Gamma random field simulation by a covariance matrix transformation method

Liou, Jyh‐Ming; Su, Yuan; Chiang, Jui-Kun; Cheng, Kit‐Yan

doi:10.1007/s00477-010-0434-8

Cited by 7 publications

(9 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Readers are referred to Cheng et al (2011) for details of the bivariate gamma simulation. Liou et al (2011) extended the BVG-FF approach to gamma random field simulation through a covariance matrix transformation method. The multisite joint gamma simulation can be considered as a simplified case of the gamma random field simulation.…”

Section: Multisite Simulation Of Event-total Rainfallsmentioning

confidence: 99%

Assessing the impact of climate change on basin-average annual typhoon rainfalls with consideration of multisite correlation

Hou

Liou

et al. 2011

Paddy Water Environ

Self Cite

View full text Add to dashboard Cite

The effects of climate change on synoptic scale storms like typhoons can have profound impacts on practices of water resources management. A stochastic multisite simulation approach is proposed for assessing the impact of climate changes on basin-average annual typhoon rainfalls (BATRs) under certain synthesized climate change scenarios. Number of typhoon events and event-total rainfalls are considered as random variables characterized by the Poisson and gamma distributions, respectively. The correlation structure of event-total rainfalls at different rainfall stations is found to be significant (higher than 0.80) and plays a crucial role in the proposed stochastic simulation approach. Basin-average annual typhoon rainfalls were simulated for the Shihmen Reservoir watershed in northern Taiwan by considering changes in the mean values of annual number of typhoon events and event-total rainfalls, while assuming the correlation structure of multisite typhoon rainfalls to remain unchanged. The simulation results indicate that changes in expected values of BATR can be easily projected with simpler models; however, changes in extreme properties of BATR are more complicated. Comparing to changes in expected values of BATRs, lesser changes in more extreme events can be observed. This is due to the reduction in coefficient of skewness of gamma distribution BATR under different climate change scenarios. With consideration of the multisite correlation structure, changes in BATRs become more significant. Thus, in assessing the impacts of climate change on many hydrological and environmental variables which exhibit significant spatial correlation pattern, the multisite correlation structure needs to be taken into consideration.

show abstract

Section: Multisite Simulation Of Event-total Rainfallsmentioning

confidence: 99%

Assessing the impact of climate change on basin-average annual typhoon rainfalls with consideration of multisite correlation

Hou

Liou

et al. 2011

Paddy Water Environ

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, many hydrological and environmental variables are asymmetric and cannot be modeled as Gaussian random fields. Liou et al (2011) proposed a covariance matrix transformation method for an isotropic non-Gaussian random field simulation in a 2D spatial domain. This study deals with variations of streamflows in both the temporal and spatial domains.…”

Section: Spatiotemporal Model Building and Stochastic Simulation Of Tmentioning

confidence: 99%

“…This study deals with variations of streamflows in both the temporal and spatial domains. Thus, an anisotropic spatiotemporal semi-variogram model was introduced into the method of Liou et al (2011) to achieve the anisotropic stochastic simulation of multi-site streamflows. Figure 5 illustrates the conceptual process for stochastic simulation of a Pearson type III random field.…”

Section: Spatiotemporal Model Building and Stochastic Simulation Of Tmentioning

confidence: 99%

“…C Z (h) and C W (h) is equivalent to conversion between the covariance matrices Σ Z and Σ W (Liou et al 2011). Since the multi-site standardized flows are modeled as a Pearson type III random field, conversion between covariance matrices of the Pearson type III random field and the standard Gaussian random field (i.e., Σ Z and Σ W , respectively) is needed for subsequent sequential Gaussian simulation.…”

Section: Spatiotemporal Model Building and Stochastic Simulation Of Tmentioning

confidence: 99%

“…Conversion between the two bivariate covariance matrices (Σ Z and Σ W ) can be achieved using the following equation (Cheng et al 2011): where ρ Z 1 Z 2 and ρ W 1 W 2 are, respectively, the correlation coefficients of the bivariate Pearson type III distribution and the bivariate standard Gaussian distribution and γ represents the coefficient of skewness of the Pearson type III distribution. The constants A, B, and C are defined by Once the covariance matrix of the standard Gaussian random field is obtained, sequential Gaussian simulation is conducted to generate realizations of the standard Gaussian random field (Liou et al 2011). Our sequential Gaussian simulation is depicted in Fig.…”

Section: Spatiotemporal Model Building and Stochastic Simulation Of Tmentioning

confidence: 99%

See 2 more Smart Citations

Water shortage risk assessment using spatiotemporal flow simulation

Hsieh

et al. 2016

Geosci. Lett.

Self Cite

View full text Add to dashboard Cite

Paddy irrigation practices in Taiwan utilize complicated water conveyance networks which draw streamflows from different tributaries. Characterizing and simulating streamflow series is thus an essential task for irrigation risk assessment and planning mitigation measures. It generally involves modeling the temporal variation and spatial correlation of streamflow data at different sites. Like many other environmental variables, streamflows are asymmetric and non-Gaussian. Such properties exacerbate the difficulties in spatiotemporal modeling of streamflow data. A stochastic spatiotemporal simulation approach capable of generating non-Gaussian ten-day period streamflow data series at different sites is presented in this paper. Historical flow data from different flow stations in southern Taiwan were used to exemplify the application of the proposed model. Simulated realizations of the spatiotemporal anisotropic multivariate Pearson type III distribution were validated by comparing parameters and spatiotemporal correlation characteristics of the simulated data and the observed streamflow data. Risks of irrigation water shortage were estimated and the effect of mitigation measures was assessed using the simulated data.

show abstract

Some enhancements to DeepKriging

Lin

Huang

Tzeng

2023

Stat

View full text Add to dashboard Cite

With an increased volume of spatial data, conventional spatial prediction methods have encountered significant challenges in handling complex data structures while maintaining statistical and computational efficiency. Recently, a spatial neural network method called DeepKriging has been proposed, which utilizes a set of basis functions as an embedded input to capture spatial information. In this study, we enhance this approach by using an ordered set of multi‐resolution thin plate spline basis functions, which offers ease of implementation and alleviates the challenges associated with basis function allocation, particularly when the data locations are highly irregular. The proposed method requires only the selection of the number of basis functions based on a validation dataset. In addition, we propose a robust version of DeepKriging, which is resistant to outliers. Several simulation experiments are conducted to show the advantages of our method over conventional statistical methods and the original DeepKriging approach. Finally, we apply the proposed method to a PM2.5 dataset in Taiwan.

show abstract

Gamma random field simulation by a covariance matrix transformation method

Cited by 7 publications

References 27 publications

Assessing the impact of climate change on basin-average annual typhoon rainfalls with consideration of multisite correlation

Assessing the impact of climate change on basin-average annual typhoon rainfalls with consideration of multisite correlation

Water shortage risk assessment using spatiotemporal flow simulation

Some enhancements to DeepKriging

Contact Info

Product

Resources

About