interpret a few features of the seismic regime and to suggest the typical scenario of the fore- and aftershock regimes of seismicity. The possibilities of application of the obtained results for earthquake prediction are discussed.

Stochastic Space‐Time Downscaling of Rainfall Using Event‐Based Multiplicative Cascade Simulations

AbstractA multiplicative cascade model called High‐resolution Downscaling of Rainfall Using Short‐Term Ensemble Prediction System (HiDRUS) is developed and tested in the greater Melbourne region (Australia) by downscaling coarse‐resolution ERA‐I rainfall to 1‐km horizontal and 6‐min temporal resolutions. The parameters required for the cascade model are computed from radar observations of rain events during 2008–2015, and a library of rainfall events and their associated synoptic conditions created. Each day, the area‐averaged rainfall and synoptic conditions are taken from ERA‐I and compared with the library. From the library, similar days are chosen randomly and downscaled using the cascade model. Ensembles of 100 realizations per day are produced for the period 1995–2004. The downscaled rainfall is compared with 6‐min rain gauges and daily gridded rain gauge data at four locations in the greater Melbourne region. HiDRUS reproduces the monthly variability of rainfall, frequency distribution of daily and 6‐min rainfall, and the autocorrelation function satisfactorily. Changes in heavy rainfall are also captured by HiDRUS but with increasing uncertainty as the intensities increase.

Multiplicative random cascades with additional stochastic process in financial markets

Multiplicative random cascade model naturally reproduces the intermittency or multifractality, which is frequently shown among hierarchical complex systems such as turbulence and financial markets. As described herein, we investigate the validity of a multiplicative hierarchical random cascade model through an empirical study using financial data. Although the intermittency and multifractality of the time series are verified, random multiplicative factors linking successive hierarchical layers show strongly negative correlation. We extend the multiplicative model to incorporate an additional stochastic term. Results show that the proposed model is consistent with all the empirical results presented here.

TEMPORAL RAINFALL DISAGGREGATION BY A SIMPLE RANDOM CASCADE MODEL

This study evaluates the utility and suitability of a simple discrete multiplicative random cascade model for temporal rainfall disaggregation. Two of a simple random cascade model, namely log-Poisson and log-Normal models are applied to simulate hourly rainfall from daily rainfall at seven rain gauge stations in Peninsular Malaysia. The cascade models are evaluated based on the capability to simulate data that preserve three important properties of observed rainfall: rainfall variability, intermittency and extreme events. The results show that both cascade models are able to simulate reasonably well the commonly used statistical measures for rainfall variability (e.g. mean and standard deviation) of hourly rainfall. With respect to rainfall intermittency, even though both models are underestimated, the observed dry proportion, log-Normal model is likely to simulate number of dry spells better than log-Poisson model. In terms of rainfall extremes, it is demonstrated that log-Poisson and log-Normal models gave a satisfactory performance for most of the studied stations herein, except for Dungun and Kuala Krai stations, which both located in the east part of Peninsula.

A minimal rupture cascade model for living cell plasticity

Under physiological and pathological conditions, cells experience large forces and deformations that often exceed the linear viscoelastic regime. Here we drive CD34+ cells isolated from healthy and leukemic bone marrows in the highly nonlinear elasto-plastic regime, by poking their perinuclear region with a sharp AFM cantilever tip. We use the wavelet transform mathematical microscope to identify singular events in the force-indentation curves induced by local rupture events in the cytoskeleton (CSK). We distinguish two types of rupture events, brittle failures likely corresponding to irreversible ruptures in a stiff and highly cross-linked CSK and ductile failures resulting from dynamic cross-linker unbindings during plastic deformation without loss of CSK integrity. We propose a stochastic multiplicative cascade model of mechanical ruptures that reproduces quantitatively the experimental distributions of the energy released during these events, and provides some mathematical and mechanistic understanding of the robustness of the log-normal statistics observed in both brittle and ductile situations. We also show that brittle failures are relatively more prominent in leukemia than in healthy cells suggesting their greater fragility.

Coupling Poisson rectangular pulse and multiplicative microcanonical random cascade models to generate sub-daily precipitation timeseries

To simulate the impacts of within-storm rainfall variabilities on fast hydrological processes, long precipitation time series with high temporal resolution are required. Due to limited availability of observed data such time series are typically obtained from stochastic models. However, most existing rainfall models are limited in their ability to conserve rainfall event statistics which are relevant for hydrological processes. Poisson rectangular pulse models are widely applied to generate long time series of alternating precipitation events durations and mean intensities as well as interstorm period durations. Multiplicative microcanonical random cascade (MRC) models are used to disaggregate precipitation time series from coarse to fine temporal resolution.To overcome the inconsistencies between the temporal structure of the Poisson rectangular pulse model and the MRC model, we developed a new coupling approach by introducing two modifications to the MRC model. These modifications comprise (a) a modified cascade model (“constrained cascade”) which preserves the event durations generated by the Poisson rectangular model by constraining the first and last interval of a precipitation event to contain precipitation and (b) continuous sigmoid functions of the multiplicative weights to consider the scale-dependency in the disaggregation of precipitation events of different durations.The constrained cascade model was evaluated in its ability to disaggregate observed precipitation events in comparison to existing MRC models. For that, we used a 20-year record of hourly precipitation at six stations across Germany. The constrained cascade model showed a pronounced better agreement with the observed data in terms of both the temporal pattern of the precipitation time series (e.g. the dry and wet spell durations and autocorrelations) and event characteristics (e.g. intra-event intermittency and intensity fluctuation within events). The constrained cascade model also slightly outperformed the other MRC models with respect to the intensity-frequency relationship.To assess the performance of the coupled Poisson rectangular pulse and constrained cascade model, precipitation events were stochastically generated by the Poisson rectangular pulse model and then disaggregated by the constrained cascade model. We found that the coupled model performs satisfactorily in terms of the temporal pattern of the precipitation time series, event characteristics and the intensity-frequency relationship.