## 1 Introduction  
Tropospheric ozone (O\({}_{3}\)) has detrimental effects on vegetation [1; 2; 3]. Current O\({}_{3}\) levels adversely affect growth and physiological functions, such as the photosynthesis of forest tree species [4; 5]. Because of this phytotoxicity, net primary production (NPP) and biomass accumulation by temperate forests were estimated to be reduced by 1-16% [6]. Therefore, O\({}_{3}\) indirectly affects radiative forcing through its adverse effects on photosynthetic CO\({}_{2}\) uptake [7]. Despite robust evidence for the negative impact of O\({}_{3}\) on plant productivity, the indirect effect of O\({}_{3}\) on radiative forcing was not mentioned in the Intergovernmental Panel on Climate Change Fifth Assessment report because of a lack of corroborating studies [8]. In Asia, an increase in the surface O\({}_{3}\) concentration is expected, although the changes in its concentration depend on the emission scenario [9; 10; 11]. In Japan, despite a decrease in the concentrations of O\({}_{3}\) precursors, the surface O\({}_{3}\) concentration has been increasing because of a reduction in NO titration and an increase in transboundary air pollution [12]. Therefore, it is necessary to quantify the negative impact of O\({}_{3}\) on the photosynthetic CO\({}_{2}\) uptake of Japanese forest tree species to account for the indirect effect of O\({}_{3}\) on radiative forcing. Ozone enters leaves through their stomata and damages their cellular components [13; 14; 15]. Because the real impacts of O\({}_{3}\) on plants mainly depend on the amounts of O\({}_{3}\) reaching the sites of damage within the leaves, these impacts can be quantified by measuring the cumulative stomatal O\({}_{3}\) uptake, defined as phytotoxic O\({}_{3}\) dose (POD) and associated response functions [16; 17; 18]. Because the degree of stomatal opening adjusts continuously to environmental changes [19], this O\({}_{3}\) flux-based approach requires the development of mathematical models to estimate the POD in leaves, using stomatal responses to environmental factors [20; 21; 22]. In Japan, several researchers have established multiplicative models to estimate the POD in the leaves of forest tree species [23; 24; 25; 26; 27]. In addition to modeling stomatal O\({}_{3}\) uptake, the degree of the O\({}_{3}\)-induced reduction in photosynthetic CO\({}_{2}\) uptake should be evaluated, based on the POD, to quantify the negative impact of O\({}_{3}\) on the NPP. According to a meta-analysis by [PERSON] et al. (2007) [28], the light-saturated net photosynthetic rate (\(A_{\text{sat}}\)) decreases at a rate of 0.22% per mmol O\({}_{3}\) m\({}^{-2}\) leaf area (LA) as POD increases. Because the relationship between POD and the percent change in \(A_{\text{sat}}\) varies with species and genotypes within species, as well as with locations and experimental conditions, little of the variability in the degree of percent change in \(A_{\text{sat}}\) is accounted for by the POD [28]. In addition to this variability, seasonal variation in the degree of O\({}_{3}\)-induced reduction in \(A_{\text{sat}}\) could explain why POD is responsible for only a small percentage of the changes in \(A_{\text{sat}}\) measured at a certain time. For example, the degree of O\({}_{3}\)-induced reduction in \(A_{\text{sat}}\) of _Populus nigra_ is lower in autumn than in summer [29], whereas POD is greater in autumn than in summer owing to the longer accumulation period. Because POD could be related to cumulative O\({}_{3}\) damage, a cumulative O\({}_{3}\) effects on net photosynthesis is an appropriate dependent variable in the response function of photosynthetic CO\({}_{2}\) uptake to POD. Therefore, it is necessary to evaluate the degree of O\({}_{3}\) damage on the cumulative photosynthetic CO\({}_{2}\) uptake at leaf-level, which could be easily incorporated into models of the carbon cycling, throughout an entire growing season, taking into consideration of seasonal and diurnal changes in the O\({}_{3}\) damage on \(A_{\text{sat}}\).