Detection of natural and artificial causes of groundwater fluctuations

Transcription

1 The Influence of Climate Change and Climatic Variability on the Hydrologie Regime and Water Resources (Proceedings of the Vancouver Symposium, August 1987). IAHSPubl. no. 168, Detection of natural and artificial causes of groundwater fluctuations Frans C. Van Geer TNO-DGV, Institute of Applied Geoscience P.O. Box 285, 2600 AG Delft, the Netherlands Peter R. Deflze ITI-TNO, Institute of Applied Computer Science P.O.Box 214, 2600 AG Delft, the Netherlands ABSTRACT Fluctuations and trends in the groundwater level are the result of a number of natural and artificial causes. Transfer/noise modelling has been applied to decompose observed groundwater level series in such a way that each cause of influence corresponds with a component of the groundwater level. In this paper two applications are presented: i) Detection of the influence of a river stage on the groundwater level, ii) Detection of an artificial trend in the groundwater level. To solve practical problems, easy to use methods are desired. Therefore transfer/noise modelling appears to be a useful addition to the existing geohydrologic modelling methods. Détection des causes naturelles et articielles de la fluctuation de l'eau souterraine RESUME Fluctuations et changements permanents dans le niveau de l'eau souterraine sont le résultat dun nombre de causes naturelles et artificielles. Le modelage transfer /bruit a été appliqué de manière que chaque cause ou influence correspond avec un constituant du niveau de l'eau souterraine. Deux applications sont présentées dans cette communication: (i) Detection de l'influence du niveau d'une rivière sur le niveau de l'eau souterraine, ii) Détection dun changement permanent dans le niveau de l'eau souterraine. Pour résoudre des problèmes pratiques, des méthodes simples sont désirées. C'eot pourquoi le modelage transfer /bruit semble être une extension utile des méthodes de modelage géohydrologiques. Introduction The presence and availability of groundwater is important for many human activities, such as agriculture and water supply. To obtain information about the behaviour of groundwater, observation wells have been placed at many locations. In the Netherlands, a primary groundwater monitoring network, maintained by TNO-DGV Institute of Applied Geoscience, serves as a reference network for regional 597

2 598 F.C. Van Geer & P.R. Defize groundwater management. The primary groundwater monitoring network consists of about 17,000 observation wells with 40,000 measurement screens. In 50% of the observation wells, the water level is measured 24 times a year, resulting in measurement series with time steps of approximately 15 days. The changes and fluctuations in the groundwater level are the result of many causes. Those causes can be split into"natural" causes (e.g. the fluctuation in precipitation, water stages in rivers) and "artificial" causes (e.g. groundwater abstraction). Often it is important to detect which part of the groundwater fluctuations is due to each particular cause. Therefore, a method is needed to decompose the groundwater level into components, representing the influence of natural and artificial causes on the groundwater. Because any method gives only an approximation of the real process, an estimate of the reliability of that approximation is also required. A well known method in systems analysis that meets these requirements is transfer modelling. The TNO-DGV Institute of Applied Geoscience in co-operation with the ITI-TN0 Institute of Applied Computer Science has tested transfer modelling for its applicability to groundwater measurement series. The method proves to be quite meritorious (Defize & Rolf 1985, Van Geer, 1986). In this paper, a brief review of the methodology is given and some specific problems encountered in applying it to groundwater are discussed. The possibilities for application of transfer modelling to groundwater are pointed out. Two case studies are presented: the detection of the influence of the stage of the river IJssel on the groundwater level and the detection whether or not the groundwater level has been lowered during the last decade in an area in the province of Noord-Brabant. Finally, some general conclusions are given. Methodology Transfer modelling is described in detail by Box and Jenkins(1976). Here only the basic conception of transfer modelling is given. The modelling process consists of three steps. (a) The causes that influence the groundwater are split into presumed dominant and minor causes with respect to the groundwater level fluctuations. The dominant causes are modelled explicitly. Each dominant cause yields a component in the groundwater level. Measurements of explicitly modelled causes are called input series. The minor causes are modelled as one single cause: the noise component. (b) All components are modelled as linear input-output models. The input of the noise model is supposed to be a zero mean white noise series, with an unknown variance. The models for the components with known input series are called transfer models, while the model with white noise as input is called the noise model. The components are the outputs of the linear models. (c) All the components and a constant are added to obtain the groundwater level. All model coefficients, including the constant and the variance of the white noise are estimated simultaneously by means of maximum likelihood. The accuracy of the estimated coefficient is given by means of the asymptotic variance-covariance matrix. The

3 Explaining groundwater fluctuations 599 validity of the model should be analysed by means of the residuals. The structure of the model or transfer/noise model, described in the three steps above, is given schematically in Figure 1. A transfer/noise is a model for discrete time series. It assumes that the input(s) and output are measured at equidistant time points. The general form of a transfer model (transfer model 1) is: h x (t) 6 X h^t-1) +.+6 h (t-r) + to x.(t) r 1 ol -co x.(t-s) (1) s 1 where: h,(t) a component of the groundwater level at time t. x-^(t) an input at time t ô^...6 r,u) 0...o) s parameters In the model (1) the terms 6 h^(t-l) (i=l...r) represent the inertia of the groundwater system. Such model structures are also known in hydrology, for example, in recession curves. The terms u) X^(t-l) (i=o...s) represent the driving force of the system. A hydrologie example of such a model structure is the unit hydrograph. The noise model has a similar form as the transfer models: n(t) = $. n(t-l) (> n(t-p)+a(t)- 6 a(t-l)-.- 6 a(t-q) q (2) where: n(t) the noise component at time t a(t) the realization of a white noise at time t c >-j_..,c )p,6]_...6 q parameters In principle, a transfer/noise model assumes stationarity. However, two types of non-stationarity can be dealt with. If the time series have seasonal fluctuations the transfer/noise model can be extended with a seasonal model. An example of a seasonal model is: n(t) = <f» n(t-l) + a(t) - 6 a(t-s) (3) where s is the seasonal period. input x,(t) transfer model 1 component h^t) input x 2 (t) transfer model 2 component h 2 (t) groundwater level h(t) constant 8, white noise a(t) noise model noise component n(t) Figure 1 Transfer/noise model.

4 600 F.C. Van Geer & P.R. Defize The second type is a polynomial trend that can be accounted for by differencing the original series a number of times, depending on the degree of the trend. A linear trend, for instance, can be modelled by taking the differences between two successive observations: z(t) = h(t) - h(t-l) (4) A quadratic trend can de dealt with by: z(t) = h(t-l) - 2h(t) + h(t+l) (5) In case of a polynomial trend the difference operation is carried out first and then the series z(t) is modelled with a transfer/noise modelo It should be noted that the structure of a transfer/noise model agrees with most common mathematical models in geohydrology, where a number of linear components (precipitation, abstraction) are superimposed, Application to groundwater A priori data manipulation Often the input series of the transfer models are abstractions of groundwater, precipitation excess (précipitation-évapotranspiration) or surface waterlevels. For convenience, throughout this discussion the input will be assumed to be precipitation. The fluctuations of the precipitation may show a totally different pattern compared with the fluctuations in the groundwater level. It is our experience that transfer modelling can be carried out successfully if the input series is transformed in such a way (by moving average, for example) that the fluctuation patterns of input and output series are of the same nature or- in other words- have the same time scale. Also, the measurement frequency of the input series may be different from that of the groundwater series. For instance in the Netherlands, most groundwater levels are measured with a frequency of 24 times per year, whereas the precipitation is measured daily. Because the groundwater measurement frequency is the lowest, this frequency (or a lower one) is used in the transfer model and the precipitation series is converted to that frequency. The measurement series of groundwater level is often smooth in comparison with the measurement series of the precipitation. Distinction can be made between two cases : (a) Shallow groundwater, where the time in which the precipitation is routed through the unsaturated zone is in the order of days. (b) Deep groundwater where the time in which the precipitation is routed through the unsaturated zone is in the order of months. In case of shallow groundwater, the fluctuations in groundwater level at time t are the result of the volume of precipitation measured in the days just before that time point. The number of days to be taken into account depends on the geohydrologic conditions. If the time scale of the groundwater fluctuations is larger than that of the converted precipitation a lower frequency can be taken (for

5 Explaining groundwater fluctuations 601 example, 12 times per year Instead of 24 times per year). Then, the volume of precipitation taken into account can be up to a monthly total. In addition to the conversion of measurement frequency, in case of deep groundwater a delay occurs between the time of precipitation and the reaction of the groundwater level. Moreover, the recharge due to precipitation will be smoothed when routing through the unsaturated zone. Similar problems occur for semi-confined groundwater. The delay time is taken into account in transfer models as an explicit parameter. The smoothing can be modelled with a moving average of the precipitation, with or without weighting factors. The time interval of the moving average and the weighting factors depend on the geohydrologic conditions. To manipulate the data in such a way that transfer models give sensible results, some experience in time series analysis as well as in geohydrologic modelling is required. There is not much guidance in the literature on this aspect. The use of a transfer/noise model The most obvious way of using transfer/noise models in geohydrology is decomposing the groundwater level time series into components related to measured input series. Very important components of groundwater levels are the fluctuations due to precipitation excess and drawdown caused by groundwater abstractions. With the aid of the decomposition, the fluctuations in and the drawdown level caused by each input can be quantified, as well as the reliability of the estimated fluctuations and drawdown. Transfer/noise models can also be used to forecast groundwater levels including confidence intervals of those forecasts. In particular, forecasting is sensible if some delay time occurs between the input and the groundwaterlevel, because then the actual measurements of the input (e.g. precipitation) can be used in the forecasting. If no delay time occurs, first forecasts of the input series are needed. Generally, with forecasted input series the confidence intervals of the forecasts will be too wide to have acceptable results. A third possible application of transfer/noise models is simulating the effects of alternative input series (e.g. for groundwater abstractions) on the groundwater level. The simulation will only give sensible results if the model structure is known in advance and will not be affected by the changes of the input. Case studies In the Netherlands, the TNO-DGV Institute of Applied Geoscience has applied transfer/noise modelling to several geohydrologic problems (Defize & Rolf 1985, Van Geer 1986). In this paper two examples are presented. (a) detection of the influence of the river IJssel on groundwater fluctuation in two observation wells. (b) detection of a possible trend in the groundwater level at a location in the province of Noord-Brabant.

6 602 F.C. Van Geer & P.R. Defize The location of the observation wells near the river IJssel (33G- 83 and 33H-27) and Noord-Brabant (51E-2) are located in Figure 2. Figure 2 Locations of the observation wells. Influence of the river IJssel on the groundwater level The observation wells 33G-83 and 33H-27 are located at distances from the river IJssel of 0*8 and 6 km respectively» The presumed dominant causes of groundwater level fluctuations are the precipitation excess and the stage of the river IJssel. The available information for the inputs were: (a) daily measurements of the river stage (b) ten-day totals of the precipitation and Penman evaporation The groundwater level is measured 24 times per year (according with a time step of about 15 days)» Both inputs have been converted to input series with a frequency of 24 times per year. The precipitation excess is calculated by: Precipitation - 0*8* Penman Evaporation. As input series for the precipitation excess the total volume during one step of 15 days is taken (Figure 3). The input series of the river stage is obtained by taking the average stage of three days, preceding the groundwater observation date (Figure 4). The results of the decomposition of the groundwater level in observation wells 23G-83 and 33H-27 are presented respectively in Figures 5 and 6. As can be seen from Figure 5, the groundwater level fluctuations in point 33G-83 are dominated by the river stage. The influence of the precipitation excess is only of minor importance. In well 33H-27 the opposite is the case (Figure 6). Here, the groundwater level is influenced little by the river stage, while the component due to the precipitation excess is a substantial part of the groundwater level.

7 Explaining groundwater fluctuations W^ 197/ ' ' ' Figure 3 Input series for precipitation excess. m ) Figure 4 ' 1974 ' 1975 ' 1976, ' 1977 ' 1978 ' 1979 ' 1980 ' 1 Input series for the water level groundwater level '^^ component of river level component of prec. excess Mr^NrM ly "\/V ^--- -v^-^-'v^m^ noise component 197A Figure 5 Decomposition of series 33G-83.

8 604 F.C. Van Geer & P.R. Defize M \AW/V groundwater level component of river level \\ / ^, / \ ' component of prec. excess r-fi "l-'i'mt ^'ix,.j!' Lv.ju --T- ^ /<[! A ^ H W K I - noise component Figure 6 Decomposition of series 33H--27. Trend detection in Noord-Brabant The observations in well 51E-2 in the province of Noord-Brabant indicate a moderate downward trend in the groundwater level during the years , A transfer/noise model has been applied to detect whether this trend is caused by changes in regional water management or it is just the result of a natural sequence of dry periods. A very important aspect of this research was the confidence interval of the estimated trend. In other words, whether or not the (artificial) trend is significant. A transfer/noise model with two inputs has been applied: precipitation excess and the "regional groundwater management". Measurements of the precipitation and Penman evaporation were available as ten-day totals. The calculated precipitation excess (precipitation * Penman evaporation) has been converted to an input series with measurement frequency of 24 times per year (the groundwater measurement frequency) in a similar way as in the previously described application. The actual changes in water management are not known, that is: not explicitly. To have an input series for the "regional water management", a linear increasing input series is generated. Of course the actual changes in water management are not known, e.g. the start of a new pumping station generally does not result in a linear increasing input series. But if the inclusion of a linear trend in the transfer/noise shows a significant improvement in comparison with a transfer/noise model without a trend, strong indications for a trend, regardless of the shape, are present. Inference about the shape of the trend demands a more thorough analysis of the water management situation than presented in this paper. The results of the transfer/noise model are given in Figure 7.

9 Explaining groundwater fluctuations 605 groundwater level ^component of precipitation excess linear trend M25_ i noise component i, f ^ l isiji'vim 1 I9&4 1 19Si ( IBSb 1 IBS/ ' I9SB* I B6I 1 I l96.1 r l9bv I96S 1 ' I 9bb' I 96?' IS6H 1! 9bï' I s/û'ïfln 1 i»;;>' 19/J 1 IS/V 19/S 1 19/b' 19^' 19/B 1 19/9* I 9<f J Figure 7 Trend analysis or series 51E-2. This figure shows a linear trend resulting in a lowering of 27cm over a period of 32 years. The standard error of this estimated lowering is 5 cm. Conclusions Applicability The applications that have been presented in this paper could also be analysed with the technique of linear regression. The model that is used with this method is a special case of the general transfer/noise model. In particular, the time aspect resulting in correlated observations, cannot be dealt with satisfactorily and therefore the more general approach of transfer/noise-analysis is preferable. For practical problems transfer/noise models are relatively easy to use. The main possibilities of applications are: (a) Decomposition of groundwater measurement series into natural and artificial components (b) short time forecasting of groundwater levels (c) simulation of changes in the groundwater regime (d) a quick-screening of the data material in preliminary investigations. Transfer/noise models can be applied if the measurement series of inputs and output are sufficiently long. The period over which measurements should be available depends mainly on the coherence (auto correlation) of the measurement series. For the interpretation of the results a qualitative knowledge of the geohydrologic conditions in situ is required. Comparison of transfer/noise models and deterministic models In comparison with the "classical" deterministic models, (e.g. finite elements, finite differences) transfer/noise models require less modelling effort, because no detailed information about the geohydrologic properties need to be collected. Moreover, generally, the

10 606 F.C. Van Geer & P.R. Defize dimensions of the computer programs for transfer/noise models are smaller than those for deterministic models. So, transfer/noise modelling can be performed in less time and for lower costs than deterministic models. Transfer/noise models are restricted to locations, where measurements are available and are not suitable for spatial interpolations. Remark In the modelling process of transfer/noise models a number of more or less arbitrary assumptions have been made (as with deterministic geohydrologic models). Therefore basic knowledge of time series analysis as well as of geohydrology is required. References Box, G.E.P. and Jenkins, G.M. (1976). Time series Analysis: forecasting and control. Holden-Day, San Francisco. Defize, P.R. and Rolf, H.L.M. (1985). Statistical analysis of some groundwater measurement series in Easter Gelderland (in dutch). DGV Report No. 0S_ Geer, F.C. van (1986). Lowering of the groundwater level in the Netherlands. Phase 1, Problem verification: Trend analyses of six groundwater measurement series in the period (In Dutch). DGV Report No. OS