A numerical model for duricrust formation by laterisation

<p>Duricrusts form near the top of or within the regolith. Once exhumed, they are resistant to erosion and are often observed capping hilltops. Two hypotheses have been proposed to explain their formation. One calls upon seasonal fluctuations in water table height causing cycles of dissolution and precipitation that concentrate hardening species transported from distant sources. The other assumes that hardening is the ultimate phase of laterisation of the regolith by progressive leaching of the soluble elements that leads to in situ concentration of the hardening species. Here we propose a numerical model for the formation of duricrusts following the latter hypothesis, which we will term the in situ or laterisation (LAT) model. In <span class="cit" id="xref_text.1"><a href="#bib1.bibx36">Fenske et al.</a> (<a href="#bib1.bibx36">2025</a>)</span>, we developed a similar model representing the other model (named here the transport or Water Table Fluctuation (WTF) model).</p> <p>The LAT model we present here assumes that the rate of hardening is a self-limiting process that takes place at a rate determined by a laterisation time scale, <span class="inline-formula"><i>τ</i>_l</span>, and is linearly proportional to precipitation rate. Laterisation is accompanied by mass loss, at a rate set by a mass loss time scale, <span class="inline-formula"><i>τ</i>_m</span>, that can potentially be different from <span class="inline-formula"><i>τ</i>_l</span> and causes lowering of the topographic surface. We also test three laterisation modes, that depend on whether laterisation takes place above the water table only (percolation mode), below the water table (saturated mode) or everywhere (everywhere mode). This model for the formation of duricrusts is embedded in a previously published model for regolith formation <span class="cit" id="xref_paren.2">(<a href="#bib1.bibx18">Braun et al.</a>, <a href="#bib1.bibx18">2016</a>)</span>.</p> <p>Here we present results obtained from the new LAT model by varying both the model parameters and the external forcing functions, namely, <span class="inline-formula"><i>U</i></span> the uplift rate and <span class="inline-formula"><i>P</i></span>, the precipitation rate. We show that duricrust formation by laterisation is favored by a small uplift rate as well as a strong precipitation rate. The smaller the laterisation time scale and the mass loss time scale, the thicker the duricrust, but if the ratio between the two time scales, <span class="inline-formula"><i>τ</i>_m</span> <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M7" display="inline" overflow="scroll" dspmath="mathml"><mo>/</mo></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="36bd7baae116a5efc17e692d563c2b51"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="esurf-14-141-2026-ie00001.svg" width="8pt" height="14pt" src="esurf-14-141-2026-ie00001.png"/></svg:svg></span></span> <span class="inline-formula"><i>τ</i>_l</span> is too small, no duricrust can form or, in the saturated mode, the duricrust is progressively buried during its formation. We also derive a simple analytical expression for the conditions under which a duricrust will form within a regolith. This relationship implies that, as shown in <span class="cit" id="xref_text.3"><a href="#bib1.bibx18">Braun et al.</a> (<a href="#bib1.bibx18">2016</a>)</span>, for regolith to form, the time scale for primary weathering, <span class="inline-formula"><i>τ</i>_w</span>, that controls the rate of propagation of the weathering front into the bedrock must be smaller than the erosion time scale, <span class="inline-formula"><i>τ</i>_e</span>, that controls the rate of surface erosion, and for a duricrust to form, the time scale for secondary weathering, or laterisation time scale, <span class="inline-formula"><i>τ</i>_l</span>, must be smaller than the primary weathering time scale.</p> <p>The model also predicts hardening (or duricrust) age distributions that can be compared to ages obtained by (U-Th) <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M12" display="inline" overflow="scroll" dspmath="mathml"><mo>/</mo></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="8pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="6bfc4ae3491d603d986b6e1d0e6866cf"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="esurf-14-141-2026-ie00002.svg" width="8pt" height="14pt" src="esurf-14-141-2026-ie00002.png"/></svg:svg></span></span> He dating of goethite in ferricretes for example. We show that these age distributions can be used to differentiate between the different modes of laterisation. We also show how peaks in age distributions appear to correlate very well with climatic events, but not with periods of enhanced uplift (or base level fall). The model also predicts the total mass loss by chemical vs. physical erosion. We show that the ratio between the two is mostly a function of the laterisation time scale and how it varies during climate or tectonic cycles.</p> <p><span id="page142"/>Finally, we show how the model predictions can be compared to those of the WTF model to help determine by which process a given duricrust formed. We also show, however, that there might be situations where the geometry, thickness and position of the duricrusts may not be unequivocal signatures of a given process.</p>