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Validation of Extreme Rainfall Estimation in an Urban Area derived from Satellite Data : A Case Study on the Heavy Rainfall Event in July, 2011 (위성 자료를 이용한 도시지역 극치강우 모니터링: 2011년 7월 집중호우를 중심으로)

  • Yoon, Sun-Kwon;Park, Kyung-Won;Kim, Jong Pil;Jung, Il-Won
    • Journal of Korea Water Resources Association
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    • v.47 no.4
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    • pp.371-384
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    • 2014
  • This study developed a new algorithm of extreme rainfall extraction based on the Communication, Ocean and Meteorological Satellite (COMS) and the Tropical Rainfall Measurement Mission (TRMM) Satellite image data and evaluated its applicability for the heavy rainfall event in July-2011 in Seoul, South Korea. The power-series-regression-based Z-R relationship was employed for taking into account for empirical relationships between TRMM/PR, TRMM/VIRS, COMS, and Automatic Weather System(AWS) at each elevation. The estimated Z-R relationship ($Z=303R^{0.72}$) agreed well with observation from AWS (correlation coefficient=0.57). The estimated 10-minute rainfall intensities from the COMS satellite using the Z-R relationship generated underestimated rainfall intensities. For a small rainfall event the Z-R relationship tended to overestimated rainfall intensities. However, the overall patterns of estimated rainfall were very comparable with the observed data. The correlation coefficients and the Root Mean Square Error (RMSE) of 10-minute rainfall series from COMS and AWS gave 0.517, and 3.146, respectively. In addition, the averaged error value of the spatial correlation matrix ranged from -0.530 to -0.228, indicating negative correlation. To reduce the error by extreme rainfall estimation using satellite datasets it is required to take into more extreme factors and improve the algorithm through further study. This study showed the potential utility of multi-geostationary satellite data for building up sub-daily rainfall and establishing the real-time flood alert system in ungauged watersheds.

Closed-Form Solutions to Free Vibration Response of Single Degree of Freedom Systems with Coulomb Friction (쿨롱마찰을 갖는 단자유도계의 자유진동응답에 관한 닫힌 해)

  • Lee, Sung-Kyung
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.33 no.1
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    • pp.9-16
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    • 2020
  • The objective of this study is to propose closed-form solutions to the free vibration response of single-degree-of-freedom (SDOF) systems, as part of fundamental research on dynamic systems with Coulomb friction. The motion of a dynamic system with Coulomb friction is described by a nonlinear differential equation, and, due to the variation in the sign of friction force term with the direction of motion, it is difficult to obtain the closed-form solution. To solve this problem, the nonlinear differential equation is directly computed by numerical integration, or an approximated solution is indirectly obtained using a linear differential equation wherein the damping effect due to Coulomb friction is replaced by an equivalent viscous damping term. However, these conventional methods do not provide a closed-form solution from a mathematical point of view. In this regard, closed-form solutions to the free vibration response of SDOF systems with Coulomb friction are derived herein by considering that the sign of the friction force term is reversed in each half-cycle of motion and by expanding it to the entire time history using the power series function. In addition, for a given initial condition, both the number of free vibration half-cycles and the response at the instant when free vibration motion stops are predicted under the condition that the motion of free vibration is stopped when the amplitude of the friction force is higher than that of the restoring force due to stiffness.