The experiment was conducted at three different locations Buture, Gembe and Degalu all in Mana district of Jimma zone, Oromia Regional state, South Western Ethiopia (7˚46'N, 36˚0'E). This area receives adequate amount of rainfall with annual average rainfall of 1595 mm per annum. In this area, the driest season lasts between December and January. The maximum and minimum air temperature is 25.9˚C and 11.2˚C, respectively with the coldest month being December [23] . The experimental areas have the potential for coffee production and each location has different altitudes. The description of the locations in terms of altitude, latitude and longitude are as shown in (Table 1).

Eight coffee Arabica genotypes have already been established since June 01, 2012 at three different locations and during this experiment, these eight genotypes (74-1, 75-227, 74-54, 74-112, 74-140, 74-148, 74-158 and 74-165) were used in May 2016. Twenty five plants (in five rows having five plants in each row) of each genotype were planted in each plot with plot size measuring 10 m × 10 m in 2 m × 2 m spacing giving a density of 2500 plants per hectare and planting depth of 0.6 m × 0.6 m. Crop management practices were similar for all locations.

The treatments were arranged in a randomized complete block design (RCBD) with three replications as indicated in the layout below. The treatments consist of eight Coffea arabica genotypes with three altitudes.

For model development, five individual plants were randomly taken for each coffee genotype at each location. For each individual plant, five twigs were sampled using cutting scissors. Then after, ten leaves per plants for each genotype at each location were collected using method of [5] . Fifty leaves were collected for each genotype per location for model development (five plants × ten leaves).

For model validation, four individual plants were randomly taken for each coffee genotype at each location. For each individual plant five twigs were sampled using cutting scissors; then after 10 leaves were cut per plant for each genotype. Forty leaves were collected for each genotype per location for model construction (four plants × ten leaves).

Totally, 1200 leaves (Fifty Leafs × eight Genotypes × three Locations) were used for model development and 960 leaves (Forty Leafs × eight Genotypes × three Locations) were used for model validation during leaf area measurements.

During measurement for model development and model validation, maximum leaf length from lamina tip to the point of petiole insertion along the midrib was measured using ruler with care. Leaf widths in centimeter at the widest point perpendicular to the midrib were measured for all leaves of the Coffea arabica genotypes using ruler [13] . We had to use leaf area meter for measuring leaf area but the leaf area meter currently available in JUCAM is not functional and even we did not find it elsewhere in the country for measuring leaf area. For this reason we used square meter to measure leaf area. Area of each leaf were measured by drawing each leaf on square paper and the squares in each leaf was counted and the number was multiplied with the area of the square to get the leaf area (cm²).

Four linear regression models, one power model and one logarithmic model were employed for model building for leaf area estimation. Leaf length (L) and leaf width (W) dimensions and LA were those variables consider in building models. The following models (Y = aL + b, Y = aW + b, Y = aLW + b, Y = aL + bW + c, Y = ax^b, Y = aLnx + b) linear, power and logarithmic models were used, respectively. Where: Y = Leaf area (cm²), L = Length (cm), W = Width (cm), a = Slope and b = intercept (cm²). All models were run for each genotype at three locations and the best model was selected based on Statistical criteria for model selection. Coefficient of determination (R²), standard error of estimates (SE) RMSE and CV were the Statistical criteria used for model selection method used by [24] . This criterion helps in evaluating the occurrence of bias and model precision and accuracy. The final model to estimate leaf area was selected based on the Statistical criteria for model selection. They are the combination of the highest R²and the lowest root mean square error (RMSE) and root mean square error (RMSE), lowest bias of linear regressed line between observed versus predicted values from the 1:1 line and lowest coefficient of variance (CV) were determined using the following formulas.

RMSE = ∑ i = 1 n ( Y i − Y o ) 2 / n (1)

Bias = ∑ ​ ( Y i − Y o ) n (2)

where “n” is the number of observations, “Yi” and “Yo” are the estimated and measured leaf area values of i^th observation. The RMSE tests the accuracy of the model which is defined as the extent to which predicted values approach a corresponding set of measured values. Beside this, coefficient of variation (CV) was also used to validate the models. CV was calculated from the following equation:

CV ( % ) = RMSE × 100 / x (3)

MSE = RMSE 1 / 2 (4)

where “x” is the mean observed values.

Equality of a set of regression models between each location for each genotype, were tested using ANCOVA (Analysis of Covariance). When no significant differences were found, data were pooled to construct a single regression. Since applying two dimensional measurements would introduce potential problems of collinearity, which would lead to poor precision in the estimates of corresponding regression coefficients, the variance inflation factor (VIF, Marquardt 1970) and the tolerance value (T, Gill 1986) cited in [25] were calculated to detect collinearity in two-dimensional models as follows:

VIF = 1 / ( 1 − r 2 ) (5)

T = 1 / VIF (6)

where: r is the correlation coefficient.

If the VIF value is higher than 10 or T value (tolerance value) smaller than 0.10, consequently one of them will be excluded from the model because the impact of collinearity on the estimates of the parameters cannot be neglected [2] [26] .

In order to validate the selected model, estimated LA was predicted using the developed model and the slopes of the regressions between observed LA and estimated LA were tested for their significant difference from the respective of the 1:1 correspondence line methods used by (Dent and Blackie, 1979 cited in [27] .

All the collected data were first tested for homogeneity using Tukey’s before being subjected to regression analysis and were analyzed with regression using SAS 9.3 Software. The differences in slopes and intercepts between models were tested using ANCOVA for testing whether two slopes and intercepts computed from two groups are significantly different.

Different prediction equations were obtained for estimating the LA of coffee Arabica involving two independent variables leaf length (L), and leaf width (W), and their product (L × W) were tested for estimating leaf area by using different equations. Among all tested linear regression models (Y = aL + b, Y = aW + b, Y = aLW + b, Y = aL + bW + c) equations using leaf length (L), and maximum leaf width (W), Y = aLW + b had strong relationships with LA and resulted in high coefficients of determination (R²) lowest standard error for all genotypes at all. For few of the genotypes, (74-140, 74-148 and 74-54 at Buture, 74-158 and 74-54 at Degalu and 74-148 at Gembe) Y = aL + bW + c had strong relationships with Leaf Area. However, this model was neglected because there was a problem of co-linearity between L and W (VIF value was higher than 10 or/and tolerance value (T value) smaller than 0.10). Therefore, for all locations and genotypes Y = aLW + b had the most predictive power than the rest models tested to estimate leaf area of Coffea arabica L. genotypes.

The models, power (Y = ax^b), logarithmic (Y = aLnx + b) and linear (Y = ax + b) models were tested. Among the three tested models (linear Y = ax + b) had the highest coefficients of determination R² and therefore, model was selected for all genotypes at all locations (Tables 2-4). However, a better fit was achieved using L * W without intercept (Y = a LW) than using L * W with intercept (Y = a LW + b) for all of the eight Coffea arabica genotypes tested (Tables 2-4).

Slopes of the models developed for each genotype at each location showed no significant difference (P > 0.05) among the genotypes (Table 5). Then the data were pooled and a single regression model was developed for each genotype at all locations (Table 6). Slopes of the models developed for each genotype at all location also showed no significant difference (P > 0.05) among the three locations.

Values followed by different letters within a column show significant differences at (p < 0.05).

All the leaf data from the eight genotypes at the three locations were pooled and a single regression model was developed for all genotypes (Table 6). Single regression model which was fitted to the combined data of all genotypes (LA = 0.6434LW) had the highest coefficient of determination (R²) and high precision (small SE) and Root mean square Error (RMSE) (Table 6). We found that the linear regression model (LA = 0.6434LW) best predicted the leaf area in respective of locations and genotypes of the eight Coffea arabica genotypes (Table 6). This finding was in agreement with other finds that developed a linear model for leaf area estimation in perennial crops [28] .

The relationship between measured LA and predicted LA using the general equation (LA = 0.6434LW) validated and had a good fit (Figure 1) for all the eight Coffea arabica genotypes. No significant difference (P > 0.01) was obtained between the slopes of the regressions between Measured Leaf Area (MLA) and Estimated Leaf Area (ELA) from the 1:1 relationship (Figure 1). The leaf area estimated by the model was strongly correlated (r = 0.99, P < 0.01, r = 0.98, P < 0.01, r = 0.99, P < 0.01, r = 0.98, P < 0.01, r = 0.99, P < 0.01, r = 0.99, P < 0.01, r = 0.98, P < 0.01, r = 0.98, P < 0.01) with the measured value of leaf area for 74-112, 74-165, 75-225, 74-54, 74-1, 74-140, 74-158 and 74-148 Coffea arabica genotypes respectively. The model overestimated the areas of 74-112 and 74-1 with 0.17% and 0.035%, respectively and underestimated the areas of 74-165, 75-225, 74-140, 74-158, 74-148 and 74-54 with 0.65%, 1.66%, 1.47%, 0.76%, 0.54% and 0.091%, respectively. The bias of estimated area from the measured area is also very small which ranges between (−0.44 to 0.06) (Figure 1) for all genotypes, showing the potential of estimating the leaf area. The findings of the present study were in agreement with many of the previous studies by Barros et al. (1973); cited in [7] for Coffea arabica (LA = 0.667LW); [21] for Coffea canephora Pierre ex Froehner var. Conilon LA = 0.6587 (LW) and LA = 0.6533 (LW); [22] , for (Coffea arabica L.) of the Castillo LA = LW * 0.6612). Many researchers also found similar results for other crops such as [29] for sweet cherry LA = 0.690LW; [30] , for Capsicum annuum L. LA = 0.587 (L × W); [28] for grapevine LA = 0.587(L × W).

The same product of linear dimensions were also successfully used to estimate leaf area, with good accuracy and excellent precision, in different agronomic species, such as [27] Kumar and Sharma (2010 and 2013) (LA = −3.44 + 0.729LW) for saffron (Salvia sclarea L.) and (Y = 0.333 + 0.603LW for Picrorhizakurroa, respectively, which depending on length multiplied by width (LW) as

independent variable gave more accurate estimation of leaf area compared to other models. Many other researchers also reported that leaf area can be estimated by linear measurement such as leaf width and leaf length in plants, such as [25] LA = 0.463 + 0.676WL Vernonia ferruginea; [12] (LA = 0.03 + 0.71LW for raspberry, LA = 1.72 + 0.69LW for redcurrant, LA = 0.90 + 0.70LW for blackberry, LA = 0.58 + 0.72LW for gooseberry, and LA = 0.54 + 0.68LW for high bush blueberry, [27] hazelnut; [31] for faba bean (Viciafaba L.) and [32] for eggplant for developing simple and non-destructive models for estimating plant leaf area by using simple linear regression measurement. Also [33] found that the best fitting equations for estimating leaf area of oleander was (LA = −22.562 + 21.209W) and (LA = −22.226 + 2.978L) with 𝑅² = 0.847 and 0.893 respectively.

On the contrary power models was found by [7] LA = 0.6626(LW)^1.0116 and [34] , LA = 0.803 (LW)^0.985 for Coffea arabica L and Jatropha curcas L respectively, which is not in agreement with this findings.