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Shanxi Academy of Forestry Sciences, Taiyuan 030012, China

1 Introduction

Shanxi is a main distribution area ofPinustabulaeformisforest in China. The area ofP.tabulaeformisis 9.999×105ha, accounting for 40.5% of the total forest land in Shanxi Province, and its productivity directly affects the forest quality of the forest in Shanxi Province[1]. Since the 1950s, extensive studies have been carried out on forest productivity worldwide, which have played an important role in vegetation restoration, operation and management. Since the 1970s, China has also carried out related work. Based on the national scale study of forest resource inventory results, Zhao Min[2]established the ChineseP.tabulaeformisbio-climate productivity (NPPa) model and estimated that the net primary productivity ofP.tabulaeformisforest was 7.82 t/(ha·year), in which the average productivity ofP.tabulaeformisforest in Shanxi Province was 7.4 t/(ha·year). Fang Jingyunetal.[3]studied the national total forest productivity and the productivity of categories of forest, and the results showed that the total forest productivity was 1.18×109t/a. According to statistics of the productivity for different age groups ofP.tabulaeformisforest by Luo Tianxiangetal.[4], the total forest productivity ofP.tabulaeformiswas 7.57 t/(ha·year). The productivity ofP.tabulaeformisin individual forest region based on the measured data[5-10]indicated that the annual net productivity of the 39-year-oldP.tabulaeformisforest in the Qinling Mountains was 4.18 t/(ha·year), the net productivity of the 35-year-oldP.tabulaeformisin the Wufeng Mountain Forest Region was 12.917 t/(ha·year), the annual productivity ofP.tabulaeformisforest in Taiyue Mountain was 6.824 t/(ha·year)[11], while there has been no report about dynamic changes in the productivity ofP.tabulaeformisforest in Shanxi Province. The previous studies focused on the arbor layer, and few studies cared about the biomass and productivity of the shrub-grass layer, lacking the estimation factors for the productivity of the forest stand, thus they could not be directly applied to guide the reasonable management of forest stand on the provincial scale.

From the provincial scale, taking artificialP.tabulaeformisforest of different age as the research object, using the method of a large number of actual measurements and growth model, we studied dynamic variations of actual productivity of the forest stand, arbor layer, shrub layer, and herb layer. Besides, using the potential productivity as the target, we predicted the potential growth space of productivity of artificialP.tabulaeformisforest in Shanxi, to provide scientific goal and practical guidance for improving the quality and increasing the efficiency of regional forest stand.

2 Materialsandmethods

2.1OverviewofthestudyareaShanxi Province (110°14′36″-114°33′24″ E，34°34′48″-40°43′24″ N) is located in the eastern part of the Loess Plateau, the middle reaches of the Yellow River, and the upper reaches of the Haihe River, covering a total area of 1.57 × 105km2. The terrain in province is diverse, including mountain, hill, tableland, valley, and plain, while mountains and hills are main parts. According to preliminary calculation, mountains, hills, and plains accounted for 40.0%, 40.3%, and 19.7%, respectively (roughly 4∶ 4∶ 2) of the total area of Shanxi Province, and most areas are located at 1 000 -2 000 m above sea level. With continental monsoon climate, Shanxi Province is dry and cold in winter and hot and rainy in summer, and short in spring and autumn. The temperature difference between space and time is very large. The annual average temperature is 4-14℃, the annual precipitation is 400-650 mm, but the rainfall distribution is not even.

There are six types of forest vegetation in Shanxi Province, namely, coniferous forest, broad-leaved forest, shrub and shrub-grass, grassland, meadow, and swamp and aquatic vegetation. The constructive species of forest community mainly include coniferous trees such asP.tabulaeformis,Pinusbungeana,Piceaasperata,Larixprincipis-rupprechtii,Platycladusorientalis, deciduous oaks such asQuercusliaotungensisandQuercusariabilis, and small-leaf deciduous trees such asPopulusdavidianaandBetulaplatyphylla.P.tabulaeformisis distributed in nine state-owned forest areas including Zhongtiao Mountain, Luliang Mountain, Taiyue Mountain, Taihang Mountain, Guandi Mountain, Guancen Mountain, Wutai Mountain, and Heicha Mountain.

2.2ResearchmethodsBased on the data of precipitation and temperature in Shanxi Province in the past 30 years, the inverse distance weighting (IDW) interpolation method was applied to form the surface data and superimposed with the forest area map. The plate area consolidation index was used to integrate the patches to form a forest ecological zone division map of Shanxi Province. The results of the division formed 11 ecological types, including northern sandstorm-stricken area (annual average temperature < 7.5℃, average annual rainfall < 400 mm sub-area; 400-500 mm sub-area), western loess hilly area (annual average temperature < 7.5℃, average annual rainfall 400-500 mm sub-area; 7.5-10℃, 400-500 mm sub-area; >10℃, >500 mm sub-area), Luliang Mountain rocky mountain area (annual average temperature < 7.5℃, average annual rainfall 400-500 mm sub-area; 7.5-10℃, 400-500 mm sub-area), and eastern rocky mountain area (annual average temperature < 7.5℃, average annual rainfall 400-500 mm sub-area; 7.5-10℃, 400-500 mm sub-area; 7.5-10℃, >500 mm sub-area; >10℃,>500 mm subarea). Based on the similarity of sample points inside the interpolation region, the IDW interpolation method calculates the weighted average value of distance from samples to adjacent regions to estimate the value of the cell, and then obtain a surface by interpolation.

Based on the classification criteria of the ecological type area and the area proportion of the forest group, 30 plots were set up, covering 14 counties of the whole province. The age range of forest stands was 5-63 year. The soil types included loessial soil, chestnut soil, cinnamon soil, gray cinnamon soil. Detailed data about sample plot were listed in Table 1.

Table1BasicdataofsampleplotofPinustabulaeformisforest

(To be continued)

(Continued)

2.2.1Standard plot survey. The arbor layer biomass survey plot was 1 ha large sample plot. We firstly surveyed and made a record of the location, slope aspect, slope and slope position, soil type, and soil thickness. The standard plot survey adopted tree measurement, DBH, and tree height. According to the diameter grade (the minimum DBH was 3 cm, and 2 cm was a grade, 8 grades in total), we selected 50 plants of sample trees. After the sample trees were cut down, we used stratification method to measure the fresh weight of trunks, branches, and fresh leaves, and sampled by mixed sampling method; root system adopted excavation method, and fresh weight was weighed for rhizome, thick roots (>5 cm), and fine roots (<5 cm). The above samples (about 800 pieces) were dried in an oven at 85℃ to a constant weight and the dry matter mass was calculated.

Based on measured data and literature data, using the relative growth equation, we established the empirical equation[12-13]and calculated the biomass per hectare of the stand. For the survey of biomass of shrub-grass layer, five 5 m × 5 m shrub plots were evenly distributed in the plot, in which 1 m × 1 m small plots were set, to survey and make a record of shrubs and herbs, and whole-harvesting method was applied to measure the biomass fresh weight of shrubs, and leaves, branches, and roots were sampled separately; in each 2 m × 2 m subsample, a 1 m × 1 m small plot was set, whole-harvesting method was applied to measure the biomass fresh weight of herbs, and leaves and roots were sampled separately; the above samples were mixed in proper proportion (>1 000 g), dried in an oven at 85℃, to calculate the dry-fresh ratio and dry matter mass of each organ.

2.2.2Calculation method of productivity. (i) Calculation method of actual productivity. The actual productivity of the stand refers to the average annual net primary productivity. It is measured using the "accumulation method" (community harvesting method or existing inventory method)[13], that is, the total amount of newly synthesized organic matter att1andt2. Specifically, the formula is as follows:

P=ΔPg/Δt

(1)

ΔPg=ΔY+ΔR+ΔL+ΔG

(2)

wherePdenotes productivity,Δtis time period,ΔPgdenotes net production,ΔYdenotes increased biomass,ΔRdenotes respiratory consumption,ΔLdenotes litter, andΔGdenotes grain consumption.

In forest ecosystems, because of the complex interrelationship, the conditions necessary to determine net production are rarely achieved, such asΔR,ΔL, andΔG. Therefore, the commonly used formula in reality is:P=ΔY/Δt. During the implementation, the existing biomass was divided by the average age (in this study, the forest age was measured using annual ring analyzer). The arbor layer biomass was determined using the average tree method, and the understory layer and herb layer were determined using sample plot harvesting method (shrub 6 year, herb 1 year)[14].

(ii) Calculation method of potential productivity. Vegetation biomass in a certain area is mainly determined by light, heat and water in the area, while the maximum productivity that the vegetation can achieve under optimum conditions of soil and climate is potential productivity, also called climate productivity. The Miami model was applied to evaluate regional productivity limiting factors; the Thornthwaite Memorial model based on evapotranspiration calculation[15]was a comprehensive representation of the hydrothermal conditions in a region that was able to relate water and heat balance to radiation and calculate the potential productivity of the climate. The climate production potential calculated by Thornthwaite Memorial model is more comprehensive and accurate than that from the Miami model[16]. In this study, we used the Thornthwaite Memorial model to calculate the potential productivity.

Miami model is as follows:

Nt= 3 000/(1+e1.315-0.119 t)

(3)

Np= 3 000(1-e-0.000 664 p)

(4)

whereNtandNpare potential productivity based on temperature and precipitation[g/(cm2·year)],tis annual average temperature (℃),pis annual average precipitation (mm), andeis the base of natural logarithm. According to Liebig’s law of limiting factors, the lower value of the two was selected as the bioproductivity value for each calculation point.

Thornthwaite Memorial model is as follows:

NE= 3 000[1-e-0.000 969 5(E-20)]

(5)

whereNEdenotes the potential productivity based on evapotranspiration[g/(cm2·year)],Edenotes actual annual average evapotranspiration (mm), andeis the base of natural logarithm. The value 3 000 refers to the maximum dry matter production of natural plants of the earth in one year per 1 m2obtained through Lieth statistics.

E=1.05p/[1+(1.05p/L)2]-0.5

(6)

L=300+25t+0.05t2

(7)

whereLdenotes the maximum annual average evapotranspiration (mm),tis annual average temperature (℃), andpis annual average precipitation (mm). Whenp>0.316 L, the formula (5) holds true; whenp<0.316 L,E=p.

2.2.3Data analysis. In the experiment, we used Microsoft Excel software and Origin software to conduct data analysis and processing.

3 Resultsandanalyses

3.1RegressionequationforsingletreebiomassThe results of statistical analysis showed that the biomass of whole plant, trunk, branches, leaves, and roots ofP.tabulaeformisare closely related to the product ofD2(square of DBH) and tree height, and the correlation coefficient was extremely significant (P<0.001, Table 2).

Table2BiomassregressionequationsoforgansofPinustabulaeformis

ItemRegressionequationR2TotalbiomasslnWt=0．6406ln(D2H)-0．23330．9122TrunkbiomasslnWS=0．7562ln(D2H)-2．19190．9291BranchbiomasslnWB=1．3450ln(D2H)-9．90350．9561LeafbiomasslnWL=0．8371ln(D2H)-4．25450．8319RootbiomasslnWR=0．9976ln(D2H)-4．81590．8200

3.2ActualproductivityofP.tabulaeformisforestinShanxiProvinceWith the increase of age ofP.tabulaeformisforest, the productivity of forest stand first increased and then decreased. The range of age with higher productivity was 39-43 year. With the increase of forest age, the productivity showed a decline trend (Fig.1). The actual average productivity ofP.tabulaeformisin Shanxi Province was 4.462 t/(ha·year), and the highest productivity was 5.736 t/(ha·year).

Fig.1Scatterdiagramforgrowthofforestproductivitywithforestage

3.2.1Productivity of layers ofP.tabulaeformisforest. According to the results of productivity of different layers ofP.tabulaeformisforest, with the change of the forest age, the arbor layer productivity remained at about 4.80 t/(ha·year) during the period of 35-45 a; later, with the increase in the forest age, the arbor layer productivity declined, in other words, although the biomass increased, the arbor layer productivity started declining in the near-mature stage; the shrub layer productivity gradually rose, and herb layer productivity gradually declined (Fig.2-Fig.3). For the different forest age groups, the arbor layer productivity reached the maximum in the near-mature stage, the average productivity was 4.843 t/(ha·year), it dropped to 4.312 t/(ha·year) in the mature stage, and the changes were the same for shrub layer and herb layer.

3.2.2Contribution of layers of forest to the productivity. The results of the contribution rate of arbor layer, shrub layer, and herb layer to the productivity of forest stand were shown in Fig.4 and Fig.5. For the arbor layer, the contribution rate in the young period was 72.17%, and later, it remained at about 85%; for the shrub layer, the contribution rate to the productivity before the mature period was 5% on average, and it reached 9.35% in the mature period, exceeding the herb layer; for the herb layer, the contribution rate to the total productivity was highest in the young period (21.16%), later, it gradually declined, and the contribution rate was 10.98%, 7.88% and 5.40%, respectively in middle-age, near-mature, and mature period.

Fig.2Changesinproductivityofdifferentlayerswithforestage

Fig.3Changesinproductivityofdifferentforestagegroups

Fig.4ChangesofcontributionrateoflayersofPinustabulaeformisforestwiththeforestage

3.3PotentialproductivityofP.tabulaeformisforestThe Thornthwaite Memorial model based on evapotranspiration calculation was a comprehensive representation of the hydrothermal conditions in a region that was able to relate water and heat balance to radiation and calculate the potential productivity of the climate. The evapotranspiration is influenced by a series of climatic factors such as solar radiation, temperature, precipitation, saturation, air pressure, and wind. The climate production potential calculated by Thornthwaite Memorial model is more comprehensive and accurate than that from the Miami model. Therefore, the potential productivity ofP.tabulaeformisforest in Shanxi Province was t/(ha·year), and the average productivity was 4.462 t/(ha·year), which is only 53% of the potential productivity.

Fig.5Contributionrateoflayersofforestwithdifferentage

Table3PotentialproductivityofPinustabulaeformisforest

t/(ha·year)

3.4PotentialofimprovingqualityandincreasingproductivityofP.tabulaeformisinShanxiProvinceAmong the research plots, the actual productivity ofP.tabulaeformisforest was the highest (5.736 t/ha·year) in Qinyuan County. Qinyuan County is situated in forest ecosystem type 10 zone (average temperature >10℃, and rainfall > 500 mm), the ratio of productivity of arbor, shrub, and herb is 60∶ 5∶ 6. Under forest, there are Acer ginnala Maxim and oaks and the soil is weakly acidic. Taking the potential productivity as the base, the actual productivity ofP.tabulaeformisforest was only 68% of the potential productivity, so there is at least 32% space for increase of the productivity.

The results show that the potential productivity ofP.tabulaeformisbased on temperature in Shanxi Province was 12.954 t/(ha·year), and the potential productivity based on rainfall was 8.172 t/(ha·year). According to Liebig’s law of limiting factors, for the potential productivity based on temperature and rainfall, we selected the lower value of the two as the productivity value of the calculation point. WhenNt-Np>0, the productivity limit factor in this area is precipitation; whenNt-Np<0, the productivity limit factor in this area is temperature. According to Table 3, the limiting factor of all distribution areas is the rainfall. Therefore, the main limiting factor of the productivity ofP.tabulaeformisforest in Shanxi Province is rainfall.

4 Conclusionsanddiscussions

The productivity ofP.tabulaeformishas a close relationship with the forest age. With the increase in forest age, the productivity ofP.tabulaeformisforest firstly increases and then gradually decreases after maturity period; the average productivity ofP.tabulaeformisforest is 4.462 t/(ha·year) on average, which is greatly different with conclusions (7.4 t/(ha·year) of Zhao Minetal.[2]. On the one hand, the latter is added with the contribution of litter, so the total productivity will increase. On the other hand, it is related to the accuracy of the data source; the arbor layer productivity is the smallest in the young stand period, the contribution rate accounts for 72.17%. With the increase of the forest age, the total biomass of forest stand continues increasing. In the transition period from near-mature and mature, the net productivity starts declining.

The maximum contribution (21.16%) of herb layer to total productivity appears in the young stand period, and later, it gradually declines; conversely, the contribution rate of shrub layer productivity gradually increases, and the contribution rate in mature stage exceeds that of the herb layer. Because of the absolute advantage of the contribution rate of the arbor layer, the contribution of shrubs and herbs is often neglected. In this study, we found that the absolute productivity and contribution rate of arbor layer start declining, and the productivity of shrub layer exceeds that of the herb layer. In the relationship between three layers, thus it is a key period for adjustment of forest stand structure.

The potential productivity ofP.tabulaeformisforest in Shanxi Province is 8.422 t/(ha·year). Taking the potential productivity as the base, there is at least 32% space for increase of the productivity ofP.tabulaeformisforest. The primary limiting factor for the productivity ofP.tabulaeformisforest is rainfall, which is consist-

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