Stand-level MCM (non-sampling & sampling errors)

In each empirical study, we ran 10000 iterations. The resulting differences in the approximations of MCM with the direct estimation were less than 0.1% when the IPCC recommendation is 1% (IPCC, 2006). This implies that the results obtained with the MCM were acceptable. The estimated RSE was 7.8, 6.0 and 3.0%, for the first, second and third empirical studies. Even when the empirical studies were not conducted in the same study area, the RSE show the effect of the sample size (Cochran, 1977) of 10, 47 and over 1600, respectively. The RSE of the third study is comparable to the RSE of 3.3% reported in the MNFI for temperate forest (CONAFOR, 2017a).

Using the MCM, the largest contribution to total uncertainty (uW), for the three empirical studies was the SE with values over 98.7%. Phillips et al. (2000) reported the SE as the most important contribution in volume estimates in South-eastern NFI USA, with over 89% of the uW. Similar results have been reported by Holdaway et al. (2014) and McRoberts & Westfall (2016) in

temperate forest carbon estimation, but do not report the contribution percentage. In contrast, Chave et al. (2004) in a rainforest found a contribution of about 50% of the SE to the uW. This indicates that the number of trees sampled in our studies is large enough so that the major source of error is attributed to sampling (McRoberts & Westfall, 2016; Phillips et al., 2000). According to McRoberts

& Westfall (2016), with a mean density of 23 trees in 400 m² plot (575 trees ha^-1), the uMes are negligible comparing to the SE. Our results confirm this last statement with a mean value of 20 trees in a 400 m² plot.

When comparing the results of uNS in the MCM and the GUM Method, in the first empirical study, a slight overestimation of the GUM Method was found. Using the same scenarios (NDn and NDnC) and comparing at plot-level the mean error estimate, resulting in an overestimation of 2% of the GUM Method (p<0.01, Tables VIII-14 and VIII-16 in Appendix IV). Assessments in

instrumentation, and material quality controls, report a range of 8 - 21% of overestimate of GUM Method results (Mahmoud & Hegazy, 2017; Sana Sediva et al., 2015; Sona Sediva & Havlikova, 2013). However, when we applied the best-fit distribution with the MCM (scenarios MCBD &

MCBDC) the uW per plot was not significantly different from the GUM Method results (scenarios NDn and NDnC) (p≥0.614, Table VIII-16 in Appendix IV). Farrance & Frenkel (2014) had similar results with no difference between these two methods, assuming independence in the variables used for the error propagation.

In the second empirical study, it was observed that the uNS decreased in proportion more than the SE, for all the scenarios evaluated when the sample size increased from 11 to 47 plots. This is evident from Caliper+Blume-Leiss (CBmod scenario) results, in which the uNS of the 11 plots equaled 0.4% of the uW, while in 47 plots was 0.1%. This behavior is explained due to the GUM Method used in the 11 plots, overestimate the MCM results in uW for the 47 plots, and according to Cochran (1977) & Taylor (1997), the SE and uNS decrease when sample size increase.

The order of the contributions to the uW, of the scenarios used in the second study, were BD<mod<BDC. The scenario mod did not have significant differences in comparison with the measured errors, and mod includes the heteroscedasticity of the measurement errors related to the size of the tree. Then, the other two scenarios underestimated (BD) and overestimated (BDC) the measurement errors.

In the second study, the contribution obtained with the use of errors made by students (Exp and Nexp) stands out since these were the only scenarios that increased the total RSE from 5.0 to 5.04%.

The Exp and Nexp scenarios represent a six-fold increase in DBH measurement errors, and a 4.5-fold increase in TH, compared to the estimated errors in repeated measurements. However, when these measurement errors are applied in the third empirical study, they are negligible with the large sample size (NFI scale) as stated by McRoberts & Westfall (2016).

V.3.5.1 MCM per source contribution

The results of the MCM in the first empirical study maintained the order of contribution from the sources of uncertainty, where SE>uAM>uTH>uDBH. The percentage of contributions per source was 98.746>1.205>0.029>0.028 and is similar to the estimated with the GUM Method.

In the second empirical study, The sources of uncertainty had a contribution to uW in the following order SE>uTH>uDBH>uAM>uρ(DBH,TH) (see Table VIII-41, Appendix V). The contribution for Caliper+Blume-Leiss measurements with mod scenario was 99.9>0.08>0.02>0.0002>0.00002, while with Tape+Vertex measurements was 99.95>0.036>0.014>0.0002>0.00001.

In the third empirical study (MNFI), the order of the contribution to the total uncertainty (uW) was like the one obtained in the first study, but also included the uncertainty of the plot design (uPlot).

The contribution to the uW was related to the scenario of measurement error estimation. The scenarios BD (best-fitted distribution) and Exp (experimented students), do not consider the size of the trees and, therefore, the contribution to the final error depends on the number of trees. In contrast, the BDC scenario (best-fitted distribution by class) estimated the contributions according to the size of the tree, furthermore, this scenario did not differ significantly from the other scenarios.

Thus, the BDC scenario does not underestimate (as BD) or overestimate (as Exp) the measurement errors in the estimation of AGB. In the BDC scenario, the order of contribution to the uW was SE>uAM>uTH≥uPlot≥uDBH. The percentage of contributions per source in MNFI of Durango was 99.41>0.53>0.03≥0.02≥0.02. The contributions from uTH, uPlot and uDBH sources were small (≥0.7%) and did not differ significantly from one another. The uPlot is uncertainty related to the shape and size of the plot, in this study its contribution was equal for the given scenarios. The contributions of uTH were larger than uDBH as the results in the first study, with no significant difference.

Using information from FIA in the South-eastern USA, Phillips et al., (2000) estimated the contributions to total carbon estimation from four sources of uncertainty. The order of the contributions is like that observed in the first and third empirical studies of this thesis, being SE>uAM>uTH>uDBH. The reported contribution percentages were 98.7>1.2>0.1>0.0. On the other hand, Holdaway et al. (2014), report a different order of contribution being SE>uMes>uAM where they estimate a larger contribution from uMes compared to uAM. The percentage

contributions were 98.9>1.0>0.09 and, within the measurement errors, the uTH were larger than the uDBH. This last is like our results in the second empirical study.

Our thesis results include the contributions of measurement, prediction, plot design and sampling uncertainties in the AGB estimation with the MNFI data for the state of Durango, Mexico. The uncertainty estimates of this thesis were made under the IPCC guidelines established for Tier 2 (IPCC, 2006), which imply the reporting of transparent, coherent, compatible, exhaustive and

precise estimates (Morfín Ríos et al., 2015). Since AGB estimation is a basic input for the estimation of GHG emissions (CONAFOR, 2014b; Gibbs et al., 2007), it is proposed that the approach used here could be considered in the development of MRV systems under REDD+ in Durango, Mexico. The MRV system in State-level (Durango strategy is under construction) aims to monitor, verify, and adapt national REDD+ strategies, incorporating practices best suited to regional characteristics (CONAFOR, 2017b). The State-level MRV system takes on greater importance since it is requested in reports of environmental management in Mexico, referring to climate change mitigation (SEMARNAT & INECC, 2017), forest carbon dynamics (Red Mex-SMIC, 2015), and including the Law of Climate Change (Chamber of Deputies, 2018b).

V.3.5.2 Uncertainty in strata and substrata of MNFI

Estimating AGB by vegetation type is a recommended method to stratify the forest for the AGB uncertainty report, according to the IPCC (IPCC, 2006). Stratification is recommended to reduce variability in estimates; however, the results of our study show the opposite trend. While in the temperate forest the RSE was 3.0%, a range from 3.3 to 10.63% of RSE was estimated in the strata and from 3.6 to 23.5% in substrata. The RSE estimates for wood volume in Durango, with

information of the MNFI (2009-2014), have an RSE range from 6.97 to 29.71% for temperate forest strata (CONAFOR, 2014a). In our study, the highest RSE (23.5%) was estimated in the substratum of secondary vegetation in the conifer forest (SCFs). This substratum has the smallest number of sampled plots (n=60). In contrast, the lowest RSE (3.6%) was in the primary vegetation of mixed forest (SMFp). This is the substratum with the largest number of sampled sites (n≥1261). The increase in measurement errors (scenarios) did not change the contribution of SE and uNS to the uW, since both estimates depend on the sample size (Cochran, 1977; Taylor, 1997). However, by stratifying, the contribution of the SE was reduced gradually; while in the temperate forest the SE was ≥99.29%, at the stratum level it was ≥97.49% and at the substratum level ≥96.39%. The scenarios were consistent in estimating uncertainties as in the temperate forest, with an

underestimation of uNS by the scenario BD (best-fitted distribution) and an overestimation of Exp (experimented students), compared to BDC (best-fitted distribution by class).

The number of clusters changed in the strata and substrata of the temperate forest and were not consistent in the periods studied. The classification of vegetation is fundamental information where the field crew applies the NFI field manual (CONAFOR, 2017a; Tomppo et al., 2010). Since classification is qualitative, as well as species identification, Morrison (2016) suggest that experience and training is required for the field crew. The difference is that classification can be only made in fieldwork and trees can be identified in the herbarium, if not possible in the fieldwork (CONAFOR, 2009b; Ricker et al., 2015). The professional profile or experience of the field crew in MNFI is not defined in the field manual. We suggest applying the findings of Tomppo et al. (2010) about the strategies used in the NFI field manuals of 37 countries to ensure the quality of MNFI information. Among these strategies are, the profile of the field crew (forest engineer or technician), training and training evaluation, cross-checking at fieldwork, a random check of the field crew, correction and validation of fieldwork (Tomppo et al., 2010).