Situ Observatory

2023-12-18-整理 Global Cryosphere 知识点 3-4章

2023/12/18 Learn 共 13233 字，约 38 分钟
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费了半天劲，LaTeX 在 Github Page 却老是不能正常的渲染出来，真的是艹了

第三章 Sea Ice

海冰

直接由海水形成的冰

  • 不包括 icebergs（陆冰崩解形成）

相关定义

  • Sea-ice concentration: The percentage of ocean area that is covered by sea ice，区域内海冰覆盖面积百分比，一般是 0-1 的一个值
  • Sea-ice extent: The total ocean area that is considered to be covered by sea ice 一般是 >=0.15 的 concentration
  • Sea-ice area: Total area covered by sea ice, taking into account the percent coverage in each pixel
  • First-year ice FYI: sea ice formed in the CURRENT season
  • Multi-year ice MYI: sea ice that survided >=1 melt season
    • Most sea ice is first-year ice, particularly in the Antarctic
    • Multi-year ice tends to be thicker and fresher than first-year ice
      多年冰更厚，含盐量更低
      • melt season -> intergranular veins -> permeable -> water and brine transport -> brine rejection 含盐量降低

海冰生长过程

  • 气温降低，水面散热，水面结冰
  • 大气温度变化是主要的结冰和融化的动力
  • speed of ice growth is limited by the (low) rate of heat conduction through the ice layer
    • typical limit is 1-2m per year
    • plow the snow so the ice keeps losing heat to the atmosphere, keeps ice growing
  • salt - lower freezing point
    • adding freshwater promotes sea ice formation
    • sea ice always has some salt in it
  • 根据海冰的中文维基百科，海水盐度大于24.69（一般都大于这个数）时，表层海水先达到结冰点，继续降温密度还会增加。在这种情况下，表层海水到达结冰点就会比底下的水密度更大，会下沉，把下面温度较高的水翻上来。所以这种情况下结冰比较慢。海冰不仅仅可以在表面形成，也可以在其他深度甚至还低形成。

Stages

frazil -> grease -> thin coherent layer -> young ice

  • Frazil ice: Disconnected crystals and needles
  • Grease ice: A bunch of frazil ice stuck together
  • thin corehent layer
    • calm: nilas
    • waves: pancakes congelation ice (凝结冰)
  • melt (melt water)
    • initial melt water gets trapped at the surface, lower the albedo
      seasonal ice-albedo feedback
    • eventually drain through cracks and channels

Movement

  • Advection: mainly the wind. ~2% of wind speed. Also ocean currents.
  • Ice floes 浮冰，裂开成一块块的海冰
    • 两个 floe 相对远离形成 leads，再远离形成 polynyas 小型开放水域。两个 floe 相向而行形成 pressure ridges
    • Leads: Narrow lines of open water between ice floes
    • Pressure ridges: Crumpled edges of ice floes where they are driven into each other
      • 向上堆起来的叫 sail，向下沉入水下的叫 keel
    • Polynyas: Larger open-water areas between floes or between sea ice and land
      • latent heat polynyas：风吹的（实际上可能仍然具备形成新海冰的条件）
      • sensible heat polynyas: 热水上涌引起的

Land-fast ice 固定冰

  • 又叫 fast ice
  • 连接到 shoreline 或者 seafloor
  • many polynyas between fast ice and mobile ice floes

一个区域的海冰受到三个因素的影响

\[\frac{dV}{dt}=\text{advection}+\text{divergence}+\text{thermodynamic growth}\]
\[\frac{dV}{dt}=V(\nabla \cdot u )-u\nabla \cdot V+\text{thermodynamic growth}\]

  • advection, v = 0, u = constant
  • divergence, v = 0 , H = constant

全球海冰趋势

  • Arctic：sea ice extent 持续降低，厚度降低，多年冰减少，九月最明显，2012年创纪录
  • Antarctic：sea ice increase, larger variability over time 可能原因有 1. ice sheet melt, 更多表层淡水输入 2. wind patterns, driving sea ice away from the continent 风吹的。 最近波动大可能是风向变了

Arctic amplification

  • ice-albedo feedback，有 seasonal and interannual 的影响
  • other variables

Bering Strait, Chukchi Sea（Alex Crawford）

  • Retreat date (RD): 区域平均 sea ice concentration 第一次低于 30% 的那天。平均值是 7月17日
  • Advance Date (AD): 在抵达了最低 concentration 之后（回升过程中），区域平均 sea ice concentration 第一次超过 30% 的那天。平均值是 10月18日

Bering Strait

  • Water flow: Pacific -> Arctic -> Atlantic
  • Local wind blows against the current

能量交换

  • More energy -> faster melting -> earlier retreat
  • More Northerly winds -> ice pushed South -> later retreat
  • More Southerly winds -> ice pushed North -> earlier retreat

海冰遥感

  • Passive microwave
    • 弱点：分辨率低（25km * 25km）
    • 常见 Sensor
      • SSM/I
      • AMSR-E
    • 地面温度也高，emissivity 越高，发射能量越强。 $E = \sigma \epsilon T^4$ 其中 $\sigma=5.67*10^{-8}\frac{W}{m^2K^4}$
    • 难点
      • mixed picels
      • surface effects (e.g. liquid water)
      • (weak) energy interact with atmosphere
  • ASCAT (scatterometer)
  • MODIS (VIS/IR)
  • ICESat (laser altimeter)
  • Cryosat (radar altimeter，可以穿透表层的雪)

Altimeter 测量海冰只能测量 freeboard，也就是海冰高出水面的部分的高度。 根据浮力的原理，$V_{ice}\rho_{ice}=V_{water}\rho_{water}$，而 $V_{ice}\rho_{ice}=V_{water}\rho_{water}=V_{ice}\rho_{water}-V_{ice}\rho_{water}$

\[h_i = h_f(\frac{\rho_w}{\rho_w-\rho_i})\]

对于激光测高数据，再把雪算上，注意雪那一项上面是学的密度，freeboard那一项上面是水的密度。 原网页链接

\[h_i = h_f(\frac{\rho_w}{\rho_w-\rho_i})+h_s(\frac{\rho_s}{\rho_w-\rho_s})\]

第四章 Glaciers and Ice Sheets

定义

  • glacier: a mass of moving ice
    • pile up, squeeze air out, turns into ice
    • drive: gravity

      冰川类型和对应名词

      Polar vs Temperate glaciers

  • Polar : below the freezing point at most depths
    • may the ice near the bed may reach the freezing (melting) point due to high pressure
  • Temperate : at the freezing point throughout

Cirque glaciers

  • bowl-shaped depressions. 冰斗

    Valley glaciers

  • cirque glaciers spill out, flow into spots between mountains

    Piedmont glaciers 山麓的冰川

  • valley glaciers flows out into an open area, spread in all directions, forming a piedmont

    Tidewater glaciers

  • 流到海里的都可以叫这个

    Ice caps and icefields

  • merged glaciers, can overtop higher elevations on an island
    • multiple outlet glaciers
    • big enough to ignore topography

      Ice sheet

  • ice cap big enough to cover a continent
    • Individual fast-flowing areas that lead to the edges are called “outlet glaciers” or “ice streams”

      ice streams

  • Fast-flowing outlets from ice sheets
  • Can be bounded by topography or by shear zones between fast- flowing and slow-flowing ice (perhaps determined by bed material)

    Ice shelves

  • The floating extensions of ice sheets
  • Floating but still connected
  • Tidewater glaciers might also have floating “ice tongues,” which are more confined than ice shelves

    Nunataks 冰原岛峰

  • exposed rock peaks protruding through an ice cap, icefield, or ice sheet

    Grounding lines

  • Where ice goes from sitting on land to floating
    • Where tidewater glaciers are not floating, the coastline is the same as the grounding line
  • Many grounding “lines” are actually grounding “zones”

    Icebergs

  • ice shelves 形成
  • 形成过程称为 “Calve”, “Calving”

    冰川地理

  • 格陵兰岛冰盖全部融化，海平面上升约7米；南极洲冰盖全部融化，海平面上升约57米
  • 全球约有 200,000个冰川
  • cryogenian 成冰纪
  • snowball earth 雪球地球
    • ~ 650 Ma
    • runaway ice-albedo feedback
  • Antarctic, ~35 Ma
  • Greenland, ~10 Ma, mostly covered by ~3 Ma
  • Pleistocene Glaciation 更新世大冰期
    • ~ 2.6 Ma
    • glacials - interglacials
    • glacial cycles
      • Milankovitch Cycles
      • Eccentricity: 100,000 years
      • Obliquity: 41,000 years
      • Precession: 23,000 years
    • Last Glacial Maximum LGM
      • Wisconsinan Glaciation; Last major glacial advance
      • Laurentide Ice Sheet: eastern North America
      • Cordilleran Ice Sheet: smaller ice sheet in Western North America
      • At its peak ~20,000 years ago, followed by retreat to current interglacial

冰川模型

质量守恒

  • 降水&蒸发，流入&流出
  • Mass gain: precipitation (mostly in the form of snow), avalanching, wind redistribution, hoar frost formation
  • Mass loss: avalanching, wind redistribution, surface melt, internal and basal melt, subaqueous melt, calving
  • Ablation zone & Accumulation zone
    • Accumulation zone: net gain (上游)
      • snow -> granular ice -> firn（粒雪） -> glacial ice
    • Ablation zone: net loss (下游)

Accumulation

  • 主要是雪
    • 有时候有冻雨，形成一层冰
    • Cirque glacier 有时候从附近悬崖的雪崩获得补给
  • 特征
    • Crevasses 冰隙
      • Snow bridges: 一层盖住 crevasse 的雪，很危险
      • Bergschrunds: largecrevasseat the head of a glacier between stagnant and flowing ice/firn
      • Seracs: crevasses 交错切割形成 tower
    • ELA Equilibrium Line Altitude
      • Equilibrium Line: annual accumulation = annual ablation
      • 温暖干燥，ELA 升高；寒冷潮湿，ELA 降低
      • On mountain glaciers, the snow line is typically close to the ELA at the end of the summer
    • AAR Accumulation Area Ratio
      • 冰川上游面积和冰川总面积之比 $\frac{\text{Accumulation Area}}{\text{Glacier Area}}$
      • steady-state 可以认为通常在 0.5-0.6 的样子

Ablation

  • Typically has blue glacial ice exposed
    • in some polar regions calving/basal melt dominate
    • Ice can only exist in the ablation zone due to glacier flow
  • Ablation Mechanisms
    surface melt, basal/subaqueous melt, ice discharge, calving
    • Surface melt
      • 气温高的地区是主要方式
        • 例如 temperate galciers
      • Measured through ablation stakes, snow pits and ice-penetrating radar, estimates of surface melt and albedo from satellite imagery…
      • 可以用类似雪的那个模型的 energy flux （例如 PDD）方法来建模
    • 大多数冰川都有 basal melt, 不过融化总量不大
    • Glaciers terminating in ice shelves or ice tongues melt from below
    • calving, ice discharge
      • As ocean-terminating glaciers accelerate, for a variety of reasons (which we’ll cover later) calving rates tend to increase, sometimes drastically
  • Ablation zone features
    • Supraglacial lakes and streams
      • Surface meltwater streams sometimes cut downwards and form canyons
    • Moulins
      • Vertical meltwater conduits that bring meltwater to the base of a glacier to some point englacially
    • Dirt cones
      • (Thick) sediments insulate the ice and slow melt
    • Cryoconite holes
      • (Thin) sediments lower albedo, warms and melts the ice

冰川的运动

  • ultimate 的驱动力是重力
  • 底部滑动+上部蠕动
  • sliding， responsible for fast velocities and rapid discharges
    • Hard-bed sliding
      • Regelation 重凝结: Movement of ice past relatively small bumps due to melting and refreezing
      • upstream : high pressure -> pressure melting -> take up latent heat -> lower temperature
      • downstream : the opposite, low pressure -> regelation -> release heat -> high temperature -> heat conduct through bump to upstream
      • bump > ~1m, 下游高压区释放的热量难以有效通过bump传回上游，但也可以通过 Glen’s Law ，高压引起高形变，加快流动
    • cavitation
    • soft-bed deformation
      • till: deposits of sediments of mixed size and angularity
      • 受到压力，冰碛物堆积形状改变
    • subglacial hydrologic evolution
      • melt season 初期，冰川底部的往往是 inefficient, distributed subglacial hydrologic system，导致 fast sliding
      • 后期，水从底部导出的效率提高，sliding 减慢
    • Trimlines
    • Moraines
      • lateral
      • terminal
      • recessional

冰川地貌

erosion process

  • Very efficient – typically 1-1000 mm/year
  • 效率取决于
    • Ice flow volume and temperature (amount of sliding and associated pressure)
    • Rock characteristics (rock type, jointing and other structures)
    • Associated processes (fluvial, mass movements from oversteepening)
    • Supply of sediments to the glacier bed

hard-bed sliding

abrasion

  • 冰川带着碎石刮擦底部，产生刮擦痕
  • 碎石太多反而减少刮擦

glacial flour

  • silt-sized pulverized (粉碎的) rock
  • a result of glacial abrasion
  • color rivers and lakes

sliding with cavitation （空化现象？）

  • 上游压力大，下游侧面压力突然减小，bedrock 容易产生裂隙

Roche moutonnée

  • 上游坡度平缓，有 striations（条纹）
  • 下游坡度较陡，基岩破碎

U-shaped valley U型谷/U形谷

  • steep sides, broad curved bottom
  • V 型谷（河流切割形成）被冰川侵蚀。
  • ~100k-year glacial cycle

Hanging valley 悬谷

  • larger glacier -> higher discharge -> more erosion

Paternoster lakes 串珠湖

  • 冰川汇合时总流量增加，基岩被侵蚀得更多，底部高度降低，形成台阶 Where discharge increases (such as where a tributary joins) erosion increases, making steps down the valley
  • Strings of lakes form in steps known as “paternoster lakes”

Fjord 峡湾

  • Big U-shaped valleys flooded by water on the edges of continent
  • Formed on the edges of big ice sheets through another flux feedback
    • 狭窄通道 - 更高流速 - 更多侵蚀 - 该区域厚度增加 - 底部压力更大 - 溶解、滑动更快 - 更多冰加入
    • Ice funneled through narrow passes must flow quickly, increasing discharge and erosion
    • Thick ice also has high pressure at bed, promoting melting and sliding
    • Pulls more ice in, causes more erosion

Cirque 冰斗

冰斗湖：tarns

Arête 刃脊

  • Sharp ridge that separates two glacial valleys
  • Between cirques or u-shaped valleys

Col 冰垭

  • 冰斗从两侧侵蚀形成的垭口 A relatively low-elevation pass where a pair of cirques eroded into each other
  • Col 本身是垭口的意思

Horn 角峰

  • From headward erosion of cirques from three or more directions

Trimlines 修剪线

  • 前面讲过了

Mountain/Alpine glaciers vs ice sheets

  • 以上主要都是 mountain/alpine glaciers 特征，只有 Roche moutonnée 和 continental ice sheets 相关，后者底部有大量碎屑降低侵蚀

冰川沉积物

  • Deposited directly by glaciers: Glacial till
  • Deposited by streams associated with glaciers: Glacial outwash
  • Deposited by lakes on ice margins: Glacial lake deposits

Outwash plains

  • Sediments often have some stratification and better sorting than glacial till

Glacial lakes

  • May be dammed by ice or sediments deposited by the ice
  • Very large lakes at the edges of ice sheets during the LGM, including where Winnipeg is now
  • 常见纹层结构 varved deposits

Movement of glacial till

  • Supraglacially 表层搬运
  • Englacially 内部搬运
    • 通过 accumulation zone, moulin （洞）， 底部带起而进入内部
  • Subglacially 底部搬运
    • 包含底部水流搬运的以及底部 till 变形带的

Moraines 碛（碛堤）

  • Piles of glacial till deposited at the edges of a glacier
  • Associated with both alpine glaciers and ice sheets
  • Medial moraines
    • often originating from the confluence of two glaciers
    • Most common with alpine glaciers
    • 随着冰川运动，接近下游的区域往往因为冰减少，露出表面面积增加，显得更宽
  • Terminal moraines
    • Size depends on length of time terminus stayed in one location, the amount of debris in the glacier, and the flux of debris- bearing ice to the margin
    • Recessional moraines: May get lines of moraines marking terminus location during stages of retreat
  • Lateral morains
    • Formed along the edges of glaciers as debris falls off the side or melts out
    • May mark previous extent of a glacier, similar to terminal moraines

冰川消退后留下来的相关地貌

Large till plains left behind by ice sheets

Subglacial landforms: drumlins, kames, eskers

Drumlins 鼓丘

  • 与 Roche moutonnée 相反，对着流动方向的一面坡度较陡，顺着流动方向的一面坡度较缓
  • 几百米到数千米长，几百米宽，几十米高
  • May be rock cored or made of sediment; erosional or depositional

Kames

  • 冰砾阜
  • englacial till
  • 冰川消融后冰面上的沉积物沉落到底床上堆积而成的一种圆形的或不规则的小丘。通常由具有层次的粉砂、细沙组成，表面有冰碛物覆盖。近圆形者称为 “kames”

Eskers

  • 蛇形丘
  • 一般两坡对称，丘脊狭窄，长度从几十米到上百公里不等，高度一般为10-30米，有时可达70米以上，其延伸方向与冰川运动方向大致相同。
  • Follow hydrologic potential, not topography - can go uphill!
  • 成因有两种
    • 在冰川开始消融时，冰融水会沿着冰裂隙流入冰川底部，形成冰下隧道，在隧道中流动的冰融水携带大量的砂砾，沿途搬运过程中不断堆积，等到冰川全部融化后，这种隧道堆积物就形成了蛇形丘。
    • 在夏季气温升高时，冰川消融产生的冰融水在冰川的末端流入冰水湖，其携带的物质则堆积形成冰水三角洲，随着冰川的节节后退，形成了一个个的冰水三角洲，它们连起来就成了串珠状的蛇形丘。

Proximal landforms: Kettles and erratics

Kettle holes and kettle ponds

  • Depressions under old ice margins, nearly circular and often filled with water
  • Form where buried blocks of ice melted out, allowing surface sediments to collapse downwards 地下的冰融化了，表面往下垮塌

Glacial erratics 冰川飞来石

  • 搬运大块岩石，和本地地层的岩石不一样

冰川模型 Glacier models

基本概念

  • Stress: The internal force that particles exert on one another due to an external force. 单位是 N/m2
  • Strain: How much a material deforms
    对液体不存在固定的形变量，因此用形变速率来描述，在此模型中等于一定方向的移动速度的梯度（加速度）
  • 二者的关系称为流变学 The relationship between a stress and a strain rate is a rheology
  • Glen’s Flow Law: $\frac{du}{dz}=A\tau^n$
    描述冰川受力流动的 “consitutive equation”
  • A 是 flow law parameter, 单位是 $Pa^{-3}yr^{-1}$
  • 在这个模型里，shear stress 简化到只有 $\tau_{zx}$
    进一步分解：$\tau_{zx}=\rho g(H-z)\sin{\left(\theta\right)}$ 其中 $\theta$是坡角，H是雪的海拔，z是地基海拔，$\rho$是冰的密度，g是重力加速度
  • 把 $\frac{du}{dz}$ 对 z 进行积分，得到 Q
    \[ Q=A\left(\rho gsin\theta\right)^3\frac{H^5}{5} \]
  • 每个节点的高度随时间的变化，与降雪/消融量（b）和流动（Q）的关系, “prognostic equation” \[ \frac{\partial H}{\partial t}=\dot{b}-\frac{\partial Q}{\partial x} \]

数值模型

步骤：

  1. 设定基本时空网格，包括地形 x（距离），z（海拔），t（时间）
  2. 设定 b ，也就是降雪和消融的参数
  3. 设定基本 flow law 参数，密度，重力加速度等
  4. 模型第一步计算当前表面高度 w 对应的 b
  5. 模型第二步计算当前雪厚度对应的各个节点之间区域的 Q ，这里需要先通过插值得到两节点之间区域的高度 H_between 以及坡度 s
  6. 通过除法算出 dQ/dx
  7. dH/dt = b - dQ/dx，再乘以 dt 得到 H
  8. H + z 等于新的表面高度 w，重新计算两节点之间的坡度 s
  • 以下是这个简单模型的 Python 代码
xmax = 50 * 1000 #length of glacier
dx = 250         # x step of glacier
x = np.arange(0, xmax+dx, dx)

zmax = 4000          #max elevation of the valley 
z = zmax - 0.04 * x  # elevation of the base, change along the valley

#temporal domain
tmax = 1500   # 1500 years
dt = 0.01   # time step = 0.01 years
t = np.linspace(0, tmax, int((tmax/dt)+1)) 

#run parameters 
A = 2.1e-16     # flow law parameter Pa-3 * yr-1
rho = 917       # ice density    kg/m3
g = 9.8         # gravity accel  m/s2

#initial conditions
H = np.zeros(len(x))     # glacier thickness 

#mass balance 
bcap = 1      # max surface mass balance rate, m/yr
gamma = 0.1  # gradient in b down the valley, m/yr/m
zELA = 3000 

Q = np.zeros(len(x)+1)   # flux 

nplot = 20 
tplot = (tmax/dt)/nplot 

w = z + H    # total height, glacier surface elevation
s = -np.diff(w) / dx    # slope 

fig = plt.figure()
ax1 = fig.add_subplot(2,1,1)
ax2 = fig.add_subplot(2,1,2)
for i in range(len(t)):
    b = gamma * (w - zELA) 
    b[b > bcap] = bcap 

    H_between = np.interp(np.arange(dx/2,xmax,dx), x, H)
    
    Q[1:-1] = A * ((rho * g * s) ** 3) * ((H_between ** 5) / 5) 
    dQdx = np.diff(Q)/dx 

    dHdt = b - dQdx 

    H = dHdt * dt + H 
    H[H<0] = 0 

    w = z + H
    s = -np.diff(w) / dx    # slope

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