Catchment sediment load limits to achieve estuary sedimentation targets

Abstract

Limits are needed to manage the cumulative effects of sediments in estuaries. A method of calculating catchment sediment load limits to achieve estuary sedimentation targets is presented. The method is based on manipulating the sediment budget and takes advantage of the inherent complexity of the estuary and its connections to different sediment source regions in the catchment. In all but the simplest of cases, there is never just one way to achieve estuary sedimentation targets. This is where opportunity lies, for some ways of achieving targets will be better than others. Management can focus on finding sediment load limits that do not fail any sedimentation targets and that are achievable, affordable and efficient. The latter is expressed in terms of sacrificing capacity of the estuary to accommodate sediment in order that no sedimentation targets are failed. The method and underlying principles are demonstrated by application to Pāuatahanui Inlet, New Zealand.

Keywords:

• estuary
• sediment
• sedimentation
• limits
• management
• New Zealand

Introduction

Background

Diffuse-source contaminants (sediments, nutrients, heavy metals, pesticides, herbicides and faecal microbes) associated with land-use intensification and change are a major cause of the continued degradation of New Zealand's aquatic ecosystems (Ministry for the Environment 2007). For estuaries, the contaminant of most concern is terrigenous sediments, which may be a legacy of earlier catchment deforestation or which may derive from present-day activities including agriculture, plantation forestry operations and urbanisation.

Catchment deforestation began about 800 years ago with the initial colonisation of New Zealand by Polynesians (McGlone 1983) and accelerated 150 years ago with European colonisation. Concurrently, there have been marked increases in sediment run-off, although large fluctuations in sediment run-off prior to colonisation are not unknown, e.g. Elliot et al. (1998). Wilmshurst (1997) showed that, at Hawke's Bay, soil structure prior to removal of vegetation was maintained by root networks and dense canopies reduced raindrop impact, but deforestation and removal of fern scrubland have left land vulnerable to erosion and landslides. Page & Trustrum (1997) found that sediment yields in the highly erodible soft-rock hill country of the East Cape region increased by up to a factor of 10 following deforestation by European settlers. Fahey et al. (2003) showed that sediment yield from a forested basin is 2–5 times less than that of an equivalent basin under pasture, but spikes in yield (up to 100 times) may occur locally following clear-felling (O'Loughlin & Pearce 1976). Williamson (1993) noted that temporary increases in sediment yield accompany construction projects associated with urbanisation. Sale (1978) noted that New Zealand's typically steep relief, large annual rainfall and weathered regolith are exacerbating factors.

Many studies have established a link between increased sediment run-off and an increase in estuarine sedimentation. Hume & McGlone (1986) found that net sedimentation rates in Lucas Creek, a tidal creek draining into the Upper Waitematā Harbour, have varied from <1 mm/year in pre-Polynesian times, to 1 mm/year under Polynesian settlement (700–110 years BP), and increasing to 3 mm/year under European settlement. Hume & Dahm (1991) found similar increases in sedimentation rates over the same timescales in other small east-coast New Zealand estuaries fed by tidal creeks. Sheffield et al. (1995) found that sedimentation rates in Whangamatā estuary, on the Coromandel Peninsula, have increased from 0.1 mm/year in pre-Polynesian times, to 0.3 mm/year under Polynesian agriculture, and to 11 mm/year after European clearance of native forest. Goff (1997) reported order-of-magnitude increases in sedimentation rate in Wellington Harbour beginning in the second half of the nineteenth century associated with European settlement, followed by further increases over the past 40–80 years due to urban growth and river channel management. Swales et al. (2002) found that sedimentation in Pakuranga estuary (Auckland) has increased from 0.2–0.5 mm/year pre-colonisation to 30 mm/year under urbanisation. Gibb & Cox (2009) found that sedimentation in Pāuatahanui Inlet has increased from a pre-colonisation rate of <1 mm/year to 5.7 mm/year (in the Onepoto Arm) and 9.1 mm/year (in Pāuatahanui Inlet) between 1974 and 2009.

The effects of sediments on estuarine ecosystems are well documented, in New Zealand at least, although Thrush et al. (2004) noted that, compared with rocky coasts and coral reefs, the vulnerability of soft-sediment estuarine communities has only recently come to be recognised globally. Acute effects of sediments include smothering of benthic communities by slugs of fine terrigenous sediment brought down from the catchment during rainstorms, which results in mortality due to the anaerobic conditions that rapidly develop underneath the slug (Norkko et al. 2002; Thrush et al. 2003a). Subsequent changes in sediment biogeochemistry and sediment food quality have been noted as factors limiting the recovery of affected areas (Cummings et al. 2003). Thinner layers of sediment that are deposited more frequently and usually over greater areas than slugs may not directly cause mortality, but they do result in long-term effects on physiological condition and behaviour of macrofauna (Lohrer et al. 2004). Chronic effects can manifest as a reduction in bed-sediment grain size, which changes sediment biogeochemistry (Thrush et al. 2004); an increase in bed-sediment mud content, which is negatively correlated with species distribution and abundance on intertidal flats (Thrush et al. 2003b); an increase in sedimentation rate, which can reduce macrofaunal diversity and cause functional shifts in populations (Ellis et al. 2004); and an increase in turbidity, which can reduce the health and change the distribution of suspension feeders (Ellis et al. 2002) and primary producers such as seagrass (Matheson & Schwarz 2007). In the upper North Island, spread of the mangrove Avicennia marina—which occurs at the expense of unvegetated sandy intertidal habitats and ultimately open water—has been well documented and linked, in the first instance, to increased estuarine sedimentation causing expansion of intertidal flats which in turn creates habitat suitable for mangrove colonisation (e.g. de Lange & de Lange 1994; Young & Harvey 1996; Ellis et al. 2004; Alfaro 2006; Lovelock et al. 2007). Lovelock et al. (2007) found that deposition of terrigenous sediments can cause mangroves to become nitrogen limited (by supply of phosphorus that accompanies sediment run-off, and by phosphorus released from anaerobic soils underneath the mangrove forest), thus allowing enhancement of tree growth in response to nitrogen enrichment from pollution. Ellis et al. (2004) found that mangrove plant health was positively correlated with bed-sediment mud content and sedimentation rate, at least up to a point, beyond which smothering of pneumatophores can occur, causing tree death. Ellis et al. also found that benthic macrofaunal diversity in mangroves and on associated mudflats was lower than expected, which they attributed to a high sedimentation rate.

Management—New Zealand

In New Zealand, the primary environmental legislation is the Resource Management Act (RMA), which has the primary purpose of promoting sustainable management of natural and physical resources. ‘Sustainable management’ is defined in the Act as providing for various well beings while leaving potential for future generations to meet their reasonably foreseeable needs; safeguarding the life-supporting capacity of ecosystems; and ‘avoiding, remedying or mitigating any adverse effects of activities on the environment’ (section 5(2c), RMA 1991). Because of the latter, management of the environment under the RMA is frequently referred to as ‘effects-based’. The ‘environment’ is rather broadly defined, including as it does ecosystems and natural and physical resources as well as amenity values, with further consideration of social, economic, aesthetic, and cultural conditions. ‘Effects’ are also broadly defined (in section 3 of the Act), and include temporary and permanent effects; past, present and future effects; and cumulative effects, which include those effects that arise over time or that occur in combination with other effects. Case law has further established that cumulative effects can include ‘additive effects of other possible but not yet occurring permitted activities and the effects of granted but not yet implemented consents’ (Milne 2008: 7), which casts a wide net.

There is a widespread view that the effects of individual activities are well managed under the Act through the consenting process, but that cumulative effects—despite them being explicitly mentioned in the Act and widely interpreted in case law—are not and are a main cause of environmental degradation, especially that associated with pastoral farming (OECD 2007). Milne (2008) explored this view and argued that it is somewhat overstated, and that the RMA is properly designed to handle cumulative effects. Nevertheless, Milne argued, there is a need to use more effectively the tools provided by the Act. There does appear to be a tension between the management of cumulative effects, which requires a catchment-wide approach, and the granting or declining of individual applications for resource consent under the RMA.

Justice Salmon (2007) argued that the best possible framework for managing cumulative effects under the RMA will be based on identifying the resource and determining its capacity, and then limiting the resource's use accordingly. This view was echoed by the Land and Water Forum (2010), which noted that (p. viii) ‘without limits it is hard to manage diffuse discharges—nutrients, microbes, sediment and other contaminants that wash into water from the land—and impossible to deal with the cumulative effects on water bodies of water takes on the one hand and diffuse and direct discharges to water on the other’. This was a key assertion of the Forum, and culminated in recommendations concerning the expression of measurable objectives at a regional level, the linking of objectives to standards and limits, and the need to employ a range of instruments to ensure that targets and limits so set are actually achieved.

Norton & Snelder (2010) distinguish between two types of limit: (1) Environmental limits are intended to give effect to objectives, which are statements of what is desired to be achieved in the environment. A standard (for water quality, for instance) is a type of environmental limit. (2) Limits to resource use are intended to give effect to environmental limits (catchment contaminant load limits or minimum lake water levels, for instance). Objectives typically derive from value-based judgements concerning the balance between the use (by people) of natural resources and the protection of the environment. Limits therefore are not really set as such; it is more correct to think of the objective as being set (or agreed), and the limits evaluated accordingly.

Aim

Setting objectives is, at least partly, a social and political process, whereas evaluating limits is a technical process. The aim of this paper is to explore that technical process as it relates to estuaries. The goal is to establish a conceptual and technical framework for limits-based management of sediment effects in estuaries. This is achieved by developing a method for calculating catchment sediment load limits (the limit to resource use) to achieve estuary sedimentation targets (the environmental limit). Whether managing for sedimentation rates will deliver the types of environmental outcomes that are desired is briefly discussed.

Application—Pāuatahanui Inlet

The framework is applied to Pāuatahanui Inlet (northern arm of Porirua Harbour, North Island of New Zealand; see Fig. 1) to demonstrate its utility. This is achieved by showing a way to calculate sediment load limits (the limits to resource use) that will give effect to a target inlet-average sedimentation rate of 1 mm/year (the environmental limit) in Pāuatahanui Inlet. The intention is to explain and demonstrate the place of the framework in the management process, not to simply calculate sediment load limits for Pāuatahanui Inlet.

Figure 1  Location maps. A, Pāuatahanui Inlet, showing sub-estuaries. (Base map: MapToaster Topo, software by Integrated Mapping, © MetaMedia Ltd.) B, Catchment, showing sub-catchments. (Base map: TUMONZ, Vision Software for Management & Technology Systems Ltd.) C, Pāuatahanui Inlet, North Island of New Zealand. (Base map: TUMONZ, Vision Software for Management & Technology Systems Ltd.)

All of Wellington City's greenfield development and half of Wellington region's urban growth over the next 20 years is planned for the Porirua Harbour catchment. Sediment effects—premature loss of the estuary due to infilling; reduced water clarity; smothering of benthic biota; loss of seagrass and fish; reduced navigability, swimming amenity and aesthetics—are recognised by Porirua City Council as the ‘greatest threat to the future usability of the harbour’ (Porirua City Council 2011). In response, and after much discussion and consultation, an initial target of reducing the inlet-average sedimentation rate to 1 mm/year was agreed, recognising that pre-human sedimentation rates were <1 mm/year (Swales et al. 2005), rates over 3 mm/year are excessive, and 1 mm/year is realistic and should be achievable (Porirua City Council 2011). A range of environmental benefits (the objectives) are anticipated on the back of the target sedimentation rate, including a healthy, functioning and productive estuarine ecosystem; no further loss of navigable waters; and improved flushing of the harbour.

International context

In the USA, limits in the form of total maximum daily loads (TMDLs) are used to achieve the goals of the Clean Water Act (CWA) (1972) related to reducing pollution of surface waters, including estuaries. The United States Environmental Protection Agency (US EPA) (1999) defines a TMDL as establishing ‘the allowable loadings for specific pollutants that a waterbody can receive without violating water quality standards’ (pp. 1–3), where ‘specific pollutants’ includes sediments. A TMDL is the sum of all the individual point-source load allocations, the load allocations for all diffuse sources, natural ‘background’ loads, and a margin of safety. In the language of this paper, a TMDL is a limit to resource use. The US EPA (1999) analyses seven components of TMDL development, which are problem statement, numeric targets, source assessment, linkage analysis, allocations, monitoring/evaluation and implementation. The method developed in this paper is a way of determining allocation, and it follows a type of linkage analysis, which is done herein by developing an estuary sediment budget.

Water quality management under the European Union (EU) Water Framework Directive (WFD) (2000) is both much less prescriptive and much broader in scope that it is under the CWA using TMDLs. Kallis & Butler (2001) describe the WFD as an ‘integrating ecosystem-based approach’ (p. 140) that formalises the environment as a user of water with status equal to that of human activities. The means to achieve an overall goal of ‘good’ and ‘non-deteriorating’ status for all waters (including coastal and estuarine) is organisation and planning at the river-basin level and the implementation of ‘supplementary measures’, when ‘basic measures’ will not achieve the goals of the WFD. Supplementary measures are the more stringent of emission controls and water quality standards, and this requirement to give priority to the more stringent action is known as the ‘combined approach’. Specific measures are not prescribed by the WFD. Kallis & Butler (2001) anticipated the use of best environmental practices for controlling diffuse-source pollution as well as prior authorisations and registrations based on binding rules. Chave (2001) noted that the measures adopted by different member states of the EU to deal with diffuse source pollution vary; in some countries the emphasis is on regulation, in others the emphasis is on best management practices. Limits to resource use may be used, but have no particular status or prominence.

Theory of sediment load limits

It is possible to define for any given period Γ a relationship between sources of sediment in the catchment and sinks of sediment in the receiving estuary at the base of the catchment:

1

where D _e is the mass of sediment deposited in sink e during the period in question; L _c is the total (sum of all sediment grain sizes) mass load of sediment that derives from source c; F _c,e is the fraction of the sediment mass from source c that deposits in sink e; and there are C sources of sediment in the catchment (for a list of symbols see the Appendix). The sedimentation rate S _e is related to D _e , and hence the source loads, by:

2

where S _e is a vertical rate of accretion with units length per time, ρ is the density of the deposited sediment and A _e is the area over which deposition occurs in sink e.

Any target S _e,TARGET will be exactly achieved for any set of source loads [L _c, c=1, C] that exactly satisfies Equation () with S _e,TARGET substituted for S _e .

Deposition of sediment in one sink

For the simplest case of one source of sediment depositing in one sink, Equation (2) becomes L ₁ F _1,1=S ₁ ρA ₁ Γ and S _1,TARGET will be exactly achieved by source load L ₁=S _1,TARGET ρA ₁ Γ/F _1,1. Hence, L _1,LIMIT, the sediment load limit for source region 1, should be chosen such that:

3

in order that the target not be failed, where L _1,LIMIT≥0. In this simplest case, there is only one sediment load limit that will exactly achieve the target, but that is not true for any other (more complicated) case.

Consider, for instance, two sources of sediment depositing in the one sink. In this case, Equation (2) becomes L ₁ F _1,1+L ₂ F _2,1=S ₁ ρA ₁ Γ and S _1,TARGET will be exactly achieved by every combination of source loads (L _1, L ₂) that satisfies L ₁ F _1,1+L ₂ F _2,1=S _1,TARGET ρA ₁ Γ, where L ₁≥0 and L ₂≥0. This implies that there is no unique combination of source loads that will exactly achieve the target. In this case, (L _1,LIMIT, L _2,LIMIT) should be chosen such that:

4

in order that the target not be failed, where L _1,LIMIT≥0 and L _2,LIMIT≥0. Furthermore, assuming that there are some minimum achievable loads (L _1,MIN__ACHIEVABLE, L _2,MIN__ACHIEVABLE) that mitigation measures in the respective source regions are at best capable of delivering, then L _1,LIMIT must exceed L _1,MIN__ACHIEVABLE and L _2,LIMIT must exceed L _2,MIN__ACHIEVABLE as well. Figure 2 shows this conjunction of conditions, denoted as ‘Valid sediment load limits’; all load limits chosen from this region will fail neither target and will be achievable by mitigation. Conversely, load limits that plot to the right of Equation (4) will fail at least one target, and load limits that plot to the left of Equation (4) but outside the region denoted by ‘Valid sediment load limits’ will not fail either target but at least one of the load limits will not be achievable. Sediment load limits chosen from outside the region denoted by ‘Valid sediment load limits’ are here termed ‘invalid’.

Inspection of Equation (4) shows that L _1,LIMIT may be no more than S _1,TARGET ρA ₁ Γ/F _1,1 if S _1,TARGET is not to be failed. Furthermore, L _1,LIMIT may only take on this value when L ₂=0. This value is termed L _1,MAX, since it is the maximum sediment load from source 1 that will not fail the target. If L _1,MIN__ACHIEVABLE>L _1,MAX then S _1,TARGET cannot be achieved. Likewise, L _2,MAX=S _1,TARGET ρA ₁ Γ/F _2,1, which can only be the case when L ₁=0, and if L _2,MIN__ACHIEVABLE exceeds L _2,MAX then S _1,TARGET cannot be achieved. This interpretation of Equation (4) highlights an important point, which is that the sediment load limits for the two sources are interdependent. This makes intuitive sense: if the limit is set low, say, in one source region, then this will allow the limit in the other source region to be set high without failing the particular target.

Equation (2) implies that for each additional source that is added to the system one more dimension is added to the analysis. Hence, for the case of three sources of sediment depositing in the one sink, Equation (2) becomes L ₁ F _1,1+L ₂ F _2,1+L ₃ F _3,1=S _1,TARGET ρA ₁ Γ and (L _1, LIMIT, L _2, LIMIT, L _3,LIMIT) accordingly should be chosen such that:

5

in order that the target not be failed. This is equivalent to requiring (L _1,LIMIT, L _2,LIMIT, L _3,LIMIT) plot on or below the plane defined by Equation (5), while at the same time noting that the limits must be greater than the respective minimum-achievable loads and L _1,MAX=S _1,TARGET ρA ₁ Γ/F _1,1, L _2,MAX=S _1,TARGET ρA ₁ Γ/F _2,1 and L _3,MAX=S _1,TARGET ρA ₁ Γ/F _3,1, (Fig. 3).

It is of course not possible for the case of four or more sources of sediment depositing in the one sink to visualise the relationships amongst the possible valid sediment load limits, as has been done in Figs 2 and 3. However, the problem readily lends itself to calculation, and a straightforward procedure can be followed to discover sediment load limits for any system of C sources of sediment depositing in the one sink. To begin, one needs to check that L _c,MIN__ACHIEVABLE≤L _c,MAX for all c, where, for the general case of sediment depositing in the one sink,

6

Figure 2  Analysis of sediment load limits for the case of two sources of sediment depositing in one sink. Sediment load limits chosen from the region denoted by ‘Valid sediment load limits’ will fail neither target and will be achievable by mitigation.

Figure 3  Analysis of sediment load limits for the case of three sources of sediment depositing in one sink. Sediment load limits chosen from the region denoted by ‘Valid sediment load limits’ will fail no target and will be achievable by mitigation.

regardless of the number of sources C. If practical mitigation measures cannot reduce the sediment load from every source to at least L _c,MAX, then it will never be possible to achieve all of the receiving-environment targets. With that check passed, i=1 to C steps are required to specify the C sediment load limits. At each step i the sediment load limit L _i,LIMIT may be freely chosen in the range:

7

where the sediment load limits [L _c,LIMIT, c=1, i−1] were chosen in the previous (i−1) steps.

Sediment load limits do not have to be set for all sources (in the sense of setting limits that are less than present-day loads). Suppose there are Λ sources for which the intention is to set sediment load limits, and these sources are numbered n _λ , λ=1 to Λ. There are Ω=C−Λ sources for which there is no intention of setting sediment load limits (in the sense noted above), and these sources are numbered n _ω , ω=1 to Ω. In this case, the sediment load limits [] should be chosen such that:

8

in order that the target not be failed, where for all λ and is given by Equation (6) for all λ.

Deposition of sediment in more than sink

Consider the case of one source of sediment depositing in two sinks. The target in sink 1 (S _1,TARGET) corresponds to a mass of deposited sediment of (say) 1000 kg, and the target in sink 2 (S _2,TARGET) corresponds to a mass of deposited sediment of 500 kg. Furthermore, 40% of sediment from the single source deposits in sink 1 (F _1,1=0.4); 50% of L ₁ deposits in sink 2 (F _1,2=0.5); and the remainder is flushed out to sea. Now, to achieve both S _1,TARGET and S _2,TARGET simultaneously, the sediment load limit L _1,LIMIT that simultaneously satisfies:

9a

9b

must be chosen. However, there is no such value for L _1,LIMIT: solving just Equation (9a) yields L _1,LIMIT=2500 kg, but this would result in 1250 kg of sediment being deposited in sink 2, which would exceed S _2,TARGET. Conversely, solving just Equation (9b) yields L _1,LIMIT=1000 kg, but this would result in 400 kg of sediment being deposited in sink 1, which would overachieve (i.e. result in a sedimentation rate less than) S _1,TARGET. In order not to fail either target, it is clearly necessary to overachieve S _1,TARGET, which can be thought of as sacrificing some of the capacity of sink 1 to accommodate sediment.

Typically, it will not be possible to find catchment sediment load limits that will deliver the exact target sedimentation rates in all parts of an estuary simultaneously. When this is the case, the guiding principle should be to find sediment load limits that do not fail any targets, noting that in so doing some other targets will be overachieved, and therefore predicted capacity of the estuary to accommodate sediment will be sacrificed.

To understand in detail how this principle works, consider two sources of sediment depositing in two sinks where, following Equation (2), the mass of sediment deposited in sink 1 is given by L ₁ F _1,1+L ₂ F _2,1 and the mass of sediment deposited in sink 2 is L ₁ F _1,2+L ₂ F _2,2. The target sedimentation rate S _1,TARGET for sink 1 is exactly achieved when:

10

and target S _2,TARGET for sink 2 is exactly achieved when:

11

If source region 2 were to be somehow switched off (i.e. L ₂ set to zero) then L ₁ could be as large as S _1,TARGET ρA ₁ Γ/F _1,1 without failing target S _1,TARGET and as large as S _2,TARGET ρA ₂ Γ/F _1,2 without failing S _2,TARGET. However, if both targets were not to be failed then L ₁ could be no more than the minimum of S _1,TARGET ρA ₁ Γ/F _1,1 and S _2,TARGET ρA ₂ Γ/F _1,2. This minimum value is termed L _1,MAX, since it is the maximum sediment load from source 1 that will not fail either target. Likewise, L _2,MAX is the minimum of S _1,TARGET ρA ₁ Γ/F _2,1 and S _2,TARGET ρA ₂ Γ/F _2,2.

It will more likely be the case that neither source will be able to be switched off, in which case L _c,LIMIT will need to be chosen to be less than L _c,MAX but greater than L _c,MIN__ACHIEVABLE. To address this case, Fig. 4 shows Equations (10) and (11) plotted on a two-dimensional graph of L ₁ (x-axis) versus L ₂ (y-axis). If neither target is to be failed, then for any value of L _1,LIMIT that is chosen to lie between L _1,MIN__ACHIEVABLE and the intersection of Equations (10) and (11), L _2,LIMIT cannot exceed (S _2,TARGET ρA ₂ Γ−L _1,LIMIT F _1,2)/F _2,2. On the other hand, if L _1,LIMIT is chosen to lie between the intersection of Equations (10) and (11) and L _1,MAX then L _2,LIMIT cannot exceed (S _1,TARGET ρA ₁ Γ−L _1,LIMIT F _1,1)/F _2,1. Joining these statements, we can say that for all values of L _1,LIMIT chosen from the range:

12

where

13

then L _2,LIMIT must lie in the range:

14

Figure 4  Analysis of sediment load limits for the case of two sources of sediment depositing in two sinks. Sediment load limits chosen from the region denoted by ‘Valid sediment load limits’ will fail no target and will be achievable by mitigation.

in order that neither target is failed. The region delineated by Equations (12–14) is denoted by ‘Valid sediment load limits’ in Fig. 4. Clearly, this region is the intersection of the valid sediment load limits corresponding to the two individual targets. Each time another sink is added to the analysis, another line is added to Fig. 4, and the region from where valid sediment load limits may be chosen is redefined accordingly.

Whereas the number of sources determines the number of dimensions in the analysis, the number of sinks determines the number of regions that intersect to bound the valid sediment load limits. For example, for the case of three sources of sediment depositing in four sinks, valid sediment load limits will be found in a region defined by the intersection of four planes (there are four sinks) in three-dimensional (L ₁−L ₂−L ₃) space (there are three sources).

As was the case for one sink, it is not possible for the case of four or more sources of sediment depositing in more than one sink to visualise the relationships amongst the possible valid sediment load limits. But, again, the problem readily lends itself to calculation, and the procedure described for finding sediment load limits for sources that deposit in one sink can be extended to apply to more than sink. As before, one needs to check that L _c,MIN__ACHIEVABLE≤L _c,MAX for all c, where, for the general case of sediment depositing in E sinks,

15

(where e=1,E) regardless of the number of sources C. If practical mitigation measures cannot reduce the sediment load from every source c to at least L _c,MAX then it will never be possible to achieve all of the receiving-environment targets. With that check passed, i=1 to C steps are required to specify the C sediment load limits. At each step i, the sediment load limit L _i,LIMIT may be freely chosen in the range:

16

where there are E sinks and the sediment load limits [L _c,LIMIT,c=1, i−1] were chosen in the previous (i−1) steps.

Again, sediment load limits do not have to be set for all sources. As before, suppose there are Λ sources for which the intention is to set sediment load limits, and these sources are numbered n _λ, λ=1 to Λ. There are Ω=C−Λ sources for which there is no intention of setting sediment load limits, and these sources are numbered n _ω , ω=1 to Ω. In this case, the sediment load limits () should be chosen such that:

17

(where e=1,E) in order that the target not be failed, where for all λ and is given by Equation (15) for all λ.

Capacity sacrifice

Capacity sacrifice—or ‘target overachievement’—in any sink e may be defined as the target sedimentation rate divided by the sedimentation rate corresponding to the chosen sediment load limits:

18

where Δ _e so defined is dimensionless; Δ _e ≥1 (because valid sediment load limits cannot fail, or ‘underachieve’ any target); Δ _e =1 corresponds to exact target achievement; and the larger Δ _e the larger the target overachievement. Figure 5 shows Δ _e for the case of two sinks e=1 and e=2 that deposit sediment from the same two sources. Δ _e is undefined for (L _1,LIMIT, L _2,LIMIT)=(0,0) and zero for all (L _1,LIMIT, L _2,LIMIT) that satisfy L _1,LIMIT F _1,e +L _2,LIMIT F _2,e =S _e,TARGET ρA _e Γ. There is only one (L _1,LIMIT, L _2,LIMIT) for which Δ₁ and Δ₂ are simultaneously zero, and this occurs at the intersection of S _1,TARGET ρA ₁ Γ=L _1,LIMIT F _1,1+L _2,LIMIT F _2,1 and S _2,TARGET ρA ₂ Γ=L _2,LIMIT F _1,2+L _2,LIMIT F _2,2:

19

The sediment load limits defined by Equation (19) can be thought of as the most efficient limits, since they sacrifice a minimum of the total estuary's capacity to accommodate sediment (within the bounds set by the sedimentation targets).

Application

Pāuatahanui Inlet drains into the Tasman Sea at the western end of Cook Strait (Fig. 1). The inlet was formed by the postglacial drowning of an ancestral river valley, which began 10,000–14,000 years ago (Irwin 1976). Since the sea stabilised at approximately its present level 7000–8000 years ago, the inlet has accumulated 7–10 m of sediment (Begg & Mazengarb 1996). The inlet covers an area of 4.7 km² and is enclosed by a spit that extends south from Mana. The tide in the inlet is semidiurnal with a spring range of 1.4 m and a neap range of 0.3 m (Blaschke et al. 2010). The mean depth of the inlet is 2.0 m, and 30% of the inlet is intertidal with high-tide water depths of less than 1 m. Residence time has been estimated as 3 days, with exchange of water to the coastal ocean being driven mainly by tides (Blaschke et al. 2010). A flood-tide delta composed of coarse sandy sediments occupies the 100-m-wide mouth of the inlet and spills into a central subtidal basin that is floored by silt (Healy 1980). Intertidal flats, which are widest along the northern and northeastern shorelines, are composed of poorly sorted muddy sand on lower flats, grading to well-sorted sand on the upper flats (Irwin 1976; Pickrill 1979; Swales et al. 2005). There are accumulations of coarser sediments in deltas built at the mouths of streams where they discharge into the harbour (Pickrill 1979).

The catchment covers an area of 109 km² and comprises six major sub-catchments (Kakaho, Horokiri, Ration Point, Pāuatahanui, Duck Creek and Browns Bay) and six small shoreline sub-catchments (Page et al. 2004) (Fig. 1). Mean freshwater input to the inlet is only about 3.3% of the tidal prism (Blaschke et al. 2010). Page et al. (2004) described historical changes in catchment land use. Māori occupation of the catchment, which began 600 years ago, had only minimal effects on vegetation cover, and at the time of European arrival in the early nineteenth century the catchment was nearly wholly forested. Widespread catchment deforestation began with European farm settlement in the early 1840s, and by the early 1940s 83% of the catchment was grassland. Since then, woody vegetation has increased to 42% of the catchment area, with much of that increase being accounted for by the planting of exotic forest. Urbanisation began around the mouth of the inlet at Mana and Golden Gate, then spread rapidly from the 1960s into the Browns Bay, Duck Creek and, most recently, Pāuatahanui sub-catchments. In 2004, 3.7% of the total catchment was urbanised, which included 58% of Browns Bay sub-catchment, 16% of Duck Creek sub-catchment and 41% of the shoreline sub-catchments. Page et al. (2004) noted that a feature of the urbanised areas is their close proximity to the inlet.

Both Swales et al. (2005) and Gibb & Cox (2009) found that sedimentation in the inlet had increased since European settlement, and that the increase has accelerated over the past 25 years. Blaschke et al. (2010) noted that changes in vegetation and land use in the catchment since the mid-nineteenth century are thought to be responsible, although they also note that there is very little information, apart from some ad hoc observations, on catchment sediment run-off and how it might have changed since catchment deforestation began (e.g. Curry 1981). Swales et al. (2005), using data from isotopic analysis and pollen dating of sediment cores, calculated the inlet-average sedimentation rate over the past 2000 years as 0.7 mm/year, rising to 2.0–2.4 mm/year (post 1850), 3.1–3.7 mm/year (post-1950) and 4.6 mm/year (post-1985). Gibb & Cox (2009), using data from sequential bathymetric surveys, calculated an inlet-average sedimentation rate between 1974 and 2009 of 9.1 mm/year. Swales et al. (2005) concluded that, if current sedimentation rates continue, even without the continued increase that does seem to be occurring, then the harbour will be infilled much sooner than would have occurred naturally.

Sediment budget for Pāuatahanui Inlet

The target inlet-average sedimentation rate of 1 mm/year set for Pāuatahanui Inlet does not make any distinction between sediment sourced from the catchment and sediment from any other source. However, all of the depositional environments landward of the flood-tide delta are thought to be dominated by catchment-sourced sediment (Gibb & Cox 2009). Hence, this analysis focuses on establishing catchment sediment load limits to achieve the target sedimentation rate in just those parts of the estuary. (The flood-tide delta is thought to be dominated by marine-sourced sediment, and a different strategy may be required to control any sedimentation issues there, e.g. dredging.)

Equation (2) first needs to be evaluated, which is akin to establishing a sediment budget for the estuary. Any of a number of catchment sediment run-off models could provide the sediment loads L _c needed for this. For evaluating the set of terms F _c,e (the total-sediment ‘fate matrix’, so-called because F _c,e describes the fate of the total sediment from each source region, where ‘total’ means the sum of all sediment particle sizes) a computational source-to-sea model of the type described by Green (2008) may be used. Green's model predicts rates and locations of estuarine sedimentation on a decadal timescale given information from a range of underlying models, including a catchment model for predicting sediment run-off and an estuarine hydrodynamics/sediment-transport model for evaluating event-scale sediment-transport and deposition patterns under a range of oceanographic and weather conditions. One output of the model is the total-sediment fate matrix (i.e. the set of terms F _c,e ), which shows how catchment sediment run-off is distributed, on average, amongst different depositional environments in the estuary at the base of the catchment.

For this exercise, a constituent-particle fate matrix, F _c,e,p , was specified (as opposed to derived from the results of a computational source-to-sea model), where the subscript p denotes sediment size fraction. Two size fractions, coarse (particle sizes >125 µm) and fine (particle sizes <125 µm), were used, which allows coarse and fine sediment to be dispersed differently from one another throughout the estuary. The constituent-particle fate matrix (F _c,e,p ) was then tested by applying to predictions of catchment sediment run-off to predict sedimentation in the harbour, and then comparing the predictions with observed sedimentation rates. Finally, the total-sediment fate matrix was calculated from the constituent-particle fate matrix for use in evaluating catchment sediment load limits. The procedure is described in more detail in the following paragraphs.

The catchment was divided into the six main source regions (sub-catchments) identified by Page et al. (2004) (Fig. 1), and the inlet was divided into the seven sinks (sub-estuaries), shown in Fig. 1. A further sub-estuary representing the coastal ocean was added to receive sediment that may be lost seawards from the inlet. Table 1 shows the constituent-particle fate matrix (F _c,e,p ), which was specified, as explained above. The timescale is annual; hence, the set of terms F _c,e,p represents annual-average sediment dispersal patterns. The constituent-particle fate matrix was contrived to prevent any deposition of catchment-sourced sediment on the flood-tide delta and, following Healy (1980), to export 20% of the fine-sediment run-off from every sub-catchment to the coastal ocean (from where it cannot return). Coarse sediment from each sub-catchment deposits primarily in the sub-estuary at the base of the respective sub-catchment, but with allowance for some longshore transport into adjacent embayments. Along the eastern and southern shorelines, coarse sediments are driven alongshore into Browns Bay, which is presumed to occur on the back of a net clockwise circulation driven by dominant northwesterly winds. The majority (70–90%) of fine sediment from each sub-catchment is deposited in the central subtidal basin on the premise that, even if initially deposited on an intertidal flat, wind waves will eventually resuspend the fines and initiate offshore transport and ultimate deposition in the more quiescent subtidal basin (Swales et al. 2005). The same presumed wind-driven clockwise circulation along the eastern and southern shorelines is also allowed to drive fine sediment into Browns Bay.

Table 1  The constituent-particle fate matrix (F _c,e,p ), which was specified.

	Flood-tide delta	Central subtidal	Kakaho intertidal	Horokiri intertidal	Pāuatahanui intertidal	Browns Bay intertidal	Browns Bay subtidal	Ocean
Coarse
Kakaho	0	0.10	0.90	0.00	0.00	0.00	0.00	0
Horokiri	0	0.10	0.15	0.50	0.25	0.00	0.00	0
Ration Point	0	0.10	0.15	0.25	0.50	0.00	0.00	0
Pāuatahanui	0	0.10	0.05	0.l5	0.60	0.10	0.00	0
Duck Creek	0	0.10	0.00	0.00	0.70	0.10	0.10	0
Browns Bay	0	0.00	0.00	0.00	0.00	0.80	0.20	0
Fine
Kakaho	0	0.64	0.08	0.00	0.00	0.00	0.08	0.20
Horokiri	0	0.70	0.00	0.02	0.00	0.00	0.08	0.20
Ration Point	0	0.60	0.00	0.00	0.04	0.00	0.16	0.20
Pāuatahanui	0	0.56	0.00	0.00	0.04	0.04	0.16	0.20
Duck Creek	0	0.54	0.00	0.00	0.02	0.08	0.16	0.20
Browns Bay	0	0.00	0.00	0.00	0.00	0.00	0.80	0.20
Note: This represents annual-average sediment dispersal patterns. Sub-catchments (c) are shown along the left and sub-estuaries (e) along the top.

To test the constituent-particle fate matrix, the constituent-particle sedimentation rate for each sub-estuary was predicted by:

20

and the total (sum of all particle sizes) sedimentation rate was calculated as:

21

where L _c,p is the mass load of sediment of grain size fraction p deriving from source (sub-catchment) c, and there are P=2 sediment size fractions. Equations (20) and (21) only account for the dispersal and deposition of catchment-sourced sediment. The density of the deposited sediment ρ was taken as 1200 kg/m³. Because the timescale of the analysis is annual, Γ is 1 year, and S _e , S _e,p and L _c are annual averages. The CLUES (Catchment Landuse for Environmental Sustainability) catchment model (Semadeni-Davies et al. 2011) was used to predict the annual-average total (sum of all grain sizes) sediment run-off L _c at the base of each sub-catchment under the present-day catchment land use (Table 2) (Wriggle Coastal Management, Nelson, unpublished data). The partitioning of the sediment run-off between the coarse and fine sediment fractions (Table 2) to give L _c,p was derived by reference to Malcolm (2011), who calculated a particle size distribution for sediment loads discharged into the estuary based on samples taken from the catchment. Table 3 shows, for each sub-estuary, the total area and the fraction of the total area over which catchment-sourced sediment was allowed to deposit. Area fractions ranged between 0.5 and 0.75. The lowest fraction (0.5) was assigned to both Browns Bay intertidal and Kakaho intertidal on the assumption that the flood-tide delta occupies a portion of both of these sub-estuaries, which reduces the area available for fine catchment-sourced sediment to deposit.

Table 2  Catchment Landuse for Environmental Sustainability (CLUES) predictions of the annual-average total (sum of all grain sizes) sediment run-off at the base of each sub-catchment under the present-day land use, and partitioning of the total sediment run-off between the two sediment size fractions.

Sub-catchment	Annual-average total sediment run-off (kg)	Fraction coarse	Fraction fine
Kakaho	2.32	0.2	0.8
Horokiri	6.87	0.2	0.8
Ration Point	0.44	0.2	0.8
Pāuatahanui	5.52	0.3	0.7
Duck Creek	1.35	0.35	0.65
Browns Bay	0.051	0.4	0.6
Note: CLUES predictions by Wriggle Coastal Management, Nelson (unpublished data).

Table 3  Sub-estuary total area and area over which catchment-sourced sediment was allowed to deposit in each sub-estuary.

Sub-estuary	Area (m^2)	Fraction of area deposition allowed
Flood-tide delta	1,171,437	0
Central subtidal	1,746,993	0.7
Kakaho intertidal	482,226	0.5
Horokiri intertidal	317,345	0.75
Pāuatahanui intertidal	520,382	0.75
Browns Bay intertidal	104,575	0. 5
Browns Bay subtidal	264,808	0.7
Ocean	–	–

The predicted total (sum of all particle sizes) sedimentation rates S _e are compared in Table 4 with total sedimentation rates calculated by Gibb (2011) by taking the difference between 1974 and 2009 bathymetric surveys. Gibb's rates are corrected for a sea-level rise of 1.95 mm/year in the period 1974–2009, and are sub-estuary averages. Also shown in Table 4 are predictions of the constituent-particle sedimentation rates S _e,p and Gibb's measured total rates broken down into constituent-particle rates by multiplying by sub-estuary-average bed-sediment composition (percentage coarse/percentage fine) derived from Malcolm (2011). Predicted S _e and S _e,p are roughly half the respective S _e and S _e,p measured by Gibb (2011). This brings the predicted values more in line with Swales et al.'s (2005) post-1985 inlet-average sedimentation rate of 4.6 mm/year, which is roughly half Gibb & Cox's (2009) inlet-average rate of 9.1 mm/year over the period 1974–2009.

Table 4  Predicted and observed total (sum of all particle sizes) and constituent–particle (total multiplied by bed-sediment composition) annual-average sedimentation rates (mm/year).

	Flood-tide delta	Central subtidal	Kakaho intertidal	Horokiri intertidal	Pāuatahanui intertidal	Browns Bay intertidal	Browns Bay subtidal	Ocean
Coarse
Predicted	–	0.3	2.5	3.4	3.7	3.7	0.2	–
Observed	–	0.5	7.3	7.5	7.3	7.1	0.8	–
Ratio	–	0.52	0.34	0.45	0.50	0.51	0.30	–
Fine
Predicted	–	5.4	0.5	0.3	0.4	3.6	6.4	–
Observed	–	10.2	0.6	0.6	0.6	7.1	14.4	–
Ratio	–	0.53	0.81	0.48	0.62	0.50	0.44	–
Total
Predicted	–	5.7	3.0	3.7	4.0	7.2	6.6	–
Observed	–	10.7	7.9	8.1	7.9	14.2	15.2	–
Ratio	–	0.53	0.38	0.45	0.51	0.51	0.44	–
Note: ‘Ratio’ is the ratio of predicted to observed.

The total-sediment fate matrix was calculated from the constituent-particle fate matrix as:

22

Table 5 shows the total-sediment fate matrix so calculated.

Table 5  The total-sediment fate matrix (F _c,e ), calculated from the constituent-particle fate matrix and sub-catchment sediment run-off (Equation 22).

	Flood-tide delta	Central subtidal	Kakaho intertidal	Horokiri intertidal	Pāuatahanui intertidal	Browns Bay intertidal	Browns Bay subtidal	Ocean
Kakaho	0	0.532	0.244	0	0	0	0.064	0.16
Horokiri	0	0.5832	0.03	0.1128	0.05	0	0.064	0.16
Ration Point	0	0.5	0.03	0.05	0.132	0	0.128	0.16
Pāuatahanui	0	0.422	0.015	0.045	0.208	0.058	0.112	0.14
Duck Creek	0	0.3886	0	0	0.2554	0.087	0.139	0.13
Browns Bay	0	0	0	0	0	0.32	0.56	0.12
Note: This represents annual-average sediment dispersal patterns. Sub-catchments (c) are shown along the left and sub-estuaries (e) along the top.

Table 6 shows the total-sediment ‘source matrix’ O _c,e , which was calculated by:

23

Table 6  The total-sediment source matrix (O _c,e ), calculated from the fate matrix and sub-catchment sediment run-off (Equation 23).

	Flood-tide delta	Central subtidal	Kakaho intertidal	Horokiri intertidal	Pāuatahanui intertidal	Browns Bay intertidal	Browns Bay subtidal	Ocean
Kakaho	–	0.15	0.65	0.00	0.00	0.00	0.10	0.15
Horokiri	–	0.48	0.24	0.74	0.18	0.00	0.30	0.44
Ration Point	–	0.03	0.02	0.02	0.03	0.00	0.04	0.03
Pāuatahanui	–	0.28	0.10	0.24	0.61	0.71	0.42	0.31
Duck Creek	–	0.06	0.00	0.00	0.18	0.26	0.13	0.07
Browns Bay	–	0.00	0.00	0.00	0.00	0.04	0.02	0.00
Note: This shows the annual-average origin of sediment that deposits in each sub-estuary. Sub-catchments (c) are shown along the left and sub-estuaries (e) along the top.

The source matrix shows the annual-average origin of sediment that deposits in each sub-estuary. For example, reading down the third column of Table 6 shows that 65% of the sediment that deposits on the Kakaho intertidal flats originates from the Kakaho sub-catchment, 24% comes from the Horokiri sub-catchment, and so on. For any particular sub-catchment to contribute significantly to the sedimentation in any particular sub-estuary, there has to be a ‘strong’ sediment-transport pathway between the two (i.e. F _c,e has to be large) and sediment run-off from the sub-catchment in question must be large relative to the other sources that deposit in the sub-estuary. Reading across the table reveals that neither Ration Point nor Browns Bay sub-catchments contribute more than a few percent to sedimentation in any part of Pāuatahanui Inlet. Hence, we can reasonably set the sediment load limit for each of these two sub-catchments at the present-day sediment run-off. To further simplify the analysis, the Kakaho and Horokiri sub-catchments are lumped together as ‘rural’ sub-catchments, and Pāuatahanui and Duck Creek sub-catchments are lumped together as ‘developing’ sub-catchments. With these decisions, and with the sub-catchment sediment loads L _c and the fate matrix F _c,e evaluated, we are now in a position to begin the discovery of sediment load limits.

Sediment load limits

Figure 6 was constructed for the analysis of Pāuatahanui Inlet. This represents just one way to apply the equations and concepts developed previously. It was chosen here because it is concise and will serve the purpose of demonstrating the place of the limits framework in the management process. Any one or more of a number of other figures could have been constructed, or the calculation scheme described above could also have been followed. Figure 6 plots Equation (24):

24

which is Equation (8) expanded and rearranged somewhat, to apply to Pāuatahanui Inlet. Here, L _DEVELOPING,e =(L _PAUATAHANUI F _{PAUATAHANUI,e} +L _DUCK F _DUCK,e ) is the annual-average mass of sediment that originates from the developing sub-catchments and deposits in sub-estuary e; L _RURAL,e =(L _KAKAHO F _KAKAHO,e +L _HOROKIRI F _HOROKIRI,e ) is the annual-average mass of sediment that originates from the rural sub-catchments and deposits in sub-estuary e;S _e,PRESENT is the present-day annual-average sedimentation rate in sub-estuary e; Φ is a fraction between 0 and 1 such that S _e,TARGET=ΦS _e,PRESENT; and the names ‘PAUATAHANUI’ and the like denote sub-catchments.

Figure 5  Analysis of capacity sacrifice for the case of two sources of sediment depositing in two sinks.

Figure 6 plots Equation (24) for Φ=0.1, 0.3, 0.5, 0.7 and 0.9 for each of the six sub-estuaries (for a total of 30 lines on the graph). Lines fall into bunches (or clusters) of six; each line in a bunch plots Equation (24) for a different sub-estuary (refer to legend in Fig. 6). A large circle has been drawn at the centre of each bunch in order to draw the eye. Beside each large circle is printed the value of Φ that applies to the lines in that bunch. The y-axis in Fig. 6 is the annual-average sediment load from the developing sub-catchments, normalised by the present-day annual-average sediment load from the developing sub-catchments. The x-axis shows the annual-average sediment load from the rural sub-catchments, similarly normalised. A value of 0.2 on either axis signifies a sediment run-off that is 20% of the present-day run-off or, equivalently, the sediment run-off that results from 80% mitigation of the present-day sediment run-off.

Figure 6  Equation (8) expanded and rearranged to apply to Pāuatahanui Inlet, plotted for a range of values of Φ for each sub-estuary, where S _e,TARGET=ΦS _e,PRESENT. Sediment run-off is normalised by present-day sediment run-off. The figure guides the discovery of sediment load limits for Pāuatahanui Inlet. Refer to the text for details.

Interpretation of Figure 6

Figure 6 shows how changes in sediment run-off from the developing and rural sub-catchments translate into changes in sedimentation in the six sub-estuaries. For example, every combination of sediment run-off that lies on the line denoted by crosses that passes through the large circle marked ‘0.3’ will result in sedimentation on the Kakaho intertidal flats that is 30% of the present-day sedimentation (which is a 70% reduction). The slope of each line reflects the relative contribution of developing and rural sources of sediment to that sub-estuary. In the extreme, a line that runs parallel to the x-axis indicates the sub-estuary deposits no sediment from rural sub-catchments (which is the case for the Browns Bay intertidal flats, which can be confirmed by referring to the sediment source matrix in Table 6), and a line that runs parallel to the y-axis indicates the sub-estuary deposits no sediment from developing sub-catchments.

It is significant that the large circles at the centre of each bunch of lines march up the graph from the origin at a slope of approximately 1:1. This suggests that the most efficient way to achieve a uniform percentage reduction in sedimentation across the entire estuary is to apply the same uniform percentage reduction in sediment run-off across the entire catchment (that is, in all sub-catchments), where ‘efficient’ is meant in the sense of minimum target overachievement (or capacity sacrifice). Figure 7 confirms this suggestion for the example case in which the target is a reduction in sedimentation of 30% in all sub-estuaries (which reduces sedimentation to 70% of present-day). Following the principles developed previously, Fig. 7A plots the valid sediment load limits. Figure 7B plots the average capacity sacrifice as a function of normalised sediment run-off from the rural and developing sub-catchments, where capacity sacrifice for each sub-estuary Δ _e is defined by Equation (18) and is the arithmetic average over all sub-estuaries:

25

Figure 7  Example case in which the target is a 30% reduction in sedimentation in all sub-estuaries. A,Valid (will not fail any sedimentation targets) and invalid (will fail at least one sedimentation target) sediment load limits. B, Average capacity sacrifice  as a function of sediment run-off from the rural and developing sub-catchments.

Estimates of are shown only for valid sediment load limits. For this case of a uniform reduction in sedimentation of 30%, the most efficient solution—that is, in the sense of minimising target overachievement—is to reduce sediment run-off from all sub-catchments by 30% (which means setting sediment load limits for all sub-catchments at 70% of the present-day sediment run-off).

Figure 7B confirms what is an intuitively obvious result (namely reduce inputs uniformly to effect a uniform reduction in outputs). However, on the one hand, it seems unlikely that it would ever be desirable to reduce sedimentation in all parts of an estuary by the same percentage in order to achieve ecological or human-amenity objectives and, on the other hand, that it would ever be cost-effective or even possible to reduce sediment run-off uniformly over an entire catchment. (Note that, in the case of Pāuatahanui Inlet, the goal to reduce sedimentation to an inlet-average of 1 mm/year is not the same as reducing sedimentation in all parts of the inlet by the same percentage.) In other words, the premise of the analysis is unlikely, and the solution offered up by the analysis is unlikely to work. However, the method of analysis encapsulated in Fig. 7 is capable of dealing with more realistic premises and of offering up solutions that are much more sophisticated, and therefore likely to work in the real world.

A more realistic goal would be to set different sedimentation targets in different parts of the one estuary, based on the premises that not all parts of an estuary may be sediment-impacted to the same degree, that there may be priorities in terms of protecting and enhancing ecological function, that there may be priorities in terms of human amenity, and that there may be a limited budget for catchment works, which would require prioritisation of resources.

The method of identifying valid sediment load limits and evaluating can be used to identify efficient solutions when sedimentation targets differ from sub-estuary to sub-estuary. For example, Fig. 8A shows the valid sediment load limits where the targets are 10% reduction in sedimentation on the Kakaho intertidal flats (which reduces sedimentation to 90% of present-day); 50% reduction in sedimentation on the Pāuatahanui intertidal flats and in Browns Bay subtidal; and 30% reduction in sedimentation in the three remaining sub-estuaries. Figure 8B shows plotted as a function of normalised sediment run-off from the rural and developing sub-catchments, for the same situation. Figure 8B shows that there is a range of possible sediment load limits that would deliver, approximately, the same minimum (which signifies minimum target overachievement), and one or other of these solutions may be preferable for one reason or another.

Figure 8  Example case in which the targets are 10% reduction in sedimentation on the Kakaho intertidal flats; 50% reduction in sedimentation on the Pāuatahanui intertidal flats and in Browns Bay subtidal; and 30% reduction in sedimentation in the three remaining sub-estuaries. A, Valid (will not fail any sedimentation targets) and invalid (will fail at least one sedimentation target) sediment load limits. B, Average capacity sacrifice as a function of sediment run-off from the rural and developing sub-catchments.

Efficiency may not in fact be an over-riding factor in the choice of sediment load limits. Other factors that could influence the choice include the cost of implementing mitigation in the catchment, opportunities for and barriers to mitigation, and political expediency. In reality, all of these factors together are likely to influence the choice of sediment load limits. This being the case, a likely real-world process for setting sediment load limits would involve finding a balance amongst all the relevant factors. Candidate sediment load limits would need to be drawn from the set of valid limits as shown in Fig. 8A. Then, for the candidate sediment load limits being considered, mitigation cost, opportunities and barriers would be evaluated using appropriate methods, and efficiency could be evaluated using the type of analysis shown in Fig. 8B. Should the evaluations be unfavourable, new candidate sediment load limits could be chosen from the set of valid load limits and the evaluation repeated, or sedimentation targets could be refined, and new candidate load limits chosen accordingly and evaluated. The process would be iterated until an acceptable set of sediment load limits was found.

It is noteworthy that, in the case of the (simultaneously) different sedimentation targets analysed in Fig. 8, there is a range of valid sediment load limits that deliver approximately the minimum and, furthermore, those limits run across the diagrams in Fig. 8 at an angle of approximately 45°. This indicates that an easing of mitigation in, say, the rural sub-catchments, can be readily offset by a strengthening of mitigation in the developing sub-catchments without losing efficiency (i.e. without increasing ). For example, setting the sediment load limits for the developing sub-catchments at 20% of the present-day run-off together with a limit for the rural sub-catchments at 80% of present-day run-off delivers approximately the same (minimum) target overachievement averaged over the entire estuary as a combination of 50% reduction in sediment run-off from the developing sub-catchments and 50% reduction in sediment run-off from the rural sub-catchments. Between those extremes, there are other combinations (found by running along the line marked ‘Valid sediment load limits that deliver approximately the minimum ’ in Fig. 8), some of which may be more favourable than others, for any of a number of reasons, as previously noted.

Where prioritisation of sedimentation targets is required (due to funding constraints, for example), it may be preferable to examine each Δ _e individually rather than examining . Furthermore, it may be useful to examine Δ _e for invalid sediment load limits (in which case 0≤Δ _e <1) in addition to valid sediment load limits. For example, Fig. 9 shows (i.e. averaged over all sub-estuaries) and Δ _e for the Browns Bay intertidal flats, which reveals how valid and invalid sediment load limits perform in delivering the Browns Bay targets. Using Fig. 9, it may be that an achievable mitigation strategy can be found at the expense of some acceptable target underachievement in Browns Bay, or that a mitigation strategy can be found that weights overachievement to a part of the estuary where values are highest. This will confer more of a safety margin than if the strategy were focused on exactly achieving the target in that high-value part of the estuary.

Figure 9  Capacity sacrifice Δ _e for an individual target of 30% reduction in sedimentation rate in the Browns Bay intertidal flats. Δ _e is plotted for invalid and valid sediment load limits, where Δ _e <1 signifies that the individual target sedimentation rate will fail to be achieved. Also shown is  for the case where the goal is to achieve simultaneous targets of 10% reduction in sedimentation on the Kakaho intertidal flats; 50% reduction in sedimentation on the Pāuatahanui intertidal flats and in Browns Bay subtidal; and 30% reduction in sedimentation in the three remaining sub-estuaries.

Offset mitigation

It is worth pointing out that, with a slight change in terminology, Equation (17) can be used to design offset mitigation, where offset mitigation is the compensation for an increase in sediment run-off from one particular source region (due to an urban development, for instance) by reducing sediment run-off from one or other source regions.

Suppose there are C sub-catchments, numbered 1 to C. Sub-catchment number α is the source region to be developed, and the sediment load from that sub-catchment is anticipated to increase by a factor of Ψ due to development. There are Λ sub-catchments available where mitigation can be undertaken to offset the increase in sediment run-off from the development, and the numbers of these sub-catchments are n _λ , where λ=1 to Λ. There are Ω sub-catchments where there is no intention of providing, or no possibility of, offset mitigation, and the numbers of these sub-catchments are n _ω , where ω=1 to Ω. The goal of the offset mitigation is to maintain the sedimentation rate in e=1,E sub-estuaries at Φ times the present sedimentation rate S _e,PRESENT, where Φ=1 to maintain the status quo. Changing terminology slightly, Equation (17) becomes:

26

where e=1, E. Load offsets L _{nλ ,OFFSET} that satisfy Equation (26) will maintain the sedimentation rate in sub-estuaries 1 to E at Φ times the present sedimentation rate S _e,PRESENT. There may be any number of such offsets that will suffice, some of which may be better than others for various reasons; these can be discovered using the same type of approach developed herein for discovering sediment load limits.

Discussion

The methods for finding sediment load limits allow for site-specific sedimentation targets throughout the estuary, which can more accurately reflect sediment effects and aspirations for the estuary as a whole. In all but the simplest of cases (one source of sediment depositing in one depositional sink), there is never just one way to manage the catchment to achieve estuary sedimentation targets. This is where opportunity lies, for some ways of achieving targets will be better than others. Management can focus on finding sediment load limits that achieve a balance amongst all the relevant factors. At the time of writing, Porirua Harbour stakeholders and management agencies are breaking down the target inlet-average sedimentation rate of 1 mm/year into sub-estuary targets and pursuing an iterative process to identify the best set of catchment sediment load limits to achieve those targets.

Having decided on the load limits, they then need to be implemented through regional and unitary plans by setting rules and providing incentives. Applications for resource consent that have the potential to elevate sediment run-off need to be assessed against sediment load limits in order to contain cumulative effects. This can be done using a catchment sediment model to predict sediment run-off associated with the proposed activity. Should the model predict that load limits will be exceeded, consent for the activity should be denied, on-site mitigation should be improved, or offset mitigation should be required (see above, for how offset mitigation can be calculated).

The type of process explored herein has not previously been applied to the management of a New Zealand estuary, although load limits have been applied in Central North Island catchments to manage nutrients in lakes (Bay of Plenty Regional Council's Rule 11 in their Regional Water and Land Plan, to manage eutrophication of the Rotorua Lakes; Waikato Regional Council's Plan Variation 5 to manage Lake Taupō). Horizons Regional Council has included load limits in their One Plan regional plan as one part of a strategy for managing the effects of point- and diffuse-source contaminants in rivers in their region, and Environment Canterbury is developing catchment load limits for managing the cumulative effects of nutrients, sediments and pathogens in rivers, lakes, wetlands and groundwater.

The limits-based approach advocated by the Land and Water Forum (and explored herein) is more aligned with the TMDLs employed in the USA under the Clean Water Act than it is with the ecosystem-based philosophy of Europe's Water Framework Directive (although limits can be used as a ‘measure’ under the WFD, or indeed under New Zealand's effects-based Resource Management Act, as evidenced by the freshwater applications mentioned above). Broadly, ecosystems-based management eschews the management of species and habitats singly and in isolation of the whole range of natural (and unnatural) interactions in an ecosystem (Christensen et al. 1996). Limits, on the other hand, are by nature prescriptive and narrowly focused. An important question, therefore, is whether managing for annual-average sedimentation rates by limits will reduce the broad spectrum of adverse sediment effects and deliver the types of environmental outcomes that are desired. Setting aside any ecological questions, it might, for instance, be more important to reduce storm-peak (as opposed to annual-average) sediment run-off to reduce the extent of smothering of shellfish beds of the type described by Norrko et al. (2002) and Thrush et al. (2003a), or to reduce the production of fine sediment to control degradation of light climate. Still, it seems unlikely that the measures required in a catchment to reduce annual-average sediment run-off would not also have mitigating effects on peak storm loads and the discharge to waterways of fine sediment. Research is required to determine the relationships between such factors and the full extent of ‘co-benefits’ associated with managing for an annual-average sedimentation rate. On the other hand, there are distinct advantages to managing for a relatively simple parameter such as an annual-average sedimentation rate. For one thing, it is easy to explain to the public and politicians, and for another it is relatively easy to measure progress towards achievement.

Where contaminants in addition to sediments are present, they may interact with the sediment to either exacerbate or moderate biological and ecological effects (e.g. Thrush et al. 2008). In some cases, it may be reasonable to treat such interactions as being purely physical. For example, the concentration, and therefore toxicity, of heavy metals in estuarine bed sediments may be increased if the metals accumulate in areas with a low sedimentation rate. In this case, the metals will be distributed through a smaller volume of sediment compared with areas where sedimentation rate is high, and vice versa. Where interactions are purely physical, it should be possible to determine joint contaminant load limits using the type of analysis presented herein for sediment in isolation. Other types of interactions may be less amenable to analysis.

Fundamentally, Fig. 6 (in the case of Pāuatahanui Inlet) shows predictions by a model of how estuarine sedimentation will change in response to changes in catchment sediment run-off. (Here, the term ‘model’ refers to the sediment budget [Equation 2], which links estuary sedimentation to catchment sediment run-off.) Furthermore, the limits-based management scheme is based squarely on those predictions. However, the predictions are uncertain since there are uncertainties in the data used to implement and test the model, and basic model assumptions may be questionable. For example, there are obviously uncertainties in the sediment fate matrix and the amount of sediment specified as being lost to sea (data used to implement the model); the model approximately reproduced Swales et al.'s (2005) measured inlet-average sedimentation rate but underpredicted that of Gibb & Cox (2009) (data used to test the model); and the sediment fate matrix may change as the estuary infills with sediment, or the density of the deposited sediment in Equation (2) may change over time if the seabed consolidates (basic model assumptions). Furthermore, the uncertainty associated with the model predictions will typically be unquantifiable. The appropriate response by management is to monitor to determine if the sedimentation predictions are accurate. This will need to be matched with monitoring of catchment sediment run-off, to check that catchment sediment load limits are actually being achieved. Furthermore, monitoring will be required to confirm the larger assumption of the limits scheme, which is that the desired environmental objectives that are intended to come along on the back of the target sedimentation rates are being achieved. With monitoring intended to confirm specific predictions and assumptions, and information gained from monitoring being used to improve predictions (by refining any component of the sediment budget model, for instance) and thereby adjust management methods (changing sediment load limits, for instance), this approach has the attributes to properly qualify as ‘adaptive management’ as defined by, for example, Stankey et al. (2005).

Conclusions

For the same reasons argued by the Land and Water Forum (2012) for freshwater, limits are required to manage the cumulative effects in estuaries of diffuse-source discharges of contaminants.

The obvious way to manage estuary sediment effects is to attempt to reduce sediment run-off uniformly from the catchment in an effort to reduce sedimentation rates uniformly throughout the estuary. However, the obvious approach is bound to fail, since it will never be cost-effective or even possible to reduce sediment run-off uniformly over an entire catchment and, in any case, it would usually not be necessary to set a goal of uniform reduction in sedimentation to achieve ecological and human-amenity objectives. The methods developed herein are aimed at finding smarter ways of managing estuary sediment effects. The key is to exploit the inherent complexity of the estuary and its connections to different sediment source regions in the catchment.

Upon implementation of catchment sediment load limits, monitoring will be required to determine that the limits are being achieved, that target sedimentation rates are being achieved, and that the desired environmental objectives that are intended to come along on the back of the target sedimentation rates are being achieved. Monitoring in the context of adaptive management is a proper course of action when management is based on predictions that will always have a degree of uncertainty.

The analysis presented herein provides a conceptual foundation and basis for calculation that may be extendable to setting joint limits for two or more contaminants such as heavy metals and sediments, and for considering interactions between stressors.

Appendix Symbols

Table

A e	Area over which deposition occurs in sink (sub-estuary) e
c	Source (sub-catchment) number
C	Number of sources (sub-catchments)
D e	Mass of sediment deposited in sink (sub-estuary) e
e	Sink (sub-estuary) number
E	Number of sinks (sub-estuaries)
F c,e	Fraction of sediment mass from source (sub-catchment) c that deposits in sink (sub-estuary) e
F c,e,p	Fraction of sediment mass of size fraction p from source (sub-catchment) c that deposits in sink (sub-estuary) e
L c	Mass load of sediment (sediment run-off) from source (sub-catchment) c
L c,e	Mass load of sediment (sediment run-off) originating from source (sub-catchment) c and depositing in sink (sub-estuary) number e
L c,LIMIT	Sediment load limit for source (sub-catchment) c
L c,MAX	Maximum mass load of sediment (sediment run-off) from source (sub-catchment) c that will not fail a particular S e,TARGET
L c,MIN_ACHIEVABLE Minimum achievable (by mitigation) mass load of sediment (sediment run-off) from source (sub-catchment) c
O c,e	Fraction of sediment mass that deposits in sink (sub-estuary) e that originates from source (sub-catchment) c
p	Sediment size fraction
P	Number of sediment size fractions
S e	Sedimentation rate (total of all sediment size fractions) in sink (sub-estuary) e
S e,p	Sedimentation rate for constituent size fraction p in sink (sub-estuary) e
S e,TARGET	Sedimentation rate target in sink (sub-estuary) e
S e,PRESENT	Present-day sedimentation rate in sink (sub-estuary) e
Γ	Period of time
Δ e	Capacity sacrifice (or target overachievement) in sink (sub-estuary) e
	Average capacity sacrifice (or target overachievement) over all sinks (sub-estuaries)
Λ	Number of sources (sub-catchments) for which the intention is to set sediment load limits or to offset mitigation
Φ	Fraction (between 0 and 1), where S e,TARGET=ΦS e,PRESENT
Ψ	Factor by which source sediment load is anticipated to increase
Ω	Number of sources (sub-catchments) for which there is no intention is to set sediment load limits or to offset mitigation
α	Number of source (sub-catchment) to be developed
η	Number of source (sub-catchment)
ρ	Density of deposited sediment
i	Index (step number, in the limit-setting process)
λ	Index (number of source)
ω	Index (number of source)