The methodological and statistical approach

Considering the importance of field trials in agricultural sciences (Spiertz 2014), adequacy of statistical methods to deal with the intrinsic spatial variability, patterns of spatial correlations and with repeated measurements in space and time are crucial in order to deliver unbiased and more precise outcomes. Here we discuss the challenges related to statistical analysis of field trials derived from constraints in randomization due to operational features. Advantages and disadvantages of field trials versus laboratory (artificially controlled) studies is also explored. Finally, we present the novelty of the method applied to analyse data from the field trials used in this study.

This study was based on data from two field trials, each one located in one site within the Brazilian Central West region on a sandy and a clay soil. Both experiments were designed with same treatments but with differences in field layout (experimental design) due to

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operational constraints. The experiment on the clay soil was established under a centre pivot for sprinkler irrigation and the experiment on the sandy soil was only rain fed. In both experiments, it was not possible to use a randomized block design due to randomization constraints. In each, there were four replicates per treatment (N x char combinations). However, on the sandy soil, the N fertilization levels were systematically allocated into strips instead of completely randomized within blocks due to limitations in area and requirements of mechanization process for sowing and fertilizer application. The same was done on the clay soil; however, in this case, plots had to be placed according to the pivot layout avoiding places nearby the wheels. Instead of a design-based approach, we adopted a contemporary statistical model based approach to overcome constraints derived from the lack of randomization in a classical experimental design (Schabenberger and Pierce 2002). This was done via linear mixed modelling of the relationship between the measured soil and plant variables and biochar and N-fertilization rate. A mixed-effects model (mixed model) comprises both fixed and random effects thus permitting inclusion of random effects, which account for times correlations and patterns of spatial dependencies (Littell 2006). In the case of the sandy soil the random effects considered were within blocks and rows within blocks because the strips corresponded to N levels (Fig. 1). On the clay soil, random effects were location of plots in columns and rows (Fig. 2). The mixed model was a sound alternative for adequate analysis in both cases, although differences in experimental design did not allow a conjoint analysis of the effects of biochar and N fertilization for both soil types. The analysis on the effects of biochar and N fertilization on soil chemical and physical properties and on aerobic rice yields was performed separately for the clay soil in Chapters 2 and 4 and for the sandy soil in Chapter 3 of this thesis.

An innovative approach developed in this study was the use of nonlinear mixed modelling to fit and compare soil water retention curves. The nonlinear mixed model allows testing differences among biochar treatments considering the overall variance of soil moisture arising from within treatments variance. Such formal testing is not possible when soil water retention curves are fitted for each biochar treatment individually by commonly used specific software such as the one proposed by Dourado-Neto et al. (2000). In our soil water retention curve modelling, we also used plot as random effect aiming to account for correlations among repeated measurements taken within the same soil sample. The idea of applying such approach derive from a study by Omuto et al. (2006), who demonstrated the relevance of considering the sources of the intra/inter relationships between individual points using mixed

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effects modelling with environmental correlates. They showed that neglecting the high variability of soil hydraulic parameters between and among soil units during modelling of the functional soil processes could lead to potential errors. The use of nonlinear mixed model to estimate parameters of soil water retention curves is presented in Chapter 3 of this thesis. In our study about the impact of biochar on N2O-N fluxes, plot was again included as a random effect in a mixed model, once repeated fluxes and related soil measurements were taken in the same plot along cropping seasons, as presented in Chapter 5. Further, the mixed model allows comparison of treatments and trends over time. According to Littell et al. (1998), this is especially important for analysis of repeated measures data because measurements taken close in time are potentially more highly correlated than those taken far apart in time. Usually this aspect is not taken into account in this type of field study, where N2O-N fluxes are assessed along a period of time, with daily or weekly intervals. Fluxes are measured via static chambers that are placed in the same spot along the field trial. In our study, we considered that measurements taken in the same chamber along the entire cropping season were correlated because they belong to a plot that is unique in itself and analysis within periods after N fertilization were also applied. According to Jungkunst et al. (2012), N2O-N fluxes are very sensitive to temporal and spatial variability and models show even higher sensitivity. To account for spatial variations of N2O-N fluxes in a regional scale is yet a challenge.

We believe our approach using mixed models is a novel contribution for agronomy research. Whereas precision and control of random effects increases under artificially controlled conditions, the opposite occurs under field trial conditions, where usually there will always be random effects to account for, i.e., consideration of environmental covariates in the estimation process will be always present. Yet, in order to develop new agronomic technologies the assessment on a field trial scale is essential, because it can mimic real farming conditions. On the other hand, laboratory studies are indispensable to deliver timely results and insights prior to planning of a field trial. Research on biochar needs to advance from artificially controlled conditions to farming conditions in order to deliver results that are more relevant and representative to real conditions (Glaser et al. 2002, Sohi et al. 2010, Jeffery et al. 2011, Liu et al. 2013, Mukherjjee and Lal 2014). This was the challenge of this thesis: to evaluate a relatively long-term effect of the use of wood biochar as a soil amendment under typical cropping systems of the Brazilian tropical Savannah.

117 F igure 1. Expe rime ntal d esign o n the sa ndy soi l at Estre la do S ul F arm in Nova Xa va nti na , M ato Gr o sso, B ra zil .

118 F igure 2. Expe rime ntal d esign o n the c lay soil a t C apivar a F arm in S anto Antonio de G oias, G oias, B ra zil .

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3. Contribution of biochar to sustainable intensification of farming systems in the