|
R
s
) such as
profit and psychological satisfaction. These are based on
material results (
R
; say yield, by-products, modification
of the system, etc.) as well as anthropic non-material
conditions
(
Rnm
;
e.g. market prices, incentives, etc.). The
decision-maker is then interested in
maximizing
the
function (
Table 1
):
R
=
R
(
R
,
R
nm
)
(1)
On the other hand both operators and researchers are
interested in production functions, i.e. in the dependence
of
R
ideally on all material factors:
R
=
R
(
f
1
,
f
2
...
f
n
)
(2)
where
f
1
,
f
2
...
f
n
=
f
i
are all known continuous or
(1)
In this paper material is strictly intended as
"made of matter" (as used by physicists).
1 9
discrete factors, including available techniques
(agricultural practices and equipment) and
external inputs (climate, pedology, other biota).
In practice, especially in research, only a limited
number of factors (
m
<
n
) can be dealt with:
R = R ( ƒ
1
, ƒ
2
… ƒ
m
)
(3)
ƒ
m + 1….
ƒ
n
where all factors from
f
m+1
to
f
n
are kept
constant (see later). Often only one factor is
considered (
m
= 1; e.g. depth of plough tillage in a
given site and year); when more than one factor is
considered their interaction must be considered. Note
that an apparent single factor might in reality be a
"compound factor" and could then be split into more
components (e.g. tillage can be split into tillage depth,
type of equipment, time of tillage, etc.) and these
components can be distributed among variables and
constants.
Factors of particular interest are the pedological
(usually but not necessarily kept as constants for
a given site), climatic and weather traits. The latter
could be taken as variables characterizing a given
cropping season when their interactions with tillage
technique are considered; in some cases events before
a given date during the cropping season are better
considered as constants characterizing the system at
that date (e.g. a rainy autumn after the primary sum-
mer plough tillage in a given type of soil defines at a
given date the conditions for the choice of subsequent
tillage and seeding operations). When one deals with
climate parameters or when variables characterizing
conditions are sampled from a more or less ample
distribution, the functions sought very frequently
apply to the average of a set of situations (e.g., to a
number of given years, or to a number of varieties of
a given crop species); in these cases the symbol {
f
i
}
is used to indicate a set of variants for the factor.
Note that some of the variables must be statistically
considered as fixed variables (soil type or imple-
ments) while others are random variables (e.g. year)
and need a different testing procedure.
A special mention must be given to the time
factor (
ft
=
t
). This might refer to the duration of
direct tillage effects (e.g. on soil bulk density,
hydraulic conductivity, etc.) or to the subtle, slow and
usually more critical modifications to the soil system
occurring after long-term applications of a given
tillage or soil management programme (the
asymptotic decrease in organic matter down to say
one half of that of the virgin soil after some decades of
arable farming is very frequent).
On the other side, as dependent variable of a function
like n. 3 in
Table 1
, one can choose any material
result, such as yield (
P
A
; production per unit area), or
quality variables of a produce, or production costs,
vegetation variables (time of harvest, crop emergence,
weed development), environmental variables
(groundwater pollution, erosion, waterbody
eutrofication). Some of these dependent variables may
enter as independent variables (or factors) in other
functions (e.g. this is the case of the effect of tillage on
the organic matter content of the soil; it affects soil
structure stability and this affects in turn the soil water
characteristics, which interact with meteorological
conditions and finally affect yield); a chain of functions
can originate in this way.
Table 1
gives some typical examples of functions
related to the study of tillage problems.
A change in tillage programme and even more so in a
whole technical package alters the previous equili-
brium in the "soil-plant-low atmosphere-other biota"
system. The system will usually move to a new
equilibrium; this can be reached almost instant-
neously (say the change in porosity brought about by
a roto-tiller) or slowly, often asymptotically (e.g.
increase in the organic matter content in the upper soil
horizon after the introduction of no-tillage; reduction
in organic matter in the whole soil profile over a
number of decades after sod breaking). Examples of
possible evolution over time of a given soil trait
when its management programme is abruptly
changed and continuously applied are given in
Fig. 2
. The decision-maker clearly needs:
°
to know the development over time of the
20
trait modification during the transient state
(this can last up to many decades and can be
non-monotone);
°
to appreciate with sufficient accuracy the final
steady state and pay attention to this and not
or at least not just the results from initial
years;
°
to know whether and up to which
development
stage the process is reversible, so that a back
transformation can be a dopted if and when
desired (e.g. to prevent
dangerous levels of
soil erosion), or a
periodic solution might be
sought (like
alternating ploughing at different
depths or
ploughing and chiselling, according
to crop rotation requirements);
°
to know whether the degradation of some
important soil trait can be corrected by other
favourable actions (say ploughing in of farm
manure replaced by crop residue mulching).
All functions of the type shown in
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