Theoretical Approaches to Water Use Optimization for Rice Irrigation Systems in the Lower Kuban

Abstract

The object of research is irrigation systems that are hydraulically connected to a large specialized agricultural complex for rice production, located in the lower part of the Kuban River basin and experiencing an acute shortage of water resources. In the last decade, rice irrigation area decreased by 50%. Calculation technology is proposed for water resources management of the Lower Kuban basin basing on integrated use of six models developed in Russia: hydrological and meteorological forecasts; simulation models of yield formation to calculate crops water demand; water balance models to develop water use schedules for irrigation systems; hydrodynamic models to calculate water use scenarios; optimization models to choose a trade-off Pareto management options; and statistical models to calculate yield losses depending on water resources deficit. This technology allows adopting optimal trade-off solutions online with the Lower Kuban water resources management in interests of agriculture.

1. Introduction

Over the long period of operation of the country’s largest Nizhnekubansky water management complex, the operational characteristics of a significant part of its hydraulic structures (HS) have changed significantly in comparison with the design ones, and some of them have lost their management functions. The need to consider the current technical HS condition is due to the fact that they are the main structural and functional elements of an integral system of the reclamation and water management complex designed to provide water resources to 215 thousand hectares of irrigated rice lands. The reclamation water management complex of the Lower Kuban includes, in addition to the Krasnodarsky one, the Kryukovskoye, Varnavinskoye, and Shapsugskoye reservoirs, the Fedorovsky retaining and Tikhovsky water distribution waterworks, more than 100 functioning pumping stations and over 550 HS, more than 3 thousand km of irrigation and discharge channels, up to 156 thousand hectares of natural fishery reservoirs [1].

Irrigation systems and hydraulic structures of the agricultural complex of the Lower Kuban are shown in Figure 1.

Figure 1.

Irrigation systems and hydraulic structures of the Lower Kuban.

The Krasnodarskoye reservoir is the main source of irrigation and performs a number of other important functions: population protection from floods, high water control with discharges up to 1200 m³/s. The main function of the reservoir is to provide water for 12 rice irrigation systems, the needs of fisheries, and navigation conditions for shipping. As a result of siltation, the capacity of the Krasnodarskoye reservoir decreased, and the value of the temporary operation level dropped below the design by 90 cm. Failures in the technical condition are also noted at other reservoirs, waterworks and HS, including pumping stations, and water supply and drainage channels, which negatively affect the water supply of rice systems. Reduction of the total volume of flood water in reservoirs, which previously, according to design parameters, made it possible to avoid a shortage of irrigation water at the most stressful time in terms of agrometeorological conditions. The low efficiency of channels, pumping stations, and other HS as a result of their unsatisfactory technical condition are also the cause of water scarcity [2].

In recent years, the area of rice crops in the Krasnodar Territory has grown to 130 thousand hectares. The average yield in the region is about 7 t/ha, with a total water intake for rice irrigation of more than 2.5 km³ [3]. An increase in air temperature and a decrease in precipitation in the rice-growing area during its growing season, associated with climate change in the Kuban, lead to an increase in irrevocable water consumption. High irrigation rates of rice, reaching an average of 20 thousand m³/ha or more, on saline soils, additionally cause a shortage of irrigation water.

The current state of the water management complex, characterized by transformation and degradation of operational characteristics, is mainly due to the processes of wear of engineering systems and their destruction under the influence of natural and industrial factors, it is impossible to return to the previous design parameters. In the current situation, one of the productive ways to reduce risks and damages from systematically observed water scarcity is not only an obvious direct opposition to degradation factors, repair and replacement of HS, reduction of rice acreage, new rice varieties resistant to water scarcity, and low-volume irrigation methods, but also a flexible management system for resource distribution and use. Adaptive properties of the rice agro complex, as an integral result of the agricultural and agro-industrial (agricultural producers) complexes’ water users operational and production activities can be achieved with the management system organically combining strategic and tactical goals. First of all, these are combined into single regional and local levels of monitoring the elements state of the rice agro complex and the distribution of water resources, static long-term, and real-time dynamic operation modes of water management and hydro-reclamation systems elements.

1. The strategic level involves the implementation of seasonal planning for the distribution of water resources in form of the most probable management scenarios, using information on rice acreage and their spatial distribution, on the technical state and characteristics of the HS for water intake and transportation to consumers and forecast data on the water content of surface and groundwater sources. Thus, already at the planning stage, water management activities are closely connected with the plans for rice-growing farms. The formation, selection, and analysis of the most suitable scenarios for water management for the upcoming cycle of agricultural production are implemented using hydrodynamic modeling of water flows in the river basin area within the boundaries of the agro-reclamation water management complex [4].

2. The tactical approach provides optimization of water use during the irrigation period basing on forecast hydrological and meteorological models in order to maintain optimal water consumption in conditions of limited water resources. The flexibility of management is achieved through the use of calculations in the operational mode of water distribution scenarios based on a hydrodynamic model, considering the requirements of water users and the available volume of water (inflow and water supply); simulation models of crop yield formation, allowing to calculate the needs of crops in irrigation water, to forecast yields considering restrictions on water resources; models of water balance of irrigation system fields for the formation of irrigation schedules and water distribution for irrigation of crop rotations within the farm; multifactorial statistical models for assessing production losses of gross yield in low-water years.

Calculations done periodically using this tool allow you to quickly respond to the supply of agricultural producers with water, adjusting the irrigation regime during the vegetation period, as well as through local redistribution and adjustment of water use. The analysis of the results obtained using the above approach at the end of the irrigation season following the harvest results will make it possible to form a water use schedule for the next year adapted to the expected environmental conditions, making the management system trainable.

The need for such an analysis arose due to the fact that, on the one hand, water demands are formed by agricultural producers, and their adjustment and implementation are carried out by the Federal State Budgetary Institution “Kubanmeliovodkhoz” management department, while the indicators of the operation service are rice yields and gross output from the entire territory of the reclamation and water management complex, forcing to control water consumption. On the other hand, water demands by agricultural producers are based on the principle of “from what has been achieved,” i.e., the more, the easier it is to carry out the technological process of cultivation, which, on the contrary, creates conditions for increasing the risk of developing water scarcity.

2. Materials and methods

The following set of initial data was used to analyze the water supply and water use of agricultural producers of the Kuban reclamation agro complex based on the water balance of rice irrigation systems lands:

1. Production data of the Federal State Budgetary Institution “Kubanmeliovodkhoz” management department on water resources use (Form 1-BX) with information on water intake from the Kuban River basin, including reuse, on water supply for irrigation of rice and non-rice fields, on watering of rivers and reservoirs, efficiency of canals, on acreage of rice and other crops, and on the volume of drainage runoff.

2. Retrospective, current, and forecast hydrometeorological data of the Kuban River basin.

3. Maps of land use, soils, and groundwater levels, as well as schemes of water supply and disposal.

4. Satellite images, digital terrain models, and topographic maps.

5. Field observations and data from literary sources.

In addition, the following computer programs and models were used:

The river inflow forecast for the estimated period was carried out according to a special model using standard data from the Hydrometeorological Center. A retrospective series of hydro and meteorological elements is selected from the database, for which the recorded inflow is close to the current and forecast values of the Hydrometeorological Center. The selected data series are adjusted by normalizing coefficients and then used as input information for calculating daily forecast values on the same model. The algorithm for forming a meteorological forecast is similar.

Crop yield models for calculating the daily parameters of water exchange of agricultural lands are similar to those presented in [5]. Based on the results of numerical experiments, water consumption schedules for rice, corn, alfalfa, and wheat during irrigation and on rainfed lands were formed. Evaporation from the water surface of rice paddy fields and water objects was calculated according to the Ivanov formula [6].

The dynamics of the water balance of a structurally heterogeneous agricultural landscape were calculated with a monthly time step according to a simplified scheme for individual landscape elements and soil layers using traditional hydrological methods. The entire territory of the considered agricultural landscape was divided into separate elements by land category, type of land use (irrigated, rainfed), and water objects (canals). For each element of the agricultural landscape, the monthly values of the water balance components were calculated according to formula 1.

$$∆S=P+M+\mathrm{Ф}+p-E-{\mathrm{Д}}_{\mathrm{р}}+\left(\overline{\mathrm{П}}-\overline{\mathrm{О}}\right)+\left(\underset{¯}{\mathrm{П}}-\underset{¯}{\mathrm{О}}\right)$$E1

where $∆\mathrm{S}$ is the change in moisture reserves for the $\left({\mathrm{S}}_2-{\mathrm{S}}_1\right)$ period; $\mathrm{P}$ is the meteorological precipitation; $\mathrm{M}$ is the irrigation rate; $\mathrm{Ф}$ is the filtration losses; $\mathrm{p}$ is the water exchange of subsoil waters and underground water basin; $\mathrm{E}$ is the evapotranspiration; ${\mathrm{Д}}_{\mathrm{р}}$ is the drainage flow; $\left(\overline{\mathrm{П}}-\overline{\mathrm{О}}\right)$ is the surface inflow and outflow of water; and $\left(\underset{¯}{\mathrm{П}}-\underset{¯}{\mathrm{О}}\right)$ is the inflow and outflow of groundwater.

Meteorological data used to calculate the water balance components are obtained from the database and forecast calculations. The water balance of each particular element of the agricultural landscape was adjusted in accordance with the interaction with neighboring elements using an assessment of the lateral inflow of groundwater.

The efficiency of irrigation water transportation from the intake to the rice fields through inter-farm and intra-farm channels was calculated considering their design, length, and efficiency. In addition, the efficiency of the channels was assessed based on the calculation of the channels’ water balance as a water object. The channels’ water balance considered evaporation from the water surface and vegetation cover of the slopes, as well as filtration losses of lateral outflow to neighboring landscape elements adjacent to the channels.

Both in case of the implementation of the optimal (calculated) version of water resources distribution between water users plan, and in accordance with the demands submitted by water users, it is necessary to have a number of hydrological and water management conditions that ensure the possibility of the waterworks functioning and the required volume of accumulated and incoming water. Production reports on water resources use of the Lower Kuban formed the basis of a water use scheme that displays the level and discharge conditions at the water intake points from the river Kuban and its branches (Kuban and Protoka) which are necessary for the functioning of rice irrigation systems (Figure 2).

Figure 2.

Water use scheme of the lower Kuban. R0 – Krasnodarskoye reservoir; R1 – Fedorovskaya irrigation system; R2 – Kubanskaya, Ponuro-Kalininskaya and Maryano-Cheburgolskaya irrigation systems; R3 – Petrovsko-Anastasievskaya irrigation system; R4 – Pump stations No. 9 and No. 10 of Petrovsko-Anastasievskaya irrigation system; R5 – Temryukskaya irrigation system; R6 – Main canal of Chernoyerkovskaya irrigation system; R7 – Pump stations No. 1, No. 2, and No. 3 of Chernoyerkovskaya irrigation system.

For this scheme, many possible water distribution scenarios were formed with priorities and requirements for various water users and rice irrigation systems, including unscheduled releases from the Krasnodarskoye reservoir. Simulation of scenarios was performed on the hydrodynamic model of the Kuban River in the MIKE 11 software using the “Control structure” module [4].

With the help of a hydrodynamic model, water use scenarios were used to calculate water levels and discharges in controlled section lines and assess possible water scarcity for irrigation systems and reservoirs’ drawdown. A matrix of water distribution strategies was constructed from the solutions obtained.

The matrix of solutions obtained in this way was analyzed in the Pareto Front Viewer software [7, 8] to form a set of optimal solutions in the sense of Edgeworth-Pareto by the beginning of negotiations between the decision-maker and water users. The choice of a particular solution is achieved by a compromise method as a result of discussing possible options.

The economic assessment of the chosen solution was carried out on a statistical model of the regional level (branch), designed to calculate crop losses depending on the acreage, weather conditions, crops’ vegetation phase, and water scarcity. Production data for the last 10 years were used to develop a statistical model.

3. Results and discussion

As a test site, three irrigation systems of the Kalininsky branch were selected, the total area of the agricultural landscape of which is about 150 thousand hectares. Rice irrigation systems’ area is 16 thousand hectares, irrigated lands on non-rice crops have an area of more than 17 thousand hectares, and the array of rainfed agriculture area is 75 thousand hectares. The total volume of water supply to the agricultural landscape of the Kalininsky branch in 2018 is more than 500 million m³.

The rice paddy fields of the branch, located on the territory of three irrigation systems (Ponuro-Kalininskaya, Kubanskaya, and Mariano-Cheburgolskaya), were divided into four groups, depending on their affiliation to the water outlet. Water supply from the Kuban River comes to the water outlet through main channels. The characteristics of the irrigation systems’ outlets of the Kalininsky branch according to 2018 data are presented in Table 1.

No.	Irrigation system	Outlet	Rice sowing area,; thousand ha	Water supply volume,; million m^3
1	Ponuro-Kalininskaya	МПК	7	270
2	Kubanskaya	А-2	1,5	20
3	Mariano-Cheburgolskaya	Р-3	2	90
4		Р-4-3	1,3	18

Table 1.

The characteristics of the irrigation systems’ outlets of the Kalininsky branch.

Drainage flow disposal is provided by 4 pumping stations to the Kirpilsky Estuary and further to the Sea of Azov.

The water capacity of rice paddy fields at the beginning of the growing season was estimated by the relief, hydrophysical parameters of soils of different categories, the groundwater level, and the amount of precipitation accumulated during the winter period. The calculated values of evaporation from the rice paddy field surface and filtration were adjusted based on the results of hourly field observations conducted during the expedition of young scientists to the Kalininskoye LLC. Meteorological and soil parameters were monitored using the Davis Vantage Pro 2—automatic weather station—and the Veles-VP—soil humidity and temperature station. The map of the surface slopes of the test area was formed according to SRTM data.

A qualitative assessment of the water balance calculations result for the vegetation months was carried out by checking the fulfillment of Eq. (2) applied to the agricultural landscape as a closed system that is part of the catchment area. The values of the agricultural landscape components balance are given in Table 2.

Month	P, mm	Qs, mm	Qu, mm	E, mm	N, mm
April	360	1022.2	63.4	81.1	391.2
May	2656	737.4	1561.2	133.8	402.5
June	2573	740.7	1444.5	178.1	333.3
July	2386	430.2	1609.0	215.7	356.2
August	2080	129.7	1451.0	145.2	306.7
September	145	251.4	260.3	27.4	321.7

Table 2.

Monthly values of the main agricultural landscape water balance components of the Kalininsky branch.

$$\mathrm{P}-\mathrm{Qs}-\mathrm{Qu}-\mathrm{E}=\mathrm{N}$$E2

where P is the water intake + precipitation; Qs is the drainage outflow; Qu + E is the filtration + evapotranspiration; and N is the groundwater and soils moisture capacity.

The high correlation, as well as the permissible variation of the residual error in fulfillment of the equality condition, indicates the applicability of the models and calculation methods used, as well as the correctness of the display of hydrological processes within the boundaries of the considered territory when solving the task (Figure 3). The results of water balance calculations were used to analyze and evaluate the effectiveness of water resources management in the region.

Figure 3.

Dynamics of the agricultural landscape water balance components of the Kalininsky branch for the vegetation period of 2018.

The calculated data compared with actual water supply volume data for the vegetation period are presented in Table 3.

Month	Irrigation rate, m^3/ha		Wetting demand, million m^3	Actual supply, million m^3	Water supply failure, million m^3
	Rice crops	Non-rice crops
May	1200	309	24.6	79.8
June	4300	444	83.1	101.1
July	5200	457	99.4	72.6	26.8
August	5500	841	114.6	112.9	1.7
September	3700	406	65.5	59.1	6.4
Total	19900	2457	387.2	425.5

Table 3.

Water supply schedule for Kalininsky branch on 2018.

Water supply failure was observed in July, August, and September, which, according to our calculations, could lead to a decrease in rice yield from the maximum by 7% (5.8 c/ha), which is lower than the average annual value.

The demand for water intake from the Kuban River formed on the basis of water balance calculations is a reasonable requirement of the water user. However, in addition to these requirements for the volume and discharge of water, gravity water intakes also need to meet the conditions on the water level in the water source. Such a requirement for the Kalininsky branch (one of the R2 water users) is the water level in the upstream of Fedorovsky waterwork, maintained at 13.4 m mark.

For the subsequent simulation of water distribution scenarios in the MIKE11 software, using the “Control structure” module, a hydrodynamic model of the Kuban River was formed, considering lateral tributaries, reservoirs, and waterworks. The model was calibrated for 7 stream gauges, the error was up to 5 cm, which indicates adequate operation and the possibility of its use for scenario calculations [4]. The inflow to the Krasnodar reservoir was set according to the calculation on the hydrological forecast model. The initial data and boundary conditions for water intakes and hydraulic structures are established in accordance with the developed scenarios of water use. The scheme of the river network calculated on the hydrodynamic model in the MIKE11 is shown in Figure 4.

Figure 4.

Scheme of river network for hydrodynamic model.

River network plotted from village Kosta Khetagurov to the Azov Sea:

• river network on river bed of the Kuban River and Kuban branch —778 km;

• river network on river bed of the Protoka branch —135 km;

• Kryukovskoye discharge canal —22 km;

• Varnavinskoye discharge canal —37 km;

Hydrodynamic model includes 195 cross sections with interval ≈ 5 km;

Reservoirs were defined by the bathygraphic function;

Boundary conditions: releases from reservoirs and waterworks, water intake by pump stations and canals, water level of the Azov Sea, lateral inflow from right and left banks.

In MIKE11, the control strategy describes the function of the gate level depending on the water level or discharge value at the controlled point. Using the “if” operator for the selected gates, it is possible to form a given management strategy, depending on water consumption, time, requirements of water users, etc. When selecting a management option, you can configure MIKE11 so that the choice is possible only between options representing different strategies. These management strategies are set using a list of “if” operators that allow you to implement a hierarchy of priorities and requirements of water users.

To form a set of alternative plans (solutions), a list of different options should be formed, usually associated with lexicographic ordering (groups of water users with the highest priority, normal priority, less significant, insignificant, etc.). The control command assigned to the first execution corresponds to the first “if” operator with a “true” condition. Therefore, it is important for the user to determine which “if” operator will be evaluated first, second, and third in the specified hierarchy. The “Control Structure” module also provides for the operation mode of the hydraulic unit according to the dispatcher schedule.

For each water user, on the basis of demands (irrigation schedules) during the vegetation period, the volumes and modes of water intake are determined based on their water requirements (nominal value and permissible “cut” or minimum level of water intake operation) in accordance with the current volume of water consumption and considering the long-term plan. The requirements are set by the level and expenditure functions from time for the particular section lines of the Kuban riverbed, branches Kuban and Protoka, and Krasnodar reservoir.

For the entire vegetation period (April-September of the current year), the water use schedule is formed in accordance with the data of the Hydrometeorological Center and the Construction Norms and Specifications-33-101-2003 daily hydrological series of flow, based on water management calculations.

The hierarchy of priorities is set in the hydrodynamic model in the “Control structure” module, which, by iteration based on the PID algorithm, allows you to select control at waterworks (Krasnodarskoye reservoir, Fedorovsky waterworks, and Tikhovsky water divider).

Depending on the method of managing releases at waterworks, calculations were made for three groups of scenarios, with priorities for different water users:

1. The management of the Krasnodar reservoir (Укгу) is aimed at maintaining the required level, at which the necessary conditions for the operation of pumping stations that take water for water users are realized: —R1—R7

   The management of releases of the Tikhovsky waterwork (Утгу) is aimed at meeting the requirements of water users located on the branches Kuban and Protoka. The distribution of water flow between the arms of the Kuban and the Protoka was set in the required proportions (54% —Protoka, 46% —Kuban; 40% —Protoka, 60% —Kuban; 60% —Protoka, 40% —Kuban).

   In the management scenario, the discharges of three water users —R1—R3 were cut by 50% in different variations, based on the consideration of reducing water supply by reducing acreage in farms.

   Scenario 01: [Укгу-R1-R2]_[Уфгу-R1-R2]_[Утгу-54]_[R3-R7 – leftover principle], where: Укгу-R1-R2 – determines the Krasnodarsky waterwork management to provide required discharges, maintaining the required level of the main channel, the water level in which ensures the normal operation of irrigation systems R1 and R2; Уфгу-R1-R2 determines Fedorovsky waterwork management to maintain required water level in R1 and R2; and Утгу-54 determines the Tihovsky waterwork management so that the accepted ratio of the water distribution between the Kuban and the Protoka is maintained in the following proportions: 54% —the Protoka and 46% —the Kuban. The requirements of other irrigation systems R3−R7 are satisfied according to the leftover principle.

2. Krasnodarskoye reservoir management was carried out to maintain the specified discharges of 405, 340, 220, 175 и 90 m³/s

   Fedorovsky waterwork management was carried out to maintain the required upstream level (13,4 m), when normal water intake was provided for water users R1 and R2, with discharges of 32 m³/s and 143 m³/s.

   The releases of the Tikhovsky waterwork were managed for discharge distribution between the Kuban and Protoka branches in the following proportions: 54% – the Protoka, 46% – the Kuban; 50% – the Protoka, 50% – the Kuban; 40% – the Protoka, 60% – the Kuban; 60% – the Protoka, 40% – the Kuban. The required distribution proportions were set for each discharge from the series (405, 340, 220, 175, and 90 m³/s), for which, as well as for different proportions of water distribution between the branches, the water intakes of three water users —R1—R3 were also cut by 50% in different variations, based on considerations of reduction acreage in farms.

   Scenario 57: [Укгу-405]_[Уфгу-R1-R2]_[Утгу-54]_[R3-R7 – leftover principle], where: Укгу-405 determines the Krasnodarsky waterwork management to maintain water discharge in controlled section line more ore equal to 405 m³/s; Уфгу – R1-R2 determines Fedorovsky waterwork management to maintain required water level in R1 and R2; and Утгу-54 determines the Tihovsky waterwork management so that the accepted ratio of the water distribution between the Kuban and the Protoka is maintained in the following proportions: 54%—the Protoka and 46%—the Kuban. The requirements of other irrigation systems R3-R7 are satisfied according to the leftover principle.

3. Krasnodarskoye reservoir management was carried out to maintain the required upstream level in R6

   Fedorovsky waterwork management was carried out to maintain the required upstream level (13,4 m), when normal water intake was provided for water users R1 and R2, with discharges of 32 m³/s and 143 m³/s.

   Management of the Tikhovsky waterwork was carried out in the interests of water user R6.

   Scenario 41: [Укгу-R6]_[Уфгу-((R1-R2)/2)]_[Утгу-R6]_[R3-R5, R7 – leftover principle], where: Укгу-R6 determines the Krasnodarsky waterwork management to provide required water level on R6; Уфгу-((R1-R2)/2) determines Fedorovsky waterwork management to maintain required water level in R1 and R-2, on R1 and R2 discharge provided half less than required; and Утгу-46 determines the Tihovsky waterwork management to maintain required water level in R6 and distribution between the Kuban and the Protoka in the following proportions: 46% и 54%, respectively. The requirements of other irrigation systems R3–R5 and R7 are satisfied according to the leftover principle.

   One hundred and fifty-two scenarios of water distribution were developed, and the results of calculations on the hydrodynamic model were transferred to the Microsoft Excel. Using a computational scheme, the deficit was calculated (as a percentage of the nominal value) for water users (R1—fos; R2—k-mch-pk-os; R3—paos; R4—paos; R5—tos; R6—chos; R7—chos), the average deficit for each water user was found (AvDef-R1-R7), and the total deficit for all water users (SumDef-R1-R7). The percentage deficit was calculated based on the difference between the required water intake and, in fact, according to irrigation data correlated to the required nominal value. For reservoirs (R0-krs), the drawdown percentage was calculated.

The water deficit, expressed as a percentage for the entire vegetation period of j-th irrigation system, is calculated by formula 3:

$$D_j=\frac{W_j-W_j^{\ast }}{W_j}\ast 100\%=1-\frac{W_j^{\ast }}{W_j}$$E3

where $W_j^{\ast }$ is the volume of water actually taken by the jth water intake of the jth irrigation system obtained as a result of modeling and $W_j$ is the volume of water demand of water user.

The assessment of the availability of irrigation water during the vegetation period is calculated by formula 4:

$$C_j=\frac{W_j^{\ast }}{W_j}\ast 100\%$$E4

For reservoirs, the calculation of water scarcity was done according to the scheme: let $V_i$ be the actual volume of the ith reservoir by the end of the growing season, obtained as a result of modeling in the MIKE11, then for the ith reservoir, the function setting the drawdown $E_i$as a percentage is determined by formula 5:

$$E_i=\frac{V_i^{\mathrm{нпу}}-V_i}{V_i^{\mathrm{нпу}}-V_i^{\mathrm{умо}}}\ast 100\%$$E5

$\text{where}{V}_i^{\mathit{нпу}}$ is the reservoir volume at the normal retaining level and $V_i^{\mathit{умо}}$ is the reservoir volume at the dead storage level [9, 10, 11].

As an example, scenario 93 was calculated based on the initial inflow data for 2018, calculated according to the scheme [Укгу-340]_[Уфгу-R1-(R2/2)]_[Утгу-50]_[R3-R7 – leftover principle].

According to the calculations results (Figure 5), it can be seen that the water level at the water intakes of water users R3 and R4 in 2018 significantly exceeds the stated requirements, but there is a shortage for water user R6.

Figure 5.

Calculation results and requirements of water users.

R3 (Petrovsko-Anastasievskaya irrigation system)—dark blue, R4 (Petrovsko-Anastasievskaya irrigation system)—blue, R6 (Chernoyerkovskaya irrigation system)—blue.

Table 4 shows the results of calculations of water user deficits and reservoir drawdown for scenarios 1, 69, 128 and 149 according to the schemes, respectively:

Scenarios	R0, %	R1, %	R2, %	R3, %	R4, %	R5, %	R6, %	R7, %	AvDef–- R1–R7, %	SumDef- R1–R7, %
Scenario 1	8	0	0	64	37	67	87	86	49	23
Scenario 93	35	0	50	7	0	8	79	81	32	15
Scenario 69	40	0	0	9	0	7	94	96	29	20
Scenario 128	68	0	0	75	0	3	94	96	38	21
Scenario 149	65	0	0	35	4	56	38	50	26	7

Table 4.

Comparison of the calculations results of scenarios based on hydrology in 2018 (deficit, %).

[Укгу-R1-R2]_[Уфгу-R1-R2]_[Утгу-54]_[R3-R7- leftover principle];

[Укгу-220]_[Уфгу-R1-R2]_[Утгу-40]_[R3-R7- leftover principle];

[Укгу-340]_[Уфгу-R1-R2]_[Утгу-40]_[(R3/2), R4-R7- leftover principle];

[Укгу-410]_[Уфгу-R1-R2]_[Утгу-60]_[R3-R7- leftover principle].

Water management systems located on the water objects of river basins include a river network with a cascade of reservoirs and hydraulic structures designed to ensure the rational use and protection of water resources. Water management systems, as a rule, are multi-purpose and serve to provide water to various water users.

Rational use of water management systems involves the adoption of compromise management decisions that minimize damages from possible failures of water users’ requirements. Decisions are made at various levels of planning and management. The ability to make informed decisions based on scientific, as well as social or political criteria is fundamental to the success of organizations involved in planning and managing water resources.

Efficiency criteria should be defined for significant water users, which provide a numerical assessment of the quality of decisions made on the water resources distribution. Some of these criteria may contradict each other (conflicting requirements of water users). In these cases, it is necessary to look for compromises between conflicting requirements of water users, which should be considered when searching for the “best” compromise solution.

Decisions made in the field of water resources management are inevitably associated with compromises among competing opportunities or goals. One of the tasks that are solved during planning is to evaluate alternative plans and identify compromises among competing opportunities, goals, or objectives. After that, the “best” compromise solution is worked out and adopted in the process of discussions and negotiations with the participation of all interested water users. The platform for such discussions in the Russian Federation is the Basin Council, and for negotiations – interdepartmental working groups, which in real time form the modes of operation of hydraulic structures included in the water management systems.

Professionals in the field of water resources who provide technically based options for compromise solutions to decision-makers should form a set of compromise options for water resources management. Their role is very important in the decision-making process since only professionals represent the full range and interrelation of problematic requirements and can form a set of compromise solutions agreed with all interested water users.

The task of regulating the water management systems’ operation modes is a multi-criteria task with probabilistic initial information. A number of specific criteria should be considered, such as: the safety of hydraulic structures, protection of the downstream from floods, reliability of water supply, characterized by the issuance of guaranteed yield, etc.

When forming the water management systems modes operation, it is necessary to use multi-criteria optimization methods to form a set of alternative solutions in accordance with the list of different options for the water users’ priorities hierarchy, to form a set of non-dominant solutions according to criteria (for example, according to the water users’ supply) and to provide visualization tools for alternative plans for discussion and decision-making.

Multi-criteria methods or multi-purpose analysis methods are not intended to determine the best solution, they provide information about trade-offs between these sets of quantitative performance criteria [12]. Any final decision will be made in the process of discussion based on qualitative and quantitative information, and not in a computer. Determining acceptable and effective plans is a simpler task than deciding which of these effective plans is the best. The multi-criteria analysis was performed on the basis of the tools developed at the Dorodnitsyn Computing Centre of the Russian Academy of Science.

For the obtained matrix of solutions (deficits), using multi-criteria analysis methods based on the method of achievable goals, Pareto boundary curves were formed, which should be used in the process of negotiations between the decision-maker (Kuban Basin Water Management) and interested water users: the directorates of reservoirs and waterworks (Krasnodarsky waterwork, Fedorovsky waterwork, Tihovsky waterwork), the “Kubanmeliovodkhoz” management department and water users (departments of reclamation systems) that are directly subordinate to them – to choose the “optimal” in the sense of Edgeworth-Pareto trade-off solution. The Computer Expert Support Group also participates in the negotiations, and prepares several initial compromise scenarios and accompanies the decision-making process.

An example of such negotiation platforms for making decisions on the regulation of reservoirs of large river basins is the Interdepartmental Working Groups conducted by Rosvodresursy.

Before the start of negotiations, the Computer Expert Support Group prepares and sends compromise scenarios to interested water users, for example, with the lowest total and average deficits for all water users (Figures 6 and 7).

Figure 6.

Trade-off scenario 148.

The drawdown of the Krasnodar reservoir (R0) is 65% and the total deficit is 7% (the smallest). The deficit for other water users is respectively: R1—Fedorovskaya irrigation system—0%, R2—Kubanskaya, Ponuro-Kalininskaya, and Maryano-Cheburgolskaya irrigation systems—0%, R3—Petrovsko-Anastasievskaya irrigation system—35%, R4—Pump stations No. 9 and No. 10 of Petrovsko-Anastasievskaya irrigation system—4%, R5—Temryukskaya irrigation system—56%, R6—Main canal of Chernoyerkovskaya irrigation system—38%, R7—Pump stations No. 1, No. 2, and No. 3 of Chernoyerkovskaya irrigation system—50%. For the following scenarios, the water users list is similar.

Figure 7.

Trade-off scenario 149.

The drawdown of the Krasnodar reservoir is 96% and the average deficit is 15% (the smallest). Deficit for other water users is respectively: 0, 0, 22, 4, 26, 27, and 28%.

The decision-maker conducts negotiations with interested water users, at which a decision is made: the reservoir will operate no more than 40% due to a small shipping operating in the water area of the Krasnodarskoye reservoir, increase water supply by R3, R4, R5 due to a slight reduction in the total deficit and “cutting” water users R6, R7.

Figure 8 shows scenario 69, in which the discharge from the Krasnodarskoye reservoir was 40%, the average deficit was 29%, and the total deficit was 20%. The deficit for other water users was, respectively: R1 = 0%, R2 = 0%, R3 = 9%, R4 = 0%, R5 = 7%, R6 = 94%, R7 = 96%.

Figure 8.

Trade-off scenario 69.

This compromise scenario has been agreed with the majority of interested water users and approved by the decision-maker.

From the perspective of multi-criteria optimization, the inclusion of economic assessment in the scale of criteria “Methods of achievable goals” for each water distribution option allows you to significantly reduce the number of options and, most importantly, additionally focus on economic indicators: rice yield forecast, gross crop yield from irrigated lands of the irrigation system, guaranteed limited damage from irrigation water shortage.

Since it is not difficult for water users to include in the technology of periodic calculation of water supply modes with the same frequency calculations of the forecast yield of rice and other agricultural crops, as well as the calculation of guaranteed damage from the loss of crop production due to a shortage of irrigation water, the choice of the optimal option becomes more economically justified and can be selected as a compromise by the decision-maker, in the process of negotiations with interested water users (Basin Council, rice irrigation systems departments).

Forecast calculations of the expected yield are performed according to weather conditions and irrigation regimes for the past period of the growing season, which can be restored based on actual data on water intakes based on materials from dispatching services.

An example of such a calculation is the regression statistical model of rice yield (Figure 9), built on the production data of the branches of “Kubanmeliovodkhoz” for the last 10 years. Currently, field experimental research on this topic is actively developing, in the direction of creating a domestic dynamic model of rice, due to the need for a detailed description of the crop formation from natural and agrotechnical factors with reference to the vegetation phase.

Figure 9.

Dependence of rice yield on irrigation rate and sum of average month temperature during vegetation period.

Thus, according to the Kalininsky branch data, in 2018, there was a failure of water supply requirements in July, August, and September, which led to a decrease in rice yield from the maximum by 5.8 centner/ha. The actual irrigation rate was 21.9 thousand m³/ha, which exceeded the declared volume for watering 2 thousand m³/ha, while the actual yield in the branch was 71.5 centner/ha against the forecast 77.2 centner/ha (the forecast error was 7.5%).

Information materials on the technical characteristics and farm irrigation network state and the structure of the sown areas made it possible to detail the irrigation regime, considering the assumption that irrigation water is used in the mode specified by agricultural technology. The formulated restriction provides such an unambiguous assessment as “guaranteed damage”—the least damage caused by violation of the water regime under all other conditions being equal [13].

To perform such calculations, the system of optimal water distribution models described above on an inter-farm irrigation system is suitable, in which the hydraulic characteristics of the irrigation network are described by a small number of parameters: the network structure, the characteristics of water supply elements (channel length, discharge, efficiency, etc.). As previously stated, the model system allows you to determine optimal irrigation schedules, optimal water supply modes in the field, optimal irrigation standards, optimal operating modes of distributors with arbitrary water intake operation and to develop a number of compromise solutions considering additional information about the forecast crop yields.

4. Conclusion

Water supply of rice irrigation systems in conditions of water scarcity is an extremely difficult task that requires improving the management of the entire structure of water use and irrigation technologies. The main direction in solving this problem is seen in the application of mathematical modeling and the latest digital technologies of communication and monitoring systems for collecting and processing information and integrating fundamental and applied disciplines.

The proposed approach to solving the problem of improving water supply and water use for rice irrigation systems is based on the development of an integrated system of tools for managing the distribution of water resources, considering the efficiency of water use by agricultural producers. In practical terms, a centralized water resources management system ensures high efficiency of their use in the implementation of the current scenario. On the other hand, the described approach makes it possible to identify the weakest links in water use, differentiated for each irrigation system, and to increase the efficiency of water use by agricultural producers. But the full solution of this set of tasks is still very far away, and we are still only at the very beginning of the planned path.

The performed studies have shown the possibility of studying the dynamics of hydrological processes under the influence of reclamation factors, analyzing water use in rice cultivation in detail, relying on models and calculation schemes. The main arrays of subject information obtained using numerical experiments on production data and standard hydrometeorological information were able to compensate for direct field measurements of water flows in the first approximation and allowed us to assess the state of water use in rice irrigation systems of the Lower Kuban.