Analysing the parameter sensitivity of the agro-ecosystem model MONICA for different crops

Europ. J. Agronomy 71 (2015) 73–87

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European Journal of Agronomy journal homepage: www.elsevier.com/locate/eja

Analysing the parameter sensitivity of the agro-ecosystem model MONICA for different crops Xenia Specka a,b,∗ , Claas Nendel b , Ralf Wieland b a b

Leibniz Centre for Agricultural Landscape Research (ZALF) e.V., Institute for Landscape Biogeochemistry, Eberswalder Str. 84, 15374 Müncheberg, Germany Leibniz Centre for Agricultural Landscape Research (ZALF) e.V., Institute for Landscape System Analysis, Eberswalder Str. 84, 15374 Müncheberg, Germany

a r t i c l e

i n f o

Article history: Received 27 March 2015 Received in revised form 28 July 2015 Accepted 6 August 2015 Available online 1 September 2015 Keywords: Sensitivity analysis Crop model Crop parameters Morris screening method Extended FAST

a b s t r a c t Sensitivity analysis (SA) has become an important tool for analysing eco-system models and for supporting the calibration activities of models. A sensitivity analysis assessment is carried out on the agro-ecosystem model MONICA for the crops winter wheat, spring barley, silage maize, sugar beet, clover grass ley and winter rape, using cutting-edge tools (Python and HPC techniques) in combination with robust and widely used methods. The aim of SA is to identify model parameters that have a considerable impact on above-ground biomass with regard to a future model calibration and an improved understanding of model response patterns. First, the Morris method was applied to identify a subset of relevant model parameters. Here, we identified 28 generally important parameters from a set of 117 analysed parameters. In the second step, these parameters were used as input for the Extended Fourier Amplitude Sensitivity Test (FAST) method. The calculation of the total sensitivity indices provided a reliable sensitivity measure for the parameters of the MONICA model. The analysis of the relevant parameter sets for the considered crops revealed that the set of important parameters differed for each crop, but for all crops the parameters related to photosynthesis and plant development had a dominant effect on above-ground biomass. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Crop models are widely applied for advisory purposes in agriculture and environmental planning. They are used to assess the impact of environmental conditions on plant growth as well as on water and nutrient dynamics in soil–plant–atmosphere systems (Ewert et al., 2015; Martre et al., 2015). Crop models are also applied to assess the impact of environmental factors or human activity on the considered ecosystem with regard to its services, such as biomass production, water availability and carbon sequestration potential (Damour et al., 2012). All simulation models are subjected to different sources of uncertainty, related to their structure, algorithms, variables and parameter values (Wallach et al., 2006; Saltelli et al., 2000). In order to be able to interpret the results of models properly, it is essential to know their inherent uncertainty.

∗ Corresponding author at: Leibniz Centre for Agricultural Landscape Research (ZALF) e.V., Institute for Landscape Biogeochemistry, Eberswalder Str. 84, 15374 Müncheberg, Germany. E-mail addresses: [email protected] (X. Specka), [email protected] (C. Nendel), [email protected] (R. Wieland). http://dx.doi.org/10.1016/j.eja.2015.08.004 1161-0301/© 2015 Elsevier B.V. All rights reserved.

Sensitivity analysis (SA) is an important method used to address the input and parameter uncertainty of a model. SA enables calibration activities to be supported by identifying parameters with the greatest degree of influence to particular outputs. Furthermore, SA provides information about how the model behaves under different conditions (Confalonieri et al., 2012) and can support simplifications and reduction activities (Jakeman et al., 2006). SA has been applied to analyse ecological models in a large number of different studies (Zhao et al., 2014; Dzotsi et al., 2013; Richter et al., 2010). Many studies concentrated on comparing different SA techniques, demonstrating their advantages and limitations (Makler-Pick et al., 2011; Manache and Melching, 2008; Francos et al., 2003). Confalonieri et al. (2010a) compared the Morris method (Morris, 1991), Monte Carlo simulation with regressionbased sensitivity measures and variance-based methods Fourier Amplitude Sensitivity Test (FAST) and Sobol’ using the example of the rice model WARM (Confalonieri et al., 2009). They found that, although variance-based methods yielded the most accurate results, similar parameter rankings could be achieved using simpler SA methods involving less computational effort. In a different study, Confalonieri et al. (2010) used the two methods proposed by Morris and Sobol’ to analyse the sensitivity of different outputs of the WARM model. Whilst the ranking achieved

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using Sobol’s indices was considered as a reference, the Morris method was found to be a suitable alternative to Sobol’s indices, although the ranking of these two methods differed slightly. They showed that the Morris method may be useful for reducing the number of parameters of a complex model before applying more elaborate methods. MONICA1 (Nendel et al., 2011) is a process-based agroecosystem simulation model which includes a generic crop model. MONICA belongs to the current set of agro-ecosystem models being applied in fundamental international studies on climate change impact and future food security (Asseng et al., 2015, 2013; Bassu et al., 2014; Pirttioja et al., 2015; Rötter et al., 2012), and the development of scaling concepts (Zhao et al., 2015; Hoffmann et al., 2015). It is currently undergoing model improvements in the context of an international effort to reduce the uncertainty of crop yield simulations (Kumudini et al., 2014; Asseng et al., 2013). With a growing number of users, we found it particulary important to demonstrate a state-of-the-art sensitivity analysis using cutting-edge tools (Python and HPC techniques) in combination with robust and widely used methods, revealing which parameters are most important in the calibration process for MONICA. Another objective was to increase our understanding of specific behavioural patterns of MONICA when applied in different studies as a basis for later improvement. In this case, the calibration of MONICA to crops recently introduced for bioenergy production in Germany triggered the application of the SA, since a lack of experimental data for these crops limited the calibration process we would usually pursue. SA enables us to focus on the most relevant parameters when designing experiments or gathering existing data for new crops. At the same time, SA provides additional insight into the behaviour of the crop model in its response to environmental factors. Our analyses included winter wheat, spring barley, silage maize, sugar beet, clover grass ley and winter rape at three study sites in Germany. The study focuses on above-ground biomass output, which best reflects the interaction between the different processes implemented in the model.

2. Material and methods 2.1. MONICA – model for nitrogen and carbon in agro-ecosystems MONICA is a process-based agro-ecosystem model developed for simulating crop growth and soil processes in Central Europe (Nendel et al., 2011). As a successor of the HERMES2 model (Kersebaum and Richter, 1991; Kersebaum and Beblik, 2001; Kersebaum, 2007), MONICA was extended to account for the carbon cycle in soil and plants, facilitating impact simulations of CO2 on biomass growth and yield formation. MONICA requires management data, soil profile information and climate data (minimum, maximum and average air temperature, precipitation, relative humidity, wind velocity and global radiation) for the simulation process. It calculates crop-related outputs such as yield, tissue N concentration, water and nitrogen uptake, as well as environmental outputs, e.g. soil moisture, groundwater recharge, N leaching and organic matter dynamics. A generic crop model, MONICA can be adapted to various crops by using specific model parameters that describe physiology and development. MONICA regards soil as a pedon with variable depth. The default temporal resolution is one day.

1 Model for nitrogen and carbon in agro-ecosystems, http://monica.agrosystemmodels.com 2 Model to describe plant growth and water and nitrogen dynamics in the soil–plant system.

Algorithms for soil moisture concentration in soil follow the capacity approach, enhanced by modifications introduced by Wegehenkel (2000). The approach considers capillary rise from groundwater. Evapotranspiration is calculated using the reference evaporation of the Penman-Monteith equation (Allen et al., 1998), adapted by crop-specific factors (Kc ). Soil temperature is calculated based on the approach by Lasch et al. (2002). Organic matter algorithms include processes of mineralisation, nitrification and denitrification. Crop growth is based on the approach pursued by the SUCROS3 model (van Keulen et al., 1982). MONICA was extended to cover the carbon cycle by calculating soil microbial population dynamics. The integrated crop growth algorithms are influenced by changes in CO2 concentration, which affects the crop’s photosynthesis rate, stomata resistance and transpiration. The agro-ecosystem model MONICA was developed using the programming language C/C++ (Stroustrup et al., 2001). The implementation of different ecological processes is separated into modules embedded in a C++ framework. The open source model is available for Linux® and Windows® or within the LandCaRe2020 Decision Support System (Wenkel et al., 2013). Model parameters are stored in a separate SQLite database that comes with the model.

2.2. Parameter selection An important step involved in SA is the selection and characterisation of the model parameters included in the analysis. This step, especially the definition of the parameter range, must be performed carefully because it has a considerable impact on the results of SA (Saltelli et al., 2000; Wallach et al., 2006). SA of the MONICA model focused on crop parameters with regard to the subsequent calibration process. Due to a lack of information on the prior probability distributions for each parameter, we assumed an independent uniform distribution for each parameter where the parameter range is limited to 30% at either side of its reference value (Song et al., 2013, 2012; Esprey et al., 2004). MONICA divides crop growth into separate developmental stages (Table 1). Some crop parameters have different values assigned for different stages. Such developmental stage-dependent parameters were analysed separately in the SA process. In the end, 117 parameters were selected for analysis using Morris SA. A full description of the analysed parameters can be found in Table A.4 in the appendix.

2.3. Site description and crop management data SA was performed using climate data and soil information obtained from an energy cropping experiment (”Development and comparison of optimised cropping systems for the agricultural production of energy crops”, Vetter et al. (2011)) at three study sites in Germany (Fig. 1). The aim of this experiment was to assess the suitability of different crop rotations across a range of site conditions (Deiglmayr et al., 2011). Ascha (12◦ 39 E, 48◦ 59 N, 430 m above sea level) in South Germany has an annual precipitation rate of 800 mm (1971–2000) and a mean temperature of 7.5 ◦ C. The soil in Ascha is characterised as a gleyic cambisol developed from loamy sand. Guelzow (12◦ 54 E, 53◦ 42 N, 10 m above sea level) in Mecklenburg-Western Pomerania has an annual precipitation of 559 mm (1971–2000) and a mean temperature of 8.4 ◦ C. Guelzow has a gleyic cambisol soil with sandy loams. Werlte (7◦ 41 E, 52◦ 51 N, 32 m above sea level) is located in Lower Saxony and has an annual precipitation rate of

3

Simple and Universal CROp growth Simulator.

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Table 1 Exemplary description of the developmental stages of the analysed crops. Six developmental stages were defined for winter wheat, spring barley, sugar beet, clover and winter rape, and seven for maize. Stage

Winter wheat Spring barley

Maize

Sugar beet

Clover Winter rape

1 2

Sowing to emergence Emergence to double ridge

Sowing to emergence Emergence to shooting

3

Double ridge to flowering

Shooting to tasselling

4

Flowering to grain filling

Tasselling to flowering

Sowing to emergence Emergence to ten leaves Ten leaves to tuber growth Tuber growth

5 6 7

Grain filling Senescence −

Flowering to grain filling Grain filling Senescence

Until harvest size After harvest size −

Sowing to emergence Emergence to beginning of generative phase Beginning of generative phase to flowering Flowering to seed ripening Seed ripening Senescence −

768 mm (1971–2000). The mean temperature is 9.57 ◦ C. The soil is characterised as a gleyic luvisol predominated with loamy sands. A four-year simulation was performed for each crop, whereby management was customised for each crop. Over the simulation period, cultivation of the crops was repeated, meaning that spring and summer crops were grown four times and winter crops only three times. Detailed information about the cultivation management of the crops is given in Table 2. In order to analyse parameter sensitivity, we used the specified crop management of Table 2 at each study site. The model output above-ground biomass (AGB) at harvest was used for SA because it is affected by numerous model processes. A sensitivity measure was calculated for each harvest date. We used the maximum value of sensitivity measures to also identify model parameters that may only be relevant in some years.

Fig. 1. Location of the three study sites in Germany.

2.4. Sensitivity analysis experiment design SA methods can be categorised into three groups: screening methods, local SA and global SA (Saltelli et al., 2000). Screening methods involve one-factor-at-a-time (OAT) experiments in which each parameter is changed individually. The main advantage of screening methods is the low computational cost involved in analysing major effects of input-output relationships. However, the results of screening methods are usually qualitative, and often produce a parameter ranking without quantifying the influence of the parameter. An overview of different SA methods is given in Saltelli et al. (2000, 2006). Local SA concentrates on the local impact of parameters, usually by creating partial derivatives. Parameters of interest are varied one at a time whilst all other parameters are fixed at nominal values. Since local SA methods do not account for interaction effects, they were not considered in this study. Global SA encompasses a group of methods used to analyse the entire range of parameters. By simultaneously varying all parameters or a subset of them, global SA accounts for interaction effects between different parameters. A further advantage of global SA is its ability to tackle non-linear relationships between model parameters and outputs. For this reason, global methods are suitable for the SA of ecological models, most of which are non-linear (Saltelli et al., 2000). One shortcoming of global SA is the computational costs involved, which increase considerably in line with the number of parameters considered. The aim of conducting SA for the MONICA model was to identify which parameters were most important for model calibration. In this study, we concentrated on global SA to include the complete range of crop parameters in the analysis. A method proposed by Morris (1991) was selected owing to its high efficiency when used with complex models. This method was applied to achieve an importance-based ranking of MONICA’s parameters and to identify a subset of relevant model parameters. We used the top-down concordance coefficient (TDCC, Iman and Conover, 1987; Confalonieri et al., 2010a) to compare different parameter rankings of the selected study sites. TDCC are characterised by emphasising the agreement between important model parameters while de-emphasising disagreements between less important ones. Values for TDCC close to one indicate a high agreement between different parameter rankings in a top-down sense (Iman and Conover, 1987). The results of Morris were used as input for the Extended FAST method (Saltelli et al., 1999). The Extended FAST method was chosen for its ability to account for model non-linearity and non-monotonicity. 2.4.1. The Morris method The Morris method (Morris, 1991) is a global screening method composed of several randomised OAT experiments. A discrete parameter space  is created by dividing the range of parameters

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Table 2 Specification of crop management applied from 2005 to 2008 for individual MONICA simulations. Cultivation of the crops was repeated over the simulation period, meaning that spring and summer crops were grown four times and winter crops only three times. Management data was derived from experiments in the energy cropping project. The fertilisation data includes information on the date, nitrogen amount and fertilisation type with KAS = calcium ammonium nitrate-based nitrogen fertiliser, Piamon = ammonium sulphate carbamid and DAP = di ammonium phosphate. Crop

Tillage

Sowing

Fertilisation

Winter wheat

13 October

14 October

31 March 5 May 4 June 17 June

88 kg N 44 kg N 55 kg N 33 kg N

KAS KAS KAS KAS

Harvest 29 July

Spring barley

11 April

12 April

15 April 6 June

65 kg N 44 kg N

KAS KAS

15 July

Sugar beet

22 March

23 March

29 March

70 kg N

Piamon

12 October

Maize

2 May

3 May

3 May 22 May

31 kg N 80 kg N

DAP KAS

22 September

Clover

15 July

16 July

2 August

40 kg N

KAS

10 October

Winter rape

21 August

23 August

18 September 14 March 29 March

50 kg N 80 kg N 80 kg N

KAS KAS KAS

29 June

into p discrete levels. The model is evaluated for r trajectories within the parameter space. The starting point of a trajectory is selected randomly. For each trajectory, every single parameter is changed separately, whereas the new point of this trajectory is an element of the parameter space. Morris proposed a sensitivity measure called the elementary effect (EE, Eq. (1)), calculated from the ratio of the variation of the model output at two different points of the input space to the variation of the input parameter. The EE of the ith input is defined as EE i =

[f (x1 , . . ., xi−1 , xi + , xi+1 , . . ., xk ) − f (x)] 

(1)

where x ∈  and x +  is still in ,  as a multiple of 1/(p − 1). Elementary effects, scaled due to different parameter ranges (Sin and Gernaey, 2009), are calculated for different trajectories within the input space. An EE is calculated each time a parameter is changed. After completing all of the model evaluations for each point of the trajectories, the result is a distribution of elementary effects for each parameter. The mean of this distribution () indicates an input with an overall influence on the output. A large standard deviation () indicates either an input with a non-linear effect on the output or an input that interacts with other parameters. In this study, the absolute values of EE for the mean (*) were used as proposed by Campolongo et al. (2007), in order to avoid cancelling out single EEs by opposite signs. The number of model evaluations n required for the Morris method is defined by n = r (k + 1), where r is the number of trajectories and k is the number of input parameters. We also implemented the improved sampling strategy of Campolongo et al. (2007) to guarantee an optimal coverage of the input space by the trajectories. 2.4.2. The Extended FAST method With variance-based methods, the sensitivity of a parameter can be described by first-order sensitivity indices (Cukier et al., 1973) that measure the variance created directly by a single parameter. The Classical FAST method is a variance-based SA method developed by Cukier et al. (1973). The output variance is separated into variances created by different inputs. The main characteristic of FAST is the sampling of the input parameter space with a transformation function (Eq. 2). Examples of different sampling functions are given in Saltelli et al. (2000). The transformation function proposed by Saltelli et al. (1999) was used in this paper. xi =



0.5 +



1 arcsin[sin(ωi s + ϕi )] 

· Ki

(2)

where xi is the ith parameter, s is the sampling range with s ∈ [− , ], ϕi is a random phase shift parameter marking the starting point of the search curve where ϕi ∈ [0, 2], ωi (i = 1, . . ., k) is the individual assigned integer frequency of parameter xi , and Ki is a scaling factor to scale the value of the transformation function that lies between 0 and 1 to the appropriate parameter range. Since the transformation function is periodic, a sampling range of 2 is sufficient for decomposition. Specification of the frequency refers to the sampling range used. A different integer frequency  must be selected for each parameter such that no single frequency is a multiple of another. Based on the transformation equation and the different frequencies  for the input parameters, a set of n (Eq. (3)) samples is generated for the model simulation. The model output can be decomposed into a Fourier series, whereas the variance of the model output is assigned to the inputs. The first-order sensitivity indices (Si ) describe the main effects of parameters by quantifying how the variance of the input contributes to the total output variance. Based on the FAST method, Saltelli et al. (1999) enhanced the method that allows both firstorder (Si ) and total sensitivity indices (TSi ) to be calculated. The new method was termed Extended FAST. Not only does the TSi include the variance of an input, it also accounts for the variance created by interaction with other parameters. The minimum number of parameter samples n (Eq. (3)) required to compute the total sensitivity indices depends on the maximum chosen frequency of the analysed parameter. According to Saltelli et al. (1999), n is defined as N = 2Mωmax + 1

(3)

where M is the maximum harmonic considered (usually 4 or higher) and ωmax is the maximum chosen frequency. 2.5. Implementation of SA SA was implemented using the scripting programming language Python (Lutz, 2010). Python combines the effectiveness of a scripting language with more high-level data structures and object-oriented programming. Numerously available extensions and libraries particularly qualify Python for scientific computing. In order to use the compiled MONICA source code within Python scripts, a new software interface of the MONICA model was created using Python/SWIG (Beazley, 2003). Python/SWIG automatically generates wrapper functions to integrate compiled source code into Python scripts. With the new interface, data structures,

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Fig. 2. Graphical display of Morris sensitivity measures * and  for maize in Ascha. For better readability, only parameters with * and  higher than 0.2 are labelled with their identification number (see Table A.4). The resulting parameter ranking based on the values of * is listed in Table 3.

variables and functions of the MONICA model could be accessed within the Python scripts. Use of the compiled MONICA software within the Python code guaranteed the fastest possible execution time of MONICA simulations. SA of the MONICA model was executed on a high-performance computer (HPC) and parallelised using MPI for Python (Dalcín et al., 2005, 2008), a Python implementation of the MPI (message passing interface) standard. MPI is an open standard for message passing used widely in high-performance computing. We calculated the speed-up S (Eq. (4)) to quantify the increasing performance of the parallel simulation compared to the sequential run. The speed-up is defined by S =

ts tp

(4)

where ts and tp are the execution time for serial and parallel simulation, respectively. Using 32 cores to calculate the main and total sensitivity indices for winter wheat at one study site, we reduced the simulation time from 160 min to 6 min with a total speed-up of 27. 3. Results 3.1. Parameter ranking by Morris As the first step of the SA of the MONICA model, a qualitative parameter ranking based on the Morris method was developed. For the Morris analysis, the parameter range for the k = 117 selected parameters was divided into p = 20 levels and analysed for  = 5/19. Among 500 randomly generated Morris trajectories, we chose r = 40 trajectories with the highest spread to guarantee a high coverage of the input space. A total of 40 trajectories necessitated a maximum of n = 4720 model evaluations when analysing all 117 model parameters. Fig. 2 depicts the results of the Morris SA for maize in Ascha obtained by calculating * and  of the elementary effects (EE). Each model parameter is represented by a point labelled with the parameter number. A large magnitude of * indicates the importance of the model parameter. A high standard deviation  implies either a non-linear relationship or interaction with other parameters. A parameter ranking for the considered crops was generated based on the main effect described by * (Table 3). Only parameters

77

with an * higher than 0.05 were ranked to exclude parameters with negligible influence. Regardless of the analysed crop, the parameter for maximum assimilation rate (maxAssimRate) was found to be important overall for AGB at each study site. Parameters defining the phenological development time of crops (stageTempSum2 − stageTempSum4 ), maintenance and growth respiration (maintRespP1, maintRespP2, growthRespP1, growthRespP2) were somewhat less sensitive, but also relevant for all crops. The number of relevant parameters differs slightly for each crop and each study site. For winter wheat, 23 sensitive model parameters were identified for Ascha, 24 for Gülzow and 25 for Werlte. When considering all analysed crops at each study site, 28 out of 117 model parameters of the MONICA model were found to be important for AGB. The parameter rankings for each study are very similar, which is substantiated by the high TDCC values (Table 3). For winter rape (TDCC=0.93) and clover (TDCC=0.95), the parameter rankings differ the most among the study sites. Although the differences are quite minor, the discrepancy of the parameter rankings for winter rape was caused by differences in the parameter ranking of Werlte with regard to the other two sites (Fig. 3). In Werlte, the parameter vernReq2 was ranked as the second most important parameter, whereas it was ranked considerably lower for the other locations. 3.2. Total sensitivity indices The second step of the sensitivity analysis was carried out based on the previous results of the Morris ranking. The most relevant model parameters identified by using the Morris method (Table 3) were analysed using the Extended FAST. Total sensitivity effect indices (TSi ) were calculated to give an additional, more detailed measure of sensitivity. We calculated both the first-order sensitivity index (Si ) and the total sensitivity index, as proposed in (Saltelli et al., 1999), to distinguish between the main effect and the interaction effect. Application of the Extended FAST method necessitated a choice of different sets of independent frequencies to calculate the total sensitivity indices. We applied the algorithm proposed by Saltelli et al. (2000) to generate the frequency sets. According to the specifications, the maximum frequency for the parameter of interest was set to ωmax =2048, hence the maximum frequency for the other parameters was 256. Since the maximum harmonic to be considered was 4, the minimum sampling size for each individual crop was set to 19,000. The resulting TSi estimates for each analysed crop are presented in Fig. 4(a)–(f). For winter wheat, the most relevant parameter at all study sites was maxAssimRate, as it is responsible for most of the variance in output (Fig. 4(a)). The second most influential parameter was vernReq2 . vernReq2 also showed high interaction effects with parameters stageTempSum3 and daylengthReq3 , since they specify the plant development time in the earlier developmental stages. The parameters defining the specific leaf area of the earlier developmental stages (specificLeafArea1 − specificLeafArea3 ) as well as the parameters for maintenance and growth respiration (maintRespP1, growthRespP1) had a minimal effect on the growth of AGB. The results of the Extended FAST for winter wheat were quite similar for all study sites. Although there were minor differences in the specific value of the TSi , the general importance of the analysed parameters was identical at all of the study sites. For spring barley, the parameter maxAssimRate also accounts for the majority of variance in output (Fig. 4(b)). stageTempSum2 − stageTempSum3 and daylengthReq2 − daylengthReq3 were found to be most relevant after maxAssimRate. The parameters for specific leaf area (specificLeafArea1 − specificLeafArea3 ) and parameters describing

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Table 3 Parameter ranking based on the results of the Morris method for the analysed crops at the three study sites (A = Ascha, G = Gülzow and W = Werlte). No

1 12 14 21 22 23 24 26 27 28 601 602 603 604 605 606 611 612 613 614 632 642 643 644 651 652 653 654

Parameter name

maxAssimRate minAvailableN canopyReflCoef maintRespP1 maintRespP2 growthRespP1 growthRespP2 minimumNConc nConcB0 nConcPN stageTempSum1 stageTempSum2 stageTempSum3 stageTempSum4 stageTempSum5 stageTempSum6 stageKcFactor1 stageKcFactor2 stageKcFactor3 stageKcFactor4 vernReq2 daylengthReq2 daylengthReq3 daylengthReq4 specificLeafArea1 specificLeafArea2 specificLeafArea3 specificLeafArea4

No. of relevant parameters TDCC

Winter wheat

Spring barley

Maize

Sugar beet

Clover

A

G

W

A

G

W

A

G

W

A

G

W

1 13 19 5 18 9 15 21 22 7 20 11 6 16 3

1 17 16 4 20 7 14 22

1 16 17 5 20 7 15 11 22 4 21 14 9 19 8

1 9 18 10 20 13 16 15 17 4 14 5 8 19 6

1 18 16 7 19 10 14 17 15 5 13 4 6 18 12

1 14 19 10 20 11 15 17 16 4 13 5 7

1 17 8 3 12 4 10

1 14 7 3 15 4 10 16

1 17 7 3 13 5 11 16

2 1 16 12

14 13 2 5 6

9 13 2 5 8 18 17

10 12 2 4 6

6 13 9 10 18

2 1 14 11 20 13 18 5 17 3 21 10 8 19

2 1 13 11 20 12 17 5 15 4 19 9 8 16

15 8 19 11

22 9 7 15

21 10 14 22

8 19 12 5 15 10

6 16 20 21

23 21 10 12 8 17 4 14 2

24 11 13 6 18 3 9 2 23

10 13 6 18 3 12 2

23

24 0.96

25

14 17 4

7 12

9 11

9 12

2 3 11

2 3 8

2 3 8 15

9 11 7 19

12 6 11

8 9 14

5 3 7 19

12 4 6 16

7 3 6 18

21

20 0.98

21

18

22 0.99

18

20

23 0.96

23

the nitrogen (N) uptake and N stress of crops (minAvailableN, nConcB0, nConcPN, minimumNConc) were less sensitive. There were no notable differences between the total sensitivity indices of the different study sites.

A

Winter rape G

W

1

1

1

12 3 10 5 7

8 2 10 3 6

7 4 10 5 6

14 2 6 8 15

13 4 7 14

12 2 8

4 9 11 13 16

5 9

3 9

12 11 15

13 11

17

16 0.95

14

A

G

W

1 17 13 4 14 8 12

1 17 13 5 15 7 14

1 18 13 7 16 11 15

15 11 2 5 6

16 18 11 2 6 9

19 14 17 5 3 6 10

9 10 3 7 16

19 8 10 3 4 12

2 9 4 8 12

18

20 0.93

20

For maize, maxAssimRate was identified as the most relevant parameter (Fig. 4(c)). The second most influential parameter was stageTempSum3 . Parameters defining the specific leaf area (specificLeafArea1 − specificLeafArea3 ) and plant development of

Fig. 3. Comparison of the different parameter rankings for each study site using TDCC. High values of TDCC indicate a higher agreement between different parameter rankings.

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Fig. 4. Total sensitivity indices of the crop-specific most relevant model parameters analysed using the Extended FAST method. Main effect denotes the part of total variance explained by the articular parameter. Interactions describe the part explained by all parameter interactions where the particular parameter is included. The sum of main effect and interactions represents the total sensitivity index (TSi ) of the parameter. A full description of the parameters shown is given in Table A.4 in the appendix.

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the later developmental stages (stageTempSum4 − stageTempSum5 ) as well as maintenance and growth respiration (maintRespP1, growthRespP1) contributed to a lesser extent to the variance in output. The biomass growth of sugar beet was primarily affected by maxAssimRate and minAvailableN (Fig. 4(d)). Whereas in Gülzow and Werlte, maxAssimRate was more important than minAvailableN, in Ascha, the influence of minAvailableN (TSi = 0.38) was considerably higher than that of maxAssimRate (TSi = 0.23). Parameters specifying the leaf area index (LAI, specificLeafArea1 − specificLeafArea3 ) as well as parameters defining the N uptake and N stress of crops (nConcPN, minimumNConc) had slightly less influence. Biomass growth of sugar beet was only minimally affected by maintenance and growth respiration parameters (maintRespP1, growthRespP1). For clover, maxAssimRate was the most relevant parameter (Fig. 4(e)). Crop growth of clover was also significantly affected by maintenance and growth respiration parameters (maintRespP1, growthRespP1) as well as by the plant development parameter stageTempSum2 . Parameters defining the daylength requirement had a minimal effect on AGB, too. No notable differences were identified when comparing the total sensitivity indices of the different study sites. For winter rape, maxAssimRate was most sensitive (Fig. 4(f)) at all study sites. In addition, AGB was mainly affected by parameters defining plant development, although the magnitude of their effect differed at each study site. In Ascha, the most important parameters after maxAssimRate were daylengthReq3 , stageTempSum5 and stageTempSum3 . In Gülzow, daylengthReq3 , vernReq2 , stageTempSum5 and stageTempSum3 were also important after maxAssimRate. In Werlte, parameters for plant development of the second developmental stage (vernReq2 , daylengthReq2 and stageTempSum2 ) exhibited high interactions between each other and significantly affected the growth of AGB. The influence of the parameter vernReq2 was high in Gülzow and Werlte, but negligible in Ascha. Only interaction effects were detected for parameters describing the nitrogen (N) uptake and N stress of crops (minAvailableN, nConcB0, nConcPN, minimumNConc) as well as for parameters defining specific leaf area (specificLeafArea1 − specificLeafArea4 ). 3.3. Comparison of the TSi for different crops As the final step of the SA of MONICA, the sensitivity of parameters was compared for different crops (Fig. 5). We used the average of the total sensitivity indices of all study sites to find a similar set of sensitive parameters that can be adapted when calibrating MONICA for different crops. The parameter maxAssimRate was ranked important for all crops. This was expected to be the case because the calculation

of assimilates developed during photosynthesis include multiplication by maxAssimRate. The higher the assimilation rate, the more assimilates are developed during crop growth. The parameters specifying the developmental stage-dependent temperature sum were − to a smaller degree in comparison to maxAssimRate − relevant for all crops. The temperature sum defines the growth period of the respective developmental stage. Any increase or reduction in this parameter has a major effect on the crop’s development, and hence on above-ground biomass (AGB). The temperature sum parameters before the flowering stage (stage 2–3, Table 1) were most important. The specific leaf area parameters of the early stages (specificLeafArea1 − specificLeafArea3) were relevant for maize and sugar beet, and also to a lesser extent for winter wheat, winter rape and spring barley. The parameters for maintenance and growth respiration, particularly the Q10 -Factors (maintRespP1 and growthRespP1), were generally relevant especially for winter wheat, maize, clover and winter rape. Maintenance and growth respiration is a temperaturedependent process influenced by the actual biomass of the crop, the parameters maintRespP1 and maintRespP2 respectively growthRespP1 and growthRespP2. maintRespP1 and growthRespP1 are scaling factors that directly influence the amount of respiration in the assimilates. The parameters maintRespP2 or growthRespP2 specify a temperature threshold that defines if the amount of assimilates required by the crop for maintenance and growth respiration will be increased (high temperature) or reduced (low temperature). The parameters nConcB0, nConcPN and minimumNConc, which describe the nitrogen (N) uptake and N stress of crops, only affected the crop growth of sugar beet. No significant effect on AGB was identified for the other crops.. For winter crops (winter wheat and winter rape), the vernalisation requirement (vernReq2 ) showed a significant influence towards AGB. This parameter defines the period a crop needs for vernalisation. If this threshold is not reached, the crop’s development will be significantly delayed, with a major impact on the AGB’s development. 4. Discussion The importance of SA is widely acknowledged in ecological modelling (Saltelli and Annoni, 2010; Saltelli et al., 2008; Cariboni et al., 2007; Saisana et al., 2005). The number of publications that focus on SA for complex ecological models has increased in recent years. In this study, we performed a global sensitivity analysis for the complex agro-ecosystem model MONICA. Although the Morris method was first introduced in 1991 (Morris, 1991), its potential was gradually recognised after the release of Saltelli’s publication (Saltelli et al., 2000), which provided an overview of important SA techniques. The Morris method is ideal

Fig. 5. Comparison of the total sensitivity indices of the analysed model parameters, averaged for all study sites. A full description of the parameters is given in Table A.4 in the appendix.

X. Specka et al. / Europ. J. Agronomy 71 (2015) 73–87

for applying SA to complex models because it requires only a few model simulations (Cariboni et al., 2007). In recent years, the Morris method – involving low computational costs – was applied more frequently in SA of ecosystem models (Makler-Pick et al., 2011; Richter et al., 2010; Mszros et al., 2009; Campolongo et al., 2007; Zador et al., 2006; Francos et al., 2003). Saltelli and Annoni (2010) showed that OAT methods, although very popular in mathematical modelling, are insufficient for a thorough sensitivity analysis and should be applied very cautiously or in combination with more sophisticated methods. Taking into account the guidance given by Saltelli and Annoni (2010), we applied the Morris method as a preliminary study to first identify the driving parameters of MONICA. Modellers’ experience shows that only a few parameters of complex models with a large number of parameters have a significant impact on the output of the model (Saltelli et al., 2000; Richter et al., 2010). Our findings support this conclusion, since only 28 out of 117 model parameters of the MONICA model were found to influence the analysed output. The preliminary SA with Morris helped to reduce the computational cost of the Extended FAST method applied subsequently. Due to the high computational costs involved, the Extended FAST method can only be used if the number of model parameters considered is small (Confalonieri et al., 2010; Saltelli et al., 2006). Although the Morris method is able to detect the main effect and the interaction effect of parameters, the result of the analysis is a qualitative parameter ranking that can only identify important parameters. Reliable information about the level of sensitivity cannot be derived using the Morris method, due to the OAT concept and the small number of model evaluations that are used (Saltelli and Annoni, 2010). Compared to the Morris method, applying the Extended FAST method by calculating the first-order and total sensitivity indices allowed us to quantify and weight the sensitivity of parameters. We were able to specify how much more important some parameters were in comparison to others. Analysis of sensitivity measures * and  calculated using the Morris method showed that highly relevant parameters, as indicated by *, also had high variances (). This suggested either the nonlinear nature of the effect or the existence of an interaction with other parameters. The calculation of the main and total effects helped us to identify highly interactional behaviour between different parameters. The parameters stageTempSum1 − stageTempSum3 , daylengthReq2 − daylengthReq4 and vernReq2 showed a high degree of interaction behaviour, as all parameters affect the calculation of the current temperature sum. The daylength requirement of a developmental stage can have a reduction effect on the calculation of the current temperature sum. The crop usually proceeds to the next developmental stage as soon as a threshold specified by the stage temperature sum (stageTempSum) is exceeded. If the specified daylength requirement is not reached, the degree-day value which is added to the actual temperature sum at this developmental stage is reduced. As a result, the crop development is delayed, as the crop remains in the current developmental stage for longer. Thus, parameters that specify the temperature sum, day length requirement and vernalisation requirement interact considerably with one another. This information is essential with regard to the calibration of the MONICA model, as all interacting parameters must be considered. Comparison of the TSi of different crops showed that there is no general parameter set that can be applied to calibrate the MONICA model for different crops. However, our investigation revealed that maxAssimRate and parameters describing the plant development (stageTempSum1 − stageTempSum3 ) as well as specific leaf area are relevant for all crops. Similar results regarding the importance of parameters specifying photosynthesis and crop phenology were found by Richter et al. (2010) and Dzotsi et al. (2013).

81

The modelling scenario used for SA was carried out using climate and soil information from three study sites in Germany. Analysing the parameter sensitivity of the MONICA model by using soil and climate information from different experimental locations revealed no significant differences. For winter wheat, spring barley, maize and clover, the parameter ranking of the Morris method as well as the total sensitivity indices of the Extended FAST produced similar results for all study sites. For sugar beet, the parameter minAvailableN, which influences the N uptake of the crop, exhibited a considerably higher influence on AGB in Ascha compared to the other locations. In Ascha, minAvailableN was even more important than the otherwise most influential parameter maxAssimRate. Simulation results showed that in Ascha, sugar beet suffers severely from nitrogen stress diminishing the development of the crop. Nitrogen stress was considerably lower at the other locations, with less influence on AGB. The parameter minAvailableN therefore had less influence in Gülzow and Werlte than in Ascha. The AGB of winter rape was affected to a greater extent by the vernalisation parameter (vernReq2 ) in Gülzow and Werlte than in Ascha. As the higher mean air temperature in Gülzow and Werlte compared to Ascha indicates, the number of cold days where vernalisation occurs was lower than in Ascha. Vernalisation has a positive effect on crop growth for winter crops. Due to the lower temperature, this requirement is met more easily in Ascha than in Gülzow or Werlte. If the vernalisation requirement cannot be met, crop growth at this stage will be impeded. The vernalisation parameter in Gülzow and Werlte therefore had a greater impact on AGB than in Ascha. Although the sensitivity analysis results for the three different study sites did not differ significantly, we expect the sensitivity of parameters to differ for simulations with significantly different climate conditions (Dzotsi et al., 2013; Richter et al., 2010). When using a scenario with limited water availability, the importance of parameters related to water stress (stageKcFactor1 − stageKcFactor7 ) is expected to increase. A further sensitivity and uncertainty analysis of the model should therefore analyse the influence of soil parameters or climate variables on the overall parameter sensitivity and the model’s uncertainty. 5. Conclusion Our study revealed that a subset of model parameters, especially parameters describing the photosynthesis and plant phenology, were relevant for the above-ground biomass of all crops. Our findings also showed that, in addition to these parameters, each analysed crop was affected by a different set of model parameters. Sensitivity analysis of MONICA was also helpful with regard to understanding and verifying model behaviour. For each analysed crop, we identified the parameters that had the greatest effect on AGB. These findings will be used to calibrate MONICA for different energy crops. The next step in our analysis of the MONICA model should include investigating sensitive parameters with regard to different outputs and quantifying the uncertainty induced by input variables such as soil and climate data. Acknowledgements This study was based on data from the project: “Development and comparison of optimised cropping systems for the agricultural production of energy crops” (FKZ 22013008). The project was funded by the German Federal Ministry of Food, Agriculture and Consumer Protection through the Agency of Renewable Resources (FNR).

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Appendix A. Parameter list for sensitivity analysis See Table A.4.

Table A.4 Description of parameters included in the sensitivity analysis process with specification of their respective nominal values. For each crop the parameter range was set to 30% at either side of the nominal value. Only uncorrelated parameters were included in the sensitivity analysis. No.

Parameter

Description

Unit

Winter wheat

Spring barley

Maize

Sugar beet

Clover

Winter rape

1

maxAssimRate

kg CO2 ha−1

52

30

96

100

45

50

2

maxCropDiameter

m

0.005

0.004

0.025

0

0.003

0.006

3 4

plantDensity rootPenRate

m−2 m ◦ C−1 d−1

220 0.0011

220 0.0011

10 0.0014

8 0.0011

600 0.0008

100 0.002

5

rootGrowthLag

◦

C

−30

−30

−30

−60

−30

−30

6

initRootingDepth

m

0.1

0.1

0.1

0.06

0.1

0.1

7

specMaxRootDepth

m

1.3

1.3

1.4

1.6

0.3

1.5

8

rootFormFactor

–

3

3

3

2

5

1.5

9

minNConcRoot

Max. assimilation rate per leaf area Maximum crop diameter Planting density of crop Vertical root growth rate Temperature sum required for root growth Initial root depth of crop Crop-specific maximum rooting depth Factor describing the pattern of root mass distribution over depth Minimum value for root nitrogen concentration Initialisation value for root concentration Maximum N uptake per root length Mineral N concentration in soil which is not available for crop N uptake Default light use efficiency Canopy reflectance coefficient

kg N kg−1

0.005

0.005

0.005

0.005

0.005

0.005

kg N kg−1

0.02

0.02

0.02

0.02

0.02

0.02

kg m Root−1

3.145

3.145

7.4

5.645

3.145

3.145

kg m−3

7.5E−4

7.5E−4

7.5E−4

7.5E−4

7.5E−4

7.5E−4

kg/ha h/J m2 s

0.5

0.5

0.5

0.5

0.5

0.5

–

0.08

0.08

0.08

0.08

0.08

0.08

– –

2.5 40

2.5 40

2.5 40

2.5 40

2.5 40

2.5 40

–

3

3

4

3

3

3

– –

6 0.5

12 0.6

9 0.35

9 0.35

9 0.35

9 0.35

–

1.3

1.3

1

1.65

1

1.1

–

0.08

0.08

0.08

0.08

0.08

0.08

◦

44

44

44

44

44

44

–

0.1

0.1

0.1

0.1

0.1

0.1

◦

38

38

38

38

38

38

–

0.5

0.3

0.5

2

1

0.3

kg kg−1

0.005

0.005

0.004

0.004

0.005

0.005

–

2

2.269

5

1.38

0

3.5

–

1.6

1.6

1

1.11

2.6

1.35

10

NConcRoot

11

maxNUptakeParam

12

minAvailableN

13

defaultRadUseEff

14

canopyReflCoef

15 16

saturationBeta stomataCondAlpha

17

stageAtMaxHeight

18 19

cropHeightP1 cropHeightP2

20

luxuryNCoeff

21

maintRespP1

22

maintRespP2

23

growthRespP1

24

growthRespP2

25

residueNRatio

26

minimumNConc

27

nConcB0

28

nConcPN

Stomata conductivity parameter Dev.-stage of maximal crop height Factor for crop height Reduction factor for crop height Coefficient describing maximum N concentration relative to critical N concentration in the crop tissue Q10 factor for maintenance respiration Temperature related scaling factor Q10 factor for growth respiration Temperature related scaling factor N concentration in crop residues relative to N concentration in marketable yield Minimum N concentration in the plant tissue Curvature of the critical N concentration curve Shape factor for critical N curve

C

C

X. Specka et al. / Europ. J. Agronomy 71 (2015) 73–87

83

Table A.4 (Continued) No. 29

30

31

32

33 34 35 36 37 38 39 40

41

42

43

44

45

46

47

48

49

50

51

52

53

Parameter specAnaerobDenit

Description

Denitrification rate under standard conditions (25◦ C) immobRateCoeffNO3 Coefficient for immobilisation rate for NO3 immobRateCoeffNH4 Coefficient for immobilisation rate for NH4 maxCropNDemand Maximum amount of soil mineral N to be taken up by the crop nitrRateCoeffStand Nitrification rate default coefficient transportRateCoeff Diffusion of nitrate to denitrification zones CNRatioSMB C to N ratio of the soil microbial biomass AOMDryMatterCont Dry matter content of added organic matter AOMNH4Content Ammonium content of added organic matter AOMNO3Content Nitrate content of added organic matter AOMCarbamidCont Carbamide content of added organic matter partAOM2AOMSlow Part of added organic matter to be assigned to slowly decomposing pool partAOM2AOMFast Part of added organic matter to be assigned to rapidly decomposing pool CNRationAOMSlow C to N ratio of slowly decomposing added organic matter CNRationAOMFast C to N ratio of rapidly decomposing added organic matter SOMSlowDecCoeffStand Soil organic matter slow decomposition rate coefficient SOMFastDecCoeffStand Decomposition rate coefficient for rapidly decomposing soil organic matter pool SMBSlowMaintRateStand Maintenance rate for slowly reproducing soil microbial biomass SMBFastMaintRateStand Maintenance rate for rapidly reproducing soil microbial biomass SMBSlowDeathRateStand Death rate of slowly growing soil microbes under standard conditions (25◦ C) SMBFastDeathRateStand Death rate of rapidly growing soil microbes under standard conditions (25◦ C) SMBUtilEff Substrate utilisation efficiency of soil microbes SOMSlowUtilEff Microbial utilisation efficiency for slowly decomposing soil organic matter pool SOMFastUtilEff Microbial utilisation efficiency for rapidly decomposing soil organic matter pool AOMSlowUtilEff Added organic matter slow utilisation efficiency

Unit

Winter wheat

Spring barley

Maize

Sugar beet

Clover

Winter rape

g gas-N g CO -C

0.1

0.1

0.1

0.1

0.1

0.1

d−1

0.5

0.5

0.5

0.5

0.5

0.5

d−1

0.5

0.5

0.5

0.5

0.5

0.5

kg m−2

6

6

6

6

6

6

d−1

0.1

0.1

0.1

0.1

0.1

0.1

kg N m−3 d−1

0.1

0.1

0.1

0.1

0.1

0.1

–

6.7

6.7

6.7

6.7

6.7

6.7

kg kg−1

0.5

0.5

0.5

0.5

0.5

0.5

kg kg−1

0.5

0.5

0.5

0.5

0.5

0.5

−1

kg kg

0.5

0.5

0.5

0.5

0.5

0.5

kg kg−1

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

0.5

100

100

100

100

100

100

25

25

25

25

25

25

d−1

4.3E−5

4.3E−5

4.3E−5

4.3E−5

4.3E−5

4.3E−5

d−1

1.4E−4

1.4E−4

1.4E−4

1.4E−4

1.4E−4

1.4E−4

d−1

0.001

0.001

0.001

0.001

0.001

0.001

d−1

0.01

0.01

0.01

0.01

0.01

0.01

0.001

0.001

0.001

0.001

0.001

0.001

0.01

0.01

0.01

0.01

0.01

0.01

0.6

0.6

0.6

0.6

0.6

0.6

0.4

0.4

0.4

0.4

0.4

0.4

0.5

0.5

0.5

0.5

0.5

0.5

0.4

0.4

0.4

0.4

0.4

0.4

2

−1

84

X. Specka et al. / Europ. J. Agronomy 71 (2015) 73–87

Table A.4 (Continued) No.

Parameter

Description

54

AOMFastUtilEff

55

AOMFastMaxC2N

56

HydrolysisKM

57

HydrolysisP1

58

HydrolysisP2

59

DiffusionCoefStand

601

stageTempSum1

602

stageTempSum2

Added organic matter fast utilisation efficiency Maximum C to N ratio of the rapidly decomposing added organic matter Parameter used to describe urea hydrolysis Parameter used to describe urea hydrolysis Parameter used to describe urea hydrolysis Diffusion coefficient in soil under standard conditions Temperature sum for dev.-stage 1 Temperature sum for dev.-stage 2 Temperature sum for dev.-stage 3 Temperature sum for dev.-stage 4 Temperature sum for dev.-stage 5 Temperature sum for dev.-stage 6 Temperature sum for dev.-stage 7 Kc factor for dev.-stage 1 Kc factor for dev.-stage 2 Kc factor for dev.-stage 3 Kc factor for dev.-stage 4 Kc factor for dev.-stage 5 Kc factor for dev.-stage 6 Kc factor for dev.-stage 7 Threshold for water deficit with consequent development acceleration for dev.-stage 1 Threshold for water deficit with consequent development acceleration for dev.-stage 2 Threshold for water deficit with consequent development acceleration for dev.-stage 3 Threshold for water deficit with consequent development acceleration for dev.-stage 4 Threshold for water deficit with consequent development acceleration for dev.-stage 5 Threshold for water deficit with consequent development acceleration for dev.-stage 6

603

stageTempSum3

604

stageTempSum4

605

stageTempSum5

606

stageTempSum6

607

stageTempSum7

611

stageKcFactor1

612

stageKcFactor2

613

stageKcFactor3

614

stageKcFactor4

615

stageKcFactor5

616

stageKcFactor6

617

stageKcFactor7

621

droughtStressThresh1

622

droughtStressThresh2

623

droughtStressThresh3

624

droughtStressThresh4

625

droughtStressThresh5

626

droughtStressThresh6

Unit

Winter wheat

Spring barley

Maize

Sugar beet

Clover

Winter rape

0.4

0.4

0.4

0.4

0.4

0.4

1000

1000

1000

1000

1000

1000

0.00334

0.00334

0.00334

0.00334

0.00334

0.00334

4.26E−12

4.26E−12

4.26E−12

4.26E−12

4.26E−12

4.26E−12

1.41E−12

1.41E−12

1.41E−12

1.41E−12

1.41E−12

1.41E−12

m2 d−1

2.14E−4

2.14E−4

2.14E−4

2.14E−4

2.14E−4

2.14E−4

◦

C

148

108

68

100

40

130

◦

C

284

284

284

300

284

284

◦

C

380

330

190

565

200

160

◦

C

200

120

250

608

400

160

◦

C

420

200

200

1600

350

900

◦

C

25

25

400

25

25

25

◦

C

25 0.4

0.4

0.4

0.4

0.6

0.6

0.7

0.6

1

0.8

0.9

1.1

1.1

1

1

1

0.93

1.3

1.1

1

1.2

1.35

0.93

1.1

0.8

0.8

1.25

0.85

0.93

0.8

0.25

0.25

1.25

0.4

0.8

0.6

1 1

0.8

0.5

1

1

1

0.9

0.8

0.5

0.7

1

0.8

1

0.8

0.5

0.8

1

0.8

1

0.75

0.5

0.8

1

0.8

0.9

0.6

0.6

0.8

1

0.8

0.8

0.5

0.6

0.7

1

1

X. Specka et al. / Europ. J. Agronomy 71 (2015) 73–87

85

Table A.4 (Continued) No.

Parameter

Description

627

droughtStressThresh7

631

vernReq1

632

vernReq2

642

daylengthReq2

643

daylengthReq3

644

daylengthReq4

651

specificLeafArea1

652

specificLeafArea2

Threshold for water deficit with consequent development acceleration for dev.-stage 7 Temperature sum required for optimum vernalisation for dev.-stage 1 Temperature sum required for optimum vernalisation for dev.-stage 2 Day length required for maximum growth for dev.-stage 2 Day length required for maximum growth for dev.-stage 3 Day length required for maximum growth for dev.-stage 4 Specific leaf area to calculate leaf area index for dev.-stage 1 Specific leaf area to calculate leaf area index for dev.-stage 2 Specific leaf area to calculate leaf area index for dev.-stage 3 Specific leaf area to calculate leaf area index for dev.-stage 4 Specific leaf area to calculate leaf area index for dev.-stage 5 Specific leaf area to calculate leaf area index for dev.-stage 6 Specific leaf area to calculate leaf area index for dev.-stage 7 Maximum value for nitrogen content in root for dev.-stage 1 Maximum value for nitrogen content in root for dev.-stage 2 Maximum value for nitrogen content in root for dev.-stage 3 Maximum value for nitrogen content in root for dev.-stage 4 Maximum value for nitrogen content in root for dev.-stage 5 Maximum value for nitrogen content in root for dev.-stage 6 Maximum value for nitrogen content in root for dev.-stage 7 Critical soil oxygen content for crop growth for dev.-stage 1 Critical soil oxygen content for crop growth for dev.-stage 2 Critical soil oxygen content for crop growth for dev.-stage 3 Critical soil oxygen content for crop growth for dev.-stage 4 Critical soil oxygen content for crop growth for dev.-stage 5 Critical soil oxygen content for crop growth for dev.-stage 6 Critical soil oxygen content for crop growth for dev.-stage 7

653

specificLeafArea3

654

specificLeafArea4

655

specificLeafArea5

656

specificLeafArea6

657

specificLeafArea7

661

stageMaxRootN1

662

stageMaxRootN2

663

stageMaxRootN3

664

stageMaxRootN4

665

stageMaxRootN5

666

stageMaxRootN6

667

stageMaxRootN7

671

critOxygenContent1

672

critOxygenContent2

673

critOxygenContent3

674

critOxygenContent4

675

critOxygenContent5

676

critOxygenContent6

677

critOxygenContent7

Unit

Winter wheat

Spring barley

Maize

Sugar beet

Clover

Winter rape

0.2

◦

C

50

0

0

0

0

35

◦

C

50

0

0

0

0

35

h

20

20

0

0

20

20

h

20

20

0

0

20

20

h

20

0

0

0

20

20

m2 kg−1

0.002

0.002

0.002

0.0009

0.002

0.002

m2 kg−1

0.0018

0.0019

0.002

0.001

0.002

0.002

−1

m kg

0.0017

0.0018

0.002

0.001

0.002

0.002

m2 kg−1

0.0016

0.0017

0.002

0.0009

0.002

0.002

m2 kg−1

0.0015

0.0016

0.002

0.0009

0.002

0.002

m2 kg−1

0.0015

0.0016

0.002

0.0009

0.002

0.002

2

−1

2

m kg

0.0012

kg kg−1

0.02

0.02

0.02

0.02

0.02

0.02

kg kg−1

0.02

0.02

0.02

0.015

0.02

0.02

−1

0.012

0.012

0.012

0.012

0.012

0.012

−1

kg kg

0.01

0.01

0.01

0.01

0.01

0.01

kg kg−1

0.01

0.01

0.01

0.009

0.01

0.01

kg kg−1

0.01

0.01

0.01

0.009

0.01

0.01

kg kg

−1

kg kg

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