1

 

Habitat Equivalency Analysis: An Overview 

Damage Assessment and Restoration Program 

National Oceanic and Atmospheric Administration 

Department of Commerce 

March 21, 1995 

(Revised October 4, 2000 and May 23, 2006) 

1. Introduction 

1.1 Goals of the paper 

 Natural resource trustees are authorized to act on behalf of the public to protect the 

resources of the nation’s environment. Serving as a trustee for coastal and marine resources, 

NOAA determines the damage claims to be filed against parties responsible for injuries to 

natural resources resulting from discharges of oil, releases of hazardous substances, or physical 

injury such as vessel groundings.1 Habitat equivalency analysis (HEA) is a methodology used to 

determine compensation for such resource injuries. The principal concept underlying the method 

is that the public can be compensated for past losses of habitat resources through habitat replacement 

projects providing additional resources of the same type. Natural resource trustees have employed 

HEA for groundings, spills and hazardous waste sites. Habitats involved in these analyses include 

seagrasses, coral reefs, tidal wetlands, salmon streams, and estuarine soft-bottom sediments.

 The goals of this paper are to present an overview of HEA and illustrate the method with 

a simple, hypothetical example. In section 1.2 below, we outline briefly the natural resource 

damage context for HEA applications and the conditions for use of HEA. An example of how 

HEA is used to estimate the appropriate level of compensation for injuries to natural resources is 

presented in section 2. Appendices A through C present an algebraic representation of the HEA 

calculations and provide detailed tables from the example. 

1 The Under Secretary for Oceans and Atmosphere (NOAA Administrator) acts on behalf of the Secretary of 

Commerce as a Federal trustee for natural resources under the Comprehensive Environmental Response, 

Compensation, and Liability Act (“CERCLA”; 42 U.S.C. § 9601 et seq.), the Clean Water Act (33 U.S.C. § 1251 et 

seq.) , the National Marine Sanctuaries Act (16 U.S.C. § 1431 et seq.), and the 1990 Oil Pollution Act (“OPA”; 33 

U.S.C. § 2701 et seq.). 
 

 

 2

 

1.2 Use of HEA in natural resource damage assessments 

 Natural resource damage claims have three basic components: (1) the cost of restoring 2

the injured resources to baseline, or “primary restoration,” (2) compensation for the interim loss 

of resources from the time of injury until the resources recover to baseline plus (3) the 

reasonable costs of performing the damage assessment.3 Following statutory requirements, all 

recovered damages are used to restore, replace, rehabilitate or acquire the equivalent of the 

injured resources (or to cover the costs of assessments). Consequently, recoveries for interim 

losses are spent on “compensatory restoration” actions providing resources and services 

equivalent to those lost. To ensure full compensation for interim losses, the trustees determine 

the scale of the proposed compensatory restoration actions for which the gains provided by the 

actions equal the losses due to the injury. The damage claim then is the cost of implementing the 

selected primary and compensatory restoration actions (plus the costs of the assessment) or 

alternatively, the responsible parties may be allowed to implement the projects themselves, 

subject to performance criteria established by the trustees. To develop the restoration plan, 

trustees must determine and quantify injury, develop restoration alternatives that consist of 

primary and compensatory actions, scale restoration alternatives, and select a preferred 

restoration alternative. This paper examines a method for scaling restoration alternatives, HEA.4

 For compensatory restoration actions, the scaling question is: what scale of compensatory 

restoration action will compensate for the interim loss of natural resources and services from the 

time of the incident until full recovery of the resources? The scale of compensatory restoration 

actions is conditional upon the choice of primary restoration actions. Consequently, for each 

2 Restoration refers to human actions taken after the removal of the cause of injury (e.g., after remediation of a 

hazardous waste site, removal of the vessel in the event of a grounding), to return an injured resource to its preinjury conditions. We use the term in its broad sense, to encompass the statutory concepts of “restoration, 

rehabilitation, replacement, and/or acquisition of the equivalent” of the injured resources. 

3 At any point in time, baseline refers to the condition of the natural resources and services that would have existed 

had the incident not occurred. If the resources are not expected to recover fully, interim losses will be calculated in 

perpetuity. 

4 This description characterizes the process outlined in the natural resource damage assessment (NRDA) regulations 

implementing OPA (15 CFR Part 990) and in the proposed statutory changes to the CERCLA NRDA provisions (43 

CFR Part 11). 
 

 

 3

 

restoration alternative under consideration, the type and scale of the primary restoration actions are 

to be identified first.5 Then the compensatory components of restoration alternatives can be scaled. 

 The process of scaling a project involves adjusting the size of a restoration action to 

ensure that the present discounted value of project gains equals the present discounted value of 

interim losses. There are two major scaling approaches: the valuation approach and the 

simplified service-to-service approach, which applies under certain conditions. 

HEA is an example of the service-to-service approach to scaling. The implicit 

assumption of HEA is that the public is willing to accept a one-to-one trade-off between a unit of 

lost habitat services and a unit of restoration project services (i.e. the public equally values a unit 

of services at the injury site and the restoration site).6 HEA does not necessarily assume a oneto-one trade-off in resources, but instead in the services they provide. Consider a marsh as the 

resource and primary productivity a resource service. Suppose the replacement project provides 

only 50 percent of the productivity per acre of marsh as the injured site would have provided, 

but-for the injury. In order to restore the equivalent of lost productivity per year, then, the 

replacement project requires twice as many acres of marsh. Habitat equivalency analysis is 

applicable so long as the services provided are comparable. 

The assumption of comparable services between the lost and restored habitats may be 

met when, in the judgment of the trustees, the proposed restoration action provides services of 

the same type and quality, and of comparable value as those lost due to injury. In this context, 

there is a one-to-one tradeoff between the resource services at the compensatory restoration site 

and the injury site. Therefore, the scaling analysis simplifies to determining the scale of a 

restoration action that provides a quantity of discounted replacement services equal to the 

quantity of discounted services lost due to the injury. 

 In cases where services at the compensatory restoration site are not of the same type and 

quality or of comparable value to those injured, then the assumption of a one-to-one trade-off 

between the resources at the injury site and the compensatory restoration site may be 

5 This includes identifying the recovery trajectory from primary restoration. 

6 The concept of services refers to functions a resource serves for other resources and for humans. For example, a 

wetland habitat may provide on-site ecological services such as faunal food and shelter, sediment stabilization, 

nutrient cycling, and primary production. Off-site services may include commercial and/or recreational fishing, bird 

watching along the flyway, water quality improvements due to on-site water filtration, and storm protection for on-
 

 

 4

 

inappropriate. In these cases, NOAA recommends that trustees evaluate whether the conditions 

for HEA are met and consider using the valuation approach as an alternative to determining the 

trade-off between injuries and compensatory restoration actions. 

 Necessary conditions for the applicability of HEA include that (1) a common metric (or 

indicator) can be defined for natural resource services that captures the level of services provided 

by the habitats and captures any significant differences in the quantities and qualities of services 

provided by injury and replacement habitats, and (2) the changes in resources and services (due 

to the injury and the replacement project) are sufficiently small that the value per unit of service 

is independent of the changes in service levels. 7 When choosing a metric to evaluate the 

quantity and quality of services provided per unit of habitat, the trustees should examine the 

capacity, opportunity and the payoff (i.e. benefits) of the services being provided as well as 

equity issues involved with the potential compensation projects ( i.e. who loses and who gains as 

a result of the injury and the potential compensation projects). On-site biophysical characteristics 

(e.g., soil, vegetative cover, and hydrology) affect the capacity of an ecosystem to provide 

ecological and human services. Landscape context affects whether the ecosystem will have the 

opportunity to supply many of the ecological and human services and strongly influences 

whether humans will value the opportunities for services.8

 Consider, for example, the wetland function of sediment trapping. A wetland’s capacity 

to provide this function depends on such factors as slope and vegetative cover. The opportunity 

for the wetland to trap sediments depends on the expected flow of sediments from adjacent land, 

which will depend upon types of upland land uses (i.e., landscape context). The total value 

generated from water quality improvements due to sediment trapping will depend upon the uses 

shore properties due to the creation of wave breaks. Human services include both use and non-use services, so the 

HEA approach measures and accounts for non-use services in the damage claim. 

7 A counterexample shows when this condition is not satisfied. Consider the value of harvesting another salmon 

when salmon are in abundant supply versus the value of another salmon when the harvest has failed in Alaska. The 

value of providing another pound of salmon may be substantially greater when the salmon are in scarce supply, all 

else equal. 

8 For a further discussion of these issues, see, Scaling Compensatory Restoration Actions, Guidance Document for 

Natural Resource Damage Assessment Under the Oil Pollution Act of 1990, National Oceanic and Atmospheric 

Administration, Damage Assessment and Restoration Program, 1997 and King, Dennis M., Comparing Ecosystem 

Services and Values, Report prepared for the National Oceanic and Atmospheric Administration, Damage 

Assessment and Restoration Program, January 1997. 
 

 

 5

 

of the affected downstream water bodies: the value will be greater if there are nearby shellfish 

beds and finfish spawning areas than if the water flows into a fast-moving river. 

The choice of a metric to characterize services is essential to determining whether HEA 

is applicable in a given context. On-site ecological attributes, such as stem density, canopy 

structure (density multiplied by height), or fish density, are sometimes used as a proxy for 

services; however, they are primarily indicators of capacity. It is critical to evaluate the role of 

landscape context to evaluate the opportunity to provide off-site, as well as on-site, ecological 

and human services. 

2. Habitat Equivalency Analysis: An Example 

 In this section we provide a simplified example to illustrate the method. To complement 

the example, we provide the algebraic formula for solving an HEA in Appendix A. 

 We construct the following hypothetical scenario.9 A heavy fuel oil released from a 

grounded tanker covered 20 acres of marsh composed primarily of smooth cordgrass (Spartina 

alterniflora) in 2000. The oil smothered significant portions of the marsh, penetrating the 

sediments in many areas and killing much of the biota. This injury impairs the function of the 

marsh habitat; the marsh provides food and shelter for animals, water quality improvements for 

downstream resources, shoreline stabilization and other natural resource services. In addition, 

the loss of marsh affects human services. For example, marsh habitat supports off-site human 

services through the production of fish that provide recreational and commercial services and 

through nutrient filtration that provides water quality enhancement.

 Trustees identified a feasible restoration action for compensation: transplanting Spartina 

alterniflora at the injury site for primary restoration and transplanting Spartina alterniflora along 

with some minor regrading at a nearby site. The projects are expected to restore the same type 

and quality of resources and services. Further, given the similar landscape context of the injury 

and restoration sites, the trustees judged the projects would restore resources and services of 

comparable value as those lost. 

9 The size and the description of the hypothetical injury are not based on actual events and have been chosen simply 

to demonstrate the HEA calculation. 
 

 

 6

3. 

 

 Under these conditions, HEA applies as a framework for scaling compensatory 

restoration. The basic steps for implementation include: 

1. Document and estimate the duration and extent of injury, from the time of 

injury until the resource recovers to baseline, or possibly to a maximum 

level below baseline; 

2. Document and estimate the services provided by the compensatory 

project, over the full life of the habitat;

 Calculate the size of the replacement project for which the total increase in 

 services provided by the replacement project equals the total interim loss 

 of services due to the injury; and 

4. Calculate the costs of the replacement project, or specify the performance 

standards in cases where the responsible party will be implementing the 

compensatory habitat project. 

 

 In the first two steps, trustees must specify numerical values for ecological parameters for 

both the injured site and the compensatory project site. For each point in time at both sites, the 

level of services must be characterized as a percent of the baseline level of services at the injured 

site. As previously noted, the baseline of services is the level of services that would have been 

provided at the injured site but for the injury. In our example, we assume that local experts 

consider grass shrimp (Palaemonetes pugio) to be a very important (or key) species in this 

habitat and they believe that the presence of grass shrimp is highly correlated with many services 

provided by the marsh. The presence and density of grass shrimp may indicate the general 

health of the marsh vegetation and the availability of food for higher trophic levels. Therefore, 

we assume that service levels for the injured site and for the compensatory project site are a 

function of the baseline mean density of grass shrimp in the marsh. Studies indicate that the spill 

reduced the mean density of grass shrimp by approximately 50%. Using the mean density of 

grass shrimp as a metric for marsh services, we assume that the service level of the injured marsh 

prior to any restoration actions is 50% of its baseline service level. 10

10 Depending on the exact nature and extent of an injury, the mean density of grass shrimp relative to the baseline 

density may or may not serve as a good metric for the services provided by the marsh. Additional potential 

indicators of marsh services might include macrofaunal abundance, fish utilization, vegetative density and percent 

vegetative cover. 
 

 

 7

 

 In step three, we calculate the size of the compensatory project for which the total 

increase in services provided by the replacement project just equals the total interim loss of 

services due to the injury. Because losses and gains are occurring in different years, we 

discount the losses and gains so that units reflect what they are worth in the present year, 2000. 

This makes units from different time periods comparable. The discount rate incorporates the 

standard economic assumptions that people place a greater value on having resources available 

in the present than on having their availability delayed until the future. This process is analogous 

to financial calculations where, if a dollar is put into the bank today at 3% interest, there will be 

$1.03 in one year. A person is willing to deposit money in such an interest bearing account only 

if having $1.03 is (at least) as good as having $1 today. There are a variety of discounting 

approaches, but mean accounting was applied in the example in this document. Mean 

accounting involves taking the arithmetic mean of service levels at the beginning and end of 

each period and crediting that resulting service level as accruing at the midpoint of the period. 

 The annual discount rate used in a HEA calculation represents the public’s preference 

towards having a restoration project in the present year, rather than waiting until next year. The 

economics literature supports a discount rate of approximately 3%. 11

 We list below the parameters necessary to complete a simple HEA. 

 Injured Area Parameters: 

• Baseline level of services at the injury site; 

• Extent and nature of the injury: the spatial extent of injury (in acres for example) 

and the initial reduction in service level from baseline at the injured site 

(characterized as a percent of the baseline level of services). These parameters 

may be combined to measure the “service-acres” of an injury; 12

11 For a further discussion of discounting see: National Oceanic and Atmospheric Administration (1999) 

Discounting and the Treatment of Uncertainty in Natural Resource Damage Assessment. Damage Assessment and 

Restoration Program, Damage Assessment Center, Resource Valuation Branch. Technical Paper 99-1. Silver 

Spring, MD, February. 

12 Service-acres may be illustrated with an example. If 30% services remain on an injured 100 acre site, the injury 

totals 70 service-acres (100 * (1-0.3) = 70). Note that the percent is represented by its decimal equivalent. 
 

 

 8

• Injury recovery function (with primary restoration or natural recovery): the rate of 

(incremental) service recovery and the maximum level of services to be achieved 

(characterized as a percent of the baseline level of services); 

• Recovery period for injured resources: the dates when recovery starts and when 

maximum level of services will be achieved. 

 Replacement Area Parameters: 

• Initial level of services at the replacement project site, measured as a percent of 

baseline services at injury site; 

• Replacement project maturity function: the rate of (incremental) service growth 

and the maximum level of services at the replacement project site (as a percent of 

the baseline level of services at injury site); 

• Maturity period for replacement resources: the dates when services begin to 

increase and when the maximum level of services will be achieved; 

• Replacement/creation project duration: lifetime of increased services. 

 Discount Rate 

• Annual real discount rate 

 In the following section, we walk through the each of the steps and show how ecological 

parameters are developed from the injury and how the HEA equation is solved. 

 Step 1: Quantifying the losses from the injury. For our example, parameter values 

characterizing the injury are listed in the table below. As shown, we denote the injury to 20 

acres of marsh function by specifying that, after injury, 20 acres provide 50% of the services 

relative to baseline at the time of the injury (2000). The site is projected to maintain a 50% 

service level until the primary restoration project (transplanting Spartina alterniflora at the 
 

 

 9

injury site) is completed in 2001. The injured area is then projected to recover in eight years 

following a linear growth path to baseline.13

Table 1: Injury Parameter Values 

Baseline Information of the Injured Resource: 

 Habitat type injured: Marsh 

 Year of injury 2000 

 # of injured acres: 20 

 Level of services in injury year (relative to baseline 

services): 

50% 

Recovery of Injured Habitat following Primary Restoration:

 Year restoration project ends and recovery starts: 2002 

 Years until full recovery: 8 

 Services at maximum recovery (relative to baseline): 100% 

 Shape of recovery function: Linear 

Discount Rate:

 Real annual discount rate 3.0% 

 The recovery of services provided by the injured habitat is illustrated in Figure 1. On the 

vertical axis is the level of services provided by the injured resource, measured in “serviceacres”. The service-acres for a given year are calculated as the product of the percent of baseline 

marsh services provided by an acre of the injured site multiplied by the number of acres 

injured.14 When the injury occurs, in year 2000, the number of service-acres drops from 20 to 

10, because 50% services remain at the site. Services increase along a linear path beginning in 

2002, until full recovery to the baseline at the end of 2009. Interim losses are represented in the 

diagram by the area labeled “L”. 

 

13 The length and shape of the recovery function are chosen in order to simplify the presentation. An alternative 

recovery function, such as a constant growth rate or other non-linear growth path, and an alternative length of 

recovery, could be chosen if applicable to the injured resource. 

14 In the multiplication, the percent is represented by the decimal equivalent, so the baseline level of acres is 

(1.00*20)=20. In 2005, the site is projected to operate at 75% of baseline, so the effective service level is 
Figure 1: 

Time 

Resource 

Services 

Baseline Services 

(if injury had not 

occurred) 

Full 

Recovery 

Start of 

Recovery 

L

2000 

Oill Spill 

2002 2009 

Resource Service Levels at the Injury Site

Recovery 

Function 

 To calculate the measure of interim loss in present value terms, we must apply the yearly 

discount factor to the losses in each year. We calculate an interim loss of 55.106 discounted 

service-acre-years by summing over all years of the injury. Appendix B presents the specific 

steps for calculating the discounted interim loss in services. 

 Step 2: Quantifying the gains from the habitat replacement project. The parameters 

characterizing the habitat creation project are listed in the table below. Prior to the 

compensation project, the nearby site offers 25% marsh services relative to the pre-injured marsh 

site. Service flows from compensation project commence when the project is completed in 

2002. We project that marsh services increase during a 10-year growth period along a linear 

path and reach a maximum service level equal to 100% of the baseline service level of the 

injured site. We further project that the site will continue to function at the maximum service 

level in perpetuity. 

 

 

 

 10

 ((1-.75) * 20) = 5. 
 

 

 11

Table 2. Replacement Project Parameters 

Replacement Project Characteristics:

Replacement habitat type: Marsh 

Initial level of services 25% 

Year creation/replacement project starts 2001 

Year services start increasing 2002 

Year in which maximum service level is reached (end of period) 2011 

Maximum service level 100% 

Shape of recovery function Linear 

Expected length of service increase Infinity 

Replacement Project Comparison Parameter: 

Ratio of maximum services per acre at the compensatory site and 

the baseline services per acre at injured habitat. 

1:1 

 The increase of services at the habitat creation site is illustrated in Figure 2. The vertical 

axis measures the services per acre of a replacement project as a percent of the baseline services 

per acre at the injured site. As shown, services begin at 25% and start increasing in 2002, 

following a linear path until the services reach full maturity in 2011. The services continue to 

function at the maximum level in perpetuity. The total increase or gain in services per acre, is 

shown as area “G”, which is the area between the maturity function and the 25% service level. 
Figure 2: 

G

Time

Resource

Service per

Acre

Maximum

service level of

Created Habitat

Grounding Compensatory

Restoration

Services Mature

2000 2002 2011

Compensatory

Restoration

Services Begin

(relative to the

injury site

baseline)

Resource Service Levels at Replacement Project Site

Maturity

Function

100%

25%

 To calculate service gains in the present value terms, we must apply the yearly discount 

factor to the gains in each year and sum over the lifetime of the replacement project. This 

calculation, presented in more detail in Appendix C, indicates that each acre of replacement 

project provides 21.015 discounted service-acre-years. 

 Step 3: Determining the Size of the Replacement Project. To determine the size of the 

compensatory project needed to compensate for the losses, we divide the total loss in discounted 

service-acre-years by the gain per acre of replacement and get 2.62 acres, as outlined in Table 3. 

 

 

 12
 

 

 13

Table 3. Determining the Size of a Project to Compensate for Interim Losses 

• Injured Area = 20 acres 

Present discounted interim losses = 55.106 service-acre-years (See Appendix B) 

• Present discounted lifetime gains per acre of replacement project = 21.015 service-acre-years 

per acre (See Appendix C) 

• Let R = # replacement habitat acres required for compensation. 

• Equating lost services and replacement project gains: 

55.106 lost service-acre-years = 21.015 service-acre-years/ acre * R acres

• Solving for the size R of the replacement project yields: 

 R = 55.106/21.015 

 = 2.62 acres of replacement habitat 

The top graph in Figure 3 illustrates the discounted service losses resulting from the 

injury and the bottom graph illustrates the discounted service gains resulting from the 

replacement project. At the time of the incident, 2000, service losses occur and, although 

recovery doesn’t start until the year restoration is completed in 2002, the value of future losses 

decreases in the year 2001 because the losses are discounted. The discounted losses reach zero 

in the year 2009, when the recovery of services at the injured site is complete. The total 

discounted service losses are equal to area “A” in the top graph. 

The replacement project begins providing service gains in the year 2002, the year the 

compensation project is completed. In 2011, the compensation project reaches maturity and 

continues providing services at the same level in perpetuity. However, the value of these 

services declines over time, eventually approaching a value very close to zero (the value of the 

service gains approaches zero asymptotically) because the value of service gains is discounted. 

The total discounted service gains are equal to area “B” in the bottom graph. A replacement 

project of 2.62 acres will provide just enough service gains to equal the service losses resulting 

from the injury. That is, area “B” in the bottom graph of Figure 3 is made equivalent to area “A” 

in the top graph. 
Figure 3: 

Discounted

Service

Losses

Time

Total Discounted AcreYears of Services Lost

Due to Injury

A

2000

Incident

 2002

Begin Recovery

of Injured and

Comp. Site

 2009

Recovery of

Services at

Injured Site

2011

Full Maturity of Services

at Compenation Site

Time

Total Discounted

Acre-Years of

Services Provided by

Replacement Project

B

2000

Incident

 2002

Begin Recovery

of Injured and

 2009

Recovery of

Services at

Comp. Site Injured Site

2011

Full Maturity of Services

at Compenation Site

Discounted

Service

Gains

 

Step 4: Calculating the Cost of the Replacement Project. Step four of HEA, which would be 

required for any damage assessment and restoration plan regardless of the methodology used in 

the assessment, occurs after the trustees have calculated the scale of the project. The damages 

claim is based on the costs of the replacement project.15 Categories of project costs include the 

following: 

 

 

 14

 

15 Again, it should be noted that the responsible parties may perform the replacement project, subject to 

performance criteria established by the trustees. 
 

 

 15

• planning and design 

• environmental impact assessment 

• permitting 

• construction 

• monitoring 

• mid-course corrections 

Some of the categories of cost can be characterized on a per-acre basis; others impose fixed costs 

(permitting). We do not calculate project costs in this example.

 
Appendix A: Algebra of HEA 

Below, we outline the generic formula employed to calculate the appropriate scale of the 

compensation project. We first provide the notation for the HEA calculations. 

Let t refer to time (in years), where the following events occur in the identified years: 

t=0, the injury occurs 

t=C, the base for discounting (when discount factor = 1.0) 

t=B, the injured habitat recovers to baseline 

t=N, the injured resource reaches maximum service provision 

t=I, compensatory project begins to provide services 

t=M, compensatory project reaches full maturity 

t=L, compensatory project stops yielding services 

Other variables in the analysis include: 

Vj , the value per acre-year of the services provided by the injured habitat (without injury) 

Vp , the value per acre-year of the services provided by the replacement habitat

xt

j

, the level of services per acre provided by the injured habitat at the end of year t

b j

, the baseline (without injury) level of services per acre of the injured habitat16 

xt

p

, the level of services per acre provided by the compensatory project at the end of year t

bp

, the initial level of services per acre of the compensatory projects 

r, is the discount rate for the time period 

J, the number of injured acres 

P, the size of the replacement project 

We select a metric, x, for capturing overall level of habitat services, or habitat function, 

which could represent a single service flow from the resource or an index that represents a 

 

16 We simplify the representation of the baseline to be constant through time. Seasonal or inter-annual (or other) 

forms of variation could be incorporated, by adding time subscripts to the baseline variable b. 

 

 

 16
weighted average of multiple service flows. In the chosen metric, we define: xt

j

 as the level of 

services per acre provided by the injured habitat at the end of year t, and bj as the baseline level 

of services of the injured habitat; consequently, (bj

 - xt

j

) is the extent of injury in year t.17 

Analogously, we define xt

p

, as the level of services provided by the replacement habitat at the 

end of year t, and bp as the initial level of services of the replacement habitat, prior to any 

enhancement activities; consequently, (xt

p

- bp) represents the increment in resource services 

provided by the replacement project - which is the relevant measure for our analysis. In our 

discussion in the text in the body of this paper, however, we referred to habitat services as a 

percent of the baseline level of services of the injured habitat, bj; in this format, (bj

 - xt

j

)/ bj

represents the percent reduction in services per acre at the injured site from the injured site 

baseline, and ( xt

p

- bp)/bj represents the percent increase in services per acre, relative to the 

injured site baseline, for the replacement site. 

 To translate the quantity in year t into its appropriate value in the year of the claim, C, we 

apply the discount factor based upon the annual discount rate, r. Finally, the number of injured 

acres is J. The goal of the habitat equivalency analysis is to solve for the size of the replacement 

project, P. 

 The equation equating the sum of the present discounted value of the services lost at the 

injured site with the sum of the present discounted value of the services provided at the 

replacement site is: 

( ) ( ) ∑ ( ) +

=

− − += +− =

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − ⎥ +

⎦

⎤ ⎢

⎣

⎡ +−

+

1

0

1 1 )1( 1* 1 * 5.0 *1**

N

t

NC

j

j

Nt

j

j

j

t

j

t

j

tC

j r

b r

xb

b

xxb

VJ r

( ) ( ) ∑ ( ) +

=

− − += +−

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − ⎥ +

⎦

⎤ ⎢

⎣

⎡ −+

+

1

1 1 )1( 1* 1 * 5.0 *1**

M

It

MC

j

p p

Mt

j

pp

t

p

t tC

p r

b r

bx

b

bxx

VP r

Under the assumption that the per unit value of replacement habitat services, , is equal to the 

per unit value of injury habitat services, , the calculation to solve for the size of the 

Vp

V j

 

 

 

 17

17 More precise estimates of the level of discounted service flows could be obtained by using smaller time periods 

(e.g. semi-annual or monthly). If smaller time periods are used the discount rate should be adjusted to keep the 

annual discount rate unchanged. 
replacement project is simplified because the term = 1

p

j

V

V

. The equation to solve for the amount 

of compensatory restoration required is: 

( ) ( ) ( )

( ) ( ) ∑ ( )

∑

+

=

− − += +−

+

=

− − += +−

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − ⎥ +

⎦

⎤ ⎢

⎣

⎡ −+

+

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − ⎥ +

⎦

⎤ ⎢

⎣

⎡ +−

+

= 1

1 1 )1(

1

0

1 1 )1(

1* 1 * 5.0 *1

1* 1 * 5.0 *1

**

M

It

MC

j

p p

Mt

j

pp

t

p

t tC

N

t

NC

j

j

Nt

j

j

j

t

j

t

j

tC

p

j

r

b r

bx

b

bxx

r

r

b r

xb

b

xxb

r

V

V

JP

The ratio of 

p

j

V

V

 is greater than one if the per unit value of the injured services is greater than the 

per unit value of the replacement services. Subsequently, more of the replacement project 

habitat would be needed than if the per unit values were equal. Less of the replacement project 

habitat would be needed if the per unit value of the injury habitat is less than the per unit value of 

the replacement habitat. 

 

 

 18
 

 

 

19

Appendix B: Interim Losses from a Marsh Oiling 

Table B1 documents the injury and recovery of services on an annual basis and presents 

the sum of total discounted service-acre-years lost. There is a unique row for each year between 

the time of injury and the time when the resource returns to baseline conditions, and these rows 

are designated in Column 1 by year. Column 2 provides some descriptive information on the 

status of the resource. Columns 3 and 4 provide information about the percent service loss at the 

beginning and end of each period, respectively. Note habitat services grow for eight years 

following a linear recovery path, starting in 2002. The beginning of period service loss in each 

period is equal to the end of period service loss in the previous period, except for the year of 

initial injury. The beginning percent service loss in the first period is equal to the service loss 

experienced by the resource immediately following the injury. The end of period service loss, 

Column 4, declines as the resource recovers toward baseline conditions. See the algebraic 

notations that follow Table 1 for the precise calculation used in Column 4. Column 5 is the 

arithmetic mean percent service loss experienced over the period, and is accurate if the overall 

recovery function is linear or can be reasonably approximated as linear within each period. 

Column 6 is the number of service-acre-years lost in each period, and is the product of the mean 

percent service loss and the area of injury. Column 7 is the discount factor, which is multiplied 

by the number of service-acre-years lost to yield the discounted service-acre-years lost in 

Column 8.
20

1 2 3 4 5 6 7 

Period Project Status % Service Loss Service-Acre- Years Lost Discount Factor Discou

Acre

Beginning 

of Period 

End 

of Period Mean 

2000 50.00% 50.00% 50.00% 10.000 1.000 

2001 Primary Restoration 50.00% 50.00% 50.00% 10.000 0.971 

2002 Recovery Begins 50.00% 43.75% 46.875% 9.375 0.943 2003 43.75% 37.50% 40.625% 8.125 0.915 2004 37.50% 31.25% 34.375% 6.875 0.888 2005 31.25% 25.00% 28.125% 5.625 0.863 2006 25.00% 18.75% 21.875% 4.375 0.837 2007 18.75% 12.50% 15.625% 3.125 0.813 2008 12.50% 6.25% 9.375% 1.875 0.789 2009 Recovery Complete 6.25% 0.00% 3.125% 0.625 0.766 

2010 0.00% 0.00% 0.000% 0.000 0.744 2011 0.00% 0.00% 0.000% 0.000 0.722 

Total Discounted Service-Acre-Years Lost = 

Table B1. Interim marsh service loss calculations. 
Algebraic notation for Table B1 calculations: 

Column 3: = j

j

t

j

b

− xb −1 , except for t=0 which = initial loss after injury 

Column 4: = j

j

t

j

b

− xb

Column 5: = ( )

j

j

t

j

t

j

b

5.0 −1 +− xxb OR 0.5 * (Column 3 + Column 4)

Column 6: = ( )

j

j

t

j

t

j

b

xxb

J 5.0 −1 +− * OR J * Column 5 

Column 7: = ( ) Ct

r − 1+

1

Column 8: = ( )

( ) j Ct

j

t

j

t

j

b r

xxb

J −

−

+

+−

1

1 * 5.0 * 1 OR Column 6 * Column 7 

 

 21
 

 

 

22

Appendix C: Service Gains from Compensatory Restoration Project 

 In Table C1, the increase in services of the compensatory habitat is calculated per acre of 

replacement project. The first five columns in Table C1 contain information analogous to that in 

Columns 1 through 5 of Table B1. As the benefits of compensatory restoration are always 

quantified per unit area (acres in this example), Table C1 does not contain a column similar to 

the service-acre-years lost. Instead, the annual discounted service-acre-years of gains per acre 

of compensatory restoration (Column G) are derived by multiplying the mean percent service 

level (Column E) by the discount factor (Column F). At the bottom of the table, the total 

discounted service-acre-years per acre are summed. 
23

A B C D E F G 

Period Project Status % Service Gain Discount Factor Discounted Se

Acre-Years Gain

Acre of Restor

Beginning 

of Period 

End 

of Period Mean 

2000 0.0% 0.0% 0.00% 1.000 0.000 2001 Replacement Project Begins 0.0% 0.0% 0.00% 0.971 0.000 

2002 Service Increase Begins 0.0% 7.5% 3.75% 0.943 0.035 2003 7.5% 15.0% 11.25% 0.915 0.103 2004 15.0% 22.5% 18.75% 0.888 0.167 

2005 22.5% 30.0% 26.25% 0.863 0.226 2006 30.0% 37.5% 33.75% 0.837 0.283 2007 37.5% 45.0% 41.25% 0.813 0.335 2008 45.0% 52.5% 48.75% 0.789 0.385 2009 52.5% 60.0% 56.25% 0.766 0.431 2010 60.0% 67.5% 63.75% 0.744 0.474 2011 Services Reach Maximum 67.5% 75.0% 71.25% 0.722 0.515 

Beyond 

2011 75.0% 75.0% 75.00% -- 18.061 

Total Discounted Service-Acre-Years Gained per Acre of Restoration = 21.015 

Table C1. Calculation of marsh service provision gains from compensatory restoration. 
Algebraic notation for Table C1 calculations: 

Column C: = j

pp

t

b

− bx −1 

Column D: = j

pp

t

b

− bx

Column E: = ( )

j

pp

t

p

t

b

−+ bxx 5.0 −1 OR 0.5 * (Column 3 + Column 4)

Column F: = ( ) Ct

r − 1+

1

Column G: = ( )

( ) j Ct

pp

t

p

t

b r

bxx

−

−

+

−+

1

1 * 5.0 1 OR Column 5 * Column 6 

 

 24