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Functions for multi-phase assessment of biomass in acacia woodlands of the Rift Valley of Ethiopia
Forest Ecology and Management 105 Ž1998. 79–90
Functions for multi-phase assessment of biomass in acacia woodlands of the Rift Valley of Ethiopia Getachew Eshete
1,)
, Goran ¨ Stahl ˚
Swedish UniÕersity of Agricultural Sciences, Faculty of Forestry, Department of Forest Resource Management and Geomatics, S-901 83 Umea, ˚ Sweden Received 14 March 1997; accepted 27 August 1997
Abstract In this article, single-tree biomass functions for acacia woodland tree species are presented. The main aim of developing the functions was for utilizing them in a multi-phase sampling design in estimating the woody biomass in acacia woodlands of the Rift Valley of Ethiopia. Eighty-five trees Ž5–35 cm diameter. were selected randomly from the five dominant tree species: Acacia tortilis ŽForsk.. Hayne, Acacia senegal ŽL. Willd., Acacia seyal Del., Acacia etbaica Schweif. and Balanites aegyptiaca ŽL. Del. Four categories of functions were developed. These were Ži. functions with crown area as independent variable, to be applied using high resolution satellite images or aerial photos; Žii. functions with crown area and tree height as independent variables, to be applied using data from aerial photos; Žiii. functions for quick estimation in ground surveys, based on the diameter at 0.8 m; and Živ. functions for thorough estimation in ground surveys, in which the diameter at 0.8 m, the diameter at stump height, and the crown area were included. Also, two sets of functions were developed, one with and one without species indicator variables. In gathering data for developing biomass functions, the selection of sample discs from trees for determining the ratio between dry weight and fresh weight is important. In addition to the functions, a robust method for the disc sampling is proposed. q 1998 Elsevier Science B.V. Keywords: Acacia tortilis; Acacia senegal; Acacia seyal; Acacia etbaica; Balanites aegyptiaca; Regression analysis; Sampling
1. Introduction As in many parts of tropical Africa, most of the energy requirement in Ethiopia is covered by traditional biomass fuels. The annual consumption of woodfuel is close to 20 = the consumption of other forest products together ŽAnonymous, 1993.. The )
Corresponding author. Tel.: q46-090-165836; fax: q46-090778116: e-mail: [email protected]. 1 Permanent address: Alemaya University of Agriculture, Faculty of Forestry, P.O. Box 138, Dire Dawa, Ethiopia.
acacia woodlands, covering nearly 11% of the total land area in the country ŽAnonymous, 1988., are important sources of woodfuel. They also provide the rural community with other forest products and benefits such as fodder, construction materials, farm implements, shade, honey, etc. The sustainable management of these woodlands, which has so far been neglected, is a priority task for the country. As outlined in the Ethiopian Forestry Action Program ŽAnonymous, 1993., it includes an optimum land-use allocation, the enforcement of property rights, and the creation of an information
0378-1127r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 8 - 1 1 2 7 Ž 9 7 . 0 0 2 7 3 - 9
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G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
basis for planning and management. The latter issue must necessarily be preceded by development of tools and techniques for the purpose, and this includes the development of methods for estimating biomass. Many studies on biomass estimation have been made over the years. Reviews of the literature are given in Hitchcock and McDonnell Ž1979. and Marklund Ž1987.. However, only a limited number of studies concerns the African forests and woodlands ŽRyan and Openshaw, 1991.. Moreover, these studies mainly consider the dry miombo woodlands of Southern and Southeastern Africa ŽStromgaard, 1985; Chidumayo, 1991; Tietema, 1993; Grundy, 1995. whereas very few treat the East African savanna woodlands ŽOlsson, 1985; Hellden, ´ 1987.. The biomass studies can be categorized into either studies concerning the estimation of wood resources ŽTietema, 1993. or ecosystem studies involving nutrient cycling, energy flow, carbon flux, comparison of plant communities, etc. ŽRochow, 1974; Brown et al., 1989.. The estimation methods used are based on direct weighing of trees or on applying functions made specifically for the purpose. In the latter case, the biomass is derived from few easily assessed tree characteristics. Regression analysis is commonly applied for developing biomass functions. The predictor variables often used, for trees in the African woodlands, are diameter at breast height ŽMalimbwi et al., 1994., diameter at stem base or ankle height ŽVertannen et al., 1993; Tietema, 1993; Grundy, 1995., crown diameter ŽOlsson, 1985; Hellden, ´ 1987; Tietema, 1993., and tree height ŽStromgaard, 1985.. In most cases the non-linear allometric equation Y s b 0 X 1b1 X 2b 2 . . . X kb k is used for modeling the relationship between the biomass Ž Y . and the predictor variablesŽ X 1 , X 2 , . . . , X k .. To enable simple estimation of the parameters Ž b s., the model is often used in its logarithmic form. The main aim of this study is to develop biomass functions on a single tree basis for the dominant tree species in the Rift Valley of Ethiopia. The species are Acacia tortilis ŽForsk.. Hayne, Acacia senegal ŽL. Willd., Acacia seyal Del., Acacia etbaica Schweif., and Balanites aegyptiaca ŽL. Del. In developing the functions, their intended use in a multi-
phase sampling design is central. Consequently, different functions are derived utilizing different sets of predictor variables, for various phases of a possible design. The study is part of a larger project aiming at developing inventory and planning techniques that could be used for the management of acacia woodlands in Ethiopia.
2. Materials and methods 2.1. Study area The study area is part of the Great Rift Valley system and is located 190 km south of Addis Ababa between latitudes 7830X and 7840X N along a strip bounded by lake Langano to the east and lakes Abiyata and Shala to the west ŽFig. 1.. It covers approximately 150 km2 out of which half of the area lies in the Abiyata Shala Lakes National Park. The area is important for migrant birds from the northern hemisphere ŽSyversten, 1995.. Climatic data for the area were obtained from the Ethiopian Meteorology Authority for the years between 1981–1995. The mean annual rainfall was 706 mm. Much of the rainfall was concentrated to a single rainy season between June and September. The mean annual temperature for the period was 20.48C with the highest temperature in March and the lowest in December. The mean monthly potential evapotranspiration ŽPET. calculated for the area from the nearest station, within the same agro-climatic zone, was 163 mm. Elevation of the area ranges between 1585–1780 m above sea level with a fairly flat to gently sloping terrain. A significant proportion of the area is subjected to cultivation and grazing and as a result the tree cover consists of remnants of acacia species scattered in the landscape. The proximity to large cities Že.g., Addis Ababa. and the main road passing through the area have made the charcoal business particularly attractive. This has contributed to the current land use pattern. 2.2. Sample tree selection To obtain a representative sample of the tree population, it is an advantage to have a picture of the
G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
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Fig. 1. Map of Ethiopia and Eritrea showing the location of the study area, which is indicated by striped lines in the magnified portion of the map.
species and size distribution of the trees prior to sampling. This was accomplished by using data from a previous study in the same area in which trees had been calipered on sample plots, within polygons. The polygons were created by automatic segmentation ŽHagner, 1990. of SPOT satellite imagery. Eighty-
five trees were selected from the list of earlier measured trees. The selection of trees was made after grouping them specieswise into 2-cm diameter classes. A random sample of trees was taken from each class, ensuring representation of trees of all species and sizes. Only trees with diameters larger
G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
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than 5 cm were included. Also, trees with a diameter larger than 35 cm were not included due to their importance as shade trees and as trees for traditional beehive keeping. Very few trees were, however, larger than 35 cm ŽFig. 2.. Moreover, trees were excluded from the sampling list if they did not belong to the natural setting Že.g., some rare Ficus trees., if they were isolated on agricultural lands, and if they were rotten, broken or had lost more than half of their crown due to lopping or natural damage. The occurrence of crown damage on trees is given in Fig. 3. The trees sampled from the list were located in the field using GPS ŽGlobal Positioning System. and by using markings from the previous inventory, conducted within the framework of the larger project. A summary of the trees sampled for felling is given in Table 1. 2.3. Measurements A number of measurements were made on the sampled trees ŽFig. 4.. The choice of variables was
guided by previous studies in similar forest types ŽStromgaard, 1985; Olsson, 1985; Tietema, 1993. and by considering the intended use of the functions within a multi-phase sampling design. While the trees were standing, the diameter at 0.8 m ŽD08. and the diameter at stump height ŽDSH., i.e., 0.3 m above ground level, were assessed in millimeter by two perpendicular caliper measurements. The reason for taking the diameter at 0.8 m instead of at 1.3 m was that close to 15% of the trees forked in the region between 0.8–1.3 m ŽFig. 5.. When the forking was below 0.8 m, the diameter of each part was measured at 0.8 m Ž d08 i . and later the equivalent diameter was calculated as D08 s
(
n
S d08 2i .
is1
The crown diameter ŽCD. was measured Žin dm. as the average value of the major Ž a. and the minor Ž b . axes of an ellipse approximation of the crown. The ab crown area ŽCA. was then calculated as P . The 4
Fig. 2. Relative frequency of trees by diameter class obtained from prior sampling in the study area.
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Fig. 3. Relative frequency of visually estimated crown damage by diameter class as percentage loss of crown. The figures are based on the results from the prior sampling.
tree height ŽTH. and the bole height ŽBH. were measured Žin dm. using a telescopic height meter. For tall trees Ž) 10 m. a Silva hypsometer was used instead. The crown height ŽCH. was determined by subtracting BH from TH. After felling, the diameter at the base of the crown ŽDC. was measured and the trees were separated into branch and stem wood components ŽFig.
4.. The stem was further crosscut into four equal parts to facilitate the disc sampling for determining the ratio of dry weight to fresh weight and ensure manageable sizes for weighing. The fresh weights of stem wood Žminimum top diameter of 5 cm. and the branch wood Žincluding leaves. components were measured to the nearest 0.01 kg using a spring balance. In case of forking below 0.8 m, the stem
Table 1 Summary data of the felled sample trees Diameter class Žcm.
5–12.9 13–18.9 19–24.9 25–30.9 31–34.9 Total
Number of trees by species A. tortlis
A. senegal
A. seyal
A. etbaica
B. aegyptiaca
3 10 7 6 1 27
5 5 5 y y 15
8 3 2 1 y 14
3 8 2 1 y 14
4 6 y 4 1 15
Mean TH Žm.
Mean DW Žkg.
5.1 6.0 6.5 7.7 9.0
34.88 69.44 193.05 343.17 372.15
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G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
Fig. 4. Sketch of an Acacia tree showing the different components and measured variables ŽCD s crown diameter, TH s total tree height, BH s bole height, DSH s diameter at stump height, D08 s diameter at 0.8 m, DC s diameter at crown base..
weight was determined by summing the weights of the parts. 2.4. Sample disc selection Two sample discs were taken from each tree, one from the branch section and another from the stem wood section. The sample disc from the stem wood Ž4 cm thick. was selected by first drawing, with equal probability, a sample of one of the four sections prepared during felling. To locate the point on
the section where the disc slice was to be removed, a uniform random number between 0–1 was multiplied by the section length. The same procedure was applied to obtain a sample disc Ž6 cm thick. from the main branches of the tree. To minimize errors from loss of moisture, the slices were measured immediately for their fresh weights to the nearest 0.01 g using an electronic balance. Later, the discs were oven-dried at a temperature of 1058C until a constant weight was obtained. 2.5. Data analysis
Fig. 5. Relative frequency of bole heights Žheights to the first forking. obtained from the prior sampling.
The total dry weight of each tree was determined by adding the dry weights of the branch and stemwood components. Each component’s weight was estimated by multiplying the fresh weight with the ratio between the oven dried and the fresh weights of the disc slices. The development of biomass functions by components was not considered in this study. Summary statistics of the main tree variables are given in Table 2. In the investigation of the empirical relationship between the total dry weight, DW, and the independent variables ŽD08, DSH, DC, CD, CA, CH, BH,
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Table 2 Summary statistics of the main tree variables of the felled sample trees Species
Mean DW Žkg.
Mean CA Žm2 .
Mean D08 Žcm.
Mean TH Žm.
Mean DSH Žcm.
A. tortilis A. senegal A. seyal A. etbaica B. aegyptiaca
118.3 103.2 86.6 108.4 107.7
35.4 33.1 28.7 26.0 16.2
19.7 16.7 13.9 15.5 19.5
6.6 5.6 6.5 5.4 6.5
20.8 17.2 14.5 16.9 21.6
TH., logarithmically transformed allometric models were fitted using least squares regression. The models used were of the kind: k
ln DW s b 0 q
Ý bi ln X i q ´
Ž 1.
is1
with the X i s being the independent variables, the b s the parameters, and ´ normally distributed error term. Several alternative functions were developed considering their potential use in a multi-phase sampling design. The functions are categorized as: Ži. Functions utilizing data from high resolution satellite images or aerial photos: such functions could be useful in the first phase of an inventory. The only variable considered in this case was CA, since it Žor CD. would be the only tree characteristic possible to assess from satellite images. Computerized methods for the determination of CA at the tree level would allow for a cost efficient first phase of biomass estimation in the acacia woodlands Žcf. Joffre and Lacaze, 1993.. Žii. Functions utilizing data from aerial photos: in addition to CA Žor CD., TH can be measured in aerial photos using stereoscopic methods. Žiii. Functions for quick estimation in ground surveys: among the variables measured on the trees, the diameter is the most reliable one for quick biomass estimation in the field. Owing to the difficulty of measuring DSH, D08 was the variable selected for the purpose. Živ. Functions for thorough estimation in ground surveys: these functions are the most accurate ones developed and are intended for use in the last phase of an inventory. They were developed by including all variables that turned out to be significant. All functions were evaluated by examining the standard deviation ŽSE. and the scatter plot of the
residuals against the different predictor variables and the predicted values. Observations were removed if they exceeded the expected value by more than three standard deviations. As a result, two to three observations were removed as outliers in developing the different functions. Two different sets of functions were developed within each category stated above. The first set of functions was developed without considering the species differences. In the second set, the potential differences were accounted for by introducing indicator variables. In the latter case the models were of the following kind: k
ln DW s b 0 q
l
Ý bi ln X i q Ý g j S j is1
k
qÝ
js1
l
Ý a i j S j ln X i q ´
Ž 2.
is1 js1
In the formula, the X i s are the basic predictor variables ŽD08, CA, etc.., and the S j s are the species
Table 3 Parameters of regression functions for above ground dry weight Žln DW. in kilogram Function Const. ln D08 ln CA ln TH ln DSH n category
R2
SE
i ii iii iv iv
0.67 0.75 0.89 0.93 0.95
0.53 0.47 0.31 0.26 0.23
1.21 y y0.26 y y2.26 2.40 y2.10 0.35 y2.36 1.00
1.09 0.97 y 1.98 0.40
y 1.01 y y y
y y y y 0.99
83 83 82 82 82
The categories of functions are indicated by Roman numbers. Units of measurements and abbreviations are the same as in the text. R 2 is the coefficient of determination and SE the standard deviation of the residuals. The functions are corrected for logarithmic bias.
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G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
indicators Žfor l q 1 species., the bi s, g j s, and a i j s are the parameters, and ´ is the error term. The significance of species differences in each category of the functions was tested by an F-test involving the extra sum of squares due to regression that arose when a certain species was introduced. A test was first made to study if g j and a i j Ž i s 1..k . together were significant for a particular species. If that was the case, it was further investigated which
of them were significant on an individual basis. The test quantity used was ŽDraper and Smith, 1981.: Fs
Ž SS reg full y SS reg hypo. r Ž p y q . MS res full
Ž 3.
where SS reg full, is the sum of squares due to regression for the full model and SS reg hypo the corresponding sum of squares for the model without indicator variables for a particular species. MS res full
Fig. 6. Studentized residuals vs. predicted values of ln DW for the different tree species. The residual plots are in Ža. for function type i Žln CA., in Žb. for type ii Žln CA, ln TH., in Žc. for type iii Žln D08., for type iv in Žd. Žln D08, ln CA. and in Že. Žln D08, ln CA, ln DSH.. All abbreviations and units are according to the text.
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Table 4 Parameters of regression functions, with indicator variables for the different species, for above ground weight Žln DW. in kilogram Function category
Predictor variable
Species
Intercept
Slope
i
ln CA
A. tortilis Žref.. A. senegal
0.83 y0.70 Ž0.223. 0.39 Ž0.015.
1.20 0.09 Ž0.524. 0.01 Ž0.016.
y0.23 0.11 Ž0.396.
0.99, 0.97 0.26, y0.78 Ž0.453, 0.639.
y3.10 1.41 Ž0.014. 1.94 Ž0.001. 0.36 Ž0.246.
2.73 y0.53 Ž0.017. y0.65 Ž0.003. y0.22 Ž0.148.
B. aegyptiaca ii
ln CA, ln TH
iii
ln D08
A. tortilis Žref.. A.senegal A.tortilis Žref.. A. senegal A. seyal B. aegyptiaca
Intercept and slope
n
R2
SE
83
0.74
0.49
83
0.78
0.45
82
0.92
0.28
Ž0.002. Ž0.005.
Ž0.012.
Ž0.033. Ž0.001. Ž0.035.
All abbreviations and units are according to the text. The numbers separated by a comma in the ‘slope’ column correspond to the predictor variables given in the same row. R 2 and SE are as in Table 3. The functions are corrected for logarithmic bias. The values in brackets indicate the p-values.
is the residual mean square of the full model. The letters p and q are the number of parameters in the full and the restricted model, respectively. Species indicators were retained only if the test quantity was higher than the tabulated quantity of an F-distribution with p–q and n–p degrees of freedom. In all tests a 5% error level was used. The final functions were corrected for logarithmic bias ŽBaskerville, 1972. by adding a correction factor to the intercept in the functions. The correction factor was calculated as: n
Ý DWi Ks
is1 n
Ž 4.
Ý exp Ž ln DWˆ i . is1
ˆ . are the true and the in which DW and exp Ž ln DW estimated dry weights, respectively. 3. Results The set of regression functions without species indicator variables, categorized according their in-
tended use, is given in Table 3. Residual scatter plots for each of these functions are shown in Fig. 6. The functions with species indicators are given in Table 4. When the interaction Žthe a i j parameters. involves more than one variable, the p-values for the interaction terms are separated with a comma. In the larger functions Žtype iv. no species differences were found to be significant.
4. Discussion Most of the biomass functions developed in previous studies ŽTietema, 1993; Malimbwi et al., 1994; Grundy, 1995. are single phase oriented. However, due to the scattered distribution of acacia woodland trees and the associated high cost of inventory, the use of multi-phase sampling should be motivated in large area biomass assessments Žcf. Olsson, 1985; Hellden, ´ 1987.. Functions of category Ži., intended for information that can be obtained from high resolution satellite images or aerial photos, were the least precise. The main reason is the limited correlation between
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G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
DW and CA. In addition, unrecognized lopped branches may have contributed to such a relationship. The precision of the function with indicator variables was significantly higher than the function without. Here, the inclusion of B. aegyptiaca was expected due to the obvious difference in crown morphology as compared to the umbrella-shaped acacias. TH and CA were used as predictor variables in the second category of functions. The correlation between DW and TH in this kind of vegetation type is inherently poor. By introducing TH together with CA, however, a significantly higher precision was obtained as compared to the corresponding functions of the first category ŽTable 3.. When accounting for species differences a reduction of the SE by 2% was obtained. The third category of functions, in which D08 was used as a predictor variable, was the best involving a single predictor variable ŽTables 3 and 4.. Hence, these functions seem to be adequate for quick ground surveys. The same result is reported in previous biomass studies ŽTietema, 1993; Malimbwi et al., 1994; Grundy, 1995.. In this category of functions, many species differences were found to be significant. Although this was the case, the difference in SE between the functions with and without species indicators was limited. The prediction of DW using DSH was less accurate ŽSE s 0.36, R 2 s 0.85. as compared to using D08, most likely due to the swelling of the stems. The fourth category of functions was the best in terms of low SE. Interestingly, no species differences were significant. The obvious interpretation is that most of the variation between the species is contained in a difference in CA, D08, and DSH. Even the function involving only D08 and CA showed no difference between the species. A limitation in using the first and second categories of functions should be mentioned. As indicated above, these functions should in practice be applied on data from high resolution satellite imagery or aerial photos. Such data were not possible to acquire in the present study. Since, instead, the measurements were made rather accurately from the ground, an inevitable propagation of measurement errors should be expected when the functions are applied on remote sensing data.
No significant differences in density were discernible between the species. At a 5% moisture level, the density varied between 0.61–0.69 grcm3 , which is comparable to results in other studies ŽMalimbwi et al., 1994.. As to the estimation of dry weight for the felled trees, it is important that this is made in a manner that ensures unbiased estimates. In the study, sample discs for drying were selected by simple random sampling. This procedure has a drawback in case there is a correlation between the fresh weight of a disc and its ratio between dry weight and fresh weight as is shown in the following. Assume a tree stem is divided into N discrete discs. The following expression for the total dry weight of the tree can then be formulated: N
DW s
Ý wi t i
Ž 5.
is1
Here, DW is the true total dry weight, wi the fresh weight of disc i, and t i the ratio between dry weight and fresh weight of disc i. The estimator used in the study, for the case when disc j is sampled from a tree, is:
ˆ s t j wtot DW
Ž 6.
In the equation, wtot is the total fresh weight of the stem. The expected value of the estimator is obtained as: N
ˆ .s E Ž DW
N
Ý pj t j wtot s Ý js1
js1
1 N
t j wtot
st wtot N
s
Ý wj t j y Ž N y 1. Cov Ž w,t .
Ž 7.
js1
where pj is the probability Ž1rN . that disc j is selected. In case the covariance term is not zero, the estimator is biased. To indicate whether or not this was the case in the present study, values of t i are plotted vs. their relative position on the stem ŽFig. 7.. The ratio between dry weight and fresh weight appears to be relatively constant, which indicates that the covariance term should be close to zero. In a PPS sampling design, with probability of selection proportional to the fresh weight of a sample
G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
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Fig. 7. The ratio between dry weight and fresh weight Žfor the disc slices. by relative position along the stem for the sampled trees Ž1 s bottom, 2 s lower middle, 3 s upper middle, 4 s top..
disc, the situation is different. In this case the estimator ŽEq. Ž6.. of total dry weight is unbiased, since: N
ˆ .s E Ž DW
N
Ý pj t j wtot s Ý js1
js1
wj wtot
N
t j wtot s
Ý wj t j js1
Ž 8. which is equal to the true dry weight. Importance sampling, the continuous analogue of PPS sampling, has been proposed for use in connection with the selection of sample discs ŽValentine et al., 1984.. The procedure for performing it is, however, slightly complicated and the thorny and numerous branches of acacia trees make the ‘path selection’ difficult. Therefore, a simple but yet robust method for the disc selection from acacia trees is proposed below. The selection of sample discs could be made in the following steps: 1. Separate the tree into components of branch and stem wood and pile them according to their relative position in the tree Že.g., bottom, lower middle, upper middle and top. 2. Weigh each pile separately 3. Select piles by PPS sampling Žprobability proportional to the weight of the pile.
4. Use random sampling to obtain discs from within the sampled piles, and estimate biomass according to Ž6. with due consideration to the number of discs selected. Finally, it should again be mentioned that the functions presented in this study are based on trees sampled from within a quite restricted area. Although no significant bias was found when the functions were tested on data Ž Acacia spp.. as reported by Olsson Ž1985., collected in Ethiopia and the Sudan, use of the functions in other areas must be made with caution. Acknowledgements We are grateful to Prof. Hakan Olsson for com˚ ments on the manuscript, to Mr. Olle Hagner for preparing the satellite imagery as a sampling frame, and to Ass. Prof. Soren Holm for statistical com¨ ments. Our thanks also go to Mr. Zeleke Ewnetu, Mr. Kassahun Embaye, Mr. Taye and Mr. Mohammed from COF in Wondo Genet., Mr. Melaku Abegaz from WUARC in Addis, Mr. Mihret Ewnetu, Mr. G. Markos W.S. and the staff of the Abiyata and Shala Lakes National Park. Financial support was obtained from the Swedish International Develop-
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ment Agency ŽSIDA. and the Alemaya University of Agriculture.
References Anonymous, 1988. National Atlas of Ethiopia, Ethiopian Mapping Authority, Addis Ababa. Anonymous, 1993. Ethiopian Forestry Action Program, Vol. 2. The challenge for development, draft final report. Ministry of Natural Resources Conservation and Development, Addis Ababa, 88 pp. Baskerville, G.L., 1972. Use of logarithmic regression in the estimation of plant biomass. Can. J. For. Res. 2, 49–53. Brown, S., Gillespie, A.J.R., Lugo, A.G., 1989. Biomass estimation methods for tropical forests applications to forest inventory data. For. Sci. 35 Ž4., 881–902. Chidumayo, E.N., 1991. Woody biomass structure and utilization for charcoal production in a Zambian miombo woodland. Bioresour. Technol. 37, 43–52. Draper, N.R., Smith, H., 1981. Applied Regression Analysis, 2nd edn. Wiley, New York, 709 pp. Grundy, I.M., 1995. Woody biomass estimation in dry miombo woodland in Zimbabwe. For. Ecol. Manage. 72, 109–117. Hagner, O., 1990. Computer aided forest stand delineation and inventory based on satellite remote sensing. In: Proc. SNSrIUFRO Workshop on the Usability of Remote Sensing for Forest Inventory and Planning, Swedish Univ. of Agricultural Sciences, Remote Sensing Laboratory, Report 4. Umea, ˚ Sweden, pp. 94–105. Hellden, ´ U., 1987. An assessment of woody biomass, community forests, land use and soil erosion in Ethiopia. A Feasibility Study on the Use of Remote Sensing and GIS-analysis for Planning Purposes in Developing Countries. Lund Studies in Geography, Ser. C. General, Mathematical and Regional Geography, No. 14, Lund, Sweden.
Hitchcock, H.C., McDonnell, J.P., 1979. Biomass measurement: a synthesis of the literature. In: Frayer, W.E. ŽEd.., Forest Resources Inventories, Vol. 2. Workshop Proc., July 23–26, 1979, Fort Collins, CO, USA, pp. 544–567. Joffre, R., Lacaze, B., 1993. Estimating tree density in oak savanna-like ‘dehesa’ of southern Spain from SPOT data. Int. J. Remote Sensing 14, 685–687. Malimbwi, R.E., Solberg, B., Luoga, E., 1994. Estimation of biomass and volume in miombo woodland at Kitungalo Forest Reserve. Tanzania J. Trop. For. Sci. 7 Ž2., 230–242. Marklund, L.G., 1987. Biomass functions for Norway spruce Ž Picea abies ŽL.. Karst. in Sweden. Swedish Univ. of Agricultural Sciences, Department of Forest Survey, Report 43. Umea, ˚ Sweden. Olsson, K., 1985. Remote sensing for fuelwood resources and land degradation studies in Kordofan, the Sudan. PhD Thesis, Meddelanden fran ˚ Lunds Universitets Geografiska Institution, Avhandlingar C, 182 pp. Rochow, J.J., 1974. Estimates of above ground biomass and primary productivity in a Missouri forest. J. Ecol. 62, 567–577. Ryan, P., Openshaw, K., 1991. Assessment of biomass resources, a discussion on its need and methodology. Energy Series Paper, No. 48, The World Bank, 78 pp. Stromgaard, P., 1985. Biomass estimation equations for miombo woodland, Zambia. Agrofor. Syst. 3, 3–13. Syversten, P.O., 1995. Wintering waterbirds on Ethiopian Rift Valley lakes. Walia 16, 3–12. Tietema, T., 1993. Biomass determination of fuelwood trees and bushes of Botswana, Southern Africa. For. Ecol. Manage. 60, 257–269. Valentine, H.T., Tritton, L.M., Furnival, G.M., 1984. Subsampling trees for biomass, volume or mineral content. For. Sci. 30 Ž3., 673–681. Vertannen, A., Johansson, S.G., Kaarakka, V., Sarajarvi, I., ¨ Sarkeala, J., 1993. Biomass equations for Acacia reficiens, Acacia zanziberica and Prosopis juliflora, and volume equations for Eucalyptus camaldulensis and Terminalia brownii E. Afr. Agric. For. J. 58, 13–21, special edn.
Functions for multi-phase assessment of biomass in acacia woodlands of the Rift Valley of Ethiopia Getachew Eshete
1,)
, Goran ¨ Stahl ˚
Swedish UniÕersity of Agricultural Sciences, Faculty of Forestry, Department of Forest Resource Management and Geomatics, S-901 83 Umea, ˚ Sweden Received 14 March 1997; accepted 27 August 1997
Abstract In this article, single-tree biomass functions for acacia woodland tree species are presented. The main aim of developing the functions was for utilizing them in a multi-phase sampling design in estimating the woody biomass in acacia woodlands of the Rift Valley of Ethiopia. Eighty-five trees Ž5–35 cm diameter. were selected randomly from the five dominant tree species: Acacia tortilis ŽForsk.. Hayne, Acacia senegal ŽL. Willd., Acacia seyal Del., Acacia etbaica Schweif. and Balanites aegyptiaca ŽL. Del. Four categories of functions were developed. These were Ži. functions with crown area as independent variable, to be applied using high resolution satellite images or aerial photos; Žii. functions with crown area and tree height as independent variables, to be applied using data from aerial photos; Žiii. functions for quick estimation in ground surveys, based on the diameter at 0.8 m; and Živ. functions for thorough estimation in ground surveys, in which the diameter at 0.8 m, the diameter at stump height, and the crown area were included. Also, two sets of functions were developed, one with and one without species indicator variables. In gathering data for developing biomass functions, the selection of sample discs from trees for determining the ratio between dry weight and fresh weight is important. In addition to the functions, a robust method for the disc sampling is proposed. q 1998 Elsevier Science B.V. Keywords: Acacia tortilis; Acacia senegal; Acacia seyal; Acacia etbaica; Balanites aegyptiaca; Regression analysis; Sampling
1. Introduction As in many parts of tropical Africa, most of the energy requirement in Ethiopia is covered by traditional biomass fuels. The annual consumption of woodfuel is close to 20 = the consumption of other forest products together ŽAnonymous, 1993.. The )
Corresponding author. Tel.: q46-090-165836; fax: q46-090778116: e-mail: [email protected]. 1 Permanent address: Alemaya University of Agriculture, Faculty of Forestry, P.O. Box 138, Dire Dawa, Ethiopia.
acacia woodlands, covering nearly 11% of the total land area in the country ŽAnonymous, 1988., are important sources of woodfuel. They also provide the rural community with other forest products and benefits such as fodder, construction materials, farm implements, shade, honey, etc. The sustainable management of these woodlands, which has so far been neglected, is a priority task for the country. As outlined in the Ethiopian Forestry Action Program ŽAnonymous, 1993., it includes an optimum land-use allocation, the enforcement of property rights, and the creation of an information
0378-1127r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 8 - 1 1 2 7 Ž 9 7 . 0 0 2 7 3 - 9
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G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
basis for planning and management. The latter issue must necessarily be preceded by development of tools and techniques for the purpose, and this includes the development of methods for estimating biomass. Many studies on biomass estimation have been made over the years. Reviews of the literature are given in Hitchcock and McDonnell Ž1979. and Marklund Ž1987.. However, only a limited number of studies concerns the African forests and woodlands ŽRyan and Openshaw, 1991.. Moreover, these studies mainly consider the dry miombo woodlands of Southern and Southeastern Africa ŽStromgaard, 1985; Chidumayo, 1991; Tietema, 1993; Grundy, 1995. whereas very few treat the East African savanna woodlands ŽOlsson, 1985; Hellden, ´ 1987.. The biomass studies can be categorized into either studies concerning the estimation of wood resources ŽTietema, 1993. or ecosystem studies involving nutrient cycling, energy flow, carbon flux, comparison of plant communities, etc. ŽRochow, 1974; Brown et al., 1989.. The estimation methods used are based on direct weighing of trees or on applying functions made specifically for the purpose. In the latter case, the biomass is derived from few easily assessed tree characteristics. Regression analysis is commonly applied for developing biomass functions. The predictor variables often used, for trees in the African woodlands, are diameter at breast height ŽMalimbwi et al., 1994., diameter at stem base or ankle height ŽVertannen et al., 1993; Tietema, 1993; Grundy, 1995., crown diameter ŽOlsson, 1985; Hellden, ´ 1987; Tietema, 1993., and tree height ŽStromgaard, 1985.. In most cases the non-linear allometric equation Y s b 0 X 1b1 X 2b 2 . . . X kb k is used for modeling the relationship between the biomass Ž Y . and the predictor variablesŽ X 1 , X 2 , . . . , X k .. To enable simple estimation of the parameters Ž b s., the model is often used in its logarithmic form. The main aim of this study is to develop biomass functions on a single tree basis for the dominant tree species in the Rift Valley of Ethiopia. The species are Acacia tortilis ŽForsk.. Hayne, Acacia senegal ŽL. Willd., Acacia seyal Del., Acacia etbaica Schweif., and Balanites aegyptiaca ŽL. Del. In developing the functions, their intended use in a multi-
phase sampling design is central. Consequently, different functions are derived utilizing different sets of predictor variables, for various phases of a possible design. The study is part of a larger project aiming at developing inventory and planning techniques that could be used for the management of acacia woodlands in Ethiopia.
2. Materials and methods 2.1. Study area The study area is part of the Great Rift Valley system and is located 190 km south of Addis Ababa between latitudes 7830X and 7840X N along a strip bounded by lake Langano to the east and lakes Abiyata and Shala to the west ŽFig. 1.. It covers approximately 150 km2 out of which half of the area lies in the Abiyata Shala Lakes National Park. The area is important for migrant birds from the northern hemisphere ŽSyversten, 1995.. Climatic data for the area were obtained from the Ethiopian Meteorology Authority for the years between 1981–1995. The mean annual rainfall was 706 mm. Much of the rainfall was concentrated to a single rainy season between June and September. The mean annual temperature for the period was 20.48C with the highest temperature in March and the lowest in December. The mean monthly potential evapotranspiration ŽPET. calculated for the area from the nearest station, within the same agro-climatic zone, was 163 mm. Elevation of the area ranges between 1585–1780 m above sea level with a fairly flat to gently sloping terrain. A significant proportion of the area is subjected to cultivation and grazing and as a result the tree cover consists of remnants of acacia species scattered in the landscape. The proximity to large cities Že.g., Addis Ababa. and the main road passing through the area have made the charcoal business particularly attractive. This has contributed to the current land use pattern. 2.2. Sample tree selection To obtain a representative sample of the tree population, it is an advantage to have a picture of the
G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
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Fig. 1. Map of Ethiopia and Eritrea showing the location of the study area, which is indicated by striped lines in the magnified portion of the map.
species and size distribution of the trees prior to sampling. This was accomplished by using data from a previous study in the same area in which trees had been calipered on sample plots, within polygons. The polygons were created by automatic segmentation ŽHagner, 1990. of SPOT satellite imagery. Eighty-
five trees were selected from the list of earlier measured trees. The selection of trees was made after grouping them specieswise into 2-cm diameter classes. A random sample of trees was taken from each class, ensuring representation of trees of all species and sizes. Only trees with diameters larger
G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
82
than 5 cm were included. Also, trees with a diameter larger than 35 cm were not included due to their importance as shade trees and as trees for traditional beehive keeping. Very few trees were, however, larger than 35 cm ŽFig. 2.. Moreover, trees were excluded from the sampling list if they did not belong to the natural setting Že.g., some rare Ficus trees., if they were isolated on agricultural lands, and if they were rotten, broken or had lost more than half of their crown due to lopping or natural damage. The occurrence of crown damage on trees is given in Fig. 3. The trees sampled from the list were located in the field using GPS ŽGlobal Positioning System. and by using markings from the previous inventory, conducted within the framework of the larger project. A summary of the trees sampled for felling is given in Table 1. 2.3. Measurements A number of measurements were made on the sampled trees ŽFig. 4.. The choice of variables was
guided by previous studies in similar forest types ŽStromgaard, 1985; Olsson, 1985; Tietema, 1993. and by considering the intended use of the functions within a multi-phase sampling design. While the trees were standing, the diameter at 0.8 m ŽD08. and the diameter at stump height ŽDSH., i.e., 0.3 m above ground level, were assessed in millimeter by two perpendicular caliper measurements. The reason for taking the diameter at 0.8 m instead of at 1.3 m was that close to 15% of the trees forked in the region between 0.8–1.3 m ŽFig. 5.. When the forking was below 0.8 m, the diameter of each part was measured at 0.8 m Ž d08 i . and later the equivalent diameter was calculated as D08 s
(
n
S d08 2i .
is1
The crown diameter ŽCD. was measured Žin dm. as the average value of the major Ž a. and the minor Ž b . axes of an ellipse approximation of the crown. The ab crown area ŽCA. was then calculated as P . The 4
Fig. 2. Relative frequency of trees by diameter class obtained from prior sampling in the study area.
G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
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Fig. 3. Relative frequency of visually estimated crown damage by diameter class as percentage loss of crown. The figures are based on the results from the prior sampling.
tree height ŽTH. and the bole height ŽBH. were measured Žin dm. using a telescopic height meter. For tall trees Ž) 10 m. a Silva hypsometer was used instead. The crown height ŽCH. was determined by subtracting BH from TH. After felling, the diameter at the base of the crown ŽDC. was measured and the trees were separated into branch and stem wood components ŽFig.
4.. The stem was further crosscut into four equal parts to facilitate the disc sampling for determining the ratio of dry weight to fresh weight and ensure manageable sizes for weighing. The fresh weights of stem wood Žminimum top diameter of 5 cm. and the branch wood Žincluding leaves. components were measured to the nearest 0.01 kg using a spring balance. In case of forking below 0.8 m, the stem
Table 1 Summary data of the felled sample trees Diameter class Žcm.
5–12.9 13–18.9 19–24.9 25–30.9 31–34.9 Total
Number of trees by species A. tortlis
A. senegal
A. seyal
A. etbaica
B. aegyptiaca
3 10 7 6 1 27
5 5 5 y y 15
8 3 2 1 y 14
3 8 2 1 y 14
4 6 y 4 1 15
Mean TH Žm.
Mean DW Žkg.
5.1 6.0 6.5 7.7 9.0
34.88 69.44 193.05 343.17 372.15
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G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
Fig. 4. Sketch of an Acacia tree showing the different components and measured variables ŽCD s crown diameter, TH s total tree height, BH s bole height, DSH s diameter at stump height, D08 s diameter at 0.8 m, DC s diameter at crown base..
weight was determined by summing the weights of the parts. 2.4. Sample disc selection Two sample discs were taken from each tree, one from the branch section and another from the stem wood section. The sample disc from the stem wood Ž4 cm thick. was selected by first drawing, with equal probability, a sample of one of the four sections prepared during felling. To locate the point on
the section where the disc slice was to be removed, a uniform random number between 0–1 was multiplied by the section length. The same procedure was applied to obtain a sample disc Ž6 cm thick. from the main branches of the tree. To minimize errors from loss of moisture, the slices were measured immediately for their fresh weights to the nearest 0.01 g using an electronic balance. Later, the discs were oven-dried at a temperature of 1058C until a constant weight was obtained. 2.5. Data analysis
Fig. 5. Relative frequency of bole heights Žheights to the first forking. obtained from the prior sampling.
The total dry weight of each tree was determined by adding the dry weights of the branch and stemwood components. Each component’s weight was estimated by multiplying the fresh weight with the ratio between the oven dried and the fresh weights of the disc slices. The development of biomass functions by components was not considered in this study. Summary statistics of the main tree variables are given in Table 2. In the investigation of the empirical relationship between the total dry weight, DW, and the independent variables ŽD08, DSH, DC, CD, CA, CH, BH,
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Table 2 Summary statistics of the main tree variables of the felled sample trees Species
Mean DW Žkg.
Mean CA Žm2 .
Mean D08 Žcm.
Mean TH Žm.
Mean DSH Žcm.
A. tortilis A. senegal A. seyal A. etbaica B. aegyptiaca
118.3 103.2 86.6 108.4 107.7
35.4 33.1 28.7 26.0 16.2
19.7 16.7 13.9 15.5 19.5
6.6 5.6 6.5 5.4 6.5
20.8 17.2 14.5 16.9 21.6
TH., logarithmically transformed allometric models were fitted using least squares regression. The models used were of the kind: k
ln DW s b 0 q
Ý bi ln X i q ´
Ž 1.
is1
with the X i s being the independent variables, the b s the parameters, and ´ normally distributed error term. Several alternative functions were developed considering their potential use in a multi-phase sampling design. The functions are categorized as: Ži. Functions utilizing data from high resolution satellite images or aerial photos: such functions could be useful in the first phase of an inventory. The only variable considered in this case was CA, since it Žor CD. would be the only tree characteristic possible to assess from satellite images. Computerized methods for the determination of CA at the tree level would allow for a cost efficient first phase of biomass estimation in the acacia woodlands Žcf. Joffre and Lacaze, 1993.. Žii. Functions utilizing data from aerial photos: in addition to CA Žor CD., TH can be measured in aerial photos using stereoscopic methods. Žiii. Functions for quick estimation in ground surveys: among the variables measured on the trees, the diameter is the most reliable one for quick biomass estimation in the field. Owing to the difficulty of measuring DSH, D08 was the variable selected for the purpose. Živ. Functions for thorough estimation in ground surveys: these functions are the most accurate ones developed and are intended for use in the last phase of an inventory. They were developed by including all variables that turned out to be significant. All functions were evaluated by examining the standard deviation ŽSE. and the scatter plot of the
residuals against the different predictor variables and the predicted values. Observations were removed if they exceeded the expected value by more than three standard deviations. As a result, two to three observations were removed as outliers in developing the different functions. Two different sets of functions were developed within each category stated above. The first set of functions was developed without considering the species differences. In the second set, the potential differences were accounted for by introducing indicator variables. In the latter case the models were of the following kind: k
ln DW s b 0 q
l
Ý bi ln X i q Ý g j S j is1
k
qÝ
js1
l
Ý a i j S j ln X i q ´
Ž 2.
is1 js1
In the formula, the X i s are the basic predictor variables ŽD08, CA, etc.., and the S j s are the species
Table 3 Parameters of regression functions for above ground dry weight Žln DW. in kilogram Function Const. ln D08 ln CA ln TH ln DSH n category
R2
SE
i ii iii iv iv
0.67 0.75 0.89 0.93 0.95
0.53 0.47 0.31 0.26 0.23
1.21 y y0.26 y y2.26 2.40 y2.10 0.35 y2.36 1.00
1.09 0.97 y 1.98 0.40
y 1.01 y y y
y y y y 0.99
83 83 82 82 82
The categories of functions are indicated by Roman numbers. Units of measurements and abbreviations are the same as in the text. R 2 is the coefficient of determination and SE the standard deviation of the residuals. The functions are corrected for logarithmic bias.
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G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
indicators Žfor l q 1 species., the bi s, g j s, and a i j s are the parameters, and ´ is the error term. The significance of species differences in each category of the functions was tested by an F-test involving the extra sum of squares due to regression that arose when a certain species was introduced. A test was first made to study if g j and a i j Ž i s 1..k . together were significant for a particular species. If that was the case, it was further investigated which
of them were significant on an individual basis. The test quantity used was ŽDraper and Smith, 1981.: Fs
Ž SS reg full y SS reg hypo. r Ž p y q . MS res full
Ž 3.
where SS reg full, is the sum of squares due to regression for the full model and SS reg hypo the corresponding sum of squares for the model without indicator variables for a particular species. MS res full
Fig. 6. Studentized residuals vs. predicted values of ln DW for the different tree species. The residual plots are in Ža. for function type i Žln CA., in Žb. for type ii Žln CA, ln TH., in Žc. for type iii Žln D08., for type iv in Žd. Žln D08, ln CA. and in Že. Žln D08, ln CA, ln DSH.. All abbreviations and units are according to the text.
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Table 4 Parameters of regression functions, with indicator variables for the different species, for above ground weight Žln DW. in kilogram Function category
Predictor variable
Species
Intercept
Slope
i
ln CA
A. tortilis Žref.. A. senegal
0.83 y0.70 Ž0.223. 0.39 Ž0.015.
1.20 0.09 Ž0.524. 0.01 Ž0.016.
y0.23 0.11 Ž0.396.
0.99, 0.97 0.26, y0.78 Ž0.453, 0.639.
y3.10 1.41 Ž0.014. 1.94 Ž0.001. 0.36 Ž0.246.
2.73 y0.53 Ž0.017. y0.65 Ž0.003. y0.22 Ž0.148.
B. aegyptiaca ii
ln CA, ln TH
iii
ln D08
A. tortilis Žref.. A.senegal A.tortilis Žref.. A. senegal A. seyal B. aegyptiaca
Intercept and slope
n
R2
SE
83
0.74
0.49
83
0.78
0.45
82
0.92
0.28
Ž0.002. Ž0.005.
Ž0.012.
Ž0.033. Ž0.001. Ž0.035.
All abbreviations and units are according to the text. The numbers separated by a comma in the ‘slope’ column correspond to the predictor variables given in the same row. R 2 and SE are as in Table 3. The functions are corrected for logarithmic bias. The values in brackets indicate the p-values.
is the residual mean square of the full model. The letters p and q are the number of parameters in the full and the restricted model, respectively. Species indicators were retained only if the test quantity was higher than the tabulated quantity of an F-distribution with p–q and n–p degrees of freedom. In all tests a 5% error level was used. The final functions were corrected for logarithmic bias ŽBaskerville, 1972. by adding a correction factor to the intercept in the functions. The correction factor was calculated as: n
Ý DWi Ks
is1 n
Ž 4.
Ý exp Ž ln DWˆ i . is1
ˆ . are the true and the in which DW and exp Ž ln DW estimated dry weights, respectively. 3. Results The set of regression functions without species indicator variables, categorized according their in-
tended use, is given in Table 3. Residual scatter plots for each of these functions are shown in Fig. 6. The functions with species indicators are given in Table 4. When the interaction Žthe a i j parameters. involves more than one variable, the p-values for the interaction terms are separated with a comma. In the larger functions Žtype iv. no species differences were found to be significant.
4. Discussion Most of the biomass functions developed in previous studies ŽTietema, 1993; Malimbwi et al., 1994; Grundy, 1995. are single phase oriented. However, due to the scattered distribution of acacia woodland trees and the associated high cost of inventory, the use of multi-phase sampling should be motivated in large area biomass assessments Žcf. Olsson, 1985; Hellden, ´ 1987.. Functions of category Ži., intended for information that can be obtained from high resolution satellite images or aerial photos, were the least precise. The main reason is the limited correlation between
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G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
DW and CA. In addition, unrecognized lopped branches may have contributed to such a relationship. The precision of the function with indicator variables was significantly higher than the function without. Here, the inclusion of B. aegyptiaca was expected due to the obvious difference in crown morphology as compared to the umbrella-shaped acacias. TH and CA were used as predictor variables in the second category of functions. The correlation between DW and TH in this kind of vegetation type is inherently poor. By introducing TH together with CA, however, a significantly higher precision was obtained as compared to the corresponding functions of the first category ŽTable 3.. When accounting for species differences a reduction of the SE by 2% was obtained. The third category of functions, in which D08 was used as a predictor variable, was the best involving a single predictor variable ŽTables 3 and 4.. Hence, these functions seem to be adequate for quick ground surveys. The same result is reported in previous biomass studies ŽTietema, 1993; Malimbwi et al., 1994; Grundy, 1995.. In this category of functions, many species differences were found to be significant. Although this was the case, the difference in SE between the functions with and without species indicators was limited. The prediction of DW using DSH was less accurate ŽSE s 0.36, R 2 s 0.85. as compared to using D08, most likely due to the swelling of the stems. The fourth category of functions was the best in terms of low SE. Interestingly, no species differences were significant. The obvious interpretation is that most of the variation between the species is contained in a difference in CA, D08, and DSH. Even the function involving only D08 and CA showed no difference between the species. A limitation in using the first and second categories of functions should be mentioned. As indicated above, these functions should in practice be applied on data from high resolution satellite imagery or aerial photos. Such data were not possible to acquire in the present study. Since, instead, the measurements were made rather accurately from the ground, an inevitable propagation of measurement errors should be expected when the functions are applied on remote sensing data.
No significant differences in density were discernible between the species. At a 5% moisture level, the density varied between 0.61–0.69 grcm3 , which is comparable to results in other studies ŽMalimbwi et al., 1994.. As to the estimation of dry weight for the felled trees, it is important that this is made in a manner that ensures unbiased estimates. In the study, sample discs for drying were selected by simple random sampling. This procedure has a drawback in case there is a correlation between the fresh weight of a disc and its ratio between dry weight and fresh weight as is shown in the following. Assume a tree stem is divided into N discrete discs. The following expression for the total dry weight of the tree can then be formulated: N
DW s
Ý wi t i
Ž 5.
is1
Here, DW is the true total dry weight, wi the fresh weight of disc i, and t i the ratio between dry weight and fresh weight of disc i. The estimator used in the study, for the case when disc j is sampled from a tree, is:
ˆ s t j wtot DW
Ž 6.
In the equation, wtot is the total fresh weight of the stem. The expected value of the estimator is obtained as: N
ˆ .s E Ž DW
N
Ý pj t j wtot s Ý js1
js1
1 N
t j wtot
st wtot N
s
Ý wj t j y Ž N y 1. Cov Ž w,t .
Ž 7.
js1
where pj is the probability Ž1rN . that disc j is selected. In case the covariance term is not zero, the estimator is biased. To indicate whether or not this was the case in the present study, values of t i are plotted vs. their relative position on the stem ŽFig. 7.. The ratio between dry weight and fresh weight appears to be relatively constant, which indicates that the covariance term should be close to zero. In a PPS sampling design, with probability of selection proportional to the fresh weight of a sample
G. Eshete, G. Stahl ˚ r Forest Ecology and Management 105 (1998) 79–90
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Fig. 7. The ratio between dry weight and fresh weight Žfor the disc slices. by relative position along the stem for the sampled trees Ž1 s bottom, 2 s lower middle, 3 s upper middle, 4 s top..
disc, the situation is different. In this case the estimator ŽEq. Ž6.. of total dry weight is unbiased, since: N
ˆ .s E Ž DW
N
Ý pj t j wtot s Ý js1
js1
wj wtot
N
t j wtot s
Ý wj t j js1
Ž 8. which is equal to the true dry weight. Importance sampling, the continuous analogue of PPS sampling, has been proposed for use in connection with the selection of sample discs ŽValentine et al., 1984.. The procedure for performing it is, however, slightly complicated and the thorny and numerous branches of acacia trees make the ‘path selection’ difficult. Therefore, a simple but yet robust method for the disc selection from acacia trees is proposed below. The selection of sample discs could be made in the following steps: 1. Separate the tree into components of branch and stem wood and pile them according to their relative position in the tree Že.g., bottom, lower middle, upper middle and top. 2. Weigh each pile separately 3. Select piles by PPS sampling Žprobability proportional to the weight of the pile.
4. Use random sampling to obtain discs from within the sampled piles, and estimate biomass according to Ž6. with due consideration to the number of discs selected. Finally, it should again be mentioned that the functions presented in this study are based on trees sampled from within a quite restricted area. Although no significant bias was found when the functions were tested on data Ž Acacia spp.. as reported by Olsson Ž1985., collected in Ethiopia and the Sudan, use of the functions in other areas must be made with caution. Acknowledgements We are grateful to Prof. Hakan Olsson for com˚ ments on the manuscript, to Mr. Olle Hagner for preparing the satellite imagery as a sampling frame, and to Ass. Prof. Soren Holm for statistical com¨ ments. Our thanks also go to Mr. Zeleke Ewnetu, Mr. Kassahun Embaye, Mr. Taye and Mr. Mohammed from COF in Wondo Genet., Mr. Melaku Abegaz from WUARC in Addis, Mr. Mihret Ewnetu, Mr. G. Markos W.S. and the staff of the Abiyata and Shala Lakes National Park. Financial support was obtained from the Swedish International Develop-
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ment Agency ŽSIDA. and the Alemaya University of Agriculture.
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