Fang Xin Yu

Parameter estimation for 3-parameter log-logistic distribution (LLD3) by Pome

The principle of maximum entropy (POME) was employed to derive a new method of parameter estimation for the 3-parameter log-logistic distribution (LLD3). Monte Carlo simulated data were used to evaluate this method and compare it with the methods of moments (MOM), probability weighted moments (PWM), and maximum likelihood estimation (MLE). Simulation results showed that POMEs performance was superior in predicting quantiles of large recurrence intervals when population skew was greater than or equal to 2.0. In all other cases, POMEs performance was comparable to other methods.

A rainfall-runoff model for small watersheds

Abstract A rainfall-runoff model was developed by combining the excess-rainfall process and the runoff-concentration process. The excess rainfall was modeled by using the two-parameter Green-Ampt infiltration approach. A six-parameter linear-discrete model was used to model the runoff hydrograph. The infiltration parameters were estimated by using the simplex method, and the runoff parameters by least squares. The model was calibrated on ten watersheds and verified on seven. The model-simulated runoff hydrographs were in close agreement with observed runoff hydrographs.

Estimating distribution parameters using optimization techniques

An improved parameter estimation procedure has been developed by using optimization techniques and applied to estimate the parameters of the log-Pearson type 3 (LP3) distribution. As a result, an improved estimation method was found. The new methods estimates the mean and the standard deviation of the log-transformed data by the method of moments and estimates the coefficient of skewness by minimizing both the relative root average square error (RRASE) and the relative average bias (RAB). Monte Carlo simulation was conducted for four selected LP3 populations. As compared with the method of moments, larger reductions in standard root mean square error (SRMSE) and standard bias (SBIAS) for quantile prediction can be achieved by the new method for small sample sizes and large return periods of quantiles. In addition, the new method can always fit the observed data better than the method of moments.

An efficient and derivative-free algorithm for finding the minimum of a 1-D user-defined function

Abstract An efficient algorithm was developed for finding the minimum or maximum of a one-dimensional (1-D) user-defined function. The algorithm combined the quadratic interpolation, the Golden search, and an additional side search into a unified optimal search. Five 1-D, four 2-D, and two 4-D functions were used to test the proposed search method and compare it with the Golden search and the Brent 1-D algorithm, for various initial points or intervals. The test results showed that the proposed search method was significantly faster than Brents search and the Golden search. The proposed search method did not experience any possible pre-termination problems either due to machine precision limit or a possible failure of interpolation. Brents search method, however, was found to yield a wrong solution (pre-termination) for one of the test functions.

A farm irrigation system (FIS) model

A mathematical model was developed to simulate farm irrigation systems (FIS). Open borders, closed borders, and/or furrows may constitute such systems. The model simulates the entire irrigation cycle of these systems. The volume balance method and some simple flow profile curves form the basis of the FIS model. Data from 25 vegetated and nonvegetated borders and six furrows were utilized to calibrate and verify the model. The test results showed that the model was accurate with less than 8% error in prediction of any of the phases of the irrigation cycle. These preliminary tests indicate that the FIS model is reasonably accurate for engineering applications.

A mathematical model for border irrigation I. Advance and storage phases

SummaryThis paper, the first in a series of three, develops a simple mathematical model for advance and storage phases of border irrigation. The model has 5 parameters which can be determined from experimental or field observations. Experimental data from 10 vegetated and nonvegetated borders were used to calibrate the model and from 15 vegetated and nonvegetated borders to verify the model. Average relative error in computed advance was less than 6% in calibration and was less than 8% in prediction. The model was particularly accurate if Reynolds number was less than 2,500.

A mathematical model for border irrigation III. Evaluation of Models

SummaryThis paper, the concluding one of a series of three, evaluates 9 border irrigation models (3 for advance, 3 for vertical recession and 3 for horizontal recession) which have closed-form solutions. Experimental data from 10 vegetated and nonvegetated borders are used to compare these models with the proposed (Singh-Yu or SY) model derived in Parts I and II. The proposed model is found to be superior in terms of accuracy, ease of application, and physical basis of parameters.

A mathematical model for border irrigation II. Vertical and horizontal recession phases

SummaryThis paper, second in a series of three, develops a mathematical model, using the volume balance approach, to simulate vertical and horizontal recession of border irrigation. An equation is proposed for computing Mannings roughness factor N in both laminar and transitional flow regimes in recession phases. The model has four parameters which can be determined experimentally. Experimental data from ten vegetated as well as nonvegetated borders were used to verify the model. Average difference (AD) between calculated and observed vertical recession times was less than 4.4 min, and between calculated and observed horizontal recession times less than 4.6 min for the ten experimental data sets. Average relative error (ARE) in computed horizontal recession was less than 13% for these data sets. The model was found to be especially accurate for Reynolds number between 1,800 and 2,500.