MODELING OF GROUNDWATER TABLE POSITION IN THE SUBSURFACE IRRIGATION ON AFFORESTED (FORMERLY ARABLE) LANDS

Tomasz Kowalczyk¹, Mieczysław Chalfen², Anna Pływaczyk^3
1 Institute of Environmental Protection and Development, Wrocław University of Environmental and Life Sciences, Poland
² Department of Mathematics, Agricultural University of Wrocław, Poland
³ Institute of Environmental Development and Protection, Agricultural University of Wrocław, Poland

ABSTRACT

The results of the model tests referring to the water conditions on afforested (formerly arable) lands in Wrocław are presented in this paper. The studies showed that regulated run-off from 90 ha catchments kept groundwater table 50 cm then the non irrigated areas. It was also found that water resources stored in Spring were depleted by June. Its rebuilding in the second part of the vegetation period was possible only when precipitation exceeded the mean value.

Key words: regulated run-off, afforested formerly arable lands, water conditions forming, mathematical modeling.

INTRODUCTION

Water resources in Poland require protection and planning due to their general scarcity and significant variability in time and space [11, 19, 23]. In agriculture and forestry there is a trend to store the excess of water in order to use it on the vegetation needs of plant in drought-spell periods. One scientifically confirmed way of increasing the environmental retention state is stopping the water in land improvement systems by damming and run-off regulation [18, 20, 21, 22]. These operations have great importance in the improvement of water conditions on afforested arable lands. In the older three stands run-off regulation and keeping the small damming up increases the forests ability to retain water and has on effect on the water balance and run-off in forest catchments [10, 13]. In forming retention resources, it is very important to improve the methods of water regulation [19] and forecasting the effect of water systems on the water conditions of the agricultural and forest habitat. The mathematical modeling is helpful because of its effective means of solving the problems of optimal irrigation control [1, 5, 8, 11, 12, 15, 16].

MATERIAL AND METHODS

The analysis of groundwater table changes was done on the background of the results of field investigations which were led in period IV 2000 – X 2002 on the afforested formerly arable land (70 ha surface) situated in the western part of Wrocław (fig. 1, phot. 1). The purpose of the surveys were to make an estimation of the effect of subsurface irrigation with the regulated run-off on the groundwater resources in the diversified hydro-meteorological conditions.

The investigated area has expanded water and a land-reclamation system. There are two main rivers – Ługowina and its tributary Ługowinka, where the regulated water management is provided based on the small natural resources of a 90 ha surface basin. For this purpose three weirs on the river are used. Its exploitation rests on the use of the run-off from the Ługowinka basin starting from the early spring (phot. 2). Depending on the course of the atmospheric conditions, water resources stored in Spring can be depleted during the vegetation period (phot. 3). In winter, the weirs are open so that the upper groundwater level does not enlarge the risk of tree damage by frost. In the Summer period, after plentiful rainfall, there is sometimes the necessity to open the weirs in order to drain the excessively dammed water. On the investigated area there are almost 5 km of ditches and 4 small water reservoirs (fig. 1).

Since the year 2000, there were provided the weekly monitoring of depths of the groundwater table in 30 piezometric wells, completed the measurements of the surface water levels in 9 sections. Collected data was the starting point to verifying the correctness of the mathematical model work.

The investigated area is covered by light and medium-cohesive soils with underlying permeable sands and gravels which are the uniform aquifer. They are characterized by a big gravity drainage capacity – the amount of water drained from macropores with a diameter > 30 ľm is several times bigger than the effective soil retention. The gravity storage coefficient ľ is about 0.20. At the soil moisture content respondent to the field water capacity, the water table rise causes the retention growth approximate on the area 24 mm on each 10 cm groundwater table growth.

The meteorological conditions were analyzed on the background of the data from the IMGW observatory Wrocław – Strachowice and AR observatory Wrocław – Swojec. (tables 1-3). It was found that the hydrological years 1999/2000 – 2001/2002 were warm, as the precipitation in this period was characterized by a big range. It allowed the estimation of the influence of regulated water management in terms of the conditions of deficiency in excess waters.

For the estimation of influence of the land reclamation system exploitation on the water conditions on the adjacent areas, the simulation program FIZ by Chalfen was used [8,11]. It is applied on the two-dimensional model in two space variables system, which is based on the Boussinesq equation:

(1)

where:

x, y – space variables, (x, y) – simulation field,
t – time,
µ – gravity storage coefficient for filtration with free water surface,
h – piezometric head,
T₁ – transmissivity in OX axis direction, T₁=k₁ (h-a),
T₂ – transmissivity in OY axis direction, T₂=k₂ (h-a),
k₁, k₂ – filtration coefficient in OX and OY axis direction,
a – aquifer bottom,
W – source function.

Equation (1) was completed with initial condition

h(x,y,0) = h₀(x,y)

where h₀ is given the function describing piezometric head at initial moment of simulation process and boundary conditions describing piezometric head or flux intensity on some fragment of aquifer boundary.

The model allows the first type boundary conditions (Dirichlet conditions)

h(x,y,t) = h₁(x,y,t) for (x,y) Î G₁

the second type (Neumann conditions)

q(x,y,t) = q₁(x,y,t) for (x,y) Î G₂

or the third type (mixed conditions)

q(x,y,t) = q_n(x,y,t) + ah for (x,y) Î G₃

where h₁, q₁ – given functions,

q_n – flux intensity in normal direction,

a – coefficient.

Equation (1) with boundary-initial conditions being solved by finite element method. First it was transformed to integral form [25]

where P is filtration domain, G is a fragment of the aquifer boundary with second or third boundary conditions. Function h minimalizes integral L is simultaneously an equation (1) solution with assumed boundary-initial conditions [6]. A domain P is divided into triangular elements. The piezometric head h throughout the entire region can be expressed by

(2)

where h_i is the head at node i, and p_i is linear shape function.

The condition for minimum integral L can be written as a linear system equations

(3)

The matrixes K, M and P are described by shape function p_i and coefficient equation (1) and boundary conditions. A differential dH/dt is approximated by the Crank-Nicholson scheme. A system of equations (3) has a symmetric matrix and it was solved by LDU- decomposition method [4].

Each node of discretization grid is defined by: filtration coefficient in OX and OY axis direction, gravity storage coefficient and as the aquifer base and roof. For determining the initial conditions, the groundwater tables for all grid-nodes were taken in accordance with real conditions on the investigated object in April 2000. The boundary conditions were marked by the course of hydroizohypses defined on the background of the real conditions on the object (Dirichlet condition), shortage of supply (Neumann condition q=0) and the closure of the simulation field by a partially penetrating stream (I condition with modification of filtration coefficient). The investigations and accessible materials referring to recognition of hydrogeological conditions on the investigated area were provided [7]. In the valley areas, the water-bearing horizon could be reduced to the schema of the homogenous aquifer [24]. Such schema was taken to modeling.

Model calibration was the next step [9, 14]. Based on the analysis of simulation results, it was assumed that the groundwater recharge by precipitation occurred when it exceeded 5 mm per day in the vegetation period; in the remaining period the precipitation is higher than 2 mm per day were included. On the basis of the model reaction in comparison to the real reaction of groundwater table on precipitation, it was determined that 50 % of precipitation infiltrated to groundwater. The evaporation take off was estimated based on the typical yearly distribution of evapo-transpiration for pine and oak – stands agreed on the basis of lysimeter researches [2, 3]. 50 % of the total use of water was taken as a direct take off from the saturated zone. The batch file was taken, it contained the daily values of supplying and take off of water from the saturated zone. The real daily sums of precipitation from IMGW Wrocław-Strachowice station diminished according to written schema were used as plus values (supplying). Daily minus values (take off water) were taken on the basis of the above mentioned lysimeter results. These initially taken foundations need revision by taking into account periodically ongoing high evaporation and saturation of the vadose water zone and thaws. The averaging groundwater tables from 3 representative piezometric wells were analyzed during the model calibration. They were compared with the ordinates calibrated by the model for the same points of the investigated area. After the verification of the different variants of input data and including 23 changes of the boundary conditions in time (according to real changes of the water levels in the streams on the object) the obtained results allowed the acceptation of the model as correctly calibrated. The results of calibrations were statistically analyzed (fig. 2). It confirmed the high compatibility of real transformation of the groundwater tables course by FIZ program (fig. 3A). Correlation coefficient (r) is 0.94, mean relative error R = 0.05 %, mean absolute error Rm = 0.04 m and maximal absolute error Rmm = 0.19 m. Finally, after testing the model, for the further simulation it was taken that: filtration coefficient k (for each grid-nodes is equal for both axis) is given depending on grid-node localization 20–30 m per day, thickness of the aquifer M is meanly 5.0 m and gravity storage coefficient is equal for the whole area 0.20. Modeling was done on the assumption that:

1. the weirs on the Ługowinka stream are always open, it meets the total give up leading of the regulated run-off,

2. the regulated run-off is led on the Ługowinka stream, and the catchment’s resources enable the permanent keeping of the given damming up the water on the weirs and providing the subsurface irrigation with constant infiltration; the ordinates of the damming up were determined in order that groundwater depth ensures the correct water conditions in soil profile.

The left conditions of simulation, also the course of precipitation-evaporation balance, were accepted on the basis of the results of the model testing. It allowed direct comparison between model results and real conditions on the object in the period April 2000 to October 2001.

RESULTS AND DISCUSSION

The simulation of the course of changes of groundwater depths were conducted on the assumption that the weirs on the Ługowinka stream were always open. This explains how big results were obtained during the run-off regulation in the analyzed period (fig. 3 B). It was stated that the biggest effects of run-off regulation were attained in April 2001, where the real groundwater table exceeded the calculated values of 20 to 50 cm. In the remaining period, the differences were smaller: from 0 to over a dozen cm. It was stated that the effects of irrigation had decayed around June. The later rebuilding of retention resources is possible only during precipitation exceeding mean value – as it did in the year 2001. On the basis of the hydroizohypses set, direction and groundwater flow velocity calculated by FIZ program stated that a big part of the area is enclosed by drain effect of the Ługowinka and connected ditches (fig. 4).

It was set that during the absence of run-off regulation ditches on the object, the Ługowinka stream clearly lowered the groundwater depths on the adjacent areas. The biggest losses in relation to the real conditions (20–50 cm) occurred at the beginning of the vegetation period, when the run-off regulation was able to store the biggest water resources.

The next stage of simulation tests was the recognition of the Ługowinka stream effect on the groundwater depths of the adjacent areas on the assumption that water resources of this stream are plentiful enough to feed the subsurface irrigation with constant infiltration (fig. 3C). The effect in the real conditions similar to the calculated results were obtained owing to run-off regulation of a short duration in the spring time in the years 2000 and 2001 as a result of the plentiful rainfall in July 2001. In the remaining period, especially from September 2000 to February 2001 and from June to October 2002, real groundwater depths were about 50 cm lower than simulated values. On the basis of the hydroizohypses set, direction and groundwater flow velocity shows that the groundwater tables increase on the whole object (fig. 5). It proved the irrigation effect of the Ługowinka stream and draining influence of the Ługowina stream. The year amplitude of the changes of the groundwater depths on the adjacent areas decreased by half owing to constantly damming up the water in the Ługowinka stream (the annual amplitude of changes measured in this object is above 50 cm). Feeding the subsurface irrigation with constant infiltration much enriched the groundwater retention resources of the area adjoining to the stream. In the soil conditions of the investigated object it is possible to store about 1200 m³ of water per hectare owing to the permanent irrigation.

The model tests showed that water resources in the Ługowinka catchments are not sufficient for feeding the subsurface irrigation with constant infiltration. During the vegetation period water levels in the stream are lower about 50 cm in relation to the simulated values. Only in the early Spring (and after summer rainfall exceed the normal value) the groundwater table on the object rose to a level close to the simulation.

On the valley areas there is a possibility to improve the water conditions and increase the resources of retention. One of these methods is by using land reclamation devices [18, 20]. These measures could be especially effective in small catchments [17, 21, 22]. The results of model and field investigations confirmed that subsurface irrigation in very small catchments brought positive effects which were limited to the period March-July in condition with a shortage of precipitation. Only during precipitation exceeding the normal value is there a possibility to regulate the water conditions in the catchments throughout the vegetation period. The time of effective influence of the subsurface irrigation is similar to the period when trees have the biggest water needs. There are differences between exploitation of subsurface irrigation of arable lands and forests founded on the small natural retention resources. On the arable lands during the period October-March the shallow groundwater depth are not dangerous for plants. However in forests, especially in coniferous forests, holding the higher groundwater depths in the winter time could risk trees damage by frost and that is why damming up is recommended in the early Spring.

CONCLUSIONS

The model tests of the influence of the run-off regulation from very small catchments groundwater depths, verified on the basis of the field investigations on the afforested formerly arable lands in Wrocław in years 2000-2002 have showed that:

1. In good hydrometeorogical conditions the leading run-off regulation enabled to keep the groundwater depths lower about 50 cm in spring time in comparison with levels during simulation with absence of run-off stoppage. It was able to store about 1200 m³ water per hectare on light soils.

2. In the shortage of precipitation in the vegetation period in small lowland catchments the water resources stored in the winter half-year as a result of run-off regulation were depleted by June. Its rebuilding in the second part of the vegetation period is possible when the precipitation exceed the mean value.

3. The simulation program FIZ is an effective instrument allowing to forecast the influence of the land reclamation systems on the groundwater table forming in adjacent areas, which was confirmed by statistical analysis. The results of tests could be used in the improvement of the exploitation of the subsurface irrigation systems in agriculture and forestry on the lowland valley areas.

REFERENCES

1. Ahlfeld, D.P., Heidari M., 1994. Applications of optimal hydraulic control to ground-water systems, ASCE J. Water Resour. Plan. and Manag., 120(3), s. 350-365.

2. Bac S., 1962. Leœne melioracje wodne. [Forest land improvement]. PWRiL, Warszawa. [in Polish].

3. Bac S., Ostrowski S., 1969. Podstawy leœnych melioracji wodnych. [Foundations of the forest land improvement]. PWRiL, Warszawa. [in Polish].

4. Bear J., Verruijt A., 1990. Modeling groundwater flow and pollution. D.Reidel Publishing Company (Dordrecht).

5. Belmans C., Wesseling J.G., Feddes R.A., 1983. Simulation model of the water balance of a cropped soil: SWATRE. J. Hydrol. 63, s. 271-286.

6. Brebbia C.A., Connor J.J., 1977. Finite Element Techniques for fluid flow. London-Boston.

7. Buksiński S. i inni, 1974. Atlas Geologiczny Wrocławia cz. I, II i III. [Wroclaw geological atlas]. Wyd. Geologiczne, Warszawa. [in Polish].

8. Chalfen M., 1990. Matematyczny model nieustalonego ruchu wód podziemnych z uwzględnieniem obiektów melioracyjnych oraz ujęć wody. [Mathematical model of non-steady movement of ground water with regard to land improvement structures and water intakes]. Zesz. Nauk. AR Wrocław nr 192, Melioracje XXXVI, s. 25-38. [in Polish].

9. Chełmicki W., Ciszewski S., Żelazny M., 2002. Model wahań zwierciadła wód podziemnych w Puszczy Niepołomickiej. [Model of the water table fluctuations in forest “Puszcza Niepolomicka”]. Czas. Techn. Polit. Krakowskiej, Inż.. Œrod. Zesz. 4-Œ/2002, Kraków, s. 19-26. [in Polish].

10. Ciepielowski A., Dšbkowski Sz., Grzyb M., 2002. Kształtowanie retencji wodnej na obszarach leœnych. [Water retention forming in the forest area]. Głos Lasu nr 3, 4, s. 10-12, 16-17. [in Polish].

11. Czamara A., 1998. Oddziaływanie wybranych urzšdzeń melioracyjnych na zasoby wód gruntowych. [Influence of the selected melioration devices on the groundwater resources]. Zesz. Nauk. AR Wrocław, nr 340, Rozprawy CLVII, Wrocław. [in Polish].

12. Dougherty, D.E., Marryott R.A., 1991: Optimal groundwater management 1. Simulated Annealing, Water Resour. Res., 27(10), s. 2493-2508.

13. Kosturkiewicz A., Czopor S., Korytkowski M., Stasik R., Szafrański Cz., 2002. Odpływ i retencja siedlisk lesnych w małych zlewniach. [Run off and forest habitat retention in the small catchment]. Roczniki AR Poznań, CCCXLII, Melior. Inż. Œrod. 23, Wyd. AR Poznań, s. 217-227. [in Polish].

14. Kowalski J., 1998. Hydrogeologia z podstawami geologii. [Hydrogeology with basic of geology]. Wyd. AR Wrocław, s. 101. [in Polish].

15. Łabędzki L., Łojek W., 2000. Sterowanie nawodnieniami podsiškowymi użytków zielonych w dolinie Noteci Górnej. [Control of the subsurface irrigations on the grassland in the Noteć Górna valley]. WMiŁ 1/2000, s. 16-19.[in Polish].

16. McDonald, M.G. & A.W. Harbaugh, 1988: A modular three-dimensional finite-difference ground-water flow model. U.S. Geol. Surv., Techniques of Water-Resources Investigations 06-A1.

17. Mioduszewski W., 1997. Formy małej retencji i warunki jej realizacji. [Forms of the small retention and conditions of its realization]. Informacje Naukowe i Techniczne SITWM, nr 1, s. 3 - 10. [in Polish].

18. Nyc K., 1994. Rola retencji gruntowej w bilansowaniu zasobów wodnych [The role of the ground retention in the water resources balance]. Zesz. Nauk. AR Wrocław nr 248, Konferencje V, Wrocław, s. 247-251. [in Polish].

19. Nyc K., 1999. Optymalizacja procesów eksploatacyjnych na systemach melioracyjnych siedlisk hydrogenicznych [Optimalization of the exploitation processes on the land improvement systems in the hydrogenic soils]. WmiŁ 1/1999, s. 54-59. [in Polish].

20. Nyc K., Pokładek R., Janus E., 1994. Kształtowanie się stanów wód gruntowych na zmeliorowanych glebach lekkich w warunkach wprowadzenia regulowanego odpływu [Forming of the groundwater depths on the ameliorated light soils in the conditions of the regulated run off]. Zesz. Nauk. AR Wrocław nr 243, Inż. Œrod. VI, Wrocław, s. 61-71. [in Polish].

21. Nyc K., Pokładek R., 2001. Ekologiczne skutki regulowanego odpływu w dolinach rzecznych Ecological effects of the run off regulation in the river valleys]. WMiŁ nr 4/2001, s. 163-165. [in Polish].

22. Pływaczyk L., Łyczko W., 1999. Wpływ eksploatacji urzšdzeń piętrzšcych na iloœć wody retencjonowanej w zlewni [The influence of the exploitation of damming devices on the amount of water retentioned in the catchment’s river]. WMiŁ 1/1999, s. 11-13. [in Polish].

23. Stšpel Z., 1995. O potrzebie i kierunkach rozwoju inzynierii melioracyjnej w zakresie regulacji stosunków wodnych gleb [Needs and directions of land improvement engineering in regulation of water conditions in the soils]. WMiŁ nr 2/95, s. 50-54. [in Polish].

24. Wišcek W., 1990. Rozrzšd wody jako element poprawy eksploatacji systemów dolinowych [Water distribution as element of betterment of the valley system exploitation]. Melioracje i gospodarka wodna w rolnictwie, ref. i donies. nauk., IMUZ, Falenty, s. 47-56. [in Polish].

25. Zienkiewicz O.C., 1972. Finite Element Method. Arkady, Warszawa.

Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.