Larch Stand Structure Analysis of Boreal Forest in Mongolia

211 2nd International Conference on Environmental Science and Technology IPCBEE vol.6 (211) (211) IACSIT Press, Singapore Larch Stand Structure Analysis of Boreal Forest in Mongolia Khongor Tsogt zandraabal@yahoo.com Narangarav Dugarsuren ndugarsuren@yahoo.com Chinsu Lin chinsu@mail.ncyu.edu.tw (Corresponding author) Tsogt Zandraabal Forestry Branch Institute of Botany Mongolian Academy of Sciences Ulaanbaatar, Mongolia ztsogt@yahoo.com Abstract The Larch tree is a dominant forest species in Mongolia. There is an increasing need to gather growth information on forest stands in natural environments to enable sustainable forest management to combat the potential impact caused by global warming. This paper aims to outline the forest structure, including diameter distribution and heightdiameter relationship, based on the sampling inventory of 6 pure stands with variant environment in Eastern Khentii, Mongolia. Exponential rise/decay, lognormal, sigmoid and Gaussian distributions are adopted in this study to fit the diameter frequency distribution and relationship between diameter and height. Results showed that a three-parameter lognormal model could explain the diameter structure of the integrated data of all 6 plots from variant forest larch stands. The Fitted model has R 2 =.99. However, individually the diameter structure of each of the plots is best explained by different models, such as exponential, lognormal, Gaussian, and piecewise linear whose R 2 varies from.68 to.99. The relationship of diameter and height also showed variant function exists among the plots. R 2 of the fitted diameter-height models are from.61 to.94. Finally, we were able to estimate forest volume using a diameter distribution model and a diameter-height model. Keywords-Larix sibirica, diameter distribution, diameter and height relationship I. INTRODUCTION The Mongolian forest is spread throughout the mountainous region located in the Northern part of Mongolia. It is in the transition zone between the Siberian forest and the Asian dry steppe where the climate condition is extreme for forest development and regeneration processes are hindered by long, cold winters and short summers. However, larch tree species are well adapted to cooler environments [1] and more than 7% of the forest area is covered by larch forest. Larch timber qualities are low (by bonitet class as IY.4) and old aged (average 156 years) [2]. Though, they serve important functions within the forest: acting as carbon sinks, sources of renewable energy, providing watershed protection, preservation of permafrost and soil erosion protection. Forest stands are dynamic and can change slowly through forest succession, or rapidly due to disturbances such as logging, fire, or insect and disease epidemics. As a result, the structure of the forest stand is changed into a different distribution shape after disturbances. To understand forest stand distributions their measureable parameters, vertical and horizontal geometric descriptions need to be obtained (e.g., diameter and height). The aims of this study are to clarify (i) the distribution frequency at variant diameters or diameter structure, and (ii) the relationship of diameter and height of larch in Mongolian forests. In order to obtain and analyze larch diameter distribution and relationship of growth parameters we used some widely applicable mathematical functions to develop empirical models. Results of both the diameter distribution model and diameter-height relationship are used to estimate volume stock of the larch forest which could be used to develop proposals for the further development of biomass and carbon storage within the larch forest. II. MATERIALS AND METHODS Inventories were conducted at 6 pure stands in Eastern Khentii, Mongolia in the summer of 28 (Tab. 1). Diameter and height were measured using a caliper and Suunto height meter. Exponential rise/decay, lognormal, sigmoid and Gaussian distributions are adopted in this study to fit the diameter frequency distribution and relationship between diameter and height. The model parameters have been estimated using Sigmaplot 1. In order to verify the distribution model of diameter frequency and the relationship between diameter and height, the empirical distribution function fitness should be considered. Empirical distribution function fitness is based on the Kolmogorov-Smirnov normality test (K-S), and constant variance test (CV). V2-123

TABLE I. DIAMETER DISTRIBUTION PARAMETERS Plot Plot area (ha) Number of stems Average DBH (cm) Diameter range (cm) Standard deviation Diameter distribution Skewness Kurtosis 1.6 552 5.4 1-46 4.773 2.34 1.66 2.5 1 11.6 2-64 12.49 2.35 4.86 3.2 282 14.7 2-39 8.27.42 -.82 4.4 61 16.5 2-77 16.16 1.62 2.24 5.2 144 19.8 1-4 7.965 -.28 -.4 6.2 12 23.9 1-56 16.58.16-1.28 The K-S test tries to determine if two datasets differ significantly. SigmaPlot tests for CV by computing the Spearman rank correlation between the absolute values of the residuals and the observed value of the dependent variable. When this correlation is significant, the constant variance assumption may be violated, and a different model should be considered. III. MATHEMATICAL MODELS For diameter distribution study, exponential decay, lognormal and Gaussian distributions were used and for diameter and height relationships study exponential rise sigmoid and linear functions were used. Here we are introducing exponentials and lognormal functions. A. Two parameter, Exponential rise/decay The exponential function is used to model phenomena when a constant change in the independent variable gives the same proportional change (increase or decrease) in the dependent variable. Exponential rise (Eq. 1) and exponential decay (Eq. 2) occurs when the growth rate of a mathematical function is proportional to the function's current value. f=a*(1-exp(-b*x)) (1) f = a*exp(-b*x) (2) where; a initial value and b rising/declining rate Initial value a is correspondent to x axis at and then it does proportionally increase/decrease by b rate. B. Three parameter, Lognormal The probability density function in the three-parameter case is expressed by Eq. 3. f=a*exp(-.5*(ln(x/x)/b) 2 ) (3) where; x scale (cm), a location, and b shape Location a value is the peak point of distribution correspondent to y axis and scale x correspondent to x axis. Shape b value is standard deviation. IV. RESULT AND DISCUSSION Tab. 1 shows the parameters of diameter distribution of plots. Plot areas range from.4-.2 m hectare. Plot 4 is the smallest plot. With consideration given to land type, slope and forest density possible rectangle areas were chosen for study plots. Small plots were developed due to stem density however plot 4 has 61 stems and plot 5 and 6 are less dense. From plot 1 to 6 average diameter increases. The diameter range of the study plots are from 1 to 77 cm and plots 2 and 4 diameter ranges 2-64 and 2-77 respectively. Even standard deviation of diameter for plots 2, 4 and 6 are bigger than 1. The kurtosis of plot 1 is the largest, 1.66 and plots 1, 2 and 4 have sharper than normal peaks. Plot 3, 5 and 6 statistically should have flatter than normal peaks. A. Diameter distributions It is first necessary to understand what pattern is expected in order to reveal forest diameter distribution. The basic idea is that as populations of trees grow and increase their size in a fixed area, their numbers must decrease. This is referred to as the self-thinning rule and exhibits a relationship between pure stand stem number and mean size [3, 4]. It has been documented that even aged forest diameter distributions follow reverse J unimodal distributions [5, 6]. Initial study of diameter distribution mathematical description was negative exponential [7]. Some researchers have found distributions that deviate from the exponential decay form such as on semi-log axes, distributions can be concave or rotated sigmoid. In even aged stands diameter distribution is non normal. Lognormal distribution is more flexible than normal distribution, which is described by the mean and variance of the sample, when the smallest diameter priori defined or assumed [8]. Weibull distribution function is a probability distribution function [9, 1]. The flexible characteristic of Weibull distribution enables researchers to model the diameter V2-124

2 Plot 1 6 5 Plot 2 6 5 Plot 3 15 1 4 3 2 4 3 2 5 1 1 2 4 6 8 1 12 14 16 18 2 22 24 26 28 3 32 34 36 38 4 42 44 46 48 4 8 12 16 2 24 28 32 36 4 44 48 52 56 6 64 68 4 8 12 16 2 24 28 32 36 4 44 2 Plot 4 5 Plot 5 25 Plot 6 16 4 2 12 8 3 2 15 1 4 1 5 4 8 12 16 2 24 28 32 36 4 44 48 52 56 6 64 68 72 76 8 4 8 12 16 2 24 28 32 36 4 44 3 8 13 18 23 28 33 38 43 48 53 58 Figure 1. Stem number-diameter class distribution of the plots frequency distribution without knowing the distribution shape. In this study we used exponential, lognormal and Gaussian distributions to explain forest diameter distributions. Explanation of diameter distribution is directly dependent on the type of mathematical function chosen. Plot 1 is the smallest diameter class stand (Tab. 1) and its diameter distributions are explained by exponential (Fig. 1). In natural forest small diameter classes are always in the majority, especially, in young stands. Significantly we observed a good fit of the exponential distribution, and the model also indicates a good status of forest regeneration. Diameter distribution of plots 2, 3 and 4 are well fitted with a lognormal function, however it can be seen that there exists a bi-modal pattern which might be influenced by some natural disturbance in the forest in the past. Plot 5 diameter distribution is normal rangeing from 4-4 cm and center at 2-cm. This distribution is very similar to the one of an artificial plantation. Also this stand has low stand density and big crown diameter. Since this plot was taken from the natural forest, it indicates that the forest has somehow been disturbed by fire. The diameter distributes from 3-58 cm in plot 6 with a piecewise or segmented linear model. Visually this stand was also influenced by natural disturbances which might have happened at the diameter point of around 28 cm and the high frequency small diameter class suggested that the forest was recovering from the disturbances. It was observed that forest fires occur frequently in Mongolia because of the dry weather condition particularly during the spring and autumn. The influence of natural disturbance, perhaps in particular forest fires, on the Mongolian forest is significant and influences the forest diameter structure. The impacts can be seen from the sample plots taken in this study. In order to confirm that proper interpretation of diameter distribution is based on reliable statistical criteria. We examined the test statistics of study plots diameter distribution modeling results in Tab 2. Plot 1 test statistics K- S test passed but failed. Plot 2 K-S test failed however all three parameters were accepted according to parameter estimate statistics. The parameter estimation statistic result was not included here. The gap in plot 2 causes the distribution model test statistic fail. As a result bigger diameter class stems cannot be predicted by this model. Plot 3, 4, 5 and 6 test statistics passed and for parameter estimation statistic all plots result show perfect fits. TABLE II. TEST STATISTICS OF THE DIAMETER DISTRIBUTION MODEL 1 Exponential decay.99 3.8.22P a.1 2 Lognormal.98 2.36.39F a.32 3 Lognormal.9 6.83.15P.7 4 Lognormal.88 2.1.29P.31 5 Gaussian.68 7.4.16P.13 6 Picewise linear.78 3.2.23P.78 a. Codes P and F represent pass and failed V2-125

TABLE III. TEST STATISTICS OF THE DIAMETER DISTRIBUTION MODEL 1 Exponential decay.98 8.33.197F. 2 Lognormal.99 6.84.187P.13 Those 6 plots were further integrated into an extended sample set of the larch forest and refitted with a diameter structure mode. All of those sample trees diameters range from 1 to 77 cm and could be well fitted with exponential and lognormal functions. The diameter distribution of trees is an indicator of structural diversity and the distribution of the total 1251 trees showed a diameter distribution with higher numbers of smaller trees. Tab. 3 showed the statistical test results of the exponential and lognormal models. R 2 are close to 1., Standard error of the model estimates SE(ŷ), showing that the lognormal model is smaller than the exponential. According to the normality assumption test, the lognormal model passed while the exponential failed. Meanwhile the has the same results. So, if an estimation only considered the prediction ability (R 2 ), both the exponential decay model and lognormal are able to provide results; but if the assumption requirements are the priority, it is recommended that the lognormal model be utilized as it is relatively more suitable or robust for further applications of volume stock and/or biomass estimation for the Khentii Range of Mongolian larch forest. B. Diameter and Height relationship Tree height and diameter are important for assessing tree volume and stand productivity, but accurate measurement of height is time consuming. Foresters often use equations to predict tree height that are made by using a few trees height diameter samples to form an estimate. Height diameter relationship differs for a given species and stand to stand, even sometimes within the same stand variation might be high [11]. Therefore no single model can explain all possible height diameter relationships [12]. In this study we used exponential, sigmoid and linear functions to explain diameter and height relationships. A characteristic of some of the simpler growth phenomena is that the rate of increase at any moment is proportional to the size already attained. During one phase in the growth of a individual tree of a forest, a number of trees follow such a law. The relationship of diameters and heights are showed in Tab. 4. Plot 1, 2, 4, and 6 predicted models test statistics passed. Plot 5 failed. Plot 5 stem density (stems/ha) is low, this suggests the plot trees are not needing to compete for light and do not have to grow so much. Instead their crown diameter are being spread from the very bottom of the stem so the relationship between diameter and height is weak. C. Stand Volume Estimation The total volume estimate of a stand or plot is important for forest quantification and management. Stand volume at a nominated age is related to the site quality, and the total at any time is important for an estimate of wood and biomass resource. Also like tree volume, stand volume is a function of stand height, and average diameter. In our case we are using a diameter distribution model and diameter and height relationship model to calculate the stand volume of 6 plots (Tab. 5). The volume estimation equation, V=aD b H c was previously published in The Mongolian forest journal [13]. Constant coefficients of a, b and c are.2291, 1.7563, and 1.453 respectively. Stand density can be calculated two ways. Those are proportionally to plot area and by the diameter distribution models of each plot. The advantage of using diameter distribution model to calculate number of stems per hectare area is that it can give us each diameter class number of stems instead of proportionally adding the total stem numbers. Further, the volume estimation of per hectare area becomes more intrinsic. Briefly, the volume calculation of a hectare forest stand is a three-step procedure. The number of stems of each diameter classes had to be firstly calculated based on the diameter distribution model, then volume estimation for each diameter class was determined using the volume model, and finally the volume of all the diameter classes were summed up. TABLE IV. TEST STATISTICS OF THE DIAMETER-HEIGHT MODEL 1 Sigmoid.93 1.5.16P.7 2 Exponential rise.93 2.4.16P.56 3 Exponential rise.88 1.9.16P.5 4 Sigmoid.94 1.45.14P.69 5 Exponential rise.61 1.23.12P. 6 Linear.73 2.7.14P.16 TABLE V. Plot RESULT OF STAND VOLUME ESTIMATION Stand density proportional to plot area ( ha) Stand density determined by model (ha) Volume (m3/ha) 1 92 9222 28 2 2 1995 598 3 141 141 299 4 1525 148 446 5 72 7 24 6 6 477 122 V. CONCLUSION The ability to predict future size distributions within a forest by suitable theoretical distributions is important for forest quantification and management. The exponential V2-126

decay and lognormal distributions were fitted to observed diameter distributions and exponential rise and sigmoid distributions were applied to diameter and height measurements in The Eastern Khentii Mongolian Larch forest to determine the distribution that best fits the data. A lognormal model was suggested as the most appropriate to describe the diameter distribution of larch forest whilst an exponential rise model was better able to describe larch diameter-height relationships. Finally, we were able to predict the stand volume of study area and this suggests the possibility for further biomass study. REFERENCES [1] A. Farjon, Pinaceae: drawings and descriptions of the genera Abies, Cedrus, Pseudolarix, Keteleeria, Nothotsuga, Tsuga, Cathaya, Pseudotsuga Larix and Picea, Koeltz Scientific Books, Ko nigstein. 199. [2] Ch. Dugarjav, Mongolian Larch Forests Монгол орны шинэсэн ой, Mongolia, 26, p. 317. [3] K. Yoda, T. Kira, H. Ogawa, and K. Hozumi, Self-thinning in overcrowded pure stands under cultivated and natural conditions, J. Biol. Osaka City Univ. vol. 14, 1963, pp. 17-129. [4] J. P. Kimmins, Forest ecology: A Foundation for sustainable forest management and environmental ethics in forestry, 3 rd Ed. Pearson Education, Inc. US, 24, p. 611. [5] A. F. Hough, Some diameter distributions in forest stands of northwestern Pennsylvania, J. For. vol. 3, 1932, pp. 933-943. [6] E. W. Jones, The structure and reproduction of the virgin forest of the north temperate zone, New Phytol. vol. 44. 1945, pp. 13-148. [7] F. De Liocourt, De l amenagement des sapinieres, Bulletin Triemestriel Societe Forestriere de Franche Comte et Belfort, Besancon, 1998, pp. 396-49. [8] Bliss and Reinker, A lognormal approach to diameter distribution in even aged stands, For. Sci, vol. (1) 3. 1964. [9] R. L. Bailey and T. R. Dell, Quantifying diameter distribution with the Weibull-function, For. Sci. vol. (2) 19. 1973, pp. 97-14. [1] C Lin, Chan M.H., Chen F.S. and Wang Y.N., Age structure and growth pattern of an endangered species, Amentotaxus formosana Li, J. of Integr. Plant Biol. vol. (49) 2, 27, pp. 157-167. [11] R. Calama, and G. Montero, Interregional nonlinear height diameter model with random coefficients for stone pine in Spain, Canadian J. of For Res. vol. 34, 24, pp. 15 163. [12] F. C. Dorado, U. Die guez-aranda, M. B. Anta, M. S. Rodrı guez, and K. V. Gadow, A generalized height diameter model including random components for radiata pine plantations in northwestern Spain For. Eco. and Man., vol. 229, 26, pp. 22 213. [13] Mongolian Forest Леса МНР 198 p.82. V2-127