Interaction between Ice Sheet and Oceanic Carbon Cycling during the Pleistocene: A Box Model Simulation
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摘要: 全球大洋深海有孔虫碳同位素(δ13C)记录中广泛发现40万年周期，这一周期可能与偏心率长周期的轨道驱动有关.1.6 Ma以来，δ13C的这一长周期拉长到50万年，且重值期不再与偏心率低值对应.目前对δ13C 40万年周期的成因及其周期拉长的机制还不明确.这里使用了包含9个箱体的箱式模型，用于研究热带过程与冰盖相互作用及其对大洋碳循环的影响.模拟结果显示当北半球高纬海区海冰迅速增大时冰盖迅速融化，进入冰消期，而当海冰快速消失后，冰盖则重新缓慢增长.冰盖变化具有冰期长，间冰期短的非对称形态.在季节性太阳辐射量的驱动下冰盖变化具有10万年冰期-间冰期旋回.当冰盖融化速率受北半球高纬夏季太阳辐射量控制时，冰盖变化的岁差周期明显加强，相位与地质记录一致，说明轨道驱动可以通过非线性相位锁定机制使冰盖变化与其在相位上保持一致.海冰的阻隔效应使大气中CO2在冰消期时增多.冰期时大洋环流减弱使大气中CO2逐渐减少.当模型只有ETP驱动的风化作用而不考虑冰盖变化时，模拟的δ13C记录显示极强的40万年周期，体现了大洋碳储库对热带风化过程的响应.当同时考虑冰盖变化和风化作用时，模拟的δ13C结果中40万年周期减弱而10万年周期加强，并且40万年周期上碳储库与偏心率的相位与不考虑冰盖变化时的相位也存在差异，反映了冰盖变化引起的洋流改组压制了大洋碳循环对热带过程的响应.Abstract: The widely discovered 400-kyr cycles of foraminiferal carbon isotopes (δ13C) from world oceans are interpreted to be linked to the forcing of Earth's eccentricity around the Sun. During the past 1.6 million years (Ma), however, this period extended to 500-kyr and the δ13C maxima of the carbon cycle didn't correspond to the eccentricity's minima. The origin of the 400-kyr cycle and the mechanism for its obscuring during the Pleistocene are elusive. Here we develop a 9-box biogeochemical model on the purpose of understanding interactions between tropical process and variability of ice sheet and their influences on oceanic carbon cycle. The simulated results show that deglaciation is concurrent with the appearance of sea ice in the northern high latitude; while when the northern high latitude is free of sea ice, the ice sheet begins to build up. The simulated building of ice sheet is slower than its retreat, thus the variability of ice sheet is asymmetric. The model can simulate asymmetric 100-kyr cycle of ice sheet under only seasonal solar insolation rather than Milankovitch forcing. By adding the summer insolation of northern high latitude into the ablation term of the ice sheet, precession components become stronger in simulated results. The onset of deglaciation is nonlinearly phase locked to the summer insolation forcing, which leads to a good comparison with geological record. The simulated concentration of atmospheric CO2 is becoming higher during deglaciation owing to the insulation effect of sea ice and is becoming lower during the decrease of ocean circulation. If the model is forced by only tropical weathering process but without the variability of ice sheet, simulated δ13C results exhibit strong 400-kyr cycles indicating a significant response of ocean carbon reservoir to tropical forcing. If the model is forced by both the variability of weathering and ice sheet, however, simulated δ13C results show weaker 400-kyr but stronger 100-kyr cycles and the phase difference between the simulated δ13C and the eccentricity at the 400-kyr band is also different from that in the simulation forced by only weathering process. Our model results seem to indicate that when ice sheet is introduced into the earth system it will result in oceanic circulation reorganization which can suppress the signal of tropical process in ocean carbon reservoir.
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Key words:
- box model /
- carbon cycle /
- tropical process /
- long eccentricity period /
- paleoclimate /
- marine geology
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图 2 封闭系统季节性太阳辐射量驱动模拟结果
a.北半球冰盖覆盖面积比例；b.北半球海冰覆盖面积比例；c.南半球海冰覆盖面积比例；d.大气CO2含量；e.箱体“B”(底层水)海水碳同位素；f.箱体“E”海水碳同位素.灰色阴影对应北半球海冰面积触发的时间段
Fig. 2. Simulated results of closed system driven by seasonal insolation
图 3 封闭系统季节性太阳辐射量驱动下北半球冰盖累积速率与融化速率变化情况
Fig. 3. Accumulation and ablation rate of closed system under seasonal insolation forcing
图 4 封闭系统太阳辐射量驱动冰盖融化速率变化条件下的模拟结果
a.LR04 δ18O合成记录(Lisiecki and Raymo, 2005)；b.北半球冰盖覆盖面积比例；c.北半球海冰覆盖面积比例；d.南半球海冰覆盖面积比例；e.大气CO2含量；f.箱体“B”(底层水)海水碳同位素；g.箱体“E”海水碳同位素
Fig. 4. Simulated results of closed system driven by Milankovitch insolation and insolation based ablation term
图 5 固定冰盖体积，河流输入DIC和ALK在ETP驱动下0~2 Ma的模拟结果
a.大气CO2含量；b.箱体“B”的海水δ13C；c.箱体“E”的海水δ13C；d.箱体“B”的碳酸根浓度；e.地球偏心率参数(Laskar et al., 2004)
Fig. 5. Simulated results of the latest 2 Ma driven by ETP based riverine inputs of DIC and ALK without variability of ice sheet
图 6 太阳辐射量轨道驱动冰盖体积变化，ETP驱动河流输入DIC和ALK变化条件下0~2 Ma的模拟结果
a.北半球冰盖覆盖面积比例；b.北半球海冰覆盖面积比例；c.大气CO2含量；d.箱体“B”的海水δ13C；e.箱体“E”的海水δ13C；f.箱体“B”的碳酸根浓度；g.地球偏心率参数(Laskar et al., 2004)
Fig. 6. Simulated results of the latest 2 Ma driven by ETP based riverine inputs of DIC and ALK and Milankovitch insolation based variability of ice sheet
图 7 封闭系统季节性太阳辐射量驱动下洋流变化模拟结果
a.北半球冰盖覆盖面积比例；b.Q1(NADW)流量；c.箱体“N”与“D”海水交换速率；d.箱体“S”与“I”海水交换速率
Fig. 7. Simulated results of ocean circulation under seasonal insolation forcing in closed system
图 8 开放系统固定冰盖体积模拟结果的小波分析
a.箱体“B”模拟δ13C连续小波谱；b.箱体“E”模拟δ13C连续小波谱；c.箱体“B”与“E”模拟δ13C的交叉小波谱；d.箱体“B”模拟δ13C与偏心率参数(Laskar et al., 2004)的交叉小波谱.其中黑色锥形实线以内为小波分析过程中不受边缘效应影响的区域，锥形线以外的结果可能因边缘效应而不可信.交叉小波结果中黑色等值线代表红噪假设下显著性水平为5%的区域.箭头表示2个时间序列间的相位关系.向右箭头表示同相位，向左箭头表示反相位，向上箭头表示δ13CB领先90°，向下箭头表示δ13CB落后90°.小波分析方法由Grinsted et al.(2004)提供
Fig. 8. Wavelet spectrums of simulated results in open system without the variability of ice sheet
图 9 开放系统冰盖体积可变时模拟结果的小波分析
a.箱体“B”模拟δ13C连续小波谱；b.箱体“E”模拟δ13C连续小波谱；c.箱体“B”与“E”模拟δ13C的交叉小波谱；d.箱体“B”模拟δ13C与偏心率参数(Laskar et al., 2004) 的交叉小波谱.其中频谱置信区间和黑色箭头代表的领先/落后关系见图 8中说明
Fig. 9. Wavelet spectrums of simulated results in open system that include the variability of ice sheet
表 1 箱式模型参数
Table 1. List of parameters
符号 描述 单位 数值 海洋模型 L1, L2, L3 箱体长度 106 m 4.15, 20, 4.15 W 箱体宽度 106 m 18 flS, flE, flN 陆地所占比例 0.5, 0.25, 0.5 λ1, …, λ5 流量参数 106 6.6, 5.1, 1.2, 4.2, 1.0 Kv1, …, Kv5 垂向扩散系数 m2/s 2.6×10-3, 6.5×10-5, 2.2×10-3, 2.4×10-3, 6.1×10-5 Kh1, …, Kh3 横向扩散系数 m2/s 2.5×103 lengthv1, …, lengthv5 垂向长度系数 m 1 500, 1 500, 1 500, 1 900, 1 900 lengthh1, …, lengthh3 横向向长度系数 106 m 17, 16, 18 upper 表层箱体间横截面积 m2 2×109 lower 下层箱体间横截面积 m2 2.8×1010 ρ0 海水参考密度 kg/m3 1 028 S0 海水参考盐度 35 D 表层箱体水深 m 200 τ 热量散失的阻尼系数 s 4.65×107 Cpw 海水热容 J·K/kg 4 180 海冰模型 Dsea-ice 海冰初始厚度 m 1.5(箱体“S”)，3(箱体“N”) τsea-ice 海冰阻尼系数 s 2.6×106 γ 海冰热阻隔系数 m 0.05 ρsea-ice 海冰密度 kg/m3 917 Tsea-ice 海水结冰温度 ℃ -2 Lf 海水融化潜热 J/kg 3.34×105 大气模型 αland 陆地反射系数 0.2 αland-ice 冰盖反射系数 0.9 αsea 海水反射系数 0.07 αsea-ice 海冰反射系数 0.65 αcloud 云层反射系数 0.3 PlwOS, …, PlwON 长波辐射系数 0.61, 0.52, 0.67 σ Stephan-Boltzmann常数 5.67×10-8 κ 常系数 0.03 pCO20 大气CO2参考值 10-6 280 Kθ 大气扩散系数 1/(s·K2) 1.5×1020 KMq 经向水汽扩散系数 m4/(s·K) 2.4×1013 Kq 高纬形体内的水汽扩散系数 m3/s 6.5×108 R 气体常数 J/(kg·K) 287.04 Cpw 定压比热 J/(kg·K) 1 004 g 重力加速度 m/s2 9.8 P0 参考大气压力 102 Pa 1 000 A 湿度计算常数 Pa 2.53×1011 B 湿度计算常数 K 5.42×103 生物地球化学模型 h 半饱和常数 mol/m3 2×10-5 r 常系数 1.2×10-8, 1.0×10-7, 2.0×10-8 
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附表 1 模型生物地球化学参数
附表 1. List of parameters for biogeochemical model
参数 描述 数值 来源 rcporg 有机质吸收C、P的比例生物吸收总C、P的比例 106 Ridgwell, 2001 rC∶P (POC+PIC) rCorg∶p/(1-rainratio) Ridgwell, 2001 rnporg 有机质吸收N、P的比例 16 Ridgwell, 2001 rALK∶P ALK与P的比例 2×rainratio×rCorg∶p -0.7×rN∶P Ridgwell, 2001 g 箱体“I”和“D”中POC和PIC的溶解比例 0.5 Toggweiler, 2008 rom POC沉积比例 0.01 本研究 DGvol+kero 火山与沉积物氧化释放CO2 7.78×1012 mol/a 本研究 Pv 海-气交换的活塞速度 3 m/d Toggweiler, 2008 εp 有机碳碳同位素分馏 -23‰ 本研究 δ13Criv 河流输入碳同位素组成 -5‰ 本研究 δ13Cvol+kero 火山与沉积物氧化释放CO2的碳同位素组成 -5‰ Kump and Arthur, 1999 rivPO43- 河流输入的磷酸盐 2.5×1010 mol/a 本研究
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