『Abstract
　The number of phases for which weathering rates can be determined by watershed geochemical mass balance is limited by the number of equations that can be constructed from elemental flux losses from the watershed and mineral stoichiometries. Mass balance studies of watershed weathering rates routinely use the flux losses of the six major cations SiO2, Al, Na, K, Mg, and Ca. Analyses of these species in water are common, but following matrix algebraic methods limits the number of weathering rates that can be calculated to six.
　For the Brubaker Run watershed located in the northern Piedmont Physiographic Province of Pennsylvania (USA), long-term (10³-10⁶ year) watershed chemical flux losses have been determined using ¹⁰Be-derived total denudation rates and zirconium-normalized total chemical concentrations from bedrock and soils. Chemical flux losses calculated from solid-phase data have three advantages: They (1) permit generation of a relatively large number of equations because both major and trace analyses are included; (2) eliminate the need for many years of regular (e.g., weekly) sampling and chemical analyses of stream water and atmospheric precipitation, and measurement of hydrologic parameters (i.e., precipitation, stream discharge, etc.); (3) long-term weathering rate calculations need not address biomass.
　For Brubaker Run, eight minerals are involved in weathering; the five primary minerals are REE-rich epidote, ankerite, almandine-spessartine garnet, muscovite, chlorite, and the three secondary products are weathered muscovite, kaolinite, and gibbsite. The long-term average weathering rates of these minerals were calculated using the major cations, and two trace elements selected from Rb, Sr, Ba, La, Pr, Nd, Sm, Gd, and Dy. Despite having the eight equations needed, geochemically reasonable weathering rates (e.g., positive primary mineral rates that reflect destruction) could not be achieved regardless of the two trace elements used in the mass balance calculations. For Brubaker Run, this is primarily attributable to the natural heterogeneity of the trace element concentrations within the host mineral grains, with trace element stoichiometries in some minerals varying by as much as an order of magnitude. Because the trace elements are hosted by a relatively small number of minerals, the computed weathering rates of other minerals become very sensitive to small variations in trace cation stoichiometry.
　REE-rich epidote, garnet, and ankerite within the Brubaker Run watershed together host nearly all of the Ca in the bedrock, and completely dissolve at or near the weathering front. Consequently, approximately all of the Ca in bedrock is lost from the regolith. In bedrock the mole-percentages of Ca hosted by REE-rich epidote, garnet, and ankerite are 49 mol%, 4 mol%, and 43 mol%, respectively, and are determined by the modal abundance of the mineral in the bedrock and its Ca stoichiometry. The weathering rates of REE-rich epidote, garnet, and ankerite can be determined by distributing to each mineral that fraction of the total watershed Ca flux loss for which it is responsible based on its mole-percent Ca in bedrock. By using a base cation that is completely lost from the regolith, and knowing the mole-percentage of that element in the mineral(s) undergoing weathering, additional equations may be added to the mass balance matrix. We term this technique the “flux distribution method.” The flux distribution method eliminates the need for additional equations established using trace elements.
　Based on the mineral weathering rates for the Brubaker Run watershed determined using the flux distribution method, the rates at which the weathering front penetrated the bedrock (the “saprolitization” rate) are 4.5 m Myr^-1 and 6.5 m Myr^-1 for chlorite and muscovite, respectively. These measured long-term average saprolitization rates compare very favorably with published theoretical values for the nearby northern Maryland Piedmont which range from 2.2 to 5.3 m Myr^-1.

Keywords: Chemical weathering; Watersheds; Mass balance; Rates; Trace elements』

1. Introduction
2. Background
　2.1. Previous work
　2.2. Study area
3. Methods
　3.1. Field sampling
　3.2. X-ray fluorescence spectrometry (XRF)
　3.3. Bulk sample trace element analyses by laser ablation-inductively coupled plasma-mass spectroscopy (LA-ICP-MS)
　3.4. Mineral electron microprobe phase analyses (EMPA)
　3.5. Mineral trace element analyses by laser ablation-inductively coupled plasma-mass spectroscopy (LA-ICP-MS)
　3.6. Watershed mass balance methods
　3.7. Determination of total denudation rates
　3.8. Flux distribution method
4. Results
　4.1. Watershed elemental flux losses
　4.2. Watershed mass balance calculations which include trace elements
　4.3. Watershed mass balance calculations using the flux distribution method
5. Discussion
　5.1. Geochemical reasons for the failure of trace elements in mass balance calculations of mineral weathering rates
　5.2. Geochemical reasonability of mineral weathering rates determined using the flux distribution method
　5.3. Saprolitization rates in the Mid-Atlantic Appalachian Piedmont
　5.4. Limitations and advantages of the flux distribution method
　5.5. Importance of accessory phases on watershed Ca budgets
6. Summary and conclusions
Acknowledgments
Appendix A. Supplementary data
References