# Table 2 Data sources and sampling designs for REDD monitoring

Data sources Sampling design Estimation procedures for means and variances of the mean (from [15])
Field plots Simple random sampling $y ¯ = ∑ i = 1 n y i n ; v( y ¯ )= ∑ i = 1 n ( y i − y ¯ ) 2 n ( n − 1 )$
Systematic sampling
Field plots & full coverage remote sensing imagery Stratified sampling
Example: field plots and Spot satellite imagery
$y ¯ st = ∑ h = 1 L A h A ∑ i = 1 n h y hi n h$
$v ( y ¯ st ) = ∑ h = 1 L ( A h A ) 2 s h 2 n h$;
Regression estimators
Example: field plots and TerraSarX (radar)
$y ¯ lr = y ¯ + b( X ¯ − x ¯ )$
$v ( y ¯ lr ) ≈ ∑ i = 1 n [ ( y i − y ¯ ) − b ( x i − x ¯ ) ] 2 n(n − 2)$
Field plots & partial coverage remote sensing imagery 2-phase sampling for stratification (double sampling for stratification)
Example: field plots & aerial photography
$y ̄ ds = ∑ h = 1 L n h ′ n’ y ̄ h = ∑ h = 1 L w h y ̄ h$

where
$s h 2 = 1 n h ′ ∑ h = 1 L ( y h i - y ¯ h ) 2$
2-phase sampling with regression estimators
Example: field plots & LiDAR
$y ¯ lr = y ¯ + b( x ¯ ' − x ¯ )$
$v ( y ¯ l r ) = s y . x 2 [ 1 n + ( x ¯ ' − x ¯ ) 2 ∑ ( x ¯ ' − x ¯ ) 2 ] + s y 2 − s y . x 2 n ' − s y 2 N$
with $s y . x 2 = 1 n − 2 [ ∑ i = 1 n ( y i − y ¯ ) 2 − b 2 ∑ i = 1 n ( x i − x ¯ ) 2 ]$
1. Where:
2. yi = observation on field plot i; xi = observation in phase-1 sampling unit i; n = sample size, nh = sample size in stratum h; b = regression coefficient; N = population size; wh = weight of stratum h = Ah/A;
3. A = inventory area; Ah = area in stratum h, h = 1, ..., L; sh2 = variance of y in stratum h;