LPJ-GUESS is a DVM optimised for regional applications but also applicable globally based on a detailed individual- and patch-level representation of vegetation structure and dynamics. For global applications, vegetation is represented as a mixture of plant functional types (PFTs) that represent the globally most abundant growth strategies of woody and herbaceous vegetation. PFTs are distinguished in terms of growth form, phenology, life history strategy, allometry, photosynthetic pathway (C3 or C4), climate-dependent scaling of physiological processes and a limited set of bioclimatic limits . The model uses climate, [CO2], soil information and N deposition as input, and plant communities evolve dynamically through competition in response to these drivers.

Recent model development includes the incorporation of land-use change dynamics together with a crop module , further developing approaches described in and . In the crop module for global-scale applications, the dominant crop types, such as wheat, maize and rice are represented as crop PFTs, which differ amongst others in management-related parameters such as baseline sowing and harvest dates. Sowing and harvest decisions are modelled based on climate variability and climatic thresholds . Irrigation, residue removal after harvest and cover crops between the main growing-seasons, are further management options available in the model.

The present study builds further on LPJ-GUESS version 3.0 which includes N-cycle dynamics for the simulation of potential natural vegetation . Soil C and N dynamics are based on the CENTURY model which represents 11 soil organic matter (SOM) and litter pools that differ in their C to N ratios (C : N) and decay rates (Kd). Both C : N and Kd are dynamic within certain limits – see for details. SOM decomposition depends on the C : N, Kd as well as soil temperature and water content, and may result in either mobilisation or immobilisation of mineral N. Plant N uptake varies between PFTs which differ in their N demand and their competitive strength for N uptake. See Sect.  and for more details.

Allocation of the net primary productivity (NPP) to different plant organs is done on a yearly basis, based on a set of C allocation rules . If a plant experiences water or N stress during the year, the C allocation scheme is flexibly adjusted so that a larger proportion of the assimilates are distributed to the roots to alleviate these stresses during the following year.

However, for crops, growing periods are less than 1 year and an annual adjustment of the allocation and growth of different plant organs is not sufficient. partly address this issue, incorporating a C allocation that operates on a daily time step. To allow for dynamic adaptation of the allocation as a response to stress, a more detailed representation of the allocation is developed in this study (see Sect. 2.1.1).

Below we describe and evaluate an updated version of LPJ-GUESS incorporating C–N interaction also for crops. The model allocates daily NPP based on the crop's development phase and allows for an adjustment of the allocation scheme based on the current nutrient and water status of the crop.

To evaluate the model's ability to simulate phenology and yields, and sensitivity to N fertiliser additions, data from nitrogen fertiliser response trials with detailed measurements of dry mass and N mass allocation from the Netherlands were used. In the trials, winter wheat was grown with different fertiliser input in the years 1983–1985. The trials were conducted on three sites (The Eest, The Bouwing and PAGV), located in the central part of the Netherlands, see Fig. . At these locations, three different N treatments were carried out for two seasons (Table ).

Based on an initial calibration of the model using leaf phenology data from Trial I, the parameters a and b in the allocation function f2 (Eq. ) were changed from 0.88 and 0.09 to 0.8 and 0.2 respectively, for this application. Daily climate data for the years 1979 to 1984 were downloaded from the Haarweg weather station, Wageningen University

http://www.met.wau.nl/haarwegdata/dayfiles/., last access: 4 February 2014

The ability of the model to simulate the observed response to elevated [CO2] treatment on yields and C : N of cropland ecosystems was tested using a FACE experiment from an experimental site close to Braunschweig, Germany (10.83∘ E, 52.82∘ N), see Fig. . Between the years 1999 and 2005 the FACE experiment was carried out on a rotation of barley, ryegrass, sugar beet and winter wheat that was repeated once. At this point the N-enabled model is not equipped to model crop rotations or sugar beet. Also LPJ-GUESS does not model wheat and barley explicitly, but temperate cereals represented by wheat (spring and winter) in the model, therefore growth of cereals was simulated for all years.

Four different trials from the experiment were simulated, high (100 % N) and low (50 % N) N input with ambient and elevated [CO2] (378/548 ppm), see Table  or Table 1 in for more details. Due to the lack of information on the timing and amount of the individual fertiliser applications, these parameters were set using the results from the regional comparison (Sect. ); total amount of N added in the experiments are listed in Table . As climate input we used the WFDEI climate data set which is a bias-corrected reanalysis data set based on WATCH and Era Interim . During the spin-up period (500 years), 30 years of detrended data (1979–2008) were used together with the ambient [CO2] from 1979.

To evaluate the model's ability to simulate wheat yields on a larger scale, 65 regions at the NUTS2 (Nomenclature of Territorial Units for Statistics in the EU; statistical administrative areas) level from northwestern mainland Europe and NUTS1 for southern England were selected based on their cereal fractions and yields taken from the EU statistics website, EUROSTAT

http://epp.eurostat.ec.europa.eu/portal/page/portal/agriculture/data/main_tables, last access: 6 May 2014.

In order to quantify the degree of agreement between simulations and the associated observations, two indices were calculated, the Willmott index of agreement (Wi, Eq. ) and the root mean square error (RMSE) (Eq. ). Wi is calculated as Wi=1-McOforM≤OcOM-1forM>O, where M denotes the sum of absolute differences between the modelled and the observed mean, O is the sum of absolute differences between the observations and the observed mean and c is scaling constant here set to 2 . Wi is without unit and ranges from 1 to -1, where 1 is a perfect agreement between the modelled and observed variances and -1 means that there is a low or no agreement between the modelled and observed variances. RMSE is calculated as RMSE=∑i=1n(oi-mi)2n, where n is the number of observations, o is the observed value and m is the modelled value.

To convert plant C to total dry matter, a conversion factor of 0.446 was used . Dry weight was converted to wet weight (used in the regional statistics) by assuming a wet fraction of 0.15 in the grains .

In the N fertiliser experiments from , 18 trials with N input ranging from 0 to 240 kg N ha-1 y-1 applied at various crop development stages were performed, resulting in grain C production from 1 to 3.5 ton C ha-1. During the growing-season, leaf C in the field trials increased until peaking around June, after which senescence commenced and leaf C decreased again (Fig. a–c). Simulations with LPJ-GUESS at these sites, and reproducing the applied fertiliser scheme broadly captured these seasonal dynamics, and the response to the different levels of N applications (Fig. a–c). Modelled grain and above-ground C mass per kg N applied (19 and 46 kg C kg N-1) were in line with the observed response of 22 and 42 kg C kg N-1, which indicates appropriate sensitivity of yield and growth to nitrogen addition. Differences between simulated and observed leaf C values were largest towards the end of the growing-season (Fig. d), especially at the highest-fertilised trial sites and in the second growing-season. As seen from the example time series in Fig. a–c, rates of senescence in the simulations were too slow, compared to measurements, which resulted also in underestimated dead-leaf C (see Fig. a–b).

The model generally simulates the observed above-ground production of biomass (C and N) well at the sites, with more accuracy in the medium- and high-input trials (2 and 3) (Fig. c–d). C content in grains and above-ground biomass is captured reasonably well, with some underestimations for the lowest N trial (Fig. c). This picture was mostly similar also for simulated N content, as a consequence average C : N were not biased towards too high or too low values (Fig. a). The C : N of the grains (Fig. b) in response to differences in N treatment was better captured than the total C mass (Fig. c). Over the growing-season there is an underestimation of the N content in the grains, especially so for the low input treatments (Fig. a–b).

At the Braunschweig FACE experimental site the mean observed yields under ambient [CO2] (∼378 ppm) were 8 and 6 ton ha-1 for the sufficiently fertilised (100 % N) and the treatment receiving 50 % N respectively, whereas the simulated yields were 9 and 7 ton ha-1, with the same pattern of higher simulated than observed yields also for the elevated [CO2] (∼548 ppm) treatments (Fig. ).

Grain yields were simulated to rise by 19 % as a response to elevated [CO2] for both the 100 and 50 % N treatments (Fig. ). The observations show a similar response with a rise of 14 % (9–19 % for 100 % N and 5–24 % for 50 % N), and neither simulations nor measurements indicated a clear impact of N treatment on the CO2 effect.

Under elevated [CO2], increased C sequestration and yields were not balanced by grain N rising at the same rate as grain C, leading to enhanced grain C : N at elevated CO2. In the observations, this increase was on average 16 % for both N treatments, whereas in the simulations the increase was 24 (100 % N) and 20 % (50 % N) (Table ).

In order to test model performance on spatial scales beyond field trials, regional modelled wheat yields were compared with yield statistics provided by EUROSTAT. The simulations were also set up to test the effects of different N management regimes (Table ) in order to derive an implementation of fertiliser application that can be adopted for large-scale models even when exact information on fertiliser timing is not available.

To do so, from the 65 regions chosen from the EUROSTAT database, a set of 50 permutations of timing and amount of N application (FT,A) was used to identify the management strategy resulting in the best agreement (lowest RMSE) with reported time series of yields (Fopt(T,A)). The optimised timing and associated amount of N input for each of the regions are listed in Table . This “optimised” simulation deviated only marginally (Fig. b) from the observed yields (Fig. a). The interannual variability in yields for individual regions was captured best for regions with a low productivity (model performance based on the Willmott index (Wi) and RMSE, Table ), whereas the interannual variability for the more productive regions was captured less well.

In the optimised simulation (Fopt(T,A)), the mean N application rates for spring-sown wheat across the entire region were a total of 129 kg N ha-1 y-1, applied in fractions of 0.11, 0.50 and 0.39 at the three development stages described in Sect. , with the main application in mid-spring. For winter wheat, on average 172 kg N ha-1 y-1 were applied with fractions 0.08, 0.19 and 0.73 for the three development stages, with the main application in late spring or early summer.

For simulation Ft,I, the mean timing obtained from the optimisation was combined with a gridded data set of N application rates , resulting in a reasonable agreement with the observed yield but with larger spread compared to Fopt(T,A) (Fig. c). In particular, overestimations were found in parts of the Netherlands, Belgium and southwestern France, and a considerable underestimation in northern France. Some of the deviations between modelled and reported yields were likely due to a lack of spatial variability in the fertiliser data input, e.g. a constant value (110 kg N ha-1 y-1) was applied for all regions in France (Table ).

Despite the spread between the model and the observations for individual years, the temporal average of the optimised set showed a good agreement (Fig. ). Even the simulation that applied the mean timing with reported fertiliser rates (Ft,I) showed a reasonable agreement, but generally overestimating the yields in low-productive areas, primarily because of a higher fertiliser application rate (regional mean N input of 188 kg N ha-1 y-1 for Ft,I, compared with 169 kg N ha-1 y-1 for Fopt(T,A)). Applying the same timing as in Ft,I with the lower constant rate of 169 kg N ha-1 y-1 (Ft,a) resulted in a much better agreement for the mean response. However, both simulations (Ft,I and Ft,a) have a smaller range of simulated yields from low-productive to high-productive areas than reported in the statistics data.

The spatial variation of the observations was captured well in all simulations except for those with maximised yields (max(FT,A)) and the C-only version (FC). As expected, optimised N management (Fopt(T,A) and Ft,A) improved the fit of the model results to spatial variation in the data, but all the C–N enabled simulations except for max(FT,A) increased the agreement between the modelled and observed variance (Table ), when compared to FC. In order to address the spatial variability in timing and rates of fertiliser application, the optimised simulation (Fopt(T,A), red line in Fig. ) was compared with two additional optimisations. In the first of these (Fopt(t,A)), timing was prescribed using the same as for Ft,a while application rates were varying. In the second optimisation (Fopt(T,a)), application rates were prescribed as for Ft,a while timing was varying. The grid-cell average yield over the region and all permutations in the Fopt(T,A) simulations was 5.2 t ha-1 y-1, ranging from 2.4 to 10.3 t ha-1 y-1 between the different application rates and timing. For Fopt(T,a) the same measures were 5.5 t ha-1 y-1 (3.1–8.7 t ha-1 y-1) and for Fopt(t,A), 5.2 t ha-1 y-1 (3.2–8.6 t ha-1 y-1). The average yields for all simulations were of the same order of magnitude. For Fopt(t,A) and Fopt(T,a) the ranges in yield were also of similar size whereas the range for the Fopt(T,A) was larger although smaller than the sum of the ranges of Fopt(t,A) and Fopt(T,a). Most importantly, both the optimisations with either fixed timing or application rate, resulted in a better agreement with the reported yields than when only using a mean uniform N management over the region (Ft,a, Table ), but optimising the application rates gave a considerably better fit than optimising the timing. While timing had a large effect, these results imply that highest priority is to obtain data on application rates.

Modelling the seasonality of growth, phenology, and the response to fertiliser is a prerequisite not only for model projections of crop yield responses to management in a changing environment, but also to aid assessments of management-related detrimental effects . Models that operate on regional to global scales are not designed to be suitable tools for detailed local-scale decision making on fertiliser use, but the improved representations of crop C–N coupling and phenology are necessary for simulating regional to global land-use-related surface–atmosphere exchange fluxes, to evaluate models against observations, and to contribute to analyses of the effects of land-use change in the climate system, including assessment of how multiple ecosystem services are affected following land conversions e.g.. For these types of questions, a chief challenge remains in representing phenology and growth responses to fertiliser application and climate in a way that is suitable for large-scale models, but still reproduces realistic results .

In LPJ-GUESS, crop phenological events, and especially the growth of the leaves throughout the growing-season were captured (Fig. ) and at the end of the growing-season, senescence was induced as a result of N retranslocation to grains from the leaves, albeit with a response that was a little too weak compared to the measurements (Fig. ). The modelled mean harvest index (HI = Y / (Y + V)) of 0.57 was in line with the value obtained from observations (0.52; Fig. a,c). Modelled grain yields and above-ground biomass were on average only slightly lower than the observations, and the overall tissue as well as grain C : N also agreed well with the corresponding ratios derived from the measurements. But there was a discrepancy in the modelled C allocated to the grains during the early parts of the grain filling period that disappeared towards the end of the growing period (Fig. a).

When making these comparisons, the need to convert dry matter to mass of C, and vice versa, added a level of uncertainty that is not associated with modelled processes, since site data often are reported as biomass (dry or wet). For instance, we used the published observations of [C] in the biomass of 44.6 % when converting the experimental site data. By contrast, in LPJ-GUESS a C content of 50 % is assumed (Smith et al., 2014), which leads to slightly higher C density in modelled output compared to the observation-derived values.

Underlying the good agreement of the tissue C : N, was an underestimation of the absolute levels of both C and N in the grains at the end of the growing-season, which were underestimated by about 30 % in many cases (Fig. a). The same pattern could also be seen for the above-ground C mass (Fig. c), suggesting that the productivity generally is too low in the model. One potential explanation for the underestimation of [C] in grains at the end of the growing period is C-retranslocation from leaves and roots to the grains during the growing-season, which has been observed in forms of sugars . Since in the current version of the model C supply originates solely from NPP, one potential source of carbon to grain filling therefore is missing. In addition, the model does not presently include other forms of molecular transport whereas the retranslocation of N from leaves to the grains is mostly in the form of amino-acids with a relatively low C : N (e.g. 4.0 in wheat; ). Accounting for such an amino-acid transport would suggest that for every unit of N that is transported to the grain, four C would have to be supplied as well. This, too, cannot be captured by the current implementation that is based on allocation of the daily NPP.

Since the C : N of the various organs plays an important role for determining N uptake and its N (re)allocation between organs, variable C : N have been suggested to be crucial when modelling vegetation C–N dynamics. This aspect might become especially important under changing climate and [CO2] environments as these can affect the chemical composition of the plant e.g., discussed in Sect. . For present-day conditions, the simulated biomass C : N agreed best with observations from the two high-N-input treatments (2 and 3) (Fig. ), although the overall agreement across treatments was acceptable, keeping in mind the assumptions that had to be made when deriving the observation-based values. Likewise, growing-season green leaf [N], which together with LAI is essential for predicting photosynthesis , was also well reproduced (results not shown). By contrast, [C] as well as [N] in the dead leaf pool were either over- or underestimated (see Fig. ), most likely because the C : N in dead leaves is set to a constant value.

Tissue C : N in dead leaves will affect C and N input to the soil through litter decomposition, and hence is arguably an important feature for representing the N cycling in ecosystems. We concentrate here on above-ground processes such as live-tissue growth, element concentrations and yields and it remains to be tested whether an implementation of C : N limits that vary over the course of the growing-season will be a necessary improvement for simulating agricultural soil processes. Moreover, a dynamic adjustment of the C and N allocation to root growth under stress (see Sect. ) might be an important future development, since as a result, less C would be partitioned towards above-ground growth, while at the same time, more N could be extracted from the soil. For the observations used here for model evaluation, no data are available on the N or C content of the roots. A flexible adjustment of the root : shoot growth is already implemented in the model as a response to N and water stress for natural vegetation, but it operates so far only on a yearly basis . Studies elsewhere have demonstrated dynamically adjusted shoot : root growth and C : N , and some published crop models like GECROS do so at higher temporal resolution. Next development phases in LPJ-GUESS will explore how to include these into the model.

In a recent intercomparison of crop models that can be applied globally, identified the CO2 fertilisation response to be one of the major sources of uncertainty of how yields might change in a future environment. When disregarding advances in breeding, the CO2 fertilisation response of crops (in particular: of the C3 photosynthesis-type) is fundamental, as this response can counteract or at least dampen effects of climate change. The chief principles are related to the carboxylation reaction of Rubisco being stimulated by enhanced levels of CO2, and by plants being able to operate at lower levels of stomatal conductance, thereby increasing the efficiency of gaining carbon per unit of water lost . The magnitude of the positive CO2 response on yields will depend on the degree of leaf-level acclimation response, and how such an acclimation would translate to the whole-plant level .

In existing crop models, the implemented CO2 response is typically based on empirical relationships between an increase in [CO2] and plant productivity, derived from e.g. FACE experiments . Adapting a more mechanistic representation of the CO2 response by replacing a radiation-use efficiency formulation with a coupled photosynthesis and stomatal conductance description (as in LPJ-GUESS) increased the overall model performance of the DSSAT model and its ability to capture responses to the combined effects of different factors affecting plant productivity .

In the study, LPJ-GUESS showed a very strong yield response to enhanced levels of atmospheric CO2. The model version used in that study did not include C–N interactions, and hence this strong response was expected, since the simulated underlying physiology was not constrained by N availability. With this constraint in place, LPJ-GUESS in the present study reproduced crop growth and productivity under elevated [CO2] with different N fertiliser treatments, as well as responses in dry matter C : N observed at the different levels of CO2, with C : N at the 100 % N treatment being somewhat above the observed values. A positive CO2 effect on yields and C : N, as well as the higher variability between years was captured in treatments that received less N input. The results shown in Sect.  were also in line with observations from previous FACE experiments that showed a mean increase of 14 % (-2 to 33 %) for wheat yields, compared to the modelled response of 20 and 24 % for the two different N treatments.

The modelled yields (ambient and elevated [CO2], 50 and 100 % N) exceeded observations only slightly. This might be explained by insufficient information on the fertiliser management at the experimental plots but also by, for instance, a too-high allocation to grains compared to other tissues. Moreover, under elevated [CO2] a relative increase in root biomass often occurs. Currently, as discussed in the previous section, there are no explicit mechanisms implemented that would yield such a dynamic growth response. A step forward, that remains to be tested, would be to set a flexible root : shoot allocation via a modification of f1 in response to water or N stress, see Sect. 2.1.1, which would result in such a response in situations when additional leaf C mass in response to elevated [CO2] induced a N demand that cannot be met by soil uptake.

Moreover, as mentioned in Sect. , SLA in the model is treated as a constant, even though it has been observed to vary over the growing-season, and in response to elevated [CO2] . found in a review of CO2 effects on different plant traits that elevated [CO2] was associated with a reduction in SLA, as the increase in leaf mass was not accompanied by a proportional increase in leaf area. These results are in line with the observed increases in leaf C : N under elevated CO2 . Currently in the model the lower limit of leaf N (Nb) is a function of SLA (Eq. ), and whether or not variable SLA would help to constrain the C : N response at variable N and CO2 treatment remains to be tested. While some studies have found elevated CO2 to also change the chemical composition of the plants and thus the C : N , others e.g. found no evidence of changes in the C : N of the senesced leaves grown under higher [CO2] implying that the fixed C : N limits and in turn the Nb are valid also under elevated [CO2], but this remains to be explored.

The implementation of C–N dynamics improved the ability of LPJ-GUESS to simulate yields not only at local scale but also across larger regions, especially when all permutations of N managements were combined (Fig. ). As expected, the comparison of the simulated yields with reported ones was best captured when considering time-averaged values (accounting only for the spatial variation) compared to the full temporal variability (difference between “mean” and “all” in Table ). The discrepancy between results from the C–N and the C-only versions of the model was striking and clearly demonstrates the need to consider C–N interactions when modelling crop processes . In addition to the improved phenology and C–N coupling, which was seen also at the FACE site, on the regional scale the representation of soil texture proved to be an additional important aspect. By incorporating the WISE map of soil mineral fractions, we were able to increase the model performance from a Wi of 0.715 using the standard soil map in LPJ-GUESS simulations with fixed mineral fractions , to 0.807. With the more detailed soil information, the heterogeneity in the growth response from fertiliser applications due to differences in physical properties could be better captured.

Still, when applied across large spatial domains, there can be multiple reasons for a disagreement between modelled and observed variability that go beyond process representation linked to the basic physiology of C–N interactions. For instance, extreme heat or freezing, pests, or water logging of soils are frequent events detrimental for crop production . Effects of extreme weather events are difficult to account for, partially because of the smoothing effect of a daily time step, and also because aggregation averaging in the production of the gridded climate input data tends to remove weather extremes. Likewise, local management decisions that are not based on weather variability, and their effects on crops and environment, are difficult to capture with the current setup.

Several approaches to modelling N limitations in agricultural ecosystems over large region scales are available in the literature. CLM e.g. includes N limitation for crops, and this model also simulates the retranslocation of N during the grain-filling period based on prescribed C : N of the plant organs pre- and post-anthesis. The C allocation scheme implemented in CLM has the same origin as the one implemented here for LPJ-GUESS. In LPJmL , an implicit nutrient limitation on yields is considered by varying production parameters (LAImax, HI, and αa) to match country or region statistics from e.g. the FAO (United Nations Food and Agriculture Organisation). This approach has the advantage that it can be applied without knowledge as to the management (fertilisation) practices that are common in a region, but lacks the possibility to assess effects of future changes in e.g. N fertiliser availability and changes in management. The crop model GEPIC – like LPJmL – has LAImax and HI as input parameters but also includes N dynamics with empirical response functions as modifiers of productivity and yields. In contrast to LPJmL, GEPIC is based on a site-scale model approach which can be extended in space via a GIS interface that facilitates input of spatially explicit management, where available. WOFOST, a detailed crop-growth model that has recently been expanded to work at larger regions , has demonstrated skills in simulating local and regional yields with a mechanistic approach to modelling crop photosynthesis as well as physiology, but the model approach assumes a continuation of current management practices, and thus cannot be applied for future simulations.

LPJ-GUESS shares several aspects of the approaches of these models: the sowing algorithm (LPJmL ), temperature limits for different CFTs (GEPIC), and a large portion of the mechanistic formulations of crop physiology (WOFOST and GECROS are “School of de Wit” models, ). Because of the dynamic PHU calculations and dynamic sowing and harvest calculations , LPJ-GUESS can be applied to all areas where suitable temperature and soil moisture conditions allow wheat growth. In addition, we have shown here also that it is possible to find a suitable timing of N fertilisation on the regional scale by relating the N application to those stages in the crop growing period when it is most needed. For globally applicable models this is an important result, since information on fertiliser application often includes total amounts per year, but typically lacks information about the seasonal distribution.