scholarly journals Runoff Potentiality of a Watershed through SCS and Functional Data Analysis Technique

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
M. I. Adham ◽  
S. M. Shirazi ◽  
F. Othman ◽  
S. Rahman ◽  
Z. Yusop ◽  
...  
Keyword(s):  
Fourier Series ◽  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Surface Runoff ◽  
Hydrological Modeling ◽  
Smooth Curve ◽  
Curve Number ◽  
Periodic Pattern ◽  
Analysis Technique

Runoff potentiality of a watershed was assessed based on identifying curve number (CN), soil conservation service (SCS), and functional data analysis (FDA) techniques. Daily discrete rainfall data were collected from weather stations in the study area and analyzed through lowess method for smoothing curve. As runoff data represents a periodic pattern in each watershed, Fourier series was introduced to fit the smooth curve of eight watersheds. Seven terms of Fourier series were introduced for the watersheds 5 and 8, while 8 terms of Fourier series were used for the rest of the watersheds for the best fit of data. Bootstrapping smooth curve analysis reveals that watersheds 1, 2, 3, 6, 7, and 8 are with monthly mean runoffs of 29, 24, 22, 23, 26, and 27 mm, respectively, and these watersheds would likely contribute to surface runoff in the study area. The purpose of this study was to transform runoff data into a smooth curve for representing the surface runoff pattern and mean runoff of each watershed through statistical method. This study provides information of runoff potentiality of each watershed and also provides input data for hydrological modeling.

Smoothing Wind and Rainfall Data through Functional Data Analysis Technique

2015 ◽  
Vol 74 (1) ◽  
Author(s):  
W. I. Wan Norliyana ◽  
Jamaludin Suhaila
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Smooth Curve ◽  
Peninsular Malaysia ◽  
Least Square ◽  
Rainfall Data ◽  
Periodic Pattern ◽  
Contour Plot ◽  
Roughness Penalty

The pattern of wind and rainfall throughout Peninsular Malaysia are varied from one region to another, because of strong influences from the monsoons. In order to capture the wind and rainfall variations, a functional data analysis is introduced. The purpose of this study is to convert the wind and rainfall data into a smooth curve by using functional data analysis method. Fourier basis is used in this study since the wind and rainfall data indicated periodic pattern. In order to avoid such overfitting data, roughness penalty is added to the least square when constructing functional data object from the observed data. Result indicated that if we use a small number of bases functions, the difference is very small between with and without roughness penalty, showing that it is safer to smooth only when required. However, when a large basis function is employed, the roughness penalty should be added in order to obtain optimal fit data. Based on the contour plot of correlation and cross-correlation functions of wind and rainfall data, the relationship between both climate functions could be determined.  

Comparing rainfall patterns between regions in Peninsular Malaysia via a functional data analysis technique

2011 ◽  
Vol 411 (3-4) ◽  
pp. 197-206 ◽  
Author(s):  
Jamaludin Suhaila ◽  
Abdul Aziz Jemain ◽  
Muhammad Fauzee Hamdan ◽  
Wan Zawiah Wan Zin
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Peninsular Malaysia ◽  
Data Analysis Technique ◽  
Analysis Technique ◽  
Rainfall Patterns

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

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