The variability and seasonality in the ratio of photosynthetically active radiation to solar radiation: A simple empirical model of the ratio

A constant ratio of photosynthetically active radiation (PAR) to solar radiation (SR) (about 0.45–0.46) has been used in many ecological studies to convert SR into PAR by multiplication. The constant ratio is useful and convenient. However, there is no general agreement on whether the ratio is 0.45 or 0.46 and how distributed globally. Accordingly, many local empirical ratios have been reported. This study aims to demonstrate a global distribution of the ratio and its changing range. Thus, we created two simple empirical models to estimate the ratio based on the in-situ climatic data to achieve the aim. The models were created based on accurate data of SR and PAR observed using a direct and diffuse separation method at Tateno in Tsukuba, Japan. At three validation sites in Japan, the ratio could be estimated with an error within 3%, a considerable reduction from 15% in using a constant. The numerical model also produced the ratio within approximately 3% errors. Using the proposed model, we demonstrated that the annual mean of the ratio had a range from 0.409 to 0.477. The results will contribute to the uncertainty estimation when using a constant ratio.