Visual_HEA Software

We have developed an interactive program, Visual_HEA, that facilitates input of HEA assumptions and parameters and provides an efficient method of calculating the required compensatory action. The program allows input of the relevant parameters necessary for analysis:

Service loss parameters:

• Injury area size
• Time history of service levels at the injury site

Service gain parameters:

• Time history of service levels at the restoration site

General program parameters:

• Relative value of lost and gained services
• Baseline level of lost and gained services
• Discount rate

Because HEA results are highly dependent upon assumptions, it is useful to examine sensitivity of results using a range of parameter values. Visual_HEA facilitates this by offering an intuitive graphical interface that allows the user to modify input parameters and quickly alter the recovery shape functions. The ability to formulate many "what-if" scenarios provides an efficient method of gauging the sensitivity of the required compensatory action scale to the analysis parameterization and time variability.

Below are the formulae used to calculate the required compensatory action (from NOAA, 2000).

Time Parameters

t=0, time when the injury occurs
t=B, time when the injured habitat recovers to baseline
t=C, time when claim is presented
t=I, time when the habitat project beings to provide services
t=M, time when the habitat replacement project reaches full maturity
t=L, time when the habitat replacement project stops yielding services

Other Variables

V_j, value per area-time of services provided by injured habitat
V_p, value per area-time of services provided by replacement habitat
x_t^p, level of services provided by replacement habitat at end of time t
b^p, initial level of services per area of replacement habitat
p_t, discount factor where pt=1/(1+r)(t-C), r is discount rate
J, number of injured area units
P, size of replacement project

Calculated Quantities

(b^j-x_t^j) extent of injury at time t
(x_t^p-b^p) increment in services provided by replacement project
(b^j-x_t^j)/b^j percent reduction in services per area for injured area
(x_t^p-b^p)/b^j percent increase in services per area for replacement area

The goal of habitat equivalency analysis is to solve for the size of the replacement project P. To accomplish this, the sum of the present discounted value of services lost as a result of the injury is set equal to the present discounted values of the services provided by the replacement project:

HEA Approach for Calculating Broward County Nearshore Mitigation Amount

This case study illustrates a plan for the renourishment of beaches in Broward County, Florida, which involved the covering of 10.1 acres of hardground coral reef community habitat with sand. Local government proposed to provide mitigation in the form of limestone boulders in order to compensate for the loss of the 10.1 nearshore acres. In order to complete the HEA, reasonable assumptions were made about the relative recovery rates of the hardground acres and the mitigation area, the discount rate, and the start times and amounts of lost and full services of the injury and mitigation.

The nearshore injury was assumed to begin in 2003 and the mitigation to also begin at the same time in 2003. The discount rate was assumed to be the long-term historical average of 3%.

Other assumptions include:

Extent of injury and loss of services of hardground

• 20% lost upon inception in 2003
• 100% lost 3 years later in 2006
• 100% loss continues in perpetuity (habitat remains sand covered forever)

It was also assumed that while the mitigation boulders will recover to 100% full services in 50 years naturally, they will recover to those 100% full services in less time (15 years) by transplanting corals onto them. By transplanting corals, the mitigation boulders will begin recovery not at 0% of full services, but at some higher value. A level of 10% was agreed upon by all parties.

Services gained by the mitigation boulders

• 10% of services upon transplantation of larger corals older than 15 years onto boulders in 2003
• 100% full services reached after 15 years in 2018
• 100% full services continues in perpetuity

The Visual_HEA program consists of a single main form. To perform an analysis, the following initial information must be provided:

• Site name: user can specify name of analysis site, analysis, etc.
• Current year: year of analysis
• Number of injured area units: size of injury site in spatial units
• Ratio of injured/restored service values: relative value of lost versus gained services per time-area unit
• Discount rate (%) per time unit: amount of discounting to reflect the relative value of present versus future service levels
• Pre-injury service level: level of services provided by the injured area prior to injury
• Pre-compensatory restoration service level: level of services provided by the restoration area prior to restoration
• Area and time units (e.g. m2, years)
• Service loss displayed years: time span of service loss analysis to be displayed
• Service gain displayed years: time span of service gain analysis to be displayed

The recovery times and service levels for both the injured site and the replacement site must be specified by placing nodes along the time axis which represent the level of services provided at a given time. This can be done either directly through the graphical interface or manually by inserting the service level and time values into a pop-up dialog box. A linear recovery function is typically used; however alternative recovery shapes could be used as well. The ease of placing and moving the service level nodes allows many different scenarios to be analyzed in a short amount of time.

Any or all of the various scenarios can be saved for later analysis by clicking the "Save HEA data" button. When specifying the time history of the injury and restoration areas, an important factor in the HEA is whether or not the services lost or gained continue in perpetuity. This can have a very significant effect on the calculated size of the replacement site.

The following panel illustrates data input for the beach renourishment project described above:

After the initial parameters and the recovery function information have been specified, the analysis can be performed by clicking "Analyze".

The following panel illustrates simplified graphical data results:

The areas under the new magenta curves represent the total levels of services lost or gained in units of effective area-time units.

Below is a more detailed summary of the HEA results, automatically generated by the program as a PostScript file:

The analysis indicates that a replacement project of 11.8 acres will provide service gains equal to the services lost in the injured area. Note the significant contribution made by having both the services lost and services gained extend forever into the future in the lines marked "Beyond" in the table above.