Cauê D Carrilho
email: cauecarrilho@gmail.com.highlights

Gabriela Demarchi

Amy E Duchelle

Sven Wunder

Carla Morsello

Permanence of avoided deforestation in a Transamazon REDD+ initiative (Pará, Brazil)

Keywords: conservation incentives, emission reductions, additionality, climate change mitigation, impact assessment

 A local REDD+ initiative in the Brazilian Amazon promoted win-win outcomes

Introduction

REDD+, short for "Reducing Emissions from Deforestation and Forest Degradation and conservation, sustainable management and enhancement of carbon stocks", is a nature-based solution devised to mitigate greenhouse gas emissions while achieving co-benefits, mainly the improvement of human well-being and biodiversity conservation [START_REF] Angelsen | A evolução de REDD+[END_REF].

Launched 15 years ago, REDD+ initially generated widespread excitement as a fresh approach to forest conservation through promoting performance-based incentives at scale. However, global carbon markets, initially envisioned to finance REDD+, have expanded insufficiently, implementation proved more complex than expected, and so far tropical deforestation has thus continued [START_REF] Angelsen | REDD+ as Result-based Aid: General Lessons and Bilateral Agreements of Norway[END_REF][START_REF] Angelsen | REDD+ enters its second decade[END_REF]. Notably, while REDD+ initially was conceived as a jurisdictional mechanism in the Paris Agreement, by far most of the action has remained in smaller-scale pilot projects (Wunder et al., 2020b).

To convincingly make conclusions about REDD+ performance, we need to focus our attention on rigorous impact evaluations vis-à-vis both REDD+ conservation and development outcomes. These evaluations allow attribution of observed outcomes to an intervention through construction of a credible counterfactual scenario (i.e., what would have happened in the absence of the REDD+ initiatives) [START_REF] Sills | Building the evidence base for REDD+: Study design and methods for evaluating the impacts of conservation interventions on local well-being[END_REF][START_REF] White | Theory-based impact evaluation: principles and practice[END_REF]. Despite the importance of REDD+ over the last decade, studies using a counterfactual approach have been scarce [START_REF] Duchelle | What is REDD+ achieving on the ground?[END_REF].

Of the few REDD+ studies using counterfactual approaches to assess deforestation reduction, most indicate moderately positive results [START_REF] Simonet | Forests and Carbon. The impacts of local REDD+ initiatives[END_REF]. For instance, a quasiexperimental assessment of 23 local REDD+ initiatives, based on different intervention mixes (e.g., restrictions on forest clearing and access, Integrated Conservation and Development Project (ICDP)type activities, and Payments for Environmental Services (PES)), in Brazil, Peru, Tanzania, Cameron, Indonesia and Vietnam, showed that half reduced deforestation, although with moderate effect sizes [START_REF] Bos | Comparing methods for assessing the effectiveness of subnational REDD+ initiatives[END_REF]. This study was undertaken as part of CIFOR's Global Comparative Study on REDD+ (GCS)1 . Likewise, a Randomized Control Trial (RCT) found a significant reduction in net tree losses in villages participating in an Ugandan PES-based carbon forestry initiative (tree cover declined 4.2% in treatment but 9.1% in control villages), which translated into an average of 5.5 ha of forestland saved per village [START_REF] Jayachandran | Cash for carbon: A randomized trial of payments for ecosystem services to reduce deforestation[END_REF]. Even more substantial were the outcomes of a mixed ICDP-PES initiative in the Brazilian Transamazon where participating households halved their yearly deforestation (Avg=4 ha/household) [START_REF] Simonet | Effectiveness of a REDD+ project in reducing deforestation in the Brazilian Amazon[END_REF]. Finally, a unique quasi-experiment of Guyana's national REDD+ program based on synthetic controls found for 2010-15 a 35% reduction in tree-cover loss (5,800 ha/year) vis-à-vis a no-REDD+ baseline, with tree-cover loss increasing after the program ended [START_REF] Roopsind | Evidence that a national REDD+ program reduces tree cover loss and carbon emissions in a high forest cover, low deforestation country[END_REF].

Other studies typically found small (significant or insignificant) effects of REDD+ initiatives on deforestation. For example, a quasi-experimental assessment of REDD+ initiatives in Mexico's Yucatan Peninsula found no overall reduction in forest cover loss using difference-in-differences (DID) regression and propensity score matching (alternatively, using synthetic controls, effects were mixed) [START_REF] Ellis | Mixed effectiveness of REDD+ subnational initiatives after 10 years of interventions on the Yucatan Peninsula, Mexico[END_REF]. For Peru, a recent review found over periods of 4-6 years insignificant forest conservation effects from a public and a private REDD+ pilot program, respectively -both implemented in the Peruvian Amazon [START_REF] Montoya-Zumaeta | Incentive-based conservation in Peru: Assessing the state of six ongoing PES and REDD+ initiatives[END_REF]. Returning to Brazil, one quasi-experiment found insignificant REDD+ deforestation impacts in Mato Grosso State's Alta Floresta municipality. This is a REDD+ like initiative under the Amazon Fund, mixing environmental land registrations with PES-ICDP incentives: land registration increased attributably in project sites, yet deforestation effects were insignificant, presumably because of already very low rates of deforestation in the pre-intervention period [START_REF] Correa | Evaluating REDD+ at subnational level: Amazon fund impacts in Alta Floresta, Brazil[END_REF]. Quite similar is the situation for the large-scale Bolsa Floresta program in Amazonas State, holding also Brazil's oldest REDD+ program in the Juma Reserve. Bolsa Floresta combines PES with collective benefits (health, education, community organization) and ICDP investments in alternative livelihoods [START_REF] Börner | Promoting Forest Stewardship in the Bolsa Floresta Programme: Local Livelihood Strategies and Preliminary Impacts[END_REF]). An evaluation using matching techniques found insignificant forest conservation effects, given that most enrolled areas proved to be remote and little threatened in the first place [START_REF] Cisneros | Impacts of Conservation Incentives in Protected Areas: The Case of Bolsa Floresta, Brazil[END_REF]. Finally, scrutinizing twelve REDD+ sites, all Amazon Fund projects spread over the Brazilian Amazon, a quasi-experiment with synthetic controls showed that only in four sites was deforestation reduced, whereas nil or negative impacts were observed in the remaining eight [START_REF] West | Overstated carbon emission reductions from voluntary REDD+ projects in the Brazilian Amazon[END_REF].

Regarding well-being and livelihoods impacts, evaluations of REDD+ initiatives most frequently indicate small, mixed (positive or negative) effects. For instance, a quasi-experiment based on publicly-available social and spatial data at 18 REDD+ sites in Indonesia suggested the strengthening of local land rights, but potentially negative effects on other welfare indicators [START_REF] Jagger | Using publicly available social and spatial data to evaluate progress on REDD+ social safeguards in Indonesia[END_REF]. The aforementioned carbon-focused project in Uganda found a significant rise in the non-food, but no impact in the food consumption of target-households monetary income [START_REF] Jayachandran | Cash for carbon: A randomized trial of payments for ecosystem services to reduce deforestation[END_REF]. In turn, [START_REF] Solis | Evaluating the Impact of REDD+ Interventions on Household Forest Revenue in Peru[END_REF] found for two REDD+ projects in the Peruvian Amazon (Madre de Dios and Ucayali) insignificant income effects, using matched DID estimations. Likewise, a comparison evaluating 22 local REDD+ initiatives in CIFOR's GCS on REDD+ did not observe any significant impact whatsoever (neither positive, nor negative) on household and village-level perceptions of wellbeing and income sufficiency [START_REF] Sunderlin | REDD+ contribution towell-being and income is marginal: The perspective of local stakeholders[END_REF]. Finally, another quasi-experiment targeting 17 of these 22 GCS REDD+ initiatives showed that impacts on subjective wellbeing of REDD+ participants depended on the composition of REDD+ interventions: a predominance of disincentives (e.g., law enforcement) negatively affected households' perceived well-being, but this negative effect was alleviated when incentives (e.g., PES, ICDP) were added [START_REF] Duchelle | Balancing carrots and sticks in REDD+: Implications for social safeguards[END_REF].

Hence, the accumulated evidence suggests local REDD+ initiatives are struggling to achieve strong win-win outcomes in terms of simultaneously delivering sizeable deforestation reductions and well-being improvements. So far, REDD+ is on average achieving moderate conservation effects, typically in a welfare-neutral manner. However, still few counterfactual evaluations exist and practically only REDD+ projects, rather than jurisdictional programs, have been evaluated [START_REF] Duchelle | What is REDD+ achieving on the ground?[END_REF]. More assessments will be needed to increase our confidence about if, when, and how REDD+ interventions are working.

Even less studied is whether REDD+ achievements persist after initiatives are suspended.

Since most of the above reviewed initiatives were evaluated only at early stages (e.g. 2-3 years after start for [START_REF] Bos | Comparing methods for assessing the effectiveness of subnational REDD+ initiatives[END_REF], [START_REF] Jayachandran | Cash for carbon: A randomized trial of payments for ecosystem services to reduce deforestation[END_REF][START_REF] Simonet | Effectiveness of a REDD+ project in reducing deforestation in the Brazilian Amazon[END_REF]), there is an understandable knowledge gap about their longer-term effects.

Theoretically, we should expect that if forest conversion paid off better than forest conservation ex ante, this will likely persist post-payment, so that deforestation should pick up again after payments stopped. Yet, under some scenarios substantial post-payment permanence could still happen. First, REDD+ initiatives might explicitly manage to achieve the lasting adoption of more benign land uses with sustained economic returns (e.g. establishing agroforestry systems). Second, REDD+ benefit transfers could have had a motivational 'crowding-in' effect, boosting landowners' altruistic motives for forest conservation -not the most common, but still a possible scenario (Ezzine- de-Blas et al., 2019). Finally, REDD+ might just have successfully bought time for the external environment to have substantially adapted in its own right (e.g. falling commodity prices, alternative employment options, or political changes), thus exogenously reducing the opportunity costs of conservation.

However, these exceptions apart, as default scenario we should rather expect the original environmental externality problem to persist: once REDD+ initiatives have ended, the incremental conversion to alternative land uses (e.g., extensive cattle ranching, swidden agriculture) will continue. Forests that were temporarily spared by the initiatives would thus likely be converted after REDD+ ends (non-permanence) [START_REF] Dutschke | How do we ensure permanence and assign liability?[END_REF]. If so, REDD+ initiatives would postpone deforestation, instead of permanently reducing it [START_REF] Angelsen | What are the key design issues for REDD and the criteria for assessing options?[END_REF]. On the livelihoods side, when REDD+ on-the-ground incentive flows (e.g., PES) end, welfare impacts may also fade, unless longer-lasting welfare-enhancing assets had been constructed from those accumulated REDD+ transferred benefits. Indeed, the two published evaluations of REDD+ outcomes' permanence that we are aware of found support for our default scenario. The first is the aforementioned quasi-experiment showing that Guyana's national REDD+ program, funded by Norway through performance-based payments for reducing deforestation, decreased tree cover loss during the implementation period (2010-2015) [START_REF] Roopsind | Evidence that a national REDD+ program reduces tree cover loss and carbon emissions in a high forest cover, low deforestation country[END_REF]). Yet, right after Norway's payments ceased, in 2016, the authors detected an increase in tree cover loss, which suggested forest protection was not guaranteed without continued payments. The second is a follow-up evaluation of the forest outcomes from the carbon-focused project in Uganda. Implemented between 2011 to 2013, the program had reduced deforestation substantially [START_REF] Jayachandran | Cash for carbon: A randomized trial of payments for ecosystem services to reduce deforestation[END_REF]). However, using satellite imagery from 2016, World Bank (2018) showed the previous PES recipients resumed forest clearing at similar rates to control group households after payments had ended; yet, importantly, without 'catching up' with the initial curve, i.e. leaving the temporary, payment-induced conservation gains intact.

The results of these two studies, therefore, would suggest REDD+ initiatives are struggling to induce self-sustained deforestation reductions. However, we cannot make sweeping generalizations from only two cases. Fortunately, drawing also on the broader family of forest carbon-focused PES interventions may help us to get a clearer picture (Wunder et al., 2020a), and they present some more optimistic evidence. One example is a natural experiment in PES permanence that occurred in Cuyabeno, Ecuador, within Socio Bosque -the national PES-like program for forest conservation. The program had attributably reduced annual deforestation on enrolled plots by annually 0.4-0.5% points during 2011-14 [START_REF] Jones | Forest conservation incentives and deforestation in the Ecuadorian Amazon[END_REF]. However, when public funds run dry during 2015-17, Socio Bosque payments were suspended for some recipients.

Even without pay, they continued to clear less forest than similar non-participating landowners, unless though they held plots close to roads or oil wells: in these plots with higher deforestation threat and presumably larger conservation opportunity costs, forest loss reverted back to rates similar to what applied to unenrolled properties [START_REF] Etchart | What happens when the money runs out? Forest outcomes and equity concerns following Ecuador's suspension of conservation payments[END_REF].

In the case of using PES as an adoption subsidy for environmentally more benign practices that pay off for land stewards ('asset-building' PES), the prospects for permanence should be better.

At least a few case studies seem to also support this empirically, in particular from the World Banksupported trinational Regional Integrated Silvo-pastoral Ecosystem Management Project (RISEMP).

This carbon-and biodiversity-focused PES program paid landowners between 2003 and 2008 for the introduction of silvopastoral practices. In Quindío (Colombia), four years after payments ended, these systems had been widely retained [START_REF] Pagiola | Evaluation of the permanence of land use change induced by payments for environmental services in Quindío, Colombia[END_REF]. Similar permanence results were reconfirmed again in 2016 [START_REF] Calle | Can short-term payments for ecosystem services deliver long-term tree cover change? Ecosyst[END_REF]. The sister silvopastoral program implemented simultaneously in Nicaragua was assessed also in 2012, showing also widespread permanence, although the evidence here is based only on a before-after comparison of various interventions, without a no-intervention control group [START_REF] Pagiola | Assessing the Permanence of Land-Use Change Induced by Payments for Environmental Services: Evidence From Nicaragua[END_REF]. The third rollout was in Costa Rica , and also here there is about a decade after (2016) evidence of a high degree of permanence [START_REF] Rasch | Permanence of PES and the role of social context in the Regional Integrated Silvo-pastoral Ecosystem Management Project in Costa Rica[END_REF]. The corollary of their findings is that inducing the lasting adoption of more benign land uses is feasible. In the REDD+ context, this could, in turn, self-sustain the deforestation reduction reached by the initiatives.

On aggregate, permanence is clearly important for the effectiveness of any conservation intervention. It is true that conservation-focused payment programs will typically strive to make conditional contracts and payment flows renewable, but we cannot guarantee funding streams will last forever. Yet, our knowledge about the degree of, and factors influencing permanence remains quite limited -not only for REDD+, but also for other types of conservation payments. Even in the developed Global North, most empirical assessments of post-intervention permanence or 'persistence' are derived from stated landowner intentions, not de facto behavior [START_REF] Swann | What factors influence the effectiveness of financial incentives on long-term natural resource management practice change?[END_REF]. It seems likely that permanence is higher for incentives that are linked to assetbuilding, rather than activity-restricting conservation action [START_REF] Dayer | Private Landowner Conservation Behavior Following Participation in Voluntary Incentive Programs: Recommendations to Facilitate Behavioral Persistence[END_REF], but surely the socio-institutional context will also matter at different scales [START_REF] Rasch | Permanence of PES and the role of social context in the Regional Integrated Silvo-pastoral Ecosystem Management Project in Costa Rica[END_REF].

In this article, we investigate the effects of a local REDD+ initiative in the Brazilian Amazon on deforestation and people's well-being, including intra-community spillover effects (leakage), scrutinizing in particular to what extent outcomes persisted after the initiative and associated 'treatments' ended, thus helping to fill a knowledge gap on REDD+ permanence. The remainder of the paper is organized as follows. In Section 2, we present the study site plus all applied REDD+ interventions. Section 3 accounts for the methods for our sampling and panel data collection. In Section 4, we present our quasi-experimental approach to estimate both short and long-term impacts of the REDD+ initiative. We then show the longitudinal effects of the REDD+ initiative on both deforestation and people's well-being (Section 5). In Section 6, we explore possible explanations for our estimation results, and in the last section, we present conclusions.

The Transamazon REDD+ initiative

As part of CIFOR's GCS REDD+, we scrutinized the Projeto Assentamentos Sustentáveis na Amazônia (PAS), a REDD+ initiative implemented by a Brazilian non-governmental organization (Instituto de Pesquisa Ambiental da Amazônia -IPAM). PAS started in 2012 but it was suspended in 2017, after IPAM had its refinancing request denied by the Amazon Fund.

Approximately 2,700 households from the western part of the Pará state (Brazil) participated in PAS (IPAM, 2016). However, our study only focused on the 350 households for which IPAM offered PES (see all interventions' description below). They lived in twelve communities located in the municipalities of Anapu, Pacajá and Senador José Porfírio, near the Transamazon highway. This is a high-deforestation area dominated by smallholders (properties up to 100 ha), mostly colonists from the northeast part of the country [START_REF] Godar | Typology and characterization of Amazon colonists: A case study along the Transamazon highway[END_REF][START_REF] Stella | O Projeto Assentamentos Sustentáveis (PAS)[END_REF]. The 350 households had participated in a previous PES-ICDP mixed federal program (Proambiente) from 2003 and 2006, where actual payments were delivered only for six months though [START_REF] Bartels | Diversifying livelihood systems, strengthening social networks and rewarding environmental stewardship among small-scale producers in the Brazilian Amazon: lessons from Proambiente[END_REF][START_REF] Simonet | Effectiveness of a REDD+ project in reducing deforestation in the Brazilian Amazon[END_REF].

Households' main economic activities were cattle ranching and swidden agriculture. Part of the production was sold (e.g., rice, cassava, cocoa), despite poor transportation infrastructure.

Secondarily, households depended on forest resources, collected mainly for auto-consumption, such as firewood for cooking, fruits, fish and bushmeat, in addition to monetary income from other sources, especially from government transfers, such as retirement pensions and the Bolsa Família conditional cash transfer program (Cromberg et al., 2014b).

The central goal of PAS was to reduce deforestation rates, mainly by increasing profitability in pasture and agricultural plots. To do that, IPAM relied on a ICDP-PES mixed approach, with project activities divided into the following four main components [START_REF] Simonet | Effectiveness of a REDD+ project in reducing deforestation in the Brazilian Amazon[END_REF].

b. Properties environmental registration

The Forest Code also requires rural landowners to register their properties in the Rural Environmental Registry (Cadastro Ambiental Rural -CAR), a public document with information on property boundaries and the location of its areas set aside for protection (Legal Reserve and Permanently Protected Area). During 2012-14, IPAM provided administrative support for CAR registration, as a main instrument for forest monitoring in Brazil. It is legally required when rural landowners want to sell cattle or to access rural credit.

c. Payments for Environmental Services

IPAM offered direct cash payments for households whose properties had at least 30% of forest cover (IPAM, 2016). Contracts were signed in 2013, and quarterly payments were provided from 2014 to 2017. Households could receive up to 1,600 BRL/year (725 USD/year, as of 07/01/2014), depending on the level of compliance with the following conditionalities (Cromberg et al., 2014a): (i) 30% of the payment was contingent upon the conservation of at least 50% of the property as forest (Legal Reserve); (ii) another 30% was contingent upon the conservation of 15 meters-wide forest riparian zones (the Permanently Protected Areas); (iii) the 40% left was based on the adoption of fire-free land management [START_REF] Simonet | Effectiveness of a REDD+ project in reducing deforestation in the Brazilian Amazon[END_REF].

d. Sustainable livelihood alternatives (ICDP component)

IPAM promoted sustainable livelihood alternatives in the project area, such as cattle ranching intensification, agroforestry (e.g., cacao -Theobroma cacao, açaí -Euterpe oleracea, babassu -Attalea speciosa), vegetables (e.g., lettuce -Lactuca sativa, cabbage -Brassica oleracea var. Treatment communities were randomly selected among the twelve communities in which IPAM intended to implement the initiative. Control communities were selected from a pool of fifteen other Transamazon communities, based on a pre-matching procedure to find communities with similar characteristics likely to influence both initiative placement and land use/well-being outcomes (e.g., forest cover, deforestation pressures, and distance to the main road) [START_REF] Sunderlin | Technical guidelines for research on REDD+ subnational initiatives[END_REF].

Sampling and data collection

For our analysis, the key unit is the household, defined here as the group of people, usually family members, living under the same roof and pooling resources [START_REF] Sunderlin | Technical guidelines for research on REDD+ subnational initiatives[END_REF]. We chose this level because households make the deforestation decisions, mainly driven by farming, and received REDD+ incentives (e.g., PES, sustainable livelihood alternatives).

In each of the four treatment and four control communities, 30 households (240 in total) were randomly selected for interviews in the baseline period. The sample in treatment communities was further stratified to include both PAS participants and non-participants, a procedure adopted to investigate intra-community spillover effects. A total of 113 households were interviewed in the three survey points (2010,2014,2019), comprising three different groups: 46 control households; 52 treatment households (i.e. participated in REDD+ initiative, receiving all interventions described in Section 2); and 35 non-participant households (i.e. did not participate in REDD+, but inhabited treatment communities).

Empirical strategy

Assessing short-term outcomes

Our first goal was to assess the outcomes of the REDD+ initiative on deforestation and household wellbeing, respectively. To do so, we adopted a DID approach also known as Before-After-Control-Impact (BACI) evaluation. Thus, we assumed that changes in outcome variables from pre-to post-intervention in the control group represented what would have happened to the treatment group without the intervention (counterfactual scenario) [START_REF] Fredriksson | Impact evaluation using Difference-in-Differences[END_REF].

For this to be credible, both groups should follow the same trend in pre-treatment outcomes (parallel trend assumption). This assumption implies that, in the absence of the treatment, outcomes for the treatment and control groups would change at the same rate [START_REF] Ryan | Now trending: Coping with nonparallel trends in difference-in-differences analysis[END_REF]. Indeed, the parallel trend assumption was confirmed using a placebo test over a pre-treatment period (2008)(2009)(2010) in which no effects were detected (Appendix A). Accordingly, we estimated the impact of the intervention on treatment households by calculating the difference between the changes in outcomes over time (between 2010 -the baseline -and 2014 -two years post the REDD+ indicative's launch) from the control and treatment groups. This is the so-called Average Treatment Effect on the Treated (ATT): ATT = E (y 1 -y 0 |D = 1), where y 1 denotes the result variable under the treatment, y 0 the same variable in the absence of treatment, and D is a dummy that takes on the value of one when the household has been treated, and zero otherwise. We adopted two outcome variables (Table 1): (i) forest cover (% of primary and secondary forest in the household property), as self-stated by household respondents, and selectively validated through remote-sensing data (cf. discussion below), as our proxy for deforestation; (ii) perceived wellbeing (self-declared by household respondents in interviews, compared to previous years: 1 = improved; 0 = not improved). As the intervention was not randomly attributed, confounders could be unevenly distributed between treatment and control groups [START_REF] Ferraro | Money for Nothing? A Call for Empirical Evaluation of Biodiversity Conservation Investments[END_REF]. Therefore, besides using DID to control for time-invariant unobserved confounders [START_REF] Deschenes | Quasi-Experimental Methods in Environmental Economics: Opportunities and Challenges[END_REF], we minimized selection bias combining DID with matching to preprocess the data and control for observable confounders [START_REF] Ho | Matching as nonparametric preprocessing for reducing model dependence in parametric causal inference[END_REF]. This means we applied the DID estimator to those households from treatment and control groups that were statistically similar in pre-treatment observable characteristics (baseline observable covariates -Table 1) [START_REF] Imbens | Nonparametric Estimation of Average Treatment Effects under Exogeneity: A Review[END_REF]. We adopted the nearest-neighbor matching estimator, by matching each treated household to two of the most similar control households [START_REF] Abadie | Implementing Matching Estimators for Average Treatment Effects in Stata[END_REF], as well as two robustness checks. For the first, we again used the nearest-neighbor, but this time matching each treated household to four of the most similar controls.

The second was the kernel-based propensity score matching, by which we compared households with the closest probability of being treated given the same set of observable covariates we used before [START_REF] Rosenbaum | The central role of the propensity score in observational studies for causal effects[END_REF].

Baseline values of observable covariates before matching were significantly different between treatment and control groups (Table 1). All normalized differences of the matching covariates, except for household members, were higher than 0.25 standard deviations. After matching, however, normalized differences dropped below 0.25, demonstrating that a plausible counterfactual was created from the matching procedure [START_REF] Imbens | Recent developments in the econometrics of program evaluation[END_REF]. To minimize the risk of bias in our household self-reported forest data, we cross-checked the estimates with remotely sensed data from the Brazilian Annual Land Use and Land Cover Mapping Project (MapBiomas) (www.mapbiomas.org). IPAM shared property boundaries from 43 of the 52 treated households in our sample. Through MapBiomas forest cover and total land area data, we analyzed changes in percent forest cover from 2010 to 2018 for these 43 overlapping households.

We found that estimates matched well to those derived from self-reported data. Paired t-test and ftest of annual differences in self-reported and observed forest cover revealed that they are not statistically significantly different in the means, as well as in standard deviations (see Appendix B).

Evaluating outcomes after the initiative ended

Our second goal was to evaluate to what extent potential outcomes persisted after the initiative ended. To this end, we also used the DID-matching estimators to compare differences in the same outcome variables (Table 1) over 2014 (during the initiative's implementation) and 2019

(two years after its end) between treatment and control groups. If the outcomes were sustained, we would expect similar results in this analysis than those with the comparison between 2010 (baseline) and 2014.

Intra-community spillover

Finally, to check for intra-community spillover effects, we reused the DID matching estimators to test for outcome variables differences between the control and the non-participant group, for 2010-14 and 2014-19, respectively. We first confirmed the parallel trend assumption for control and non-participant groups running another placebo test (Appendix A). We also compared the normalized differences of the matching covariates before and after matching, concluding once more that a plausible counterfactual had been constructed (Appendix C).

Results

Longitudinal impact assessment

Our results show that the REDD+ initiative achieved positive outcomes in terms of both forest conservation and perceived well-being improvement (Table 2). Aligned with the results of the earlier study on the effectiveness of PAS in reducing deforestation [START_REF] Simonet | Effectiveness of a REDD+ project in reducing deforestation in the Brazilian Amazon[END_REF], ATT for forest cover was significant for all DID matching estimators in the first period . This implies an average of 7.80% to 10.32% of forest cover was saved by the initiative, or the equivalent of 6.20 to 8.20 ha per farm, given that the average land area of the treatment group was 79.45 ha in 2014 (Table 1). Moreover, ATT for perceived wellbeing was also positively significant in this first period: the REDD+ initiative increased the probability of improved enrollee perception of wellbeing by 27% to 44%. Cohens' d for forest cover (0.32 -Table 3) and perceived wellbeing (0.37) were numerically similar, both indicating small-to-medium effect sizes according to [START_REF] Sawilowsky | Very large and huge effect sizes[END_REF] (0.01 = very small; 0.2 = small; 0.5 = medium; 0.8 = large; 1.2 = very large; 2.0 = huge). However, according to our estimates, deforestation resumed after the initiative ended (Table 2). Indeed, for the second period (2014-2019), we found that ATT from all DID matching estimators were non-significant for forest cover. We also detected a significant negative impact on perceived well-being for the same period.

The results for forest cover change from the nearest neighbor estimator, using two matched observations as controls, are provided in Figure 3. We observe that forest cover continued to decrease from 2008 to 2019 in both treatment and control groups. However, there is a break in the forest loss trend between 2010 and 2014 in the treatment group. Despite that, from 2014 and 2019, the treatment group lost forests again in a similar trend to the control group. Note: Treated households: 52 that had participated in the REDD+ initiative. Matched control households: 40 that matched to treated households using nearest neighbor estimator with two matched observations as controls, from the total of 46 households living in the control communities. Forest cover was estimated in 2008 as a recall period from the 2010 survey. The REDD+ initiative started in 2012 and ended in 2017 (see Figure 1).

Intra-community spillover

We found no evidence for intra-community spillover effects for the REDD+ initiative (Appendix D). ATT from all DID matching estimators were insignificant for forest cover and perceived well-being in both periods (2010-2014; 2014-2019).

Discussion

Short-term effects on forests and well-being

Our results indicate the REDD+ initiative investigated here for the group of ICDP-cum-PES treated households achieved win-win outcomes in terms of reducing deforestation and improving well-being while it was being implemented. These findings therefore add to the emerging evidence that REDD+ initiatives have demonstrated statistically significant success in reducing deforestation [START_REF] Simonet | Forests and Carbon. The impacts of local REDD+ initiatives[END_REF]. Moreover, our findings highlight positive impacts on perceived well-being, which differ from observations in other REDD+ initiatives that evidenced insignificant impacts [START_REF] Sunderlin | REDD+ contribution towell-being and income is marginal: The perspective of local stakeholders[END_REF].

Notably, we found no evidence that deforestation reduction reached by the REDD+ initiative was offset by intra-community spillover. This means that, according to our estimations, reducing deforestation in REDD+ participant properties did not lead to an increase in deforestation in nonparticipant properties. This could have occurred, for instance, if participants had shifted their deforestation activities to non-enrolled plots, which would have reduced REDD+ net impacts as a consequence [START_REF] Pfaff | Spillovers from conservation programs[END_REF].

As this REDD+ initiative was based on a mix of on-the-ground interventions (see Section 2),

we might want to also discuss the likely efficiency across different components. We conjecture the original deforestation reduction likely resulted more from PES than from the ICDP-type sustainable livelihood alternatives or CAR registration, for two reasons. First, in 2014, households were surveyed when the REDD+ initiative was still beginning (Figure 1), therefore before the main If the initial outcomes did result mostly from PES, as we believe, our findings corroborate the majority of studies employing counterfactual designs, showing the potential effectiveness of PES in forest conservation (e.g., [START_REF] Shapiro | Forest Conservation and Slippage: Evidence from Mexico's National Payments for Ecosystem Services Program[END_REF][START_REF] Costedoat | How effective are biodiversity conservation payments in Mexico?[END_REF][START_REF] Jayachandran | Cash for carbon: A randomized trial of payments for ecosystem services to reduce deforestation[END_REF][START_REF] Montoya-Zumaeta | Adding rewards to regulation: The impacts of watershed conservation on land cover and household wellbeing in Moyobamba, Peru[END_REF][START_REF] Robalino | Ecopayments and deforestation in Costa Rica: A nationwide analysis of PSA's initial years[END_REF][START_REF] Scullion | Evaluating the environmental impact of payments for ecosystem services in Coatepec (Mexico) using remote sensing and on-site interviews[END_REF], and in delivering small but often significant wellbeing improvements (e.g., income, assets) (e.g., [START_REF] Duan | The Effects of the Sloping Land Conversion Program on Poverty Alleviation in the Wuling Mountainous Area of China[END_REF][START_REF] Hegde | Performance of an agro-forestry based Payments-for-Environmental-Services project in Mozambique: A household level analysis[END_REF]; Jack and Cardona Santos, 2017; Sims and Alix-Garcia, 2017; [START_REF] Uchida | Are the poor benefiting from China's land conservation program?[END_REF], despite fewer studies finding null impacts (e.g., [START_REF] Arriagada | Analysing the impacts of PES programmes beyond economic rationale: Perceptions of ecosystem services provision associated to the Mexican case[END_REF][START_REF] Arriagada | Combining qualitative and quantitative methods to evaluate participation in costa rica's program of payments for environmental services[END_REF][START_REF] Sánchez-Azofeifa | Costa Rica's payment for environmental services program: Intention, implementation, and impact[END_REF][START_REF] Wiik | Experimental evaluation of the impact of a payment for environmental services program on deforestation[END_REF]. The moderately positive outlook on PES for delivering these win-win outcomes is supported by more recent meta-studies and systematic reviews [START_REF] Snilsveit | Incentives for climate mitigation in the land use sector-the effects of payment for environmental services on environmental and socioeconomic outcomes in low-and middle-income countries: A mixed-methods systematic review[END_REF]Wunder et al., 2020a).

Our findings also align with the emerging evidence showing the effect size of PES on forest conservation outcomes is limited, even if our estimated effect sizes (0.32 - areas, certification, decentralized forest management) and they all exhibit small effect sizes in general [START_REF] Börner | The effectiveness of forest conservation policies and programs[END_REF]. In fact, PES has larger impacts than these other interventions, though differences are small (Wunder et al., 2020a).

Long-term effects of the REDD+ initiative

In our study, deforestation reductions and wellbeing improvements were more temporary than permanent -both improving trends reversed post-treatment. However, the REDD+ initiative still left a lasting gain for the environment: the treatment group cleared forests again as quickly as the control group, but without exceeding it to 'catch up' on the earlier mitigations, meaning there was a net forest gain over time [START_REF] Skutsch | Understanding permanence in REDD[END_REF]. Our findings therefore match very well with the aforementioned evaluation of the permanence outcomes from the PES RCT in Uganda (see Section 1) (World Bank, 2018). The study showed deforestation resumed among former PES recipients once payments ended, but without exceeding the reference scenario; thus, leaving the initial conservation gains intact.

Notably, the literature on PES permanence suggested that asset-building PES ('active establishment') may have better chances of locking in forest gains than activity-reducing ('passive conservation') PES, to the extent the former manage to lastingly boost the adoption of environmentally desirable land uses established (e.g. agroforestry systems) (see Section 1). In fact, this was the main goal of the REDD+ initiative investigated here when providing the ICDP investments in alternative livelihoods (see Section 2). Following this logic, one possible explanation for why deforestation reduction was not sustained after the REDD+ initiative ended could be that the alternative livelihood activities promoted did not take off, leastways at a desirable scale.

Notably, during the 3 rd data collection phase, 27 treated interviewees (i.e., 52%) declared they did not adopt alternative livelihood activities between 2014 (when the main ICDP-type support started) and 2019. Studies accessing conservation outcomes of ICDP-type programs indeed most indicate failures rather than successes [START_REF] Hughes | Integrating conservation and development experience: a review and bibliography of the ICDP literature, Biodiversity and Livelihoods Issues[END_REF][START_REF] Roe | Are alternative livelihood projects effective at reducing local threats to specified elements of biodiversity and/or improving or maintaining the conservation status of those elements?[END_REF]. This may be because programs often rely on upfront subsidies instead of conditional payments to promote alternative livelihood activities, which increases the risk of non-compliance [START_REF] Pagiola | Assessing the Permanence of Land-Use Change Induced by Payments for Environmental Services: Evidence From Nicaragua[END_REF]. Therefore, despite that targeted households had received technical assistance and free agricultural inputs, a significant part of them may have not adopted sustainable livelihood alternatives. Otherwise, lasting deforestation reduction outcomes might have been possible.

Concluding remarks

We presented one of the first evaluations of the permanence of a local REDD+ initiative's outcomes. We found that the PAS initiative reduced deforestation in the Transamazon region and improved the perceived well-being of treated households, while being actively implemented. Postintervention, deforestation resumed at a similar pace as the control group, yet without 'catching up' on the temporary forest gains made. Our results, therefore, suggest that temporary performancebased REDD+ benefit flows may effectively delay, though not permanently eradicate deforestation.

Still, they can be important in mitigating the climate change challenge the world is facing.

As long as the basic environmental externality persists, i.e. that standing forests privately cannot compete with the yields from alternative land uses, we should not expect the miracle that a temporary payment would permanently change the logic of the productive system. ICDP type of investments try to achieve exactly this type of change, but have typically been little successful, as also seems the case, at first sight, in the PAS initiative we analyzed. PES used as adoption subsidies for environmentally beneficial land uses seem to have a somewhat better record (see Section 1).

As for perceived wellbeing impacts, we failed to detect permanence of improvements; perceptions clearly improved during REDD+ implementation but were then negatively impacted after the initiative ended. Does that mean the project left no permanent welfare gains behind? We would be cautious to press such an extreme interpretation, given that ex-post stated negative subjective wellbeing can also sometimes be seen as a vote of protest against the sudden withdrawal of benefits that were expected to be steadily provided anew -and still go perfectly hand in hand with lastingly higher incomes (e.g. [START_REF] Montoya-Zumaeta | Adding rewards to regulation: The impacts of watershed conservation on land cover and household wellbeing in Moyobamba, Peru[END_REF].

We close by highlighting that the external validity of our study must be approached with two cautions. First, our analysis relied on a subsample of households that were targeted for PES payments; thus from this we cannot extrapolate to the entire PAS project (see Section 2). Second, REDD+ as implemented on the ground is a basket of interventions, which includes incentives (direct payments and alternative livelihood activities), disincentives (e.g., law enforcement) and enabling measures (e.g., tenure clarification) [START_REF] Duchelle | Balancing carrots and sticks in REDD+: Implications for social safeguards[END_REF]

  a. Awareness-raising meetings on environmental legislation and tenure regularization Between 2013 and 2017, IPAM conducted farmer meetings, explaining the processes involved in land tenure regularization (many local properties were not titled) and Brazilian environmental legislation, especially the Forest Code (Law 12.651/2012), which requires for rural properties in the Amazon to retain a fixed proportion of 50-80% of land covered with native vegetation (Legal Reserve). Failing to comply, landowners could be fined by environmental agencies, such as the federal Brazilian Institute for the Environment and Renewable Natural Resources (Instituto Brasileiro do Meio Ambiente e dos Recursos Renováveis -IBAMA).

  capitata) and black pepper (Piper nigrum). Between 2013 and 2016, IPAM developed customized property management plans together with household heads to decide which economic activities to develop. From 2014 to 2017, IPAM offered technical assistance through regular visits, and free inputs (e.g., wire for fences, fertilizers). According to IPAM, each household could choose a list of inputs valued at up to 5,000 Brazilian reais (BRL) (2,267 USD, as of 07/01/2014) for the planned activities.

Figure 1

 1 Figure 1 synthetizes the timeline of PAS activities, including data collection.

Figure 1 -

 1 Figure 1 -PAS implementation and CIFOR-GCS data collection timeline. Source: own elaboration, based on Cromberg et al. (2014b) and IPAM (2016).

  Identical survey instruments were employed through face-to-face interviews in four treatment and four control communities (Figure 2) in three time periods: June-July 2010 (baseline period), February-March 2014 (~2 years after the REDD+ initiative's onset) and March-May 2019 (~7 years after onset and 2 years after the initiative ended).

Figure 2 -

 2 Figure 2 -Location of both treatment and control communities along the Transamazon highway (Brazil).

Finally, following

 following [START_REF] Börner | The effectiveness of forest conservation policies and programs[END_REF] andWunder et al. (2020), we calculated normalized effect sizes (Cohen's d) as indicators of the magnitude of the initiative's impact on both forest cover and perceived well-being. The effect size is the standardized mean difference of the outcome variables between control and treatment groups[START_REF] Coe | It's the Effect Size, Stupid. What effect size is and why it is important[END_REF]. The formula is d = M1 -M0 / SDpooled, where M1 denotes the mean of the treatment group, M0 denotes the mean of the control group, and SDpooled = SD1 2 (N1 -1) + SD0 2 (N0 -1) / N0 -N1 -2, where SD1 2 and SD0 2 are the square of the respective standard deviations, and N1 and N0 are the respective sample sizes[START_REF] Acock | A Gentle Introduction to Stata[END_REF].

Figure 3 -

 3 Figure 3 -Forest cover (% of forest of the household property) change among treated and their matched control households.

  livelihood alternatives (technical assistance, free agricultural inputs) were delivered. Although the first conditional payment also occurred soon after the 2014 survey, PES contracts were signed earlier (beginning of 2013). It is therefore reasonable to suppose that households could have reduced deforestation in the dry season of 2013 (when they usually convert forest to pasture/crops) in anticipation of conditional payments that would begin around March 2014. Similarly, perceived wellbeing improvements could have resulted from an expectation of the payments that would start soon. Second, besides IPAM, several other organizations offered administrative support in the Transamazonian region for registering households' properties under CAR. As a result, most of the control households received the same intervention from elsewhere, as already noted by Simonet et al. (2019).

Table 1 -

 1 Summary statistics for treatment and control groups.

	Variables	Treatment group	Control group	ND
	Pre-treatment variables	Mean	Std dev.	Mean	Std dev.	Raw	Matched
	Forest cover in 2008 (% of land area)*	0.75	0.16	0.64	0.23	0.55	0.09
	Forest cover in 2010 (% of land area)*	0.70	0.16	0.60	0.23	0.52	0.04
	Total land area in 2010 (ha)*	79.45	35.19	91.61	54.39	-0.26	-0.01
	Total income in 2010 (BRL)*	27,931.35 21,525.78 34,906.54 25,455.53	-0.29	0.06
	Household head age in 2010 (years)*	48.48	11.45	53.91	11.42	0.47	0.12
	Household members in 2010 (number)*	5.54	2.45	5.33	2.63	0.08	0.07
	Perceived well-being in 2010 (1 =	0.65	0.48	0.59	0.50	-	-
	improved; 0 = not improved)
	Post-treatment variables
	Forest cover in 2014 (% of land area)	0.65	0.19	0.50	0.24	-	-
	Forest cover in 2019 (% of land area)	0.54	0.23	0.45	0.24	-	-
	Perceived well-being in 2014 (1 =	0.79	0.41	0.46	0.50	-	-
	improved; 0 = not improved)
	Perceived well-being in 2019 (1 =	0.58	0.50	0.35	0.48	-	-
	improved; 0 = not improved)
	Total land area in 2014 (ha)	79.45	35.19	91.61	54.39	-	-
	Note: *matching covariates. Treatment group: 52 households that participated in the REDD+ initiative. Control group:
	46 households living in the control communities. ND: normalized differences between the two groups. Forest cover was
	estimated for 2008 as a recall period from the 2010 survey.

Table 2 -

 2 Longitudinal forest and wellbeing impacts of the REDD+ initiative on the treatment group.

	DID-matching	Forest cover	Perceived well-being
	estimator	(%)		(1 = improved; 0 = not improved)
		2010-2014	2014-2019	2010-2014	2014-2019
		Coeff a (S.E.) b	Coeff (S.E.)	Coeff (S.E.)	Coeff (S.E.)
	NNM(2X)	7.80* (4.36)	-1.75 (4.67)	0.45** (0.19)	-0.31** (0.15)
	NNM(4X)	8.08* (4.57)	-1.73 (5.29)	0.44** (0.18)	-0.28* (0.15)
	PSM(kernel)	10.32** (4.00)	-3.65 (4.87)	0.27* (0.16)	-0.17*** (0.15)
	Note: Significance level: *=10%; **=5%; ***= 1%. DID-matching estimators: nearest neighbor using four matched
	observations as controls (NNM(4X)) and using two matched observations (NNM(2X)); kernel-based propensity score
	matching (PSM(kernel)).

a Coefficient represents ATT (treated are the treatment group: 52 households that participated in the REDD+ initiative). b Standard errors in parentheses.

Table 3 -

 3 Normalized effect sizes (Cohen's d) of the outcomes. Treated households: 52 that had participated in the REDD+ initiative. Matched control households: 40 that matched to treated households using nearest neighbor estimator with two matched observations as controls, from the total of 46 households living in the control communities.

	Variables	Cohens' d	Treatment group	Matched control
					households
			Mean	Std dev.	Mean	Std dev.
	Δ Forest cover between 2010-2014 (%	0.32	0.05	0.11	-0.10	0.20
	of land area)
	Δ Perceived well-being between 2010-	0.37	0.13	0.63	-0.13	0.79
	2014 (1 = improved; 0 = not improved)
	Note:

  Table 3) were above average. Based on data from 19 studies measuring PES outcomes for forest conservation,Wunder et al. (2020a) showed Cohens' d effect size ranged from 0.0 to ~0.5, with an average value around 0.2.According to[START_REF] Sawilowsky | Very large and huge effect sizes[END_REF] interpretation of Cohens' d, this means PES effect size varies in reviewed studies from very small to medium, being small on average. However, to make a fair evaluation, PES must be compared with other forest conservation interventions (e.g., protected

  . Thus, any generalization to other REDD+ sites must consider, besides the local context, the type of interventions applied. *matching covariates. Non-participant group: 35 households from treatment communities that had not participated in the REDD+ initiative. Control group: 46 households living in the control communities. ND: normalized differences for the two groups. Forest cover was estimated in 2008 as a recall period from the 2010 survey.

	Forest cover in 2008 (% of land area)*	0.72	0.20	0.64	0.23	0.41	-0.04
	Forest cover in 2010 (% of land area)*	0.68	0.19	0.60	0.23	0.38	-0.08
	Total land area in 2010 (ha)*	117.70	101.30	91.61	54.39	0.32	0.17
	Total income in 2010 (BRL)*	43,224.72 74,367.73 34,906.54 25,455.53	0.16	0.20
	Household head age in 2010 (years)*	50.91	13.48	53.91	11.42 -0.29	-0.10
	Household members in 2010 (number)*	5.06	2.38	5.33	2.63 -0.13	-0.10
	Perceived well-being in 2010 (1 =	0.59	0.50	0.59	0.50	-	-
	improved; 0 = not improved)
	Post-treatment variables
	Forest cover in 2014 (% of land area)	0.61	0.21	0.50	0.24	-	-
	Forest cover in 2019 (% of land area)	0.55	0.22	0.45	0.24	-	-
	Perceived well -being in 2014 (1 =	0.62	0.49	0.46	0.50	-	-
	improved; 0 = not improved)
	Perceived well -being in 2019 (1 =	0.53	0.51	0.35	0.48	-	-
	improved; 0 = not improved)
	Total land area in 2014 (ha)	118.22	102.78	91.61	54.39	-	-
	Note:

As part of GCS REDD+, CIFOR and partners have assessed the outcomes of

local REDD+ initiatives in Brazil, Peru, Indonesia, Vietnam, Cameroon, and Tanzania. See more in: https://www.cifor.org/gcs/

Acknowledgments

We sincerely thank our fieldwork team, hosting families during fieldwork, and interviewees, as well as valuable comments from CIFOR workshop participants. This research is part of CIFOR's Global Comparative Study on REDD+ (www.cifor.org/gcs). The funding partners that have supported this research include the Norwegian Agency for Development Cooperation (Norad), the Australian Department of Foreign Affairs and Trade (DFAT), the European Commission (EC), the International Climate Initiative (IKI) of the German Federal Ministry for the Environment, Nature Conservation and Nuclear Safety (BMU), the United Kingdom Department for International Development (UKAID), and the CGIAR Research Program on Forests, Trees and Agroforestry (CRP-FTA), with financial support from the donors contributing to the CGIAR Fund. C.D.C. was funded by a studentship from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brasil (CAPES) -Finance Code 001. We thank the University of São Paulo (USP) for providing infrastructural support.

Appendix A. Impact on treatment and non-participant groups over 2008 and 2010 (placebo test).

DID-matching estimator

Forest cover (%) Treatment group Coeff a (S.E.) b Non-participant group Coeff (S.E.) NNM(4X) 0.00 (0.00) 0.00 (0.00) NNM(2X) 0.00 (0.00) 0.00 (0.00) PSM (kernel) -0.71 (0.01) -0.45 (0.01) Note: Treatment group: 52 households that had participated in the REDD+ initiative. Non-participant group: 35 households from treatment communities that had not participated in the REDD+ initiative. No statistically significant effects were detected to both groups in comparison to the control group over the pre-treatment period (2008)(2009)(2010) N=52). The paired t-test of annual differences and the f-test of equality of variances revealed that self-reported and observed forest cover were not statistically significantly different both in the means and in standard deviations, confirming the validity of our self-reported data. We used MapBiomas data from the preceding years to our interview surveys because the Amazon dry season, when households usually convert forest to pasture/crops, runs between May-September, but interviews were conducted before this period or in its beginning (see Section 2).

Appendix C. Summary statistics for non-participants and control group.


Luis Romero
email: luis.romero.ben@upc.edu

Joaquim Blesa

Débora Alves

Gabriela Cembrano

Vicenç Puig

Eric Duviella

LEAK LOCALIZATION IN WATER DISTRIBUTION NETWORKS USING DATA-DRIVEN AND MODEL-BASED APPROACHES

Keywords: leak localization, water distribution network, model-based, data-driven, multi-leak problem

The worldwide growing demand of water supply requires a proper management of the available hydraulic resources. One of the major concerns in the operation of water distribution networks (WDNs) is the existence of leakages, due to the high operational costs for the water utilities. Leaks can produce substantial economic losses, infrastructure damage and even health risks. Therefore, leak detection and isolation methodologies are widely researched.

One the one hand, model-based approaches exploit the existence of a hydraulic model of the considered WDN, as well as the availability of hydraulic measurements like inlet flow and pressure, and sensorized inner nodes pressure, to tackle the leak localization task. The suitability of these methods has been confirmed by numerous works during the years. On the other hand, the sources of information in the majority of water networks are rather limited, and other interesting measurements are not available, like water demands at the junctions, flows between inner nodes, etc. Thus, datadriven approaches, which have a reduced or non-existent dependency on a hydraulic model, can be helpful to locate leaks in WDNs that lack the mentioned measurements and modelling. This abstract presents the combined utilization of a model-based and a novel data-driven methodology to locate leaks in the concrete case of the challenge proposed at BattLeDIM 2020. The division of the introduced network (L-Town) in three areas allows to determine the usage of one of the approaches at each one of these areas, depending on their concrete characteristics.

Besides, both methods allow to solve the multi-leak problem in a proper way, which entails a further step with regard to the classical single-leak assumption.

INTRODUCTION

In the last ten years, our research team, with a solid experience in fault diagnosis applied to different real applications, have developed several leak localization methods that include model-based methods [START_REF] Pérez | Methodology for leakage isolation using pressure sensitivity analysis in water distribution networks[END_REF], data-driven methods [START_REF] Soldevila | Leak Localization Method for Water-Distribution Networks Using a Data-Driven Model and Dempster-Shafer Reasoning[END_REF] and hybrid methods [START_REF] Soldevila | Leak localization in water distribution networks using a mixed model-based/data-driven approach[END_REF], which have successfully been applied to real WDNs. These methods considered inlet pressure and flow measurements, that are usually gathered in WDN for control purposes, and some pressure measurements in inner nodes from installed sensors that are easy and relatively cheap to install. The L-Town challenge in BattLeDIM 2020 introduces multi-leak scenarios including abrupt and incipient leaks. Additionally, the three areas composing the network present different kind and amount of sensors. These facts have motivated the development of two new leak localization methods: A new data-driven approach that benefits from the high density of pressure sensors installed in Area A and a new model-based method that benefits from demand measurements provided by Automated Metered Readings (AMRs) in most of the nodes of Area C. The model-based method has also been applied to Area B, where there is a very low density of pressure measurements to apply the datadriven method. In the following, both leak localization methods that are able to tackle the multi-leak problem are described in more detail.

DATA-DRIVEN APPROACH

An explicative diagram of the novel data-driven leak localization procedure is displayed in Figure 1. It consists of a two-phase process:

1. From the hydraulic measurements gathered by the installed pressure sensors, as well as the topology of the WDN, the complete state of the network is estimated. The sensorized nodes state value will correspond to their exact hydraulic head, whereas the state of the rest of the nodes will consist of an approximation of the actual hydraulic head. 2. From the analysis of the current and nominal complete states, achieved from the network state interpolation of the current leaky data and historical non-leaky data respectively, a specific area of the network is considered as the source of the leak. An estimation of a more precise location of the leak is derived from the distance metric that is exploited to select the candidates.

As mentioned above, this methodology has been applied to Area A, due to the existence of 29 sensors distributed among the 659 nodes contained in the area. To face the presented challenge, the method is extended to locate pipe leaks by assuming the leak to be located in the pipe that connects the best node candidates.

Network state interpolation

The proposed state estimation method is based on two main ideas:

1. To introduce a simplification in the relation between the states of nodes of the network. The information of the measured nodes would be extended to the rest of nodes by means of a simple and linear equation. Hence, the state of the network does not represent exact hydraulic variables (except for the sensorized nodes), although it properly estimates them. 2. To exploit the graph associated to the WDN structure to perform the estimation of the states.

This translates to the utilization of the nodes adjacency and the network flows directionality to induce a better approximation of the states. , being 𝑛 the total number of nodes. 𝒘 𝑖 stands for the i th row of a weight matrix 𝑊, achieved from the lengths of the pipes of the network (these distances must be inverted so that close nodes share a high weight value). The second part of the cost function, together with the inequality constraint, allow to impose a condition about the flow directionality by means of the incidence matrix 𝐵 , in order to obtain more accurate state interpolations. Finally, the equality constraint sets the sensorized nodes states to their respective head value, achieved from the sensors measurements.

An example of the obtained results by means of this interpolation method is shown in Figure 2.

Leak candidate selection method (LCSM)

The key idea of the second part of the method consists of considering the state of a healthy situation of the network, 𝒙 𝑛𝑜𝑚 , and the state of the scenario with leak, 𝒙 𝑙𝑒𝑎𝑘 , to be the 𝑥 -𝑦 coordinates of 𝑛 points in ℝ 2 . Then, the best fitting line for the obtained points cloud is computed, and the perpendicular distance, with sign, from each individual point to the line is computed. The importance of the sign lies in the assumption that leaky points tend to undergo a larger pressure value reduction in comparison to non-leaky nodes. This effect would be more noticeable in nodes which are close to the leaky one. The produced line directly depends on the values of all the nodes, and hence the distance between a certain node location in ℝ 2 and this line not only encodes information about the change of state in that node, but also the relation among states of nodes of the network.

Due to the large set of nodes that may fulfil the requirement of having a positive distance value, they need to be filtered. To solve this problem, the standard deviation of the distance vector is computed, using the achieved value as a threshold.

The set of final candidates for the presented example is displayed in Figure 4. Additionally, a detailed image is presented in the form of a colour map. The colour of each node depends on the distance value provided by the LCSM method: the greener the node, the higher the distance. The proximity of the red and blue ellipses illustrates the good performance of the proposed method. Nevertheless, notice that the goal of the method is to find a location area that contains the leak, but some degree of error may exist.

MODEL-BASED APPROACH

The model-based leak localization method developed and applied to Areas C and B relies on the scheme depicted in Fig. 4, based on computing pressures for different the leak scenarios (hypothesis) and matching actual pressure measurements with the most probable leak hypothesis. . Therefore, a leak detection algorithm is necessary to determine at which time a leak is present in every area and to provide an estimation of its magnitude. In this work, leak detection and estimation is carried out by means the analysis of two inlet flows evolutions: the total inlet flow minus the pump flow to reservoir of Area C to detect and estimate leaks in area A and B and the output flow of reservoir of Area C compared with AMRs measurements to detect and estimate leaks in Area C.

BATTLE APPLICATION and CONCLUSIONS

This abstract presents a combined leak localization model-based/data-driven approach, applying each technique depending on the characteristics of the network. This methodology was used for the BattLeDIM 2020 challenge, and was applied, as stated, for the training and testing datasets. About the training results, some key aspects can be highlighted:

-About the data-driven method, the eight leaks of 2018 in Area A, that are said to be located and fixed by the water utility of L-TOWN, were found by the leak localization approach, as they were contained by the candidates set. There was a mean distance of 5.6 pipes from the leak to the best candidate, regarding that two of the leaks (p232 & p369) highly increase this mean value. If they are not considered, the mean is reduced to 3.5 pipes. It was discovered that this behaviour is caused by the pipe distance from the leaks to the sensors. If considering only the problematic leaks, the mean distance from the nearest sensors to the leak is 337.1 m, while this value is 158.7 m for the mean of the rest of the leaks. -About the model-based technique, the reported leak of 2018 in Area C was detected and located at the pipe level. In addition, a non-reported leak was also detected and located. On the other hand, the leak of 2018 in Area B, was detected and located with an error of one pipe.

The testing results are included at the attached text file. The 2019 dataset implies a higher level of difficulty, due to the existence of several incipient leaks that are not fixed, which hinder the performance of the data-driven method, as well as the leak estimation for the model-based method.

The proposed approach is applicable to a broad class of water networks and leak situations, since it considers different options, e.g. for networks where no hydraulic model is available, taking advantage of a deployment of pressure sensors, or for networks with AMR and a reliable hydraulic model. Similarly, it considers single-leak and multiple-leak situations.

Figure 1 :

 1 Figure 1: Workflow scheme of the complete data-driven leak localization approach.

Figure 2 :

 2 Figure 2: Comparison between the complete network state estimation, obtained for three different scenarios: a hydraulic simulation of a nominal situation, a graph-based interpolation of a nominal situation and a graph-based interpolation of a situation with a leak.

Figure 3 :

 3 Figure 3: Representation of the set of candidates (right) together with a colour map of the distance value for each candidate (left). The red ellipse encircles the actual leaky pipe, while the blue ellipse indicates the zone with higher distances in the LCSM method.

Figure 4 :

 4 Figure 4: Workflow scheme of the model-based leak localization approach (left) and localization result for the fixed leak in Area C during 2018 (right). Note that pressures of leak hypothesis are computed by an Epanet WDN model that considers user demands measured (if there are AMRs) and non-leak demands computed by the expected total demand distribution of the effective inlet flow (measured inlet flow minus leak estimation magnitudes) where there are not AMR measurements. In addition, the estimation of leaks produced in previous instants 11 11 .... N j jN ll    are introduced in the nodes where the leak have been located in

  Both objectives can be reached by solving the following optimization problem to obtain the network state estimator 𝒙: 𝐿, and 𝐷 and 𝐿 are the degree matrix and the Laplacian of the graph associated to the WDN topology, respectively. In this way, the first part of the cost function introduces the simplification of the relation among nodes by means of the harmonization property, i.e., 𝒙 𝑇 𝐻𝒙 =

		𝑚𝑖𝑛 𝒙 𝑠. 𝑡.	1 2 𝐵 ⋅ 𝒙 ≤ 𝜸 [𝒙 𝑇 𝐻𝒙 + 𝜏𝛾 2 ]
			𝑆 ⋅ 𝒙 = 𝒙 𝑠
	where 𝐻 = 𝐿𝐷 -2 ∑ [𝑥 𝑖 -1 𝑑 𝑖𝑖 𝒘 𝑖 𝒙 ] 𝑖=1 𝑛	2


Marine Paucsik

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Self-compassion and savouring buffer the impact of the first year of the COVID-19 on PhD students' mental health

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