Global Teleconnections Operators (GTO) (exam questions)

1. Question #1-1

To estimate the Global Teleconnections Operators (GTO), we assume that the mean state of

atmospheric response to anomalous sea surface temperature (SST) forcing can be regarded

as a linear process. In other words, the regional climate response for given region can be

the summation of the responses to individual SST forcings. Therefore we can calculate the

sensitivity matrix Gjk to characterize the sensitivity of regional climate (at location j) to

particular SST forcings (at location k) using this equation:

(1) Rj =

X

k

GjkTkAk + “j ;

, where Gjk the sensitivity of polar climate response at location j to anomalous SST at

location k. Tk is the SST anomaly at location k and Ak is the size of the grid box of SST at

location k. And Rj is the polar climate response at location j, which could be any climate

variables of interest (e.g. temperature, precipitation etc.). The “j is the error term arising

from nonlinearities that cannot be captured by the linear method, or other physical processes

that are not determined by SST changes (and it is speci c at region j). One can run several

ensemble members to get Rj with di erent SST forcings Tk. The more the ensemble members

are run, the more robust the relation between climate responses and SST forcings can be

characterized through a linear regression representing by Gjk. If the Gjk is high, we might

expect there is a close relation between the SST forcings Tk at location k and the responses.

In other words, the regional climate Rj is sensitive to SST forcings at location k.

2. Question #1-2

Torn and hakim [1] use ensemble sensitivity technique to analyze sensitivity of a forecast

metric (in their case, sea level pressure or precipitation over given boxes) to the initial

conditions, which could be determined from the observations on sea level pressure, 850-hPa

temperature, and 500-hPa height. This can be done using the ensemble sensitivity equation

which states that for an ensemble of size M, the sensitivity of the ensemble-mean value of

the forecast metric J to variable of interest x can be determined by:

(2)

@J

@x

=

cov(J; x)

var(x)

;

cov indicates the covariance between J at predicted time and x at initial time and var is

the sum of variance of x at initial time and predicted time. This usually are also analyzed

through large ensemble members in order to provide robust estimate to characterize statistically

signi cant sensitivity at certain (e.g. 95%) con dence level. Corresponding to how I

estimate the GTO, in which cov(J;x)

var(x) (the ensemble correlation) is analogous to the sensitivity

matrix Gjk that we try to characterize for any region of interest. However, what NWP use

has time evolution that the sensitivity can be traced back to the variables (e.g. SLP) several

hours before so that it can help scientists to know if the observed SLP at that location can

be improved in order to provide more accurate forecast for the SLP or precipitation at another

places (in terms of asking scienti c questions to determine which locations required to

improve what observations). However, for climate, which has longer timescale, the propagation

of Rossby wave from perturbed SST is within the time scale of months/seasons. Thus,

we haven’t looked at the \\time evolution” of sensitivity between seasons (but it might also

worth trying).

3. Question #1-3

The EOF analysis uses a set of orthogonal functions to represent a time series of climate

elds and it can explore the structure of the variability within a data set (e.g. winter SLP

during certain years) and how much those patterns can explain the variability we observe.

However, the EOF results might be hard to interpret because the atmospheric modes are

not always orthogonal and the EOF structure tends to be domain dependent as well. One

can use EOF analysis to extract di erent modes of variability such as the Arctic Oscillation

(AO), usually is the EOF1 of winter SLP during certain years and we can see the pressure

anomalies in the Arctic and midlatitudes

4. Question #1-4

El Ni~no is a teleconnection phenomena causing by the periodic

uctuation in equatorial

Paci c SSTs and the overlying pressure of the overlying atmosphere (this refers to Southern

Oscillation). During the normal conditions, the higher SST occurs at tropical western Paci c,

which provide a favorable conditions for convections and precipitations (upward motion) over

surrounding area. However during El Ni~no years, the warm pool occurs near the tropical

eastern Paci c, which could bring anomalous rain over Chile (South America) and creating

a relatively dry environment for regions at western Paci c (e.g. Australia).

2

References

[1] R. D. Torn and G. J. Hakim. Ensemble-Based Sensitivity Analysis. Monthly Weather Review, 136(2):663{

677, 2008.

3

COMPREHENSIVE WRITTEN EXAM

CHII-YUN TSAI (JUDY)

April 5. 2016

1. Question #2-1

Before getting more details in exploring internal variability using climate models with dif-

ferent initial conditions, it’s worth revisiting the sources of uncertainty in projecting climate

using climate models and the empirical methods to study those di erent types of uncertainty.

The uncertainty in simulating climate could arise from three main sources: (1) forcings, in

which di erent greenhouse gases, aerosols and many others could be speci ed by scientist to

provide plausible scenario. (2) model-response uncertainty can occur when di erent climate

models developed from di erent research institutes are used. This is because di erent mod-

els use di erent parameterization, di erent model physics, di erent resolutions and di erent

numerical methods (dynamical cores) to solve the equations. This is what the Coupled

Model Intercomparison Project (CMIP) has tried to resolve these uncertainty by collecting

the simulations using more than 30 models worldwide (with same forcing). (3) The last

source of uncertainty is the internal variability that I include in this project, which is not yet

widely addressed in this community for now. Comparing to other two uncertainties that can

be explored through changing the forcings, model resolutions, dynamical cores, in order to

study the internal variability, the climate community typically run a small or large ensemble

(based on available computational resources) with di erent initial conditions but with the

same forcing and same models. In terms of justi cations, it can go back to what Lorenz

found from chaos theory that even for a simple set of nonlinear di erential equations, the

evolution of the solutions could be di erent by small perturbations to the initial conditions.

Given that the climate models is composed of a large set of nonlinear equations that describe

the physics of the changes of climate. Thus, to explore the internal variability, from a climate

modeling perspective, we seek to represent internal variability uncertainty in using di erent

initial conditions. The evolutions of the solutions are di erent between ensemble members

because the climate elds would undergo nonlinear feedback within coupled climate system,

which ends up with yielding di erent results as time evolves.

Because each single realizations could be the \\real” climate that we want to capture, we

need to run multiple simulation to represent uncertainty estimate for climate projections.

I understand that the more ensemble members we can generate, the more robust estimate

we can make for estimating future climate change. However, I agree that we might slightly

underestimate the true internal variability given that we cannot run climate model for in nite

ensemble members. But in terms of capturing the \\trend” of climate signal, I think the 50

ensemble members might be enough for quantifying the distributions of possible outcome,

and in this case, increasing more ensemble members might have minimal e ect of changing

the distribution. As for way to check this, I think one can randomly select 5, 10, 20, 30, 40,

and 50 ensemble members (within the 50 ensemble members) and examine the distributions

formed by these ensemble members and calculate the standard deviation. I expect that the

standard deviation won’t change too much as the number of ensemble members increase to

certain threshold. But again, the internal variability can be di erent from the location of

the regions (e.g. tropics and high latitude regions) and the spatial/temporal averages of the

variabiles.

2. Question #2-2

If the same climate model with same parameters are used, with di erent initial conditions

(let’s say, I rerun the SFK15 experiment with other sets of initial conditions), I expect that

the spread of the internal variability might be really similar (this could be regarded as adding

50 more ensemble members). However, in SFK15, they perturbed the initial conditions of

all climate components, including initial atmospheric elds, sea-ice elds, land elds, and

ocean elds. This actually adds another layer of assessing the internal variability in terms of

including the internal variability from a fully coupled climate system. And this is why SFK15

ensemble is di erent from other large ensemble experiments generated from NCAR, in which

they only perturbed the initial atmospheric elds and have all the other components start

with the same initial conditions (ps. SFK15 use the climate model developed from NCAR,

although it’s a di erent version). I think it would be interesting to compare the ice sheet

responses to these di erent large initial-condition-ensembles (i.e., SFK15 and those from

NCAR) in order to investigate if the purely atmospheric internal variability could be large

enough to cause the di erent responses of ice sheet changes or if it necessary to include the

internal variability from all climate components to cause the di erent ice sheet responses.

3. Question #2-3

I think the rst thing I can do from examining the 4 sets of results would be identifying the

atmospheric circulation changes either in di erent smaller regions (e.g. east/west coast of

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North America, north polar caps, or even Asia) or in larger hemispheric scales. The variables

that I’m interested in would be (1) the pressure systems and if and how much the pressure

patterns can be changed (this can be quanti ed by either calculating the pressure gradient,

or identifying changes in the centers of low/hight pressure). (2) precipitation pattern changes

(this is related to pressure changes) and this is of interest to many regions in terms of water

availability or more/less stormy events. Honestly, this simulation can help us to answer lots

of research questions and understand the possible underlying physical process and changes

that we might experience if the Greenland ice sheet melted. Usually, those variables changes

could be simply quanti ed by taking the di erences between the control simulations (in my

case, present Greenland topography) and the simulations of decreased surface elevations.

Perhaps more sophisticated quanti cations for climate variable changes can be applied in

the course of this project if it is necessary. In addition, I will also examine the seasonal

changes of precipitation to identify in which season the precipitation might be more a ected

by Greenland surface elevation decrease. The reasons for using only four sets of surface

elevations are because I would like to provide a topography forcing that is \\large” enough

for changing atmospheric circulations (if the forcing is too small, then the atmosphere will

adjust itself back to previous equilibrium because of inertia). The reasons for adding 2

intermediate decreases of ice sheet is to explore if there’s a physical process for circulations

adjustment that could explain the last case of extreme topography decrease (comparing to

many literatures have been only looking at the cases for no Greenland and with present

Greenland). Also, this can provide an estimate to see if the extent of intermediate decrease

is large enough to change the atmospheric and oceanic circulations.

3

COMPREHENSIVE WRITTEN EXAM

CHII-YUN TSAI (JUDY)

April 5. 2016

Considering 3 cases:

(a) Remove the sea ice

(b) Remove the ice sheet

(c) Remove the sea ice and ice sheet

1. Question #3-1 1st order responses, changes in internal variability, factors

a ecting instability

If we removed a large amount of sea ice (in terms of large enough to change climate re-

sponses), the 1st order response of that would be having more open water which can provide

unlimited moisture to the atmosphere. Meanwhile the open Arctic Ocean can absorb more

solar radiation so that the sea surface temperature (SST) would rise a lot compared to that

with sea ice atop. This could warm the Arctic region and decrease the meridional temper-

ature gradient between the tropics and the Arctic and the mid-latitudes and the Arctic.

According to recent observations about decreasing sea ice, the jet stream tends to be more

\\wavy” compared to the past. And the resulting more blocking events would happen at

mid-latitude regions. The decreased meridional temperature gradient would weaken the po-

lar vortex (analogous to a extreme negative phase of the Arctic Oscillation) and jet stream

considering the thermal wind relation, and this would brings warm weather to high latitude

regions but cold, stormy weather to mid-latitude regions. The removal of large amount of

sea ice could a ect the internal variability in terms of ice-albedo feedback through decreasing

albedo because of deceasing sea ice. Again, this allows more solar radiation absorbed in the

ocean and warm the ocean. Warmer ocean can heat the atmosphere aloft and increase the

amount of moisture that atmosphere can hold (based on the Clausius{Clapeyron equation),

this might increase precipitation. Meanwhile open ocean provide sources of moisture which

could accelerate this process. This nonlinear ice-albedo feedback described above could cre-

ate a catastrophic transition (or tipping point) to extreme stage (e.g. catastrophic decrease

of sea ice or even no sea ice) once it is triggered and the factors involved in the feedback are

all responsible for a ecting instability of the climate system.

If we removed the ice sheet, the 1st order response we might see is the wind can penetrate

inland. If the remaining bedrock is high enough for providing favorable environment for

precipitation, we might slowly build the ice sheet back through snow accumulation if the

climate there is cold enough to permit this. On the other hand, removing ice sheet can be

regarded as removing a barrier within the air

ow, which might also change the wind pattern

surrounding the ice sheet (e.g. semi-permanent Icelandic low could shift if the Greenland

ice sheet is removed). This can also have a more remote impact by changing the Northern

Hemispheric circulation and the jet stream position because Greenland used to provide an-

ticyclone there with its cold inland. If we remove a large amount of ice sheet, from a surface

energy balance perspective, the surface albedo feedback involved in the ice-sheet-climate

feedback would play a dominant role to cause a consistent ice sheet decrease, which is unsta-

ble again. As the ice sheet decreases, the high albedo surface decreases, which make ice sheet

absorb more incoming shortwave radiation and decrease the amount of shortwave radiation

to be re

ected back. This positive feedback could accelerate the speed of decreasing ice

sheet. Another way that the removal of ice sheet can a ect climate is through adding fresh

water to the ocean (assuming that the ice sheet is turned into water because mass needs

to be conserved). Because the fresh water is buoyant compared to the deep dense water, it

can shut down the deep thermohaline circulation that are responsible for modulating heat

(and materials) transport to balance the Earth’s climate. The slowdown of the thermohaline

circulation could stop transporting warmer water from the tropics to higher latitudes and

make the climate colder over there (which is a negative feedback that high latitudes climate

tries to cool down to build the ice sheet back).

If we removed the ice sheet and sea ice, considering the combination of e ects we might have

mentioned previously, we might experience more warmer high latitude climate because we

remove those high-re

ective ice. The changes of atmospheric circulations could be similar to

those mentioned for removing sea ice, with weaker polar vortex, wavy jet streams and wind

patterns that can penetrate into the center of ice sheet. However, the increasing moisture

availability could also bene t the rebuilt of ice sheet if the wind can carry those moisture

and precipitate on the bedrock in the form of snow. If the ice sheet can be rebuilt, the dis-

charge of the iceberg could be bene cial for reforming of sea ice and \\cool” the ocean surface.

(I think my answers for the rst questions somehow cover those factors. I will just highlight

those factors again for questions #3-2 and #3-3)

2

2. Question #3-2 key

uid dynamics factors

Generally, for

uid dynamics factors that a ect the new quasi-equilibrium would be the

wind velocity of wind patterns changes (for sea ice removal: jet stream changes; for ice sheet

removal: both jet stream or semi-permanent pressure system change and the wind that can

penetrate inland). Also, the strength or direction of ocean overturning circulation might

change as well.

3. Question #3-3 key thermodynamics factors

Generally, for thermodynamics factors that a ect the new quasi-equilibrium would be the

temperature changes (either warming Arctic could decrease temperature gradient for removal

of sea ice or the increase of polar temperature if both highly re

ective sea ice and ice sheet

are removed). Also, the bare bedrock after removing the ice sheet could also absorb more

to the atmosphere.

Another factor is density (of atmosphere or ocean). The warmer ocean tends to increase

buoyancy of the atmosphere and favors convections, so the precipitation might increase if

those ice are removed. If the ice sheet melted and transformed into fresh water to the ocean,

it could also change the density of the surface ocean (e.g. the slowdown of the thermohaline

circulation). Density can relate the dynamical changes and thermal dynamical changes, so I

highlight this one here.

3

COMPREHENSIVE WRITTEN EXAM

CHII-YUN TSAI (JUDY)

April 5. 2016

ps. The answers are based on my understanding and references in [1], [2]

1. Question #4-1

The main physical ways that climate and ice sheets interact can be probed through exam-

ining the changes of ice sheet mass, which consist of surface mass balance, ice discharge to

the ocean, and bottom or ocean melt. Typically, ice sheets can gain mass via precipitation

(liquid or snowfall) and loss mass via surface melt and meltwater runo , sublimation or

evaporation, ocean melt of

oating ice shelf, calving, and bottom melt by geothermal heat

ux. As precipitation is one of the primary components a ect ice sheet, it can be a ected

by how the wind patterns/circulations are around the ice sheet. For example, the sharp

di erences of the heights of ice sheet and sea level can provide upslope environment that

is favorable for precipitation, but it in turn limits the moisture availability inland, which

usually creates a dry area with the center part of the ice sheet. If the ice surface elevation

decreases, it might be possible that the wind can penetrate inland and provides more pre-

cipitation there. The timescale of this depends on the location of ice sheet; for Greenland,

which could have signi cant melt within 3000 years. Also, the calving or discharge of the ice

berg could provide more sea ice coverage around the ice sheet, which might also limit the

moisture availability and inhibit the ice sheet grow from gaining precipitation.

As for surface energy balance, which can directly a ect ice melt in a thermal dynamical way,

is determined by the sum of net shortwave radiation, net longwave radiation, latent heat

ux and sensible heat

ux. The surface albedo feedback involved in the ice-sheet-climate

feedback would be primary feedback. As the ice sheet decreases (in response to the warm-

ing Arctic), the high albedo surface decreases, which make ice sheet absorb more incoming

shortwave radiation and decrease the amount of shortwave radiation to be re

ected back.

This positive feedback could accelerate the speed of decreasing ice sheet, in the timescale

around thousands years (for Greenland).

Another way that ice sheet can a ect climate is through adding fresh water to the ocean

and cause sea level rise. In addition, because the fresh water is buoyant compared to the

deep dense water, it can shut down the deep thermohaline circulation that are responsible

for modulating heat (and materials) transport to balance the Earth’s climate. The slowdown

of the thermohaline circulation could stop transporting warmer water from the tropics to

higher latitudes and make the climate colder over there (which is a negative feedback that

high latitudes climate tries to cool down to build the ice sheet back). The timescale of this

feedback could be millennial.

2. Question #4-2

The main issues in coupling climate models and ice sheet models are that both have large

di erences in spatial (i.e., in terms of model grids, GCM typically has >100’s km and ice

sheet model has 10’s km) and temporal scales (i.e., GCM or weather has timescale of

days/seasons/years but ice sheet has 104 to 106 years). Thus, running climate models more

than several centuries or millennia simulations is not really feasible in terms of requiring large

computational cost. However, several techniques have been used to solve these mismatch in

order to perform long-term ice sheet simulations using climate information.

To solve temporal mismatch, one can use:

(1) Using energy balance models (EBM)

A simple energy balance model can crudely address radiation, heat transport and horizontal

di usion of heat for Earth’s climate. This kind of model can then be coupled with explicit

ice-sheet models, by prescribing snowfall-melt pattern with respect to height and latitude

changes. Later in 1990’s, anomaly method was used to apply climate di erences in EBM on

the modern observed climatology in order to resolve climate model bias.

(2) Using asynchronous method

Because ice sheet changes have longer timescale to the order of 106 years, it is not feasible to

run GCM simulations for this time span. Scientist have been using GCM snapshots to deal

with timescale mismatch. Typically, the ice sheet model is run continuously while GCM is

run only a few decades to provide a “snapshot” climate representing particular climate for

that time to force ice sheet model (e.g. provide mass balance forcing).

(3) GCM look up table

Before running ice sheet model, one can assemble a collection of GCM snapshots within

di erent external forcings or ice sheet sizes to represent all possible scenarios for the runs.

2

The look up table can only consist of two extreme climate members (i.e., modern and Last

Glacial Maximum).

(4) Climate parameterization

If a 3D climate elds cannot be read in the ice sheet model (or if one wants to save compu-

tational cost), climate parameterization can be used to achieve this. For example, a zonally

symmetric snowfall-snowmelt pattern can be applied to reduce x-y spatial dimension. Some

temperature record can also be parameterized by analyzing isotope data for the past. Some

scientists also use regression analyses to parameterize modern Antarctic temperature and

precipitation given that the observations are sparse.

To solve spatial mismatch, several methods can be used as follows:

(1) Using simple interpolation

Typically people use bilinear interpolation to horizontally interpolate GCM variables (i.e.,

surface air temperature, precipitation elds) to ice sheet model grid. However, because

GCM cannot characterize ice sheet topography (especially along the ice margin) well with

its coarse grid. A simple lapse rate correction is used to correct the climate elds to account

for di erence between interpolated-GCM topography and the actual ice surface elevation.

(2) Using regional climate models (RCM) or stretched-grid GCMs

In order to resolve some sophisticated processes (e.g. upslope precipitation and katabatic

winds along the ice sheet margin). GCM results can be used to force atmospheric RCM

within particular domains. RCM can also be embedded in GCM to simulate smaller-scale

process under ner grid. As for using stretched-grid GCM, it is usually done with running

the simulations with specifying a region with ner grids.

3

References

[1] D. Pollard. A retrospective look at coupled ice sheet{climate modeling. 100(1):173{194, 2010.

[2] M. Vizcano. Ice sheets as interactive components of Earth System Models: progress and challenges.

Wiley Interdisciplinary Reviews: Climate Change, 5(4):557{568, 2014.

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