Bayesian networks estimate regulating-service assets for Oslo’s urban tree canopies

A study of Oslo’s built zone estimated the present value of regulating services associated with 406,000 mapped tree canopies at 5.42 billion Norwegian kroner in 2014. The proof-of-principle ecosystem account combined ground observations of 16,189 municipally owned trees with an ecosystem-service model, high-resolution laser mapping and spatial Bayesian networks. It covered four modelled services: air-pollution removal, avoidance of stormwater runoff, carbon sequestration and building-energy savings. The resulting citywide total was an estimate, not a direct market valuation, and the researchers emphasized that uncertainty limits its use for fine-scale policy decisions and legal compensation.

The approach responds to a research and development agenda in the UN System of Environmental-Economic Accounting, which seeks methods for monetary accounts of ecosystem assets in urban areas. Asset accounting places a present value on expected future flows of ecosystem services rather than adding only the annual value of those flows. For each sampled tree, the researchers used i-Tree Eco to estimate annual monetary benefits and then discounted those benefits over the tree’s expected lifetime at a 1.4% social discount rate, a rate recommended for investment in climate-change mitigation. The sampled inventory included tree characteristics and location data augmented through a geographic information system method.

Extending the model to private and other unmanaged trees was the central challenge. The researchers used lidar data, digital terrain maps, municipal tree inventories, building information and land-use data to identify canopy height, crown area and other characteristics for 406,000 tree crown polygons across Oslo’s built zone. A polygon can contain more than one trunk, but the number beneath it was unobserved, so each polygon was represented as one asset and canopy area was used as a proxy for leaf area index. This spatial coverage did not imply that every individual tree in Oslo had been surveyed, and the approach introduced extra uncertainty for carbon estimates derived from canopy size rather than measured stem dimensions.

At the centre of the analysis, a Bayesian network emulated the joint relationships between inputs to i-Tree Eco and its asset-value outputs. Machine learning retained canopy height, diameter at breast height, crown area and air pollution as the variables most strongly associated with service values in the municipal-tree sample. The network represented uncertainty as probability distributions rather than producing one fixed estimate for every location. Its structure was guided by known relationships, including the influence of pollution zones on tree characteristics, and it was used to assess the consequences of estimating values for trees whose trunk diameter had not been measured directly.

The need to retain individual predictions became especially important because Oslo’s mapped trees had a highly skewed distribution of value. Small, young trees were much more numerous than large, older trees. Across the mapped trees, the average predicted 5th-percentile asset value was 3,414 kroner per tree, the median was 12,005 kroner and the 95th percentile was 25,912 kroner. Summing the model’s individual predictions produced the 5.42-billion-kroner total for the built zone in 2014. By contrast, multiplying a mean value per square metre of canopy by the area in each height class gave 7.31 billion kroner, demonstrating the potential inflation that can arise when averages are transferred to a population with a strongly non-normal distribution.

Air pollution was the dominant driver of the simulated values, accounting for about 200 of the roughly 220 kroner in annual regulating-service value for an average tree and approximately 94% of the asset value in the i-Tree simulation. The network also captured associations among pollution, crown size, height, stem width and species composition. The largest canopies were commonly located in lower-pollution zones with less dense development, whereas trees in highly polluted areas tended to have smaller crowns and different species distributions. Municipal trees were concentrated in streets and parks, particularly near the city centre and major roads, and are actively managed; these characteristics may not represent privately managed or unmanaged trees.

The authors applied the account to Oslo’s Small House Regulation Plan, an area of about 3,000 hectares containing roughly 28,000 properties. Lidar-derived modelling indicated a net canopy loss of 70 decares, or 70,000 square metres, between 2011 and 2017, about 1% of canopy cover. That total was smaller than the estimated error of the lidar classification and tree-segmentation model, so the researchers did not regard it as a significant aggregate change over the six-year period. Differences in lidar resolution and classification between periods may also have affected the estimates. Tree height nevertheless showed a clearer pattern: gains were concentrated among trees below 15 metres, while established trees above that height declined.

When the Bayesian-network model was linked to the physical extent-and-condition account, the inferred value of regulating-service assets in the regulation area fell by about 21 million kroner, or approximately 2%, over 2011–2017. That decrease was not significant relative to the combined uncertainty from tree segmentation and asset-value inference. At the aggregate level, therefore, the study found no significant loss of regulating services, and the expanded canopy area of numerous small trees numerically compensated for the loss of fewer large trees. The spatial results were less even: areas closer to the centre on Oslo’s northwestern side were more likely to show net losses, whereas the southeastern part of the city had a mixed pattern.

The study identified several applications with different accuracy requirements. A large aggregate estimate can raise awareness of tree canopies as infrastructure, while time-series accounts can track canopy extent, condition and modelled service values during urban development. Spatial accounts can also support priority-setting by locating neighbourhoods with canopy losses or potential gains. Yet the study warned that a total conceals locally unequal benefits from pollution removal, runoff control and energy savings. It also found that, after adjustment to 2019 prices, the estimated value of regulating services from all mapped trees was equivalent to about 0.42% of the value of Oslo’s building stock, highlighting the scale of urban nature without treating the two asset classes as interchangeable.

Several limitations remain. The analysis did not include cultural services such as views, and accounting prices and the discount rate were fixed rather than varying across space. The monetary model assumed that current air-pollution levels would persist over each tree’s expected life; declining pollution could therefore cause pollution-removal benefits, and their discounted asset value, to be overstated. Calculations also excluded replacement planting when a tree reached the end of its life, while the use of present-day tree size for future flows may underestimate young trees that have not reached their growth potential. Future work identified in the study includes testing alternative management assumptions and accounting for changes in climate, air quality, carbon prices and stormwater costs. The Oslo results therefore demonstrate a way to extend scarce field data across an urban accounting area while preserving uncertainty, rather than a definitive price for every urban tree.

Subject of Research: Spatial Bayesian estimation of regulating-service asset values for urban tree canopies in Oslo’s built zone

Article Title: Value ‘generalisation’ in ecosystem accounting – using Bayesian networks to infer the asset value of regulating services for urban trees in Oslo

Article References: Barton, D. N. (2023). Value ‘generalisation’ in ecosystem accounting – using Bayesian networks to infer the asset value of regulating services for urban trees in Oslo. One Ecosystem, 8, Article e85021. https://doi.org/10.3897/oneeco.8.e85021

Image Credits: AI Generated

DOI: 10.3897/oneeco.8.e85021

Keywords: urban trees, ecosystem accounting, Bayesian networks, i-Tree Eco, lidar mapping, natural capital, regulating services, Oslo, urban planning, value generalisation, Value, generalisation