Debate

analysis

PCA was computed on the correlation matrix (i.e. variables were re-scaled to have unit variance) of the linearly detrended December sea surface temperature record defined separately for each cell. The first four components explain 19%, 8%, 7%, 6% of the variance of the field.

1.5.4

Zonal wind PC1 prediction model

We use a weighted k-nearest neighbor model. We compute distance via euclidean distance and use a Gaussian kernel.

The weighted k-nearest neighbor model proceeds as follows:

1. Call the year of interest t∗. Compute the distances between t∗ and each year in the training sample based on the distance between the predictor(s). When more than one predictor is used, the predictors are scaled to have equal variance. 2. Retain the k years that are closest to t∗. Call this repainted sample t* 0. 3. Predict the t∗ year response as:

ˆ PJFM_t∗ = k

X

X

Where i indexes the k years contained within the t* 0 set and ci is the weight

of the ith _{observation, which is inversely proportional to distance (d) in the}

predictor space with the form: ci = √1_2πexp

n_−d2 i

2

o

. JFM is January-March.

Repeat this 1000 times for each year by bootstrapping the training set (re-sampling with replacement and maintaining the original sample size). This bootstrapping pro- vides us with confidence intervals for estimates for all training and testing years. The predictor set for Mod 1 is one dimensional and includes SST PC1D_t−1. The predictor set for Mod 2 includes SST PC1D_t−1, SST PC2D_t−1, SST PC3D_t−1, SST PC4D_t−1. Where

t is year and D is December. The training sample included the years 1950 up until 2015 and the testing set included the year 2016. We use a neighborhood size of 8 for each of the PC1 prediction models based on the general neighborhood size guidance of k ≈√n. All modeling was conducted in the R package kknn.

Chapter 2

Chapter II: Regional extreme precipitation events:

robust inference from credibly simulated GCM

variables

Abstract

General Circulation Models (GCMs) have been demonstrated to produce estimates of precipitation, including the frequency of extreme precipitation, with substantial bias and uncertainty relative to their representation of other fields. Thus, while the- ory predicts changes in the hydrologic cycle under anthropogenic warming, there is generally low confidence in future projections of extreme precipitation frequency for specific river basins. In this paper, we explore whether a GCM simulates large-scale atmospheric circulation indices that are associated with regional extreme precipi- tation (REP) days more accurately than it simulates REP days themselves, and thus whether conditional simulation of the precipitation events based on the circu- lation indices may improve the simulation of REP events. We show that a coupled Geophysical Fluid Dynamics Laboratory GCM simulates too many springtime REP days in the Ohio River Basin in historical (1950-2005) simulations. The GCM, how- ever, does credibly simulate the distributional and persistence properties of several indices (which represent the large-scale atmospheric pressure features, local atmo- spheric moisture content, and local vertical velocity) that are shown to modulate the likelihood of REP occurrence in the reanalysis/observational record. We show that simulation of REP events based on the GCM-based atmospheric indices greatly re- duces the bias of GCM REP frequency relative to the observed record. The simulation is conducted via a Bayesian regression model by imposing the empirical relationship between observed REP occurrence and the reanalysis-based atmospheric indices. Ap- plication of this model to future (2006-2100) representative concentration pathway

8.5 scenario suggests an increasing trend in springtime REP incidence in the study region. The proposed approach of simulating precipitation events of interest, partic- ularly those poorly represented in GCMs, with a statistical model based on climate indices that are reasonably simulated by GCMs could be applied to subseasonal to seasonal forecasts as well as future projections.

Citation: Farnham, David J., James Doss-Gollin, and Upmanu Lall

(2018). Regional extreme precipitation events: Robust inference from cred-

ibly simulated GCM variables. Water Resources Research, 54, 38093824.

2.1

Introduction

Floods are responsible for significant loss of life and economic damages both within the United States (US) and worldwide. Flood impacts in the US are estimated at $USD 8 billion (in 2014 dollars) and 82 fatalities per year from 1984 to 2013 (NWS Internet Services Team, 2015), while worldwide flood losses were estimated to be about $USD 85 billion (in 2012 US dollars) in 1993 alone (Kundzewicz et al., 2013). Furthermore, trends in population and urbanization are expected to increase exposure to hydroclimate extremes (including floods) into the future (Jongman, Ward, and Aerts, 2012). Given that projections of extreme precipitation changes remain highly uncertain (IPCC, 2012), particularly in the mid-latitudes, improved estimation of future hydroclimate extremes is a key ingredient for the mitigation of future flood impacts.

The poor representation of precipitation fields (particularly extreme precipitation) in general circulation model (GCM) simulations (Dai, 2006; Stephens et al., 2010; Kendon et al., 2012) complicate the projections of future hydroclimate extremes. Simulated precipitation fields are often used as inputs to hydrologic models (e.g. Kundzewicz et al., 2010; Hirabayashi et al., 2013; Lehner et al., 2006; Winsemius et al., 2015) after some form of bias correction (e.g. quantile-quantile mapping; Gudmundsson et al., 2012)) or downscaling is applied. However, It is often difficult to justify a bias correction approach, especially for extrapolation into the future, since there is no accompanying insight as to the underlying cause for the bias, or whether the bias correction used would be applicable in the future. In this paper we

explore whether some atmospheric variables that are closely related to the occurrence of regional extreme precipitation (REP) are well simulated by GCMs, such that their use for conditional prediction of REPs under seasonal forecasts or for climate change projections can be an effective strategy.