A null model for global root depth distributions: Analytical solution and comparison to data

Authors: HARMAN, CIARAN - Johns Hopkins University; Lapides, Dana

Submitted to: Ecohydrology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 3/16/2025
Publication Date: 4/25/2025
Citation: Harman, C.J., Lapides, D.A. 2025. A null model for global root depth distributions: Analytical solution and comparison to data. Ecohydrology. 18(3). Article e70023. https://doi.org/10.1002/eco.70023.
DOI: https://doi.org/10.1002/eco.70023

Interpretive Summary: Evapotranspiration is the largest terrestrial water flux, and storage and release of carbon in root systems plays an essential (but difficult to observe) role in the global carbon cycle. As a result, root systems are an important source of uncertainty in hydrological and carbon cycle models. Here, we develop an analytical solution to a previously proposed model for rooting distribution. The solutions show that root distributions in arid and humid environments both follow an exponential distribution and are shallower than root distributions in mesic environments, which follow a power law distribution. In arid environments, moisture is not available at depth, so roots grow only to the depth where water is available. In humid environments, water is always available at depth, so plants only need to grow enough roots to meet their water needs in the time between infiltration events. In mesic environments, deep moisture is just as likely to be available as not, so root water uptake may be very deep to take advantage of semi-reliable deep water supply. We compared the analytical solutions to a newly-compiled database of observed rooting distributions and an existing database of root depth observations. Our findings show that the analytical model is a good shallow bound for rooting depths and distributions and performs similarly to or better than existing models in the literature. Model performance can be explained well by deviations from the idealized climate assumed by the analytical model.

Technical Abstract: To accurately predict earth system response to global change, we must be able to predict the responses of important properties of that system, such as the depths over which plant roots are distributed. In 2008, H. J. Schenk proposed a model for the depth distribution of plant roots based on a simple hydrological scheme and the assumptions that plants will take up the shallowest water available first and will distribute their roots in proportion to long-term mean uptake at each depth. Here, we derive an analytical solution to the Schenk model under an idealised climate (in which infiltration events are treated as a marked Poisson process), explore properties of the result and compare with data. The solution suggests that in very humid and arid climates, the soil wetting and drying cycles induced by root water uptake are generally confined to a characteristic depth below the surface. This depth depends on the typical magnitude of rainfall events (most strongly so in arid climates), the typical total transpiration demand between rainfall events (most strongly in humid climates) and the plant-available water holding capacity of the soil. Root water uptake (and thus predicted root density) in very humid and arid landscapes decreases exponentially with depth at a rate determined by this characteristic depth. However, in a mesic climate, soils may be wet or dry to greater depths below the near-surface, and the duration spent in each state increases with depth. Consequently, root water uptake and root density in mesic climates more closely resemble a power law distribution. When the aridity index is exactly 1, the characteristic depth diverges and the mean rooting depth approaches infinity. This suggests that the most skewed root depth distributions might occur in mesic environments. We compared this model to another analytical solution and a compiled database of root distributions (159 combined locations). For a larger comparison dataset, we also compared 99th percentile rooting depth to rooting depths modeled by two other frameworks and a database of observed rooting depths (1271 combined locations). Results demonstrate that the analytical formulation of the Schenk model performs well as a shallow bound on rooting depths and captures something of the nonexponential form of root distributions, and its error is similar to or less than that of other modeling frameworks. Errors may be partly explained by the deviation of real climate from the idealisations used to obtain an analytical solution (exponentially distributed infiltration events and no seasonality).