Abstract: Renewed interest in heat stress effects on livestock productivity derives from climate change, which is expected to increase temperatures and the frequency of extreme weather events. This study aimed at evaluating the effect of temperature and humidity on milk production in highly selected dairy cattle populations across 3 European regions differing in climate and production systems to detect differences and similarities that can be used to optimize heat stress (HS) effect modeling. Milk, fat, and protein test day data from official milk recording for 1999 to 2010 in 4 Holstein populations located in the Walloon Region of Belgium (BEL), Luxembourg (LUX), Slovenia (SLO), and southern Spain (SPA) were merged with temperature and humidity data provided by the state meteorological agencies. After merging, the number of test day records/cows per trait ranged from 686,726/49,655 in SLO to 1,982,047/136,746 in BEL. Values for the daily average and maximum temperature-humidity index (THIavg and THImax) ranges for THIavg/THImax were largest in SLO (22-74/28-84) and shortest in SPA (39-76/46-83). Change point techniques were used to determine comfort thresholds, which differed across traits and climatic regions. Milk yield showed an inverted U-shaped pattern of response across the THI scale with a HS threshold around 73 THImax units. For fat and protein, thresholds were lower than for milk yield and were shifted around 6 THI units toward larger values in SPA compared with the other countries. Fat showed lower HS thresholds than protein traits in all countries. The traditional broken line model was compared with quadratic and cubic fits of the pattern of response in production to increasing heat loads. A cubic polynomial model allowing for individual variation in patterns of response and THIavg as heat load measure showed the best statistical features. Higher/lower producing animals showed less/more persistent production (quantity and quality) across the THI scale. The estimated correlations between comfort and THIavg values of 70 (which represents the upper end of the THIavg scale in BEL-LUX) were lower for BEL-LUX (0.70-0.80) than for SPA (0.83-0.85). Overall, animals producing in the more temperate climates and semi-extensive grazing systems of BEL and LUX showed HS at lower heat loads and more re-ranking across the THI scale than animals producing in the warmer climate and intensive indoor system of SPA.

Abstract: Eddy covariance data from four European grassland sites are used to probabilistically invert the CARAIB (CARbon Assimilation In the Biosphere) dynamic vegetation model (DVM) with 10 unknown parameters, using the DREAM((ZS)) (DiffeRential Evolution Adaptive Metropolis) Markov chain Monte Carlo (MCMC) sampler. We focus on comparing model inversions, considering both homoscedastic and heteroscedastic eddy covariance residual errors, with variances either fixed a priori or jointly inferred together with the model parameters. Agreements between measured and simulated data during calibration are comparable with previous studies, with root mean square errors (RMSEs) of simulated daily gross primary productivity (GPP), ecosystem respiration (RECO) and evapotranspiration (ET) ranging from 1.73 to 2.19, 1.04 to 1.56 g C m(-2) day(-1) and 0.50 to 1.28 mm day(-1), respectively. For the calibration period, using a homoscedastic eddy covariance residual error model resulted in a better agreement between measured and modelled data than using a heteroscedastic residual error model. However, a model validation experiment showed that CARAIB models calibrated considering heteroscedastic residual errors perform better. Posterior parameter distributions derived from using a heteroscedastic model of the residuals thus appear to be more robust. This is the case even though the classical linear heteroscedastic error model assumed herein did not fully remove heteroscedasticity of the GPP residuals. Despite the fact that the calibrated model is generally capable of fitting the data within measurement errors, systematic bias in the model simulations are observed. These are likely due to model inadequacies such as shortcomings in the photosynthesis modelling. Besides the residual error treatment, differences between model parameter posterior distributions among the four grassland sites are also investigated. It is shown that the marginal distributions of the specific leaf area and characteristic mortality time parameters can be explained by site-specific ecophysiological characteristics.

Abstract: As a part of the MACSUR task L2.4, we probabilistically calibrated the CARAIB dynamic vegetation model by Markov chain Monte Carlo (MCMC) simulation with the DREAMZS sampler. CARAIB is a mechanistic model that calculates the carbon assimilation of the vegetation as a function of the soil and climatic conditions, and can thus be used for simulating grassland production under cutting or grazing management. Bayesian model inversion was performed at 4 grassland sites across Europe: Oensingen, CH; Grillenburg, DE; Laqueuille, FR and Monte-Bodone, IT. Four daily measured variables from these sites: the Gross Primary Productivity (GPP), Net Ecosystem Exchange (NEE), Evapotranspiration (ET) and Soil Water Content (SWC) were used to sample 10 parameters related to rooting depth, stomatal conductance, specific leaf area, carbon-nitrogen ratio and water stresses. The maximized likelihood function therefore involved four objectives, whereas the applied Bayesian framework allowed for assessing the so called parameter posterior probability density function (pdf), which quantifies model parameter uncertainty caused by measurement and model errors. Sampling trials were performed using merged data from all sites (all-sites-sampling) and for each site (site-specific sampling) separately. The derived posterior parameter pdfs from the all-sites sampling and site-specific sampling runs showed differences in relation with the specificities of each site. Analysis of these distributions also revealed model sensitivity to parameters conditioned on the measured data, as well as parameter correlations.