Master Thesis

Climate Change in the Arctic:

Analysis of model simulations

Author:

Florian Schneider

Supervisor:

Dr. Johannes Quaas

Co-Supervisor:

Dr. Manfred Wendisch

15th December 2015

Abstract

The Arctic climate change is ampli�ed compared to the global climate change. Individual

feedback e�ects contribute to Arctic Ampli�cation. Radiative climate feedbacks diag-

nosed by means of the combined �Partial Radiative Perturbation method� (PRP-method)

from an idealized climate change experiment for abruptly changed CO2-concentration

to the quadruple (�abrupt4xCO2�) of the pre-industrial concentration (�piControl�) of

13 models from the Coupled Model Intercomparison Project Phase 5 (CMIP5) are pre-

sented and compared for a global and an Arctic average, de�ned as the area between

70◦N and 90◦N. Signi�cant discrepancies between the Arctic and global averaged feed-

backs are found. For a global average, the water vapor feedback is the strongest positive

feedback (1.91 ± 0.19Wm−2K−1) while the surface albedo feedback is the dominating

positive feedback for an Arctic average (3.97 ± 1.28Wm−2K−1).The strongest negative

feedback is the Planck feedback for both area averages, but it is more than twice as

strong for the Arctic average. The globally averaged cloud feedback shows the largest

intermodel di�erences (±0.24Wm−2K−1), con�rming earlier results, but this does not

account for the Arctic average. The Arctic surface albedo feedback (±1.28Wm−2K−1)

shows the biggest intermodel di�erences due to huge intermodel di�erences in the con-

trol surface temperature and sea-ice fraction. The strength of the Arctic surface albedo

feedback is independent of the control sea-ice fraction, but its global complement shows

a dependency. The lapse-rate feedback is due to the missing deep convection and tem-

perature inversions in the Arctic positive and six times stronger (2.90± 0.63Wm−2K−1)

in absolute value than for a global average (−0.47± 0.20Wm−2K−1). The global change

of the surface temperature is correlated to the strength of the surface albedo and lapse-

rate feedback, whereat for an Arctic average also the strength of the cloud and Planck

feedback are dependent of the magnitude of warming. The cloud feedback is changing

sign for a greater Arctic warming to positive because of a greater impact of the trapped

emitted longwave radiation from surface by clouds. The Arctic surface albedo feedback

shows the strongest correlation with the total Arctic radiative feedback, which is corre-

lated to the strength of Arctic warming. Hence, the Arctic temperature feedbacks play

only a secondary role for the total Arctic feedback parameter, causing Arctic warming.

Contents

1. Introduction 1

2. Fundamentals 4

2.1. Radiation balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2. Climate feedbacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1. Planck feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.2. Lapse-rate feedback . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.3. Water vapor feedback . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.4. Surface albedo feedback . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.5. Cloud feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3. Data/Methodology 11

3.1. Models and simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2. Feedback quanti�cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4. Results 15

4.1. Climate feedbacks of 4× CO2-simulation . . . . . . . . . . . . . . . . . . 15

4.2. Model variability of climate feedbacks . . . . . . . . . . . . . . . . . . . . 21

4.3. Summer vs. winter Arctic feedbacks . . . . . . . . . . . . . . . . . . . . . 25

4.4. Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.5. Control climate sea ice extent . . . . . . . . . . . . . . . . . . . . . . . . 31

4.6. BW-PRP assuming preindustrial CO2 . . . . . . . . . . . . . . . . . . . . 31

5. Conclusion and Outlook 34

A. Appendix 39

iii

1. Introduction

The human in�uence on the climate and its global changing is evident [Graÿl, 1995,

IPCC, 2013]. The Fifth Assessment Report (AR5) of the Intergovernmental Panel of

Climate Change (IPCC) reports that human impacts on the climate system are extremely

likely the main reason for the global warming observed since the 1950s. Observations

and instrumental detection of climate variables began in the 19th century and due to this

we know today that the global surface temperature over land and ocean from 1880 to

2012 increased by 0.85 (0.65 to 1.06)K [IPCC, 2013]. Other important parameters apart

from temperature are snow and ice masses which have reduced signi�cantly. Je�ries et al.

(2013) showed in his work that the models are not able to predict the sea-ice declining.

The measured sea-ice extent is declining faster.

Measurements of the last 130 years show that the earth is in a phase of global warming

in comparison to the mean surface temperature of the period from 1961-1990 (Fig. 1.1).

It is remarkable that the high latitudes of the northern hemisphere have a much stronger

warming than any other region on earth. Climate Change is more pronounced in the

high latitude Arctic than in the rest of the world [Serreze and Francis, 2006]. This

process is called Arctic Ampli�cation.

Arctic Ampli�cation is prominent when the rises in increasing surface air temperature

in response to increasing greenhouse gases (GHG) will be larger in the Arctic compared

to the global surface air temperature change as a whole. Arctic Ampli�cation is run by

several physical and non-physical processes, e.g. loss of sea-ice extent due to melting.

The Arctic is in many physical processes unique and di�erent from the rest of the globe.

Most of the Arctic Ocean is covered by sea-ice, which results in a high surface albedo.

The Atmosphere of the Arctic shows a complex vertical structure with inversions of tem-

perature and humidity in the lower troposphere [Boé et al., 2009]. Beesley and Moritz

(1999) showed that the Arctic is cloudy 80% of the year and by contrast to the general

cooling e�ect of clouds, in the Arctic the clouds heat up the atmosphere stronger than

they cool the Earth's surface.

Holland and Bitz (2003) documented the Arctic Ampli�cation in coupled models out

1

CHAPTER 1. INTRODUCTION

of the Coupled Model Intercomparison Project Phase 2 (CMIP2). The range of simu-

lated polar warming in the Arctic was from 1.5 to 4.5 times the global mean warming

[Holland and Bitz, 2003]. Those big intermodel discrepancies are the result of di�er-

ent parametrizations [Holland and Bitz, 2003] and the missing understanding of climate

processes.

Feedback analyzes are an important quantity to understand the processes of climate

development [Bony et al., 2006]. From a global perspective, it is most important to

calculate, understand, and verify global mean radiative feedbacks. These are, however,

a result of a large number of regional and local physical processes.

Earlier studies investigated the feedbacks from a global perspective as global mean ra-

diative feedbacks [Soden and Held, 2006, Klocke et al., 2013, Tomassini et al., 2013].

They analyze the main physical climate feedbacks such as temperature, water vapor,

and albedo. The largest uncertainty between models shows up for the cloud feedback

[Klocke et al., 2013]. However, Pithan and Mauritsen (2014) focused on the warming

contribution of the individual feedback mechanisms in a global and a polar point of view.

They reported that the albedo feedback is not the primary contributor to Arctic Am-

pli�cation as said by Taylor et al. (2013). Instead, the temperature feedbacks dominate

the Arctic Ampli�cation in climate models from the Coupled Model Intercomparison

Project Phase 5 (CMIP5).

Figure 1.1. � Annual and zonal mean of measurements of temperature anomalies from 1880-2020in comparison to the period of 1961-1990. Grey areas are missing measurements. This map isprovided by the National Aeronautics and Space Administration (NASA) Goddard Institute forSpace Science (GISS): www.data.giss.nasa.gov/gistemp/maps/.

2

CHAPTER 1. INTRODUCTION

This study is focusing on the Arctic and therefore the Arctic Ocean (70◦N to 90◦N).

The topic of this thesis is to quantify the individual radiative feedback parameters for 13

CMIP5 models of the Arctic area and to compare those to the global feedback param-

eters. The di�erences between the summer and winter feedbacks are also investigated.

Additionally, relations between the radiative feedbacks and the surface temperature

change are analyzed. Therefore a complete feedback analysis is performed

Chapter 2 introduces the theoretical background to climate feedbacks, radiative forcing

and the radiative transfer model. Chapter 3 describes the Partial Radiative Perturba-

tion (PRP) method and gives an overview about the CMIP5 models and how the data

was implemented into the o�ine radiation transfer model. The Results are presented

and discussed in Chapter 4. Chapter 5 will conclude the thesis and gives an outlook.

3

2. Fundamentals

2.1. Radiation balance

There are several emitters in the atmosphere e.g. the sun, which has a temperature of

around 6000K, terrestrial bodies and surfaces, atmospheric gases and the present clouds

and aerosol particles [Kraus, 2004]. The Stefan-Boltzmann law describes the relationship

of the total emitted radiation energy F per unit area and time of such a grey body.

F = eσT 4 (2.1)

Where σ is the Stefan-Boltzmann constant and e the emissivity. The emissivity for a

black body, which completely absorbs the received radiation, has value of 1. A body

which is not completely absorbing the incident radiation is called grey body and has an

emissivity smaller than 1. Each body acts as a grey body and emits radiation back to its

surroundings depending on its temperature and emissivity after the Stefan-Boltzmann

law 2.1. The radiation �ux density (also called irradiance) out of equation 2.1 describes

the total energy of the radiation passing through or hitting a surface per unit time and

per unit area.

The sun is emitting an irradiance of 6× 107Wm−2 and due to its distance to Earth and

the sphere likely shape of the Earth this value is reduced to 1/200000 of the outgoing

irradiance from the sun. Thus, the global mean of the extraterrestrial irradiance which

hits the Earth is 342Wm−2. The sun is therefore heating the Earth and thus increas-

ing the Earth's surface temperature. Due to assumption of equilibrium, this incoming

irradiance has to be compensated by the emitted and re�ected irradiance [Kraus, 2004].

This is called radiation balance.

The solar and the terrestrial spectrum ranges roughly from 0.2 to 4µm and 3.5 to 100µm,

respectively. For practical purpose, they can be treated separately.

Absorption and emission of radiation by gases described by the spectral irradiance Fλ

are extremely wavelength dependent. To obtain the �ux F of a certain spectrum, the

4

2.1. RADIATION BALANCE CHAPTER 2. FUNDAMENTALS

spectral irradiance has to be integrated over the intended spectrum [λ1, λ2].

F (λ1, λ2) =

λ2∫λ1

Fλdλ (2.2)

The short- and longwave irradiances are calculated by integrating over its spectral range.

Figure 2.1 shows which fraction of the solar and terrestrial radiation is re�ected and/or

emitted in the Earth radiation system.

Figure 2.1. � The radiation balance of the atmosphere. The unit is Wm−2. Solar and terrestrialradiation are colored in yellow and brown, respectively [Trenberth et al., 2009].

The total radiation balance Fnet can be written:

Fnet = (Fsw ↓ +Flw ↓)− (Fsw ↑ +Flw ↑) = (S +D − Fsw ↑) + (Flw ↓ −A−R) (2.3)

Fsw ↓ is the downward solar radiation that can be separated into a direct solar radiation

S and a di�use solar radiation D. Fsw ↑ is the solar re�ected radiation leaving the

system at top of atmosphere (TOA). Flw ↓ is the downward terrestrial radiation and

Flw ↑ stands for the total upward terrestrial radiation which can be separated close to

5

2.2. CLIMATE FEEDBACKS CHAPTER 2. FUNDAMENTALS

the surface in the emission of the surface (A) and the re�ected part of the downward

terrestrial radiation that is emitted by the atmosphere (R) [Kraus, 2004].

All the following values in this section accord to the fraction of the solar constant divided

by 4. The incident solar irradiance is scattered and absorbed by clouds, aerosol particles

and gases in the atmosphere. Hence only 49% of the measured incident solar irradiance

at TOA reaches the Earth surface, thereof only 23% is direct solar radiation. 30% of the

incident irradiance is re�ected back to space. The missing 70% to reach equilibrium at

TOA are given by the emitted longwave irradiance from the surface and the atmosphere

[Kraus, 2004]. The short- and longwave irradiances are not compensating each other

(+28% to much energy in the system), that means that there other �uxes are needed to

reach equilibrium. The latent and turbulent heat �uxes are compensating the missing

�uxes. Those heat �uxes are not further investigated in this thesis.

Upward and downward �uxes are de�ned that upward-directed �uxes have a negative

sign and downward-directed �uxes a positive sign.

2.2. Climate feedbacks

The climate system is often described as it is in equilibrium. This means that there is

no global change in surface temperature (Ts) averaging about a long enough time period

and the net radiation balance on TOA is zero (∆R = 0). Considering the radiation

balance by Mauritsen et al. (2013),

∆R = F + λ∆T, (2.4)

it is obvious that an imposed external forcing F (e.g. change of greenhouse gas con-

centration) is generating a temperature change ∆T that the net radiation balance at

TOA will be zero again (∆R = 0). An external forcing will depart the radiative budget

at TOA from zero, and the climate system can be described as o�-equilibrium. The

climate system responds by changing the global mean surface temperature. This leads

to increased energy being radiated back into space, so that the system can return to

equilibrium [Klocke et al., 2013]. Therefore, the total feedback parameter λ must be

negative to ensure a stable climate system [Mauritsen et al., 2013]. This feedback pa-

rameter can be estimated from the change of equilibrium temperature and the strength

of the forcing.

6

2.2. CLIMATE FEEDBACKS CHAPTER 2. FUNDAMENTALS

λ = − F

∆T(2.5)

The temperature change a�ects other temperature-dependent climate processes. If those

processes in turn have an e�ect on the radiation budget (and hence on the temperature),

they are referred to as climate feedbacks [Klocke et al., 2013]. Those temperature-

dependent climate processes or parameters are e.g. temperature, water vapor, surface

albedo and clouds.

The feedback parameter can be de�ned after Klocke et al. (2013):

λ =∂R

∂Ts=

∑x

∂R

∂x

∂x

∂Ts+ φ(∂2) ≈

∑x

λx (2.6)

with

λx =∂R

∂x

∂x

∂Ts(2.7)

whereas x stands for the individual feedbacks. The second order term and all higher

order terms are standing for the interactions in between the di�erent feedbacks. However,

for a linear approximation, the higher order terms are neglected [Klocke et al., 2013].

With the approach of linearity the total physical feedback parameter can be split into a

temperature (λT ), a water vapor (λWV ), a surface albedo (λA) and a cloud component

(λC):

λ = λPL + λLR + λWV + λA + λC (2.8)

The temperature feedback can further be separated into a homogeneous temperature

change, which is called the Planck feedback (λPL), and the change of the vertical tem-

perature gradient in the troposphere, called lapse-rate feedback (λLR). The chemical

feedbacks are not considered in this thesis.

Feedbacks can have amplifying (positive feedback) and dampening (negative feedback)

e�ects on the initial perturbation of the TOA radiation budget [Klocke et al., 2013].

2.2.1. Planck feedback

The Planck feedback is the dominating part of the temperature feedback and the strongest

negative physical feedback [Soden and Held, 2006]. It describes the homogeneous change

of the temperature throughout the troposphere, assuming that the troposphere is per-

7

2.2. CLIMATE FEEDBACKS CHAPTER 2. FUNDAMENTALS

fectly mixed. Convection will pass the increase in surface temperature to all layers in

the troposphere. Due to the warmer tropospheric temperatures, the emitted longwave

radiation to space will increase. Hence the Planck feedback is a negative feedback. The

Planck feedback is generally overlooked as a contributor to Arctic Ampli�cation. A given

increase in emitted radiation requires a larger temperature increase at colder background

temperatures (see eq. 2.1). As the Arctic is colder than the tropics, the Planck feedback

in itself causes Arctic Ampli�cation [Pithan and Mauritsen, 2014].

2.2.2. Lapse-rate feedback

The second part of the temperature feedback is the lapse-rate feedback, which describes

the radiation e�ect of the change of the tropospheric lapse rate due to an initial per-

turbation. It acts both positive and negative. This feedback is known to contribute to

stronger Arctic than tropical warming [Manabe and Wetherald, 1975, Bintanja et al.,

2012, Pithan and Mauritsen, 2014]. Air parcels rising in deep convective clouds create a

tight coupling between surface and upper tropospheric temperatures. These air parcels

steepen the moist-adiabatic lapse rate in a warming climate due to more latent heat and

hence cause greater warming in the upper troposphere than at the surface. To o�set

a given TOA radiation imbalance at TOA or at surface (SFC), a stronger warming is

needed at TOA compared to SFC due to eq. 2.1 [Pithan and Mauritsen, 2014]. Thus

the stronger temperature increase in upper troposphere gives rise to enhanced longwave

radiation emission to space which cools the atmosphere. Thus the lapse-rate feedback

in this case is negative. In contrast, an increase (�attening) of the lapse-rate leads to

less longwave emission to space. Hence more energy stays inside the atmosphere which

results in an enhanced greenhouse e�ect, warming the atmosphere. Therefore the lapse-

rate feedback in this case is positive [Colman, 2002]. The lapse-rate feedback is also

special in the Arctic. Due to cold dense air close to the surface which is hardly mixed

with the lighter air aloft, radiation is the primary coupling mechanism. A certain lapse-

rate is not imposed by radiative coupling which leads to a surface based warming that

remains con�ned to the lowermost part of the atmosphere. Under this bottom-heavy

warming pro�le, a larger increase in surface temperature is required to o�set a given

TOA imbalance, causing a local negative lapse-rate feedback in the Arctic [Pithan and

Mauritsen, 2014].

8

2.2. CLIMATE FEEDBACKS CHAPTER 2. FUNDAMENTALS

2.2.3. Water vapor feedback

In a warmer climate the atmosphere contains more water vapor, and because water vapor

is itself a greenhouse gas, this yields the positive water vapor feedback. Higher water

vapor concentrations in the atmosphere increase the absorption of longwave radiation

inducing a further warming of the climate. This is by far the strongest feedback acting

in the atmosphere [Soden and Held, 2006, Klocke et al., 2013, Mauritsen et al., 2013,

Tomassini et al., 2013]. In the case of a CO2 doubling in the atmosphere, the water

vapor alone increases the global temperature by a factor of two [Bony et al., 2006].

This feedback is much weaker in the Arctic region. Looking at the Clausius-Clapeyron

equation, which describes the saturation water vapor pressure as nearly exponential with

temperature, it is obvious that the change in water vapor concentration is much higher

in the tropics than in the Arctic, because of higher tropospheric temperatures.

2.2.4. Surface albedo feedback

A warmer climate leads to snow and ice retreat, which consequently exposes land [Je�ries

et al., 2013] and ocean surfaces that are much less re�ective of solar radiation. This gives

rise to a higher absorption of solar radiation that results in higher atmospheric warming,

especially in the region of the snow and ice reduction [Hall, 2004]. Thus, the surface

albedo feedback is positive because the initial warming of the climate is strengthened.

Surface albedo is not only changing due to snow and ice retreat. It is changing e.g.

due to warmer temperatures when grasslands of the tundra in the Arctic are replaced

by shrubs or even forest, which both have a lower albedo than grasslands [Kessler and

Jaeger, 1999], or due to the human in�uence by replacing forest with a more re�ective

vegetation like crops.

In the Arctic the surface albedo is dominated by sea ice and water. Thus, melting sea ice

to an open water area leads to a massive change in surface albedo. It is well established

that this gives rise to an enhanced warming in the Arctic [Serreze and Francis, 2006,

Serreze et al., 2009, Holland and Bitz, 2003]. Pithan and Mauritsen (2014) showed that

in a perspective of warming contribution to Arctic Ampli�cation, the surface albedo

feedback plays only a secondary role.

2.2.5. Cloud feedback

The cloud cover can exert a large in�uence upon climate due to its shortwave re�ecting

and longwave absorbing abilities. The net radiative in�uence of clouds on the climate

9

2.2. CLIMATE FEEDBACKS CHAPTER 2. FUNDAMENTALS

system depends on the cloud optical properties, the cloud amount and its vertical distri-

bution. The cloud feedback has the biggest intermodel spread of all radiative feedback

processes [Soden and Held, 2006, Klocke et al., 2013, Tomassini et al., 2013, Cess et al.,

1990] which is not accounting for an Arctic average.

It is important to understand how the climate change is a�ecting the cloud properties

of di�erent cloud types like high or low clouds. Low clouds do have a cooling e�ect

because of their high cloud albedo, which leads to a strong shortwave radiation re�ec-

tion, leading to less energy in the earth climate system. High clouds, in turn, warm

the Earth's system because they transmit almost all solar radiation, but absorb strongly

the longwave radiation and therefore trap the energy in the system, which ampli�es the

Earth's greenhouse e�ect.

This warming or cooling e�ect is not working in the same way in the Arctic due to its

complex vertical structure of the atmosphere. Low clouds are the main cloud type in the

Arctic region and in contrast to the general cooling e�ect of those low clouds in a global

perspective, they warm the atmosphere stronger than they cool the Earth's surface most

of the year. Only in summer, when the re�ection of incoming radiation is higher, the

clouds cool the Earth's surface [Wielicki et al., 1995].

10

3. Data/Methodology

3.1. Models and simulations

The feedback analysis is based on two di�erent experiments of the �fth phase of the

CMIP5 [Taylor et al., 2012], called �piControl� and �abrupt4xCO2�. The �piControl� ex-

periment is the preindustrial control run, where the CO2-concentration is at the preindus-

trial level and only changed due to natural variability. The �abrupt4xCO2� experiment

is the experiment where the preindustrial CO2-concentration is abruptly quadrupled and

then hold �xed. In both experiments all other external forcings are kept at their prein-

dustrial values.

For the feedback analysis, 13 di�erent global climate models are considered: MPI-ESM-

LR [Stevens et al., 2012], CanESM2 [Chylek et al., 2011], NorESM1-M [Seland et al.,

2008], GFDL-ESM2G [Dunne et al., 2012, 2013], bcc-csm1-1 [Wu et al., 2014], BNU-

ESM [Ji et al., 2014], inmcm4 [Volodin et al., 2010], FGOALS-s2 [Bao and Coauthors,

2013], MIROC5 [Watanabe et al., 2010], MRI-CGCM3 [Yukimoto et al., 2011], GISS-

E2-R and GISS-E2-H [R. L. Miller, 2014], and CCSM4 [Gent et al., 2011].

Other models are missing due to limited access to required variables.

All model data is regridded with the cdo command �cdo remapbil,t63grid� on the T63

grid, which has a gridsize of 192 × 96 (longitude×latitude) over the whole earth. Fur-

thermore, 4-dimensional variables (time,level,latitude,longitude) are level inverted with

the cdo command �cdo invertlev� that the �rst level in the array is the top of atmosphere

(TOA) and the last level in the array is the level directly upon the surface (SFC). Vari-

ables, which have a vertical pressure level grid (�plev�) are 1st grade interpolated (linear)

on the vertical hybrid levels. If there is a hybrid level with a practical value (not missing

value) below the last pressure level with a practical value, the variable will be linearly

extrapolated to this hybrid level. The used variables and their dimensions are listed in

table 3.1.

11

3.2. FEEDBACK QUANTIFICATION CHAPTER 3. DATA/METHODOLOGY

Table 3.1. � All required variables

variable long name dimensions level type unit

cl cloud fraction time,lev,lat,lon hybrid %cli cloud ice mass fraction time,lev,lat,lon hybrid 1clw cloud water mass fraction time,lev,lat,lon hybrid 1hur relative humidity time,plev,lat,lon pressure %hus speci�c humidity time,plev,lat,lon pressure 1ta air temperature time,plev,lat,lon pressure Kts surface temperature time,lat,lon - Kps pressure at surface time,lat,lon - Pa

rsdscs shortwave downward radiation clear sky time,lat,lon - W/m2

rsuscs shortwave upward radiation clear sky time,lat,lon - W/m2

sic sea ice cover fraction time,lat,lon - %

3.2. Feedback quanti�cation

To determine the feedback parameters for the individual feedbacks, the �Partial Radia-

tive Perturbation�-method (PRP-method) is used. This method was �rst introduced

by Wetherald and Manabe (1988). Colman (2003) and Soden and Held (2006) used

this method in an ensemble of atmosphere-ocean coupled general circulation models

(AOGCM).

The climate system of the model is in thermal equilibrium,:

∆R̃ = ∆S̃ + ∆F̃ = 0 (3.1)

where the tilde indicates a global mean value. S̃ stands for the annually averaged

downward solar irradiance and F̃ represents the annually averaged downward longwave

irradiance at TOA. The ∆S̃ and ∆F̃ stand both for the di�erence between the thermal

equilibrium between the �piControl� and the �abrupt4xCO2� experiment in the atmo-

sphere in their respective spectrum. For a su�ciently small perturbation of the climate,

it is assumed that the feedbacks are independent and can be considered separately.

Hence, the additive approximation can be assumed:

∆R̃ = ∆xR̃ + ∆T R̃ + ∆rR̃ + ∆AR̃ + ∆CR̃ (3.2)

x, A, T , C and r stand for the carbon dioxide concentration, surface albedo, temper-

ature, clouds, and mixing ratio of water vapor, respectively. The same approximation

can be done for ∆S̃ and ∆F̃ .

To retrieve the net TOA �ux changes ∆Ri due to a speci�c feedback i, o�ine radiation

calculations need to be performed. In this thesis the o�ine radiation calculations, which

12

3.2. FEEDBACK QUANTIFICATION CHAPTER 3. DATA/METHODOLOGY

Table 3.2. � Substituted variables for individual feedback.

Feedback substituted variables

Surface albedo feedback rsusucs, rsdscsCloud feedback cl, cli, clw

Water vapor feedback hur, husLapse rate feedback taPlanck feedback ts

means calculated outside of the climate model [Klocke et al., 2013], are performed for

150 years. The radiation algorithm of the model is used to determine the standard �uxes

of S̃i and F̃i at each grid point for the monthly mean of the temperature, water vapor,

albedo and cloud cover from the preindustrial simulation �piControl�. This calculation

must be performed a second time, where all variables stay unchanged, except for one

variable, which is substituted by the value from the (perturbed) climate change simu-

lation �abrupt4xCO2�. The annual mean �ux changes ∆Ri are divided by the annual

mean temperature changes ∆Ts and then averaged over several simulation years - in this

thesis the last 50 years of the calculated 150 years - to consider the interannual variabil-

ity of the �ux and surface temperature change. The �rst 100 years are not used because

the climate is adjusting to the external forcing and therefore changing the surface tem-

perature to achieve equilibrium again (see �g. A.1). Fig. A.1a shows that there is no

distinct change in global surface temperature for the last calculated 50 years, so that

the assumption of equilibrium is valid. Table 3.2 shows which variable is substituted to

achieve the speci�c radiative feedback, e.g. the variables �cl�,�cli�,�clw� are substituted

to achieve the cloud feedback.

Every value of eq. 3.2 is determined by the di�erence of the calculated radiation �uxes of

the standard �piControl� run and the perturbed �piControl� run. However, the �piCon-

trol� run and the �abrupt4xCO2� run are from now be called the reference and perturbed

climate, respectively.

Hence, the feedback parameter can be de�ned for each variable i as follows:

λi =∆iR̃

∆i

∆i

∆T̃s(3.3)

This method calculates the partial derivative directly. However, it must be considered

that the interaction between the individual feedbacks are neglected. Besides, the changed

signal from the total derivative of i is calculated with the temperature Ts instead of

using the partial derivative. Furthermore, it is possible that the discrepancies between

13

3.2. FEEDBACK QUANTIFICATION CHAPTER 3. DATA/METHODOLOGY

the reference and the perturbed climate are not small enough, leading to the problem

that the discreet approximation (eq. 3.2) is not su�cient.

To avoid biases due to the assumption of uncorrelated variables, the PRP-method has

to be computed twice [Colman and McAvaney, 1997]. Once forward (FW-PRP), where

a variable from the perturbed climate is substituted into the reference climate, and once

backward (BW-PRP), where the same variable is substituted from the reference climate

into the perturbed climate. The �nal solution is obtained by averaging the FW-PRP

and the BW-PRP calculations [Klocke et al., 2013]:

∆Ri =∆RFW

i −∆RBWi

2(3.4)

Note that if FW-PRP leads to a positive �ux change, BW-PRP will cause a negative

�ux change. Therefore the �ux change of the BW-PRP must be multiplied by −1.

In this study the feedback parameters will be quanti�ed for the Arctic region, which

is de�ned in this study as the area from 70◦N to 90◦N. Globally averaged feedback

parameters are also calculated to compare the Arctic feedback parameters with the

global ones.

To execute the calculations, the radiation transfer calculations must be done o�ine.

This makes the method very complex to implement and computationally very expensive.

However, this method is used in this thesis because it provides the possibility of a full

feedback analysis. Other methods are struggling to calculate or estimate the cloud

feedback because of its strong vertical non-linearity (radiative kernel method - Soden

and Held, 2006).

14

4. Results

4.1. Climate feedbacks of 4× CO2-simulation

The climate feedbacks for the case of an abruptly quadrupled atmospheric CO2 simula-

tion are described in this section. Once for a global mean and once for an Arctic average

(70◦N - 90◦N).

Fig. 4.1 shows the global distribution of the individual feedback parameters as a multi-

model average. The combined PRP-method leads to the presented results. To avoid

interannual and natural variability, the feedback parameters are averaged over 50 years

after 100 years of acclimatization due to the external forcing. The weighted multi-model

global mean value of each individual feedback parameter is written at the upper left of

each subplot and listed in table 4.1. Furthermore, the multi-model standard deviation

of each feedback parameter is listed in table 4.1. All values from now on are multi-model

averaged except otherwise identi�ed.

On a global scale the strongest positive feedback is the water vapour feedback with a

strength of 1.91 ± 0.19Wm−2K−1 averaged over all 13 models, which is slightly higher

than the multi-model mean of 1.80±0.18Wm−2K−1 [Bony et al., 2006], who investigated

a doubling of the preindustrial CO2-concentration. The strength of the water vapour

feedback has its maximum in the tropics and diminishes polewards. This is accused to

the speci�c humidity which arises most in the tropics, due to the warmer temperatures

Table 4.1. � Feedback parameters for abruptly quadrupling CO2 simulation for the (FW+BW)PRP calculation. Given are the multi-model averages and their standard deviation.

λx global mean [Wm−2K−1] Arctic mean [Wm−2K−1]λA 0.42 ± 0.11 3.97 ± 1.28λC 0.18 ± 0.24 −0.20 ± 0.32λWV 1.91 ± 0.19 1.30 ± 0.14λLR −0.47 ± 0.20 2.90 ± 0.63λPL −3.33 ± 0.08 −7.49 ± 1.18

15

4.1. CLIMATE FEEDBACKS OF 4× CO2-SIMULATION CHAPTER 4. RESULTS

Figure 4.1. � Multi-model average of the global geographical distribution of net albedo, cloud,water vapour, lapse rate and Planck feedback parameters for CO2 quadrupling at TOA for thecombined (FW+BW) PRP calculation. Positive values denote increased downward radiation.

16

4.1. CLIMATE FEEDBACKS OF 4× CO2-SIMULATION CHAPTER 4. RESULTS

Figure 4.2. � multi-model zonal mean surface temperature change between the 4×CO2-simulationand the piControl-simulation. The black line shows the multi-model average and the shadedarea includes all indiviudal model surface temperature changes. The box-whisker plots show theminimum, the 25th percentile, the median, the 75th percentile and the maximum of the surfacetemperature of all models for the Arctic (70◦N - 90◦N) [red], the tropics (20◦N - 20◦ S) [green]and Antarctica (70◦ S - 90◦ S) [blue], respectively.

in comparison to the poleward located regions, even though the Arctic region has a

greater multi-model warming than the tropics between the 4× CO2-simulation and the

prehistorical CO2-concentration simulation (piControl) (see �g. 4.2,4.3). The surface

temperature change is varying much more in the Arctic than in the tropics.

In contrast, the multi-model Planck feedback is by far the strongest negative feedback

with a global multi-model mean value of −3.33±0.08Wm−2K−1, which is slightly higher

than the value reported by Soden and Held (2006) with −3.21 ± 0.04Wm−2K−1. It

dominates the climate response to an external forcing. The global distribution pattern

of the TOA �ux changes is accorded to the global distribution of the surface temperature

change (shown in �g. 4.3 and �g. 4.2). The highest values are in the high latitudes

where large surface warming occurs, especially over sea-ice and snowy land regions.

The largest intermodel di�erences on a global scale produces the multi-model cloud

feedback with a value of 0.18± 0.24Wm−2K−1. It is strongly heterogeneous and it has

17

4.1. CLIMATE FEEDBACKS OF 4× CO2-SIMULATION CHAPTER 4. RESULTS

Figure 4.3. � Geographical distribution of the surface temperature change, averaged over the last50 years of the o�ine calculations, between the �abrupt4xCO2�- and the �piControl�-experiment.∆T=Tsfc,4xCO2

−Tsfc,piControl.

local values between +2 and −3Wm−2K−1. It is remarkable that the cloud feedback

shows negative values in the Arctic Ocean and at the coastal regions of Antarctica,

where more sea-ice is located. However, the global mean multi-model cloud feedback

calculated in this thesis is smaller than the reported value by Bony et al. (2006) with

0.69± 0.38Wm−2K−1. This di�erence is remarkable and is probably resulting from the

not-perturbed cloud droplet number concentration in this thesis for the FW- and BW-

PRP.

The multi-model lapse-rate feedback shown in �g. 4.1 has a weighted global average,

which is negative with −0.47 ± 0.20Wm−2K−1 and not in good agreement with the

reported multi-model value of −0.84± 0.26Wm−2K−1 by Bony et al. (2006), who inves-

tigated a doubling of CO2. Its global distribution has a clear cut between the negative

values in low latitudes and even the midlatitudes above the oceans. Further poleward

it is positive above the ocean and the continents. All in all the lapse-rate feedback is

stronger, independent of sign, above the sea. This distinct pattern can be explained by

the structure of the temperature change. The surface temperature increases stronger

at high latitudes than the surface temperature at higher altitudes, causing a negative

18

4.1. CLIMATE FEEDBACKS OF 4× CO2-SIMULATION CHAPTER 4. RESULTS

feedback. At low latitudes, it is reversed due to the deep convection, leading to a tight

coupling between the surface temperature and the upper tropospheric temperatures (see

Chapter 2.2.2). Higher values above the sea result from the higher temperature di�er-

ence between the surface temperature (in this case the uppermost water temperature)

and the temperature in high altitudes, because the sea water has a higher e�ective heat

capacity and, consequently, heats up less by the same energy input, leading to a smaller

temperature increase at surface compared to the continental land masses. The di�erence

between the lapse-rate feedback parameter resulting from this thesis and the one of Bony

et al.(2006) is due to higher surface temperature changes in the Arctic under an external

forcing of 4xCO2 than 2xCO2, which leads to a stronger positive lapse-rate feedback in

the Arctic and therefore a smaller negative globally averaged lapse-rate feedback param-

eter.

The global distribution of the multi-model albedo feedback shows noteworthy changes at

TOA �ux in the high latitudes and at the Himalayan mountain system, where snow and

sea-ice melting due to a warmer climate are present. Stronger radiative perturbations

at TOA are limited to the sea-ice regions in the Arctic and on the southern hemisphere.

However, this gives rise to a small positive global mean albedo feedback parameter of

0.42±0.11Wm−2K−1 which is of similar size compared to 0.26±0.08Wm−2K−1 reported

by Bony et al. (2006), keeping in mind that Bony et al. (2006) had a transient doubling

of the CO2 concentration. That leads to a lower surface temperature warming than the

4× CO2-simulation, consequently causing less and slower melting of ice and snow.

On an Arctic point of view the multi-model Arctic mean for the water vapour, Planck,

cloud, lapse-rate and albedo feedback parameter with values of 1.30 ± 0.14Wm−2K−1,

−7.49 ± 1.18Wm−2K−1, −0.20 ± 0.32Wm−2K−1, 2.90 ± 0.63Wm−2K−1 and 3.97 ±1.28Wm−2K−1, respectively, show great di�erences to the global ones.

Comparing all the multi-model global mean feedback parameters to the multi-model

Arctic mean feedback parameters, listed in table 4.1, it is obvious that there is a need

to distinguish between a global and an Arctic perspective.

From an Arctic perspective the strongest positive feedback is the albedo feedback and

not the water vapour feedback. The Planck feedback is more than twice as strong in

the Arctic average than on global average, but it has quite big intermodel di�erences

(±1.18Wm−2K−1), which result from the big intermodel di�erences in the tempera-

ture change (see �g. 4.2). The biggest intermodel di�erences has the albedo feedback

(±1.28Wm−2K−1), which is three times bigger than the global average albedo feedback

parameter. The di�ering sea-ice cover fractions (see �g. 4.10) and thicknesses in the

19

4.1. CLIMATE FEEDBACKS OF 4× CO2-SIMULATION CHAPTER 4. RESULTS

control simulation of each model [Holland and Bitz, 2003] and the highly diverse tem-

perature changes in the Arctic region for the di�erent models (see �g. 4.2) lead to such

deviations in between the models. Hence, the sea-ice melting di�ers strongly in between

the models, leading to strong di�erences in the calculation of the albedo feedback. Jef-

fries et al. (2013) reported that although the models provide qualitative support for

Arctic ampli�cation and future sea-ice loss, they have limited value for quantitative pro-

jections. The models have de�ciencies in ocean circulation, cloud physics, atmospheric

dynamics, and albedo parameterization - details that go beyond sea-ice pyhsics per se -

all contributing to the spread among model predictions [Je�ries et al., 2013].

The cloud feedback is quite consistent between the di�erent models in comparison to the

albedo and Planck feedback, although its intermodel di�erence is bigger than on global

average. The multi-model average is negative for an Arctic average and therefore causing

a loss of energy in the climate system per one Kelvin warming while the positive global

cloud feedback leads to more energy in the climate system per one Kelvin warming.

The biggest contrast in between global and Arctic average has the lapse-rate feedback,

which is not only positive in the Arctic region but also almost 6 times larger in absolute

value than the global average. Hence to this feedback, the surface temperature is warm-

ing more in the Arctic than in the tropics, where there is a stronger negative feedback.

Pithan and Mauritsen (2014) showed earlier that the lapse-rate feedback is the largest

contributor to Arctic ampli�cation due to its Arctic warming and tropical cooling which

would explain the strong di�erence between the global and Arctic average.

All of the feedbacks show signi�cant di�erences between the global and Arctic regions.

Furthermore, the Arctic feedback parameters do all have higher greater intermodel dif-

ferences than on a global average, except of the water vapor feedback. Conidering this,

it seems quite challenging for the models to simulate Arctic ampli�cation. Fig. A.1

shows the global and the Arctic surface temperature history. All of the models di�er

very much in the control surface temperature. Up to 2K for a global average and even

up to 8K for an Arctic average. This discrepancies in the control surface temperature

lead to discrepancies in the surface temperature change and consequently in the sea-ice

cover fraction of the Arctic between the models, so that the temperature feedbacks and

the albedo feedback di�er in between the models.

20

4.2. MODEL VARIABILITY OF CLIMATE FEEDBACKS CHAPTER 4. RESULTS

4.2. Model variability of climate feedbacks

This section describes the model variability for each individual feedback and how strong

they di�er between all the models for a global average and an Arctic average (70◦N -

90◦N).

Fig. 4.4 shows the intermodel spread of the individual feedback strengths versus the

total global warming in individual models. All feedback strengths are listed in table 4.2.

The water vapor and Planck feedback parameter strength are independent of the total

global surface temperature warming in a global scale. The other feedback parameters,

in particular albedo, lapse-rate and cloud feedback, are dependent of the strength of

the global surface temperature warming. They tend to be slightly bigger in a warmer

climate compared to a climate where the surface temperature increased not that much.

It is also remarkable that all the models di�er in their strength of global warming from

Figure 4.4. � Intermodel spread of the globally averaged individual feedback parameter strengthsversus total global warming in individual models. Lines are linear regressions of feedbackstrengths against global warming. The right-hand side shows the spread of the individualfeedback strengths in the analysed models. Boxes show the median, 25th and 75th percentile,and whiskers show the full ensemble spread.

21

4.2. MODEL VARIABILITY OF CLIMATE FEEDBACKS CHAPTER 4. RESULTS

Figure 4.5. � Intermodel spread of the individual feedback parameter strengths, averaged over theArctic, versus total Arctic warming in individual models. Lines are linear regressions of feedbackstrengths against Arctic warming. The right-hand side shows the spread of the individualfeedback strengths in the analysed models. Boxes show the median, 25th and 75th percentile,and whiskers show the full ensemble spread.

almost 3K to more than 6K.

The total Arctic warming di�ers more between the models with values from 6K to more

than 16K than the total global warming. In an Arctic point of view, the Planck feedback

parameter is dependent of the total Arctic warming as well. The albedo and the Planck

feedback parameter, averaged over the Arctic, have the largest intermodel di�erences

and they tend to be anti-correlated for a higher Arctic warming.

The correlations will be further discussed in Chapter 4.4.

The cloud feedback parameter is positive for a higher increase in Arctic surface tem-

perature and negative for a lower increase. This feedback acts as negative feedback in

the shortwave spectrum due to the clouds re�ection and as a positive feedback in the

longwave spectrum due to a emitted radiation from surface, which is trapped by the

clouds. For a small Arctic warming the shortwave feedback dominates, whereat for a

22

4.2. MODEL VARIABILITY OF CLIMATE FEEDBACKS CHAPTER 4. RESULTS

Table 4.2. � Feedback parameter strengths for each model for a global average and an Arcticaverage.

modelglobal average [Wm−2K−1] Arctic average [Wm−2K−1]λA λC λWV λLR λPL λA λC λWV λLR λPL

bcc-csm1-1 0.32 0.10 1.74 -0.31 -3.24 2.65 -0.25 1.21 2.63 -6.82BNU-ESM 0.62 0.29 1.73 -0.24 -3.22 3.55 0.56 1.34 3.06 -7.64CanESM2 0.34 0.57 1.94 -0.54 -3.30 2.75 0.43 1.36 2.25 -6.87CCSM4 0.51 0.13 1.68 -0.31 -3.29 3.45 0.24 1.08 2.84 -6.93FGOALS-s2 0.49 -0.31 2.04 -0.42 -3.32 4.15 -0.15 1.07 3.19 -7.10GFDL-ESM2G 0.28 0.22 2.29 -1.01 -3.31 2.89 0.04 1.37 2.78 -7.41GISS-E2-H 0.33 0.32 1.84 -0.40 -3.36 3.33 -0.13 1.30 3.23 -8.86GISS-E2-R 0.25 0.29 1.99 -0.62 -3.40 1.59 -0.10 1.18 2.00 -6.40inmcm4 0.37 -0.17 1.91 -0.50 -3.39 2.06 -0.71 1.18 2.72 -6.49MIROC5 0.49 0.10 2.01 -0.50 -3.39 6.84 0.03 1.51 4.48 -10.65MPI-ESM-LR 0.32 0.51 2.13 -0.28 -3.51 3.72 0.13 1.45 3.04 -7.51MRI-CGCM3 0.44 0.22 1.79 -0.48 -3.25 3.65 -0.20 1.12 3.63 -8.48NorESM1-M 0.40 0.14 1.68 -0.38 -3.23 4.34 -0.07 1.34 3.45 -8.42

greater Arctic warming the longwave and shortwave feedback cancel each other and for

an even greater Arctic warming the longwave feedback is stronger due to the greater

amount of trapped energy, so that the Arctic cloud feedback becomes all in all positive.

Comparing both �gures 4.4 and 4.5, it's obvious that a high total global warming leads

to a high total Arctic warming and vice versa. Nonetheless, the �MIROC5�-model has

an extraordinary high Arctic warming in comparison to its moderate global warming.

It shows also the highest albedo, lapse rate and Planck feedback parameters in absolute

values for the Arctic average, whereat these parameters are close to their multi-model

average for the global average (shown in �g. 4.6). The albedo feedback is connected to

the surface albedo change in the Arctic. For the �MIROC5�-model the surface albedo

is changing most of all models (shown in �g. A.2). Due to this strong surface albedo

change, the albedo feedback is much stronger than in other models, e.g. �GISS-E2-R�

(A.2c) or �CCSM4� (A.2d). If there is less sea-ice, more heat can be stored in the Arc-

tic Ocean which consequently leads to a higher warming in the Arctic. This warming

is mostly in the near-surface region of the atmosphere which would explain the higher

lapse-rate feedback. A higher surface temperature change would lead to a higher Planck

feedback but in this case, the �BNU-ESM�-model should have the highest Planck feed-

back, which is not the case (shown in �g. 4.6a). This phenomena is not fully understand

at this point.

23

4.2. MODEL VARIABILITY OF CLIMATE FEEDBACKS CHAPTER 4. RESULTS

(a) Arctic average

(b) global average

Figure 4.6. � Individual feedback parameter strengths for each model.

24

4.3. SUMMER VS. WINTER ARCTIC FEEDBACKS CHAPTER 4. RESULTS

4.3. Summer vs. winter Arctic feedbacks

There is a strong di�erence between the seasonal feedbacks in the Arctic region. Espe-

cially for the Arctic summer (June, July, August; JJA) and winter (December, January,

February; DJF), due to polar day and night, respectively. During polar day there is

strong incident shortwave radiation which is completely missing during polar night.

These two special seasons are described in this section. All individual northern hemi-

spheric winter and summer (from now on called winter and summer) feedback parameter

strengths for the Arctic are listed in A.1.

Fig. 4.7 shows the individual feedback parameter strengths for each model for the sum-

mer (4.7a) and the winter (4.7b).

Naturally, during winter the surface albedo feedback is close to zero, whereat it is

strongest feedback during summer. The surface albedo feedback is acting in the short-

wave spectrum. This leads, consequently, to a small (or even zero) surface albedo feed-

back in the Arctic winter, because of the polar night. In summer, during polar day,

when sea-ice already started to melt, the surface albedo feedback is strong due to open

water areas which absorb solar radiation. This causes a strong positive perturbation at

the TOA radiation balance. This is in good agreement with earlier results (e.g. Crook

et al., 2011). There are large intermodel di�erences in the summer surface albedo feed-

back depending on the change of surface albedo as mentioned before.

The cloud feedback parameter is changing sign from summer to winter and it has a larger

impact on the TOA radiation balance (in absolute values) in summer than in winter.

Wielicki et al. (1995) showed that the re�ection in Arctic summer is higher than in other

periods, leading to a cooling of the Earth's surface. This is in good agreement with the

calculated cloud feedback parameters for the summer period. During winter, the clouds

in the Arctic give rise to a warming of the Earth's surface [Beesley and Moritz, 1999],

which explains the positive albeit small cloud feedback parameter during winter.

It is obvious that the water vapor feedback has to be smaller during the winter months

in comparison to the summer months in the Arctic, because of warmer atmospheric

temperatures and a higher possible change of the speci�c humidity per Kelvin at higher

temperatures (see Chapter 2.2.3). In winter, when the Arctic vertical temperature gra-

dient is even smaller than the annual mean, the water vapor feedback is especially small

and can even become negative [Colman, 2001, 2003b]. The intermodel di�erences are

smallest for the seasonal water vapor feedback, which shows that the physics in behind

are quite well understood and implemented in the di�erent models.

25

4.3. SUMMER VS. WINTER ARCTIC FEEDBACKS CHAPTER 4. RESULTS

(a) Arctic summer JJA average

(b) Arctic winter DJF average

Figure 4.7. � Individual feedback parameter strengths for each model as an Arctic average forthe winter (DJF) and the summer (JJA) period. The �(m)� behind some model names standsfor missing data.

26

4.4. CORRELATIONS CHAPTER 4. RESULTS

The lapse-rate and Planck feedback in the Arctic are directly dependent of the tem-

perature change close to the surface or at surface due to the missing deep convection.

The surface and near-surface temperature change for the �abrupt4xCO2�-simulation are

much bigger during the winter months than during the summer months (e.g. Boé et al.,

2009), leading to a stronger lapse-rate and Planck feedback (in absolute values) dur-

ing the winter months. The lapse-rate feedback is strongly positive due to the strong

temperature inversion in the atmosphere and the nonexistent deep convection, causing

stronger warming in lower parts of the tropospheric atmosphere than in higher regions

close to the tropopause. Both seasonal feedbacks agree quite well compared to earlier

results (e.g. Crook et al., 2011, Taylor et al., 2011).

4.4. Correlations

This section describes the possible correlations between individual feedbacks and surface

temperature changes as well as between individual feedbacks and the total radiative

feedback λ (see eq. 2.8) for the di�erence between the 50-year-average �piControl�- and

�abrupt4xCO2�-simulation of all given models. The analysis is performed for both global

and Arctic average. This section takes a closer look on the intermodel spread and the

relations between the global or local warming and the individual feedback parameter

strength.

Fig. 4.8 shows exemplary the relation between the surface albedo feedback parameter

and the warming (top) or the total radiative feedback (bottom) as a global (left) or

Arctic average (right).

At the top left of each subplot stands the coe�cient of determination. All coe�cients

of determination for each individual feedback are listed in table 4.3.

Table 4.3. � Coe�cients of determination (R2) for each individual feedback parameter versus theglobal or Arctic warming or the total global or total Arctic feedback parameter.

Feedback parametertotal warming total radiative feedback parameterglobal Arctic global Arctic

surface albedo 0.50 0.65 0.25 0.86cloud 0.26 0.66 0.71 0.47water vapor -0.10 0.37 -0.11 0.39lapse-rate 0.50 0.50 0.38 0.66Planck 0.21 -0.48 0.10 -0.52

27

4.4. CORRELATIONS CHAPTER 4. RESULTS

Figure 4.8. � Top plots show the relation between the surface albedo feedback parameter and thetotal warming. Bottom plots show the relation between the surface albedo feedback parameterand the total radiative feedback parameter. Left and right coloumn show the correlations as aglobal and an Arctic average, respectively. The lines are linear regressions. On the upper leftof each plot is the coe�cient of determination.

28

4.4. CORRELATIONS CHAPTER 4. RESULTS

Fig. 4.8 shows that the Arctic surface albedo feedback parameter shows a linear depen-

dency of the total Arctic feedback parameter (R2 = 0.86). It is also linear correlated to

the total Arctic warming albeit weaker (R2 = 0.65). The larger the Arctic warming the

stronger is the surface albedo feedback because of the stronger sea-ice melting which, in

turn, leads to a greater absorption of solar radiation, followed by a stronger heat �ux in

the winter months from the Arctic Ocean to the air when the air temperature is cooler

than the ocean water temperature [Boé et al., 2009, Screen and Simmonds, 2010]. This

gives rise to a warmer air temperature close to the ground, consequently damping the

formation of ice.

These correlations are much weaker on a global average for the global surface albedo

feedback parameter because, �rst, the sea-ice is just covering a small area in comparison

to the global surface which leads to a smaller impact of the melting sea-ice on a global

scale and, secondary, the sea-ice loss is not the same close to Antarctica and in the Arc-

tic Ocean and therefore not comparable. Additionally, the atmospheric composition is

di�erent between the Arctic and the sea-ice areas close to Antarctica, leading to di�erent

warming. This give rise to non-linear dependencies.

The Arctic cloud feedback parameter shows a linear dependency to the total Arctic

warming with a coe�cient of determination of 0.66, whereat there tend to be no relation

between the global cloud feedback and the global total warming (shown in �g. A.3).

The top right of �g. A.4 shows the geographical distribution of the cloud feedback in

the Arctic (70◦N - 90◦N). The cloud feedback tend to be homogeneous in the Arctic,

whereat it is heterogeneous on a global scale (see top right of �g. 4.1). This could allow

a linear dependency of the cloud feedback and the total warming for the Arctic region.

In turn, the water vapor feedback shows just a low linear dependency to the warming

or the total radiative feedback parameter for a global or an Arctic average (see table

4.3). Approving this dependency, Curry et al. (1995) found out that there is no simple

relationship existing between the surface temperature and the precipitable water over

the Arctic Ocean because of the lack of convective coupling between the surface and the

atmosphere.

The lapse-rate feedback shows only low linear correlations on a global scale for both,

the total global warming and the total radiative feedback parameter, while it shows a

stronger linear correlation on an Arctic average for the total Arctic feedback parameter.

Comparing the global and the Arctic Planck feedback parameter correlations, it is obvi-

ous that the Planck feedback parameter has a low linear correlation to the total global

warming and a noteworthy linear anti-correlation to the total Arctic warming. A higher

29

4.4. CORRELATIONS CHAPTER 4. RESULTS

Figure 4.9. � Left: Shows the correlation between the total Arctic radiative feedback parameterand the total Arctic warming. Right: Shows the correlation between the total global radiativefeedback parameter and the total global warming. On the top left of each plot stand thecoe�cient of determination.

total Arctic warming leads to a bigger negative Arctic Planck feedback as expected by

eq. 2.1.

The anti-correlation between the water vapor and the lapse-rate feedback of other stud-

ies (e.g. Soden and Held, 2006) was con�rmed by a coe�cient of determination of -0.68.

Fig. 4.9 shows the linear correlation between the total radiative feedback and the total

warming for the global and the Arctic average. Both, global and Arctic, show a linear

dependency. The stronger positive the total radiative feedback parameter, the higher

is the global and/or Arctic warming. The total radiative feedback can be negative and

there is still a warming. The outcome of this is that other parts like the chemical feed-

backs or the meridional transport of heat cannot be neglected for an accurate study of

the Arctic Ampli�cation.

30

4.5. CONTROL CLIMATE SEA ICE EXTENT CHAPTER 4. RESULTS

4.5. Control climate sea ice extent

This section describes the relation between the surface albedo feedback parameter strength

and the control sea-ice cover fraction from the �piControl�-simulation.

The top left column of the �g. 4.10 shows the dependency of the sea-ice cover fraction

and the surface albedo feedback parameter annually averaged. There is a linear correla-

tion of R2 = 0.554 which shows that if there is a higher sea-ice cover fraction averaged

over the year, the surface albedo feedback parameter is higher because more sea-ice can

melt in a warmer environment. This dependency is independent of the month as shown

in the middle and the bottom left of �g. 4.10. The right column of �g. 4.10 shows

the relation between the Arctic control sea-ice cover fraction and the Arctic surface

albedo feedback parameter for an annual average and a monthly average of september

and march. In contrast to the global average, there is no correlation, as expected, be-

tween the Arctic surface albedo feedback parameter and the sea-ice cover fraction of

the �piControl�-simulation. A greater sea-ice covered area in the Arctic is not leading

linearly to a stronger Arctic surface albedo feedback parameter, which consequently

gives rise to the assumption that the surface albedo feedback parameter is independent

of the given control sea-ice cover fraction in the �piControl�-simulation for the de�ned

Arctic region. This is not directly comparable to the result of Holland and Bitz (2003),

who found out that there is a correlation between the control sea-ice cover and the po-

lar ampli�cation, and that the polar ampli�cation is also dependent of the control ice

thickness. Due to the linear dependency between the surface albedo feedback parameter

and the total Arctic warming, which leads to Arctic Ampli�cation, it was expected to

have a correlation between the control sea-ice cover and the surface albedo feedback, if

there is a provided correlation of the sea-ice cover and the polar ampli�cation as said

by Holland and Bitz (2003). It was shown that there is no correlation. Consequently, a

more accurate and speci�ed research is needed, whereat ice-thickness, ice micro-physics

and age of the ice are included, to achieve a relation between the control sea-ice cover

and the surface albedo feedback parameter.

4.6. BW-PRP assuming preindustrial CO2

For a PRP method where the BW-PRP method is changed not only in the needed

variable to quantify the individual feedback but also in the CO2-concentration from a

31

4.6. BW-PRP ASSUMING PREINDUSTRIAL CO2 CHAPTER 4. RESULTS

Figure 4.10. � Shows the relation between the surface albedo feedback parameter and the sea-icecover fraction averaged over the whole year (top), september (middle) and march (bottom).The left column shows global average and the right column the Arctic average.

32

4.6. BW-PRP ASSUMING PREINDUSTRIAL CO2 CHAPTER 4. RESULTS

4xCO2-concentration to the prehistorcial CO2-concentration, the error in the resulting

individual feedback parameters are noteworthy. Note, this is not a PRP method where

the CO2-concentration in the FW-PRP method was also changed.

By means of the small mistake of always assuming prehistorical CO2-concentration in

the o�ine radiation transfer calculation, the error propagation is larger than estimated.

Table 4.4 lists the multi-model deviations from the correct individual feedback parame-

ters of the used PRP method.

The relative deviation on a global average is largest for the surface albedo feedback pa-

rameter and second largest for the lapse-rate feedback parameter, which has the largest

intermodel di�erences in this experiment. The change of CO2-concentration seems to

have the largest relative impact on the surface albedo feedback (20.35 ± 12.18 %) and

the largest absolute impact on the Planck feedback (-0.19Wm−2K−1). The multi-model

Planck feedback parameter of this experiment is even larger then the MPI-ESM-LR

Planck feedback parameter of the original quanti�cation (see 4.2), which is the largest

Planck feedback parameter in the multi-model analysis. The cloud feedback parameter,

however, has the smallest deviation in relative and absolute values, although it has the

biggest intermodel di�erences for the global feedback.

Considering only the Arctic region, the surface albedo feedback parameter produces also

the largest relative deviation. The lapse-rate feedback shows in absolute values the same

deviation as on a global average. The cloud feedback has by far the largest intermodel

di�erences in the relative deviation due to values close to zero, making this value in-

comparable to the other feedbacks. On an Arctic average, the surface albedo feedback

parameter shows the largest absolute deviation (0.70Wm−2K−1), short followed by the

Planck feedback parameter (-0.60Wm−2K−1).

Finally, the in�uence of the changed CO2-concentration in the o�ine radiation transfer

calculation tend to have quite a large impact on the result, mainly for the Planck and

surface albedo feedback, which are the strongest feedback parameters in the Arctic.

Table 4.4. � Multi-model deviations of the wrong PRP method to the correct PRP method (seetable 4.1). Left: Global average. Right: Arctic average.

λxglobal average Arctic average

BW-PRP 1xCO2 [Wm−2K−1] Deviation [%] BW-PRP 1xCO2 [Wm−2K−1] Deviation [%]λA 0.47 ± 0.11 20.35 ± 12.18 4.61 ± 1.53 39.42 ± 35.25λC 0.19 ± 0.25 1.71 ± 5.74 −0.19 ± 0.33 −7.62 ± 187.06λWV 1.99 ± 0.19 4.48 ± 0.70 1.31 ± 0.14 3.40 ± 1.40λLR −0.51 ± 0.19 14.54 ± 21.83 2.97 ± 0.62 −1.70 ± 2.06λPL −3.52 ± 0.07 6.06 ± 0.95 −8.09 ± 1.25 5.62 ± 0.85

33

5. Conclusion and Outlook

Radiative feedback processes such as the surface albedo, cloud, water vapor, lapse-rate

and Planck feedbacks are investigated, especially for the Arctic region, de�ned as the

area from 70◦N to 90◦N. Therefore, the monthly model data of two experiments from

13 CMIP5 models is taken into account. The �piControl�- and the �abrupt4xCO2�-

experiment are used to determine the feedback parameters for a climate under abruptly

increased CO2-concentration by the factor of four from the pre-industrial CO2-concentration

(�piControl�). The combined �Partial Radiative Perturbation� method is used. This work

compares the feedback parameter strengths between a global and an Arctic average. It

also investigates summer and winter seasonal feedbacks for the Arctic. Furthermore,

the relations between the individual feedbacks and on the one hand the total global or

Arctic warming and on the other hand the total global or Arctic feedback are examined.

The following feedback parameters are averaged after 100 years of acclimatization over

50 years to counteract the interannual variability of the individual feedbacks. All glob-

ally averaged multi-model feedbacks disagree slightly or more from earlier results (e.g.

Soden and Held, 2006, Bony et al., 2006), except the water vapor feedback. The Planck

feedback agrees spatially to earlier results, but it is slightly higher, probably due to a

more ampli�ed Arctic warming for a climate having four times higher CO2-concentration

than in the preindustrial time. The biggest intermodel di�erences has the cloud feed-

back, whereat some models show a negative feedback and most a positive feedback on

global average. All in all the cloud feedback is smaller than the value reported by Bony

et al. [2006], probably due to the not perturbed cloud droplet concentration in this thesis.

Nevertheless, the lapse-rate feedback is also smaller in absolute values than the reported

one by Bony et al. [2006], which means that there must be either stronger positive values

in the Arctic or less negative values in the lower or midlatitudes. The 4xCO2 external

forcing leads to a higher surface temperature change and therefore a stronger lapse-rate

in the Arctic due to the missing deep convection, leading to a stronger positive lapse-rate

34

CHAPTER 5. CONCLUSION AND OUTLOOK

feedback in the Arctic. The surface albedo feedback acts noteworthy only in the high

latitudes, where there is sea-ice and snow. It is slightly higher as the value by Bony

et al. [2006].

For the Arctic average, the strongest positive feedback is the surface albedo feedback

(3.97Wm−2K−1). The positive feedbacks are balanced by a strong negative Planck feed-

back, which is compared to its global average more than twice as strong. The intermodel

di�erences for the Arctic averages, except of the water vapor feedback, are all larger than

for the global average. The surface albedo feedback parameter intermodel di�erences

are with ±1.28Wm−2K−1 three times larger than the globally averaged surface albedo

feedback, leading to the assumption that the control surface temperature and the control

sea-ice cover fraction of the �piControl�-experiment of each model plays an important

role for the strength of the surface albedo feedback in the Arctic. This was con�rmed

for the Arctic surface warming but not for the control sea-ice cover fraction. While a

higher surface warming in the Arctic leads to a higher Arctic surface albedo feedback, a

higher or lower Arctic control sea-ice cover fraction does not lead to a stronger or weaker

Arctic surface albedo feedback. The latter accounts not for the global average of the

surface albedo feedback and the global sea-ice cover fraction. A higher global control

sea-ice cover fraction leads to a higher global surface albedo feedback. Hence, it is not

clear why this accounts for the global average but not for the Arctic average.

The Arctic cloud feedback is in comparison to the other feedbacks quite consistent in

between the models, but its intermodel di�erences are bigger than on the global aver-

age. The Arctic lapse-rate feedback has to be featured because it is in comparison to its

global average (-0.47Wm−2K−1) not only changing sign from negative to positive but

also more than six times larger in absolute values (2.90Wm−2K−1). A di�erent vertical

structure of the atmosphere makes this possible. Due to the missing deep convection

and the temperature and humidity inversions close to the ground, the heat and therefore

warming is trapped to the lower levels of the troposphere leading to a larger temperature

di�erence between the lower and the upper levels of the troposphere. Deep convection in

the tropics and partly in the midlatitudes gives rise to a steepening of the vertical tem-

perature pro�le because the heat is transported to uppermost part of the troposphere,

leading to more warming close to the tropopause than near the ground.

Signi�cant discrepancies between the Arctic and global averaged feedbacks are found.

Not only that the feedbacks are mostly larger in absolute values for the Arctic average

but also the intermodel di�erences are larger, leading to the assumption that the in-

dividual model control surface temperature, which di�ers on a global scale by 2K and

35

CHAPTER 5. CONCLUSION AND OUTLOOK

on an Arctic scale by 6,K between the models, has a huge in�uence on the resulting

feedbacks.

Each model simulates a di�erent warming for a global and an Arctic average. The

global surface temperature change di�ers between almost 3K and around 6K between

the models. The global water vapor, cloud and Planck feedback show low correlations to

the total global warming, leading to the assumption that their strength is independent

of the total global warming. The global lapse-rate and surface albedo feedback correlate

stronger to the total global warming, leading to a stronger global surface albedo feed-

back for a greater global warming and a global lapse-rate feedback closer to zero or even

positive.

For an Arctic average the intermodel di�erences are larger than for the global average.

The Arctic averaged surface temperature warming for the individual models is between

6K and more than 16K from the �piControl�- to the �abrupt4xCO2�-experiment. Low

surface temperature changes for an Arctic average accompany to a lower surface tem-

perature change for a global average, thus, the Arctic Ampli�cation is present for each

model. However, since for a global average only the lapse-rate and surface albedo feed-

back show linear dependencies to the magnitude of global warming, for an Arctic average

every radiative feedback of this thesis shows stronger correlations. Albeit the water va-

por feedback shows a low linear correlation. The Arctic cloud feedback is changing sign

from negative to positive for a greater Arctic warming. This feedback acts as negative

feedback in the shortwave spectrum due to the clouds re�ection and as a positive feed-

back in the longwave spectrum due to emitted radiation from surface, which is trapped

by the clouds. For a small Arctic warming the shortwave feedback tends to dominate.

For a greater Arctic warming the longwave and shortwave feedback cancel each other

and for an even greater Arctic warming the longwave feedback is stronger due to the

greater amount of trapped energy, so that the Arctic cloud feedback becomes all in all

positive. A more accurate investigation of the shortwave and longwave feedbacks could

give a better result.

The Arctic surface albedo feedback is getting stronger for a greater Arctic warming,

which is expected, due to greater sea-ice and snow melting, which has huge in�uence

on the surface albedo. Both temperature feedbacks show correlations to the strength of

Arctic warming. Greater Arctic warming gives rise to a stronger Planck feedback and,

due to the vertical structure of the atmosphere in the Arctic, the near surface levels will

36

CHAPTER 5. CONCLUSION AND OUTLOOK

receive greater warming than the upper regions of the troposphere, causing a stronger

positive Arctic lapse-rate feedback.

All the global individual feedback parameters except of the cloud feedback show weak

correlations to the global total radiative feedback parameter. The global cloud feedback

tends to be positive for a higher total radiative feedback and negative for a lower total

radiative feedback. Those relations cannot be con�rmed for an Arctic average. In par-

ticular the Arctic surface albedo feedback shows a strong correlation to the total Arctic

radiative feedback parameter, consequently making it to the feedback which has the

greatest impact on the total Arctic feedback. The Arctic temperature feedbacks tends

to play a secondary role for the total Arctic feedback parameter, which in turn shows a

linear dependency to the Arctic total warming.

The Arctic is also special due to its polar night and day in northern hemispheric winter

and summer, respectively. From now on called winter and summer respectively. The

seasonal feedbacks for both seasons were analyzed. The Arctic surface albedo feedback

behaves as expected and is around zero in the winter and is the strongest Arctic feedback

in summer, due to the incident shortwave radiation and the melting sea-ice, where the

sea can absorb almost all the energy of the incident radiation. The intermodel di�er-

ences are much larger in summer for the Arctic surface albedo feedback depending on

the strength of the Arctic warming for each speci�c model and not on the control sea-

ice cover as already mentioned above. The cloud feedback changes sign from negative

(summer) to positive (winter) due to high re�ection of solar radiation in summer and

trapping of outgoing longwave radiation from the surface in the winter, respectively. The

Arctic water vapor feedback is smaller in winter than in summer and can even become

negative [Colman, 2001, 2003b]. The Arctic temperature feedbacks are both stronger in

Arctic winter than summer due to a greater surface temperature warming during the

winter months.

The hereby used combined PRP-method uses for the o�ine radiation calculations once

the preindustrial environment (FW-PRP) and once the perturbed environment with

4xCO2-concentration (BW-PRP). Not using the perturbed CO2-concentration causes

strong error propagation. For instance, the multi-model global surface albedo feedback

is 20% higher than under correct circumstances and the global Planck feedback deviates

by -0.19Wm−2K−1, which is larger than the di�erence between the correct global Planck

37

CHAPTER 5. CONCLUSION AND OUTLOOK

feedback and the result by Bony et al. (2006). For the Arctic feedbacks, the deviations

are stronger, e.g. the surface albedo feedback has the highest absolute deviation with

0.70Wm−2K−1, which is even higher than the global surface albedo feedback. While the

cloud feedback shows minimal deviations on a global average, it has by far the biggest

intermodel di�erence for an Arctic average. Hence, the error of not changing the CO2-

concentration does not cause a certain shift of the feedbacks in one direction as seen by

the cloud feedback and the error leads to larger mistakes for an Arctic average than for a

global average. The error is not negligible, in turn, it has quite large impacts especially

for the Arctic.

To achieve better intermodel results and to minimize the deviations in between the

models for the Arctic feedbacks, all models should have almost the same control surface

temperature, which is not the case for the models of CMIP5, although they simulate the

same time periods.

A more accurate investigation of the seasonal Arctic feedbacks in comparison to the

global ones would probably give a better understanding of the relations between the

feedbacks and the physics in the Arctic. Additionally, a di�erentiation between the

shortwave and longwave spectrum would lead to a better understanding of the feedbacks

and therefore the dynamics in the Arctic.

Other physical processes like the meridional heat transport should be compared to the

individual feedback strengths in the Arctic to understand their relative impact for the

Arctic Ampli�cation, especially for a seasonal average and perspective. It would be of

great interest to investigate the impact of polar night and day on the climate dynamics

in the Arctic.

38

A. Appendix

Table A.1. � Feedback parameter strengths for each model for the Arctic winter (December,January, February) and summer (June, July, August) averaged from 70◦N to 90◦N.

modelArctic summer [Wm−2K−1] Arctic winter [Wm−2K−1]λA λC λWV λLR λPL λA λC λWV λLR λPL

bcc-csm1-1 3.59 -1.80 1.70 -0.06 -3.45 0.71 0.48 0.65 4.22 -8.85BNU-ESM 3.90 0.52 2.08 0.65 -5.18 1.09 0.25 0.67 4.92 -9.91FGOALS-s2 7.17 -1.75 1.60 0.82 -4.09 0.31 0.28 0.43 4.22 -8.26GFDL-ESM2G 6.01 -0.96 1.93 -0.17 -3.85 0.04 0.19 0.80 4.27 -9.40GISS-E2-H 5.51 -1.55 1.67 0.64 -4.61 0.28 0.37 0.69 4.99 -11.84GISS-E2-R 4.78 -1.15 1.62 0.66 -4.56 -0.05 0.26 0.55 2.62 -7.11inmcm4 4.81 -2.01 1.67 0.17 -3.39 0.31 0.26 0.63 4.31 -11.40MPI-ESM-LR 8.68 -0.35 2.28 0.83 -4.00 0.06 0.50 0.76 5.16 -11.16MRI-CGCM3 10.37 -2.29 1.78 0.47 -3.81 0.04 0.42 0.45 5.35 -11.40

39

APPENDIX A. APPENDIX

(a) global average

(b) Arctic average

Figure A.1. � Surface temperature history from 1850 to 2000 for each model for the �piControl�-and �abrupt4xCO2�-experiment.

40

APPENDIX A. APPENDIX

(a) MIROC5 (b) NorESM1-M

(c) GISS-E2-R (d) CCSM4

Figure A.2. � Change of surface albedo in the Arctic for the 4xCO2 simulation. Shown area isfrom 70◦N to 90◦N. On the upper left of each graphic is the Arctic mean albedo change. Theaverage values are -0.29, -0.21, -0.11, -0.20 for the �MIROC5�, �NorESM1-M�, �GISS-E2-R� and�CCSM4� model, respectively.

41

APPENDIX A. APPENDIX

Figure A.3. � Top plots show the relation between the cloud feedback parameter and the totalwarming. Bottom plots show the relation between the cloud feedback parameter and the totalfeedback parameter. Left and right coloumn show the correlations as a global and an Arcticaverage, respectively. The lines are linear regressions. On the upper left of each plot is thecoe�cient of determination.

42

APPENDIX A. APPENDIX

Figure A.4. � Multi-model average of the Arctic geographical distribution (70◦N - 90◦N) of netalbedo, cloud, water vapour, lapse rate and Planck feedback parameters for CO2 quadrupling atTOA for the combined (FW+BW) PRP calculation. Positive values denote increased downwardradiation.

43

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Statement of authorship

I hereby certify that this master thesis has been composed by me and is based on my

own work, unless stated otherwise. This work has not been submitted for any other

degree.

I agree on the publishing of my master thesis.

Florian Schneider, Leipzig, 15th December 2015

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