Table 2 Summary of methods used for crown biomass estimation in this study
From: Evaluation of sampling strategies to estimate crown biomass
Methods | Equations for total crown biomass | Selection probability | Inclusion probability |
|---|---|---|---|
Simple random sampling | |||
SRS | \( {\widehat{\tau}}_i=N{B}_i\left(\frac{1}{n}{\displaystyle \sum_{j=1}^n}{y}_{ij}\right) \) | \( {\left(\frac{1}{N{B}_i}\right)}^n \) | \( \frac{n}{N{B}_i} \) |
SRS-RAT | \( {\widehat{\tau}}_i=\frac{{\displaystyle {\sum}_{j=1}^n}{y}_{ij}}{{\displaystyle {\sum}_{j=1}^n}B{D}_{ij}^2}{\displaystyle \sum_{j=1}^{N{B}_i}}B{D}_{ij}^2 \) | \( {\left(\frac{1}{N{B}_i}\right)}^n \) | \( \frac{n}{N{B}_i} \) |
PPS | \( {\widehat{\tau}}_i={\displaystyle \sum_{j\in S}}\frac{y_{ij}}{\pi_{ij}^{PPS}} \) | \( {\pi}_{ij}=\frac{B{D}_{ij}^2}{{\displaystyle {\sum}_{j=1}^{NB}}B{D}_{ij}^2} \) | \( {\pi}_{ij}^{PPS}=1-{\left(1-{\pi}_{ij}\right)}^n \) |
Systematic sampling | |||
SYS | \( {\widehat{\tau}}_i=N{B}_i\left(\frac{1}{n}{\displaystyle \sum_{j=1}^n}{y}_{ij}\right) \) | \( \frac{n}{N{B}_i} \) | \( \frac{n}{N{B}_i} \) |
SYS-RAT | \( {\widehat{\tau}}_i=\frac{{\displaystyle {\sum}_{j=1}^n}{y}_{ij}}{{\displaystyle {\sum}_{j=1}^n}B{D}_{ij}^2}{\displaystyle \sum_{j=1}^{N{B}_i}}B{D}_{ij}^2 \) | \( \frac{n}{N{B}_i} \) | \( \frac{n}{N{B}_i} \) |
Stratified sampling | |||
STR | \( {\widehat{\tau}}_i={\displaystyle \sum_{h=1}^H}{\displaystyle \sum_{j=1}^{n_h}}\frac{N_{ih}}{n_h}{y}_{ijh} \) | \( \frac{B{D}_{ij}^2}{{\displaystyle {\sum}_{j=1}^{NB}}B{D}_{ij}^2} \) | \( \frac{n_h}{N_{ih}} \) |
STR-RAT | \( {\widehat{\tau}}_i=\frac{{\displaystyle {\sum}_{h=1}^H}{\displaystyle {\sum}_{j=1}^{n_h}}\frac{N_{ih}}{n_h}{y}_{ijh}}{{\displaystyle {\sum}_{h=1}^H}{\displaystyle {\sum}_{j=1}^{n_h}}\frac{N_{ih}}{n_h}B{D}_{ijh}^2} \) | \( \frac{B{D}_{ij}^2}{{\displaystyle {\sum}_{j=1}^{NB}}B{D}_{ij}^2} \) | \( \frac{n_h}{N_{ih}} \) |
STR-PPS | \( {\widehat{\tau}}_{i\left(STR-PPS\right)}={\displaystyle \sum_{h=1}^H}{\displaystyle \sum_{j\in {S}_h}}\frac{y_{ijh}}{\pi_{ijh}^{\left(STR-PPS\right)}} \) | \( \frac{B{D}_{ijh}^2}{{\displaystyle {\sum}_{j=1}^{N{B}_{ih}}}B{D}_{ijh}^2} \) | \( {\pi}_{ij}^{STR-PPS}=1-{\left(1-{\pi}_{ij}\right)}^n \) |