TY - JOUR

T1 - Detection of mean-field bias of the radar rain rate using rain gauges available within a small portion of radar umbrella

T2 - A case study of the Donghae (East Sea) radar in Korea

AU - Yoo, Chulsang

AU - Yoon, Jungsoo

AU - Ha, Eunho

N1 - Funding Information:
This work was supported partly by a Korea University Grant and partly by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST) (No. 2010-0014566). All contributions are gratefully acknowledged.

PY - 2013/2

Y1 - 2013/2

N2 - Observation of a storm approaching from the ocean to the in-land area is very important for the flood forecasting. Radar is generally used for this purpose. However, as rain gauges are mostly located within the in-land area, detection of the mean-field bias of radar rain rate cannot be easily made. This problem is obviously different from that with evenly-spaced rain gauges over the radar umbrella. This study investigated the detection problem of mean-field bias of radar rain rate when rain gauges are available within a small portion of radar umbrella. To exactly determine the mean-field bias, i. e. the difference between the radar rain rate and the rain gauge rain rate, the variance of the difference between two observations must be small; thus, a sufficient number of observations are indispensable. Therefore, the problem becomes determining the number of rain gauges that will satisfy the given accuracy, that being the variance of the difference between two observations. The dimensionless error variance derived by dividing the expected value of the error variance by the variance of the areal average rain rate was introduced as a criteria to effectively detect the mean field bias. Here, the variance of the areal average rain rate was assumed to be the climatological one and the expectation for the error variance could be changed depending one the sampling characteristics. As an example, this study evaluated the rainfall observation over the East Sea by the Donghae radar. About 6. 8 % of the entire radar umbrella covered in-land areas, where the rain gauges were available. It was found that, to limit the dimensionless error variance to 2 %, a total of 26 rain gauges are required for the entire radar umbrella; whereas, a total of 24 rain gauges would be required within the in-land area with available for the rain gauge data.

AB - Observation of a storm approaching from the ocean to the in-land area is very important for the flood forecasting. Radar is generally used for this purpose. However, as rain gauges are mostly located within the in-land area, detection of the mean-field bias of radar rain rate cannot be easily made. This problem is obviously different from that with evenly-spaced rain gauges over the radar umbrella. This study investigated the detection problem of mean-field bias of radar rain rate when rain gauges are available within a small portion of radar umbrella. To exactly determine the mean-field bias, i. e. the difference between the radar rain rate and the rain gauge rain rate, the variance of the difference between two observations must be small; thus, a sufficient number of observations are indispensable. Therefore, the problem becomes determining the number of rain gauges that will satisfy the given accuracy, that being the variance of the difference between two observations. The dimensionless error variance derived by dividing the expected value of the error variance by the variance of the areal average rain rate was introduced as a criteria to effectively detect the mean field bias. Here, the variance of the areal average rain rate was assumed to be the climatological one and the expectation for the error variance could be changed depending one the sampling characteristics. As an example, this study evaluated the rainfall observation over the East Sea by the Donghae radar. About 6. 8 % of the entire radar umbrella covered in-land areas, where the rain gauges were available. It was found that, to limit the dimensionless error variance to 2 %, a total of 26 rain gauges are required for the entire radar umbrella; whereas, a total of 24 rain gauges would be required within the in-land area with available for the rain gauge data.

KW - Donghae radar

KW - Mean-field-bias

KW - Radar rain rate

KW - Rain gauge density

UR - http://www.scopus.com/inward/record.url?scp=84872500625&partnerID=8YFLogxK

U2 - 10.1007/s00477-012-0644-3

DO - 10.1007/s00477-012-0644-3

M3 - Article

AN - SCOPUS:84872500625

VL - 27

SP - 423

EP - 433

JO - Stochastic Environmental Research and Risk Assessment

JF - Stochastic Environmental Research and Risk Assessment

SN - 1436-3240

IS - 2

ER -