Impacts of Enhanced Weathering on biomass production for negative emission technologies and soil hydrology

. Limiting global mean temperature changes to well below 2°C likely requires a rapid and large-scale deployment of Negative Emission Technologies (NETs). Assessments so far showed a high potential for biomass based terrestrial NETs, but only few included effects of the commonly found nutrient deficient soils on biomass production. Here, we investigate the deployment of Enhanced Weathering (EW) to supply nutrients to phosphorus (P) deficient areas of Afforestation/Reforestation and naturally growing forests (AR) and bio-energy grasses (BG), besides the impacts on soil hydrology. Using stoichiometric ratios and biomass estimates from two established vegetation models, we calculated the nutrient demand of AR and BG. By comparing the inferred AR P demand to differentInsufficient geogenic P supply scenarios, we estimated that 3 – 98 Gt limits C of the predictedstorage in biomass accumulation cannot be realized due to insufficient soil. For a mean P demand by AR 535 and a low geogenic P supply for an AR scenario considering natural N , AR would sequester 119 Gt C in biomass; for high geogenic P supply. An and low AR P demand scenario, 187 Gt C would be sequestered in biomass; and for a low geogenic P supply and high AR P demand, only 92 Gt C would be accumulated by biomass. An average amount of 2 – 362~150 Gt basalt powder applied byfor EW would be needed to coverclose global P gaps and completely sequester projected amounts of 190 Gt C during years 2006 – 2099. The for the mean AR P demand scenario (2 – 362 Gt basalt powder for the low AR P 540 demand and for the high AR P demand scenarios would be necessary respectively). The average potential of carbon sequestration by EW until 2099 is ~11 Gt C (~0.6 – 97.8 Gt CO 2 for the same scenario.2 – ~27 Gt C) for the specified scenarios (excluding additional carbon sequestration via alkalinity production). For BG, 8 kg basalt m -2 a -1 might, on average, replenish the exported potassium (K) and P by harvest. Using pedotransfer functions, we show that the impacts of basalt powder application on soil hydraulic conductivity and plant available water, for closingto close predicted P gaps, would depend on basalt and soil texture, but in general the impacts are marginal. We show that EW could potentially close the projected P gaps of an AR scenario, and exported nutrients by BG harvest, which would decrease or replace the use of industrial fertilizers. Besides that, EW ameliorates soilthe soils capacity to retain nutrients, and soil pH, and renewrestocks soil nutrient pools. LastLastly, EW applicationsapplication could improve plant available water capacity depending on deployed amounts of rock powder - adding a new dimension to the coupling of land-based biomass NETs with EW. for estimates for limits done for downward We show that EW can be an important part of the solution to the problem of nutrient limitation AR and BG might from. Specifically, the potential for hydrological management of soils was shown and it could be used in areas where seasonality and droughts might affect the biomass growth. The use of Enhanced Weathering for hydrological management coupled to land based NETs is worth to investigate. A global management of the carbon pools will need a full ecosystem understanding, addressing nutrient fluxes, and related soil mineralogy changes, soil hydrology, impacts on soil microorganisms, and responses of plants on the diverse array of soil types and climates. Applied ecosystem engineering is likely a future nexus discipline which needs to link local ecosystem processes with a global perspective on carbon pools within a universal effort to manage the cycle.


220-233
: What about the grain size of the rock powder be applied? Does that matter at all? I assume it would be based on reactive transport simulations such as those by Maher (2010, 2011) for example. And relatedly how fine the rock is powdered will change the texture described in the next section right?

100
Yes, the grain size matters since it will influence on the exposed reactive surface area (generally fine textured basalt powd er would have a high reactive surface area than a coarser textured basalt powder) and consequently the weathering rates. However, in our approach we considered that the grain sizes would range in between 0.6 -90 µm (for the fine basalt powder) which is enough to completely dissolve the deployed rock powder after one year . For the coarse basalt 105 powder ~70% of its granulometry fall into the 0.6 -90 µm range and from the other 30%, at least 20% would be dissolved in one year . The finest grain size we can consider is the clay size which comprehends grains >1 µm and <3.9 µm. If a basalt powder would have only clay size granulometry, the effects on soil hydraulic conductivity would decrease in average by 37% for deployment amount of 30 kg basalt m -2 (for the same deployment amount and for the fine rock powder used in our work, the hydraulic conductivity would decrease by 2%). However, the finer the grain gets the higher the energy A discussion on the applicability of the conclusions drawn from the paper to alternative scenarios should be included.
We included the discussion on chapter 4.1 in lines 461 to 467 considering the results from others AR model that assumes RCP8.5 for an RCP4.5 land evolution scenario. And we have also acknowledged your point (that "even using only one model 270 induces uncertainty" the general message of the study would not change) in the last sentence.
We included a discussion for the harvest rates obtained from the MAgPIE simulations. In this discussion we assume a hypothetical one order of magnitude increase in the maximum harvest rate. The discussion is presented on chapter 4.2 in line 488 to 498.

For the carbon sequestration from afforestation you mention (line 260) that the available estimates of carbon uptake vary between 0.3 and 3.3 GtC/a, while in the paper a value of 2 GtC/a is used.
This is the value for the AR scenario from Kracher (2017), the same model shows a carbon sequestration of ~2.4 Gt C a -1 if 280 N supply is unlimited. We have shown that it can fall to ~1.3 Gt C a -1 if geogenic P supply scenario one for mean P content within wood and leaves is selected. This number would change for another AR scenario. But the main message is that the estimated C sequestration by biomass on terrestrial carbon cycle models can fall if nutrient supply is accounted for.
On the other hand, a lot of weight in the uncertainty is given to e.g. the P concentration in basalt (5-95th percentiles).

285
To my understanding it seems that this uncertainty is not so relevant for the present study, as I assume that for the use in EW basalt with relatively high P concentrations could in principle be selected. Would the interquartile range possible provide a more appropriate measure of the uncertainty in this parameter?
For EW, we need to firstly know rock mineralogical composition and petrography. Therefore, it is more interesting a basalt 290 with high pyroxene group minerals content (especially the ones rich in Ca and Mg like Diopside) since these minerals would weather more rapidly (cf. Table 1 at Hartmann et al. (2013)) and less olivine or sulfide minerals content (Olivine can have high content of Nickel and Chromium that are trace elements problematic for agriculture (Edwards et al., 2017); Sulfide minerals can cause acid rock drainage if pyrite (a sulfide mineral) concentration is within 1% or 2% (Earle, 2018)). As an example, Alkali basalt can have P concentration >3000 ppm , but it is rich in olivine (John, 295 2001;Irvine and Baragar, 1971). Therefore, in this study we have adopted a more strict data selection from the EarthChem database. We selected only the rocks exclusively named as rhyolite, dacite, andesite, and basalt. This resulted in 2985 samples for rhyolite, 3008 samples for dacite, 11099 samples for andesite, and 23816 samples for basalt. Comparing our P concentration values to other works, we see that the median P value of 916 ppm from  is higher than ours (500 ppm of P). This occurs because  did a broader classification, resulting 300 in 97895 used samples, and neglected possible unwanted side-effects of trace minerals in basalt mineralogy. Therefore, the selected quartiles for rock chemistry (either for Basalt or other rock used in our study) are a conservative estimation and assuming interquartile values would decrease even more the consideration of potential rock sources for EW.
In general in the paper it is difficult to immediately associate the uncertainty ranges to uncertainty sources.

305
We re-structured the paper. The results are discussed in a separate section. We also renamed the old section "results and discussion" to Discussion and implications, which contain the discussion for the presented results and implications to rock powder deployment.

310
For AR it seems that the largest uncertainty is related to the geogenic P-supply, with scenario two showing basically no 315 P limitation. Is there really no observation-based evidence to suggest that one or the other scenario is more realistic? This is a fundamental question for the purpose of the paper, because if P limitation is not an issue the benefit of EW in these areas will be limited to the direct CO2 consumption by weathering.
Basically, the uncertainties for the AR scenario are from biomass P demand and the geogenic P supply, with the later 320 influencing the most our results as it was seen. Unfortunately, given current understanding of bioavailability of soil P and soil P estimates uncertainties are large with respect to how much P is available to support future plant growth (detailed analysis and discussion is found in Sun et al. (2017)) and thus AR and BG. Mineral P is likely limiting biomass production in European forests today (Jonard et al., 2015), tropical forest (Turner et al., 2018), boreal forests , as well as agricultural areas (e.g., Ringeval et al., 2019 in discussion;. This situation is likely to deteriorate in the 325 future. Therefore, considering that the inorganic and organic labile P pools will be completely available for tree nutrition is unlikely to occur. Thus, Geogenic supply Scenario 2 is a very optimistic assumption that might not correspond to reality based on the already observed P limitation on different ecosystems (Elser et al., 2007). However, we cannot rule out that gradual shifts in soil organic P fractions occur, which make comparable amounts of P as in scenario 2 available over time, We therefo re opted to show both scenarios as these are a major source of uncertainty with respect to P effects on future plant growth (as 330 has been demonstrated by Sun et al. (2017)).
In the main text there are many references to supplementary materials. References to supplementary material should be limited as much as possible for a better readability of the paper, considering also that papers in Biogeosciences are not subject to strict length limitations. Since the main paper contains only relatively few figures, I would suggest to 335 move some of the figures from the supplementary to the main paper. For example Figs S1,S2,S3 could be merged into one figure and added to the paper. It would help to get an idea of the numbers that could then be more easily compared with e.g. the P gap in Fig. 2. I would also strongly suggest to add Fig. S8 to the main paper.
We appreciate your suggestions and have considered them. Now the Figs. S1 to S3 is the Fig. 3 in the mains text. The Fig. S8 340 now is the Fig. 4 in the main text (which also include the estimated P gaps for the AR scenario).  Beerling et al., 2018;Amann and Hartmann, 2019).
Under intensive growth scenarios, nutrient supply is a critical factor. According to Liebig's law of the minimum, supplying high amounts of nitrogen (N) might shift growth limitation to other nutrients (von Liebig and Playfair, 1843). Some U.S.
forests already show changes from N-limited to a Phosphorus (P) limited system caused by increases in N atmospheric 570 deposition (Crowley et al., 2012) along with magnesium (Mg), potassium (K) and calcium (Ca) deficiencies (Garcia et al., 2018;Jonard et al., 2012). Poor nutrient supply, related to deficient mineral nutrition, may reduce tree growth (Augusto et al., 2017). Impacts on biomass production due to poor tree nutrition is observed in European forests (Knust et al., 2016;Jonard et al., 2015) decreasing the carbon sequestration of forest ecosystems (Oren et al., 2001)a factor rarely included in climate models leading to overestimated CDR potentials.

575
Specifically, global simulations with a N-enabled land surface model (Kracher, 2017) suggest that insufficient soil nitrogen availability for a RCP4.5 AR scenario  could lead to a reduction in the cumulative forest carbon sequestration between year 2006 -2099 by 15%. Goll et al. (2012) showed that carbon sequestration during the 21 st century in the JSBACH land surface model was 25% lower when N and P effects were considered.
P is rather immobile soil nutrient and only a small fraction of soil P is readily available for plant uptake limiting plant growth in a wide range of ecosystem (Shen et al., 2011;Elser et al., 2007). P content in soils is a result of a process controlled by the 595 interactions of parent material (primary rocks) with climate, tectonic uplift, and erosion history through geological time . The processes of P transfer between biologically available and recalcitrant P pools influence at most P availability . Orthophosphate (H2PO4or HPO4 2-) is the chemical species adsorbed by plants (Shen et al., 2011) and its solubility is controlled by soil pH as de-protonation occurs when pH increases. Ideal pH conditions for orthophosphate availability are from 5 to 8 (Holtan et al., 1988). Soil with soil moisture influencing soil P availability seems 600 to be influenced by soil moisture for different crops (He et al., 2005;He et al., 2002;Shen et al., 2011), and natural ecosystems .
The inclusion of soil hydraulic properties in the evaluation of EW effects is important as the soil water content has a strong influence on average crop yield. Practices that increase the plant available water (PAW) are thought to mitigate drought effects on crops (Rossato et al., 2017). The water content of soils also seems to influence soil erosion rates and surface runoff 605 (Bissonnais and Singer, 1992). In addition, soil water content influences soil pCO2 production, which is a relevant agent for mineral dissolution .
Deploying land-based NETs would imply large changes in a local landscape nutrient and water cycles. At least 65% of worldwide soils (6.8 billion hectares of land) have unfavorable soil conditions for biomass production (Fischer et al., 2001).
Therefore, we assess if applications of rock mineral based P sources could close eventual nutritional gaps in an environment 610 with natural N supply (N-limited) and with N fertilization (N-unlimited), using a global afforestation scenario. In addition, we investigate the effects of coupling nutrient supplying (EW) to nutrient demanding (AR and BG) land-based NETs by focusing on the efficiency of different upper limits of basalt powder to supply nutrients. We hypothesize that large-scale EW deployment potentially changes soil texture. Therefore, threshold values for impacts on soil hydraulic conductivity, and plant available water will be determined.

Methods
Since phosphorus (P) is a limiting nutrient in a wide range of ecosystems (Elser et al., 2007), we performed a P budget for an N stock-based P demand from an AR scenario considering natural N supply (hereafter N-limited) and N fertilization (hereafter N-unlimited). We choseselected two N supply scenarios since the related P demand is proportional to biomass N stock, but in 620 the main text we discuss only the N-limited AR scenario. BasedWe estimated the balanced supply of Mg, Ca, and K for each supplied P based on ideal Mg, Ca, and K demand of AR derived from databases of biomass Mg, Ca, and Knutrient content, we estimated the balanced supply of these nutrients for each supplied P . Balanced nutrient supply is necessary to avoid shift of growth limitation to other nutrients, which can occur according to Liebig's Law (von Liebig and Playfair, 1843). is observed for some U.S. forests that changed from a N-limited to a Phosphorus (P) limited after increase in atmospheric N deposition 625 (Crowley et al., 2012). Based on minimum and maximum harvest rates of bio-energy grass (BG), we estimated the related exported P and K export by harvest from the fields. We choosedecide on these nutrients for BG since crops require large amounts of K and P, once N demand is covered. The amount of rock powder for Enhanced Weathering (EW) to cover projected P gaps and to replenish exported nutrients was estimated. The projected impacts on soil hydrology due to EW deployment were done by pedotransfer functions since they are used to estimate soil hydraulic properties (Schaap et al., 2001;Whitfield 630 and Reid, 2013;Wösten et al., 2001) and such approximations have proven to be a suitable approach (Vienken and Dietrich, 2011).
The additional AR P demand, obtained for the 21 st century for an N-unlimited and N-limited AR scenario (Kracher, 2017) was approximated by stoichiometric P:N ratios for mean and range (5 th and 95 th percentiles), which is a similar approach done by Sun et al. (2017). The ratios were derived from databases of hard-and softwood (Pardo et al., 2005) and foliar biome-specific 635 nutrient content (Vergutz et al., 2012). We then compared the inferred P demand to geogenic P supply given by observationbased estimates of soil inorganic labile P and organic P (Yang et al., 2014a), observation-based estimates of P release  from weathering corrected to future temperature increase, since the uncertainty on future hydrological cycle is too high  and estimated atmospheric P depositions from Wang et al. (2017) to derive the potential geogenic P deficits, (i.e, the P gap,) during the 21 st century. Since the geogenic P supply cannot cope with N stock-based P 640 demand from the different AR scenarios within P gapped areas, the biomass production and biomass C sequestration, predicted by the AR scenarios, will be lower. Based on the amount of missing P, we estimated the C-stock reduction within P gapped areas by using stoichiometric C:P ratios. The C:P ratios were derived from simulated C stock content (Kracher, 2017) and inferred N stock-based P demand.
Necessary Mg, Ca, and K supply for balanced tree nutrition based on P supply were derived from N stock-based Mg, Ca, and

645
K additional demand normalized to the N stock-based additional P demand (Fig. 1). The nutrient demand of bio-energy grass was estimated based on stoichiometric P:N and K:N ratios, used in Bodirsky et al. (2012), for minimum and maximum exported N proportional to harvest rates of the 1995 -2090 period obtained from the agricultural production model MAgPIE (Fig. 1).

Formatted: Font: Not Italic
Later on, the necessary amount of rock to cover the P gaps of AR scenario and to resupply the exported nutrients by BG harvest was estimated (Fig. 1). In addition, the potential impact of deploying rock powder into the topsoil was done. Detailed 650 description on used data and assumptions are given below.

Afforestation/Reforestation
The idealized simulations for the AR system from Kracher (2017)  The net primary productivity (NPP) calculation was based on atmospheric CO2 concentrations, stomatal conductance, and water availability. JSBACH considers mass conservation, a supply-demand ansatz, and fixed C:N ratios (Goll et al., 2012). Kracher (2017), considered forest regrowth on abandoned croplands, which in the long term become acidic and consequently 665 favor leaching of nutrients and heavy metals (Hesterberg, 1993), natural shift in natural vegetation, and future CO2 increase leading to CO2 fertilizationThe coupled terrestrial nitrogen-carbon cycle model was selected since it: (i) considered forest regrowth on abandoned croplands (which in the long term become acidic and consequently favor leaching of nutrients and heavy metals (Hesterberg, 1993)); (ii) considered natural shift in natural vegetation; (iii) considered a natural N supply scenario (N-limited) and a N fertilized scenario (N-unlimited); (iv) considered future CO2 increase leading to CO2 fertilization; and (v) 670 explicitly consider large-scale afforestation.
We retrieved the annual changes in N and C content of different pools, i.e., Wood (above and below ground, also including litter) and foliar (above and below ground, also including litter) for temperate, cold, tropical, and subtropical climate growing forests and shrubs plant functional types for years 2006 -2099 and annual model output.

675
Simulations of BG nutritional needs from the agricultural production model MAgPIE, a framework for modeling global landsystems (Dietrich et al., 2018;Lotze-Campen et al., 2008;Popp et al., 2010) were used. The objective of MAgPIE is to minimize total costs of production for a given amount of regional food, bio-energy demand and climate target (here RCP4.5)., to keep correspondence to the AR simulations). In its biophysical core, the yields in the model are based on LPJmL (Bondeau et al., 2007;Müller and Robertson, 2013), a dynamic global vegetation model, which is designed to simulate

685
The MAgPIE output had a frequency of 10 years and the global minimum, and maximum of each output year was taken to obtain the potential bio-energy grass minimum (0.7 kg m -2 a -1 ) and maximum (3.6 kg m -2 a -1 ) harvest rate for the simulation period, which is 0.7 and 3.6 kg m -2 a -1 for the areas with bio-energy plantations.

690
The P, Mg, Ca, and K additional demand is defined as the amount of P, Mg, Ca, and K needed to realize the state of ecosystem N variables in each grid cell and year according to JSBACH output ( Fig. 1). It was estimated from the spatially explicit information on average forest N content of each stock and plant functional type for an N-unlimited, and an N-limited AR scenario from Kracher (2017). Since P limits forest growth in a wide range of ecosystems (Elser et al., 2007), we performed a P budget for each AR scenario. The ideal P, Mg, Ca, and K biomass additional demand were based on the difference in the where ∆ , [kg m -2 a -1 ] is the average N stock-based Mg, Ca, K, or P demand for a given time in the future simulation time range (2007 -2099) within a cell for biome i. ∆ [kg m -2 a -1 ] is the average N stock change of pool j. n is the number of N pools. The N pools considered are: Wood (above and below ground, including litter) and foliar (above and below ground, 700 including litter).
The P, Mg, Ca, K, and N content of leaves obtained from a global leaf chemistry database (Vergutz et al., 2012) was used to derive the Mg:N, Ca:N, K:N, or P:N ratios (Table 1), which was already biome classified. For wood, the tree chemical composition database of US forests (Pardo et al., 2005) was used in order to derive the global ratios, which were assumed to represent the chemical composition of all biomes (Table 1).

705
The AR C content ( Fig. 2) from Kracher (2017) and the resulting N stock-based Mg, Ca, and K demand were normalized by the N stock-based P demand to estimate the mean and range C:P, Mg:P, Ca:P, and K:P ratios of each grid cell. The stoichiometric C:P, Mg:P, Ca:P, and K:P ratios were used to derive the C-fixation reduction due to P deficiencies and the necessary Mg, Ca, and K supply for a balanced biomass nutrition based on supplied P (Fig. 1).

710
The BG yield was obtained by the spatially explicit harvest rates within a grid cell for an output frequency of 10 years and a period of 95 years (1995 -2090). The minimum 0.7 kg m -2 a -1 and maximum 3.6 kg m -2 a -1 harvest rate were used. With the information on exported N by each harvest rate, the exported K or P from cultivation fields (eqEq. 2) were estimated based on the P:N, and K:N stoichiometric ratios used in Bodirsky et al. (2012). We have chosen these nutrients, since crops require large amounts of K and P.

715
Differently from the AR scenario forests, which are perennial, bio-energy grasses are harvested regularly due to their use as biomass feedstock for BECCS. Thus, the natural system's nutrient supply is insufficient to maintain successive and constant yields, and the exported nutrients by harvest need to be replenished (Cadoux et al., 2012) to maintain high yields. The exported nutrient was calculated following Eq. (2):(2): where corresponds to the exported nutrient P or K [kg m -2 a -1 ] by harvest. is the P:N or K:N stoichiometric ratio used 720 in Bodirsky et al. (2012). ℎ is the exported N for a minimum 0.7 kg m -2 a -1 or a maximum 3.6 kg m -2 a -1 harvest rate.
The harvest rate value was based on the MAgPIE output for each grid cell, representing the minimum and maximum projected global harvest rate for a period of 95 years.

Geogenic P supply for AR
Since theThe geogenic P source databases have different spatial resolution (Table 2), we resampled each of them to 2°×2° 725 spatial resolution fields by nearest neighbor interpolation.a coarser 2°×2° spatial resolution fields by nearest neighbor interpolation to minimize distortions of location (Pontius, 2000). Nearest neighbor interpolation method reliably retain the overall proportions of an original fine resolution map (Christman and Rogan, 2012). As the uncertainty on which P pool is available for long-term plant nutrition is high (Johnson et al., 2003), two scenarios for soil P supply were investigated: scenario one considering P from weathering and atmospheric P deposition. Scenario two the same as scenario one plus inorganic labile 730 P and organic P (Yang et al., 2014a)(Supplement S1 Fig. S2)..
where [kg m -2 ] is the cumulative atmospheric P deposition of the 2006 -2099 period. (Fig. 3a). [kg m -2 a -1 ] is the atmospheric P deposition of each year i within a grid cell.
The total soil P map from Yang et al. (2014a) was used as estimation of the projected long term available P in the soil system thickness  and calibrated on 381 catchments in Japan . A relationship between air temperature and weathering rate was used, which was derived from reconstructed weathering rates and different climate change scenarios for the recent past (1860-2005) using the weathering model applied here. The relationship in which P weathering increases by 9% per 1ºC increase  implicitly accounts for changes in soil hydrology. Without accounting for P concentration changes in primary and secondary P minerals. Due to the large uncertainties in projected 750 changes in soil hydrology we omitted a more detailed representation of hydrological effects on weathering.

Estimating geogenic P gap, related C-fixation reduction, and balanced Mg, Ca, and K supply for AR
The potential P gap ( [kg m -2 ]) was estimated as the difference between additional mean and range (95 th and 5 th percentiles) P demand estimated from the N stock for the two different AR scenarios (section on Afforestation/Reforestation nutrient demand), and the geogenic P supply from the different supply scenarios ( [kg m -2 ]) within the cover fraction for a grid cell the plant C-fixation reduction was estimated based on the P gap and calculated following Eq. (5): where [kg m -2 ] is the plant reduced C-fixation due to the projected P gap. is the used stoichiometric C:P ratio based on mean and range (5 th and 95 th percentiles) chemistry for wood and leaves derived from the N-limited and N-unlimited AR scenario N stock as described in subsection 2.2.1.

760
The Mg, Ca, and K necessary supply for balanced biomass nutrition ( [kg m -2 ]) should be proportional to the supplied P ( [kg m -2 ]) and was calculated following Eq. (6): (6): with being equal to the projected since the it is covered by P from Enhanced Weathering according to Eq. (7): where is the used stoichiometric ratio Mg:P, Ca:P, K:P obtained by normalizing the N stock based additional Mg, Ca, and K demand to the N stock based additional P demand.

770
The nutrient supply was estimated assuming complete rock powder dissolution in the system, which is expected over long timescales depending on the grain size (i.e., one year for grain sizes between 0.6 -90 µm ). The results and discussion will focus on basalt rock powder considering median values and range (5 th and 95 th percentiles), as basalt is abundant worldwide (Amiotte Suchet et al., 2003;Börker et al., 2018) and has a high P content. Other rock types are included, but the results are provided in the supplementary text (Supplement S1 section S4). The necessary mass of rock powder to 775 supply macronutrient (Mg, Ca, K, or P) was calculated following Eq. (8): To cover the potential of different igneous rocks for EW strategies, rhyolite and dacite (acidic rocks), andesite (intermediate rock) and basalt (basic rock) were selected to project necessary amounts to cover P gaps from the AR scenarios. Data on macronutrient concentrations (Mg, Ca, K, P) in weight percent within these rocks were downloaded from the Earthchem web portal ( Fig. 4; http://www.earthchem.org, accessed on 2017-07-14). The data was selected for rocks named as rhyolite, dacite, 780 andesite, and basalt. Neglecting intermediate compositions between different lithotypes (i.e., a trachybasalt that has its chemical composition lying in between trachyte and basalt). Rocks that were under any metamorphism grade (e.g., metabasalt) were neglected because metamorphism can change rock mineralogy. We neglected rocks known to have high content of minerals rich in trace elements (e.g., an alkali basalt can have P concentration >3000 ppm ), but it is rich in olivine Irvine and Baragar, 1971) that contains elevated concentrations of nickel and 785 chromium (Edwards et al., 2017)). Nickel and chromium are trace elements problematic for agriculture (Edwards et al., 2017).
Thus, following the classification criteria, the number of selected data to calculate descriptive statistics for Mg, Ca, K, P content within rocks were 2985 chemical analysis for rhyolite, 3008 chemical analysis for dacite, 11099 chemical analysis for andesite, and 23816 chemical analysis for basalt.
The nutrient supply was estimated assuming complete rock powder dissolution in the system considering median and ranges 790 (5 th or 95 th percentile) chemical composition. The duration of complete rock powder dissolution varies depending on the grain size (i.e., one year for grain sizes between 0.6 -90 µm  for basalt). The results and discussion will focus on basalt rock powder considering median P values (500 ppm) and range (5 th (157 ppm  . The necessary mass of rock powder to supply macronutrients (Mg, Ca, K, or P) was calculated following Eq. (8): where [kg rock m -2 or kg rock m -2 a -1 ] represents the mass of a rock type to cover AR or BG nutritional needs, [kg m -2 or kg m -2 a -1 ] is the mass of required nutrient for AR or BG, (e.g., P to cover a P gap, obtained by Eq. (4)), and [-] is the median and range (5 th or 95 th percentile) fractions of interest nutrient within the chosen rock, i.e, for P in basalt a median 800 of 500 ppm and ranges of 157 ppm for 5 th percentile and 1833 ppm for 95 th percentile is expectedselected rock.
However, the potential nutrient supply by EW for different amounts of rock powder being deployed was also estimated following Eq. (9):(9): where [kg m -2 or kg m -2 a -1 ] represents the macronutrient input by dissolving a chosen rock.
[kg rock m -2 or kg rock m -2 a -1 ] is the mass of rock added to the natural system. 805

Related impacts on soil hydrology from Enhanced Weathering deployment
Large scale deployment of rock powder on soils is expected to influence soil'sits texture. The deployed amount and texture of rock powder will somehow affect hydraulic conductivity, water retention capacity, and specific soil surface area. Pedotransfer functions (PTFs) are used to estimate soil hydraulic properties (Schaap et al., 2001;Whitfield and Reid, 2013;Wösten et al., 2001) based onand such approximations have proven to be a suitable approach (Vienken and Dietrich, 2011). PTFs make use 810 of statistical analysis Wösten et al., 2001), artificial neural networks, and or other methods applied to large soil databases of measured data (Wösten et al., 2001).
The impacts of basalt powder application on soil hydrology are estimated for soils corresponding to P gap areas from the Nunlimited AR scenario as a function of rock powder deployment by the use of PTFs fromThe equations from Saxton et al. (1986) performed the best estimations of soil hydraulic properties (Gijsman et al., 2002). Later on, Saxton and Rawls (2006) 815 (Supplement S1 section S5). The N-unlimited AR scenario was chosen since this scenario would have the highest P deficiencies requiring more rock powder to cover the P gaps.improved Saxton et al. (1986) PTFs and they are used to estimate the effects The potential changes in soil hydraulic properties, due to the application of a fine basalt texture (15.6% clay, 83.8% silt, and 0.6% fine sand) or a coarse basalt texture (15.6% clay, 53.8% silt, and 30.6% fine sand) were estimated as a function of rock 820 powder deployment for soils corresponding to P gap areas from the N-unlimited AR scenario. According to the international organization for standardization, the man-made materials can be classified according to their grain sizes; therefore, here the clay comprehends grain diameters ≤ 2 µm, silt comprehends grain diameter 2 -63 µm, and fine sand comprehends = 33 + ( −33) − 0.097 × + 0.043, wherewith:    Supplement S1 section S5), and is the slope of the logarithmic tension-moisture curve (Supplement S1 section S5). The numbers in front of each described variable are regression coefficients .
The initial hydrologic properties of topsoil were estimated for a depth of 0.3 m, as it is the average depth usual machinery can 840 homogeneously mix topsoil (Fageria and Baligar, 2008). Greater depths can be reached but under higher energy and labor costs (Fageria and Baligar, 2008). The global data set of derived soil properties (Batjes, 2005), which had textural information with: where represents the initial topsoil texture (sand, silt, and clay content) of a specific raster cell [-].
[km 3 ] is the raster cell volume obtained by multiplying the area [km 2 ] to the soil depth of 0.3×10 -3 km.

_
[kg] is the total soil mass of a raster cell.
[-] is the corrected soil texture (sand, silt, and clay content).
The necessary rock powder mass was estimated by Eq. (8) to close the obtained by Eq. (4). The effect of basalt powder application in soil and PAW was estimated by assuming a homogeneous mixture between applied basalt powder and topsoil.
The changes on initial soil organic matter (SOM) concentration within a raster grid-cell were obtained by normalizing the 855 SOM to the sum of applied basalt mass, mass of soil, and initial SOM mass by Eq. (21). This was necessary since the SOM concentration at the moment of basalt deployment would have a relative decrease compared to initial SOM concentration: with: where [wt %] is the corrected soil organic matter content, [kg] is the organic matter mass within the raster cell.

860
The impacts in soil texture by rock powder application considered the textures of applied basalt mass added to the initial soil mass by Eq. (23). It was assumed a content of 15.6% clay, 83.8% silt, and 0.6% fine sand for fine basalt powder and 15.6% clay, 53.8% silt, and 30.6% fine sand for a coarse basalt powder. Besides texture and organic matter, intrinsic grain properties (e.g., the shape of grains and pores, tortuosity, specific surface area, and porosity) should be considered (Bear, 1972). The equations from Beyer (1964) are based on the non-uniformity of 870 grain size distribution and density of the grain packing to estimate soil properties. Carrier III (2003) uses information on the particle grain size distribution, the particle shape, and the void ratio on his equations to estimate soil properties. However, such detailed information on a global scale is missing turning Beyer (1964) and Carrier III (2003) equations not applicable to our analysis.

Afforestation/Reforestation P gaps and Enhanced Weathering as nutrient source
The global C sequestration for the N-limited AR scenario is 190 Gt C, while for the N-unlimited AR scenario it is 34 Gt C higher. The AR model from Kracher (2017) shows an increase in biomass production in tropical and temperate zones (Fig. 2).
The results only focus on the N-limited scenario since it considered natural N supply, but the results for the N-unlimited scenario are presented only in the supplement (Supplement S1 section B ii). The calculated P budgets according to Eq. (4) for 880 the AR time of 2006 -2099 (Fig. 5) considered different geogenic supply scenarios (scenario one: P from weathering and atmospheric P deposition; scenario two: the same as scenario one plus inorganic labile P and organic P) and the average and range N stock-based P demand (calculated following Eq. 1) for the AR simulation from Kracher (2017).
The ideal P biomass additional demand (calculated from Eq. (1)), to sequester 190 Gt C (N-limited AR scenario) amounts to 200 Mt P on global scale for a mean wood and leaves P content; for 5 th and 95 th percentile, the estimated P demand would be 885 71 and 345 Mt P respectively. The P budget (estimated from Eq. (4)) for geogenic P supply scenario one suggest that P deficiency areas are distributed around the world, but with more frequent occurrences in the northern hemisphere (Fig. 5a) and the P gaps can potentially reach up to ~17 g P m -2 (~4 -~30 g P m -2 for 5 th and 95 th quartiles of wood and leaves chemistry; Table 3) or a global P gap of ~77 Mt P (~9 -181 Mt P 2 for 5 th and 95 th quartiles of wood and leaves chemistry; Table 3).
However, for geogenic P supply scenario two, the P deficiency areas are predominantly located in the southern hemisphere 890 (Fig. 5c) and the P gaps can potentially reach up to ~7 g P m -2 (~2 -~12 g P m -2 for 5 th and 95 th quartiles of wood and leaves chemistry; Table 3) or a global P gap of ~10 Mt P (1 -~35 Mt P 2 for 5 th and 95 th quartiles of wood and leaves chemistry; Table   3).
The P and N limitation cause an average C reduction of 47% for the geogenic P supply scenario one and 19% for the geogenic P supply scenario two (obtained by accounting the C reduction from N limitation, which is 34 Gt C plus the C reduction from 895 Table 3 and then normalized by the global sequestration for the N-unlimited scenario of 224 Gt C) or ~-1.1 and ~-0.5 Gt C a -1 , respectively. In some areas, the C sequestration can be reduced by up to 100% compared to the predicted C sequestration of the AR models (Fig. 6). Accounting for N and P limitation on AR suggests that the biomass production will be affected, consequently decreasing the C sequestration potential of AR strategies (Table 3 and Fig. 6). Therefore, supplying the demanded P would positively contribute to biomass to reach the predicted growth of the specific AR scenario.

900
Besides removing carbon from the atmosphere, EW can also amend soils by supplying nutrients and increasing alkalinity fluxes (Leonardos et al., 1987;Nkouathio et al., 2008;Beerling et al., 2018;Hartmann et al., 2013;Anda et al., 2015). Since basalt has higher P content compared to acidic and intermediate rocks , it could be used as raw material for EW to cover the estimated P gaps of Fig. 5a and Fig. 5c. For a median Basalt P content of 500 ppm (cf., subchapter 2.5), it would be necessary to apply ~33 and ~13 kg basalt m -2 ( Fig. 5b and Fig. 5d) in areas of high P deficiency 905 (~17 and ~7 g P m -2 , Fig. 5a and Fig. 5c respectively), considering the AR time span, the deployment rates would be less than 1 kg basal m -2 a -1 , if full congruent dissolution occurs as assumed for further given scenarios.
The total amount of basalt powder to close the estimated P gaps from Fig. 5 would depend on the assumed geogenic P supply scenario and chemical composition of wood and leaves, but for a mean P chemical composition, at least ~153 Gt basalt would be necessary for geogenic P supply scenario one and ~20 Gt basalt for geogenic P supply scenario two. Basalt has a carbon 910 capture potential of ~0.3 t CO2 t -1 basalt (Renforth, 2012), resulting in ~46 Gt CO2 (~12.4 Gt C) and 6 Gt CO2 (1.6 Gt C) capture by closing the P gaps from Fig. 5a and Fig. 5c, respectively. If wood and leaves P concentration correspond to 5 th percentiles (Table 1) ~2 Gt basalt would be needed for closing the P gaps from a geogenic P supply scenario two (Supplement S1 Fig. S1), which would potentially sequester ~0.6 Gt CO2 (~0.2 Gt C) due to weathering. If wood and leaves P concentration correspond to 95 th percentiles (Table 1) ~362 Gt basalt for closing the P gaps from a geogenic P supply scenario one 915 (Supplement S1 Fig. S3) would be necessary, which would potentially sequester ~98 Gt CO2 (~27 Gt C) due to weathering.
The amount of basalt needed was estimated for a P content of 500 ppm and an increase in basalt P concentrations would represent a decrease in the necessary amounts of basalt powder. Incongruent dissolution of basalt might occur consequently increasing the necessary amounts of deployed basalt to cover the estimated P gaps.
Basalt deployment can also guarantee a balanced supply of Mg, Ca, and K for different deployment rates (Fig. 7), potentially 920 preventing the shift of growth limitation to some of these nutrients within the P gapped areas (Fig. 5). Besides basalt, rhyolite, dacite or andesite could alternatively be used as a source of P, but these rocks generally have lower P content (Fig. 4). As a consequence, the necessary amounts of rhyolite, dacite or andesite would be higher than that for basalt. Even though, for a median rock nutrient content, if these rocks are used to close the projected P gaps, they potentially can supply the necessary amount of Ca, Mg, and K for balanced tree nutrition (Fig. 8).

Enhanced Weathering coupled to bio-energy grass production
For the simulation time spam of 1995 -2090 the minimum and maximum biomass growth yield amounts to 0.7 and 3.6 kg m -2 a -1 , which represent a K export of 4.2 -22 g m -2 and a P export of 0.7 -3.6 g m -2 according to Eq. (2). To guarantee maximum bioenergy grass yield, the exported nutrients should be replaced. For a high nutrient content (95 th quartile) deploying up to 1.5 kg basalt m -2 a -1 could meet the K needs of bio-energy grass (Fig. 9) and would be able to replenish up to 75% of the 930 exported P, if the maximum bio-energy grass yield is considered (Fig. 9). Industrial fertilizer co-application would be indicated to completely replenish exported P reducing industrial fertilizers dependency. Deploying 8 kg basalt m -2 a -1 would be enough to replenish exported K and P by harvest assuming median nutrient content of basalt powder, congruent and complete dissolution (Fig. 9).

935
The baseline hydraulic properties for soils within the P gap areas from the N-unlimited AR scenario, since this scenario represents the maximum effect, were estimated by Eq. (10), and they show high variability. The projected hydraulic conductivity ( ) of top soils for areas corresponding to those of P budget from geogenic P supply scenario one (Supplement S1 Fig. S7a), for the N-unlimited AR scenario encompass values ranging from 1.5 × 10 -7 and 7.8 × 10 -5 m s -1 and for PAW of 4% and 32% (  Fig. 10 and Fig. 11). The average values for PAW increase together with the increase of the upper limits of rock powder application, but for a coarse basalt powder some areas might experience a decrease in the PAW ( Fig. 10 and Fig. 11).
Closing the observed P gap areas from the N-unlimited AR scenario would require a maximum deployment of 34 kg basalt m -2 if geogenic P supply scenario one is assumed and 13 kg basalt m -2 if geogenic P supply scenario two is assumed (Supplement S1 Fig. S7). Filling the P gaps from scenario two by a coarse or fine basalt powder (given complete dissolution of P-bearing 950 minerals) the related changes in soil hydrology would remain below ±10% for most of the areas (Supplement S1 Fig. S12). If the geogenic P supply from scenario one, for the N-unlimited AR scenario (Supplement S1 Fig. S7a), is assumed and a fine basalt powder is applied, the changes on hydraulic conductivity range between 58% and -11% (Fig. 12a). Decrease on PAW could be neglected for most of the deployment areas, but some would have an increase of up to 31% from 13.8% to 18.2% (Fig. 12c). A coarse basalt powder would, in general, cause fewer impacts to soil hydraulic properties ( Fig. 12b and Fig. 12d).

Enhanced Weathering coupled to Afforestation/Reforestation
Phosphorus (P) is a limiting nutrient in a wide range of ecosystems (Elser et al., 2007). and in temperate and tropical climate zones (Du et al., 2020). P deficiency might affect biomass growth of tropical (Herbert and Fownes, 1995;Tanner et al., 1998;Wright et al., 2011) and northern forests (Menge et al., 2012;. The numerical simulations of Kracher

960
(2017) predict biomass growth for the 21 st century (Supplement S1 Fig. S5) considering natural water supply, CO2 fertilization, and N-unlimited and N-limited scenario. In the present text, we will focus on the results from the N-limited scenario since it considers natural N supply. In the supplement, the results for the N-unlimited scenario are presented. The predicted C sequestration by the N-limited AR scenarios from with mineral P already limiting biomass production in European forests (Jonard et al., 2015) and in Forests from USA (Garcia et al., 2018), as well as agricultural areas Kvakić 965 et al., 2018). The uncertainty on which P pool is available for long-term plant nutrition is high (Johnson et al., 2003;Sun et al., 2017) and we tackled this uncertainty assuming two potential geogenic P supply scenarios. Geogenic supply scenario two, assuming P from weathering and atmospheric deposition plus inorganic labile P and organic P, is a very optimistic assumption that might not correspond to reality based on the already observed P limitation on different ecosystems (Elser et al., 2007).
However, we cannot rule out that gradual shifts in soil organic P fractions occur, which make comparable amounts of P as in 970 scenario two available over time.
The numerical simulations of Kracher (2017) is 2.0 Gt C a -1 .predicted biomass growth for the 21 st century (Fig. 2) considering natural water supply, CO2 fertilization, and N-unlimited and N-limited scenario for an RCP4.5 greenhouse gas concentration trajectory and land use transitions. The predicted C sequestration by the N-limited AR scenarios from Kracher (2017) is  (2017) can drop to ~1.3 Gt C a -1 if geogenic P supply scenario one for mean P content within wood and leaves is selected. If geogenic P supply scenario two for mean P content within wood and leaves is selected, it drops to ~1.9 Gt C a -1 .
The here estimated P demand based on the predicted biomass growth to sequester 190 Gt C (N-limited AR scenario) amounts 980 to 200 Mt P on global scale for a mean wood and leaves P content. Since there are more than 60,000 tree speciesMore than 60,000 tree species are recorded worldwide (Beech et al., 2017) and a precise estimation on tree chemistry represents a challenge. Based on global and US specific databases,, which we attempted to represent by the rangeconsidered ranges of N stock-based additional P demand is 71 / 345 Mt P; 5 th / 95 th percentile for wood and leaves chemistry.
The P budget for geogenic P supply scenario one, with P supply by weathering and atmospheric deposition, suggest that P 985 deficiency areas are distributed around the world, but with more frequent occurrences in the northern hemisphere (Fig. 2a).
from the databases. However, for geogenic P supply scenario two, which is the same as geogenic P supply scenario one plus geogenic P from soil inorganic labile P and organic P pools, the P deficiency areas are predominantly located in the southern hemisphere (Fig. 2b). If N and P are limiting nutrients, it is expected a C reduction of 16.5 -59.0%, with mean C reduction of 47.0% for the geogenic P supply scenario one and 19.0% for the geogenic P supply scenario two. Therefore, accounting for N 990 and P limitation on AR suggests that, in average; the biomass production will be more affected, which decreases the C sequestration potential of AR strategies (Table 3). In some areas, the C sequestration can be reduced by up to 100% compared to the predicted C sequestration of the AR models (Fig. 3).
Differentdifferent pathways and mechanisms control soil P availability to the plant (Vitousek et al., 2010), and they are not considered in our estimations leading to conservative predictions. Adding soil P dynamics to models would allow to reliably 995 quantify the C sequestration potential of AR, e.g., using P enabled land surface models (e.g., using P enabled land surface models; Sun et al., 2017;Wang et al., 2017;Goll et al., 2012;Goll et al., 2017;Wang et al., 2010;Yang et al., 2014b). Kracher (2017) has shown that N can limit biomass production and consequently C sequestration. To achieve the projected C sequestration of 190 Gt C for N-limited scenario, the estimated P gaps must be closed. Potential P sources are industrial fertilizers, like diammonium phosphate (DAP) or rock powder, (e.g., basalt.). However, DAP potentially represents an extra 1000 input of ammonium to the groundwater and it is expected, in the long-term, that DAP deployment acidifies the soil (!!!

INVALID CITATION !!! ).
Most of the world soils are acidic, with some being strongly acidic (IGBP-DIS, 1998), which generally favors the sorption of orthophosphate onto Fe-and Al-(hydro)oxides surfaces and clay minerals, essentially demobilizing P (Shen et al., 2011).
Besides that, the long AR time span can undermine the effectiveness of DAP to supply P for forests due to the high soil 1005 acidification potential of DAP. Therefore, rock powder application can be an alternative as nutrients are slowly released and an increase of alkalinity fluxes is expected (!!! INVALID CITATION !!! ), which can raise and stabilize the pH of soils. Rhyolite, dacite or andesite could alternatively be used as a source of P, but these rocks generally have lower P content than basalt. As a consequence, the necessary amounts of each rock to cover P gap of each P budget scenario for the AR scenarios, based on chemical composition, will be higher. Therefore, basalt powder is more effective to supply P for the estimated P gap 1020 areas due to relative high P content.
To avoid shifts of nutrient limitation, the supply of macronutrients like Mg, Ca, and K shouldmight be proportional to P supply since Mg is required as an essential element in chlorophyll, Ca has a structural role, and K is responsible for water and ionic balance (Hopkins and Hüner, 2008). Rock powder can be used as source of these nutrients, as suggested by different authors (Beerling et al., 2018;Hartmann et al., 2013;Straaten, 2007). Therefore, we investigated if these macronutrients are supplied 1025 by EW for balanced tree nutrition. Assuming median rock nutrient content, the different rock types under study can supply the necessary amount of Ca, Mg, and K for balanced tree nutrition if they are used to close the projected P gaps (Supplement S1 Fig. S6). The and according to our results from Fig. 7 and Fig. 8. However, the potential of basalt powder to supply K, based on chemical composition, is lower than for other analyzed rocks. For median values, rhyolite has the highest content of K; however, if occurring in K-feldspars it will not be plant available. Blending these rocks in different proportions could result in 1030 a more balanced macronutrient supply (Leonardos et al., 1987).
For a rock chemical composition corresponding to the 95 th percentile of P content, 10 kg basalt m -2 would cover the maximum projected P gaps for all P supply scenarios. For a median chemical composition of rock, deploying 33 kg basalt m -2 would cover all the P gaps of the two geogenic P supply scenarios. For the 5 th percentile, the necessary amount of rock would be even higher. Besides successfully covering the estimated P deficiencies, basalt powder seems to supply enough K, Mg, and Ca to 1035 the afforested system contributing to balanced biomass nutrition (Fig. 4) and, as expected, avoiding shift of growth limitation to other nutrients.
RCP8.5 scenario predicts that global agricultural areas (crop land and pastures) are going to increase in the course of 21 st century due to a decrease in forested area (Sonntag et al., 2016). Assuming a future scenario of high atmospheric CO2 levels (RCP8.5), but using the land use transitions and wood harvest rates from a RCP4.5 scenario (Sonntag et al., 2016), a similar 1040 forest cover fraction than the one presented in Fig. 2 is expected (cp. Figure 1 Sonntag et al. (2016)) and geogenic P supply would also limit the predicted biomass growth. Similar areas of forest growth were observed in Figure 2c presented in the study from Yousefpour et al. (2019) by comparing it to Fig. 2. Though using only one model induces uncertainty, however, it would not change the general message of this work.

1045
Generally, natural soil P content is inadequate for long-term cultivation of agricultural plants. To overcome this issue, P is supplied by fertilizers to reach or maintain optimum levels of crop productivity (Sharpley, 2000) after several harvest rotations.
In order to keep a positive CO2 balance, an alternative to industrial fertilizers shouldmight be used to replenish the exported nutrients by harvest. Rock powder application could increase the soil macro-and micronutrient stocks, maintaining or increasing biomass yields without decreasing CDR efficiency. For a high nutrient content (95% confidence intervals) 1050 deploying up to 1.5 kg basalt m -2 a -1 could meet the K needs of bio-energy grass (Fig. 5) and would be able to replenish up to 75% of the exported P, if the maximum bio-energy grass yield is considered (Fig. 5). Industrial fertilizer co-application would be indicated to completely replenish exported P reducing industrial fertilizers dependency. Deploying 8 kg basalt m -2 a -1 would be enough to replenish exported K and P by harvest assuming median nutrient content of basalt powder (Fig. 5).
The chemical composition of rocks is highly variable (Supplement S1 Fig. S4). Different (Fig. 4) and different rock types can 1055 be used for EW and ideal. Ideal rock types need to be chosen in order to resolve a specific plant nutrient deficiency, and enhance the nutrient reservoir of a target soil besides increasing the soil pH, the CEC (Anda et al., 2015;Anda et al., 2009), improve the C-and N-mineralization (Mersi et al., 1992), the soil organic carbon (Doetterl et al., 2018) and the supply of Si (Beerling et al., 2018;Hartmann et al., 2013). In the case of oxisols, which are found over about 8% of the glacier-free land surface and common in tropical and subtropical agricultural regions, application of 8 kg m -2 basalt powder can increase the 1060 CEC by 150 -300% (Anda et al., 2015;Anda et al., 2009). For ultisols, which are found over about 8% of the glacier-free land surface, application of ~7 kg m -2 basalt powder can increase the CEC by 44% (Noordin et al., 2017).
Overall, rock application couldhas the potential to resupply the harvest exported nutrients, and partially or totally close the short-and long-term nutrient gaps in soil. Individual rock types, from basic (Mg, Ca) to acidic (K, Na), contain varying amounts of target nutrients and mixing them might increase the overall nutrient supply capacity (Leonardos et al., 1987). Intrinsic 1065 mineralogical and or petrographic structures can influence the release of nutrients (Ciceri et al., 2017), which makes them plant unavailable in some cases. K can also limit plant growth; it occurs in K-feldspars as a plant unavailable form, in the case of acidacidic rocks, but becomes accessible after hydrothermal treatment (Liu et al., 2015;Ma et al., 2016a;Ma et al., 2016b).
However, research on release processes of other macro-and micronutrients and on nutrient-release optimization, (e.g., by hydrothermal decomposition,) is necessary to be able to parameterize this effect in the soil environment.

1070
Harvest rates will control the nutrient export from bioenergy grass fields. Therefore, an increase in harvest rate represent an increase in nutrient export and vice-versa. Thus, to keep with a sustainable nutritional balance of soils, the exported nutrients Formatted: Font: Not Italic must be replenished, otherwise maintaining the high harvest rates become an unsustainable situation. Accounting for other simulation setup or a numerical model different from MAgPIE might change the harvest rates of this study. If we assume that the maximum harvest rate of 3.6 kg m -2 a -1 would hypothetically increase by one order of magnitude, the maximum exported 1075 nutrients would be of ~0.2 kg K m -2 a -1 and ~0.04 kg P m -2 a -1 , which would demand a basalt deployment rate of ~13 kg m -2 a -1 and ~20 kg m -2 a -1 (considering 95 th percentiles of chemical composition for basalt) to respectively replenish the exported nutrients. If median K and P concentrations on basalt powder are assumed, the basalt deployment rate increase to ~48 kg m -2 a -1 and 73 kg m -2 a -1 to respectively replenish the exported nutrients (Supplement SI Fig. S11). However, such an increase in harvest rates might not correspond to reality. Harvest rates smaller than 0.7 kg m -2 a -1 (the minimum) represent less nutrient 1080 export, decreasing the basalt powder deployment rates necessary to replenish the exported nutrients by harvest.

Impacts on soil hydrology
AR and BECCS demand huge quantities of irrigation water (Boysen et al., 2017b;Bonsch et al., 2016), and it is projected that climate change will affect the water balance, and consequently influence crop yields (Kang et al., 2009). Soils with higher water holding capacity will better tolerate the impacts of drought (Kang et al., 2009). Therefore, practices that improve water 1085 availability to plants at the root system are used as strategies to mitigate drought effects (Rossato et al., 2017). We investigated if deployment of rock powder can change the top soil hydraulic conductivity, and plant available water (PAW) for different application ranges.
To show baseline hydraulic properties for soils with any sort of P gap, the initial hydraulic properties were estimated, and they show high variability. The projected hydraulic conductivity ( ) of top soils for areas corresponding to those of P budget from 1090 geogenic P supply scenario one (Supplement S1 Fig. S21a), for the N-unlimited AR scenario encompass values ranging from 1.5 × 10 -7 and 7.8 × 10 -4 m s -1 and for PAW of 4% and 32% (Table 4). Neglecting the topography, soils having low , e.g., values of 1.5 × 10 -7 m s -1 , would experience the lowest water infiltration rate. The impacts of deploying a fine basalt texture Impact of rock-powder deployment could be neglected, in average, for upper limits until 50 and 205 kg basalt m -2 respectively for a fine and a coarse textured rock powder being deployed. However, deviations from what is expected for the mean might occur ( Fig. 6 and Supplement S1 Fig. S23 for P gap from geogenic P supply scenario two). The average values for PAW increase together with the increase of the upper limits of rock powder application, but for a coarse basalt powder some areas 1100 might experience a decrease in the PAW (Fig. 6 and Supplement S1 Fig. S23 for P gap from geogenic P supply scenario two).
However, overloading the soil system with rock powder can trigger plant suffocation, if gas exchange is prevented by water saturation of pores (Sairam, 2011). reach PAW threshold values to trigger biomass productivity (Sadras and Milroy, 1996). In general, the average changes on 1105 topsoil PAW related to basalt powder application would not be enough to trigger biomass growth, e.g.,. Therefore, areas showing PAW changes from 14% to 21% would not trigger leaf and stem expansion of maize, wheat or soybean, but could increase leaf and stem expansion of pearl millet (Sadras and Milroy, 1996), but could increase leaf and stem expansion of pearl millet (Sadras and Milroy, 1996) after deploying 50 kg basalt m -2 with a fine texture. 50 kg basalt m -2 of coarse powder changes PAW by 19% consequently not triggering biomass productivity.

1110
Concrete effects of EW on biomass productivity would depend if the changes in the initial PAW values for top soils would reach PAW threshold values to trigger biomass productivity (Sadras and Milroy, 1996). In general, the average changes on topsoil PAW related to basalt powder application would not be enough to trigger biomass growth, e.g.,. Therefore, areas showing PAW changes from 14% to 21% would not trigger leaf and stem expansion of maize, wheat or soybean, but could increase leaf and stem expansion of pearl millet (Sadras and Milroy, 1996), but could increase leaf and stem expansion of pearl 1115 millet (Sadras and Milroy, 1996) after deploying 50 kg basalt m -2 with a fine texture. 50 kg basalt m -2 of coarse powder changes PAW by 19% consequently not triggering biomass productivity.
The equations fromfinest grain size Saxton and Rawls (2006) do not consider changes in the rock powder mineralogy, e.g., by clay mineral formation, which can potentially increase the water holding capacity of soils, and subsequently change the PAW.equations can consider is the clay fraction (grains diameter >1 µm and <3.9 µm). Fine grain sizes influence the exposed 1120 reactive surface area of rock powder, which will affect the weathering rates. The fine basalt would have the grain sizes ranging in between 0.6 -90 µm which might be enough to completely dissolve the deployed rock powder after one year . For the coarse basalt powder, ~70% of its granulometry fall into the 0.6 -90 µm range and from the other 30%, about 20% might be dissolved in one year . Based on the used pedotransfer functions, If a basalt powder would contain only grains on the clay size fraction, the effects on soil hydraulic conductivity would decrease by 37% for 1125 deployment amount of 30 kg basalt m -2 (for the fine rock powder used in our work, the hydraulic conductivity would decrease by only 2%). The finer the grain gets the higher the energy input for grinding is, which can drastically affect the costs of EW (it can reach up to 500$ tCO2 -1 sequestered; . Since grains of different diameters need different times for complete dissolution, a rock powder with different grain sizes would act as a constant source of nutrients to soil. During the weathering of rock powder, clay mineral genesis can occur and potentially increase the water holding capacity of 1130 soils (Gaiser et al., 2000), which can subsequently change the estimated PAW. The added fresh silicate minerals to the soil by EW will have high reactivity releasing a significant amount of nutrients, which increases soil nutrient pools. The increased nutrient availability will increase the potential of soils to stabilize carbon (Doetterl et al., 2018) and a positive effect on PAW is expected to occur based on Eqs. (15) to (17) and according to Olness and Archer (2005). The suitable amounts of rock powder applied depend on the target changes of the chosen soil, and on its intrinsic grain size distribution and organic matter 1135 content. Intrinsic grain properties like the shape of grains and pores, tortuosity, specific surface area, and porosity should be considered (Bear, 1972). Field for the evaluation of changes in soil hydraulic properties by pedotransfer functions and its consequences to dissolution kinetics. A large set of data from field and laboratory experiments covering different soil types, climatic regions, and plant species would enable a qualitatively, and quantitatively reliable assessment of soil hydrology impacts., but also dissolution rates and changes on soil's mineralogy. The impactseffects on soil microorganisms should be 1140 taken into account in order to correct the limits of rock powder deployment. The potential of rock powder to trigger plant suffocation, if gas exchange is prevented by water saturation of pores (Sairam, 2011), should also be considered before deployment.

Challenges of rock powder deployment
Average tillage depth common machinery can reach is 0.3 m and greater depths causecan be reached with higher energy, and 1145 labor costs (Fageria and Baligar, 2008). Since annual crops have an effective rooting depth typically in the range of 0.4 -0.7 m (Madsen, 1985;Aslyng, 1976;Munkholm et al., 2003;Olsen, 1958), a deployment depthsdepth of 0.3 m seems to be reasonable.
OnceSince tillage can trigger soil carbon loss (Reicosky, 1997;La Scala et al., 2006), deploying rock powder at soil surface might be a solution. At the soil surface, the long-term water percolation, and /or bioturbation (Fishkis et al., 2010;Taylor et al., 2015) can transport and mix fine-grained material to deeper regions within the soil profile, which potentially can change the 1150 , and PAW at crop rooting zones. Groundwater recharge rates might change if clogging of pores at deeper regions of soil profile occurs. or if the changes in soil hydraulic properties due to rock deployment can significantly influence the initial soil hydraulic conditions for a constant water precipitation. Taylor et al. (2015) argue that downward transport of a silt-textured powder deployed at a soil surface would easily reach the rooting zone of trees, which is in its majority in a depth up to 0.4 m.
The authors suggest that in tropical regions higher depths might be reached due to intensive rain and bioturbation.

1155
Detailed field studies to better comprehend downward transport of grained material through the soil profile, changes on soil water residence time, PAW, mineralogy, nutrient pools, CEC (Anda et al., 2015(Anda et al., , 2013, and bioavailability of released trace metals (Renforth et al., 2015) are necessary, to be able to. This would provide management recommendations for the diverse existing settings for EW application. In the present study, estimates for different basalt powder application upper limits are done for changes in soil hydraulic properties without accounting for downward transport of fine particles through the soil 1160 profile.
Besides avoiding clogging of pores of the top soil layer by rock powder application in a certain extent, downward transport of rock powder can contribute freshly ground material being in contact with roots of trees or crops, which can enhance the weathering rates and create new sites to retain nutrients Anda et al., 2015).
Once the freshly ground material is in contact with the soil, different factors control the nutrient supply efficiency of rock

1170
Full dissolution is a simplification based on modelled scenarios (Taylor et al., 2015;. Under field conditions, soil water could rapidly reach near-equilibrium concentrations (Grathwohl, 2014), which would decrease weathering rates. The opposite would occur if near-equilibrium conditions could be disturbed by a sink of nutrients by nutrient root uptake (Stefánsson et al., 2001) or by percolation of water un-equilibrated with soil porous water (Calabrese et al., 2017).
The nutrient (Mg, Ca, K, P, etc.) content of rocks can vary significantly. Besides that, deploying rock powders with grain sizes 1175 > 90 µm would decrease the reactive surface area of deployed rock powder decreasing the weathering fluxes (Goddéris et al., 2006). The median and the ranges (5 th or 95 th percentile) values for Mg, Ca, K, P content obtained from the EarthChem database considered chemical analysis of 2985 rhyolites, 3008 dacites, 11099 andesites, and 23816 basalts. Broadening the classification criteria for these rocks would change median and the ranges (5 th or 95 th percentile) for chemical composition; however, the selected median and the ranges of this study are conservative estimates. As an illustration,  1180 adopted another selection criteria, for the same database, which resulted in a total of 97895 samples and estimated a median Besides the potential to be used to rejuvenate soil nutrient pools (Leonardos et al., 1987), silicate rock powder can be used to reduce the risk of nitrate mobilization, being indicated for regions in which special care to water preservation is needed.
However, extra input of sodium (Na) to the system, if the rock is rich in this element, could disturb this amelioration effect 1190 (Von Wilpert and Lukes, 2003)However, extra input of sodium (Na) to the system, if the rock is rich in this element, could disturb this amelioration effect (Von Wilpert and Lukes, 2003). Besides decreasing nitrate mobilization, co-application of rock powder with other fertilizers can increase the biomass production of crops (Anda et al., 2013;Leonardos et al., 1987;Theodoro et al., 2013).
An additional challenge of the application of rock products will be the assessment of the fate of weathering products, which 1195 might be transported eventually into river systems and alter geochemical baselines as evidenced by past land use changes in some large rivers Raymond and Hamilton, 2018).

Conclusions
Our results illustrate the potential of Enhanced Weathering (EW) to act as a nutrient source to nutrient demanding AR and BG.
This is an important, yet often overlooked, aspect of EW besides CO2 sequestration. The investigated scenarios show that areas 1200 with undersupply of P exist, and a C-stock reduction is expected to occur if P is the only limiting nutrient. Considering N, and P deficiency together for a low geogenic P supply and high biomass P demand, the C-stock reduction increaseswill be up to 59% of the projected total global C sequestration potential of 224 Gt C from the N-unlimited AR scenario. Potential P deficiencies were here based on the soil P availability and P demand scenarios, indicating that the inclusion of P cycles in AR models is necessary to accurately project the C sequestration of forests. Industrial fertilizers can be used to alleviate the P 1205 deficiency but the extra input of ammonium along with it can undermine the carbon budget and acidify the soils. Furthermore, acidic soil conditions generally favors the sorption of orthophosphate onto Fe-and Al-(hydro)oxides surfaces and clay minerals, essentially demobilizing P (Shen et al., 2011).
Besides the high chemical P content and relative fast weathering rates, the equilibrated supply of Ca, K, and Mg put the use of basalt powder one step ahead as a potential alternative to industrial fertilizers. Regrowth of forests on abandoned agricultural 1210 land is a passive landscape restoration method (Bowen et al., 2007). In most of the cases soils become acidic in abandoned agricultural land in the long term (Hesterberg, 1993), which favors the leaching of nutrients (Haynes and Swift, 1986) and heavy metals (Hesterberg, 1993). As a consequence, the regrowth rate of forests might be limited in acidic soils. The use of basalt powder will keep a positive carbon budget, increase the soil pH (Anda et al., 2015;Anda et al., 2009) [g P m -2 ] 0 -1.1 1.1 -3.1 3.1 -5.9 5.9 -14.8 14. 8 -16.6 [g P m -2 ] 0 -1.1 1.1 -3.1 3.1 -5.9 5.9 -6.7    (Table 1). a) Geogenic P supply scenario one (geogenic P from weathering plus atmospheric P deposition as source of P). bb) Basalt deployment necessary to close P gaps from P budget 1710 scenario of Fig. 5a. c) Geogenic P supply scenario two (geogenic P from soil inorganic labile P and organic P pools plus atmospheric P deposition and P from weathering as source of P). d) Basalt deployment necessary to close P gaps from P budget scenario of Fig.  5c. Map generated with ESRI ArcGIS 10.67 (http://www.esri.com). Fig. 6: Reduction on forest C sequestration due to geogenic P limitation. C-reduction estimated from stoichiometric C:P ratios for the N-limited AR scenario assuming P concentrations within foliar and wood material corresponding to mean values (Table  1). On Fig. 2b we present the C sequestration potential if geogenic P supply is not limiting biomass growth. a) C-reduction based 1720 on P gaps of Fig. 2Fig. 5a, obtained for geogenic P supply scenario one (geogenic P from weathering plus atmospheric P deposition as source of P). b) C-reduction based on P gaps of Fig. 2bFig. 5c, obtained for geogenic P supply scenario two (geogenic P from soil inorganic labile P and organic P pools plus atmospheric P deposition and P from weathering as source of P). For resulting global C reduction check 1730 and minimum (<<1 g P m -2 ) gap of each geogenic P supply scenario for P and derived Mg, Ca, and K demand for balanced tree nutrition assuming mean foliar and wood material chemistry (Table 1). a) Based on minimum and maximum P gap values of <1 g P m -2 and 17.116.6 g P m -2 , which were obtained for a geogenic P supply scenario one (geogenic P from weathering plus atmospheric P deposition as source of P). b) Based on minimum and maximum P gap values of <1 g P m -2 and 6.67 g P m -2 , which were obtained for a geogenic P supply scenario two (geogenic P from soil inorganic labile P and organic P pools plus 1735 atmospheric P deposition and P from weathering as source of P).

1740
Median and ranges (5 th and 95 th percentiles) of potential supply based on rock chemistry. Fig. 9: Projected K and P supply (logarithmic curve) by basalt dissolution given as median ranges (5 th and 5/95% confidence interval95 th percentiles) for bioenergy grasses K and P demand (horizontal filled boxes) based on global minimum 0.7 kg m -2 a -1 and maximum 3.6 kg m -2 a -1 harvest 1745 rates for simulation years of 1995 -2090. The amount of exported nutrients by several harvest rates higher than the minimum and lower than the maximum harvest rates are represented by the vertical filled boxes. and PAWini is the estimated initial PAW of different soils. a) Application of a fine basalt texture (15.6% clay, 83.8% silt, and 0.6% fine sand). b) Application of a coarse basalt texture (15.6% clay, 53.8% silt, and 30.6% fine sand) for areas corresponding to P gaps of geogenic P supply scenario one, for the N-unlimited AR scenario (Supplement S1 Fig. S7a). Mean and standard deviations for n=15318 grid cells. cf., Supplement S1 section D for impacts on initial and PAW of fine or coarse basalt powder texture on soils of P gap areas from (Supplement S1 Fig. S7c).

Fig. 11: Relative impacts on soil saturated hydraulic conductivity ( ) and Plant Available Water (PAW). Kbas and PAWbas respectively represents the estimated soil and PAW after basalt application. Kini is the estimated initial soil
and PAWini is the estimated initial PAW of different soils. a) Application of a fine basalt texture (15.6% clay, 83.8% silt, and 0.6% fine sand). b) Application of a coarse basalt texture (15.6% clay, 53.8% silt, and 30.6% fine sand) for areas corresponding to P budget scenario two, for the N-unlimited AR scenario (Supplement S1 Fig. S7c). Mean and standard deviations for n=2525 grid cells. Fig. 12: Relative impacts on soil saturated hydraulic conductivity ( ) and Plant Available Water (PAW). Kbas and PAWbas respectively represent the estimated soil and PAW after basalt application. Kini is the estimated initial soil and PAWini is the estimated initial PAW of different soils. a) Application of a fine basalt texture (15.6% clay, 83.8% silt, and 0.6% fine sand). b) Application of a coarse basalt texture (15.6% clay, 53.8% silt, and 30.6% fine sand) for areas corresponding to P gaps of geogenic P 1760 supply scenario one, for the N-unlimited AR scenario (Supplement S1 Fig. S21a). Mean and standard deviations for n=1525 grid cells. cf., Supplement S1 section S5 for impacts on initial and PAW of fine or coarse basalt powder texture on soils of P gap areas from b.: Impacts on soil hydrology estimated according to Saxton and Rawls (2006) equations for basalt deployment mass coincident to areas with potential P gap for the nutrient budget of the N-unlimited AR scenario assuming P concentrations within foliar and wood material corresponding to mean values (Supplement Fig. S7a). a) Hydraulic conductivity (K) changes relative to initial soil 1765 values for a fine basalt texture (15.6% clay, 83.8% silt, and 0.6% sand) being deployed. b) Hydraulic conductivity (K) changes relative to initial soil values for a coarse basalt texture (15.6% clay, 53.8% silt, and 30.6% fine sand) being deployed. c) Plant available water (PAW) changes relative to initial soil values for a fine basalt texture (15.6% clay, 83.8% silt, and 0.6% sand) being deployed. d) Plant available water (PAW) changes relative to initial soil values for a coarse basalt texture (15.6% clay, 53.8% silt, and 30.6% fine sand) being deployed. Map generated with ESRI ArcGIS 10.7 (http://www.esri.com).  (Vergutz et al., 2012). b Stoichiometric ratios derived from a US soft-and hardwood database (Pardo et al., 2005). cf., SI-table.xlsx file for used database.

P source Resolution
Geogenic P supply scenario one Geogenic P supply scenario two Reference Soil organic P and inorganic labile P 0.5° X (Yang et al., 2014a) Atmospheric P deposition 1° X X (Wang et al., 2017) Geogenic P release ratesP from weathering 1 km 2 X X    Table 4: Minimum and maximum soil hydraulic conductivity for areas coincident to the P gap areas of each geogenic P supply scenario one, for the N-unlimited AR scenario (Supplement S1 Fig. S21aS7a).
Geogenic P supply scenario one Geogenic P supply scenario two Formatted Table   Formatted Table