scholarly journals SolveSAPHE-r2: revisiting and extending the Solver Suite for Alkalinity-PH Equations for usage with CO<sub>2</sub>, HCO<sub>3</sub><sup>−</sup> or CO<sub>3</sub><sup>2−</sup> input data

2021 ◽  
Author(s):  
Guy Munhoven

Abstract. The successful and efficient approach at the basis of SolveSAPHE (Munhoven, 2013), which determines the carbonate system speciation by calculating pH from total alkalinity (AlkT) and dissolved inorganic carbon (CT), and which converges from any physically sensible pair of such data, has been adapted and further developed for work with AlkT &amp; CO2, AlkT &amp; HCO3− and AlkT &amp; CO32−. The mathematical properties of the three modified alkalinity-pH equations are explored. It is shown that the AlkT &amp; CO2 and AlkT &amp; HCO3− problems have one and only one positive root for any physically sensible pair of data (i.e., such that, resp., [CO2] > 0 and [HCO3−] > 0). The space of AlkT &amp; CO32− pairs is partitioned into regions where there is either no solution, one solution or where there are two. The numerical solution of the modified alkalinity-pH equations is far more demanding than that for the original AlkT-CT pair as they exhibit strong gradients and are not always monotonous. The two main algorithms used from SolveSAPHE v.1 had to be revised in depth to reliably process the three additional data input pairs. The AlkT &amp; CO2 pair is numerically the most challenging. With the Newton-Raphson based solver, it takes about five times as long to solve as the companion AlkT &amp; CT pair, while AlkT &amp; CO2 requires about four times as much time. All in all, it is nevertheless the secant based solver that offers the best performances. It outperforms the Newton-Raphson based one by up to a factor of four, to reach equation residuals that are up to seven orders of magnitude lower. Just like the pH solvers from routines from the v.1 series, SolveSAPHE v.2 includes automatic root bracketing and efficient initialisation schemes for the iterative solvers. For AlkT &amp; CO32− pairs of data, it also determines the number of roots and calculates non-overlapping bracketing intervals. An open source reference implementation in Fortran 90 of the new algorithms is made publicly available for usage under the GNU Lesser General Public Licence v.3 or later.

2021 ◽  
Vol 14 (7) ◽  
pp. 4225-4240
Author(s):  
Guy Munhoven

Abstract. The successful and efficient approach at the basis of the Solver Suite for Alkalinity-PH Equations (SolveSAPHE) (Munhoven, 2013), which determines the carbonate system speciation by calculating pH from total alkalinity (AlkT) and dissolved inorganic carbon (CT), and which converges for any physically sensible pair of such data, has been adapted and further developed to work with AlkT–CO2, AlkT–HCO3-, and AlkT–CO32-. The mathematical properties of the three modified alkalinity–pH equations are explored. It is shown that the AlkT–CO2, and AlkT–HCO3- problems have one and only one positive root for any physically sensible pair of data (i.e. such that [CO2]>0 and [HCO3-]>0). The space of AlkT–CO32- pairs is partitioned into regions where there is either no solution, one solution or where there are two. The numerical solution of the modified alkalinity–pH equations is far more demanding than that for the original AlkT–CT pair as they exhibit strong gradients and are not always monotonous. The two main algorithms used in SolveSAPHE v1 have been revised in depth to reliably process the three additional data input pairs. The AlkT–CO2 pair is numerically the most challenging. With the Newton–Raphson-based solver, it takes about 5 times as long to solve as the companion AlkT–CT pair; the AlkT–CO32- pair requires on average about 4 times as much time as the AlkT–CT pair. All in all, the secant-based solver offers the best performance. It outperforms the Newton–Raphson-based one by up to a factor of 4 in terms of average numbers of iterations and execution time and yet reaches equation residuals that are up to 7 orders of magnitude lower. Just like the pH solvers from the v1 series, SolveSAPHE-r2 includes automatic root bracketing and efficient initialisation schemes for the iterative solvers. For AlkT–CO32- data pairs, it also determines the number of roots and calculates non-overlapping bracketing intervals. An open-source reference implementation of the new algorithms in Fortran 90 is made publicly available for usage under the GNU Lesser General Public Licence version 3 (LGPLv3) or later.


2021 ◽  
Author(s):  
Guy Munhoven

&lt;p&gt;SolveSAPHE, the Solver Suite for Alkalinity-PH Equations (Munhoven, 2013, DOI:10.5194/gmd-6-1367-2013), hereafter SolveSAPHE v.1, was the first carbonate chemistry speciation package that was able to securely and reliably calculate pH for any physically meaningful pair of total alkalinity (Alk&lt;sub&gt;T&lt;/sub&gt;) and dissolved inorganic carbon (&lt;em&gt;C&lt;/em&gt;&lt;sub&gt;T&lt;/sub&gt;) values. We have now revised and extended the solution approach developed for SolveSAPHE v.1 so that Alk&lt;sub&gt;T&lt;/sub&gt; &amp; CO&lt;sub&gt;2&lt;/sub&gt;, Alk&lt;sub&gt;T&lt;/sub&gt; &amp; HCO&lt;sub&gt;3&lt;/sub&gt; and Alk&lt;sub&gt;T&lt;/sub&gt; &amp; CO&lt;sub&gt;3&lt;/sub&gt; problems can be processed as well.&lt;/p&gt;&lt;p&gt;The mathematical analysis of the modified alkalinity-pH equations reveals that the Alk&lt;sub&gt;T&lt;/sub&gt; &amp; CO&lt;sub&gt;2&lt;/sub&gt; and Alk&lt;sub&gt;T&lt;/sub&gt; &amp; HCO&lt;sub&gt;3&lt;/sub&gt; problems have one and only one positive root for any physically sensible pair of data (i.e., such that, resp., [CO&lt;sub&gt;2&lt;/sub&gt;] &gt; 0 and [HCO&lt;sub&gt;3&lt;/sub&gt;&lt;sup&gt;&amp;#8211;&lt;/sup&gt;] &gt; 0). For Alk&lt;sub&gt;T&lt;/sub&gt; &amp; CO&lt;sub&gt;3&lt;/sub&gt; the situation is completely different: there are pairs of data values for which there is no solution, others for which there is one and still others for which there are two. Similarly to its predecessor, the new SolveSAPHE-r2 offers automatic root bracketing and efficient initialisation schemes for the iterative solvers. The Alk&lt;sub&gt;T&lt;/sub&gt; &amp; CO&lt;sub&gt;3&lt;/sub&gt; problem is furthermore autonomously and completely characterised: for any given pair of data values, the number of solutions is determined and non-overlapping bracketing intervals are calculated.&lt;/p&gt;&lt;p&gt;The numerical solution of the alkalinity-pH equations for the three new pairs is far more difficult than for the Alk&lt;sub&gt;T&lt;/sub&gt; &amp; &lt;em&gt;C&lt;/em&gt;&lt;sub&gt;T&lt;/sub&gt; pair. The Newton-Raphson and the secant based solvers from SolveSAPHE v.1 had to be reworked in depth to reliably process the three additional data input pairs. The Alk&lt;sub&gt;T&lt;/sub&gt; &amp; CO&lt;sub&gt;2&lt;/sub&gt; pair is computationally the most demanding. With the Newton-Raphson based solver, it takes about five times as long to solve as the companion Alk&lt;sub&gt;T&lt;/sub&gt; &amp; &lt;em&gt;C&lt;/em&gt;&lt;sub&gt;T&lt;/sub&gt; pair, while Alk&lt;sub&gt;T&lt;/sub&gt; &amp; CO&lt;sub&gt;3&lt;/sub&gt;&lt;sup&gt;2&amp;#8211;&lt;/sup&gt; requires about four times as much time. All in all, the secant based solver offers the best performances. It outperforms the Newton-Raphson based one by up to a factor of four and leads to equation residuals that are up to seven orders of magnitude lower. For carbonate speciation problems posed by Alk&lt;sub&gt;T&lt;/sub&gt; and either one of [CO&lt;sub&gt;2&lt;/sub&gt;], [HCO&lt;sub&gt;3&lt;/sub&gt;&lt;sup&gt;&amp;#8211;&lt;/sup&gt;] or [CO&lt;sub&gt;3&lt;/sub&gt;&lt;sup&gt;2&amp;#8211;&lt;/sup&gt;] the secant based routine from SolveSAPHE-r2 is clearly the method of choice; for calculations with Alk&lt;sub&gt;T&lt;/sub&gt; &amp; &lt;em&gt;C&lt;/em&gt;&lt;sub&gt;T&lt;/sub&gt;, the SolveSAPHE v.1 solvers will perform better, due to the mathematically favourable characteristics of the alkalinity-pH equation for that pair.&lt;/p&gt;


2009 ◽  
Vol 6 (11) ◽  
pp. 2421-2431 ◽  
Author(s):  
M. Chierici ◽  
A. Fransson

Abstract. In the summer of 2005, we sampled surface water and measured pH and total alkalinity (AT) underway aboard IB Oden along the Northwest Passage from Cape Farewell (South Greenland) to the Chukchi Sea. We investigated the variability of carbonate system parameters, focusing particularly on carbonate concentration [CO32−] and calcium carbonate saturation states, as related to freshwater addition, biological processes and physical upwelling. Measurements on AT, pH at 15°C, salinity (S) and sea surface temperature (SST), were used to calculate total dissolved inorganic carbon (CT), [CO32−] and the saturation of aragonite (ΩAr) and calcite (ΩCa) in the surface water. The same parameters were measured in the water column of the Bering Strait. Some surface waters in the Canadian Arctic Archipelago (CAA) and on the Mackenzie shelf (MS) were found to be undersaturated with respect to aragonite (ΩAr<1). In these areas, surface water was low in AT and CT (<1500 μmol kg−1) relative to seawater and showed low [CO32−]. The low saturation states were probably due to the likely the effect of dilution due to freshwater addition by sea ice melt (CAA) and river runoff (MS). High AT and CT and low pH, corresponded with the lowest [CO32−], ΩAr and ΩCa, observed near Cape Bathurst and along the South Chukchi Peninsula. This was linked to the physical upwelling of subsurface water with elevated CO2. The highest surface ΩAr and ΩCa of 3.0 and 4.5, respectively, were found on the Chukchi Sea shelf and in the cold water north of Wrangel Island, which is heavily influenced by high CO2 drawdown and lower CT from intense biological production. In the western Bering Strait, the cold and saline Anadyr Current carries water that is enriched in AT and CT from enhanced organic matter remineralization, resulting in the lowest ΩAr (~1.2) of the area.


2017 ◽  
Author(s):  
Jacoba Mol ◽  
Helmuth Thomas ◽  
Paul G. Myers ◽  
Xianmin Hu ◽  
Alfonso Mucci

Abstract. The Mackenzie Shelf in the southeastern Beaufort Sea is a region that has experienced large changes in the past several decades as warming, sea-ice loss, and increased river discharge have altered carbon cycling. Upwelling and downwelling events are common on the shelf, caused by strong, fluctuating along-shore winds, resulting in cross-shelf Ekman transport, and an alternating estuarine and anti-estuarine circulation. Downwelling carries inorganic carbon and other remineralization products off the shelf and into the deep basin for possible long-term storage in the world oceans. Upwelling carries dissolved inorganic carbon (DIC) and nutrient-rich waters from the Pacific-origin upper halocline layer (UHL) onto the shelf. Profiles of DIC and total alkalinity (TA) taken in August and September of 2014 are used to investigate the cycling of inorganic carbon on the Mackenzie Shelf. The along-shore transport of water and the cross-shelf transport of inorganic carbon are quantified using velocity field output from a simulation of the Arctic and Northern Hemisphere Atlantic (ANHA4) configuration of the Nucleus of European Modelling of the Ocean (NEMO) framework. A strong upwelling event prior to sampling on the Mackenzie Shelf is analyzed and the resulting influence on the carbonate system, including the saturation state of waters with respect to aragonite and pH, is investigated. TA and the oxygen isotope ratio of water (δ18O) are used to examine water-mass distributions in the study area and to investigate the influence of Pacific Water, Mackenzie River freshwater, and sea-ice melt on carbon dynamics and air-sea fluxes of carbon dioxide (CO2) in the surface mixed layer. Understanding carbon transfer in this seasonally dynamic environment is key to quantify the importance of Arctic shelf regions to the global carbon cycle and provide a basis for understanding how it will respond to the aforementioned climate-induced changes.


2018 ◽  
Author(s):  
Haoyi Yao ◽  
Wei-Li Hong ◽  
Giuliana Panieri ◽  
Simone Sauer ◽  
Marta E. Torres ◽  
...  

Abstract. We report on a rare observation of a mini-fracture in near-surface sediments (30 cm below the seafloor) visualized using rotational scanning X-ray of a core recovered from the Lomvi pockmark, Vestnesa Ridge west of Svalbard (1200 m water depth). Porewater geochemistry and lipid biomarker signatures revealed clear differences in the geochemical and biogeochemical regimes of this core compared with two additional ones recovered from pockmarks sites at Vestnesa Ridge, which we attribute to differential methane transport mechanisms. In the sediments core featuring the shallow mini-fracture at pockmark Lomvi, we observed high concentrations of both methane and sulfate throughout the core in tandem with moderately elevated values for total alkalinity, 13C-depleted dissolved inorganic carbon (DIC), and 13C-depleted lipid biomarkers (diagnostic for the slow-growing microbial communities mediating the anaerobic oxidation of methane with sulfate – AOM). In another core recovered from the same pockmark about 80 m away from the fractured core, we observed complete sulfate depletion in the top centimeters of the sediment and much more pronounced signatures of AOM than in the fractured core. Our data indicate a gas advection-dominated transport mode in both cores facilitating methane migration into sulfate-rich surface sediments. However, the more moderate expression of AOM signals suggest a rather recent onset of gas migration at the site of the fractured core, while the geochemical evidence for a well-established AOM community at the second coring site at the Lomvi pockmark suggest that gas migration has been going on for a longer period of time. A third core recovered from Lunde pockmark was dominated by diffusive transport with only weak geochemical and biogeochemical evidence for AOM. Our study highlights that advective fluid and gas transport supported by mini-fractures can be important in modulating methane dynamics in surface sediments.


2013 ◽  
Vol 10 (5) ◽  
pp. 8283-8311 ◽  
Author(s):  
M. Wakita ◽  
S. Watanabe ◽  
M. Honda ◽  
A. Nagano ◽  
K. Kimoto ◽  
...  

Abstract. Rising atmospheric CO2 contents have led to greater CO2 uptake by the oceans, lowering both pH due to increasing hydrogen ions and CaCO3 saturation states due to declining carbonate ion (CO32−). Here, we used previously compiled data sets and new data collected in 2010 and 2011 to investigate ocean acidification of the North Pacific western subarctic gyre. In winter, the western subarctic gyre is a source of CO2 to the atmosphere because of convective mixing of deep waters rich in dissolved inorganic carbon (DIC). We calculated pH in winter mixed layer from DIC and total alkalinity (TA), and found that it decreased at the rate of −0.001 ± 0.0004 yr−1 from 1997 to 2011. This decrease rate is slower than that expected under condition of seawater/atmosphere equilibration, and it is also slower than the rate in the subtropical regions (−0.002 yr−1). The slow rate is caused by a reduction of CO2 emission in winter due to an increase in TA. Below the mixed layer, the calcite saturation horizon (~185 m depth) shoaled at the rate of 2.9 ± 0.9 m yr−1 as the result of the declining CO32− concentration (−0.03 ± 0.01 μmol k−1yr−1). Between 200 m and 300 m depth, pH decline during the study period (−0.0051 ± 0.0010 yr−1) was larger than ever reported in the open North Pacific. This enhanced acidification rate below the calcite saturation horizon reflected not only the uptake of anthropogenic CO2 but also the increase in the decomposition of organic matter evaluated from the increase in AOU, which suggests that the dissolution of CaCO3 particles increased.


2021 ◽  
Author(s):  
Sina Bold ◽  
Justus E.E. van Beusekom ◽  
Yoana G. Voynova ◽  
Marius Cysewski ◽  
Bryce Van Dam ◽  
...  

&lt;p&gt;Estuaries are crucial in transforming matter fluxes from land to sea. To better understand and quantify these processes and respective fluxes, it is important to determine the input into an estuary accurately. To allow for such studies in the Elbe estuary in Germany, a state-of-the-art research platform is currently being set-up just upstream of the weir in Geesthacht at the entrance of the estuary. Here, we report on small-scale spatial dynamics of organic matter and associated processes from several cross and longitudinal profiles around the planned location and the implications for the set-up of the aforementioned research platform.&lt;/p&gt;&lt;p&gt;Based on preliminary data obtained in August 2020 during a period of relatively low discharge, we present the following results: (1) In three cross profiles along a 10 km transect of the Elbe upstream of the weir, we observed considerable small-scale gradients regarding currents and various biogeochemical parameters. In comparison to the fairway, water from the riverbanks was depleted in suspended particulate matter, chlorophyll a, dissolved oxygen, and nitrate, and enhanced in ammonium, phosphate and silicate, as well as total alkalinity and dissolved inorganic carbon paralleled by decreasing pH. This suggests that in the summer, organic matter is deposited and remineralised at the riverbanks, resulting in the release of ammonium, phosphate and silicate, and in the removal of nitrate, presumably by denitrification. (2) Along the 10 km transect towards the weir, we observed that concentrations of suspended particulate matter, chlorophyll a, dissolved oxygen, nitrate and pH were decreasing. In contrast, we found that ammonium, phosphate and silicate, total alkalinity and dissolved inorganic carbon increased towards the weir. This suggests an increased sedimentation and subsequent remineralisation due to the reduced flow velocities in front of the weir. (3) An analysis of a 10-year time series from the weir supports this by showing higher ammonium concentrations when discharges were relatively low. The implications of these findings for the set-up of the research platform in this area, as well as for optimising estimates of budgets are discussed. The research platform will contribute to understand further such variations in biogeochemical parameters at the entrance of the Elbe estuary over time.&lt;/p&gt;&lt;p&gt;The research platform is set-up in cooperation with the Helmholtz initiative MOSES (&amp;#8220;Modular Observation Solutions for Earth Systems&amp;#8220;) and will be incorporated in the Elbe-North Sea Supersite of DANUBIUS-RI (&amp;#8220;International Centre for Advanced Studies on River-Sea Systems&amp;#8220;). Funding is provided by European Regional Development Funds, the federal state of Schleswig-Holstein, the Helmholtz Association and the Helmholtz-Zentrum Geesthacht. The research platform, planned to be operational in autumn 2021, will also be open for users e.g. to develop and test new methods and technologies. Data will be made available through the &amp;#8220;Helmholtz Coastal Data Centre&amp;#8221; (HCDC).&lt;/p&gt;


2021 ◽  
Author(s):  
Kunal Madkaiker ◽  
Vinu Valsala

&lt;p&gt;The Indian Ocean (IO) is witnessing acidification of its surface waters as a consequence of the continuous rising of atmospheric CO&lt;sub&gt;2&lt;/sub&gt; concentration thus disrupting the biological and chemical balance of the ecosystem in the region. The basin wide spatial variability of biogeochemical properties induces spatial variability of surface water pH. This study investigates the seasonality and trends of surface pH over the IO bioprovinces and regionally assesses the individual contribution of the factors affecting its variability. Simulations from global ocean models (OTTM and ROMS) coupled with suitable biogeochemical modules were validated with pH observations over the basin, and used to discern the regional response of pH seasonality (1990-2010) and trend (1961-2010) to changes in ocean temperature (SST), Dissolved Inorganic Carbon (DIC), Total Alkalinity (ALK) and Salinity (S). DIC and SST are the major contributors to the seasonal variability of pH in almost all bioprovinces consistent in both model simulations. The acidification in IO basin of 0.0675 units during 1961-2010 is attributed to 69.28% contribution of DIC followed by 13.82% contribution of SST. For most of the regions DIC remains a dominant contributor to changing trend in pH except for the Northern Bay of Bengal and Around India (NBoB-AI) region, wherein pH trend is dominated by ALK (55.6%) and SST (16.8%). The interdependence of SST and S over ALK is significant in modifying the carbonate chemistry and biogeochemical dynamics of NBoB-AI and a part of tropical, subtropical IO. The strong negative correlation between SST and pH infers the increasing risk of acidification in the bioprovinces with the rising SST.&lt;/p&gt;&lt;p&gt;This study is an attempt to identify the regional influencers of pH variability so that adequate mitigation action can be planned and the acidification can be decelerated in near future.&lt;/p&gt;


2021 ◽  
Author(s):  
Uliana Kazakova ◽  
Alexander Polukhin

&lt;p&gt;The Kara Sea receives about 55 % of the total continental runoff to the Siberian Arctic. Water of the Yenisei and Ob Rivers with low salinity (mineralization), flowing into the sea, forms a surface desalinated layer. The desalinated layer spreads over the sea area under the influence of hydrological and meteorological factors. Meltwater generated by the melting of marine and riverine ice and precipitation contribute to the formation of a surface desalinated layer along with continental runoff.&lt;/p&gt;&lt;p&gt;Determining the amount of fresh water is not accurate enough if only the salinity of surface water is considered. It is possible to identify riverine water and meltwater using hydrochemical proxies. The ratio of the major ions in seawater differs from that in riverine and meltwater. River waters are characterized by an increased content of silicate and reduced values of total alkalinity. At the same time, it is possible to identify the waters of the Ob and Yenisei Rivers by the estimated values of the total alkalinity and dissolved inorganic carbon obtained during the research expeditions to the Kara sea from 1993 to 2020.&lt;/p&gt;&lt;p&gt;The calculation of the parts of waters of different origin is done as a result of solving a system of equations. It includes the salinity and alkalinity values of the observed surface waters and those presumably involved in the mixing process. The salinity and alkalinity values of meltwater are taken as 0 and 134 &amp;#181;M respectively.&lt;/p&gt;&lt;p&gt;The total contribution of the Ob and Yenisei runoff ranges from 20 to 90% as it approaches the estuarine areas. The correlation coefficient between the proportion of river water and the salinity of the surface layer is quite high, it is equal to -0.9. This characterizes the inverse linear relationship. The separate contribution of the waters of the Yenisei differs from the contribution of the waters of the Ob, which is related to the hydrological conditions of the rivers.&lt;/p&gt;&lt;p&gt;The contribution of meltwater to the formation of the surface layer of the Kara Sea did not exceed 20%, with the exception of the coastal zone of the Novaya Zemlya. In this coastal zone, meltwater provides the greatest contribution compared to the other sources, which is associated with glacial runoff.&lt;/p&gt;&lt;p&gt;The work is implemented in the framework of the state assignment of the Shirshov Institute of Oceanology RAS (theme No. 0149-2019-0008), with the support of the Russian Scientific Foundation (project &amp;#8470; 19-17-00196) and the grant of President of Russian Federation &amp;#8470; MK-860.2020.5.&lt;/p&gt;


2015 ◽  
Vol 12 (6) ◽  
pp. 1671-1682 ◽  
Author(s):  
J. Meyer ◽  
U. Riebesell

Abstract. Concerning their sensitivity to ocean acidification, coccolithophores, a group of calcifying single-celled phytoplankton, are one of the best-studied groups of marine organisms. However, in spite of the large number of studies investigating coccolithophore physiological responses to ocean acidification, uncertainties still remain due to variable and partly contradictory results. In the present study we have used all existing data in a meta-analysis to estimate the effect size of future pCO2 changes on the rates of calcification and photosynthesis and the ratio of particulate inorganic to organic carbon (PIC / POC) in different coccolithophore species. Our results indicate that ocean acidification has a negative effect on calcification and the cellular PIC / POC ratio in the two most abundant coccolithophore species: Emiliania huxleyi and Gephyrocapsa oceanica. In contrast, the more heavily calcified species Coccolithus braarudii did not show a distinct response when exposed to elevated pCO2/reduced pH. Photosynthesis in Gephyrocapsa oceanica was positively affected by high CO2, while no effect was observed for the other coccolithophore species. There was no indication that the method of carbonate chemistry manipulation was responsible for the inconsistent results regarding observed responses in calcification and the PIC / POC ratio. The perturbation method, however, appears to affect photosynthesis, as responses varied significantly between total alkalinity (TA) and dissolved inorganic carbon (DIC) manipulations. These results emphasize that coccolithophore species respond differently to ocean acidification, both in terms of calcification and photosynthesis. Where negative effects occur, they become evident at CO2 levels in the range projected for this century in the case of unabated CO2 emissions. As the data sets used in this meta-analysis do not account for adaptive responses, ecological fitness and ecosystem interactions, the question remains as to how these physiological responses play out in the natural environment.


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