Selecting Reference Cities for i-Tree Streets

Background

The primary goal behind finding the best match is to produce benefit estimates that are as accurate as possible. In other words, total benefits obtained using reference city X are closer to actual than obtained using reference city Y or Z. Because i-Tree Streets is a simulation model, its results can only approximate reality. Determining the magnitude and source of errors is difficult due to the complex collection of input data and simulation models. A systematic analysis of the sensitivity of i-Tree Streets’ output to the probabilistic range of possible input values has not been undertaken. However, all model inputs have been identified with errors grouped into six categories.

1. Sampling error. A sampling error expresses how well a tree sample reflects the actual tree population. There is no sampling error for a complete inventory.

2. Formulaic error. Errors of this type are related primarily to formulation and application of tree growth models. Within-class errors result from using dbh class midpoints to quantify benefits, when in reality tree sizes may be distributed throughout each size class. Tree size and growth errors are confidence intervals for each dimension that depict increasing variability with size. Species assignment errors result from matching species not sampled to one of the 22 species sampled in the reference city. The magnitude of this error depends on the proportion of population assigned, as well as goodness of fit in terms of matching sizes and annual growth for leaf area, dbh, and other size parameters.

3. Pricing errors. These are errors concerning the selection of values for pricing benefits and costs.

4. Resource unit errors. Resource unit or RU (engineering units such as cubic meters of rainfall intercepted), model errors are related to selection of input data, parameterization of individual models that produce RUs (e.g., building energy use, pollutant deposition, biomass formulas), choice of adjustment factors (e.g., adjacent shade, VOC emission rates), and their assignment to species.

5. Temporal errors. These are errors related to the selection of a particular year of input data. Different years may be used for different numerical models.

6. Spatial errors. Errors related to using data separated by some distance from the region of interest, the use of point measurements of air quality concentrations, precipitation, and other meteorological data for a large area.

Sources of errors that pertain to reference city selection are formulaic: species assignment errors due to a lack of sampled tree species and inaccurate tree dimensions. Also, spatial errors result in inaccurate estimates when reference city meteorological and other geographic data are not representative of the subject city.

Criteria

The approach adopted here attempts to simplify the selection process by limiting the analysis to several criteria: species composition, heating and cooling degree days, and annual precipitation. These criteria were selected because the data are widely available and highly relevant to tree benefit estimation. The approach can include other criteria, such as air pollutant concentrations. For example, if the subject city has very clean air, selecting a reference city with unclean air will result in overestimates of pollutant deposition. However, substantial resources may be required to obtain and manipulate raw data to derive useful indicators for comparison purposes.

Analysis

To determine which reference city (RC) best matches the subject city (SC) the analyst calculates the root mean squared error (RMSE) for each reference city. The city with the lowest RMSE is the best match. The RMSE is calculated as:

where,

• HDD_SC and HDD_RCi are Heating Degree Days for the subject city and reference city i

• CDD_SC and CDD_RCi are Cooling Degree Days for the subject city and reference city i

• AP_SC and AP_RCi are annual precipitation for the subject city and reference city i

• TM_RCi is the percentage of tree species/genera that match for reference city i (whole number)

• a, b, c, and d are nonnegative coefficients that add to 1.0 and express the relative importance of each criterion.

This approach requires two-steps. First, raw and difference values for each criterion are normalized so that they range from 0 to 10. Lower values indicate a better match with the reference city than higher values. The second step weights each of the four criteria based on its relative importance. It is recognized that the Tree Match criterion is fundamentally different than the others because the raw value remains the value of interest. For the other criteria, the value of interest is a difference value obtained by subtracting reference city raw values from subject city raw values. Because the Tree Match values are unique, the types of statistical analyses that can be conducted to identify the best match are limited.

First, to normalize data the ranges of raw values are identified for each criterion and 10 equal intervals are calculated. Each of the raw and difference values are normalized and given a value between 0 and 10. Linear interpolation is used to calculate the normalized values.

The second step is to assign a weight value to each coefficient that reflects its relative importance. For example, if the criteria are equally important, 0.25 is assigned to each of the four coefficients. The coefficient values must sum to 1.0. Factors influencing the relative importance of each criterion include extent of annual tree growth, severity of the climate, seasonality of rainfall, and total amount of annual rainfall. For example, in a northern latitude city with cold, snowy winters and cool, dry summers, it is more important to match HDDs than CDDs or annual precipitation. In a coastal region with mild temperatures and much rainfall, it is more important to match annual precipitation than HDDs and CDDs.

Comparable Reference Cities

Initially, the number of candidate reference cities is pared down from sixteen by excluding cities that are obvious mismatches and cities with similar values for the selection criteria. Comparing reference city data (Appendix; Tables 1–2) with values for Lisbon, Portugal (Table 3) indicate annual rainfall (622 and 702 mm, respectively) and CDDs (383 and 474, respectively), in Minneapolis, MN, are good matches with Lisbon. CDDs and the tree species composition in Fort Collins, CO, also have much in common with Lisbon (Table 3). Claremont, Santa Monica, and Modesto, CA, share Lisbon’s Mediterranean climate. HDDs in Charleston, SC, closely match HDDs in Lisbon (1,171 and 1,084, respectively).

Six reference cities passed this initial screening. Fort Collins, Colorado, rests at the foot of the Rocky Mountains (elevation 1,500 m) and has a semi-arid climate. Winters are cold, with snow staying on the ground for days or weeks. The growing season ranges from 75 to 150 days (Brenzel 1997). The area receives approximately 457 mm of rain and 1,397 mm of snow per year.

Minneapolis, Minnesota, sits along the Mississippi River and has a humid continental climate. Winters can be very cold, with expected lows ranging from −29°C to −34°C. Summer air masses moving north from the Gulf of Mexico can result in hot, humid weather. Annual precipitation averages 747 mm, with nearly one-half falling in June, July, and August.

Claremont, California, is located in the valley east of Los Angeles and 70 km from the Pacific Ocean. The Mediterranean climate is warm during summer, when the average maximum temperature in August is 32°C and all-time highs reach 45°C. Mild winters are marked by occasional frost. The annual average precipitation is 432 mm. Winter months are wetter than summer months.

Santa Monica, California, is located along the Pacific Ocean and adjacent to Los Angeles. It has a mild marine climate with mild winters and cool summers. Record low temperatures are above 0°C. In mid-summer, temperatures rarely exceed 30°C. Annual precipitation averages 338 mm and falls primarily from November through March. Because of its oceanside location, ozone concentrations are usually lower in Santa Monica than they are inland.

Modesto, California, is located in the Central Valley and has cool, damp winters and very warm, dry summers. A layer of ground fog is common during winter. Average January temperatures are a maximum 12°C, averaging 20 days with freezing temperatures (0°C) or lower. Average July temperatures are a maximum 34.6°C and on average there are 80 days with highs 32°C or higher. Average annual rainfall is 310 mm. Summer months are usually very dry.

Charleston, South Carolina, is located along the Atlantic Ocean in the southeast U.S. It has a humid subtropical climate with mild winters and hot, humid summers. Winter is short and mild, with temperatures seldom dropping below freezing. Summer is the wettest season; almost half of the annual rainfall occurs during the summer months in the form of thundershowers. Annual rainfall averages 1,438 mm.

Compiling Data

Street trees were sampled throughout Lisbon and the population totalled 41,247, with a standard error of 6,312 (Soares 2006). European hackberry (Celtis australis) and basswood (Tilia spp.) are the most common street trees, each accounting for 16% of the population, while black poui (Jacaranda mimosifolia) account for 10% (Table 4). Other important species belong to the sycamore (Platanus), maple (Acer), and cottonwood (Populus) genera. Tree inventory data were assembled for each of the six reference cities (see Appendix).

Lisbon has 1,084 HDDs and 474 CDDs with a base of 18°C (Energy Plus 2009) (Table 3). Average annual precipitation in Lisbon is 702 mm (World Climate 2010). Annual HDD, CDD, and precipitation data were compiled and shown as raw values for each reference city. Differences between Lisbon and each reference city were tabulated as absolute values (Table 3).

Tree Matching

The species of trees measured to develop growth curves in each reference city inventory (from Appendix) were matched at the species and genus level with the most abundant street trees in Lisbon’s population (from Table 4). To quantify the extent of tree matching in each reference city, the percentage (i.e., relative abundance expressed as percentage of the population) of matching taxon in each reference city were summed (Table 3).

Normalizing the Values

To normalize the values, ranges were calculated for each criterion and 10 equal intervals calculated (Table 5). For example, HDD values ranged from 0 to 4,354. Ten intervals, each 435 in size, were established and assigned the appropriate normalized value ranging from 0 to 10.

Linear interpolation was used to calculate the normalized value for each difference value (Table 5). For example, the HDD difference value for Fort Collins is 2,168 (3,252–1,084). This value falls within the normalized value range of 5 to 4 (1,742–2,177). After linear interpolation the normalized value is 4.98, close to the value of 5.0 because the difference value 2,168 is close to the interval value of 2,177.

Accounting for Importance

In this step, the coefficient for each criterion is weighted to reflect its relative importance. The analyst’s best judgment is used to assign weighted values. If the criteria are equally important, 0.25 is assigned to each of the four coefficients. Unequal weighting can be done to accentuate or diminish the relative importance of individual criterion. The rationale for a weighting scheme applied in the Lisbon example is discussed as follows.

Final Analysis

When coefficients are weighted equally, the best matching reference cities are Modesto (RMSE = 2.6) and Fort Collins (2.8) (Table 6). The worst matches are Charleston (5.96), Santa Monica (4.95), and Claremont (4.04), due largely to inferior tree matching.

Weighting the coefficients unequally gives a different result. Tree matching is considered relatively unimportant in this analysis (0.1), while HDD (0.3) and annual precipitation are weighted as most important (0.4). Because of this unequal weighting, the Mediterranean climate cities Modesto (RMSE = 2.41) and Claremont (2.71) are the best choices for use with Lisbon’s tree inventory in i-Tree Streets (Table 6). Fort Collins (3.02) and Santa Monica (3.21) are better fits than Minneapolis (4.14) and Charleston (5.15). Although Modesto is the best choice using both equal and unequal weighting, Claremont jumped from fourth- to second-best choice with unequal weighting. Weighting that accentuated the importance of HDDs emphasized the large difference in HDDs between Fort Collins and Lisbon (2,168 HDDs) relative to Claremont (845 HDDs). The relatively low weighting for tree matching also advantaged Claremont relative to Fort Collins and Minneapolis. The winter season rainfall pattern, summer irrigation, and longer growing season in Modesto and Claremont are likely to result in tree growth patterns more similar to those found in Lisbon than those found in Minneapolis and Fort Collins.