3.1. Entropy Production in Ecosystems of the Southern Taiga
Figures of the diurnal course of the entropy production and EMEP at the studied sites in different weather conditions (Figure 2
) show that the WS and DS forests were very similar, but entropy production in the bog was much lower than in the forests. The most significant difference of σ
values between the forests and the bog was associated with sunny conditions. The σ
/EMEP at forest sites increased slightly (insignificant in comparison to the standard deviation) with increasing cloudiness. The σ
/EMEP rose significantly only at the bog site and on overcast days (σ
/EMEP = 0.842 ± 0.015) compared to clear days (σ
/EMEP = 0.801 ± 0.019).
Entropy production has a distinctive seasonal pattern (Figure 3
), which is typical for a boreal climate. The efficiency of entropy production (Figure 4
) in the forests varied from 0.78 (WS) and 0.81 (DS) in winter to 0.91 (WS) and 0.90 (DS) in summer. In some winter months, the σ
/EMEP in forests dropped to 0.5–0.6, but on average it was relatively high. The wet spruce forest in summer had a slightly higher efficiency than the dry one. The maximal efficiency in forests was formed in April, just after the snow melted; it then decreased during May and remained constant for the rest of the growing season. The June–October levels of the σ
/EMEP in forests were quite stable and consistent between forests in different years.
The efficiency of entropy production at the bog site had significant day-to-day and month-to-month variations during the growing season (Figure 4
). The bog station was in operation only during spring-autumn periods of 1998–2000, so we had only 27 days of radiation data while the bog was covered with snow. These data show that the bog under snow had a very low entropy production efficiency of about 0.4. With the snow melting, the σ
/EMEP at the bog site rose rapidly, reaching the spring peak, and then gradually decreased during the first half of summer, and increased again to the autumn peak. In November, the entropy production efficiency of the bog reached the level of the forest sites. Fluctuations of the σ
/EMEP in the warm periods at the bog site were much greater than at the WS site.
Though in warm periods the monthly entropy production in the long-wave radiation balance in the spruce forests rarely exceeded 2% of σQS, in late autumn and in winter σQL sometimes reached 5%–7% of σQS. Entropy production in the long-wave radiation balance at site B during April–October was higher than at the WS site by a factor of 1.4.
sums for 2000–2005 in wet and dry spruce forests were almost identical, i.e., 10.6 ± 0.7 and 10.4 ± 0.5 W·m−2
) in WS and DS, respectively (Figure 5
). The bog monthly σQS
sums in the growing season of 1999 were lower by 8%–18% than in the WS forest, and the cumulative sum of σQS
for April–October at B was 11.6% lower than in the WS forest. Annual σQL
at WS and DS sites reached 0.8 and 1.0% of σQS
Radiative entropy production in the studied ecosystems had strong diurnal and seasonal courses and inter-annual variation at a level of 10%. Most (90%) of the annual entropy production in spruce forests was associated with the snow-free period determined by the level of albedo. According to tower measurements, the 2000–2008 snow-free period lasted from 27 March to 4 November (222 days). Wet and dry spruce forests were very close in terms of entropy production, but entropy production at the bog in April–October of 1999 was 11.6% lower than in the wet spruce forest. The efficiency of entropy production in spruce forests during the growing season was stable and exceeded 90%, but it strongly fluctuated in winter and decreased by 10%–20% in comparison with the summer level. The efficiency of entropy production at the bog during the growing season significantly increased after rains, as well as in April and November, in comparison with mid-summer, and dropped sharply when the bog was snow-blanketed.
3.2. Factors Affecting Entropy Production
According to Equation (2), there are two groups of factors affecting entropy production: radiation (changes in Qs,in and albedo) and surface temperature. We will estimate the importance of these two groups on different time-scales for the studied sites.
The monthly sums of incident radiation (Qs,in
) at all three sites were very close, suggesting that the studied ecosystems receive approximately the same amount of solar energy. Net short-wave radiation, Qs,net
, in the boreal climate of the CFBR was 3183 ± 167 (1999–2006) and 3110 ± 170 (2000–2008) MJ·m−2
at WS and DS, respectively. For comparison, two-year means of Qs,net
in temperate-climate ecosystems of the Duke Forest (Durham, NC, USA) were 4395 (Old Field), 4912 (Planted Pine) and 4736 (Hardwood) MJ·m−2
]. The albedo of the bog in April–October was significantly higher and Qs,net
was about 10.1% lower than that of spruce forests.
The low-productive paludified forest has a slightly lower short-wave daily albedo (α
), calculated as the daily sums of Qs,in
, during the summer months than the highly productive nemorose forest, namely 0.080 versus 0.094, but in other seasons the α
of WS was slightly higher (Figure 6
). From June to September α
was quite stable in the two spruce forests. On the contrary, the bog α
varied over a wide range, from 0.15 to 0.20, and dropped by 0.025–0.05 after each rain event. The albedo did not depend on cloudiness for the spruce forests, but α
at the bog was significantly lower on “overcast” days (under our criteria, see Section 2.2
). It is explained by the fact that, on these days, precipitation events usually took place and the water level, water area, and peat moistening of the bog increased, whereas water has a lower α
than the bog plant cover. The highest difference in α
between the bog and forests was recorded at the end of periods without rain. Twice a year, just after the snow melted and just before the formation of snow cover, a distinctive decrease in α
at all sites took place, which is probably linked with phenological changes of herbs and mosses and/or the flooding of soil and mosses with water. In these few spring and autumn days, the ecosystem α
came to its annual low, i.e., 0.07 at the spruce sites and 0.10–0.12 at the bog site. The considerable difference between the bog and spruce sites was also found in the winter level of α
: while the snow-blanketed bog reflected 40%–80% of the incident solar radiation, the evergreen spruce forests sent back only 15%–30%. The low α
of the bog under snow was also the cause of the low entropy production efficiency.
According to Equation (2), the seasonal variation of entropy production in the boreal climate followed the dynamics of the net short-wave radiation (see Figure 3
). Averaged for all given years, QS,net
in December at WS (25.5 MJ·m−2
) was 22 times lower than in July (563.6 MJ·m−2
), while (1/Tsurf
) ranged only from 0.003746 (with an average temperature of −6.2 °C) to 0.003416 (with a temperature of +19.6 °C), which makes up a difference of 9.2% between the minimal and the maximal values. At DS, QS,net
in December (on average for all measurement periods) was 23 times lower than in July, while (1/Tsurf
) differed by 8.9%. So, in CFBR, QS,net
variations were 240–260 times greater than variations of (1/Tsurf
), which allows us to conclude that temperature plays a minimal role in the seasonal variation of radiative entropy production.
The inter-annual variation of entropy production also was driven by variations in short-wave radiation. In “sunny” 2002, QS,net as well as QS,in were maximal among all years of measurements, and the σ sum also reached its highest level, whereas in “cloudy” 2003, both QS,net and σ were minimal. The coefficient of variation (CV) of the temperature term (1/Tsurf − 1/Tsun) between different years at WS was 0.19% and at DS it was 0.21%, while the CV of QS,net was at 6.13% at WS and at 5.47% at DS. In other words, the inter-annual variation of QS,net was 32-fold (at WS) or 26-fold (at DS) larger than the inter-annual variation of (1/Tsurf − 1/Tsun). Inter-annual changes in solar radiation were much more important for entropy production in comparison to changes in temperature. Annual entropy production was at its highest in 2002 and 2015 with dry and sunny summers. Therefore, in southern taiga forests, drought had a positive role in entropy production.
For CFBR spruce forests, the full-year albedo of WS was slightly lower (by 0.3%) and Qs,net was a bit higher than that of DS, but this difference was of the same order for the final value of σ as the random fluctuation of the simultaneous incoming radiation (due to changing cloudiness) between the sites. The surface temperature was almost equal for the two spruce forests. The bog site was characterized by both lower Qs,net and 1/Tsurf than the WS forest. The bog was usually warmer than the forest: the average radiative surface temperature at B in April–October was 0.63 °C higher than at WS, but on some summer days it was 2–4 °C higher. On some November days the difference between the daily-averaged temperature at B and WS reached 6 °C because the bog was still left snow-free due to the high heat storage capacity of the incorporated water. However, even this 6 °C difference resulted only in a 2.3% difference in the daily entropy production, whereas the November albedo difference resulted in a 4% difference in σ. During daytime in the warm period of 1999, the temperature term of Equation (2) varied only from 0.0030 to 0.0036 K−1 both at the WS and B sites, while the radiation term varied from 0 to more than 900 Wt·m−2. Therefore, for analysis of the significance of the two terms for the integral σ, we may regard the temperature term as almost constant. Through the rates of the averaged temperature terms at the two sites, the integral radiation terms at the two sites, and the integral entropy production at the two sites, we may evaluate the relative importance of the two terms for the increased σ of the WS forest in comparison to the bog. The temperature effect on the larger value of σ at WS than at B was only about one-eighth, and seven-eighths of the entropy increment was associated with higher radiation absorption by the forest.
The tentative calculations for the entropy production in the WS forest under higher temperatures, but the same radiation, showed that if the surface temperature increased by 2, 4, and 6 °C, respectively, the annual sum of σ, averaged for 2000–2005, would decrease only by 0.8%, 1.6%, and 2.3%.
The above-given calculations demonstrate that changes in the incoming solar radiation (linked with changes in cloudiness) had a much larger effect on the daily, seasonal, and inter-annual variability of entropy production than changes in the surface temperature. Changes in temperature became more significant if the annual sums of entropy production were compared at different sites. The entropy production efficiency in spruce forests during all of the growing seasons was high and very stable due to the stable albedo. Temperature changes in warm periods had a minor effect on the entropy production. When moistening of the bog increased (after rains and in mid-seasons), the albedo significantly decreased and the efficiently of the entropy production increased.