If you are enrolled in the class, make sure you use the GitHub Classroom link from the Ed Discussion Board rather than downloading directly.

Overview

Instructions

• Problem 1 asks you to use Optimize.optim() to calibrate a semi-empirical sea-level rise model to temperature and sea-level data.

• Problem 2 asks you to use SNEASY, a Simple Nonlinear EArth SYstem model, to propagate climate-system uncertainty through to sea-level rise.

Problems (Total: 100 Points)

Problem 1 (60 points)

In this problem, we will work with the semi-empirical sea-level model from Rahmstorf (2007). This model links global mean temperature $T(t)$ to global mean sea-level $H(t)$ through the equation:

where $T_0$ is the temperature (in $^\circ C$) where sea-level is in equilibrium ($dH/dt = 0$), and $\alpha$ is the sea-level rise sensitivity to temperature. Discretizing this equation using the Euler method and using an annual timestep ($\delta t = 1$), we get

Our goal in this problem is to load temperature and sea-level datasets and calibrate the model by finding parameter values which are consistent with historical observations. We will select parameters which minimize the root-mean-square-error (RMSE) of the data-model residuals. The following function can be used to compute the RMSE.

using Statistics

rmse(y, ŷ) = sqrt(mean((y - ŷ).^2))

rmse (generic function with 1 method)

Problem 1.1 (15 points)

Load the sea-level and temperature datasets into DataFrames. The sea-level dataset is provided in data/CSIRO_Recons_gmsl_yr_2015.csv, and the temperature dataset is provided in data/HadCRUT.5.0.1.0.analysis.summary_series.global.annual.csv. You'll need to correct the years in the sea-level rise data to remove the half-year, and then align the two data sets on the common period 1880 – 2013. Plot each of the resulting data sets after this "cleaning" process on different axes.

Problem 1.2 (30 points)

Write a function for the above model, and find the parameter values which minimize the RMSE using Optim.optimize() (here is documentation on how to use Optim.optimize() to minimize a function. This will involve writing a function which takes in a vector of parameter values and the data, simulates the model, and computes the RMSE. Optim.optimize() maps a parameter vector to a function, and since you'll be passing auxiliary data to your function, you may want to use anonymous function to wrap your simulation function, as in

optimize(p -> f(p, aux), ...)

Problem 1.3 (15 points)

Plot the sea-level data as points, and overlay a line with the model hindcast. How well do you think the model fits the data? Are there any key trends or features that you notice?

Problem 2 (40 points)

Your goal in this problem is to see how scenario and parametric uncertainty in climate models propagates through the simple semi-empirical sea-level model from Problem 1. You'll be using SNEASY, and we have provided the same set of functions in src/sneasy_model_functions.jl that you used in Lab 3.

Problem 2.1 (10 points)

Use 1000 samples from the parameter set for MimiSNEASY (found in params/parameters_subsample_sneasybrick.csv) to compute and plot 95% uncertainty intervals for global mean temperatures from 1880 – 2100 for RCPs 2.6, 4.5, 6.0, and 8.5.

Problem 2.2 (10 points)

Run your calibrated model from Problem 1 on the ensemble of temperatures for each RCP from Problem 2.1. Plot the 95% uncertainty intervals and the median trajectory from 1880 & ndash;.

Problem 2.3 (10 points)

Use Plots.density() to plot the distribution of global mean sea levels in 2100 for each RCP (put these density plots on the same axes for easier comparison).

Problem 2.4 (10 points)

What do you notice about the contributions of parametric and scenario uncertainty to the variability in sea levels over the rest of the century? Are there any interesting trends?

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