The study was conducted in the Juaboso and Bia West districts of the Western North region in Ghana’s cocoa landscape. Juaboso and Bia West districts are among the highest cocoa - producing districts in Ghana. The study area is situated between latitude 6˚13'N and 6˚50'N and longitude 2˚40'W and 3˚16'W, covering an area of 2571.26 square kilometres (Figure 1Figure 1). Cocoa farming is the major land-use system, which occupies a greater percentage of the land in the area. Apart from cocoa farms, other land use/cover which include food crop farms, fallow lands, patches of grassland and also communities in relatively low-lying areas. Within the study area are Krokosua Hills forest reserve, a portion of Bia Tributaries North forest reserve, and Bia National Park [39].

Figure 1. Map of the study area showing the cocoa mosaic landscape of Juaboso and Bia West districts of Ghana (Image source: Landsat and Copernicus from Goggle Earth Engine).

With a mean annual temperature between 25.5˚C and 26.5˚C, the area has a tropical climate marked by warm temperatures. The annual rainfall levels are between the ranges of 1250 - 2000 mm, with June and October as its peak months. The area is very undulating, with the elevation of the terrain ranging between 137 and 594 m above mean sea level. The study area falls within Moist Evergreen, Moist Semideciduous Northwest and Moist Semideciduous Southeast subtypes of ecological zones [40]. The soils are mainly Oxysols and Ochrosols [41] with underlying Birimian and Hornblende parent rocks.

Field data were collected from 40 square plots, each of dimensions 30 m × 30 m, with an area of 900 m², from 5^th to 19th January 2022. Enumeration was carried out for only live cocoa trees with a diameter at breast height (DBH) ≥ 5 cm. For each cocoa tree, DBH was measured and recorded (Appendix 1).

Two Landsat 8 level-2 product 2022 scenes were downloaded; details of the Landsat 8 data used in this study are shown in Table 1.

Table 1. Landsat 8 data used in this study.

Two ALOS-2 PALSAR-2 level 2.1 scenes from 2022 were downloaded with a resolution of 25 m, and details are shown in Table 2.

Table 2. ALOS-2 PALSAR-2 mosaic data used in this study.

For Landsat 8, image processing entails pre-processing and post-processing. For the pre-processing, the original unscaled digital numbers (DNs) were converted to scaled surface reflectance values using Equation (1)

ρ = (DN × 0.0000275) − 0.2(1)

where,

ρ is scaled surface reflectance, DN is pixel value in the Landsat band, 0.0000275 is reflectance scale factor and −0.2 is reflectance additive offset.

Cloud, cloud-shadow and other low-quality pixels were identified and removed using the QA_PIXEL quality-assurance band. The post-processing activities performed include deriving the various Vegetation Indices (VIs) from the scaled surface reflectance values and retrieving VIs values using the sample plot points. In this study, five (5) VIs were computed. Details of the VIs are summarized in Table 3.

These VIs were selected for this study because they reveal both the abundance of green vegetation cover and biomass [47]. The shapefiles of the sample plot points were imported into the VIs to extract their values.

Table 3. Vegetation indices and equations used.

For ALOS-2 PALSAR-2, the sample plot points shapefiles were imported on both the HH and HV polarized images to extract their digital values. The digital values extracted do not represent the radar backscatter coefficient (γ˚); therefore, they were converted to the radar backscatter coefficient in decibel units using Equation (2).

γ˚(dB) = 10log₁₀(DN²) − 83.0(2)

where,

γ˚ (dB) is the radar backscatter coefficient in decibels, DN is the digital number, and −83 is the calibration factor for ALOS-2 PALSAR-2.

Supervised image classification was performed with Sentinel-2 imagery to derive Land Use Land Cover (LULC) classes of the study area. The classification resulted in five (5) LULC classes of: closed forest, open forest, cocoa, other vegetation and settlement/bare surface. The study area was divided into grids of 5 km by 5 km after an exploratory analysis of the entire study area and the grids that were on the cocoa LULC class were selected. The cocoa LULC class was found to occupy a total area of 135329.87 ha (52.63%) of the study area. Using a sample intensity of 0.003%, 40 sample plots were generated, and they were uniformly distributed over the cocoa farms.

The number of cocoa trees enumerated in the 40 sample plots totaled 4367 trees. The parameter measured in the field for the cocoa trees was Diameter at Breast Height (DBH); thus, diametre measured at 1.3 cm from the ground. Table 4 displays the descriptive statistics of the cocoa trees across all sample plots.

Table 4. Descriptive statistics of the sample plots’ cocoa trees.

Allometric equation developed by [48] (Equation (3)) was used to calculate the AGB of cocoa trees in the sample plots

AGB = 0.7217ρ(D²)^0.921(3)

where,

AGB is aboveground biomass for cocoa tree (kg), D is the measured cocoa tree diameter at breast height (cm), and ρ is cocoa wood density, which is 0.4 g/cm³. This model was most appropriate, as it was developed to estimate AGB for cocoa plantations in Ghana. Biomass estimates from local site-specific equations are considered accurate in forestry and plantation applications [49].

The descriptive statistics of the AGB (Mg/ha) for all the sample plots are shown in Table 5.

Table 5. Descriptive statistics of the AGB (Mg/ha) for the sample plots.

Different models were developed, namely: simple linear model (Equation (4)), power model (Equation (5)), and exponential model (Equation (6)). The predictive performance of each model was evaluated based on its coefficient of determination (R²) (Equation (7)) and root mean squared error (RMSE) (Equation (8)). The chosen model for AGB estimation was the model with the highest R² and the lowest RMSE.

Multi-linear regression (MLR) (Equation (9)) was performed using the parameters of the best model for both Landsat 8 and ALOS-2 PALSAR-2 as the independent variables and their corresponding measured AGB as the dependent variable. Validation of the MLR model was carried out by assessing the coefficient of determination (R²) and the root mean squared error (RMSE). To obtain a more reliable and robust estimate of model predictive performance, a repeated 10-fold cross-validation procedure was performed over five independent repetitions. The mean R² and mean RMSE and their associated uncertainties were calculated to test whether the model transfer across the study area. Regression diagnostics were also conducted to assess whether the assumptions underlying the multiple linear regression model were reasonably satisfied. Regression diagnostics performed include: residual behaviour, influential observations and correlation between the satellite parameters. Residual behaviour was evaluated using residual-versus-fitted plots and normal Q-Q plots. The Shapiro-Wilk test was used to assess the distribution of residuals. Influential observations were evaluated to identify data points that have unusually large effect on the fitted multiple-linear-regression model using Cook’s distance and leverage test. The Pearson correlation (r) was used to evaluate the association between the two satellite parameters, while the variance inflation factor (VIF) was calculated to quantify the extent of multicollinearity among the predictors prior to fitting the multiple-linear-regression model.

Simple Linear Model: AGB = β₁X + β₀ (4)

where,

AGB is aboveground biomass (dependent variable), X is the independent variable, β₁ is the model coefficient for X, and β₀ is the intercept.

Power Model: AGB = aX^b (5)

where a is a non-zero coefficient, a ≠ 0, and b is a real number.

Exponential Model: AGB = ae^bx (6)

where a is a non-zero coefficient, a ≠ 0, and b is a real number.

e = exponential constant = 2.7182818

where y i , y ^ i represent the measured and predicted values, respectively, and N is the sample size.

Multi-Linear Regression: AGB = β₀ + β₁X₁ + β₂X₂ (9)

where,

AGB is aboveground biomass, X₁ is vegetation index, X₂ is backscatter coefficient, β₀ is the intercept, β₁ is the model coefficient for X₁ and β₂ is the model coefficient for X₂.

The study area was divided into grids with each grid cell of dimension 2 km × 1 km after exploratory analysis, which yielded 1273 grids and the grids centre coordinates were extracted. The difference vegetation index (DVI) model of Landsat 8 and the HV model of ALOS-2 PALSAR-2 were the best models using R² and RMSE as validation metrics. The extracted plot points shapefiles were imported onto the DVI raster file to extract their DVI values as well as those of HV of ALOS-2 PALSAR-2 to extract their DN values. The DN values were converted to radar backscatter coefficients in decibels. A multilinear regression model (Equation (10)) was used to calculate the predicted AGB for all 1273 grids.

AGB (Mg/ha) = 6.97 * 10⁻⁴DVI + 3.56HV + 74.88(10)

Geostatistics interpolation techniques using universal kriging (UK), ordinary kriging (OK), inverse distance weighting (IDW), and radial basis function (RBF) were tested, and the best method was used to develop AGB map of cocoa plantations in the study area. Forty (40) observations were used to validate UK, OK, IDW, and RBF interpolation methods. Efficiency-based and error-based metrics were used to assess the performance of the interpolation methods. The efficiency-based metrics used in this research include the R² (Equation (7)), the Index of Agreement (I_A) (Equation (11)), and P-values.

where y i , y ^ i and y ¯ i represent the measured, predicted, and mean AGB, respectively, whereas n is the sample size.

Error-based metrics considered include RMSE (Equation (8)) and Mean Absolute Error (MAE) (Equation (12)).

where y i , y ^ i represent the measured and predicted AGB, respectively, whereas n is the sample size.

Fifteen (15) models were developed: simple linear regression, power, and exponential models with their R² and RMSE (Mg/ha) as the evaluation metrics. The output models with their R² and RMSE (Mg/ha) are shown in Table 6.

Table 6. Models of AGB and VIs of Landsat 8.

From Table 6, difference vegetation index (DVI) using a linear model (Equation (13)) gives the highest predictive accuracy with R² (0.79) and RMSE (0.97 Mg/ha), and EVI gives the lowest accuracy performance with R² (0.43) and RMSE (1.57 Mg/ha) using an exponential model. From the best model, 79% of the estimated AGB was explained by the observed AGB.

AGB = 0.00115DVI + 27.6(13)

Six (6) models were developed: simple linear regression, power, and exponential models using measured AGB with HV and HH backscatter coefficients. The R² and RMSE (Mg/ha) were used as performance metrics, and the output models are presented in Table 7.

Table 7. Models of AGB with backscatter coefficients of HV and HH.

From Table 7, HV using linear model (Equation (14)) gives the highest accuracy of R² (0.63) and RMSE (1.29 Mg/ha) and HH gives the least accuracy with R² (0.04) and RMSE (1.85 Mg/ha) using the exponential model. From the best model, about 63% of the estimated AGB was explained by the observed AGB.

AGB = 6.17HV + 114.28(14)

The Multi Linear Regression (MLR) model using DVI and HV is shown in Equation (15).

AGB (Mg/ha) = 6.97 * 10⁻⁴DVI + 3.56HV + 74.88(15)

where,

AGB = predicted aboveground biomass, DVI = difference vegetation index of Landsat 8, and HV = HV backscatter coefficient of ALOS-2 PALSAR-2.

The model produced: R² = 0.83, RMSE = 0.96 Mg/ha. Thus, 83.0% of the variation in measured AGB was explained jointly by DVI and HV in the fitted model.

The repeated 10-fold cross-validation process with five repetitions showed that the AGB model had very good and consistent predictions in validation. The mean validation R² was 0.81 ± 0.006, showing that 81% of the variation in the observed AGB was explained by the model in validation, and the corresponding mean validation RMSE was 0.99 ± 0.015 Mg/ha. This RMSE indicates low prediction error in AGB. The little variation in R² and RMSE for the repeated cross-validation also shows consistent model performance. The above-mentioned results show that the model had good predictive accuracy and robust validation performance for estimating AGB.

The regression diagnostics results demonstrated strong relationships between measured AGB and both remotely sensed parameters. The DVI exhibited a strong positive relationship with AGB (r = 0.83); this indicates that plots with greater DVI values generally had greater measured biomass. The HV showed an even stronger relationship with AGB, but the relationship was negative (r = −0.90); thus, increasing HV values were associated with decreasing AGB. The two predictors were also strongly negatively correlated (r = −0.82); the negative correlation means that higher DVI values tend to occur with lower HV values. The variance inflation factor (VIF) for both DVI and HV was approximately 3.07. Although DVI and HV were strongly correlated (r = −0.82), the VIF values were below commonly used thresholds of 5 to 10. Therefore, the model did not exhibit severe multicollinearity according to the VIF criterion.

Residual-versus-fitted plot (Figure 2Figure 2) was examined to assess linearity and homoscedasticity, while Q-Q plot (Figure 3Figure 3) was used to assess the approximate normality of residuals. Shapiro-Wilk test gave result of W = 0.986, which indicates that there is insufficient evidence to reject normality of the residuals.

Figure 2. Residuals vrs fitted plot.

Figure 3. Normal Quantile-Quantile(Q-Q) plot.

From Figure 2Figure 2, the residuals are evenly spread around zero with no systematic curvature or changes in distribution across fitted AGB values, suggesting that the linear model seems to be appropriate for the relationship between the satellite data-derived predictors and the AGB.

From Figure 3Figure 3, the normal Q-Q plot indicated that the model residuals were approximately normally distributed, as most observations closely followed the theoretical normal distribution line, with only minor deviations at the tails.

The influence diagnostics (Figure 4Figure 4 and Figure 5Figure 5) indicated that the most extreme observations were observation 3 and observation 14. Observation 14 had a Cook’s distance of 0.154 and a leverage of 0.063, while observation 3 had the largest value of Cook’s distance (0.164) and the largest value of leverage (0.161). The maximum Cook’s distance of 0.164 was well below the conventional threshold of 1.0, indicating that no individual observation exerted extreme influence on the fitted multiple-linear-regression model. Although observations 3 and 14 were flagged for diagnostic screening based on commonly used influence and leverage criteria, they were not excluded because influence does not necessarily indicate error measurements. The observations were therefore retained because they may represent genuine field measurements in aboveground biomass and/or the associated satellite-derived DVI and HV measurements.

Figure 4. Cook’s distance observation influence.

Figure 5. Leverage observation influence.

Table 8 presents the best model of Landsat 8 and ALOS-2 PALSAR-2 as well as the MLR model with their R² and RMSE.

Table 8. Results of the best models of Landsat 8, ALOS-2 PALSAR-2 and MLR model.

Results from Table 8 showed that the MLR model, AGB = 6.97 * 10⁻⁴DVI + 3.56HV + 74.88, produced the highest performance (R² = 0.83, RMSE = 0.96 Mg/ha); hence, this model was used to predict AGB of cocoa plantations for the study area.

Combining DVI and HV using multi linear regression produced R² of 0.83 and RMSE of 0.96 Mg/ha as presented in Table 8. This shows that combining Landsat 8 and ALOS-2 PALSAR-2 parameters improved AGB estimates. This result is in line with the findings of research conducted by [17], where they pointed out that combining Landsat and SAR images can increase the accuracy of estimating AGB. In this study, Landsat 8 data could only be used to estimate cocoa AGB with moderate accuracy, whereas ALOS-2 PALSAR-2 data alone would produce poor AGB estimates for cocoa AGB. Integration of Landsat 8 data and ALOS-2 PALSAR-2 produced the highest AGB estimation; this shows that combining images from different sensors improves AGB estimation.

Table 9 displays the performances of the UK, OK, IDW, and RBF interpolation methods.

Table 9. Performances of the interpolation methods.

Quantitative comparisons of these four interpolation methods, UK, OK, IDW, and RBF, are based on their efficiencies (R², I_A, P-value) and their errors (RMSE and MAE) associated with their predictions. Selection of the best interpolation method is based on the highest R², the highest I_A, the lowest P-value, and the smallest error values. The R² ranged from 0.67 to 0.86, with the UK having the highest value of 0.86 and the lowest, 0.67, obtained by RBF. The R² performance of OK is 0.85, which is very close to the UK. The I_A has a minimum value of 0.79 for RBF and a maximum of 0.89 for UK. The lowest P-value of 2.20 × 10⁻¹⁶ is for the UK and the highest value of 1.18 × 10⁻¹⁰ is for RBF.

The RMSE ranged from 0.71 to 1.05 and MAE from 0.59 to 0.82, with UK and RBF obtaining the lowest and highest errors, respectively. In all aspects of the comparison, the performance of OK is close to UK (Table 9). The best interpolation method based on R², I_A, P-value, RMSE, and MAE is UK, followed by OK, IDW and the least is RBF. The UK interpolation method was used to produce the final AGB map with total AGB in the range (4973833.80 - 5240128.92) Mg for cocoa plantations in the study area.

Universal kriging was used to model the AGB with satellite-derived predictors and the residual spatial component. The trend component was specified as a multiple linear regression of AGB on DVI and HV, expressed as AGB(s) = β₀ + β₁DVI(s) + β₂HV(s) + ε(s), where ε(s) represents spatial residual component. Data set of 40 observations was used in fitting the trend component; the fitted trend equation was AGB = 74.88 + 6.97 * 10⁻⁴DVI + 3.56HV, with R² of 0.83. The residual semi variogram estimated from pairwise distances between observations and fitted using spherical, exponential and Gaussian models. The models were assessed using the residual sum of squared (RSS) differences and the model with the least RSS was selected. Model comparison based on the RSS differences identified the Gaussian model as the best-fitting candidate, although its advantage over the spherical model was small (Table 10). The fitted variogram indicated a relatively large nugget term and weak partial sill, suggesting limited residual spatial dependence within the sampled area. Leave-one-out cross validation was used to evaluate the predictive performance of the model, whereby each observation was withheld sequentially and predicted from the remaining observations. The resulting cross-validated RMSE was 0.98 Mg/ha, MAE was 0.79 Mg/ha, and cross-validated R² was 0.81. These results indicate good predictive performance, while the weak residual spatial structure suggests that most of the predictive information was provided by the DVI and HV trend component.

Table 10. Model statistics.

Equation (15), AGB = 6.97 * 10⁻⁴DVI + 3.56HV + 74.88, was used to predict AGB for 1273 plots and to develop a map of AGB for cocoa plantations in the study area (Figure 6Figure 6). The AGB estimates ranged between 30.4 and 42.2 Mg/ha; the estimated AGB range is a little lower than the field AGB (Table 5).

Figure 6. AGB distribution map of cocoa plantations in Juaboso and Bia West Districts, Ghana.