Data Tables Buhler Piqueux JGR 2021

We have provided data tables for figures 3-6 and model routines used in Buhler and Piqueux (2021), JGR. Figures 3 and 6 We have provided ten data tables: as_zreg.txt, matm.txt, mcap.txt, mreg.txt, matm_hist.txt, mcap_hist.txt, mreg_hist.txt, obl.txt, obl_hist.txt, and t_hist.txt. These tables contain the information shown in Fig. 3 and Fig. 6 in the text. as_zreg.txt is a 1-dimensional array of length 7 that contains the product of the specific surface area and regolith thickness zreg used in each of the seven model outputs, corresponding to the caption in Fig. 3 and Fig. 6. The data for Fig 3 is contained in: matm.txt, mcap.txt, mreg.txt, and obl.txt. obl.txt is a 1-dimensional array of length 91, spanning 0 to 90, that contains obliquity values in degrees. matm.txt, mcap.txt, and mreg.txt are each 2-dimensional arrays of shape (7, 91) that provide our model output solution for atmosphere mass (matm.txt), cap mass (mcap.txt), and adsorbed CO2 mass (mreg.txt) in kilograms as a function of obliquity (along the axis of length 91; corresponding to obl.txt) and regolith thickness (along the axis of length 7; corresponding to zreg.txt). All values were calculated assuming regolith thermal conductivity kreg = 1.0 W m-1 K-1 and regolith albedo Areg = 0.25. The data for Fig. 6 is contained in: matm_hist.txt, mcap_hist.txt, mreg_hist.txt, obl_hist.txt, and t_hist.txt. t_hist.txt is a 1-dimensional array of length 1000 with values of time referenced to J2000 in units of 1000 years. obl_hist.txt is a 1-dimensional array of length 1000 with values of obliquity in units of degrees from Laskar et al. (2004). matm_hist.txt, mcap_hist.txt, and mreg_hist.txt are each 2-dimensional arrays of shape (7, 1000) that provide our model output solution for atmosphere mass (matm.txt), cap mass (mcap.txt), and adsorbed CO2 mass (mreg.txt) in kilograms as a function of time (along the axis of length 1000; corresponding to t_hist.txt) and regolith thickness (along the axis of length 7; corresponding to as_zreg.txt). All values were calculated assuming regolith thermal conductivity kreg = 1.0 W m-1 K-1 and regolith albedo Areg = 0.25. Figure 4 MCMC_chains.txt is a table of size 3 x 1e7. The axis of length 1e7 correspond to steps in the MCMC simulation. Values in the first row are the regolith thermal conductivity (k; W m-1 K-1) value, values in the second row are the regolith thickness (z_reg; m) value, and values in the third row are the regolith specific surface area (a_S; m2 kg-1) value at each timestep. Figure 5 mtothistx.txt is a table of size 1 x 100 containing the bin value total obliquity-timescale exchangeable inventory (kg).mtothisty_norm is a table of size 1 x 100 containing the normalized probability density (unitless) for the corresponding mass bin index. Figure 7 Figure 7 comprises an ensemble of 5e6 draws of model results for MCID bounding layer elevations and total obliquity-timescale exchangeable CO2 reservoirs taken from the model input parameter probability distributions shown in Figure 4.elevs0.txt is a table of size 1 x 5e6 containing the fraction of the MCID modeled to be below the topmost bounding layer of water ice (unitless).elevs1.txt is a table of size 1 x 5e6 containing the fraction of the MCID modeled to be below the second topmost bounding layer of water ice.elevs2.txt is a table of size 1 x 5e6 containing the fraction of the MCID modeled to be below the third topmost bounding layer of water ice.elevs3.txt is a table of size 1 x 5e6 containing the fraction of the MCID modeled to be below the bottommost bounding layer of water ice. mtots.txt is a table of size 1 x 5e6 containing the total obliquity-timescale exchangeable CO2 reservoir corresponding to elevation indices in elevs0.txt, elevs1.txt, elevs2.txt, and elevs3.txt. Model Routines Construct Subsurface Temperature Arrays.py is a 1d thermal diffusion model that constructs subsurface temperature arrays as a function of latitude, depth, and insolation (based on orbit parameters) in sub-sol time steps. Construct mean annual subsurface arrays_v0.3.py creates the mean annual subsurface profile from the output of Construct Subsurface Temperature Arrays.py for more efficient calculation in Pressure_reg_only_iterator_v8.py.Pressure_reg_only_iterator_v8.py is a joint atmosphere-regolith equilibration model (without a CO2 ice cap) that calculates the atmospheric pressure in equilibrium with a regolith of given defined properties as a function of orbit parameters, using as input the mean annual temperature profiles output from Construct Subsurface Temperature Arrays.py. These equilibrium solutions are an input that improves numerical stability for Pressure_MCID_reg_iterator_v8.py. Pressure_MCID_reg_iterator_v8.py is the full joint cap-atmosphere-regolith equilibration model that calculates the equilibrium atmospheric pressure, cap mass, and adsorbed CO2 as a function of orbit parameters, using as input the mean annual temperature profiles output from Construct Subsurface Temperature Arrays.py and regolith-atmosphere equilibrium solutions from Pressure_reg_only_iterator_v8.py. The difference in cap mass at each of the previous obliquity maxima can then be used to find the model-predicted layer thicknesses of the MCID as input to MCMC.py. MCMC.py is the Markov Chain Monte Carlo model that compares modeled stratigraphy to the observed stratigraphy of the MCID. References Laskar, J., Correia, A.C.M., Gastineau, M., Joutel, F., Levrard, B., Robutel, P., 2004. Long term evolution and chaotic diffusion of the insolation quantities of Mars. Icarus 170, 343–364

本数据集提供了Buhler与Piqueux（2021，《地球物理学研究杂志》（Journal of Geophysical Research，JGR））一文中图3至6及所用模型程序对应的数据表格。本次共提供10个数据表：as_zreg.txt、matm.txt、mcap.txt、mreg.txt、matm_hist.txt、mcap_hist.txt、mreg_hist.txt、obl.txt、obl_hist.txt及t_hist.txt，上述表格包含正文图3与图6展示的相关信息。
as_zreg.txt为长度7的一维数组，包含7组模型输出中所用的比表面积与风化层厚度zreg的乘积，对应图3与图6的图例说明。
图3的相关数据包含于matm.txt、mcap.txt、mreg.txt及obl.txt中。其中obl.txt为长度91的一维数组，取值范围为0至90，单位为度，包含黄赤交角数值。matm.txt、mcap.txt及mreg.txt均为形状(7, 91)的二维数组，分别提供大气质量（matm.txt）、冰盖质量（mcap.txt）与吸附态二氧化碳（CO₂）质量（mreg.txt）的模型输出解，单位为千克，其数值随黄赤交角（沿长度为91的轴，对应obl.txt）与风化层厚度（沿长度为7的轴，对应as_zreg.txt）变化。所有数值均基于风化层热导率kreg=1.0 W·m⁻¹·K⁻¹、风化层反照率Areg=0.25的假设计算得到。
图6的相关数据包含于matm_hist.txt、mcap_hist.txt、mreg_hist.txt、obl_hist.txt及t_hist.txt中。t_hist.txt为长度1000的一维数组，数值为以J2000为基准的时间，单位为1000年。obl_hist.txt为长度1000的一维数组，单位为度，包含来自Laskar等人（2004）的黄赤交角数值。matm_hist.txt、mcap_hist.txt及mreg_hist.txt均为形状(7, 1000)的二维数组，分别提供大气质量、冰盖质量与吸附态CO₂质量的模型输出解，单位为千克，其数值随时间（沿长度为1000的轴，对应t_hist.txt）与风化层厚度（沿长度为7的轴，对应as_zreg.txt）变化。所有数值均基于风化层热导率kreg=1.0 W·m⁻¹·K⁻¹、风化层反照率Areg=0.25的假设计算得到。
图4 对应的MCMC_chains.txt为尺寸3×10⁷的数据表，长度为10⁷的轴对应马尔可夫链蒙特卡洛（Markov Chain Monte Carlo，MCMC）模拟的步数。第一行的数值为各时间步的风化层热导率（k；W·m⁻¹·K⁻¹），第二行的数值为风化层厚度（z_reg；m），第三行的数值为风化层比表面积（a_S；m²·kg⁻¹）。
图5 对应的mtothistx.txt为尺寸1×100的数据表，包含分箱后的总黄赤交角时间尺度可交换储量，单位为千克。mtothisty_norm为尺寸1×100的数据表，包含对应质量分箱索引的归一化概率密度，无量纲。
图7 包含5×10⁶组模型结果的集合，对应取自图4所示模型输入参数概率分布的MCID边界层高程及总黄赤交角时间尺度可交换CO₂储量。elevs0.txt为尺寸1×5×10⁶的数据表，包含模拟得到的低于最顶部水冰边界层的MCID占比，无量纲。elevs1.txt为尺寸1×5×10⁶的数据表，包含模拟得到的低于第二顶部水冰边界层的MCID占比。elevs2.txt为尺寸1×5×10⁶的数据表，包含模拟得到的低于第三顶部水冰边界层的MCID占比。elevs3.txt为尺寸1×5×10⁶的数据表，包含模拟得到的低于最底部水冰边界层的MCID占比。mtots.txt为尺寸1×5×10⁶的数据表，包含对应elevs0.txt、elevs1.txt、elevs2.txt及elevs3.txt中高程索引的总黄赤交角时间尺度可交换CO₂储量。
模型程序 Construct Subsurface Temperature Arrays.py 为一维热扩散模型，基于轨道参数构建随纬度、深度及日照辐射变化的地下温度数组，时间步为亚太阳时步。Construct mean annual subsurface arrays_v0.3.py 基于Construct Subsurface Temperature Arrays.py的输出生成年均地下温度剖面，以用于Pressure_reg_only_iterator_v8.py中的高效计算。Pressure_reg_only_iterator_v8.py为联合大气-风化层平衡模型（不含CO₂冰盖），基于Construct Subsurface Temperature Arrays.py输出的年均温度剖面作为输入，计算给定属性的风化层与轨道参数对应的平衡大气压强。该平衡解可作为输入提升Pressure_MCID_reg_iterator_v8.py的数值稳定性。Pressure_MCID_reg_iterator_v8.py为完整的联合冰盖-大气-风化层平衡模型，基于Construct Subsurface Temperature Arrays.py输出的年均温度剖面及Pressure_reg_only_iterator_v8.py得到的风化层-大气平衡解作为输入，计算轨道参数对应的平衡大气压强、冰盖质量与吸附态CO₂含量。可利用各前序黄赤交角极大值处的冰盖质量差异，得到模型预测的MCID层厚度，作为MCMC.py的输入。MCMC.py为马尔可夫链蒙特卡洛模型，用于将模拟地层与MCID的观测地层进行比对。
参考文献 Laskar, J., Correia, A.C.M., Gastineau, M., Joutel, F., Levrard, B., Robutel, P., 2004. 火星日照参数的长期演化与混沌扩散. 《伊卡洛斯》（Icarus）170, 343–364