System Earth 5a

Cryosphere

Misha Velthuis

m.velthuis@uva.nl

Tue 1 Oct 2024

Content

Some stuff

Snow

Glaciers

Sea ice

Permafrost

My average location (lat,lon)

41.76006345520992, -13.607610755529738

lat_medellin = 6.246236906580691
lon_medellin = -75.5715966473171

lat_amsterdam = 52.36808956713812
lon_amsterdam = 4.901112303056097

# Spent 398 of the last 1727 days in Medellin.

frac = 398/1727

average_lat = lat_medellin * 0.23 + lat_amsterdam * (1-0.23)
average_lon = lon_medellin * 0.23 + lon_amsterdam * (1-0.23)

41.76006345520992 North latitude 13.607610755529738 West longitude

Distance between longitudes vs latitude

The distance between meridians decreases with latitude.

So using average coordinates underestimates my zonal movement (moving 1° zonally near Amsterdam implies less zonal movement than moving 1° zonally near Medellín).

import matplotlib.pyplot as plt
import math

r = 6370

def circumf(lat):
    degrees2rad = lat*(2*math.pi/360)
    radius = math.cos(degrees2rad)*r
    circumference = 2*math.pi*radius
    return(circumference)

degrees = range(0,90)
store_circumf = []

for i in degrees:
    circumf(i)
    store_circumf.append(circumf(i))

plt.plot(degrees,store_circumf)
plt.title("Latitude vs zonal circumference")
plt.xlabel('Latitude (°N)')
plt.grid(True)
plt.ylabel('Zonal circumference (km)')
plt.savefig('/home/misha/Nextcloud/mnotes/org-roam/presentations/images/latitude_vs_zonal_circumference.png')
plt.close()

My average location (distance)

Proper calculation: indeed, the original location underestimated zonal movement.

Link to supportive sketches

def average_location(lat1,lon1,lat2,lon2,frac):

    lat1=math.radians(lat1)
    lon1=math.radians(lon1)

    lat2=math.radians(lat2)
    lon2=math.radians(lon2)

    # Turn coordinates in radians to coordinates in 3-dimensional space
    # See accompanying sketches for details
    x1 = math.cos(lat1)*math.sin(lon1)
    y1 = math.sin(lat1)
    z1 = math.cos(lon1)*math.cos(lat1)

    x2 = math.cos(lat2)*math.sin(lon2)
    y2 = math.sin(lat2)
    z2 = math.cos(lon2)*math.cos(lat2)

    # Calculate distance between the two points (in the 3d space) in a straight line
    MA = (((x1-x2)**2)+((y1-y2)**2)+((z1-z2)**2))**0.5

    # The angle we're looking for is two times the inverse sine of half of that distance
    alpha = math.asin(MA/2)*2

    # The full distance between the two coordinates
    full_distance = alpha * r
    print("The distance between the two points is: %s" % (full_distance))

    # If on the sphere, the distance should be frac, what should
    # be the frac on the straight line connecting the two points?
    gamma = (math.pi-alpha)/2
    alpha1 = alpha * (1-frac)
    beta = math.pi-alpha1-gamma
    MF = math.sin(alpha1)/math.sin(beta)
    frac_real = (MA-MF)/MA

    # Point F lies at frac_real of MA
    x3 = x1 + frac_real*(x2-x1)
    y3 = y1 + frac_real*(y2-y1)
    z3 = z1 + frac_real*(z2-z1)

    # The radius is 1. So dividing point F (x,y,z)
    # with it's distance from O, you get point F'
    distance_to_origin = (((x3**2+z3**2)**0.5)**2+y3**2)**0.5
    x3 = x3/distance_to_origin
    y3 = y3/distance_to_origin
    z3 = z3/distance_to_origin

    # Turning the 3d space back to coordinates
    # (basically reverting what happens above)
    lat3 = math.asin(y3)
    lon3 = math.asin(x3/math.cos(lat3))

    # Printing latitude, longitude
    lat_average=(lat3/(2*math.pi))*360
    lon_average=(lon3/(2*math.pi))*360

    print("%s%% of %s is %s" % (frac*100,full_distance,frac*full_distance))
    print("%s from point 1, is %s°N and %s°E" % (frac*full_distance, lat_average,lon_average))

lat_medellin = 6.246236906580691
lon_medellin = -75.5715966473171

lat_amsterdam = 52.36808956713812
lon_amsterdam = 4.901112303056097
average_location(lat_amsterdam,lon_amsterdam,lat_medellin,lon_medellin,0.23)

I'm almost on top of the midoceanic ridge.

It has, overall, cost 21 tonnes of CO2.

Average annual per capita CO2 emissions in the Netherlands: 8.5 tonnes.

Average annual per capita CO2 emissions in Colombia: 1.9 tonnes.

Make up for it by fighting for the energy transition?

Pushing for to a world where net zero intercontinental travel is possible (returns)?

Gulf stream stories

Question Louis

Answer (uncontroversial)

Role of Gulf stream?

Cryosphere😭

Cryosphere

Continental ice sheets + ice shelves
Mountain glaciers
Sea ice
River and lake ice
Snowcover
Permafrost

What is the role of the cryosphere?

Energy:

Albedo: reflects high percentage of sunlight (80-90%)
As such it plays an important role in the energy balance.
The fact that we have ice caps at the poles contributes to the latitudinal energy imbalance, which in turn powers the movement of the atmosphere, which in turn powers the movement of the oceans. Which both ar involved in the latitudinal redistribution of energy
Fluctuations in the angle of the axis of the earth, and the shape of our orbit around the sun cause fluctuations in incoming solar radiation, but these fluctuations are strengthened by growing and shrinking ice: glacials and interglacial.
But it also plays a key role in the thermohaline circulation, which we saw is powered by the density increase that results from the freezing of sea ice.

Connects to the carbon cycle (which itself connects to the energy balance of course):

The thermohaline circulation (see above) plays a role in carbon cycle.
Permafrost captures (and releases) carbon.
Long term inorganic carbon cycle (sea level fluctuation exposes fluctuating rock surface to silicate weathering).

What to focus on?

Snow

Current snow cover

Formation of snow

Vaporization curve: we have seen this before:

In both graphs (on the slide and the speaker notes) you can see the "water vapor pressure - temperature"-combination at which condensation equals evaporation at a gas-liquid interface.

At 0°C this balance emerges at a water vapor pressure of about 6 milibar (graph in speaker notes) or ≈ 4.58 Hgmm (graph on slide).

Atkins (2016):

"If one of the phases is a vapor, the pressure corresponding to this equilibrium is the vapor pressure of the substance."
"The solid–liquid boundary … show[s] the pressures and temperatures at which solid and liquid coexist in equilibrium."

Graph in slide:

The lines represent the (vapor) pressure at which the phases exist in equilibrium (for a certain temperature).

Above vaporization curve: condensation exceeds evaporation.

If net condensation causes water vapor pressure to go down (i.e. no re-supply water vapor), system returns to vaporization curve.
If there is a re-supply of water vapor (water vapor pressure stays the same), the system keeps turning new water vapor into liquid water.

Below vaporization curve: evaporation exceeds condensation.

If net evaporation causes water vapor pressure to go up (i.e. water vapor accumulates, does not leave the system), system returns to vaporization curve.
If the water vapor leaves the system/ interface, the system keeps turning liquid water to water vapor (my mug, right here, with water).

Sublimation curve shows "water vapor pressure - temperature"-combination at which sublimation equals deposition at a gas-solid interface.

Above sublimation curve: deposition exceeds sublimation. If there is no re-supply of water vapor, system returns to sublimation curve.
Below sublimation curve: sublimation exceeds deposition. If net sublimation causes water vapor pressure to go up, system returns to sublimation curve. If water vapor is removed from interface, ice is turned to water vapor.

Melting point curve shows "pressure - temperature"-combination at which melting equals freezing at solid-liquid interface.

Above melting point curve: melting exceeds freezing.
Below melting point curve: freezing exceeds melting.
Note that at for example -10°C, under relatively low pressure ice is solid, but at higher pressures ice becomes liquid! (The temperature at which water melts (the melting point curve) goes down with pressure).

Formation of snow

Snow crystals

Thermal inertia

Glaciers

From snow to glacier ice

Snow accumulates

Higher pressure → higher density + ductile

Form	Density
Snow	50-70 kg/m³
Firn	400-800 kg/m³
Glacier ice	850-900 kg/m3

Mountain glaciers

Continental glaciers

Greenland

Antarctica

Ice sheet

Greenland and antarctic

Ice also flows without an inclined bed (relatively high pressure in the middle).

Antarctic ice sheet = snow-fed. But very slowly, because very dry (see also later).

This is useful for studying the composition of air bubbles captured in the ice.

To maitain chronologic order → sample from stable part of ice sheet.

Polar deserts:

Low temperature = water "can contain" only little vapor.
Polar high pressure zone = little convection.
Wiki:
- "Polar deserts are the regions of Earth that fall under an ice cap climate (EF under the Köppen classification). Despite rainfall totals low enough to normally classify as a desert, polar deserts are distinguished from true deserts (BWh or BWk under the Köppen classification) by low annual temperatures and evapotranspiration. Most polar deserts are covered in ice sheets, ice fields, or ice caps, and they are also called white deserts."

Past melting

Asymmetry in increase and decline

Current melting

Continental glaciers in the Netherlands

Sea ice

Not snow from above, but sea water from below

Freezing point at typical ocean salinity = -1.8°C

Arctic sea ice

Sea ice - atmosphere feedback loops

Arctic sea ice trend

Polar amplification

Permafrost

Basic structure

Thermokarst in the Netherlands

Permafrost degradation

Greenhouse gases in permafrost

Link to FAQ AR6 WGI

"The Arctic is the biggest climate-sensitive carbon pool on Earth, storing twice as much carbon in its frozen soils, or permafrost, than is currently stored in the atmosphere."

"The projections from these permafrost carbon models show a wide range in the estimated strength of a carbon–climate vicious circle, from both carbon dioxide and methane, equivalent to 14–175 billion tonnes of carbon dioxide released per 1°C of global warming. By comparison, in 2019, human activities have released about 40 billion tonnes of carbon dioxide into the atmosphere." (Using higher estimate of 175 GT: 1.5°C warming causes greenhouse gases equivalent to (175*1.5)/40=6.56 years (using 2019 emissions).

"…the models do not identify any one amount of warming at which permafrost thaw becomes a ‘tipping point’ or threshold in the climate system that would lead to a runaway global warming. However, models do project that emissions would continuously increase with warming, and that this trend could last for hundreds of years."