I. SCOPE, APPLICABILITY AND PARAMETERS Scope


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1 D Executve Board Annex 9 Page A/R ethodologcal Tool alculaton of the number of sample plots for measurements wthn A/R D project actvtes (Verson 0) I. SOPE, PIABIITY AD PARAETERS Scope. Ths tool s applcable f sample plots are used for montorng purposes. The tool estmates the number of permanent sample plots needed for montorng changes n carbon pools at a desred precson level. Permanent sample plots are to be used because forest nventory nvolves: easurements taken at specfc tme ntervals; Hgh covarance s expected between observatons at successve samplng events.. Permanent sample plots are statstcally effcent n estmatng changes n forest carbon stocks because typcally there s a hgh covarance between observatons at successve samplng events. However, sample plots must be treated n the same way as other lands wthn the project boundary, e.g., durng ste and sol preparaton, weedng, fertlzaton, rrgaton, thnnng, etc., and should not be destroyed over the montorng nterval. Ideally, staff nvolved n management actvtes should not be aware of the locaton of montorng plots. Where local markers are used, these should not be vsble. Applcablty 3. Ths tool s applcable under the followng condton: Varables under consderaton are normally dstrbuted or may be transformed nto a normal dstrbuton. 4. ormal dstrbuton can be assumed when: any small (ndependent) effects contrbute to each observaton n an addtve fashon. Parameters 5. Ths tool provdes procedures to determne the followng parameters: Parameter SI Unt Descrpton n Dmensonless Sample sze (total number of permanent sample plots requred) n the project area Dmensonless Sample sze for stratum n
2 D Executve Board Annex 9 Page II. PROEDURE ethod I (samples drawn wthout replacement) 6. It s assumed that the followng parameters are known from the project set up, preproject estmates (e.g., results from a plotstudy) or lterature data: A Total sze of all strata (A), e.g., the total project area; ha A Q st Index for stratum; dmensonless Total number of strata; dmensonless Sze of each stratum ; ha Sample plot sze (constant for all strata); ha Quantty beng estmated (usually the forest carbon stocks); t ha  Standard devaton of Q for each stratum ; dmenson the same as Q ost of establshment of a sample plot for each stratum ; e.g., US $ then: A = ; A = () axmum possble number of sample plots n the project area axmum possble number of sample plots n stratum 7. The number of sample plots s estmated as beng dependent on accuracy and costs. 8. In addton to the assumptons and parameters lsted under Intal calculatons ), t s further assumed that the followng parameters are known from the project set up, preproject estmates (e.g., results from a plotstudy) or lterature data: Q P then: Approxmate expected value of the estmated quantty Q, (e.g., aboveground wood volume per hectar); e.g., m 3 ha  Target precson for estmaton of Q (e.g., 0%, expressed as a fracton); dmensonless E = Q p () E Allowable error of the estmated quantty Q 9. Wth the above nformaton, the sample sze (mnmal number of sample plots to be establshed and measured) can be estmated as follows:
3 D Executve Board n = = st E z + = = st Annex 9 Page 3 (3) n Sample sze (total number of sample plots requred) n the project area z /,, 3, project strata  s probablty that the estmate of the mean s wthn the error bound E Value of the statstc z (embedded n Excel as: nverse of standard normal probablty cumulatve dstrbuton), for e.g.,  = 0.05 (mplyng a 95% confdence level) z / = The value n calculated accordng to formula () s the mnmal number of sample plots that allows the estmate of the mean to be wthn the error bound E wth probablty . Ths value s optmal n such sense that t mnmzes the sum of costs of establshment and the mantenance of sample plots. The data on costs may be approxmate, but shall reflect relatve dfferences of costs among strata. st = n = E + z = st (4) n z / Sample sze for stratum,, 3, project strata  s probablty that the estmate of the mean s wthn the error bound E Value of the statstc z (embedded n Excel as: nverse of standard normal probablty cumulatve dstrbuton), for e.g.  = 0.05 (mplyng a 95% confdence level) z / =.9599
4 D Executve Board Annex 9 Page 4. When no nformaton on costs s avalable or the costs may be assumed as constant for all strata, then: n = E z = st + = (5) n = E z h= st + = st (6) It s possble to reasonably modfy the sample sze after the frst montorng event based on the actual varaton of the carbon stocks determned from takng the n samples. ethod II (samples drawn wth replacement). It s assumed that the followng parameters are known from the project set up, preproject estmates (e.g., results from a plotstudy) or lterature data: A Total area of all strata (.e., the total project area); ha A st Index for a stratum; dmensonless Total number of strata; dmensonless Area of each stratum ; ha Standard devaton of the estmated quantty Q for each stratum ; dmenson the same as Q ost of establshment of a sample plot for each stratum ; e.g., US $ Q Approxmate expected value of the estmated quantty Q, on a per plot bass (e.g., m 3 aboveground wood volume per plot); e.g., m 3 p then: Desred level of precson (e.g., 0%, expressed as a fracton); dmensonless = A A (7)
5 D Executve Board Annex 9 Page 5 Share of area of stratum n the project area A and: E = Q p (8) E Allowable error of the estmated quantty Q 3. The number of permanent samplng plots for montorng of an A/R D project actvty may be estmated by means of the followng approxmate formula accordng to Wenger (984): tn, n = st st E = = (9) st n = n st h= (0) t n, Student s tdstrbuton value for a confdence level  (e.g. for =0.05 the confdence level equals 95%) and n degrees of freedom E Absolute value of allowable error per plot (e.g., m 3 ) 4. The standard devaton of each stratum (st ) can be determned through ex ante estmates of varance of carbon stock n pools consdered by the methodology. Student s tdstrbuton value for 95% confdence level s approxmately equal to when the number of sample plots s over 30. As the frst step, use as the t n, value and f the resultng n s less than 30, use the new value of n to get a new t n, value (from statstcal tables or the embedded functon n Excel  nverse of Student s tdstrbuton) and conduct a recalculaton. Ths teratve process shall be repeated untl the calculated value of n s stablzed. 5. It s good practce to reasonably modfy the sample sze after the frst montorng event based on the actual varaton of the carbon stock changes determned from takng the n samples. If modfed sample sze s smaller than the ntally estmated one, then the measurements shall be contnued on all sample plots ntally dentfed; If modfed sample sze s greater that the ntally estmated one, then the relevant number of new sample plots shall be parttoned among the project areas of land proportonally to number of already establshed sample plots. The new sample plots shall be dstrbuted n approxmately unform way over the areas of land and located n centers of cells of the exstng sample plot grd. Wenger, K.F. (ed) Forestry handbook (nd edton). ew York: John Wley and Sons.
6 D Executve Board Annex 9 Page 6 Sample plot sze (for both methods) 6. The plot area has major nfluence on the samplng ntensty and tme and resources spent n the feld measurements. The area of a plot depends on the stand densty. Therefore, ncreasng the plot area decreases the varablty between two samples. Accordng to Freese (96), the relatonshp between coeffcent of varaton and plot area can be denoted as follows: V = V () where and represent dfferent sample plot areas and ther correspondng coeffcent of varaton (V). Thus, by ncreasng the sample plot area, varaton among plots can be reduced permttng the use of small sample sze at the same precson level. Usually, the sze of plots s between 00 m for dense stands and 000 m for open stands. Determnng plot locaton (for both methods) (a) It s recommended that permanent sample plots be located usng the approach of algned systematc samplng. In ths approach a grd s lad over the entre project area, and the centre ponts of a permanent sample plots are taken as those grd ntersecton ponts that fall wthn a stratum. The grd shall have a random orgn (.e. the orgn s a randomly selected set of map coordnates), and optonally a random orentaton (a randomly selected compass orentaton); (b) To obtan the correct number of permanent sample plots n each stratum, vary the spacng of the grd (the dstance between grd ntersectons) untl the necessary number of grd ntersectons n a stratum s obtaned. It s not necessary to retan the same grd spacng for each stratum; however the same orgn and orentaton should be retaned for the grd; (c) Havng assgned the centre ponts of the permanent sample plots usng the above procedure, t s possble that, due to nherent and unavodable uncertanty n mappng and/or sample plot locaton, durng sample plot nstallaton part of a sample plot may be found to fall outsde of the area that s forested. In ths case, move the plot centre towards the centre of the parcel of land such that the outer edge of the plot concdes wth the estmated poston of the outer edge of the forest canopy at tree maturty. The drecton of movement of the plot centre shall be at rghtangles to the edge of the parcel of land; (d) Suffcent sample plots should always be allocated to a stratum so that t s possble to omt any sample plots that prove to be naccessble whle stll mantanng the mnmum number of sample plots calculated n Secton II. or II Freese, F. 96. Elementary Forest Samplng. USDA Handbook 3. GPO Washngton, D. 9 pp
7 D Executve Board Annex 9 Page 7 Hstory of the document Verson Date ature of revson(s) 0, Annex 9 5 arch 009 Further clarfcaton of practcal aspects on locaton of permanent sample plots for data collectng and mprovement n clarty of formulae 0 EB 3, Annex 5 04 ay 007 Intal adopton.
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