Essay: Global Teleconnections Operators (GTO) (exam questions)

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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
2
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
solar radiation, which could increase temperature through releasing longwave radiation back
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. Vizcano. 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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