Huidae Cho

A derivation of the number of minima of the Griewank function

The Griewank function is commonly used to test the ability of different solution procedures to find local optima. It is important to know the exact number of minima of the function to support its use as a test function. However, to the best of our knowledge, no attempts have been made to analytically derive the number of minima. Because of the complex nature of the function surface, a numerical method is developed to restrict domain spaces to hyperrectangles satisfying certain conditions. Within these domain spaces, an analytical method to count the number of minima is derived and proposed as a recursive functional form. The numbers of minima for two search spaces are provided as a reference.

Let-It-Rain: a web application for stochastic point rainfall generation at ungaged basins and its applicability in runoff and flood modeling

We present a web application named Let-It-Rain that is able to generate a 1-h temporal resolution synthetic rainfall time series using the modified Bartlett–Lewis rectangular pulse (MBLRP) model, a type of Poisson stochastic rainfall generator. Let-It-Rain, which can be accessed through the web address http://www.LetItRain.info, adopts a web-based framework combining ArcGIS Server from server side for parameter value dissemination and JavaScript from client side to implement the MBLRP model. This enables any desktop and mobile end users with internet access and web browser to obtain the synthetic rainfall time series at any given location at which the parameter regionalization work has been completed (currently the contiguous United States and Republic of Korea) with only a few mouse clicks. Let-It-Rain shows satisfactory performance in its ability to reproduce observed rainfall mean, variance, auto-correlation, and probability of zero rainfall at hourly through daily accumulation levels. It also shows a reasonably good performance in reproducing watershed runoff depth and peak flow. We expect that Let-It-Rain can stimulate the uncertainty analysis of hydrologic variables across the world.

Application of Multimodal Optimization for Uncertainty Estimation of Computationally Expensive Hydrologic Models

The generalized likelihood uncertainty estimation (GLUE) framework has been widely used in hydrologic studies. However, the extensive random sampling causes a high computational burden that prohibits the efficient application of GLUE to costly distributed hydrologic models such as the soil and water assessment tool (SWAT). In this study, a multimodal optimization algorithm called isolated- speciation-based particle swarm optimization (ISPSO) is employed to take samples from the search space. A comparison between the ISPSO- GLUE, proposed here, and traditional GLUE approaches shows that the two approaches generate similar uncertainty bounds, but that the convergence rate to stable uncertainty bounds is much faster for ISPSO-GLUE than for GLUE. That is, ISPSO-GLUE needs a much smaller number of samples than GLUE to arrive at a very similar answer. Although ISPSO-GLUE slightly underestimated the prediction uncertainty and missed a number of observed values, the proposed approach is considered to be a good alternative to the typical GLUE approach that employs random sampling. DOI: 10.1061/(ASCE)WR.1943-5452.0000330.

Development and Application of an Storm Identification Algorithm that Conceptualizes Storms by Elliptical Shape

A storm identification algorithm conceptualizing the storm with an elliptical shape was developed. The developed algorithm identifies the center, major and minor axis, and the inclination angle of the ellipse that contains the maximum volume of rainfall for a given area using the isolated particle swarm optimization algorithm. The developed algorithm was applied to radar precipitation imagery of 10 major storms observed in Korea during the year 2008 and 2012. The algorithm successfully identified the storm shapes for all time steps of all 10 major storms. The following conclusion was drawn from the result of the storm identification: (1) as the size of the ellipse becomes smaller, the diversity of the storm shape increased, and the diversity decreased as the size of the ellipse increases; (2) the temporal variation of the storm center identified by the ellipse is not always continuous; (3) the tracking capability of the algorithm is expected to be improved as the center and the shape of the ellipse at the previous time step is considered in the objective function of the optimization algorithm.

Efficient Uncertainty Analysis of TOPMODEL Using Particle Swarm Optimization

We applied the ISPSO-GLUE method, which integrates the Isolated-Speciation-based Particle Swarm Optimization (ISPSO) with the Generalized Likelihood Uncertainty Estimation (GLUE) method, to the uncertainty analysis of the Topography Model (TOPMODEL) and compared its performance with that of the GLUE method. When we performed the same number of model runs for the both methods, we were able to identify the point where the performance of ISPSO-GLUE exceeded that of GLUE, after which ISPSOGLUE kept improving its performance steadily while GLUE did not. When we compared the 95% uncertainty bounds of the two methods, their general shapes and trends were very similar, but those of ISPSO-GLUE enclosed about 5.4 times more observed values than those of GLUE did. What it means is that ISPSOGLUE requires much less number of parameter samples to generate better performing uncertainty bounds. When compared to ISPSO-GLUE, GLUE overestimated uncertainty in the recession limb following the maximum peak streamflow. For this recession period, GLUE requires to find more behavioral models to reduce the uncertainty. ISPSO-GLUE can be a promising alternative to GLUE because the uncertainty bounds of the method were quantitatively superior to those of GLUE and, especially, computationally expensive hydrologic models are expected to greatly take advantage of the feature.