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Model of long-term water-table dynamics at Doñana National Park
Pergamon PIh S0043-1354(97)00098-5
War. Re.~.Vol. 31, No. 10, pp. 2586-2596, 1997 © 1997ElsevierScienceLtd. All rights reserved Printed in Great Britain 0043-1354/97 $17.00 + 0.00
MODEL OF LONG-TERM WATER-TABLE DYNAMICS AT DOlqANA NATIONAL PARK FRANCISCO DE CASTRO OCHOA'* and JOSI~ C. MUlqOZ REINOSO 2 tDepartment of Biology, University of Puerto Rico, P.O. Box 23360, Rio Piedras, 00931-3360, Puerto Rico, U.S.A. and 2Department of Biologia Vegetal y Ecologia, Universidad de Sevilla, Aptdo. 1095 41080, Sevilla, Spain (Received September 1996; accepted in revised form March 1997) Akstract--A model of long-term (10 years) dynamics of the water-table in the Dofiana National park is presented. The model is based on a linear regression analysis of data from a group of 24 piezometers, predicting the increments of the water-table at given time-steps. Rainfall, present depth of the water-table, average maximum temperatures and lapse time between two measurements have been used as independent variables. The regressions reach r2-valuesover 0.8. The model prediction of the water-table dynamics based on the regression equations fits the data for most of the measurement points. Differences in the coefficients of variables obtained for the piezometers reflect the different dynamics of the water-table of ponds and the dune area. © 1997 Elsevier Science Ltd Key words--model, simulation, water table, multiple regression, Dofiana
INTRODUCTION Dofiana National Park, located in south-western Spain, is one of the most important wetlands in Western Europe. The marshes and ponds of the park are the wintering area for a large number of migrating waterfowl species from Northern Europe and Central Africa. Also, the Dofiana National Park is one of the last habitats for seriously endangered vertebrate species such as the Imperial Eagle (Aquila adalberti) and the Iberian Linx (Lynx pardina). The Dofiana National Park (35 000 ha) was established in 1969. The Dofiana Biological Reserve (7500 ha), the study area, is a section of the park with a special degree of legal protection. In 1989 much of the area surrounding the park (54 250 ha) was also protected with the legal category of Natural Park to create a buffer zone around the National Park. The flooding height of the marsh, the ponds of the park and the soil water-table depth, are strongly influenced by the underlying aquifer's conditions. It has been shown (Allier et al., 1974; Garcia Novo, 1979) that the composition and growth of vegetation on sandy soils is largely dependent on the soil water-table depth. The subterranean water dynamics strongly influence the ecology of the park at various levels. The aquifer system of Dofiana belongs to the regional "A1monte-Marismas" aquifer, covering an area of 2400km 2, dominated by continental deposits of *Author to whom all correspondence should be addressed. TIf. [1] (787) 764 0000 ext: 2036. Fax: [1] (787) 764 3875. Emaih [email protected],edu.
gravel and sands belonging to the Plio-Quaternary period. Within the park, two zones can be distinguished: the unconfined aquifer in the sandy substrates, and the confined aquifer under the impermeable sediments of the marsh. The superficial water-table, the objective of this study, which presents communications in some points with the regional aquifer, fluctuates approximately 1 m, and the aquatic systems are quite sensitive to small variations in the superficial phreatic surface. The regional aquifer is subjected to water exploitation outside the park at two sites. In the north, a large (14000ha) government-sponsored irrigation plan, with yearly extractions estimated between 25 and 35 hm 3 (Custodio, 1992). In the west and close to the sea shore, a second pumping site provides water for "Matalascafias", a large tourist resort with peak summer occupation of 200 000 people and yearly water extraction of 4-5 hm 3 (Custodio, 1992). The influence of the aquifer on the ecology of the park, together with the importance of the area, has promoted the development of several research programs since the 1960s (FAO, 1970; IGME, 1982; Olias Alvarez et al., 1991). The data obtained in these programs facilitated the development of different numerical models of the Dofiana aquifer dynamics (IGME 1982, 1983, 1987; Virg6s et al., 1983). Other papers have focused on phenomena of a reduced scale (Vela et al., 1991; Sacks, 1992). Most of the models cited above are focused on the large-scale hydrological aspects of the aquifer and were not designed to simulate the smaller-scale dynamics of the soil surface
2586
Linear regression model of water-table dynamics water, which, in turn, are responsible for the ecological performance of vegetation and the superficial water ecosystems. The relative regularity of the superficial water table fluctuations and the close relationship between precipitation and the phreatic surface variation led us to the development of a simple numerical model to simulate the fluctuations of the water in the discharge areas of the sands, where the water-table lies close to the soil surface. The main objectives were 1) to identify the parameters influencing the water table level fluctuations under the mobile dune area; 2) to develop expressions to estimate unknown values of the water-table level for periods during which records were not available; 3) to compare the equations obtained for different points of the study area as a way to detect local differences in the dynamics of the aquifer; and 4) to explore the detection of persistent deviations of the water level between the model and records, in order to identify the input of new regulatory processes using the model. The work is focused on the data from a set of 15 piezometers located at the mobile dune system in an interdune slack described below. Other sampling points were used fo:~comparison with the main set of data. The use of dynamic models, based on systems of differential equations or finite elements analysis, commonly found in the literature (IGME 1982, 1983, 1987; Rai and Singh, 1992), was beyond the scope of this project, It was not intended to study the flow of water into the larlge "Almonte-Marismas" aquifer system, nor the spatial distribution of water-table fluctuations, which can be studied with those models (FE/FD). The aim was to stimulate, through a simple mathematical treatment, the local level of temporal fluctuations of the water-table, as a tool to predict its behaviour and tc outline hypotheses about its dynamics and its ecological consequences. DESCRIPT][ON OF T H E STUDY AREA
Dofiana National Park is located on the southwestern coast of Spain (Fig. 1). The climate is a
t,
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Fig. 1. Map of the study area, located on the south-western coast of Spain.
2587
Mediterranean subhumid type with some Atlantic influence. Average rainfall is 570 mm, 80% of which falls between October and March. The summer is dry with high temperatures, July and August being the hottest months, with a daily mean temperature of 24.6°C. December and January are the coldest months, with a daily mean temperature of 9.3 degrees. The National Park includes two distinct geomorphologic structures: the marsh and the sands (mobile and stabilized). The stabilized sands have a rolling topography without a defined drainage network. The presence of a shallow water-table, along with the high permeability of the sandy substratum, makes higher zones very arid in summer, while depressions are humid with occasional flooding in winter. The present vegetation is dominated by a Mediterranean forest and scrub, whose floristic composition closely follows the local topography (Garcia Novo et al., 1977; Granados Corona et al., 1988; Garcia Novo and Merino Ortega, 1993; Pou, 1977) the effect being mediated by soil water availability (Merino Ortega et al., 1976). Scrub species largely belong to the Cistaceae and Labiatae families. METHODS AND DATACOLLECTION The records of the piezometric level in the Dofiana National Park dune field for ecological purposes were started in 1971 by the Department of Ecology of the Sevilla University with two main objectives: (1) to study the relationship between vegetation and the shallow soil water-table; and (2) to study the demography of Pinus pinea populations in the slacks of the mobile dune area. A set of permanent piezometers was established in the mobile dune area and the water-table level was recorded on a regular basis. The number of measuring points largely increased in 1989 as part of the "Dofiagua" research program, focused on long-term trends of the influenceof water availability on vegetation within the park. All the measuring points are located within the zone of the park with the highest degree of legal protection, Dofiana Biological Reserve. The monitored area include several types of vegetation. The measurements from 1983 to 1989 were taken monthly, while the periodicity from 1989 up to present varies from 7 to 30 days. Piezometers are made up of PVC pipes, of 4 cm diameter, fitted with a filter of nylon fabric at the end. They are buried vertically into the ground to a variable depth, usually ranging from 1 to 2.5 m. The water-table level is recorded with a phreatic depth electric sensor. The data are more frequently recorded from a set of 15 piezometers aligned in a 300-m transect, spaced 20 m apart, in an interdune slack known as "Corral Largo". The transect was established in 1973 in the mobile dune area, although regular water-table data are available only from 1983 onwards. The "Corral Largo" area is identified with the number 10 in Fig. 2. In the figures and tables, each piezometer of the transect is denoted by the letter "D" (dune) followed by a number. The water-table level next to some of the larger ponds in the area has been also recorded on a regular basis from 1989, and the data are used for a comparison with the water-table under the mobile dune field. These piezometers are identified with the letter "P" (pond) followed by a number (Fig. 2). Finally, a piezometer recorded on a continuous basis, located at the marsh border, is denoted as M9 (Fig. 2).
2588
F. de Castro Ochoa and J. C. Mufioz Reinoso
x,,
Fig. 2. Enlarged view of the Dofiana Biological Reserve, with the location of the piezometers. Numbers PI to P8 are placed next to permanent (P8) or temporal (PI-P7) ponds. The names of the ponds are (1) Navazo, (2) Ojillo, (3) Brezo, (4) Charco del Toro, (5) Zahillo, (6) Taraje, (7) Dulce, (8) Santa Olalla. Number M9 ("Palacio") is a piezometer located at the marsh border which is recorded in a continuous basis. Number 10 marks the location of the "Corral Largo", a dune area where a transect of 15 piezometers is located (D1-D15).
The data used for the calculations described below were those from Oct. 1989 to Dec. 1993. The reasons to select that period were (1) during that period rainfall measurements from a pluviometer located next to the piezometers are available for the same dates of the recordings of the phreatic level, and (2) the measurements were more frequent in that period than before, the phreatic surface level and rainfall being recorded almost each fortnight.
DESCRIPTION
OF THE MODEL
The calculations refer mainly to the data obtained from the transect of piezometers at the " C o r r a l Largo". The same kind o f analysis has been performed using the data from the set o f p o n d s a n d the results are c o m p a r e d with t h a t o f the transect. Multiple linear regression analysis was chosen to develop the model o f the phreatic surface. A l t h o u g h the a u t h o r s are aware t h a t it is n o t the most conventional m e t h o d for analysis o f time series (compared with m o v i n g averages (MA), autoregression (AR) or A R I M A models), they think t h a t multiple regression is the m e t h o d best suited for their particular purposes. The reasons for choosing multiple linear regression are as follows. (1) In order to apply analysis tools as those mentioned, the time-lag between two consecutive m e a s u r e m e n t s has to be c o n s t a n t t h r o u g h o u t the series (Priestly, 1981). This condition is not met by the present set o f data. The time-lag in this series varies from 7 to 60 days. (2) The m e n t i o n e d analyses (AR, M A or A R I M A ) do n o t take into account the effect of external variables in the fit o f the model, which is one o f the a u t h o r s ' main interests.
(3) The subset o f the data best suited to fit the model are that from Oct. 1989 to Dec. 1993, because, during that period, as previously mentioned, the data were recorded m u c h more frequently a n d accurately t h a n before. The years 1989-1993 were not very typical in their climatic conditions a n d the watertable dynamics reflect it. A n y A R or M A model fitted with that data would p r o b a b l y be less accurate predicting the phreatic surface in a n average year. (4) The multiple regression analysis allowed us to include the effect o f climatic variables into the model, m a k i n g it more flexible a n d able to m a k e accurate predictions even for years with climatic characteristics very different from those from which the model is fitted. A multiple linear regression has been calculated for each o f the piezometers. The d e p e n d e n t variable of the regressions is the increment (Ah) o f the phreatic surface d e p t h between two consecutive measurements, being positive if the water level rises a n d negative if it drops. So the values o f all the i n d e p e n d e n t variables are referred to the time interval between two consecutive measurements. A n autocorrelation analysis of the dependent variable (phreatic d e p t h increment) for four o f the piezometers is shown in Table 1. A u t o - c o r r e l a t i o n values are very low a n d are significative only in a few cases. The i n d e p e n d e n t (predictive) variables used are rainfall (r, dm), time lapse (At, days), present d e p t h (h, m) and, for some o f the piezometers, average m a x i m u m t e m p e r a t u r e between t a n d t + At (T, °C). The general expression o f the e q u a t i o n fitted to the data is A h = ao + m A t + a2h + a3er + a4T
The e q u a t i o n is fitted to the data o f each piezometer separately, instead o f fitting a single e q u a t i o n to the whole set o f data, because one o f the purposes of the model is to distinguish differences in the water-table dynamics of different zones, t h r o u g h the c o m p a r i s o n o f the p a r a m e t e r s al-a4 for each piezometer. Table 1. Results of the auto-correlation test of the dependent variable (phreatic depth increments) for four of the piezometers at the "Corral Largo" area (D1, D9, DI4 and D15) LAG DI D9 DI4 D15 1 0.013 0.093 0.027 0.464a 2 0.383" 0.355" 0.305a 0.452~ 3 - 0.022 0.160 0.079 0.288 4 0.222 0.141 0.102 0.202 5 - 0.157 0.028 0.019 0.048 6 0.077 0.096 0.064 0.027 7 - 0.111 - 0.087 - 0.056 - 0.075 8 - 0.042 - 0.061 - 0.108 - 0.133 9 - 0.029 0.052 0.048 - 0.052 10 - 0.030 - 0.071 - 0.004 - 0.072 11 - 0.100 - 0.034 - 0.076 0.106 12 0.043 0.042 0.003 - 0.133 13 - 0.155 - 0.268 - 0.235 14 0.023 - 0.015 aSignificance at 0.05 level.
Linear regression model of water-table dynamics
2589
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Rainfall
Time lapse
It is assumed that the rainfall is the main source of recharge of the dune aquifer, and so it is included as a primary indepe]adent variable in the regression analysis. The sand'.¢ texture of the soil in most of the area implies a low field capacity (18%), and so most of the rainfall may percolate directly to the water-table. It is to be noted that the phreatic surface increments shows an exponential relationship with precipitation (Fig. 3), so the variable that has been used for a better adjustment is the exponential of the precipitation. Some of the rainfall values are exceptional (130 rnm in 2 weeks) and the exponential function (e') increases significantly, causing numerical overflow during the calculations. To avoid that, the precipitation values are expressed in decimeters instead of millimeters.
The main loss of water from the phreatic aquifer is assumed to be the evapotranspiration, depending on the time lapse and the temperature, although water discharge in other directions are not excluded, i.e. to the sea, to the regional aquifer, etc. A rate of 0.1 cm/day has been calculated for bare sand in June 1989 (Coleto Fiafio and G6mez Martos, 1992). The discharge from the aquifer to the sea and to the nearby ponds has not been taken into account as an independent variable due to the lack of data about these processes, although they are not discarded. The longer the period between two measurements the larger the water-table drop. During periods without precipitation (usually from July to mid-September), it can be seen that the drop of the phreatic surface remains quite constant (Fig. 4). It is assumed, thus, that a more or less constant loss of water is produced,
2590
V. de Castro Ochoa and J. C. Mufioz Reinoso
and this suggested use of the time interval (in days) as an independent variable.
Present depth The present depth of the water-table influences the effect of the rainfall. As an initial hypothesis, it was assumed that if the water-table is shallow a given amount of water may produce a noticeable rise, while when the water-table was deep, say 2 or 3 m, the effect could be negligible. The regression analysis, however, revealed a different result, which will be explained in the discussion. The present depth can be considered as a auto-regressive component in the model.
through the warming of the soil. Also, higher temperatures promote an increment in the vegetation transpiration up to a given point in which the plant closes its stomata and transpiration ceases. Both processes may promote the descent of the watertable. To include temperature in the regression analysis the average maximum temperatures during the time-lapse between two measurements is used as an independent variable. Temperature was included in the analysis only for four of the piezometers, for reasons explained below. The results of the regression analysis for all the piezometers and ponds can be seen in Tables 2 and 3. The r2-values range from 0.547 to 0.83, many of them being over 0.7.
Temperature It is assumed that the temperature has both direct and indirect effects on the water-table. Higher temperatures produce higher evaporation rates
SIMULATION OF THE WATER-TABLE DYNAMICS
The regressions calculated for each piezometer allow us to simulate the evolution of the phreatic level 2.5
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Fig. 4. Descent of the phreatic surface in four piezometers of the "Corral Largo" dune area, in periods without precipitation (usually from July to September there is virtually no rainfall). The slope of the lines is quite constant, indicating a regular discharge of the water-table to other areas.
2591
Linear regression model of water-table dynamics Table 2. Regression coefficients for the ponds~ Pond Navazo (PI) Ojillo (P2) Brezo (P3) Charco (P4) Zahillo (P5) Taraje (P6) Dulce (P7) St Olalla (P8) Palacio (P9)
:intercept (ao)
At (a~)
h (a2)
e¢ (a3)
F
r2
n
0.5418 0.1322 0.1235 0.5297 0.5039 0.4144 0.509 0.42 0.1939
0.0062 0.0025 - 0.0012 0.0072 0.0057 0.0041 0.0023 0.0035 0.0108
- 0.2432 - 0.0397 0.0418 - 0.3994 - 0.3619 - 0.3665 - 0.2981 - 0.2756 - 0.1182
0.3185 0.0906 0.0955 0.2572 0.308 0.284 0.1935 0.1922 0.1742
10.68 7.08 4.53 16.88 36.72 14.43 21.44 22.94 45.22
0.604 0.57 0.382 0.62 0.78 0.599 0.712 0.697 0.638
25 20 26 35 35 33 30 34 81
aThe first column indicates the name of the pond and its number in Fig. 2. Other columns show the coefficients obtained for the independent variables: At (time lapse), h (phreatic depth) and e' (rainfall expressed as the exponential of the actual value).
in the past. G i v e n a n initial, actual p h r e a t i c surface d e p t h , a n d p r o v i d e d the p r e c i p i t a t i o n and, if n e e d e d , t e m p e r a t u r e values, it is possible to calculate the successive p h r e a t i c levels by iteration a p p l y i n g the a d e q u a t e regression e q u a t i o n s a n d w o r k i n g o u t the p h r e a t i c level i n c r e m e n t for the next time-step. A d d i n g this i n c r e m e n t to the p r e s e n t d e p t h , the next o n e is o b t a i n e d and so on. T h e s e kind o f s i m u l a t i o n s have b e e n r u n for f o u r p i e z o m e t e r s (Figs 5 a n d 6). T h e f o u r p i e z o m e t e r s were selected b e c a u s e they o b t a i n e d b e t t e r results in t h e regression analyses, a n d b e c a u s e l o n g record:s o f d a t a were available for t h e m . T h e c o m p a r i s o n b e t w e e n the real a n d p r e d i c t e d values ( S p e a r m a n c o r r e l a t i o n test) gives n o significant differences (p < 0.001) in a n y o f the four d a t a series. T h e actual d a t a used in the simulations c o m p a r i s o n are different f r o m t h o s e used for the calculation o f the regressions. T h e initial c o n d i t i o n is t h a t o f Oct. 1983, a n d the s i m u l a t i o n s are run with a time-step o f 10 days. T h e m a x i m u r a a n d a v e r a g e differences b e t w e e n o b s e r v e d a n d p r e d i c t e d values for the f o u r simulations c a n be seen in Table 4. T h e p r e c i p i t a t i o n a n d t e m p e r a t u r e values n e e d e d for the s i m u l a t i o n s were o b t a i n e d f r o m historical r e c o r d s o f a m e t e o r o l o g i c a l s t a t i o n located s o m e 15 k m a w a y f r o m the " C o r r a l L a r g o " area. A regression analysis o f p r e c i p i t a t i o n values for " C o r r a l L a r g o " (Pcl) a n d the M e t e o r o l o g i c a l s t a t i o n (Pms) d u r i n g the p e r i o d 1989-1993 s h o w s a very g o o d reilationship ( r 2 = 0 . 8 4 8 5 , n = 55)
Piezometer
with the f o r m u l a Pcl = 0.8562 + 1.5749 P m s This f o r m u l a was used to e s t i m a t e t h e p r e c i p i t a t i o n values at " C o r r a l L a r g o " for the s i m u l a t i o n p e r i o d 1983-1989, for w h i c h n o direct r e c o r d s are available. Implicitly, it is a s s u m e d t h a t the r e l a t i o n s h i p o b s e r v e d in the p e r i o d 1989-1993 h a s been t h e s a m e f r o m 1983 to 1989, w h i c h is c o n s i d e r e d to be a reasonable assumption. RESULTS AND DISCUSSION
Variables influencing the water-table fluctuations T h e regressions reached, in general, a c c e p t a b l e r2-values, t a k i n g into a c c o u n t the kind o f system being m o d e l l e d , thus suggesting t h a t the i n d e p e n d e n t variables c a n explain to a large degree the v a r i a t i o n s in the levels o f the shallow w a t e r - t a b l e in t h e s t u d y area. T o a large extent, the i n c r e m e n t s in the w a t e r - t a b l e level can be explained just by local precipitation, w h i c h suggests t h a t the d u n e a q u i f e r is very sensitive to local m e t e o r o l o g i c a l c o n d i t i o n s a n d follows its o w n d y n a m i c s , s o m e w h a t i n d e p e n d e n t o f the regional aquifer a n d t h e regional rainfall. T h e regression analysis s h o w s t h a t the soil w a t e r - t a b l e u n d e r the d u n e area has a very quick r e s p o n s e , since the effect o f the p r e c i p i t a t i o n c a n be n o t i c e d in few days. T h e soil w a t e r - t a b l e c a n be c o n s i d e r e d as a local s u b s y s t e m i n d e p e n d e n t o f the regional " A l m o n t e -
Table 3. Regression coefficients for the Corral Largo piezometers~ Intercept (ao) At (a0 h (a2) er (a~)
F
r2
n
D 1 -5 xx 0.2054 0.0039 - 0.048 0.166 132 0.8302 85 D2 -3 0.2725 0.0033 - 0.037 0.216 114.4 0.8148 75 D3 2 0.2074 0.0038 - 0.042 0.169 113.5 0.8156 81 D4 3 0.277 0.0032 - 0.035 0.220 104.1 0.8088 68 D5 5 0.18991 0.0038 - 0.057 0.152 69.5 0.6880 64 D6 7 0.22945 0.0050 - 0.072 0.148 60.3 0.6333 75 D7 8 0.14725 0.0035 - 0.048 0.120 65.3 0.6601 82 D8 12 0.14703 0.0033 - 0.035 0.127 69.2 0.6874 78 D9 15 0.1781 0.0036 - 0.045 0.149 125.3 0.8277 48 D10 19 0.15977 0.0035 - 0.041 0.135 70.0 0.6977 63 DI I 23 0.14404 0.0066 - 0.079 0.145 57.5 0.5474 83 DI2 26 0.13703 0.0033 - 0.019 0.129 70.2 0.7854 63 DI3 30 0.17268 0.0035 - 0.077 0.107 125.1 0.8259 48 D14 17 0.15609 0.0394 - 0.049 0.143 71.1 0.7940 68 DI5 28 0.14306 0.0035 - 0.019 0.128 90.11 0.7997 75 "The first column indicates the number of the piezometer. The second column is the interception point of the regression at y axis. The rest of the columns show the coefficients obtained for the independent variables: At (time lapse), h (phreatic depth) and er (rainfall expressed as the exponential of the actual value).
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2594
F. de Castro Ochoa and J. C. Mufioz Reinoso
Table 4. Maximumand average differencesbetweenobserved and predicted valuesof phreatic depth for four of the piezometers Piezometer Max. difference Averagedifference (cm) (cm) DI 36 10 D9 46 13 DI4 29 7.7 DI5 39 I1
Marismas" aquifer. This fact can have profound implications in the ecology of the vegetation in the area, since it strongly depends on the phreatic surface. The model can be used to simulate the variations of water-table depth in the past and to make estimates of drought or flooding in the different points of the area, depending on the local topography, which could help in the interpretation of vegetation changes and succession.
Developing expressions to estimate unknown values of the water-table The simulation through the calculated regressions of the phreatic surface dynamics in the past shows no significant differences with the actual phreatic surface depth. The average of the differences between the actual and calculated values (average error) lies between 7.8 cm and 11.3 cm. The model predictions during periods where records do not exist can be considered as good approximations to the unrecorded phreatic surface depth and could be used in other studies on the ecology of vegetation, as pointed out above.
If the temperature (average maximum daily temperature) is included as an independent variable, the r2-value of the regressions slightly increases, except in one out of the four piezometers tested, but the increments were not significant in any of the four cases. Thus, the temperature is not included as an independent variable in the final formulation of the model. As a further confirmation, a stepwise regression applied to the four data sets did not include the temperature as a predictive variable in any case.
Comparison of local water-table characteristics The coefficient of the rainfall variable is positive in all cases, as expected. More intense precipitation produces obviously higher increments in the watertable. The coefficient for the time-lapse is negative, again for all the piezometers. This result is also consistent, since it is assumed that the loss of water from the water-table takes place on a constant basis, and so the longer the period without input of water the deeper the phreatic surface. The coefficient for the present-depth variable is positive for all the regressions. This means that a given rainfall (r) in a given time interval (At) will promote a large rise of the water-table if it is deep, but only a slight rise if the water-table is shallow. This result can be explained by special distribution of the rainfall throughout the year. At the end of the summer the water-table is at its lowest level, after almost 3 months virtually without precipitation. Eighty percent (80%) of the yearly rainfall is concentrated at the
0.03
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Fig. 7. Result of the correspondence analysis of regression coefficients of all the piezometers.
Linear regression model of water-table dynamics beginning of the autumn (Oct. and Nov.), which causes a steep rise of the water-table. The coincidence of both factors, i.e. lowest level and maximum rise, is predicted irt the regression analysis and so the coefficient for the present-depth variable is positive. The set of coefficients for each regression reflects the behaviour of the water-table at each measurement point, To find out if different groups of piezometers may be distinguished by their behaviour, a correspondence analysis was done, with the coefficients of the regressions ao-a4 as variables and piezometers as cases. Prior to the analysis the coefficients were transformed to [log (x + 2)], where x is the value of the coefficient. This transformation is applied to normalize the data set (Zar, 1984), which is a requisite of the correspondence analysis. Two is added to every value to avoid figures less than l, because their logarithms are negative, which is not allowed in the correspondence analysis. The result is depicted in Fig. 7. The analysis clearly separate the ponds (all except number 2 and 3, in the negative part of the axis l) from the piezometers located in the "Corral Largo" area, all in the positive part of the axis. The pond number one (Navazo) is apart from the rest (4-8), which means a very different and particular response of that pond to external conditions. The group of piezometers at "Corral Largo" is distributed along the axis 2, with three (D2, D4 and D5) apart from the others. Two of the ponds exhibit a behaviour closer to the piezometers at "Corral Largo" (a dryer area) than to the rest of ponds (Fig. 7). They are ponds closer to the touristic resorL of "Matalascafias", which can have a definite influence in the dynamics of the phreatic level near the ponds. These ponds show a low response to rainfall. That can be due to several reasons, for instance the water extractions from the aquifer for the supply of the touristic resort "Matalascafias" or the discharge of the aquifer to the nearby ocean (Fig. 1). Except for the two cases mentioned in the previous paragraph (2 and 3), the piezometers placed next to the ponds have higher coefficient values titan those obtained for the "Corral Largo" area, specially for the precipitation and the present depth of phreatic surface. That suggests that the water-table under or next to the ponds has a stronger response to precipitation and that the recharge of the water-table of the ponds takes place more readily, spec,ially when it is very deep. Both results can be explained by the special characteristics of the ponds: first, they are depressed areas where some of the run-off is collected; second, they are discharge areas fed by the aquifer. Some of the relQ:ressions had a low r2-value, even with a sufficient number of observations. It suggests that some processes exist in some zones which affect the soil water-table that have not been considered in the regressions. The low r2-values of ponds 2 and 3 ("Ojillo" and "Brezo"), as suggested above, could be
2595
due to water extractions which have not been taken into account. Use of the model as a tool to detect changes in the aquifer dynamic The close agreement between actual and calculated phreatic surface depths should allow the use of the regression expressions as a tool to detect variations in the phreatic dynamics, for instance those due to extractions of water for irrigation or other purposes. The rainfall values need to be known to run the model. In spite of this, the model can be applied to rainfall values representative of different kinds of years (very dry, dry, humid, very humid, etc.) to obtain a prediction of the phreatic depth for that kind of year. Acknowledgements--Part of this work was supported by the project DOIqAGUA (Confederacirn Hidrogr~ifica del Guadalquivir). Manuel Olias kindly allowed us the use of data from the piezometer number M9 (Palacio). The Estacirn Biol6gica de Dofiana allowed us to take the field measurements inside the Biological Reserve. The Instituto Nacional de Meteorologia provided the authors with the rainfall and temperature data needed for some of the calculations. They gratefully acknowledge the useful comments from Dr Francisco Garcia Novo, Dr R. Maidment and four anonymous referees.
REFERENCES
Allier C., Gonz~ilez Bernaldez F. and Ramirez Diaz L. (1974) Mapa ecolrgico de la Reserva Biol6gica de Dofiana. CSIC, Estaci6n Biolrgica de Dofiana. Coleto Fiafio I. and G6mez Martos M. (1992) El proceso de recarga del aquifero del entorno del Parque Nacional de Dofiana. I. Evaporaci6n. V Simposio de Hidrogeologia, Alicante. Hidrogeol. Recursos Hidr~ul. Vol. XVII, 383-393. Custodio E. (1992) Comportamiento y papel de las aguas suberr~ineas en Dofiana: consecuencias de las extracciones. Meeting "Cambios sociales y ecol6gicos en Dofiana y su entorno". Universidad Hispanoamericana de Santa Maria de la R~bida. Garcia Novo F. (1979) The ecology of vegetation of the dunes in Dofiana National Park (South-West Spain). In Ecological Processes in Coastal Environments (Edited by Jefferies R. L. and Davy A. J.), pp. 571-592. Blackwell, Oxford. Garcia Novo F. and Merino Ortega J. (1993) Dry coastal ecosystems of southwestern Spain. In Dry Coastal Ecosystems: Polar Regions and Europe Edited by Van der Maarel, E. Elsevier. Garcia Novo F., Merino Ortega J., Ramirez Diaz L., Rodenas Larios M., Sancho Royo F., Torres Martinez A., Gonzalez Bernaldez F., Diaz Pineda F., Allier C., Bresset V. and Lacoste A. (1977) Dofiana, Prospeccirn e Inventario de Ecosistemas. Monografia 18, ICONA, Madrid. Granados Corona M., Martin Vicente A. and Garcia Novo F. (1988) Long-term vegetation changes on the stabilized dunes of Dofiana National Park (SW Spain). Vegetatio 75, 73-80. 1GME (1982) Actualizaci6n de datos hidrogeolrgicos en los acuiferos de Almonte-Marismas y Mioceno de base. Modelo matem~iticobidimensionaldel sistema acuifero n° 27. Technical Report, Unidad Almonte-Marismas, Madrid.
2596
F. de Castro Ochoa and J. C. Mufioz Reinoso
IGME (1983) Hidrogeologia del Parque Nacional de Dofiana y su entorno. Colecci6n lnforme, Madrid. IGME (1987) Simulaci6n de la evoluci6n piezom&rica del aquifero Almonte-Marismas: horizonte afio 2010. Merino Ortega J., Garcia Novo F. and Sanchez Diaz M. (1976) Annual fluctuations of water potential in the xerophitic shrub of the Dofiana Biological Reserve (Spain). Oecol. Plant. 11(1), 1-11. Olias Alvarez M., Cruz San Julian J., Benavente Herrera J., Garcia Novo F. and Mufioz Reinoso J. C. (1991) New data about the Almonte-Marismas aquifer from the hydrogeological monitoring (1989-1990). In Proceedings
of the XXIII I.A .H. Congress "Aquifer overexploitation", Vol. 1., pp. 159-162. Pou A. (1977) Implicaciones paleoclim~iticas de los sistemas dunares de Dofiana. IN: V. Reuni6n de Climatologla Agricola. Univ. Santiago de Compostela. Priestley M. B, (1981) Spectral Analysis and Time Series. Academic Press,
Rai S. N. and Singh R. N. (1992) Water table fluctuations in an aquifer system owing to time-varying surface infiltration and canal recharge. J. Hydrol. 136, 381-387. Sacks L. A., Herman J. S., Konikow L. F. and Vela A. L. (1992) Seasonal dynamics of groundwater-lake interactions at Dofiana National Park, Spain. J. Hydrol. 136, 123-154.
Vela A., Rodriguez J. and Tenajas J. L. (1991) An~lisis de los efectos de la explotaci6n del acuifero costero en las proximidades del Parque Nacional de Dofiana. In
Proceedings of the XXIII I.A.H. Congress "Aquifer Overexploitation", Vol. 1, 179-182. Virg6s L., Martinez Alraro P. E., L6pez Vilchez L. and Martin Machuca M. (1983) Estudio del funcionamiento hidrol6gico del aquifero Almonte-Marismas (Sistema n '~ 27) mediante un modelo digital bidimensional. Hidrol. Recursos Hidr{ml. (Madrid) IX, 103-124. Zar J. H. (1984) Biostatistical Analysis. Prentice-Hall.
War. Re.~.Vol. 31, No. 10, pp. 2586-2596, 1997 © 1997ElsevierScienceLtd. All rights reserved Printed in Great Britain 0043-1354/97 $17.00 + 0.00
MODEL OF LONG-TERM WATER-TABLE DYNAMICS AT DOlqANA NATIONAL PARK FRANCISCO DE CASTRO OCHOA'* and JOSI~ C. MUlqOZ REINOSO 2 tDepartment of Biology, University of Puerto Rico, P.O. Box 23360, Rio Piedras, 00931-3360, Puerto Rico, U.S.A. and 2Department of Biologia Vegetal y Ecologia, Universidad de Sevilla, Aptdo. 1095 41080, Sevilla, Spain (Received September 1996; accepted in revised form March 1997) Akstract--A model of long-term (10 years) dynamics of the water-table in the Dofiana National park is presented. The model is based on a linear regression analysis of data from a group of 24 piezometers, predicting the increments of the water-table at given time-steps. Rainfall, present depth of the water-table, average maximum temperatures and lapse time between two measurements have been used as independent variables. The regressions reach r2-valuesover 0.8. The model prediction of the water-table dynamics based on the regression equations fits the data for most of the measurement points. Differences in the coefficients of variables obtained for the piezometers reflect the different dynamics of the water-table of ponds and the dune area. © 1997 Elsevier Science Ltd Key words--model, simulation, water table, multiple regression, Dofiana
INTRODUCTION Dofiana National Park, located in south-western Spain, is one of the most important wetlands in Western Europe. The marshes and ponds of the park are the wintering area for a large number of migrating waterfowl species from Northern Europe and Central Africa. Also, the Dofiana National Park is one of the last habitats for seriously endangered vertebrate species such as the Imperial Eagle (Aquila adalberti) and the Iberian Linx (Lynx pardina). The Dofiana National Park (35 000 ha) was established in 1969. The Dofiana Biological Reserve (7500 ha), the study area, is a section of the park with a special degree of legal protection. In 1989 much of the area surrounding the park (54 250 ha) was also protected with the legal category of Natural Park to create a buffer zone around the National Park. The flooding height of the marsh, the ponds of the park and the soil water-table depth, are strongly influenced by the underlying aquifer's conditions. It has been shown (Allier et al., 1974; Garcia Novo, 1979) that the composition and growth of vegetation on sandy soils is largely dependent on the soil water-table depth. The subterranean water dynamics strongly influence the ecology of the park at various levels. The aquifer system of Dofiana belongs to the regional "A1monte-Marismas" aquifer, covering an area of 2400km 2, dominated by continental deposits of *Author to whom all correspondence should be addressed. TIf. [1] (787) 764 0000 ext: 2036. Fax: [1] (787) 764 3875. Emaih [email protected],edu.
gravel and sands belonging to the Plio-Quaternary period. Within the park, two zones can be distinguished: the unconfined aquifer in the sandy substrates, and the confined aquifer under the impermeable sediments of the marsh. The superficial water-table, the objective of this study, which presents communications in some points with the regional aquifer, fluctuates approximately 1 m, and the aquatic systems are quite sensitive to small variations in the superficial phreatic surface. The regional aquifer is subjected to water exploitation outside the park at two sites. In the north, a large (14000ha) government-sponsored irrigation plan, with yearly extractions estimated between 25 and 35 hm 3 (Custodio, 1992). In the west and close to the sea shore, a second pumping site provides water for "Matalascafias", a large tourist resort with peak summer occupation of 200 000 people and yearly water extraction of 4-5 hm 3 (Custodio, 1992). The influence of the aquifer on the ecology of the park, together with the importance of the area, has promoted the development of several research programs since the 1960s (FAO, 1970; IGME, 1982; Olias Alvarez et al., 1991). The data obtained in these programs facilitated the development of different numerical models of the Dofiana aquifer dynamics (IGME 1982, 1983, 1987; Virg6s et al., 1983). Other papers have focused on phenomena of a reduced scale (Vela et al., 1991; Sacks, 1992). Most of the models cited above are focused on the large-scale hydrological aspects of the aquifer and were not designed to simulate the smaller-scale dynamics of the soil surface
2586
Linear regression model of water-table dynamics water, which, in turn, are responsible for the ecological performance of vegetation and the superficial water ecosystems. The relative regularity of the superficial water table fluctuations and the close relationship between precipitation and the phreatic surface variation led us to the development of a simple numerical model to simulate the fluctuations of the water in the discharge areas of the sands, where the water-table lies close to the soil surface. The main objectives were 1) to identify the parameters influencing the water table level fluctuations under the mobile dune area; 2) to develop expressions to estimate unknown values of the water-table level for periods during which records were not available; 3) to compare the equations obtained for different points of the study area as a way to detect local differences in the dynamics of the aquifer; and 4) to explore the detection of persistent deviations of the water level between the model and records, in order to identify the input of new regulatory processes using the model. The work is focused on the data from a set of 15 piezometers located at the mobile dune system in an interdune slack described below. Other sampling points were used fo:~comparison with the main set of data. The use of dynamic models, based on systems of differential equations or finite elements analysis, commonly found in the literature (IGME 1982, 1983, 1987; Rai and Singh, 1992), was beyond the scope of this project, It was not intended to study the flow of water into the larlge "Almonte-Marismas" aquifer system, nor the spatial distribution of water-table fluctuations, which can be studied with those models (FE/FD). The aim was to stimulate, through a simple mathematical treatment, the local level of temporal fluctuations of the water-table, as a tool to predict its behaviour and tc outline hypotheses about its dynamics and its ecological consequences. DESCRIPT][ON OF T H E STUDY AREA
Dofiana National Park is located on the southwestern coast of Spain (Fig. 1). The climate is a
t,
S~I~~
Ivlr
Fig. 1. Map of the study area, located on the south-western coast of Spain.
2587
Mediterranean subhumid type with some Atlantic influence. Average rainfall is 570 mm, 80% of which falls between October and March. The summer is dry with high temperatures, July and August being the hottest months, with a daily mean temperature of 24.6°C. December and January are the coldest months, with a daily mean temperature of 9.3 degrees. The National Park includes two distinct geomorphologic structures: the marsh and the sands (mobile and stabilized). The stabilized sands have a rolling topography without a defined drainage network. The presence of a shallow water-table, along with the high permeability of the sandy substratum, makes higher zones very arid in summer, while depressions are humid with occasional flooding in winter. The present vegetation is dominated by a Mediterranean forest and scrub, whose floristic composition closely follows the local topography (Garcia Novo et al., 1977; Granados Corona et al., 1988; Garcia Novo and Merino Ortega, 1993; Pou, 1977) the effect being mediated by soil water availability (Merino Ortega et al., 1976). Scrub species largely belong to the Cistaceae and Labiatae families. METHODS AND DATACOLLECTION The records of the piezometric level in the Dofiana National Park dune field for ecological purposes were started in 1971 by the Department of Ecology of the Sevilla University with two main objectives: (1) to study the relationship between vegetation and the shallow soil water-table; and (2) to study the demography of Pinus pinea populations in the slacks of the mobile dune area. A set of permanent piezometers was established in the mobile dune area and the water-table level was recorded on a regular basis. The number of measuring points largely increased in 1989 as part of the "Dofiagua" research program, focused on long-term trends of the influenceof water availability on vegetation within the park. All the measuring points are located within the zone of the park with the highest degree of legal protection, Dofiana Biological Reserve. The monitored area include several types of vegetation. The measurements from 1983 to 1989 were taken monthly, while the periodicity from 1989 up to present varies from 7 to 30 days. Piezometers are made up of PVC pipes, of 4 cm diameter, fitted with a filter of nylon fabric at the end. They are buried vertically into the ground to a variable depth, usually ranging from 1 to 2.5 m. The water-table level is recorded with a phreatic depth electric sensor. The data are more frequently recorded from a set of 15 piezometers aligned in a 300-m transect, spaced 20 m apart, in an interdune slack known as "Corral Largo". The transect was established in 1973 in the mobile dune area, although regular water-table data are available only from 1983 onwards. The "Corral Largo" area is identified with the number 10 in Fig. 2. In the figures and tables, each piezometer of the transect is denoted by the letter "D" (dune) followed by a number. The water-table level next to some of the larger ponds in the area has been also recorded on a regular basis from 1989, and the data are used for a comparison with the water-table under the mobile dune field. These piezometers are identified with the letter "P" (pond) followed by a number (Fig. 2). Finally, a piezometer recorded on a continuous basis, located at the marsh border, is denoted as M9 (Fig. 2).
2588
F. de Castro Ochoa and J. C. Mufioz Reinoso
x,,
Fig. 2. Enlarged view of the Dofiana Biological Reserve, with the location of the piezometers. Numbers PI to P8 are placed next to permanent (P8) or temporal (PI-P7) ponds. The names of the ponds are (1) Navazo, (2) Ojillo, (3) Brezo, (4) Charco del Toro, (5) Zahillo, (6) Taraje, (7) Dulce, (8) Santa Olalla. Number M9 ("Palacio") is a piezometer located at the marsh border which is recorded in a continuous basis. Number 10 marks the location of the "Corral Largo", a dune area where a transect of 15 piezometers is located (D1-D15).
The data used for the calculations described below were those from Oct. 1989 to Dec. 1993. The reasons to select that period were (1) during that period rainfall measurements from a pluviometer located next to the piezometers are available for the same dates of the recordings of the phreatic level, and (2) the measurements were more frequent in that period than before, the phreatic surface level and rainfall being recorded almost each fortnight.
DESCRIPTION
OF THE MODEL
The calculations refer mainly to the data obtained from the transect of piezometers at the " C o r r a l Largo". The same kind o f analysis has been performed using the data from the set o f p o n d s a n d the results are c o m p a r e d with t h a t o f the transect. Multiple linear regression analysis was chosen to develop the model o f the phreatic surface. A l t h o u g h the a u t h o r s are aware t h a t it is n o t the most conventional m e t h o d for analysis o f time series (compared with m o v i n g averages (MA), autoregression (AR) or A R I M A models), they think t h a t multiple regression is the m e t h o d best suited for their particular purposes. The reasons for choosing multiple linear regression are as follows. (1) In order to apply analysis tools as those mentioned, the time-lag between two consecutive m e a s u r e m e n t s has to be c o n s t a n t t h r o u g h o u t the series (Priestly, 1981). This condition is not met by the present set o f data. The time-lag in this series varies from 7 to 60 days. (2) The m e n t i o n e d analyses (AR, M A or A R I M A ) do n o t take into account the effect of external variables in the fit o f the model, which is one o f the a u t h o r s ' main interests.
(3) The subset o f the data best suited to fit the model are that from Oct. 1989 to Dec. 1993, because, during that period, as previously mentioned, the data were recorded m u c h more frequently a n d accurately t h a n before. The years 1989-1993 were not very typical in their climatic conditions a n d the watertable dynamics reflect it. A n y A R or M A model fitted with that data would p r o b a b l y be less accurate predicting the phreatic surface in a n average year. (4) The multiple regression analysis allowed us to include the effect o f climatic variables into the model, m a k i n g it more flexible a n d able to m a k e accurate predictions even for years with climatic characteristics very different from those from which the model is fitted. A multiple linear regression has been calculated for each o f the piezometers. The d e p e n d e n t variable of the regressions is the increment (Ah) o f the phreatic surface d e p t h between two consecutive measurements, being positive if the water level rises a n d negative if it drops. So the values o f all the i n d e p e n d e n t variables are referred to the time interval between two consecutive measurements. A n autocorrelation analysis of the dependent variable (phreatic d e p t h increment) for four o f the piezometers is shown in Table 1. A u t o - c o r r e l a t i o n values are very low a n d are significative only in a few cases. The i n d e p e n d e n t (predictive) variables used are rainfall (r, dm), time lapse (At, days), present d e p t h (h, m) and, for some o f the piezometers, average m a x i m u m t e m p e r a t u r e between t a n d t + At (T, °C). The general expression o f the e q u a t i o n fitted to the data is A h = ao + m A t + a2h + a3er + a4T
The e q u a t i o n is fitted to the data o f each piezometer separately, instead o f fitting a single e q u a t i o n to the whole set o f data, because one o f the purposes of the model is to distinguish differences in the water-table dynamics of different zones, t h r o u g h the c o m p a r i s o n o f the p a r a m e t e r s al-a4 for each piezometer. Table 1. Results of the auto-correlation test of the dependent variable (phreatic depth increments) for four of the piezometers at the "Corral Largo" area (D1, D9, DI4 and D15) LAG DI D9 DI4 D15 1 0.013 0.093 0.027 0.464a 2 0.383" 0.355" 0.305a 0.452~ 3 - 0.022 0.160 0.079 0.288 4 0.222 0.141 0.102 0.202 5 - 0.157 0.028 0.019 0.048 6 0.077 0.096 0.064 0.027 7 - 0.111 - 0.087 - 0.056 - 0.075 8 - 0.042 - 0.061 - 0.108 - 0.133 9 - 0.029 0.052 0.048 - 0.052 10 - 0.030 - 0.071 - 0.004 - 0.072 11 - 0.100 - 0.034 - 0.076 0.106 12 0.043 0.042 0.003 - 0.133 13 - 0.155 - 0.268 - 0.235 14 0.023 - 0.015 aSignificance at 0.05 level.
Linear regression model of water-table dynamics
2589
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60
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175
Rainfall (ram) Fig. 3. Exponential relationship between rainfall and phreatic increments. The points are data values; the line represents the adjustment of data to an exponential curve.
Rainfall
Time lapse
It is assumed that the rainfall is the main source of recharge of the dune aquifer, and so it is included as a primary indepe]adent variable in the regression analysis. The sand'.¢ texture of the soil in most of the area implies a low field capacity (18%), and so most of the rainfall may percolate directly to the water-table. It is to be noted that the phreatic surface increments shows an exponential relationship with precipitation (Fig. 3), so the variable that has been used for a better adjustment is the exponential of the precipitation. Some of the rainfall values are exceptional (130 rnm in 2 weeks) and the exponential function (e') increases significantly, causing numerical overflow during the calculations. To avoid that, the precipitation values are expressed in decimeters instead of millimeters.
The main loss of water from the phreatic aquifer is assumed to be the evapotranspiration, depending on the time lapse and the temperature, although water discharge in other directions are not excluded, i.e. to the sea, to the regional aquifer, etc. A rate of 0.1 cm/day has been calculated for bare sand in June 1989 (Coleto Fiafio and G6mez Martos, 1992). The discharge from the aquifer to the sea and to the nearby ponds has not been taken into account as an independent variable due to the lack of data about these processes, although they are not discarded. The longer the period between two measurements the larger the water-table drop. During periods without precipitation (usually from July to mid-September), it can be seen that the drop of the phreatic surface remains quite constant (Fig. 4). It is assumed, thus, that a more or less constant loss of water is produced,
2590
V. de Castro Ochoa and J. C. Mufioz Reinoso
and this suggested use of the time interval (in days) as an independent variable.
Present depth The present depth of the water-table influences the effect of the rainfall. As an initial hypothesis, it was assumed that if the water-table is shallow a given amount of water may produce a noticeable rise, while when the water-table was deep, say 2 or 3 m, the effect could be negligible. The regression analysis, however, revealed a different result, which will be explained in the discussion. The present depth can be considered as a auto-regressive component in the model.
through the warming of the soil. Also, higher temperatures promote an increment in the vegetation transpiration up to a given point in which the plant closes its stomata and transpiration ceases. Both processes may promote the descent of the watertable. To include temperature in the regression analysis the average maximum temperatures during the time-lapse between two measurements is used as an independent variable. Temperature was included in the analysis only for four of the piezometers, for reasons explained below. The results of the regression analysis for all the piezometers and ponds can be seen in Tables 2 and 3. The r2-values range from 0.547 to 0.83, many of them being over 0.7.
Temperature It is assumed that the temperature has both direct and indirect effects on the water-table. Higher temperatures produce higher evaporation rates
SIMULATION OF THE WATER-TABLE DYNAMICS
The regressions calculated for each piezometer allow us to simulate the evolution of the phreatic level 2.5
2.5
DS
DI
,.-
A
=. Q. ® t2
O-O'~
A
E 1~ Q.
.,.,.f.,.f'" .f.,.-""
1
1
IIV
05
0.5
0
Iii O
O
,q"
~
i ; ; ; i i i i : i : : i I I i i ii 0 ¢:) r,4
I : I , ('o -
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2.5
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0.4
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,.,.,...,.--"".,.,.....-'/
)sO*'O'~o'*O Sa'O*e*OSO
g
O,,.ooO *'O*W'OSe
1 0.5
I I ', ', ', ', ', ', ', I ', ', I ', ', I ', T I ', ', [
-0.1
O
T-
Time
Time
Fig. 4. Descent of the phreatic surface in four piezometers of the "Corral Largo" dune area, in periods without precipitation (usually from July to September there is virtually no rainfall). The slope of the lines is quite constant, indicating a regular discharge of the water-table to other areas.
2591
Linear regression model of water-table dynamics Table 2. Regression coefficients for the ponds~ Pond Navazo (PI) Ojillo (P2) Brezo (P3) Charco (P4) Zahillo (P5) Taraje (P6) Dulce (P7) St Olalla (P8) Palacio (P9)
:intercept (ao)
At (a~)
h (a2)
e¢ (a3)
F
r2
n
0.5418 0.1322 0.1235 0.5297 0.5039 0.4144 0.509 0.42 0.1939
0.0062 0.0025 - 0.0012 0.0072 0.0057 0.0041 0.0023 0.0035 0.0108
- 0.2432 - 0.0397 0.0418 - 0.3994 - 0.3619 - 0.3665 - 0.2981 - 0.2756 - 0.1182
0.3185 0.0906 0.0955 0.2572 0.308 0.284 0.1935 0.1922 0.1742
10.68 7.08 4.53 16.88 36.72 14.43 21.44 22.94 45.22
0.604 0.57 0.382 0.62 0.78 0.599 0.712 0.697 0.638
25 20 26 35 35 33 30 34 81
aThe first column indicates the name of the pond and its number in Fig. 2. Other columns show the coefficients obtained for the independent variables: At (time lapse), h (phreatic depth) and e' (rainfall expressed as the exponential of the actual value).
in the past. G i v e n a n initial, actual p h r e a t i c surface d e p t h , a n d p r o v i d e d the p r e c i p i t a t i o n and, if n e e d e d , t e m p e r a t u r e values, it is possible to calculate the successive p h r e a t i c levels by iteration a p p l y i n g the a d e q u a t e regression e q u a t i o n s a n d w o r k i n g o u t the p h r e a t i c level i n c r e m e n t for the next time-step. A d d i n g this i n c r e m e n t to the p r e s e n t d e p t h , the next o n e is o b t a i n e d and so on. T h e s e kind o f s i m u l a t i o n s have b e e n r u n for f o u r p i e z o m e t e r s (Figs 5 a n d 6). T h e f o u r p i e z o m e t e r s were selected b e c a u s e they o b t a i n e d b e t t e r results in t h e regression analyses, a n d b e c a u s e l o n g record:s o f d a t a were available for t h e m . T h e c o m p a r i s o n b e t w e e n the real a n d p r e d i c t e d values ( S p e a r m a n c o r r e l a t i o n test) gives n o significant differences (p < 0.001) in a n y o f the four d a t a series. T h e actual d a t a used in the simulations c o m p a r i s o n are different f r o m t h o s e used for the calculation o f the regressions. T h e initial c o n d i t i o n is t h a t o f Oct. 1983, a n d the s i m u l a t i o n s are run with a time-step o f 10 days. T h e m a x i m u r a a n d a v e r a g e differences b e t w e e n o b s e r v e d a n d p r e d i c t e d values for the f o u r simulations c a n be seen in Table 4. T h e p r e c i p i t a t i o n a n d t e m p e r a t u r e values n e e d e d for the s i m u l a t i o n s were o b t a i n e d f r o m historical r e c o r d s o f a m e t e o r o l o g i c a l s t a t i o n located s o m e 15 k m a w a y f r o m the " C o r r a l L a r g o " area. A regression analysis o f p r e c i p i t a t i o n values for " C o r r a l L a r g o " (Pcl) a n d the M e t e o r o l o g i c a l s t a t i o n (Pms) d u r i n g the p e r i o d 1989-1993 s h o w s a very g o o d reilationship ( r 2 = 0 . 8 4 8 5 , n = 55)
Piezometer
with the f o r m u l a Pcl = 0.8562 + 1.5749 P m s This f o r m u l a was used to e s t i m a t e t h e p r e c i p i t a t i o n values at " C o r r a l L a r g o " for the s i m u l a t i o n p e r i o d 1983-1989, for w h i c h n o direct r e c o r d s are available. Implicitly, it is a s s u m e d t h a t the r e l a t i o n s h i p o b s e r v e d in the p e r i o d 1989-1993 h a s been t h e s a m e f r o m 1983 to 1989, w h i c h is c o n s i d e r e d to be a reasonable assumption. RESULTS AND DISCUSSION
Variables influencing the water-table fluctuations T h e regressions reached, in general, a c c e p t a b l e r2-values, t a k i n g into a c c o u n t the kind o f system being m o d e l l e d , thus suggesting t h a t the i n d e p e n d e n t variables c a n explain to a large degree the v a r i a t i o n s in the levels o f the shallow w a t e r - t a b l e in t h e s t u d y area. T o a large extent, the i n c r e m e n t s in the w a t e r - t a b l e level can be explained just by local precipitation, w h i c h suggests t h a t the d u n e a q u i f e r is very sensitive to local m e t e o r o l o g i c a l c o n d i t i o n s a n d follows its o w n d y n a m i c s , s o m e w h a t i n d e p e n d e n t o f the regional aquifer a n d t h e regional rainfall. T h e regression analysis s h o w s t h a t the soil w a t e r - t a b l e u n d e r the d u n e area has a very quick r e s p o n s e , since the effect o f the p r e c i p i t a t i o n c a n be n o t i c e d in few days. T h e soil w a t e r - t a b l e c a n be c o n s i d e r e d as a local s u b s y s t e m i n d e p e n d e n t o f the regional " A l m o n t e -
Table 3. Regression coefficients for the Corral Largo piezometers~ Intercept (ao) At (a0 h (a2) er (a~)
F
r2
n
D 1 -5 xx 0.2054 0.0039 - 0.048 0.166 132 0.8302 85 D2 -3 0.2725 0.0033 - 0.037 0.216 114.4 0.8148 75 D3 2 0.2074 0.0038 - 0.042 0.169 113.5 0.8156 81 D4 3 0.277 0.0032 - 0.035 0.220 104.1 0.8088 68 D5 5 0.18991 0.0038 - 0.057 0.152 69.5 0.6880 64 D6 7 0.22945 0.0050 - 0.072 0.148 60.3 0.6333 75 D7 8 0.14725 0.0035 - 0.048 0.120 65.3 0.6601 82 D8 12 0.14703 0.0033 - 0.035 0.127 69.2 0.6874 78 D9 15 0.1781 0.0036 - 0.045 0.149 125.3 0.8277 48 D10 19 0.15977 0.0035 - 0.041 0.135 70.0 0.6977 63 DI I 23 0.14404 0.0066 - 0.079 0.145 57.5 0.5474 83 DI2 26 0.13703 0.0033 - 0.019 0.129 70.2 0.7854 63 DI3 30 0.17268 0.0035 - 0.077 0.107 125.1 0.8259 48 D14 17 0.15609 0.0394 - 0.049 0.143 71.1 0.7940 68 DI5 28 0.14306 0.0035 - 0.019 0.128 90.11 0.7997 75 "The first column indicates the number of the piezometer. The second column is the interception point of the regression at y axis. The rest of the columns show the coefficients obtained for the independent variables: At (time lapse), h (phreatic depth) and er (rainfall expressed as the exponential of the actual value).
-+
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3
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Depth (m) --=
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L
i
mm==m~.
=,---
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J
Depth (m) 4~
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2594
F. de Castro Ochoa and J. C. Mufioz Reinoso
Table 4. Maximumand average differencesbetweenobserved and predicted valuesof phreatic depth for four of the piezometers Piezometer Max. difference Averagedifference (cm) (cm) DI 36 10 D9 46 13 DI4 29 7.7 DI5 39 I1
Marismas" aquifer. This fact can have profound implications in the ecology of the vegetation in the area, since it strongly depends on the phreatic surface. The model can be used to simulate the variations of water-table depth in the past and to make estimates of drought or flooding in the different points of the area, depending on the local topography, which could help in the interpretation of vegetation changes and succession.
Developing expressions to estimate unknown values of the water-table The simulation through the calculated regressions of the phreatic surface dynamics in the past shows no significant differences with the actual phreatic surface depth. The average of the differences between the actual and calculated values (average error) lies between 7.8 cm and 11.3 cm. The model predictions during periods where records do not exist can be considered as good approximations to the unrecorded phreatic surface depth and could be used in other studies on the ecology of vegetation, as pointed out above.
If the temperature (average maximum daily temperature) is included as an independent variable, the r2-value of the regressions slightly increases, except in one out of the four piezometers tested, but the increments were not significant in any of the four cases. Thus, the temperature is not included as an independent variable in the final formulation of the model. As a further confirmation, a stepwise regression applied to the four data sets did not include the temperature as a predictive variable in any case.
Comparison of local water-table characteristics The coefficient of the rainfall variable is positive in all cases, as expected. More intense precipitation produces obviously higher increments in the watertable. The coefficient for the time-lapse is negative, again for all the piezometers. This result is also consistent, since it is assumed that the loss of water from the water-table takes place on a constant basis, and so the longer the period without input of water the deeper the phreatic surface. The coefficient for the present-depth variable is positive for all the regressions. This means that a given rainfall (r) in a given time interval (At) will promote a large rise of the water-table if it is deep, but only a slight rise if the water-table is shallow. This result can be explained by special distribution of the rainfall throughout the year. At the end of the summer the water-table is at its lowest level, after almost 3 months virtually without precipitation. Eighty percent (80%) of the yearly rainfall is concentrated at the
0.03
[] P4
D30
0.02
aP8
I
a P7 [] P6
0.01
" Dtl e
M9
P2
D12° eD7
D8 D14 •
ID15 DP3
2
._W
I -0.15
I -0.1
~ -0.05
e"u~ D9 0.05
D6
(1
D1
a P5 -0.01
D3 -0.02
• D5 -0.03 • D2 I)4 -0.04 -
ta Pt
Axis
I
Fig. 7. Result of the correspondence analysis of regression coefficients of all the piezometers.
Linear regression model of water-table dynamics beginning of the autumn (Oct. and Nov.), which causes a steep rise of the water-table. The coincidence of both factors, i.e. lowest level and maximum rise, is predicted irt the regression analysis and so the coefficient for the present-depth variable is positive. The set of coefficients for each regression reflects the behaviour of the water-table at each measurement point, To find out if different groups of piezometers may be distinguished by their behaviour, a correspondence analysis was done, with the coefficients of the regressions ao-a4 as variables and piezometers as cases. Prior to the analysis the coefficients were transformed to [log (x + 2)], where x is the value of the coefficient. This transformation is applied to normalize the data set (Zar, 1984), which is a requisite of the correspondence analysis. Two is added to every value to avoid figures less than l, because their logarithms are negative, which is not allowed in the correspondence analysis. The result is depicted in Fig. 7. The analysis clearly separate the ponds (all except number 2 and 3, in the negative part of the axis l) from the piezometers located in the "Corral Largo" area, all in the positive part of the axis. The pond number one (Navazo) is apart from the rest (4-8), which means a very different and particular response of that pond to external conditions. The group of piezometers at "Corral Largo" is distributed along the axis 2, with three (D2, D4 and D5) apart from the others. Two of the ponds exhibit a behaviour closer to the piezometers at "Corral Largo" (a dryer area) than to the rest of ponds (Fig. 7). They are ponds closer to the touristic resorL of "Matalascafias", which can have a definite influence in the dynamics of the phreatic level near the ponds. These ponds show a low response to rainfall. That can be due to several reasons, for instance the water extractions from the aquifer for the supply of the touristic resort "Matalascafias" or the discharge of the aquifer to the nearby ocean (Fig. 1). Except for the two cases mentioned in the previous paragraph (2 and 3), the piezometers placed next to the ponds have higher coefficient values titan those obtained for the "Corral Largo" area, specially for the precipitation and the present depth of phreatic surface. That suggests that the water-table under or next to the ponds has a stronger response to precipitation and that the recharge of the water-table of the ponds takes place more readily, spec,ially when it is very deep. Both results can be explained by the special characteristics of the ponds: first, they are depressed areas where some of the run-off is collected; second, they are discharge areas fed by the aquifer. Some of the relQ:ressions had a low r2-value, even with a sufficient number of observations. It suggests that some processes exist in some zones which affect the soil water-table that have not been considered in the regressions. The low r2-values of ponds 2 and 3 ("Ojillo" and "Brezo"), as suggested above, could be
2595
due to water extractions which have not been taken into account. Use of the model as a tool to detect changes in the aquifer dynamic The close agreement between actual and calculated phreatic surface depths should allow the use of the regression expressions as a tool to detect variations in the phreatic dynamics, for instance those due to extractions of water for irrigation or other purposes. The rainfall values need to be known to run the model. In spite of this, the model can be applied to rainfall values representative of different kinds of years (very dry, dry, humid, very humid, etc.) to obtain a prediction of the phreatic depth for that kind of year. Acknowledgements--Part of this work was supported by the project DOIqAGUA (Confederacirn Hidrogr~ifica del Guadalquivir). Manuel Olias kindly allowed us the use of data from the piezometer number M9 (Palacio). The Estacirn Biol6gica de Dofiana allowed us to take the field measurements inside the Biological Reserve. The Instituto Nacional de Meteorologia provided the authors with the rainfall and temperature data needed for some of the calculations. They gratefully acknowledge the useful comments from Dr Francisco Garcia Novo, Dr R. Maidment and four anonymous referees.
REFERENCES
Allier C., Gonz~ilez Bernaldez F. and Ramirez Diaz L. (1974) Mapa ecolrgico de la Reserva Biol6gica de Dofiana. CSIC, Estaci6n Biolrgica de Dofiana. Coleto Fiafio I. and G6mez Martos M. (1992) El proceso de recarga del aquifero del entorno del Parque Nacional de Dofiana. I. Evaporaci6n. V Simposio de Hidrogeologia, Alicante. Hidrogeol. Recursos Hidr~ul. Vol. XVII, 383-393. Custodio E. (1992) Comportamiento y papel de las aguas suberr~ineas en Dofiana: consecuencias de las extracciones. Meeting "Cambios sociales y ecol6gicos en Dofiana y su entorno". Universidad Hispanoamericana de Santa Maria de la R~bida. Garcia Novo F. (1979) The ecology of vegetation of the dunes in Dofiana National Park (South-West Spain). In Ecological Processes in Coastal Environments (Edited by Jefferies R. L. and Davy A. J.), pp. 571-592. Blackwell, Oxford. Garcia Novo F. and Merino Ortega J. (1993) Dry coastal ecosystems of southwestern Spain. In Dry Coastal Ecosystems: Polar Regions and Europe Edited by Van der Maarel, E. Elsevier. Garcia Novo F., Merino Ortega J., Ramirez Diaz L., Rodenas Larios M., Sancho Royo F., Torres Martinez A., Gonzalez Bernaldez F., Diaz Pineda F., Allier C., Bresset V. and Lacoste A. (1977) Dofiana, Prospeccirn e Inventario de Ecosistemas. Monografia 18, ICONA, Madrid. Granados Corona M., Martin Vicente A. and Garcia Novo F. (1988) Long-term vegetation changes on the stabilized dunes of Dofiana National Park (SW Spain). Vegetatio 75, 73-80. 1GME (1982) Actualizaci6n de datos hidrogeolrgicos en los acuiferos de Almonte-Marismas y Mioceno de base. Modelo matem~iticobidimensionaldel sistema acuifero n° 27. Technical Report, Unidad Almonte-Marismas, Madrid.
2596
F. de Castro Ochoa and J. C. Mufioz Reinoso
IGME (1983) Hidrogeologia del Parque Nacional de Dofiana y su entorno. Colecci6n lnforme, Madrid. IGME (1987) Simulaci6n de la evoluci6n piezom&rica del aquifero Almonte-Marismas: horizonte afio 2010. Merino Ortega J., Garcia Novo F. and Sanchez Diaz M. (1976) Annual fluctuations of water potential in the xerophitic shrub of the Dofiana Biological Reserve (Spain). Oecol. Plant. 11(1), 1-11. Olias Alvarez M., Cruz San Julian J., Benavente Herrera J., Garcia Novo F. and Mufioz Reinoso J. C. (1991) New data about the Almonte-Marismas aquifer from the hydrogeological monitoring (1989-1990). In Proceedings
of the XXIII I.A .H. Congress "Aquifer overexploitation", Vol. 1., pp. 159-162. Pou A. (1977) Implicaciones paleoclim~iticas de los sistemas dunares de Dofiana. IN: V. Reuni6n de Climatologla Agricola. Univ. Santiago de Compostela. Priestley M. B, (1981) Spectral Analysis and Time Series. Academic Press,
Rai S. N. and Singh R. N. (1992) Water table fluctuations in an aquifer system owing to time-varying surface infiltration and canal recharge. J. Hydrol. 136, 381-387. Sacks L. A., Herman J. S., Konikow L. F. and Vela A. L. (1992) Seasonal dynamics of groundwater-lake interactions at Dofiana National Park, Spain. J. Hydrol. 136, 123-154.
Vela A., Rodriguez J. and Tenajas J. L. (1991) An~lisis de los efectos de la explotaci6n del acuifero costero en las proximidades del Parque Nacional de Dofiana. In
Proceedings of the XXIII I.A.H. Congress "Aquifer Overexploitation", Vol. 1, 179-182. Virg6s L., Martinez Alraro P. E., L6pez Vilchez L. and Martin Machuca M. (1983) Estudio del funcionamiento hidrol6gico del aquifero Almonte-Marismas (Sistema n '~ 27) mediante un modelo digital bidimensional. Hidrol. Recursos Hidr{ml. (Madrid) IX, 103-124. Zar J. H. (1984) Biostatistical Analysis. Prentice-Hall.