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Section 5. Information technology
DOI: http://dx.doi.org/10.20534/ESR-16-11.12-28-33
Djumanov Jamoljon Xudaykulovich, head of department Tashkent University of Information Technologies, Tashkent, Uzbekistan E-mail: timanet4u@gmail.com
Mathematical modeling of geofiltrational of processes of the regional hydrogeological systems
Abstract: In the article has considered a wide range of subjects from computer modeling to experience with water user associations and vary in content from directly applicable research to more basic studies, on which applied work ultimately depends on the example of the Ferghana Valley. Some researchers are narrowly focused, applied and detailed empirical studies; others are wide-ranging and overviews of generic problems.
Keywords: Mathematical modeling, geofiltrational of processes, boundary conditions, manage aquifer recharge, estimation an optimal regime, groundwater extraction, groundwater for irrigation.
Study Area. The Fergana Valley depression is the area spread between the mountains of Kuramin and Chatkal on the north, Ato-inak and Fergana on the east, and Alai and Turkestan on the south (Lange 1964). The Fergana Valley covers a central part of the depression bounded by the outcrops of the Mesozoic and Paleozoic formations. This study is limited to the part of the Fergana Valley within Uzbekistan with an area of 17,000 km 2 The irrigated area totals to 897,000 ha. The climate is semi-arid with low quantity of precipitation and high summer temperatures. The annual precipitation rate varies from 100 to 200 mm in the central part of the valley and increases to 300 mm in the piedmont areas. The mean average temperature is at 14 oC. The altitude increases from west to east from 330 meters above sealevel (masl) to 600 masl. The valley is filled with alluvial deposits of rivers washed out in the mountain zone. Mirzaev (1974) specified three hydrogeological zones in the Fergana Valley: (1) groundwater natural recharge and transit (Zone A); (2) spring (Zone B); and (3) groundwater dispersion (Zone C) (see Figure 1). By source of supply, the rivers of the Fergana Valley are glacier- and glacier-snow type. The Karadarya and Narin Rivers and its tributaries are of snow glacier type.
Sources available for managed aquifer recharge (MAR) are (1) free winter flow of small rivers; (2) the flow of small rivers, which can be released by the adoption of water-saving technologies or increasing groundwater irrigation; (3) precipitation in Zone A (see Figure 1); (4) subsurface inflow from the upstream; and (5) the winter flow of the Naryn River. Winter flow of small rivers can be used for increasing natural recharge in Zone A, which spread above the main canal commands. Natural recharge can be enhanced by increasing the leakage from the riverbed and the floodplain, canal and stream channels. The winter flow of the Naryn River can be stored underground by: a) increasing the leakage from the canals; b) installing infiltration basins; and c) boreholes or shafts. Sources available for MAR are (1) free winter flow of small rivers; (2) the flow of small rivers, which can be released by the adoption of water-saving technologies or increasing groundwater irrigation; (3) precipitation in Zone A; (4) subsurface inflow from the upstream; and (5)
the winter flow of the Naryn River. Winter flow of small rivers can be used for increasing natural recharge in Zone A, which spread above the main canal commands. Natural recharge can be enhanced by increasing the leakage from the riverbed and the floodplain, canal and stream channels. The winter flow of the Naryn River can be stored underground by: a) increasing the leakage from the canals; b) installing infiltration basins; and c) boreholes or shafts.
As a result of the growing demand for food and energy, the competition for water between upstream and downstream users in the Syrdarya River Basin has increased. The change in the upstream reservoir operation from a conjunctive irrigation/hydropower mode to exclusively hydropower generation resulted in reducing the river flow downstream in the summer and increasing it in the winter.
Modeling studies for the estimation an optimal regime of groundwater extraction, which would facilitate the prevention of freshwater and saline water mixing, and thereby maintain the water quality in the lenses at the supply level that is acceptable for drinking purposes until the next high water season.
Used a mathematical model based on a system of differential equations describing the time-dependent planned flows of groundwater in the interconnected aquifers of parabolic type, having the following form (Habibullaev et al, 1995):
^ = kh + H + f ~SQ* (1)
dt dx ^ dx ) dy ^ dy) with the initial conditions,
h (x, y, t0)= 91(x, y, t0); (x, y) e G; t0=0 (2)
and with the boundary conditions,
h(x,y, t)=p2(x,y, t); (x,y) er; t>t0 (3)
-khdh = & (x,y,0 x, yer; t>t0; (4)
dn
dh
-kh— = y(hr -h) ,x, yer; t>t0; (5)
dn
where, ^ — water loss rate of the aquifer (dimensionless), h=h (x, y, t) — groundwater level of water level to the free surface, m; (x,y) e G — filtering domain — G, with boundary — r; x,y-spatial
and t -temporal coordinates; k — filtration coefficient, m/day; f (x, y> t)=Qr-Qc-Qp — infiltration feeding of ground water, the sum ofthe parts of rainfall and irrigation water (filtration of r — river c — channels), percolating into the aquifer, p — evaporation from the groundwater level; Q„=Q. (t)S (x-x0, y-y0) t>t0; S — Dirac function; f1, f2, — given functions; j-characterizes the hydrogeological conditions of the relationship underground and surface waters; Decisions of the equation (1) with the boundary conditions (2) — (5) used a numerical method (AA. Samarskiy 1983), the transition from differential to record the difference method.
Then the equation (1) takes the following form: H;; - h
0.5ÀT
-I = A ,-05 j -A
where, A,.-0 5j =- (kh )
0.5, j 1 1 ,'+0.5, j h....- h
-1, j
A,',j+0.5 +((,j - W01 j)i (6)
hi+l,j- hi, j
-0.5, j
l
> A,+0.5, j =-(kh )
i +0.5, j
hi ,j = h .
After some transformations we obtain a standard equation
a ,jhi -w - b. ,jhi, j- ci ,jhi+i,j = -d, (7)
For the solution of this equation using the method of so-called locally — dimensional circuitry solutions, (A. A. Samarsky, 1983) sweep method and a solution will be sought in the form
C:
+ ßi+1, j, where,
b ,j - a a
' ßi+i, j
di ,j + ai ,j ßi ,j
bi j- a a
and we obtain the equation for hi, j, in the case of boundary conditions of type I,
ai,j = o Pi,j =Wi,j here \j , aN,j = o Pn,j = Vn,j here hN,j = yN,,, (7)
in the case of boundary conditions of type II,
a,
o,j
Y + ao,j a„
ßj =
Y ho,j + Q
N j
Y + a
->P
Y + ao,j
YhN, j + Qj + Sy
N ,j
N, j
Y+a
N ,j
u aN j ßN ,j + YhN ,j + Qj + Sy here hN ,j =-;
Y + aN ,j + aN ,jaN ,j in the case of boundary conditions of type III,
(8)
a,
0,j
Y + Y + ao, j a„
N ,j
Y + Y + aN, j
ßN.j =
= yho,j -jHb + Q
Y + Y + ao,j YhN ,j + YhB + Q Y + Y + aN ,j
here hN ,j =
ßN, j +YhN ,j +YhB + Q
N, jHN, j
(9)
N, j ßN ,j
are computed, and h ^.
Y + Y + aN ,j
Thus, all the coefficient values aNj-i,j As an initial approximation we accept the initial condition of the boundary value problem (9) sequentially calculate h^-i,r+i'h,!>++-2,r+2'"-'h,!>++-m>r+m and will check the condition max\hj - hi j I <s, s > 0 Ifthe condition is satisfied, the calculation is terminated, otherwise the entire calculation process is repeated for the next iteration. The values of the mesh function satisfying the condition, used as problem solving.
Developed the software to implement such an approach, focused on solving routine and specialized tasks geofiltration presumably includes blocks that implement algorithms for solving boundary value problems for groundwater flows.
Model Description. A three-dimensional regional model of the Fergana valley aquifer (Figure 2) is a widely used GIS-technology. The Fergana aquifer model covers approximately 380 km2. Grid spacing in the x and y model dimension is 250 m x 250 m, and in the areas with dense irrigation canals and drainage ditches the model has 50 m x x 50 m resolution.
The model boundary conditions were set based on the results of the hydrogeological studies carried out by the HYDROENGEO. The surface of the groundwater level acted as a recharge boundary. The loamy/clay layer that is 300 m deep was set as a noflow boundary to represent the lower boundary condition. In the south, there is the subsurface inflow from the uplands through the valley of the river. The groundwater level in the northeast is sourced by the Syrdarya River and in the northwest it is provided by a constant head. There is a zone of natural groundwater recharge on the south and a discharge zone to the north of the Big Fergana Canal (BFC) (Figure 1).
The water-saving model has tree layers; first layer are represented by gravel and shingle deposits in the recharge zone and by loam and second zone are represented by sandy loam deposits in the discharge zone. Groundwater is unconfined in the recharge zone and confined in the discharge zone in layers two to tree. Main canals in the upper part are given in the model as a 'recharge boundary condition' because of their deep groundwater level. Canals that spread in the discharge zone are given as a 'river boundary condition' because they supply the groundwater in summer and drain it in winter. Recharge of a 'boundary condition' also includes percolation losses of precipitation and infiltration losses of irrigation water.
Figure 1. Hydrogeological zones in the Fergana Valley
i, j
«u =
Initial values of the parameters were determined from pumping tests, carried out by the Institute HYDROENGEO in the study area from 1980-1985. During that time 13 pumping tests were carried out including 9 in the unconfined zone and 4 in the confined zone. Location of the monitoring wells was dependent on the hydro-geological profile. For a uniform profile, the number of the observation wells taken was 2-3 in the upstream, 3-4 in spring zone and 4-10 on the periphery of the basin with a confined aquifer. According to these estimates, transmissivity of the water-bearing deposits varies in the range of 40-555 m 2/day and specific yield from 0.13-0.22 in the unconfined zone and at 0.0001 in the confined zone.
Model Calibration and Verification. Simplified models were compiled for each of the 13 wells exploited for pumping tests. The size of each model was 1,000 m x 1,000 m. The simplified models were represented by tree layers, repeating the layers of the main model of the aquifers (Djumanov 2015).
The model grid was non-uniform — 50 m near the well and was increased to 250 m closer to the border of the model. In total, the model had 328 rows and 912 columns. The boundary of the model was taken as the constant head considering that short-term pumping will not affect the water levels at 500 m distance from the well. A low permeable clay layer that is 300 m deep was taken as an impermeable layer to represent the lower boundary of the model.
In the beginning, the models were run using values of the parameters, coefficient of filtration and specific yield, determined from an analytical solution. Later, correct values of the parameters by increasing the convergence with actual data obtained during the pumping tests.
The comparison of the actual and the model calculated values of the water elevations showed a coefficient of correlation at 0.85-0.95. Based on the values of the parameters obtained from the model, the values of the coefficient of filtration and specific yields were corrected. Subsequently, the historical groundwater budget data, obtained by the HYDROENGEO Institute from April 1, 1981 22 to April 1, 1983, were used for model calibration.
This emphasizes the need for alternative additional storage capacities. One potential option is associated with subsurface storage. The upstream of Fergana Valley in the Syrdarya River Basin has favorable hydrogeology conditions to store extra winter flows for summer use. Two main and multiple small tributaries form and feed the Syrdarya River. Subsurface storage, which at this stage is almost full, is estimated to be 200 km 3 (Mavlonov et al. 2006).
First attempts to implement MAR were exploited in Uzbekistan for municipal water supply (Mirzaev 1974; Akramov 1991). During this period, a number of aquifers were identified as having a high potential for aquifer recharge. They were Narin, Iskovat-Pish-karan, Osh-Aravan, Isfara and Sokh in the Fergana Valley (Akramov Table 1. - Free capacities of the sut
1991). Free capacities of the Osh-Aravan Aquifer were estimated at 500 Mm 3, and at 200 Mm 3 in the Sokh Aquifer. The main difference in agricultural water use in the Syrdarya River Basin as compared to other countries ofAsia is that agriculture, which is entirely dependent on the canal system with furrow irrigation, produces a major part of groundwater recharge (Djumanov 2016).
Concept and Examples. MAR is intended to regulate groundwater recharge to increase water resources, improve water quality in subsurface horizons and regulate return flow from irrigated lands. The adoption of MAR practices may yield the following benefits: temporarily storing ('banking') water in subsurface horizons for later use; sustaining groundwater levels and preventing groundwater depletion or raising the water level, minimizing salinity and waterlogging; reducing non-processed water depletions for evaporation, flow to sink and pollution; flood control; improving surface water and groundwater quality; environmental gains (for example, stored water intended for landscape irrigation or baseflow to rivers).
Various methods of MAR and preparatory activities can be applied in agriculture, including the following: regulating groundwater natural recharge; creating artificial groundwater recharge to increase or replenish groundwater storages; adoption of water-saving technologies to reduce areal or linear groundwater recharge caused by saline fluxes from the vadoze zone; using groundwater extraction to increase leakage from riverbeds, floodplains, canals and drains; using groundwater extraction to create free subsurface horizons; effecting changes in the cropping pattern and soil tillage.
Results. The data given in Table 1 indicates that free capacities exceeding 3,000 Mm 3 in Zone A are available for storing the winter flow of small rivers, which varies within a range of 1,0001,200 Mm 3/year and are predominantly allocated for winter crop irrigation. The indicated area is located at higher altitudes above the commands of the main canals, which deliver water from the Naryn River to water-short areas of the Fergana Valley. Free capacities available and those that potentially can be created within the main canal commands. Additional capacities which can be released by lowering the groundwater level are estimated at 186 Mm 3 per meter of groundwater level drawdown.
These data show availability of subsurface horizons for storing the winter flow. However, detailed Results The data given in Table 1 indicates that free capacities exceeding 3,000 Mm 3 in Zone A are available for storing the winter flow of small rivers, which varies within a range of 1,000-1,200 Mm 3/year and are predominantly allocated for winter crop irrigation. The indicated area is located at higher altitudes above the commands of the main canals, which deliver water from the Naryn River to water-short areas of the Fergana Valley.
face horizonsof the Fergana Valley.
№ Aquifers Recharge zone
Area* (ha) Free capacity ^m 3)
1 2 3 4
1 Almaz-Varzyk 19,825 231
2 Kukumbai 2,658 54
3 Kasansai 4,351 30
4 Iskovat-Pishkaran 19,439 359
5 Sokh 34,589 1,452
6 Altyaryk-Beshalysh 7,366 28
7 Namangan 5,196 77
8 Isfara 4,385 90
9 Mailisu 17,513 22
10 Karaungur 3,944 35
1 2 3 4
11 Naryn 28,393 167
12 Chust-Pap 7,936 147
13 Andij an- Shahrihan 7,919 16
14 Chimien-Aval 3,651 88
15 Osh-Aravan 21,223 324
16 Nanai 4,349 71
17 Syrdarya 5,810 32
18 Yarmazar 2,210 67
Total 198,737 3,861
Source: Mavlonov A., Djumanov J., et al. 2006.
Note:* The area within the recharge zone where free capacities are
Free capacities available and those that potentially can be created within the main canal commands. The data indicate free subsurface capacities in the zone of the main canals, available for water banking, totaling 760 Mm 3. Additional capacities which can be released by lowering the groundwater level are estimated at 186 Mm 3 per meter of groundwater level drawdown. These data show availability of subsurface horizons for storing the winter flow. However, detailed modeling and economic analysis are required to estimate the optimal level of groundwater abstraction and recharge. MAR has to be preceded by increasing the groundwater abstraction to lower the water table. The areas suitable for groundwater irrigation and conjunctive use in the Fergana Valley are illustrated in Figure 2.
The estimates show that the area suitable for groundwater irrigation totals to 290,000 ha and 243,000 ha for conjunctive use. The rest of the area can be kept irrigated using canal water.
The potential volumes of groundwater extraction depend on hydrogeology conditions (Zones A and B) and the replenishable groundwater resources.
Total groundwater recharge in Zones A and B (Figure 1) is estimated to be in the range of5,624-6,005 Mm 3/year in low and high water years, respectively.
available.
Expanding the area under conjunctive use and the adoption of water-saving technologies will decrease the groundwater recharge in summer due to reducing losses from canals and irrigated fields. Recharge deficit (~1,000 Mm 3/year) can be compensated using the winter flow of the Naryn River and small rivers. The data given above indicate the potential for MAR at the regional level and the next step is assessing the MAR potential at the pilot aquifer level.
The actual values of the groundwater budgets and elevations were compared with the model simulation results. The comparison showed a high convergence.
The value of the coefficient of correlation was at 0.989. Changes in the groundwater budget (groundwater extraction, recharge and evaporation) since 1980 were considered in the formulation of the modeling.
Modeling Results. Results of the modeling is shown in Figure 3 and indicate high groundwater levels under the current baseline scenario 1 and forming the free capacities under scenario 2. A significant lowering of the groundwater level under scenario 3 is the consequence of the intensive groundwater extractions exceeding the groundwater recharge.
Figure 2. General view study area
The regime of filling and draw off of the subsurface reservoir under scenario 1 of minimum extraction levels of groundwater for irrigation, the subsurface reservoirs are filled during summer and drawn off in winter for subsurface outflow and discharge to the drain system. Intensive groundwater extraction for irrigation results in
on the geofilterational of model
drawing off water levels in summer and minor filling happening in the winter. This increases the risk of groundwater depletion and degradation in quality due to saline fluxes from the Vadoze Zone and surrounding inter-fan depressions.
Managed aquifer recharge in scenario 4 sustains the groundwater storages and maintains the water quality, since 100 Mm 3 of freshwater will be stored underground. Groundwater storages are
depleted in summer by intensive groundwater extraction but replenished in winter by managed aquifer recharge.
Figure 3. The areas with favorable hydrogeology conditions for storing winter flow of the Fergana Valley
This combination aims at sustaining groundwater storages and quality in the long run. Location of the monitoring wells was dependent on the hydrogeological profile. For a uniform profile, the number of the observation wells taken was 2-3 in the upstream, 3-4 in spring zone and 4-10 on the periphery of the basin with a confined aquifer. The pumping tests were carried out with fixed yields of the wells so as to simplify the analysis of the obtained data. The yields were from 25 to 100 l/s and the groundwater level drawdown by 3-4 m in the exploited well.
The yields of the wells were selected to achieve quasi-stationary regime and groundwater level drawdown by 20 cm in the remote well after 5-10 days. Duration of the pumping test was 10-15 days in the unconfined zone and 15-20 days in the confined zone. Groundwater level drawdown data was collected for each 1-10 minutes at the beginning of the pumping and three times per day at the end stages and at the remote well. The hydrogeology parameters were estimated using groundwater level drawdown and restoration data (Figure 4).
Figure 4. Sharing use surfase and aquifers water of the Fergana Valley. 1 - Rivers, 2 - Canals, 3 - Border of the aquifers, 4 - Aquifers water use; 5 - Surfase and aquifers water on complecs use; 6 - Surfase water use
The concentration of the dissolved ions is much higher in the affecting the quality of the groundwater of the aquifer: i) the leakage groundwater of the inter-fan depressions. There are two main factors from the riverbed contributes to the sustenance of the water quality;
and ii) the subsurface inflow from the inter-fan depressions and the upstream and saline fluxes from the topsoil, increase the concentrations of the dissolved solids.
During the field studies carried out in 2010, it was found that when the river flow exceeded the transporting capacity of the main canals, it is released to the headwork downstream. Using the relation obtained for 2010, the leakage from the riverbed was calculated for 1995-2010. Changes in the groundwater salinity in the study area from 1995 to 2010 indicate tight relations between the river flow and the groundwa-ter. Data show that the losses from the riverbed in the summer varies from 98 Mm 3 in low water years to 137 Mm 3 in high water years. The salinity of the groundwater, as and when affected by the leakage from the riverbed, begins to decrease in the spring and continues to the fall. The gradual increase in the share of the saline water in the groundwater budget indicates the need for measures to sustain the quality of the water.
There are at least two ways to sustain the water quality: i) to adopt water-saving technologies to reduce losses from the irrigated fields and to increase the natural recharge from the riverbed and oth-
er recharge structures; and ii) to restrict irrigation in the upstream of the river. This concept of adopting water-saving technologies for conserving water for enhancing natural recharge of groundwater was further tested through MAR modeling.
Conclusions. The study followed the stepwise procedure of implementing manage in the Fergana Valley. The first step is the regional assessment of the potential for MAR and for shifting from canal irrigation to conjunctive surface water-groundwater use. The second step is the application of MAR for aquifers, located in the tail end of main canals. The next step is to move to the next aquifers along the main canals. When the process is complete for all of the separate aquifers along the main canals, MAR implementation for the entire Fergana Valley is considered. The regional assessments in the Fergana Valley show that over 500,000 ha or 55% of the currently irrigated land can be shifted from canal irrigation to conjunctive surface water-groundwater use, which will reduce the return flow to the river by 30%, or by 1,000 Mm3/year, and form free storages of 500 Mm 3 in the command areas of the main canals.
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