Isoprene and monoterpene emission rate variability: model evaluations and sensitivity analyses

The emission of isoprene and monoterpenes from plants is influenced by light and leaf temperature, which account for almost all short-term variations (minutes to days) and a large part of spatial and long-term variations. The temperature dependence of monoterpene emission varies among monoter- penes, plant species, and other factors, but a simple exponential relationship between emission rate (E) and leaf temperature (T), E = E s [exp (/3(T - Ts))], provides a good approximation. A review of reported measurements suggests a best estimate of/3 - 0.09 K-1 for all plants and monoterpenes. Isoprene emissions increase with photosynthetically active radiation up to a saturation point at 700-900 tzmol m -2 s -(cid:127) . An exponential increase in isoprene emission is observed at leaf temperatures of less than 30øC. Emissions continue to increase with higher temperatures until a maximum emission rate is reached at about 40øC, after which emissions rapidly decline. This temperature dependence can be described by an enzyme activation equation that includes denaturation at high temperature. Algorithms developed to simulate these light and temperature responses perform well for a variety of plant species under laboratory and field conditions. Evaluations with field measurements indicate that these algorithms perform significantly better than earlier models which have previously been used to simulate isoprene emission rate variation. These algorithms account for about 90% of observed diurnal variability and can predict diurnal variations in hourly averaged isoprene emissions to within 35%.


INTRODUCTION
Isoprene and monoterpenes are volatile hydrocarbon compounds that are produced by vegetation and emitted into the atmosphere in significant quantities. Emissions of biogenic hydrocarbons are estimated to equ•aal or exceed anthropogenic emissions even in industrialized nations such as the United States [Lamb et al., 1987]. Biogenic and anthropogenic hydrocarbons can influence the chemical composition of the atmosphere by controlling the oxidation capacity of the troposphere [Chameides et al., 1988]. In regions with sufficient levels of oxides of nitrogen and sunlight, this influence can include photochemical production of ozone and peroxides [Liu et al., 1987]. Highly reactive biogenic hydrocarbons play a major role in photochemical oxidant production even when they are present in the atmosphere at concentrations that are much lower than those of anthropogenic hydrocarbons [Chameides et al., 1992].
Numerical tropospheric photochemistry models typically use time steps of less than 1 min [e.g., Roselle et al., 1991]. Diurnally varying boundary conditions must be specified for sources such as biogenic hydrocarbon emissions, which can vary several orders of magnitude in a 24-hour period. Diurnal variations in biogenic hydrocarbon emissions are controlled by changes in light and/or temperature. Light and Copyright 1993 by the American Geophysical Union.
In this paper we describe and evaluate models which simulate short-term variations in isoprene (section 2) and monoterpene (section 3) emissions from plants. In section 2.1 we describe two isoprene emission rate data bases which are referred to in this paper. A laboratory measurement data base was used in the development of an isoprene emission model, and a field measurement data base was used to evaluate the new model and eight previously published models. Section 2.2 provides a detailed description of the new isoprene emission model and brief descriptions of the other eight models. The performance of each model is evaluated in section 2.3, and the results of sensitivity analyses are included in section 2.4. A simple model for monoterpene emissions is described and evaluated in section 3.1, and model sensitivity analyses are discussed in section 3.2. These results are summarized in section 4, and specific recommendations for biogenic isoprene and monoterpene emission rate modeling are provided.

Isoprene Emission Rate Measurements
A data base of isoprene emission rate measurements from individual leaves of sweet gum (Liquidambar styracifiua) and aspen (Populus tremuloides) trees at nine light intensities and 12 leaf temperatures was made for this study. These 12,609 were measured at intervals of 30 minutes to 2 hours for periods of up to 18 hours. Six different trees were sampled for a total of 94 measurements. Leaf temperature, enclosure temperature, relative humidity, PAR, and general sampling conditions were recorded for each measurement. Photosynthesis, transpiration, and stomatal conductance measured with a LICOR 6200 system indicated that the physiological behavior of these trees was within normal limits. Table 1 contains brief descriptions of nine models which can be used to predict the effects of environmental variables on isoprene emission rates. These models include approaches developed by Guenther and coworkers (G91, G93), Tingey and coworkers (T400, T800, BEIS), Evans and coworkers (EES, ESS), Lamb and coworkers (L87), and Chameides and coworkers (HR). Each of these models except G93 has been described previously; G93 is described below.

Isoprene Model Descriptions
A variety of factors influence isoprene emission rates. Although the mechanisms controlling isoprene emission are not well known, recent studies have correlated both longterm and short-term variations in isoprene emission with isoprene synthase activity [Kuzma and Fall, 1993;Monson et al., 1992]. Normal variations in humidity, CO2 concentration, and stomatal conductance play a minor role in controlling short-term variations in isoprene emissions [e.g., Guenther et al., 1991;Fall and Monson, 1992]. These studies suggest that PAR and leaf temperature can account for short-term variations in isoprene emissions. One model listed in Table 1 (HR) uses only time of day, which is a general indicator of both temperature and PAR, as a model input. Three models (T400, T800, and L87) use only temperature as an input and assume that emissions fall to zero at night. The other five models use both temperature and PAR as model inputs. were nearly constant for all tested leaves. The best fit value of the coefficient T M varied significantly. This coefficient influences the predicted emission behavior at high temperatures (above 30øC). Similar ranges in estimates of T• were determined for each of the plant species tested, which suggests that this variation is not species dependent. Growth conditions may play a role in determining the response of isoprene emission to high temperatures . It is difficult to describe the behavior of isoprene emission at high temperatures because two opposing biochemical processes appear to be occurring: (1) the enzyme isoprene synthase is activated with increasing temperature, resulting in increased emissions; and (2) at high temperatures (e.g., >33øC) the enzyme denatures, decreasing emissions . Figure 1 shows that at temperatures above 33øC, an increase in temperature results in an initial increase in isoprene emission followed by a slow decline in emission. It is important that descriptions of measurements of isoprene emission at high temperature be accompanied by the amount of time that the leaf was at the temperature at which the measurement was made.

Isoprene Model Evaluations
In this section, we evaluate the performance of each of the isoprene emission models described in Table 1. The general behavior of the models is discussed and compared to measurements of isoprene emission rates from four plant species. The overall performance of each model is evaluated by using a field data set.
The normalized isoprene emission rates shown in Figure 2 initially increase linearly with increasing PAR but saturate at higher PAR levels. Similar behavior was observed for all four plant species. Figure 2 also demonstrates the ability of models G91, G93, BEIS, ESS, and EES to simulate this behavior. The other four models described in Table 1 Table 1  The field measurements of isoprene emissions described in section 2.1 were used to evaluate each isoprene emission model. The results of this evaluation are summarized in Table 2. To evaluate only the ability to predict diurnal emission rate variations, observed emission rates were normalized by the estimated emission rate at the standard condition of 30øC and 1000/xmol m-2 s-•. Emission rates at this standard condition were estimated by using each model to relate emissions under observed conditions to expected emissions under standard conditions. Examples of these standardized rates for a red oak leaf are given in Table 2. The -1 wide variation in the standardized rates (34 to 71/xg of C g h -1) estimated by using the various models demonstrates the importance of estimating standardized rates with a model that can accurately simulate emission rate variations. Table 2 show that 86 to 89% of the total variation in diurnal isoprene emission rates can be accounted for by models G91 and G93. Models T400, T800, BEIS, L87, and ESS account for 77 to 81% of diurnal variations, while models EES and HR account for only 61 and 33%, respectively. Percent differences between observed and predicted daily and hourly emission rates are also shown in Table 2. The hourly emission rates predicted by models G93 and G91 were within 21 to 53% of observed emissions. The mean percent differences were 36% (model G93) and 37% (model G91). Percent differences in predicted and observed hourly emissions ranged from 25 to 78% (mean = 43 to 48%) for the other seven models. The percent   *r 2, correlation coefficient; %AD^¾, mean percent difference in daily emission rates. The M score (defined by equation (4)) and standard deviation of the M score (aM) were determined by using bootstrap methods [Efron, 1982].

The correlation coefficients listed in
?Observed emissions were normalized by rates estimated for 30øC and 1000/xmol m -2 s -1 by each model. The mean normalized emission rates estimated for the same red oak leaf, E (in micrograms of C per gram per hour), are shown as an example. differences in the daily emission rates predicted by models G91 and G93 were within 0.2 to 10% of observed daily total emission rates. Mean percent differences in observed and predicted daily rates were 3.5% for model G93 and 3.9% for model G91. Mean percent differences between observed and predicted daily rates ranged from 20 to 42% for the other seven models. Table 2 provides an overall score of model performance.

The normalized mean square error (M) listed in
where Ee is the emission rate predicted by the model, Ee is the mean predicted emission rate, E o is the observed emission rate, and E o is the mean observed emission rate. The M score is a function of three statistical scores (t, F, and r). The t is a measure of the bias of magnitude, F is a measure of the bias of variance, and the correlation coefficient (r) is a measure of the intensity of association. A lower M score indicates better overall model performance. Based on the M scores and standard deviations, the nine models can be grouped into three categories with significantly different model performances. The standard deviations were estimated with 500 bootstrap iterations by using the methods described by Efron [1982]. Models G91 and G93 displayed the best performance (M = 0.11 to 0.14) and were followed by models T400, T800, L87, and ESS (M = 0.23 to 0.26) and models BEIS, HR, and EES (M = 0.50 to 0.66). Figure 4 shows the ability of model G93 to simulate short-term variations in isoprene emission rates from red oak, willow oak, and sweet gum leaves under field conditions. Isoprene emission rates varied over more than 2 -1 orders of magnitude in each case (<0.5 to >50/•g of C g h-l). The predicted daily total isoprene emissions, i.e., integrated over the entire day, are all within 2% of observed values. Emissions vary by as much as a factor of 5 within a 1-hour period, suggesting that a biogenic emission model should have a time step equal to or less than 1 hour. Over half the predicted emission rates shown in Figure 4 are within 20% of the observed values, and 90% are within a factor of 2.

Model Sensitivity Analysis
In this section, we consider the sensitivity of model G93 to the coefficients a (equation (2) and TM (equation (3)). The purpose of this analysis is to determine the magnitudes of the emission rate uncertainties associated with the potential range of values which could be assigned to these two coefficients. The upper portion of Table 3 contains results predicted for a maximum temperature of 35øC and a maxi- Table   3 illustrates that the results of this analysis are sensitive to both daily maximum temperature and light intensity.  Table 1). period (daily total), a 3-hour period between 0600 and 0900 UT (morning total), and a 6-hour period between 0900 and 1500 UT (midday total).

We generated sets of 24 hourly average temperatures by using a sine function to vary between the assigned daily minimum (Tmin) and daily maximum temperatures (Tmax).
Hourly average PAR fluxes were generated similarly except that PAR was set equal to zero before 0600 and after 1800 UT. We used model G93 to estimate variations in hourly average emission rates for two sets of 24-hour periods. Emission rates in the first set were calculated by using model G93 with a = 0.0027 and TM = 314. Emissions for the second set were calculated with a range of values for a (0.0007-0.0057) and T M (310-318), which is similar to the range observed in laboratory experiments. In each case we calculated the percent difference in the daily (24 hour) total, morning (0600-900 UT) total, and midday (0900-1500 UT) total emission rates. Results of this analysis are in the top section of Table 3. If the assumed value of a is less than the actual value, the model will underestimate emissions when L < 1000/xmol m -2 s -1 and overestimate when L > 1000 /xmol m -2 s -1 . If the assumed value of TM is less than the actual value, the model will underestimate emissions at high (>33øC) temperatures.
The PAR and temperature regimen used for the following analysis (Tmi n = 20øC; Tma x = 35øC; Lma x = 1500/xmol m -2 s -1) represents a hot summer day at temperate latitudes, which provides the potential for very high isoprene fluxes.

M = Ms .exp (/3(T-Ts)) (5)
where M is monoterpene emission rate at temperature T (K), Ms is monoterpene emission rate at a standard temperature

Ts (K), and/3 (K -1) is an empirical coefficient. Equation (5)
can account for diurnal variations in monoterpene emissions but may not fully account for seasonal variations [ Yokouchi and Ambe, 1984].
The coefficient Ms, the emission rate at a standard temperature, scales emissions to account for emission rate variation not specifically resulting from temperature. This may include differences due to genotype, nutrient availability, phenology, relative humidity, foliar moisture, or stresses. The value of Ms can vary over more than 3 orders of magnitude among different plant species and monoterpenes. Table 4   data from which the estimates of/3 in Table 4  Detailed monoterpene emission rate models which base monoterpene emission rates on environmental conditions, leaf morphology, and needle resin content have been proposed [e.g., Tingey et al., 1991]. These detailed models cannot be evaluated with existing field measurement data sets and require input variables which are not currently available on regional scales. The model developed by Tingey et al. [1991] predicts that the temperature dependence of monoterpene emissions will vary with vegetation species and the monoterpene being emitted.

The coefficient/3 establishes the temperature dependence of emission rate in equation (5). The estimates of/3 listed in
Estimates of /3 range from 0.067 to 0.14 for a single monoterpene, a-pinene, from 10 plant species listed in Table  4. Estimates of/3 for five different monoterpenes range from 0.067 to 0.0769 for Pinus elliottii [Tingey, 1981] and 0.057 to 0.114 for Picea engelmannii [Evans et al., 1985]. There are also differences in the estimates of/3 for a single monoterpene, a-pinene, from the same plant species: 0.089 and 0.139 for Pinus taeda and 0.067 and 0.091 for Pinus elliottii. Dement et al. [1975] report that/3 is also dependent on the temperature of the plant before measurement. The estimates of/3 shown in Table 4 do not indicate a clear relationship between /3 and monoterpene or vegetation species. A systematic investigation is required to understand the observed variability in/3.

Model Sensitivity Analysis
In this section, we consider the sensitivity of equation (5) to the coefficient/3. This analysis relates uncertainty in the value of/3 to the resulting uncertainties in estimated monoterpene emission rates. The upper portion of Table 5 contains results for a day with a minimum temperature of 22øC and maximum temperature of 37øC. The bottom part of Table 5 shows how the results of this analysis are sensitive to daily minimum and maximum temperatures. The hourly average temperatures used for this analysis were generated by using the procedures described above in section 2.2.
We simulated two sets of hourly average emission rates for 24-hour periods by using equation (5) with Ts = 303.15 K. In the first set,/3 was equal to our best estimate of 0.09.  Table 4 (0.057-0.144) was used to represent /3 in the second set of emission rates. The percent differences between emissions calculated with the different values of/3 were calculated for each 24-hour period (daily total), for a 12-hour period between 0600 and 1800 UT, for hour 0600 (hour of Tmin), and for hour 1800 (hour of Tmax). The upper portion of Table 5 shows that if we use equation (5) with /3 = 0.09, we can expect percent differences in hourly emission rates to be less than 25% if the actual value of/3 is between 0.065 and 0.115. The percent difference in estimated total daily (24 hour) and total daytime (12 hour) variations are considerably less than 10%. The lower percent differences in total emissions occur because if the model overestimates emissions when T < T s, i.e., the assumed value of /3 is less than the actual value, then the model underestimates emissions when T > T s.

The range of values shown in
To assess the sensitivity of these results to the daily temperature regimen, we set /3 = 0.065 and examined the effect of varying either the temperature range (middle section of Table 5) or the daily average temperature (bottom of Table 5). These results show that the error associated with uncertainties in/3 is sensitive to both the mean daily temperature and the range of temperatures encountered. An increase in the difference between the daily average temperature and the temperature to which emissions rates have been normalized, Ts, can significantly increase errors in fluxes estimated with equation (5). The errors in daily and daytime variations in emissions increase from around 10% or less if the daily average temperature is within 5øC of T s to around 50% if T s is 20øC greater than the daily average temperature.

SUMMARY AND RECOMMENDATIONS
The chemical time steps used in regional tropospheric photochemical models vary depending on chemical reaction rates but typically range from 10 to 60 seconds [e.g., Roselle et al., 1991]. Accurate simulation of diurnal biogenic hydrocarbon emission rate variations is required to provide realistic hydrocarbon concentrations at each chemical time step. Leaf temperature plays the major role in determining diurnal monoterpene emission rate variations, while diurnal isoprene emission rate variations are determined by both leaf temperature and light intensity. Light and temperature also play an important role in controlling seasonal, year-to-year, and spatial variations.
The temperature dependence of isoprene emission appears to be associated with isoprene synthase enzyme activity . Isoprene emissions respond to light with a linear increase up to a light saturation point. We recommend using model G93, described in Table 1, to simulate isoprene emission rate variations associated with light and temperature. This model performs well for a variety of plant species and performs significantly better than other models which have been used to simulate isoprene emission rate variation. The improved performance of this model is probably a result of its partial basis in the biochemical mechanisms that control isoprene emissions. It should be noted that the computational expense and data input requirements of model G93 are not prohibitive and that the model can be easily incorporated into regional and global biogenic hydrocarbon emission models. While this model provides a good first-order approximation, there may be additional factors which influence short-term variations in isoprene emission rates. These factors include but are not limited to growth environment, species-to-species variations among plants, maximum emission rates, leaf age, and season.
The temperature dependence of monoterpene emission rates is related to monoterpene vapor pressure and increases exponentially with increasing temperature. Monoterpene emission rate behavior varies among monoterpenes, vegetation species, and other factors, but a simple exponential relationship between temperature and emission provides a good first-order approximation. On the basis of existing data, we recommend that equation (5) be used with a value of/3 = 0.09 K -1 .
Short-term (hours to days) monoterpene and isoprene emission rate variation can be simulated by using the models described above. The uncertainties vary depending on environmental conditions but are typically <25% for individual hours and < 10% for daily totals estimated for the hot sunny days associated with high biogenic hydrocarbon fluxes at temperate latitudes. More accurate descriptions of biogenic emission rate variations may be obtained by incorporating second-order effects into these general models. This can occur only if model improvements are accompanied by a means of estimating the variables needed to initialize and drive additional model components.