[논문]선형혼합모형을 활용한 표준강수지수 계산 인자들의 불확실성에 대한 기여도 평가

신지예; 이배성; 윤현철; 권현한; 김태웅

doi:10.3741/jkwra.2023.56.8.509

선형혼합모형을 활용한 표준강수지수 계산 인자들의 불확실성에 대한 기여도 평가
Evaluating the contribution of calculation components to the uncertainty of standardized precipitation index using a linear mixed model 원문보기

Journal of Korea Water Resources Association = 한국수자원학회논문집, v.56 no.8, 2023년, pp.509 - 520

신지예 (한양대학교(ERICA) 공학기술연구소) , 이배성 (한양대학교 대학원 건설환경시스템공학과) , 윤현철 (국립재난안전연구원 국가통합가뭄센터) , 권현한 (세종대학교 건설환경공학과) , 김태웅 (한양대학교(ERICA) 건설환경공학과)

초록
AI-Helper

가뭄은 강수량, 토양수분 그리고 유출량 등 여러 가지 요인으로부터 영향을 받으며, 가뭄의 상황 판단을 위하여 다양한 가뭄지수가 널리 활용되고 있다. 가뭄지수의 산정에 활용되는 수문기상학적 자료와 가뭄지수 산정공식에 따라서 지수값은 달라지며, 가뭄 상황에 대한 판단에도 차이가 발생 할 수 있다. 본 연구에서는 국내외에서 널리 활용되는 표준강수지수(SPI)의 산정과정에서 결정해야 하는 강수량의 자료길이, 누적기간, 확률분포 모형, 매개변수 추정기법 등을 불확실성 영향 요인으로 가정하고, 각각의 조합에 대한 불확실성을 평균제곱근오차와 선형혼합모형(LMM)을 활용하여 평가하였다. 평균제곱오차는 SPI 산정과정에 발생되는 전반적인 오차를 추정하며, LMM은 영향 요인들의 상대적인 불확설성을 평가하는데 활용되었다. 그 결과, SPI 산정에 활용된 자료의 기간과 누적기간이 길어질수록 평균제곱오차가 감소하였다. LMM을 통하여 불확실성 영향요인들의 기여도를 비교한 결과, SPI의 불확실성에는 자료기간의 영향이 가장 크게 나타났다. 또한, 자료기간이 증가하면, 자료기간에 의한 불확실성은 감소하고 누적기간과 매개변수 추정기법에 의한 불확실성이 상대적으로 증가하였다. 본 연구 결과, SPI 산정과정에서 발생되는 불확실성을 줄이기 위해서는 장기간의 자료 확보가 우선이며, 자료의 특성을 적절히 반영하는 확률분포모형과 매개변수 추정기법이 적용되어야 한다.

Abstract ▼ AI-Helper

Various drought indices are widely used for assessing drought conditions which are affected by many factors such as precipitation, soil moisture, and runoff. The values of drought indices varies depending on hydro-meteorological data and calculation formulas, and the judgment of the drought condition may also vary. This study selected four calculation components such as precipitation data length, accumulation period, probability distribution function, and parameter estimation method as the sources of uncertainty in the calculation of standardized precipitation index (SPI), and evaluated their contributions to the uncertainty using root mean square error (RMSE) and linear mixed model (LMM). The RMSE estimated the overall errors in the SPI calculation, and the LMM was used to quantify the uncertainty contribution of each factor. The results showed that as the accumulation period increased and the data period extended, the RMSEs decreased. The comparison of relative uncertainty using LMM indicated that the sample size had the greatest impact on the SPI calculation. In addition, as sample size increased, the relative uncertainty related to the sample size used for SPI calculation decreased and the relative uncertainty associated with accumulation period and parameter estimation increased. In conclusion, to reduce the uncertainty in the SPI calculation, it is essential to collect long-term data first, followed by the appropriate selection of probability distribution models and parameter estimation methods that represent well the data characteristics.

주제어

표/그림 (11)

표 Table 1. The meteorological stations information in this study
그림 Fig. 1. Conceptual diagram showing the SPI calculation process (gray line) and the reference precipitation calculation process (red line) corresponding to the SPI (=-1)
그림 Fig. 2. Uncertainty assessment procedure performed in this study
그림 Fig. 3. SPI values calculated by precipitation corresponding to the SPI (=-1)
그림 Fig. 4. Histogram of the RMSE. The RMSE is calculated for the refer-ence precipitation correponding to the SPI (=-1)
그림 Fig. 5. Boxplots of RMSE for individual stations. Gray line displays the average value of RMSE
표 Table 2. Reference precipitation of 3-month SPI (SPI=-1.0) (unit: mm)
그림 Fig. 6. Histograms of the RMSE for different sample sizes and the different accumulation periods of SPI
그림 Fig. 7. Relative uncertainty components for individual stations
표 Table 3. Relative uncertainty contributions for individual stations
그림 Fig. 8. Relative uncertainty contributions of influence factors

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