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6MATHEMATICAL MODEL FOR REMOTE MONITORING CONTROL TECHNOLOGY BIOPRODUCTION PROCESSES IN WATER ECOSYSTEMS USING FLOATING PLANTS
Abstract
The urgency of the problem being studied due to the need to develop a wide range of control technologies and correction of bioproduction processes to address emerging threats in emergency situations Biosafety drinking and other uses, located in the vast territories of aquatic ecosystems, in particular - the technology is used for the correction of floating plants and remote sensing - to monitor the status of the aquatic ecosystem. The purpose of the research is to study using the original having the world novelty, the mathematical apparatus, the structure of relations colorimetric parameters of the water surface, measured remotely with a relatively simple and inexpensive methods. The leading method to the study of this problem is a formalized description of this structure with the help of a new class of mathematical models, called discrete models of dynamic systems - DMDS. Our results show the possibility of using the DMDS, certain aspects of bioproduction processes in aquatic ecosystems, aspects that are important in terms of technology to eliminate, with floating plants, water consumption biosecurity threats in extreme conditions. Article submissions may be helpful to a better understanding of the systemic aspects of the functioning of aquatic ecosystems and, in practical terms, to create technologies control and correction of character bioproduction processes in reservoirs and streams to eliminate, in extreme situations, threats biosafety consumption.
Keywords
discrete models of dynamic systems, water ecosystems, remote determination of the ecological status, ponds and streams, water consumption biosecurity threats
AUTHORS
Elena Vysotskaya
PhD, Professor of Department of Biomedical Engineering Kharkov National University of Radio Electronics Kharkov, Ukraine evisotska@maH.ru
Yurii Bespalov
MS, Senior research fellow,
School of Mathematics and Mechanical Engineering V.N. Karazin Kharkiv National University Kharkov, Ukraine bezpalof@bk.ru
Alexander Betin
PhD in Engineering, Professor Head of Department of Chemistry, Ecology and Expertise Technology National Aerospace University "Kharkiv Aviation Institute" Kharkov, Ukraine
Introduction. Serious threats to biosecurity drinking and other water uses in the in conditions of global climate change, may be due to imbalances processes, not related to human activities in aquatic ecosystems. The resonant example of this kind was observed in the summer of 2013 in the Kharkiv region (Ukraine) on the Seversky Donets River and the White Lake in a conservation area, near the Biological Station of Kharkiv National University named after V.N. Karazin.
Floating tropical plant Pistia stratiotes, cultured in medium latitudes only in aquariums and ornamental pools, which fell, unknown, in the Seversky Donets, it gave her a flash of biomass, which is in a different place would pose a serious threat to biosafety - caused by the release of failure the water intake, which scored this living and dead biomass.
Experts do not rule out the threats of biosafety related to the creation of favorable conditions for the development of the dying biomass of microorganisms - causative agents of dangerous infectious diseases. It should be noted that the development Pistia stratiotes, as well as other floating plants, in many cases relatively easily regulated by simple means - such as floating barriers. It is practiced in the tropical and subtropical regions of the world where cultivated Pistia stratiotes: as a fodder plant, or, as in some parts of Central Asia, for purification of waste water. But the massive development of mid-latitude tropical plant is a sign of disturbance of homeostasis of aquatic ecosystems - natural mechanisms to protect, for the time being, by threats biosafety that may arise as a result of outbreaks of biomass is much more dangerous than Pistia stratiotes, organisms - alien or mutant.
For example - toxic cyanobacteria development which is an important source of drinking water for Israel Lake Kinneret, it creates now a major concern of biosafety threat. And in other cases, not the least we can talk about the threats biosafety drinking water, which can lead to other threats - public and national security. Parry these threats will require in the near future the development of technologies of water ecosystems - in cases of catastrophic breach of their natural homeostatic mechanisms.
The above example of such violations suggests at first glance - a paradoxical, the idea of using such technologies Pistia stratiotes, used as described above for purification of wastewater. and abilities, he tells us said a sad but instructive precedent in a short time to complete its entire surface biomass such as the Seversky Donets River for more than ten kilometers, By creating this huge over the surface of a biofilter with a complex organism, promotes mineralization of organic substances and disposal of waste water. Note that a biofilter would be very useful in the same Kharkiv region in the summer of 1995, during the catastrophe at Dikanevskoy biological treatment plant. When the river in Kharkov was thrown a huge amount of untreated wastewater, What experts say NATO has created a real danger of epidemics of infectious diseases, not only in Ukraine and neighboring countries, but also in Western Europe, the biofilter of Pistia stratiotes or other floating plants in such a situation would have to function over a wide area. Its operation will require methods of control and correction - in order to optimize processes increase plant biomass, acting as agent, water purification and removal of excess biomass, acting as agent, water purification and removal of excess biomass, which can be a source of secondary pollution of water by the withering away and cause a malfunction in the hydraulic structures.
Control of the vast water areas is also necessary to prevent pressure uncontrolled development of aquatic plants, which can cause ecological catastrophe - like above the Seversky Donets River in the summer of 2013. The vastness of the area controlled by making use of perspective in the case of a relatively simple and inexpensive methods for determining the distance of aquatic ecosystems (hydrobiocenoses). Such, for example, digital photography from the board of light unmanned aerial vehicles (UAVs). Digital photography was used for this purpose during the experiment on introdutsirovaniyu Pistia stratiotes in one of the ornamental ponds Kharkov Zoo (1).
In this case, digital photography, with the fixation of the colorimetric parameters associated with the presence in the water of the pond chlorophyll and other plant pigments that give factual material for mathematical modeling of the dynamics of bioproduction processes hydrobiocenoses. As a result of the simulation was to explain the causes for which, Pistia stratiotes in the pond, although received some development, but not as massive as the at the same time in the Seversky Donets. To simulate the use of genuine having world novelty developed in Kharkiv National University named after VN Karazin class of mathematical models, called discrete models of dynamic systems (DMDS) (1-7). DMDS allows the structure analysis of correlations between the system components, to give a qualitative description of the structure of the formalized interconnect
relationship ECOTOR structure can be represented as a matrix or graph. In her (it) can be the basis for a certain combination of the initial values of components built idealized trajectory of the system (ITS), which reflects a shift, characterized by different combinations of the values of the components of the phases. In some cases, there is no need of constructing DMDS in a series of observations of the modeled system over a period commensurate with the cycle of changing its states (5, 7).
This is possible when we observe practically simultaneously a certain set of objects that can be described by the same DMDS and have the same ITS, according to which vary in one and the cycle, but are in different phases of its - components differing values. Along with the components, physical and biological meaning of which is known prior to the construction of DMDS is used (1, 7) latent components (LK) for which initially know is that the values of their correlations with other components - zero. Such correlation values are observed, in particular, when relationships between the components of the feedback type "+, -" characteristic, established the principle of Le Chatelier's a state of dynamic equilibrium relationship of components within a pair, whose members can be interpreted as indicators of the performance and the result of a process. This type of communication can be described as the relationship "predator-prey". As a result of DMDS corresponding interpretation of LC can be an expert to operate the system of information decision support system information support of decision-making (IDSS). As part raised in this article concerns biosafety focus should be on developing IDSS possessing databases (DB), which contain a variety of environmental information, including - get remote methods. With the use of DMDS using imaged with a digital photograph factual information, you can simulate the conditions, where Pistia stratiotes can quickly increase its biomass and fill it all the mirror of water.
This is necessary for activities to prevent pressure endanger Biosafety different types of water consumption catastrophic outbreaks of Pistia stratiotes (and other floating aquatic plants), and to determine the conditions necessary to create in emergency situations as soon as possible in natural waters biofilters Pistia stratiotes using as a water treatment agent. Based on the results of mathematical modeling using remote sensing methods of collecting the factual material, methods for determining these conditions must, in our view, be an essential component of the knowledge-based biotechnology perspective of water ecosystems using floating aquatic plants. This mathematical modeling is the subject of this paper.
Materials and Methods.
DMDS was performed using pirrsonovskoy correlation and ideology based on Liebig's law (3), using the results produced by natural sunlight white digital photography disc diameter of 100 mm and dive to a depth of 200 mm in the water two decorative ponds Kharkov Zoo. In one of them, hereinafter referred to as the pond N1, Pistia stratiotes although pprisutstvovala, but takes no more than one or two percent of the water surface, basically - the coast. In the other, hereinafter referred to as the pond N2, Pistia stratiotes occupied more than half the area of the mirror pond. Photographing performed at distances of 2 to 3 meters from the fifteenth of July to 15 August 2013 of camera Canon E OS - D Mark III 22.3 MN .
Photos were processed using the software package Image processing Toolbox MATLAB. As the values of the three "color", reflecting the color of the phytoplankton, the system components, were the following values: G / B, identified with the concentration of chlorophyll (the living, young, actively dividing cells of algae) in the water of the pond, R / G, identified with the "yellow-green index" reflecting the ratio of chlorophyll and yellow-orange plant pigments, (R + G) / B, identified with the total concentration in the water of the pond live and dead cells of algae, where R, G and B - the number of the red,
green and blue pixel elements. The fourth was a latent component (LK) - the value of the correlation coefficient is all the first three ("color") is equal to zero.
Results. As a result of using DMDS mathematical modeling was carried out a formalized description of the structure of relations between the components, characterizing the state of bioproduction processes in the pond N1, where no significant development of Pistia stratiotes in the pond, N 2, where it has developed considerably. These are the following components named above under , see ""Materials and Methods". Three "color" colorimetric: G / B, R/G, (R+G)/B, as well as LK. Thus, the correlation coefficient values with all three aforementioned colorimetric zero, which may be an indication of a connection type "-, +". The resulting simulation graphs relationships between these components, for the two pools are presented in Figure 1 and Figure 2.
FIGURE 1. GRAPH OF RELATIONS BETWEEN THE COMPONENTS OF THE AQUATIC ECOSYSTEM IN THE POND N1. THE BOXES - COMPONENTS. THE SOLID ARROWS INDICATE THE DIRECTION OF THE NEGATIVE EFFECTS OF INTERCONNECT, INTERMITTENT - POSITIVE
From Fig. 1 shows that the main role played by the influence of latent component colorimetric components whose relationship with colorimetric components allow us to interpret it as an indicator of development in the pond zooplankton organisms are filter feeders: population growth that occurs in high concentrations in the water, both living and dead cells of microalgae (( R + G) / B), the power of filter reduces the concentration of zooplankton (values G / B, (R + G) / B) and providing the prevalence of young actively dividing "green" cell reduces the R / G.
f
GIB r- RJG ... + iGM <-
\|lkT
FIGURE 2. GRAPH OF RELATIONS BETWEEN THE COMPONENTS OF THE AQUATIC ECOSYSTEM IN THE POND N2. THE BOXES - COMPONENTS. THE SOLID ARROWS INDICATE THE DIRECTION OF THE NEGATIVE EFFECTS OF INTERCONNECT AND VNUTRIKOMPONENTNYH, INTERMITTENT - POSITIVE
125
Column relationship shown in Fig. 2, latent component, a positive effect on G / B, (R + G) / B) and R / G and the associated G / B according to the "+, -", can be interpreted as an expression of the concentration of microalgae in water available forms of nutrients, which contribute to high values: ascending concentrations in the water of the living and the dead cells of microalgae (LK positive effect on G / B and (R + G) / B), and, in this case - "aging" phytoplankton increase therein proportion of dead and old unable to actively dividing and nutrition, cell microalgae (ascending values R / G). The negative impact of G / B on the LC corresponds to the absorption of water young, actively dividing and feeding, microalgal cells available for phytoplankton forms of biogenic elements.
The comparison graphs relationship shown in Fig. 1 and Fig. 2 may state an important distinction structures relations components of aquatic ecosystems ponds N1 and N 2. Namely, in the pond N 2 are connected by direct dependence of growth of phytoplankton (increase value G / B and (R + G) / B) and its "aging", reduction of the share in it of young, actively dividing and feeding, the cells of algae (increased values of R / G). In the field of relations of components in the ecosystem of the pond 1 N signs direct dependence of phytoplankton growth and "aging" no.
Based on the graph relationship shown in Fig. 1 and Fig. 2, to determine the initial values of the components built idealized trajectory of the system, reflect a cycle of component values. Fig. 3 and 4 shows that are based on those of the ITS, directed graphs that reflect these cycles in the phase shift differing nature of the changes in the values of components associated with the growth of phytoplankton (G / B) and its "aging" (R / G). The edges of a directed graph indicate the direction of phase change, which corresponds to the vertex of the graph. The phases are different nature of the change component values at the current step, compared with the previous, and in some tops, component values. As with conditional steps ITS time, these specific values are given in conventional points: low - one point, the average - two points, high - three points.
Rt+1 < Rt
Rt+1 = Rt
Rt+1 > Rt
FIGURE 3 DIRECTED GRAPH OF PHASE CHANGE CHANGES ITS POND ECOLOGICAL SYSTEM N1; ARROWS - EDGES OF A DIRECTED GRAPH, RECTANGLES - THE TOP OF IT; GT + 1 -VALUES OF G / B AT THE CURRENT TIME STEP IS CONDITIONAL, GT - THE PREVIOUS, RT + 1 - VALUES OF R / G AT THE CURRENT TIME STEP IS CONDITIONAL, RT - THE PREVIOUS. A,
B, C - LETTERING GRAPH VERTICES
A Gt+1 < Gt Rt+1 < Rt » ■ E Gt+1 = Gt =3 Rt+1 Rt =3
J
1 t
B Gt+1 = Gt =1 Rt+1 = Rt =1 D Gt+1 > Gt Rt+1 = Rt
1 r
c Gt+1 = Gt Rt+1 > Rt
FIGURE 4. DIRECTED GRAPH OF PHASE CHANGE CHANGES ITS ECOLOGICAL SYSTEM OF THE POND N2; ARROWS - EDGES OF A DIRECTED GRAPH, RECTANGLES - THE TOP OF IT; GT + 1 - VALUES OF G / B AT THE CURRENT TIME STEP IS CONDITIONAL, GT - THE PREVIOUS, RT + 1 - VALUES OF R / G AT THE CURRENT TIME STEP IS CONDITIONAL, RT - THE PREVIOUS. A,
B, C, D, E - LETTERING GRAPH VERTICES
From a comparison of Fig. 3 and Fig. 4 shows that the dynamics of the ecosystem of the pond N1 present phase change (from the top edge to the top in C), at which the "aging" of phytoplankton growth ahead of it in the number of active young cells of algae. Zooplankton-filter-alike consume both young and old and dead cells of algae, saturating the water with their metabolites, that are available for phytoplankton form of nutrients. By the active removal of the water of these metabolites can only young cells of algae. Therefore, in situations where the "aging" of phytoplankton growth ahead of it, likely to accumulate in the water available for plant nutrients forms. This creates a favorable environment for the development in the water, along with other plants, phytoplankton, in our case, Pistia stratiotes.
As follows from the results in this paper mathematical modeling, the advance growth of phytoplankton its "aging" is accompanied by detectable using DMDS changes in the structure and dynamics of the relationship of the measured values of the color of the remote pond water. These are the parameters fixed by remote digital photography - using a relatively simple and inexpensive equipment that can be establish, for example, on board a light UAV. This, in our view, suggests the prospect of application DMDS to address threats biosafety related to the violation of stability bioproduction processes in aquatic ecosystems.
Discussions
The subject of this article from the perspective of theoretical biology refers to the problems of the organization at the level of biological communities. More specifically - to the research nature of the relationship of structure and dynamics of communities with their resistance. Including - with resistance to factors that promote conditions for accompanying flashes of some organisms violation of the existing biological equilibrium. Such studies have long been used by a wide range of mathematical methods, among which should be noted is still popular with environmentalists methods based on indicators shennovskih diversity (8). R. Margalef, one of the first to propose such an approach, once wrote, "ecologist sees any expression of diversity as possible to build a system with feedback" (""the ecologist sees in any measure of diversity an expression of the
possibilities of constructing feedback systems, or any sort of links, in a given assemblage of species'') (9). As used in this work allows the unit DMDS based on relatively small in terms of the actual material to give direct formal description of the structure of feedback systems between the components of different nature (1-7), including - biological communities (1, 2, 7). Possibility of using DMDS, to also formalized description of the idealized cycle value changes of system components allows you to explore the relationship between the stability of the system and the parameters of its diversity. R. Margalef at the time showed that aquatic ecosystems for these parameters, along with others, can act, reflecting the ratio of plant pigments in it (10). As part of this operation such as parameter the ratio R / G, which is determined in such a relatively simple and inexpensive manner as a digital photograph. The structure of the feedback that other parameters of phytoplankton modeled using DMDS.
In connection with the practical task of determining the extent related to the possibility of a mass of toxic cyanobacteria, threatening drinking water consumption biosafety conducted studies of phytoplankton and its relations with other components of the ecosystem of Lake Kinneret mentioned above. The results of these studies are reflected in the works Hambright K., Pinchasov Y., Recknagel F (11-13). We know of no papers on aspects of solutions to major biosecurity threats such as Lake Kinneret waters through technology using floating aquatic plants, technologies, for understandable reasons, in such cases difficult to be realized. We know of no papers on aspects of biosafety decisions threats on large bodies of water such as Lake Kinneret, through technology, using floating aquatic plants, technologies, for understandable reasons, in such cases difficult to be realized. The closest to the content of this article is to work Grygoryev A. (1), which is devoted to mathematical modeling of bioproduction processes in a small pond, which has been introduced Pistia stratiotes. Presented in this work model, which is built using the DMDS and data obtained by a digital photo of the colorimetric parameters of phytoplankton, it describes the conditions under which the possibility of a mass in the water Pistia stratiotes absent, but does not describe the conditions are favorable for such development. This paper presents and compares models describing both favorable and unfavorable conditions for mass development of Pistia stratiotes. What matters for the development of technologies to eliminate the dangers of water consumption using Biosafety Pistia stratiotes and to prevent pressure uncontrolled its development - carrying such threats.
Conclusion The results obtained in this paper are the results, in our opinion, some interest from the point of view of theoretical biology - creating certain prerequisites for the expansion of ideas about the structure and dynamics of the feedback parameters of the aquatic ecosystem. However, these results are also highly relevant to the present time associated with the pressing problems of biosafety practical value - to develop, with the use of DMDS, relatively simple methods of remote control of bioproduction processes in the aquatic ecosystem. It's about control methods needed to address, with a rapidly increasing its biomass of floating plants, water consumption biosecurity threats arising in emergency situations, as well as - in situations where these threats arise from uncontrolled development of these plants.
Can recommend The results presented in this article are, in our opinion, have a certain interest to specialists in the field of theoretical biology. Their practical importance due to the elimination of threats to biosecurity and prevent pressure water consumption through the use of emergency biofilters of floating plants. Technology of creation of biofilters and remote monitoring of their operation on large areas is often difficult terrain must be equipped with the new structures with comprehensive capabilities and powers that effectively provide liquidation and prevent pressure biosecurity threats of various
kinds of water consumption resulting from natural disasters and man-made disasters. The need to create such structures in the near future in the interest of not only environmental, but also social and national security. For such structures should be developed DSS, allowing, in particular, to determine the optimal strategy to use, along with other agents of self-purification of water, also floating plants, taking into account the information received by remote methods, to implement some of which are described in this article.
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