# Height-Diameter Allometry for Tree Species in Tanzania Mainland

Authors: W. A. Mugasha; E. W. Mauya; A. M. Njana; K. Karlsson; R. E. Malimbwi; S. Ernest
Journal: International Journal of Forestry Research
 (2019)

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## Abstract

Total tree height (H) and diameter at beast height (D) are important independent variables in predicting volume, biomass, and other forest stand attributes. However, unlikeD measurement, which is easy to measure with high accuracy,H measurement is laborious. This study, therefore, developedH-D relationships for ten different forest types in Tanzania Mainland. Extents in which climate and forest stand variables explain the variation inH-D allometry were also assessed. A total of 31782 sample trees covering miombo woodlands, humid montane, lowland forests, bushlands, grasslands, mangroves, cultivated land, wetlands forests, and pines andEucalyptus species plantations were used for model development. TheH estimating model without climate and forest stand variables referred herein as “base model” was first developed followed by “generalized model” which included climate and stand variables. All the data were fitted using nonlinear mixed effect modelling approach. Results indicated that generalizedH estimating models had better fit than the base models. We therefore confirm a significant contribution of climate and forest structure variables in improvingH-D allometry. Among the forest structure variables, basal area (BA) was far more important explanatory variable than other variables. In addition, it was found that the mean treeH tends to increase with the increase of mean precipitation (PRA). We therefore conclude that forest specific generalizedH model is to be applied when predictingH. When forest type information is not available, generalized regional model may be applied. Base model may be applied when forest stand or climate information are missing.


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## Body

## 1. Introduction

Diameter at breast height (D) and tree height (H) are among the important single tree parameters that describe forest structure and other forest characteristics [1–3]. Most tree variables, which are difficult to measure directly such as tree biomass and volume, are highly correlated withD andH [1, 4]. Consequently, single tree biomass and volume are estimated by means of allometric models which useD andH as predictor variables. On the other hand, these parameters are also highly correlated. A good example is the relationships betweenH andD, D and crown diameter, andD and stem height [4–7].Often,H has been excluded and onlyD or a combination ofD and wood basic density is often applied to estimate biomass [8–10]. This assumes that the ratio ofH-D,stem taper, and crown mass fraction is constant from smaller to larger trees. However, this assumption may result in systematic error for biomass and other stand level variables estimates since the relationship betweenHandD is not linear [3]. This is because in tropicsH-D relationship varies within the same species with different sizes, stand density, species composition, and site conditions [1, 2]. In addition, whileD increases at a more or less constant rate until the tree is lost to mortality,H normally reaches an upper limit asymptotically [11]. Consequently, variousH patterns affect other tree variable such as individual tree biomass and volume [9, 12, 13]. A good example is the reported reduction of allometric model standard error and relative root mean square error from 357 kg to 228 kg and from 47% to 33% when applying biomass and volume allometric equation for miombo woodlands of Tanzania Mainland, respectively, withD as sole predictor and with bothD andHas predictor variables [4, 14].Conventionally, when carrying out forest inventory all trees in sample plots are measured forD and few sample trees are measured forH [15]. The measured sample trees are used to develop simpleH-D equations and applied to estimateHof unmeasured trees. This approach is often used because measuringH of all trees is laborious and time consuming especially in the tropical forests. The amount of work involved is aggravated by situations encountered in the field such as steep terrain, wide tree crown, and obstruction of tree tops by other trees crowns and leaning trees [16, 17]. Advantage of this approach is that it takes consideration of site conditions, e.g., climate and structural variation at plot level. However, often, the number of sample trees is inadequate to capture theH-D allometry variations which may jeopardize the precision and accuracy of estimatedH and other associated forest stand parameters such as volume and biomass (e.g., [8]). SuchHestimating models which utilize onlyD have been applied for decades [1, 18–21]. Studies have reported thatH-D allometry is regulated by other factors, particularly abiotic factors such as soil nutrients, depth, and availability of water and biotic factors such as those describing the interactions of trees, e.g., competition for soil and light resources [2, 22–24]. These factors have been reported to trigger tree species specific phenotypic responses which affect allocation of biomass in tree parts. Irrespective of the reported significant effects of abiotic factors inH-D, there are a limited number of studies particularly in the tropical forests of Tanzania which have attempted to report the effect of abiotic factors on the treeH-D relationship. In this study we consider that in addition toD,H is also modulated by forest structure and climate variable.At local scale where the climate gradient is relatively negligible, precipitation and temperature at spatial scale may not have effect onH. At large scale where climate variation is substantial there is indication thatH-D allometry also varies significantly among sites [2]. It has been shown that environmental resources especially water affect carbon allocation in tree compartments which may eventually affectH-D allometry. For example, Ledo et al. [22] have reported root-shoot ratio to decrease with the increase in water stress. It has been further reported that maximum attainedH corresponds to amount of precipitation while forDirregular pattern has been observed [25, 26]. In Tanzania Mainland where in most cases altitude coincides with moisture availability and precipitation, trees found in miombo woodlands at an altitude ranging from 300 m to 1100 m, on average, are shorter than trees in humid montane forest found at an altitude above 1000 m [27, 28]. Despite such remarkable and obvious effect of climate and other associated abiotic factor, to date, there is no study which has attempted to report evidence suggesting the effect of climate on bothH andD simultaneously in the miombo woodlands and other vegetation types in Tanzania. On the other hand, forest stand variables which describe density, e.g., basal area per unit area (BA; m2 ha−1), may vary considerably within a given site compared to precipitation. The effect of forest stands variables onH-D allometry had been reported elsewhere [29]. It is well known that trees of the same size in diameter growing in a dense stand are taller compared to tree growing in less dense stand [29] although Zahabu et al. [30] reported taller trees in widely spaced than in closely spaced teak. Since these studies investigated and reported the effect of forest stand variables to only one dimension of the tree, i.e.,H, there is no adequate evidence on their effect onH-D allometry.RobustH estimating models developed from adequate sample trees and which consider other factors that modifyH-D allometry are prerequisite for explaining majority ofH variations. FewH estimating models have been developed in Tanzania Mainland but with some limitations; e.g., they covered single species [31] or utilized limited number of sample trees [32, 33]. It is until recent whereH estimating models for miombo woodlands (1,392 sample trees), humid montane (751), and lowland forest (314) were developed for few selected sites [14, 28]. However, like other previously developed models, they do not incorporate climate variables. Due to heterogeneity ofH-D allometry associated with differences in climate and topography in Tanzania, application of these models beyond their range may not be appropriate. In addition, Tanzania has made an effort to develop accurate volume and biomass allometric equations where those utilizingH in addition toD have better performance in terms of mean prediction error [4, 34, 35]. These efforts will be wasted ifH is not accurately estimated and therefore risk tree volume and biomass estimates.This study utilized large data set generated from the first National Forest Inventory (NFI) in Tanzania popularly known as National Forest Resources Monitoring and Assessments (NAFORMA) with the aim of developingH-D relationship and assessing the contribution of climate and forest structure variables to theH-D allometry. The developed models will mainly serve the following purposes, i.e., (1) increase precision of forest biomass and volume which utilizeH as predictor in addition to other variables, e.g.,D and wood basic density and (2) reduce forest inventory costs associated withH measurements.


## 2. Methodology

### 2.1. Site Description

Data used in this study were obtained from a network of plots established by NAFORMA in Tanzania Mainland (Figure1). Data were collected over the entire Tanzania Mainland covering all primary vegetation types. The country has a diverse climate with mean annual rainfall ranging from below 400 mm to over 2000 mm per annum. The rainfall for large parts of the country is bimodal with short rains from October to December and long rains from March to May. The biodiversity of forests in Tanzania Mainland is high consisting over 10,000 plant species, hundreds of which are nationally endemic. Of the plant species, 305 are identified as threatened in the IUCN Red List, with 276 species classified as endangered (IUCN 2013). The main forest types include miombo woodlands, humid montane forest, lowland forest, bushland, grassland, mangroves, wetlands, cultivated areas, and plantations [36]. Some of these vegetation types are described briefly in subsequent subsections.Figure 1
Distribution of the NAFORMA sample plots within the entire Tanzania Mainland.


#### 2.1.1. Woodlands and Bushlands

The woodlands constitute the largest vegetation type in Tanzania Mainland, occupying about 44.7 million hectares which is equivalent to 93% of the entire forest area [36]. The woodland has three subtypes: Closed (>40% canopy cover), Open (10–40% canopy cover), and Woodland with scattered cropland. The height ranges between 5–20 m although occasionally being taller than 20 m.


#### 2.1.2. Humid Montane and Lowland Forest

The humid montane and lowland forest occupy 995,000 and 1,656,500 ha, respectively, in Tanzania Mainland which is altogether about 5.5% of the countries forest area. These forests are characterized by high richness of flora and fauna and have high catchment values [43].


#### 2.1.3. Grassland

Grassland is another vegetation type possessing marked variety, with four subtypes [44]. For the most part, this type occurs as its subtypes in combination with either a limited Wooded or Bushed component, or with scattered subsistence cultivation. The grassland subtypes are Wooded grassland, Bushed grassland, Grassland with scattered cropland, and Open grassland.


#### 2.1.4. Cultivated Land

The cultivated land is a type of land with four vegetation subtypes [44]. The physiognomy varies widely in accordance with the significance of the tree and crop component associated with each unit. The agroforestry systems which contain permanent tree crops (timber and fruit) that are mixed with permanent and annual agricultural crops (yam, beans, banana, coffee, etc.) are recognized as one vegetation subtype. The tree crops (Grevillea, Albizia, Cordia, Citrus,Acrocarpus, etc.) which form the upper canopy act as shade to the lower canopy crops (banana, coffee, beans). The other cultivated land subtype is where the woody crops are mixed in varying proportions of fruit tree species such as mango, coconut, citrus, and cashew.


#### 2.1.5. Mangroves

Mangroves are forests found in the tropical and subtropical coastlines between 30° south and north of equator [45]. Mangroves comprise trees and shrubs which grow in or adjacent to the intertidal zone. They are found at primarily along sheltered shorelines where freshwater (rainfall or river flow) dilutes the ocean. At the eastern coast of Africa, 14 mangrove species are growing naturally, and 10 among these are found in Tanzania Mainland.Avicennia marina (Forssk.) Vierh,Sonneratia alba J. Smith, andRhizophora mucronata Lam. are the three most dominant mangrove species in Tanzania [35].


#### 2.1.6. Pine and Eucalyptus Species

Pine andEucalyptus species are among the planted exotic tree species in Tanzania Mainland. Pine species in Tanzania Mainland includePinus patula, P. elliottii,andP. caribaea. These species are the dominant species in most of the government and private plantations with about 78% of the total area planted and the remaining 22% is shared among hardwoods and other softwood species. In Tanzania Mainland, the area underEucalyptus species is estimated to be 25,000 ha [46] of which 4,665 ha. The plantedEucalyptus species includeE. saligna, E. grandis, E. camaldulensis, E. globulus, E. viminalis, E. citriodora, E. regnans, andE. microtheca [46].


### 2.2. Sampling Design and Field Measurements

Data used in this study were collected during the first ever NFI in Tanzania carried out in year between 2010 and 2014. The double sampling for stratification approach was applied. The sampling was designed based on a simulation study described by Tomppo et al. [47]. The first-phase sample consisted of clusters of plots on a 5×5 km grid. The first-phase clusters were stratified based on predicted growing stock, time consumption for cluster measurements, and slope of the terrain. Altogether, the first-phase clusters that contain 6 to 10 plots were assigned to 18 predefined strata. The second-phase samples were systematically selected from the first-phase sample, with different sampling intensities in each of the 18 strata following an optimal allocation procedure with cost functions tailored for each stratum (see. [47]). Greater sampling intensity was allocated to strata with large predicted growing stock and smaller sampling intensity to strata with small-predicted growing stock. Only the clusters selected during the second phase of sampling were measured in the field. The distance between field plots within a cluster was 250 m, while the distance between clusters varies from 5 km to 45 km. For each cluster plots spaced 250 m apart varied from 6 to 10 depending on estimated difficulty to access the cluster (Figure 2). Accordingly, a total of 3,420 clusters with 32,660 plots were adopted. However, during the fieldwork, a total of 3,219 clusters which are equivalent to 30,773 plots were actually measured. Some clusters were not measured for various reasons, mainly difficult terrain and remoteness. Circular fixed area nested plot designs were applied. The nested plots included 1, 5, 10, and 15 m radius concentric plots.Figure 2
The NAFORMA cluster and plot design [36].Measurements ofD for all the trees within the plot were in accordance with the tree size and distance from plot centre where larger trees where measured in larger plot and vice versa [47]. For all the trees measured in the plot, species names were recorded both botanical and local names. Every fifth tree in the cluster was selected as sample tree and measured forH using Suunto hypsometers. We refer the readers to MNRT [36] for more details on the field measurements.


### 2.3. Data Preparation

Following data cleaning to remove outliers in the NAFORMA data, a total of 31782 observations were obtained for analysis. During preliminary data analysis scatterplots revealed relationships betweenH andD varying with vegetation types. Accordingly, for modelling purpose, the entire data were grouped into vegetation types in order to account for variations inH-D allometry that might be attributed by the tree allometry associated with the specific vegetation type. The relationship between response and predictor variables was assessed by means of scatter plots. TheH-Dplots indicated nonlinear relationship (Figure 3). Summary statistics for variable under consideration for each forest type is presented in Table 1.Table 1
Descriptive statistics of total tree height (H) and diameter at breast height (D).
Variable Forest Type Statistics Bushlands Cultivated Eucalyptus Grasslands Lowland Mangroves Montane Pines Wetlands Miombo All H Number of trees 3669 1866 100 934 2278 307 2111 340 97 20080 31782 Min. 1.35 1.50 5.00 1.50 1.50 1.50 1.50 3.00 2.00 1.30 1.30 Max. 28.00 35.00 36.00 33.00 35.00 27.00 45.00 35.00 25.00 36.00 45.00 Mean 6.72 8.45 16.47 7.61 10.67 7.53 12.89 18.00 9.78 9.24 9.30 CV 0.49 0.52 0.42 0.49 0.52 0.49 0.50 0.47 0.48 0.46 0.52  D Min. 1.00 1.00 5.20 1.00 1.00 1.00 1.00 1.80 2.20 1.00 1.00 Max. 83.10 149.90 82.50 75.00 122.40 46.40 141.00 54.20 93.00 123.40 149.90 Mean 12.44 21.64 19.41 17.42 18.42 11.13 22.65 22.69 24.31 18.52 18.21 CV 0.85 0.74 0.65 0.68 0.81 0.62 0.78 0.45 0.76 0.63 0.71  BA Min. 0.08 0.09 1.59 0.07 0.39 0.91 0.26 0.60 0.52 0.27 0.07 Max. 104.05 88.27 74.96 72.53 138.59 59.75 204.37 53.50 61.88 105.69 204.37 Mean 10.98 9.10 21.66 8.01 22.90 17.57 32.79 26.37 14.74 13.48 14.93 CV 0.92 1.06 0.87 0.86 0.57 0.55 0.71 0.57 1.12 0.58 0.81  CI Min. 0.04 0.04 0.22 0.02 0.02 0.09 0.03 0.22 0.23 0.04 0.02 Max. 4.54 2.98 2.06 2.56 4.47 2.95 4.18 1.75 2.55 4.91 4.91 Mean 0.91 0.94 0.99 0.94 0.85 0.88 0.85 0.97 0.99 0.92 0.91 CV 0.58 0.43 0.33 0.43 0.66 0.45 0.63 0.26 0.43 0.51 0.53  PRA Min. 475.00 520.00 841.00 440.00 560.00 936.00 683.00 841.00 479.00 366.00 366.00 Max. 2025.00 2266.00 1666.00 1865.00 1865.00 1257.00 1913.00 1913.00 2323.00 2323.00 2323.00 Mean 825.41 1072.53 1272.74 1100.06 1119.53 1116.83 1184.12 1199.17 1045.08 997.58 1012.76 CV 0.30 0.25 0.15 0.27 0.25 0.09 0.21 0.12 0.27 0.24 0.26  Dry Min. 4.00 3.00 4.00 4.00 4.00 5.00 4.00 4.00 5.00 4.00 3.00 Max. 11.00 10.00 8.00 11.00 11.00 8.00 9.00 8.00 10.00 11.00 11.00 Mean 7.69 6.63 6.39 6.91 6.83 6.54 6.36 6.95 7.27 7.11 7.07 CV 0.15 0.14 0.16 0.13 0.09 0.09 0.14 0.08 0.11 0.14 0.15Figure 3
Scatter plots ofH-D allometry.


#### 2.3.1. Climate Data and Forest Stand Parameters

Climate data of 2.5 min resolution were downloaded fromhttp://worldclim.org/version2 covering a period between 1970 and 2000 [48]. Climate data parameters of interest were mean annual precipitation (PRA), number of months with precipitation below 100 mm (dm) and mean annual temperature (TEA). Candidate stand forest parameter variables tested were stand level competition variables, i.e., basal area (BA, m2 ha−1), a distance-independent tree-level competition index (CI, a ratio ofD to the plot-level quadratic mean diameter (e.g., [49]). Summary statistics of climate and stand forest variables are shown in Table 1.


### 2.4. Modelling

#### 2.4.1. Height Estimating Base Models

Several models describingH-D relationships have been reported in the past [2, 19, 28]. No uniformly best function has been recommended, suggesting thatH-D allometry differs significantly among forests (e.g., [21, 50]). We first developedH estimating models which had only D as sole explanatory variable herein referred as “base model”. This was necessary so as to make comparison of base models with otherH estimating models which include climate and forest stand variables herein referred as “generalized models”. In addition,H base models are required for estimatingH when forest structure and climate variables are not available. Furthermore, we fittedH estimating models to all data set combined herein referred as “regional models”. We fitted six commonH estimating model forms, i.e., three with two parameters and other three with three parameters (Table 2).Table 2
Height base model forms.
Model # Model form Reference 1 H = 1.3 + ( D 2 / ( ∅ 0 × D + ∅ 1 ) 2 ) [37] 2 H = 1.3 + exp ⁡ ( ∅ 0 - ∅ 1 × ( D + 1 ) - 1 ) [38] 3 H = 1.3 + ∅ 0 × (  D / ( 1 + D ) ) ∅ 1 [18, 39] 4 H = 1.3 + ∅ 0 × ( 1 - exp ⁡ ( - ∅ 1 × D ) ) ∅ 2 [40] 5 H = 1.3 + ∅ 0 × exp ⁡ ( ∅ 1 / ( D + ∅ 2 ) ) [41] 6 H = 1.3 + ∅ 0 × ( 1 - exp ⁡ ( - ∅ 1 × D ∅ 2 ) ) [42] ∅’s are parameters to be estimated.


#### 2.4.2. Generalized Tree Height Models

For complex models with several independent variables, i.e., forest structure and climate variables (generalized model), simple log-log model has been preferred partly because it is easy to converge when estimating model parameters [2]. Limitation associated with log-log model include problem of back transformation and lack of flexibility to set maximumH a tree must not exceed [21, 50]. It is through this background that in this study we decided to fit nonlinear models which agree with known biologicalH-D allometry. We included climate and forest structure variables into six nonlinearH model forms (Table 2) and refitted the models. It was apparent that majority of the fitted model forms failed to converge. Weibull model was the most successful in terms of convergence and fit and therefore was selected to fit generalized H models (see [51]). The formulation of three parameters Weibull model is presented in equation (1)(1)H=1.3+α1-exp⁡-β1Dβ2+∈where α, β1, and β2 are model parameters to be estimated and ∈ is unexplained variation inH. Parameter α describes the maximumH the model can predict; β1describes the rate of change ofH with change inD and β2 describes the shape of the curve.The NAFORMA data represent a hierarchical structure where the field plots were nested within the clusters. In this case, nonlinear mixed effect modelling approach was considered to be an ideal for developing predictive models that will account for dependence of the plots within the clusters. In addition, to account for variation (i.e., heteroscedasticity due to cluster andD) not accounted by the random effects, we also included power variance function structure, i.e.,varPower, implemented in thenlme packages of R software for nonlinear and linear models [52]. Preliminary model fitting showed that model with plots nested in cluster was not able to converge probably due to few observations [21] in some vegetation types. Model with only cluster as random variable converged successful. Therefore, the fixed effects (equation (1)) are common to all subjects, while random effect parameters are specific to each subject (in this case cluster) [52], (Zuur et al. 2009). At the beginning, we allowed all model parameters to vary between clusters through inclusion of random effects. The model fitted data well by only allowing random effect on parameter β2. With the inclusion of random effects, the following equation (2) emerged: (2)H=α1-exp⁡-β1Dβ2+Ri+∈where Ri expresses the difference in parameter β2 of clusteri from mean value obtained from (1) or typical cluster.The next step was to ascertain the effect of forest structure and climate parameters onH-D allometry. We refer this model as “generalized model”. Before fitting generalizedHestimation models, we explored relationship of climate and forest structure variables withH in each vegetation type. Preliminary results show that at least one of the dependent variables (BA,CI,PRA, anddm) is highly correlated withH of the studied forest types (Figure 4). We consider forest structure and climate variables to mostly affect asymptotic parameter, i.e., α. The parameter α was further expanded as shown in (3). The generalized model variables, i.e.,PRA, CI, dm and BA were allowed to enter into the model linearly for easy evaluation of their contribution (equation (3)). (3)α=θ0+θ1PRA+θ2CI+θ3dm+θ4BAwhere θ′s are model parameters.Figure 4
The relationship of total tree height (H) with forest stand (BA,CI) and climatic variables (number of dry month and precipitation). Different letters indicate significant differences among groups. Q1, Q2, Q3, and Q4 are quantiles.


### 2.5. Model Fitting and Performance Evaluation

Height-diameter models were fitted by considering the contribution of the random effect associated with clusters. In addition, to account for variation (i.e., heteroscedasticity due to clusters andD) not accounted by the random effects, we included power variance function, i.e.,varPower, implemented in thenlme packages of R software for nonlinear regression equations [52, 53]. The models were fitted using Maximum Likelihood procedure. To ensure that our modelling strategy has accounted for heteroscedasticity, models were assessed using residuals plots. We assessed the contribution of forest stand and climate variables by looking at the significance of their respective parameters. Variables with nonsignificant parameter were considered irrelevant toH-D allometry.To present generalizedHestimation models for practical application, we selected those with low Akaike Information Criterion (AIC) and evaluated the best first three models. Percentage Root Mean Square Error (SE%) was also assessed. We also assessed the models by means of residuals plots where models with more balanced residuals were selected.In addition, preliminary findings (Figures3 and 4) show that climate variables specificallyPRA varies among forest types which consequently may affectH-D allometry. Variation ofH among forest types of Tanzania Mainland has been reported also by other scholars [27, 54]. Therefore, assuming that the variation inPRA within the same forest type may not necessarily influenceH-D allometry significantly, it is expected that other factors such as competition expressed in terms ofCI andBA may have the role of modifyingH-D allometry. With large data set, collected from NAFORMA, it is expected that large variation associated with species, site condition, and stand structure difference has been adequately covered. Since the regional models have some of these potential variables, we therefore tested mean prediction error (PE %) of the regional models with and without climate and/or stand forest variables to ascertain which one may adequately predictH of all forest types. The mean prediction error was calculated using the following equation: (4)PE%=∑H^-H/Hn×100where H^ andH are predicted and observed total tree height, respectively andn is the number of sample trees.


## 2.1. Site Description

Data used in this study were obtained from a network of plots established by NAFORMA in Tanzania Mainland (Figure1). Data were collected over the entire Tanzania Mainland covering all primary vegetation types. The country has a diverse climate with mean annual rainfall ranging from below 400 mm to over 2000 mm per annum. The rainfall for large parts of the country is bimodal with short rains from October to December and long rains from March to May. The biodiversity of forests in Tanzania Mainland is high consisting over 10,000 plant species, hundreds of which are nationally endemic. Of the plant species, 305 are identified as threatened in the IUCN Red List, with 276 species classified as endangered (IUCN 2013). The main forest types include miombo woodlands, humid montane forest, lowland forest, bushland, grassland, mangroves, wetlands, cultivated areas, and plantations [36]. Some of these vegetation types are described briefly in subsequent subsections.Figure 1
Distribution of the NAFORMA sample plots within the entire Tanzania Mainland.


### 2.1.1. Woodlands and Bushlands

The woodlands constitute the largest vegetation type in Tanzania Mainland, occupying about 44.7 million hectares which is equivalent to 93% of the entire forest area [36]. The woodland has three subtypes: Closed (>40% canopy cover), Open (10–40% canopy cover), and Woodland with scattered cropland. The height ranges between 5–20 m although occasionally being taller than 20 m.


### 2.1.2. Humid Montane and Lowland Forest

The humid montane and lowland forest occupy 995,000 and 1,656,500 ha, respectively, in Tanzania Mainland which is altogether about 5.5% of the countries forest area. These forests are characterized by high richness of flora and fauna and have high catchment values [43].


### 2.1.3. Grassland

Grassland is another vegetation type possessing marked variety, with four subtypes [44]. For the most part, this type occurs as its subtypes in combination with either a limited Wooded or Bushed component, or with scattered subsistence cultivation. The grassland subtypes are Wooded grassland, Bushed grassland, Grassland with scattered cropland, and Open grassland.


### 2.1.4. Cultivated Land

The cultivated land is a type of land with four vegetation subtypes [44]. The physiognomy varies widely in accordance with the significance of the tree and crop component associated with each unit. The agroforestry systems which contain permanent tree crops (timber and fruit) that are mixed with permanent and annual agricultural crops (yam, beans, banana, coffee, etc.) are recognized as one vegetation subtype. The tree crops (Grevillea, Albizia, Cordia, Citrus,Acrocarpus, etc.) which form the upper canopy act as shade to the lower canopy crops (banana, coffee, beans). The other cultivated land subtype is where the woody crops are mixed in varying proportions of fruit tree species such as mango, coconut, citrus, and cashew.


### 2.1.5. Mangroves

Mangroves are forests found in the tropical and subtropical coastlines between 30° south and north of equator [45]. Mangroves comprise trees and shrubs which grow in or adjacent to the intertidal zone. They are found at primarily along sheltered shorelines where freshwater (rainfall or river flow) dilutes the ocean. At the eastern coast of Africa, 14 mangrove species are growing naturally, and 10 among these are found in Tanzania Mainland.Avicennia marina (Forssk.) Vierh,Sonneratia alba J. Smith, andRhizophora mucronata Lam. are the three most dominant mangrove species in Tanzania [35].


### 2.1.6. Pine and Eucalyptus Species

Pine andEucalyptus species are among the planted exotic tree species in Tanzania Mainland. Pine species in Tanzania Mainland includePinus patula, P. elliottii,andP. caribaea. These species are the dominant species in most of the government and private plantations with about 78% of the total area planted and the remaining 22% is shared among hardwoods and other softwood species. In Tanzania Mainland, the area underEucalyptus species is estimated to be 25,000 ha [46] of which 4,665 ha. The plantedEucalyptus species includeE. saligna, E. grandis, E. camaldulensis, E. globulus, E. viminalis, E. citriodora, E. regnans, andE. microtheca [46].


## 2.1.1. Woodlands and Bushlands

The woodlands constitute the largest vegetation type in Tanzania Mainland, occupying about 44.7 million hectares which is equivalent to 93% of the entire forest area [36]. The woodland has three subtypes: Closed (>40% canopy cover), Open (10–40% canopy cover), and Woodland with scattered cropland. The height ranges between 5–20 m although occasionally being taller than 20 m.


## 2.1.2. Humid Montane and Lowland Forest

The humid montane and lowland forest occupy 995,000 and 1,656,500 ha, respectively, in Tanzania Mainland which is altogether about 5.5% of the countries forest area. These forests are characterized by high richness of flora and fauna and have high catchment values [43].


## 2.1.3. Grassland

Grassland is another vegetation type possessing marked variety, with four subtypes [44]. For the most part, this type occurs as its subtypes in combination with either a limited Wooded or Bushed component, or with scattered subsistence cultivation. The grassland subtypes are Wooded grassland, Bushed grassland, Grassland with scattered cropland, and Open grassland.


## 2.1.4. Cultivated Land

The cultivated land is a type of land with four vegetation subtypes [44]. The physiognomy varies widely in accordance with the significance of the tree and crop component associated with each unit. The agroforestry systems which contain permanent tree crops (timber and fruit) that are mixed with permanent and annual agricultural crops (yam, beans, banana, coffee, etc.) are recognized as one vegetation subtype. The tree crops (Grevillea, Albizia, Cordia, Citrus,Acrocarpus, etc.) which form the upper canopy act as shade to the lower canopy crops (banana, coffee, beans). The other cultivated land subtype is where the woody crops are mixed in varying proportions of fruit tree species such as mango, coconut, citrus, and cashew.


## 2.1.5. Mangroves

Mangroves are forests found in the tropical and subtropical coastlines between 30° south and north of equator [45]. Mangroves comprise trees and shrubs which grow in or adjacent to the intertidal zone. They are found at primarily along sheltered shorelines where freshwater (rainfall or river flow) dilutes the ocean. At the eastern coast of Africa, 14 mangrove species are growing naturally, and 10 among these are found in Tanzania Mainland.Avicennia marina (Forssk.) Vierh,Sonneratia alba J. Smith, andRhizophora mucronata Lam. are the three most dominant mangrove species in Tanzania [35].


## 2.1.6. Pine and Eucalyptus Species

Pine andEucalyptus species are among the planted exotic tree species in Tanzania Mainland. Pine species in Tanzania Mainland includePinus patula, P. elliottii,andP. caribaea. These species are the dominant species in most of the government and private plantations with about 78% of the total area planted and the remaining 22% is shared among hardwoods and other softwood species. In Tanzania Mainland, the area underEucalyptus species is estimated to be 25,000 ha [46] of which 4,665 ha. The plantedEucalyptus species includeE. saligna, E. grandis, E. camaldulensis, E. globulus, E. viminalis, E. citriodora, E. regnans, andE. microtheca [46].


## 2.2. Sampling Design and Field Measurements

Data used in this study were collected during the first ever NFI in Tanzania carried out in year between 2010 and 2014. The double sampling for stratification approach was applied. The sampling was designed based on a simulation study described by Tomppo et al. [47]. The first-phase sample consisted of clusters of plots on a 5×5 km grid. The first-phase clusters were stratified based on predicted growing stock, time consumption for cluster measurements, and slope of the terrain. Altogether, the first-phase clusters that contain 6 to 10 plots were assigned to 18 predefined strata. The second-phase samples were systematically selected from the first-phase sample, with different sampling intensities in each of the 18 strata following an optimal allocation procedure with cost functions tailored for each stratum (see. [47]). Greater sampling intensity was allocated to strata with large predicted growing stock and smaller sampling intensity to strata with small-predicted growing stock. Only the clusters selected during the second phase of sampling were measured in the field. The distance between field plots within a cluster was 250 m, while the distance between clusters varies from 5 km to 45 km. For each cluster plots spaced 250 m apart varied from 6 to 10 depending on estimated difficulty to access the cluster (Figure 2). Accordingly, a total of 3,420 clusters with 32,660 plots were adopted. However, during the fieldwork, a total of 3,219 clusters which are equivalent to 30,773 plots were actually measured. Some clusters were not measured for various reasons, mainly difficult terrain and remoteness. Circular fixed area nested plot designs were applied. The nested plots included 1, 5, 10, and 15 m radius concentric plots.Figure 2
The NAFORMA cluster and plot design [36].Measurements ofD for all the trees within the plot were in accordance with the tree size and distance from plot centre where larger trees where measured in larger plot and vice versa [47]. For all the trees measured in the plot, species names were recorded both botanical and local names. Every fifth tree in the cluster was selected as sample tree and measured forH using Suunto hypsometers. We refer the readers to MNRT [36] for more details on the field measurements.


## 2.3. Data Preparation

Following data cleaning to remove outliers in the NAFORMA data, a total of 31782 observations were obtained for analysis. During preliminary data analysis scatterplots revealed relationships betweenH andD varying with vegetation types. Accordingly, for modelling purpose, the entire data were grouped into vegetation types in order to account for variations inH-D allometry that might be attributed by the tree allometry associated with the specific vegetation type. The relationship between response and predictor variables was assessed by means of scatter plots. TheH-Dplots indicated nonlinear relationship (Figure 3). Summary statistics for variable under consideration for each forest type is presented in Table 1.Table 1
Descriptive statistics of total tree height (H) and diameter at breast height (D).
Variable Forest Type Statistics Bushlands Cultivated Eucalyptus Grasslands Lowland Mangroves Montane Pines Wetlands Miombo All H Number of trees 3669 1866 100 934 2278 307 2111 340 97 20080 31782 Min. 1.35 1.50 5.00 1.50 1.50 1.50 1.50 3.00 2.00 1.30 1.30 Max. 28.00 35.00 36.00 33.00 35.00 27.00 45.00 35.00 25.00 36.00 45.00 Mean 6.72 8.45 16.47 7.61 10.67 7.53 12.89 18.00 9.78 9.24 9.30 CV 0.49 0.52 0.42 0.49 0.52 0.49 0.50 0.47 0.48 0.46 0.52  D Min. 1.00 1.00 5.20 1.00 1.00 1.00 1.00 1.80 2.20 1.00 1.00 Max. 83.10 149.90 82.50 75.00 122.40 46.40 141.00 54.20 93.00 123.40 149.90 Mean 12.44 21.64 19.41 17.42 18.42 11.13 22.65 22.69 24.31 18.52 18.21 CV 0.85 0.74 0.65 0.68 0.81 0.62 0.78 0.45 0.76 0.63 0.71  BA Min. 0.08 0.09 1.59 0.07 0.39 0.91 0.26 0.60 0.52 0.27 0.07 Max. 104.05 88.27 74.96 72.53 138.59 59.75 204.37 53.50 61.88 105.69 204.37 Mean 10.98 9.10 21.66 8.01 22.90 17.57 32.79 26.37 14.74 13.48 14.93 CV 0.92 1.06 0.87 0.86 0.57 0.55 0.71 0.57 1.12 0.58 0.81  CI Min. 0.04 0.04 0.22 0.02 0.02 0.09 0.03 0.22 0.23 0.04 0.02 Max. 4.54 2.98 2.06 2.56 4.47 2.95 4.18 1.75 2.55 4.91 4.91 Mean 0.91 0.94 0.99 0.94 0.85 0.88 0.85 0.97 0.99 0.92 0.91 CV 0.58 0.43 0.33 0.43 0.66 0.45 0.63 0.26 0.43 0.51 0.53  PRA Min. 475.00 520.00 841.00 440.00 560.00 936.00 683.00 841.00 479.00 366.00 366.00 Max. 2025.00 2266.00 1666.00 1865.00 1865.00 1257.00 1913.00 1913.00 2323.00 2323.00 2323.00 Mean 825.41 1072.53 1272.74 1100.06 1119.53 1116.83 1184.12 1199.17 1045.08 997.58 1012.76 CV 0.30 0.25 0.15 0.27 0.25 0.09 0.21 0.12 0.27 0.24 0.26  Dry Min. 4.00 3.00 4.00 4.00 4.00 5.00 4.00 4.00 5.00 4.00 3.00 Max. 11.00 10.00 8.00 11.00 11.00 8.00 9.00 8.00 10.00 11.00 11.00 Mean 7.69 6.63 6.39 6.91 6.83 6.54 6.36 6.95 7.27 7.11 7.07 CV 0.15 0.14 0.16 0.13 0.09 0.09 0.14 0.08 0.11 0.14 0.15Figure 3
Scatter plots ofH-D allometry.


### 2.3.1. Climate Data and Forest Stand Parameters

Climate data of 2.5 min resolution were downloaded fromhttp://worldclim.org/version2 covering a period between 1970 and 2000 [48]. Climate data parameters of interest were mean annual precipitation (PRA), number of months with precipitation below 100 mm (dm) and mean annual temperature (TEA). Candidate stand forest parameter variables tested were stand level competition variables, i.e., basal area (BA, m2 ha−1), a distance-independent tree-level competition index (CI, a ratio ofD to the plot-level quadratic mean diameter (e.g., [49]). Summary statistics of climate and stand forest variables are shown in Table 1.


## 2.3.1. Climate Data and Forest Stand Parameters

Climate data of 2.5 min resolution were downloaded fromhttp://worldclim.org/version2 covering a period between 1970 and 2000 [48]. Climate data parameters of interest were mean annual precipitation (PRA), number of months with precipitation below 100 mm (dm) and mean annual temperature (TEA). Candidate stand forest parameter variables tested were stand level competition variables, i.e., basal area (BA, m2 ha−1), a distance-independent tree-level competition index (CI, a ratio ofD to the plot-level quadratic mean diameter (e.g., [49]). Summary statistics of climate and stand forest variables are shown in Table 1.


## 2.4. Modelling

### 2.4.1. Height Estimating Base Models

Several models describingH-D relationships have been reported in the past [2, 19, 28]. No uniformly best function has been recommended, suggesting thatH-D allometry differs significantly among forests (e.g., [21, 50]). We first developedH estimating models which had only D as sole explanatory variable herein referred as “base model”. This was necessary so as to make comparison of base models with otherH estimating models which include climate and forest stand variables herein referred as “generalized models”. In addition,H base models are required for estimatingH when forest structure and climate variables are not available. Furthermore, we fittedH estimating models to all data set combined herein referred as “regional models”. We fitted six commonH estimating model forms, i.e., three with two parameters and other three with three parameters (Table 2).Table 2
Height base model forms.
Model # Model form Reference 1 H = 1.3 + ( D 2 / ( ∅ 0 × D + ∅ 1 ) 2 ) [37] 2 H = 1.3 + exp ⁡ ( ∅ 0 - ∅ 1 × ( D + 1 ) - 1 ) [38] 3 H = 1.3 + ∅ 0 × (  D / ( 1 + D ) ) ∅ 1 [18, 39] 4 H = 1.3 + ∅ 0 × ( 1 - exp ⁡ ( - ∅ 1 × D ) ) ∅ 2 [40] 5 H = 1.3 + ∅ 0 × exp ⁡ ( ∅ 1 / ( D + ∅ 2 ) ) [41] 6 H = 1.3 + ∅ 0 × ( 1 - exp ⁡ ( - ∅ 1 × D ∅ 2 ) ) [42] ∅’s are parameters to be estimated.


### 2.4.2. Generalized Tree Height Models

For complex models with several independent variables, i.e., forest structure and climate variables (generalized model), simple log-log model has been preferred partly because it is easy to converge when estimating model parameters [2]. Limitation associated with log-log model include problem of back transformation and lack of flexibility to set maximumH a tree must not exceed [21, 50]. It is through this background that in this study we decided to fit nonlinear models which agree with known biologicalH-D allometry. We included climate and forest structure variables into six nonlinearH model forms (Table 2) and refitted the models. It was apparent that majority of the fitted model forms failed to converge. Weibull model was the most successful in terms of convergence and fit and therefore was selected to fit generalized H models (see [51]). The formulation of three parameters Weibull model is presented in equation (1)(1)H=1.3+α1-exp⁡-β1Dβ2+∈where α, β1, and β2 are model parameters to be estimated and ∈ is unexplained variation inH. Parameter α describes the maximumH the model can predict; β1describes the rate of change ofH with change inD and β2 describes the shape of the curve.The NAFORMA data represent a hierarchical structure where the field plots were nested within the clusters. In this case, nonlinear mixed effect modelling approach was considered to be an ideal for developing predictive models that will account for dependence of the plots within the clusters. In addition, to account for variation (i.e., heteroscedasticity due to cluster andD) not accounted by the random effects, we also included power variance function structure, i.e.,varPower, implemented in thenlme packages of R software for nonlinear and linear models [52]. Preliminary model fitting showed that model with plots nested in cluster was not able to converge probably due to few observations [21] in some vegetation types. Model with only cluster as random variable converged successful. Therefore, the fixed effects (equation (1)) are common to all subjects, while random effect parameters are specific to each subject (in this case cluster) [52], (Zuur et al. 2009). At the beginning, we allowed all model parameters to vary between clusters through inclusion of random effects. The model fitted data well by only allowing random effect on parameter β2. With the inclusion of random effects, the following equation (2) emerged: (2)H=α1-exp⁡-β1Dβ2+Ri+∈where Ri expresses the difference in parameter β2 of clusteri from mean value obtained from (1) or typical cluster.The next step was to ascertain the effect of forest structure and climate parameters onH-D allometry. We refer this model as “generalized model”. Before fitting generalizedHestimation models, we explored relationship of climate and forest structure variables withH in each vegetation type. Preliminary results show that at least one of the dependent variables (BA,CI,PRA, anddm) is highly correlated withH of the studied forest types (Figure 4). We consider forest structure and climate variables to mostly affect asymptotic parameter, i.e., α. The parameter α was further expanded as shown in (3). The generalized model variables, i.e.,PRA, CI, dm and BA were allowed to enter into the model linearly for easy evaluation of their contribution (equation (3)). (3)α=θ0+θ1PRA+θ2CI+θ3dm+θ4BAwhere θ′s are model parameters.Figure 4
The relationship of total tree height (H) with forest stand (BA,CI) and climatic variables (number of dry month and precipitation). Different letters indicate significant differences among groups. Q1, Q2, Q3, and Q4 are quantiles.


## 2.4.1. Height Estimating Base Models

Several models describingH-D relationships have been reported in the past [2, 19, 28]. No uniformly best function has been recommended, suggesting thatH-D allometry differs significantly among forests (e.g., [21, 50]). We first developedH estimating models which had only D as sole explanatory variable herein referred as “base model”. This was necessary so as to make comparison of base models with otherH estimating models which include climate and forest stand variables herein referred as “generalized models”. In addition,H base models are required for estimatingH when forest structure and climate variables are not available. Furthermore, we fittedH estimating models to all data set combined herein referred as “regional models”. We fitted six commonH estimating model forms, i.e., three with two parameters and other three with three parameters (Table 2).Table 2
Height base model forms.
Model # Model form Reference 1 H = 1.3 + ( D 2 / ( ∅ 0 × D + ∅ 1 ) 2 ) [37] 2 H = 1.3 + exp ⁡ ( ∅ 0 - ∅ 1 × ( D + 1 ) - 1 ) [38] 3 H = 1.3 + ∅ 0 × (  D / ( 1 + D ) ) ∅ 1 [18, 39] 4 H = 1.3 + ∅ 0 × ( 1 - exp ⁡ ( - ∅ 1 × D ) ) ∅ 2 [40] 5 H = 1.3 + ∅ 0 × exp ⁡ ( ∅ 1 / ( D + ∅ 2 ) ) [41] 6 H = 1.3 + ∅ 0 × ( 1 - exp ⁡ ( - ∅ 1 × D ∅ 2 ) ) [42] ∅’s are parameters to be estimated.


## 2.4.2. Generalized Tree Height Models

For complex models with several independent variables, i.e., forest structure and climate variables (generalized model), simple log-log model has been preferred partly because it is easy to converge when estimating model parameters [2]. Limitation associated with log-log model include problem of back transformation and lack of flexibility to set maximumH a tree must not exceed [21, 50]. It is through this background that in this study we decided to fit nonlinear models which agree with known biologicalH-D allometry. We included climate and forest structure variables into six nonlinearH model forms (Table 2) and refitted the models. It was apparent that majority of the fitted model forms failed to converge. Weibull model was the most successful in terms of convergence and fit and therefore was selected to fit generalized H models (see [51]). The formulation of three parameters Weibull model is presented in equation (1)(1)H=1.3+α1-exp⁡-β1Dβ2+∈where α, β1, and β2 are model parameters to be estimated and ∈ is unexplained variation inH. Parameter α describes the maximumH the model can predict; β1describes the rate of change ofH with change inD and β2 describes the shape of the curve.The NAFORMA data represent a hierarchical structure where the field plots were nested within the clusters. In this case, nonlinear mixed effect modelling approach was considered to be an ideal for developing predictive models that will account for dependence of the plots within the clusters. In addition, to account for variation (i.e., heteroscedasticity due to cluster andD) not accounted by the random effects, we also included power variance function structure, i.e.,varPower, implemented in thenlme packages of R software for nonlinear and linear models [52]. Preliminary model fitting showed that model with plots nested in cluster was not able to converge probably due to few observations [21] in some vegetation types. Model with only cluster as random variable converged successful. Therefore, the fixed effects (equation (1)) are common to all subjects, while random effect parameters are specific to each subject (in this case cluster) [52], (Zuur et al. 2009). At the beginning, we allowed all model parameters to vary between clusters through inclusion of random effects. The model fitted data well by only allowing random effect on parameter β2. With the inclusion of random effects, the following equation (2) emerged: (2)H=α1-exp⁡-β1Dβ2+Ri+∈where Ri expresses the difference in parameter β2 of clusteri from mean value obtained from (1) or typical cluster.The next step was to ascertain the effect of forest structure and climate parameters onH-D allometry. We refer this model as “generalized model”. Before fitting generalizedHestimation models, we explored relationship of climate and forest structure variables withH in each vegetation type. Preliminary results show that at least one of the dependent variables (BA,CI,PRA, anddm) is highly correlated withH of the studied forest types (Figure 4). We consider forest structure and climate variables to mostly affect asymptotic parameter, i.e., α. The parameter α was further expanded as shown in (3). The generalized model variables, i.e.,PRA, CI, dm and BA were allowed to enter into the model linearly for easy evaluation of their contribution (equation (3)). (3)α=θ0+θ1PRA+θ2CI+θ3dm+θ4BAwhere θ′s are model parameters.Figure 4
The relationship of total tree height (H) with forest stand (BA,CI) and climatic variables (number of dry month and precipitation). Different letters indicate significant differences among groups. Q1, Q2, Q3, and Q4 are quantiles.


## 2.5. Model Fitting and Performance Evaluation

Height-diameter models were fitted by considering the contribution of the random effect associated with clusters. In addition, to account for variation (i.e., heteroscedasticity due to clusters andD) not accounted by the random effects, we included power variance function, i.e.,varPower, implemented in thenlme packages of R software for nonlinear regression equations [52, 53]. The models were fitted using Maximum Likelihood procedure. To ensure that our modelling strategy has accounted for heteroscedasticity, models were assessed using residuals plots. We assessed the contribution of forest stand and climate variables by looking at the significance of their respective parameters. Variables with nonsignificant parameter were considered irrelevant toH-D allometry.To present generalizedHestimation models for practical application, we selected those with low Akaike Information Criterion (AIC) and evaluated the best first three models. Percentage Root Mean Square Error (SE%) was also assessed. We also assessed the models by means of residuals plots where models with more balanced residuals were selected.In addition, preliminary findings (Figures3 and 4) show that climate variables specificallyPRA varies among forest types which consequently may affectH-D allometry. Variation ofH among forest types of Tanzania Mainland has been reported also by other scholars [27, 54]. Therefore, assuming that the variation inPRA within the same forest type may not necessarily influenceH-D allometry significantly, it is expected that other factors such as competition expressed in terms ofCI andBA may have the role of modifyingH-D allometry. With large data set, collected from NAFORMA, it is expected that large variation associated with species, site condition, and stand structure difference has been adequately covered. Since the regional models have some of these potential variables, we therefore tested mean prediction error (PE %) of the regional models with and without climate and/or stand forest variables to ascertain which one may adequately predictH of all forest types. The mean prediction error was calculated using the following equation: (4)PE%=∑H^-H/Hn×100where H^ andH are predicted and observed total tree height, respectively andn is the number of sample trees.


## 3. Results

### 3.1. Height Base Model

Performance of base models is shown in Table3. The SE% were found to range from 25.4% to 41.3% across forest types. Forests with highest SE% were found to be bushlands followed by lowland and montane forests. Forests with low SE% were pines (26.5%) andEucalyptus (25.5%) plantations and mangroves forest (28.1%) for natural forests. In terms of performance, based on AIC, Model (6) had a good fit in all forest types except for wetland forests. Model (1) was the second in performance. Model (1), i.e., Ratkowsky [41], was selected for wetland forests while for other forests Model (6), Weibull [42], was selected. Parameter estimates and mode expressions are provided in Table 4.Table 3
Parameters estimates and performance of height base models.
Forest Model SE % AIC Forest SE % AIC Forest SE % AIC Forest SE % AIC BU 1 34.8 15752 CUL 40.7 9408 EUC 25.5 561 GRA 36.0 4311 2 35.5 15783 41.2 9439 25.7 563 36.4 4331 3 36.1 15915 41.3 9464 25.9 563 36.5 4344 4 32.4 15430 40.3 9388 25.4 564 35.6 4290 5 33.0 15510 40.4 9389 25.5 563 35.7 4288 6 32.4 15428 40.2 9386 25.4 564 35.5 4290  LO 1 34.9 11893 MAN 28.5 1316 HUM 34.3 11779 ALL 42.7 156220 2 36.1 11987 28.8 1320 35.2 11862 36.3 157410 3 36.2 12069 29.1 1326 35.3 11906 36.5 158053 4 33.7 11703 27.9 1312 33.5 11685 34.5 154230 5 33.8 11721 28.1 1314 33.6 11706 34.6 154460 6 33.7 11703 27.8 1311 33.5 11684 34.5 154229  WET 1 31.6 486 MIO 31.2 96575 PIN 26.5 2007 2 31.9 490 31.8 97303 26.2 2008 3 32.1 491 31.9 97616 26.2 2009 4 31.7 486 30.7 95686 26.1 2003 5 31.6 485 30.7 95757 26.3 2007 6 31.7 486 30.7 95683 26.0 2001 BU: Bushlands; LO: Lowland; WET: Wetlands; CU: Cultivated land; MAN: Mangroves; EUC: Eucalyptus species; HUM: Humid montane; GRA: Grasslands; and PIN: Pines species.Table 4
Best selected height base models.
Model Forest type Model expression Weibull [42] Bushlands 1.3 + 37.0396 × ( 1 - exp ⁡ ( - 0.03778 × D 0.6063 ) ) Weibull [42] Cultivated land 1.3 + 13.6509 × ( 1 - exp ⁡ ( - 0.06223 × D 0.8600 ) ) Weibull [42] Eucalyptus species 1.3 + 29.3684 × ( 1 - exp ⁡ ( - 0.03148 × D 1.1061 ) ) Weibull [42] Grasslands 1.3 + 14.7261 × ( 1 - exp ⁡ ( - 0.0536 × D 0.8637 ) ) Weibull [42] Lowland 1.3 + 24.9862 × ( 1 - exp ⁡ ( - 0.0579 × D 0.7682 ) ) Weibull [42] Mangroves 1.3 + 15.8607 × ( 1 - exp ⁡ ( - 0.0705 × D 0.8520 ) ) Weibull [42] Humid montane 1.3 + 25.6752 × ( 1 - exp ⁡ ( - 0.0536 × D 0.8234 ) Weibull [42] Pine species 1.3 + 28.5979 × ( 1 - exp ⁡ ( - 0.0064 × D 1.6174 ) ) Ratkowsky [41] Wetlands 1.3 + 20.4098 × exp ⁡ ( - 23.1909 / ( D + 6.7727 ) ) Weibull [42] Woodlands 1.3 + 24.3701 × ( 1 - exp ⁡ ( - 0.0405 × D 0.8070 ) ) Weibull [42] Reginal 1.3 + 30.2116 × ( 1 - exp ⁡ ( - 0.0379 × D 0.7451 ) )


### 3.2. Height Estimating Models with Climate and Forest Stand Variables

#### 3.2.1. Regional Generalized Height Models

The findings show that all parameters of the fitted regional models were significant; i.e., all fitted variables had significant contribution in explainingH(Table 5).The magnitude of importance of independent variables decreased in the following order,BA,PRA,dm, andCI. Based on AIC, the model which combines all the independent variables was found to have best fit. Positive parameters forPRA andBA suggest that as precipitation and stand density increases, the meanH also increases (e.g., Figure 5). Trend of meanPRA versus meanHis shown in Figure 4.Table 5
Performance of different combination of climate and forest parameters on regional and forest type specificHestimating models.
Variables Akaike Information Criterion (AIC) Regional Lowland Montane Miombo Bushland Cultivated Grassland Mangroves Pines Eucalyptus Wetlands BA 150932 11667 11552 94685 15272 9223 4191 1366 1866 535 487BA CI 153650 11697 11634 95401 15403CI 9369 4288CI 1388CI 1927 555 488CI Dry 153316 11699 11686dm 95131 15315 9343 4290dm 1410dm 2003dm 565dm 487dm PRA 153006 11675 11672 94853 15363 9349 4234 1409PRA 2003PRA 564PRA 487PRA BA, CI 150842 11668CI 11546 94579 15262 9222CI 4193CI 1362CI 1855 536CI 486BA,CI BA, Dry 150416 11664 11554dm 94271 15176 9201 4193dm 1367dm 1868dm 530 486BA,dm BA,PRA 150232 11645 11550 94096 15244 9207 4162 1368PRA 1867PRA 522 488BA,PRA CI, Dry 152871 11693 11636dm 94908 15282CI,dm 9327 4289CI,dm 1390CI,dm 1929dm 556dm 488CI,dm CI,PRA 152518 11673CI 11628 94557 15329CI,PRA 9335 4233CI 1390PRA,CI 1928PRA 555PRA 488CI,P Dry,PRA 152871 11650 11671dm 94783 15314PRA 9337 4228 1411P,dm 2002PRA,dm 566dm,PRA 485dm,P BA, CI, dry 150352 11665CI 11548d 94191 15159 9199CI 4194CI,dm 1363C,dm 1857dm 532dm 486CI,dm BA, CI,PRA 150149 11646CI 11545PRA 93966 15228PRA 9206CI 4164CI 1364PRA,CI 1856PRA 524CI 487CI,PRA,BA CI,PRA, Dry 152421 11649CI 11627dm 94514 15279CI,PRA 9322 4226CI 1392C,PRA,dm 1930PRA,dm 557dm 486CI,PRA,dm BA, Dry,PRA 150156 11625 11552dm,PRA 94035 15177PRA 9200PRA 4158 1369dm,PRA 1868PRA,dm 523dm 482BA,dm,PRA BA, CI, Dry,PRA 150083 11626CI 11547dm,PRA 93922 15161PRA 9198PRA,CI 4160CI,dm 1365dm,PRA,CI 1857PRA,dm 524dm,CI 481CI Powered letters are nonsignificant of the respective variables, i.e.,dm: number of dry months; CI: competition index; PRA: precipitation; and BA: basal area.Figure 5
Effect of precipitation to total tree height distributed in diameter classes.PRAvalues above the box are in mm. BUS: Bushland; GRA: Grassland; LOW: Lowland; MAN: Mangroves; MIO: Miombo; MON: Montane; and WET: Wetlands.


#### 3.2.2. Generalized Height Models for Lowland and Montane

For both forest types, all parameters estimates were significant when forest structure and climate variables were included in the model one by one except fordm in the montane forest (Table 5). The magnitude of importance of independent variables for lowland and montane forests decreased in the following order:BA >PRA>CI andBA >CI >PRA>dm, respectively. In many cases combinations which include CI, CI were found to be nonsignificant. For example, for lowland, a model with a combination ofBA andCI andPRAandCI consistently yielded nonsignificant parameters forCI. For the lowland, the five best models in decreasing order of model fit had the following combination of variables, i.e.,BA,dm,PRA>BA,PRA>dm,PRA >BA,dm >BA while for the montane they wereBA,CI >BA,PRA >BA >CI,PRA>CI.


#### 3.2.3. Generalized Height Models for Miombo Woodlands

All variable combinations yielded significant model parameters. Model with all variables had the best fit. The importance of stand and climate variables decreased in following order:BA >PRA>CI >dm. The models fit decreased in the following order of combination: BA, CI,dm,PRA>BA,CI,PRA>BA,dm,PRA>BA,PRA>BA,CI,dm.


#### 3.2.4. Generalized Height Models for Mangroves and Wetlands

Climate variables were not found to influenceH-D allometry in both wetlands and mangroves forests. Except for mangroves whereBA was a significant variable, forest stands variables did not improve theHestimating model fit in wetlands. This implies thatH base models were found to describeH-D allometry adequately for wetland forests (Table 5). In mangroves, model with BA included had better fit than base model.


#### 3.2.5. Generalized Height Models for Bushland, Cultivated, and Grasslands

The PRA in combination withdm and/orCI did not improve model fit for bushlands. Important variables in decreasing order wereBA,dm, andPRA. In cultivated lands,BA,dm, andPRA were found to be important in that order in describingH-D allometry whileCI was found to be nonsignificant. In grasslands,CI anddm did not add value to the model while BA was the most significant variable followed byPRA. The combination with good fit in decreasing order in the bushlands was found to beBA, CI,dm >BA,PRA >BA,dm > BA, for the grassland,BA, dm, PRA>BA,PRA>BA >dm, PRA >PRA, and for cultivated lands, BA,dm >BA > CI,dm.


#### 3.2.6. Generalized Height Models for Pines and Eucalyptus Species

The most important variables describing variation inH were found to be forest stand variables, i.e.,BA andCI for both plantation tree species ofEucalyptus and pines. Climate variables, i.e.,PRA anddm, were found to be nonsignificant. WhenPRAordm are combined withBA, the climate variables were found to be important in describingH-D allometry forEucalyptus species.


### 3.3. Application of the Developed Models

AlthoughHestimating models with climate and forest structure variables proved to be superior, except for wetlands forest (failure to converge),H base models for all forest types are also presented for practical reasons, i.e., to be applied when climate and forest stand variables are not available (Table 4; e.g., [14, 28]). Of the fitted generalizedHestimating models (Table 5), we selected at least two best models for each forest type and regional models for further evaluation except for mangrove forest (one model selected) and wetlands (none was selected). We prioritize and select simple and practical models instead of complex models with large number of variables.The selected models were refitted by allowing stand and climate variables to enter into the model nonlinearly. This is becauseH increases to asymptote with the increase of climate and stand variables. However, not all the models were able to converge, e.g., bushlands, grasslands, mangroves, andEucalyptus species, while also for some, we maintained variables getting into the model linearly due to poor model fit. Models in which climate or forest stand variables were not significant are not presented in Table 6. It was evident thatBA was an important variable for every vegetation except wetlands. Addition ofPRA improved model fit for reginal model, lowland, miombo, and grassland forests (Table 6). TheCI improved model fit for montane, miombo, bushland, and pine forests. ThePRA, however, was not important to wetlands, mangroves, montane forest, and pine species when BA enters into the model nonlinearly. The number of dry month (dm) improved the model fit for only cultivated land and bushlands.Table 6
Parameter estimates and their performance of the selectedHestimating models.
Forest Variables Model expression SE% AIC Regional BA H = 1.3 + 13.1646 × B A 0.1844 × 1 - exp ⁡ - 0.0537 × D 0.7896 31.4 140977 BA&PRA H = 1.3 + 0.0045 × P R A + 9.3717 × B A 0.2143 × 1 - exp ⁡ - 0.0544 × D 0.7925 31.0 140308   Lowland BA H = 1.3 + 16.0867 × B A 0.1052 × 1 - exp ⁡ - 0.0634 × D 0.7997 33.0 11645 BA&PRA H = 1.3 + 0.0033 × P R A + 12.4099 × B A 0.1197 × 1 - exp ⁡ - 0.0654 × D 0.8006 32.8 11621   Montane BA H = 1.3 + 14.2044 × B A 0.1373 × 1 - exp ⁡ - 0.0592 × D 0.8624 32.5 11536 BA&CI H = 1.3 + - 1.6404 × C I + 18.3007 × B A 0.1173 × 1 - exp ⁡ - 0.049 × D 0.856 32.5 11533   Miombo woodlands BA H = 1.3 + 13.4969 × B A 0.1491 × 1 - exp ⁡ - 0.0492 × D 0.8423 29.7 94421 BA&PRA H = 1.3 + 0.0047 × P R A + 9.5937 × B A 0.1734 × 1 - exp ⁡ - 0.0491 × D 0.8449 29.1 93966 BA&CI H = 1.3 + - 2.0170 × C I + 19.2910 × B A 0.1284 × 1 - exp ⁡ - 0.0363 × D 0.8449 29.1 93870   Bushlands BA H = 1.3 + 14.6667 × B A 0.1190 × 1 - exp ⁡ - 0.0736 × D 0.6525 31.3 15193 BA&  dm H = 1.3 + 23.3673 + 0.1416 × B A - 0.9164 × d m × 1 - exp ⁡ - 0.0738 × D 0.68119 30.8 15176 BA&CI H = 1.3 + - 1.36 × C I + 20.9768 × B A 0.1088 × 1 - exp ⁡ - 0.0531 × D 0.6485 31.1 15184   Cultivated lands BA H = 1.3 + 9.2773 + 0.6193 × B A 0.6688 × 1 - exp ⁡ - 0.0666 × D 0.9273 38.3 9220 BA&  dm H = 1.3 + 13.3441 - 0.6336 × d m + 0.7211 × B A 0.6151 × 1 - exp ⁡ - 0.0667 × D 0.9309 38.5 9196   Grasslands BA H = 1.3 + 10.8129 + 0.2606 × B A × 1 - exp ⁡ - 0.0601 × D 0.8927 33.5 4191 BA&PRA H = 1.3 + 7.5584 + 0.00318 × P R A + 0.2275 × B A × 1 - exp ⁡ - 0.0583 × D 0.8968 32.3 4162   Mangroves BA H = 1.3 + 12.9657 + 0.2318 × B A × 1 - exp ⁡ - 0.0746 × D 0.7705 26.3 1366   Pine species BA H = 1.3 + 8.8207 × B A 0.3323 × 1 - exp ⁡ - 0.0294 × D 1.1772 20.6 1857 BA&CI H = 1.3 + - 8.0292 × C I + 19.7312 × B A 0.2076 × 1 - exp ⁡ - 0.0169 × D 1.2614 20.5 1850   Eucalyptus species BA H = 1.3 + 14.0897 × B A 0.1935 × 1 - exp ⁡ - 0.0538 × D 1.0275 19.8 520 BA&PRA H = 1.3 + 4.1385 + 0.0106 × P R A + 0.2292 × B A × 1 - exp ⁡ - 0.0470 × D 1.1205 19.3 522At this end, the best regional models were found to be that which consist of soleBA and a combination ofBA andPRA. Base model had the poorest performance. The residual box plot and mean prediction error (PE %) for the three regional models are shown in Figure 6 and Table 7, respectively. The performance of the model with soleBA and that ofBA andPRAwhen evaluated against forest types did not differ significantly. The prediction error ranged between -1.26% and -21.68%. The two models produced relatively lower prediction error to the bushlands, lowlands, mangroves, montane, and miombo woodlands. The two models consistently produced similar pattern of residuals; i.e., both were biased to wetlands and grassland trees (Figure 6). ThePE% for the basic model were found to be relatively high to all forest types except for lowland and mangrove forests (Table 7). This was also evident when evaluating the model by means of residuals (Figure 6).Table 7
Prediction error of the fitted base and generalized regional models to the studied forest types.
Forest Type Prediction error (%) D D & BA D, BA & PRA Bushlands -18.41 -11.32 -8.09 Grasslands -32.48 -16.83 -21.68 Lowlands 4.49 -1.88 -3.10 Mangroves -6.17 -9.50 -11.29 Montane 10.78 0.82 -1.26 Wetlands -20.12 -13.51 -14.67 Woodlands -12.79 -11.06 -10.72Figure 6
Evaluation of regional models to the studied from types BUS: Bushland; GRA: Grassland; LOW: Lowland; MAN: Mangroves; MIO: Miombo; MON: Montane; and WET: Wetlands.


## 3.1. Height Base Model

Performance of base models is shown in Table3. The SE% were found to range from 25.4% to 41.3% across forest types. Forests with highest SE% were found to be bushlands followed by lowland and montane forests. Forests with low SE% were pines (26.5%) andEucalyptus (25.5%) plantations and mangroves forest (28.1%) for natural forests. In terms of performance, based on AIC, Model (6) had a good fit in all forest types except for wetland forests. Model (1) was the second in performance. Model (1), i.e., Ratkowsky [41], was selected for wetland forests while for other forests Model (6), Weibull [42], was selected. Parameter estimates and mode expressions are provided in Table 4.Table 3
Parameters estimates and performance of height base models.
Forest Model SE % AIC Forest SE % AIC Forest SE % AIC Forest SE % AIC BU 1 34.8 15752 CUL 40.7 9408 EUC 25.5 561 GRA 36.0 4311 2 35.5 15783 41.2 9439 25.7 563 36.4 4331 3 36.1 15915 41.3 9464 25.9 563 36.5 4344 4 32.4 15430 40.3 9388 25.4 564 35.6 4290 5 33.0 15510 40.4 9389 25.5 563 35.7 4288 6 32.4 15428 40.2 9386 25.4 564 35.5 4290  LO 1 34.9 11893 MAN 28.5 1316 HUM 34.3 11779 ALL 42.7 156220 2 36.1 11987 28.8 1320 35.2 11862 36.3 157410 3 36.2 12069 29.1 1326 35.3 11906 36.5 158053 4 33.7 11703 27.9 1312 33.5 11685 34.5 154230 5 33.8 11721 28.1 1314 33.6 11706 34.6 154460 6 33.7 11703 27.8 1311 33.5 11684 34.5 154229  WET 1 31.6 486 MIO 31.2 96575 PIN 26.5 2007 2 31.9 490 31.8 97303 26.2 2008 3 32.1 491 31.9 97616 26.2 2009 4 31.7 486 30.7 95686 26.1 2003 5 31.6 485 30.7 95757 26.3 2007 6 31.7 486 30.7 95683 26.0 2001 BU: Bushlands; LO: Lowland; WET: Wetlands; CU: Cultivated land; MAN: Mangroves; EUC: Eucalyptus species; HUM: Humid montane; GRA: Grasslands; and PIN: Pines species.Table 4
Best selected height base models.
Model Forest type Model expression Weibull [42] Bushlands 1.3 + 37.0396 × ( 1 - exp ⁡ ( - 0.03778 × D 0.6063 ) ) Weibull [42] Cultivated land 1.3 + 13.6509 × ( 1 - exp ⁡ ( - 0.06223 × D 0.8600 ) ) Weibull [42] Eucalyptus species 1.3 + 29.3684 × ( 1 - exp ⁡ ( - 0.03148 × D 1.1061 ) ) Weibull [42] Grasslands 1.3 + 14.7261 × ( 1 - exp ⁡ ( - 0.0536 × D 0.8637 ) ) Weibull [42] Lowland 1.3 + 24.9862 × ( 1 - exp ⁡ ( - 0.0579 × D 0.7682 ) ) Weibull [42] Mangroves 1.3 + 15.8607 × ( 1 - exp ⁡ ( - 0.0705 × D 0.8520 ) ) Weibull [42] Humid montane 1.3 + 25.6752 × ( 1 - exp ⁡ ( - 0.0536 × D 0.8234 ) Weibull [42] Pine species 1.3 + 28.5979 × ( 1 - exp ⁡ ( - 0.0064 × D 1.6174 ) ) Ratkowsky [41] Wetlands 1.3 + 20.4098 × exp ⁡ ( - 23.1909 / ( D + 6.7727 ) ) Weibull [42] Woodlands 1.3 + 24.3701 × ( 1 - exp ⁡ ( - 0.0405 × D 0.8070 ) ) Weibull [42] Reginal 1.3 + 30.2116 × ( 1 - exp ⁡ ( - 0.0379 × D 0.7451 ) )


## 3.2. Height Estimating Models with Climate and Forest Stand Variables

### 3.2.1. Regional Generalized Height Models

The findings show that all parameters of the fitted regional models were significant; i.e., all fitted variables had significant contribution in explainingH(Table 5).The magnitude of importance of independent variables decreased in the following order,BA,PRA,dm, andCI. Based on AIC, the model which combines all the independent variables was found to have best fit. Positive parameters forPRA andBA suggest that as precipitation and stand density increases, the meanH also increases (e.g., Figure 5). Trend of meanPRA versus meanHis shown in Figure 4.Table 5
Performance of different combination of climate and forest parameters on regional and forest type specificHestimating models.
Variables Akaike Information Criterion (AIC) Regional Lowland Montane Miombo Bushland Cultivated Grassland Mangroves Pines Eucalyptus Wetlands BA 150932 11667 11552 94685 15272 9223 4191 1366 1866 535 487BA CI 153650 11697 11634 95401 15403CI 9369 4288CI 1388CI 1927 555 488CI Dry 153316 11699 11686dm 95131 15315 9343 4290dm 1410dm 2003dm 565dm 487dm PRA 153006 11675 11672 94853 15363 9349 4234 1409PRA 2003PRA 564PRA 487PRA BA, CI 150842 11668CI 11546 94579 15262 9222CI 4193CI 1362CI 1855 536CI 486BA,CI BA, Dry 150416 11664 11554dm 94271 15176 9201 4193dm 1367dm 1868dm 530 486BA,dm BA,PRA 150232 11645 11550 94096 15244 9207 4162 1368PRA 1867PRA 522 488BA,PRA CI, Dry 152871 11693 11636dm 94908 15282CI,dm 9327 4289CI,dm 1390CI,dm 1929dm 556dm 488CI,dm CI,PRA 152518 11673CI 11628 94557 15329CI,PRA 9335 4233CI 1390PRA,CI 1928PRA 555PRA 488CI,P Dry,PRA 152871 11650 11671dm 94783 15314PRA 9337 4228 1411P,dm 2002PRA,dm 566dm,PRA 485dm,P BA, CI, dry 150352 11665CI 11548d 94191 15159 9199CI 4194CI,dm 1363C,dm 1857dm 532dm 486CI,dm BA, CI,PRA 150149 11646CI 11545PRA 93966 15228PRA 9206CI 4164CI 1364PRA,CI 1856PRA 524CI 487CI,PRA,BA CI,PRA, Dry 152421 11649CI 11627dm 94514 15279CI,PRA 9322 4226CI 1392C,PRA,dm 1930PRA,dm 557dm 486CI,PRA,dm BA, Dry,PRA 150156 11625 11552dm,PRA 94035 15177PRA 9200PRA 4158 1369dm,PRA 1868PRA,dm 523dm 482BA,dm,PRA BA, CI, Dry,PRA 150083 11626CI 11547dm,PRA 93922 15161PRA 9198PRA,CI 4160CI,dm 1365dm,PRA,CI 1857PRA,dm 524dm,CI 481CI Powered letters are nonsignificant of the respective variables, i.e.,dm: number of dry months; CI: competition index; PRA: precipitation; and BA: basal area.Figure 5
Effect of precipitation to total tree height distributed in diameter classes.PRAvalues above the box are in mm. BUS: Bushland; GRA: Grassland; LOW: Lowland; MAN: Mangroves; MIO: Miombo; MON: Montane; and WET: Wetlands.


### 3.2.2. Generalized Height Models for Lowland and Montane

For both forest types, all parameters estimates were significant when forest structure and climate variables were included in the model one by one except fordm in the montane forest (Table 5). The magnitude of importance of independent variables for lowland and montane forests decreased in the following order:BA >PRA>CI andBA >CI >PRA>dm, respectively. In many cases combinations which include CI, CI were found to be nonsignificant. For example, for lowland, a model with a combination ofBA andCI andPRAandCI consistently yielded nonsignificant parameters forCI. For the lowland, the five best models in decreasing order of model fit had the following combination of variables, i.e.,BA,dm,PRA>BA,PRA>dm,PRA >BA,dm >BA while for the montane they wereBA,CI >BA,PRA >BA >CI,PRA>CI.


### 3.2.3. Generalized Height Models for Miombo Woodlands

All variable combinations yielded significant model parameters. Model with all variables had the best fit. The importance of stand and climate variables decreased in following order:BA >PRA>CI >dm. The models fit decreased in the following order of combination: BA, CI,dm,PRA>BA,CI,PRA>BA,dm,PRA>BA,PRA>BA,CI,dm.


### 3.2.4. Generalized Height Models for Mangroves and Wetlands

Climate variables were not found to influenceH-D allometry in both wetlands and mangroves forests. Except for mangroves whereBA was a significant variable, forest stands variables did not improve theHestimating model fit in wetlands. This implies thatH base models were found to describeH-D allometry adequately for wetland forests (Table 5). In mangroves, model with BA included had better fit than base model.


### 3.2.5. Generalized Height Models for Bushland, Cultivated, and Grasslands

The PRA in combination withdm and/orCI did not improve model fit for bushlands. Important variables in decreasing order wereBA,dm, andPRA. In cultivated lands,BA,dm, andPRA were found to be important in that order in describingH-D allometry whileCI was found to be nonsignificant. In grasslands,CI anddm did not add value to the model while BA was the most significant variable followed byPRA. The combination with good fit in decreasing order in the bushlands was found to beBA, CI,dm >BA,PRA >BA,dm > BA, for the grassland,BA, dm, PRA>BA,PRA>BA >dm, PRA >PRA, and for cultivated lands, BA,dm >BA > CI,dm.


### 3.2.6. Generalized Height Models for Pines and Eucalyptus Species

The most important variables describing variation inH were found to be forest stand variables, i.e.,BA andCI for both plantation tree species ofEucalyptus and pines. Climate variables, i.e.,PRA anddm, were found to be nonsignificant. WhenPRAordm are combined withBA, the climate variables were found to be important in describingH-D allometry forEucalyptus species.


## 3.2.1. Regional Generalized Height Models

The findings show that all parameters of the fitted regional models were significant; i.e., all fitted variables had significant contribution in explainingH(Table 5).The magnitude of importance of independent variables decreased in the following order,BA,PRA,dm, andCI. Based on AIC, the model which combines all the independent variables was found to have best fit. Positive parameters forPRA andBA suggest that as precipitation and stand density increases, the meanH also increases (e.g., Figure 5). Trend of meanPRA versus meanHis shown in Figure 4.Table 5
Performance of different combination of climate and forest parameters on regional and forest type specificHestimating models.
Variables Akaike Information Criterion (AIC) Regional Lowland Montane Miombo Bushland Cultivated Grassland Mangroves Pines Eucalyptus Wetlands BA 150932 11667 11552 94685 15272 9223 4191 1366 1866 535 487BA CI 153650 11697 11634 95401 15403CI 9369 4288CI 1388CI 1927 555 488CI Dry 153316 11699 11686dm 95131 15315 9343 4290dm 1410dm 2003dm 565dm 487dm PRA 153006 11675 11672 94853 15363 9349 4234 1409PRA 2003PRA 564PRA 487PRA BA, CI 150842 11668CI 11546 94579 15262 9222CI 4193CI 1362CI 1855 536CI 486BA,CI BA, Dry 150416 11664 11554dm 94271 15176 9201 4193dm 1367dm 1868dm 530 486BA,dm BA,PRA 150232 11645 11550 94096 15244 9207 4162 1368PRA 1867PRA 522 488BA,PRA CI, Dry 152871 11693 11636dm 94908 15282CI,dm 9327 4289CI,dm 1390CI,dm 1929dm 556dm 488CI,dm CI,PRA 152518 11673CI 11628 94557 15329CI,PRA 9335 4233CI 1390PRA,CI 1928PRA 555PRA 488CI,P Dry,PRA 152871 11650 11671dm 94783 15314PRA 9337 4228 1411P,dm 2002PRA,dm 566dm,PRA 485dm,P BA, CI, dry 150352 11665CI 11548d 94191 15159 9199CI 4194CI,dm 1363C,dm 1857dm 532dm 486CI,dm BA, CI,PRA 150149 11646CI 11545PRA 93966 15228PRA 9206CI 4164CI 1364PRA,CI 1856PRA 524CI 487CI,PRA,BA CI,PRA, Dry 152421 11649CI 11627dm 94514 15279CI,PRA 9322 4226CI 1392C,PRA,dm 1930PRA,dm 557dm 486CI,PRA,dm BA, Dry,PRA 150156 11625 11552dm,PRA 94035 15177PRA 9200PRA 4158 1369dm,PRA 1868PRA,dm 523dm 482BA,dm,PRA BA, CI, Dry,PRA 150083 11626CI 11547dm,PRA 93922 15161PRA 9198PRA,CI 4160CI,dm 1365dm,PRA,CI 1857PRA,dm 524dm,CI 481CI Powered letters are nonsignificant of the respective variables, i.e.,dm: number of dry months; CI: competition index; PRA: precipitation; and BA: basal area.Figure 5
Effect of precipitation to total tree height distributed in diameter classes.PRAvalues above the box are in mm. BUS: Bushland; GRA: Grassland; LOW: Lowland; MAN: Mangroves; MIO: Miombo; MON: Montane; and WET: Wetlands.


## 3.2.2. Generalized Height Models for Lowland and Montane

For both forest types, all parameters estimates were significant when forest structure and climate variables were included in the model one by one except fordm in the montane forest (Table 5). The magnitude of importance of independent variables for lowland and montane forests decreased in the following order:BA >PRA>CI andBA >CI >PRA>dm, respectively. In many cases combinations which include CI, CI were found to be nonsignificant. For example, for lowland, a model with a combination ofBA andCI andPRAandCI consistently yielded nonsignificant parameters forCI. For the lowland, the five best models in decreasing order of model fit had the following combination of variables, i.e.,BA,dm,PRA>BA,PRA>dm,PRA >BA,dm >BA while for the montane they wereBA,CI >BA,PRA >BA >CI,PRA>CI.


## 3.2.3. Generalized Height Models for Miombo Woodlands

All variable combinations yielded significant model parameters. Model with all variables had the best fit. The importance of stand and climate variables decreased in following order:BA >PRA>CI >dm. The models fit decreased in the following order of combination: BA, CI,dm,PRA>BA,CI,PRA>BA,dm,PRA>BA,PRA>BA,CI,dm.


## 3.2.4. Generalized Height Models for Mangroves and Wetlands

Climate variables were not found to influenceH-D allometry in both wetlands and mangroves forests. Except for mangroves whereBA was a significant variable, forest stands variables did not improve theHestimating model fit in wetlands. This implies thatH base models were found to describeH-D allometry adequately for wetland forests (Table 5). In mangroves, model with BA included had better fit than base model.


## 3.2.5. Generalized Height Models for Bushland, Cultivated, and Grasslands

The PRA in combination withdm and/orCI did not improve model fit for bushlands. Important variables in decreasing order wereBA,dm, andPRA. In cultivated lands,BA,dm, andPRA were found to be important in that order in describingH-D allometry whileCI was found to be nonsignificant. In grasslands,CI anddm did not add value to the model while BA was the most significant variable followed byPRA. The combination with good fit in decreasing order in the bushlands was found to beBA, CI,dm >BA,PRA >BA,dm > BA, for the grassland,BA, dm, PRA>BA,PRA>BA >dm, PRA >PRA, and for cultivated lands, BA,dm >BA > CI,dm.


## 3.2.6. Generalized Height Models for Pines and Eucalyptus Species

The most important variables describing variation inH were found to be forest stand variables, i.e.,BA andCI for both plantation tree species ofEucalyptus and pines. Climate variables, i.e.,PRA anddm, were found to be nonsignificant. WhenPRAordm are combined withBA, the climate variables were found to be important in describingH-D allometry forEucalyptus species.


## 3.3. Application of the Developed Models

AlthoughHestimating models with climate and forest structure variables proved to be superior, except for wetlands forest (failure to converge),H base models for all forest types are also presented for practical reasons, i.e., to be applied when climate and forest stand variables are not available (Table 4; e.g., [14, 28]). Of the fitted generalizedHestimating models (Table 5), we selected at least two best models for each forest type and regional models for further evaluation except for mangrove forest (one model selected) and wetlands (none was selected). We prioritize and select simple and practical models instead of complex models with large number of variables.The selected models were refitted by allowing stand and climate variables to enter into the model nonlinearly. This is becauseH increases to asymptote with the increase of climate and stand variables. However, not all the models were able to converge, e.g., bushlands, grasslands, mangroves, andEucalyptus species, while also for some, we maintained variables getting into the model linearly due to poor model fit. Models in which climate or forest stand variables were not significant are not presented in Table 6. It was evident thatBA was an important variable for every vegetation except wetlands. Addition ofPRA improved model fit for reginal model, lowland, miombo, and grassland forests (Table 6). TheCI improved model fit for montane, miombo, bushland, and pine forests. ThePRA, however, was not important to wetlands, mangroves, montane forest, and pine species when BA enters into the model nonlinearly. The number of dry month (dm) improved the model fit for only cultivated land and bushlands.Table 6
Parameter estimates and their performance of the selectedHestimating models.
Forest Variables Model expression SE% AIC Regional BA H = 1.3 + 13.1646 × B A 0.1844 × 1 - exp ⁡ - 0.0537 × D 0.7896 31.4 140977 BA&PRA H = 1.3 + 0.0045 × P R A + 9.3717 × B A 0.2143 × 1 - exp ⁡ - 0.0544 × D 0.7925 31.0 140308   Lowland BA H = 1.3 + 16.0867 × B A 0.1052 × 1 - exp ⁡ - 0.0634 × D 0.7997 33.0 11645 BA&PRA H = 1.3 + 0.0033 × P R A + 12.4099 × B A 0.1197 × 1 - exp ⁡ - 0.0654 × D 0.8006 32.8 11621   Montane BA H = 1.3 + 14.2044 × B A 0.1373 × 1 - exp ⁡ - 0.0592 × D 0.8624 32.5 11536 BA&CI H = 1.3 + - 1.6404 × C I + 18.3007 × B A 0.1173 × 1 - exp ⁡ - 0.049 × D 0.856 32.5 11533   Miombo woodlands BA H = 1.3 + 13.4969 × B A 0.1491 × 1 - exp ⁡ - 0.0492 × D 0.8423 29.7 94421 BA&PRA H = 1.3 + 0.0047 × P R A + 9.5937 × B A 0.1734 × 1 - exp ⁡ - 0.0491 × D 0.8449 29.1 93966 BA&CI H = 1.3 + - 2.0170 × C I + 19.2910 × B A 0.1284 × 1 - exp ⁡ - 0.0363 × D 0.8449 29.1 93870   Bushlands BA H = 1.3 + 14.6667 × B A 0.1190 × 1 - exp ⁡ - 0.0736 × D 0.6525 31.3 15193 BA&  dm H = 1.3 + 23.3673 + 0.1416 × B A - 0.9164 × d m × 1 - exp ⁡ - 0.0738 × D 0.68119 30.8 15176 BA&CI H = 1.3 + - 1.36 × C I + 20.9768 × B A 0.1088 × 1 - exp ⁡ - 0.0531 × D 0.6485 31.1 15184   Cultivated lands BA H = 1.3 + 9.2773 + 0.6193 × B A 0.6688 × 1 - exp ⁡ - 0.0666 × D 0.9273 38.3 9220 BA&  dm H = 1.3 + 13.3441 - 0.6336 × d m + 0.7211 × B A 0.6151 × 1 - exp ⁡ - 0.0667 × D 0.9309 38.5 9196   Grasslands BA H = 1.3 + 10.8129 + 0.2606 × B A × 1 - exp ⁡ - 0.0601 × D 0.8927 33.5 4191 BA&PRA H = 1.3 + 7.5584 + 0.00318 × P R A + 0.2275 × B A × 1 - exp ⁡ - 0.0583 × D 0.8968 32.3 4162   Mangroves BA H = 1.3 + 12.9657 + 0.2318 × B A × 1 - exp ⁡ - 0.0746 × D 0.7705 26.3 1366   Pine species BA H = 1.3 + 8.8207 × B A 0.3323 × 1 - exp ⁡ - 0.0294 × D 1.1772 20.6 1857 BA&CI H = 1.3 + - 8.0292 × C I + 19.7312 × B A 0.2076 × 1 - exp ⁡ - 0.0169 × D 1.2614 20.5 1850   Eucalyptus species BA H = 1.3 + 14.0897 × B A 0.1935 × 1 - exp ⁡ - 0.0538 × D 1.0275 19.8 520 BA&PRA H = 1.3 + 4.1385 + 0.0106 × P R A + 0.2292 × B A × 1 - exp ⁡ - 0.0470 × D 1.1205 19.3 522At this end, the best regional models were found to be that which consist of soleBA and a combination ofBA andPRA. Base model had the poorest performance. The residual box plot and mean prediction error (PE %) for the three regional models are shown in Figure 6 and Table 7, respectively. The performance of the model with soleBA and that ofBA andPRAwhen evaluated against forest types did not differ significantly. The prediction error ranged between -1.26% and -21.68%. The two models produced relatively lower prediction error to the bushlands, lowlands, mangroves, montane, and miombo woodlands. The two models consistently produced similar pattern of residuals; i.e., both were biased to wetlands and grassland trees (Figure 6). ThePE% for the basic model were found to be relatively high to all forest types except for lowland and mangrove forests (Table 7). This was also evident when evaluating the model by means of residuals (Figure 6).Table 7
Prediction error of the fitted base and generalized regional models to the studied forest types.
Forest Type Prediction error (%) D D & BA D, BA & PRA Bushlands -18.41 -11.32 -8.09 Grasslands -32.48 -16.83 -21.68 Lowlands 4.49 -1.88 -3.10 Mangroves -6.17 -9.50 -11.29 Montane 10.78 0.82 -1.26 Wetlands -20.12 -13.51 -14.67 Woodlands -12.79 -11.06 -10.72Figure 6
Evaluation of regional models to the studied from types BUS: Bushland; GRA: Grassland; LOW: Lowland; MAN: Mangroves; MIO: Miombo; MON: Montane; and WET: Wetlands.


## 4. Discussion

### 4.1. Height Base Models

This study aimed at developingH estimating models for different forest types in Tanzania Mainland using the National Forest Inventory data collected through NAFORMA program. We also assessed how climate and forest stand variables modifyH-D allometry. This is the first study withH estimating models developed from sample trees covering the entire country of Tanzania. As such the models developed from this study are robust enough to account for different tree allometry variations which might be attributed by differences in forest types as well as climatic conditions. SeveralH estimating model forms were tested and evaluated but generally Weibull model turned out to be the best and was able to smoothly converge when climate and forest stand variables are included (Tables 5 and 6). In addition, the fact that the model form has asymptotic characteristics complies with biological features ofH growth. This characteristic may explain why Weibull model has been reported to be more appropriate for prediction of above ground biomass and reduces errors for trees of extremeD compared to nonasymptote which tend to overestimate biomass of extreme trees [50]. With such a big data set used in this study where the confidence that most ofH-D variation has been captured is high, e.g., good presentation of trees which have reached maximumH growth, the asymptotic Weibull model may be more appropriate than the log-log model.The Weibull model was found to be superior in all forest types except in wetland. The performance of Weibull models has been widely reported and used to describe tree allometric relationships, especiallyH-D relationships reported by other scholars [19, 50, 55–57]. The SE% for the base model was found to be relatively higher than that of generalized models (Tables 3 and 6). This may be explained by large variations inH which could not be explained byD alone. However, the error margin corresponds to the reported findings elsewhere [19, 28, 57]. Mangroves and plantation tree species, i.e., pine and Eucalyptus, had relatively lower SE% compared to other forest types. Mangroves have rather fewer woody tree species [35] which may translate to lowH variation. This also applies to pines andEucalyptus trees species which have more uniform allometry in plantation.


### 4.2. Height-Diameter Allometry and Climate

The findings show meanH of all forest types which were affected byPRA anddm in a regular pattern (Figure 2) and show high coefficient of variation of bothPRA anddm (Table 1);PRA anddm were also found to affect theH-D allometry significantly. The affected forest types include all data combined, bushlands, cultivated land, grasslands, miombo woodlands, and lowlands (Table 1). The observed trend may be explained by the fact that the reported forest types are widely distributed in the country and therefore exposed to differentPRA and dm patterns (Table 1; [36]). Taking an example of lowland forests, where two subclasses exist, i.e., semideciduous normally found inland receiving relative low rainfall compared to evergreen forests in the coastal regions [58] with more or less comparable tree species composition, it was found that trees in coastal regions were taller than those found inland [10]. Phenotypic plasticity of trees responses to climate and other environmental conditions such as altitude and soil characteristics may explain these differences [59]. This pattern is also supported by Vizcaíno-Palomar et al. [13] who studied the effect of climate and population origin to theH-D allometry and found that some species modifyH-D allometry (e.g.,Pinus halepensis andPinus pinaster) when growing in environment with varyingPRA while others maintain theH-D allometry (e.g.,Pinus sylvestris andP. nigra). However, pines andEucalyptus species were not affected byPRA and dm. Dominant pine species grown in Tanzania Mainland at large scale isPinus patula in southern and northern highlands [60]. These areas experience similar climatic conditions which may explain why this study did not findH-D allometry variation associated withPRA. On the other hand,Eucalyptus species is widely distributed in both dry and wet areas where we would expect to find the effect ofPRA anddm on theirH-D allometry. However, the effect ofPRA anddm were insignificant suggesting inconsistentH-D allometry response to climatic condition [61, 62].Furthermore, when comparing meanH of forest types, the findings show that meanH increases with the increase ofPRA (Figure 5) and decreases with the increase ofdm with few exceptions, i.e., grasslands (Figure 4). Generally, these findings are in line with those reported by Burgess et al. [27] who found that maximumH decreases with decreasingPRA in this order, i.e., montane, lowland, closed woodlands, and open woodlands. The contradicting results with grassland maybe due to the fact that the vegetation type is mainly found in the southern highlands which experience highPRA and also in patches woodlands with moderatePRA. In the grasslands trees are normally scattered and therefore it is likely that they are not struggling for light resource for vertical growth and therefore invest more on branches (horizontal growth; [63, 64]). This is further justified by nonsignificant parameter forCI as shown in Table 5 since the trees experience no competition. On the other hand, although wetlands and mangroves forests receive moderatePRA, it was expected that trees would be taller than those found in other forests since these areas are wetter throughout the year. This implies that there are other factors other than PRA such as genetics, soils fertility and depth, winds, and humidity which also modifyH-D allometry which were not captured in our data set [2, 59]. Trend observed in this study provides vital information on tree allometry response to climatic condition. Climate fluctuations are even more urgent because climate changes are expected to cause stronger climatic variability, with increased frequency of extreme dry years which will affect distribution, allometry of tree species and consequently forest biomass [65–68].


### 4.3. Height-Diameter Allometry and Forest Structure Variables

The findings from this study show that BA in most cases (except for wetlands forests) have a strong influence onH-D allometry, i.e., increasing ofH with increasing BA. This pattern suggests thatH-D allometry varies within forest type, i.e., among plots. This implies that when excluding BA as a predictor, differentH-D equation would be required for each plot [69]. There are contradicting findings reported on the effect of stand density toH (e.g., [70]). Other scholars have claimed that the vertical and horizontal dimensional change of a tree is linked with the availability of resources: solar radiation, water, and nutrients. Consequently, site quality has been conventionally determined by dominantH which is considered to be less sensitive to stand density such asBA [71]. Dunning [72] and Baker [73] have shown thatH may be affected by stand density. However, the inconsistence of the reported findings has been shown to be attributed by size of plots and variable responses of different tree species to stand density [70]. Data collected in larger plots have shown to be more explanatory to this phenomenon than those collected in small plots [70]. Due to the consistence of our findings, we rule out that the plot size applied in this study was adequate to explainH-stand density relationships. In addition, while few tree species are shade tolerant, light demanders in a tightly packed setup may be forced to shoot upward in pursuit of sunlight [74, 75]. On the other hand, trees growing in a densely packed stems are not susceptible to wind damage due to sheltering effect and therefore they are likely to invest inH thanD since mechanical support may not be the priority [2, 76].While increase inBA aggravates competition for resources and affects tree growth, the magnitude of the impact may be experienced differently from one tree to another depending on their sizes [77, 78]. This is when the tree status in terms ofCI becomes important, thus explaining how a tree is affected by neighboring trees. It is expected that tree with largeCI to have “proportionally” largeH, i.e., larger trees have more advantages in resources capturing than the small trees [22]. However, this interaction favorsD growth rather thanH. For example, Mugasha et al. [79] reported diameter increment to be positively linked toCI. This imply that while small trees have narrow ground for resources since adjacently they are outmatched with larger trees [80], they capitalize onH growth in pursuit for sunlight [75]. Therefore, it is not surprising that in this studyCI was inversely proportional toH in all forest types except for wetland whereCI was not significant but maintained similar trend. InsignificantCI parameter for wetland forest may be associated with the limited number of observations used in modelling, i.e., 97 observations (Table 1).


### 4.4. Application of Height-Diameter Models

Prediction ofH is critical step when estimating other forest parameters such as forest biomass and volume (e.g., [1]). The accuracy of the estimates will depend on the prediction power ofH estimating models. Comparison between the fitted base and generalizedH estimating model forHpredictions of forest types indicated that for montane, mangrove, and wetlands, parameters forPRA were not significant suggesting that whenBA enters into the model nonlinearly, the model explains most ofH andPRA remain redundant. We dropped models having insignificant parameter forPRA. It was expected that the pattern displayed byPRA to the lowland and humid montane forest to be the same as shown in Table 5 (positive and significantPRA parameters). However, whilePRA was important for lowland forests in modifyingH-D allometry, it was not the case for humid montane forest. This may be explained by wide distribution scale of lowland forests to various precipitation patterns [58]. The fact that humid montane forests occur in wetter areas, i.e., leeward of eastern, southern and northern mountains (elevated areas and therefore low evapotranspiration; [43]), may explain whyPRA were found insignificant toH-D allometry.As expected climate and forest structure variables were highly significant when fitting generalized regionalH estimating model since the modelling data covers large spatial variability in terms of climate and forest structure which consequently affectsH-D allometry (e.g., [2]). However, the magnitude of their contribution in explainingH-D allometry varied. The residuals of generalized regional model withBA included were far more balanced than base model. Addition ofPRA on top ofBA did not improve the residual plots. This is further indicated byPE% values where generalized regional model withBA hadPE% below 12% except for grassland and wetland forest. These findings indicate that generalized regional model can adequately predictH of trees found in the studied forests with exception of few when climate and forest stand variables are available [2]. For improved accuracy, however, forest specific generalizedH estimating models are recommended. Forest specificH estimating model is recommended when climate and stand variables information is not available.


## 4.1. Height Base Models

This study aimed at developingH estimating models for different forest types in Tanzania Mainland using the National Forest Inventory data collected through NAFORMA program. We also assessed how climate and forest stand variables modifyH-D allometry. This is the first study withH estimating models developed from sample trees covering the entire country of Tanzania. As such the models developed from this study are robust enough to account for different tree allometry variations which might be attributed by differences in forest types as well as climatic conditions. SeveralH estimating model forms were tested and evaluated but generally Weibull model turned out to be the best and was able to smoothly converge when climate and forest stand variables are included (Tables 5 and 6). In addition, the fact that the model form has asymptotic characteristics complies with biological features ofH growth. This characteristic may explain why Weibull model has been reported to be more appropriate for prediction of above ground biomass and reduces errors for trees of extremeD compared to nonasymptote which tend to overestimate biomass of extreme trees [50]. With such a big data set used in this study where the confidence that most ofH-D variation has been captured is high, e.g., good presentation of trees which have reached maximumH growth, the asymptotic Weibull model may be more appropriate than the log-log model.The Weibull model was found to be superior in all forest types except in wetland. The performance of Weibull models has been widely reported and used to describe tree allometric relationships, especiallyH-D relationships reported by other scholars [19, 50, 55–57]. The SE% for the base model was found to be relatively higher than that of generalized models (Tables 3 and 6). This may be explained by large variations inH which could not be explained byD alone. However, the error margin corresponds to the reported findings elsewhere [19, 28, 57]. Mangroves and plantation tree species, i.e., pine and Eucalyptus, had relatively lower SE% compared to other forest types. Mangroves have rather fewer woody tree species [35] which may translate to lowH variation. This also applies to pines andEucalyptus trees species which have more uniform allometry in plantation.


## 4.2. Height-Diameter Allometry and Climate

The findings show meanH of all forest types which were affected byPRA anddm in a regular pattern (Figure 2) and show high coefficient of variation of bothPRA anddm (Table 1);PRA anddm were also found to affect theH-D allometry significantly. The affected forest types include all data combined, bushlands, cultivated land, grasslands, miombo woodlands, and lowlands (Table 1). The observed trend may be explained by the fact that the reported forest types are widely distributed in the country and therefore exposed to differentPRA and dm patterns (Table 1; [36]). Taking an example of lowland forests, where two subclasses exist, i.e., semideciduous normally found inland receiving relative low rainfall compared to evergreen forests in the coastal regions [58] with more or less comparable tree species composition, it was found that trees in coastal regions were taller than those found inland [10]. Phenotypic plasticity of trees responses to climate and other environmental conditions such as altitude and soil characteristics may explain these differences [59]. This pattern is also supported by Vizcaíno-Palomar et al. [13] who studied the effect of climate and population origin to theH-D allometry and found that some species modifyH-D allometry (e.g.,Pinus halepensis andPinus pinaster) when growing in environment with varyingPRA while others maintain theH-D allometry (e.g.,Pinus sylvestris andP. nigra). However, pines andEucalyptus species were not affected byPRA and dm. Dominant pine species grown in Tanzania Mainland at large scale isPinus patula in southern and northern highlands [60]. These areas experience similar climatic conditions which may explain why this study did not findH-D allometry variation associated withPRA. On the other hand,Eucalyptus species is widely distributed in both dry and wet areas where we would expect to find the effect ofPRA anddm on theirH-D allometry. However, the effect ofPRA anddm were insignificant suggesting inconsistentH-D allometry response to climatic condition [61, 62].Furthermore, when comparing meanH of forest types, the findings show that meanH increases with the increase ofPRA (Figure 5) and decreases with the increase ofdm with few exceptions, i.e., grasslands (Figure 4). Generally, these findings are in line with those reported by Burgess et al. [27] who found that maximumH decreases with decreasingPRA in this order, i.e., montane, lowland, closed woodlands, and open woodlands. The contradicting results with grassland maybe due to the fact that the vegetation type is mainly found in the southern highlands which experience highPRA and also in patches woodlands with moderatePRA. In the grasslands trees are normally scattered and therefore it is likely that they are not struggling for light resource for vertical growth and therefore invest more on branches (horizontal growth; [63, 64]). This is further justified by nonsignificant parameter forCI as shown in Table 5 since the trees experience no competition. On the other hand, although wetlands and mangroves forests receive moderatePRA, it was expected that trees would be taller than those found in other forests since these areas are wetter throughout the year. This implies that there are other factors other than PRA such as genetics, soils fertility and depth, winds, and humidity which also modifyH-D allometry which were not captured in our data set [2, 59]. Trend observed in this study provides vital information on tree allometry response to climatic condition. Climate fluctuations are even more urgent because climate changes are expected to cause stronger climatic variability, with increased frequency of extreme dry years which will affect distribution, allometry of tree species and consequently forest biomass [65–68].


## 4.3. Height-Diameter Allometry and Forest Structure Variables

The findings from this study show that BA in most cases (except for wetlands forests) have a strong influence onH-D allometry, i.e., increasing ofH with increasing BA. This pattern suggests thatH-D allometry varies within forest type, i.e., among plots. This implies that when excluding BA as a predictor, differentH-D equation would be required for each plot [69]. There are contradicting findings reported on the effect of stand density toH (e.g., [70]). Other scholars have claimed that the vertical and horizontal dimensional change of a tree is linked with the availability of resources: solar radiation, water, and nutrients. Consequently, site quality has been conventionally determined by dominantH which is considered to be less sensitive to stand density such asBA [71]. Dunning [72] and Baker [73] have shown thatH may be affected by stand density. However, the inconsistence of the reported findings has been shown to be attributed by size of plots and variable responses of different tree species to stand density [70]. Data collected in larger plots have shown to be more explanatory to this phenomenon than those collected in small plots [70]. Due to the consistence of our findings, we rule out that the plot size applied in this study was adequate to explainH-stand density relationships. In addition, while few tree species are shade tolerant, light demanders in a tightly packed setup may be forced to shoot upward in pursuit of sunlight [74, 75]. On the other hand, trees growing in a densely packed stems are not susceptible to wind damage due to sheltering effect and therefore they are likely to invest inH thanD since mechanical support may not be the priority [2, 76].While increase inBA aggravates competition for resources and affects tree growth, the magnitude of the impact may be experienced differently from one tree to another depending on their sizes [77, 78]. This is when the tree status in terms ofCI becomes important, thus explaining how a tree is affected by neighboring trees. It is expected that tree with largeCI to have “proportionally” largeH, i.e., larger trees have more advantages in resources capturing than the small trees [22]. However, this interaction favorsD growth rather thanH. For example, Mugasha et al. [79] reported diameter increment to be positively linked toCI. This imply that while small trees have narrow ground for resources since adjacently they are outmatched with larger trees [80], they capitalize onH growth in pursuit for sunlight [75]. Therefore, it is not surprising that in this studyCI was inversely proportional toH in all forest types except for wetland whereCI was not significant but maintained similar trend. InsignificantCI parameter for wetland forest may be associated with the limited number of observations used in modelling, i.e., 97 observations (Table 1).


## 4.4. Application of Height-Diameter Models

Prediction ofH is critical step when estimating other forest parameters such as forest biomass and volume (e.g., [1]). The accuracy of the estimates will depend on the prediction power ofH estimating models. Comparison between the fitted base and generalizedH estimating model forHpredictions of forest types indicated that for montane, mangrove, and wetlands, parameters forPRA were not significant suggesting that whenBA enters into the model nonlinearly, the model explains most ofH andPRA remain redundant. We dropped models having insignificant parameter forPRA. It was expected that the pattern displayed byPRA to the lowland and humid montane forest to be the same as shown in Table 5 (positive and significantPRA parameters). However, whilePRA was important for lowland forests in modifyingH-D allometry, it was not the case for humid montane forest. This may be explained by wide distribution scale of lowland forests to various precipitation patterns [58]. The fact that humid montane forests occur in wetter areas, i.e., leeward of eastern, southern and northern mountains (elevated areas and therefore low evapotranspiration; [43]), may explain whyPRA were found insignificant toH-D allometry.As expected climate and forest structure variables were highly significant when fitting generalized regionalH estimating model since the modelling data covers large spatial variability in terms of climate and forest structure which consequently affectsH-D allometry (e.g., [2]). However, the magnitude of their contribution in explainingH-D allometry varied. The residuals of generalized regional model withBA included were far more balanced than base model. Addition ofPRA on top ofBA did not improve the residual plots. This is further indicated byPE% values where generalized regional model withBA hadPE% below 12% except for grassland and wetland forest. These findings indicate that generalized regional model can adequately predictH of trees found in the studied forests with exception of few when climate and forest stand variables are available [2]. For improved accuracy, however, forest specific generalizedH estimating models are recommended. Forest specificH estimating model is recommended when climate and stand variables information is not available.


## 5. Conclusion

TheH-D allometry was developed with comprehensive data set collected from NFI covering eight main forest types in Tanzania Mainland. The findings indicated that spatial variability inH-Dallometry in Tanzania Mainland is significant. The mean tree height tends to increase with the increase of mean precipitation (PRA). Total tree height increases with the increase inBA. TheBA in addition toD was far more important explanatory variable than other climate and forest stand variables. We therefore confirm a significant contribution of climate and forest structure variables in modifyingH-D allometry. Consequently, generalizedH models turned out to be the best compared to base models. It is therefore recommended the forest specific generalizedH model to be applied when predictingH. When forest type information is not available, generalized regional model may be applied. Height base model may be applied when forest stand or climate information are missing.



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*Source: 4832849-2019-04-21.xml*