| Quercus variabilis Blume (Cork oak) is both useful in the national economy and environmental protection. However, wood quality of Quercus variabilis Blume is low and benefits of Quercus variabilis Blum can not be brought into full play due to the lack of management. Therefore, mathematical models establishment is requied, basing on which the forests can be managed reasonably and the forests growth dynamic can be grasped.Quercus variabilis Blume (Cork oak) is mainly distributed in the areas of Taihang Mountain and Yan Mountain in North China. Basing on the data from 107 plots and 178 stem analysed trees in 7 sites:(1) The logarithmic curves were selected as oriented curves from 12 mathematical models which were respectively lgH=-0.2059+0.7700lgA (natural forests) and lgH=-0.2505+ 0.84431gA (planted forests). The datum ages for natural forests and planted forests were respectively 50 years and 40 years. Exponential distance for them were both 2 m. Six site index curves (7-17 m) of natural forests and five site index curves (10-14 m) of planted forests were developed. Finally, site index tables by the method of adjusting standard deviation for different stand origins were established. Tested by correlation coefficient, fit significance and forecast accuracy, the results showed that the site index tables had promising precision, and they could be used on Quercus variabilis forests site evaluation.(2) According to the specific models forms for oak trees in Forest Vegetation Simulation (FVS) in America, several mixed effects models with site as a random factor (i.e., FVS model) for different stand origins were built, including:Diameter growth models:DF= 2.023+0.985 x DBHobO (for natural forests); DF= 0.930 x DBHobO+0.184 x SI(for planted forests);Height-diameter models:Logistic equation (for natural forests):H= exp(2.756+-7.753/ (DBHob+1))+1.3; Parabola equation (for planted forests):H= 2.087+0.767 x DBHob+-0.014 x DBHob2;Bark ratio models:DBHib= 0.926 x DBHob0.946(for natural forests); DBHib= 0.781 x DBHob1.020 (for planted forests);Volume models:Vib= 0.00006 x DBHob1.645× H1.001 (for natural forests); Vib= 0.00004 x DBHob1.808 x H1.057 (for planted forests);Crown width models:Bechtold equation (for natural forests):CW= 0.183+0.251× DBHob-0.002 × DBHob2+0.394 × CR-0.028 × BA; linear equation (for planted forests): CW=0.848+0.191×DBHob；Crown ratio models:CL=-0.661+0.617 ×H+0.060×DBHob-0.033×BA(for natural forests)；CL=0.743×H-0.072×BA(for planted forests).(3)Basing on several theretical equations,using dummy Variables to combine the models of different stand orgins,several mixed effects models with site as a random factor(i.e.,self-built model)were built,including:Diameter model:Mitscherlish equation DBHib=(14.921+0.455×DOMTH)×(1一 (0.732×N0.049)×exp(-(0.016×D1+0.018×D2)×A))；Height-diameter model:Richards equation H=1.3+(4.632×DOMTH0.454)×(1一 exp(-0.065×DBHob))0.991xD2+0.913xD1；Crown width model:Logistic equation CW=6.081/(1+exp((((10.726+0.206 x BA)× D1+(10.044+0.183×H)×D2)-DBHob)/(3.810+0.223×DoMTH)))；Crown ratio model:CL=-0.050×BA+0.052×DBHob+0.650×H-0.591×D1.Also,after Box-Cox transformations of variables,compatible taper and Volume models with tree number and stand origins as the random factors were created,including:Bark thickness model:bt=(0.538×tbt+1)(1/0.53B), tbt=-O.881-0.277×tdid5/104+0.669×tdib4/103-O.495×tdib3/102+0.278× tdib-3.182×Rh+8.094×Rh2-8.695×Rh3+3.327×Rh4+0.089×naturalVolume model:vib=(0.000009×tvib+1)(1/0.000009),tvib=-3.879+0.081×td2h-0.021×tHTaper model: (4)After Box-Cox transformations of variables,three sets of additive biomass models were built and compared,including sum of mixed effect models with site as a random factor("sum of lme"),sum of ordinary models("sum of lm")and seemingly unrelated regression(SUR).The"sum of lme"models turned out to be the least biased,the models were as follows:Wood biomass:tWwood=-1.710+1.345×tDBHH+0.391 × D1；Bark biomass:tWbark=-2.687+2.000×loge(DBH)；Branch biomass:tWbranch=-2.988+0.563×td2h+-O.194×H；Foliage biomass:twfoliage=-2.126+-0.122×H+0.349×td2h-0.311×D1.For the FVS models,self-built models and biornass models,relative testing such as the coefficienls of determination(R2),root mean square error(RMSE),jackknife testing or independent testing,confidence interval of predictions(CI),residuals plots and histograms of residuals verified that the prediction accuracies of those models were high within specific tree diameter at breast height and height ranges.Therefore,the models can be used to evaluate site quality and predict tree growth, biomass or carbon stocks of cork oak forests in North China... |
