# Spatial determinants of biomass and root exploration heterogeneity at watershed scale

Enguerrand Burel<fnref n="1" />* – Nathalie Jarosz-Pellé<fnref n="1" /> – Rémy Fieuzal<fnref n="1" /> – Sébastien Verrier<fnref n="1" /> – Julie Betbeder<fnref n="2" /> – Sylvain Ferrant<fnref n="1" /> – Vincent Bustillo<fnref n="1" />

## Introduction

Determinants of crops spatial heterogeneity have to be identified in order to optimize food production. This is essential to manage crops more accurately and better fit to crop requirements. Watersheds gather repetitive geomorphologic, climatic and soil properties patterns that are recognized to be the main spatial determinants of crop development (Cambardella et al., 2004, Oddershede et al., 2015). Soil and climatic conditions diagnosis as part of crop management, including precision agriculture, is necessary to identify key variables at watershed scale. Spatial distribution of these variables has been drawn using inversion models method (Varella et al., 2010), remote sensing data assimilation (Lagacherie et al., 2008) or empirical relationships (Sreelash et al., 2012).

In this study, we aim at determining relationships between indicators of crop spatial heterogeneity and the variable of interest on a catchment area of 25 ha in the South of France covered by wheat crop in 2015. Based on multilinear model selection from multi-model inference, we assessed the statistical significance of the relationships in order to assess the relative importance of the explanatory variables on the descriptors. Average models allows incorporating several competing multilinear models in the estimation process and may therefore provide a better estimation method than the best model one (Hoeting et al., 1999). The statistical significance of regression coefficients was evaluated using standard t-student test. Finally, the predictability of averaging models was tested by cross-validation procedure.

## Materials and Methods

In this study, crop heterogeneity is characterized by maximum rooting depth (Rootmax) and above ground biomass (AGB) as measured just before harvest. Rootmax gives the maximum depth at which plant is able to access soil nutrients and water resources. AGB at harvest is a quite good estimate of yield as it includes straw and grain production. These variables were measured in 15 sample points defined by Latin Hypercube sampling method (Minasny and McBratney, 2006) which requires as inputs spatially distributed variables over the area. These 6 selected variable inputs are the same as those used for multiple linear regressions: (i) a hydrological convergence index as determined by the topography soil index, TSI (Beven et al., 1978), (ii) the altitude z (iii) soil conductivity, Rs (iv) the maximum leaf area index, LAImax, (v) a precocity index, Pi, and (vi) the spatialized incident global radiation, Rg, depending on the slope and exposure (Allen et al. 2006).

## Results and Discussion

<figure><img src="image_1.png" /><figcaption>**Figure 1:** Weight coefficients of explanatory variables in describing above ground biomass (AGB) and maximal rooting depth (Rootmax). Weight coefficients below 15% are not significant. Here, Rs is the soil conductivity, LAImax the maximum leaf area index, Rg the spatialized incident global radiation, Pi a precocity index, TSI the topography soil index and z is the altitude,</figcaption></figure>

We performed 200 bootstrap iterations (with 3 < n samples < 15) in order to test significance and stability of regression coefficients. To achieve stable coefficients, 10 and 5 values were required for AGB and Rootmax, respectively. This means that the sample size defined for Latin Hypercube sampling method is correct to give robust relationships. We found a Relative Root Mean Squared Error (RRMSE) 0.23 and 0.22 for Rootmax and AGB, respectively on the validation dataset. These values are acceptable considering the measurements accuracy and assumption of a linear relationship.

<footnote n="1">¹ CESBIO UMR 5126 24 rue d'Embaquès 32000 Auch – France</footnote>

<footnote n="2">² INRA SAD-Paysage 65, rue de St-Brieuc 35042 Rennes – France</footnote>

<footnote>* Correspondence: enguerrand.burel@iut-tlse3.fr</footnote>
Figure 1 shows the relative importance of the explanatory variables tested in average models on AGB and Rootmax. LAImax and Pi are complementary since they capture the crop sensitivity to stress occurring at two distinct phenological stages. TSI appears as the most significant explanatory variable for both descriptors. It underlines the importance of taking into account the redistribution of water and nutrients by lateral water flow (Ferrant et al., 2016). Finally, the altitude that is strongly correlated to soil depth appears to be a prevailing explanatory factor of Rootmax. The colinearity with the TSI may partly explain the low weight of Rg. Moreover, the global radiation has only a small effect on crop canopy growth (Ferrant et al., 2016) than nutrients accessibility. Soil conductivity only explains the depth of root exploration. This result was unexpected as soil properties are highly relevant on the description of crop canopy heterogeneity, including crop yield. One hypothesis is that the crop plants adapt their root exploration in order to avoid water stress. This could explain why soil properties effect is stronger on Rootmax than AGB.

## Conclusions

This work provides a simple approach to represent the spatial heterogeneity of crops. This constitutes a first step towards the elaboration of yield maps or intermediate variables (e.g., soil water-holding capacity) that are useful to inform mechanistic biophysical models. In this study the choice of explanatory variables has been shown to be relevant for stable and significant relationships between local variables and high resolution gridded datasets used as covariates. Also the Latin Hypercube sampling method enabled to optimize the minimum sample size useful to represent crop heterogeneity.

However it appears in this study that relevant variables for the description of aboveground biomass are not necessarily the same as for the description of other biophysical measurements (e. g. rooting depth). Therefore the spatialization method is not directly portable.

## Acknowledgements

This work is supported by the Midi-Pyrénées region, Grand Auch Intercommunality as well as CNRS.

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