=Paper=
{{Paper
|id=Vol-2258/paper48
|storemode=property
|title=Application of Fuzzy Logic Elements under the Moisture Supply Evaluation in the Plant-Soil-Air System
|pdfUrl=https://ceur-ws.org/Vol-2258/paper48.pdf
|volume=Vol-2258
|authors=Viktor Alekseev,Sergey Vasilyev
}}
==Application of Fuzzy Logic Elements under the Moisture Supply Evaluation in the Plant-Soil-Air System==
https://ceur-ws.org/Vol-2258/paper48.pdf
Application of fuzzy logic elements under the moisture supply
evaluation in the plant-soil-air system
V V Alekseev1 and S A Vasiliev2
1
Department of Information Technologies and Mathematics, Cheboksary Cooperative Institute,
428025, Cheboksary, Russia
2
Department of applied mechanics and graphics, Chuvash state University, 428015,
Cheboksary, Russia
Abstract. Making the right decisions in the everyday practical activities of the
agrotechnologist is the most important component determining the conditions for the growth
and development of plants. It takes special importance in the conditions of incomplete (fuzzy)
information. One of the perspective directions of solving problems of forecasting and modeling
natural and human-corrected phenomena and processes is fuzzy logic. Works of many Russian
and foreign scientists are devoted to studying of weather forecasting and the least costly
creation of optimal conditions for the growth and development of agricultural plants.
Accordingly, there are various and sometimes contradictory points of view on the definition of
predicted norms and the timing of irrigation. The relationships obtained in most of the studies
and the calculation formulas describing the relationship between the volumes of water entering
the sediments and watering with the processes of its infiltration into the soil are in many cases
specialized for certain soils under specific conditions and are not always portable from soil to
soil. In this regard, the paper discusses the modeling of the frequency and intensity of
precipitation from long-term observations, as well as numerical calculations of the intensity of
water absorption into the soil under natural precipitation and irrigation. This approach allows
planning erosion-safe irrigation, which, in combination with natural precipitation, provides a
favorable regime in the plant-soil-air system and, accordingly, obtaining high yields for the
tested land. The state of the soil at different times determines in many respects, on the one
hand, the proportion of soaking water, and, on the other hand, the proportion of running water.
Moreover, if the first part is directly connected with the moisture supply of plants, the second
directly determines the danger of erosion processes. The rate of water absorption into the soil is
influenced by factors such as specific surface area, soil porosity, initial humidity, structural and
water resistance of aggregates, root system and plant density, etc.
1. Introduction
For modeling and forecasting weather conditions (in our case, time, frequency, duration and intensity
of precipitation), the use of fuzzy logic laws is quite promising. The use of the fuzzy system apparatus
is connected with the fact that the task has the uncertainty and inaccuracy of the initial information.
The decision-making process in this case is multi-criteria and rather complex. Uncertainty and
inaccuracy of information results from the processing of the abovementioned precipitation data over a
50-year period. The use of cluster analysis has made it possible to break the entire data array into 5-6
most likely cases. Within each cluster, according to the laws of mathematical statistics, information
about the time, frequency, duration and intensity of precipitation is revealed for the cluster. That is,
after analysis, their mean values (ranges) and corresponding probabilities for each rain in the cluster
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under consideration were determined. Conditionally, fuzzy subsets divide the intensity and duration of
precipitation.
Since the intensity of moistening and evaporation of water from the soil depends both on its
properties and on external conditions, conclusions on the moisture state in the soil obtained with the
help of fuzzy logic can be used. The factors that determine evaporation and the rate of soaking are not
well understood, and therefore a number of difficulties arise in forecasting. There are no common
universal methods for describing evaporation and moistening of soil in the literature, and existing
models are limited to application only under certain conditions because of the assumptions made.
The moisture consumption from the soil can be conditionally divided into two types: productive –
the consumption of moisture by plant cover and unproductive – evaporation from the soil surface,
infiltration, runoff, etc. After a runoff and infiltration, the largest proportion of the flow is due to
evaporation from the soil surface. The soil can then dry up to a depth of 20 cm, and in arid regions up
to 40 cm or more. In addition to soil properties, the evaporation rate depends on external conditions
such as temperature, wind speed, surface shape and plant cover.
Evaporation of water largely depends on the temperature, which determines the energy of soil
moisture. When considering evaporation, however, we take into account the additional energy costs
associated with the fact that in the soil, as the volume of moisture decreases, the surface area of the
condensed phase increases [1,2]. Obtained in most studies of Russian and foreign scientists, the
dependencies and design formulas describing the infiltration processes are in many cases specialized
for specific soils under specific conditions and are not always portable from soil to soil [3].
2. Conditions, materials and methods of research.
We implement the well-known mechanism of logical inference. Let us consider, for example, the
duration. In view of the fact that for different rains in a cluster the duration T is different and it is
absolutely certain that it has never been less than Tmin and has never exceeded Tmax, then the operand
assignment function has the following form:
x Tmin Tmax x
D( x) : max min ,1, ,0 .
(1)
T Tmin Tmax T
1
0.8
0.6
D ( x)
0.4
0.2
0
0 12 24 36 48 60 72 84 96 108 120
x
Figure 1. The graph of the assignment function for the duration (minutes) of the average “autumn”
rain Tmin = 65, T = 80, Tmax = 92.
When considering the rain intensity, the assignment function can look like this (Figure 2):
x I min I x
A( x) : max min ,1, max ,0 .
(2)
I 0 I min I max I1
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1
0.8
0.6
A ( x)
0.4
0.2
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x
Figure 2. The graph of the assignment function μA (x) for the intensity (mm per minute) of the
average “autumn” rain Imin = 0.12, I0 = 0.25, I1 = 0.40, Imax = 0.56.
Figure 2 shows that the intensity varies between 0.25 and 0.40, but has never been less than 0.12
and has never been greater than 0.56.
Similarly, if it is a time interval between rains, then the assignment function can have the form
(Figure 3):
x 120 x 145 x 115
A( x) : max min ,1, max 1 ,1 ,0 .
180 115
(3)
128 120 150 145
Figure 3. Time interval between rains (hours).
Having described mathematically fuzzy statements, we gave complete information about the
moisture entering the soil.
Absorption of water in the soil is a complex process. The moisture flux is defined as the volume of
water absorbed into the soil per unit of time through unit of area: q=Q/St. Factors such as specific
surface area, soil porosity, initial moisture content, structural and water resistance of aggregates, root
system, etc. influence the rate of water absorption into the soil.
The determination of the filtration coefficient is often carried out using vertical soil monoliths. The
volume of the absorbed water is measured, maintaining a constant thickness of the water layer on the
surface of the monolith. There are non-pressure filtration (with a single hydraulic gradient) and
pressure filtration (the gradient is greater than one).
The absorbing intensity that decreases with time describes the equation of Kostyakov A.N. [4]:
K t K 0 t , (4)
where Kt – intensity of absorption at the time t, K0 – intensity at the beginning of soaking, α –
coefficient.
Averyanov S.F. and others have improved the formula (4) by adding a constant equal to the
filtration coefficient Kf, because, after a certain time, after filling the pores with water, the flow
stabilizes and water filtration through the soil begins i.e. K t K ф K 0 t [4]. However, this type of
model is not standard and its linearization for statistical processing is non-trivial, so the use of
spreadsheets in order to obtain interesting numerical values is difficult.
In a number of papers, the factor еi ( is an empirical factor, i is the slope) is added to the formula
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(4).
Not absorbed water causes the threat of erosion-hazardous water runoff. Therefore, many
researchers have been offered all sorts of solutions to improve absorption: discrete watering with
regulation of intensity; use of short-term irrigation for a certain time to the main one in order to
increase the coefficient of moisture conductivity (preliminary wetting); magnetization of water;
mechanical loosening of the soil and its splitting; increase of soil texture using polymeric materials.
As mentioned earlier, the equation of Kostyakov A.N. has a power-like form K t K 0 t , and,
therefore, is included in the set of standard functions of modern spreadsheets (power), according to
which equations of non-linear regression are obtained. Therefore, the search for numerical values of
the coefficients of the model K0, and α does not present difficulties in the statistical processing of data.
However, the formula by Averyanov S.F. is more precise [4] Kt = Kf + K0 t-α (Kf is the filtration
coefficient). It is obtained from the formula by Kostyakov A.N. by adding a constant equal to the filter
coefficient. This is due to the fact that after a while, after filling the pores with water, filtration of
water through the soil begins.
However, from the standpoint of mathematical statistics, the type of model proposed by Averyanov
S.F. is not standard and the use of spreadsheets for its processing is difficult. If it is necessary to obtain
regression dependences of the absorption rate on the porosity and specific surface area of the soil, the
following solution is available. In the work [1, 4], to calculate the coefficient of moisture conductivity,
the following formula was obtained:
0 w
2
2
K 1 1 , (5)
0S 2 1 0 0
where η is the viscosity of water, Pa c; S is the cross-sectional area of the soil sample, m2; through
which gas flows; α, λ – constants depending on the form of the three-dimensional model, 0 – volume
specific surface, m2/m3; w – volumetric moisture, m3/m3, П0 – porosity, in fractions.
The formula is valid for cases when water flows through soil partially filled with water. The
equation (5) shows the ratio between the coefficient of moisture conductivity and moisture in an
explicit form and makes it possible to take into account the properties of the soil, since it depends on
both porosity and the specific surface area of the solid phase of the soil.
3. Analysis and discussion of the results
When using the formula for calculating the coefficient of moisture conductivity (5), for the value (K –
Kf) the dependence is reduced to a statistically easily processed power form, which makes it possible
to determine the numerical values. The use of the developed programs makes it possible to study the
dependence of Kf, K0, α on porosity, specific surface and humidity.
When modeling the intensity of water absorption into the soil, the maximum possible amount of
absorbing moisture is determined for the current time under the current conditions. To do this, a
constant zero potential ψ is set in the upper soil layer and, according to the Darcy formula, the possible
volume of moisture transferred to the underlying layer, is calculated under the given conditions. The
work of the software for calculating the intensity of absorption is shown in Figure 4.
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Figure 4. Work of the software for calculating the absorption rate.
The task of determining the wetting profile during sprinkling is one-dimensional, therefore a layer-
by-layer (50 layers) moisture transfer with layer thickness Δh = 5 mm was calculated (Figure 5). When
calculating the potential difference of soil moisture in the layers, a gravitational potential gΔh was
added.
Figure 5. Operation of the software for calculating humidification profiles for sprinkling and drip
irrigation.
The implementation of the software for calculating the humidification profile is carried out by
specifying the moisture volume entering the upper layer per unit of time, arrays of porosity values,
specific surface area, and initial moisture for each layer, for which the coefficients of moisture
conductivity and soil moisture pressure were calculated. According to Darcy's formula, the volumes of
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moisture that flowed from layer to layer were calculated. The number of cycles of allocation
approximately corresponds to the time of passage of the sprinkler through the area.
4. Conclusion
The developed software for calculating the profiles of moistening and the intensity of soaking can use
data of soil moisture, time and intensity of precipitation obtained with fuzzy logic. The comparison of
the values obtained from the formulas with the experimental data confirmed the statistical significance
and, consequently, the justification of the proposed calculation method for describing the conditions of
moisture availability in soils. Due to the fact that the physical and hydrophysical properties of a
specific soil are taken into account in a specific area, their use is economically effective for
agromeliorative measures, as well as for numerical modeling of the processes of water absorption into
the soil during sprinkling and drip irrigation.
5. References
[1] Alekseev V V and Maksimov I I 2013 Aerodynamic method for obtaining the soil water
retention curve Eurasian J. Soil Sci 46(7) pp 751–757 DOI: 10.1134/S1064229313070028
[2] Sysuev V A et al 2013 Soil water retention curves based on idealized models Russian Agr. Sci.
39(5-6) pp 522–525
[3] Maksimov I I et al 2016 Simulation of channel development on the surface of agrolandscapes
on slopes Eurasian J. Soil Sci 49(4) pp 475–480 DOI: 10.1134/S1064229316040074
[4] Maksimov I I and Alekseev V V 2017 Hydrophysics of soils in land improvement (Cheboksary:
New Time) p 280
[5] Sysuev V A et al 2013 The catchment area of small rivers as an object of anthropogenic
agrolandscape Agr. Sci. Euro-Northeast 5 (36) pp 59–65
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