Skip to main content

Advertisement

SpringerLink
Log in

Modeling Production Efficiency and Greenhouse Gas Objectives as a Function of Forage Production of Dairy Farms Using Copula Models

  • Published:
Environmental Modeling & Assessment Aims and scope Submit manuscript

A Correction to this article was published on 20 May 2022

This article has been updated

Abstract

Dairy farms are systems with multiple dependent variables whose practices influence their economic and environmental performances. Decisions made and actions taken to improve environmental performances of dairy farms carry the risk of decreasing farm profitability. Correlations among multiple variables must therefore be considered to reliably assess risks of improving environmental performances of farms. We applied copula models to a dataset of conventional dairy farms surveyed in France to decscribe relationships among their characteristics, such as forage dry matter (DM) production, milk production, and greenhouse gas (GHG) emissions. By modeling relationships among farm characteristics, copula models can identify the characteristics’ joint distributions, unlike other statistical methods. For dairy farms, copula models are useful for estimating probabilities of reaching a milk production goal or not exceeding a regulatory emission limit as a function of forage production. For instance, when a farm produced at least 4,500 kg DM/livestock unit (LU)/year of maize silage, the probability of producing at least 7,000 l milk/cow/year was 75%, while the probability of emitting less than 7,000 kg CO2 eq./LU/year (a value close to the mean of 6669 kg CO2 eq./LU/year for all of the farms) was 48%. When the same amount of grass from pasture was produced, these probabilities changed to 48% and 78%, respectively (i.e., decreased probability of reaching a production goal, but increased probability of not exceeding an emission threshold). Farmers must make trade-offs, since increased milk production goals are likely to increase GHG emissions per LU and/or reduce GHG emission intensities per l of milk, but are less likely to be reached for a given amount of forage DM. By providing information about relationships among farm characteristics that other statistical approaches cannot, copula models are useful for investigating these trade-offs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data Availability

Not applicable.

Code Availability

Not applicable.

Change history

References

  1. Pellerin, S., Bamiere, L., Angers, D., Béline, F., Benoit, M., Butault, J., et al. (2013). How can French agriculture contribute to reducing greenhouse gas emissions? Abatement potential and cost of ten technical measures. Synopsis of the study report. Paris.

    Google Scholar 

  2. Dollé, J.-B., Agabriel, J., Peyraud, J.-L., Faverdin, P., Manneville, V., Raison, C., et al. (2011). Les gaz à effet de serre en élevage bovin : évaluation et leviers d'action. In B. R. Doreau M., Perez J.M. (Ed.), Gaz à effet de serre en élevage bovin : le méthane (Vol. 24, pp. 415–432): Dossier, INRA Productions Animales.

  3. Flysjö, A., Cederberg, C., Henriksson, M., & Ledgard, S. (2012). The interaction between milk and beef production and emissions from land use change–critical considerations in life cycle assessment and carbon footprint studies of milk. Journal of Cleaner Production, 28, 134–142.

    Article  Google Scholar 

  4. Baumman, H., & Tillman, A. (2004). The hitch hiker’s guide to LCA: An orientation in life cycle assessment methodology and application. Studentlitteratur, Lund, Sweden.

  5. Rogers, K., Seager, T., & Linkov, I. (2008). Multicriteria Decision Analysis and Life Cycle Assessment. In Dordrecht, 2008 (pp. 305–314, Real-Time and Deliberative Decision Making): Springer Netherlands.

  6. Prado, V., & Heijungs, R. (2018). Implementation of stochastic multi attribute analysis (SMAA) in comparative environmental assessments. Environmental Modelling & Software, 109, 223–231. https://doi.org/10.1016/j.envsoft.2018.08.021

    Article  Google Scholar 

  7. Cucurachi, S., Borgonovo, E., & Heijungs, R. (2016). A protocol for the global sensitivity analysis of impact assessment models in life cycle assessment. Risk Analysis, 36(2), 357–377. https://doi.org/10.1111/risa.12443

    Article  CAS  Google Scholar 

  8. Ventura, A., Senga Kiessé, T., Cazacliu, B., Idir, R., & van der Werf, H. M. G. (2015). Sensitivity analysis of environmental process modeling in a life cycle context: A case study of hemp crop production. Journal of Industrial Ecology, 19(6), 978–993. https://doi.org/10.1111/jiec.12228.

    Article  CAS  Google Scholar 

  9. Groen, E. A., & Heijungs, R. (2017). Ignoring correlation in uncertainty and sensitivity analysis in life cycle assessment: What is the risk? Environmental Impact Assessment Review, 62, 98–109. https://doi.org/10.1016/j.eiar.2016.10.006

    Article  Google Scholar 

  10. Niu, M., Kebreab, E., Hristov, A. N., Oh, J., Arndt, C., Bannink, A., et al. (2018). Prediction of enteric methane production, yield, and intensity in dairy cattle using an intercontinental database. Global Change Biology, 24(8), 3368–3389. https://doi.org/10.1111/gcb.14094

    Article  Google Scholar 

  11. Li, D.-Q., Jiang, S.-H., Wu, S.-B., Zhou, C.-B., & Zhang, L.-M. (2013). Modeling multivariate distributions using Monte Carlo simulation for structural reliability analysis with complex performance function. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 227(2), 109–118. https://doi.org/10.1177/1748006x13476821

    Article  Google Scholar 

  12. Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de l’Université de Paris, 8, 229–231.

    Google Scholar 

  13. Joe, H. (1993). Parametric families of multivariate distributions with given margins. Journal of Multivariate Analysis, 46, 262–282.

    Article  Google Scholar 

  14. Coles, S., Heffernan, J., & Tawn, J. (1999). Dependence measures for extreme values analyses. Extremes, 24, 339–365.

    Article  Google Scholar 

  15. Embrechts, P., Mcneil, A., Straumann, D. (2002). Correlation and dependence in risk management: Properties and pitfalls. In Risk Management: Value at Risk and Beyond (pp. 176–223): Cambridge University Press.

  16. Hao, Z., & AghaKouchak, A. (2013). Multivariate Standardized Drought Index: A parametric multi-index model. Advances in Water Resources, 57, 12–18. https://doi.org/10.1016/j.advwatres.2013.03.009

    Article  Google Scholar 

  17. Kao, S.-C., & Govindaraju, R. S. (2010). A copula-based joint deficit for droughts. Journal of Hydrology, 380, 121–134. https://doi.org/10.1016/j.jhydrol.2009.10.029

    Article  Google Scholar 

  18. Shiau, J.-T., Modarres, R., & Nadarajah, S. (2012). Assessing multi-site drought connections in Iran using empirical copula. Environmental Modeling & Assessment, 17(5), 469–482. https://doi.org/10.1007/s10666-012-9318-2

    Article  Google Scholar 

  19. Patton, A. J. (2012). A review of copula models for economic time series. Journal of Multivariate Analysis, 110, 4–18. https://doi.org/10.1016/j.jmva.2012.02.021

    Article  Google Scholar 

  20. Favre, A.-C., El Adlouni, S., Perreault, L., Thiémonge, N., & Bobée, B. (2004). Multivariate hydrological frequency analysis using copulas. Water Resources Research, 40(1). https://doi.org/10.1029/2003wr002456

  21. Ilić, A., Prohaska, S., Radivojević, D., & Trajković, S. (2021). Multidimensional approaches to calculation of design floods at confluences—PROIL model and copulas. Environmental Modeling & Assessment. https://doi.org/10.1007/s10666-021-09748-8

    Article  Google Scholar 

  22. Gil, R., Bojacá, C. R., & Schrevens, E. (2021). Accounting for correlational structures in stochastic comparative life cycle assessments through copula modeling. The International Journal of Life Cycle Assessment, 26(3), 604–615.

    Article  Google Scholar 

  23. Opio, C., Gerber, P., Mottet, A., Falcucci, A., Tempio, G., MacLeod, M., et al. (2013). Greenhouse gas emissions from ruminant supply chains – A global life cycle assessment. Rome: Food and Agriculture Organization of the United Nations (FAO).

  24. Sauvant, D., Giger-Reverdin, S., & Eugene, M. (2018). Enteric methane emissions. In D. Sauvant, L. Delaby, & P. Noziere (Eds.), INRA feeding system for ruminants. The Netherlands: Wageningen Academic Publishers.

  25. Moraes, L. E., Strathe, A. B., Fadel, J. G., Casper, D. P., & Kebreab, E. (2014). Prediction of enteric methane emissions from cattle. Global Change Biology, 20(7), 2140–2148. https://doi.org/10.1111/gcb.12471

    Article  Google Scholar 

  26. IPCC. (2006). Chapter 10: Emissions from livestock and manure management. In Guidelines for National Greenhouse Gas Inventories: International Panel on Climate Change.

  27. Sauvant, D., & Noziere, P. (2016). Quantification of the main digestive processes in ruminants: The equations involved in the renewed energy and protein feed evaluation systems. Animal, 10(5), 755–770. https://doi.org/10.1017/S1751731115002670

    Article  CAS  Google Scholar 

  28. Arvalis Institut du végétal. (2015, janvier 2015). Maïs et tournesol: Performances des variétés et conduite des cultures. Aravalis-Cetiom Infos.

  29. Nadarajah, S., Afuecheta, E., & Chan, S. (2018). A compendium of copulas. Statistica, 77(4), 279–328.

    Google Scholar 

  30. Nagler, T. (2014). Kernel methods for vine copula estimation. Technische Universität München,

  31. Genest, C., & Favre, A.-C. (2007). Everything you always wanted to know about copula modeling but where afraid to ask. Journal of hydrologic engineering, 12(4), 347–368. https://doi.org/10.1061//ASCE/1084-0699/2007/12:4/347

    Article  Google Scholar 

  32. R Core Team. (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.

  33. Schepsmeier, U., Stoeber, J., Brechmann, EC., et al. (2015). VineCopula:Statistical Inference of Vine Copulas. R package version 1.6–1.

  34. Nagler, T. (2019). VC2copula: Extend the 'copula' package with families and models from 'VineCopula'. R package version 0.1.0.

  35. van der Werf, H. M. G., Knudsen, M. T., & Cederberg, C. (2020). Towards better representation of organic agriculture in life cycle assessment. Nature Sustainability. https://doi.org/10.1038/s41893-020-0489-6

    Article  Google Scholar 

  36. Henriksson, M., Flysjö, A., Cederberg, C., & Swensson, C. (2011). Variation in carbon footprint of milk due to management differences between Swedish dairy farms. Animal, 5(9), 1474–1484. https://doi.org/10.1017/S1751731111000437

    Article  CAS  Google Scholar 

  37. Baldini, C., Gardoni, D., & Guarino, M. (2017). A critical review of the recent evolution of Life Cycle Assessment applied to milk production. Journal of Cleaner Production, 140, 421–435.

    Article  Google Scholar 

  38. Zehetmeier, M., Gandorfer, M., Hoffmann, H., Müller, U. K., de Boer, I. J. M., & Heißenhuber, A. (2014). The impact of uncertainties on predicted greenhouse gas emissions of dairy cow production systems. Journal of Cleaner Production, 73, 116–124. https://doi.org/10.1016/j.jclepro.2013.09.054

    Article  CAS  Google Scholar 

  39. Coquil, X., Béguin, P., & Dedieu, B. (2013). Transition to self-sufficient mixed crop–dairy farming systems. Renewable Agriculture and Food Systems, 29(3), 195–205. https://doi.org/10.1017/S1742170513000458

    Article  Google Scholar 

  40. Senga Kiessé, T., Corson, M. S., Le Galludec, G., & Wilfart, A. (2020). Sensitivity of greenhouse gas emissions to extreme differences in forage production of dairy farms. Livestock Science, 232, 103906. https://doi.org/10.1016/j.livsci.2019.103906

    Article  Google Scholar 

  41. Gerber, P. J., Steinfeld, H., Henderson, B., Mootet, A., Opio, C., Dijkman, J., et al. (2013). Tackling climate change though livestock – A global assessment of emissions and mitigation opportunities. Rome: Food and Agriculture Organization of the United Nations (FAO).

  42. Rotz, C. A., Montes, F., & Chianese, D. S. (2010). The carbon footprint of dairy production systems through partial life cycle assessment. Journal of Dairy Science, 93(3), 1266–1282. https://doi.org/10.3168/jds.2009-2162

    Article  CAS  Google Scholar 

  43. Aguirre-Villegas, H. A., & Larson, R. A. (2017). Evaluating greenhouse gas emissions from dairy manure management practices using survey data and lifecycle tools. Journal of Cleaner Production, 143, 169–179. https://doi.org/10.1016/j.jclepro.2016.12.133

    Article  CAS  Google Scholar 

  44. Delaby, L., Faverdin, P., Michel, G., Disenhaus, C., & Peyraud, J. L. (2009). Effect of different feeding strategies on lactation performance of Holstein and Normande dairy cows. Animal, 3(6), 891–905. https://doi.org/10.1017/S1751731109004212

    Article  CAS  Google Scholar 

  45. Kolver, E. S. (2007). Nutritional limitations to increased production on pasture-based systems. Proceedings of the Nutrition Society, 62(2), 291–300. https://doi.org/10.1079/PNS2002200

    Article  Google Scholar 

  46. Buckley, F., Dillon, P., Rath, M., & Veerkamp, R. F. (2018). The relationship between genetic merit for yield and live weight, condition score, and energy balance of spring calving Holstein-Friesian dairy cows on grass based systems of milk production. BSAP Occasional Publication, 26(2), 297–303. https://doi.org/10.1017/S0263967X00033814

    Article  Google Scholar 

  47. Leblanc, S. (2010). Assessing the association of the level of milk production with reproductive performance in dairy cattle. Journal of Reproduction and Development, 56(S), S1-S7.

  48. Ghahramani, A., Howden, S. M., del Prado, A., Thomas, D. T., Moore, A. D., Ji, B., et al. (2019). Climate change impact, adaptation, and mitigation in temperate grazing systems: A review. Sustainability, 11(24), 7224.

    Article  CAS  Google Scholar 

  49. Aas, K., Czado, C., Frigessi, A., & Bakken, H. (2009). Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics, 44(2), 182–198.

  50. Graux, A.-I., Gaurut, M., Agabriel, J., Baumont, R., Delagarde, R., Delaby, L., et al. (2011). Development of the pasture simulation model for assessing livestock production under climate change. Agriculture, Ecosystems & Environment, 144(1), 69–91.

    Article  Google Scholar 

Download references

Acknowledgements

We thank the French Livestock Institute (IDELE) for providing the dataset.

Funding

The study was financially supported by the the AgreenSkills international postdoctoral fellowship program. The AgreenSkills program was co-funded by the European Union and coordinated by INRAE, in collaboration with Agreenium-IAVFF, the French Agricultural, Veterinary and Forestry Institute.

Author information

Authors and Affiliations

  1. UMR SAS, INRAE, Institut Agro, 35000, Rennes, France

    Tristan Senga Kiessé & Michael S. Corson

  2. Department of Operations Analytics, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

    Reinout Heijungs

  3. Institute of Environmental Sciences, Department of Industrial Ecology, Leiden University Leiden, Leiden, The Netherlands

    Reinout Heijungs

Authors
  1. Tristan Senga Kiessé
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Reinout Heijungs
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael S. Corson
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Tristan Senga Kiessé: methodology, writing — original draft; Reinout Heijungs: writing — original draft, supervision; Michael S. Corson: writing — original draft, reviewing.

Corresponding author

Correspondence to Tristan Senga Kiessé.

Ethics declarations

Ethics Approval

Not applicable.

Consent to Participate

Not applicable.

Consent for Publication

Not applicable.

Conflict of Interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (DOCX 452 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Senga Kiessé, T., Heijungs, R. & Corson, M.S. Modeling Production Efficiency and Greenhouse Gas Objectives as a Function of Forage Production of Dairy Farms Using Copula Models. Environ Model Assess 27, 413–424 (2022). https://doi.org/10.1007/s10666-021-09812-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10666-021-09812-3

Keywords

Search

Navigation