Uncertainty in silicate mineral weathering rate estimates: source partitioning and policy implications

Silicate mineral weathering is a cornerstone ecosystem service. The biological, chemical and physical dissolution of the silicate rocks which comprise 90% of Earth's crust is the ultimate source of most essential plant nutrients including phosphorus and base cations (BC; i.e. calcium, magnesium, sodium and potassium). Other processes including atmospheric deposition, litter fall, release from organic matter and fertilization only recycle mineral weathering products (Ouimet and Duchesne 2005). Precise and accurate estimates of silicate mineral weathering rates are vital for defining polices to meet environmental targets for forestry and agriculture (Kuylenstierna et al 2001, Sverdrup and Rosén 1998); long-term sustainability (Azar et al 1996) and achieving cost-effective control of soil and surface water acidification (Hodson and Langan 1999, Skeffington 2006 and McDonnell et al 2010). In addition to influencing the chemical composition of all soils, freshwaters and oceans (Roelandt et al 2010), weathering is also a driver of atmospheric CO₂ concentrations over geological time-scales (Brady 1991, Hilley and Porder 2008). Anthropogenically enhanced weathering has been proposed as a countermeasure to mitigate increasing atmospheric CO₂ concentrations (Köhler et al 2010).

Obtaining accurate estimates of weathering rates is difficult because weathering is a slow process that occurs over very long periods of time (Hatton et al 1987, Palviainen et al 2012). Management decisions related to plant growth (Kuylenstierna et al 2001, Sverdrup and Rosén 1998) and ecosystem ability to buffer acid deposition (Hodson and Langan 1999, Skeffington 2006, McDonnell et al 2010) rely on creditable estimates of silicate mineral weathering rates. However, several studies have questioned the use of single estimates of silicate mineral weathering rates because of large associated uncertainties (Kolka et al 1996, Starr et al 1998, Hodson and Langan 1999, Whitfield et al 2006). For example, the uncertainty range in seven different published silicate weathering rates at a single catchment was significantly greater than the expected difference in BC removal associated with different forest harvest scenarios (Klaminder et al 2011b), calling into question the utility of weathering estimates as an effective tool for forestry management. Some of this variability occurs because estimation methods differ substantially in their boundary conditions (depth of the weathering zone); spatial (pedon versus catchment) and temporal (contemporary environment versus historic) scales and assumptions regarding the processes which drive weathering; hence, there will always be inter-method biases in weathering rate estimates. Nevertheless, decisions need to be made for mitigating acid deposition, sustainable forest harvesting and assessing the feasibility of geo-engineering projects. When making such decisions, it is of crucial importance to recognize the bias associated with different weathering rate estimates derived from single approaches and what implications such biases might have.

To assess the magnitude and sources behind differences in available estimates of silicate mineral weathering rates, we assembled a data set of published BC weathering and release rates to address the following questions: (i) what is the range of published BC weathering and release rates for individual sites; (ii) what are the sources of variability in estimated rates of BC weathering and release; (iii) how many weathering rate estimates are needed to achieve an acceptable level of precision at a single site and (iv) how do MAGIC and PROFILE, two of the most commonly used weathering models, differ in their predictions? We compiled available peer-reviewed literature data including 394 individual silicate mineral weathering rate estimates from 82 poorly buffered, silicate mineral dominated locations across the world where at least three published estimates of BC weathering or release were available.

2.1. Site selection

2.2. Methods for estimating weathering rates

2.3. Resolving the research questions

We found substantial variability in BC weathering and release rates estimated using different methods at individual locations (figure 1). The differences in BC weathering and release rates between log₁₀(Max) and log₁₀(Min) at each site had a minimum of 0.055 and a maximum of 1.7 with a median value of 0.77. This equates to a median difference of ∼600% between maximum and minimum estimated weathering rates. Approximately 34% of the sites had maximum estimates exceeding the minimum weathering rate estimates by more than 10 times. Clearly, this large variation illustrates that without a well-defined set of criteria for choosing a method of estimating weathering rates, a high degree of uncertainty will result. There was no relationship between number of rate estimates reported at individual sites and variability in the estimate. Approximately 44% of the weathering rates were between 0.6 and 1.8 times the mean value for a site; an additional 34% were between either 0.2–0.6 or 1.8–5 times the site mean.

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Estimated sources of uncertainty contributing to overall variability of BC weathering rate estimates were quantified and partitioned into individual sources. The relative magnitude of different sources of uncertainty increased as follows: structural uncertainty (including depth of the weathering zone)  <  parameter uncertainty  <  input data uncertainty (table 1). The contribution of data uncertainty to overall variability in BC weathering and release rates was high (69–135 times) when laboratory data were used (data, overall in table 1). Similar estimates of the effect of using different data sets from the same site on prediction ranges were reported to give 8–9 times difference in estimated weathering rates (data, non-laboratory in table 1). The estimated contribution of model parameter uncertainty to overall variability related to PROFILE and MAGIC were relatively small ranging from 1.7 to 2.1 for the two models, respectively. For PMB, the parameter uncertainty resulted in a range in the weathering estimate of 8.6 times. Although an inter-comparison of uncertainties in model parameters between different studies should be avoided, the results indicate that model parameter values are an important source of uncertainty. The estimated contribution of structural uncertainty relating to the depth of the weathering zone indicated a 2X difference in BC weathering and release rates, where rates doubled as deeper soil depths were used (table 1).

To determine whether or not different methods ranked sites congruently from high to low weathering rates within a region, we assembled data from the seven most extensive studied sites, each including up to eight weathering methods at numerous sites (table 2). A two-way rank ANOVA was performed to test whether or not different estimation methods ranked weathering rates congruently across sites. In five of seven studies where different weathering rate estimation methods were applied to a series of sites, a similar rank ordering of weathering rates was observed (table 2).

Precision in weathering rate estimates could be increased substantially as the number of members in an ensemble of weathering rate estimates increase, suggested by the outcome of our Monte Carlo simulation (figure 2). A single weathering rate estimate was estimated to be within a factor of 3 (i.e. between 33% and 300%) of the best estimate  < 80% of the time. An ensemble of three estimates was calculated to be within a factor of 2 approximately 80% of the time, while ten estimates were calculated to be within a factor of 1.5 approximately 80% of the time.

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PROFILE-estimated weathering rates and MAGIC-simulated BC release rates were available for 30 sites (figure 3). A paired t-test comparing log₁₀ estimated weathering rates for the two models showed on average log₁₀ MAGIC estimates rates were on average 0.35 (2.2 times) higher than log₁₀ PROFILE estimates (t = 4.76, p ≤ 0.01, SE = 0.074, lower₉₅ = 0.2, upper₉₅ = 0.5).

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This synthesis indicates that there is a significant difference between methods estimating silicate weathering rates (figure 1), supporting previously raised concerns about the usefulness of using data derived from single methods as a basis for land management decisions (Hodson and Langan 1999, Langan et al 2001, Skeffington 2006, McDonnell et al 2010). However, the differences between methods can to a large extent be identified and attributed in an increasing order of relevance to structural uncertainties (including depth of the weathering zone)  <  parameter uncertainty  <  input data uncertainty. In other words, while assumptions about key processes and the manner in which BC are released contributes to total uncertainty as part of a structural component, greater uncertainties are associated with the assumptions made about data and parameter values to use when estimating weathering rates. We highlight this finding and suggest that, in contrast to previous suggestions (Klaminder et al 2011b), the largest source of uncertainty can be related to input data and not to different conceptual understanding of the weathering process. This conclusion is especially problematic when attempting to up-scale point scale measurements using individual or a few soil samples to model weathering and BC release rates for an entire catchment or even region.

Despite large discrepancies in absolute values of weathering rates estimated by different methods, most rank relative weathering rates between sites in a similar way, which is very encouraging (table 2). In other words, if the main goal is to identify sites with relatively low or alternatively relatively high weathering rates, then single estimates from any of the reviewed methods will be informative. The two models which have been most widely used to make assessments of weathering rates for environmental decision making are MAGIC (Cosby et al 2001) and PROFILE (Sverdrup and Warfvinge 1993). These two models represent the landscape in different ways. PROFILE provides estimates for a shallow one-dimensional soil pedon whereas MAGIC integrates weathering processes for the whole catchment including deep soil weathering. Therefore, lower weathering rate estimates are expected from PROFILE in comparison to MAGIC, considering that deep soil weathering could constitute an important source of BC in catchment weathering (Klaminder et al 2011a), which is also the general resulting trend (figure 3). As indicated in our analysis of sources of differences between estimates of weathering rates (table 1), differences in the depth of the weathering zone are unlikely to be the main explanation for the discrepancy but rather uncertainties in the input data. However, it is very encouraging that PROFILE (pedon based) and MAGIC (watershed based) rank site BC weathering rates similarly, considering their frequent use.

The large ranges in weathering rates reported by different studies at a given site are commonly the result of estimates made using the mass-balance method. This is not surprising given the age of most of the soils in the studies and the difficulties in sampling the deepest horizon. For example, Duan et al (2002) highlight the important role of secondary minerals in old soils since the formation of secondary minerals may lead to erroneous weathering rate estimates when Ca and Mg are accumulated in B horizons. Other large observed ranges in our assembled data set are due to the occurrence of clays of undefined stoichiometry and their role in weathering (Kolka et al 1996, Langan et al 1996, van der Salm 2001).

One key finding from this work is that precision in weathering rate estimates increases as the number of members in an ensemble of weathering rate estimates increases (figure 2). A single weathering rate estimate will be within a factor of 3 (i.e. between 33% and 300%) of the best estimate  < 80% of the time. An ensemble of three estimates will be within a factor of 2 approximately 80% of the time, while ten estimates be within a factor of 1.5 approximately 80% of the time. This suggests that single estimates of weathering rates must be interpreted with extreme caution. Ensembles of three estimates may provide a minimum acceptable level of precision but likely still not sufficiently precise to support management decision making.

Many well established decisions about environmental management rely on precise and accurate silicate mineral weathering rate estimates. In both Europe and North America, estimates of acceptable levels of acid deposition and forest management recommendations have all been based on single model results of BC weathering rates using a critical loads concept (Akselsson et al 2007, Menz and Seip 2004). The credibility of these calculations has been questioned due to uncertainty in estimated weathering rates (Hodson and Langan 1999, Langan et al 2001, Skeffington 2006, McDonnell et al 2010). While there are substantial differences between weathering estimates at a given site (figure 1), the credibility of estimates would be significantly improved if ensembles (n ≥ 3) of weathering rates were used in critical load calculations. Decreasing uncertainty of input data would further improve calculations of critical loads (table 1).

Uncertainties in silicate mineral weathering rates were likely less of a problem for policymakers during the 1980s. Despite the substantial uncertainty in estimates of both acid deposition and weathering rates, it was clear that the effects of the large amount of acid deposition in many regions could not be offset by the relatively small, albeit uncertain weathering rate. This was clearly manifested by negative environmental impacts of acid deposition on soils and surface waters across large regions of northern Europe and northeastern North America. With present deposition load, which has decreased dramatically in recent decades (Skjelkvåle et al 2005, Fowler et al 2007), forest uptake is currently the dominant BC sink in many regions (Akselsson et al 2007). The importance of this sink will probably be enhanced by shorter rotation times for forest harvesting that are to be expected in a future warmer and wetter climate (Laudon et al 2011). With a greater pressure on forests as an alternative to fossil fuels, new management strategies including whole-tree harvesting (all above-stump tree biomass) and full-tree harvesting (all tree biomass including the stump) as well as an increased use of fertilizers and genetically improved seedling stocks are being implemented. All of these strategies have the potential to cause BC removal from forest soils faster than they can be replaced through mineral weathering. The external pressure on BC sustainability of forest soils and surface waters will shift from being a regional problem caused by long-range atmospheric transport of air pollution to a more local issue caused by excessive forest harvesting. This paradigm shift in the causality of BC depletion underscores the need for scientifically sound forest management guidelines and hence weathering rate estimates. Whereas environmental managers during the acid deposition era merely could observe, or at best stop the symptoms of soil and water acidification, the likelihood of unacceptable levels of BC depletion can be minimized by avoiding intensive forestry practices in the most sensitive areas. Here, all reviewed methods can play an important role in identifying these sensitive areas. However, in order to reach these goals better measures of weathering rate are greatly needed as uncertainties associated with currently used methods are unacceptably large.

Using an ensemble approach which includes multiple estimates of BC weathering and release rates at a single location using multiple independent estimation methods is the only credible way forward with present modeling tools for making decisions related to BC cycling and environmental sustainability. Estimates should be classified according to their scale (pedon versus catchment based), soil age (importance of secondary minerals for weathering) and the role of clays in general (mineral stoichiometry). Ensembles of BC weathering and release rate estimates produce more realistic results and provide some estimate of uncertainty. Only by using ensembles of comparable results (i.e. pedon or watershed based), can managers and decision makers produce credible quantitative estimate of local sensitivity to BC losses caused short and long term by changes in climate, air pollution and land use.

Management decisions made on the basis of single weathering rate estimates should be interpreted with a great deal of caution. There are large uncertainties associated with silicate mineral weathering rates. However, these uncertainties can be reduced through better input data, an improved appreciation of the conceptual differences between estimation methods and the use of ensembles of weathering rate estimates. Better input data based on more extensive field sampling will reduce uncertainty in weathering rate estimates The two most widely used models for management decision making, MAGIC and PROFILE, can give widely different weathering rate estimates, mainly due to differences in their conceptual approach. However, they can give similar rankings for weathering rates across sites. As precision increases with larger ensembles of weathering rate estimates, we recommend the use of three independent estimates to provide a minimum acceptable level of precision.

This research was funded by the MISTRA Future Forests program and the FORMAS ForWater strong research environment. We are grateful to D Kothawala, S Löfgren and anonymous reviewers for comments which improved the manuscript.