Risk-aware Delineation of Wellhead Protection Zones

A classical approach to manage the risk of well exposure is to ban all hazards from a travel-time based area, which is known as delineating a wellhead protection zone. Questions by water stakeholders and managers such as (1) ’What is the current overall safety level of an exist-ing delineated wellhead protection area?’ or ’Can we provide the same reliability level with a smaller protection area at lower costs than the existing one?’ (2) ’How much can the system reliability be improved without additional areal costs?’ and (3) ’What reliability level can be achieved at only little additional areal costs?’ (4) ’How much can the system reliability be improved with additional and more accurate data?’ will now be answered by providing four corresponding management options based on the VIP maps.

The four suggested management strategies are conceptually shown in Fig. 6.2. These strate-gies will help water stakeholders to support robust and transparent decisions under uncer-tainty, while keeping the additional costs relatively small or even leading to smaller delin-eated areas. Costs in this context are so-called areal costs associated with the area of land delineated as wellhead protection zone, as land has a monetary value.

The required size of delineated wellhead protection zones under uncertainty is easily larger than the actual size of the truly required wellhead protection areaA_true (see Fig. 6.3). The delineated area depends on the degree of uncertainty (areal demand) and on the desired safety levelβ = 1−α of the stakeholders. α is denoted as the risk acceptance level, i.e., the accepted probability that the system may fail. The choice ofβ orα is often limited by financial constraints of the water stakeholder. A no risk (α = 0) situation is unachievable (e.g., Pollard et al., 2008). There always exists the chance of something unexpected happen-ing to the groundwater, endangerhappen-ing safe water supply. Furthermore, delineation outline ofβ = 100%would lead to excessively large wellhead protection zones that are in conflict with the stakeholders interest in the delineated land. In particular, the agricultural sector is a strong stakeholder blocking many delineation processes in Germany².

2Personal communication with Mr. M ¨uller, Ministry for Environment, Agriculture, Food, Wine and Forest of the State of Rheinland-Pfalz

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Figure 6.2.: Risk management with the VIP framework, showing increased areal delineation costs with increasing reliability level.

If a delineation process has not been considered yet, water managers are free in their deci-sion to choose an acceptable probability level of non-compliance with the well vulnerability criterion (i.e. an (non-)exceedance probability level, depending on the respective criterion).

The desired reliability levelβ^∗defines a consistent outline of the wellhead protection zone, corresponding to the probability isolines of each VIP.

(I) Current Delineation Reliability Level and Smaller Consistent Area

As basis for further analysis, the current safety level of an existing wellhead protection area A⁽⁰⁾ is assessed first. This is of special interest for water supply companies with no sophis-ticated post-treatment facilities, as they usually fully rely on perfect groundwater quality, or for supply wells, which have to be abandoned from the first day of contamination. The areal demand for source water protection increases with the desired reliability levelβ^∗, as illustrated in Fig. 6.2. The areaA_β^∗needed to maintain this reliability levelβ^∗is the integral over the entire domainΩ:

A_β^∗ = Z

Ω

I(P1 ≤β^∗)dΩ, (6.3)

where P1 is the exceedance probability for a given well vulnerability criteria, here peak arrival (k= 1), and a certain critical levelW V C_critaccording to Eq. (4.2).

Now, the maximum consistent safety levelβ⁽⁰⁾of an existing protection zoneA⁽⁰⁾is defined.

In case of an existing protection zone it is theβ-value of the largest isopercentile, which is still fully enclosed by the wellhead areaA⁽⁰⁾.

In many practical situations, parts of the current protection zoneA⁽⁰⁾will be located outside the VIP contour lineβ⁽⁰⁾. Therefore, already a smaller protection zoneA⁽⁻⁾ with the same consistent reliability levelβ⁽⁰⁾ as the current wellhead protection can be defined. This can be achieved by simply cropping the wellhead protection area exactly along theβ⁽⁰⁾VIP line, freeing up an excess area∆A⁽⁻⁾=A⁽⁰⁾−A⁽⁻⁾(see Fig. 6.2).

(II) Area - Neutral New Delineation

As a possible next step, the areaA⁽⁰⁾of an existing protection zone can be re-allocated within an optimized outline. To this end, the excess area∆A⁽⁻⁾from step (I) is re-invested towards an increased safety levelβ⁽⁺⁾. The new outline will have the same area A⁽⁰⁾ but with the largest possible consistent reliability level β⁽⁺⁾ that can be achieved with A⁽⁰⁾. The new outline is found by choosing a consistent safety level β⁽⁺⁾, such that the new area A⁽⁺⁾ is just as large as the old area A⁽⁰⁾, but the new outline follows exactly a VIP line β^∗ (see Fig. 6.2):

β⁽⁺⁾: A⁽⁺⁾≡A⁽⁰⁾. (6.4)

(III) Reliability Increase at Minimum Costs

Reallocation or cropping of wellhead protection zones is not always possible, e.g., due to political interests, or due to existing long-term rights and concerning land use. Also, the general public, regulators and customers might not accept the fact that some parts of the existing protection zone are removed in the above management option, as there may or may have been other plausible or even possibly subjective (based on the public risk perception) reasons behind the existing delineation. Please remember, wellhead delineation is enforced by the regional municipalities in Germany (see Section 3.4). Even in such a complex local situation, the probabilistic reliability information contained in the VIPs may be used to im-prove the safety of water supply, without competing against the locally established need for the current protected area. The key argument is the model-based and probabilistic character of VIPs, and the plain, yet objective, quantitative and transparent language spoken by the contour maps.

Therefore, the optimized areaA⁽⁺⁾ from step (II) is complemented by minimal additional area in order to increase the reliability levelβ⁽⁺⁾to some larger levelβ⁽⁺⁺⁾. The area△A⁽⁺⁾ needed for this improvement is exactly the area between the VIPs with the two safety levels β⁽⁺⁾andβ⁽⁺⁺⁾. Thus, the cost function for the increase of reliability△β =β⁽⁺⁺⁾−β⁽⁺⁾is directly given by∆A⁽⁺⁾=A β⁽⁺⁺⁾

−A β⁽⁺⁾

=A⁽⁺⁾−A⁽⁰⁾in Fig. 6.2.

An intermediate alternative is to keep A⁽⁰⁾ without cropping and to complement it with pieces △A^(∗) that are missing in order to reach any desired safety level β^(∗) > β⁽⁰⁾. The corresponding cost function is more complex and cannot be plotted in a generalized man-ner (as a function of isopercentiles and their enclosed area only), as it depends on the actual geometry ofA⁽⁰⁾. However, it would better respect the specific local situation, and leave the other plausible and possibly subjective arguments untouched.

(IV) Increased Reliability Level with Additional and More Accurate Data

The area sacrificed to uncertainty can be reduced, when additional, more accurate and the most beneficial type of data is incorporated to the delineation model. This inevitably leads to the following two questions:

(a) What is the best catchment investigation strategy to achieve a pre-defined reliability level at lowest costs?

(b) What is the highest achievable reliability level at no additional costs?

Fig. 6.2 illustrate these two questions schematically. With additional data, the reliability of the wellhead delineation (x-axis) is expected to increase up to a certain limit at no additional or only small pre-defined costs (Fig. 6.2, IV(b)). Likewise, a given reliability level can be achieved with less areal demand, when uncertainty in areal delineation is reduced (Fig. 6.2, IV(b)). Each sampling design would result in an additional risk-aware delineation curve (gray curve) and thus add to the increased information gain. The benefit of using additional and better data decreases with more sophisticated sampling techniques and more data (dis-tance between lines). Thus, an uncertainty measure is defined that can follow the marginal benefit curve given in Fig. 6.1 in order to know how beneficial additional or better data is.

In this study, this is done for sampling type, quality of measurement and sample size and illustrated for a synthetic test case (Section 8.5). In order to find an optimal sampling design case in light of monetary costs, decision analysis is employed to identify the best scenario for question (a) or (b) among pre-defined sampling designs. Given the fact that stakeholders pre-define an acceptable safety level (compare Fig. 3.2, step: risk objective), it is now possi-ble to find the cost-optimal situation, where the marginal costs for sampling outweigh the benefit in reducing areal demand as far as possible (see IV(a), Fig. 6.2). The same is true for fixed costs, where additional data pay for themselves in order to improve system reliabil-ityβ(see IV(b), Fig. 6.2).

The concept of risk-aware delineation of wellhead protection zones (I-III) is demonstrated for a real test site in Chapter 9. The uncertainty reduction due to additional and better data is demonstrated along a synthetic test case in Chapter 8.

6.3. Uncertainty and Economic Risk Measures within the VIP