Dome A Inverse Model

This is the result of a geophysical inversion for the ice sheet and basal hydrological state around Dome A, East Antarctica. The datasets used to constrain the inversion are observations of basal water, basal freeze-on, internal layers, and a geothermal flux prior. The inversion solved for best-fit geothermal flux and accumulation rate fields, along with their respective uncertainty and skewness, and also partitioned the fractional contribution of each individual data type towards constraining the final answer. Note that skewness fields are not statistically significant, but they are provided here for completeness anyway.Also included is the ice sheet state produced by the best-fit forward model, including: englacial and basal temperatures, basal melt/freeze rate and water flux, strain heating, hydraulic heating (ie, the combined thermal effect of PMP changes and viscous dissipation in the water system), ice velocity, strain rate, viscosity, and shape function; plus post-processing variables like ice age, best-fit H* in a D-J model, freeze-on thickness, model echo-free-zone thickness, isotopic smoothing due to diffusion, the oldest useful ice for ice coring, and the normalized elevation at which the oldest useful ice is found. Parameters included in the inversion results for both geothermal flux and accumulation rate: output of evolutionary algorithm, local optimization correction, best-fit fields, uncertainty estimate, skewness estimate, and fractional constraints contributed by the five constraints used in the inversion (water observations, freeze-on observations, internal layer observations, GHF prior, and smoothness contraint). Also contains an estimate of the bias in geothermal flux induced by the use of smoothed gridded topography that does not fully capture the deep narrow valleys where water is present. All inversion results variables are 2D.Best-fit model results include: englacial temperature (3D), basal temperature (2D), basal logical state (wet/dry; 2D), basal melt rate (2D), basal water flux (2 components plus magnitude, 2D), hydraulic heating (sum of viscous dissipation and supercooling in basal hydrological system, 2D), ice velocity (3 components, 3D), vertically averaged ice velocity (2 components plus magnitude, 2D), effective strain rate (3D), effective viscosity (3D), horizontal velocity shape function (3D), strain heating (3D), corner elevation in best-fit D-J model (2D), freeze-on thickness (2D), ice age (3D), spreading length from isotopic diffusion (3D), echo-free-zone thickness (2D), oldest useful ice for ice coring (2D), and the normalized elevation of the oldest useful ice (2D). Best-fit model also includes a misfits structure describing the misfit with the observational constraints.Units: all velocities (including accumulation rate and basal melt rate) are in m/yr. Water flux is in m^2/yr. Strain rate is in 1/yr. Ice age is in yr. All other variables are in MKS units (temperature is in K, geothermal heat flux and hydraulic heating are in W/m^2, strain heating is in W/m^3, viscosity is in Pa*s, etc). Files are provided in both .mat format and netcdf format. The mat-files have slightly more information, such as the model parameters and the data constraints. The netcdf files have 2D and 3D grids only. The inversion was run twice, once with BedMachine as the basal topography input and once with Bedmap2 as the basal topography input. Both versions use Martos et al. (2017) as the GHF prior. The version with BedMachine is considered the preferred version. Full explanation given in a pair of papers publishd in JGR: Earth Surface: Wolovick, M. J., Moore, J. C., & Zhao, L. (2021). Joint Inversion for Surface Accumulation Rate and Geothermal Heat Flow From Ice-Penetrating Radar Observations at Dome A, East Antarctica. Part I: Model Description, Data Constraints, and Inversion Results. Journal of Geophysical Research: Earth Surface, 126(5), e2020JF005937. https://doi.org/10.1029/2020JF005937 Wolovick, M. J., Moore, J. C., & Zhao, L. (2021). Joint Inversion for Surface Accumulation Rate and Geothermal Heat Flow From Ice-Penetrating Radar Observations at Dome A, East Antarctica. Part II: Ice Sheet State and Geophysical Analysis. Journal of Geophysical Research: Earth Surface, 126(5), e2020JF005936. https://doi.org/10.1029/2020JF005936 Edit for Version 3, October 7, 2024: I added the actual scripts for the model itself, along with the input files used to run the model. I also updated the desciption with the references to the actual published papers. Edit for Version 4, May 20, 2025: I forgot to include one script (makerednoise2.m), so I uploaded that script.本数据集为南极东部穹顶A（Dome A）周边冰盖（ice sheet）及基底水文状态（basal hydrological state）的地球物理反演（geophysical inversion）结果。用于约束该反演的数据集包括基底水体（basal water）观测、基底冻结（basal freeze-on）观测、内部层位（internal layers）观测以及地热通量（geothermal flux）先验数据。本次反演求解得到了最优拟合的地热通量与累积率（accumulation rate）场，及其对应的不确定性（uncertainty）与偏度（skewness），并量化了各单一数据类型对最终反演结果的分数贡献（fractional contribution）占比。需注意，偏度场不具备统计学显著性，但为保证数据集完整性仍予以提供。 此外还包含由最优拟合正演模型（forward model）生成的冰盖状态数据，具体包括：冰内温度（englacial temperature）、基底温度（basal temperature）、基底融/冻速率（basal melt/freeze rate）与水通量（water flux）、应变生热（strain heating）、水力加热（hydraulic heating，即基底水系中压力熔点（pressure melting point, PMP）变化与粘性耗散（viscous dissipation）的综合热效应）、冰流速（ice velocity）、应变率（strain rate）、粘度（viscosity）以及形状函数（shape function）；同时包含后处理变量（post-processing variables），如冰龄（ice age）、D-J模型（D-J model）中的最优拟合H*值、冻结厚度（freeze-on thickness）、模型无回波区（echo-free-zone）厚度、扩散（diffusion）作用导致的同位素平滑（isotopic smoothing）效应、冰芯钻探（ice coring）可用最古老冰体，以及该最古老冰体所在的归一化海拔（normalized elevation）。 本次反演结果中，地热通量与累积率均包含以下参数：进化算法（evolutionary algorithm）输出结果、局部优化（local optimization）校正结果、最优拟合场、不确定性估计、偏度估计，以及反演所用五类约束（水体观测、冻结观测、内部层位观测、地热通量先验、平滑性约束（smoothness constraint））各自的分数贡献占比。数据集还包含了因使用平滑网格化地形（未能完全捕捉存在水体的深窄谷地）而导致的地热通量偏差估计。所有反演结果变量均为二维数据。 最优拟合模型结果包括：冰内温度（三维）、基底温度（二维）、基底逻辑状态（湿/干；二维）、基底融速率（二维）、基底水通量（2个分量加幅值，二维）、水力加热（基底水系粘性耗散与过冷效应总和，二维）、冰流速（3个分量，三维）、垂直平均冰流速（2个分量加幅值，二维）、有效应变率（effective strain rate，三维）、有效粘度（effective viscosity，三维）、水平流速形状函数（horizontal velocity shape function，三维）、应变生热（三维）、最优拟合D-J模型中的拐角海拔（二维）、冻结厚度（二维）、冰龄（三维）、同位素扩散引发的延展长度（spreading length from isotopic diffusion，三维）、无回波区厚度（二维）、冰芯钻探可用最古老冰体（二维），以及该最古老冰体的归一化海拔（二维）。最优拟合模型还包含描述与观测约束之间拟合偏差的残差结构（misfit structure）。 单位说明：所有流速（包括累积率与基底融速率）单位为米每年（m/yr）。水通量单位为平方米每年（m²/yr）。应变率单位为1/年（1/yr）。冰龄单位为年（yr）。其余所有变量均采用国际单位制（MKS，米-千克-秒制）：温度单位为开尔文（K），地热通量与水力加热单位为瓦每平方米（W/m²），应变生热单位为瓦每立方米（W/m³），粘度单位为帕秒（Pa·s）等。 数据集同时提供.mat格式与netCDF格式文件。.mat格式文件包含更多信息，例如模型参数与数据约束项。netCDF格式文件仅包含二维与三维网格数据。本次反演共开展两次：一次以BedMachine作为基底地形输入，另一次以Bedmap2作为基底地形输入。两次反演均以Martos等人（2017）的研究作为地热通量（GHF）先验基准。其中以BedMachine为输入的版本为推荐版本。 完整说明见发表于《地球物理研究杂志：地球表面（*Journal of Geophysical Research: Earth Surface*）》的两篇论文： Wolovick, M. J., Moore, J. C., & Zhao, L. (2021). 南极东部穹顶A穿冰雷达观测的地表累积率与地热热流联合反演：第一部分：模型描述、数据约束与反演结果. *Journal of Geophysical Research: Earth Surface*, 126(5), e2020JF005937. https://doi.org/10.1029/2020JF005937 Wolovick, M. J., Moore, J. C., & Zhao, L. (2021). 南极东部穹顶A穿冰雷达观测的地表累积率与地热热流联合反演：第二部分：冰盖状态与地球物理分析. *Journal of Geophysical Research: Earth Surface*, 126(5), e2020JF005936. https://doi.org/10.1029/2020JF005936 2024年10月7日 版本3更新：补充了模型本体的实际运行脚本与模型运行所需的输入文件，并更新了已发表论文的引用说明。 2025年5月20日 版本4更新：补传了遗漏的脚本makerednoise2.m。