Analysis Patrick Breach M.E.Sc Candidate pbreach@uwo.ca Outline - PowerPoint PPT Presentation

Climate Change Impact Analysis Patrick Breach M.E.Sc Candidate pbreach@uwo.ca

Outline July 2, 2014 • Global Climate Models (GCMs) • Selecting GCMs • Downscaling GCM Data • KNN-CAD Weather Generator • KNN-CADV4 Example

Global Climate Models (GCMs)

Global Climate Models (GCMs) • In IPCC AR4 socio-economic driven SRES were used • In IPCC AR5 representative concentration pathways • Future GHG concentrations converted to radiative forcing of climate

Global Climate Models (GCMs)

Global Climate Models (GCMs)

Selecting GCMs • Multiple Model Ensembles (MME) approach is recommended to encompass uncertainty in model structure and parameterization • Large number of GCMs available • Multiple emissions scenarios (4 RCPs) • Multiple realizations for each GCM-Scenario combinations • Methods are needed for model selection

Selecting GCMs • 1) Selection of GCMs by required climate variables for hydrologic modelling during time of interest (e.g. 2050’s , 2090’s) • 2)GCM reanalysis data is used to compare with historical data

Selecting GCMs • 3) Calculate skill score of each probability density function for each GCM 𝑜 𝑇 𝑡𝑑𝑝𝑠𝑓 = ෍ min 𝑎 𝑛 , 𝑎 𝑝 1 • Cumulative minimum value measures common area between probability density functions • User defined weights can be applied to each bin to provide higher influence to models that can reproduce range

Selecting GCMs • 4) After models have been selected further reduction can take place by graphical methods Scatter Plot Method • Selections of models encompossing scenarios likely to produce hydrologic extremes

Selecting GCMs Percentile Method • Selection of future GCM-Scenario combinations corresponding to 5 th , 25 th , 50 th , 75 th , and 95 th , percentile

Downscaling GCM data GCM Change Factor Statistical Dynamic Methodologies Regional Transfer Regression- Weather Weather Climate Models functions Based Generators Classification (RCMs) Parametric Non-Parametric Semi-Parametric

Downscaling GCM data • Use transfer functions based on average GCM conditions in different time slices Simple Change Factor Methods

Downscaling GCM data Dynamic Regional Climate Models (RCMs)

Downscaling GCM data • Develops relationship between large scale “predictor” & single site “ predictand ” variables Statistical Regression- Standard Regression Model: Based Weather Classification • Multiple regression, Artificial Neural Networks, Weather Generators Canonical correlation, etc.

Downscaling GCM data • Meteorological data is related to discrete Statistical weather patterns Regression- Based • Relationships are developed using conditional probability distributions Weather Classification • Future climate simulations developed using Weather Generators large scale GCM models

Downscaling GCM data • Most popular technique for statistical Statistical downscaling Regression- Based • Ability to generate synthetic climate data of any length Weather Classification • Statistically reproduces attributes of climate variables include mean and standard deviation Weather Generators • Main types are parametric, non-parametric, and semi-parametric

Downscaling GCM data Parametric Statistical • Markov chains to determine wet or dry day Regression- probability Based • Probability distributions are derived for Weather precipitations amounts, temperatures and Classification other variables Weather • Spatial correlation must be assumed for multi- Generators site applications

Downscaling GCM data Semi-Parametric Statistical • Empirical / parametric components Regression- Based • Each model uses a different approach Weather • Spatial correlations must be assumed for multi- Classification site applications Weather • Examples: Generators • Statistical Downscaling Model (SDSM) • LARS-WG

Downscaling GCM data Non-Parametric Statistical • Resampling is used to select daily weather Regression- Based • No underlying statistical assumptions are Weather needed regarding the probability distribution Classification of weather variables Weather • KNN approach from Young (1994) Generators

KNN-CAD • KNN - “K” Nearest Neighbor algorithm (Yates, 2003) • Reshuffles daily climate data for multiple stations • Potential neighbors are determined within temporal window • Potential neighbor averages compared to current day averages using Mahalanobis distance • Closest “K” nearest neighbors selected • Next days weather from KNNs randomly selected from probability distribution

KNN-CAD • KNN-CAD version 1 (Sharif and Burn, 2006) • Perturbation component is added • KNN-CAD version 2 (Prodanovic and Simonovic, 2008) • Leap year modification • KNN-CAD version 3 (Eum and Simonovic, 2008) • Principal component analysis for calculation of Mahalanobis distance • KNN-CAD version 4 (King, McLeod, and Simonovic, 2012) • Improved perturbation scheme • Block bootstrapping method

KNN-CAD • KNN algorithm consists of 9 steps Step 1 – Compute regional means of p variables (x) across all q stations for each day in the historical record 𝑌 𝑢 = 𝑦 1,𝑢 , 𝑦 2,𝑢 , … , 𝑦 𝑞,𝑢 ∀𝑢 = 1,2, … , 𝑈 𝑟 𝑦 𝑗,𝑢 = 1 𝑘 𝑟 𝑥ℎ𝑓𝑠𝑓, 𝑟 ෍ 𝑦 𝑗,𝑢 ∀𝑗 = {1,2, … , 𝑞} 𝑦 𝑗,𝑢 = 1 𝑘 ℎ𝑓𝑠𝑓, 𝑟 ෍ 𝑦 𝑗,𝑢 ∀𝑗 = {1,2, … , 𝑞} 𝑘=1 𝑘=1

KNN-CAD Step 2 – Choose temporal of length “w” and select a subset of potential neighbors “L” days long for “N” years 1 2 3 4 5 6 7 8 9 N . . . . . . 1 2 3 4 5 6 7 8 9 3 1 2 3 4 5 6 7 8 9 2 1 2 3 4 D 6 7 8 9 1 Year <------------------ w/2 ------------------> <------------------ w/2 ------------------> 𝑀 = 𝑂 ∗ 𝑥 + 1 − 1

KNN-CAD Step 3 – Compute mean of “L” potential neighbors, 𝑌 𝑚 for each day 𝑦 1,1 ⋯ 𝑦 1,𝑞 𝑌 𝑚 = ⋮ ⋱ ⋮ 𝑦 𝑀,1 ⋯ 𝑦 𝑀,𝑞 Step 4 – Compute covariance matrix 𝐷 𝑢 for day 𝑢 with 𝑌 𝑚 𝑤𝑏𝑠 𝑦 1,1 ⋯ 𝑑𝑝𝑤 𝑦 1,1 , 𝑦 1,𝑞 𝐷 𝑢 = ⋮ ⋱ ⋮ 𝑑𝑝𝑤 𝑦 𝑞,1 ⋯ 𝑤𝑏𝑠 𝑦 𝑞,𝑞

KNN-CAD Step 5 – Random selection of first simulation day from historical record consisting of “p” variables at “q” stations from the “N” years Step 6 a) Calculate eigenvector ( 𝐹 ) & eigenvalue (e) from 𝐷 𝑢 b) Retain 𝐹 with highest e c) Calculate first principal component using 𝐹 𝑄𝐷 𝑢 = 𝑌 𝑢 𝐹 𝑄𝐷 𝑚 = 𝑌 𝑚 𝐹 ∀𝑚 = {1,2, … , 𝑀}

KNN-CAD d) Calculate Mahalanobis distance 𝑄𝐷 𝑢 − 𝑄𝐷 𝑚 2 𝑒 𝑚 = 𝑤𝑏𝑠(𝑄𝐷) TMX 𝐹 TMN PPT

KNN-CAD Step 7 – Sort the Mahalanobis calculated for each potential neighbor from smallest to largest and retain the “K” nearest neighbors 𝐿 = 𝑀 Yates et al. (2003) Step 8 – Use discrete probability distribution weighting closest neighbors the highest for resampling one of the “K” nearest neighbors 1/𝑙 𝑘 𝑞 𝑘 = σ 𝑗=1 𝑥 𝑙 = ∀𝑙 = 1,2, … , 𝐿 𝑥 𝑗 𝑙 σ 𝑗=1 1/𝑗

KNN-CAD Step 9 – Generate random number, 𝑣 0,1 , to determine current neighbor from probability distribution

KNN-CAD Step 10 – Resample block of data preceding selected day - - - NN NN + 1 NN + 2 NN + B Step 11(a) – Perturbation of resampled temperature values 𝑘 𝑘 𝑧 𝑗,𝑢+𝑐 = 𝜇 𝑢𝑓𝑛𝑞 ∗ 𝑦 𝑗,𝑢+𝑐 + 1 − 𝜇 𝑢𝑓𝑛𝑞 𝑎 𝑢+𝑐 From KNN where, 𝑐 = 1,2, … , 𝐶 𝑎 𝑢+𝑐 ~ 𝑂 𝜈, 𝜏 𝑘 𝑎 𝑢+𝑐 ~𝑂 𝑦 𝑗,𝑢+𝑐 , 𝜏 𝑗,𝑢

KNN-CAD Step 11(b) – Perturbation of resampled precipitation values 𝑘 𝑘 𝑧 𝑞𝑞𝑢,𝑢+𝑐 = 𝜇 𝑞𝑞𝑢 ∗ 𝑦 𝑞𝑞𝑢,𝑢+𝑐 + 1 − 𝜇 𝑞𝑞𝑢 𝑎 𝑢+𝑐 Where, 𝑎 𝑢+𝑐 = 𝑓 𝐵𝑛 𝑘,𝑢 +𝐶𝑛 𝑘,𝑢 ∗𝑨 𝑢 𝐵𝑛 𝑘,𝑢 = log 𝑦 𝑘,𝑢 − 𝐶𝑛 𝑘,𝑢 2 2 𝜏 𝑘,𝑢 𝐶𝑛 𝑘,𝑢 = log + 1 𝑦 𝑘,𝑢 𝜏 𝑘,𝑢 From LNN

KNN-CAD Step 12- Repeat process until end of historical record is reached *Process can be repeated any number of times for longer generated climate records *Longer records are extremely useful for risk analysis in hydrologic modelling