Introduction

The USA is the largest producer of biofuels in the world and is converting nearly 40 % of its corn production into 14 billion gallons per year of corn ethanol. Further increases in biofuel production from cellulosic feedstocks are mandated by the Renewable Fuel Standard (RFS), established by the Energy Independence and Security Act, 2007, which mandates production of at least 16 billion gallons per year of cellulosic biofuels by 2022 [1].

Although conversion of cellulosic biomass to fuel is not yet commercially viable, considerable research is underway on high-yielding feedstock sources that could provide abundant biomass for large-scale cellulosic biofuel production. Among all non-grain feedstocks, two perennial crops, switchgrass (Panicum viragatum) and Miscanthus (Miscanthus × giganteus), have been identified as among the best choices for low-input and high dry matter yield per hectare in the USA and Europe [2–4]. Miscanthus is a C4 perennial rhizomatous grass. It has been extensively grown in Europe for over 20 years and is recently being grown in field trials in the USA [3]. Switchgrass is also a C4 native warm-season grass from the USA and has historically been used as forage. Studies suggest that latitude-of-origin of different bioenergy grasses determines their varied adaptability to edaphic conditions, such as winter hardiness, day length, heat, dry and cold conditions, etc. [5]. Miscanthus × giganteus is more adapt to the region below the US plant hardiness zone (PHZ) 5 [6]. On the other hand, switchgrass cultivars are usually divided into upland and lowland. Upland cultivars, such as Cave-in-Rock, are more adapted to middle and northern latitudes (PHZ 4–PHZ 7). Lowland cultivars, such as Alamo, grow better in lower latitudes (PHZ 6–PHZ 9) [7, 8]. The detailed physiological differences between upland and lowland switchgrasses, as well as their differences with Miscanthus, have been discussed in previous studies [4, 8].

While these perennial grasses have potential to help meet future energy demand, the extent to which this potential can be realized will depend on the biophysical potential to grow these grasses while minimizing the diversion of land from food production. We evaluate this potential by assessing the productivity of these perennial grasses under different environmental conditions in the USA. A number of crop productivity modeling studies have estimated the biomass yields for Miscanthus and switchgrass in the USA. For example, Jager et al. [9] have developed empirical models to estimate yield from factors associated with climate, soils, and management for both lowland and upland switchgrass cultivars. However, these model estimates are usually limited by available observation data from field trials and have limited representation of diverse climate, soil, and topographical conditions across the USA [10]. No attempt has been made to evaluate the biomass yield for Miscanthus using an empirical-based approach, mainly because field trials for Miscanthus are sparser than for switchgrass and usually centralized in the Midwest region [3, 11]. Several attempts have therefore been made using mechanistic models to estimate the yield and the spatial and temporal variability in yield of bioenergy grasses, including ALMANAC [12], MISCANMOD [13, 14], MISCANFOR [15], EPIC [16], WIMOVAC (BIOCRO) [17], Agro-IBIS [18], Agro-BGC [19], and TEM [20]. Nair et al. [10] reviewed the differences among these models. According to Nair et al. [10], the ALMANAC, MISCANMOD, MISCANFOR, and EPIC models use relatively simple radiation use efficiency method to simulate the biomass yields, while other models use a more mechanistic biophysical approach to simulate the carbon uptake and assimilation rates. Partitioning of carbon among leaves, stem, root, and rhizome pools are based on fixed carbon allocation fraction at each phenology stage. WIMOVAC (BIOCRO) only accounts for the water limitation on biomass allocation, whereas the ALMANC and EPIC models not only account for water limitation effect on biomass allocation but also temperature, nitrogen, and aeration limitations on plant phenology and biomass yield. Moreover, ALMANC and EPIC are the only two models that account for full hydrological cycle processes. Nitrogen cycle dynamics processes are only considered in the EPIC, ALMANAC, and Agro-BGC models.

This study builds upon and extends the approaches of the models discussed above and aims to integrate the dynamic crop growth processes for Miscanthus and two cultivars of switchgrass perennial grasses into a land surface model, the Integrated Science Assessment Model (ISAM), to estimate the biomass yields for these three grasses in the USA. The western USA, where bioenergy grasses could not survive due to drier conditions [7], is excluded in this study (irrigation is not addressed in this study). The adaptability of three bioenergy grasses at different latitudes is determined by accounting various environmental factors, which vary with day length, the effect of soil texture, soil slope, bedrock layer depth on water uptake by the grasses, and tolerance to winter hardiness, heat, dry, and cold conditions.

While ISAM methodologies to model carbon assimilation, water and energy fluxes, and carbon and nitrogen dynamics for various plant functional types have been described elsewhere [21–25], this study extends ISAM model by accounting additional dynamic structural properties of vegetation, which are specific to the perennial bioenergy grasses. These include the following: (1) a specific phenology development scheme and its variation with latitude, which is controlled by thermal, photoperiod, and extreme meteorological conditions (e.g., frost and drought); (2) a dynamic carbon allocation process to allocate assimilated carbon among root, rhizome, leaf, and stem based on resource availability (e.g., light, water, and nutrient); (3) parameterization of N resorption rate; (4) parameterization of leaf area index (LAI) growth process, which is sensitive to photoperiod.

The objectives of this study are to (1) calibrate and validate different parameters of the above parameterization schemes for three perennial grasses: Miscanthus and two switchgrass cultivars, Cave-in-Rock and Alamo; (2) evaluate ISAM-calculated carbon assimilation rate, LAI, and aboveground/belowground biomass yields for three energy crops using observational data; (3) estimate spatial and temporal biomass yield patterns for the period 2001–2012 in the USA; and (4) compare ISAM-estimated biomass yields with other published studies.

Methods

Model Description

ISAM is a land surface model, which coupled biogeochemical (carbon and nitrogen) module [25] and biogeophysical (energy and hydrology) module [26, 27]. The model calculates carbon, nitrogen, energy, and water fluxes at 0.5 × 0.5° spatial resolution and at multiple temporal resolutions ranging from half-hour to yearly time steps. The details about the model structure, parameterization, and performance have been introduced in previous studies [21–25]. In the following, we provide the details of the processes added to the model, which are specific for this study.

Model Extension

The formulations for dynamic growth processes considered for bioenergy grasses—such as allocation of assimilated carbon among above- and belowground vegetation pools and development of vegetation structure (LAI, canopy height and root depth), etc.—are the same as for the row crops described by Song et al. [24]; here, we describe the calibration of model parameters and model validation, specific to the model of energy grasses. However, the phenology for bioenergy grasses is different than row crops and is described in “Phenology Development”. In addition, we added a rhizome pool and implemented the carbon reallocation between root and rhizome for the bioenergy grasses (Carbon Allocation). The parameterization of N resorption and the sensitivity of LAI growth to photoperiod are also considered (Parameterization of N Resorption Rate for Bioenergy Grasses and LAI Calculation). In the following, we described dynamic processes that had been implemented in ISAM for the current study.

Phenology Development

Miscanthus is planted through rhizomes and switchgrasses through seeds. During the growing season, phenology is divided into five stages: emergence period, initial vegetative period, normal vegetative period, initial reproductive period, and post reproductive period (Fig. 1). After post reproductive period, bioenergy grasses go to the winter dormancy stage, which lasts until the rhizomes emerge next year. The grasses are harvested each year at the beginning of winter dormancy time.

Fig. 1
figure 1

The phenology scheme for bioenergy perennial grasses. The description of each variable is provided in the Table 8

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The planting date for Miscanthus rhizomes is determined based on the shallow soil layers’ temperature and air temperature [24]. The seeding dates for switchgrass are determined by both soil and surface air thermal conditions and accumulated precipitation over a week time just prior to the planting date. Since switchgrasses may not adapt to the region in the west of the 100th meridian [7], and Miscanthus may have difficulty to survive in the region with less than 0.75 m of annual accumulated precipitation [28], we exclude those regions which experience such environmental conditions—viz. the western USA. Switchgrass seeds are planted when the accumulated precipitation over the previous week is greater than the grass-specific minimum precipitation requirement (P crit) [29] (Table 8). Each year after planting bioenergy grasses, the transitions of the different phenology stages are determined by thermal conditions and other factors, which are dependent on latitude of each grid cell [8, 30].

The thermal condition for each grid cell is expressed as the heat unit index above 0 °C (HUI0) (Eq. 1).

$$ \mathrm{H}\mathrm{U}\mathrm{I}0=\frac{\mathrm{GDD}0}{\mathrm{GDD}{0}_{\max }} $$
(1)

Here, GDD0 is the accumulated growing degree days above 0 °C summed from the first day of the year to the current day. GDD0max is the yearly summation of growing degree days above 0 °C averaged for the past 33 years (1980–2012), which represents the climatological thermal conditions [31]. The threshold values of HUI0 for classifying five phenology stages are listed in Table 8. The total number of days during each phenology stage does not exceed the maximum number of growing days of each phenology stage (D), as prescribed in the Table 8.

Latitudinal variability in the onset of the emergence stage and the initial reproductive stage (flowering time) is controlled by the photoperiod [5], which is expressed as the total day length and civil twilight of each day (L day) in terms of hours. The onset of the emergence stage begins when the photoperiod value is above the critical photoperiod value for emergence (L e). At the same time, the past week mean daily air temperature is above the base temperature (T base) and soil temperature is above the critical emergence soil temperature (T soil_crit). The values for T base and T soil_crit vary with bioenergy grasses due to their difference in tolerance to temperature (Table 8). The value for Le varies with the origin of each bioenergy grass (Table 8). Alamo, which is originally from central Texas, can emerge at much shorter photoperiod than that for Cave-in-Rock and Miscanthus, which originally grew in southern Illinois [8]. In addition, the regression analyses of bioenergy grass yields on photoperiod [5, 32] indicate that growing Miscanthus and Cave-in-Rock in the south of its origin (Southern Illinois) will flower earlier due to exposure to shorter than normal day length in the summer, while growing Alamo switchgrass north of its origin (Central Texas) will cause it to flower late due to exposure to longer than normal day length in the summer. To parameterize this effect, the onset of the initial reproductive stage is initialized when the following two conditions are satisfied: (1) the estimated photoperiod value is less than the grass-specific critical photoperiod value for flowering (L f), which is 13 h for Miscanthus and Cave-in-Rock, but 12 h for Alamo [33–35]; (2) the minimum heat required for flowering (GDD v1), which is expressed as the GDD above T base from emergence to flowing time. Here GDD v1 is defined as a function of latitude (Eq. A1). The function is attained through regressing observed GDD v1 values from available sites with the latitude values of corresponding observation sites [36, 37]. If above two conditions are not satisfied, the initial reproductive stage can also be initiated when LAI values reach the grass-specific maximum LAI values (LAImax) (Table 8).

Besides the normal phenology development, extreme environmental conditions can speed up or slow down the development of different phenology stages (Fig. 1). For example, spring frost can delay the onset of initial vegetative stage, whereas fall frost can trigger the earlier onset of the dormancy stage.

Alamo has been reported to be high heat tolerant, but sensitive to extreme cold and dry conditions [32, 38]. In contrast, Miscanthus is more sensitive to extreme hot and dry conditions than Cave-in-Rock and Alamo. Relative to Miscanthus and Alamo, Cave-in-Rock has higher cold and drought tolerances [32]. In addition, Moser and Vogel [39] suggest that warm-season grass species generally do not move more than 500 km north of their origin due to potential stand and rhizomes losses from over-winter injury. Calser [7] reports that Cave-in-Rock will have difficulty surviving in the regions above the PHZ 3, whereas the survival rates of Alamo in the region above the PHZ 6 are low. Heaton et al. [40] finds that Miscanthus is able to survive with −20 °C of air temperature and −6 °C of soil temperature in Illinois, but experiences 90 % of loss in Wisconsin. Past field experiments have failed to establish Miscanthus in the PHZ 3 and PHZ 4 [personal communication with M. Casler].

ISAM accounts for sensitivity of bioenergy grasses to extreme cold, dry, or hot conditions, as discussed above. The spring and fall frost are triggered when previous 3 days average daily minimum temperature (T min3) is less than the grass-specific critical air minimum temperature for frost (T frost). Extreme cold conditions, expressed as previous 6 days (T 6) average daily temperature below T base, during the initial vegetative stage can force the transition from the initial vegetative stage to the initial reproductive stage. Extreme cold weather conditions during the normal vegetative and the initial reproductive stages can induce the onset of the post reproductive stage with initiation of plant senescence [31]. Cold weather conditions are triggered when any of the following conditions are satisfied (Fig. 1): (1) the daily minimum temperature averaged for previous week (T min7) is less than T base; (2) the T min3 is less than the annual minimum temperature averaged for 1980–2012 (T ytmin); (3) the daily soil temperature of root zone is less than the critical temperature for root zone (T soil_s2). Extreme hot and dry conditions can also make the transition to the post reproductive stage earlier without flowering [37]. Extreme hot conditions are triggered when one of the following conditions is met: (1) the mean daily temperature averaged for the last month is larger than the grass-specific maximum temperature (T max_crit); (2) the previous 3 days average daily maximum temperature (T max3) is larger than the annual maximum temperature averaged for 1980–2012 (T ytmax). Dry conditions are activated when the daily mean soil water availability for previous week (Wa7) is below the critical values of water availability for initiation of dry condition (Wacrit). Here, soil water availability (Wa) is the weighted summation of water availability over the total number of soil layers (Eq. A2). The Wa is expressed as an index ranging from 0 to 1, which depends on the combined effects of precipitation, topography, soil texture, root depth, and its distribution in soil layers. The closer that Wa is to 1, the more soil water is available for grass growth. If extreme hot and dry conditions are met simultaneously, onset of the post reproductive stage is triggered. The over-winter injury is triggered when the average annual extreme minimum temperature (T avg_min) is less than T frost. The values for T frost, T base, T ytmin, T soil_s2, T max_crit, T ytmax, and Wa7 (Table 8) are grass specific. Cave-in-Rock is parameterized with lower T frost, T soil_s2, and Wa7 than that for Miscanthus and Alamo due to high tolerance to cold and dry condition, whereas Alamo is parameterized with higher T max_crit than Miscanthus and Cave-in-Rock due to its high tolerance to hot condition.

Carbon Allocation

Besides leaves, stem, roots, and production (seeds or flowers) carbon pools, here we added rhizome pool, which store carbon and nitrogen for the perennial growth. The emergence from rhizome and the carbon allocation among leaves, stems, roots, production, and rhizome are introduced as follows.

The amount of carbon in switchgrass seeds during germination is simulated as a function of seed weight and hydro and thermal conditions (Eqs. A3–A5) [41]. The carbon stored in switchgrasses seeds during the germination is allocated to root and leaf pools to build the root and initiate leaf development (Eq. A6). In the establishment year, the growing season starts with the germination of the seed. In the spring of the following years, the growing season starts with the emergence of rhizome. During the emergence of rhizomes, a fraction of rhizome carbon is allocated to leaf, stem, and root pools according to Eq. A7. After the emergence stage, leaves start assimilating carbon and the assimilated carbon is allocated to stem and root, as well as production pools. The amounts of the carbon allocation fractions at each model time step are determined dynamically based on the availability of water, light, and nitrogen as described in Song et al. [24].

Initial carbon allocation fractions to leaf (Al), stem (As), root (Ar), and rhizome (Arh_r) during each phenology stage (Table 8) are parameterized based on different growth requirements of canopy, stem, root, flowers, seeds, and rhizomes at each phenology stage. The canopy needs to be developed during the initial vegetative stage by keeping a large fraction of leaf-assimilated carbon in the leaf pool, but transferring a small fraction of leaf-assimilated carbon into root and stem. During the normal vegetative stage, the stem is elongated through increasing the fraction of assimilated carbon that allocates to stem. During the initial and post reproductive stages, leaf-assimilated carbon is transferred entirely to production and root pools to develop flowers and roots. Rhizomes grow over time through reallocation of a part of the root carbon pool to the rhizome pool. The reallocation fractions from root to rhizome are dynamically adjusted as a function of Wa (Eq. A8). In order to elongate the root to acquire more water under water stress conditions, the reallocation carbon fractions from root to rhizome pool are reduced according to Eq. A8. During the post reproductive stage, seed is produced for switchgrasses through increasing the fraction of leaf-assimilated carbon given to production pools. However, no carbon is allocated to production pools for Miscanthus, which has no seed production. Finally, the dynamic carbon allocation factor for each vegetation pool is modified by examining whether the minimum belowground/aboveground ratio (RSmin) is sufficient to maintain the structure of each grass. If this condition is not satisfied, all new assimilated carbon is allocated to root and rhizome. The senescence process follows the initiation of flowering. The leaf, stem, root, and rhizome senesce at fixed turnover rates (rlt leaf, rlt stem, rlt root, rlt rhizome) (Table 8), while leaf loss can be intensified due to dry or cold conditions. If the spring frost damage is triggered, the mortality of rhizomes, roots, and aboveground biomass increases linearly according to the Eqs. A9–A10. The fraction of rhizome mortality due to over-winter injury is assumed to be an exponential function of latitude (Eq. A11). The function is developed by regressing the reported values of standing/rhizome fraction loss [5, 42] on T avg_min.

Parameterization of N Resorption Rate for Bioenergy Grasses

Temperate perennial grasses can mobilize N from actively growing tissues to rhizomes in response to winter or dry conditions [43]. This N can be reallocated to actively growing tissues in the following year and thus is important to maintain long-term N availability for growth of bioenergy grasses. N resorption for natural vegetation has been implemented in N cycle process in ISAM and the N availability on carbon assimilation is parameterized by linearly adjusting potential maximum carboxylation rate (V max) with N availability [21, 22, 25]. Here, we parameterized N resorption rate (R cyc) for bioenergy grasses based on measured seasonal variability in standing N and biomass for Miscanthus and Cave-in-Rock at Urbana, IL, site [43] (Table 8). It is assumed that R cyc is uniform across the different region and Alamo has the same R cyc value as Cave-in-Rock in this study.

LAI Calculation

LAI is calculated as a function of leaf carbon and specific leaf area (SLA, defined as a ration of leaf area to leaf biomass). SLA for bioenergy grasses can vary with photoperiod. According to Van Esbroeck et al. [34], variation of leaf area with photoperiod differs among switchgrass cultivars. They found that the leaf size and number for Cave-in-Rock increased when the photoperiod increased from 12 to 16 h, but the reverse was true for Alamo. These results indicate that SLA for the northern cultivar (Cave-in-Rock) decreases from north to south due to exposure to shorter than normal day length in the summer, while SLA for southern cultivar (Alamo) decreases from south to north due to exposure to longer than normal day length in the summer. To parameterize photoperiod-sensitive SLA, we take the SLA in the natural origin of each cultivar (SLA0) (Table 8) as a reference value and calculate SLA at each grid cell as a function of day length during the vegetative stage according to Eq. A12. It is assumed that the function between SLA and day length for Miscanthus is the same as that for Cave-in-Rock in this study.

Model Calibration and Evaluation Using Data from Various Sites

Description of Sites and Database

The field observation data for Miscanthus and Cave-in-Rock and Alamo switchgrasses from three sites in the USA were used to calibrate the model (Table 1). The choice of these sites for calibrations was due to the availability of the comprehensive observation data sets to calibrate the model parameters and processes. The Champaign-Urbana site 1 (CU1) for Miscanthus represents the earliest Miscanthus-growing region in the USA, whereas the CU2 site and Temple, TX (TE), site are at Cave-in-Rock’s and Alamo’s origin. The detailed soil and climatic characteristics as well as data available for different variables for each site are listed in Table 1.

Table 1 The location of the calibrated site, its soil and climate characteristics, and a list of available data that are used to calibrate the model
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The yield data collected at 17 Miscanthus planting sites (M1–M17), 28 Cave-in-Rock planting sites (C1–C28), and 22 Alamo planting sites (A1–A22) (Table 10) were used to evaluate the model performance in diverse environmental conditions. This measurement database aims to include available field experiments that could represent diverse environmental conditions and different geographical region. Field experiments with more than one time of harvest frequency per year and/or irrigation are excluded in this database, since current model has not considered these management practices. This database covers a large geospatial area of the USA, ranging from 26.68°N to 41.17°N for Miscanthus, from 26.22°N to 46.88°N for Cave-in-Rock switchgrass, and from 26.22°N to 39.62°N for Alamo switchgrass (Fig. 3). The soil texture and climatic characteristics are quite diverse at evaluated sites (Table 10). The annual mean air temperature during study years varies along the latitude gradient from 8 °C at the most northern site (Mandan, ND) to 24.5 °C at the most southern site (Weslaco, TX). The validation sites for Miscanthus cover five PHZs (PHZ 5–10a) with an average minimum air temperature of −28.9 to 1.7 °C. The validation sites for Cave-in-Rock include more northern PHZs ranging from PHZ 4a to PHZ 9b, with an average minimum temperature of −34.4 to −1.1 °C. Field experiments usually fail to establish Alamo switchgrass from PHZ 1a–5b due to extreme cold winter condition [personal communication with M. Casler]; thus, the validation sites for Alamo switchgrass only cover the region from PHZ 6a to 9b. The annual total precipitation follows the distinct longitude pattern with relatively less precipitation at the western sites and relative more precipitation at the eastern sites (Table 10). At most of validation sites have made efforts to mitigate the edge effect through excluding sampling from the edge of the plot, adjusting alley width, subsample size, planting density, harvest length, etc. [32, 37]. Detailed management information, such as planting time, seedling/rhizome planting weights, harvest frequency and time, fertilizer and irrigation, etc., were collected from references listed in Table 10.

Model Calibration

Hourly climate data for mean surface air temperature, precipitation rate, the incoming shortwave radiation, long-wave radiation, wind speed, and specific humidity are taken from North American Land Data Assimilation System (NLDAS-2) climate database (0.5 × 0.5°) [44]. Soil texture data is taken from the State Soil Geographic Database (STATSGO2) [45]. Both of these are used to drive the model simulation for each calibrated and validated site at an hourly time step. We start the modeling calculations for each site by prescribing current land cover distribution and atmospheric CO2 concentrations of 369 ppm, representative of approximate condition in 2000, to allow soil water and soil temperature to reach an initial steady state, which takes approximately 200 years of model runs. Then, we assume that each site is fully covered with the corresponding bioenergy grasses (Miscanthus/Cave-in-rock Rock/Alamo) and run the model based on site-specific planting time, seed weight, and harvest time for each site [40, 46–49].

The model parameters are calibrated and validated by minimizing the total sum of the squares of the difference between simulated and observed data for each bioenergy grass at each calibrated site [24]. The calibrated processes and corresponding parameters are listed in the Table 2.

Table 2 Calibrated parameter values for individual process. The three calibrated parameter values separated by comma (,) are for Miscanthus, Cave-in-Rock, and Alamo  
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Best Fit Model Results for Carbon Assimilation, LAI, and Above- and Belowground Biomass

We use the refined Willmott’s index (dr) [50] to quantify the degree to which observed carbon assimilation rates, LAI, and biomass (aboveground, root, and rhizome biomass) are captured by the model. The dr is calculated as Eq. 2 and varies from −1 to 1. The value of 1 indicates perfect agreement between the modeled and observed values, while a dr of −1 indicates either lack of agreement between the model and observation or insufficient variation in observations to adequately test the model. The dr is calculated as:

$$ dr=\left\{\begin{array}{ll}1-{\displaystyle {\sum}_{i=1}^N\left|{P}_i-{O}_i\right|/2}{\displaystyle {\sum}_{i=1}^N\left|{O}_i-\overline{O}\right|}\hfill & if\ {\displaystyle {\sum}_{i=1}^N\left|{P}_i-{O}_i\right|}\le 2{\displaystyle {\sum}_{i=1}^N\left|{O}_i-\overline{O}\right|}\hfill \\ {}2{\displaystyle {\sum}_{i=0}^N\left|{O}_i-\overline{O}\right|/{\displaystyle {\sum}_{i=1}^N\left|{P}_i-{O}_i\right|}-1}\hfill & if\kern0.5em {\displaystyle {\sum}_{i=1}^N\left|{P}_i-{O}_i\right|}>2{\displaystyle {\sum}_{i=1}^N\left|{O}_i-\overline{O}\right|}\hfill \end{array}\right. $$
(2)

Here, P i and O i are the individual modeled and observed data, respectively. Ō is the mean of observed values. N is the number of the paired observed and modeled data. Based on the availability of observed carbon assimilation rate, we compare modeled with measured gross carbon assimilate rates (A) for Miscanthus and Cave-in-Rock as well as modeled with measured net carbon assimilation rate (An = A-leaf respiration) for Alamo switchgrass.

The dr values for A/An vary between 0.73 and 0.76 (Table 3), indicating that the model is able to capture the measured variations in carbon assimilation rates for all grasses. Modeled and measured carbon assimilation rates compare favorably across different growing seasons (Fig. 2a–c). The measured data is only available for Cave-in-Rock, and the comparisons between the modeled and measured hourly gross carbon assimilation rates for Cave-in-Rock at canopy level show close agreement (dr = 0.75) (Figure S1), suggesting that the model is not only able to capture the daily assimilation rates for energy grasses but also the measured diurnal variability in carbon assimilation. The model also captures the seasonal development of LAI and its inter-annual variability for each three of energy grasses (Fig. 2d–f). The dr values calculated with all available data for three grasses vary between 0.78 and 0.90 (Table 3).

Table 3 The calculated Willmott index, dr, for various variables of Miscanthus, Cave-in-Rock, and Alamo
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Fig. 2
figure 2

Measured and model simulated carbon assimilation rates (A/An) (a–c), LAI (d–f), and biomass (aboveground, root and rhizome) (h–j) for Miscanthus at Urbana, IL, Cave-in-Rock at Urbana, IL, and Alamo at Temple, TX, sites. Here A is the daily gross carbon assimilation rate at leaf level for Miscanthus and the hourly gross carbon assimilation rate at canopy level for Cave-in-Rock. An is the net carbon assimilation rate for Alamo at leaf level. The data for Miscanthus is for the time period 2007–2008, for Cave-in-Rock 2005–2006, and for Alamo 1995–1997. The biomass data for Cave-in-Rock is only available as the multiyear mean values over the time period 2005–2006

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The modeled aboveground biomass production across two Miscanthus-growing seasons and three Alamo-growing seasons is in good agreement with the measured intra-annual and inter-annual variations (Fig. 2h, j), with an exception for a slight underestimation of peak biomass for Miscanthus at the CU1 site. The dr values are 0.83 and 0.87 for Miscanthus and Alamo grasses (Table 2). Because of the unavailability of the measured data for Miscanthus, we have not compared the modeled belowground biomass results with measurements. More importantly, the modeled root biomass for Alamo grass at the end of two continuous growing seasons is close to measured values (Fig. 2j), indicating that the model is able to predict continuous root growth across multiple years for Alamo grass. The model also accurately predicts the mean biomass partitioning among aboveground biomass, root, and rhizome across three continuous years for Cave-in-Rock (Fig. 2i). The relatively low dr values of 0.54 for root and 0.51 for rhizome are attributed to the overestimations of root and rhizome biomass at the end of growing season. These overestimations are due to the overestimation of carbon allocation to belowground pools at the end of growing season, when the minimum belowground/aboveground ratio (RSmin) is not satisfied to maintain the grass structure and thus model allocates all assimilated carbon to root and rhizome. This happens due to the uncertainty in parameterization of RSmin, which is attained in this study based on the measurement of a greenhouse experiment [51] and is assumed that its value does not vary spatially. However, the modeled root and rhizome biomass values still fall within the maximum measured uncertainty range values (Fig. 2i). Overall, the calibrated model is able to capture the diurnal and daily carbon assimilation rate and intra-annual and inter-annual variation in LAI and biomass production.

Model Evaluation

We evaluate model performance for estimated yields for each bioenergy grass across all evaluation sites discussed in Description of Sites and Database. First, the modeled and observed multi-year yields are averaged over the measured years to calculate the modeled and observed mean yield for each evaluation site. Then, the degrees to which observed mean yield across all sites are captured by modeled values are quantified by dr as discussed in Best Fit Model Results for Carbon Assimilation, LAI, and Above- and Belowground Biomass. The averaged tendency of the modeled yields relative to measured yields for each site is evaluated by calculating percent bias (PBIAS) (Eq. 3) [52]. Here, Y o i and Y m i are the modeled and measured yearly yields for the year i at each site. N is numbers of available data for each site. The closer the value of PBIAS is to zero, the higher the accuracy of the model results is and the smaller the bias in the model results is. Positive PBIAS indicates the model underestimates the yield, and negative PBIAS indicates that the model overestimates the yield. The standard deviations (SD) from the mean for modeled and measured yields are calculated for each site using Eq. 4. Here, Y i is the yearly yield for the year i and \( \overline{Y} \) is the mean yield over N numbers of measured years for each site. The ± SD in mean yield represents the range of modeled and measured yields at each site. The comparison between modeled and observed SDs determines whether the model is able to capture the yearly yield variability at each site.

$$ \mathrm{PBIAS}=\frac{{\displaystyle {\sum}_{i=1}^N}\left({Y}_i^o-{Y}_i^m\right)}{{\displaystyle {\sum}_{i=1}^N}{Y}_i^o}\times 100\% $$
(3)
$$ \mathrm{S}\mathrm{D}=\sqrt{\frac{{\displaystyle {\sum}_{i=1}^N}{\left({Y}_i-\overline{Y}\right)}^2}{N-1}} $$
(4)

Evaluation of Model Estimated Yields

Overall, the modeled yields for Miscanthus, Cave-in-Rock, and Alamo are in good agreement with measured yields at evaluation sites, with dr values of 0.87, 0.83, and 0.66, respectively. Except for the sites where the peak yield for growing season is harvested, the modeled mean harvested yield is around 30 % lower than the simulated mean peak yield for each grass (Table 4). This is in agreement with recommended harvest management, which suggests that harvest until winter or early spring will induce approximately 33 % reduction from peak biomass [4]. However, there are still some specific sites where the model is unable to accurately capture the observed yields.

Table 4 Mean and standard deviation (SD) from the mean for modeled and measured yields, modeled peak yield for growing season, sampling variability in measured yield, relative percent bias (PBIAS) in modeled yield for each validation site (Miscanthus: M1-M17; Cave-in-Rock: C1-C28; Alamo: A1-A22). Here N is the number of years for measured data and mean is calculated for N years
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The PBIAS values for Miscanthus yield are −66.7 % for Booneville, AR, site, −35.7 % for Stillwater, OK, site, and 54.6 % for Kingsville, TX, site, respectively (Table 4), indicating the overestimation of Miscanthus yield at Booneville and Stillwater sites, but the underestimation at the Kingsville site. The sampling variability (Table 4) is equal to 58, 60, and 66 % of measured mean yields at Booneville, Stillwater, and Kingsville, respectively. The higher sampling variability at the three sites suggests that there is a large environmental heterogeneity at each site, and ISAM is unable to capture the heterogeneity effect on spatial yield.

For Cave-in-Rock (Table 4), ISAM underestimates yield at two TX sites: Weslaco (PBIAS = 57.8 %) and Kingsville (PBIAS = 34.2 %). The sampling variability is also high at these two sites, which is equal to around 50 % of measured mean yields. This indicates that ISAM fails to capture large environmental heterogeneity at these two sites. The higher model bias is also observed at the Brownstown, IL, site, where the modeled yield for Cave-in-Rock is about 31 % higher than observed yield (Table 4). According to Dohleman [53], this site has a poor soil quality and weed pressure that might have slowed down the establishment of Cave-in-Rock and thus produced relatively low yield. However, ISAM is not able to capture the poor soil quality effect due to uncertainty in soil data used in our calculation, nor ISAM accounts for weed pressure effects.

In the case of Alamo yield, the largest model bias is observed at Jackson, TN, site, where the model overestimates yield with the bias magnitude of 45.1 % (Table 4). The Jackson site has a shallow soil depth and thus low water capacity, which limits the root development and lowers the yield due to water stress conditions [54]. The model is unable to simulate shallow soil depth and its effects on soil water capacity due to lack of high-resolution bedrock data, leading to overestimation of Alamo yield at this site. Otherwise, higher PBIAS values (Table 4) at the Kingsville, TX (PBIAS = 41.4 %) and the Weslaco, TX (PBIAS = 32.2 %) sites indicate that the model also underestimates Alamo yields at two sites due to the same reason discussed above.

The comparisons between modeled and measured SD values for yields at different sites indicate that the model is able to capture the measured yearly yield variability at most of the sites (Table 4), with the following exceptions: at the Elsberry, MO, site, the measured yearly yield variability for Miscanthus (16.1 t/ha) is seven times higher than the modeled yield variability (2.2 t/ha). Kiniry et al. [32] indicates that the maximum Miscanthus LAI at this site increases from 3.6 in 2010 to 7.6 in 2011 and thus leads to almost two times of increase in yield from 2010 to 2011. However, the model is unable to capture this yearly increase in maximum LAI and thus the yield during the second and the third year after establishment. For Cave-in-Rock, the measured yield variability at the Kingsville, TX, site (1.6 t/ha) is seven times higher than the modeled yield variability (0.2 t/ha). The mismatch between modeled and measured yearly yield variability at this site could be due to the same reasons as discussed above. The apparent underestimation of modeled yearly variability in Alamo yield is shown at the Nacogdoches site, the Blacksburg site, the Jackson site, and the Kingsville site (Table 4). The underestimation of yearly variability in Alamo yield at the Nacogdoches site is due to underestimation of yearly maximum LAI variability during the second and the third year after establishment, while the disagreement between modeled and measured yearly yield variation at the Jackson site and Kingsville site is due to lack of high-resolution bedrock data or lack of large spatial heterogeneity of environmental factors within the site as discussed above. The Blacksburg site is situated on a steep slope and thus has a low water infiltration [55], which leads to a strong sensitivity of Alamo yield to precipitation. ISAM currently fails to capture steep slope conditions and hence the lower water infiltration. Most of the trial sites selected for our analysis have multiple years of data sets, with the exception of three Miscanthus sites in Florida. We include these three sites in our model analysis because there are not many sites available in the literature for Miscanthus yield data in Florida. The statistical analysis suggests that accounting of these three sits does not skew the statistics for evaluating the model performance on Miscanthus yield simulation. The recalculate dr value without including these three sites was as high as 0.85, which was not significantly different than with including case value of 0.87.

In summary, the model is able to capture observed mean yields and their variations for three energy grasses under diverse environmental conditions in the USA. The high model biases for some sites in extreme southern TX are due to site-level environmental heterogeneity not captured in the model. The uncertainty in bedrock and slope data sets also explains the model biases in Alamo yields and their variations at specific sites.

Estimating Yield Zones Based on Spatial and Temporal Variations for Biomass Yield for Energy Grasses

Information on potential bioenergy yields in space and time will be crucial in order to improve estimation of feedstock supply areas for biorefineries and to reduce biomass producer risk [56]. However, spatial variations for bioenergy feedstock could vary with time and space due to changes in environmental conditions, such as temperature and precipitation, and soil characteristics. Here, we carried out quantitative analysis of biomass yield of bioenergy grasses to identify the spatial and temporal trends in the USA using the methodology described by Blackmore et al. [57] and later on applied by other studies [56]. This methodology identifies the regions where yields could be high or low and stable or unstable in time.

In order to estimate spatial and temporal pattern of biomass yields over the period 2001–2012, the model is first initialized with NLDAS-2 climate [44] and STATSGO2 soil database [45] along with current land cover and atmospheric CO2 concentrations for year 2000 until soil temperature and moisture reach steady state. Energy grasses were then planted with commonly reported seedling and rhizome planting densities, which were 4,850 rhizomes/acre (approximately 600 kg/ha) for Miscanthus [58] and 8.5 kg/ha of seeds for Cave-in-Rock and Alamo [59]. We follow the agronomic practices to grow switchgrass and Miscanthus at site level calculations based on the information provided in the literature for each site. For the US-scale calculations, we prescribe agronomic practices based on Lee et al. [60].

Here, we use spatial yield patterns estimated by ISAM at 0.5° × 0.5° to assess the regions which continuously produce higher (or lower) yields due to favorable (or unfavorable) conditions, such as soil and topography characteristics and regional climate conditions. A single spatial yield pattern of each bioenergy grass is presented as the arithmetic mean (AM) of yearly yield for the period 2001–2012 at each grid point. Here, we exclude low and unstable yield in the establishment year at each grid point. The thresholds, which classify high and low yield zones, are defined as the median value of the AM of yield over the period 2001–2012 for all grid cells. To quantify the effects of environmental factors on spatial yield pattern, the statistical significance of the differences in environmental variables between high and low yield zones is analyzed by rank-sum test [61] and comparing the median values of each environmental variable for high and low yield zones. The environmental variables considered here include the following: mean air temperature (T), mean short wave radiation (Ra), accumulated precipitation (P), and mean Wa during the growing season and photoperiod during the vegetative stage (L day). The value of each environmental variable at each grid point is expressed as its multi-year mean values over the time period 2001–2012.

The yearly variations in yield over the period 2001–2012 at each model grid are used to assess the extent to which yields vary temporally. The degree of temporal variability in yields is measured as temporal variance defined as the square of the standard deviation (SD2) at each grid cell [57]. The lower the variance is, the lower the extent to which yield varies temporally due to variation in weather conditions, and thus the greater the temporal yield stability. The threshold values of temporal variance in yield are used to define stable (SD2 ≤ threshold) and unstable (SD2 > threshold) yields for each bioenergy grass. The threshold value for temporal variance in yield can be assigned according to multiple criteria and could include choosing a fraction of the coefficient of variation or relating it to potential management practices [57]. We assign the threshold value of temporal variance for each bioenergy crop where SD (the square root of the temporal variance) is about 16 % of the bioenergy’s median crop yield (values defined above). A sensitivity analysis suggests that choosing a threshold value based on SD being greater than about 16 % results in an insignificant number of grid points being identified as unstable.

To quantify how variability in climate variables influences temporal yield variability, we calculate the coefficient of variation (CV) for each climate variable over the time period 2001–2012 at each grid cell. CV defines as the percentage fraction of standard deviation of each climate variable to its mean value over the time period 2001–2012, and thus indicates the relative variability of each climate variable relative to its mean value. The significance of difference in CV values of each climate variable between stable/unstable yields zone is firstly tested through rank-sum test and then quantified by comparing estimated median values for CV in stable/unstable yield zones. Since soil texture can influence the sensitivity of yield to variability in climate variables, here we also calculate the CV values for Wa over the same period and compare its difference between stable/unstable yield zones.

After assigning the threshold values for high/low yield classification and stable/unstable yield classification, the spatial trend and temporal variations are then grouped together into four yield class zones: high and stable yield zone (HS), high and unstable yield zone (HU), low and stable yield zone (LS), and low and unstable yield zone (LU). The HS yield zone is more appropriate to grow bioenergy grasses with stable high yields, whereas the yield in HU zone is sensitive to the variance in weather variables. The LS yield zone is not appropriate to grow bioenergy grasses due to unfavorable climate and soil characteristics. Finally, yields in LU zones are uncertain due to high variance. Future climate change that may increase precipitation may increase the yield in this zone.

Estimated Spatial Yield Patterns for Energy Grasses

The model simulates no establishment of Miscanthus in the region above the PHZ 4 (Fig. 3a). This is in agreement with most field experiments, which fail to establish Miscanthus in upper Michigan, the northern part of lower Michigan, as well as northern Vermont, New Hampshire, and Maine. The extreme low over-winter temperatures in these regions induce almost 100 % rhizome mortality and thus no survival of Miscanthus. In addition, the model also simulates no survival of Miscanthus in the western Great Plains (Fig. 3a) where accumulated precipitation over the growing season is estimated to be less than 400 mm (Figure S2a). Except for region with no survival of Miscanthus, there are large spatial variations with average annual yields for the time period 2001–2012 ranging between 2 and 25 t/ha. High-yield zones with yield of more than 15 t/ha are located in the central Midwest, Kentucky, Tennessee, and the upper south Atlantic region. The results suggest that there are significant differences in P, mean Wa, mean Ra, and mean T g during the growing season and mean photoperiod during the vegetative stage (Table 5) between high/low yield zone for Miscanthus. In addition, the results indicate that high yields are supported by high precipitation (P > 600 mm), moist soil condition, T g less than 296 K, and longer mean photoperiod during the vegetative stage (Figure S2a, g, j). In contrast, low precipitation amount reduces Wa for the Miscanthus growth in the eastern Great Plains, leading to less than 10 t/ha of yield (Fig. 3a), whereas the low Miscanthus yields in the southern USA are due to too warm conditions (T g > 296 K). High temperature reduces carbon assimilation rates and thus the yield in this region. Moreover, too warm condition here delays the senescence process and reduces N translocation, leading to N limitation for the growth in the following year. In addition, shorter than normal day length in the southern USA induces earlier flowering time, which reduces leaf size and number and thus carbon assimilation [34].

Fig. 3
figure 3

The spatial yield patterns (Miscanthus (a), Cave-in-Rock (b), and Alamo (c)), the temporal yield variance maps (Miscanthus (d), Cave-in-Rock (e), and Alamo (f)), and the spatial and temporal yield trend maps (Miscanthus (g), Cave-in-Rock (h), and Alamo (i)) for three energy crops. In the legend of figures g, h and i the HS represents high and stable yield zone, HU high and unstable yield zone, LS low and stable yield zone, and LU low and unstable yield zone

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Table 5 Annual median values for various environmental factors averaged over the period 2001–2012. The values are provided for high and low yield zones for three energy crops
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Similar to Miscanthus, the model simulates no survival of Cave-in-Rock in the western part of Great Plains, mainly the region located in the west of the 100th meridian. Limited precipitation together with poor soil texture in the northwest of Nebraska induces strong water limitation on the establishment of Cave-in-Rock. Cave-in-Rock could survive in most of the rest part of the eastern USA, except for region above PHZ 3, where grass may not survive due to too cold winter conditions. The Cave-in-Rock yield in its establishment region has an estimated range between 2 and 15 t/ha, with the critical value for classifying high/low yield zone of 9.4 t/ha. Cave-in-Rock can share the same high yield zone as that for Miscanthus (Fig. 3b). In addition, there is also high yield in Iowa, eastern Nebraska, eastern Kansas, and eastern Oklahoma. Table 5 suggests that the high Cave-in-Rock yield zones are attributed to high precipitation (P > 500 mm), moist soil condition, and suitable temperature (T g >296 K) during the growing season and longer mean photoperiod during the vegetative stage (Figure S2b, h, k). Yields in central Great Plains (Fig. 3b) are low due to less than 500 mm of precipitation during the growing season together with poor soil texture, which limits the water availability for Cave-in-Rock growth (Figure S2b, k). As discussed for Miscanthus, lower Cave-in-Rock yields (<6 t/ha) in the southern USA are due to too hot conditions and shorter than normal day length.

Unlike Miscanthus and Cave-in-Rock, Alamo may not be established in most of the northern USA. This is agreement with the field experiments, which suggest that Alamo usually could not adapt to the region above PHZ 6 because unfavorable cold winter conditions, which could induce almost 100 % of rhizome mortality [7]. In addition, Alamo may not survive in the western Texas due to too dry condition in this region. Alamo yields in the rest of the eastern USA have the range between 4 and 17 t/ha, with the critical value for classifying high/low yield zone of 11 t/ha. The most parts in the bottom of the Midwest, Atlantic Plains, and most of the southern USA are identified as high yield zones, except for central Kansas, central Oklahoma, and central Texas. Table 5 shows that P and mean Wa during the growing season are significantly higher in the high Alamo yield zone than that in the low yield zone, whereas photoperiod during the vegetative stage is significantly lower in the high yield zone than that in the low yield zone. This analysis suggests that high precipitation (P > 600 mm), moist soil condition during the growing season (Figure S2 c, l), and relatively short photoperiod results in the high Cave-in-Rock yield. Low yields in central Kansas, central Oklahoma, and central Texas are attributed by low precipitation and thus low Wa in the region.

Temporal Yield Variations for Energy Grasses

The estimated SD2 range between 0 and 64 (t/ha)2 for Miscanthus, 0–13 (t/ha)2 for Cave-in-Rock, and 0–24 (t/ha)2 for Alamo over the USA (Fig. 3d–f). Given the median yield values for three bioenergy crops, the threshold values for classifying stable/unstable yield zones are therefore 7.0 (t/ha)2 for Miscanthus, 2.5 (t/ha)2 for Cave-in-Rock, and 3.0 (t/ha)2 for Alamo. Figure 4 shows the distribution of SD2 across all grid points, as well as the thresholds for temporally stable yields. This curve indicates that the percentage of the total number of grid cells with temporally stable yield apparently increases with increasing level of temporal variance, but with gradually decreasing rates, as indicated by the first deviation of the curve in Fig. 4. The total grid cells that have temporal yield variances lower than or equal to these thresholds are 75 % of Miscanthus, 89 % of Cave-in-Rock, and 84 % of Alamo. However, only 21 % of these stable yield zones for Miscanthus, 41 % of stable yields zones for Cave-in-Rock, and 16 % of stable yields zones for Alamo can be considered as high yield zones.

Fig. 4
figure 4

The bar chart shows the distribution of total number of grid points falling into the each bin of variance interval and the curve shows the variation of the percentage of total number of grid points, with increasing values of the temporal yield variance for Miscanthus, Cave-in-Rock, and Alamo yields over the US domain. The green vertical line shows the threshold value for temporal variance for classifying stable/unstable yield zones

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Except for the region in bottom of the Midwest, western Kentucky, western Tennessee, as well as central Texas, southern Oklahoma, and eastern Nebraska, Miscanthus yields in the rest of the eastern USA are unstable (Fig. 3d). Table 6 shows that the CV values for both precipitation and Wa in the unstable yield zones are significantly higher than that in the stable yield zone. These results explain unstable Miscanthus yields in eastern Kansas and northern Oklahoma, where more than 20 % of relative variability in precipitation together with poor soil texture induces more than 10 % of relative variability of Wa (Figure S3a, d) and thus drives high yield variations for Miscanthus. Relative to these regions, similar variability in precipitation does not induce high variability in soil water availability in moist southern USA (Figure S3a, d). Table 6 indicates significant difference in radiation and temperature between stable/unstable Miscanthus yield zones. Our study indicates that more than 4 % of relative variability in radiation following variability in precipitation amount (Figure S3g) drives unstable Miscanthus yields in the southern USA (Fig. 3d). The higher radiation and temperature variability (>6 %) in the unstable yield zones mainly control the higher yield variability in the central Midwest, such as northern Missouri, northern Illinois, southern Michigan, Ohio, and the western Pennsylvania in the northeastern USA (Fig. 3d).

Table 6 Annual median values of coefficient of variance (CV) averaged over the period 2001–2012 for various input variables. The values are provided for stable and unstable yield zones for three energy crops
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Unlike Miscanthus, Cave-in-Rock yield is stable in most of the eastern USA, except the regions discussed as follows. Table 6 suggests that high variability of precipitation, Wa, radiation, and temperature induce unstable Cave-in-Rock yield. The unstable yields in the eastern Great Plains (Fig. 3e) are due to more than 20 % of precipitation relative variability and thus high variability in Wa (Figure S3b, e). In addition, high relative variability in temperature (CV > 7 %) (Figure S3k) also attributes to the unstable Cave-in-Rock yield in South Dakota and North Dakota (Fig. 3e). Cave-in-rock yields in southern Arkansas and northern Mississippi are very sensitive to radiation variation (Figure S3h), even 3 % of relative variability in radiation could induce more than 5 (t/ha)2 of yield variation in this region.

For Alamo, the unstable yield zones are mainly located in eastern Kansas, eastern Oklahoma, eastern Texas, and the connection region between Arkansas and Louisiana (Fig. 3f). The significant difference in precipitation and Wa between stable/unstable yield zones (Table 6) indicates that high Alamo yield variability here is the response to high precipitation and Wa variability (Figure S3c, f). In addition, there is also unstable Alamo yield in West Virginia and Maryland (Fig. 3f), which is related to high relative variability of temperature in this region (Figure S3l).

Homogeneous Spatial Zones Based on the Spatial and Temporal Trends in Yield for Energy Grasses

Figure 3g–i shows that all three zones (HU, LU, LS) are usually successively distributed, northward, southward, and westward from HS zones for Miscanthus and Cave-in-Rock, but northward and westward from HS zones for Alamo.

There are some common trends for three bioenergy grasses in the distribution of yield zones in the USA. The HS yield zones for three bioenergy grasses are in southern Missouri, northwestern Arkansas, southern Illinois, southern Indiana, southern Ohio, western Kentucky, and part area of northern Virginia (Fig. 3g–i). The highest Miscanthus yield is almost 1.8 and 1.5 times higher than that for Cave-in-Rock and Alamo in these regions. The LS yield zones for Miscanthus and two cultivars of switchgrasses are located in the upper part of north central, northeastern, and northern New England as well as western parts of Great Plains (Fig. 3g–i). Three bioenergy grasses usually could not be established in these regions (Fig. 3a–c).

Parts of the Midwest region, such as northern Illinois, Indiana and Ohio, and eastern Kentucky are HU yield zones for Miscanthus (Fig. 3g) and HS zones for Cave-in-Rock (Fig. 3h), but LS yield zones for Alamo (Fig. 3i). Most of the areas in Tennessee, southern Virginia, and North Carolina are HS yield zones for Cave-in-Rock and Alamo, but HU yield zone for Miscanthus. Most areas of the southern USA are the HS yield zone for Alamo, but the LU yield zone for Miscanthus and LS yield zone for Cave-in-Rock. In eastern parts of Great Plains, both Cave-in-Rock and Alamo show the transition from HU to LU yield zones along an east-to-west gradient. However, Miscanthus is usually low and unstable in this region.

Overall, the HS yield zones for the three bioenergy grasses discussed here are more suitable to grow bioenergy grasses with minimum natural resource investment. Extra management practices such as irrigation, especially in the dry year, might help to increase the stability of bioenergy grass yields in the HU yield zones. Upper part of north central, northeastern, and northern New England and western parts of Great Plain, defined as LS yield zones, are not appropriate to grow Miscanthus and Cave-in-Rock and Alamo switchgrasses. There could be some other bioenergy crops or other switchgrasses cultivars that may be grown in this region.

Comparing ISAM Estimated Bioenergy Yields with Other Studies

We compare ISAM estimated biomass yields for energy crops with previously published model studies that simulate bioenergy yields either at a regional or US scale, including Miguez et al. [17, WIMOVAC (BIOCRO) model], VanLoocke et al. [18, Agro-IBIS model], Zhuang et al. [20, TEM model], Jager et al. [9, empirical model], Thomson et al. [16, EPIC model], and Behrman et al. [12, ALMANAC model]. The major characteristics and the main results of these models along with ISAM are listed in Table 7. All models, with the exception of Jager et al. [9], are process-based models, which simulate carbon assimilation and allocation processes for Miscanthus and/or switchgrasses. Among these models, the EPIC and ALMANAC models use radiation use efficiency to calculate switchgrass yields [12, 16], while other models use more detailed biophysical methods to simulate carbon assimilation. The major distinction between ISAM and other models is that ISAM is the only model which accounts for dynamic response of carbon allocation, LAI growth, as well as root growth and distribution among the soil layers to environmental factors, such as precipitation, temperature, and radiation. Similar to EPIC and ALMANAC model, ISAM also parameterizes Cave-in-Rock and Alamo separately.

Table 7 Comparison of simulated yields among different models
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In terms of Miscanthus yield, ISAM estimates consistently higher yields in the central and southern Midwest Corn belt, which is similar to BIOCRO, Agro-IBIS, and TEM models. However, the ISAM estimated highest yield in this region, which is 25 t/ha and similar to TEM estimated highest yield value of 21.5 t/ha, is almost 38 % lower than the BIOCRO model estimated highest yield of 40.5 t/ha and 31 % lower than the Agro-IBIS estimated highest harvested yield of 36 t/ha. This difference could be due to the fact that these two models use different sets of observation data to calibrate the model parameters. ISAM is calibrated based on the observation data from a large plot at Champaign-Urbana (plot size 0.2 ha) site, whereas BIOCRO and Agro-IBIS are calibrated based on observed data from a small plot at the same site (plot size 0.01 ha). Due to edge effects, the observed aboveground biomasses for the small plot for years 2007 and 2008 are as high as 2.9 times as compared to the observed data for the large plot [53, 62]. In addition, ISAM and BIOCRO model estimated spatial yield patterns differ in the south USA. ISAM estimated Miscanthus yield in the southern states, including eastern Texas, Louisiana, Mississippi, Alabama, Georgia, and Florida, is lower than 8 t/ha, but BIOCRO model estimated yield is usually higher than 20 t/ha in this region. Observed data (Table 4) from sites in Arkansas, Texas, Oklahoma, and Florida suggests that ISAM estimated Miscanthus yield in the southern USA is consistent with measured values at these sites, whereas BIOCRO model may have overestimated Miscanthus yield in the southern US.

For Cave-in-Rock switchgrass, all models, including ISAM, estimate higher yield for Illinois, Indiana, Ohio, Iowa, and Missouri. ISAM estimated highest yield for Cave-in-Rock in these states is 15 t/ha, which is consistent with ALMANAC estimated yield of 14 t/ha, but slightly higher than EPIC estimated highest yield of around 12 t/ha and TEM estimated highest yield of 10.8 t/ha (Table 7).

For Alamo switchgrass, all models simulate higher yield in the southern US states, including Louisiana, Mississippi, and Alabama. ISAM estimated highest yield for Alamo in these states is 17 t/ha. This estimated yield is consistent with EPIC estimated highest yield of 16 t/ha in this region and falls in the range (15–20 t/ha) of BIOCRO model estimated yields in this region. However, ISAM estimated yield along the Gulf coast and Florida (15–17 t/ha) is lower than ALMANAC estimated higher yield (>18 t/ha) for the same region. One of the reasons for this difference could be due to the fact that the two models follow different N management practices. The simulation with ALMANC applies 100 kg/ha N per year after establishment, whereas ISAM assumes no N fertilizer applications. This may have led to N limitation on Alamo growth in the ISAM simulated yield.

Overall, ISAM is able to simulate yields for bioenergy grasses under diverse environments conditions in the USA, especially in central and south of study domain, where model performances have been widely validated by the observed data. In north central, northeastern, and northern New England, an empirical function has been introduced to simulate the rhizome and stand mortality due to over-winter injury. Our model estimates less than 8 t/ha of Miscanthus yields in the most south part of Michigan, which is consistent with reported Miscanthus yield range (1.47 to 9.0 t/ha) in this state [63]. This result suggests that the model is able to capture the effect of rhizome mortality due to over-winter injury. However, model estimated yield for Cave-in-Rock in this region is slightly higher (6.0–10.0 t/ha) as compared to measurements [63] (2.9 to 7.3 t/ha). We suggest that more observed data is needed in north central, northeastern, and northern New England to further validate our model performance. In addition, as discussed in model validation section, the model underestimates yields of bioenergy grasses at the bottom of southern Texas due to lack of large spatial heterogeneity of environmental factors within specific sites. Thus, the potential yields of bioenergy grasses need to be further evaluated with high-resolution data for environmental variables, such as soil slope, soil depth, etc.

Conclusions

The study implements dynamic growth processes, including dynamic carbon allocation and root distribution, into a land surface model, ISAM, with specific phenology development schemes for Miscanthus and Cave-in-Rock and Alamo. The simulated carbon assimilation rates, LAI, and carbon allocation among aboveground and belowground biomass for the three bioenergy grasses are in good agreement with observed data from Urbana, IL, site for Miscanthus and Cave-in-Rock, and a Temple, TX, site for Alamo. The modeled mean yield and its variation over measured years at 43 different evaluation sites are in good agreement with measured yields. The model calibration and evaluation results indicate that ISAM is able to capture the spatial and temporal variations in biomass yields for bioenergy grasses in the US.

Based on simulated mean bioenergy grass yields and their variances over the period 2001–2012 in the USA, we identify four yield zones: a high and stable yield zone (HS), a high but unstable yield zone (HU), a low and stable yield zone (LS), and a low and unstable yield zone (LU). Our results indicate that regional precipitation, temperature, soil water availability, and day length control the spatial distribution of high and low yields zones in the USA, whereas relative temporal variability in precipitation, temperature, and radiation determines the temporal stability and instability in the USA. The HS zone for the three bioenergy grasses is mainly located in the regions with precipitation greater than 600 mm and mean temperature 292–294 K during the growing season, and includes southern Missouri, northwestern Arkansas, southern Illinois, southern Indiana, southern Ohio, western Kentucky, and parts of northern Virginia. The highest yield for Miscanthus in these regions is 25 t/ha, which is about 1.8 and 1.5 times higher than the highest yield for Cave-in-Rock and Alamo in these regions. Besides the HS zones discussed above, Cave-in-Rock yields are also high and stable in northern Illinois, northern Indiana, and northern Ohio. Alamo yields are also high and stable in most areas of the southern USA, except for eastern Texas, the region between Arkansas and Louisiana, and the connect region among Tennessee, Georgia, and South Carolina. However, the lower part of the southern USA is usually a LU yield zone for Miscanthus and LS yield zone for Cave-in-Rock.

There are certain yield patterns, which are common to all three bioenergy grasses. These include the following: low and stable yield for all three grasses in the western Great Plains, such as western part of South Dakota, western Nebraska, western Kansas, western Texas, etc., due to poor soil texture and low precipitation; low and stable biomass yields in upper part of north central, northeastern, and northern New England due to cold temperature conditions. These LS yields zones are not suitable to grow three specific bioenergy grasses considered in this study, but it is likely possibly that other bioenergy crops or other switchgrasses cultivars perform better in these zones. However, the calculations of other bioenergy crops or switchgrasses cultivars are beyond the scope of this study and will be implement in the future modeling studies.

Overall, the ISAM-estimated spatial yields patterns for bioenergy grasses in the USA are in agreement with previous model studies. In addition, ISAM can simulate the adaption of different bioenergy grasses across the latitudes ranging between 26°N and 41°N for Miscanthus and between 26°N and 46°N for switchgrasses by accounting the effect of photoperiod on phenology and leaf development and the effect of extreme environmental conditions on establishment, carbon assimilation, and phenology. There are significant differences between the ISAM and other models estimated highest yields due to differences in the treatment of environmental stress factors in different models. With more comprehensive treatment of environmental factors, such as water, temperature, light, and nitrogen, on plant phenology and carbon allocation, ISAM estimated highest yield for bioenergy grasses is lower than BIOCRO and Agro-IBIS estimated values. For Miscanthus, these differences are also due to different observational data that is used for model calibration. ISAM is calibrated by data from a large plot at the Urbana-Champaign, IL, site, while BIOCRO and Agro-IBIS model are calibrated by data from a small plot. The observed aboveground biomasses from smaller plots were much higher than that from the larger plots due to the edge effects, and this effect should be accounted for if small plots are used for model calibration. The close agreement between the ISAM modeled and measured yields at extended evaluation sites (ranging from 26.68°N to 46.88°N) suggests that ISAM is able to simulate bioenergy grasses across diverse environments in the USA. Further evaluation of modeled yields in southern Texas is needed with high-resolution of soil depth and slope data. More measured yields data in north central, northeastern, and northern New England is also needed to further assess the model’s performance in these areas.

The identification of four yield zones for bioenergy grasses in the eastern USA indicates that HS yield zones over most of eastern USA are more suitable to grow bioenergy grasses, whereas yield instability needs to be considered when assessing the potential yields of bioenergy grass in the HU yield zones. The LS yield zones in the upper part of north central, northeastern, and northern New England usually could not grow bioenergy grasses due to winter-injury. Bioenergy grasses also may not survive in western parts of Great Plains. Climate change may increase the uncertainty in yield variance in the HU and LU zones by altering the precipitation amount and frequency.