2. Methods of Estimating Aboveground Net Primary Productivity
39
seen that the size of the overestimation error depends on the variance and the true value of productivity. The larger the variance and the lower the
true value of productivity, the larger is the overestimation error.
The larger the variance of the estimates of biomass used in calculating NPP, the greater will be
the possibility of having only by chance a negative
difference between biomass at time 0 and time 1
when in fact the true difference was positive. Similarly, the smaller the true value of productivity and
of the true difference in biomass (B 1 - BO), the
higher will be the probability of obtaining by
chance only a negative value of B 1 - BO. Equation
2.6 indicates that the magnitude of the overestiMean = 110 g m·2
SO = 10
80
100
I
I
I
I
I
I
I
P < 0 = 0.33 I P > 0 = 0.67
I
I
-20
·10
o
10
A
120
140
c
20
30
40
mation error depends on the probability of obtaining by chance a negative value for B 1 - BO.
Biondini et al. (1991) developed an example for
a grassland with a biomass at time 0 BO = 110
g m- 2 , SD = 10, and a biomass at time 1 Bl
= 120, SD = 20 g m -2 (Fig. 2.5). The distribution
of B 1 - BO had a mean of 10 g m - 2 and a SD of
22.4, and the probability of B 1 - BO being less
than 0 was 0.33. The mean and standard deviation
of NPP can be calculated using the distribution calculated by Sala et al. (1988). In this example, NPP
had a mean of 14.6 g m -2, SD 16.3, the probability
of NPP being equal to 0 was 0.33, and the probability of NPP being greater than 0 was 0.67. The
overestimation error was 4.6 g m - 2 and it was calMean = 120 g m·2
50=20
80
10
100
120
20
B
140
160
D
30
40
FIGURE 2.5. Example of the occurrence of overestimation error in estimates of productivity. A, Frequency distribution
of biomass estimates at time O. B, Frequency distribution of biomass estimates at time 1. C, Frequency distribution
of the B 1 - BO. D, Frequency distribution of net primary productivity (NPP) estimates. Note that although the real
difference between Bl - BO is 10 g m -2, in 33% ofthe cases, the difference Bl - BO is negative. Because negative
values are discarded, NPP estimates are biased and an overestimation error occurs. The mean of B 1 - BO is 10
g m -2, the mean of NPP is 14.6 g m -2, and the overestimation error is 4.6 g m -2. For calculation details see text
and Biondini et al. (1991).
39
seen that the size of the overestimation error depends on the variance and the true value of productivity. The larger the variance and the lower the
true value of productivity, the larger is the overestimation error.
The larger the variance of the estimates of biomass used in calculating NPP, the greater will be
the possibility of having only by chance a negative
difference between biomass at time 0 and time 1
when in fact the true difference was positive. Similarly, the smaller the true value of productivity and
of the true difference in biomass (B 1 - BO), the
higher will be the probability of obtaining by
chance only a negative value of B 1 - BO. Equation
2.6 indicates that the magnitude of the overestiMean = 110 g m·2
SO = 10
80
100
I
I
I
I
I
I
I
P < 0 = 0.33 I P > 0 = 0.67
I
I
-20
·10
o
10
A
120
140
c
20
30
40
mation error depends on the probability of obtaining by chance a negative value for B 1 - BO.
Biondini et al. (1991) developed an example for
a grassland with a biomass at time 0 BO = 110
g m- 2 , SD = 10, and a biomass at time 1 Bl
= 120, SD = 20 g m -2 (Fig. 2.5). The distribution
of B 1 - BO had a mean of 10 g m - 2 and a SD of
22.4, and the probability of B 1 - BO being less
than 0 was 0.33. The mean and standard deviation
of NPP can be calculated using the distribution calculated by Sala et al. (1988). In this example, NPP
had a mean of 14.6 g m -2, SD 16.3, the probability
of NPP being equal to 0 was 0.33, and the probability of NPP being greater than 0 was 0.67. The
overestimation error was 4.6 g m - 2 and it was calMean = 120 g m·2
50=20
80
10
100
120
20
B
140
160
D
30
40
FIGURE 2.5. Example of the occurrence of overestimation error in estimates of productivity. A, Frequency distribution
of biomass estimates at time O. B, Frequency distribution of biomass estimates at time 1. C, Frequency distribution
of the B 1 - BO. D, Frequency distribution of net primary productivity (NPP) estimates. Note that although the real
difference between Bl - BO is 10 g m -2, in 33% ofthe cases, the difference Bl - BO is negative. Because negative
values are discarded, NPP estimates are biased and an overestimation error occurs. The mean of B 1 - BO is 10
g m -2, the mean of NPP is 14.6 g m -2, and the overestimation error is 4.6 g m -2. For calculation details see text
and Biondini et al. (1991).