A Statistical Method for the Accurate and Rapid Sampling of Urban Street Tree Populations

Zonation

The first step in the sampling and estimation procedure is to stratify, or partition, the city’s area into zones. Stratification is useful for two reasons. First, it provides a way of spreading the sample areas appropriately across the city, by dividing the city into regions and then looking at the trees within each region. Second, stratification into relatively small regions allows for the investigation of planting patterns and trends within each region, allowing the tree manager to examine tree populations in discrete sections.

To facilitate the stratification of a city, we now introduce the terminology to be used. A zone type is a major land use category and may refer to a residential or commercial neighborhood, a physical street layout, or a time of development. The city’s area is divided into nonoverlapping regions, each of which is categorized as one of the zone types, except that regions in the city known to contain no street trees (e.g., natural vegetation, parks, etc.) are omitted. The three zone types used in the research reported here are Rectilinear Residential (RR). Curvilinear Residential (CR), and Downtown (DT).

Rectilinear Residential (RR) neighborhoods usually contain the majority of street trees found in the city. These areas, consisting primarily of rectangular blocks, are often the neighborhoods that were first developed around the core of the city (9), and usually contain sidewalks and street tree planting areas.

Curvilinear Residential (CR) zones, on the other hand, were usually developed later within a city, and the layout of these neighborhoods often does not include sidewalks and specified tree pits. The streets in CR zones usually do not form a grid-like pattern.

The third zone type is the Downtown (DT) or central business district. Because of high tree mortality rates, the prevalence of new construction, and the general clustering of trees in downtown urban areas, downtown areas are substantially different from residential areas, thus warranting a separate zone type classification. The streets in DT zones usually form a grid-like pattern.

These three zone type classifications are sufficient for the analysis of many cities. The general attributes of a particular city’s composition may, however, suggest different categories. If a city contains areas that do not fall within the above descriptions, new zone types can and should be defined.

A zone segment is a contiguous region of a single zone type containing between 20 and 500 sampling units (city blocks in RR or DT regions). To the greatest extent possible, zone segments should be constructed to have areas as nearly equal as possible. A contiguous region of a single zone type should be subdivided into two or more adjacent zone segments if it contains potentially important natural or political boundaries or if it is too large to constitute a single zone segment. This process is illustrated in Figures 1 and 2. It is within the individual zone segments that the random sampling is performed.

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Figure 1

Example of a city partitioned into three different zone types

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Figure 2

Example of zone segments and street units.

In the stratified random sampling procedure described here, each zone segment is sampled. Within each zone segment, a simple random sample is drawn, ensuring that every block has an equal probability of being selected. Stratification allows us to combine the results of the simple random samples from all zone segments to obtain the final composite result (4). Estimates from a stratified sample of blocks selected within zone segments will be more precise than those from a simple random sample of blocks taken from the city as a whole, since the stratified sample will give improved coverage of the entire city. If stratification is not used, then there is an increased probability that the random sampling process could miss, underrepresent, or overrepresent large sections of the city.

Establishment of a uniform sampling entity

The elements that are chosen during the random sampling process to form the sample are called sampling units. In our approach, each zone segment is divided into sampling units called street units. These are the elements that will be randomly sampled throughout the city. A street unit in a Rectilinear Residential or Downtown zone segment is defined to be the inside perimeter of a block; for convenience, we will usually refer to this simply as a block. A block is the preferred sampling unit in RR and DTzone segments fortwo reasons. First, it is easy to drive completely around a single block, sampling trees from only the inside perimeter of the block, thus eliminating the chance of observing the same individual tree twice as part of two separate street units (Fig. 3). Second, neighborhoods tend to be developed as several contiguous blocks at the same time. Street trees on a single block have a higher chance of having come from the same nursery or of being planted in soil of the same general type than trees on different blocks. This aspect of heterogeneity between blocks and homogeneity within blocks is often referred to as clustering (8).

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Figure 3

Example of one street unit or block, selected to be observed (one side only) within a Rectilinear Residential or Downtown zone segment.

It is usually difficult, or impossible, to drive around a block in a Curvilinear Residential neighborhood, because the streets do not form blocks. Therefore, a different kind of basic sampling unit is needed in OR zone segments. To define a CR sampling unit called a street segment, we began by estimating the average rectilinear block perimeter length from all Rectilinear Residential zone segments. This length was called A. Using A as the size of the sampling unit, we subdivided the curvilinear streets into sections of that size. It was convenient in sampling CR zone segments to observe the trees on both sides of the street, so a CR street segment consisted of both sides of a section of street having a length of A/2 (Fig. 4). This method established an equivalent length of street observed between RR and CR zone segments. Small sections of street remaining at intersections, and at the edges of the CR zone segments, could be included in any adjoining street segment.

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Figure 4

Example of the street segments that comprise street units within a Curvilinear Residential area. Trees are recorded on both sides of the street.

Finally, within a block or street segment, each individual street tree was observed. A street tree was defined as any tree u nder the control of the city, and bounded on one side by a curb or street edge and on the other by a sidewalk. Trees in median strips were also included with the adjacent block. If a sidewalk was not present, then a distance of approximately 8 feet in from the street edge, comprising the public right-of-way, may be used as the criterion defining a street tree. Certain trees on private property can act as street trees but are not generally considered in an inventory, since the city often has no control over them. Areas of natural vegetation along street edges are not generally part of an inventory. In downtown areas, street trees are often planted in special isolated planters or pits. These plantings have to be within the right-of-way to qualify as street trees.

Sampling at the block level instead of randomly selecting individual street trees out of the total population offers advantages when sampling in large, widespread zone segments. Typically we find that in cluster (block) sampling:

1. the cost per tree is much lower, due to the lower cost of locating and observing each tree within a block;

2. the variance between blocks is higher than the variance within blocks, due to the usual, though irregular, heterogeneity of trees between clusters; and

3. the complexity of statistical analysis is greater. Cluster sampling is preferred over individual selection when the lower cost per tree more than compensates for the more complex structure (7).

The pre-sample

A preliminary sample, or presample, was used to estimate two important quantities: a) the average block perimeter length over all Rectilinear Residential zone segments, and b) the number of street trees in every zone segment. A random sample of block perimeters was measured in each zone segment, and the average perimeter length for each of the random samples was calculated. The average perimeter lengths were combined, using weighted averaging, to give A, the estimated average block perimeter length over all blocks in all RR zone segments. As described earlier, this estimated average length was then used to divide the streets in CR zone segments into street segments of length A/2. In all zone segments, random samples of these street segments were then drawn for pre-sampling and sampling of street trees.

Pre-sampling also helped in estimating the number of street trees in each zone segment, and throughout the entire city. Foreach zone segment, we estimated the tree density, or average number of trees per street unit, from the street u nits (blocks for RR or DT, street segments for CR) in the presample. We estimated the total number of street trees in each zone segment as the product of the estimated number of trees per street unit in a given zone segment and the total number of street units in that zone segment. These estimated total numbers of street trees for all zone segments were than summed to provide an estimate for the total number of street trees within the city. This pre-sampling technique also allowed estimation of the percentage of the city’s trees that are in each zone segment. This had an important role in the distribution of the sample of 2,000-2,300 trees across the city.

The rationale for 2,000 - 2,300 trees

Statistical sampling theory shows that a suitably selected random sample consisting of only a small fraction of the population can often be used to estimate the characteristics of the entire population with an acceptably high level of accuracy, i.e., an acceptably low degree of error (4). The sample selection procedure may be complex, as in the multistage sampling method described fully below, in which the city is divided into zone segments, a sample of street units is drawn from each zone segment, and the trees in each of these street units are inspected. This is done in a way that gives all individual trees in the population approximately the same probability of being selected. In this situation, a sample of 2,000 - 2,300 trees is sufficient to attain the stated goals of accurate estimation of the city (population) total number of street trees, tree species diversity, and other variables. The degree of error in these estimates can also be estimated, and is an important criterion for judging and comparing estimates.

Increasing the sample size used in asampling and estimation procedure will increase the level of accuracy of the estimates. However, the improvement may not be substantial. The extra cost of conducting a survey with a sample of more than 2,000 - 2,300 trees, in time, personnel, and data analysis, generally seems not to be justified by the limited increase in accuracy and information available. Note that selecting a sample of known size, e.g., 2,300 trees, is much easier than sampling a known percentage of the total population for two reasons: 1) it is often impossible to know the population size, even approximately, before conducting the survey, and 2) percentage sampling of a very large population requires a very large sample.

The sample

The actual sampling used in our procedure was performed by observers in an automobile. We found that each observer could usually handle two different kinds of observations. For example, one observer could be responsible for species identification and dbh class, while a second observer could assess tree condition and tree planting opportunities. To expedite the sampling procedure, it was helpful to have a person in addition to the driver whose sole responsibility was navigation. Data were recorded onto tape using a microphone, or could be entered directly into a handheld laptop computer. Every data entry had to be identified with a specified street unit at the time of observation. This was necessary because the data from each observed street unit were weighted by the zone segment they were in when estimates were calculated.

Weighting of results

The results of the presampling phase of this procedure allowed us to estimate not only the total number of street trees in the city, but also the percentage of those trees located in each zone segment. After estimating the proportions of all the individual species in each zone segment from the counts observed during the actual sample, the values were multiplied by the estimated percentage of the city’s street trees located in each zone segment. This weighting procedure adjusted the estimated proportions to reflect the number of street trees expected in a given zone segment. For example, if a zone segment were estimated to contain 20% of the total street trees in the city, then the species proportions estimated from counts observed in that zone segment were weighted (multiplied) by 0.20. For each species, summing these weighted values over all zone segments provided an accurate estimate of the number of street trees of that species within the city.

Total Number of Trees

Four cities in New York State were surveyed between the fall of 1989 and summer of 1990 to evaluate the accuracy of this technique. The four cities, Ithaca, Syracuse, Rochester, and Brooklyn, NY, were chosen because they represented areas ranging from 5.6 square miles (Ithaca) to 78.5 spare miles (Brooklyn). Brooklyn, although only a part of New York City, would be the fifth largest city in the U.S. if considered on its own. The three smaller cities had either complete or partially existing inventories against which we could check the accuracy of our samplebased estimates; Brooklyn had only a total count of street trees to compare to our data.

The four cities had street tree populations ranging from 5,571 for Ithaca to 113,000 forBrooklyn (Table 1). Rochester had only a partial inventory of one area of the city, completed in 1988. At that time, a gross estimate of 60,000 trees was given by the partial inventory, but was not supported by any methodology or data. The other three cities had data against which to compare our sample-based results. For these cities, for total number of street trees, we were well within the ± 10% accuracy desired for the method (Table 1).

Species Composition

During the 1990 sample conducted in Ithaca, NY, we observed a total of 56 species, compared to 103 species during the 1988 full inventory. As can be seen from Table 2, the top four species, three of which are maples, comprise 66.9% of all street trees in the city of Ithaca. The accuracy of the sample was well within our statist!-cal objectives (Table 2). However, between 1988 and 1990, there were 82 Acer saccharum removed from Ithaca, NY, and none has been replanted. Therefore, the percentage of total existing Acersaccharum changed from 19.1 % to 17.5%, so the estimate of 17.0% is within our goal of ±10% of the actual fraction of existing trees of that species.

In Syracuse, NY, four species comprised 58.6% of the total street trees in the city (Table 3). Syracuse Parks and Recreation records showed that between 1978 and 1988, approximately 1000 silver maples were removed. This would adjust the 1978 inventory percentage for Acer saccharinum to approximately 13.4%, keeping it within the desired bounds of statistical accuracy.

Over 50% of the trees inventoried in the Downtown zone segment were Gleditsia triacanthos. This species has been heavily planted within the last 10 years. Also, within the last 10 years Tilia cordata, Fraxinussp., and Acer rubrum have become very popular street trees, and their numbers have increased dramatically. Taking into consideration these changes related to us by the Syracuse City Forester, our sample provides acceptable levels of accuracy.

During the 1989 sample conducted in Syracuse, NY, we doubled the size of our sample from 2,300 to 4,600 sampled street trees in order to calculate the effect of increased sample size (Table 3). While ourgoal was 2,000-2,300 sampled trees, we actually observed 1,922 trees from one side of the street, 2,080 from the opposite side of the street, and a total of 980 street trees from the Downtown zone segment. As can be seen from Table 3, doubling the sample size did not change the results appreciably.

The 1988 inventory results for Rochester, NY, shown in Table 4, are from a partial inventory conducted in one section of the city during the summer of 1988 (1). Our 1990 results reflect a sample drawn from the entire city. In Rochester, four species make up over 65% of the street tree population, with Acer platanoides again, as in Ithaca and Syracuse, making up about one-third of the population. Gleditsia triacanthos, Acer saccharum and A. saccharinum also played important roles in all three cities.

Brooklyn, New York was the first city we sampled where there was no known existing street tree inventory. The same sample size of 2,000 - 2.300 trees that was used in the three previous cities was also used for Brooklyn. The pre-sample for Brooklyn took 1 day, the actual sample took 2 days, and the analysis of the data took approximately another week. Table 5 shows that two species were the major street trees in the city, and the top four species comprised approximately 75% of the street trees within the city.

For all four cities, four or fewer species made up the majority of street trees, Maples figured heavily in all cities, but in Brooklyn, Platanus x acerífolia(London plane) comprised the largest proportion. The overplanting of a few species leaves that city vulnerable to attack by insect or disease. These results suggest that greater diversity is necessary when planting street trees in these cities.

DBH Class

For Ithaca, Rochester, and Brooklyn, we also took data on dbh size class, by species. This is a good indicator of the age of any population of trees within the city. Table 6 shows the distribution of dbh size classes for all species making up >1% of the street tree population in Ithaca, NY. For example, Acerplatanoides comprised 33.8% of the city’s street trees. Of these Acer platanoides, 20.4% were in dbh class 1” - 5”, 51.3% were in dbh class 6” - 12”, etc. The dbh proportions were calculated by exactly the same method as species composition, i.e., the number of a particular species observed in each dbh class was weighted by the percentage of trees expected in the zone segment within which they were observed. Values from all zone segments were then totaled for the city.

Of the four main species comprising 57.8% of the street trees in Rochester, three were distributed nicely throughout the lower dbh classes (Table 7), whereas only one, Acer platanoides was showing signs of aging.

The two most common species observed in Brooklyn both had more than 50% of their trees in the 13”-24” dbh range (Table 8). This suggests that the top two species, which together are estimated to comprise 60.9% of the street trees in Brooklyn, are beginning to reach maturity.

For all cities, Acer saccharinum clearly comprised the oldest tree population, followed by Acer saccharumand, in Brooklyn, Platanusx acerifolia. Although Acer saccharinum is not planted today because of its defect-prone nature, it must be admired for its adaptability and longevity in the urban environment.

Tree Condition

During the observation of the Brooklyn sample, one observer also noted the condition of each sampled tree, a subjective rating of the overall health, soundness, and shape of the Tree (Table 9). Acer platanoides and Quercus palustris stood out as being in poorer condition than the other species. Of the trees observed that fell into the categories of Good and Poor, Acer platanoides had the largest number of trees showing crown dieback and foliage scorch (Table 10).

Dieback of tree crowns was clearly the most common symptom of tree decline, followed by the presence of trunk wounds. The prevalence of trunk wounds generally followed the age or size of the tree population, with the youngest group, Pyrus calleryana showing no wounds, and the oldest, Acer saccharinum, showing the most. Chlorosis was most prevalent in Quercuspalustris, a species known to be intolerant of alkaline urban soils. The percentage of 30% is not as great as has been noted for this species in Ithaca, NY, where 70% has been recorded (3).