218 reading, it has the potential to overestimate the num- ber of starts and stops in growth, resulting in a very high number of 5-minute growth periods (the record- ing interval of the data logger). We used a Hidden Markov Model (HMM) to summarize the ZG model intervals and make them more suitable for statistical analysis. The HMM assigned each time point to one of two latent variable states: “growth” or “deficit” (Durbin et al. 1998; Eddy 2004). The model was trained using emitted states of the Zweifel et al. (2016) ZG model. We used the Baum-Welch algorithm to infer model parameters from the full data for each tree, and we used the Viterbi algorithm to infer the most likely state of the latent variable at each point (Durbin et al. 1998). All HMM code was implemented using the package “HMM” in R (R Development Core Team 2018; Himmelmann 2010). For downstream statistics, we isolated the HMM-identified “growth” periods that overlapped with more than two data points. From these growth periods, we derived our response variables and our predictors. The response variables are: (1) the net change in the ZG model through the growth interval (“total growth”; yend − ystart ) and (2) the value from (1) divided by the duration of the growth interval (“slope”). The value of (2) corresponds to the slope of a line passing through the ZG model values at the begin- ning and end of the growth interval. The predictors are environmental variables. We calculated their val- ues using the mean through the growth interval. Linear Models As most of growth occurs at night, we conducted a multiple regression analysis on the HMM-identified growth periods when solar radiation was equal to zero. The models were applied separately to each tree and to the total growth and slope response variables for each interval. During each interval, we used the mean of each environmental factor and their interactions as the explanatory variables. Conditional Inference Trees (CITs) While the linear models test for the effect of a variable across all of the data, interactions between variables could result in cases where a particular explanatory variable only has a significant influence over the response in a particular part of another variable’s range. With this in mind, we fit conditional inference Griffin et al: Stem Radius Fluctuations in Urban Trees trees (CITs) to further examine the association between the explanatory and response variables. In compari- son to the linear models, which tested the influence of each variable across the full data, the CITs repeatedly partitioned the data using the predictors. For exam- ple, even though “variable X ” might not show an influence on the whole data—so a linear model would show no significance—“X ” might instead have a sig- nificant influence for the subset of the data, where a different “variable Y ” has a high value. The CITs were fit on the HMM-identified growth periods for each tree, with response variables being the “total growth” and “slope” metrics defined in the previous section. The predictors were the mean values of the environmental variables through each interval. We performed CIT analysis using the partykit pack- age in R (Hothorn and Zeileis 2015). RESULTS Micrometeorological Conditions Air temperature during our experiment varied from a low of 4.8 °C (2019 May 1) to a high of 32.0 °C (2019 July 14), with a mean temperature of 19.37 ± 5.18 °C (Figure 2). Daytime temperatures were on average 3 °C degrees warmer than nighttime temperatures, 20.6 ± 5.15 °C and 18.0 ± 4.84 °C, respectively, during the experimental period. Soil temperatures varied between 24.4 °C (2018 August 9) and 8.7 °C, with a mean of 18.3 ± 4.26 °C (Figure 2). Total precipitation was 1,012 mm (Figure 2). The combination of rain and irrigation resulted in a mean volumetric soil water content of 0.38 ± 0.26 m3 m−3 . The wind was primar- ily onshore, coming from the south/southwest (201°) (data not shown). The total solar energy received during the experimental period was 8.9 MW m−2 a daily average of 816.6 W m−2 , with d−1 . Stem Diameter The study trees were of average size in this planted landscape, similar to most other trees within 100 m. Over the duration of the experiment, these trees grew by an average of 11%, reaching final diameters of 13.4, 15.9, and 17.34 cm (Table 1, Figure 3). In 2019, the period of rapid diameter growth for spruce began on 14 April ± 10 days and ended on 7 September ± 10 days, and for cedar began on 26 April ± 5 days and ended on 3 November ± 5 days (dotted vertical lines on Figure 3). Note a small portion of the 2018 early ©2021 International Society of Arboriculture
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