『Abstract
　Weathering of silicate minerals impacts many geological and ecological processes. For example, the weathering of basalt contributes significantly to consumption of atmospheric carbon dioxide (CO2) and must be included in global calculations of such consumption over geological timeframes. Here we compare weathering advance rates for basalt (wD^β), where D and β indicate the scale at which the rate id determined and surface area measured, respectively, from the laboratory to the watershed scales. Data collected at the laboratory, weathering rind, soil profiles and watershed scales show that weathering advance rate of basalt is a fractal property that can be described by a fractal dimension (dr≒2.3). By combining the fractal description of rates with an Arrhenius relationship for basalt weathering, we derive the following equation to predict weathering advance rates at any spatial scale from weathering advance rates measured at the BET scale:
　wD^β = k0 (β/a)^dr-2 e^-Ea/RT.
Here, k0 is the pre-exponential factor (1.29×10⁷ mm³ mm^-2 yr^-1). Ea is the activation energy (70 kj mol^-1), and a is a spatial constant related to the scale of measurement of BET surface area (10^-7 mm) The term, (β/a)^dr-2, is the roughness. The roughness fractal dimension can be conceptualized as a factor related to both the thickness of the reaction front and the specific surface area within the reaction front. However, the above equation can also be written in terms of a surface fractal dimension and the hypothetical average grain radius. These fractal dimensions provide insight into reaction front geometry and should vary with lithology. Once the surface area discrepancy has been accounted for using this method, we find a one to two order of magnitude range in weathering advance rates measured at any scale or temperature that can be attributed to factors such as changes in erosional regime, parent lithology, mechanism, climate, composition of reacting fluid, and biological activity. Our scaled equation, when used to predict global basalt CO2 consumption based upon global lithologic maps, yields an uptake flux (1.75×10¹³ mol CO2 yr^-1) within the predicted error of fluxes estimated based upon riverine measurements.

Keywords: basalt; weathering; fractal dimension; fractals; surface area; cation denudation rates; weathering advance rates; scaling』

1. Introduction
2. Weathering advance rates
　2.1. Laboratory scale
　2.2. Weathering rind and soil profile studies
　2.3. Watershed studies
3. Calculation of weathering advance rates
　3.1. Advance rates from water chemistry
　3.2. Advance rates calculated from regolith thickness
4. Results and discussion
　4.1. BET surface area-normalized rates
　4.2. BET surface area-normalized rates from fractal dimensions
　4.3. Predicting weathering advance rates across scales
5. Fractal dimensions and reaction front geometry
6. Conclusions
Acknowledgements
References