Ecoinformatics Problems of the World Ocean - New Ecoinformatics Tools in Environmental Science: Applications and Decision-making - page 291

2 , the function p(h) is the product of the nondecreasing
and nonincreasing functions. Hence, in

1 [ X

In the set X ¼ X

ʩ − p(h) is either nondecreasing, or non-
increasing or has a maximum. Since for 8 h 2 X

F ðÞ=

N ðÞ [ m , then p(h)willbe

the nonincreasing function at 8 h 2 H 0 ¼ f h : h h 0 g , where

Z

h 0

p ð 0 Þ ¼ w ð y Þ exp ½ uð y Þ dy

0

The multitude of values h ≥ 0, for which the following condition is valid, are

denoted by H 1 :

Z w ðÞ exp

1 exp w ðÞ F ðÞ vN ðÞ ½ u ðÞþ ½ u ðÞ dy p ðÞ

[

.
The obtained results are formulated as the following theorem.
Theorem The function p(h) is nonincreasing at 8 h 2 H þ [ð H 0 \ H Þ[ð H 1 \
H Þ and nondecreasing at 8 h 2 H \ð E n H 0 Þ\ð E n H 1 Þ , where E ={h: h

Then p(h) will be the nonincreasing function at 8 h 2 H 1 \ X

≥ 0}.

In a more general case @ p =@ can be presented in the form of the sum:

@ p =@ z ¼ ð@ p =@ z Þ EB þð@ p =@ z Þ O þð@ p =@ z Þ s þð@ p =@ z Þ M þð@ p =@ z Þ Z

þð@ =@

z Þ T ;

ð 4 :

44 Þ

p

where each of the terms on the right-hand side re ects a change of the phyto-

plankton biomass due to changes in illumination and concentration of nutrient
elements (EB), sedimentation (O), temperature changes (

fl

), mortality (M), con-
sumption by zooplankton (Z) and turbulent mixing (T). According to Eq. ( 4.43 ), it
can be supposed that

˄

Þ ¼Af 1 ðÞ f 2 ðÞ ½1 10 c p

ð@ p =@ z Þ EB Ft ð ; p ; z :

At ʳ p << 1 we obtain

p 1

ð@ p =@ z Þ EB Af 1 ðÞ f 2 ðÞ:

With an increasing depth in other stationary conditions the water temperature is
known to monotonically decrease, dropping sharply in the layer of the thermocline
(i.e., (

@ =@

z) ˄ ≤

@ =@

z) M has the form of the sectionally
continuous non-positive function. However, due to the physical processes of
mixing a situation can appear when this monotonicity gets broken.
The values of the constituent (

p 0). The similar term ( p

@ p =@ z) Z depend on the distribution of N(z).

The term ( @ p =@ z) T is totally determined by the hydrological conditions through the