measurements has been used in the form of double 
sampling or two-phase sampling. The principles 
of two-phase sampling were introduced by Neyman 
(1938) and applied to forest inventory in con 
nection with remote sensing by Bickford (1932). 
Thereafter, designs have been described and app 
lications illustrated by many authors, e.g. 
Frayer (1979), LaBau and Winterberger (1988), 
Mattila (1985), Peng (1987), Poso (1972, 1988). 
Two-phase sampling is a sensible method if there 
is access to inexpensive auxiliary data. The 
first phase data does not necessarily have to be 
remote sensing data, but should be well corre 
lated to the ground truth data. If several aux 
iliary data sources, possibly from many diffe 
rent dates, Landsat TM, SPOT, NOAA, digital ter 
rain model, old forest resource inventory data, 
and general map data, the stratification and the 
whole system tend to become very complicated. 
The technique suggested here is based on the 
idea that each auxiliary data source is used 
either separately or in a simple combination, 
e.g. the combination of Landsat TM and a gene 
ral map, for stratification. This results in se 
veral different strata for each first phase 
sample unit. The principles of the technique 
have been described in specific applications 
used in Finland (e.g. Poso et al. 1984, Peng 
1987, Harma 1988). Accordingly, the procedure 
of using several different stratifications pro 
duces several sets of inventory data for each 
first phase sample unit. 
The methodology is illustrated in Figure 1. In 
the first phase, units are defined on the basis 
of a homogeneous grid and stratified on the ba 
sis of Landsat TM imagery to 5 strata. In the 
second phase, each first phase plot belonging 
to stratum 1 receives the same ground variable 
estimates from matrix Mi based on ground mea 
surements. Correspondingly, plots belonging to 
stratum 2 receive the ground variable estimates 
from matrix M2. The procedure is carried out for 
each stratum and results in formally complete 
ground variable estimates for each first-phase 
plot. 
STEP 1: 
Each plot is supplied 
with first phase data 
2 
2 
3 4 
2 
STEP 2: 
2 
3 
4 2 
4 
Each plot is stratified 
into homogeneous strata on 
3 
3 
4 2 
5 
the basis of first phase 
data, xi 
3 
4 
4 5 
1 
3 
5 
1 1 
1 
STEP 3: 
Y ll> 
Y 12’ •' 
... Yip 
Measurement of ground truth 
M h = 
Y21» 
Y 22 » •• 
... Y 2p 
data for each stratum, h, 
Ymhl > 
Ymh2 »• 
resulting in a ground truth 
Ymh >p 
matrix Mf, (h=l,2,..5) 
Y 2 
y 2 
Y 3 Y 4 
y 2 
STEP 4: 
Each plot is supplied with 
Y2 
Y3 
Y4 y 2 
Y4 
ground truth values from 
the relevant matrix Mh to 
Y3 
Y3 
y 4 y 2 
Y5 
be used as the final 
estimates, Yj-, 
Y3 
Y 4 
Y 4 Y 5 
Yl 
(h=index for a stratum) 
Y 3 
y 5 
-< 
-< 
Yl 
Figure 1. Steps in two-phase 
sampling approach