Visual_HEA: Haia Equivalency Analysis sofware o calculae compensaory resoraion following naural resource inury Kevin E. KOHLER * and Richard E. DODGE Naional Coral Reef Insiue, Nova Souheasern Universiy Oceanographic Cener, 8 Norh Ocean Drive, Dania Beach, FL 334, USA * Corresponding auhor: K.E. Kohler Tel.: 954-262-3641, Fax: 954-262-4158, e-mail: kevin@nova.edu Asrac Haia Equivalency Analysis (HEA) is a means o deermine he amoun of compensaory resoraion required o provide services ha are equivalen o he inerim loss of naural resource services following an inury. HEA includes a discouning procedure o accoun for asse valuaion in ha he oal asse value is equal o he discouned value of he fuure sream of all services from he naural resource or he compensaory resource. Discouning is used o include he relaive valuaion of loss and gain of ecological services of he resources over ime. Visual_HEA is a compuer program developed o calculae he amoun of compensaory resource services ha would e required o mach hose los following an inury o naural resources. The program acceps inpu of parameers necessary o deermine long-erm service loss from he inury and long-erm service gain from he desired compensaory resoraion acion. HEA resuls are highly dependen upon assumpions, and consequenly i is useful o examine sensiiviy of resuls o a range of parameer values. Visual_HEA offers an inuiive graphical inerface ha allows he user o inpu or modify inpu parameers and hence quickly creae or aler he los and gain service level shape funcions. The ailiy o calculae resuls of many scenarios allows ready comparisons ha may assis in deerminaion of he mos appropriae compensaory acion. Keywords haia equivalency analysis, ecosysem resoraion, ecosysem models, cos-enefi analysis, sofware Inroducion Because of pervasive degradaion of coral reefs gloally as a resul of oh naural and anhropogenic causes, here has een a urgeoning ineres in mehods ha could resore reefs. One of he ways ha has een used in he Unied Saes has een o aemp o deermine he naure and degree o which a resoraion proec migh provide adequae replacemen for an inured resource via Haia Equivalency Analysis (Dunford e al. 24; ilon and Dodge 21; azzoa e al. 1994; Unsworh and Bishop 1994) In overview, Haia Equivalency Analysis (HEA) is a means o deermine he amoun of compensaory resoraion required o provide services ha are equivalen o he inerim loss of naural resource services following an inury. HEA uses a discouning procedure o accoun for asse valuaion in ha he oal asse value is equal o he discouned value of he fuure sream of all services from he naural resource or he compensaory resource. Discouning is used o deermine he relaive valuaion of he loss and gain of ecological services of he resources over ime relaive o ime of analysis. Therefore, he HEA approach is paricularly well suied for analysis ecause i can e used o quanify he amoun of loss and gain of resources and services over ime. We have developed a compuer program, Visual_HEA, ha acceps inpu of user-defined parameers represening HEA assumpions relaed o loss of services from a naural resources inury and gain of services from a desired compensaory acion. Visual_HEA illusraes many of he parameers graphically and calculaes he amoun of compensaion required o offse he loss of services. I is he purpose of his paper o descrie he feaures of his program. The reader should refer o he Haia Equivalency Analysis references given aove for more informaion on he HEA procedure. Visual_HEA does no provide exhausive opions for all HEA coningencies, ye many of he more common ariues commonly required y users have een incorporaed, and herefore should e useful o a wide range poenial user applicaions. Program resricions are idenified in his paper. Fuure releases of he sofware will hopefully address some of hese resricions. HEA ehodology The following is an overview of he HEA mehodology used in he Visual_HEA program. The same or similar naming convenions as found in NOAA (1995, 2) are employed. In order o mee lengh resricions of he Proceedings, he reader is direced o 1611
hese references for a more deailed discussion of inpu parameers and mehodology. To perform an HEA analysis, a variey of inpu parameers are required. Each of hese quaniies is descried elow. Relaive value of pre-inury services and compensaory (a equilirium) services. These parameers indicae he value per area of services provided oh a he inury sie (pre-inury) and a he resoraion sie. In his formulaion of he Visual_HEA program, he relaive values are held consan hroughou he analysis. Baseline levels of services. These percenage values indicae he level of services eing provided y he inury sie prior o inury and he level of services provided y he resoraion sie prior o any resoraive acion. Tha is, in he case of he inury sie, he aseline represens he level of services ha would have een provided y he sie had inury no occurred. For example, he aseline level of services of a haia prior o inury migh e considered o e 1% (full services) or a some lower value depending upon he condiion of he haia. The services level provided y he resoraion sie immediaely prior o resoraion acion migh e % (no services) or migh e some higher value again depending upon he condiion of ha haia. For he purposes of he curren configuraion of Visual_HEA, hese aseline levels are considered ime-invarian hroughou he ime of analysis. Discoun rae. This parameer incorporaes he assumpion ha services provided sooner are more highly valued han hose provided laer. Since service losses and gains occur a differen imes, hey mus e adused in order o e direcly compared. This adusmen is accomplished using a discoun facor which decreases he value of fuure services and increases he value of pas services in order o reflec how much he pulic values fuure (or pas) service enefis oday. This discoun rae is specified as a percenage rae per ime uni. Year of claim. This is he year in which he claim is eing made. The claim could e in a legal sense or, more generally, simply as an anchor poin in ime. The HEA calculaions use he claim year as he reference poin in calculaing discouned service levels, i.e., he discoun level a his year is 1.. loss parameers from he inury. This includes he size of he inury area and he ime hisory of he loss of services a he inury sie, i.e. he duraion and level of service loss from ime of inury hrough naural or assised recovery, if any. gain parameers from he compensaory acion (resoraion). This includes he ime hisory of service levels of he compensaory acion, i.e., he duraion and levels of services gained from iniiaion of he compensaory acion hroughou is persisence. HEA resuls are highly dependen upon he inpu parameers descried aove. I is herefore ofen useful o calculae resuls using a range of parameer values. Visual_HEA sofware faciliaes muliple runs y offering a graphical user inerface where he user can easily modify inpu parameers and he ime srucure of he service loss and gain shape funcions. The ailiy o formulae and deermine he resuls of many scenarios can provide an indicaion of he sensiiviy of he required compensaory acion scale o various inpu parameers. The relevan variales required for performing HEA analysis are shown in Tale 1. Time variales = Time when inury occurs Time when inured area recovers o = B aseline levels = C Time when he claim is presened = I Time when he haia proec = egins o provide services Time when he haia replacemen proec reaches full mauriy Time when he haia replacemen sops yielding services = L Oher variales V value per area-ime of services provided y inured haia V value per area-ime of services p provided y replacemen haia level of services provided y inured x haia a end of ime he pre-inury aseline level of services per area of inured haia p level of services provided y x replacemen haia a end of ime p iniial level of services per area of replacemen haia discoun facor, where ρ ( ) ( C ) ρ = 1/ 1+ r, r=discoun rae per ime uni J numer of inured area unis size of compensaory replacemen P proec Calculaed quaniies ( x ) Exen of inury a ime p p ( x ) Incremen in services provided y replacemen proec ( x percen reducion in services per area for inured area, relaive o he inury sie aseline level of services p p ( x percen increase in services per area for replacemen sie, relaive o he inury sie aseline level of services Tale 1. Parameers used in Haia Equivalency Analysis The ulimae goal of Haia Equivalency Analysis is o solve for he size of he compensaory replacemen proec P. To accomplish his, he sum of he presen 1612
value of services los as a resul of he inury is se equal o he presen value of he services provided y he replacemen proec: B L p p V ( x J = V p ρ ( x P = ρ (1) = I I is useful o define wo quaniies, λ and γ which represen he discouned effecive area los and he discouned effecive service gain per uni area, respecively. They are given y: J ( x p p ( x λ = ρ (2) γ = ρ (3) The unis of λ are in area unis, while γ is nondimensional. If V and V p are considered ime invarian, P can hen e solved for as: P ( x ) B B ρ / * J V = V = = = L L Vp p p Vp ρ ( x γ = I = I There are wo special cases o e addressed: 1) when he service levels a he inury sie never aain heir preinury aseline levels and 2) when here is no ime limi when he resoraion haia sops yielding services. ahemaically, his is equivalen o oh B and L approaching infiniy. For hese cases, Visual_HEA gives he user he opion of having he service levels of eiher or oh of he inury sie and resoraion sie remain in perpeuiy. This requires adding on he amoun of services gained or los from he ime of mauriy () o infiniy. In he case where V and V p are ime-dependen, he user has o run he analysis far enough such ha he muliplicaive discoun facor renders addiional erms insignifican. However, in he case where V and V p are considered ime invarian, he addiional erm can e calculaed as follows. (The derivaion given elow is for services los a he inury sie. A similar echnique can e used for he resoraion sie). Define S o e he addiional erm o e calculaed, i.e. he conriuion o he sum of services los due o perpeuiy. ' = V J ( m c m= + 1 (1 + r) x ) λ (4) S (5) Define he erm S ( x ) = V J c (1 + r) This erm is he conriuion o he discouned effecive area a ime =. Grouping addiional ime-independen erms in (5) yields: (6) ( x ) 1 m S' = V J = S α c m (1 + r) m= 1 (1 + r) m= 1 1 α =. (7) 1 + r where Dividing each side of (7) y α yields: S' = α S m= α Suracing (7) from (8) yields: 1 S '( 1) = α m S or S S = r (8) ' (9) Thus, for ime-independen values of V and V p, he conriuion due o perpeuiy can e exacly deermined. This is he form used in he curren version of Visual_HEA. Case Sudy o Illusrae Use of Visual_HEA: Calculaing he Amoun of Nearshore Compensaory Acion for Beach Renourishmen Inury o a Coral Reef Communiy A eer undersanding of he parameerizaion and operaion of Visual_HEA can e faciliaed y discussion of a relaively simple case sudy (alhough more complex cases are possile). This case sudy is a plan for he renourishmen of eaches ha anicipaes covering 1.1 acres (4.1 ha) of nearshore hardground coral reef communiy haia wih sand used for each renourishmen. Assume local governmen proposed o provide miigaion (compensaory acion) in he form of limesone oulders as haia in order o compensae for he loss of he 1.1 nearshore reef haia acres (4.1 ha). An HEA was performed o calculae amoun of he compensaory acion ha would e needed. In order o complee he HEA, various assumpions were made aou he loss of services of he hardground acres o e covered and he gain of services from he compensaory acion, he discoun rae, and he sar imes and amouns of los and gained services of he inury and compensaory resoraion. Assumpions included he following: General program parameers: Relaive value of los and gained services I was assumed ha he raio of he value of services of he inury area (pre-inury) versus for he compensaory acion (afer i reaches full services) was 1.. This assumpion means ha he value of services per acre of he nearshore hardoom communiy efore inury was equal o he value of services per acre provided y he oulders a he resoraion sie. This doesn have o e he case for all formulaions. One migh imagine compensaory acions which would only evenually provide half he services of he pre-inury aseline. In such a case, he appropriae raio would e 2.. 1613
Discoun rae The hisorical value of 3% was used. Specific program parameers: Exen of inury and loss of services of he nearshore reef hardground The nearshore inury egins in 23 2% of he 1.1 acres (4.1 ha) was los immediaely when sand was placed in 23 1% of he 1.1 acres (4.1 ha) was los 3 years laer in 26 1% loss of he 1.1 acres (4.1 ha) coninues in perpeuiy (i.e., he haia remains sand covered forever) I was assumed ha he iniial placemen of he renourishmen sand on he each in 23 would cover only aou 2% of he associaed nearshore hardoom. As he each sand equiliraed o he naural wave climae, i was assumed he coverage of he hardoom would exend o 1% of he 1.1 acres (4.1 ha) afer 3 years in 26. I was conservaively esimaed ha he 1.1 acres (4.1 ha) would remain covered ad infinium. (I is possile ha he nearshore acreage would e uncovered y each erosion wihin decades. Such an evenualiy could e facored ino he HEA hrough appropriae node placemen. For example 1% loss migh end afer 2 years in 226 whereupon naural recovery migh egin). s gained y he compensaory acion (miigaion oulders) The compensaory acion (miigaion) also egins a he same ime in 23. 1% of services gained upon ransplanaion of sony corals (from he area o e inured) older han 15 years ono oulders in 23. The oulders are assumed o e ransplaned immediaely and so he 1% services gain is also immediae. 1% full services reached afer 15 years in 218 1% full services coninues in perpeuiy. I was assumed ha while he miigaion oulders will recover o 1% full services in 5 years naurally, hey will recover o 1% full services in less ime (15 years) y ransplaning corals ono hem. 15 years was chosen ecause all corals greaer han 15 years old were o e removed from he area slaed for inury. These would e used for ransplanaion. By ransplaning corals, he miigaion oulders will egin recovery no a % of full services, u a some higher value. A level of 1% immediae gain of services was assigned. (This analysis assumed ha he oulders would reach services of 1% and ha hese services would persis forever. Oher assumpions migh have included ha oulder services would only reach some level less han full services or ha he oulders would only persis for a finie ime period, e.g., ioerosion migh e invoked o desroy he oulders in 5 years a 253, hence eliminae any services provided eyond ha ime.) HEA Program Operaion The HEA program inerface consiss of a single main form. To perform an analysis, he following iniial informaion mus e enered (Tale 2). Values used in he case sudy are provided in he righmos column. Parameer: Explanaion Sie name: name of analysis sie, analysis, ec Presen year: year of analysis. This gives he reference ime from which discouned service losses and gains are calculaed. Numer of inured area unis: size of inury sie in spaial unis Raio of inured/resored service values: relaive value of los versus gained services per ime-area uni Discoun rae (%) per ime uni: amoun of discouning o reflec he relaive value of presen versus fuure service levels Pre-inury service level: level of services provided y he inured area prior o inury Iniial compensaory service level: level of services provided y he compensaory acion area a he onse of he compensaory acion Area and ime unis loss display years: ime span of service loss o e displayed on he graphs (and o have as discree calculaion resuls in he prinous gain display years: ime span of service gain o e displayed on he graphs (and o have as discree calculaion resuls in he prinous Case sudy parameer value Beach Renourishmen 23 1.1 1. 3% 1% 1% acres, years 22-22 22-22 Nodes of service gain and loss Inury: s a 8% in 23 and % a 26 (coninues in perpeuiy). Compensaory acion: s a 1% in 23 and 1% 15 years laer in 218 (coninues in perpeuiy). Tale 2. Explanaion of HEA parameers and values used in he case sudy. The recovery imes and service levels for oh he inured sie and he compensaory acion mus e specified y placing nodes along he ime axis which represen he level of services provided a a given ime. This can e done eiher direcly hrough he graphical inerface or manually y insering he service level and ime values ino a pop-up dialog ox. In is presen form, Visual_HEA allows only a linear recovery funcion eween specified nodes. General curvilinear shapes can e specified y muliple closely-spaced nodes. (Laer versions of Visual_HEA may incorporae addiional recovery funcions, e.g. quadraic or exponenial). The ease of placing and moving he service level nodes allows differen scenarios o e quickly visualized and analyzed. Scenarios can e saved for laer analysis y clicking he Save HEA daa uon. Fig. 1 shows a Visual_HEA panel of daa inpu for he each renourishmen proec case sudy descried aove: 1614
The analysis indicaes ha a compensaory replacemen proec of 11.8 acres (4.8 ha) will provide service gains equal o he services los over ime in he inured area. The shaded areas in each panel of Fig. 3 shows he acual amoun of services los and gained over ime in a graphical form. The upper plo is a graph of λ, while he lower panel is a plo of γ. The plos span he period from 22 212 in order o show how he effec of discouning provides a closure mechanism for he shaded areas. Acual closure occurs a infiniy. Fig. 1. A screensho of he main form of Visual_HEA. General program parameers are enered in he op secion, and he ime hisory shape funcions of los and gained services are enered on he wo graph areas elow. Afer he iniial parameers and he recovery funcion informaion have een specified, he analysis can e performed y clicking Analyze. The resuls are displayed in an inser laeled HEA resuls placed aove he upper panel graph, as shown in Fig. 2. Fig. 2. A screensho of he resuls secion of Visual_HEA. Fig. 3. Graphs of discouned effecive services los (upper panel) and discouned effecive services gained per uni area (lower panel). In order o see he yearly calculaion deails, he Deails uon is clicked. A new window appears, displaying he values of λ and γ for each year of analysis. Tale 3 shows a summary of hese yearly values. Year % Level s los a he inury sie % Loss Effecive area los (acre) Discoun Facor Discouned effecive area los (acre) s gained a he compensaory sie Year % Level % Increase Discoun Facor Discouned effecive area los (acre) 22 1... 1.3. 22.. 1.3. 23 53.33 46.67 4.713 1. 4.713 23 16. 16. 1..16 24 26.67 73.33 7.47.971 7.191 24 22. 22..971.214 25. 1. 1.1.943 9.52 25 28. 28..943.264 26. 1. 1.1.915 9.243 26 34. 34..915.311 27. 1. 1.1.888 8.974 27 4. 4..888.355 28. 1. 1.1.863 8.712 28 46. 46..863.397 29. 1. 1.1.837 8.459 29 52. 52..837.435 21. 1. 1.1.813 8.212 21 58. 58..813.472 211. 1. 1.1.789 7.973 211 64. 64..789.55 212. 1. 1.1.766 7.741 212 7. 7..766.536 213. 1. 1.1.744 7.515 213 76. 76..744.566 214. 1. 1.1.722 7.296 214 82. 82..722.592 215. 1. 1.1.71 7.84 215 88. 88..71.617 216. 1. 1.1.681 6.878 216 94. 94..681.64 217. 1. 1.1.661 6.677 217 1. 1..661.661 218. 1. 1.1.642 6.483 218 1. 1..642.642 219. 1. 1.1.623 6.294 219 1. 1..623.623 22. 1. 1.1.65 6.111 22 1. 1..65.65 Beyond 23.689 Beyond 2.167 Toal discouned effecive acre-years los: 338.765 Toal discouned effecive acre-yrs/acre gained: 28.763 Replacemen haia size (acres): 11.778 Tale 3. Resuls from he HEA case sudy of Beach Renourishmen proec 1615
In he summary window, opions are provided o save hese daa in one of wo formas. The daa can e saved as a ex file ha can e impored ino word processing sofware. Also, a PosScrip file can e creaed, which can e convered o.pdf forma using sofware such as Aode Disiller. The PosScrip file conains a graph of he ime hisory shape funcions of los and gained services, as well as yearly aulaions of λ and γ. Discussion The assumpions made regarding he ime hisory of los and gained services form he core of HEA calculaions. Visual_HEA allows he user o quickly modify hese ime hisories and analyze various inury and compensaory scenarios. When specifying he ime hisory of he inury and compensaory acion, an imporan assumpion in he HEA is wheher or no he services los or gained coninue in perpeuiy. This assumpion can have a significan effec on he calculaed size of he replacemen sie. For example, in he case sudy assume all as aove, u ha he compensaory acion egins degrading 1 years afer reaching full services (in 228) and services cease compleely 1 years laer in 238. The compensaory acion required for his case is 23.6 acres (9.6 ha), versus he 11.8 acres (4.8 ha) required previously. This is ecause he compensaory acion provides gained services which las only a finie amoun of ime, and hence more compensaory area is required o alance he loss of services. The opposie siuaion arises when here is recovery a he inury sie. In his case, he amoun of los services is less, and hence less compensaory acion is required o offse hese losses. When using Visual_HEA, i is imporan o e aware of he convenions used regarding he placemen of nodes. When placing a node a a given ime, e.g. year, he ic marks on he ime axis indicae he eginning of he corresponding year lael. Also o e noed is he fac ha he compensaory summary deails give he amoun of los and gained services a he end of any given year, as is cusomary in exising HEA lieraure. I is possile o use quarer-years insead of years as he ime uni for Visual_HEA. The imporan iem o rememer is he user should adus he discoun rae inpu value per ime sep so as o mainain he desired annual discoun rae. For he case sudy, a landscape HEA has een applied o resource inuries. This is useful for relaively uniform landscapes wih lile difference in iological funcions across he inured area. A populaion HEA approach (ilon and Dodge 21) could also have een considered where he oal inury area would have een allocaed ino porions ased on a percen conriuion of organism caegories of ineres. An individual HEA would hen have een performed for each appropriae caegory using is allocaed area. The curren version of Visual_HEA conains limiaions which he auhors may e ale o address in fuure released versions if here is demand. Among hese are ime-dependen values for V and V p, non-linear ime recovery funcions, and monhly or oher imeseps. Summary Visual_HEA is a compuer program ha faciliaes inpu of HEA assumpions and parameers and calculaes he compensaory acion required for a given se of assumpions aou inury and compensaion. The program allows inpu of he relevan parameers necessary for analysis, and hrough he use of an inuiive graphical inerface, he inpu parameers and recovery funcions can e quickly changed. The ailiy o formulae many scenarios using he graphical inerface is useful o evaluae alernaive compensaion sraegies. Fuure work includes adding more sophisicaed capailiies o several aspecs of he program, including non-linear ime recovery funcions and addiional imesep opions. Acknowledgemens We would like o hank anonymous reviewers for heir helpful commens which improved he manuscrip. This work is a resul of research funded y he Naional Oceanic and Amospheric Adminisraion Coasal Ocean Program under award #NA3NOS42646 o Nova Souheasern Universiy for he Naional Coral Reef Insiue (NCRI). This is NCRI conriuion No. 64. References Dunford RW, Ginn TC, Desvousges WH (24) The use of haia equivalency analysis in naural resource damage assessmens. Ecol Econ 48 (1): 49-7. azzoa J, Opaluch JJ, Grigalunas TA (1994) Naural resource damage assessmen: The role of resoraion. Na Resour J 34 (Winer): 153-178. ilon JW, Dodge RE (21) Applying haia equivalency analysis for coral reef damage assessmen and resoraion. Bull ar Sci 69 (2): 975 988. NOAA (1995) Haia Equivalency Analysis: An Overview. NOAA Damage Assessmen and Resoraion Program, Policy and Technical Paper Series, No. 95-1, (Revised 2). NOAA (1997) Scaling compensaory resoraion acions, guidance documen for naural resource damage assessmen under he Oil Polluion Ac of 199. Damage Assessmen and Resoraion Program. Unsworh RE, Bishop RC (1994) Assessing naural resource damages using environmenal annuiies. Ecol Econ 11: 35-41. 1616