Basal area and AGB in the estimation

Using the stepwise regression models and applying the results to the Landsat imagery, the basal area (G) and AGB (W) were estimated in the temperate forest of Durango, Mexico. Then, the statistics (mean and standard deviation) for the variable estimates of the temperate forest (TF) and per-vegetation stratum were calculated (Table IV-23). In this table, the total area where Landsat imagery information was properly acquired and applied to the models was included (non-temperate forests and clouds were excluded). In the bold character rows, the results of applying the stepwise model in TF (n=1662 in 2007 and n=1635 in 2013) are shown for both response variables. For the W estimate, the calculation of total storage was included (Tg). Similarly, G and W statistics for each vegetation stratum were estimated (SCF, SMF, and SOF). With the stratum estimates, a single layer of temperate forest merged was made (TFM).

Time Area Basal area (G) Aboveground biomass (W)

𝜇̂ 𝜎̂ RMSE 𝜇̂ 𝜎̂ RMSE storage

2007 ha m² ha^-1 Mg ha^-1 Tg

TF (n=1662) 5152172.76 12.58 5.33 4.28 58.56 31.43 24.50 301.70 TFM (n=1662) 5152172.76 12.16 5.53 - - 55.36 31.28 - - 285.25 SCF (n=292) 2356073.28 13.72 5.59 4.33 62.11 31.27 24.21 146.34 SMF (n=1033) 1906699.05 12.32 5.41 4.23 56.57 32.73 24.71 107.86 SOF (n=337) 889400.43 7.70 2.35 3.33 34.90 15.38 17.05 31.04

2013

TF (n=1635) 5104018.71 12.42 5.61 4.11 57.03 32.51 23.93 291.09 TFM (n=1635) 5104018.71 11.99 5.83 - - 53.57 32.01 - - 273.42 SCF (n=216) 2338481.43 14.03 6.16 4.24 61.64 33.97 23.20 144.15 SMF (n=1156) 1883999.43 11.65 5.12 4.19 52.18 31.59 25.18 98.31 SOF (n=263) 880943.85 7.33 2.68 3.06 35.10 14.88 16.06 30.92

𝜇̂= estimated mean, 𝜎̂=estimated standard deviation RMSE=root mean square error

Table IV-23. Basal area (G) and AGB (W), estimate for temperate forest in Durango, Mexico.

Basal area models estimated values less than zero for 0.17% of the area in 2007 and 0.27% of the area in 2013. Moreover, from applying the AGB models, the area with values less than zero was 1.90% in 2007 and 1.78% in 2013. Values less than zero were estimated because the range of predictor variables used (PV) to fit the regression models has not covered all the range of PV values in the study area, previously referred to as gaps (Section I.2.2.2.2). In this study, it was the above-mentioned percentage of area for basal area and AGB. These values less than zero were replaced by

0.1 (m² ha^-1/Mg ha^-1) with no modification to the estimates of 𝜇̂ and 𝜎̂. Los valores menores a ceros se obtuvieron

IV.4.3.1 Basal area (G) estimates for Durango temperate forest

In 2007, the G estimate using the TF model (𝜇̂=12.58 m² ha^-1) was larger than the TFM estimate (𝜇̂=12.16 m² ha^-1). In contrast, 𝜎̂ was larger in TFM (5.33 m² ha^-1). Estimates of G for 2013 were like in 2007, with a larger 𝜇̂ in TF (12.42 m² ha^-1) than in TFM (11.99 m² ha^-1). The 𝜎̂ in 2013 was smaller in TF than in TFM (5.61 and 5.83 m² ha^-1).

The 𝜇̂ G values across the different vegetation strata were largest for SMF in 2007, with a value of 12.32 m² ha^-1. However, in 2013, the SCF and SOF estimates were the largest (14.03 and 7.33 m² ha

-1). Furthermore, the 𝜎̂ was smaller in 2007 for SCF and SOF (5.59 and 2.35 m² ha^-1) but was smaller for SMF in 2013 (5.12 m² ha^-1).

IV.4.3.2 AGB (W) estimates for the Durango temperate forests

The 2007 𝜇̂ W estimates were larger in TF compared to TFM (58.56>55.36 Mgha^-1). Therefore, storage was also larger for TF at 301.70 Tg (Tg=10⁶ Mg). The 𝜎̂ was smaller in TFM, with a value of 31.28 Mgha^-1. The 2013 trends were the same, in which TF had a 𝜇̂ of 57.03 Mgha^-1, 𝜎̂ of 32.51 Mgha^-1 (CV=0.6), and storage of 291.09 Tg.

For the vegetation strata in 2007, the 𝜇̂ W estimates were larger in the SCF and SMF (62.11 and 56.57 Mg ha^-1), while the larger SOF estimate occurred in 2013 (35.10 Mg ha^-1). The 𝜎̂ was smaller in 2007 for SCF, with 31.27 Mg ha^-1. However, for SOF and SMF, it was smaller in 2013 (14.88 and 31.59 Mg ha^-1).

IV.4.3.3 Basal area and AGB maps of Durango, Mexico

Using the models per stratum described above, the basal area (G) and AGB (W) maps were

produced for the State of Durango. The results, presented in Figure IV-13, show the G estimated by the stepwise regression models using Landsat satellite imagery and the INEGI vegetation series.

The values in the figure for the Landsat 5 imagery (2007) range from 0 to 35.14 Mg ha^-1 and from 0 to 35.49 Mg ha^-1 for the Landsat 8 imagery (2013). Surfaces with the presence of clouds were excluded in the Landsat 8 images (right), located in the far west of the state in two blank areas. This surface spanned 48,154 ha without information in 2013. However, the same land area was able to be analyzed in 2007 and averaged a 15.43 m² ha^-1 basal area.

In 2007, 88.6% of the evaluated area in the temperate forest (TF) registered less than 20 m² ha^-1 of G. The class with the largest area was (10 to 15] m² ha^-1, comprising 30.5% of the TF. Moreover, with the information from 2013, 87.1% of the surface recorded less than 20 m² ha^-1. The largest surface class in this year was (5 to 10 cm] m² ha^-1, covering 32.2 % of the TF in Durango (see Table VIII-43, Appendix VIII).

MNFI (2004-2009) and Landsat 5 (2007) MNFI (2009-2014) and Landsat 8 (2013) Figure IV–13. Basal area in the temperate forest of Durango, Mexico, with information from the MNFI and Landsat imagery.

MNFI (2004-2009) and Landsat 5 (2007) MNFI (2009-2014) and Landsat 8 (2013) Figure IV–14. AGB in the temperate forest of Durango, Mexico, with information from the MNFI and Landsat imagery.

Figure IV-14 shows the distribution of the W in the temperate forest of Durango. This map was produced by applying the stepwise regression models of W to Landsat imagery. The W range in 2007 was 0 to 199.48 Mg ha^-1 and in 2013 was 0 to 201.79 Mg ha^-1. According to the 2007

estimates, 77.5% of W was contained in classes less than 100 Mg ha^-1, which represented 89.9% of the temperate forest area. Similarly, in 2013, the two classes less than 100 Mg ha^-1 covered 89.6%

of the area, with an estimate of 76.03% of the AGB in TF. Thus, classes ≥100 Mgha^-1 increased surface in 2013 (see Table VIII-44, Appendix VIII). For the area covered by clouds in 2013, a storage of 3.8 Tg in 2007 was calculated.

IV.4.3.4 Comparison of model-based and sampling-based estimations

The estimates of linear regression models (Table IV-23) were compared with the estimates from the sampling-based method made in the MNFI (Section IV.3 of this study). In this case, the estimators (𝜇̂, 𝜎̂, SE, RE) calculated for both methods are available in Table IV-24. In this table, the calculation of AGB storage (Tg) and the uncertainty in estimating AGB storage (uTg) using the 𝜇̂ and SE estimators were included. Calculations are given for the total reported area of the temperate forest (TF) and the per-strata vegetation in Durango to estimate total storage using both estimation methods. Estimates by stratum were summed up and reported as temperate forest merged (TFM).

Time area Basal area (G) Aboveground biomass (W)

Table IV-24. Estimates of basal area (G) and AGB (W) using methods based on forest inventory sampling and regression models, applied in the temperate forests of Durango, Mexico.

The results from both methods in the temperate forest (TF) showed that in the first study period the sampling-based value of 𝜇̂ was larger than the model-based value (bold rows in Table IV-24). This observation was valid for the two variables and both study periods. It was also found that the sampling-based method produced larger estimates of 𝜇̂ in the second period of the MNFI, while the opposite result was achieved with the model-based method.

At the stratum level, was observed similar behavior as in TF for most strata. Nevertheless, when the sampling-based method was applied in the mixed forest stratum (SMF), the 𝜇̂ value was smaller in the second period for both variables. On the other hand, the model-based method in G estimation calculated an increase in the estimation in the second period for the conifer forest stratum (SCF, 14.03>13.72 m² ha^-1). This result was also observed in the oak forest stratum (SOF) for W (34.90<35.10 Mg ha^-1).

SOF estimates were similar for both methods and for both variables, with ranges of 7.33 to 7.82 m² ha^-1 for G and 34.90 to 36.84 Mg ha^-1 for W. In the other two strata, the dominance alternated according to the estimation method. While SCF had the largest 𝜇̂ in the sampling-based method, SMF had the largest estimate in model-based method.

W storage behaved like the 𝜇̂ estimator. Thus, the largest storage from the sampling-based method came from the SMF, with values of 147.73 Tg for the first MNFI and 137.76 Tg for the second MNFI. Meanwhile, the largest storage in the model-based method was in the SCF.

Comparing the W stored in the TF (bold rows in Table IV-24) to the sum of W stored by stratum, an overestimation of the W in TF was observed. The sampling-based estimate from all sampled clusters of the TF was 13% larger than the sum of the estimates per vegetation stratum. Likewise, the overestimate of W in the model-based method was 6%.

In Figure IV-15, the storage values of AGB with information from the two estimation methods were plotted (sampling-based and model-based). This figure included the uncertainty confidence interval (CI95% -95% of probability-), using SE for the sampling-based and model-based method,

respectively.

SB=sampling-based method, MB=model-based method

Figure IV–15. AGB storage and uncertainty in AGB storage using information from two methods of estimation in the temperate forests of Durango, Mexico.

Figure IV-15 shows that AGB's estimates in temperate forest (TF) were higher than those observed for temperate forest merged (TFM). However, the confidence intervals of the two methods of AGB

0 50 100 150 200 250 300 350

SCF SMF SOF TFM TF

W(Mg ha-1)

SB MNFI 04-09 SB MNFI 09-14 MB MNFI 04-09 MB MNFI 09-14

estimation showed overlap in the TFM estimates; this overlap was not observed in the results for TF. This figure shows also the AGB overestimate in the results of the model-based method for the conifer forest stratum (SCF), as well as the underestimate of the same method for the mixed forest stratum (SMF), compared to the sampling-based estimations. In the figure is shown the difference in CI95% by the model-based method (±2.44 to ±11.57 Mg ha^-1) compared to the CI95% by the sampling-based method (±3.72 to ±27.61 Mg ha^-1). These differences in uncertainty estimation was used to calculate the relative efficiency (RE) for the two periods of study. In TF the RE for 2004-2009 was 5.1 and decreased to 4.7 in the second period. This reduction of RE was also observed in SMF (6.4 to 5.4). However, in SCF and oak forest stratum (SOF) an increase in RE was observed (3.7 to 5.9 in SCF, 2.3 to 2.8 in SOF).