Download Climate Change Risk and Uncertainty Exercise 1: Temperature

Climate Change Risk and Uncertainty
Exercise 1: Temperature Increase in New York
City
by
Prof. Reto Knutti & Prof. David Bresch
Tutorials
Anina Gilgen ([email protected])
Kathrin Wehrli ([email protected])
Martin Stolpe ([email protected])
Department of Environmental System Sciences - ETH Zurich
Zurich, February 27, 2017
1
Introduction
In this exercise, we will examine the annual mean near surface temperatures in New York City
(40.99°N/74.56°W). The observational time series we will analyse is based on dierent meteorological stations located in New York and is quality-controlled (Figure 1). For more information
about the individual stations and the adaptations conducted to homogenize the data, you can visit the following webpage
http://berkeleyearth.lbl.gov/station-list/?phrase=new+york.
In the rst part of the exercise, we will create a toy model based on the observed time series.
After that, we will compare the observations and our toy model with results from two global
climate models (CESM and MPI-ESM). In the end, we will calculate impact costs associated with
future temperature increase and compare them to mitigation costs. There are some voluntary
questions denoted with a *, which give you extra points. Feel free to ask us any question during
the tutorials or by email. For many of the questions dierent possible solutions exist. Hence, it
is important that you explain and reason your solution process.
12
Observed Temperatures in New York
11.5
Temperature (° C)
11
10.5
10
9.5
9
8.5
8
annual
11-year moving average
7.5
1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000
Year
Figure 1:
Observed annual mean temperatures in New York from 1800 to 2012 (in blue) and
after smoothing with a 11-year moving average (in red). In the exercise we will mainly focus
on the observations since 1960. Source:
99N-74. 56W .
1
http: // berkeleyearth. lbl. gov/ locations/ 40.
Toy Model
Download the mat-les (observations_new_york_short.mat ;
cesm_new_york.mat ; mpi_new_york.mat )
from the lecture homepage and store them in your local MATLAB folder. Load the observations
(by double-clicking or by using the function
load)
in MATLAB. This loads six matrices: the
annual mean surface temperature (tas) and the years for the observations, for CESM, and for
MPI-ESM. As you can see, the les span dierent time periods.
Note that
tas_cesm contains 29 rows. Each row is one ensemble member; more details will
follow in Section 2.
1. In the following, we only use the observations from 1960 to (and including) 2000 using the
le
observations_new_york_short.mat. Plot the observations for this time period (plot).
2
2. Estimate the trend over this period using linear regression (e.g.
3. Is the trend signicant on the
5 %-level?
(e.g.
polyt).
regstats)
4. Since when is the trend signicant? Hint: Starting from 1960, analyse the trend over longer
and longer time periods.
detrend) to get the noise.
5. Detrend the observations (
How large is the standard deviation
of the noise?
6. Is the noise normally distributed? Create a qq-plot (
qqplot),
hist),
a histogram (
and a
Tuckey-Anscombe plot (plotting residuals against tted values) to answer this question.
So far, we have estimated the trend as well as the noise of the time series. From that, we will
now create a simple toy model:
T = a + b · t + µ,
where
T
is the estimated temperature,
µ
time, and
is the noise.
a
and
b
are the coecients of the linear regression,
t
is
In your toy model, you can assume that the noise is normally and
randomly distributed, i.e. use the function
normrnd
to generate the (white) noise with the
previously estimated standard deviation.
7.* Some time series are serially correlated, meaning that the data points of the time series
linearly depend on previous values. Examine if the noise of this time series is auto-correlated
(e.g. use
autocorr and parcorr).
If the is noise is serially correlated, how would you adjust
the toy model to account for it?
8. Using the toy model, calculate at least 1000 simulations for the time period 1960 to 2012 and
plot them into one gure. Use your
≥1000
simulations to answer the following questions.
9. Calculate and plot also the 5th, 50th and 95th percentiles as well as the mean of these
simulations.
10. Now compare your model results with observations (especially with the time period from
2001 to 2012, which was not used to create your toy model.
Use the le
observati-
ons_new_york_full.mat that contains observations until 2012). Comment on your results.
11. Use your toy model to estimate the probability that the annual mean temperatures exceed
◦
11.5 C for each year from 1960 to 2012. How does the probability change over time?
12. What are limitations of this toy model? Name and shortly explain at least two of them.
2
Comparison with Climate Model Data
Earth system models are used to simulate the climate system, including the atmosphere, oceans,
land surface, sea ice and the interactions between them. Now you will examine the output of two
1
such state-of-the-art climate models, the Community Earth System Model Version 1 (CESM1 )
2
and the Max Planck Institute Earth System Model (MPI-ESM-LR ). Observed changes in the
greenhouse gas concentrations, aerosols, the solar activity, the land use and further forcing agents
are used to drive these climate models. For the future the models are forced with the business
as usual scenario RCP8.5 that assumes strong increases in the concentration of greenhouse gases
1
Meehl et al. (2013), Climate Change Projections in CESM1(CAM5) Compared to CCSM4, in
Climate, http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-12-00572.1
2
Journal of
Giorgetta et al., (2013), Climate and carbon cycle changes from 1850 to 2100 in MPI-ESM simulations
for the Coupled Model Intercomparison Project phase 5, in Journal of Advances in Modeling Earth Systems,
http://onlinelibrary.wiley.com/doi/10.1002/jame.20038/full
3
3
during the 21st century . To quantify the role of unpredictable internal variability, CESM1 is
run 29 times from 1920 to 2100 with sightly diering atmospheric initial conditions (e.g. Deser
et al. (2012)
4 used a large ensemble to address similar questions as you will). You nd each of
the 29 simulations in
cesm_new_york.mat. MPI-ESM-LR spans the period from 1850 to 2100
and consists of three ensemble members. In
mpi_new_york.mat you nd the mean time series
of these three members.
1. Plot the 29 CESM1 ensemble members, the ensemble mean and median, the MPI-ESM-LR
simulation, together with the observations for the period 1960 to 2000.
2. Compare the observations with the model results.
a) Compare the mean climate in the models and observations. Comment on your results
and give at least one possible reason for dierences.
b) Compare the simulated with observed interannual variability. Comment on your results
and the assumptions you used to estimate the interannual variability from observations
and model.
c) Compare the simulated interannual variability of CESM1 and MPI-ESM-LR. Comment
on your results.
d) Compare the simulated trends by CESM1 from 1960 to 2000 with the observed trends
over the same period (e.g. look at histograms of the trends). Fit an appropriate distribution
to the modeled trends. Is there a signicant dierence between the modeled and observed
temperature trends? Comment on your results.
e*) Compare the simulated temperature trends of CESM1 and MPI-ESM for dierent
periods (you have free choice). Are there signicant dierences? What is the inuence of
the trend length? Give at least one possible reason for dierences.
5
3.* Detection of a climate signal .
As you have seen, there is both interannual variability
(i.e. noise) and a long-term trend in the observations and the model simulations. It takes
a while until the warming is strong enough so that it emerges from the natural range of
variability. The concept of Time of Emergence (ToE) relates the signal, S, to the noise, N:
T oE =
Here,
σ
S
S
=
N
2σ
denotes the internal variability you estimated earlier from the observed/modeled
temperatures. ToE is reached, when S is
≥ 2σ
and does not fall into the band of internal
variability again. Figure 2 illustrates the concept of ToE.
a*) Has ToE already occurred within the observations? If yes, when?
b*) When does ToE occur in each of the 29 CESM1 ensembles? Use the simulated internal
variability for
σ.
How many years of spread occur between the members with the earliest
and latest ToE? Use the full CESM simulations until 2100 to answer this question.
3
Representative Concentration Pathway (RCP) that reaches a radiative forcing of 8.5 W m−2 in 2100 compared
to pre-industrial values. For comparison: A doubling of the CO2 concentration causes a radiative forcing of about
3.7 W m−2 .
4
Deser et al., (2012), Communication of the role of natural variability in future North American climate, in
Nature Climate Change, http://www.nature.com/nclimate/journal/v2/n11/full/nclimate1562.html
5
Mahlstein et al. (2011), Early onset of signicant local warming in low latitude countries, in Environmental
Research Letters, http://iopscience.iop.org/article/10.1088/1748-9326/6/3/034009
4
Time of Emergence of a Climate Signal
1.2
annual time series
1
Temperature Anomaly (°C)
0.8
0.6
0.4
0.2
0
−0.2
−0.4
Figure 2:
ToE
1860
1880
1900
1920
1940
Year
1960
1980
2000
2020
Concept of the Time of Emergence. The grey shaded area indicates the range of
internal variability (the noise) and the time series the signal. Around 1970 the observed temperatures exceed the internal variability permanently. Also before 1970 the signal is sometimes
larger than the internal variability, but then falls back into the internal variability envelope within
a few years.
3
Impact and Mitigation Cost
6
Imagine you are one of the last commercial urban apple tree farmers in New York . At the moment, you breed the apple variety Gala. Since Gala is susceptible to the temperature-dependent
apple scab disease (Apfelschorf ), you fear that climate change might lead to more frequent
outbreak of this disease and therefore to a smaller harvest.
Assume that your monetary los-
ses associated with this reduced agricultural productivity can be described with the following
function:
T < 11 ◦C : no
◦
loss
◦
11 C < T < 12 C : loss = 10000
USD
T > 12 ◦C : loss = 10000
USD
◦
C−1 · (T − 11 ◦C)
+ (T − 12 ◦C) · 50000
USD
◦
C−1
You consider now to cultivate the more resistant apple variety Resi. With Resi, apple scab is
not an issue and you expect no temperature-dependent loss in yield. However, to switch from
Gala to Resi, you have additional initial investment costs of 10000 USD. Use your toy model to
answer the following questions.
1. At which temperature will the investment costs be outweighed?
6
Urban
farming:
The
green
answer
urban-farming-green-answer-to-city-growth/
to
5
city
growth?,
https://share.america.gov/
2. Which apple variety is more protable in 2030, 2050, and 2070?
distribution of temperature into account for your calculations (e.g.
neglect discounting and interest rates.
6
Take the probability
pd and cdf ).
You can