Dynamic modelling of weathering rates – Is there any benefit over steady-state modelling ?

Weathering rates are of considerable importance in estimating the acidification sensitivity and recovery capacity of soil, and are thus important in the assessment of the sustainability of forestry in a time of changing climate and growing demands for forestry products. In this study, we modelled rates of weathering in mineral soil at two forested sites in southern Sweden included in the SWETHRO monitoring network using two models. The aims were to determine whether the 10 dynamic model ForSAFE gives comparable weathering rates as the steady-state model PROFILE, and whether the ForSAFE model provided useful extra information on weathering behaviour. The average weathering rates calculated with ForSAFE were very similar to those calculated with PROFILE for the two modelled sites. The differences between the models regarding the weathering of certain soil layers seemed to be due mainly to differences in calculated soil moisture. The weathering rates provided by ForSAFE vary seasonally with temperature and 15 soil moisture, as well as on longer time scales, depending on environmental changes. Long-term variations due to environmental changes can be seen in the ForSAFE results, for example: the weathering of silicate minerals is suppressed under acidified conditions due to elevated aluminium concentration in the soil, whereas the weathering of apatite is accelerated by acidification. The weathering of both silicates and apatite is predicted to be enhanced by increasing temperature during the 21st century. In this part of southern Sweden, precipitation is assumed to be similar to today’s level 20 during the next forest rotation. However, in parts of Sweden with projected decreasing soil moisture, weathering might not increase despite increasing temperature. These results show that the dynamic ForSAFE model can be used for weathering rate calculations and that it gives average results comparable to those from the PROFILE model. However, dynamic modelling provides extra information on the variation in weathering rates with time, and offers much better possibilities for scenario modelling. 25

Comment: "Furthermore, the dynamic ForSAFE model, by definition is bound to provide more detailed and seasonal results 10 and information, making the answers to the question posed by the title and to the hypotheses some-what self-evident."

Answer:
We have changed the title to "Dynamic modelling of weathering ratesthe benefit over steady-state modelling" (P1L2), as suggested by the second reviewer. We have also added a bit to the second objective (P2L31-32): "…scenarios, representing important ecological issues: acidification, climate change and nutrient removal through land use.", since a large part of the paper describes the weathering response to environmental drivers (i.e. describes in detail some benefits that 15 can be gained by dynamic modelling). By doing those changes, the title and the second objective fits better to what we actually do in the paper -describing the benefits and the dynamics in weathering. For example, we show that even though ForSAFE weathering rates vary a lot, averages over the same period represented in the PROFILE modelling, fall so close to PROFILE values, which gives credit to the ForSAFE weathering. We didn´t know this before we performed the study.
Comment: "I think the paper could be substantially improved if there were more focus on and calibration of the ForSAFE 20 model with empirical field data; for example, with measured soil temperature, soil moisture, forest growth (base cation uptake) and leaching data." Answer: ForSAFE is not calibrated with empirical field data except base saturation and soil carbon and nitrogen. Other data can be used for comparisons with model results. Unfortunately we don't have measurements of soil moisture or soil temperature for these sites. Since soil moisture and temperature are very important parameters, a very good next step would 25 be to compare ForSAFE modelled soil moisture and soil temperature to measured data, but that is outside the scope of this paper, as that would have to be on other sites. We include this suggestion in the discussion (P9L28-30) as a suggested future study. There are measured forest growth and soil water concentrations for these sites, but there are already papers comparing ForSAFE modelled values with these kinds of measurements (Yu et

SPECIFIC COMMENTS
Comment : "p. 1, l. 20 (and p. 4, l. 31). Annual precipitation may remain similar but what about the seasonal distribution?
How will temperature change affect snowfall and snowmelt, surely a very important feature of climate change in such latitudes, the water cycle and weathering?" Answer: In this part of Sweden, there is already very little snow. Otherwise is would probably be an important feature. The 5 seasonal distribution of precipitation does change in this scenario, with less precipitation in summer in the second half of the century. The last decades the yearly precipitation increases somewhat too, about 8%.We corrected the text in the abstract with regards to seasonal distribution of precipitation and did the same in the chapter about scenarios (2.4) and in the discussion l. 19 (and p. 8,l.11). Why/how are base cations, Al3+ and organic acids inhibitors of weathering? Do you 10 mean that if the concentrations of weathering products in the soil solution increase, the weathering reaction slows down as equilibrium concentrations are reached? But then aren't the weathering products being continually take away through up take, leaching or adsorption by the soil allowing weathering to proceed?" Comment: "p. 5, l.16. Furthermore, thickness of the mineral soil horizons at Hissmossa is 55 cm (and not 50 cm; Table 2) and how/why is the organic layer included where surely it is a question of organic matter decomposition rather than mineral weathering? It is not stated how stoniness was derived and if the hydraulic parameter values (Table 3) have been corrected for stone content. Given the concluded importance of soil moisture, the fixed value used in PROFILE and same value for all 30 layers (0.2) seems rather crude. The field capacity values in Table 3 also seem somewhat lowis this because of stone content correction? How have any time related changes in organic layer thickness (and therefore soil moisture content) been taken into account?" Answer: The modelled soil horizon at Hissmossa is 55 cm+organic layer, but the root zone is still 50 cm+organic layer. We included the C-horizon in the modelling, even though it lies below the root zone, but we did not include it in calculations representing the weathering in the root zone. We clarified this in the text to figure 1. The organic layers do contain some 5 mineral soil and the modelled weathering in those layers is from the minerals, not from the organic matter. They are included in the modelling since they are important for the modelled ecosystem and thus for the soil water chemistry for the rest of the layersfor example much of the nutrient uptake takes place here, especially of nitrogen. Stoniness is estimated at the soil sampling. We added this in chapter 2. 3 (P4L22-26 figure 2). The field capacity values are calculated according to Balland (2008). Dynamic changes in layer thicknesses are not modelled by any of the models.
Comment: "P. 4, l. 31: by "rainfall" you mean annual precipitation?" Answer: Yes, thanks. I have changed the text (P5L5). 15 Comment: "p. 5, l. 6-11. The description of the scenarios is unclear, at least to me. For example, does the base scenario mean there are two thinnings and a clear cut every 70 years (and starting from the year of planting - Table 1), deposition loads constant from "todays" (which year?) levels into the future plus climate change temperature (but no change in precipitation)? What is the whole tree harvesting treatment: stems + branches or stems + branches + stumps? Is it carried out every 70 years during the 1900-2100 period? It would be useful to number or letter the scenarios and refer to them in the text 20 and, tables and figures."

Answer:
We have given the scenarios three letter abbreviations and use those throughout the text and figures, as suggested.
We have clarified the scenario descriptions, both the description of the base scenario (BSC) and how the others differ from the BSC scenario (P4L31-P5L20). Yes, the BSC has forestry with a clear cut approximately every 70 years (Västra Torup: 1940, 2010, 2080. Hissmossa: 1972, 2040, 2100 and thinnings at about 25  changes less and without trend, but summer precipitation is lower in 2050-2100 than before and winter and spring precipitation is higher. Whole tree harvest is, in the WTH scenario of this study, stems and 60% of branches, treetops and needles, but stumps are not removed. Whole tree harvest in the WTH scenario is carried out in thinning and clear cutting from the clear cutting in 2010 (Västra Torup) or 2040 (Hissmossa) and forward.
Comment: "Which scenario is used for Figure 1?" Answer: Base scenario (BSC). We gave the scenarios abbreviations and clarified in the running text and in the figure texts which scenario was used. 5 Comment: "Doesn't the 70 year rotation period cover a different set of years between the two sites (20112080 vs. 2041-2100), when the climate change has changed the climate. Doesn't this explain the differences in weathering between the two sites rather than differences in soil texture (p. 5, l. 21), which anyway would also affect the soil hydraulic properties besides Hissmossa would have had the higher weathering rates and not the lower. Also, the difference between the sites exist also in 15 the scenarios with no climate change (NCC and BGR). See also P6L2-5. According to our calculations of soil hydraulic properties following Balland (2008), field capacity is slightly lower in Hissmossa than in Västra Torup, which means that soil moisture also is slightly lower, which should affect the weathering rates as calculated by ForSAFE, but not those calculated by PROFILE, since we used the same soil moisture value for both sites in PROFILE. And the differences in weathering rates between the sites are as large in the PROFILE calculations as in the ForSAFE ones (see figure 1). 20 Comment: "As weathering largely takes place by acid (proton) attack, why is silicate weathering decreased by acidified Answer: Apatite weathering is increased by more acid conditions because there are more protons in solution, and not at the same time high concentrations of something that inhibits weathering. Silicate weathering was not increased by the more acid conditions on those two sites, according to ForSAFE. Those two sites had high concentration of Al in soil solution during the acidified conditions, as Al is more soluble in acid conditions, and Al inhibits weathering of silicates in ForSAFE, but not of apatite since there is no Al in apatite. We added a little text in the discussion (P9L11-12) to clarify this. 5 Comment: "Doesn't the base scenario include harvesting effects besides climate change effects (p. 6, l. 29)? See also p. 8, l.

21-24. "
Answer: Yes, but so does the NCC scenario. Forestry and acidification are equal in the NCC and the BSC scenario. Only climate differs. We clarified the scenario descriptions a bit (chapter 2.4).
Comment: "p. 7. l. 19: by "more detailed forestry plans" do you mean timing of thinning and timing and intensity of 10 harvesting?" Answer: . And with additional soil data, at least on soil texture, differences within a stand or a couple of nearby stands could also be modelled, so that more sensitive areas within the stand could get a less intensive forestry.  Piirainen et al. (2004). After 20 whole tree harvesting, where branches and treetops, with most of the needles, are removed, there will be less decomposable litter on the site, which should mean that concentrations in soil water do not increase as much after WTH as after stem only harvest (as discussed in Ågren et al., 2010). The concentrations in the soil water in its turn affect the weathering rates. See

P8L31-P9L2.
Comment: "p. 8. L. 25-. The contribution of your C-horizon is small (Table 2). And if the material is less weathered, then 25 there would be more weatherable minerals and therefore potential or weathering? Is the explanation for taking silica concentrations into account the same as mentioned above, i.e. equilibrium concentrations reached? " Answer: The contribution of the C-horizon is small because we only model a small portion of it. But the rates of weathering per volume in the C-horizon are equivalent to the rates in the horizons above, in the modelling. The material in the Chorizon is less weathered since the weathering in the C-horizon is smaller than in the B-horizon, even though there is more and not be a C horizon), probably because of slow water movements, so that some reactants are depleted and some products of the weathering build up and inhibit further weathering. And Si is one of the products that are building up, one that we do not model with ForSAFE and PROFILE yet. We added a little text in the discussion to clarify this, P9L33-P10L4, P10L16-
Comment: "Conclusions: I appreciate the recognition of the importance of soil moisture to weathering (and decomposition) and for the reasons stated (time step). However, wouldn't a model with a daily time step be more suited to forest stand nutrient/biogeochemical cycling studies rather than modelling long-term climate change effects. " Answer: A daily time step is more suited for modelling of hydrology, which in its turn affects all other processes both on 10 short term and possibly also their long term averages. The effects on long term averages might be large, if average soil moisture is affected significantly or if the dynamic shows that the timing of different processes produce for example lack of soil moisture at high temperatures or lack of nutrients when vegetation needs them. In any case, studying if the daily time step that has been implemented in another version of ForSAFE has an impact seems like a reasonable next step. We clarified the text on model development (4.3) somewhat (P9L24). 15 Comment: "Units: Wouldn't it be more correct to present weathering in units of moles charge rather than equivalents? And why sometimes meq m-2 yr-1 and sometimes meq m-3 y-1 (Fig. 2, 3,4,5). Is it somehow because the latter refer to a specific layer (of differing thicknesses) rather than to the fixed organic layer + 50 cm layer or simply a typo? " Answer: To our understanding, moles of charge and equivalents are equivalent in this case. We used weathering per area in figure 1 to make it easy to sum up the weathering from the different layers, even though they have different thicknesses, and 20 to show how much each layer contributes to the total weathering. But since the layers have different thicknesses, the total weathering per forest floor area for a layer is not as easily comparable to other soils in other studies as weathering per soil volume, and therefore we converted the weathering rates into meq m-3 y-1 for the text and the rest of the figures. We clarified the use of different unit in figure 1 in the caption to figure 1. Table 1. Coordinates are decimal degree latitude (N) and longitude (E). 25 Answer: Yes, thank you. We added unit in the table. 25 difference in weathering in the two models. This can be more easily seen now when the soil moisture is shown in a new figure 2. In Västra Torup the differences between soil moisture in the two models are small, except in the organic layer, and differences between weathering rates between the two models are also small, except in the organic layer. There are other differences between the models that affect the difference in weathering rates too, but soil moisture has a large role. See Comment: "P9L15-L19. These are not surprising conclusions (and more-or-less were previously known)."  Abstract. Weathering rates are of considerable importance in estimating the acidification sensitivity and recovery capacity of soil, and are thus important in the assessment of the sustainability of forestry in a time of changing climate and growing demands for forestry products. In this study, we modelled rates of weathering in mineral soil at two forested sites in southern Sweden included in a monitoring network, using two models. The aims were to determine whether the dynamic model 10 ForSAFE gives comparable weathering rates as the steady-state model PROFILE, and whether the ForSAFE model provided believable and useful extra information on the response of weathering to changes in acidification load, climate change and land use.
The average weathering rates calculated with ForSAFE were very similar to those calculated with PROFILE for the two modelled sites. The differences between the models regarding the weathering of certain soil layers seemed to be due mainly 15 to differences in calculated soil moisture. The weathering rates provided by ForSAFE vary seasonally with temperature and soil moisture, as well as on longer time scales, depending on environmental changes. Long-term variations due to environmental changes can be seen in the ForSAFE results, for example: the weathering of silicate minerals is suppressed under acidified conditions due to elevated aluminium concentration in the soil, whereas the weathering of apatite is accelerated by acidification. The weathering of both silicates and apatite is predicted to be enhanced by increasing 20 temperature during the 21st century. In this part of southern Sweden, yearly precipitation is assumed to be similar to today's level during the next forest rotation, but with more precipitation in winter and spring and less in summer, which leads to somewhat drier soils in summer, but still increased weathering. In parts of Sweden with bigger projected decrease in soil moisture, weathering might not increase despite increasing temperature.
These results show that the dynamic ForSAFE model can be used for weathering rate calculations and that it gives average 25 results comparable to those from the PROFILE model. However, dynamic modelling provides extra information on the variation in weathering rates with time, and offers much better possibilities for scenario modelling.

Introduction
Most parts of Sweden are covered with glacial till, composed largely of slowly weathering minerals of granitic origin, the type of rugged landscape with mostly very shallow soil depth described in Krabbendam and Bradwell (2014). This makes both soils and lakes sensitive to acidification. Two thirds of Sweden is covered by boreal and northern temperate forests, mostly consisting of Norway spruce and Scots pine, together with birch and a few other deciduous trees. Forests are one of Sweden's most important natural resources, and are used for timber (32 million m 3 y -1 in 2013, Christiansen, 2014), pulp wood (31 million m 3 y -1 in 2013) and biomass for energy production (6 million m 3 y -1 in 2013). The last is especially important due to the need to replace fossil fuels with renewable sources of energy (Chu and Majumdar, 2012). Forests and 5 their soil also determine the water quality of most lakes and streams, since the catchments of most lakes are forested and surface water is filtered through forest soils.
During the 1960s, lakes in Scandinavia became increasingly acidified (Odén, 1968). The cause of this was found to be air pollution in the form of atmospheric sulphur and nitrogen (Overrein, 1972), much of it from fossil fuel combustion. The regions most severely affected were those with high deposition of acidifying substances on shallow soils containing base 10 cation poor minerals with low weathering rates and release of base cations (i.e. calcium, magnesium, potassium and sodium) (Galloway et al., 1983). In 1979, the Convention on Long-Range Transboundary Air Pollution (CLRTAP) was formulated by the United Nations Economic Commission for Europe (UNECE). CLRTAP was extended by the addition of several protocols for the mitigation of air pollutants, where participating countries were urged to submit data on emissions of pollutants and ecosystem sensitivity. A need thus emerged for ways of assessing ecosystem sensitivity, and different 15 methods of estimating critical loads of acidity for sulphur and nitrogen for forest and lake ecosystems were developed . One of these was the PROFILE model, developed by researchers at Lund University during the 1990s (Sverdrup and Warfvinge, 1993;Sverdrup et al., 2005). CLRTAP led to a considerable reduction in the emission of acidifying pollution, and lakes and soils in large parts of acidified areas in Europe slowly started to recover (Engardt et al., 2017;Garmo et al., 2014;Johnson et al., 2018). However, 20 acidifying pollution is still a large and increasing problem in some parts of the world, for example, Southeast Asia (Cho et al., 2016). Forestry is also a potentially acidifying practice, as buffering base cations are removed during harvest (Farley and Werritty, 1989;Akselsson et al., 2016;Zetterberg et al., 2013). Furthermore, as the demand for forest products is growing, while both climate conditions and atmospheric deposition are changing, there is an increasing need to evaluate the sensitivity of forest soils and the weathering of base cations in greater detail, as an aid in forestry planning and regulation. The dynamic 25 ecosystem model ForSAFE (Wallman et al., 2005;Belyazid et al., 2006), which consists of a dynamic development of the PROFILE model, together with models for tree growth and decomposition, has the potential to do this.
The aims of this study were: • to investigate whether ForSAFE gives comparable weathering rates to those estimated with the PROFILE model, and to explain the results based on differences in the formulation of the models, and 30 • to investigate the seasonal, inter-annual and decadal weathering dynamics provided by ForSAFE for different scenarios, representing important ecological issues: acidification, climate change and nutrient removal through land use.

Methods
The PROFILE and ForSAFE models were applied to two spruce forest sites in southernmost Sweden, Västra Torup and Hissmossa, included in the Swedish Throughfall Monitoring Network (SWETHRO) (Pihl Karlsson et al., 2011). Different scenarios for the input parameters were modelled with ForSAFE. ForSAFE-modelled weathering for the base scenario was averaged over the 21st century forest rotation and compared with PROFILE-modelled weathering. The weathering rates 5 from the different scenarios from the ForSAFE model were examined in detail.

PROFILE
The PROFILE model is a steady-state mechanistic biogeochemistry model, developed at Lund University in the 1990s (Sverdrup and Warfvinge, 1993;Warfvinge and Sverdrup, 1995). It has been widely used for calculations of critical loads of acidification, weathering as an aid to improving the sustainability of forestry in Europe (including Iceland with its very 10 different mineralogy), North America and East Asia, and has even been applied to agricultural land Erlandsson et al., 2016;Phelan et al., 2014;Fumoto et al., 2001;Holmqvist et al., 2003;Stendahl et al., 2013). The ecosystem in PROFILE is represented by a soil profile divided into layers, each with its own chemical and physical properties, to which water, nutrients and pollutants are added via atmospheric deposition and litterfall from trees, and from which water, nutrients and pollutants are removed via uptake by trees and downward leaching. Chemical equilibrium 15 reactions and weathering take place in the soil profile. Weathering is modelled using transition state theory, and the parameters affecting it are soil temperature, soil moisture, mineralogy, soil texture, expressed as the exposed mineral surface area, soil density, and the concentrations of H + , organic ligands and carbon dioxide, as well as the concentrations of inhibitors: base cations (Ca, Mg, K and Na), Al 3+ (products of the weathering reaction) and organic acids.

ForSAFE 20
The ForSAFE model consists of a dynamic development, SAFE, of the PROFILE model (Alveteg et al., 1995;Martinsson et al., 2005), together with the DECOMP model of the decomposition of soil organic matter (Wallman et al., 2006;Walse et al., 1998), the PnET model of tree growth (Aber and Federer, 1992) and the hydrological PULSE model (Lindström and Gardelin, 1992). ForSAFE was developed to better model the process of recovery from acidification and the effects on ecosystems of forestry and climate change, with dynamic feedbacks between soil chemistry and forest growth. Many 25 parameters used as input data in the PROFILE model are modelled by the ForSAFE model. These include runoff, soil moisture, decomposition of litter and the uptake of nutrients by trees. The model is being continuously developed (Belyazid et al., 2011;Phelan et al., 2016;Zanchi et al., 2014;Yu et al., 2016;Rizzetto et al., 2016;Gaudio et al., 2015). In this study, a ForSAFE version with monthly time steps was used.

Site descriptions
The characteristics of the two SWETHRO sites, at Västra Torup and Hissmossa, are presented in Table 1 and Table 2. SWETHRO is a Swedish network started in the 1980's to monitor deposition of acidifying substances to Swedish managed forest and how the forest and forest soil is affected by the deposition. Each site consists of a 30 m x 30 m square plot in a forest stand, where throughfall deposition is measured every month, and soil water chemistry parameters are measured with 5 lysimeters at a depth of 50 cm three times per year; at Västra Torup since 1996, and at Hissmossa since 2010. Open field deposition is measured near the stands. Soil chemistry, texture and other properties as well as forest parameters have been measured previously (Tables 1 and 2). Västra Torup has previously been modelled by Belyazid et al. (2006) with an earlier version of the ForSAFE model, using less detailed input data. Zanchi et al. (2014) have also modelled this site using the same version of ForSAFE as in the present 10 study, as well as most of the input data, with the aim of describing changes in forest ecosystem services in a changing climate.
The forest at Västra Torup was clear cut in 2010, and the site at Hissmossa, 5 km to the north, was introduced into SWETHRO as a replacement site. Hissmossa has previously been modelled with ForSAFE, with the aim of explaining why this site shows continuously elevated concentrations of nitrate in soil water, while Västra Torup did not, prior to clear cutting 15 (Olofsson et al., manuscript). Hissmossa has courser, very sandy soil. Both soils are high in quartz and feldspars. Both sites are highly productive sites for Norway spruce, but was probably grazing lands up to the beginning of the 20 th century. The soils are assessed as transition types.
The soil parameters used in the modelling are given in Table 3. Values of the field capacity and wilting point were calculated using the equations given by Balland et al. (2008). Mineral content was calculated from total soil chemistry data using A2M, 20 a mathematical model that uses total chemistry of the soil samples to come up with possible mineral compositions (Posch and Kurz, 2007). For the uppermost, organic layers, mineralogy and texture from the second layers were used, since there are no texture analyses for the organic layers and the total chemistry analyses of the organic layers include the ash of the organic matter. The soil moisture input value for PROFILE is an estimated site specific value based on observations at the sites. In this case the soil moisture value is equal at both sites: 0.2 m 3 soil water volume m -3 soil volume for all layers. The fraction of stones in 25 the soils is also estimated at the time of the soil sampling.

Scenarios and time series of driver parameters
ForSAFE uses time series of climate parameters, forest management and the deposition of atmospheric pollutants and base cations to the site. A set of these time series, from 1900 to 2100, is here called a scenario. The purpose of the different scenarios used in this study is to investigate how ForSAFE-modelled weathering rates responded to changes in the driving 30 parameters. Thus, the scenarios used consist of a base scenario (BSC), four scenarios in which one aspect of the environment differs from the BSC scenario and a background scenario (BGR) without forestry, acidification and climate change.
The BSC scenario represents the actual drivers at the sites from 1900 to today, followed by a reasonably realistic future to the year 2100 with regards to forestry management, climate and deposition. This scenario has been used by Zanchi et al. (2014), and Olofsson et al. (manuscript). The future climate is based on a high-CO 2 emission scenario (SRESA2, modelled with ECHAM5: Nakićenović et al., 2000;Roeckner et al., 2006), with an approximately exponentially increasing temperature during the 21st century. Annual precipitation is almost unaffected by the climate change in this scenario for this 5 part of Sweden up to 2080, after which it increases, but only by about 8%. The distribution of precipitation during the year changes after 2050, with more precipitation during winter and spring and less during summer. Past and future forest management of the sites in the BSC scenario is based on normal, but not intensively, managed forestry in Sweden today, with two thinnings (at approximately 30 and 45 years after planting) and clear cuttings approximately every 70 years, where only stem wood is removed. The deposition of pollutants and base cations is based on data from the EMEP programme 10 (Simpson et al., 2012), with SOx-deposition peaking in 1970 and decreasing sharply after that and nitrogen deposition peaking in 1985 with a smaller decrease after that. Future deposition is assumed to be constant after 2020.
Five scenarios were compared with the BSC scenario, where climate, deposition or forest management were changed (for the whole or part of the period 1900 -2100), while the other input parameters were as in the BSC scenario. The scenarios were: • BSC: Base scenario, described above. 15 • NFO: No forestry: no thinning or clear cutting between 1900 and 2100. Deposition and climate change as in BSC.
• WTH: Whole-tree harvest at clear cutting and thinning from 2010. Deposition and climate change as in BSC.
• NAC: No acidification: no increase in acidifying deposition after 1900. Forestry and climate change as in BSC.
• NCC: No climate change: no increase in temperature between 1900 and 2100. Forestry and deposition as in BSC.
• BGR: Background: no clear cutting or thinning, no increase in acidifying deposition and no climate change. 20

Weathering rates from PROFILE and ForSAFE
The total weathering rates obtained with ForSAFE with the BSC scenario, averaged over a forest rotation, were similar to the weathering rates obtained with PROFILE for all soil layers and modelled elements, and almost equal for many of them ( Figure 1). At Västra Torup, the total annual weathering rate of the base cations (Ca, Mg, K and Na) in the root zone 25 (organic layer plus the 50 uppermost cm of the mineral soil, L1-L5) was 115 meq m -3 y -1 on average, according to ForSAFE (varying for different months between 51 meq m -3 y -1 and 260 meq m -3 y -1 ), and 106 meq m -3 y -1 according to PROFILE. At Hissmossa, the total weathering rate of base cations in the root zone (L1-L4) estimated with ForSAFE was 38 meq m -3 y -1 (varying from 16 meq m -3 y -1 to 86 meq m -3 y -1 ) and 45 meq m -3 y -1 according to PROFILE.
The estimated weathering rate of base cations is lower at Hissmossa than that at Västra Torup according to both models. This 30 is due to the coarser soil texture at Hissmossa, leading to a significantly lower exposed mineral surface area. Also, according to field measurements, Hissmossa has a more acid soil solution than Västra Torup, with twice the concentration of inorganic aluminium at Västra Torup. Dissolved inorganic aluminium, a product of the weathering of silicate minerals, inhibits the weathering of silicate minerals. The rotation periods at Västra Torup and Hissmossa are not the same, so average rates for the forest rotation are not directly comparable since climate changes during the period. The differences in weathering rates between the sites are much larger than the changes in rates because of climate change in the two to three decades differing in rotation period. 5 Differences in the weathering rates predicted by the two models are greater for soil layers where the differences between the values of soil moisture are higher between the two models (Figure 2), i.e. in the organic layers (where weathering is very small, due to very small mineral mass) and in L4 in Hissmossa. The input value for PROFILE was 0.2 m 3 soil water volume m -3 soil volume for all layers at both these sites. The soil moisture is dynamically modelled in ForSAFE, with average values close to the defined field capacity for the respective layers (Table 3). The average soil moisture at Västra Torup, for the forest 10 rotation 2011 -2080, was 0.18 -0.21 in the mineral layers and 0.29 in the thin organic upper layer. In the sandy soil at Hissmossa the average soil moisture in ForSAFE (for the forest rotation 2041 -2100) was 0.13 -0.18 in the mineral soil layers and 0.4 in the organic soil layer. The difference between the value of soil moisture used in PROFILE and that calculated by ForSAFE is thus greater at Hissmossa, and the differences in weathering rates between the two models are thus also greater at Hissmossa than at Västra Torup. 15

Seasonal, yearly and decadal variation in weathering rates from ForSAFE
The weathering rates obtained with ForSAFE vary seasonally with temperature and soil moisture, as well as on longer time scales, depending, for example, on forest stage, the acidification status of the soil and the climate (Figure 3). On the seasonal scale, weathering is lowest in winter and highest in the warmest period of summer, unless the soil is too dry. Weathering rates during the warmest month of the year are typically 3 to 4 times higher than during the coldest month, except for Ca and 20 P, where weathering in the warmest month is 5 to 8 times higher than in the coldest month. On longer time scales, the yearly average weathering rates can vary by a factor of two during a forest rotation.

Effect of forestry on weathering
Thinning and clear cutting at Västra Torup increased the weathering of base cations by 9 % in the future forest rotation (2011 -2080) in the BSC scenario, compared to the NFO scenario with no clear cutting or thinning (Figure 4). Whole-tree 25 harvesting in the WTH scenario increased the weathering by a further one percent. At Hissmossa the increase in weathering between the NFO scenario and the BSC scenario was 14 % for the forest rotation between 2041 and 2100, with a further increase of 2 % for the WTH scenario. The difference in weathering between scenarios occurs during the first half of the forest rotation.

Effect of acidification on weathering
In ForSAFE, the weathering of silicate minerals is decreased by the acidified conditions in the soils during the second half of the 20th century in the BSC scenario, whereas the weathering of the only P-containing mineral, apatite, is enhanced ( Figure   5). The effect of acidification on weathering is smaller than the effects of temperature and soil moisture. For the forest rotation 1941 -2010 in Västra Torup, the weathering of base cations was 11 % lower in the BSC scenario than in the non-5 acidification NAC scenario, while the P weathering was 11 % higher. At Hissmossa, for the forest rotation 1973 -2040 (i.e., mostly after the most acidified period), the weathering of base cations was 6 % lower and the weathering of P 17 % higher in the BSC scenario than in the NAC scenario.

Effect of climate change on weathering
Temperature has a considerable effect on weathering rates. In the BSC scenario, the yearly average temperature increased 10 from 7˚C in the 1990s to 11˚C in the 2090s. This leads to an increase in ForSAFE weathering rates of the base cations of 7 % per degree increase in temperature. The increase in temperature is greatest in winter (6˚C difference between 1900 -1930 and 2080 -2100) and smallest in summer (4˚C difference between 1900 -1930 and 2080 -2100). In Hissmossa, the weathering rates of Ca in L4 are 44 % to 49 % higher in 2080 -2100 in the BSC scenario than in the constant climate scenario, NCC, for all seasons (Figure 6). 15

Overall effect of forestry, acidification and climate change
The overall effect of human practices on weathering rates, as in the BSC scenario: forestry, historical acidification and climate change, is positive, compared to the background scenario, BGR. Climate change and forestry have a positive effect on silicate weathering, while acidification has a negative effect, but not of such a magnitude that it cancels out the first two.
For apatite weathering, the combined effect of climate change, forestry and decreasing acidification is an increase of the 20 weathering in the future, especially for newly planted forest. The weathering-enhancing effect of forestry is also seen in the first part of a forest rotation for silicate weathering, whereas an aging forest has slightly decreasing weathering rates.
Increasing temperatures combined with the forestry induced weathering dynamic with higher weathering in young forest, produces a step-like increase in weathering rates of silicates in the BSC scenario (Figure 7).

Implications of model differences
The weathering calculations in PROFILE and ForSAFE are based on the same equations, but in ForSAFE they are dynamic, while PROFILE has no time dimension. The models also differ in that several processes are only given as input data into PROFILE while they are modelled dynamically with ForSAFE and that feedbacks between these processes affect the system in ForSAFE. In the PROFILE model, lack of nutrients because of low weathering can never affect tree growth, since uptake of nutrients to trees are input data. Low soil moisture during summers can also never affect weathering rates in PROFILE, because there are neither seasons nor modelled soil moisture values. PROFILE was developed at a time when climate change was usually not considered, to answer the question of what long term loads of acidity the ecosystem could tolerate (under the premise of unchanging forestry and climate), and for this it was sufficient. As acidification loads decreased, the role of 5 forestry intensity for recovery from acidification increased (Iwald et al., 2013), A more complex model was needed and ForSAFE was developed, which include these processes and feedbacks. We have shown that despite their differences, the two models produce comparable estimates of weathering rates on these two sites.
The PROFILE model has often been used for critical load assessments and weathering estimates. This study shows that the more advanced model ForSAFE is as reliable as the PROFILE model and can be used to gain more information on the 10 variation in weathering rates due to forestry practices, climate changes and temperature change, which could increase our understanding of the dynamics of ecosystem sensitivity. General conclusions regarding acid sensitivity, critical loads and the sustainability of forestry would not change significantly, but our ability to make customised or more detailed forestry plans with regards to intensity of harvest or to take acidification countermeasures would be improved.

Weathering dynamics in a changing environment 15
Another parameter that has a significant influence on weathering rates is the temperature. The climate is becoming warmer, and in some regions in Sweden, as elsewhere, it is possibly also becoming drier in the summer (Kjellström et al., 2018).
Higher temperatures increase weathering, as shown in our simulations. However, drier conditions inhibit weathering, and dry periods in the summer, when weathering otherwise would be much higher than in the rest of the year, might affect the yearly weathering considerably. These two sites, although having lower soil moisture in the summer on average (Figure 2), does not 20 seem to experience really dry summers more often in these future scenarios than during the 20 th century, for the same forest stand age. Future studies, on regions that are believed to become much drier in summer in the future may help elucidate this. Akselsson et al. (2016) calculated the increase in weathering rate due to climate change in the 21st century in Sweden, using the PROFILE model. They found that the increase in weathering rates due to temperature increase up to 2050 varied at different locations in Sweden. The median increase in base cation weathering rate was 20 % for the ECHAM projection and 25 33 % for the HADLEY projection, which are both equivalent to about 10 % ˚C -1 . This is slightly higher than our result of a 7 % increase per degree increase in temperature. The difference is due to the fact that ForSAFE is a more complex model, with dynamic feedbacks between the uptake by trees, soil solution chemistry, soil moisture and weathering.
Forestry also affects weathering. After clear cutting, both soil moisture and soil temperature increase, leading to an increase in weathering rate. As uptake of nutrients to trees are halted and as the remaining litter starts to decompose, concentrations of 30 base cations start to increase (Piirainen et al. 2004). Base cations in soil solution inhibit weathering of base cations in the model (like inorganic aluminium inhibit weathering of aluminium), but the increase in base cations is not sufficient to reduce the rate of weathering, since the soil moisture is still high. With whole-tree harvesting, much of the litter is removed, so that there are less base cations to be released to soil water through decomposing, and the concentrations of base cations should not increase as much as with stem only harvesting (Ågren et al. 2010). This might be the reason for the very slight increase in weathering following whole-tree harvesting compared to stem only harvesting, found in this study. If base cation concentrations do not increase as much after whole-tree harvesting as after stem only harvesting, this also leads to less leaching of base cations after whole-tree harvest than after stem only harvest. The slightly increased weathering rate and the 5 decreased leaching may explain the diminishing difference in soil conditions with time between whole-tree harvesting and stem harvesting that has been seen in field experiments, despite the fact that a large quantity of base cations is removed from the ecosystem by whole-tree harvesting (Zetterberg et al., 2013).
According to ForSAFE, the weathering of silicate minerals is considerably suppressed by the atmospheric deposition of acidifying substances, whereas the weathering of apatite (P and some of the Ca) was enhanced. The reason for this is the 10 combined effects of H + as a driver of weathering and Al 3+ as an inhibitor of silicate weathering, but not of apatite weathering, since apatite does not contain Al. The solubility of Al increases with lower pH, thus inhibiting the weathering of silicates as the soil acidifies.

Model limitations and development
The results of this study demonstrate the importance of soil moisture on weathering rates. In PROFILE the soil moisture is 15 an input, previously known from uncertainty studies to be of great importance for the weathering rates (Jönsson et al. 1995, Barkman andAlveteg, 2001), but often based on observation of the site and rough assumptions, whereas it is modelled in ForSAFE with soil texture, precipitation and temperature as inputs. For these two sites, average soil moisture modelled by ForSAFE is similar to the rough estimates of moisture used as input for PROFILE for most of the soil layers. The soil moisture modelled by ForSAFE is also close to the calculated field capacity most of the time. Average soil moisture being 20 close to field capacity could partly be an effect of the monthly time step, which evens out precipitation and gives enough time for draining of excess water each time step. A new version of ForSAFE with a daily time step is under development. A daily time step, with a more realistic time distribution of precipitation, with rainfall events and dry periods in between, affects the calculations of soil moisture on the short term, might affect the seasonal average soil moisture values and might thus affect the predicted weathering rates; giving a greater variability in weathering between drier and wetter periods and 25 potentially shifting the average. A shorter time step would potentially give more accurate results, given that soil moisture is an important parameter for weathering and soil moisture is highly variable on a shorter time scale than monthly.
In the SWETHRO sites, soil moisture and soil temperature are not measured and thus modelled soil moisture can't be compared to measured values. Another future study could model sites were such measurements are made and compare these, for the weathering important parameters, with measurements. 30 Both the PROFILE model and the ForSAFE model are known to overestimate weathering in the lower soil layers Zanchi, 2016). The soil horizon C consists of the less weathered parent material at the bottom of the soil profile, where weathering rates are low because the conditions in the soil inhibits weathering, despite the relative abundance of weatherable minerals. Both PROFILE and ForSAFE currently calculate rather high weathering rates in the C horizon, if this soil layer is included in the calculations. In the modelling presented in this paper only a few centimetres of the C horizon are included, thus the total contribution of weathering from horizon C is small, but the rates per soil volume are equivalent to the layers above. Most of the C-horizon is usually located below the root zone, usually defined as the uppermost 50 cm of mineral soil for spruce forests in Sweden, where more than 90 % of the spruce roots can be located (Rosengren and 5 Stjernquist, 2004) and therefore not included in the modelling. The overestimation of weathering in the lower soil layers by these two models is likely to be, at least partly, due to the lack of calculation of the concentrations of dissolved silica in the soil water in both models. The dissolved silica, being a product of weathering of silicate minerals, acts as an inhibitor on the weathering of these minerals, i.e. all the minerals modelled in this study except apatite. The concentration of dissolved silica in the soil water is currently being included in the ForSAFE model. 10 When the PROFILE and ForSAFE weathering profiles at Västra Torup and Hissmossa are compared to weathering rates at a nearby site, Skånes Värsjö, calculated with the depletion method , PROFILE and ForSAFE predict substantially higher weathering rates in the lower soil horizons, in line with the above discussion on overestimation in the lower layers. The weathering rates modelled in the upper horizons by PROFILE and ForSAFE are, on the other hand, lower than the rates obtained with the depletion method. However, the depletion method does not calculate present-day weathering, 15 but average weathering in the soil layer since deglaciation. The weathering rates have varied with time, both because new soils have more easily weatherable material and weathers much faster than older soils (Starr and Lindroos, 2006) and because environmental conditions have varied since the end of the last glaciation. This means that weathering rates calculated with methods that calculate average weathering since the deglaciation, such as the depletion method, should generally be higher than PROFILE and ForSAFE weathering rates, except for the lower soil layers, since the weathering 20 front moves down .

Conclusions
We have shown that despite the differences between PROFILE and ForSAFE, the two models give comparable estimates of annual weathering rates.
The PROFILE model has often been used for critical load assessments and weathering estimates. This study shows that the 25 more advanced model, ForSAFE, can be used to gain much more information on the variation in weathering rates in response to forestry and climate change.
The results from ForSAFE presented in this paper demonstrate that weathering rates vary considerably; between seasons, between years and on longer time scales. This dynamic behaviour can be of importance in nutrient leaching and nutrient availability to the trees: during seasons with high nutrient demand there might be risk of nutrient deficiency, even though 30 there might be higher availability of nutrients than demand and nutrient losses through leaching during other seasons.  Table 2. Measured soil parameters for the five soil layers (O, A, AB, B and C) at the two sites. Above: thickness of layer, bulk density, percentage organic matter, estimated percentage stones, measured size fractions, pH, exchangeable ions, cation exchange capacity, base saturation, fraction of carbon and nitrogen. Below: total chemistry of all dry soil matter. Table 3. Soil input data to the models, standard values (partial pressure of CO 2 and gibbsite constant) or calculated from measured soil parameters at the two sites (mineral area, field capacity, wilting point, field saturation and percentage of minerals). The modelled layers L1 -L5 correspond to soil layers O, A, AB, B and C in the two soils. Hissmossa L5 is below the modelled root zone of 50 cm. 0