38
Singh et al. (1984) and Lauenroth et al. (1986)
demonstrated that there are other kinds of errors
when estimating NPP that always lead to overestimation of NPP. These are the errors leading to
overestimation (ELOs), which stem from the fact
that random errors in estimates of biomass do not
compensate but accumulate, leading to a positive
bias when estimating NPP (Sala et al. 1988). ELDs
result directly from the estimation of NPP. In all
cases, NPP is estimated as the increase in biomass
during a period of time. An increase in biomass
during a time period is considered an estimate of
production. However, a decrease in biomass in the
same interval yields a production equal to zero.
Consider the case in which the real value of biomass at time 0 (BO) is equal to biomass at time 1
(Bl) (Fig. 2.4). Both BO and Bl are random variables and therefore, when sampling them, sometimes B 1 will be larger than BO, sometimes BO will
be larger than B 1, and occasionally they will be
equal. Because of the definition of productivity (increments in biomass), when Bl > BO it is considered an estimate of production, but when B 1 < BO
the estimate of production will be zero. In synthesis, when random errors result in a positive difference, it is accepted as productivity, but when they
result in a negative difference, it is ignored.
Singh et al. (1984) and Lauenroth et al. (1986)
developed simulation models that yielded "true"
~
III
III
11\
E
.2
ID
1
2
3
TIME (months)
4
Osvaldo E. Sala and Amy T. Austin
values of below- and aboveground biomass and
production. They sampled biomass from both models, calculated productivity using several of the
standard methods, and compared them against the
true values of production from the models. They
found that the ELDs were very large; belowground
NPP estimates were up to 5 times higher than the
true value (Singh et al. 1984) and aboveground estimates were up to 33% higher than the true value
(Lauenroth et al. 1986).
The works of Singh et al. (1984) and Lauenroth
et al. (1986) were empirical demonstrations of
ELDs and their magnitude. Sala et al. (1988) later
calculated the distribution function of the estimator
of productivity NPP which is nonnormal and demonstrated analytically that NPP derived from
changes in biomass is a biased estimator of the
true value of productivity. Based on the distribution function of NPP, it was possible to calculate
the distribution function of the overestimation error (OE) and to assess the determinants of its
magnitude.
DE = (cr/ ji;.)e -112(!licr)2 - qll (2.6)
where Il is the true difference in biomass between
time 1 and time 0, cr is the standard deviation of
the difference, and q is the probability of B 1 - BO
::5 O. Independently of the mathematical reasoning
that led to the distribution function of DE, it can be
FIGURE 2.4. Example demonstrating
how random errors in estimates of
biomass do not compensate but
rather accumulate and result in a
positive bias in estimates in productivity. The horizontal line represents
the true value of biomass which, in
the example, does not change. Biomass estimates are random variables
that have a normal distribution and a
mean that coincides with the real
mean. Sampling from this normal
distribution yields, by chance, values
that are slightly higher or lower than
the true value. Increases in biomass
through time are accepted as productivity but decreases are considered as
zero.
Singh et al. (1984) and Lauenroth et al. (1986)
demonstrated that there are other kinds of errors
when estimating NPP that always lead to overestimation of NPP. These are the errors leading to
overestimation (ELOs), which stem from the fact
that random errors in estimates of biomass do not
compensate but accumulate, leading to a positive
bias when estimating NPP (Sala et al. 1988). ELDs
result directly from the estimation of NPP. In all
cases, NPP is estimated as the increase in biomass
during a period of time. An increase in biomass
during a time period is considered an estimate of
production. However, a decrease in biomass in the
same interval yields a production equal to zero.
Consider the case in which the real value of biomass at time 0 (BO) is equal to biomass at time 1
(Bl) (Fig. 2.4). Both BO and Bl are random variables and therefore, when sampling them, sometimes B 1 will be larger than BO, sometimes BO will
be larger than B 1, and occasionally they will be
equal. Because of the definition of productivity (increments in biomass), when Bl > BO it is considered an estimate of production, but when B 1 < BO
the estimate of production will be zero. In synthesis, when random errors result in a positive difference, it is accepted as productivity, but when they
result in a negative difference, it is ignored.
Singh et al. (1984) and Lauenroth et al. (1986)
developed simulation models that yielded "true"
~
III
III
11\
E
.2
ID
1
2
3
TIME (months)
4
Osvaldo E. Sala and Amy T. Austin
values of below- and aboveground biomass and
production. They sampled biomass from both models, calculated productivity using several of the
standard methods, and compared them against the
true values of production from the models. They
found that the ELDs were very large; belowground
NPP estimates were up to 5 times higher than the
true value (Singh et al. 1984) and aboveground estimates were up to 33% higher than the true value
(Lauenroth et al. 1986).
The works of Singh et al. (1984) and Lauenroth
et al. (1986) were empirical demonstrations of
ELDs and their magnitude. Sala et al. (1988) later
calculated the distribution function of the estimator
of productivity NPP which is nonnormal and demonstrated analytically that NPP derived from
changes in biomass is a biased estimator of the
true value of productivity. Based on the distribution function of NPP, it was possible to calculate
the distribution function of the overestimation error (OE) and to assess the determinants of its
magnitude.
DE = (cr/ ji;.)e -112(!licr)2 - qll (2.6)
where Il is the true difference in biomass between
time 1 and time 0, cr is the standard deviation of
the difference, and q is the probability of B 1 - BO
::5 O. Independently of the mathematical reasoning
that led to the distribution function of DE, it can be
FIGURE 2.4. Example demonstrating
how random errors in estimates of
biomass do not compensate but
rather accumulate and result in a
positive bias in estimates in productivity. The horizontal line represents
the true value of biomass which, in
the example, does not change. Biomass estimates are random variables
that have a normal distribution and a
mean that coincides with the real
mean. Sampling from this normal
distribution yields, by chance, values
that are slightly higher or lower than
the true value. Increases in biomass
through time are accepted as productivity but decreases are considered as
zero.