Huynh Ngoc Phien

Efficient algorithms for Bézier curves

For evaluating Bezier curves, the de Casteljau algorithm is commonly used. Even though it is simple and stable, this algorithm is not efficient. Using the relationships between Bezier curves and two generalized Ball curves, this paper proposes three more efficient algorithms, of which the best has a linear time complexity.

Maximum likelihood estimation of the parameters and quantiles of the general extreme-value distribution from censored samples

Abstract The General Extreme Value (GEV) distribution has become increasingly popular, as has the use of historic information, in flood frequency analysis during recent years. Both call for a systematic investigation of the properties of the maximum likelihood (ML) estimators obtained from censored samples. In this study, such an investigation was made for the type-1 censoring believed to be more frequently encountered in practical situations. All the mathematical equations needed for obtaining the ML estimators of the parameters and the quantiles (represented by the T- year event) were derived and Monte Carlo experiments were carried out to determine their sampling properties. It was found that censoring may reduce the bias of the parameter estimators but does not necessarily increase the variances. It was also found that the variances-covariances of the parameter estimators, and hence the variance of the T- year event, are better approximated by using the observed rather than the Fisher information matrix.

Reservoir storage capacity with gamma inflows

Abstract Reservoir storage capacity determined by the double-cycling sequent peak algorithm has been investigated in previous studies for normal and log-normal inflows. Since annual streamflows have also been found to follow the gamma distribution, it is necessary to consider this situation and to cater for other possible situations. This paper considers the distribution of the storage capacity of reservoirs with gamma inflows that are either independent or first-order autoregressive. Empirical formulae for the mean and standard deviation of the non-dimensional capacity are obtained from Monte Carlo experiments for both full and partial regulation and for the entire realistic range of the lag-one autocorrelation coefficient. It is also confirmed that the standardized capacity may be represented by a three-parameter log-normal distribution.

Applications of the log Pearson type-3 distribution in hydrology

Abstract Although the log Pearson (LP3) type-3 distribution was recommended specifically for flood-frequency analysis, its applicability to annual maximum rainfall, annual streamflow and annual rainfall was also considered in this study. It was found that the LP3 distribution was applicable in most cases; however, for annual flood and maximum rainfall intensity, the existence of an upper bound to the distribution, in some cases, may cause some concerns, while this fact may indicate the suitability of the LP3 distribution for other variables such as annual streamflow and annual rainfall.

A review of single-site models for monthly streamflow generation

Abstract Four important models for the generation of monthly streamflows are considered and modified when needed with the view to reproducing the mean, standard deviation and skewness coefficient of each monthly sequence of the historical records. To evaluate these models, the number of negative values generated and the computer time required are also considered. From the results obtained in actual applications, a suitable model is then recommended.

Rational Wang?Ball curves

Although rational Bézier curves have been commonly used as a base model for curve modelling, rational Wang?Ball curves have been found to be more efficient. The present study introduces rational Wang?Ball curves which are derived from non-rational Wang?Ball curves. It is shown that a rational Wang?Ball curve is a rational Bézier curve of the same degree and vice versa. The relationships between two rational curves established in this paper, allow conversion from one curve to the other. A recursive algorithm for plotting rational Bézier and Wang?Ball curves is obtained from the de Casteljau and Wang algorithm using homogeneous coordinates. An efficient algorithm for evaluating a rational Wang?Ball curve is attained and has a linear time complexity. Finally, another algorithm for rational Bézier curves which has linear time computation is also devised.

A statistical analysis of the sediment volume accumulated in reservoirs

Abstract A statistical method is used to investigate the reservoir sedimentation problem by: (1) correlating the annual sediment discharge and the annual river discharge; (2) using the resulting correlation either to generate a sediment sequence having the same length as the river discharge, or to obtain the distribution of the sediment discharge by means of a transformation of variable; and (3) expressing the accumulated volume as the cumulative sum of a sequence of random variables. Assuming a reservoir trap efficiency equal to unity, this cumulative sum is the partial sum of annual sediment discharges. The investigation then concentrates on the derivation of the mean and variance of the sediment volume accumulated in the design lifetime of the reservoir.

Rainfall distribution in northeastern Thailand / Sur la distribution de pluie dans le nord-est de Thailande

Abstract Rainfall is the main source of irrigation water in the northeastern part of Thailand where the inhabitants derive their income primarily from farming. In order to improve their economic conditions, the efficient use of available water is essential and this requires a sound understanding of the distribution of rainfall in space and in time. The present study aims at providing basic information on rainfall sequences in the region, such as their amount and their distribution in space and time. Several other statistical properties such as the persistence, the periodicity and the degree of irregularity of rainfall and the transition probabilities between rainy and non-rainy days are presented. An assessment of the availability of water for irrigation is also made.

Estimating the Parameters of the Generalized Gamma Distribution by Mixed Moments

Having three parameters but many possible forms, the generalized gamma (GG) distribution can be a good candidate for flood frequency analysis. In this study, four methods of parameter estimation were introduced, and sampling variances and covariances of the parameter estimators ewrw analytically derived along with the variance of the T-year flood event. For 45 sets of annual flood data taken from different sources, the GG distribution was found to provide good fits when the above methods were employed. Moreover, it was also found that although the sampling variances of the estimators were high, the percent standard error of the T-year flood was relatively small. Thus use of the GG distribution and these methods would provide good design flood magnitudes at appropriately determined return periods.

Applicability of the Johnson SB-curve to annual stream-flow distributions

Abstract The applicability of the Johnson S B -curve to the modelling of annual streamflows is evaluated with the use of actual data. The methods for its parameter estimation are summarized and later discussed based on the results obtained.