杉木人工林断面积生长规律及动态模拟
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摘要
断面积生长预估是林分生长和收获预估体系中的核心因子和基础。本研究以杉木密度试验林和密度间伐试验林为研究对象,在全林分、径阶和单木三个水平上,全面探讨断面积生长动态规律及其与林分因子之间的关系并采用相应模型对断面积生长动态进行模拟。主要结果如下:
1.密度试验林断面积生长的关系规律
对于密度试验林,分别对相同初始林分密度、立地条件下林分断面积进行比较分析;采用Chapman-Richards’方程计算林分累积胸高断面积曲线的拐点年龄(A*),应用回归模型讨论初始林分密度和立地质量与林分生长率的关系。结果表明:在幼龄林阶段,初始林分密度(单位面积林木株数)越大,立地条件越好,则林分断面积越大,林分断面积生长率也越大,达到最大生长率时间最短,这一阶段立地条件对林分的生长起主要作用;初始林分密度越大,立地条件越好的林分,进入郁闭的时间也越早。在达到最大断面积生长率后,初始林分密度大的小区其断面积生长率降低的幅度较初始林分密度小的小区大。当林分进入竞争阶段,尽管林分断面积生长率下降,但林分断面积仍旧与初始林分密度呈正相关,初始林分密度大的林分林分断面积仍旧大;当林分开始自疏并达到稳定状态时,林分单木死亡导致的断面积减小则由存活木的高生长率所弥补。林分断面积虽然还在增加,但增加幅度逐渐变小。最终,一定初始林分密度范围内,林分断面积趋于一致。对于相同立地下,同密度小区的林分断面积生长率基本相同,而不同密度小区之间林分断面积生长率差异明显。低于一定林分密度(2m×1m)下的林分几乎没有自疏现象发生。
在相同林分密度下,立地指数越小,枯死木出现的时间越早。而立地指数越大,枯死木断面积比例也越大。随着林分密度由低到高,枯死木的断面积值达到最高点的时间逐渐变短。对于相同初始密度,同一立地指数级的小区枯损趋势比较接近,但是由于立地条件的差异,枯损的数量有所不同。
林分雪灾受害比例大体上随着林分密度的增加呈现上升趋势。立地指数高,雪压受损程度小。位于坡度大的小区林木受害的面积比例远大于坡度小的小区。
2.间伐对林分断面积的影响
在立地相同的条件下,间伐次数和间伐强度均随着林分初始密度的增大而增大。在林分密度相同条件下,立地指数大的小区间伐强度明显大于立地指数小的小区。林分密度越大,立地条件越好,首次间伐时间也越早。对同一小区间伐前后断面积分布比较可知:间伐后各个小区在低径阶上的断面积分布比重明显减小。在对不同小区进行首次间伐后,不同径阶上的断面积随径阶增大出现左偏趋势。但随着间伐次数的增加,断面积随径阶左偏的趋势逐渐减弱,并有趋于正态分布的趋势。经过最后一次间伐(小区密度为1667n/hm-1)后,多数小区则又呈现左偏趋势。
对同立地条件下不同时期间伐后的保留密度小区与临近密度的小区林分断面积比较可知:对于立地条件差的小区(SI=14),小断面积的林木所占比例大。对于立地条件好的小区(SI=16),间伐后与同密度未间伐小区林分断面积相比呈现一定的规律性:随着间伐次数的增多,大、中径阶所对应的林分断面积逐渐增加。
相同立地、初始密度下,间伐与未间伐林分断面积比较:对于中(C)、高(E)密度的林分,在立地条件差(SI=14)的情况下,经过间伐的林分的断面积远小于没有间伐的林分;而立地条件好(SI=16)的林分,间伐林分的断面积与未间伐的林分断面积趋同。
3.林分断面积生长的动态模拟
以三个广为应用的方程(Korf、Hossfeld和Bertalanffy-Richards)作为基础方程,应用广义代数差分(GADA)模型对密度试验林和密度间伐试验林断面积生长动态进行模拟。模拟结果显示:(1)由于GADA可以消除异方差问题,从而获得了对林分生长模拟更高的模拟精度;(2)在给出的10个GADA形式的模型中,以两个与立地有关参数(a1、a2)的KorfⅢ方程最为合适的模拟方程。其具体形式为:
4.径阶水平断面积生长规律
径阶划分与模拟精度之间有着非常紧密的关系。断面积误差%( PS )与径阶距(a )成正相关和平均直径(d )成负相关。具体关系为: P_S = ( a/(2d))~2(%).
通过径阶整化和添加方程极值的方法,增加用来模拟的数据对,从而达到了提高模拟精度的目的。通过对不同方程模拟得到的R a2dj、Root MSE、RSS进行比较检验。最终,按照模拟精度从高到低前4位分别是:Champan-Richards’> Richards’>Weibull(3参数)>Logistic。采用径阶累加作比的方法,令极值为常数1。这样模拟得到的结果与渐近值作为参数时结果极为接近,完全可信。按照方程参数与林分因子之间的关系,方程稳定性顺序为:Weibull(3参数)>Logistic>Richards’>Champan-Richards’。
6.单木断面积生长规律及模拟
Chow检验的结果显示:雪灾发生前后,单木断面积生长趋势没有发生显著差异。不论优势木、中间木还是被压木,单木的断面积都随着林龄的增加而增加。同一初始林分密度下,立地指数大的林分单木的断面积大,并且断面积增长趋势接近。对于同一密度,优势木随株数变化的累积断面积最大,中间木其次,被压木最小。在相同立地下,高密度林分的株数变化范围大,但是对应的累积断面积变化范围较小。对于同一林层单木,初始林分密度越小,单木断面积增长幅度越大,密度对单木断面积的影响越显著。对于被压木,低密度林分的断面积增长要远高于中、高密度林分。
通过对年珠和青石湾样地单木断面积蓄积生长量进行面板数据分析,可以得到以下结论:(1)单木断面积蓄积生长量受立地条件影响最大,立地条件越好,单木断面积蓄积生长量越大;(2)在一定立地条件下,单木断面积蓄积生长量与林分密度呈负相关,密度越大,单木断面积蓄积生长量越小;(3)采用竞争指数可以很好的反映单木断面积的生长规律;(4)间伐是减小单木竞争,保证保留木有足够生长空间的有效方式,同时,间伐对于单木断面积生长的影响非常明显。
Basal area growth system is a key componmet of stand-level models, since basal area is directed related to other very important variables.In this paper, relationship between basal area and stand factors, which is based on spacing and thinning trials at whole- stand, size-class and individual tree levels at the Chinese fir plantations.
Stand basal area growth trends with spacing trials have shown at the initial same growing space or site indexes; variance analysis is used to explain stand density effect; Richard’model was chosen as the cumulative stand basal area function and the ages of the growth curves inflection points were found by determining the age at which the second partial derivate of the Richard’model; regression analysis is used to illustrate relationship between stand basal area growth rate and stand density, site quality.Inspection of these data revealed that stand basal area is well correlated with stand density, site quality. The cumulative stand basal area and growth rate increase progressively with increasing initial density and better site quality.The age at which the growth rate culminates increases as initial stocking density decreases. After culmination the growth rate declines much faster for higher stocking densities, causing the growth rate for the higher densities to drop below those for the lower densities. Stand basal growth rate decreases at competition stage, while cumulative stand basal area increases slightly. When stand growth reaches a dynamic stable balance, the cumulative stand basal area converges to one at a certain initial stand density level. Self-thinning has no begin under a certain initial stand density level.
At the same stand density, the low site index lead to high natural mortality. Stand density become from low to high, when the snag basal area reaches the maximum value early.
The higher stand density, snow damage is higher; the higher site index, snow damage lower. Compared with the low slope, snow damage ratio is larger at the high slope.
Thinning indiciates: after thinning was done, the different size-class logs can be gained and the remained trees growth is promoted. When trees were planted with higher site and stand density, the small size-class timber was gained. Above a certain stand site, the cumulative stand basal area between thinned and unthinned converges to one.
Three well-known growth functions (Korf, Hossfeld and Bertalanffy-Richards) were considered for developing a stand basal area growth system for the different spacing and thinning artificial trials. Among the ten dynamic equations finally evaluated for basal area projection, the Generalized Algebraic difference Approach (GADA) formulation from the Korf equation that considered parameters a1 and a2 to be site specific was selected. The concrete formulation is fllowing:
The basal area erroris is in proportion to diameter class and inversein proportion to mean diameter. That is P_S = ( a/2d)~2(%).
The results were showed with basal area at the size-class level that (1)well relationship between size-class and simulation precision; (2) compared with R a2dj, Root MSE and RSS, Champan-Richards’has the higher precision gains than those, then Richards’, Weibull (3 parameters) and Logistic. Furthermore, the interval estimation with the model parameters also proved to the identical results; (3) applying size-class cumulating method, the asymptote value equals to 1. As a result, the number of the model parameters decrease and the estimated results is parallel with that the parameters is unequal to 1; ( 4) the model stability was gained by relationship between model parameters and stand factors: Weibull(3 parameters)higher, then Logistic, Richards’and Champan-Richards’.
The results were showed that snow damage didn’t changed individual tree growth trends using Chow test with spacing and thinning artificial trials. The panel data provides a useful model of individual tree basal area grow trends. (1) the basal area increment is well correlated with site quality; (2) at a certain site index level, the basal area increment decreases while stand density increases; (3)by adding competition indexes, the basal area growth outperforms; (4)thinning decreases inter-individual tree competition and makes the remained trees gain enough growth resource.
1.密度试验林断面积生长的关系规律
对于密度试验林,分别对相同初始林分密度、立地条件下林分断面积进行比较分析;采用Chapman-Richards’方程计算林分累积胸高断面积曲线的拐点年龄(A*),应用回归模型讨论初始林分密度和立地质量与林分生长率的关系。结果表明:在幼龄林阶段,初始林分密度(单位面积林木株数)越大,立地条件越好,则林分断面积越大,林分断面积生长率也越大,达到最大生长率时间最短,这一阶段立地条件对林分的生长起主要作用;初始林分密度越大,立地条件越好的林分,进入郁闭的时间也越早。在达到最大断面积生长率后,初始林分密度大的小区其断面积生长率降低的幅度较初始林分密度小的小区大。当林分进入竞争阶段,尽管林分断面积生长率下降,但林分断面积仍旧与初始林分密度呈正相关,初始林分密度大的林分林分断面积仍旧大;当林分开始自疏并达到稳定状态时,林分单木死亡导致的断面积减小则由存活木的高生长率所弥补。林分断面积虽然还在增加,但增加幅度逐渐变小。最终,一定初始林分密度范围内,林分断面积趋于一致。对于相同立地下,同密度小区的林分断面积生长率基本相同,而不同密度小区之间林分断面积生长率差异明显。低于一定林分密度(2m×1m)下的林分几乎没有自疏现象发生。
在相同林分密度下,立地指数越小,枯死木出现的时间越早。而立地指数越大,枯死木断面积比例也越大。随着林分密度由低到高,枯死木的断面积值达到最高点的时间逐渐变短。对于相同初始密度,同一立地指数级的小区枯损趋势比较接近,但是由于立地条件的差异,枯损的数量有所不同。
林分雪灾受害比例大体上随着林分密度的增加呈现上升趋势。立地指数高,雪压受损程度小。位于坡度大的小区林木受害的面积比例远大于坡度小的小区。
2.间伐对林分断面积的影响
在立地相同的条件下,间伐次数和间伐强度均随着林分初始密度的增大而增大。在林分密度相同条件下,立地指数大的小区间伐强度明显大于立地指数小的小区。林分密度越大,立地条件越好,首次间伐时间也越早。对同一小区间伐前后断面积分布比较可知:间伐后各个小区在低径阶上的断面积分布比重明显减小。在对不同小区进行首次间伐后,不同径阶上的断面积随径阶增大出现左偏趋势。但随着间伐次数的增加,断面积随径阶左偏的趋势逐渐减弱,并有趋于正态分布的趋势。经过最后一次间伐(小区密度为1667n/hm-1)后,多数小区则又呈现左偏趋势。
对同立地条件下不同时期间伐后的保留密度小区与临近密度的小区林分断面积比较可知:对于立地条件差的小区(SI=14),小断面积的林木所占比例大。对于立地条件好的小区(SI=16),间伐后与同密度未间伐小区林分断面积相比呈现一定的规律性:随着间伐次数的增多,大、中径阶所对应的林分断面积逐渐增加。
相同立地、初始密度下,间伐与未间伐林分断面积比较:对于中(C)、高(E)密度的林分,在立地条件差(SI=14)的情况下,经过间伐的林分的断面积远小于没有间伐的林分;而立地条件好(SI=16)的林分,间伐林分的断面积与未间伐的林分断面积趋同。
3.林分断面积生长的动态模拟
以三个广为应用的方程(Korf、Hossfeld和Bertalanffy-Richards)作为基础方程,应用广义代数差分(GADA)模型对密度试验林和密度间伐试验林断面积生长动态进行模拟。模拟结果显示:(1)由于GADA可以消除异方差问题,从而获得了对林分生长模拟更高的模拟精度;(2)在给出的10个GADA形式的模型中,以两个与立地有关参数(a1、a2)的KorfⅢ方程最为合适的模拟方程。其具体形式为:
4.径阶水平断面积生长规律
径阶划分与模拟精度之间有着非常紧密的关系。断面积误差%( PS )与径阶距(a )成正相关和平均直径(d )成负相关。具体关系为: P_S = ( a/(2d))~2(%).
通过径阶整化和添加方程极值的方法,增加用来模拟的数据对,从而达到了提高模拟精度的目的。通过对不同方程模拟得到的R a2dj、Root MSE、RSS进行比较检验。最终,按照模拟精度从高到低前4位分别是:Champan-Richards’> Richards’>Weibull(3参数)>Logistic。采用径阶累加作比的方法,令极值为常数1。这样模拟得到的结果与渐近值作为参数时结果极为接近,完全可信。按照方程参数与林分因子之间的关系,方程稳定性顺序为:Weibull(3参数)>Logistic>Richards’>Champan-Richards’。
6.单木断面积生长规律及模拟
Chow检验的结果显示:雪灾发生前后,单木断面积生长趋势没有发生显著差异。不论优势木、中间木还是被压木,单木的断面积都随着林龄的增加而增加。同一初始林分密度下,立地指数大的林分单木的断面积大,并且断面积增长趋势接近。对于同一密度,优势木随株数变化的累积断面积最大,中间木其次,被压木最小。在相同立地下,高密度林分的株数变化范围大,但是对应的累积断面积变化范围较小。对于同一林层单木,初始林分密度越小,单木断面积增长幅度越大,密度对单木断面积的影响越显著。对于被压木,低密度林分的断面积增长要远高于中、高密度林分。
通过对年珠和青石湾样地单木断面积蓄积生长量进行面板数据分析,可以得到以下结论:(1)单木断面积蓄积生长量受立地条件影响最大,立地条件越好,单木断面积蓄积生长量越大;(2)在一定立地条件下,单木断面积蓄积生长量与林分密度呈负相关,密度越大,单木断面积蓄积生长量越小;(3)采用竞争指数可以很好的反映单木断面积的生长规律;(4)间伐是减小单木竞争,保证保留木有足够生长空间的有效方式,同时,间伐对于单木断面积生长的影响非常明显。
Basal area growth system is a key componmet of stand-level models, since basal area is directed related to other very important variables.In this paper, relationship between basal area and stand factors, which is based on spacing and thinning trials at whole- stand, size-class and individual tree levels at the Chinese fir plantations.
Stand basal area growth trends with spacing trials have shown at the initial same growing space or site indexes; variance analysis is used to explain stand density effect; Richard’model was chosen as the cumulative stand basal area function and the ages of the growth curves inflection points were found by determining the age at which the second partial derivate of the Richard’model; regression analysis is used to illustrate relationship between stand basal area growth rate and stand density, site quality.Inspection of these data revealed that stand basal area is well correlated with stand density, site quality. The cumulative stand basal area and growth rate increase progressively with increasing initial density and better site quality.The age at which the growth rate culminates increases as initial stocking density decreases. After culmination the growth rate declines much faster for higher stocking densities, causing the growth rate for the higher densities to drop below those for the lower densities. Stand basal growth rate decreases at competition stage, while cumulative stand basal area increases slightly. When stand growth reaches a dynamic stable balance, the cumulative stand basal area converges to one at a certain initial stand density level. Self-thinning has no begin under a certain initial stand density level.
At the same stand density, the low site index lead to high natural mortality. Stand density become from low to high, when the snag basal area reaches the maximum value early.
The higher stand density, snow damage is higher; the higher site index, snow damage lower. Compared with the low slope, snow damage ratio is larger at the high slope.
Thinning indiciates: after thinning was done, the different size-class logs can be gained and the remained trees growth is promoted. When trees were planted with higher site and stand density, the small size-class timber was gained. Above a certain stand site, the cumulative stand basal area between thinned and unthinned converges to one.
Three well-known growth functions (Korf, Hossfeld and Bertalanffy-Richards) were considered for developing a stand basal area growth system for the different spacing and thinning artificial trials. Among the ten dynamic equations finally evaluated for basal area projection, the Generalized Algebraic difference Approach (GADA) formulation from the Korf equation that considered parameters a1 and a2 to be site specific was selected. The concrete formulation is fllowing:
The basal area erroris is in proportion to diameter class and inversein proportion to mean diameter. That is P_S = ( a/2d)~2(%).
The results were showed with basal area at the size-class level that (1)well relationship between size-class and simulation precision; (2) compared with R a2dj, Root MSE and RSS, Champan-Richards’has the higher precision gains than those, then Richards’, Weibull (3 parameters) and Logistic. Furthermore, the interval estimation with the model parameters also proved to the identical results; (3) applying size-class cumulating method, the asymptote value equals to 1. As a result, the number of the model parameters decrease and the estimated results is parallel with that the parameters is unequal to 1; ( 4) the model stability was gained by relationship between model parameters and stand factors: Weibull(3 parameters)higher, then Logistic, Richards’and Champan-Richards’.
The results were showed that snow damage didn’t changed individual tree growth trends using Chow test with spacing and thinning artificial trials. The panel data provides a useful model of individual tree basal area grow trends. (1) the basal area increment is well correlated with site quality; (2) at a certain site index level, the basal area increment decreases while stand density increases; (3)by adding competition indexes, the basal area growth outperforms; (4)thinning decreases inter-individual tree competition and makes the remained trees gain enough growth resource.
引文
[1]张建国,段爱国.理论生长方程与直径结构模型的研究.北京:科学出版社, 2004. 1-3
[2]张守攻.工业人工林的培育和高效利用.北京:中国林业出版社, 2002. 1-4
[3]雷加富.中国森林资源.北京:中国林业出版社.2005.172.
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