This study investigated the inter-relationships between weather parameters in the Kyushu–Okinawa region of Japan using the correlation coefficients derived for each pair of weather parameters. Clear and stable relationships were confirmed among precipitation, solar radiation, and cloud cover throughout the year. Precipitation tended to increase with increasing cloud availability and decreasing solar radiation. The impact of precipitation, solar radiation, and cloud cover on air temperature is more complicated and has seasonality or regionality, especially in winter. In the summer months, air temperature tended to be high when there was little precipitation, strong solar radiation, or less cloud cover, implying that solar radiation dominantly controlled air temperature on a monthly timescale. However, their impacts on air temperature turned to be opposite or unclear in winter, probably because the relative impact of the longwave energy budget increases in winter as compared to the shortwave energy budget. Some regional differences in the inter-relationships were observed among northern Kyushu, southern Kyushu, and Okinawa. While the air temperature–precipitation relationship has been of public interest, this study suggests the importance of considering cloud and solar radiation because the relationships were formed via cloud and solar radiation circumstances.

  The Darcy–Weisbach equation describes the flow in a pipe, and the coefficient of friction loss, f, depends on the Reynolds number, Re. The authors proposed using f=aRe^-b for pipes in the near-hydraulically smooth transition zone for practical flows of the order, 10⁵<Re<10⁶. For coefficients a and b, we collected data from hydraulic experiments on various types of inner coatings and resin pipes. However, hydraulic experiments are complex, and data collection is challenging. Takakuwa (1972) derived a new discharge equation by combining the coefficient of friction loss from the Colebrook equation with the Hazen–Williams equation. The power number of hydraulic gradient I, in the new equation is obtained from the equivalent roughness k, inner diameter D, and Reynolds number Re. The authors obtained coefficient b from the power number, verified the relationship between Re ~ b, Re ~ a, and b ~ a, and expressed a as a function of b. Furthermore, we propose a process for determining the hydraulic gradient I, friction loss head h_f, and discharge Q using the average discharge equation incorporating f=aRe^-b based on pipe inner surface conditions of k, a, b and hydraulic design conditions of D.

  In this study, the authors examined a method for estimating the coefficients a and b of f=aRe^-b, which linearly expresses the relationship between the friction loss coefficient f and the Reynolds number Re. Takakuwa (1972) proposed a theoretical method for combining the Colebrook equation with an arbitrary exponential-type average flow formula. The indexes of pipe diameter and hydraulic gradient were obtained using the equivalent roughness of the inner surface of the pipe. Combining this joint formula with the general Hazen-Williams formula, the coefficients a and b can be obtained theoretically using the exponents of the hydraulic gradient. However, the theoretical method requires numerical calculations, making computational complexity an issue. Therefore, the authors investigated a method to derive a combination of coefficients a and b that can guarantee f=aRe^-b from hydraulic experiment results while maintaining the computational simplicity of the Hazen-Williams formula. Consequently, they proposed a simple linearization method between the two points Re and f for a pipe in the transition zone close to the hydraulic smooth surface of a practical flow of approximately 10⁵ < Re < 10⁶.