Above-ground tree carbon storage in response to nitrogen deposition in the U.S. is heterogeneous and may have weakened

Forest Inventory data

Tree growth, tree survival, and plot-level basal area data were compiled from the Forest Inventory and Analysis (FIA) program database (accessed on January 24, 2017, FIA phase 2 manual version 6.1; http://www.fia.fs.fed.us/). Aboveground tree biomass was estimated from tree diameter measurements⁴⁴ and then multiplied by 0.5 to estimate aboveground C. Tree growth rates were calculated from the difference in estimated aboveground C between the latest and first live measurement of every tree and divided by the elapsed time between measurements to the day. Tree species that had at least 2000 individual trees after the data filters were applied were retained for further growth and survival evaluation. The probability of tree survival was calculated using the first measurement to the last measurement of a plot. Trees that were alive at both measurements were assigned a value of 1 (survived) and trees alive at the first and dead at the last measurement were assigned a value of 0 (dead). The duration between the first and last measurement was used to determine the annual probability of tree survival. Trees that were recorded as dead at both measurement inventories and trees that were harvested were excluded from the survival analysis.

Predictor data: Climate, deposition, size, and competition

There were six predictors that were related to the response rate of growth or survival for each individual tree: mean annual temperature, mean annual precipitation, mean annual total nitrogen deposition, mean annual total S deposition, tree size, and plot-level competition.

To obtain total N and S deposition rates for each tree, we used spatially modeled N and S deposition data from the National Atmospheric Deposition Program’s Total Deposition Science Committee³². Annual N and S deposition rates were then averaged from the first year of measurement to the last year of measurement for every tree so that each tree had an individualized average N deposition based on the remeasurement years, and each species had an individualized range of average N deposition exposure based on its distribution. Monthly mean temperature and precipitation values were obtained in a gridded (4 x 4 km) format from the PRISM Climate Group at Oregon State⁴⁵ for the contiguous US and averaged between measurement periods for each tree in a similar manner. Tree size was represented by estimated aboveground tree C (previously described). Because the climate and deposition predictors were tailored to each plot, the years assessed varied by plot, but spanned 2000–2016. Thus, the results from the earlier study⁶ used conditions from the 1980–1990s, whereas the results from this study used more recent environmental and stand conditions. Tree competition was represented by a combination two factors: (1) plot basal area and (2) the basal area of trees larger than the focal tree being modeled. How all six variables were statistically modeled is discussed below.

Modeling tree growth and survival

We developed in ref. ²⁰ multiple models to predict tree growth (G; kg C year⁻¹) and survival (P(s); annual probability of survival). Our growth model (Eq. 1 and 2) assumes that there is a potential maximum growth rate (a) that is modified by up to six predictors in our study (which are multipliers from 0 to 1): temperature (T), precipitation (P), N deposition (N), S deposition (S), tree size (m), and competition. The potential full growth model included all six terms (Eq. 1 for the general form and Eq. 2 for the specific form). The size effect was modeled as a power function (z) based on the aboveground biomass (m). N deposition may affect the allometric relationships between tree diameter and aboveground tree biomass⁴⁶, but these relationships are not yet accounted for in U.S. inventories⁴⁴. Competition between trees was modeled as a function of plot basal area (BA) and the basal area of trees larger than that of the tree of interest (BAL) similar to the methods of⁴⁷. The environmental factors (N deposition, S deposition, temperature, precipitation) were modeled as two-term lognormal functions (e.g., t₁ and t₂ for temperature effects, n₁ and n₂ for nitrogen deposition effects). The two-term lognormal functions allowed for flexibility in both the location of the peak (determined by t₁ for temperature, for example), and the steepness of the curve (determined by t₂ for temperature, for example). Thus, the full growth model is presented in Eq. 2.

We examined a total of five different growth models: (1) a full model with the size, competition, climate, S deposition, and N deposition terms (Eq. 2); (2) a model with all terms except the N deposition term; (3) a model with all terms except the S deposition term; (4) a model with all terms but without S and N deposition terms; and (5) a null model that estimated a single parameter for the mean growth parameter (a in Eq. 2).

The annual probability of survival (P(s)) was estimated similarly as for growth, except that the probability was a function of time and we explored two different representations for competition. The general form of the model is shown in Eq. 3, and the full survival model in Eqs. 4, 5 for the two competition forms.

A total of nine survival models were examined: four using the formulation for size and competition in Eq. 4 (with the same combinations of predictors as above for growth), four using formulation for size and competition in Eq. 5, and a null survival model in which a mean annual estimate of survival (a) was raised to the exponent of the elapsed time.

Parameters for each of the growth and survival models above were fit for a given species using maximum likelihood estimates through simulated annealing with 100,000 iterations via the likelihood package (v2.1.1) in Program R. Akaike’s Information Criteria (AIC) was estimated for all models. The best model was the model with the lowest AIC, and statistically indistinguishable models are those with a delta AIC < 2⁴⁸. We used the simplest model (i.e., the one with the fewest parameters) among the set of statistically indistinguishable models as the basis for dC/dN. The variation explained in the models in ref. ²⁰ was good for growth (R² averaged 24% for the 94 species +/− 15% standard deviation) and was not reported for survival. Additional details can be found in²⁰.

Estimating dC/dN from individual responses from N and S deposition

Individual tree growth and survival equations were combined to estimate the relationships between N deposition and aboveground tree C calculated as the change in aboveground tree C accumulation vs change in N deposition rates (△ kg C ha⁻¹yr⁻¹/△kg N ha⁻¹ yr⁻¹ or dC/dN). The estimated amount a tree grows after 1 year is simply its annual growth rate (G). The estimated amount of aboveground tree biomass for a single surviving tree that carries over from one time period to the next is the initial biomass plus the growth (Eq. 6).

For the FIA database, at the landscape level the amount of forest biomass associated with a tree is the amount of biomass associated with that tree (Eq. 6), multiplied by the FIA expansion factor (f in Eq. 7; because the FIA tree represents many trees), multiplied by the probability of survival (P(s) in Eq. 7, because not all expanded trees will survive).

At the plot level, the expansion factor is not needed and the equation for the amount of tree biomass simplifies to (Eq. 8). The annual aboveground tree C accumulation, for established trees, is the difference in the initial aboveground tree C (C_i) and the aboveground tree C after 1 year in kg C tree⁻¹ yr⁻¹ (Eq. 9).

We estimated the rate of change in aboveground tree C accumulation vs N deposition (dC/dN) by estimating the annual aboveground tree C accumulation (Eq. 9) at the local rate of N deposition and the local rate of N deposition plus 0.01 kg N ha⁻¹yr⁻¹, allowing us numerically calculate the slope of the relationship between C accumulation and N deposition. Subtracting these two calculations of annual C accumulation provides the change in C associated with a small change in N (dC). We normalized this calculation by dividing the small change in N deposition (0.01 kg N ha⁻¹ yr⁻¹) to estimate dC/dN for each tree within a plot. To scale the individual tree estimates to the plot level, individual tree (dC/dN) values were summed up by FIA plot and divided by the plot area. To scale from the plot level to the landscape, plot dC/dN values were then averaged within each 20 x 20 km pixel and weighted by its corresponding plot expansion factor (see FIA manual).

Comparison of responses in 2000–2016 with 1980s–90s

The relationships from the study focused on the 1980s–90s⁶ did not include sulfur deposition, thus, those relationships are better described as the effect from N deposition when only N is included in the model (i.e., does not try to account for S deposition). In the study focused on 2000–2016²⁰ we ran models with only N, with only S, and with both. Thus, to optimize the comparison with the earlier study we selected the model in²⁰ that only included N, regardless of whether it was the best overall model. These comparisons are shown in Figs. 3, 4. N and S were only weakly associated in much of this region (Fig. 5 from ref. ²⁰). Also note, we examined three different allometric scaling methods estimating C from FIA diameter measurements (CAG, BAI, and Jenkins). The most appropriate comparison with⁶ is Jenkins, while the others were included to examine sensitivity to the method for future work. To further compare to the estimates of dC/dN from 1980–90s in ref. ⁶, we ran a second analysis using stand-level C increment between two measurements periods (rather than the up-scaled species response curves described above) to assess the relationship between N deposition on annual C increment of all surviving trees in a plot (i.e., as in Table 2 in ref. ⁶). Following⁶, we first ran a model with climate and size (i.e., carbon stock at the first measurement period) terms. Then we added N deposition to that model to see if the AIC value decreased by 2 or more. Although the addition of N deposition led to a significant improvement of the stand-level model in ref. ⁶ in the Northeastern U.S. for the 1980s–90s, it did not in this analysis of the 2000–2016 period.

Source: Ecology - nature.com