6. Case Histories

In each of the following case studies, the only sources of data are:

Daily values of land surface recharge estimated from a water balance model. These are summed to monthly totals for use with monthly groundwater level data.
Records of groundwater (piezometric) level from a few observation wells, either at daily or monthly time intervals.

Reprints of portions of topographical maps are shown, to illustrate the location of observation wells and the scale of the aquifer.

Details of the water balance model and geological information about the aquifers are not presented here.

6.1.1 Preliminary Assessment with Limited Data

Figure 6 shows the results of an eigenmodel calibration with one year of daily data for Rossiters Well (Figure 5). This is a good set of data because there is a significant land surface recharge event that has caused a strong piezometric response in the aquifer.

Figure 5: Location of observation wells in the Motueka Aquifer

The results (Figure 6) show that only one eigenvalue was required to provide a good fit (R2 = 0.91) to the data. The important result is that the storage residence time (T1) is only 22 days. This means that the contribution of land surface recharge is unlikely to be adequate because half of this storage is lost by natural drainage in about 15 days (0.69 × 22). Therefore, this aquifer appears to be primarily a transport medium for river recharge. Now we examine the additional information provided by the use of five years of daily data for the three observation wells shown in Figure 5.

6.1.2 Assessment with Additional Data

The eigenmodel results and simulation plots for Wratts, Rossiters and Horrells observation wells (Figure 5) are shown in Figures 7 to 9. The relevant parameter values from these results are summarised in Table 1.

Table 1: Summary of eigenmodel results for the Motueka Aquifer

Observation well	Wratts	Rossiters	Horrells
Eigenvalues (d-1)	0.260, 0.010	0.039	0.031
Residence time (d)	99	25	32
LSR effect (mm)	373	368	510
GWL base amsl (mm)	8697	3212	1576
Eigenmodel fit R2	0.53	0.75	0.85

At Rossiters and Horrells, there is only one significant eigenvalue and it is similar for both locations, as are the storage residence times (inverse of the smallest eigenvalue). This similarity is expected from aquifer dynamics (Section 5.2.1). These values are also comparable to the eigenvalue of 0.045/d (residence time of 22 days) determined from the short data record (Section 6.1.1).

The well at Wratts exhibits an apparently anomalous value for the smallest eigenvalue, of 0.01/d. This could be caused by a piezometric response to the adjacent Motueka River, which reflects the storage characteristics of the river catchment rather than the aquifer. This signal is likely to be rapidly damped with distance from the river and therefore not detected at the other wells. The larger eigenvalue at this well (0.260/d) is an order of magnitude greater than the first eigenvalue of any of the wells, which is typical (Section 5.1.1).

The average piezometric effect of land surface recharge (LSR effect) is similar for Wratts and Rossiters (373 mm, 368 mm). This indicates that the Motueka River is not a fixed-head boundary near Wratts, otherwise the LSR effect would be relatively smaller.

Horrells Well has the largest value of LSR effect (510 mm), and this suggests that it is further from fixed-head outflow boundaries. This may suggest the presence of a no-flow boundary to the south of this well.

The GWL base and the LSR effect at Horrells can be compared with the bed level and stage of the Motueka River as part of any investigation of the nature of the connection between river and aquifer. This is not included in the present case study.

Comparison of the average piezometric heads (GWL base + LSR effect) at the three wells indicates groundwater flow to the southeast quarter.

The eigenmodel fit (R2) is poorest at Wratts (0.53) because of the influence of the Motueka River, and because the eigenmodel treats river effects as a constant. The fit improves with distance from the river at Rossiters (0.75) and Horrells (0.85). The primary source of model error appears to be the low piezometric head during summer drought, when abstractions are high. These periods are indicated (Figures 7 to 9) by piezometric levels (GWL) below the GWL base values.

The conclusions from this eigenmodel assessment of the Motueka aquifer are as follows:

There is insufficient aquifer storage to carry-over land surface recharge from winter months through the dry spring-summer period;
The aquifer is a transport medium for river recharge, which is the primary water resource;
The connection between the Motueka River and the aquifer is probably not directly interactive, but the nature of this connection is very important for managing abstraction from the aquifer, in terms of the magnitude of the resource.

Figure 6: Eigenmodel results for short data record at Rossiters Well, Motueka

Figure 7: Eigenmodel results for Wratts Well, Motueka

Figure 8: Eigenmodel results for Rossiters Well, Motueka

Figure 9: Eigenmodel results for Horrells Well, Motueka

6.2 Central Plains Aquifer, Canterbury

Figure 10 shows the location of four observation wells in the Central Canterbury Plains, which will be the basis of the next case study. The Central Plains aquifer is much larger than the Motueka aquifer, and the dynamic behaviour can be adequately described by the use of monthly values of piezometric head. The land surface recharge is still estimated from a daily water balance model but the results are summed to provide monthly totals. The piezometric data are in units of metres (rather than millimetres as for the Motueka data).

Figure 10: Location of observation wells and a river gauging station in the Central Canterbury Plains

Figure 10 also shows the location of a flow gauging station on the Halswell River. The relationship between streamflow and piezometric levels in the aquifer will be examined in Section 7.4.

6.2.1 Preliminary Assessment with Individual Short Records

Figures 11 to 14 show the simulation results and parameter values for the four wells (Figure 10), based on five years of monthly data for 1995-1999. This is quite a short data record for an aquifer of this size, given the climatic variability of the Canterbury Plains. The results are summarised in Table 2.

Table 2: Eigenmodel results for 5 years’ data, Central Canterbury Plains, for individual calibration at each location

Observation well	L35/0163	L36/0092	M35/1080	M36/0255
Eigenvalues (mth-1)	N/A	0.011	0.189	0.043, 0.339
Residence time (mth)	N/A	95	5.3	23
LSR effect (m)	N/A	62.3	2.0	3.6
GWL base amsl (m)	N/A	0	44.9	30.0
Eigenmodel fit R2	N/A	0.95	0.90	0.90

In general, these results are quite unsatisfactory. The following explanations include some additional physical knowledge of the aquifer:

The eigenmodel could not be fitted to L35/0163 during this period of record because the variations in piezometric head were caused primarily by recharge events from the adjacent Waimakariri River. There is also a general decline in piezometric head which looks as though it is associated with decreasing land surface recharge but this signal has been swamped by the river recharge effect.
The model fit (R2 = 0.95) appears to be very good for L36/0092, but physical realism is poor. The GWL base of zero corresponds to sea level, and this was because this value is a constraint in the calibration procedure. The LSR effect of 62.3 m is questionably large. The physical explanation of this poor performance may be that this well is in a semi-confined layer and the response is damped by the storage characteristics of perched groundwater. This is usually simulated by the vadose zone storage element of the eigenmodel.
The results for M35/1080 and M36/0255 are physically realistic, but the storage residence times are very different. According to eigenmodel theory (Section 4.2.1), the dominant residence times should be similar.

6.2.2 Reassessment with Combined Short Records

The eigenmodels for the four observation wells were then optimised simultaneously, with incorporation of the requirement that the eigenvalues are the same at all locations. The revised results are shown in Table 3.

Table 3: Eigenmodel results for 5 years’ data, Central Canterbury Plains, for simultaneous calibration at all locations

Observation well	L35/0163	L36/0092	M35/1080	M36/0255
Eigenvalues (mth-1)	0.015, 0.197	0.015	0.197	0.197
Residence time (mth)	67	67	5.1	5.1
LSR effect (m)	11.1	26.1	2.4	2.0
GWL base amsl (m)	68.1	33.7	44.9	30.4
Eigenmodel fit R2	0.89	0.95	0.90	0.89

The effect of combining the data is that Well L35/0163 now has a result, because the eigenvalues have been forced to "sensible" values by the influence of knowledge gained from the other observation wells. The model fit has hardly changed for these wells, but the realism of the parameter values remains questionable. In the next section, the influence of a longer data record will become apparent.

Figure 11: Eigenmodel results for the 5-year record at well L35/0163

Figure 12: Eigenmodel results for the 5-year record at well L36/0092

Figure 13: Eigenmodel results for the 5-year record at well M35/1080

Figure 14: Eigenmodel results for the 5-year record at well M36/0255

6.2.3Assessment with Longer Time Series

Table 4 shows the eigenmodel results for the four wells (Figure 10) from up to 28 years of monthly data (June 1972 to May 2000). The corresponding simulation plots and detailed results are shown in Figures 15-18.

Table 4: Eigenmodel results for 28 years’ data, Central Canterbury Plains, for individual calibration at each location

Observation well	L35/0163	L36/0092	M35/1080	M36/0255
Eigenvalues (mth^-1)	0.053	0.048	0.049, 0.629	0.052, 1.649
Residence time (mth)	19.0	20.8	20.5	19.1
LSR effect (m)	20.8	19.1	3.2	4.9
GWL base amsl (m)	80.1	59.5	44.0	28.9
Vadose storage (mth)	2.7	4.4	0.6	0.6
Eigenmodel fit R²	0.87	0.91	0.82	0.85

These results are much more satisfactory than those reported in Section 6.2.1 for the 5-year record. Discussion of particular features follows:

The first eigenvalues are all similar, as are the corresponding storage residence times. This residence time of about 20 months suggests that the aquifer has significant inter-seasonal storage, and therefore land surface recharge is an important water resource.
The values of GWL base correspond to a gradient of about 0.002 up the Plains from the lower fixed-head boundary at Lake Ellesmere. This suggests that river recharge is also a significant contribution to groundwater.
The values of LSR effect correspond to the distance of wells from surface water boundaries, except for L35/0163. This well has the highest LSR effect (20.8 m), which suggests that the aquifer does not directly interact with the Waimakariri River at this location. In other words, the river is perched above the aquifer.
The vadose residence time is much larger for L35/0163 and L36/0092, which is probably due to the slow drainage of perched groundwater into the semi-confined aquifers tapped by theses two wells.
A second eigenvalue is significant only for M35/1080 and M36/0255. This is because these two wells are closer to fixed head, surface-water boundaries, for which there is a component of more-rapid transient drainage.

The simulation plot for L35/0163 (Figure 15) shows several peaks in the piezometric record, which are not simulated by the eigenmodel. Examination of the dates of these events suggests that the peaks are caused by recharge during floods in the Waimakariri River, over and above the more steady component of river recharge. A similar departure, caused by a major flood in the Selwyn River, can be seen in the 1986-1988 period of the record for L36/0092 (Figure 16).

In general, the improved model results for the longer records are due to including the earlier years when land surface recharge was more significant than during the recent years of relative drought.

6.2.4. Assessment with Combined Longer Series

Table 5: Eigenmodel results for 28 years' data, Central Canterbury Plains, for simultaneous calibration at all locations

Observation well	L35/0163	L36/0092	M35/1080	M36/0255
Eigenvalues (mth^-1)	0.949	0.949, 0.285	0.949, 0.285	0.949, 0.285
Residence time (mth)	19.3	19.3	19.3	19.3
LSR effect (m)	20.9	18.7	3.1	5.0
GWL base amsl (m)	80.0	59.9	44.1	28.8
Vadose storage (mth)	2.7	5.3	1.3	0.1
Eigenmodel fit R²	0.87	0.91	0.82	0.85

Comparison of Table 4 with Table 5 shows that simultaneous calibration of the four longer well records has not made a significant difference to the model parameters. This result demonstrates the value of a long period of record for assessing the overall storage capability of a large aquifer. Increasing the number of observation well records has only a marginal effect on defining this particular property.

Figure 15: Eigenmodel results for the 28-year record at well L35/0163

Figure 16: Eigenmodel results for the 28-year record at well L36/0092

Figure 17: Eigenmodel results for the 28-year record at well M35/1080

Figure 18: Eigenmodel results for the 28-year record at well M36/0255

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