International Journal of Forestry Research
Volume 2019 (2019), Article ID 1876329, 15 pages
https://doi.org/10.1155/2019/1876329

Research Article

Biomass and Volume Models Based on Stump Diameter for Assessing Degradation of Miombo Woodlands in Tanzania

Bernardol John Manyanda,1,2 Wilson Ancelm Mugasha,¹ Emannuel F. Nzunda,¹ and Rogers Ernest Malimbwi¹

¹Department of Forest Resources Assessment and Management, College of Forestry, Wildlife and Tourism, Sokoine University of Agriculture, P.O. Box 3013, Chuo Kikuu, Morogoro, Tanzania
²Forestry Training Institute, Olmotonyi, P.O. Box 943, Arusha, Tanzania

Correspondence should be addressed to Bernardol John Manyanda; bernardoljohnm@gmail.com

Received 29 May 2018; Revised 11 November 2018; Accepted 27 December 2018; Published 15 January 2019

Academic Editor: Scott D. Roberts

Copyright © 2019 Bernardol John Manyanda et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Models to estimate forest degradation in terms of removed volume and biomass from the extraction of wood fuel and logging using stump diameter (SD) are lacking. The common method of estimating removals is through estimating diameter at breast height (D) by applying equations relating measured D and SD. The estimated D is then used to estimate biomass and volume by means of allometric equations, which utilize D. Through this sequence of procedures, it is apparent that there is an accumulation of errors. This study developed equations for estimating volume, aboveground biomass (ABG), and belowground biomass (BGB) using SD in miombo woodlands of mainland Tanzania. Volume models were developed from 114 sample trees while AGB and BGB models were developed from 127 and 57 sample trees, respectively. Both site specific and regional models were developed. Over 70% of the variations in BGB, AGB, and volume were explained by SD. It was apparent that SD is inferior compared to measured D in explaining variation in volume and BGB but not AGB. However, the accuracy of BGB and volume estimates emanating directly from SD were far better than those obtained indirectly, i.e., volume or BGB estimates obtained from estimated D from SD, since the latter is affected by accumulation of regression equation errors. For improved accuracy of ABG, BGB, and volume estimates, we recommend the use of site specific models. However, for areas with no site specific models, application of regional models is recommended. The developed models will facilitate the addition of forest degradation as a REDD+ activity into the forthcoming FREL.

1. Introduction

Miombo woodlands are lands dominated by deciduous trees of the genera Brachystegia, Julbernadia, and Isoberlinia [1, 2]. They cover an area of approximately 2.7 million km² equivalent to 9% of the African land area spanning across ten countries in southern and eastern Africa including Tanzania [1, 3–6]. In Tanzania, woodlands cover about 93% of the total forest area of 48.1 million ha [7, 8]. Miombo woodlands can be divided into dry (annual precipitation <1000 mm) and wet miombo (annual precipitation>1000 mm). Dry miombo are found in Zimbabwe, central Tanzania, southern areas of Mozambique, Malawi, and Zambia [6]. Wet Miombo are found in eastern Angola, northern Zambia, central Malawi, and south western Tanzania [6].

Miombo woodlands offer both direct and indirect benefits. Direct benefits include energy (fuel wood and charcoal), construction and craft materials, medicines, employment, income, food (fruits, mushrooms, honey, and edible insect), and fodder for animals. These benefits are either for domestic consumption or for local sale [3, 5]. On the other hand, indirect benefits encompass soil nutrient inputs through nutrient cycling and through nitrogen fixation and environmental services such as soil and water conservation, biodiversity, and carbon sequestration [9–12].

Miombo woodlands are under pressure from increasing demands for land-based products and services. This has led to forest degradation and deforestation [13, 14]. Forest degradation jeopardizes the capacity of forests to function as regulators of the environment. Consequently, increasing flooding, erosion, reduced soil fertility, and loss of plant and animal diversity have been common [13]. Sustainable provision of goods and services from the miombo woodlands requires effective forest management efforts, which ultimately may make a significant contribution to national goals for Reduction of Emission from Deforestation and Forest Degradation “plus,” the role of conservation, sustainable management of forests, and enhanced carbon stock (REDD+). Implementation of REDD+ as a carbon credit market approvals among others requires measurement and monitoring of carbon emissions from forest degradation and deforestation.

While deforestation is relatively easy to estimate, forest degradation is more challenging [8]. Recently, Tanzania has engaged in developing Forest Reference Emission Level (FREL) standards [14]. Deforestation and conservation are the only REDD+ activities among the five activities, which have been included in the Tanzania FREL. Degradation has not been included due to inadequate data for establishing baselines and monitoring. Forest degradation is taking place throughout the country. Monitoring degradation by means of remote sensing techniques poses a significant challenge since degraded forests frequently maintain a closed canopy. The main drivers of forest degradation are extraction of wood fuel (charcoal and firewood), logging, grazing, and wildfire. Techniques to estimate forest degradation need to be developed following a stepwise approach. One of the techniques is the use of Stump diameter (SD) which may be included during forest inventories as a means of assessing forest degradation.

Diameter at breast height (D) and total tree height have often been used as standard predictors of biomass (both above- and belowground biomass) and volume [3–5, 15]. This is because these variables are highly correlated with biomass and volume. The common method of estimating removals is through estimating D by developing equations relating D and SD from sample trees measured for both D and SD [16–18]. The estimated D is then used to estimate biomass and volume by means of allometric equations. Through this sequence of procedures, it is apparent that there is an accumulation of errors from the estimation of D to the estimation of biomass or volume [16, 19–21]. In this case, it is considered more precise to estimate biomass and volume directly from SD. In addition, the recent National Forest Monitoring and Assessment (NAFORMA) included SD for monitoring forest degradation. Therefore, having biomass/volume – SD allometric equations will facilitate the estimation and monitoring of forest degradation in Tanzania associated with extraction of wood fuel and logging.

To date, there is only one biomass/volume – SD allometric equation that was developed from limited sample trees (30 trees) from only a single site in Tanzania [22]. Topography, soil, climate, and species are the main factors, which affect stand architectural variability in miombo woodlands [22]. Therefore, adequate sample trees collected from different sites are imperative to cover the variability in SD, D, and H of trees. Thus, this study developed aboveground biomass (AGB), belowground biomass (BGB), and volume-SD allometric equations that utilize SD as the sole predictor for estimating removal and emission from forest degradation associated with extraction of fuel wood and timber in miombo woodlands.

2. Materials and Methods

2.1. Study Area Description

The data for developing biomass and volume models were collected in Tanzanian miombo woodlands of Manyara, Lindi, and Tabora regions (Figure 1). In Manyara region, data were collected in Ayasanda and Duru Haitemba Village Land Forest Reserves. The dominant miombo woodlands tree species in these reserves include Albizia versicolor, Brachystegia microphylla, Julbernardia globiflora Brachystegia spiciformis, Brachystegia boehmii, Combretum collinum, Parinari curatellifolia, Markhamia obtusifolia, Tamarindus indica., and Senegalia nigrescens (Acacia nigrescens). Likewise, Brachystegia spp., Julbernadia spp., and Pterocarpus angolensis are common miombo woodlands trees found in Angai Village Forest Reserve in the Lindi region. Furthermore, in Tabora region, the data were collected in Nyahua Forest Reserve in which Pterocarpus angolensis, Afzelia quanzensis, Dalbergia melanoxylon, Burkea africana,Pterocarpus tinctorius, and Swartzia madagascariensis are the common tree species. Details on locations and conditions of the study sites are described in Table 1.

Table 1: Study sites descriptions.

Region
Forest
Location
Dominant soil Type
Altitude (m)
Mean annual temperature (°C)
Mean annual rainfall (mm)

Min
Max

Manyara
Ayasanda and Duru Haitemba
4°20′S, 35°47′E
Clay alluvial soils
1 300–1 800
15
26
854

Lindi
Angai Villages Forest Reserve
9°47′S, 37°55′E
Sandy loam soils
330–600
20
31
873

Tabora
Nyahua Forest Reserve
5°18′S, 32°58′E
Sandy clay loam soils
1 096–1 103
17
30
771

Figure 1: Study sites (Manyara, Lindi, and Tabora) locations as seen in the map of Tanzania. Modified from [5].

The weather conditions for all sites may be divided into three categories, i.e., a hot dry season from mid-August to the end of October, a hot wet season from November to the beginning of April, and a relatively cool dry season from April to mid-August. Furthermore, two rainfall regimes exist. In the southern, southwestern, central, and western parts of the country, including Lindi and Tabora, the rainy season starts in mid-November and ends in mid-May. In the north and in the northern coastal zone, including Manyara, the rain is distributed over two shorter periods (October–December and March–May).

2.2. Data Collection

2.2.1. Sampling Design

This study utilized a data set that was collected to develop biomass and volume models utilizing D and H [3, 5]. Additionally, SD of the sampled trees was measured. The SD was measured over bark immediately under the cutting point (felling cut). When a tree was irregular, the SD was measured at a higher point where a regular shape commenced but must be below D. Circular sample plots of 15 m radius were distributed within the study sites where 40 plots in each site were systematically established making a total of 120 plots across all three sites. Tree size and species distribution of this inventory were used as the target distribution for the selection of sample trees. One or two trees in each plot were selected for destructive sampling in order to match the target distribution. Some of the sampled trees were selected outside the plot area, i.e., large trees that were not present inside the plot.

2.2.2. Destructive Sampling

Before felling, species of each sample tree was recorded and the tree was measured for D and SD. The SD was measured at least 30 cm from the ground. In case of irregularity of the stump, we moved further above up to a point where irregularity ends. However, the measured point was always breast height. The selected sample trees were divided into two main parts, i.e., aboveground and belowground components. The aboveground component included all biomass above a point of SD measurement.

Aboveground Component. The aboveground component (Table 2) was divided into three sections, merchantable stem and branches including tops (up to a minimum diameter of 2.5 cm) and twigs (with diameter less than 2.5 cm). For small trees with D < 10 cm, no merchantable stem part was considered. For trees with D ≥ 10 cm, no specific minimum diameter was set to distinguish between merchantable stem biomass and branch biomass, but the decision was based on a subjective judgment of the length of the stem that could be used to produce timber. Leaves were excluded from twigs and thus not included in the modelling. Stems and branches were trimmed and cross cut into manageable sections ranging from 1 to 2.5 m in length and weighed for green weight. Mid-diameter and length were measured for each log section. At least two sample disks (depending on the length) from stem and branches were extracted and weighed for determination of the dry to green weight ratio (DG-ratio). Twigs were collected into separate bundles and the green weight of each twig was recorded. Small sample disks were collected from each bundle, labelled, and measured for green weight ready for drying in laboratory.

Table 2: Stump diameter descriptive statistics of volume, above- and belowground biomass data.

Component
Site
Stump diameter (cm)

n
Mean
Min
Max

Volume
Manyara
36
37.08
5
80

Lindi
39
34.25
4.5
82

Tabora
39
37.05
1.8
102

All
114
36.10
1.8
102

AGB
Manyara
40
38.31
2.4
80

Lindi
47
38.48
1.9
114

Tabora
40
37.27
1.8
102

All
127
38.05
1.8
114

BGB
Manyara
19
33.25
5
55

Lindi
19
36.61
10.2
72

Tabora
19
48.94
13
102

All
57
39.60
5
102

Belowground Component. For the belowground component (57 sample trees) (Table 2), areas around the sample tree were excavated to expose all of the roots emanating from the root crown. Three main roots (largest, medium, and smallest in diameter) were selected and excavated in full, measured for diameter at the branching point from the root crown, and weighed. Up to three side roots were selected from the excavated main roots, measured for diameter at the branching points from the main root, and weighed. Other side roots from the excavated main roots were measured for diameter at the branching point. For trees with a tap root, excavation was done until reaching a diameter corresponding to the largest selected main roots (down to 4 m depth). Diameter was measured and the remaining portion was treated as a side root (Figure 2). All main roots that were not excavated were measured for diameter at the branching point of the root crown. The root crown was also recorded for green weight. Details on excavation and sampling procedures for BGB are described in [3].

Figure 2: Belowground tree section illustrating different parts of the root (stump, root crown, main roots, and side roots). The points at diameter of main roots mark the beginning of main roots and the end of root crown. The points at diameter of side roots mark the beginning of side roots and the end of main root. Adopted from [3].

In order to obtain estimates of the dry weights of the belowground components, at least two samples were taken from all main and side roots and at least two from the root crown. All were weighed for green weight, labelled, and prepared for the laboratory procedures. In the laboratory, all above- and belowground samples were oven-dried to a constant weight at 105°C for stems, branches, and twigs for at least 48 hours and weight was recorded after every 6 hours until they maintain constant weight.

2.3. Data Analysis

2.3.1. Determination of Tree Volume

Each log section volume was calculated by multiplying the cross-sectional area at the midpoint of each log by its length. The volume of the merchantable stem and branches for a tree was obtained by summing the volumes of the respective sections for that specific tree. Total tree volume was finally obtained through summation of the volumes of the merchantable stem and the branches. Summary statistics for total observed volume over sites are shown in Table 3.

Table 3: Descriptive statistics of volume, above- and belowground biomass.

Site
AGB (Kg)
BGB (kg)
Volume(m³)

n
Mean
Min
Max
n
Mean
Min
Max
n
Mean
Min
Max

Manyara
40
1126
0.77
5143
19
199
2.90
643
36
1.26
0.0015
7.87

Lindi
47
1463
0.12
10418
19
308
17.20
1130
39
1.21
0.0016
5.79

Tabora
40
1149
0.19
8790
19
486
18.72
2355
39
1.42
0.0002
7.53

All
127
1258
0.11
10418
57
331
2.89
2356
114
1.30
0.0002
7.87

2.3.2. Determination of Aboveground Biomass

Dry to green weight (DG) ratios were determined for each tree component, i.e., stem, branches, and twigs [3]. The mean DG for each tree component was computed. The dry weight of each component (merchantable stem, branches, and twigs) was obtained as a product of mean DG-ratio and the green weight of the respective tree component. Finally, total AGB was computed as the sum of the dry weights of merchantable stem, branches, and twigs. Summary statistics for the AGB for each site are presented in Table 3.

2.3.3. Determination of Belowground Biomass

Dry to green weight (DG) ratios were determined for each belowground components, i.e., root crown, main roots, and side roots [3]. Since few sample roots were measured for green weight in the belowground section, it was necessary to develop a green weight-root diameter relationship to be able to establish the green weight of unexcavated roots, which were only measured for diameter. Once the green weight of each root was determined, green weight of each section (main roots, side roots, and root crowns) was converted to biomass by multiplying its green weight and its respective DG. The BGB of a tree was obtained by summing the dry weights of the roots and that of the root crown. Details on the procedures and uncertainty associated with these equations are described in [3]. Summary statistics for BGB for each site are shown in Table 3.

2.3.4. Model Development

Prior to model fitting, and to avoid blind fittings, response variables were plotted against the explanatory variable to examine the patterns and extent of variance for each site and for the combination of sites. The scatter plots (Figures 3, 4, and 5) displayed a positive nonlinear relationship between volume/biomass and SD. As a rule of thumb, a best model emanates from fitting several models since tree allometry differs due to biotic and abiotic factors [3–5, 19, 23, 24]. Since all trees during data collection were cut to a height of at least 30 cm above ground level, the stump height was not included in the models as an independent variable. We fitted three model forms, i.e., one nonlinear and two linear models.

where Y is volume (m³ tree⁻¹), AGB, or BGB (kg tree⁻¹); SD is stump diameter (cm); Ɛ is the error term (or residual); and a, b, and c are the regression parameters to be estimated.

Figure 3: Scatter plots of sample trees volume distribution versus stump diameter for the three sites and all sites combined.

Figure 4: Scatter plots of sample trees belowground biomass distribution versus stump diameter for the three sites and for all sites combined.

Figure 5: Scatter plots of sample trees aboveground biomass distribution versus stump diameter for the three sites and for all sites combined.

Modelling data used in this study represent a hierarchical structure, i.e., three sites and tree species nested into sites. In this case, a nonlinear mixed effect modelling approach was considered ideal for developing predictive models that would account for dependence of the species within sites and for preservation of original scale. The list of species is presented in the Appendix. Preliminary findings showed a significant improvement of model with mixed effect compared to models without mixed effect. In addition, to account for variation (i.e., heteroscedasticity due to SD) not accounted for by the random effects, we also included a power variance function structure, i.e., varPower, implemented in the nlme packages of R software for nonlinear and linear models [25, 26]. Model (1) (nonlinear) was fitted with an nlme function while models (2) and (3) (linear models) were fitted with the lme function in the nlme package [27] in R software (R Development Core Team 2018). We developed regional as well as site specific AGB, BGB, and volume models. Models were fitted by allowing random effects on all model parameters (see (1)). With the inclusion of random effects, (4) emerged.

where represents model parameters a, b, and c and expresses the difference in parameter of site i and tree species j from the mean value obtained from (1), (2), and (3) or typical site or tree species and Ri is the random effects.

2.3.5. Model Selection and Evaluation

To select the best models for volume, AGB, and BGB, we computed Root Mean Square Error (SE%), Coefficient of Determination (R²), Mean Prediction Error percentage (E%), and Akaike Information Criterion (AIC). Models with small values of SE%, E%, AIC, and high R² were considered to have a good fit. Mean prediction error percentage (E%) was computed using (5) based on fixed effects parameters only. However, with an increase in model parameters, SE% tends to be smaller and R² becomes higher regardless of the contribution of the added parameters. Therefore, to address this problem we used AIC to select the best model (see (6)). The selected models were further examined by using residual plots.

where Y is observed AGB, BGB, or volume; is predicted AGB, BGB, or volume; and n is the number of observations (i.e., number of trees).

where L is the value of the likelihood and k is the number of parameters.

In addition, we tested the previously developed volume, BGB, and AGB models from similar data sets except that their independent variables were D and total tree height. The aim was to gauge the strength of SD relative to D. We further evaluated the performance of regional models to the studied sites using E%.

3. Results

3.1. Volume Models

Table 4 presents parameter estimates and performance criteria of the fitted volume models. Parameter estimates of all fitted models were significantly different from zero (p < 0.05). Model (1) was consistently the best in all cases, i.e., smallest AIC and E%, and therefore was selected for further evaluation. For the selected models, the coefficient of determination (R²) was found to be greater than 70% except for Tabora (62%). With the exception of Manyara (absolute E% = 0.85%), E% were found to range from 9.6% to 11.8%. Residual plots of selected models are shown in Figure 6. Residual plots did not show any pattern that indicates model bias.

Table 4: Volume model coefficients and performance.

Site
Model forms
Model coefficients
AIC
SE
SE%
E%
R²

a
b
c

Tabora

0.000031
2.78805

-41.0
0.72
45.7
-11.79
0.62

-0.00234
0.00054

-1.257
1.01
63.93
-67.2
0.79

0.00443
-0.0034
0.00059
-24.66
0.98
61.96
-14.5
0.80

Manyara

0.000035
2.77406

1.348
0.51
42.10
-0.85
0.89

-0.0129
0.00050

23.85
1.06
88.12
-13.55
0.536

0.0205
-0.0077
0.00079
9.75
0.79
65.04
-9.51
0.75

Lindi

0.000026
2.8908

-39.2
0.81
56.2
-9.6
0.789

-0.0137
0.00059

2.132
0.88
61.39
-17.0
0.749

0.0385
-0.01237
0.00098
-27.2
0.53
36.6
-9.80
0.91

Regional

0.000032
2.7992

-90.16
1.01
71.7
-10.5
0.709

-0.00294
0.00056

30.7
0.99
70.4
-48.3
0.719

0.00557
0.0041
0.00066
-41.8
0.91
64.6
-15.3
0.76

Note: Bold type indicates selected model.

Figure 6: Residual plots of selected sites and regional volume models.

3.2. Above- and Belowground Biomass Models

The parameter estimates and performance criteria of the AGB and BGB models are presented in Tables 5 and 6, respectively. Model (1) was consistently the best for AGB in all cases based on the lowest E% and AIC (Table 7). Since selection was based on models with smallest AIC, model (1) was selected for all cases. Coefficient of determination (R²) of the selected regional AGB model was 0.92, while R² for the selected site specific models ranged from 0.88 to 0.94. The E% of the selected models ranged from 9.7% to 11.1%. Residual plots of selected AGB models are shown in Figure 7. Residual plots did not show any pattern to indicate model bias.

Table 5: Aboveground biomass model coefficients and performance.

Site
Model
Model coefficients
AIC
SE
SE%
E%
R²

a
b
c

Tabora

0.0391
2.6491

485.9
483.22
42.9
-11.1
0.925

-1.3626
0.3755

524.9
986.72
87.6
-39.6
0.687

3.0632
-2.4073
0.4559
501.8
848.17
75.3
-13.4
0.76

Manyara

0.0605
2.5490

511.7
649.61
44.4
9.3
0.88

-1.4551
0.35343

544.3
1319.70
90.2
-10.3
0.52

5.5304
-3.1894
0.5021
516.3
1035.86
70.8
-9.7
0.70

Lindi

0.02821
2.7508

552.8
482.84
42.0
-9.7
0.94

-0.7873
0.2337

620.5
1640.49
142.7
-10.3
0.28

1.9440
-1.6667
0.3871
598.9
1300.21
113.1
8.3
0.55

Regional

0.03785
2.6700

1541.1
551.00
43.8
-7.9
0.92

-1.1067
0.3194

1679.6
1419.02
112.8
-14.9
0.49

2.9345
-2.2779
0.4551
1614.6
1124.65
89.4
-8.96
0.68

Note: Bold type indicates selected model.

Table 6: Belowground biomass model coefficients and performance.

Site
Model forms
Model coefficients
AIC
SE
SE%
E%
R²

a
b
c

Tabora

0.0882
2.1386

222.8
87.69
44.05
-13.59
0.86

-10.1727
0.1590

228.2
90.88
45.65
-13.31
0.85

-5.8520
-0.3781
0.1651
230.2
89.98
45.2
-13.31
0.85

Manyara

0.1434
2.0144

199.6
122.52
39.72
-8.36
0.78

0.7040
0.1546

199.0
122.12
39.59
-9.27
0.79

-8.9545
1.9007
0.0945
196.2
141.96
46.02
-3.18
0.71

Lindi

0.08147
2.1896

211.2
180.71
37.18
-13.42
0.89

0.1553
0.1454

212.6
259.78
53.45
6.15
0.77

41.0525
-4.9379
0.25975
212.6
157.47
32.4
-10.84
0.91

Regional

0.1056
2.1035

623.5
154.01
46.5
-12.2
0.86

-0.8040
0.1526

624.9
164.67
49.72
-11.41
0.84

0.9476
-0.3688
0.1631
626.5
158.98
48.0
-12.04
0.85

Note: Bold type indicates selected model.

Table 7: Evaluation of some previous developed models for estimation of tree volume/biomass.

Site
Component
Reference
Equation
E

Tabora
AGB
Mugasha et al. (2013)

-3.9

BGB
Mugasha et al. (2013)

-2.7

Volume
Mauya et al. (2014)

2.0

Manyara
AGB
Mugasha et al. (2013)

-12.5

BGB
Mugasha et al. (2013)

-11.8

Volume
Mauya et al. (2014)

1.1

Lindi
AGB
Mugasha et al. (2013)

-10.1

BGB
Mugasha et al. (2013)

-8.8

Volume
Mauya et al. (2014)

0.2

Regional
AGB
Mugasha et al. (2013)

-8.9

BGB
Mugasha et al. (2013)

-7.8

Volume
Mauya et al. (2014)

-0.6

Figure 7: Residual plots of selected sites and regional belowground biomass models.

All parameter estimates for BGB models were significantly different from zero. Except for Manyara where model (3) had a good fit, model (1) performed well in Lindi and Tabora and for the regional model (Table 6). These models had lower AIC and lower E% values and therefore were selected for further evaluation. The selected BGB model for Tabora, Manyara, and Lindi had R² of 0.86, 0.71, and 0.86, respectively. The E% of the selected models ranged from 3.2% to 13.6%. Residual plots of selected models are shown in Figure 8. Residual plots did not show any pattern indicating model bias.

Figure 8: Residual plots of selected sites and regional aboveground biomass models.

3.3. Evaluation of Previously Developed Models

The prediction power of the previously developed volume and biomass models for Miombo woodlands which utilize D as sole independent variable was also tested on the current data set (Table 7). The tested volume and biomass models were developed from similar data [3, 5]. The E% for AGB, BGB, and volume model over the sites ranged from -2.7 to 11.8, -3.9 to 12.5, and 1.1 to 2.0, respectively. These values were slightly higher than those produced by the current developed models.

3.4. Performance of Developed Regional Models to Study Sites

Performance of the regional models relative to study sites results is presented in Table 8. The findings show that regional models E% were not significantly different from zero (p > 0.05) except for Tabora region.

Table 8: Performance of regional AGB, BGB, and volume models for study sites.

Site
E%

BGB
AGB
Volume

Manyara
-8.0
-7.7
-9.1

Lindi
-9.5
-10.5
-0.7

Tabora
-19.4
-21.2
31.4

4. Discussion

4.1. Modelling Data

This study developed volume and biomass models using a comprehensive data collected from three regions rich in miombo woodlands in Tanzania, i.e., Tabora, Lindi, and Manyara. Sampling was guided by the observed species distributions from previous systematic sample plot inventories carried out in each site so that the most frequently occurring genera of miombo woodlands, such as Brachystegia, Pterocarpus, Julbernadia, and Combretum, were as representative as possible (see the Appendix). Such considerations were not made in the development of models [18, 22] that are currently applied for removed volume and biomass estimation in the miombo woodlands of Tanzania. The data covered a wide range of growth conditions such as climate, topography, and soils. In addition, the data also covered a large number of observations (AGB = 127; BGB = 57; and volume = 114) and wide range of tree sizes (minimum SD of 1.8cm to maximum SD of 102 cm) for modelling which ensured that the majority of volume and biomass variation is explained by SD. Trees of large sizes were also included to avoid extrapolation beyond the data ranges. The inclusion of larger trees is of particular importance for mature forests because large trees account for the largest part of the volume and biomass and drives the model fits [3, 5, 6]. With such data set characteristics, we are confident that the developed models are superior to the previously developed volume and biomass model from a single site and limited data in eastern Tanzania that also utilized SD as a sole predictor [21, 22].

4.2. Volume Models

Model (1) was selected in all cases (site specific and for regional models). Similar model forms had also fitted well to the same data utilizing D as the explanatory variable [3, 5]. When comparing R² with other studies, [21] found R² ranging from 0.70 to 0.81 which are in line with those obtained in the present study. This also suggests that SD may explain over 70% of variation in tree volume.

The lower E% which was also not significantly different from zero indicates that the developed models were unbiased (Table 4). Generally, based on E%, models for individual sites were superior to regional models as expected since by combining all data sets there is an increase of volume, AGB, and BGB variations which were not able to be explained by only SD [3, 5]. Evaluation of previously developed volume, AGB, and BGB models shows that E% was slightly lower than those of earlier models except for Manyara. This trend suggests that D is a slightly better explanatory variable than SD when estimating standing trees volume. However, when estimating removed volume, the most viable option is to utilize a model with SD as sole predictor. Furthermore, the findings show that application of regional models for all components was limited to Manyara and Lindi where prediction errors were not significantly different from zero. It is not clear why prediction was poor in Tabora. However, differences in tree allometry, especially at root collar, may explain the difference.

4.3. Aboveground Biomass Models

Model (1) was selected in all cases with lower AIC and E%. This goodness of fit and flexibility of this model form have been reported by other scholars [3, 5, 6, 22, 24]. It is apparent in most cases that models are applied outside their modelling data. However, models which are simple (e.g., model (1) with few coefficients) are flexible and mostly unbiased relative to more complex models (with large number of coefficients) which are more specific and therefore biased when applied outside their range [28].

The selected site specific and regional models for AGB had R² values ranging from 0.91 to 0.93. These values are similar to previously reported values for models developed for miombo woodlands that utilize SD as the predictor [22] and lowland forest in Dindili forest reserve in Morogoro that utilize D as the predictor [29] with R² ranging from 83% to 89%. This implies that, for miombo woodlands, SD is adequate to explain majority of variation in AGB, as does D. This is further supported by residual plots, which did not show any indication of model bias. In addition, E% obtained from evaluation of previous model to the current data set were similar to the E% obtained for the models developed in the current study (Tables 5 and 7). Therefore, the conventional approach of estimating degradation (trees removal) by first estimating D from SD and then applying estimated D to estimate AGB may jeopardize the estimates accuracy more than using SD directly as suggested in this study.

4.4. Belowground Biomass Models

Model (1) for all sites and for the regional models was selected as the preferred model except for Manyara region. The inconsistency of model (1) performance for Manyara region was also reported by [3] for BGB. In comparison with R² values reported by [3], i.e., R² ranging from 0.89 to 0.94, R² reported in this study was relatively lower. Similarly, E% values also followed that trend. For example, the current regional model had an E% of 12.2% while the previous regional model using D as the predictor had an E% of -7.8%. This suggests that not all variation in BGB explained by D can adequately be explained by SD. In addition, the accuracy of BGB estimates dropped when using SD as the predictor rather than D.

There are several studies, which have modelled BGB with SD as the explanatory variable to make a concrete comparison. However, [30] reported findings that are contrary to the current findings. They found in Pinus densiflora in Samcheok that root collar diameter had a higher correlation with BGB than D. The fact that this study dealt with multiple tree species growing in different environmental conditions, i.e., soil depth, different moisture stress (climate) [30], and topography, may explain the inconsistency between the two studies.

5. Conclusion

Predicting volume and biomass directly from SD is useful in situations where D is not available. This study developed robust volume, AGB, and BGB models utilizing SD as the predictor that can be used to estimate forest degradation carried out through tree cutting in miombo woodlands. These models will facilitate the addition of forest degradation as a REDD+ activity in the forthcoming FREL. It was apparent that SD was inferior to D in explaining variation in volume and BGB but not AGB. However, the accuracy of BGB and volume estimates emanating directly from SD are far better than those obtained indirectly, i.e., volume or BGB estimates obtained from estimated D from SD, since the latter are affected by the accumulation of regression equation errors. For improved accuracy of ABG and BGB and volume estimates, it is recommended that site specific models be used. However, for areas where no site specific models exist, application of regional models is recommended.

Appendix

See Table 9.

Table 9: Tree species used in modelling.

Site
Tree species
SD (cm)

Manyara
Brachystegia microphylla
55

Manyara
Brachystegia microphylla
45

Manyara
Lannea schimperi
32

Manyara
Julbernadia globiflora
77

Manyara
Strychnos spinosa
34

Manyara
Brachystegia microphylla
55

Manyara
Brachystegia microphylla
51

Manyara
Julbernadia globiflora
30.9

Manyara
Brachystegia microphylla
53

Manyara
Grewia sp.
8

Manyara
Julbernadia globiflora
46

Manyara
Brachystegia microphylla
10

Manyara
Brachystegia microphylla
37

Manyara
Vernonia exserstiflora
5

Manyara
Julbernadia globiflora
36

Manyara
Lannea schimperi
32

Manyara
Brachystegia spiciformis
29

Manyara
Brachystegia spiciformis
9.5

Manyara
Brachystegia microphylla
22.7

Manyara
Brucea antidysenterica
34.5

Manyara
Brachystegia microphylla
78

Manyara
Rhus vulgaris
2.4

Manyara
Brachystegia spiciformis
40

Manyara
Brachystegia microphylla
68

Manyara
Julbernadia globiflora
80

Manyara
Brachystegia spiciformis
32

Manyara
Julbernadia globiflora
28

Manyara
Julbernadia globiflora
54

Manyara
Brachystegia microphylla
69

Manyara
Brachystegia microphylla
67

Manyara
Albizia antunesiana
63

Manyara
Julbernadia globiflora
40

Manyara
Grewia sp.
31.5

Manyara
Julbernadia globiflora
29

Manyara
Brachystegia microphylla
26.3

Manyara
Brachystegia spiciformis
10.9

Manyara
Brachystegia microphylla
17

Manyara
Julbernadia globiflora
52

Manyara
Lannea schimperi
25.7

Manyara
Brucea antidysenterica
16

Lindi
Pterocarpus angolensis
72

Lindi
Dichrostachys sp.
18

Lindi
Lonchocarpus laxiflorus
11

Lindi
Pterocarpus angolensis
37

Lindi
Deinbollia borbonica
18

Lindi
Pterocarpus angolensis
32

Lindi
Pterocarpus angolensis
41.7

Lindi
Pterocarpus angolensis
60

Lindi
Pterocarpus angolensis
28.1

Lindi
Pterocarpus angolensis
54

Lindi
Pterocarpus angolensis
29.8

Lindi
Brachystegia boehmii
29.2

Lindi
Julbernadia globiflora
46.5

Lindi
Zanha africana
27.5

Lindi
Pterocarpus angolensis
16.7

Lindi
Brachystegia spiciformis
71

Lindi
Ficus natalensis
11.5

Lindi
Sterculia appendiculata
65.2

Lindi
Brachystegia boehmii
29

Lindi
Brachystegia spiciformis
82

Lindi
Pseudolachnostylis maprouneifolia
41

Lindi
Vangueria acutiloba
12

Lindi
Lonchocarpus bussei
6.2

Lindi
Sterculia appendiculata
33

Lindi
Pseudolachnostylis maprouneifolia
24.2

Lindi
Bridelia scleroneura
65

Lindi
Brachystegia spiciformis
25

Lindi
Cordyla africana
54

Lindi
Afzelia quanzensis
48

Lindi
Diplorhynchus condylocarpon
29

Lindi
Deinbollia borbonica
32

Lindi
Ficus natalensis
34.2

Lindi
Lonchocarpus laxiflorus
2.4

Lindi
Deinbollia borbonica
1.9

Lindi
Hugonia castaneifolia
30.2

Lindi
Julbernadia globiflora
54

Lindi
Deinbollia borbonica
86

Lindi
Afzelia quanzensis
39

Lindi
Annona senegalensis
18.2

Lindi
Brachystegia spiciformis
114

Lindi
Brachystegia spiciformis
98

Lindi
Deinbollia borbonica
19

Lindi
Combretum apiculatum
24.2

Lindi
Dodonaea viscosa
80

Lindi
Lonchocarpus bussei
10.2

Lindi
Brachystegia spiciformis
43

Lindi
Julbernadia globiflora
4.5

Tabora
Acacia robusta
41.5

Tabora
Terminalia sericea
34

Tabora
Afzelia quanzensis
31

Tabora
Combretum zeyheri
25

Tabora
Combretum molle
12.5

Tabora
Pericopsis angolensis
92

Tabora
Isoberlinia globiflora
82.8

Tabora
Bridelia scleroneura
51

Tabora
Schrebera koiloneura
22

Tabora
Combretum zeyheri
13

Tabora
Brachystegia boehmii
55.3

Tabora
Lannea amaniensis
27

Tabora
Lannea schimperi
28

Tabora
Unknown
29

Tabora
Brachystegia boehmii
70

Tabora
Pterocarpus angolensis
32.7

Tabora
Brachystegia boehmii
51.7

Tabora
Albizia antunesiana
45.9

Tabora
Brachystegia spiciformis
102

Tabora
Brachystegia spiciformis
89

Tabora
Dalbergia melanoxylon
17.2

Tabora
Screrocaria birrea
36

Tabora
Pericopsis angolensis
36.5

Tabora
Psorospermum febrifugum
3.8

Tabora
Antiaris toxicaria
5.5

Tabora
Tamarindus indica
4.3

Tabora
Brachystegia spiciformis
77

Tabora
Lonchocarpus bussei
17

Tabora
Cordyla africana
1.8

Tabora
Garcinia sp.
19

Tabora
Dalbergia melanoxylon
12

Tabora
Swartzia madagascariensis
46

Tabora
Erythrophleum africanum
25

Tabora
Bridelia scleroneura
55

Tabora
Kigelia africana
39

Tabora
Combretum zeyheri
25

Tabora
Strychnos pungens
6.5

Tabora
Brachystegia spiciformis
60

Tabora
Xeroderris stuhlmannii
35

Tabora
Dichrostachys glomerata
34

Data Availability

The data regarding this research work will be readily available when requested.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

Acknowledgments

The authors gratefully thank the Tanzania Forest Services Agency for giving them a permit to conduct destructive sampling in all the study sites.

References

P. Frost, “The ecology of Miombo woodlands,” in The Miombo in Transition: Woodlands and Welfare in Africa, B. M. Campbell, Ed., pp. 11–57, Center for International Forestry Research, Bogor, Indonesia, 1996.

I. Backéus, B. Pettersson, L. Strömquist, and C. Ruffo, “Tree communities and structural dynamics in miombo (Brachystegia-Julbernardia) woodland, Tanzania,” Forest Ecology and Management, vol. 230, no. 1–3, pp. 171–178, 2006.

W. A. Mugasha, O. M. Bollandsås, R. E. Malimbwi et al., “Allometric models for prediction of above- and belowground biomass of trees in the miombo woodlands of Tanzania,” Forest Ecology and Management, vol. 310, pp. 87–101, 2013.

E. Mwakalukwa, E. Meilby H, and T. Treue, “Volume and aboveground biomass models for dry Miombo woodland in Tanzania,” International Journal of Forestry Research, vol. 11, 2014.

E. W. Mauya, W. A. Mugasha, E. Zahabu, O. M. Bollandsås, and T. Eid, “Models for estimation of tree volume in the miombo woodlands of Tanzania,” Southern Forests: Journal of Forest Science, vol. 10, pp. 1–11, 2014.

D. J. Kachamba, T. Eid, and T. Gobakken, “Above- and belowground biomass models for trees in the miombo woodlands of Malawi,” Forests, vol. 7, no. 38, pp. 1–22, 2016.

J. M. Abdallah and G. C. Monela, “Overview of Miombo woodlands in Tanzania. MITMIOMBO–Management of indigenous tree species for ecosystem restoration and wood production in semi-arid Miombo woodlands in eastern Africa,” Working papers of the Finnish Forest Research Institute, vol. 50, pp. 9–23, 2007.

United Republic of Tanzania, National Forest Resources Monitoring and Assessment of Tanzania Mainland, (NAFORMA): Main Results, Ministry of Natural Resources & Tourism, Tanzania Forest Services Agency, The Government of Finland and Food and Agriculture Organization(FAO) of the United Nations, 2015.

P. K. T. Munishi and T. H. Shear, “Carbon storage in afromontane rain forests of the eastern arc mountains of Tanzania: their net contribution to atmospheric carbon,” Journal of Tropical Forest Science, vol. 16, no. 1, pp. 78–93, 2004.

E. Zahabu, Sinks and Sources: A Strategy to Involve Forest Communities in Tanzania in Global Climate Policy [Thesis for Award of PhD Degree at University of Twente], 2008.

N. D. Burgess, B. Bahane, T. Clairs et al., “Getting ready for REDD+ in Tanzania: a case study of progress and challenges,” Oryx, vol. 44, no. 3, pp. 339–351, 2010.

P. A. Dewees, B. M. Campbell, Y. Katerere et al., “Managing the miombo woodlands of southern Africa: policies, incentives and options for the rural poor,” Journal of Natural Resources Policy Research, vol. 2, no. 1, pp. 57–73, 2010.

Food Agriculture Organization, Global Forest Resources Asssessment, vol. 163, Food and Agriculture Organization of the United Nations, Rome, Italy, 2010.

United Republic of Tanzania, Tanzania’s Forest Reference Emission Level Submission to the United Nations Framework Convention on Climate Change (FREL), Ministry of Natural Resources and Tourism, Dar es Salaam, Tanzania, 2017.

J. S. Makero, R. E. Malimbwi, T. Eid, and E. Zahabu, “Models Predicting Above- and Belowground Biomass of Thicket and Associate Tree Species in Itigi Thicket Vegetation of Tanzania,” Agriculture, Forestry and Fisheries, vol. 5, no. 4, pp. 115–125, 2016.

R. B. Heiligmann, M. Golitz, and M. E. Dale, “Predicting board-foot tree volume from stump diameter for eight hardwood species in Ohio,” Journal of Science, vol. 84, no. 5, pp. 259–263, 1984.

J. J. Corral-Rivas, M. Barrio-Anta, O. A. Aguirre-Calderón, and U. Diéguez-Aranda, “Use of stump diameter to estimate diameter at breast height and tree volume for major pine species in El Salto, Durango (Mexico),” Forestry, vol. 80, no. 1, pp. 29–40, 2007.

T. C. Sawe, P. K. T. Munishi, and S. M. Maliondo, “Miombo of Tanzania: Implications on conservation and carbon stocks,” International Journal of Biodiversity and Conservation, vol. 6, no. 3, pp. 230–237, 2014.

H. I. Aigbe, W. W. Modugu, and B. A. Oyebade, “Modeling volume from stump diameter of Terminalia ivorensis (a. chev) in sokponba forest reserve, edo state, Nigeria,” Journal of Agricultural and Biological Science, vol. 7, no. 3, pp. 146–151, 2012.

S. B. Shamaki and S. O. Akindele, “Volume estimation models from stump diameter for Teak (Tectona grandis Linn f) plantation in Nimbia forest reserve Nigeria,” Journal of Environmental Science and Water Resources, vol. 2, no. 3, pp. 89–94, 2013.

V. B. Carl, “Volume prediction from stump diameter and stump height of selected species in Louisiana, New Orleans, United States of department of agriculture,” Research Paper, no. SO-182, 1982.

S. A. O. Chamshama, A. G. Mugasha, and E. Zahabu, “Stand biomass and volume estimation for Miombo woodlands at Kitulangalo, Morogoro, Tanzania,” Southern African Forestry Journal, vol. 200, pp. 59–70, 2004.

A. M. Masota, E. Zahabu, R. E. Malimbwi, O. M. Bollandsås, and T. H. Eid, “Volume models for single trees in tropical rainforests in Tanzania,” Journal of Energy and Natural Resources, vol. 3, no. 5, pp. 66–76, 2014.

M. Henry, N. Picard, C. Trotta et al., “Estimating tree biomass of sub-Saharan African forests: A review of available allometric equations,” Silva Fennica, vol. 45, no. 3, pp. 477–569, 2011.

N. Picard, L. Saint-André, and M. Henry, “Manual for building tree volume and biomass allometric equations: from field measurement to prediction,” Food and Agriculture Organization of the United Nations, vol. 215, 2012.

B. R. Parresol, “Modeling multiplicative error variance - An example predicting tree diameter from stump dimensions in baldcypress,” Forest Science, vol. 39, no. 4, pp. 670–679, 1993.

F. Baty and M. L. Delignette-Muller, Tools for Nonlinear Regression Diagnostics, 2018, http://cran.r-project.org/web/packages/nlstools/index.html.

W. A. Mugasha, T. Eid, O. M. Bollandsås, and L. Mbwambo, “Modelling diameter growth, mortality and recruitment of trees in miombo woodlands of Tanzania,” Southern Forests, vol. 79, no. 1, pp. 51–64, 2017.

W. A. Mugasha, E. E. Mwakalukwa, E. Luoga et al., “Allometric models for estimating tree volume and aboveground biomass in lowland forests of Tanzania,” International Journal of Forestry Research, vol. 2016, Article ID 8076271, 13 pages, 2016.

A. Ledo, K. I. Paul, D. F. R. P. Burslem et al., “Tree size and climatic water deficit control root to shoot ratio in individual trees globally,” New Phytologist, vol. 217, no. 1, pp. 8–11, 2018.