Structural water self-organization in river flow

BOHR International Journal of Civil Engineering
and Environmental Science
2023, Vol. 1, No. 2, pp. 80–86
DOI: 10.54646/bijcees.2023.10
www.bohrpub.com
METHODS
Structural water self-organization in river flow
O. M. Rozental1 and V. Kh. Fedotov2*
1Water Problems Institute, Russian Academy of Sciences, Moscow, Russia
2Chuvash State University, Cheboksary, Russia
*Correspondence:
V. Kh. Fedotov,
fvh@inbox.ru
Received: 28 August 2023; Accepted: 11 September 2023; Published: 22 September 2023
Application of neural-network methods revealed relationships between hydrological and hydrochemical
characteristics of water flow, suggesting structural self-organization of substances dissolved in water in the form
of micro layering. In particular, the coefficient of correlation between the concentrations of such substances in
some cases reaches its nearly maximal value (0.99), combining with the high weights of neural network edges.
This can be supposed to be due to the mechanical and chemical interactions in river flow with the participation of
Van der Waals forces, hydration, and sorption. Other factors, not taken into account, can also have their effect, in
particular those responsible for the fluctuations of the parameters of order, determining the singular contributions
to the dynamic characteristics of the non-linear system under consideration. Such can be the cyclic oscillations of
the characteristics under control with an amplitude decreasing with a decrease in the intensity of the pollution/self-
purification processes in water medium and increasing with an increase in this intensity. The obtained information,
in addition to its direct purpose as a means to study the nature and properties of fresh water, is a necessary
condition for the effective control of water resource quality and water management activity.
Keywords: artificial neural networks, industrial waste discharges, neural-network analysis, pair and multiple
correlations, water quality, water-monitoring site
Introduction
The quasiperiodic variations of river water quality
characteristics (1) suggest the structural self-organization
taking place in it, i.e., the process of reordering of the
parameters of water composition and properties due to
internal factors. The importance of further studies into this
process is determined not only by scientific and informative
objectives but also by the need to more reliably manage the
economic activity under the stricter requirements of water
use and the maintenance of water-environmental safety.
There is no single and easily comprehensive model of
the structural self-organization of impurities in water (2,
3). However, for water management, it is quite enough to
answer the question of whether there exist pair or multiple
correlations between hydrodynamics and hydrochemical
characteristics for any individual water object. This study
is focused on the Iset River (a tributary of the Tobol
River) in Sverdlovsk oblast territory, where large-scale water
consumption and disposal imply the processes of either
formation or destruction of mutual correlations between the
monitored characteristics at different sites of hydrochemical
and hydrodynamic monitoring.
Experimental data
The study was based on the results of monthly monitoring
of river water in 1990–2010 performed by the Ural
Department of the Federal Agency for Hydrometeorology
and Environmental Monitoring.
The selected data have been collected at the following
stations (Figure 1):
– 5.2 km upstream Ekaterinburg (Palkino Vil. station no.
1),
– within city boundaries (2),
80

10.54646/bijcees.2023.10 81
FIGURE 1 | Hydrographic scheme of the Iset River within Sverdlovsk oblast (the circles show hydromonitoring stations). Translation of
geographical names in the diagram: : Palkino; : Ekaterinburg; : Bol’shoi Istok; : Aramil; :
Kolyutkino; : Kamensk-Ural’skii.
FIGURE 2 | Copper concentration in the first 10 months of 2008 at stations with numbers corresponding to those of data series.
FIGURE 3 | Mean copper concentration (black triangular markers), suspended matter concentration (squares), and water discharge (circles), as
well as the root-mean-square deviations of these characteristics, given by appropriate gray markers at each of the eight observation points.
– 7 km downstream (Bol’shoi Istok Settl., 3),
– 19.1 km downstream (Aramil Town, 4),
– further downstream (Kolyutkino Vil., 5),
– 21.3 km upstream of Kamensk-Ural’skii C. (6),
– 5.3 km upstream of this city (7), and
– 9.3 km downstream (8).

82 Rozental and Fedotov
TABLE 1 | A list of the neural networks studied for the observation
sites (a fragment).
Site Type Inputs Hidden Output TError VError TeError Training
1 Linear 3 – 4 1.03 1.08 1.24 PI
1 MLP 1 13 4 1.05 1.05 1.25 BP16b
1 RBF 3 5 4 0.65 0.74 0.82 KM,KN,PI
2 Linear 3 – 4 2.15 3.48 2.14 PI
2 MLP 1 58 4 2.20 3.53 2.14 BP50,CG2b
2 RBF 2 4 4 1.01 1.02 0.95 KM,KN,PI
3 Linear 3 – 4 2.35 1.61 1.65 PI
3 MLP 3 8 4 8.23 7.86 7.88 BP0b
3 RBF 3 5 4 1.32 0.95 1.15 KM,KN,PI
4 Linear 3 – 4 8.23 13.58 42.29 PI
4 MLP 3 4 4 4.34 14.30 15.00 BP0b
4 RBF 3 13 4 1.94 5.36 2.66 KM,KN,PI
5 Linear 3 – 4 1.96 2.03 3.30 PI
5 MLP 1 8 4 5.39 5.06 5.85 BP0b
5 RBF 3 20 4 0.87 1.45 2.57 KM,KN,PI
6 Linear 3 – 4 1.32 1.12 2.44 PI
6 MLP 1 12 4 4.34 4.30 5.00 BP0b
6 RBF 2 2 4 0.90 0.88 1.47 KM,KN,PI
7 Linear 3 – 4 2.19 2.15 2.40 PI
7 MLP 1 25 4 2.27 2.06 2.36 BP6b
7 RBF 3 2 4 1.03 0.81 1.10 KM,KN,PI
8 Linear 3 – 4 2.19 1.93 1.93 PI
8 MLP 1 88 4 2.82 2.48 2.53 BP0b
8 RBF 3 6 4 0.92 0.87 0.71 KM,KN,PI
Denotations of the columns and networks. Type is network architecture type (Lin,
linear; MLP, multilayer perceptron; RBF, radial; Inputs: number of neurons at the
network entry; Hidden, number of neurons in the intermediate (hidden) network layer;
Output, number of neurons at the exit from the network; TError, error on the learning
set; VError, error on the verification set; TeError, error on the test set; Training, training
algorithms (PI, pseudo invert; BP, back propagation). For example, MLP «1–13–4»
means a three-layer MLP-network, including 1 input neuron, 13 hidden neurons, and
4 output neurons.
The geochemical character of the provinces where the
river’s channel lies causes a higher natural pollution of river
water. For example, the mean concentrations of iron, copper,
nickel, and zinc that are standardized by their maximal
allowable concentrations reach 10 units and more at all
stations. At the same time, the chaotic character of the
time series, which is partly due to wastewater discharges,
hampers the identification of regularities in the variations of
the monitored characteristics. As a result, the only conclusion
that can be derived, for example, from Figure 2 is that at
all hydromonitoring stations in the industrial region under
consideration, the concentration of copper compounds is far
in excess of the maximal allowable value for water bodies used
in the economy, one of which is the Iset River.
It is more difficult to identify any regularities in large
data bodies for water-polluting substances over longer time
intervals. As can also be seen from Figure 3, variations in the
arithmetic mean concentration of impurities at observation
sites in some cases disagree with the values of the root-
mean-square deviation of the respective characteristics. This
indicates the heteroscedasticity of the system, which is due
to the heterogeneity and non-stationarity of the data series.
That is why numerical technologies of intellectual analysis are
required to achieve the goal.
Neural-network method of study
The numerical analysis of data was based on artificial neural
networks (ANN) in the specialized neural-network software
package Statistica Neural Networks (SNN) (4). For the
detailed study of the available time series, neural regressions
were constructed with the use of networks with four types of
architecture (topologies): linear two-layer networks (Linear),
non-linear three-layer and four-layer perceptrons [multi-
layer perceptron (MLP)], non-linear networks with a radial
basis function [radial basis function (RBF)], and non-
linear generalized regressive networks [generalized regressive
neural network (GRNN)].
The data were prepared by separating each time series into
subsets:
– Training, the major portion, not less than 50%,
– Verification, confirming the result by its comparison
with experimental data, up to 25%,
– Test, showing how well the system can analyze new
data, up to 25%.
Such a distribution was made taking into account
the structure and completeness of the available source
data (up to 250 for each characteristic involved in each
observation section).
The cause-and-effect relationships were studied by
observing the effect of three input (Input) characteristics
[water discharge (m3/s), water temperature (◦C), and
suspended matter concentration (mg/dm3)] on four output
(Output) water chemistry characteristics (the concentrations
of iron, copper, zinc, and nickel, all in mg/dm3).
The network architectures were formed by superimposing
experimental data arrays, considering their preparation, on
all types of network architectures that correspond to the
idea of the problem.
Network training was made with the use of only training
and verification samples by more than 10 algorithms of linear
and non-linear optimization, including back propagation of
error, pseudo invert, and so on.
The test samples intended for forecasting were not used
in training. The setting of detailed parameters for these
algorithms, such as the number of training epochs, noise,
accuracy, etc., was taken as standard by default.
In the estimation of ANN training, an algorithmic
characteristic (criterion) of good quality was taken to be
the small enough absolute errors of training (TError),

10.54646/bijcees.2023.10 83
TABLE 2 | Neural regression statistics for linear «3–4» network at site 6.
Tr. Fe Ve. Fe Te. Fe Tr. Cu Ve. Cu Te. Cu Tr. Zn Ve. Zn Te. Zn Tr. Ni Ve. Ni Te. Ni
Data mean 0.47 0.44 0.57 19.70 18.54 26.32 30.26 26.61 31.55 9.84 9.75 9.37
Data S.D. 0.46 0.44 0.73 13.49 12.77 36.23 23.87 17.90 33.16 13.80 9.01 6.96
Error mean 0 0.01 −0.13 0 0.68 −5.96 0 2.35 −0.28 0 −0.34 0.38
Error S.D. 0.44 0.36 0.70 13.28 13.22 35.45 23.45 18.97 31.93 13.71 8.53 6.92
Abs E. mean 0.33 0.25 0.39 9.58 10.31 16.67 15.78 15.33 17.83 7.01 6.31 5.71
S.D. ratio 0.94 0.81 0.96 0.98 1.03 0.97 0.98 1.05 0.96 0.99 0.94 0.99
Correlation 0.32 0.70 0.31 0.17 −0.28 0.27 0.18 −0.21 0.28 0.11 0.46 0.15
Data Mean is the mean concentration at a site. Data Standard Deviation (S.D.) is the standard deviation of the concentration at the site from the value Data Mean. Error Mean is the
mean error, i.e., the mean residual difference between the measured and calculated (by neural network) values at the site. Error S.D. is the standard deviation of the source data from
those calculated by the neural network. Abs E. Mean is the absolute mean error (the arithmetic mean of the modules of differences between the source and calculated values at the
site). S.D. Ratio: Error S.D./Data S.D. is the relative error of neural regression. Correlation is multiple correlation coefficient.
verification (VError), and testing (TeError). The main
statistical characteristics of ANN training were Pearson’s
multiple correlation coefficients and the values of the weight
coefficients of neural network links.
The analytical means for network operation estimation
included the results of calculating correlation-regression
statistics, optimal weights of links, sensitivity analysis (testing
the response to small variations of weights), and analysis
of what-if type (testing the response to small variations of
source data). The graphical means included illustrations of
network architecture and its response surface.
The issue of the choice of the network architecture that can
give an acceptable model for a problem remained open (it
has no unique solution), and, in practice, it was solved by the
search of variants. Therefore, more than a hundred different
acceptable network architectures were examined for each set
of data collected at observation stations.
The number of neurons at the entry and in the inner layer
of the network was varied.
The number of neurons at the exit of the network (Output)
remained constant and equal to the number of metals
involved in the study.
The teaching parameters were taken as
standard (by default).
Several best networks with minimal training and
testing errors were chosen for detailed study and making
conclusions. The first approximation was taken in the form
of linear networks. Non-linear networks were used to test
and improve the obtained neural-network relationships, as
shown in Table 1.
It was found that, at all hydromonitoring gages, linear and
non-linear neural networks, with the use of different training
algorithms, showed similar and relatively high quality in
revealing possible relationships between network elements,
which makes the results of neural network studies given
below quite reliable.
TABLE 3 | Weights of the links in linear «3–4» neural network at site 6.
Fe Cu Zn Ni
Water discharge 0.49 −0.11 −0.05 0.06
Water temperature 0.06 −0.01 −0.06 −0.01
Concentration of suspended particles −0.13 0.26 0.22 0.02
Results of neural-network study of
the data
The results mentioned in the head of this section include:
1. Statistics of linear and non-linear neuro-regressions of
the chosen type of network architecture with successive
specification of.
– the number of input characteristics, such
as water discharge, suspended particle
concentration, and the temperature;
– the number of intermediate (hidden) neurons;
and
– the numbers of output parameters.
Thus, the record of the type linear «3–4» means
that the network used in the study was a two layer
perceptron, containing 3 input neurons (discharge,
temperature, and suspended particles), 0 hidden
neurons, and 4 output neurons (iron, copper,
nickel, and zinc).
2. The weights of the links of linear/non-linear neural
networks with specified numbers of input and output
characteristics.
Tables 2 and 3 exemplify the results of the study obtained
with the use of the data at an observation site.
The value of Error Mean (Table 2) was close to zero at
all sites, thus demonstrating that the neural network, trained
on the results of preliminary measurements, reproduced
the source data almost without errors, at least taking into

FIGURE 4 | The largest detected values of the coefficients of pair
linear correlations for concentration of metals (the full line), neuro
correlations of the type «3–4» (long-dash line), and the weights
of neuro correlations in the systems of suspended particles-metal
(short-dash line), and water discharge-metal (dotted line).
account the measurement errors in the source data. At the
same time, the scatter of the calculated values of Error
standard deviation (S.D.) was commonly less than the scatter
of the original values. In addition, the level of Abs E. Mean
remained higher than the Error Mean, i.e., the signs of
the differences between the measured and calculated values
alternated almost uniformly and, in the calculation of Error
Mean, they compensated one another. In addition, the total
relative error of neural regression S.D. Ratio was most often
less than unit. This was most typical of copper and iron
concentrations, such that the standard deviations for these
two metals were much less than the standard deviations for
the source data, thus suggesting the high accuracy of the
neural regressions.
The effect of temperature on metal concentrations was
found to be negligible for all sites, as can be seen in Table 3.
The key results of studies by neural network method
are given in Figure 4. One can distinctly see the high
correlation of the metals with one another and with the
concentration of suspended particles at the fourth site,
likely after active discharges of these substances near the
observation sites 2 and 3, where many industrial plants-
water users are concentrated. The weight of the neural link
between water discharge and metals, i.e., the hydrodynamic
and hydrochemical characteristics, also somewhat increases
here, although the maximal values of this characteristic
were recorded in the zones near sites 6 and 8, which
can be naturally attributed to the least effect of the factor
of concentration scatter here because of the decrease in
the rate of industrial waste discharge in this part of the
industrial region.
Overall, Figure 4 indicates the existence of processes
of reordering (self-organization) of water composition and
properties in river flow, lower in the zone of intense
technogenic impact and higher at its decrease. This can be
seen from multiple and pair correlations, which, depending
on the level of impact mentioned above, vary from
weak (with a regression coefficient of 0.2−0.4) to very
strong (0.99), synchronous with the values of weights of
neural network edges.
In the use of the ANN, it was taken into account that
each layer of the neural network depends not only on
the state of the entry neurons but also on an additional
(Threshold) neuron, the state of which determines the
threshold of activation of the input neuron (4). In this
study, the input and output neurons correspond to the
dynamic and chemical characteristics incorporated in the
model. The threshold neurons do not correspond to any
of them; therefore, in the protocols of studying the edge
weights of neural networks, they were denoted as factors
not taken into account. As can be seen from Figure 5, the
values of these factors for all observation sites are negative,
meaning that they accelerated the activation of the output
neuron. As to their absolute values, it was found that, for
these factors, they show periodic oscillations. As can be seen
from Figure 5, such oscillations are relatively low for the
concentrations of iron and zinc, and they are higher for
nickel after the third observation site. The nature of this
phenomenon requires additional studies; however, we can
suppose that, for the non-linear system under consideration,
i.e., the water matrix, which contains admixture particles,
this is a consequence of the dissipation of the energy of
microstructure self-organization and regular restructuring
of the system, i.e., bifurcation, caused by this restructuring.
FIGURE 5 | Unaccounted for factors that arise at evaluating neural network weight for the concentrations of iron (full line), copper (long-dash
line), nickel (short-dash line), and zinc (dotted line).

10.54646/bijcees.2023.10 85
Developing in time, this process resembles cyclic oscillations
of the characteristics of the composition and properties of
natural water with an amplitude decreasing at moderate
rates of pollution/self-purification and increasing when these
processes accelerate (5).
Conclusion
The problems with recording non-linear correlations
between varying chemical and dynamic water characteristics
in river flow required the use of intellectual information
technologies (neural networks) as a way to generalize
classical correlation-regression methods. This made it
possible to reveal hidden non-linear relationships between
seemingly unordered data arrays without a priori analytical
specification of the form of the expected relationships.
Experiments revealed a correlation between the
concentrations of dissolved substances and their relationship
with water discharges at the observation sites with a narrower
scatter of the examined characteristics, which forms under
the effect of heavy use of water in the industrial region under
consideration. This indicates the structural self-organization
of water in the flow and ordering in the form of micro
layering of foreign particles.
The self-organization processes can be assumed to proceed
under the effect of forces of physical, chemical, and
mechanical nature (hydration, sorption, and hydraulics).
In particular, the elastic forces caused by deformations of
the hydrogen bond grid in water push particles in water
toward grid defects, thus forming micro layering, which
counteracts the diffusion leveling of the concentration (2). At
the same time, the hydrodynamic structure of the water flow,
examined by the analysis of the complete system of equations
describing the dynamics of fluid flow, revealed its structural
elements, such as waves, vortices, and high-gradient layers (6,
7), which contribute to the structural self-organization.
Discussion
The factors that counteract the self-organization described
above include the technogenic activity, in particular
wastewater discharge and diffusion, which tend to level the
concentrations of admixture particles. The effects that appear
at the predominance of some tendency, i.e., admixture micro
layering or its concentration leveling, can be seen at the
joining of water volumes with different compositions and
properties:
1. If the differences are not large, the diffusion does not
cope with the layering, and, after joining in a single
channel, the water flows with different compositions
run over a long distance without mixing (8). Similar
are examples of river water which spreads over the
ocean surface, forming haloclines in tidal estuaries
(9). Also known are other stratifications, for example,
at jumps in temperature (thermoclines) or density
(pycnocline) (10).
2. Another picture is formed when the minimal
admissible concentration difference between the
touching water objects with different compositions is
high enough for the interphase tension to be higher
than the elasticity coefficient of the grid of hydrogen
bridges. In such cases, judging by laboratory data (11,
12), turbulent mass transport forms near the phase
interface, accompanied by density fluctuations,
protuberance formation, opalescence, and an
increase in the megahertz dielectric permittivity.
Such phenomena should be expected in the zones near
sites where high-pollution wastewater is discharged
into river flow.
Energy exchange in multicomponent water medium,
containing various foreign substances, includes several
processes, some of which are slow dissipative (diffusion)
and some are relatively fast processes controlled by ion-
molecular interactions (5) and hydrodynamic forces in forced
flows (6). The dynamics of fluid flows can be described
by a system of equations of transport of matter, density,
momentum, and total energy–analogs of the conservation
laws for isolated systems (13). The high rank of the system of
fundamental equations for weakly dissipative media is related
to the existence of fine-structure components of periodic
and non-steady-state flows (7). The simplest leveling of the
concentration works only in a stationary phase. Accordingly,
the hypothesis of an inert admixture has no grounds, except
for J. Taylor’s declaration (14).
According to the general scientific knowledge, the factors
that have an effect on the revealed non-linearity in the
examined characteristics of natural waters are fluctuations of
the parameters of order (15), which determine the singular
contributions to the dynamic characteristics of water flow.
Author contributions
OR: Analysis of water problems. VF: Neural
network data analysis.
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