The shape of temperature dependence functions for J max and Vc max

The three thermodynamic parameters of the temperature dependence function (equation (30)) from the evaluation of nitrogen classes with RACCIA did not show a clear dependence on nitrogen content per area. Range and average values for J_max- and Vc_max-specific activation energies H_a, deactivation energies H_d and entropy terms S for leaves of both investigated trees are listed in table 6.

Table 6: range and average values of temperature dependence parameters

Quantity Unit Beech Gr12 ∅ Oak Gr13 ∅

Fig. 91: Influence of relatively small changes of parameter Hd on the shape of the temperature dependence function for Vcmax and Jmax, when S is held constant at the average Vcmax-specific value of beech Gr12 (608 J/(K * mol)). Hd is 185 kJ/mol in the left graph and 195 kJ/mol in the right graph, while the approximation to the measured data yielded an average value of 189 kJ/mol. The influence of parameter Ha can be seen from the third axis in the figure. The fourth parameter (rate at 25°C) was held constant equalling 100 µmol/(m²*s).

In equation (30), the optimum temperature at which maximum rates are achieved is mainly determined by the parameters S and H_d, which interact in its third term. The ratio between both quantities is decisive for the result of this term and even small variations in one of both quantities without change of the other one were found to have an immense effect on the optimum temperature (Fig. 91). The high sensitivity of the shape of equation (30) on the ratio between both parameters is probably the reason for a strong correlation, that has been found between all the derived values for Jmax - and Vcmax -specific parameters S and Hd (Fig. 92).

The found linear relationship gave also a good approximation to previously published values, indicating the narrow range of reasonable values for these parameters, given that the optimum temperature lies somewhere between 20°C and 40°C. C onsidering the strong impact of small variations, the regression line in Fig. 92 was not forced through the origin.

S and H_d do not impose fundamental changes on the ecophysiologically interesting part of the temperature response curve, when their values move along the found linear relationship. Higher S and H_d values lead in this case to a more pronounced, peak-like temperature optimum with

Fig. 92: Strong linear correlation between entropy terms and deactivation energies of equation (32) from the derived values for beech Gr12, oak Gr13, and beech seedlings (left graph). The same regression line gives a good approximation to previously published values (right graph).

y = 0.311x - 0.8521

0 200 400 600 800 1000 1200

S ( J / (K * mol) ) Hd(kJ/mol)

oak Gr13 beech seedlings beech Gr12

y = 0.311x - 0.8521

Falge et al. 1996 Harley et al. 1992 Niinemets & Tenhunen 1997 y = 0.3102x - 0.1568

Dreyer et al. 2001 Falge et al. 1996

Harley et al. 1992 Niinemets & Tenhunen 1997

(30)

Fig. 93: Effect of simultaneously changing parameters S and Hd on the shape of the temperature dependence function for Jmax and Vcmax (equation (30)). S and Hd were changed according to the linear relationship Hd = 0.311S - 0.8521, using the derived minimum value of S from oak Gr13 (left graph) and the maximum value from beech Gr12 (right graph). The rate at 25°C equals 100 µmol/(m²*s).

rate µmol/(m²*s) rate

µmol/(m²*s)

more steeply ascending and descending slopes (Fig. 93), but the found differences in S-values and in Hd -values of different leaves or nitrogen classes induce only relatively small numerical changes in the resulting rates over the temperature range from 0°C to 40°C (Fig. 94). The effects of these differences on the optimum temperature were dependent on H_a, but also small.

Ha mainly determines the curvature of the ascending slope of the temperature dependence curve, as can be seen in Figs. 93 and 94. While the rates below 25°C become lower, the rates above 25°C may easily become much higher when H_a-values are increased. Thus, rate calculations with equation (30) are more sensitive to the rate at 25°C and Ha than to parameters S and H_d, when the average linear relationship between S and H_d is assumed.

While J_max and Vc_max at 25°C have been shown to be strictly nitrogen de pendent (Fig. 89), a weaker tendency was found for activation energies, Ha increasing with nitrogen per area (r² = 0.35 (Vc_max) and 0.25 (J_max) for all beech data and r² = 0.27 (Vc_max) and 0.01 (J_max) for oak Gr13, data not shown). Stronger relationships were observed between J_max at 25°C and H_a and between Vcmax at 25°C and Ha (Fig. 95). The unique Ha vs. Jmax relationship for beech seedlings and beech Gr12 had a very high coefficient of determination (0.91), while the Vc_max-specific relationship was weaker (0.45), similar to that of oak Gr13 (r²=0.47). No clear relationship was found between Jmax and Ha of oak Gr13 leaves (r² = 0.03), which may be due to the low number

Fig. 94: Comparison of temperature dependence functions with minimum parameters of beech Gr12 (S

= 448 J/(K*mol), Hd = 138.5 kJ/mol , solid lines) and with maximum parameters of beech Gr12 (S = 867 J/(K*mol), Hd = 268.8 kJ/mol, dashed lines). While the rate at 25°C was held constant at 100

µmol/(m²*s), activation energy H_a equals 30 kJ/mol in the left graph and 100 kJ/mol in the right graph.

0 10 20 30 40

Fig. 95: Relative increase of activation energies Ha for Vcmax (left graph) and Jmax (right) with their appertaining rates at 25°C. Equations and coe fficients of determination in the upper left corner are for beech and those in the bottom right corner of each graph are for oak.

y = 6.74x^0.5161

oak Gr13 beech Gr12 and beech seedlings

y = 29.683x^0.0927

oak Gr13 beech Gr12 and beech seedlings

of data points for the whole investigation, since the exclusion of only three points would result in an r² of 0.73.

As stated above, the ratio between S- and Hd-values was not really constant due to the addition of a small, but possibly powerful constant value. Thus, the term S / (Hd + 0.8521) may be seen as constant in a first approximation. The examination of the small deviations from this approximation showed no clear tendency in relation to nitrogen or other leaf-related quantities, but the weak correlations that were found in relation to Ha (r² ≤ 0.3) fundamentally improved, when the constant value was arbitrarily increased to a number close to 7.8 (Fig. 96). This was valid for Jmax and Vcmax data from oak Gr13, beech Gr12, and beech seedlings. The empirical relationship between Ha and S/(Hd+7.8) was nearly the same for beech seedlings and beech Gr12, while it was different for oak Gr13.

Thus, Jmax and Vcmax are fully determined by nitrogen content and temperature:

- Jmax and Vcmax at 25°C are dependent on nitrogen (Fig. 89).

- Ha may be expressed as function of Jmax or Vcmax at 25°C (Fig.95), though the coefficients of determination for oak were low.

- Two equations (Figs. 92 and 96) describe the relationship between S and Hd, when Ha is known, and may be solved simultaneously for the determination of S and Hd.

If all found relationships between parameters of equation (30) and the relationship from Fig. 89 may be accepted as empirical relationships (which can only be proven in further investigations that increase the number of data points), Jmax and Vcmax of Fagus sylvatica and Quercus petraea would be determined by temperature and nitrogen per area as is shown in Fig. 97.