• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.295-309
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• 2023

The Richards' equation attracts the attention of several scientific researchers due to its importance in the hydrogeology field especially porous soil. This work presents a numerical method to solve the two dimensional Richards' equation. The pressure form and the mixed form of Richards' equation are solved numerically using a bivariate diamond finite volumes scheme. Euler explicit scheme is used for the time discretization. Different test cases are done to validate the accuracy and the efficiency of our numerical model and to compare the possible numerical strategies. We started with a first simple test case of Richards' pressure form where the hydraulic capacity and the hydraulic conductivity are taken constant and then a second test case where the hydrodynamics parameters are linear variables. Finally, a third test case where the soil parameters are taken according the Van Gunchten empirical model is presented.

• Journal of Forest and Environmental Science
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• v.13 no.1
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• pp.66-80
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• 1997

Pinus koraiensis is one of the major speciese which have been recently planted for ten years and consists of 31% of total plantation. Presently young stand less than 30 years consists of 87% of total forest, but tending thinning of it is hardly carried out and the desirable direction for the thinning is not established yet. The objective of the study is to introduce the optimum thinning plan and thinning method through the long-run experiment of tending thinning for the Pinus koraiensis stand. The experiments carry out to interprete its growth model on the subject of two thinning experimental plots and yield table of Pinus koraiensis. As the basic step for understanding the thinning process, a theoretical growth model which is suitable to express the growth process is required. For that purpose, three growth functions (Mitscherlich, 4 parameter Richards, 3 parameter Richards) are applied to the diameter growth of the sample trees which are taken in the two plots. The results show that 3 parameter Richards is the most suitable. It is also verified that the diameter growth, the height growth, and the decrease in the number of stocks can be estimated by this function. To estimate the growth change of single tree, growth model including parameter h which is related to the occupation area of single tree are introduced. The parameter h can be estimated by using the data of the diameter growth obtained from the established experimental plots. Therefore, if both verification and modification of the usefulness of the model suggested is made, equations which tell about the thinning effects could be drived by estimating the growth process of single tree in advance.

• Journal of Korean Society of Forest Science
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• v.88 no.1
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• pp.47-54
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• 1999

To estimate optimal tree diameter and height growth function in Pinus thunbergii stands with site index of 12 class, quoted from two linear models of linear transformation(1) and linear transformation (2) and four non-linear models of exponential, Gompertz, Chapman-Richards, and Weibull etc.. Analyzed correlation among the estimated tree diameter and height by these function models, and observed diameter and height growth were compared. In the results of tree diameter and height growth estimation by stand age, non-linear models showed better appropriation than linear model and Chapman-Richards model was most fitted for tree height growth but few, if any, differences among their nonlinear models. Therefore, it is consider to be much more study about non-linear model to estimate tree diameter and height growth in the actual stands hereafter.

• Communications for Statistical Applications and Methods
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• v.29 no.5
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• pp.499-512
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• 2022

Intervention measures have been implemented worldwide to reduce the spread of the COVID-19 outbreak. The COVID-19 outbreak has occured in several waves of infection, so this paper is divided into three groups, namely those countries who have passed the pandemic period, those countries who are still experiencing a single-wave pandemic, and those countries who are experiencing a multi-wave pandemic. The purpose of this study is to develop a multi-wave Richards model with several changepoint detection methods so as to obtain more accurate prediction results, especially for the multi-wave case. We investigated epidemiological trends in different countries from January 2020 to October 2021 to determine the temporal changes during the epidemic with respect to the intervention strategy used. In this article, we adjust the daily cumulative epidemiological data for COVID-19 using the logistic growth model and the multi-wave Richards curve development model. The changepoint detection methods used include the interpolation method, the Pruned Exact Linear Time (PELT) method, and the Binary Segmentation (BS) method. The results of the analysis using 9 countries show that the Richards model development can be used to analyze multi-wave data using changepoint detection so that the initial data used for prediction on the last wave can be determined precisely. The changepoint used is the coincident changepoint generated by the PELT and BS methods. The interpolation method is only used to find out how many pandemic waves have occurred in given a country. Several waves have been identified and can better describe the data. Our results can find the peak of the pandemic and when it will end in each country, both for a single-wave pandemic and a multi-wave pandemic.

• Journal of The Korean Society of Agricultural Engineers
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• v.52 no.6
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• pp.19-26
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• 2010

Batch experiments were conducted to investigate growth and nutrient removal performance of microalgae Chlorella vulgaris by using piggery wastewater in different concentration of pollutants and the common growth models (logistic, Gompertz and Richards) were applied to compare microalgal growth parameters. Removal of nitrogen (N) and phosphorus (P) by Chlorella vulgaris showed correlation with biomass increase, implying nutrient uptake coupled with microalgae growth. The higher the levels of suspended solids (SS), COD and ammonia nitrogen were in the wastewater, the worse growth of Chlorella vulgaris was observed, showing the occurrence of growth inhibition in higher concentration of those pollutants. The growth parameters were estimated by non-linear regression of three growth curves for comparative analyses. Determination of growth parameters were more accurate with population as a variable than the logarithm of population in terms of R square. Richards model represented better fit comparing with logistic and Gompertz model. However, Richards model showed some complexity and sensitivity in calculation. In the cases tested, both logistic and Gompertz equation were proper to describe the growth of microalgae on piggery wastewater as well as easy to application.

• Korean Journal of Environmental Biology
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• v.20 no.4
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• pp.378-385
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• 2002

Growth of Pacific oystey, Crassostrea gigas, in Kamak Bay, Korea was modeled using Von Bertalanffy growth function, seasonal Von Bertalanffy growth function and generalized growth equation of Schnute and Richards' growth model, based on shell length and wet weight frequency data of 9208 oysters. Carrying capacity in the oyster culture ground was also estimated using Schaefer's and Fox's surplus production model. The present results suggest that the generalized growth equation of Schnute and Richards' model is fitter to describe the length growth pattern of C. gigas than Von Bertalanffy growth functions. This results also suggest that the current number of culture facility per unit area in 2000 is similar to the number of facility that produces the maximum production of oyster per unit area.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.33-33
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• 2016

산사태 발생 예측은 재해를 예방하고 대처하기 위한 가장 근본적이며 효과적인 방법이나, 과학기술의 발전과 많은 노력에도 불구하고 아직 산사태의 발생 장소와 시기를 예측하는 것은 매우 어려운 일이다. 산사태 발생 예측 기법은 크게 경험론적 지수기법, 통계적 해석기법, 물리적 해석 기법으로 나뉠 수 있다. 이 세 방법은 각기 장단점이 있으나 일반적으로 후자로 갈수록 많은 데이터가 요구되고, 해석에 시간이 필요하며, 보다 신뢰할만한 결과를 도출할 수 있다. 경험론적 지수 기법은 국내에서 실무적으로 널리 활용되고 있으며, 통계적 해석기법에 관한 연구도 수행된 바 있다. 하지만 이 두 방법론은 일정량 또는 일정강도 이상의 강우 발생 시 산사태의 발생 위험도를 공간적으로 예측할 수 있으나, 산사태의 발생 시점과 연속적인 강우량 또는 강우강도의 관계를 정량적으로 분석하기 힘든 한계가 있어 최근에는 이러한 한계를 극복하기 위해 최근 무한사면안정 모형과 토양수분침투 모형을 결합한 시변 사면안정모형들이 활용되기 시작하고 있다. 대표적으로는 TRIGRS가 있으며, 이 모형에서는 선형화한 1차원 Richards 방정식의 해석해를 활용하여 토양수분량을 계산한 후 이 정보를 무한사면안정모형에 반영하여 시변적인 사면안정도를 구하고 있다. 하지만 Richards 방정식을 선형화하기 위해서 제한된 토양수분-압력 관계식이 사용되며, GUI가 제공되지 않아 전처리 및 후처리가 번거로운 한계가 있다. 본 연구에서는 이러한 한계를 개선하기 위해 3차원 Richards방정식을 수치적으로 계산하여 보다 다양한 토양수분-압력 모형과 초기조건을 반영할 수 있게 하였다. 또한 GUI를 지원하여 사용자가 보다 손쉽게 해석모형을 사용할 수 있도록 하였다.

• Journal of Forest and Environmental Science
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• v.31 no.4
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• pp.255-260
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• 2015

Height growth models for Pinus thunbergii in Jeju Island were developed in this study using four widely used nonlinear growth models; Exponential, Modified Logistic, Chapman-Richards, and Weibull. All functions were found to be significant at the 1% level. Chapman-Richards model for height-DBH allometry and Weibull model for height-age allometry was chosen as the best model on the all validation. All the model curves showed the similar pattern. Additionally, there was no abnormal pattern when the previous studies were compared. Therefore, these models are highly expected to be used to estimate the tree height using DBH or age for Pinus thunbergii especially in Jeju Island.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.3
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• pp.243-259
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• 2016

The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

• Journal of Forest and Environmental Science
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• v.31 no.3
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• pp.202-206
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• 2015

Site index curves were developed for Larix kaempferi and Pinus koraiensis in Gangwon and North Gyeongsang provinces in Korea. For the development of site index, Schumacher and Chapman-Richards model were applied using the data collected from 2012 to 2014. Base age was set to 40 years for Larix kaempferi and Pinus koraiensis in site index of this study. Coefficient of determination and root mean square error of site index models were provided by species, and the models were compared with the previous studies to check the suitability. Overall, site index models developed in this study fitted in the current data well. Thus, the site indexes are considered to be properly used in Gangwon and North Gyeongsang provinces.