• Title/Summary/Keyword: Polynomial model

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Studies on the Time Distribution of Heavy Storms (暴雨의 時間的 分布에 關한 硏究)

  • Lee, Keun-Hoo
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.26 no.2
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    • pp.69-84
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    • 1984
  • This study was carried out to investigate the time distribution of single storms and to establish the model of storm patterns in korea. Rainfall recording charts collected from 42 metheorological stations covering the Korean peninsula were analyzed. A single storm was defined as a rain period seperated from preceding and succeeding rainfall by 6 hours and more. Among the defined single storms, 1199 storms exceeding total rainfall of 80 mm were qualified for the study. Storm patterns were cklassified by quartile classification method and the relationship between cummulative percent of rainfalls and cummulative storm time was established for each quartile storm group. Time distribution models for each stations were prepared through the various analytical and inferential procedures. Obtained results are summarized as follows: 1. The percentile frequency of quartile storms for the first to the fourth quartile were 22.0%, 26.5%, 28.9% and 22.6%, respectively. The large variation of percentile frequency was show between the same quartile storms. The advanced type storm pattern was predominant in the west coastal type storm patterns predominantly when compared to the single storms with small total rainfalls. 3. The single storms with long storm durations tended to show delayed type storm patterns predominantly when compared to the single storms with short storm durations. 4. The percentile time distribution of quartile storms for 42 rin gaging stations was estimated. Large variations were observed between the percentiles of time distributions of different stations. 5. No significant differences were generally found between the time distribution of rainfalls with greater total rainfall and with less total rainfall. This fact suggests that the size of the total rainfall of single storms was not the main factor affecting the time distribution of heavy storms. 6. Also, no significant difference were found between the time distribution of rainfalls with long duration and with short duration. The fact indicates that the storm duration was no the main factor affecting the time distribution of heavy storms. 7. In Korea, among all single storms, 39.0% show 80 to 100mm of total rainfall which stands for the mode of the frequency distribution of total rainfalls. The median value of rainfalls for all single storms from the 42 stations was 108mm. The shape of the frequency distribution of total rainfalls showed right skewed features. No significant differences were shown in the shape of distribution histograms for total rainfall of quartile storms. The mode of rainfalls for the advanced type quartile storms was 80~100mm and their frequencies were 39~43% for respective quartiles. For the delayed type quartile storms, the mode was 80~100mm and their frequencies were 36!38%. 8. In Korea, 29% of all single storms show 720 to 1080 minutes of storm durations which was the highest frequency in the frequency distribution of storm durations. The median of the storm duration for all single storms form 42 stations was 1026 minutes. The shape of the frequency distribution was right skewed feature. For the advanced type storms, the higher frequency of occurrence was shown by the single storms with short durations, whereas for the delayed type quartile storms, the higher frequency was shown gy the long duration single storms. 9. The total rainfall of single storms was positively correlated to storm durations in all the stations throughout the nation. This fact was also true for most of the quartile storms. 10. The third order polynomial regression models were established for estimating the time distribution of quartile storms at different stations. The model test by relative error method resulted good agreements between estimated and observed values with the relative error of less than 0.10 in average.

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Optimization of microwave-assisted extraction process for blue honeysuckle (Lonicera coerulea L.) using response surface methodology (반응표면분석법을 이용한 댕댕이 기능성성분의 마이크로웨이브추출조건 최적화)

  • Park, Daehee;Lee, Jae-Jun;Park, Jongjin;Park, Sanghwan;Lee, Wonyoung
    • Food Science and Preservation
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    • v.24 no.5
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    • pp.623-630
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    • 2017
  • Functional compounds including flavonoids, anthocyanins, polyphneols and antioxidants were extracted from blue honeysuckle (Lonicera caerulea L.) using highly efficient microwave-assisted extraction. And extraction process was modeled and optimized according to response surface methodology (RSM). The independent variables ($X_n$) were ethanol concentration ($X_1$: 0, 25, 50, 75, 100%), irradiation time ($X_2$: 1, 3, 5, 7, 9 min), and microwave power ($X_3$: 60, 120, 180, 240, 300 W). Dependent variables ($Y_n$) were total flavonoid contents ($Y_1$), total anthocyanin contents ($Y_2$), total polyphenol contents ($Y_3$) and antioxidant activity ($Y_4$). Four-dimensional response surface plots were generated based on the fitted second-order polynomial models to get optimal conditions. Estimated optimal conditions for 4 responses were ethanol concentration of 54-72%, irradiation time of 7.1-7.6 min, and microwave power of 243-251 W. Ridge analysis predicted the maximal responses of total flavonoid content, total anthocyanin content, total polyphenol content and antioxidant activity were 38.00 mg RE/g, 6.80 mg CGE/g, 14.90 mg GAE/g, 89.10%, respectively. Verification experiment was carried out at predicted optimal conditions and experimental values for total flavonoid content, total anthocyanin content, total polyphenol content and antioxidant activity were 38.10 mg RE/g, 6.72 mg CGE/g, 14.91 mg GAE/g and 89.13%, respectively. No significant difference was observed between predicted and experimental values, indicating good fitness of fitted model and successful application of RSM.

Optimization for Extraction of ${\beta}-Carotene$ from Carrot by Supercritical Carbon Dioxide (초임계 유체에 의한 당근의 ${\beta}-Carotene$ 추출의 최적화)

  • Kim, Young-Hoh;Chang, Kyu-Seob;Park, Young-Deuk
    • Korean Journal of Food Science and Technology
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    • v.28 no.3
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    • pp.411-416
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    • 1996
  • Supercritical fluid extraction of ${\beta}$-carotene from carrot was optimized to maximize ${\beta}$-carotene (Y) extraction yield. A central composite design involving extraction pressure ($X_1$ 200-,100 bar), temperature ($X_2,\;35-51^{\circ}C$) and time ($X_1$$ 60-200min) was used. Three independent factors ($X_1,\;X_2,\;X_3$) were chosen to determine their effects on the various responses and the function was expressed in terms of a quadratic polynomial equation,$Y={\beta}_0+{\beta}_1X_1+{\beta}_2X_2+{\beta}_3X_3+{\beta}_11X_12+{\beta}_22X_3^2+{\beta}_-12X_1X_2+{\beta}_12X_1X_2+{\beta}_13X_1X_3+{\beta}_23X_2X_3,$ which measures the linear, quadratic and interaction effects. Extraction yields of ${\beta}$-carotene were affected by pressure, time and temperature in the decreasing order, and linear effect of tenter point (${\beta}_11$) and pressure (${\beta}_1$) were significant at a level of 0.001(${\alpha}$). Based on the analysis of variance, the model fitted for ${\beta}_11$-carotene (Y) was significant at 5% confidence level and the coefficient of determination was 0.938. According to the response surface of ${\beta}$-carotene by cannoical analysis, the stationary point for quantitatively dependent variable (Y) was found to be the maximum point for extraction yield. Response area for ${\beta}$-carotene (Y) in terms of interesting region was estimated over $10,611{\mu}g$ Per 100 g raw carrot under extraction.

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