Recent advances in research on gene drives have produced genetic constructs that could theoretically spread a desired gene (payload) into all populations of a species, with a single release in one place. This attribute has advantages, but also comes with risks and ethical concerns. There has been a call for research on gene drive systems that are spatially and/or temporally self‐limiting. Here, we use a population genetics model to compare the expected characteristics of three spatially self‐limiting gene drive systems: one‐locus underdominance, two‐locus underdominance and daisy‐chain drives. We find large differences between these gene drives in the minimum release size required for successfully driving a payload into a population. The daisy‐chain system is the most efficient, requiring the smallest release, followed by the two‐locus underdominance system, and then the one‐locus underdominance system. However, when the target population exchanges migrants with a nontarget population, the gene drives requiring smaller releases suffer from higher risks of unintended spread. For payloads that incur relatively low fitness costs (up to 30%), a simple daisy‐chain drive is practically incapable of remaining localized, even with migration rates as low as 0.5% per generation. The two‐locus underdominance system can achieve localized spread under a broader range of migration rates and of payload fitness costs, while the one‐locus underdominance system largely remains localized. We also find differences in the extent of population alteration and in the permanence of the alteration achieved by the three gene drives. The two‐locus underdominance system does not always spread the payload to fixation, even after successful drive, while the daisy‐chain system can, for a small set of parameter values, achieve a temporally limited spread of the payload. These differences could affect the suitability of each gene drive for specific applications. This abDrosophila with the new constructs  and have relatively low levels of fitness cost. However, we also adapt our model for an initial comparison of these gene drives when the goal is to suppress a population. We find large differences in the efficiencies as well as the levels of localization of the three gene drives. We discuss the relative suitability of the different gene drives for applications in different scenarios.2We use population genetic models to separately simulate the spread of a desired “payload” allele with each of the three types of gene drive in an isolated diploid population. We also compare the within and among population spread of the payload allele by the three gene drives when the target population exchanges migrants with a neighboring population.sp, while the cost to heterozygotes is modified for specific dominance patterns of the payload allele. We show results in the main text only for multiplicative cost of the payload allele. Results with additive, recessive and dominant payload costs are provided in the online Appendix We follow the spread of the payload allele after a single initial introduction of individuals homozygous for the complete drive constructs into the target population. The payload allele fitness cost can be varied depending upon whether the gene drive is intended for population suppression or for population replacement. The fitness cost associated with being homozygous for the payload allele is given by We model a life cycle with nonoverlapping generations. We assume that the population is very large, and model only gene frequency‐based dynamics (no multigeneration density‐dependent dynamics). The gene drives addressed here differ in the mechanisms that result in their spread in a population—the daisy‐chain drive relies on homology‐directed repair (HDR) following double‐stranded breaks in the DNA, while the underdominance drives use lower fitness  of transgene‐wild‐type heterozygotes for their propagation. The variation in genotypic fitnesses caused by these driving mechanisms results in natural selection. The payload allele may further add to variation in genotypic fitnesses. In our model, natural selection due to the drive mechanism and due to the fitness costs imposed by the payload allele occurs in immature stages or in adults before reproduction. Migration occurs after natural selection and is followed by reproduction within a population. Individuals in our model mate randomly with respect to the alleles at the gene drive loci. Offspring are produced following free recombination.2.1Below we describe the structure of the three gene drives that we compare. The constructs used to build each of the gene drives can be modified to exhibit a large variety of properties, such as tissue‐specific or sex‐specific patterns of expression, condition‐dependent fitness costs. For the comparative analysis here, we mainly model the basic forms of these gene drives. But, for the comparison of the capacity for population suppression, we model these drives with female‐limited payload gene expression. We also assume that the payload allele is carried at only one locus and has the same phenotypic expression with each gene drive.2.1.1A is driven by a second, independently segregating allele at locus B, which in turn is driven by a third independently segregating allele at locus C  and are haplo‐insufficient. This design, in combination with the multiple double‐stranded cuts, is expected to reduce the likelihood of appearance of genotypes that are resistant to the drive mechanism  and a wild‐type allele (represented by subscript “w”). The Bt allele is dominant and drives the At allele by making multiple double‐stranded cuts at all copies of the wild‐type Aw allele . In heterozygous cells, the cut at the Aw allele can be repaired through homologous recombination (homology‐directed repair or HDR) using the uncut At allele as a template, thus rendering the cell homozygous for the At allele after repair. Similarly, the Ct allele is dominant and converts BtAw heterozygotes to BtBt homozygotes. HDR can occur only in heterozygotes. Homozygotes for the wild‐type allele at locus A and B can only be repaired through nonhomologous end joining (NHEJ) that would result in a deletion at the location of the multiple cuts, resulting in nonfunctional alleles.Following Noble et al. , there aAt allele includes a payload gene sequence. This payload can alter an individual's characteristics  or decrease fitness. The drive components of the transgenic alleles at the B and C loci are, by design, only expressed in germline cells, so that homing only occurs in the germline. It is assumed that even a single copy of a Bt allele always results in complete cutting of all Aw alleles in the cell . Similarly, a Ct allele always cuts all copies of the wB allele. The frequency of successful HDR after a wild‐type allele is cut is referred to as “homing efficiency” and is denoted by the parameter H. In the absence of HDR after a cut, NHEJ results in a nonfunctional allele and the germline cell fails to produce gametes (or produce gametes that fail to produce viable offspring) due to haplo‐insufficiency of the genes. An individual with genotype AtAw and at least one copy of the Bt allele would thus lose a fraction (1‐H) of its functional gametes and only produce H functional gametes relative to an individual that does not have any cuts occurring. BtBw individuals pay a similar cost when they also inherit a copy of the Ct allele. As in Noble et al. .In the 3‐element daisy‐chain drive, the e et al. , the cosH) of 95% throughout, unless noted otherwise.The CRISPR‐based gene drives have been shown to exhibit homing efficiencies as high as 99%  occurs at each locus. The terms σ and τ modify the equation to account for whether cutting occurs at a loci B and A, respectively, and also whether a transgenic template is available for HDR when cutting does occur. The modifiers θ and ε modify the cost of inefficient homing for zero, one or two loci. Their values for the different genotypes arewhere sp. Here, we describe genotypic fitness assuming multiplicative cost of the payload. Equations for other patterns of payload costs are given in Appendix AxByCz, which is attributed to the payload allele, is given byAs mentioned previously, the payload allele confers a homozygous fitness cost where AxByCz after selection due to the drive mechanism and due to the payload allele is then given by the product,The relative fitness of a genotype In the analyses shown here, we assume that the nonpayload transgenic alleles do not impose any direct fitness costs, besides the costs that arise through the drive mechanism. Analyses with additional fitness costs of the nonpayload elements are provided in Appendix 2.1.2Davis et al.  describeThe one‐locus underdominance drive is modeled to consist of two engineered constructs, each of which is composed of four tightly linked elements—i) a gene coding for a lethal toxin, ii) a cis‐promoter for the toxin gene, iii) a suppressor specific for the other construct's promoter and iv) a payload gene Figure a.A.” The two constructs are referred to as alleles A1 and A2. Wild‐type alleles at the locus A are denoted as A0. Individuals that inherit one copy of each transgenic allele (genotype A1A2) are viable, because the suppressor on each construct blocks the cis‐promoter on the other allele, thus preventing the production of the toxin  are not viable, as the toxin is not suppressed. Wild‐type homozygotes (genotype A0A0) are, of course, viable. The expression of the toxins on each construct can be timed to occur at any desired life stage. The payload allele confers a multiplicative fitness cost of sp when homozygous. Note that for the one‐locus underdominance drive, the multiplicative cost pattern is indistinguishable from other dominance patterns (such as additive or dominant costs) because heterozygotes are not viable. The relative fitnesses of the different diploid genotypes for the one‐locus underdominance system are given in Table The elements within each construct are tightly linked by design, and therefore each construct can be modeled as an allele at a single locus “A,” and locus “B” carries the second construct. Each of the loci can thus have either a transgenic allele (denoted by subscript t) or a wild‐type allele (denoted by the subscript w), with the allele At representing construct 1 and allele Bt representing construct 2. It is assumed that even one copy of a suppressor (heterozygous state at one of the loci) is sufficient to block all copies of the corresponding promoter on the other construct . The island is modeled to receive an influx of wild‐type emigrants at a rate given by the parameter 2.2.2In reality, migration is rarely completely unidirectional. To compare the level of localization of the different gene drives, we also analyze a scenario with bidirectional migration between the target population and a neighboring population of similar size.μ” is equal in both directions, that is, the same fraction of individuals migrate out of each population. When both populations have an equal number of fertile adults before migration, a fraction μ of each population after migration in each generation is composed of migrants from the other population. This population of emigrants and residents would form the breeding adult population in each generation.We assume that the base migration rate “μT for migration into the target population and μN for migration into the neighboring population. These effective immigration rates are functions of the base migration rate and the relative genetic load on the two populations in a given generation. The genetic load represents a reduction in the population size from birth to fertile adults. The ratio of the sizes of the two fertile adult populations in a given generation then is given byAlthough we assume that the two populations initially have equal sizes, the fitness costs imposed by the gene drive can cause genetic load on the population and reduce the fertile adult population size within a generation. If the two populations differ in size, this would lead to an asymmetry in the effective migration rate, or the immigration rate, because more individuals would leave the larger population than the smaller population . This assumption is justified when density‐dependent compensation occurs through changes in offspring production or density‐dependent offspring survival. We recognize that such compensation may not be effective when the genetic load is extremely high. A more accurate estimation of the changes in the sizes of the two populations across generations would require explicitly incorporating density‐dependent population dynamics, which would depend upon the species‐specific ecological details  irrespective of the genetic load on each population. This does not qualitatively change the results described below (see Appendix 2.3X1X1) are introduced (see description above). For the two‐locus underdominance and the daisy‐chain drive, individuals homozygous for the gene drive are introduced. Our goal is to compare the efficiency of the three gene drives in spreading the payload allele into the target population, the level of localization of the payload allele to the target population , and the degree of permanence of the payload gene in the targeted population. To this end, we calculate the mean frequencies  of the payload allele in both the target and the neighboring populations in the first 100 generations after the initial introduction . These mean frequencies are used for comparing the level of population alteration caused by the different gene drives in the target and the neighboring populations. The mean payload allele frequency gives a better measure of the fraction of population altered within 100 generations compared to the equilibrium frequency, especially when alteration may be temporary (see Results). For organisms such as mosquitoes in the tropics, 100 generations would correspond to approximately a period of 10 years.We simulate the spread of the gene drives after a single initial introduction of transgenic individuals into the target population. For the one‐locus underdominance drive, transgenic heterozygotes .All three gene drives studied here exhibit a threshold for the introduction frequency, below which the drive fails to successfully spread the payload allele into a population. The threshold introduction frequencies are the lowest for the daisy‐chain drive, highest for the one‐locus underdominance drive, with the two‐locus underdominance drive having relatively intermediate threshold introduction frequencies Figure a,b and c−15 of 1) or are eliminated from the population. The daisy‐chain drive can, under a narrow set of conditions . This is because most wild‐type alleles at the A locus  are present in a heterozygous state. Moreover, if the toxin produced by the underdominance drive is lethal during early (pre‐adult) life stages, the equilibrium genotypic frequency of the payload  in the adult population practically reaches fixation (>99.99%). This is because any individuals born homozygous for the wild‐type allele at the A locus would die before reaching adulthood if they also possess a copy of the transgene at the B locus . Depending on when lethality occurs, this difference between the drives can be critical for certain applications, where the maintenance of a few wild‐type alleles in the population may be detrimental.Another important difference between the gene drives is that the daisy‐chain drive and the one‐locus underdominance drive do not have stable internal equilibria for the payload allele frequency. Both the drives either push the payload to near fixation  to fixation with a release of far fewer engineered individuals than are needed for either of the underdominance drives. Compared to the one‐locus system, the two‐locus underdominance drive requires a lower threshold introduction frequency for drive to occur. In addition to the differences in the threshold introduction frequencies required for each gene drive, they also differ in the extent to which they alter an isolated population even when successful drive does occur, which may affect their utility for different applications. The daisy‐chain system does not have a stable internal equilibrium in the scenarios studied here . However, within a very narrow range of fitness costs and release numbers Figure . This prOnce the single‐locus underdominant drive system reaches fixation, eliminating it from an isolated population would require release of a large number of wild‐type individuals, or release of engineered individuals that disable the drive system . Eliminating a two‐locus underdominance drive after it reaches an equilibrium above the threshold introduction frequency would require similar releases. Additionally, over time the intermediate equilibrium frequency could enable recombination events that disable the two‐locus underdominance drive and/or result in breakdown of the payload . The one‐locus underdominance system is the most localized of the three systems and does not spread to the nontarget population, even when the payload cost is 5%. Thus, concern about unintended spread is highest with the daisy‐chain system and lowest with the one‐locus system. It must be noted that we did not examine spread to a secondarily connected population, one that does not exchange migrants with the target population, but does so with the “neighbor” population. One possibility is that as the daisy‐chain system spreads into secondarily connected populations, each subsequently connected population may receive fewer elements of the daisy chain, or receive them at progressively smaller frequencies relative to the payload. However, the equilibrium frequencies for each given element of the daisy chain in the two populations that are modeled here are equal, giving no indication of sequential removal of daisy‐chain elements across populations.In our models, we always assume only a single release of the engineered individuals. Depending upon the specific application, multiple smaller releases, as examined by Davis et al.  and MagoOne factor that may greatly influence the localization of gene drives to target populations is genotype‐dependent variation in migration rates. In our analyses, we assume that the migrating group of individuals is perfectly representative of the source population. If the payload or other components of a gene drive reduce the likelihood of migration for the individuals bearing them, the risk of unintended spread would be greatly reduced compared to the results shown here. Genes that reduce the mobility of organisms, for example, through physical deformities or by reducing desiccation tolerance, may therefore prove ideal for designing gene drives that can reduce population fitness and also have a lower risk of unintended spread.Our analysis of localization in this study was limited to a two‐population scenario, with no heterogeneity between the populations. The dynamics of these gene drive systems would certainly be different in a scenario with a more complex spatial structure with multiple populations spread across two dimensions. For one, the target population may receive more wild‐type immigrants, which may make all three gene drives more difficult to establish in the target population. The exact dynamics would depend upon the particular two‐dimensional pattern of migration between the different populations (e.g., Láruson & Reed, In isolated populations, all three drive systems are able to spread a payload into a population as long as the fitness cost associated with it is low, as could be the case if the payload was built to change a characteristic such as ability to transmit a pathogen. However, if the goal of a release is to suppress an isolated population to very low density or cause local elimination, the daisy‐chain drive with a female‐limited payload cost can be much more efficient than the underdominance drives. Migration in one or two directions is likely to reduce the capacity of the gene drives for suppression, because migration reduces the ability of a gene drive to spread in the target population, and even after successful suppression, migration may restore the population.The general models presented here could be expanded to include more population ecology and structure, and parameters could then be adjusted to fit specific targeted populations. It would also be useful to expand modeling efforts to include economic estimates regarding the financial and time costs involved in development of each of these drive systems. Given the genetic engineering tools available today, the cost for developing a daisy‐chain system is likely to be greater than the costs for developing the underdominance systems. For example, the daisy‐chain system requires that at least two chromosomes be engineered to express multiple guide RNAs and that the targets of the guide RNAs on at least two chromosomes are essential genes that are haplo‐insufficient. Moreover, it must be possible to insert a construct with the replacement haplo‐insufficient gene along with Cas9 and guide RNAs without a substantial fitness cost (Noble et al., Another factor that our analysis does not consider is the evolution of resistance to the gene drives. Wild‐type alleles resistant to CRISPR‐Cas9‐based homing drives can be present in genetically diverse populations and can arise through nonhomologous end joining (Champer, Liu et al., A number of authors and committees have emphasized the need for development of spatially limited gene drive systems (e.g., Gould, Mathematica code for the models will be made available without restriction upon request to the authors. Click here for additional data file.


Star Wars Scroll Illusion is a dynamic version of the Leaning Tower Illusion. When two copies of a Star-Wars-like scrolling text are placed side by side (with separate vanishing points), the two scrolls appear to head in different directions even though they are physically parallel in the picture plane. Variations of the illusion are shown with one vanishing point, as well as from an inverted perspective where the scrolls appear to originate in the distance. The demos highlight the conflict between the physical lines in the picture plane and perspective interpretation: With two perspective points, the scrolling texts are parallel to each other in the picture plane but not in perspective interpretation; with one perspective point, the texts are not parallel to each other in the picture plane but are parallel to each other in perspective interpretation. The size of the effect is linearly related to the angle of rotation of the scrolls into the third dimension; the Scroll Illusion is stronger than the Leaning Tower Illusion for rotation angles between 35° and 90°. There is no effect of motion per se on the strength of the illusion.The  One implication of this principle is that any object that recedes into the distance should be able to create an effect similar to the Leaning Tower Illusion; the leaning tower effect opens a valuable method for studying how we construct a three-dimensional perceptual world from objects in a picture plane.The Leaning Tower Illusion  won firsStar Wars movies. The Star Wars scroll is perhaps one of the most iconic demonstrations of a simple object appearing to move into the distance, and therefore serves to illustrate the generality of the principle underlying the Leaning Tower Illusion. The basic version of the Star Wars Scroll Illusion is shown in Here, I reproduce the leaning tower effect with scrolling text similar to the scrolling introduction in the If the texts scroll to a single vanishing point, the reverse effect is created: The scrolling texts are parallel in perspective view but not parallel in the picture plane. This can be seen in Star Wars Scroll Illusion functions from a variety of viewing angles. appearing text: That is, the two scrolls appear to start scrolling in the distance, from a point at the bottom of the screen. The scrolls expand as they approach the top of the screen, as if the scrolling text were viewed from an imaginary planet inside a Star Wars movie . When there are two appearing points, the scrolls appear to converge even though the lines are parallel in the picture plane; when there is a single appearing point, the texts appear to scroll in parallel. As with The x-axis at 0, −30°, −60°, and −90° . The scrolling texts are identical but translated laterally from each other. At 0°, the texts appear to scroll in parallel in the picture plane. With each successive rotation, the apparent direction of the left scroll deviates further from the right scroll.As shown in Movie 3, the strength of the illusion is determined primarily by the rotation of the scrolling texts into the third dimension. x-axis rotation, we presented observers with five stimulus conditions: The four conditions in accept setting button, and the next trial commenced. The five stimulus conditions were presented six times each, for a total of 30 trials in the session. The magnitude of the effect was taken as the average of the angle set for the right line minus the average of the angle set for the left line; a value of zero indicates that the observer saw the tilt of both objects to be moving/leaning in the identical direction.To measure the extent of the tilt as a function of R2 = 0.99). All seven observers showed similar linear relationships ; however, observers differed in the slopes of the best-fit line (from 0.1 to 0.31). Thus, while there was always a (remarkably) linear relationship between the perceived difference in tilt and the rotation angle, observers differed substantially in the reported magnitude of the effect. At this point, we cannot determine whether individual differences are due to observers’ perception or to a response bias in how observers set the orientation of the lines.The results, presented in Star Wars Scroll Illusion appears to have a larger magnitude than the Leaning Tower Illusion is that the images used to create the effects differ in their rotation into the third dimension. Observer settings for the Leaning Tower Illusion showed an average difference between the towers of 8.24°. The red line on the plot shows that the average difference produced by the Star Wars Scroll Illusion would be equivalent to a backward tilt of 35.2°—a magnitude equivalent to a relatively small rotation for the Star Wars Scroll Illusion  for each condition are as follows: still, short text = 20.2 ± 4.9; moving, short text = 24.1 ± 4.1; still, long text = 23.5 ± 4.2; and moving, long text 22.7 ± 4.1. An analysis of variance with correlated samples showed no significant difference between the conditions . There was a trend for the still, short text condition to have less magnitude than the other conditions , but there could be a number of reasons for the short, still text to have a less defined angle. Also, as with the previous experiment, there was a strong correlation for observer settings for each condition; the correlation matrix had r values ranging .86 to .99. Thus, while the average values were similar across groups, individual observers either had a strong response bias or they were quite consistent in the magnitude of the effect relative to other observers.The motion of the text itself as the scroll moves does not seem to be a contributing factor to the strength of the illusion. An experiment similar to that described earlier was conducted for eight naïve observers. There were four stimulus conditions: The text was either fully scrolled (long text) or partially scrolled (as if the text were only 1/3 of the display); the text was either still or moving. The stimulus conditions were presented eight times each, in random order, making 32 trials total. Figures all had an work because they create a conflict between multiple reasonable interpretations. The central conflict in the Star Wars Scroll Illusion and the Leaning Tower Illusion seems to be between the picture plane and the perspective interpretations. With two perspective points, the scrolling texts are parallel to each other in the picture plane but not in perspective interpretation; with one perspective point, the texts are not parallel to each other in the picture plane but are parallel to each other in perspective interpretation. A major question for understanding how we see and interpret images concerns how the visual system can simultaneously maintain both of these types of representations.Many illusions Leaning Tower-type effects seem to give insight into how we construct perspective interpretations. Geometric illusions have a history of generating multiple types of explanation , so, undStar Wars Scroll Illusion and the Leaning Tower Illusion concerns the interaction between global construction of perceptual space and local perspective information. As commented on by Perhaps the most remarkable insight from the


A multiple dependent state (MDS) sampling plan is developed based on the coefficient of variation of the quality characteristic which follows a normal distribution with unknown mean and variance. The optimal plan parameters of the proposed plan are solved by a nonlinear optimization model, which satisfies the given producer’s risk and consumer’s risk at the same time and minimizes the sample size required for inspection. The advantages of the proposed MDS sampling plan over the existing single sampling plan are discussed. Finally an example is given to illustrate the proposed plan. Nowadays, quality is one of the most important consumer decision factors. It has become one of the main strategies to increase the productivity of industries and service organizations. Therefore, the companies are trying to enhance the quality of their products by using various statistical techniques and tools. Acceptance sampling plans are important tools that have been widely used for lot sentencing in the industries. The inspection of the final product is always done on the basis of acceptance sampling scheme. There are two major types of acceptance sampling plans: attribute sampling plans and variable sampling plans. The major advantage of a variable sampling plan is that it has the same protection as an attribute acceptance sampling plan with a smaller sample size. When destructive testing is employed, variables sampling is particularly useful in reducing the costs of inspection. For more detail about the applications of the acceptance sampling plan can be found in Wu , Liu et The coefficient of variation (CV), which is defined as the ratio of the standard deviation to the mean, is widely used to measure the relative variation of a variable to its mean. CV has been widely used in many practical applications. It is used as a measure of the reliability of an assay in chemistry and medicine  of the quality characteristics are usually considered to measure the quality of products. However, in certain scenarios, the practitioner is not interested in the changes in the mean or the standard deviation but is instead interested in the relative variability compared with the mean  is a statistic defined as the ratio of the standard deviation Assume that t distribution, i.e. n − 1 is the degrees of freedom, and Iglewicz et al.  noticed Step 1: Choose the values of Step 2: Select a random sample of size n,  and the single sampling plan for two cases: (a) (n = 28 while the MDS plan with m = 1 requires n = 19 in case (a). In addition, all of the OC curves show that the probability of acceptance will become smaller as the value of CV increases, which is as expected from the theory. Since the MDS sampling plan requires fewer sample size to give the desired protection, the cost of inspection will greatly be reduced. Therefore, it is reasonable to conclude the MDS plan has a better performance.In order to show the efficiency of the proposed sampling plan, Fig. m = 1, 3) and the single plan with different values of n of three sampling plans all decreases as the value of n is larger as the value of In order to compare the sample sizes required for inspection in the MDS plan m = 1,  and the m = 1, 2, and 3) in Table m = 1, 227 for m = 2, and 240 for m = 3, while the single plan is 318. Therefore, the proposed sampling plan will give the desired protection with the less required sample size so that the MDS plan is economically superior to the single plan.On the other side, we also list the sample sizes required for the single sampling plan and MDS plan  lots have been accepted under the condition of Based on our proposed methodology, we can obtain the plan parameters as  sampling plan for accepting a lot whose quality characteristic follows a normal distribution based on the coefficient of variation (CV) is presented. Several tables are given for practical use. By comparison with the single sampling plan propose by Tong and Chen  in terms


The response of a well‐type chamber should remain constant to within 1.2% when exposed to a constant dose from an external beam unit, if reference conditions can be reproducibly established. However, the uncertainty for establishing reference conditions for output measurements for an orthovoltage unit can be reduced, which would justify a reduction of the tolerance for constancy measurements.Constancy checks of a well‐type ionization chamber should be performed regularly as part of a quality assurance regime. The goal of this work was to test the feasibility of using a linear accelerator and an orthovoltage unit to check the constancy of a well‐type chamber's response to an external radiation source. The reproducibility, linearity with dose, variation with dose‐rate, and variation between energy‐matched units of the well‐type chamber response when exposed to 6 MV beams was examined. The robustness to errors in establishing the measurement conditions, including setting the source‐to‐surface distance and gantry angle, rotation of the chamber around the central axis of the beam, and the effect of changing the length of the chamber cable exposed to the field, were tested. The reproducibility and linearity with dose of the chamber response, and robustness to errors in establishing the measurement conditions for 100 kVp and 250 kVp beams from an orthovoltage unit, were also examined. The combined uncertainty, including contributions from errors in establishing the reference conditions, for well‐type chamber measurements using a 6 MV beam from a linear accelerator is 1.0%. The combined uncertainties for measurements using 100 and 250 kVp beams were 1.8% and 1.5%, respectively. When focus‐source distance errors were reduced to PACS numbers: 87.55.Qr, 87.56.Fc I.137Cs source or an external beam 60Co unit.60Co teletherapy units are rarely used in developed countries, and many departments no longer use 137Cs sources for brachytherapy. We have developed an alternative means of checking the constancy of a well‐type chamber to external beam sources using a linear accelerator and an orthovoltage X‐ray unit. The purpose of this study was to demonstrate that external beam units can be used as part of a quality assurance system for well‐type chambers by assessing the constancy of the chamber measurements when exposed to external X‐ray beams and the reproducibility of positioning the chamber under each external beam unit.Well‐type ionization chambers are used for calibration of both high‐ and low‐dose‐rate brachytherapy sources. A quality assurance program for any instrument used for dose calibration is essential, and should include a regular check of the constancy of the instrument calibration.II.A.The response of a well‐type ionization chamber to 6 MV beams on a pair of energy‐matched Elekta Precise linear accelerators  was assessed. The well‐type chamber readings were corrected for dose output of the specific linear accelerator, as measured under reference conditions with a PTW  Farmer chamber type 30013, connected to a PTW UNIDOS E electrometer, and for air temperature and pressure.20 cm×20 cm, a dose rate of approximately 600 monitor units (MUs) per min, and a gantry and collimator angle of 0°, with the center of the well‐type chamber positioned at the intersection of the light‐field crosshairs. Unless stated, all measurement conditions were set to these standard conditions. No source calibration insert was used. The collection voltage on the electrometer was set to 400 V and the electrometer range set to ‘High’ (corresponding to a range of 20 nC−65 mC). The chamber and electrometer were left to stabilize for 10 min. The chamber was then exposed to five beams, each delivering 200 monitor units (MU), equivalent to approximately 1.1 Gy at the surface of the chamber. The median of the electrometer readings was considered to be the reference reading, and all results are reported as a percentage of the reference reading.A PTW well‐type chamber, connected to a PTW UNIDOS E electrometer, was positioned on the treatment couch of a linear accelerator, as illustrated in Fig. 1. The standard conditions for the measurements were a source‐to‐surface distance (SSD) of 100.0 cm, a field size of Reproducibility was calculated as the standard deviation (SD) of the five readings delivered under reference conditions. Variation with dose rate was assessed by delivering two beams of 200 MU at dose rate of 300 MU per min, and reported as the difference between the reference reading and the median of the readings recorded at lower dose rate. Linearity with dose was assessed by delivering beams of 50, 100, 200, and 400 MU. The variation of linearity with dose reported as maximum difference between the measured accumulated charge per MU and the reference reading. The uncertainty associated with establishing the standard conditions for measurements were simulated by delivering two beams of 200 MU at gantry angles from 0.1° to 0.5° at 0.1° intervals, and then with the SSD set to 100.2 cm and the gantry angle set to 0.0°. The effects of gantry angle and SSD errors were reported as the difference between the reference reading and the median of the readings obtained with the nonreference gantry angles and with the nonreference SSD, respectively. The variation between energy‐matched machines was assessed by positioning the chamber on a second linear accelerator, under standard conditions, and delivering five beams of 200 MU. The variation was reported as the difference between the median of the five readings and the reference reading.The effects of rotation of the chamber and of exposing the co‐axial cable connecting the chamber to the electrometer were assessed using a different well‐chamber and electrometer, as the original set was no longer accessible. A Standard Imaging HDR 1000 PLUS  well‐type ionization chamber, connected to a second PTW UNIDOS E electrometer, was positioned on the treatment couch of an Elekta Precise linear accelerator. A new reference reading was obtained by exposing the chamber to five beams of 200 MU under the standard conditions described above. The effect of rotating the chamber about the central axis of the beam was examined by delivering four beams of 200 MU with the chamber rotated by 90° between beams and reported as the difference between the median of these readings and the reference reading. The effect of exposing the cable was assessed by increasing the length of cable within the X‐ray field on the treatment couch from approximately 5 cm to approximately 95 cm (the full length of the well‐type chamber cable) and delivering four beams of 200 MU. The cable effect was reported as the difference between the median of these readings and the reference reading.B.The response of a Standard Imaging HDR 1000 PLUS well‐type ionization chamber, connected to a PTW UNIDOS E electrometer, to 100 kVp and 250 kVp X‐rays from a Gulmay D3225 orthovoltage unit  was assessed. All well‐type chamber readings were corrected for air temperature and pressure.10 cm×10 cm applicator with an open end and a focus–surface distance (FSD) of 30.0 cm was used for all 100 kVp measurements, while a 10 cm×10 cm applicator with a closed end and an FSD of 50.0 cm was used for all 250 kVp measurements. The experimental setups for the 100 kVp and 250 kVp measurements are shown, respectively, in Figs. 2 and 3. The center of each applicator was positioned over the center of the chamber. For the 250 kVp measurements, the surface of the applicator was flush with the surface of the chamber and, for the 100 kVp measurements, the edges of the open‐ended applicator were flush with the chamber surface. The gantry angle was set to 0°. No source calibration insert was used. Unless stated, all measurement conditions were set to these standard conditions. The respective dose rates measured in air at 100 kVp and 250 kVp are 442 cGy per min and 88 cGy per min at the end of the applicator and cannot readily be adjusted. The collection voltage of the electrometer was set to 400 V, the electrometer range set to ‘High’, and the chamber and electrometer were left to stabilize for 10 min. The potential voltage of the orthovoltage unit was set to 250 kVp and the chamber was then exposed to five beams of 200 cGy. A further five beams of 200 cGy were delivered with the potential voltage set to 100 kVp. The medians of each set of five readings were considered the 250 kVp and 100 kVp reference readings. All results obtained at each potential voltage are reported as a percentage of the corresponding reference reading.The well‐type chamber was positioned on the treatment couch of the orthovoltage unit. A Reproducibility of readings, linearity with dose, and uncertainty associated with establishing the standard measurement conditions, including off‐axis positioning of the chamber, were assessed at both voltage settings. Reproducibility and linearity with dose were assessed as described for the linear accelerator measurements. The effects of errors in positioning the chamber under the X‐ray source were tested at both voltage settings by delivering two beams of 200 cGy with the gantry angle set to 0.5° and with the FSD increased by 0.2 cm. The effects of gantry angle and FSD errors were reported as the difference between the reference reading and the median of the readings obtained with the nonreference gantry angle and FSD, respectively. Note that when the gantry angle was adjusted, the end of the applicator was no longer parallel with the surface of the chamber. The effect of positioning the chamber off the central axis of the beam was assessed by shifting the chamber 0.2 cm on each cardinal axis, and delivering a beam of 200 cGy at each new position. The effect was reported as the difference between the median of the readings at each off‐axis position and the reference reading. The effect of rotation of the chamber was examined at 250 kVp, as described for the linear accelerator measurements. No assessment of the effect of increasing the length of cable included in the X‐ray field was made, as the chamber occupied most of the area of the primary field.III.uc, for well‐type chamber measurements for the external beam units was calculated using the formula in Eq. (1). The combined uncertainty comprises the uncertainty for absolute calibration of the unit, uabs_cal, the uncertainty associated with establishing reference conditions for the well‐type chamber measurements, uref_cond, and the sources of variability of the measurements, uvar.The results for the linear accelerator and orthovoltage measurements are shown in Tables 1 and 2, respectively. The combined uncertainty, ustability, and the uncertainty associated with establishment of reference conditions, uabs_ref_cond. The uncertainty associated with establishing reference conditions for the well‐chamber measurements, shown in Eq. (3), includes the uncertainties arising from setting the SSD (or FSD for orthovoltage measurements), uSSD, and the gantry angle, ugantry, the variations introduced by the chamber rotation, uangle, and the length of cable irradiated by the beam, ucable. The variability of the well‐type chamber measurements, uvar, given in Eq. (4), comprises the uncertainty associated with reproducibility of the measurements, urep, linearity with dose, ulinear, variation with dose rate, udose_rate, and variation between linear accelerators, ulinac.The uncertainty for absolute calibration of the external beam unit, calculated using Eq. (2), comprises the long‐term stability of the dosimeter used for beam calibration, 60Co unit.The combined uncertainty for well‐type chamber measurements using a 6 MV beam from a linear accelerator is 1.0% of the reference dose measurement, which is with the same as the recommended tolerance of ± 1.0% for constancy of chamber readings using a ±1.0%, after correction for beam output and air temperature and pressure, and the required accuracy of positioning of the chamber in the beam is achievable. The small variation of 0.5% between readings obtained on machines with TPR20,10 values of 0.588 and 0.592 indicates that the chamber readings will not be unduly affected by the variations of beam energy within the recommended tolerance of 1.0% of TPR20,10 from baseline.Thus, it is reasonable to expect that chamber readings for 6 MV beams from a linear accelerator should be constant within The combined uncertainty for well‐type chamber measurements using 250 kVp and 100 kVp beams from an orthovoltage unit are 1.5% and 1.8%, respectively. Nonlinearity with dose constitutes the largest source of error of the 100 kVp measurements; the accumulated charge per cGy is 1.1% lower for the 50 cGy beam than the 200 cGy beams, whereas the accumulated charge per cGy for the 100 and 400 cGy beams are within 0.1% of the accumulated charge per cGy for the reference readings. The observed nonlinearity also includes nonlinearity of the output of the orthovoltage unit and/or timer errors. The results demonstrate the importance of restricting the dose used for constancy checks to the linear region of the dose‐response curve of the well‐type chamber and of the output of the orthovoltage unit.≤1mm and the dose restricted to the linear region of the dose‐response curve, the overall uncertainties for the measurements using 250 kVp and 100 kVp beams are reduced to 1.2% and 1.1%, respectively. If a closed‐ended applicator is used, or if the size of an open‐ended applicator is selected so that the edges of the applicator are in contact with the surface of the chamber, the requirement that the FSD error be no greater than 0.1 cm can more readily be imposed. Otherwise, each department should assess the precision of establishing the FSD for open‐ended applicators and determine the corresponding tolerance for constancy checks of the well‐type chamber.When the uncertainty associated with establishing the FSD is reduced to Absolute dose calibration of the external beam units is performed monthly using an appropriate ionization chamber. The relative standard uncertainty associated with the long‐term stability of the dosimeter is 0.3%, and the uncertainties associated with establishment of reference conditions for measurements in a water phantom on a linear accelerator and for medium energy X‐ray beam are 0.4% and 1.0%, respectively.Checking the constancy of the well‐chamber response to both megavoltage and orthovoltage X‐rays ensures that the chamber response is stable over a broad spectrum of photon energies, but checking the response using either unit alone would provide a check of the chamber stability. However, it should be noted that the dose rates of external beam units are orders of magnitude higher than those for low‐dose‐rate brachytherapy, although similar to dose rates obtained using an high‐dose‐rate brachytherapy source. The radiation from the linear accelerator is delivered as a pulsed rather than continuous beam. Reducing the dose rate of the linear accelerator changes the pulse repetition frequency rather than the dose (or dose rate) per pulse. A comparison of the response of the well‐type chamber to linear accelerator beams of different dose rates, therefore, does not approximate a comparison of the response of the well‐type chamber to high‐ and low‐dose rate continuous X‐ray radiation. The dose rate, or dose per pulse, to the surface of the well‐type chamber cannot feasibly be reduced to less than 2 Gy per hr by increasing the SSD or FSD, or by inserting absorbent materials between the source and the chamber. Hence, it is also essential to check the chamber and electrometer leakage as part of the quality assurance program for the well‐type chamber.IV.Provided reference conditions can be reproducibly established, the response of a well‐type chamber should remain constant to within 1.0% and 1.2% when exposed to a constant dose from a linear accelerator and an orthovoltage unit, respectively. However, the uncertainty for establishing reference conditions for output measurements for an orthovoltage unit can be reduced, which would justify a reduction of the tolerance for constancy measurements.Supplementary MaterialClick here for additional data file.


Temperature variations have significant effects on propagation of Lamb wave and therefore can severely limit the damage detection for Lamb wave. In order to mitigate the temperature effect, a temperature compensation method based on baseline signal reconstruction is developed for Lamb wave-based damage detection. The method is a reconstruction of a baseline signal at the temperature of current signal. In other words, it compensates the baseline signal to the temperature of current signal. The Hilbert transform is used to compensate the phase of baseline signal. The Orthogonal matching pursuit (OMP) is used to compensate the amplitude of baseline signal. Experiments were conducted on two composite panels to validate the effectiveness of the proposed method. Results show that the proposed method could effectively work for temperature intervals of at least 18 °C with the baseline signal temperature as the center, and can be applied to the actual damage detection. Recently, Lamb wave-based damage detection has received much attention from the research community because Lamb waves can travel over long distances and are sensitive to a range of types of damage including cracks, corrosion, and delaminations ,7,8,9,10In order to mitigate the temperature effect, many researchers have conducted theoretical and experimental investigations on the change in guided waves propagation caused by temperature fluctuations within the last decade ,15,16,17In addition, most temperature compensation methods for baseline subtraction need model training. However, it may not be possible to gather model training data for all possible combinations of structural and environmental changes. Furthermore, as far as we know, at present, the effectiveness of the temperature compensation methods are usually validated by the first few wave packets, and are rarely validated by the whole waveform. This validated temperature compensation method is not suitable for the damage detection situation that the damage is far from the sensing path.This study presents a temperature compensation method based on baseline signal reconstruction. It compensates the baseline signal to the temperature of current signal. The Hilbert transform is used to compensate the phase of baseline signal. The Orthogonal matching pursuit (OMP) is used to compensate the amplitude of baseline signal. Experiments are conducted on two composite panels to validate the proposed method.The remainder of this paper is organized as follows. In the baseline subtraction approach, the damage signal is the difference between the current signal and the baseline signal. So this temperature compensation method compensates the baseline signal to the temperature of current signal. It achieves the reconstruction of the baseline signal at the temperature of the current signal.According to the literatures , the temAccording to the above-mentioned, the temperature-related shift of the Lamb wave signals can be compensated as follows. According to Equation (1), it needs two Lamb wave signals with different temperature before the compensation. Among the two Lamb wave signals, one is the baseline signal which is compensated to the temperature of the current signal, the other is the reference signal which together with the baseline signal is used to determine the relation between the instantaneous phase difference and the temperature difference. It assumes that Then it needs to compensate the amplitude of The problem of Equation (3) can be changed as:In order to solve the problem of Equation (4), the OMP  can be uThis study uses the OMP to calculate the representation coefficient Finally, the temperature compensation signal of the baseline signal S. The thickness of each layer is 0.125 mm. Two Lead Zirconate Titanate (PZT) wafers were bonded on the specimen with the GLEIHOW302 adhesive. One was used as actuator, the other was used as sensor. The PZT wafers have a diameter of 8 mm and thickness of 0.45 mm. Their positions are shown in The experiment was carried on a carbon fiber composite panel with the size of 150 mm × 100 mm × 3 mm. The material of composite panel is T700/BA9916. The stacking sequence is [45/0/−45/90/0/45/0/−45/0/45/90/−45]The experimental procedure is as follows: The temperature was gradually increased from 20 °C to 68 °C at the heating rate of 1 °C/min, and for every 3 °C increase, it was held for 20 min. From 20 °C, pitch-catch signal of the transducers was collected at every 3 °C increase. The excitation signal was a five-cycle tone burst with different center frequencies modulated by a Hanning window. Data were collected for central frequencies from 50 to 210 kHz with a step of 20 kHz. The sampling rate was 10 MHz. The collected signal length was 0.9 ms.To quantify the difference between two time-domain signals, In order to judge the temperature compensation results, The change in temperature has effects on both signal amplitude and TOF for Lamb wave. For example, signals with frequency 50 kHz for the pitch-catch signal at different temperatures in this study are illustrated in In order to proof hypothesis of the proposed temperature compensation method, the relationship between the instantaneous phase difference and the temperature difference was studied. Using the instantaneous phase of the signals at 20 °C as benchmark, the instantaneous phase differences between signals at other temperatures and the signals at 20 °C were calculated. The calculated instantaneous phases of signals were unwrapped. The relationships between the instantaneous phase difference and the temperature difference for some signal points at three frequencies are shown in Before the temperature compensation, the experimental signals are processed by band pass filter, and the electronic crosstalk is removed. Then the experimental signals are processed by the proposed temperature compensation method using different baseline signals and reference signals. As an example, when the baseline signal temperature is 44 °C and the reference signal temperature is 47 °C, the temperature compensation results are shown in The reasons for the results of In order to study the effect of temperature difference between the baseline signal and the reference signal on the temperature compensation, the baseline signal temperature is 44 °C and the reference signal temperatures are selected as 50 °C and 53 °C, respectively. The temperature compensation results are shown in According to the above results, the temperature compensation effectiveness of the proposed method is better when the temperature difference between the baseline signal and reference signal is small. In order to determine the temperature interval of effective temperature compensation, the temperature compensation was achieved by keeping the temperature difference between the reference signal and the baseline signal for 3 °C. Several baseline signals at different temperatures were used for temperature compensation, and the baseline signals are listed in (a)Baseline signals were collected at 18 °C without damage.(b)Reference signals were collected at 20 °C without damage.(c)Damage was produced by an impact on the specimen with a hammer.(d)Environment temperature was increased to 26 °C.(e)Current signals with damage were measured at 26 °C.The proposed temperature compensation method was also verified with damage detection on a carbon fiber composite panel which was the same with the 0 mode amplitude is dominant. So A0 mode was used for damage imaging. The damage detection results are shown in The experimental signals were processed with the delay-and-sum damage imaging algorithm . Under tIn this paper, a temperature compensation method based on baseline signal reconstruction has been developed to enhance the robustness and effectiveness of Lamb wave-based damage detection. The method does not need model training. It only requires a baseline signal and a reference signal for temperature compensation. The effectiveness of the proposed method was validated by the experiments conducted on two composite panels. Results show that: (1) the instantaneous phase difference of the two Lamb wave signals with different temperature is proportional to the temperature difference, with the limit range of temperature; (2) the proposed method could effectively work for temperature intervals of at least 18 °C with the baseline signal temperature as the center; (3) the temperature compensation performance is degraded by the temperature difference between the baseline signal and the reference signal increase; (4) the damage signal extraction was effective after the temperature compensation; (5) the proposed method can improve the damage detection for temperature variation and can be applied to actual damage detection. In practical application, this method can be combined with OBS for damage detection.


In this paper we present a case study of integrated ecosystem and economic accounting based on the System of Environmental Economic Accounting — Experimental Ecosystem Accounts (SEEA-EEA). We develop accounts, in physical and monetary terms, for the water purification ecosystem service in Europe over a 20-year time period (1985–2005). The estimation of nitrogen retention is based on the GREEN biophysical model, within which we impose a sustainability threshold to obtain the physical indicators of capacity – the ability of an ecosystem to sustainably supply ecosystem services. Key messages of our paper pertain the notion of capacity, operationalized in accounting terms with reference to individual ecosystem services rather than to the ecosystem as a whole, and intended as the stock that provides the sustainable flow of the service. The study clarifies the difference between sustainable flow and actual flow of the service, which should be calculated jointly so as to enable an assessment of the sustainability of current use of ecosystem services. Finally, by distinguishing the notion of ‘process’ (referred to the ecosystem) from that of ‘capacity’ (pertaining specific services) and proposing a methodology to calculate capacity and flow, we suggest an implementable way to operationalize the SEEA-EEA accounts. •We present a case study of ecosystem accounting based on the SEEA-EEA framework.•Accounts for water purification are developed in physical and monetary terms.•Flow accounts include both actual and sustainable flows.•Capacity is assessed as Net Present Value of the sustainable flow.•Replacement cost is the exchange value technique used for the monetary valuation. An essential part of integrated assessments is the identification of the links between ecosystem functions and processes and human wellbeing, a task to which theoretical frameworks, principles, definitions and classifications have been devoted by numerous studies e.g. .Europe 2020 strategy has the manifest intention of mainstreaming environmental issues into other policy areas  and biotic (biodiversity) components, and the depletion of its stock - the natural capital - may cause the loss of multiple services now and in the future. This is the reason why ecosystem accounts, aimed at monitoring the capacity of ecosystems to deliver services, are the focus of increasing attention within economic-environmental accounting .The Land and Ecosystem Accounting framework (LEAC) is an early attempt at ecosystem accounting . In LEACcapacity  aggregation of the various ecosystem services within a spatial area; ii) aggregation of a single ecosystem service across multiple areas within a country, and iii) aggregation of all ecosystem services across multiple areas within a country. Our case study falls within the second approach, as we account for a single ecosystem service across multiple river catchments in Europe.2.21.Identify the ecosystem service classification and the underlying conceptual framework.2.Quantify in physical terms the targeted ecosystem service. The quantification procedure can range from simple to complex, or can be multi-tiered3.Translate the quantitative assessment into monetary terms by choosing an economic valuation technique that as much consistently as possible links to the biophysical model.4.Populate SEEA-EEA tables consistently with the resulting data.To align with SEEA-EEA definitions and methods, we use a four step procedure:In step 1 we use the Common International Classification for Ecosystem Services (CICES) as proposed in the SEEA-EEA. The underlying conceptual framework is the ecosystem services cascade model . In the Step 2 involves the physical quantification of the selected ecosystem service. The approach most compatible with SEEA-EEA to quantify the capacity of the ecosystem to provide a service is to measure ecosystem conditions (from the ecosystem asset set of tables) using indicators such as biomass index and soil fertility. In the SEEA-EEA handbook ecosystem condition provides a link between ecosystem capacity and ability to supply ecosystem services. Here we use a biophysical model to quantify the actual flow of the ecosystem service, i.e. the amount used by society. In the supply-use accounting table the sustainable flow corresponds to the service supply, while the actual flow plus the difference between sustainable and actual flow corresponds to service use. In The actual flow of an ecosystem service is not necessarily sustainable. In overfished fisheries, for example, the actual flow exceeds the capacity of the marine ecosystem to maintain the stock, with a resulting declining stock value and the risk of collapse. A sustainable use of ecosystems requires the actual flow of the service to be equal or lower than the maximum sustainable flow that the ecosystem is able to provide. For management purposes it is therefore important to measure or estimate the sustainable flow – which remains a challenge for regulating services because it is hard to establish thresholds for sustainability.sustainable flow. The changes to be recorded are the actual flow of the ecosystem service that is used by humans. The capacity is not the maximum theoretical flow the river system can generate for e.g. one year, but it represents the current and future flows measured at a sustainable rate. Capacity is thus intended as a stock (measured with NPV in money terms) and not as a flow. Consistently with these definitions, the actual flow can be higher, equal or lower than the sustainable flow, but not higher than the capacity (i.e. NPV of sustainable flows).Here we define capacity as the stock generating a sustainable flow and quantify its value by estimating the Net Present Value (NPV) of the present and future sustainable flow. We think that for accounting purposes capacity should be quantified with reference to single ecosystem services, rather than for ecosystems as a whole. In the accounting terminology, the opening stock in our approach is the capacity of the ecosystem to generate a given specific service, and it is calculated as the NPV of the ecosystem service When the actual flow of the ecosystem service is lower than sustainable flow the implication is no degradation. Actual and sustainable flows are separate (but interconnected) tables and maps. In economic terms you might choose to only value actual flow, however the sustainable flow remains whether or not a monetary value is estimated.If actual flow is lower than sustainable flow the capacity to provide the service remains intact. Conversely, if actual flow exceeds sustainable flow, the stock will be degraded and the capacity will be reduced. Population density, for example, affects capacity only when it drives the actual flow beyond the sustainability threshold, and its specific role can be identified provided it is explicitly included in the modelling equations behind the biophysical assessment. However, it must be acknowledged that the basis for these assumptions about capacity is that there are no other changes in the ecosystem, i.e. we assume that the condition of the ecosystem is not affected by any other changes.Step 3 translates biophysical quantities into monetary terms. Following the SEEA-EEA guidelines, it is important to distinguish between welfare values relevant in some public policy decision making contexts, and exchange values, relevant in an accounting context. The former include consumer surplus,1.Accounting for actual flow of services received by economic sectors and households;2.Accounting for the sustainable flow of services;3.Accounting for the capacity of ecosystems to provide a sustainable flow of the ecosystem service, calculated as the NPV of the sustainable flow.Step 4 reports the physical and monetary outputs in accounting tables in three ways:2.3The empirical objective of this case study is to value the water purification service taking place in rivers in Europe. The retention of Nitrogen (N) from point and diffuse sources is used as a proxy for water purification. Excessive nitrogen loading is a leading cause of water pollution in Europe and globally which makes nitrogen a useful indicator substance for water quality . We defi2.3.1We use the Geospatial Regression Equation for European Nutrient losses (GREEN) model  to estim2  and phosphorus (P) flows to surface water in large river basins. The model is developed and used in European basins with different climatic and nutrient pressure conditions  and is s2 . For eaci, 103 kg N year−1) is expressed as following:i (103 kg N year−1) is the sum of nitrogen diffuse sources in each catchment i, PSi (103 kg N year−1) is the sum of nitrogen point sources in each catchment i, Ui (103 kg N year−1) is the nitrogen load received from upstream sub-catchments, and BRi and RRi  are the estimated nitrogen basin retention and river retention, respectively. In the model, BRi is estimated as a function of rainfall while RRi depends on the river length. For more details on model parameterisation and calibration see For each sub-catchment i the annual nitrogen load estimated at the sub-catchment outlet  in combination with the critical nitrogen concentration (1 mg l−1), we can calculate the critical nitrogen loading  - the critical threshold below which no environmental damage is expected. Substituting the nitrogen loading Li with Lcrit in Eq. retained we obtain:crit is the critical nitrogen removal by the river network (103 kg N year−1), assuming a critical loading Lcrit.Using data on average river flow , Ncrit is the critical removal of nitrogen (103 kg N year−1), L is the nitrogen loading at the outlet of each catchment (103 kg N year−1), and Lcrit is the critical loading of nitrogen at 1 mg N l−1 (103 kg N year−1).Next, we use the critical nitrogen load and the critical nitrogen removal function, which assumes that at or below the critical nitrogen load, the removal of nitrogen by the different ecological processes that take place in the ecosystem is sustainable and results in the optimal use of the ecosystem from an ecosystem services point of view. However, increases in nitrogen loading far above the critical loading will result in costs due to the degradation of most other ecosystem services. This hypothesis allows thus for the use of nitrogen from anthropogenic sources and the subsequent nitrogen inputs to river systems up to a level at which nitrogen concentrations reach a critical threshold. In the monetary valuation calculations nitrogen removal will be valued the most at critical nitrogen loads. The following equation is used to estimate the sustainable removal of nitrogen:crit as value for Nsustainable without applying the exponent function.Eq. 2.3.3For the monetary valuation of water purification we adopt a ‘cost-based approach’. We do not use a ‘damage-based approach’ because of the difficulty to exhaustively identify all the benefits that could be lost if the water purification service offered by the ecosystem is no longer available. These benefits range from the availability of clean water for drinking or swimming, to the presence of fisheries, to the aesthetic perception that influences both recreational activities and real estate markets. The benefits from water purification also overlap in many cases with benefits from other ecosystem services, which risks to give rise to double counting. By using, instead, a cost-based approach rather than methodologies based on stated preferences we make an attempt to get closer to SEEA-EEA guidelines that preferably ask for exchange value estimatesThe rationale of a cost-based approach to valuation is well known. By  cleaning up discharges from human activities, aquatic ecosystems provide for free a valuable ecosystem service and thus avoid a degradation of the ecosystem that would impact on human health and living conditions. Since human activities will not stop, there will always be the need for this ecosystem service even after river bodies will not be able to provide it any longer. The operational hypothesis of our valuation exercise is that an artificial replacement would be required in order to maintain the water purification service, and replacement would entail a cost. Considering the relevant pollution sources , the best proxy we can use as replacement cost are constructed wetlands. Wastewater treatment plants would be inappropriate because: (i) they are not applicable to the primary sector (agriculture and livestock activities) and (ii) what is discharged by the secondary sector  and by households is already treated by wastewater treatment plants before reaching water bodies.ad hoc for the specific engineering works hypothesized.Differently from previous applications undertaken on water purification  the moneThe typologies of CW are differentiated according to the types of pollutant sources .Free Water Surface (FWS) CWs are densely vegetated basins that contain open water, floating vegetation and emergent plants. They basically need soil to support the emergent vegetation. The FW constructed wetlands reproduce closely the processes of natural wetlands, attracting a wide variety of wildlife, namely insects, mollusks, fish, amphibians, reptiles, birds and mammals . FWS-CWsHorizontal subsurface Flow (HF) CWs consist of waterproofed beds planted with wetland vegetation  and filled with gravel. The wastewater is fed by a simple inlet device and flows slowly in and around the root and rhizomes of the plant and through the porous medium under the surface of the bed in a more or less horizontal path until it reaches the outlet zone. HF-CWs represent the best choice for treating point sources.•s: surface of the CWs (m2)A•e: outlet concentration (mg l−1)c•i: inlet concentration (mg l−1)c•−1c*: background concentrations, for nitrate assumed at 0 mg l•−1); for nitrogen removal k is temperature dependent: K˭K20∙θ(T-20) k: areal constant of first order (m year•−1)Q: hydraulic load (m year•3 day−1)q: mean flow (m3 day−1) by using population data and by assuming person equivalents .The flow Q is separated in two different sub-flows: a first one containing only nitrogen from diffuse sources, which is calculated as the product of surface basin and annual precipitation (supposing a completely impervious basin); and a second one containing only nitrogen from point sources, whereby the point input sources (kg) were converted according to Eq. i and ce Li: Diffuse sources at catchment (103 kg year−1)DSi: Basin retention (dimensionless)BRFWS: 1 - Percentage of point sources% N 3 kg year−1)NR: In-stream nitrogen retention (10i=Load at catchment inlet (103 kg year−1)Li=Point input sources to the river at catchment (103 kg year−1)PSHF=Percentage of point sources% N3 kg year−1)NR: In-stream nitrogen retention  a fixed component ; (2) labour costs; (3) filling materials costs.−2) is obtained as the sum of fixed costs, labour costs and filling material cost for HF and as sum of fixed costs and labour cost for FWS. On the ground of a series of case studies examined, we assume an operating and maintenance (O&M) cost equal to 3850 € ha-1 for FWS and 7700 € ha−1 for HF.For each country the total cost (€ ma: yearly amount of building costs (euro)Y: total building costsi: discount rate (in our application set at 3%LE: Life Expectancy of the CW (20 years).The building value that we calculate refers to the whole building project. What we need in our valuation is an annual flow, we thus need to calculate it. For the estimation of the annual flow from the total building costs, we can use the standard equation:We should take into account on one hand the economy of scale effect, and on the other hand the fact that different countries in Europe have different costs. The two aspects cannot be calculated together because the imposition of fake thresholds would unrealistically affect the final result. We thus calculate separately the economy of scale effect and the price difference effect. After few simulations were run , the mos143We present the accounts at two spatial scales: i) at the European scale, to show how service capacity and service flow can be quantified through the accounting tables proposed by the SEEA-EEA, and; ii) at the country scale, to put sustainable and actual flow and valuation estimates into context. We report monetary estimates in constant year 2000 values: valuation is used here as a translation in monetary terms of the biophysical assessment, and including inflation in the estimates would overshadow their comparability over time. Using current rather than constant prices is obviously feasible and may be desirable for different purposes.In Europe, over the 20-year time period considered (1985–2005), total nitrogen input to river basins varies between 50 and 80 million ton, the largest share originating from the agricultural sector and entering the basin as diffuse sources. This total represents the combined input of different nitrogen sources on the land after take up by crops. After basin retention (i.e. the nitrogen that is retained in soils and groundwater), around 5 million tons reach the river network. Nitrogen emissions from industries and households enter the river network as point sources and amount to 1.1 million ton of nitrogen.15The flows of total annual service vary between 21 and 31 billion euro assuming sustainable service delivery. The actual service flow aggregated at the European scale is worth around 16 billion euro annually . EconomiThe separation between the primary sector and other economic activities and households has been determined by the features of the biophysical model that explicitly differentiate retention values for diffuse source (that are indeed mostly due to agriculture activities) and point sources. The possibility to frame the results according to economic sectors (by using of course the same classification) offers the possibility to integrate this information with economic accounts, all expressed in monetary terms.3 kg km−1 year−1and euro km−1 year−1, so as to assess sustainability independently of the size of the country. Total values are mapped in In Furthermore, The apparently contrasting results between A few important points are worth highlighting. (i) The capacity to generate sustainable nitrogen retention, shown in Interesting observations emerge also from the monetary flow accounts . FirstlyThe accounts reported in Finally, it should be recalled that the nitrogen retention takes place in soils, surface water including streams, river and lakes, wetlands, and coastal and marine sediments. Our accounts, however, are limited to the river network.4versus actual flow is what we define as sustainable flow versus actual flow. In The crucial note we address with this case study is the definition, in accounting terms, of stocks and flows of ecosystem services. Ecosystem services depend on the functioning and health of the ecosystem as a whole. Ecosystem resilience is related to the capacity of ecosystems to generate ecosystem services, now and in the future. However, the notion of capacity is controversial. In Our application identifies several challenges that need to be addressed before a standard framework for integrated ecosystem and economic accounting can be proposed. The first is the difference between potential flows and sustainable flows. Potential flow is the maximum flow of a given service that the ecosystem is able to generate; sustainable flow is the flow that does not exceed the regeneration rate. For provisioning services it is possible to quantify the difference between the two. For regulating and maintenance services it is possible to measure the sustainable flow once a sustainability threshold has been identified, but it is unclear whether it would be possible to measure potential flow. This is a key point that needs to be addressed in order to make the accounting for ecosystem services operational and rigorous. Even establishing a sustainability threshold is not trivial because the conditions and vulnerability of ecosystems vary in space and time.One feature of our application that needs to be highlighted is the use of constructed wetlands for valuing the NPV of water purification sustainable flow. Ideally the quantification of ecosystem capacity (in our application: the NPV of the sustainable flow) and services  should be based on the assessment undertaken in physical terms and not be dependent on the valuation methodology. In many cases, however, this turns out to be not possible. In our case study, for example, the available biophysical model (GREEN) is based on a statistical approach, using regression analysis to build a statistical relation between retention and explanatory variables such as land cover, climate, and so on. The model does not include equations representing the physical functions of the ecosystem. For future applications and wherever possible, process-based models should be used to quantify stock-capacity and flow-service.17Directly related with the choice of using CWs as replacement cost is the choice of lifetime of the resource and of the discount rate used in calculating the Net Present Value (i.e. the lifetime of the resource in terms of number of years depends on constructed wetlands as an engineering work rather than on water purification as an ecosystem service). Moreover, we not only consider operation and maintenance costs  but we also 'incorporate' building costs considered over the 20 years of the CW life. One important consequence is that fixed costs play the most important role, consistently with our hypothesis that substitute costs  have to be incurred once natural processes have been impaired. Underlying assumptions must however be kept in mind when comparing monetary values resulting from different valuation techniques. Finally, although CW are likely to affect the concentration of other pollutants and to provide other ecosystem services, we only related CW to nitrogen emissions, the pollutant we used as proxy of anthropic pressure on the water purification service. In a future application the application of the whole cost should be maybe re-proportionated based on feasible hypotheses.Another point highlighted by our application is the critical role played by the way in which the sustainability threshold is calculated and spatially differentiated according to physical conditions. The latter, in fact, causes the sustainable flow be very sensitive to changes in emissions. A sensitivity analysis (available as As a final note, the exercise presented in this paper shows once more that quantifying and valuing ecosystem services often involves complex, fit for purpose models. This imposes heavy reliance on derived data. If developing data standards is generally considered one of the objectives of ecosystem service accounting, we therefore suggest that a standard on metadata settings e.g. , in addi5Ecosystem service accounting is in its infancy and substantial work is needed to refine and test methods for use in National Accounts. Our case study addresses the issue of capacity in integrated ecosystem and economic accounting by structuring ecosystem services within a consistent stocks and flows perspective – something not fully addressed in previous applications of ecosystem services accounting.The first key message from our application is that capacity can be calculated for ecosystem services one-by-one. The second key message is that capacity can be intended as the stock that provides the sustainable flow of the service. The third key message is that the sustainable flow must be calculated jointly with the actual flow. Current use of any ecosystem service should be assessed against sustainable use. The capacity should describe the sustainable flow of each service that the ecosystem can generate, even if not currently fully exploited. The common underlying element underneath the first two messages is that the physical flow accounts provide the basis upon which other accounting tables are built.By calculating capacity and flow, in our case study, we demonstrate how to make the theory and concepts described in the SEEA-EEA operational for use in upcoming standards of integrated ecosystem and economic accounting.