An electrical analogue to design subirrigation systems

Agricultural Water Management, 6 (1983) 3 2 1 - - 3 3 3 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

321

AN ELECTRICAL ANALOGUE TO DESIGN SUBIRRIGATION SYSTEMS

F. HOMMA ICW, Institute for Land and Water Management Research, Staringgebouw, Postbus 35, 6700 AA Wageningen (The Netherlands) (Accepted 6 January 1983)

ABSTRACT Homma, F., 1983. An electrical analogue to design subirrigation systems. Agric. Water Manage., 6: 321--333. To prevent drought damage to crops on reclaimed peat soils in the northeastern part of the Netherlands subsurface, irrigation is used. High water losses due to deep seepage often prevent the building up of sufficiently high groundwater tables, however. To investigate this problem field data of a subsurface irrigation experimental field were used to construct resistor network models to simulate the groundwater flow in the field and its surroundings. The model results showed very good agreement with the field data. Further, the models were used to simulate other conditions to detect the influence of ditch water levels and the effect of irrigation applied over a larger area. A description of the field experiment and the set-up and use of the models are given.

INTRODUCTION In h u m i d areas s u c h as n o r t h w e s t e r n E u r o p e an excess o f w a t e r o c c u r s d u r i n g winter. In T h e N e t h e r l a n d s , w h e r e d r a i n a g e s y s t e m s are usually welld e v e l o p e d , d a m a g e t o c r o p s b e c a u s e o f w a t e r l o g g i n g o f t h e soil rarely occurs, b u t d u r i n g s u m m e r a w a t e r s h o r t a g e m a y o c c u r , c a u s e d b y high e v a p o t r a n s p i r a t i o n rates. In o r d e r t o o v e r c o m e possible d a m a g e f r o m a w a t e r s h o r t a g e in s u m m e r , t h e w a t e r level in t h e d i t c h a n d canal s y s t e m in several areas is k e p t high b y l e t t i n g w a t e r in. Filling t h e drainage s y s t e m w i t h w a t e r causes an inf l o w i n t o t h e soil, p r e v e n t i n g a g r o u n d w a t e r t a b l e d r o p , so t h e c r o p s are fed b y g r o u n d w a t e r t h r o u g h o u t t h e g r o w i n g season. This s y s t e m k n o w n as subs u r f a c e irrigation is a p p l i e d in t h e m a j o r p a r t o f t h e D u t c h polders. T h e s a m e s y s t e m can be a p p l i e d in several relatively fiat areas in t h e eastern p a r t o f t h e c o u n t r y if s u f f i c i e n t d r a i n a g e canals are available. A n a r e a w h e r e t h e s e c o n d i t i o n s are f o u n d , are t h e r e c l a i m e d high m o o r p e a t soils in t h e n o r t h e a s t e r n p a r t o f t h e c o u n t r y . H e r e t h e original b o g p e a t has b e e n dug, dried a n d u s e d f o r h e a t i n g p u r p o s e s . B e f o r e digging s t a r t e d ,

0378-3774/83/$03.00

© 1983 Elsevier Science Publishers B.V.

322 canals had to be excavated in the sandy subsoil to lower the groundwater and thus enable the peat land to dry. After the peat had been cut, these canals were used not only for transport of the dried peat but also for agricultural products and materials. From the original bog peat a layer of about 0.5 m was left. The soils then were prepared for agricultural use by leveling the surface and covering it with a layer of 10 to 20 cm of Pleistocene sand originating from the canal bottoms. By plowing every year, the sand layer was mixed with a small a m o u n t of peat. This resulted into a soil very suitable for growing arable crops (potatoes, sugar beets, grain crops). With centuries of use the peat layer gradually vanished through oxidation and nowadays the profile is reduced to a plow layer with a high organic matter content overlying the original Pleistocene podsolic sand profile. The water holding capacity of the profile is considerably reduced and measures to prevent drought damage are often necessary. A possible solution for this problem is to supply extra water by using the existing canal and ditch system which has lost its transport function as a result of the development of road transport. The problems to be solved are, to determine what groundwater level is needed to attain a sufficient water supply for crop production, what levels should be maintained in the canal system to maintain this groundwater level and finally how much surface water is to be supplied. As a preliminary experiment the canal and ditch water levels in a small area were raised during summer. The a m o u n t of water infiltrating into the soil from a canal section was measured and by means of piezometers the shape of the groundwater table was determined. Analysis of the data collected gave hydrological properties of the profile which were used to construct some relatively simple resistor network models. With these models the groundwater flow in the region was simulated. The results of these simulations were used to find the water levels required and the amounts of water needed to obtain a sufficient water supply for the crops. FIELD EXPERIMENTS Fig. 1 shows the open water system in the pilot area. In the neighbourhood of the experimental site the distance between the secondary canals ('wijken'} is about 200 m. They are generally situated perpendicular to the main canals indicated by 'vaart' or 'kanaal'. Secondary canals will be referred to as "ditches" and main canals indicated as "canals". As also indicated in Fig. 1, the area between two ditches was chosen as the experimental site. Both ditches (wijk N and wijk S} are in open contact with the canal Catovaart. The southern ditch (see Fig. 2) was closed at two sites by means of wooden weirs provided with turbine water meters, The readings of these meters gave the a m o u n t of water lost by the ditch section. Perpendicular to the ditches two series of piezometers were placed as depicted in the lower part of Fig. 2. The groundwater tables in the middle of

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the site were recorded by means of an Alpina Werke P10 level recorder. The other piezometers were measured dally or weekly depending on the weather conditions. Apart from the hydrological observations, air temperature, humidity, windspeed and rainfall were measured locally. Solar radiation data were obtained from a meteorological station about 40 km North of the experimental site. Soil water c o n t e n t was determined weekly in the rows of piezometers by means of gamma ray radiation equipment. With the aid of the data collected a water balance was calculated for three periods of the summer of 1973 (Table I). The balances show an average discharge rate of 1.06 mm day -1 over the longest period. Detailed information over the measuring years 1972 and 1973 showed that periods of subirrigation were alternated with periods of drainage, because of the rapidly changing weather conditions. The a m o u n t of subirrigation obtained from the water meters was considerably higher than that calculated with the water balance. Average groundwater tables during selected periods in 1973, given in Fig. 3, show that the shape of the water table between the ditches is not symmetrical. Moreover, the height of the water table in the ditches differs despite the fact t h a t both have an open connection with the canal. Furthermore it was proven from groundwater observations in the surroundings of the pilot area that an additional South-North groundwater flow exists. For these reasons the data collected were not sufficient to describe the groundwater flow and a further analysis was required.

325 TABLE I Water balance for three periods in the summer of 1973 (after Homma, 1976) 1973 1973 1973 22/5--10/7 22/5--18/6 12/6--9/7 (mm per 49 days) (mm per 28 days) (mm per 28 days) Rainfall Soil water extraction Supply from groundwater

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Theoretical analysis T h e g r o u n d w a t e r levels given in Fig. 3 can be c o n s i d e r e d t o consist o f diff e r e n t c o m p o n e n t s : (a) drainage o f p r e c i p i t a t i o n f r o m t h e p i l o t p l o t ; (b) radial f l o w f r o m a n d t o t h e ditches; (c) h o r i z o n t a l subsoil flow in t h e area.

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The drainage of precipitation from an isotropic soil by ideal drains reaching to a depth equal to at least a quarter of their spacing (Fig. 4A) gives according to Ernst (1962) the following water table gradients: Q'(x~

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where h' stands for the hydraulic head, k for the conductivity and D for the thickness of the so~alled equivalent layer. The discharge Q' is related to the rainfall intensity N by Q' = N L , where L is the spacing between the drains.

327 Under the same conditions mentioned above the infiltration from the ditches can be described by (Fig. 4B) h"(xO -- h"(x2) =

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Addition o f the three flow components will result in a water table shape as depicted in Fig. 4D (dotted line). For values of N < 1 m m day -1 and a transmissivity k D = 1 400 m 2 day-1 (see below), h'(0) - h' (100) = 0.36 cm and therefore drainage can be neglected. When the difference in water levels between the two ditches is ascribed to a horizontal flow c o m p o n e n t only, the measured values can be corrected proportionally with the distance. The remaining differences then indicate the effect of radial flow. Substituting corrected values for h(1) and h(9) and taking the value of Q" obtained from the water meters yields of k-values ranging from 1 to 7 m day -~ with an average of k = 3.1 m day -~. The horizontal flow c o m p o n e n t due to outflow from the ditches, calculated from Eq. 1 gives k D = 1631 m 2 day -~. For the radial flow in the neighbourhood of the ditches the piezometers 1 and 9 were used. An additional entrance resistance (We) can, however, exist separate from the radial resistance Wr. The total resistance We + Wr obtained from field data is 0.2 day m -~. This brings k to 1.62 m day -1. When the entrance resistance is thought to be concentrated in a thin layer of say 0.5 m thick around the b o t t o m of the drain then the conductivity of this layer is, according to the theory of Widmoser (1968}, equal to 0.43 m day -~. When the loss in head due to radial flow according to Eq. 2 is subtracted from the piezometer readings, the loss in head due to the entrance resistance amounts to 3 cm. This points to a value of k = 0.39 m day -1 . As such analysis of the hydrological data did not lead to exact values for the hydrological constants of the area. In order to further improve the insight in the hydrological situation and to get better founded data for the design of a subsurface irrigation system, two resistor n e t w o r k models were built. ELECTRICAL MODELS The first model indicated in Fig. 5 represents a 1500 m long North-South cross-section. This model was built to investigate the groundwater flow in the pilot area. A second model was restricted to deal with the cross-section over the experimental site.

328 In order to be able to simulate field conditions, the models should at least include: the entrance resistances of ditches and canals; the unequal losses from the ditches; a horizontal flow beneath the ditches. To construct the models more field data were necessary on stratification and conductivity of the aquifer and on the intensity o f the horizontal flow component. For this purpose two borings to a depth of 25 m, of which one in the experimental site, were made. Analysis of the cores showed that the water bearing aquifer consists of two different parts. Calculations of k-values from grain size distributions resulted in kl = 8 m day -1 for the upper 12 m. For the lower part, consisting of much coarser material, a k2 of 37 m day -1 was computed. According to the geological map (Rijks Geol. Dienst, 1975) the Tertiary {Miocene) clay in the area is found between 40 and 60 m. Since this clay can be considered to be impermeable, D2 was taken to be 38 m. From piezometers installed at different depths in the bore holes and a number of additional shallow groundwater observation wells in the region, a contour map of the hydraulic heads of the groundwater was constructed {Humbert, 1976). From this map a South-North gradient of 1:1 000 was found for the groundwater flow. For a k D = 1500 following from the above data, the flux q = 1.5 m3day -1 and the flow velocity v = 0.03 m day -1. The model depicted in Fig. 5 was based on the above data, hence k l / k 2 = 1/4.75 and D I / D 2 = 12/38. The lower part of the aquifer was simulated by a strip of conductive paper (Teledeltos), the upper part by a network of resistors. The ditches were given a radial resistance equivalent of 27 k~2. Because of a loss o f water from the Catovaart the potential along the canal had to be reduced. This was done by inserting potentiometers along this line. Model tests now were carried out by introducing observed ditch and canal water levels. The potentiometers in the line of the canals then were adjusted in such a way that the water table midway between the ditches in the experimental site agreed with field measurements. In this way the loss from the canals and ditches and the horizontal flow component were established. The flow in the experimental site was 1.6 c m d a y -1, increasing to 8.6 c m d a y -1 near the Willemsvaart. ScholtenskanaaL Cato v a a r t

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329

The results of the model were used to test the shape of the groundwater in the experimental site. For this purpose the resistor network model given in Fig. 6 was constructed. By carrying out test runs with the horizontal flow component beneath the area and the waterlosses from the ditches both ob__

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330 tained f r o m the first model, groundwater table shapes in the pilot area were constructed. Fig. 7 gives the results for two periods in 1973. The agreement between field and model data is very good, indicating t hat the flow components were established correctly. As a n e x t step, the potentials in the first time period in the nodes of the model were used to construct equipotentials and streamlines. The result is given in Fig. 8. Computations based on this pattern give k, = 4.6 t o d a y -1 near the southern and k, = 4.7 t o d a y - ' near the n o r t h e r n ditch. For the lower part o f the aquifer the values were 30.3 and 29.7 m d a y - ' , respectively. The above data poi nt to a transmissivity o f 1200 m 2 day-'. For the kDvalues used in the next part o f this paper an average value of 1/~(1 600 + 1 200) = 1 400 was t he r ef or e used. 3o2928 27

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Fig. 8. Streamlines and equipotentials obtained with the model of Fig. 6 used for checking the hydrological constants of the soil. SUBSURFACE IRRIGATION SYSTEM As p o in ted out, the main problem for subirrigation is to establish a sufficiently high water table in the soil. The required increase in ditch water level height can be t h o u g h t to consist of three parts: a raise equal to the required raise o f the groundwater table; a raise to overcome the loss o f head due to the induced capillary flow; a raise to overcome the loss o f water towards the subsoil and deep groundwater flow. The groundwater table depth in a subirrigated field must be such that the capillary rise is sufficient to provide a crop with adequate water. According to Feddes (1969, 1971) a p o t a t o crop for example, requires a soil water tension below 4 kPa (pF = 2.6) for good growth. Taking a r o o t zone dept h of 0.35 m with a soil water tension of 4 kPa Van der Spelt (1976} c o m p u t e d the steady state capillary flow for various depths of the water table for soil types typical for the area under discussion. These data are represented by line A in Fig. 9. For the same water table depths the loss of water due to deep seepage flow could be calculated (taking kD = 1 400 m 2 day-'). This resulted in line B. As a n ex t step, the water levels required to realize the groundwater tables in t h e ditches were c o m p u t e d . For this purpose first the difference in head

331 ditch revel

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Fig. 9. The relation between water table depth and capillary rise (curve A, left hand scale), between ditch water level and deep seepage (curve B, right hand scale) and between ditch water level and groundwater table depth (curve C, right hand scale). Curves represent calculated results, the data pertain to model results.

between ditch level and groundwater table depth was computed with the aid of the equation (Ernst, 1962) L Ah = qcL (8kD + Wr + We)

(4)

where qc is the relevant rate of capillary rise. The value of kD was taken to be 1 400 m 2 day -1 and the radial and entrance resistances as based on the hydraulic conductivity of the upper part of the aquifer and the size of the ditches, were taken to be 0.055 and 0.1 day m -1 respectively. The decrease in resistances as a result o f a higher water level in the ditches will be very small and therefore has been neglected. In the computations the L-value was increased from the actual 200 m to 300 m to take into account that the seepage from the southern ditch is twice that from the northern one. The total head necessary to sustain the different flow components is indicated by line C in Fig. 9.

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f r o m S o u t h to N o r t h in the pilot area (see Fig. 1); M = Margrietvaart, W = Willems1 4 6 and 1 1 0 c m b e l o w the surface respectively. B o t t o m : the same w i t h a high level Willemskanaal; the upper curve gives the c o n d i t i o n s w i t h a drainage rate o f 3 m m in contrast to the o t h e r curves w h i c h give subinfiltration situations.

The results were tested with a second resistor n e t w o r k model. The results o f this test are given as data in Fig. 9. The calculated relationship between ditch level and groundwater table dept h agree very well with the calculated line. The deep flow is overestimated to some e x t e n t by the computations. It is a typical o u t c o m e t ha t the groundwater table should not fall t oo much below 80 to 90 cm depth in order to get sufficient capillary rise. Deep seepage, however, increases with higher ditch water levels. In order to overcome this, the levels o f canals and ditches should be raised over a large area. In t hat case a more favourable ratio o f capillary rise to deep seepage is to be expected. To investigate this aspect the model for the larger area was again used. In Fig. 10 the water table curves derived with the model are given to establish average water tables of 110 and 146 cm below the soil surface in the experimental site. Due to water losses .the level of the canals decreases from South to North and the effect o f subirrigation in the plots North of the experimental site will be small due to low groundwater tables.

333 A t t h e b o t t o m side o f Fig. 10 t h e s a m e s u m m e r s i t u a t i o n is given w h e n a high w a t e r level is also m a i n t a i n e d in t h e Willemskanaal. F o r a w a t e r t a b l e o f 1 4 6 c m b e l o w t h e s u r f a c e in t h e e x p e r i m e n t a l site t h e s i t u a t i o n b e c o m e s f a r m o r e f a v o u r a b l e t h a n w i t h o u t a high level in t h e Willemsvaart. W h e n a w a t e r t a b l e o f 1 1 0 c m is t o be m a i n t a i n e d in t h e e x p e r i m e n t a l site, t h e w a t e r t a b l e s d e v i a t e less f r o m t h e s i t u a t i o n as given a t t o p o f Fig. 10. Drainage c o n d i t i o n s can also be s i m u l a t e d . T h e u p p e r c u r v e in t h e b o t turn p a r t o f Fig. 10 p e r t a i n s t o a d r a i n a g e o f 3 m m d a y -1 o v e r t h e e n t i r e area. T h e raise o f t h e w a t e r t a b l e as c o m p a r e d t o a s u b i n f i l t r a t i o n s i t u a t i o n is r a t h e r small. This is d u e t o t h e relatively large t r a n s m i s s i v i t y o f t h e a q u i f e r a n d t h e small d i s t a n c e s b e t w e e n t h e ditches. T h e a b o v e clearly s h o w s t h e a d v a n t a g e o f h a v i n g a m o d e l available t o solve these types of water m a n a g e m e n t problems. When the hydrological constants o n w h i c h t h e m o d e l is b a s e d are available v a r i o u s c o n d i t i o n s c a n b e simulated.

REFERENCES Ernst, L.F., 1962. Grondwaterstromingen in de verzadigde zone en hun berekening bij aanwezigheid van horizontale evenwijdige open ledingen (Groundwater flow in the saturated zone and its calculation when parallel horizontal open conduits are present). Thesis, Univ. Utrecht, The Netherlands, 189 pp. Feddes, R.A., Beregeningsprogramma's (Irrigation programs). Meded. Dir. Tuinbouw, 32(10/11): 440--453. Misc. Repr. ICW 105. Feddes, R.A., 1971. Water, heat and crop growth. Meded. Landbouwhogesch. Wageningen, 71(12), 184 pp. Homma, F., 1976. ElektTisch modelonderzoek naar infiltratie vanuit evenwijdige wijken (Electrical model research of infiltration from parallel ditches). Nota ICW 920, 52 pp. Humbert, H., 1976. Isohypsenkaarten van het Waterschap De Runde (Piezometric elevation maps of the drainage district De Runde). Not published. Rijks Geol. Dienst, 1975. Inventarisatie geologische gegevens van Emmen en omgeving (Inventary of geological data on Emmen and surroundings). Rapp. 10151, Rijks Geologische Dienst, Haarlem, The Netherlands, 5 pp. Van der Spelt, T.S.B., 1976. Gewenste grondwaterstand in de jonge Veenkoloni~n (Desired groundwater level in the young peat-colonies). Nota ICW 911, 17 pp. Widmoser, P., 1968. Der Einfluss von Zonen ge~inderter Durchl~issigkeit im Bereich von Drain- und Brunnenfilterrohren (The influence of zones of changed permeability within reach of drainage and well filterpipes). Schweiz. Bauztg, 86 (9): 135--144.