Carbon Status and Regression Model for Tree Carbon by Crown Cover for Sal Forest of Nepal

Background: Volume, biomass and carbon of forest ecosystem are generally estimated using lookup tables or allometric equations known as models. These general equation-based models are usually exclusively based on dimensional measurement such as diameter at breast height (DBH) and/or height, which sometimes makes it dicult to judge applicability of equation to given forest condition or types. It is therefore important to estimate carbon stock and develop models to predict biomass or carbon stock with stratication by categorical variables like crown cover, slope, forest types, etc. Stratication of forest by remote sensing approach while designing forest inventory not only improves the reliability of the estimation but also reduces the cost of measurement and uncertainty in estimation. Taking crown coverage (<25%, 25-50%, 50-75% and >75%) and slope (0-8.5%, 8.5-19%, 19-31% and >31%) as a categorical variable, this study assessed the status of carbon stock and develop a regression model to predict carbon stock for each canopy class of Sal (Shorea robusta) forest in Nepal. DBH and height were measured for trees with more than 7 cm DBH in 82 sample plots (18, 22, 22 and 20 for <25%, 25-50%, 50-75% and >75 % respectively). Results: On average 297 stands per hectare were recorded with 94.80 m 3 /ha growing stock. Carbon stock was highest for >75% crown cover class (89.83 ton C/ha) and lowest for <25% crown cover class (27.47 ton C/ha) with average 60.41 ton C/ha, where per tree carbon stock was lowest in crown cover class 25-50% (0.16 ton C/tree). TukeyHSD shows that four pairs of crown cover classes have signicant difference in carbon stock at 95% condence interval. However, with increase in slope carbon stock per hectare was decreasing. Regression model with natural logarithm of DBH 2 and total tree height (i.e. log transformed polynomial equation) was best tted for estimation of carbon stock per tree in different crown cover class with adjusted R 2 >0.99 and residuals were normally distributed.


Background
Forest ecosystem stores carbon by sequestering a substantial amount of carbon dioxide from the atmosphere, globally accounting around 92% of all terrestrial biomass storing approximately 400Gt of carbon (Dixon et al. 1994 ton/ha above ground carbon in lower slope compared to 187.49 ton/ha in higher slope and also concluded that variation in total carbon stock by aspect for Gedo forest of Ethiopia. An experiment conducted in mixed deciduous and evergreen broadleaf forest by International Center for Integrated Mountain Development (ICIMOD) knowledge park Nepal shows that the carbon stock density of dense forest strata was higher than that of the sparse strata, whereas soil organic carbon was lower (164.02 ton C/ha) in dense forest strata compared to in sparse strata (180.93 ton C/ha) in which mean soil organic carbon ( ne fractions) percentage was 5.27% and 6.01% for sparse and dense forest strata, respectively (Karki et al. 2016). Similarly, Sharma and Kakchapati (2018) also concluded that the stem density has signi cant association with the total biomass carbon content, where plots with less than 20 trees per plot showed higher carbon stock. (DFRS) (2015) Sal forest alone accounts for 15.27% of total forest area. In addition, the study also found that another 24.61% of forest area exists in the form of tropical mixed hardwood forest resulting in Sal representing total of 26-28% of stem volume in Nepal whose carbon stock distribution varies spatially by species composition, cover condition site quality and edaphological factor. So, developing regression equation for estimation of carbon stock for natural Sal forest by crown cover will not only estimate the accurate carbon stock for REDD + bene ts but also helps to remove uncertainty in estimation of biomass and carbon due to site quality resulting in variation in crown coverage. Therefore, this study aimed to estimate carbon stock by crown cover class and develop regression models to estimate carbon stock for various crown cover measuring DBH and total height of tree at eld level and classifying crown cover with remote sensing for cost effective carbon estimation in tropical Sal forest.

Results
Crown cover classi cation Division of forest into four different crown cover classes shows that majority of forest areas fall under crown cover class 50-75% whereas only around 50 ha of forest was covered by crown cover class < 25% (Table 1). Cohen's kappa coe cient calculated from the error matrix shows that the overall accuracy of the classi cation was more than 85%. Carbon stock There was a uctuation in the number of stems with increase in crown cover, where on an average 297 stems per hectare were recorded in study area with highest number of stems in crown cover class >75 %.
Similarly, per tree growing stock and carbon stock was highest for crown cover class >75 % and lowest for 25-25 % crown cover class despite having the second largest number of stems per ha in the class.
Growing stock (GS), above ground biomass (AGB), total biomass (TB) and carbon stock (CS) was observed to have increased with increase in crown coverage. Table 2 shows that estimated variables by crown cover class and weighted average for the whole area. Four estimated variables (GS, AGB, TB, CS) were plotted against crown cover in Box-whisker plot for displaying the variation in data by crown cover class. It shows that the variability in data was seen more in crown cover class >75 % for all four estimated variables and less in crown cover class <25 %.
One-way ANOVA showed a signi cant difference in total carbon stock with crown cover class at 95 % con dence interval. TukeyHSD, test to explore the signi cance between different pairs of crown cover, showed that three pairs of crown cover category (<25 to 25-50, <25 to 50-75 and 25-50 to >100) signi cantly differ at 95 % con dence interval (Table 3) whereas <25 to >100 pairs were signi cantly different at 99.9 % con dence interval.

Model for Carbon Stock Estimation
Regression equation to model each crown cover class was developed from DBH and height as independent variables where crown cover was used as a categorical variable. Models were selected after the intercept of DBH and height were positive, adjusted R 2 value was above 0.99 and residual areas normally distributed and homogeneous.
Fitted model for estimating carbon stock where DBH and Height are independent variables with base of natural logarithm is given as: Where, CS is in kg/tree, DBH in cm and Height in m.  (Table 3) and residuals are normally distributed ( Figure 6). Selected models were plotted with natural logarithm of DBH and height along with estimated carbon stock in 3d scatter diagram as shown in Figure 4.

Discussion
We found that linear model with natural logarithm of DBH 2 and height is best t to predict carbon stock  also concluded that CS is low in higher slope compared to lower with 570.67ton/ha in lower slope in Gedo forest of Ethiopia. Steep slope / Higher slope areas contains little vegetation compared to lower slope areas (Maggi et al. 2005) and soil depth for root and stem growth gets washed away due to erosion due to step slope (Feyissa, Soromessa, and Argaw 2014; Şükrü Teoman Güner 2012) resulting in lower carbon stock per hectare.
Equations available for predicting biomass of a single tree mostly use a function of easily measured variable like DBH and tree height and are usually developed for particular species or species group. So, we regress the carbon stock by crown cover from predictors (DBH and height) to develop allometric equation to estimate carbon stock. This is consistent with the previous studies in which DBH

Conclusions
There is a relation between total biomass carbon and degree of crown coverage for Sal forest. The application of strati ed sampling for developing model for measurement of carbon stock by crown cover class is more precise and accurate which should be used for estimation of carbon stock of Sal forest. Therefore, we strongly recommend the inclusion of crown cover as strata for better estimation of biomass and carbon stock. This equation will help managers for better management of forest for maximum carbon sequestration and accurate and cost-effective methods to estimate carbon stock.
Developing such models for other forest type can be linked with result-based payment like REDD + which requires accurate and precise measurement of sequestrated carbon.

Study Area
The study was conducted in Hetauda sub-metropolitan city ward no 14, entirely located in Chure region of Nepal (Fig. 1)

Data collection and analysis
Using Strati ed random sampling, 160 plots were randomly established representing the whole forest area with sampling intensity of at least 1% for all crown cover class (Fig. 2). Sample plots were randomly selected after strati cation by crown cover class in each stratum and eld measurements were only con ned to plots in which all stands (poles/trees) were Sal. Measurement of DBH and height was carried out for all trees more than 7 cm DBH. Even though there were 40 plots (pre-located) in each stratum only 82 plots in total were valid for measurement ( Availability of data and material The data set during and/or analyzed during the current study available from the corresponding author on request.

Competing interest
The author declares that no competing interest exists.

Finding
The author received no speci c funding for this work.

Authors' Contribution
Mr. Prashant Paudel-Research design, data collection, analysis and writing Mr. Rupesh Kalakheti-Data collection, data entry and data analysis Prof. Tek Maraseni (PhD)-guidance, supervision and editing