# Radiative Entropy Production along the Paludification Gradient in the Southern Taiga

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory, Methods, and Data

#### 2.1. Theory

_{S,in}), short-wave outgoing (Q

_{S,out}), long-wave incoming (Q

_{L,in}), and long-wave outgoing (Q

_{L,out}) radiation.

_{n}is formed as the difference of the incoming and outgoing radiation fluxes:

_{S,in}and Q

_{S,out}are the incoming and outgoing short-wave radiation, respectively; Q

_{L,in}and Q

_{L,out}are the incoming and outgoing long-wave radiation, respectively; net short-wave radiation Q

_{S,net}= Q

_{S,in}− Q

_{S,out}; and net long-wave radiation Q

_{L,net}= Q

_{L,in}− Q

_{L,out}. All terms are in W·m

^{−2}.

_{sun}is the sun’s surface temperature, which approximately equals 5780 K; T

_{surf}is the radiometric surface temperature, calculated from Q

_{L,out}using the Stefan-Boltzmann equation:

_{surf}is the surface emissivity calculated as:

_{S,out}divided by Q

_{S,in}. Note that in Equation (2), Q

_{S,net}depends on full-day, rather than noontime, albedo.

_{sky}is the temperature of the sky and it also can be accessed from Q

_{L,in}using the Stefan-Boltzmann equation:

_{sky}, was assumed to be 0.85 and A was again assumed to be one.

_{S}and σQ

_{L}:

_{S,net}is assumed to be equal to Q

_{S,in}and T

_{surf}is replaced by T

_{air}:

_{QL,max}is often two orders of magnitude less than ${\sigma}_{Qs,max}$ [22], so the total EMEP is approximately equal to ${\sigma}_{Qs,max}$:

_{surf}ranges from –80 °C to +80 °C (approximate temperature limits on Earth’s surface), 1/T

_{surf}ranges from 0.05177 to 0.02832 K

^{−1}, while 1/T

_{sun}= 0.000173 K

^{−1}, i.e., 1/T

_{sun}amounts to 3.3%–6.1% of 1/T

_{surf}. If we suppose (1) the diurnal temperature ranges from 0 to 40 °C; (2) consequent day-to-day temperature changes from 10 to 20 °C; and (3) inter-annual temperature changes from 20 to 25 °C (in most real ecosystems the range is usually smaller), the temperature term $\left(\frac{1}{{T}_{surf}}-\frac{1}{{T}_{sun}}\right)$ will vary by about 14.4% around the average value in the first case, by about 3.7% in the second case, and by about 1.8% in the third case. By contrast, the radiative term Q

_{S,net}may range from 0 to more than 1000 W·m

^{−2}during the day, three-fold (hundreds W·m

^{−2}) from an overcast day to a clear day, and by 10%–20% from year to year. Consequently, using real data, Q

_{S,net}usually shows much greater variation at different time-scales than $\left(\frac{1}{{T}_{surf}}-\frac{1}{{T}_{sun}}\right)$.

#### 2.2. Methods

_{S,in}), short-wave outgoing (Q

_{S,out}), long-wave incoming (Q

_{L,in}), and long-wave outgoing (Q

_{L,out}) radiation, collected at eddy covariance sites with a native half-hourly time-step (see Section 2.3). Quality control of the used data included spike removal, the exclusion of non-physical values, like non-zero short-wave radiation at night (which sometimes takes place due to instrument biases), examination of congruence of in- and outgoing short-wave radiation using albedo values, excluding days in December–February with too low short-wave radiation for albedo calculations, etc. WinABD software (Deshcherevskii, IPE RAS, Moscow, Russia [33,34,35]) was used for the analysis of long-term data with unavoidable gaps. For the calculation of daily, monthly, and annual entropy sums, missed data on radiation were filled. However, missed data rates in the key parameters for our calculation, i.e. fluxes of short-wave radiation, did not exceed 4% of all data for the studied periods (see Section 2.3). Incoming short-wave radiation was filled using data on photosynthetically active radiation at the same site (correlation coefficients for available quaility-controlled data were 0.99), or extrapolation from neighboring site (correlation coefficients were more than 0.96). Reflected radiation was filled using the average duirnal course of the albedo in the same season multiplied by Q

_{S,in}after filling of Q

_{S,in}. Long-wave outgoing radiation was filled using air temperature above the canopy, because these parameters demonstrated an excellent correlation (>0.99). If such information was absent, we used a running mean (in case of 30 min–2 h gaps), running average diurnal course, or mean diurnal course for the same month in other years (for gaps from a few days to few weeks). To analyze how entropy production and σ/EMEP change under varying weather conditions in the mid-growing-season, only data from 15 May to 31 July were chosen. Sunny, variable clouds, and overcast days were selected using the following rough approximation: for each site, separately, 10% of days with the highest Q

_{S,in}sums were determined as “sunny”, 10% of days with the lowest Q

_{S,in}sums were determined as “overcast”, and days from the 45th percentile to the 55th percentile of Q

_{S,in}sums were considered as “variable cloud” days. The first sample was in a good agreement with sunny days distinguished by the regular diurnal course, though a few days with low cloud amounts were also regarded as “sunny”.

#### 2.3. Sites and Data

## 3. Results

#### 3.1. Entropy Production in Ecosystems of the Southern Taiga

_{S}, in late autumn and in winter σQ

_{L}sometimes reached 5%–7% of σQ

_{S}. 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.

_{S}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}·K

^{−1}·year

^{−1}(Table 2) in WS and DS, respectively (Figure 5). The bog monthly σQ

_{S}sums in the growing season of 1999 were lower by 8%–18% than in the WS forest, and the cumulative sum of σQ

_{S}for April–October at B was 11.6% lower than in the WS forest. Annual σQ

_{L}at WS and DS sites reached 0.8 and 1.0% of σQ

_{S}, respectively.

#### 3.2. Factors Affecting Entropy Production

_{s,in}and albedo) and surface temperature. We will estimate the importance of these two groups on different time-scales for the studied sites.

_{s,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, Q

_{s,net}, in the boreal climate of the CFBR was 3183 ± 167 (1999–2006) and 3110 ± 170 (2000–2008) MJ·m

^{−2}·year

^{−1}at WS and DS, respectively. For comparison, two-year means of Q

_{s,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}·year

^{−1}[14]. The albedo of the bog in April–October was significantly higher and Q

_{s,net}was about 10.1% lower than that of spruce forests.

_{s,in}/Q

_{s,out}, 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.

_{S,net}in December at WS (25.5 MJ·m

^{−2}·month

^{−1}) was 22 times lower than in July (563.6 MJ·m

^{−2}·month

^{−1}), while (1/T

_{surf}− 1/T

_{sun}) 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, Q

_{S,net}in December (on average for all measurement periods) was 23 times lower than in July, while (1/T

_{surf}− 1/T

_{sun}) differed by 8.9%. So, in CFBR, Q

_{S,net}variations were 240–260 times greater than variations of (1/T

_{surf}− 1/T

_{sun}), which allows us to conclude that temperature plays a minimal role in the seasonal variation of radiative entropy production.

_{S,net}as well as Q

_{S,in}were maximal among all years of measurements, and the σ sum also reached its highest level, whereas in “cloudy” 2003, both Q

_{S,net}and σ were minimal. The coefficient of variation (CV) of the temperature term (1/T

_{surf}− 1/T

_{sun}) between different years at WS was 0.19% and at DS it was 0.21%, while the CV of Q

_{S,net}was at 6.13% at WS and at 5.47% at DS. In other words, the inter-annual variation of Q

_{S,net}was 32-fold (at WS) or 26-fold (at DS) larger than the inter-annual variation of (1/T

_{surf}− 1/T

_{sun}). 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.

_{s,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 Q

_{s,net}and 1/T

_{surf}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.

## 4. Discussion

^{−1}·year

^{−1}and WS was a carbon source of 1800 kg·C·ha

^{−1}·year

^{−1}in 1999–2004 [41].

^{14}C year BP), the increasing winter temperature resulted in the expansion of mixed coniferous broad-leaved forests, while cooling and moistening of the area resulted in an increasing area of pure spruce forests and the development of oligotrophic sphagnum bogs [51]. Under excessive moistening, some types of bogs exhibit intensive vertical growth, carbon accumulation, and may expand rapidly toward surrounding forests [25]. Modern investigations of [24] using remote sensing data showed that in 1986–2010, in the Central Forest Biosphere Reserve, the total bog area increased from 8% to 10% of the territory. Swamping of territories may result in the increasing instability of the energy balance and entropy production in the landscape of the southern taiga.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Vegetation cover in the southeastern part of the Central Forest Biosphere Reserve. Wet Spruce (WS), Dry Spruce (DS), and Bog (B) are the studied sites (see below). The yellow line is the boundary of the core of the reserve and red points mark the boundary of the buffer zone.

**Figure 2.**Diurnal course of entropy production (σQS) and EMEP at the wet spruce (WS), dry spruce (DS), and bog (B) sites in the Central Forest Biosphere Reserve in sunny conditions (

**a**); variable clouds (

**b**); and overcast conditions (

**c**). See Section 2.1 and Section 2.2 for details of the data sample method and period.

**Figure 3.**Daily entropy production (σQ

_{S}) in short-wave radiation balance at bog (B), wet spruce (WS), and dry spruce (DS) sites in the Central Forest Biosphere Reserve.

**Figure 4.**Efficiency of entropy production in radiation balance (σ/EMEP) at bog (B), wet spruce (WS), and dry spruce (DS) sites (mean for all years, B data with 10 day smoothing). σ/EMEP at B in March and mid-November was 0.5–0.8.

**Figure 5.**Cumulative sums of observed entropy production (Σσ) and EMEP at the wet spruce (WS), dry spruce (DS), and bog (B) sites in the Central Forest Biosphere Reserve in 2000 (

**a**); 2001 (

**b**); 2002 (

**c**); 2003 (

**d**); 2004 (

**e**); and April–October of 1999 (

**f**).

**Figure 6.**(

**a**) Seasonal course of albedo (α) at the dry spruce (DS), wet spruce (WS), and bog (B) sites; (

**b**) Albedo (α) and daily precipitation sums (Pr) at the bog site in 1999; α of B in March and mid-November was 0.4–0.6 and 0.6–0.8, respectively.

Dry Spruce Forest (DS) | Wet Spruce Forest (WS) | Bog (B) | |
---|---|---|---|

Site coordinates | 32.9239° N, 56.4617° E | 32.9039° N, 56.4476° E | 33.0325° N, 56.4750° E |

Site altitude, m a.s.l. | 265.00 | 262.50 | 253.75 |

Vegetation type | Mature nemorose spruce forest with broad-leaved species | Mature paludified shallow-peat spruce forest with birch | Oligotrophic peat bog |

Measurement period | 2000–2008, second half of 2015 | 1998–2005, 2nd halves of 2006 and 2014, 2015 | Warm periods of 1998–2000 |

**Table 2.**Average entropy production and meteorological parameters

^{1}at the bog (B), wet spruce (WS), and dry spruce (DS) sites in the CFBR.

Site (Period) | σQ_{S} | σQ_{L} | EMEP | σ/EMEP | Q_{s,net} | α | T_{surf} |
---|---|---|---|---|---|---|---|

W·m^{−2}·K^{−1} | W·m^{−2} | K | |||||

WS (2000–2005) | 0.3316 | 0.0026 ^{2} | 0.3642 | 0.919 | 100.25 | 0.114 | 279.28 |

DS (2000–2005) | 0.3277 | 0.0033 ^{2} | 0.3653 | 0.901 | 99.55 | 0.117 | 279.19 |

WS (Apr–Oct 1999) | 0.5164 | 0.0041 | 0.5662 | 0.912 | 159.15 | 0.076 | 286.73 |

B (Apr–Oct 1999) | 0.4563 | 0.0057 | 0.5686 | 0.802 | 143.01 | 0.166 | 287.35 |

^{1}Entropy production in short-wave radiation balance (σQ

_{S}) and long-wave radiation balance (σQ

_{L}), empirical maximum entropy production (EMEP), net short-wave radiation (Q

_{s,net}), noon albedo (α), and surface temperature (T

_{surf}).

^{2}Averaged for 2000–2003.

© 2017 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Kuricheva, O.; Mamkin, V.; Sandlersky, R.; Puzachenko, J.; Varlagin, A.; Kurbatova, J.
Radiative Entropy Production along the Paludification Gradient in the Southern Taiga. *Entropy* **2017**, *19*, 43.
https://doi.org/10.3390/e19010043

**AMA Style**

Kuricheva O, Mamkin V, Sandlersky R, Puzachenko J, Varlagin A, Kurbatova J.
Radiative Entropy Production along the Paludification Gradient in the Southern Taiga. *Entropy*. 2017; 19(1):43.
https://doi.org/10.3390/e19010043

**Chicago/Turabian Style**

Kuricheva, Olga, Vadim Mamkin, Robert Sandlersky, Juriy Puzachenko, Andrej Varlagin, and Juliya Kurbatova.
2017. "Radiative Entropy Production along the Paludification Gradient in the Southern Taiga" *Entropy* 19, no. 1: 43.
https://doi.org/10.3390/e19010043