A.N.Morozov

WATER-SALT REGIME FORECAST METHODS.

Reasoning from the set goals and considering technical possibilities for realization of the tasks being solved, the models have been used, in those a comparatively simple mathematical tool is applied, which represents the main mechanisms of moisture and salt transfer.
Balance models apply known ideas of moisture balance in a certain soil layer. The following dependences are in its basis:

 

here Q -irrigation; O -precipitation; E - total evaporation; I -moisture exchange of the root-inhabited zone with lower layers; G -water discharge to lower horizons. It is supposed that the all variables are deterministic, and there are functional dependences upon time and moisture. In particular, total evaporation:

here - parameter characterizing vegetation influence; Eo -evaporability; W -moisture reserves in the soil.

The dependence of replenishment from the lower horizons can be approximated:

here - , - constants, are determined through modeling.
Mineralization computation is carried out according the root-inhabited zone?s salt balance equation:

here, Cv - irrigation water mineralization; Cq - soil moisture mineralization that comes to the lower horizons; S - convection-diffusion salt transfer from the lower horizons, is approximated by the dependence:

For moisture arrival time, one ought to check whether it will result in saturation of the root-inhabited zone up to field moisture capacity and further moisture discharge to the lower horizons.

The value calculated is compared to the moisture deficit Ot in the root-inhabited zone:

(7)

if there is irrigation water excess (Pt > Ot), discharge to the lower horizons arises, and in the root-inhabited zone, moisture is formed, which is equal to the field moisture capacity ? HB. If there is no water excess (Pt < Ot), the irrigation water is accumulated in the aeration zone:

(8)

The discharge is:

otherwise, Gt = 0
Crop capacity is determined by the formula:

here, - number of "stressful" days j for jth time interval; - dimensionless reduction factor of crop capacity characterizing crop decrease per one "stressful" day j of jth time interval ().

Stress days are determined as days in those the total soil moisture potential Pt exceeds the critical level (see below).
In the first model modification, water-salt balance of the field is computed and the design crop capacity is defined subject to the given conditions and irrigation regime assigned.
The first modification, using the previous model, determines an irritation regime excluding crop losses, but without taking into account reducing income from costs for irrigation and water itself.
The third modification model carries out searching for the optimal from economic standpoint irrigation regime. A standard inter-irrigation regime is set therein, as it is in common practice mostly, and several possible irrigation rates. The program makes full searching of all probable combinations of irrigation rates and terms for a vegetation period, and then selects the most efficient.
The imitation model of moisture and salt transfer in soil based on the researches of L.M.Reks, I.P.Aydarov, A.I.Golovanov, and other authors as well is described in detail in the work by V.A.Zlotnik and A.N.Morozov (1983).
Two interconnected blocks are used in the model:
- one of water regime which forecasts moisture and filtration rate;
- one of salt regime that forecasts salt transfer.
The flow scheme of modeling of soil water-salt regime (WSR) state and irrigation regime control is shown on figure 1.

Input information in the form of soil-meliorative and climatic indices, characteristics of irrigated lands state, technical features of the hydromeliorative service, and crop requirements to growth conditions is processed in state forecasting blocks, is controlled by the control block which, in the case of need, issues commands to make vegetation irrigation.
The known equation of moisture transfer accepted in the model looks as follows:

(11)

here, t - day time;
Z - vertical coordinate, m;
K( 0) - hydraulic conductivity factor, m/day;
T(Z,t) - moisture withdrawal rate by plant roots, m3/day per ha;
Qq - drainage effluent, m3/day per ha;
O - volume moisture;
H(Z,t) - water head, m;
b - delta function.
Target function is and H. Vertical filtration rate used in salts transfer calculation is determined via the formulae:

Boundary conditions on soil surface are specified by an irrigation regime ensuring certain fixed conditions in the root-inhabited layer. The decision describes changes of moisture and filtration rate used further for the salt transfer calculation. The equation defining C(Z,t) concentration in the salt transfer model is as follows:

(13)

here, D - hydraulic dispersion factor;
Zq - drainage location depth.

The value of hydrodynamic dispersion factor is computed through the dependence:

here, Do - salts molecular diffusion factor;
^ - dispersion parameter

Salts flow in the aeration zone is calculated by the formulae:

Solving the assigned task gives a forecast of pore solution mineralization and the value of salt carry-over to drainage along with infiltration feeding. When solving the task, a few functions are applied, which determine:
- hydraulic conductivity factor;
- dependence of moisture capillary-sorption potential in soil;
- evaporation and transpiration dependence upon soil moisture;
- dependence of drainage effluent on the effective head value.
Dependence of the hydraulic conductivity factor on moisture K(O) is taken by the S.F.Averyanov? formulae (1978). At that, K(O) is determined via the filtration factor (Kf), porosity (m), moisture of plant growth delay (PGDM):

The exponent n, according to analyses of a number of researchers? actual data, can be accepted in the range of 2-7 depending on soil constituent stratum properties, and can be selected in such a way that to provide the best approximation of the experimental data.
Dependence of the soil moisture capillary-sorption potential Y(O) is accepted single-valued (without consideration of the hysteresis) and must be determined for every soil constituent stratum. It is set in a table form.
Head dependence on moisture is written as follows:

To calculate plants transpiration, in view of extreme approximateness of the experimental data, a model with constant rate of moisture withdrawal by the roots in depth (S.V.Nerpin and others, 1976):

(18)

here, Ec(t) - evapotranspiration, mm/day;
a(t) - physical evaporation part.
Evapotranspiration value is computed taking into account soil moisture by the GGI methods (Recommendations on evaporation calculation form the land surface, 1976), applied for the conditions of the Central Asia region (D.F.Solodennikov, 1981):

here, …®(t) - evaporability from water surface, mm/day;
- factor representing crop peculiarities in a certain vegetation period;
ECM - evaporation cessation moisture;
LMC - least moisture capacity.
The drainage effluent value is approximated by a linear function of the effective head (A.I.Golovanov, 1975):

here, A - drainage degree factor, l/day;
h(t) - groundwater depth, m.
Conditions and parameters of relation between groundwater and head water horizons are defined by materials of hydro-geological investigations with operation observations.
Assignment of regular fixed-rate irrigation, providing agro-technical conditions in the root-inhabited layer, is made in the model by the irrigation control block. Irrigation is automatically assigned every time when the total potential in the soil moisture, expressed via the equivalent pressure (Pc) and determined as the average value in the root-inhabited layer l(t), reaches the critical value (Pk) in the current time (see above).
Conditions for irrigation assignment is written in the form:

here, Pc(Z) = |P(Z)| + 0.36*C(Z),
P(Z) - capillary-sorption potential in soil moisture;
C(Z) - soil solution mineralization.
This task is solved by the numerical method, using the conservative difference scheme (A.A.Samarskiy, 1977; G.I.Marchul, 1977), and realized in FORTRAN-77 language.
Adaptation of these models through field determination of the parameters specifically characterizing soil conditions in the area of the use can considerably promote settling problems related to all possible water saving per a crop unit produced.

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