Fig 1.
Flowering phenology dates of Neodani Usuzumi-zakura from 1989 to 2024 published on the Motosu City Web site.
Fig 2.
Relationship between probability distributions of estimated true dates of (a) FFL, (b) FFB, (c) LFB, and (d) LFL from 1924 to 2024 (α1t and α2t in Eqs 4 & 8) by the proposed Bayesian statistical state space model based on temperature data at Gifu weather station and observed values in records from Motosu City, the literature, and a private collection (y1t and y2t in Eqs 5 & 9).
Table 1.
Medians of estimated variables μ1t and μ2t as the intercept, coefficient β1t of ex1t as explanatory variable 1, coefficient γ1t of ex2t as explanatory variable 2, and coefficient β2t of ex3t as explanatory variable 3 based on air temperature data recorded at the Gifu weather station.
As an example, in the case of the estimated model for the true date of FFL, we show the probability distributions of estimated variable μ1t and coefficients β1t and γ1t in Fig 3.
Fig 3.
Probability distributions of estimated (a) variable μ1t as the intercept, (b) coefficient β1t of ex1t as explanatory variable 1, and (c) coefficient γ1t of ex2t as explanatory variable 2 (μ1t, β1t, and γ1t in Eqs 1−3) in the case of the estimated model for the true date of FFL.
Fig 4.
Relationship between probability distributions of estimated true dates of (a) FFL, (b) FFB, (c) LFB, and (d) LFL from 1979 to 2024 (α1t and α2t in Eqs 4 & 8) by our Bayesian statistical state space model based on temperature data at Tarumi weather station and observed values in records from Motosu City (y1t and y2t in Eqs 5 & 9).
Table 2.
Medians of estimated variables μ1t and μ2t, and coefficients β1t, γ1t, and β2t based on air temperature data recorded at the Tarumi weather station.
Fig 5.
(a) Probability distributions of the estimated true date of FFB from 1924 to 2024 (α1t in Eq 4) by the proposed Bayesian statistical state space model based on temperature data at Gifu weather station, and both flowering phenology records of the tree from the literature and a private collection before 1989 (1928−1937: Literature and photograph; 1955−1980: Private collection of Hakuryu Fujiwara; and 1981−1988: Unpublished data of Motosu City [Motosu City {Unpublished}]) and observed data published on a website since 1989 as the observed value of FFB date (y1t in Eq 5). Probability distributions of estimated (b) variable μ1t as the intercept, (c) coefficient β1t of ex1t as explanatory variable 1, and (d) coefficient γ1t of ex2t as explanatory variable 2 (μ1t, β1t, and γ1t in Eqs 1−3) in the case of this estimated model for the true date of FFB.