7. Application to Groundwater Management

7.1. SUSTAINABLE LIMITS TO GROUNDWATER ALLOCATION

There has been much debate about definitions of "sustainable yield" from aquifers. We take the view that sustainable yield is meaningful only in the context of potential effects on values to be protected. Some of the more important effects of groundwater abstraction, such as low flow in spring-fed streams and salt water intrusion, depend on piezometric levels in the aquifer. As discussed in Section 4.1.1, variations in piezometric levels are caused primarily by variation in land-surface recharge. If abstractions can be considered as negative land-surface recharge, then the eigenmodel method can be used to estimate the piezometric effects and hence the environmental effects. We examine this concept in more detail in Section 8.2.

This approach seems to imply that river recharge is not being considered as a groundwater resource, but this not the case. River recharge, in some aquifers, provides the steady piezometric surface upon which is superimposed the dynamic fluctuations caused by land surface recharge. The long-term effect of abstractions is to lower the steady piezometric surface to an amount that depends on the connection between river and aquifer. The eigenmodel approach assumes that the river does not increase recharge in response to abstraction, which is a conservative view. However, if this assumption proves to be grossly incorrect then the model is easily updated when new piezometric data become available.

7.2. SHORT-TERM AND LONG-TERM EFFECTS OF ABSTRACTION

The theory of groundwater wells shows that the piezometric effect of groundwater abstraction propagates away from the well in a radial direction, and that this effect decreases in magnitude with distance. Most applications of this theory are directed to estimating the effects of drawdown from a well, in terms of interference with other wells or influence on stream-aquifer interaction. The distance scale of these investigations is usually up to a few kilometres, and the time scale is up to a few months. These methods are well established and are not considered any further in this report. However, it is important to realise that these applications of well theory limit the estimation of effects to magnitudes that are significant or are practically measurable.

Any abstraction from an aquifer has an effect that eventually propagates throughout the whole aquifer. This effect may be a lowering of piezometric levels or induced additional recharge from a river. The effect from any one well may be infinitesimal in terms of practical measurement, but the cumulative long-term effects of many wells can be very significant. This is an issue that can be addressed by means of the eigenmodel approach, because the cumulative effects can be considered as a (negative) change to the land surface recharge over the whole aquifer.

One of the assumptions of the eigenmodel (Section 4.1.2) is that the spatial pattern of recharge is fixed, and that the time-variation is the same everywhere. It is obvious that this does not appear to be true for a developing pattern of abstraction wells that operate out of season to winter recharge from soil water drainage, for example. Our experience to date suggests that this assumption is not a serious limitation to application of the method. As aquifer development proceeds, the eigenmodel can be re-calibrated to account for any systematic changes. Therefore, our initial working assumptions for estimating the aquifer-wide, long-term effects of abstraction are:

The cumulative effect of abstractions is spread throughout the whole aquifer
The time pattern of total abstraction can be applied as an input to the eigenmodel.

7.3. ANALYSIS OF AQUIFERS WITH UNKNOWN ABSTRACTION

Many of the aquifers that are likely to require improved management are already under stress from abstractions for which there are insufficient data on actual use in contrast to permitted allocation. This situation is demonstrated in the case histories considered in Section 6, for which the simulation plots show marked departures from the eigenmodel predictions, especially during drought periods. Our experience is that the eigenmodel calibrations are quite robust for aquifers with climatically driven, land surface recharge that is relatively larger than total abstraction.

7.4. CASE STUDY: EFFECTS OF GROUNDWATER ABSTRACTION ON THE HALSWELL RIVER

7.4.1. Relationship between Groundwater Level and Streamflow

Figure 19 shows the relationship between flow at a gauging station on the Halswell River and piezometric levels at Well M36/0255, which is about 14 km from the river (Figure 10).

Figure 19: Relationship between groundwater levels and low flow in the Halswell River

The low-flow base of the Halswell River is clearly related to the piezometric level at the observation well, and this base is given by the linear scaling:

Halswell River low-flow (L/s) = 200 × GWL@M36/0255 (m amsl) - 6000 (24)

We have an eigenmodel for predicting groundwater level at this indicator well M36/0255 (Table 3, Figure 18), and therefore it seems feasible to use it, in combination with equation (24), to predict the effects of Central Plains land surface recharge on the low-flow regime of the Halswell River.

7.4.2. Eigenmodel Predictions of Low Flow

Figure 20 shows the eigenmodel prediction of piezometric levels at M36/0255 for the same time period as in Figure 19. Predictions are quite satisfactory for the earlier part of the record but during the two consecutive "drought" seasons of 1997/98 and 1998/99 the observed groundwater levels were well below predictions. Therefore, low flow in the Halswell River would have been overestimated. Was this just a local effect caused by nearby groundwater abstraction, or was it part of an overall depletion of aquifer resource? Figure 21 shows the four well records, standardised by means of the Base and LSR effect parameters, for convenient comparison.

Figure 20: Eigenmodel predictions at indicator well for low-flow effects

Figure 21: Comparison of standardised well records for the droughts of 1997/98 and 1998/99

For the first season (1997/98), the two well records for the upper part of the Central Plains (L35/0163, L36/0092) follow the eigenmodel prediction, whereas the two well records for the lower part of the plains (M35/1080, M36/0255) are significantly lower. This suggests that there is a component of "short-range, short-term" effect caused by abstraction in the lower plains, which has a direct effect on low-flow in the Halswell River. What is the role of the eigenmodel predictions in this scenario?

One solution would be to update the eigenmodel to account for observed departures from what has been predicted, and to use this information in operational management of the groundwater resource. In fact the mathematical structure of the eigenmodel is well suited to this kind of "real-time" updating.

7.4.3. A First Look at "sustainable yield"

Although the example shown in Figures 20 and 21 demonstrates that an environmental effect may be determined by local and temporal stresses, it is useful to be able to quantify the expected effect of allocating a proportion of the total groundwater resource to a particular use. Figure 22 shows the effect on the predicted indicator well levels of allocating 15% of average land surface recharge to be used for irrigation each year during November to February. The total land surface recharge can be estimated from the total land area overlying the Central Plains aquifer, multiplied by the average recharge calculated from the water balance model. Then, the allocation can be expressed as an annual volume of water, for example.

Figure 22: Effect on groundwater level of a specified water allocation

7.5. A TOOL FOR ADAPTIVE MANAGEMENT

The eigenmodel can be a useful tool for adaptive management of groundwater because it provides a means of expressing, as a simple concept, the overall dynamic behaviour of the groundwater resource in response to natural recharge and the abstraction stresses imposed by human use of the resource. This simple conceptual model is expressed in a mathematical form that is the key to a large body of theory that has been developed in the applied fields of control engineering and econometrics. Some of these theories are concerned with issues related to managing dynamic systems with uncertain knowledge of processes and poor quality data. The following section illustrates one example of these applications.

7.6. UPDATING THE EIGENMODEL FOR REAL-TIME FORECASTING

Appendix II describes how the difference equation (10) of the eigenmodel can be further augmented to a "forecast" form that is suitable for real-time operations in which the model is continually updated with the latest observations of piezometric levels. The resulting difference equation is:

(25)

in which the coefficients are related to the coefficients of equation (10), as given in Appendix II. The complete procedure for forecasting is not presented in this report and equation (25) is shown above only to illustrate the process. The input data for the forecasting procedure are the recent history of:

Observed piezometric data h_n relative to the Base parameter (U_n)
Estimated land surface recharge R_n
Forecasting errors e_n

Future values of land surface recharge are not usually known because the climatic events are yet to occur. However, in a drought situation the future recharge can be assumed to be zero in order to forecast the worst-case. If restrictions on abstraction are being considered, then these can be estimated in terms of negative land surface recharge and used in the forecast equation.

The effect of incorporating the recent history of forecasting errors is to produce a feedback signal for the model to help it track unknown influences such as unrecorded abstractions and recharges. In order to operate the forecasting procedure, these data must be collected and processed in every time interval (e.g., monthly). This requirement can act as a focal point for the stakeholders involved in adaptive management.

The case study described in the next section illustrates the benefit of applying a forecast model to managing groundwater for environmental objectives. A forecast model of this type had previously been developed for Well L36/0092 by Bidwell et al. (1991).

7.7. FORECASTING THE EFFECTS OF ABSTRACTION

We now reconsider the case study of Section 7.4.2 in which prediction of low flow in the Halswell River was considered to be unsatisfactory during the 1997-99 droughts because unrecorded abstraction caused unexpected low piezometric levels in the indicator well (Figure 20). Figure 23 shows the result of applying the forecast version of the eigenmodel to the data from this well, in order to obtain forecasts of piezometric level one month ahead. These forecasts can than be transformed to low-flow estimates for the Halswell River by use of equation (24).

Figure 23: Eigenmodel forecasts at indicator well for low-flow effects

Figure 23 shows that the one-month forecasts provide warning of significant departures from model prediction, quite similar to what was subsequently observed. This kind of information could be used to justify implementation of restrictions on abstraction if the low-flow forecasts were to violate agreed environmental values.