Subtropical Floods and Tropical Cyclones Daniel A. Shaevitz

Extreme weather: subtropical ﬂoods and tropical cyclones

Daniel A. Shaevitz

Submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences

COLUMBIA UNIVERSITY

Extreme weather: subtropical ﬂoods and tropical cyclones

Daniel A. Shaevitz

Extreme weather events have a large effect on society. As such, it is important to understand these events and to project how they may change in a future, warmer climate. The aim of this thesis is to develop a deeper understanding of two types of extreme weather events: subtropical floods and tropical cyclones (TCs). In the subtropics, the latitude is high enough that quasi-geostrophic dynamics are at least qualitatively relevant, while low enough that moisture may be abun- dant and convection strong. Extratropical extreme precipitation events are usu- ally associated with large-scale flow disturbances, strong ascent, and large latent heat release. In the first part of this thesis, I examine the possible triggering of convection by the large-scale dynamics and investigate the coupling between the two. Specifically two examples of extreme precipitation events in the subtropics are analyzed, the 2010 and 2014 floods of India and Pakistan and the 2015 flood of Texas and Oklahoma. I invert the quasi-geostrophic omega equation to decompose the large-scale vertical motion profile to components due to synoptic forcing and diabatic heating. Additionally, I present model results from within the Column Quasi-Geostrophic framework. A single column model and cloud-revolving model are forced with the large-scale forcings (other than large-scale vertical motion) computed from the quasi-geostrophic omega equation with input data from a reanalysis data set, and the large-scale vertical motion is diagnosed interactively with the simulated convection. It is found that convection was triggered primarily by mechanically forced orographic ascent over the Himalayas during the India/Pakistan flood and by upper-level Potential Vorticity disturbances during the Texas/Oklahoma flood. Furthermore, a climate attribution analysis was conducted for the Texas/Oklahoma flood and it is found that anthropogenic climate change was responsible for a small amount of rainfall during the event but the intensity of this event may be greatly increased if it occurs in a future climate. In the second part of this thesis, I examine the ability of high-resolution global atmospheric models to simulate TCs. Specifically, I present an intercomparison of several models’ ability to simulate the global characteristics of TCs in the current climate. This is a necessary first step before using these models to project future changes in TCs. Overall, the models were able to reproduce the geographic distribution of TCs reasonably well, with some of the models performing remarkably well. The intensity of TCs varied widely between the models, with some of this difference being due to model resolution. Table of Contents

List of Figures iii

List of Tables x

1 Introduction 1

I Subtropical ﬂoods: Dynamical inﬂuences on vertical motion and precipitation 4

2 The 2010 and 2014 floods in India and Pakistan 10 2.1 Introduction ...... 10 2.2 Data ...... 13 2.3 Description of flood events ...... 13 2.3.1 2010 first event: 07-20-10 to 07-23-10 ...... 14 2.3.2 2010 second event: 07-27-10 to 07-30-10 ...... 14 2.3.3 2014 event: 09-04-14 to 09-07-14 ...... 16 2.4 Quasi-geostrophic Omega Equation ...... 20 2.4.1 Alternative lower boundary ...... 27 2.5 Historical comparison ...... 29 2.6 Conclusion ...... 33

3 The May 2015 ﬂood in Texas and Oklahoma 35 3.1 Introduction ...... 35 3.2 Data ...... 37

i 3.3 Description of ﬂood event ...... 38 3.4 Quasi-geostrophic Omega Equation ...... 42 3.5 Column model simulations ...... 47 3.5.1 Single Column Model ...... 50 3.5.2 Cloud Resolving Model ...... 58 3.6 Conclusions ...... 62

II Tropical Cyclones in climate models 64

4 Characteristics of tropical cyclones in high-resolution models in the present climate 67 4.1 Introduction ...... 67 4.2 Models and data ...... 69 4.3 Results ...... 72 4.3.1 Climatology ...... 72 4.3.2 Interannual variability ...... 86 4.4 Conclusions ...... 89

5 Conclusions 93

Bibliography 95

ii List of Figures

2.1 Topography map. The black rectangle represents the flood region and the blue outlines the border of Pakistan...... 14 2.2 Three-day accumulated precipitation. (a)-(c) are for ERA-Interim and (d)-(f) is for TRMM. (a) and (d) are for the 2010 First event: 07-20-10 to 07-23-10. (b) and (e) are for the 2010 Second Event: 07- 27-10 to 07-30-10. (c) and (f) are for the 2014 Event: 09-04-14 to 09-07-14. The black rectangles define the domain used for time series calculations...... 15 2.3 Time series of the area averaged ERA-Interim precipitation, TRMM precipitation, and precipitable water. (a) 2010 events, (b) 2014 event. 16 2.4 Three day average height anomalies of the 500-hPa surface (top) and precipitable water anomalies (bottom). (a) and (d) 2010 First Event: 07-20-10 to 07-23-10. (b) and (e) 2010 Second Event: 07-27-10 to 07-30-10. (c) and (f) 2014 Event: 09-04-14 to 09-07-14...... 17 2.5 Sequence of maps showing the evolution of one day average height anomalies of the 500-hPa surface and one day average moisture flux at 700-hPa (arrows) from 07-24-10 to 07-29-10...... 18 2.6 Sequence of maps showing the evolution of one day average height anomalies of the 500-hPa surface (colors) and one day average moisture flux at 700-hPa (arrows) from 08-31-14 to 09-05-14...... 19 2.7 Sequence of maps showing the evolution of one day average precipitable water anomalies from 08-31-14 to 09-05-14...... 20

iii 2.8 Potential Vorticity at θ = 330K during the three events. The top row shows the first events of 2010, the middle row shows the second event of 2010, and the bottom row shows the 2014 event. PVU=10−6 K m2 kg−1 s−1 ...... 21 2.9 Top row: Area-average reanalysis (red) and geostrophic (blue) velocities as a function of pressure above the surface for the peak of the first event of 2010 (07-22-10 0000), (a) and (b), and the peak of the second event of 2010 (07-29-10 0600), (c) and (d). (a) and (c) show the magnitude of the velocity and (b) and (d) show the velocity direction. Middle and bottom rows: reanalysis vertical velocity (blue) as well as topographic forced vertical velocity using the reanalysis wind (red) and geostrophic wind (yellow). (e) is for the vertical velocity at the surface and (f) is for the vertical velocity at the top of the boundary layer, defined as 150 hPa above the surface. The gray bars indicate the precipitation events...... 24 2.10 Area average vertical velocity, w, profiles from inverting the omega equation. Shown are the contribution from the advection terms (blue), the heating term (red), the boundary condition (yellow), the sum of all terms (purple), and the Reanalysis vertical velocity (black). The top plots are for points-in-time and the bottom plots are three-day averages during each event. 2010 First Event: (a) 07-22-10 0000 and (e) three-day average from 07-20-10 and 07-23-14. 2010 Second Event: (b) 07-29-10 0600 and (f) three-day average from 07-20-10 and 07-23-14. 2014 Event: (c) 09-04-14 0600 and (g) three-day average from 09-04-14 to 09-07-14...... 26 2.11 2010 event. Area average vertical velocity through time from inverting the omega equation. Shown are the contribution from (a) the advection terms , (b) the heating term, (c) the sum of all terms, and (d) the Reanalysis vertical velocity. The black lines bound the time of the flood events...... 28

iv 2.12 2014 event. Area average vertical velocity through time from inverting the omega equation. Shown are the contribution from (a) the advection terms , (b) the heating term, (c) the sum of all terms (without the boundary condition), and (d) the Reanalysis vertical velocity. The black lines bound the time of the flood event...... 29 2.13 Map of 350 hPa vertical velocity from inverting the omega equation. Only contributions from the advection terms are included. (a) 07-22- 10 0000, (b) 07-29-10 0600, and (c) 09-05-14 0600...... 30 2.14 Same as figure 2.10 except using a lower boundary at 700 hPa as discussed in section 2.4.1...... 31 2.15 Average precipitable water and topographic forced vertical velocity. The colors are precipitation rate in mm/day. The first event of 2010 is shown with black squares, the second event of 2010 is shown with black diamonds, and the 2014 event is shown with black circles. Time range is June - September 2004-2014. (a) One-day averages, (b) Three-day averages...... 32 2.16 (a) Average Potential Vorticity anomaly at θ = 330K for the 13 days with the largest topographic forced vertical velocity in the flood region. (b) Linear regression of Potential Vorticity at θ = 330K onto the topographic forced vertical velocity in the flood region...... 33

3.1 Four-day accumulated precipitation from 5/23/15 to 5/26/15. (a) ERA-Interim reanalysis, (b) CPC Rain Gauge data. Blue rectangles: flood region...... 38 3.2 (a) Area-averaged Precipitation (both reanalysis and CPC rain gauge) and Precipitable Water in the flood region. (b) Area-averaged Poten- tial Vorticity at θ = 330K in the upstream region shown in pink in figure 3.4 ...... 39 3.3 Sequence of maps showing daily average quantities. Colors: Precip- itable Water. Black arrows: 850 hPa wind vectors. Blue rectangle: flood region...... 40

v 3.4 Sequence of maps showing daily average quantities. Colors: Potential Vorticity at θ = 330K. Black contours: height of the 500-hPa surface. Black shading: Areas where the precipitation exceeds 25 mm/day. Blue rectangle: flood region. Pink rectangle: upstream region used for PV averaging in figure 3.2 ...... 41 3.5 Area average pressure vertical velocity, ω, profiles from inverting the omega equation. Shown are the contribution from the advection terms (blue), the heating term (red), the boundary condition (yellow), the sum of all terms (purple), and the Reanalysis vertical velocity (black). (a) Four-day average during the flood. (b) Peak of the flood: 05-24-15 0000 ...... 44 3.6 Daily and area averaged pressure vertical velocity, ω, profiles from inverting the omega equation. The colors are the same as in figure 3.5 45 3.7 Area average vertical velocity through time from inverting the omega equation. Shown are the contribution from (a) the advection terms , (b) the heating term, (c) the sum of all terms, and (d) the Reanalysis vertical velocity. The black lines bound the time of the flood event. . 46 3.8 Time series of precipitation estimated from each ω component using equation 3.4 and the reanalysis precipitation (black)...... 47 3.9 Area averaged quantities to force the SCM. (a) specific humidity advection, (b) vorticity avection, and (c) temperature advection. The black lines bound the time of the flood event...... 49 3.10 Time series comparison of reanalysis quantities with SCM simulation. (a) Precipitation and (b) precipitable water...... 52

vi 3.11 Comparison of pressure vertical velocity, ω, profiles from inverting the omega equation between the reanalysis and the SCM simulation. (a) Four-day average during the flood, ERA: 3D inversion, (b) peak of the flood: 05-24-15 0000 , ERA: 3D inversion, (c) four-day average during the flood, SCM: 1D inversion, and (d) peak of the flood: 05- 24-15 0000, SCM: 1D inversion. The colors are the same as in figure 3.5...... 53 3.12 Area average vertical velocity through time from the SCM simulation. Shown are the contribution from (a) the advection terms , (b) the heating term, (c) the sum of all terms, and (d) the Reanalysis vertical velocity. The black lines bound the time of the flood events...... 54 3.13 Time series of precipitation estimated from each ω component using equation 3.4. (a) Reanalysis (also shown in figure 3.8) and (b) SCM. The black line in (a) represents the reanalysis precipitation and the black line in (b) represents the SCM precipitation...... 55 3.14 Precipitation time-series for SCM model simulations with only a single forcing applied. The black curve in all panels represents the control case (with all forcings) precipitation. The red curves in (b)-(d) represent the precipitation from the SCM forced solely by: (b) the PV advection terms, (c) q advection, and (d) the boundary conditions. The red curve in (a) represents the sum of the red curves in (b)-(d) minus 8 mm/day as multiple-counted mean precipitation. The blue curve in (a) represents the precipitation of the SCM with all forcings applied, but without the convective feedback on ω...... 57 3.15 Time series comparison of reanalysis quantities with CRM simulation. (a) Precipitation and (b) precipitable water...... 59

vii 3.16 Comparison of pressure vertical velocity, ω, profiles from inverting the omega equation between the reanalysis and the CRM simulation. (a) Four-day average during the flood, ERA: 3D inversion, (b) peak of the flood: 05-24-15 0000 , ERA: 3D inversion, (c) four-day average during the flood, CRM: 1D inversion, and (d) peak of the flood: 05- 24-15 0000, CRM: 1D inversion. The colors are the same as in figure 3.5...... 60

4.1 Distributions of the number of TCs per year for models and observations. The horizontal line inside the boxes shows the median number of TCs per year, the top and bottom of the boxes represent the 75th and 25th percentiles respectively, with the whiskers extending to the maximum and minimum number of TCs per year in each case. CAML: Low-resolution CAM5.1, CAMH: High-resolution CAM5.1, HadL: Low-resolution HadGEM3, HadM: Medium-resolution HadGEM3, HadH: High-resolution HadGEM3...... 72 4.2 Mean number of TCs formed in each basin for models and observations. The top panel shows the total number of TCs, while the bottom panel shows the percentage of TCs in each basin. The basins are defined as: SI (South Indian), AUS (Australian), SP (South Pa- cific), NI (North Indian), WNP (Western North Pacific), ENP (Easter North Pacific), NATL (North Atlantic). The model names follow the definitions in Fig. 4.1...... 74 4.3 TC track density in models and observations. Track density is defined as the mean number of TC transits per 5◦ x 5◦ box per year. . . . . 76 4.4 TC genesis density in models and observations. Genesis density is defined as mean TC formation per 5◦ x 5◦ box per year...... 77 4.5 TC lysis density in models and observations. Lysis density is defined as mean TC lysis per 5◦ x 5◦ box per year...... 78

viii 4.6 Mean number of TC genesis per year in models and observations as a function of latitude (top panel), longitude (middle panel), and month (bottom panel)...... 79 4.7 Mean TC genesis per year and month in models and observation in various basins (as defined in Fig. 4.2) ...... 81 4.8 Total accumulated cyclone energy (ACE) for models and observations (top panel). The bottom panel shows the percentage of the total ACE in each basin for models and observations. Basins and models are defined as in previous figures...... 82 4.9 Distributions of TC maximum intensity in models and observations (top panel). The horizontal line shows the median of each distribution, the left and right edges of the box represent the 75th and 25th percentiles respectively, and the whiskers extend to the maximum and minimum values in each case. Histograms of TC maximum intensity for two horizontal resolutions of the CAM5.1 model (middle panel) and three model resolutions of the HadGEM1 model (bottom panel). The vertical lines show the boundaries of the Saffir-Simpson hurricane classification scale. TD: Tropical Depression, TS: Tropical Storm, C1-C5: Category 1-5 hurricanes. LR: Low resolution, MR: Medium resolution, HR: High resolution...... 84 4.10 Distributions of TC life-time (or duration) for models and observations. The horizontal line shows the median of each distribution, the left and right edges of the box represent the 75th and 25th percentiles respectively, and the whiskers extend to the maximum and minimum values in each case. The histograms of TC durations in the CAM5.1 and HadGEM3 models for different resolutions are shown in the middle and bottom panel, respectively. LR: Low resolution, MR: Medium resolution, HR: High resolution...... 85

ix 4.11 Number of TCs per year (top panel) in the globe and in a few of the Northern Hemipshere basins (Western North Pacific, Eastern North Pacific, and North Atlantic). For the models, when more than one ensemble simulation was available, the ensemble mean number of TCs in each year is shown.s ...... 87 4.12 Difference of TC genesis density in El Niñoand La Niñaseasons in models and observations. The genesis density is defined as the mean TC formation per 5◦ x 5◦ box per year...... 90 4.13 Mean TC genesis location in the western and eastern North Pacific in El Niño(triangles) and La Niña(circles) years in models and observations...... 91

x List of Tables

3.1 Four-day total area-average precipitation during the ﬂood for diﬀerent climate scenarios...... 62

4.1 Table of model parameters. LR: Low Resolution, MR: Medium Reso- lution, HR: High Resolution. Roeckner/Scoccimarro: Roeckner (2003) and Scoccimarro et al. (2011). Hodges/Bengtsson: Hodges (1995) and Bengtsson et al. (2007b). Mizuta/Murakami: Mizuta et al. (2012) and Murakami et al. (2012) ...... 71 4.2 Models that performed interannual simulations...... 86 4.3 Correlation of yearly ACE and model-ACE (MACE) in each basin and the yearly observed ACE, shown as ACE / MACE. Asterisks denote correlations that are statistically significant. Basins are defined as: SI (South Indian), AUS (Australian), SP (South Pacific), NI (North Indian), WNP (Western North Pacific), ENP (Easter North Pacific), NATL (North Atlantic)...... 88 4.4 El Niñoand La Niñaseasons for the northern and southern hemispheres, using the warm and cold ENSO (El NiñoSouthern Oscilla- tions) definitions of Climate Prediction Center. The northern (southern) hemisphere seasons definitions as based on the state of ENSO in the August - October (January - March) seasons. Note that the southern hemisphere TC seasons are defined from July to June, encompassing 2 calendar years...... 89

xi Acknowledgments

I first and foremost want to express my gratitude to my advisor, Adam Sobel. I first started working with Adam about fifteen years ago and he is responsible for introducing me to this field and to scientific research in general. I also wish to thank Ji Nie whose depth of knowledge and willingness to always answer any and all questions were invaluable to me in completing the first part of this thesis. Additionally, I want to thank Suzana Camargo for guiding me through the second part of this thesis; it was an honor to work with a leading expert in this field. Finally I want to thank Larry Rosen, Naomi Henderson, and Montse Fernandez-Pinkley for providing computer, data management, and administrative support.

xii CHAPTER 1. INTRODUCTION 1

Chapter 1

Introduction

Extreme weather events cause the loss of tens of thousands of lives and enormous economic losses each year (Karl and Easterling, 1999). These events include floods, droughts, extreme heat and cold, hurricanes, and many others. Because of their huge impact on society, it is important to develop an understanding of these events and how they might change. Of particular interest is how extreme weather events depend on climate and what impact anthropogenic global warming may have on these events in the future. Rising greenhouse gas emissions over the last 150 years have led to a global warming of the climate. The warming during the late twentieth century is most likely attributable to anthropogenic causes (Hegerl et al., 2007). The effects on climate and weather have been extensively studied (see Solomon et al. 2007). Fore- casts using General Circulation Models (GCMs) of the climate system allow for the prediction of future climate states for different scenarios of greenhouse gas emissions. These forecasts predict that the climate is expected to continue to warm in the future. Due to this likelihood of further warming, it is imperative to develop a better understanding of extreme weather events and their dependence on climate. My focus in this work is on two types of extreme weather events: floods (specifically in the subtropics) and tropical cyclones (commonly referred to as hurricanes and typhoons). Floods affect people all over the planet. It is estimated that in the period from CHAPTER 1. INTRODUCTION 2

1970 to 1995, floods affected more than 1.5 billion people; over 300,000 people were killed and more than 80 million people became homeless. Economically, floods were responsible for more than $200 billion in damages from 1991-1995, which is 40% of the economic damage of all natural disasters during that period (Pielke and Downton, 2000). In GCM simulations for the 21st century, extreme precipitation events are predicted to increase globally (Kharin et al., 2007; Sun et al., 2007). This change in precipitation is generally thought to be a consequence of increased atmospheric water vapor due to increased temperatures, though recent work has demonstrated the extreme precipitation events that are highly convective may increase at a faster rate than predicted by the increase in water vapor alone (e.g. Lenderink and van Meij- gaard 2008; Berg et al. 2013). This increase in extreme precipitation is expected to lead to an increase in the number of floods (O’Gorman and Schneider, 2009). Tropical cyclones (TCs) are the natural disasters that cause the most economic damage in the United States and account for a significant fraction of damage, injury, and loss of life from natural hazards (Pielke and Landsea, 1998; Emanuel, 2005). On average, hurricanes cause $7.5 billion dollars (inflation adjusted to 2016) in damage in the continental United States per year. GCMs have also been used to simulate TCs in climate change scenarios. The general consensus of the models is for a decrease in the overall global frequency of TCs, an increase in the intensities of the strongest TCs, an increase in the precipitation rates, and an increase in the risk of storm surge due to sea level rise caused by global warming (Walsh et al., 2016). This thesis consists of two parts. Part I involves an analysis of three subtropical floods, the 2010 and 2014 floods in India and Pakistan in chapter 2 and the 2015 flood in Texas and Oklahoma in chapter 3. I focus on two factors that contributed to the extreme precipitation events: the source of moisture and the causes of vertical motion that drove the convection and precipitation. These flooding events involve a large amount of moist convection, and I investigate possible mechanisms that triggered the convection. Specifically, the quasi-geostrophic (QG) omega equation CHAPTER 1. INTRODUCTION 3 is used to determine what factors were important in triggering the convection. It will be shown in chapter 2 using the QG omega equation applied to reanalysis data that during the floods in India and Pakistan the dominant trigger of convection was orographically forced mechanical ascent due to low-level winds blowing towards the Himalayan mountains. It will also be concluded that extreme precipitation in this region has been historically associated with a combination of anomalously high moisture content and orographically forced ascent. In contrast, it will be shown in chapter 3 that the convection during the flood of Texas and Oklahoma was triggered by the advection of an upper-level potential vorticity anomaly. This will be demonstrated in an application of the QG omega equation to reanalysis data as well as model simulations that use the QG omega equation to parameterize the large-scale motion. Additionally, these model simulations will be used in a climate attribution analysis for this event. It is concluded that climate change contributed to a small portion (4%) of the rainfall during the event, but this event in a future warmer climate scenario would have produced 25% more rainfall. Part II consists of chapter 4 which is an intercomparison of several GCMs’ ability to simulate the global characteristics of TCs in the current climate. This is a necessary first step before using these GCMs to project future changes in TCs. The climatological spatial, temporal, and intensity distributions of TCs are examined as well as the interannual variability of TCs. Overall, the models were able to reproduce the geographic distribution of TCs reasonably well, but there was a wide range in TC intensities between the models. 4

Part I

Subtropical ﬂoods: Dynamical inﬂuences on vertical motion and precipitation 5

Introduction

Convective precipitation is related to large-scale ascending motion of air. Large- scale ascent is the result of strong ascent in updrafts with limited horizontal scale combined with descent over much larger scales1 (Yanai et al., 1973). Thermody- namic budgets in both models and reanalysis data sets are typically separated into large-scale vertical advection and subgrid-scale diabatic heating terms that capture the effects of convective updrafts. These terms are distinct but they interact, so understanding the magnitude of convective precipitation requires an understanding of the large-scale vertical motion and its coupling to small-scale convective processes. Any attempt to understand or model convective precipitation must, therefore, also include an understanding or model of the vertical motion. In particular, consider the simple example of a Single Column Model (SCM) of the atmosphere. In an SCM, one typically specifies the large-scale vertical velocity profile, which along with a convection parameterization2 determines the precipitation rate. Since the precipitation depends on the imposed vertical velocity, it is not possible to model the precipitation as a a function of boundary forcings (e.g. the equilibrium precipitation rate of an atmospheric column over an ocean as a function of the Sea Surface Temperature (SST)). There is a need to parameterize the vertical velocity in a SCM to be able to model the precipitation. Sobel and Bretherton (2000) introduced the Weak Temperature Gradient (WTG) approximation to allow for the modeling of tropical convection and precipitation in a single column. WTG exploits the fact that horizontal temperature gradients are small in the tropics and can be neglected. The prognostic temperature tendency equation: ∂T + u · ∇T + ωS = Q (1.1) ∂t h then becomes a diagnostic equation that can be used to estimate the steady-state

1In the case of stratiform clouds, there is weaker ascent over large areas, as opposed to descent.

2As well as a representation of radiation, specified surface fluxes and initial temperature and moisture profiles. 6

∂p pressure vertical velocity ω = ∂t :

ωS = Q (1.2)

where T is temperature, uh is the horizontal velocity, S is the static stability, and Q is the diabatic heating. The vertical advection of temperature in WTG is balanced by the convective heating. Using the WTG set up of an SCM, Sobel and Bretherton (2000) were able to make a prediction of the precipitation rate in the tropics as a function of underlying SST that matched observations well. The WTG approximation and other related approaches that parameterize the large-scale dynamics, as opposed to imposing or neglecting them altogether, have been used in many modeling studies of the tropical atmosphere. As in the WTG example briefly described above, these approximations parameterize the large-scale vertical velocity as functions of the local column state variables and prescribed large-scale parameters of the environment (Nie and Sobel, 2016). These include studies using SCMs (Chiang and Sobel 2002; Shaevitz and Sobel 2004; Bergman and Sardeshmukh 2004; Sobel et al. 2007; Sobel and Bellon 2009; Ramsay and Sobel 2011; Zhu and Sobel 2012) and studies using Cloud Resolving Models (CRMs) (Mapes 2004; Raymond and Zeng 2005; Raymond 2007; Kuang 2008; Blossey et al. 2009; Kuang 2011; Sessions et al. 2010; Wang and Sobel 2011; Anber et al. 2014; Nie and Sobel 2015). All of these approaches to parameterize the large-scale vertical motion were developed for the tropics and are not valid in the extratropics because they neglect all sources of vertical motion that are not related to diabatic heating. As will be further explored in chapter 3, Hoskins et al. (1983) described the impact of upper- level Potential Vorticity (PV) anomalies on the vertical motion. These dry adiabatic dynamical processes are critically important outside of the tropics and are unable to be captured in the tropical parameterizations described above. Nie and Sobel (2016) introduced the column QG (CQG) framework, a parameterization that includes the effects of QG dynamics and can be used in the extratropics. Similar to WTG, CQG models an atmospheric column. The tendencies of horizontal advection are prescribed and the large-scale vertical motion is parameterized with 7 the QG omega equation. The QG omega equation (equation 2.1 in chapter 2) is a diagnostic equation for the quasi-geostrophic pressure vertical velocity, ω, and includes both dry QG and convective forcings (this equation is discussed in detail in chapters 2 and 3). The dry QG forcings lead to vertical motion that alters the temperature and moisture profiles and can lead to triggering of convection through either a destabilization of the column. The convection in turn feeds back into the large-scale vertical motion. The QG omega equation is a linear equation for ω, so it is possible to attribute precipitation events to different large-scale forcings and the associated convective feedback. Thus, the CQG framework is ideal for studying the interaction of large-scale dynamics and convection outside of the tropics. It is expected to be particularly useful for precipitation events in the subtropics, where the latitude is high enough that the dry adiabatic QG dynamics are important but low enough that there is a large amount of moisture in the atmosphere that can lead to strong moist convection and associated latent heating. The QG omega equation has previously been used to study the forcing mechanisms of extratropical cyclones (Clough et al., 1996; Deveson et al., 2002). Typically, the convection term is ignored and only the dry QG forcings are considered3. In particular, Gray and Dacre (2006) used the omega equation applied to reanalysis data to examine the forcing mechanisms of 700 extratropical cyclones and classify the cyclones into different types based on the relative importance of the different forcings. The analysis in this part extends this approach by including the convection term, and thus allows for analysis of subtropical events with a large contribution from convection. In this part, I analyze two examples of subtropical extreme precipitation events that had a strong convective component using the QG omega equation, the 2010 and 2014 floods of India and Pakistan in chapter 2 and the May 2015 flood of Texas and Oklahoma in chapter 3. For both examples, I invert the full three-

3The alternative case where dry QG forcings are ignored and only convection is considered is equivalent to the WTG approximation (Nie and Sobel, 2016). 8 dimensional QG omega equation using reanalysis data and decompose the vertical velocity into components forced by the dry QG forcings, the surface forcing, and convection. Additionally, I employ the CQG modeling framework (which involves a one-dimensional form of the QG omega equation) and show simulation results of the May 2015 flood of Texas and Oklahoma using an SCM and a CRM in chapter 3. It will be seen that the dominant triggering mechanism of convection during the India/Pakistan floods was topographically forced ascent of low-level winds blowing towards the Himalayas and that the dominant triggering mechanism of convection during the Texas/Oklahoma flood was an upper-level PV anomaly. In chapter 3, I also describe a climate attribution analysis for the Texas/Oklahoma flood using the CQG framework. Attribution analyses of extreme weather events in the context of climate change is a new and emerging area of study (National Academies of Sciences, Engineering, and Medicine, 2016; Peterson et al., 2012, 2013; Herring et al., 2014, 2015). Attribution analyses examine individual extreme weather events and attempt to quantify the degree to which the event was influenced by anthropogenic climate change. The analysis can determine the effect of climate change on the frequency of the event, the intensity of the event, or both. National Academies of Sciences, Engineering, and Medicine (2016) classifies attribution studies into three categories: unconditional, conditional, and highly conditional. The conditionality refers to how the study is conditioned on certain climate scenarios. For example, an unconditional study could use a coupled atmosphere- ocean climate model. In contrast, a conditional study could use an atmosphere only climate model with specified SSTs; the study being conditioned on the imposed SST distribution. Finally, a highly conditional study could take an actual weather event and model the intensity for different climate scenarios. An example of an unconditional attribution study is Zwiers et al. (2011), which used coupled atmosphere-ocean climate models to examine return periods of daily temperature extremes. They found that the return periods of 20-year extreme annual maximum daily maximum temperatures from the 1960s had decreased to fewer than 15 years. 9

An example of a conditional attribution study is Zhao et al. (2009), which studied hurricane frequency using a high-resolution atmosphere model with specified SSTs. They used both observed SSTs from the present climate as well as projected SSTs from a warmer climate obtained from coupled atmosphere-ocean models. An example of a highly conditional attribution study focusing on Hurricane Sandy is Lackmann (2015). This study used a nested modeling technique; high- resolution numerical simulations were initialized with analyses from the midpoint of Sandy’s track. These simulations were run with thermodynamic conditions that represent the present day, as well as scenarios for the 1880s and 22nd century obtained from a coupled climate model ensemble. The CQG modeling framework is a useful tool for performing highly conditional attribution analyses. The large-scale dynamics that force the omega equation can be taken from the actual extreme event while the background thermodynamic environment can be altered for different climate scenarios. Chapter 3 includes a highly conditional attribution analysis for the Texas/Oklahoma flood using a CRM and the CQG framework. The dry QG forcing of the omega equation is taken from the actual event, while the convection and precipitation are simulated. Three background thermodynamic profiles are compared: present day, a past climate, and a warmer climate derived from coupled climate model projections. The rest of this part consists of chapter 2 which analyzes the 2010 and 2014 flood of India and Pakistan and chapter 3 which analyzes the May 2015 flood of Texas and Oklahoma. CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 10

Chapter 2

The 2010 and 2014 ﬂoods in India and Pakistan

2.1 Introduction

In early September 2014, near the end of the monsoon season, heavy rains caused landslides and flooding in the Jammu and Kashmir region of India and nearby regions of Pakistan, killing hundreds of people (Mishra, 2015). Extreme rainfall in roughly the same region (the precipitation region can be seen in figure 2.1) led to historic floods of the Indus river basin in northeast Pak- istan, submerging a significant fraction of the country and causing over 2000 deaths (Akthar, 2011). The July 2010 floods were related to an extratropical blocking anticyclone event that also led to an intense heat wave in Russia (Lau and Kim, 2011). A southeasterly flow was present over India during the end of July 2010, caused by an intense pressure gradient between an anticyclone over the Tibetan Plateau and a low pressure disturbance traveling westward across India (Houze et al., 2011; Rasmussen et al., 2015). This southeasterly flow brought moisture into northwest India and eastern Pakistan, where the moist air stream was lifted as it reached the slopes of the Himalayas. I am interested in gaining a deeper understanding of the dynamics of these events of 2010 and 2014, as well as other similar events (e.g. Rahmatullah (1952) described CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 11 a flood in the region during August 1949 that was also related to a southeasterly flow over India due to a mid-tropospheric trough). Two necessary conditions for an extreme precipitation event are upward motion and a sufficient supply of moisture. The events occurred in the western foothills of the Himalayas, a region with a very steep gradient of topography (figure 2.1). Steep topography gradients are well known to be able to produce orographic precipitation when moist air flow impinges on them (Roe, 2005; Smith, 2006). These events occur in a sufficiently warm, humid environment that the precipitation may be convective, at least in part, with some of the vertical motion connected to diabatic heating which allows air parcels to ascend across potential temperature surfaces. At the same time, upper-level disturbances can cause ascent through quasi-adiabatic potential vorticity dynamics. I attempt here to quantify the roles of each of these processes in the 2010 and 2014 events. The events of 2010 were extensively studied in Martius et al. (2013) and Galarneau et al. (2012). It was concluded that the transport and convergence of moist air into the flood region was driven by monsoonal low-level flow features and that positive potential vorticity anomalies at upper levels, reaching Pakistan from the extratropics, induced a surface wind field that had a significant component directed orthog- onal to the topographic barrier. It was also suggested that the upward motion was mainly driven by the forcing of topography and that forced quasi-geostrophic ascent from the upper-level large-scale flow was fairly weak. In this chapter, I extend these two studies in three ways. First, I perform a more in-depth analysis of the factors influencing large-scale vertical motion in greater detail for the 2010 event, including examining the vertical profiles of vertical motion attributable to different factors via quasi-geostrophic omega equation. Second, I apply the same approach to the 2014 event. Third, I place both events in longer historical context by examining the association of extreme precipitation events over a ten-year period with the factors identified as likely causal influences in the 2010 and 2014 events. The quasi-geostrophic omega equation (Clough et al., 1996; Gray and Dacre, 2006) is a useful framework for understanding and quantifying the factors associated with vertical motion outside the deep tropics. While the assumptions of CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 12 quasi-geostrophic theory are not technically valid in this application, due to the large topographic variation in the region of interest as well as other possible vio- lations, it is nonetheless a useful exercise to apply the theory and see how well it works. The results in section 2.4 demonstrate that the omega equation captures the dynamics quite well. A great advantage of the quasi-geostrophic omega equation is that it is linear, allowing for direct decomposition of the vertical motion into components forced by the large-scale quasi-adiabatic dynamics, diabatic heating, and orography. A more exact nonlinear model would not allow such a straightforward decomposition. The inclusion of the contributions of diabatic heating and orography, not considered in previous work, allows for a direct comparison with the actual vertical velocity and thus provides confirmation of the validity of using this model for these events, as well as a more complete description of the vertical motion. These precipitation events involve deep convection, large diabatic heating in the troposphere, and thus vertical motion directly associated with that heating in the omega equation. What is not so easily apparent is the role of each of the possible factors in causing the convection. One possibility is that the large scale circulation induces upward motion that forces the convection. Another possibility is that when surface winds are aligned towards the topographic barrier, the upward motion forced mechanically near the surface then triggers the convection. To fully understand what is driving the vertical motion, it is necessary to understand the interactions of the large-scale circulation and topographically forced lifting with the convective heating. The current analysis is limited to analyzing observational data, takes the heating rate as a given, and thus cannot explicitly determine what causes that heating. However, the analysis developed here is used to provide forcing terms which are used in the modeling study by Nie et al. (2016), using the column quasi-geostrophic method of Nie and Sobel (2016) in order to more directly separate the influences of causal understanding of the controls exerted by orographic lifting and upper- level disturbances on the convection. Here I establish, as necessary prerequisites to that analysis, that the convection is the essential component of both the 2010 and 2014 events, in that the diabatic heating is the dominant forcing term in the omega CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 13 equation. I also show that the magnitude of the vertical motion directly forced by orographic lifting is consistently larger than that of the synoptic forcing due to the upper-level disturbances, which suggests that the orographic forcing is the more important influence on the convection. Additionally, the full three-dimensional omega inversion carried out here compares well to the single-wavenumber inversion in Nie et al. (2016), which gives additional confidence to the usefulness of the single- wavenumber inversion. In the rest of this chapter I focus on the extreme rainfall events of September 4-17, 2014, and on the two three-day extreme rainfall events of July 20-23 and 27- 30, 2010, referred to hereafter as the first and second event of 2010, respectively. The data that are used are discussed in section 2.2, a description of the three flood events and the moisture transport is given in section 2.3, diagnoses of the influences on vertical motion using the quasi-geostrophic omega equation are given in section 2.4, analysis of a longer historical record to place the 2010 and 2014 events in context is in section 2.5, and concluding remarks are given in section 2.6.

2.2 Data

The ERA-Interim reanalysis dataset (Dee et al., 2011) was used for the analysis discussed in this chapter. Most of the ERA-Interim fields that were used have a 6-hourly temporal resolution and a spatial resolution of 0.7◦. The ERA-Interim precipitation field used is the 12-hour ECMWF forecast, which is available at 12- hourly temporal resolution. The ERA-Interim precipitation was also compared to the 3B42 Tropical Rainfall Measuring Mission (TRMM) precipitation data, which has a 3-hourly temporal resolution and a 0.25◦ spatial resolution (Huffman et al., 2001, 2007). A flood domain used for area-averaged time-series calculations was defined as the region from 70◦ to 77◦ longitude and 30◦ to 37◦ latitude. This region can be seen in figure 2.1. CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 14

m 50 7000

45 6000 40 5000 35 4000 30 3000 25 2000 20

15 1000

10 0 50 60 70 80 90 100

Figure 2.1: Topography map. The black rectangle represents the ﬂood region and the blue outlines the border of Pakistan.

2.3 Description of ﬂood events

Figure 2.2 shows the three-day accumulated precipitation of both 2010 events and the 2014 event for both the ERA-Interim and TRMM datasets. Both the ERA- Interim and TRMM datasets show extreme rainfall totals in the respective flood domains for all three events and there is relatively good spatial agreement between the two datasets. One discrepancy is that TRMM shows less rainfall than does ERA-Interim for the 2010 first event. The maximum total rainfall for a single grid point in the flood domain for the 2010 first event was 196 mm and 219 mm from ERA-Interim and TRMM, respectively; the maximum total rainfall for a single grid point for the 2010 second event was 212 mm and 310 mm; and the maximum total rainfall for a single grid point in the flood domain for the 2014 event was 212 mm and 430 mm. The differences in the maxima between the two datasets may be due in part to the TRMM data’s higher spatial resolution than the ERA-Interim data. CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 15

(a) ERA-Interim 2010 First Event (b) ERA-Interim 2010 Second Event (c) ERA-Interim 2014

(d) TRMM 2010 First Event (e) TRMM 2010 Second Event (f) TRMM 2014

0 50 100 150 200 250 mm

Figure 2.2: Three-day accumulated precipitation. (a)-(c) are for ERA-Interim and (d)-(f) is for TRMM. (a) and (d) are for the 2010 First event: 07-20-10 to 07-23-10. (b) and (e) are for the 2010 Second Event: 07-27-10 to 07-30-10. (c) and (f) are for the 2014 Event: 09-04-14 to 09-07-14. The black rectangles deﬁne the domain used for time series calculations.

2.3.1 2010 ﬁrst event: 07-20-10 to 07-23-10

Figure 2.3(a) shows area-averaged time series of precipitation and column precipitable water during July 2010. Prior to the first precipitation event, a heat low was present to the northwest of Pakistan (Martius et al., 2013). This region of low pressure can be seen in the 500-hPa height anomalies shown in figure 2.4(a) along with a high-pressure anomaly located over the Bay of Bengal. These low and high pressures led to southwesterlies that transported moisture from the Arabian Sea into the flood region. The precipitation event commenced on July 20th and the precipitable water rose above 35 mm.

2.3.2 2010 second event: 07-27-10 to 07-30-10

Between July 25 and 28, a low pressure system traveled from the Bay of Bengal westward across India to the Arabian Sea, while a weaker low pressure system formed CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 16

(a) 2010 Events 70 50

60 45

50 40

40 35

30 30 PW (mm) 20 25 Precip (mm/day) 10 20

0 15 07/15 07/20 07/25 07/30

(b) 2014 Event 70 50

P 60 ERA-Interim 45 P TRMM 50 PW 40 40 35

30 30 PW (mm) 20 25 Precip (mm/day) 10 20

0 15 08/26 08/31 09/05 09/10

Figure 2.3: Time series of the area averaged ERA-Interim precipitation, TRMM precipitation, and precipitable water. (a) 2010 events, (b) 2014 event. over the Bay of Bengal and an extreme high pressure anomaly was located over the Tibetan Plateau and northern India (Houze et al., 2011). These systems (seen in figures 2.4(b) and 2.5) provided a very strong pressure gradient which resulted in southeasterly flow that transported moisture from the Bay of Bengal into the flood region (Martius et al., 2013; Galarneau et al., 2012)). These large pressure gradients (as well as the pressure gradients in the first 2010 event) are very unusual in this region. Romatschke and Houze (2010) found that for typical rainstorms in the western Himalayan foothills, dry air advected into the region from the Afghan Plateau surrounds intense convective clouds and does not permit their growth into larger storms with large precipitation areas. This stands in contrast to this event, where the large pressure gradient brought an extreme amount of moisture into the region and allowed for very large storms to develop. As seen in figure 2.3(a), the CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 17 strong pressure gradient resulted in a dramatic increase in area-average precipitable water to 45 mm. The very large amount of precipitable water can also be seen in figure 2.4(e).

-25

-50

(d) 2010-1: PW (e) 2010-2: PW (f) 2014: PW mm 30

-10

-20

-30

Figure 2.4: Three day average height anomalies of the 500-hPa surface (top) and precipitable water anomalies (bottom). (a) and (d) 2010 First Event: 07-20-10 to 07-23-10. (b) and (e) 2010 Second Event: 07-27-10 to 07-30-10. (c) and (f) 2014 Event: 09-04-14 to 09-07-14.

2.3.3 2014 event: 09-04-14 to 09-07-14

Figure 2.3(b) shows area-averaged time series of precipitation and precipitable water during September 2014. Similar to the 2010 events, the evolution of precipitable water shows pre-moistening for several days before the onset of rainfall, with the precipitable water peaking during the middle of the precipitation events and then decreasing. Figure 2.4(f) shows that there was anomalously high precipitable water over all of Pakistan, which is similar, though less intense, to the state during the second event of 2010 (ﬁgure 2.4(e)). CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 18

(a) 07-24-10 (b) 07-25-10 (c) 07-26-10

(d) 07-27-10 (e) 07-28-10 (f) 07-29-10

-100 -80 -60 -40 -20 0 20 40 60 80 100

Figure 2.5: Sequence of maps showing the evolution of one day average height anomalies of the 500-hPa surface and one day average moisture ﬂux at 700-hPa (arrows) from 07-24-10 to 07-29-10.

Figure 2.4 (a-c) also shows large variability in the height field. The first event of 2010 has a northwest-southeast dipole, the second event of 2010 has a southwest- northeast dipole, and the 2014 event has a west-east dipole. These dipoles are consistent with the low level flow which transported moisture into the flood region: the moisture for the first event of 2010 came form the Arabian sea, while the moisture for the second event of 2010 and the 2014 events came from the Bay of Bengal (figures 2.5 and 2.6). Figure 2.6 shows the time evolution of the 500 hPa height field anomaly along with the 700 hPa moisture flux. From 08-31-14 to 09-03-14 there was a similar pressure configuration to the second event of 2010, with a strong depression moving westward over India and a high pressure anomaly over the Tibetan Plateau, which resulted in southeasterlies transporting moisture from the Bay of Bengal into India and Pakistan and the area-average precipitable water in the flood region increasing from roughly 20 mm to 35 mm (figure 2.3(b)). The similarity of the evolution of CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 19

(a) 08-31-14 (b) 09-01-14 (c) 09-02-14

(d) 09-03-14 (e) 09-04-14 (f) 09-05-14

-100 -50 0 50 100

Figure 2.6: Sequence of maps showing the evolution of one day average height anomalies of the 500-hPa surface (colors) and one day average moisture flux at 700-hPa (arrows) from 08-31-14 to 09-05-14. this flow pattern can be seen in comparing figures 2.6 and 2.5. The Tibetan anticyclone dissipated in the 2014 event instead of persisting like the 2010 event, but the position and timing of the transit of the low pressure across India is very similar. The moisture transport induced by the flow in the 2014 event can be seen in figure 2.7, which shows that a diffuse area of anomalously high precipitable water over the Indian subcontinent, as well as over the Bay of Bengal and Arabian Sea, was transported northwest and became concentrated over Pakistan. Subsequent to the low pressure transit, the high pressure anomaly weakened and a new depression formed over the Bay of Bengal. As discussed below, a key driver of these extreme precipitation events is low- level flow oriented towards the Himalayan mountains which results in orographic lifting. Martius et al. (2013) found that there was a positive upper-level Potential Vorticity (PV) anomaly to the north of Pakistan during both events of 2010. They CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 20

(a) 08-31-14 (b) 09-01-14 (c) 09-02-14

(d) 09-03-14 (e) 09-04-14 (f) 09-05-14

-30 -20 -10 0 10 20 30

Figure 2.7: Sequence of maps showing the evolution of one day average precipitable water anomalies from 08-31-14 to 09-05-14. further performed a piecewise PV inversion which showed that these PV anomalies resulted in a lower-tropospheric wind ﬁeld aligned perpendicular to the Himalayan mountains in northern Pakistan. Figure 2.8 shows the upper-level PV during all three events. Similar to the 2010 events, there was a positive PV anomaly to the north of Pakistan during the 2014 event. While I have not performed a PV inversion, the similar PV anomaly during the 2014 event suggests that the upper-level PV may have also led to low-level ﬂow oriented towards the mountains. This examination of PV is further analyzed in section 2.5. CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 21

7/20/10 7/21/10 7/22/10 50 50 50 40 40 40 30 30 30 20 20 20 10 10 10

40 60 80 100 40 60 80 100 40 60 80 100

7/27/10 7/28/10 7/29/10 50 50 50 40 40 40 30 30 30 20 20 20 10 10 10

40 60 80 100 40 60 80 100 40 60 80 100

9/4/14 9/5/14 9/6/14 50 50 50 40 40 40 30 30 30 20 20 20 10 10 10

40 60 80 100 40 60 80 100 40 60 80 100

0 1 2 3 4 5 6 7 8 PVU

Figure 2.8: Potential Vorticity at θ = 330K during the three events. The top row shows the ﬁrst events of 2010, the middle row shows the second event of 2010, and the bottom row shows the 2014 event. PVU=10−6 K m2 kg−1 s−1 .

2.4 Quasi-geostrophic Omega Equation

The quasi-geostrophic omega equation is a diagnostic equation for the quasi-geostrophic pressure vertical velocity, ω:

2 2 2 f0 ∂ f0 ∂ 1 2 ∇ + 2 ω = vg · ∇ ∇ Φ + f σ ∂p σ ∂p f0 1 ∂Φ + ∇2 v · ∇ − σ g ∂p κ − ∇2Q (2.1) σp CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 22

◦ RT0 dlnθ0 where f is the coriolis parameter, f0 here is f at a latitude of 33.5 , σ = − p dp is κ p0 the static stability, R is the gas constant, T is temperature, θ = T p is potential temperature, v = 1 kˆ×∇Φ is the geostrophic velocity, Φ is the geopotential, κ = R , g f0 cp 2 cp is the specific heat, ∇ is the horizontal Laplacian, and Q is the heating rate. The first term on the right hand side of Eq. (2.1) represents differential vorticity advection, the second term is the horizontal Laplacian of temperature advection, and the third term is the horizontal Laplacian of diabatic heating. The first two terms can be combined to yield the total forcing by PV advection (Trenberth, 1978) and I shall refer to them as contributions from the large-scale circulation, or as synoptic forcing. The right hand side of Eq. (2.1) can be computed solely from the geopotential, Φ, and the heating rate, Q. Φ is available in the ERA-Interim reanalysis, but Q is not. Q, therefore, is diagnosed from the temperature tendency equation: ∂ ∂Φ κQ + v · ∇ − − σω˜ = (2.2) ∂t g ∂p p whereω ˜ is the actual pressure vertical velocity, which need not be identical to the quasi-geostrophic one, ω, derived from (2.1). Here I obtainω ˜ from the ERA-Interim reanalysis. Equation (2.1) was inverted for the three flood events between 550 hPa and 175 hPa using finite-differences for the derivatives1 and Stone’s method, also known as the strongly implicit procedure, (Stone, 1968) to invert the Laplacian on the left side of the equation. Stone’s method is an iterative procedure to approximate the LU decomposition of sparse matrices arriving from the discretization of elliptical partial differential equations. In order to decompose ω, the inversion is first carried out with only the first two forcing terms on the right hand side of equation 2.1 (referred to as the contribution of the synoptic advection terms) and a lower boundary condition of ω set to zero. Secondly, the inversion is carried out with only the third term on the right hand side of equation 2.1 (referred to as contribution of the convective heating

1The ﬁrst derivatives were approximated with standard second-order diﬀerences and the Lapla- cians were approximated using a least-squares polynomial approximation to obtain a smoother solution. CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 23 term) and a lower boundary condition of ω set to zero. Thirdly, the inversion is carried out with no forcing terms on the right hand side of equation 2.1 (referred to as the contribution of the boundary condition) and a lower boundary condition of

ω set to a topographic omega, ωqg(ps), which is described below. The decomposition of ω is, therefore,

ω = ωPV + ωQ + ωBC (2.3) where ωPV is the component forced by the advection terms, ωQ is the component forced by the heating, and ωBC is the component forced by the lower boundary condition. The lower boundary of 550 hPa was chosen because the flood regions have a very large topographic gradient inside them which leads to time-mean surface pressures ranging from 990 hPa to 585 hPa. Choosing a lower boundary at 550 hPa ensures that the entire domain is above the surface.2 The upper boundary of 175 hPa was chosen as a nominal tropopause. The domain used to perform the inversion was ◦ ◦ ◦ ◦ from 0 to 55 latitude and 25 and 100 longitude. ωqg was set to zero at the horizontal boundaries and at the upper boundary. The horizontal domain size is large enough that the horizontal boundary conditions have no effect on the solution in the flood region. The resolution used in the inversion is the same as the resolution of the ERA- Interim data, which has horizontal resolution of 0.7◦ and vertical resolution of 25 hP a in the lower troposphere and 50 hP a in the mid-troposphere.

The topographic vertical velocity, w(ps), is computed using the geostrophic velocities at the surface:

w(ps) = vg(ps) · ∇h (2.4) where vg(ps) is the geostrophic velocity linearly interpolated to the local surface pressure, ps, and h is the height of the topography. The topographic vertical velocity is then converted to the topographic omega using the hydrostatic approximation:

ω(ps) = −ρgw(ps) (2.5)

2An alternative approach is detailed in section 2.4.1 CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 24

In the presence of a sloping lower boundary, the natural boundary condition to use is the topographically forced vertical velocity by the geostrophic wind at a level close to the surface. Here I consider the appropriate level to use for this purpose. Figures 2.9 (a)-(d) show the magnitude and direction of the reanalysis and geostrophic velocities as a function of the pressure above the surface. While the reanalysis velocities are well approximated by the geostrophic velocities in the free troposphere, there is clearly a planetary boundary layer (PBL) near the surface where frictional effects cannot be neglected and the velocity is not geostrophic. Figure 2.9 (e) shows a comparison of the reanalysis vertical velocity at the surface, the topographic forced vertical velocity by the surface reanalysis winds, and the topographic forced vertical velocity by the surface geostrophic winds. The reanalysis vertical velocity and the topographic forced vertical velocity by the surface reanalysis winds closely match and show a strong diurnal cycle with no visible signal during the flood events. Due to the mismatch of the reanalysis and the geostrophic winds at the surface, the topographic forced vertical velocity by the surface geostrophic winds do not match the others and is the only one to have an upward vertical velocity signal during the flood events. Figure 2.9 (f) shows a comparison of the reanalysis vertical velocity at the top of the PBL, the topographic forced vertical velocity by the reanalysis winds at the top of a nominal PBL, defined as a level 150 hPa above the surface, and the topographic forced vertical velocity by the geostrophic winds at the top of the PBL. Now, all of the velocities match well and show a positive vertical velocity signal during the flood events. Other PBL heights were tested (not shown) and a height of 150 hPa was found to deliver the best match. It is high enough to ensure that the reanalysis winds are well approximated by the geostrophic winds and low enough to ensure that the reanalysis vertical velocity matches the topographic forced vertical velocity. Therefore, the topographic forced vertical velocity by the geostrophic winds at a PBL height of 150 hPa was used as the lower boundary condition for the inversion of the omega equation.

ω(ps) is deﬁned at the top of the PBL. This level ranges from a pressure of CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 25

(a) First Event: Magnitude (b) First Event: Direction (c) Second Event: Magnitude (d) Second Event: Direction 400 400 400 400 Reanalysis Geostrophic 300 300 300 300

200 200 200 200

100 100 100 100

Pres above surface (hPa) 0 Pres above surface (hPa) 0 Pres above surface (hPa) 0 Pres above surface (hPa) 0 0 10 20 30 0 100 200 0 10 20 30 0 100 200 Wind Speed (m/s) Wind Direction (Deg) Wind Speed (m/s) Wind Direction (Deg)

(e) w at surface 0.04 0.03 0.02 0.01 0 w (m/s) -0.01

-0.02 Reanalysis Topo Reanalysis Topo Geostrophic -0.03 07/11 07/18 07/25 08/01 08/08

(f) w at top of PBL (150 hPa above surface) 0.04 0.03 0.02 0.01 0 w (m/s) -0.01 -0.02 Reanalysis Topo Reanalysis Topo Geostrophic -0.03 07/11 07/18 07/25 08/01 08/08

Figure 2.9: Top row: Area-average reanalysis (red) and geostrophic (blue) velocities as a function of pressure above the surface for the peak of the first event of 2010 (07-22-10 0000), (a) and (b), and the peak of the second event of 2010 (07-29-10 0600), (c) and (d). (a) and (c) show the magnitude of the velocity and (b) and (d) show the velocity direction. Middle and bottom rows: reanalysis vertical velocity (blue) as well as topographic forced vertical velocity using the reanalysis wind (red) and geostrophic wind (yellow). (e) is for the vertical velocity at the surface and (f) is for the vertical velocity at the top of the boundary layer, defined as 150 hPa above the surface. The gray bars indicate the precipitation events. roughly 840 hPa to 440 hPa, so using it as the lower boundary condition at 550 hPa is somewhat artificial. Nevertheless, it is a simple method for attempting to include the effects of orographic forcing. Figures 2.10(a) and 2.10(e) show area-averaged profiles of w from inverting the omega equation, split into the contributions from the synoptic advection terms, the convective heating term, and the boundary condition, as well as the reanalysis w for the first event of 2010. Shown are point-in-time profiles at 07-22-10 0000 (which CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 26 was the time of maximum vertical velocity for this event) and a three-day average over the whole event from 07-20-10 to 07-23-14. Both the point-in-time and time- averaged solutions match the reanalysis profile well, with the point-in-time solution overestimating slightly in the mid-troposphere. In the point-in-time solution, while the contribution of the heating term is greatest, the advection terms contribute significantly, with the advection terms contribution being roughly half of the heating term contribution at mid-levels. For the time-averaged solution, the advection terms’ net contribution is of the same order as the heating term contribution. The effect of the topographic lower boundary condition decays with height, as expected, and the boundary condition underestimates the reanalysis vertical velocity at 550 hPa. Similarly, figures 2.10(b) and 2.10(f) show area-averaged profiles of w from inverting the omega equation as well as the reanalysis w for the second event of 2010. Again, shown are point-in-time profiles at 07-29-10 0600 (which was the time of maximum vertical velocity for this event) and a three-day average over the whole event from 07-27-10 to 07-30-14. Both the point-in-time and three-day average solutions again match the reanalysis profiles closely. In contrast to the first event, the heating term dominates to a larger extent. In particular, the contribution of the advection terms in the point-in-time solution is much weaker than in the first event. Figures 2.10 (c) and 2.10 (g) show area-averaged profiles of w from inverting the omega equation as well as the reanalysis w for the 2014 event. Shown are point-in- time profiles at 09-05-14 0600 (which was the time of maximum vertical velocity for this event) and a three-day average over the whole event from 09-04-14 to 09-07-14. As with the 2010 events, the overall agreement between the total solution and the reanalysis profile is quite good. The heating term completely dominates in both the point-in-time and time-averaged solutions, which is similar to the second event of 2010 but to an even greater extent. For all three events, the magnitude of the lower boundary condition on the vertical velocity is of the same order as the interior maxima associated with the heating term. This closeness in magnitude suggests that the topographic forced lifting of CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 27

(a) 07-22-10 0000 (b) 07-29-10 0600 (c) 09-04-14 0600 200 200 200

250 250 250

300 300 300

350 350 350

400 400 400 Pressure (hPa) Pressure (hPa) Pressure (hPa) 450 450 450

500 500 500

550 550 550 0 0.05 0.1 0.15 0 0.05 0.1 0.15 0 0.05 0.1 0.15 w (m/s) w (m/s) w (m/s)

(e) 3-day Average: 2010 First Event (f) 3-day Average: 2010 Second Event (g) 3-day Average: 2014 Event 200 200 200

250 250 250

300 300 300

350 350 350

400 400 400 Pressure (hPa) Pressure (hPa) Pressure (hPa) 450 450 450

500 500 500

550 550 550 0 0.02 0.04 0.06 0 0.02 0.04 0.06 0 0.02 0.04 0.06 w (m/s) w (m/s) w (m/s)

Advection Terms Heating Boundary Condition All Terms Reanalysis

Figure 2.10: Area average vertical velocity, w, profiles from inverting the omega equation. Shown are the contribution from the advection terms (blue), the heating term (red), the boundary condition (yellow), the sum of all terms (purple), and the Reanalysis vertical velocity (black). The top plots are for points-in-time and the bottom plots are three-day averages during each event. 2010 First Event: (a) 07-22-10 0000 and (e) three-day average from 07-20-10 and 07-23-14. 2010 Second Event: (b) 07-29-10 0600 and (f) three-day average from 07-20-10 and 07-23-14. 2014 Event: (c) 09-04-14 0600 and (g) three-day average from 09-04-14 to 09-07-14. the lower boundary condition may be a significant trigger for the convective heating. Further investigation of this inference using cloud-resolving model simulations of the 2010 events is presented by Nie et al. (2016), where we found that the lower boundary condition is indeed the major trigger of convection during the events. Figure 2.11 shows the time evolution spanning both 2010 events of the w profiles from inverting the omega equation and the reanalysis. Shown are the sum of the CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 28 contributions from the two advection terms (which captures the effect of the large scale circulation), the contribution of the heating term, the sum of all terms, and the reanalysis. The total solution matches the reanalysis w well for both events, with the exception of the first weak peak of the first event which the solution underestimates. As seen in the previous two figures, the advection terms, and thus the large scale circulation, have a much larger effect during the first event than the second event, which was also found by Martius et al. (2013). Figure 2.12 shows the time evolution of the w profiles from inverting the omega equation and the reanalysis for the 2014 event. Like the second event of 2010, there is no discernible signal in the advection terms during the flood event, with all of the vertical velocity being forced by heating.

(a) Adv Terms 200 300 400 500 Pressure (hPa) 07/11 07/16 07/21 07/26 07/31 (b) Heating 200 300 400 500 Pressure (hPa) 07/11 07/16 07/21 07/26 07/31 (c) All Terms 200 300 400 500 Pressure (hPa) 07/11 07/16 07/21 07/26 07/31 (d) Reanalysis 200 300 400 500 Pressure (hPa) 07/11 07/16 07/21 07/26 07/31

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 m/s

Figure 2.11: 2010 event. Area average vertical velocity through time from inverting the omega equation. Shown are the contribution from (a) the advection terms , (b) the heating term, (c) the sum of all terms, and (d) the Reanalysis vertical velocity. The black lines bound the time of the ﬂood events. CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 29

(a) Adv Terms 200 300 400 500 Pressure (hPa) 08/27 08/28 08/29 08/30 08/31 09/01 09/02 09/03 09/04 09/05 09/06 09/07 09/08 09/09 (b) Heating 200 300 400 500 Pressure (hPa) 08/27 08/28 08/29 08/30 08/31 09/01 09/02 09/03 09/04 09/05 09/06 09/07 09/08 09/09 (c) All Terms 200 300 400 500 Pressure (hPa) 08/27 08/28 08/29 08/30 08/31 09/01 09/02 09/03 09/04 09/05 09/06 09/07 09/08 09/09 (d) Reanalysis 200 300 400 500 Pressure (hPa) 08/27 08/28 08/29 08/30 08/31 09/01 09/02 09/03 09/04 09/05 09/06 09/07 09/08 09/09

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 m/s

Figure 2.12: 2014 event. Area average vertical velocity through time from inverting the omega equation. Shown are the contribution from (a) the advection terms , (b) the heating term, (c) the sum of all terms (without the boundary condition), and (d) the Reanalysis vertical velocity. The black lines bound the time of the ﬂood event.

Figure 2.13 shows maps of the large-scale circulation forced w at 350 hPa during the peaks of the three events. As expected, the solution is more active poleward of the flood regions where there are larger wind velocities due to the jet stream. As seen before, only the first event of 2010 has significant forced lifting by the circulation.

2.4.1 Alternative lower boundary

The omega equation inversion described above involved a complication due to the fact that the ﬂood region contains very tall mountains that extend up to 585 hPa. In order to ensure that the entire domain is above the surface, the lower boundary CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 30

(a) 07-22-10 0000 (b) 07-29-10 0600 (c) 09-05-14 0600

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 m/s

Figure 2.13: Map of 350 hPa vertical velocity from inverting the omega equation. Only contributions from the advection terms are included. (a) 07-22-10 0000, (b) 07-29-10 0600, and (c) 09-05-14 0600. was set to 550 hPa and the topographic vertical velocity was applied at this level. An alternative approach that is considered here is to use a lower boundary that is below the surface in some locations. This involves computing a solution below the surface at some locations and setting the forcing terms in Eq. (2.1) to zero below the surface. It was shown in section 2.4 that the geostrophic velocities at 150 hPa above the surface work well when computing the topographic vertical velocity. The alternative approach sets the lower boundary at 700 hPa because this is the level that is roughly 150 hPa above the mean surface pressure in the flood region. With this lower boundary, the boundary condition was defined at each location as either the reanalysis vertical velocity at 700 hPa (if the surface is below 700 hPa) or at the surface (if the surface is above 700 hPa). Figure 2.14 is the same as figure 2.10 but using this alternative approach with the lower boundary at 700 hPa. The profiles show area-averages in the flood region, where only locations above the surface are used in the averaging at each level. Both approaches show that the solutions match the reanalysis velocity profiles well. Both approaches also show that the heating term is of much more important than the advection terms for all events except the first event of 2010. CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 31

(a) 07-22-10 0000 (b) 07-29-10 0600 (c) 09-04-14 0600 200 200 200 250 250 250 300 300 300 350 350 350 400 400 400 450 450 450 500 500 500 Pressure (hPa) 550 Pressure (hPa) 550 Pressure (hPa) 550 600 600 600 650 650 650 700 700 700 0 0.05 0.1 0.15 0 0.05 0.1 0.15 0 0.05 0.1 0.15 w (m/s) w (m/s) w (m/s)

(e) 3-day Average: 2010 First Event (f) 3-day Average: 2010 Second Event (g) 3-day Average: 2014 Event 200 200 200 250 250 250 300 300 300 350 350 350 400 400 400 450 450 450 500 500 500 Pressure (hPa) 550 Pressure (hPa) 550 Pressure (hPa) 550 600 600 600 650 650 650 700 700 700 0 0.02 0.04 0.06 0 0.02 0.04 0.06 0 0.02 0.04 0.06 w (m/s) w (m/s) w (m/s) Advection Terms Heating Boundary Condition All Terms Reanalysis

Figure 2.14: Same as ﬁgure 2.10 except using a lower boundary at 700 hPa as discussed in section 2.4.1.

2.5 Historical comparison

The above analysis suggests that the amount of precipitable water and the topographic forced vertical velocity were the dominant causes of the three flood events. It is useful to determine if the relationship between these forcings and extreme amounts of precipitation in this region found for the 2010 and 2014 events also exists historically. This will also reveal how often the levels of precipitable water, topographic forced lifting, and precipitation rate seen during the flood events occur in this region. To this end, the monsoon seasons were examined from 2004 through 2014. Figure 2.15(a) shows flood-domain averaged precipitation rate for one-day averaged time periods for June though September of the years 2004 though 2014 as CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 32 a function of the amount of precipitable water and the topographic forced vertical velocity. The three flood events examined in this chapter are indicated with black outlines. There is a clear relationship between the precipitation and the other two variables, with days with high levels of precipitable water and topographic forcing corresponding to days with high levels of precipitation.

(a) One-day Average mm/day (b) Three-day Average mm/day 0.15 0.1 25 20

18 0.1 20 16

0.05 14 0.05 15 12

10 0 10 8 Topo w (m/s) Topo w (m/s) 0 6

-0.05 5 4

2 -0.1 -0.05 10 20 30 40 50 10 20 30 40 50 Precip water (mm) Precip water (mm)

Figure 2.15: Average precipitable water and topographic forced vertical velocity. The colors are precipitation rate in mm/day. The ﬁrst event of 2010 is shown with black squares, the second event of 2010 is shown with black diamonds, and the 2014 event is shown with black circles. Time range is June - September 2004-2014. (a) One-day averages, (b) Three-day averages.

Figure 2.15(b) is similar to ﬁgure 2.15(b) but with three-day averages instead of one-day averages. There is again a clear relationship between the precipitation and the other two variables, with the two events of 2010 being particularly extreme in all variables and the 2014 event somewhat weaker. Given that the precipitation in this region is related to the amount of moisture and the topographic forced vertical velocity, a natural followup question to ask is what is causing the high values of topographic forced vertical velocity associated with large amounts of precipitation. As discussed previously, there were positive upper-level PV anomalies to the north of Pakistan during the three events studied in this chapter and the 2010 PV anomalies were found by Martius et al. (2013) to induce low-level winds directed towards the Himalayan mountains in northern Pakistan and thus resulting in topographically forced lifting. CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 33

In order to determine if upper-level PV might be related to other extreme precipitation events in this region, figure 2.16(a) shows the average PV anomaly at a potential temperature of 330K for the 13 days with the highest average topographic forced vertical velocity in the flood region, which represent the highest 1% of the days during the monsoon seasons of 2004 to 2014. There is indeed a region of anomalously high PV to the north and west of the flood region, indicating that positive PV anomalies are associated with the most extreme days of topographic forced vertical velocity. Furthermore, figure 2.16(b) shows the linear regression of PV at 330K onto the average topographic forced vertical velocity in the flood region. Similar to figure 2.16(a), there is a large, well defined region of high regression slopes to the north of the flood region. While I did not perform a PV inversion to quantify this relationship, these results suggest that the upper-level PV is a dominant driver of the topographic forced vertical velocity in this region during the monsoon season.

(a) Top 1% of days (b) Regression 2 0.5

50 50 0.4 1.5 45 45 0.3 40 1 40 0.2 35 0.5 35 0.1 30 30 0 0 25 PVU 25

-0.1 PVU / (m/s) 20 -0.5 20 -0.2 15 -1 15 10 10 -0.3 -1.5 5 5 -0.4

-2 -0.5 40 60 80 100 40 60 80 100

Figure 2.16: (a) Average Potential Vorticity anomaly at θ = 330K for the 13 days with the largest topographic forced vertical velocity in the ﬂood region. (b) Linear regression of Potential Vorticity at θ = 330K onto the topographic forced vertical velocity in the ﬂood region.

Previous studies (Webster et al., 2011; Galarneau et al., 2012; Rasmussen et al., 2015) using the ECMWF Ensemble Prediction System (EPS) have shown the ability to accurately forecast that conditions that favor floods of this type in northeast Pakistan with up to 1-2 weeks lead time. The results shown here that extreme CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 34 precipitation in this region is chiefly associated with moisture influx and topographic lifting could be a physical reason for the ability of the forecasts to predict these types of events.

2.6 Conclusion

Devastating floods in northeast Pakistan and north India occurred in July 2010 and September 2014. These floods were the result of three extreme precipitation events (two in July 2010 and one in September 2014). This chapter has compared the events and attempted to describe the factors that supported the events, specifically the circulation that brought moisture into the region and the driving factors of the upward motion that led to the precipitation. The vertical motion was analyzed through inverting the quasi-geostrophic omega equation, which allowed for the contribution of the large-scale circulation forcing to be quantified. The omega equation solutions matched the reanalysis vertical motion fairly well for all three events. The topographic forced vertical motion was also calculated using the geostrophic winds at the top of the PBL. All three events had anomalously high amounts of moisture in the region due to the configuration of the flow field that transported moisture into the region from either the Bay of Bengal or the Arabian Sea. Large amounts of moisture can induce unusually extreme precipitation events from the orographic forcing due to the large topographic gradient of the Himalayas (Houze et al., 2011). It is found that while all three events had large pre-moistening prior to the onset of rainfall, the 500 hPa height surfaces and moisture sources show differences. The specific flow pattern and moisture source in the 2014 event were similar to those in the second event of 2010. During these events, there was a strong high pressure over the Tibetan plateau that, along with a depression that traveled from the Bay of Bengal northwest across India, caused southeasterlies which transported moisture from the Bay of Bengal onto the continent and into the flood region. In contrast, during the first 2010 event, a high pressure in the Bay of Bengal and a low pressure CHAPTER 2. THE 2010 AND 2014 FLOODS IN INDIA AND PAKISTAN 35 northeast of Pakistan led to southwesterlies and moisture transport northeastward from the Arabian Sea. In contrast to the synoptic analysis, all three events show quite similar features when focusing only on the local air column and performing the quasi-geostrophic omega decomposition. The heating term is dominant, which explains the need for pre-moistening. The topographic forced upward motion is found to be the main triggering factor of the convection, with the synoptic forcing due to vorticity and temperature advection being relatively weak. This is consistent with earlier work of Sanders (1984) which computed the quasi-geostrophic ω for a monsoon depression in 1979 and found that the direct synoptic forcing of ω was only marginally detectible. The conclusion drawn from these three events are also supported by studying historical data of this region. An examination of the monsoon season over eleven years demonstrates that topographic forced ascent and moisture content are the main drivers of extreme precipitation. By identifying common features among those extreme events, the conclusion of this chapter improves our understanding of the dynamics of these events, and highlights the two most relevant environmental factors which regulate their occurrence. CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 36

Chapter 3

The May 2015 ﬂood in Texas and Oklahoma

3.1 Introduction

Floods in India and Pakistan were analyzed in Chapter 2 using the quasi-geostrophic omega equation. It was found for these events that the topographically forced ascent of low-level winds blowing towards the Himalayas was the dominant triggering mechanism of convection, and that the potential vorticity (PV) forcing of the advection terms in the omega equation was relatively weak. To further explore the state-space of convection triggers during subtropical floods, in this chapter I analyze a May 2015 flood event in Texas and Oklahoma in which the PV forcing is dominant and topographic forcing is negligible. More than a week of heavy rainfall preceded record breaking floods which were caused by a slow moving storm system that, along with low-level moisture inflow from the Gulf of Mexico, produced large amounts of precipitation across much of Texas and Oklahoma during the nights of May 24-26, 2015 (Gaskill and Wines, 2015) killing more than 30 people (Associated-Press, 2015). This system also produced deadly tornados in both the US and Mexico (Robbins, 2015). This event occurred during an El Niñoand it is known that an El Niñocan increase springtime precipitation in the southern Great Plains (Lee et al., 2014). CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 37

Wang et al. (2015) analyzed the flood event in the context of this El Niñotelecon- nection in a warmer climate. They conducted an attribution analysis study and concluded that when anthropogenic greenhouse gases are taken into account, there is a significant increase in the El Niño-inducedprecipitation anomalies in Texas and Oklahoma and this had an impact on the May 2015 event. As explained in chapter 2, necessary conditions for extreme precipitation include upward motion and a sufficient supply of moisture. I will again attempt to determine the source of the moisture supply as well as use the quasi-geostrophic omega equation to decompose the vertical velocity during this event. Similar to the India/Pakistan floods, this event involved deep convection, large diabatic heating in the troposphere, and thus vertical motion directly associated with the heating in the omega equation. I will again examine possible factors in causing the convection. There are no large mountains in this region, so topographic forced ascent is not expected to play a role during this event, unlike in the Pakistan/India floods. The upward motion induced by the large-scale PV forcing is then a prime suspect among the possible triggers of the convection. I will first use the observational data, taking the heating rate as a given, to decompose the vertical motion with the omega equation. As was the case in chapter 2, this will allow for the examination of the relative magnitudes of the possible convection triggers, but can not explicitly determine what is causing the convection. In this chapter I will go one step further by performing modeling simulations using the Column Quasi-Geostrophic (CQG) framework introduced in Nie and Sobel (2016) and applied to the 2010 Pakistan flood in Nie et al. (2016). The CQG model can be used to explicitly simulate convection1 when the large-scale forcings are applied. This allows for an explicit attribution of the convection to specific forcings, and not just a suggestion of this attribution that is possible when solely using observational data. Finally, I will describe a climate attribution analysis using the CQG modeling framework. As discussed in the introduction to this part, attribution studies attempt

1Or parameterize convection in the case of a Single Column Model. CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 38 to quantify the impact that climate change had on a weather event. The CQG modeling framework is a useful tool for performing highly conditional attribution analyses. The large-scale dynamics that force the omega equation are taken from the actual extreme event while the background thermodynamic environment are altered for different climate scenarios. A highly-conditional attribution analysis of the Texas/Oklahoma event was performed using the CQG framework with a Cloud Resolving Model. The dry QG forcing of the omega equation is taken from the actual event, while the convection and precipitation are simulated. Three background thermodynamic profiles are compared: present day, a past climate, and a warmer climate derived from coupled climate model projections. In the rest of this chapter I focus on the extreme rainfall event of May 2015 in Texas and Oklahoma. That data that are used are discussed in section 3.2, a description of the flood event and the moisture transport is given in section 3.3, diagnoses of the influences on vertical motion using the quasi-geostrophic omega equation applied to reanalysis data is given in section 3.4, column model simulations and the attribution analysis are discussed in section 3.5, and concluding remarks are given in section 3.6.

3.2 Data

The ERA-Interim reanalysis dataset (Dee et al., 2011) was used for the analysis discussed in this chapter. Most of the ERA-Interim fields that were used have a 6-hourly temporal resolution and a spatial resolution of 0.7◦. The ERA-Interim precipitation field used is the 12-hour ECMWF forecast, which is available at 12- hourly temporal resolution. The ERA-Interim precipitation was also compared to the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center (CPC) quarter-degree Daily U.S. Unified Precipitation Dataset2 (Higgins et al., 1996), which are daily rain gauge data that has been interpolated onto a

2CPC US Uniﬁed Precipitation data provided by the NOAA/OAR/ESRL PSD, Boulder, Col- orado, USA, from their Web site at http://www.esrl.noaa.gov/psd/ CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 39

0.25◦ spatial grid using the algorithm of Xie et al. (2007). A flood domain used for area-averaged time-series calculations was defined as the region from -101◦ to -92◦ longitude and 31◦ to 40◦ latitude. This region can be seen in figure 3.1. An upstream region used for PV averaging in figure 3.2 was defined as the region from -110◦ to -101◦ longitude and 31◦ to 40◦ latitude. This region can be seen in figure 3.4.

3.3 Description of ﬂood event

Figure 3.1 shows the four-day accumulated precipitation during the flood event for the ERA-Interim (reanalysis) and CPC rain gauge datasets. The two datasets match reasonably well and a large region of extreme precipitation can be seen which covers most of Oklahoma and Kansas and parts of Texas, Missouri, Arkansas, and Louisiana. The maximum total rainfall in one location was 144 mm for the reanalysis dataset and 275 mm for the rain gauge data set. The differences in the maxima between the two datasets may be due in part to the rain gauge data’s higher spatial resolution than the reanalysis data Anomalously high precipitation fell in this region over the month of May 2015 (Wang et al., 2015) which likely saturated the soil before the event and caused the extreme rainfall from May 23 to May 26 to lead to a large amount of flooding and damage. Figure 3.2(a) shows area-averaged time series of precipitation (both reanalysis and CPC rain gauge) and column precipitable water. Both the reanalysis and rain gauge data show increased precipitation from May 23 to May 27 with the largest sustained precipitation occurring on May 24. The reanalysis and rain gauge precipitation show good agreement overall. Figure 3.3 shows daily-averaged maps of column precipitable water and 850 hPa wind vectors. At the onset of the event, the low-level wind field brought moisture from the Gulf of Mexico into the flood region. The column precipitable water in the flood region doubled from May 22 to May 24 (figure 3.2(a)). The onset of the rainfall led to a decrease in precipitable water that was partly offset by sustained CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 40

(a) Reanalysis (b) Rain Gauge 45 45

40 40

35 35

30 30

25 25

20 20 -110 -100 -90 -80 -110 -100 -90 -80

0 10 20 30 40 50 60 70 80 90 100 mm

Figure 3.1: Four-day accumulated precipitation from 5/23/15 to 5/26/15. (a) ERA- Interim reanalysis, (b) CPC Rain Gauge data. Blue rectangles: ﬂood region.

(a) Precipitation and Precipitable Water 40 40 Precip - Reanalysis Precip - Gauge PW

20 30 PW (mm) Precip (mm/day)

0 20 05/18 05/20 05/22 05/24 05/26 05/28 05/30

(b) Potential Vorticity 5 PV 4

2 PV (PVU) 1

0 05/18 05/20 05/22 05/24 05/26 05/28 05/30

Figure 3.2: (a) Area-averaged Precipitation (both reanalysis and CPC rain gauge) and Precipitable Water in the flood region. (b) Area-averaged Potential Vorticity at θ = 330K in the upstream region shown in pink in figure 3.4 CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 41 advection of moisture from the Gulf of Mexico by the low-level flow.

5/22 5/23 5/24 55 50 45 40 35 30 25 20

5/25 5/26 5/27 55 50 45 40 35 30 25 20 -120 -100 -80 -120 -100 -80 -120 -100 -80

0 10 20 30 40 50 60 70 mm

Figure 3.3: Sequence of maps showing daily average quantities. Colors: Precipitable Water. Black arrows: 850 hPa wind vectors. Blue rectangle: ﬂood region.

Figure 3.4 shows daily-averaged maps of PV on the 330 K potential temperature surface, 500 hPa heights, and regions of extreme precipitation3. A region of high upper-level PV (and corresponding low 500 hPa height) can be seen over the west coast of the US on May 22. The high PV moves slowly eastward until it covers most of the western half of the US on May 24 and is directly adjacent to the ﬂood region. The high PV stalls at this location and then dissipates while moving towards the northeast. The extreme precipitation in the ﬂood region is highly variable in space and time. Extreme precipitation occurs only in the northwest corner of the region on May 23, over nearly the entire region on May 24, hardly at all on May 25, and only on the eastern edge of the region on May 26.

3Deﬁned as regions with reanalysis precipitation greater than 25 mm/day. CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 42

5/22 5/23 5/24 55 5700 5700 5400 5500 5400 50 5500 5600 5400 5600 5700 5500 45 5700 5600 5700 5800 40 5800 5800 5800 5700 35 5700 5700 5900 30

25 5900

20 5900

5/25 5/26 5/27 55 5500 5600 5600 5600

50 5700 5700 5700 45 5800 5700 5700

40 5800 5800 355800 5900 30 5900 25

20 5900 -120 -100 -80 -120 -100 -80 -120 -1005900 -80

0 2 4 6 8 10 PVU

Figure 3.4: Sequence of maps showing daily average quantities. Colors: Potential Vorticity at θ = 330K. Black contours: height of the 500-hPa surface. Black shading: Areas where the precipitation exceeds 25 mm/day. Blue rectangle: ﬂood region. Pink rectangle: upstream region used for PV averaging in ﬁgure 3.2

Upper-level PV anomalies can reduce the convective stability of the troposphere (Hoskins et al., 1985; Juckes and Smith, 2000). The upward curvature of isentropes in the troposphere related to a moving PV anomaly causes tropospheric ascent ahead of the depressed tropopause and descent behind the depressed tropopause. This ascent ahead of the PV anomaly can result in the development of deep convection through the release of potential instability (Russell et al., 2012). Figure 3.2(b) shows a time-series of PV on the 330 K potential temperature surface averaged over the upstream region shown in figure 3.4. It can be seen that the upstream PV is associated with precipitation in the flood region; upstream PV is very high during the flood event and elevated during May 19-20, which is also a period of relatively high precipitation. Additionally, the reanalysis precipitation is low after 5/26 even though there is an increase in moisture presumably because there is no upper-level CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 43

PV forcing to induce upward motion and precipitation. The strong association between upstream PV and precipitation in this region suggests that the ﬂood event was likely driven by upward motion induced by upper-level PV dynamics. This is further explored in the rest of this chapter.

3.4 Quasi-geostrophic Omega Equation

I analyzed the vertical motion during the India/Pakistan floods in chapter 2 using the quasi-geostrophic omega equation. I perform a similar analysis for the Texas/Oklahoma flood in this chapter and repeat the omega equation here. The quasi-geostrophic omega equation is a diagnostic equation for the quasi- geostrophic pressure vertical velocity, ω: 2 2 2 f0 ∂ f0 ∂ 1 2 ∇ + 2 ω = vg · ∇ ∇ Φ + f σ ∂p σ ∂p f0 1 ∂Φ + ∇2 v · ∇ − σ g ∂p κ − ∇2Q (3.1) σp ◦ where f is the coriolis parameter, f0 here is f at a latitude of 35.5 , σ = κ RT0 dlnθ0 p0 − p dp is the static stability, R is the gas constant, T is temperature, θ = T p is potential temperature, v = 1 kˆ × ∇Φ is the geostrophic velocity, Φ is the geopo- g f0 tential, κ = R , c is the specific heat, ∇2 is the horizontal Laplacian, and Q is the cp p heating rate. The first term on the right hand side of Eq. (3.1) represents differential vorticity advection, the second term is the horizontal Laplacian of temperature advection, and the third term is the horizontal Laplacian of diabatic heating. The first two terms can be combined to yield the total forcing by PV advection (Trenberth, 1978) and I shall refer to them as contributions from the large-scale circulation, or as synoptic forcing. The right hand side of Eq. (3.1) can be computed solely from the geopotential, Φ, and the heating rate, Q. Φ is available in the ERA-Interim reanalysis, but Q is not. Q, therefore, is diagnosed from the temperature tendency equation: ∂ ∂Φ κQ + v · ∇ − − σω˜ = (3.2) ∂t g ∂p p CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 44 whereω ˜ is the actual pressure vertical velocity, which need not be identical to the quasi-geostrophic one, ω, derived from (3.1). Here I obtainω ˜ from the ERA-Interim reanalysis. Equation (3.1) was inverted for the flood event between 1000 hPa and 175 hPa using finite-differences for the derivatives4 and Stone’s method, also known as the strongly implicit procedure, (Stone, 1968) to invert the Laplacian on the left side of the equation. Stone’s method is an iterative procedure to approximate the LU decomposition of sparse matrices arriving from the discretization of elliptical partial differential equations. In order to decompose ω, the inversion is first carried out with only the first two forcing terms on the right hand side of equation 3.1 (referred to as the contribution of the synoptic advection terms) and a lower boundary condition of ω set to zero. Secondly, the inversion is carried out with only the third term on the right hand side of equation 3.1 (referred to as contribution of the convective heating term) and a lower boundary condition of ω set to zero. Thirdly, the inversion is carried out with no forcing terms on the right hand side of equation 3.1 (referred to as the contribution of the boundary condition) and a lower boundary condition of 5 ω set toω ˜(ps) from the reanalysis . The decomposition of ω is, therefore,

ω = ωPV + ωQ + ωBC (3.3)

where ωPV is the component forced by the advection terms, ωQ is the component

forced by the heating, and ωBC is the component forced by the lower boundary condition. Figures 3.5(a) and 3.5(b) show area-averaged proﬁles of ω from inverting the

4The ﬁrst derivatives were approximated with standard second-order diﬀerences and the Lapla- cians were approximated using a least-squares polynomial approximation to obtain a smoother solution.

5This is in contrast to the topographic boundary condition used in chapter 2 due to the fact that for the Texas/Oklahoma case studied here, there are no large topographic gradients in the flood region. The choice of boundary conditions does not significantly alter the results and was chosen to provide a better fit near the surface. CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 45 omega equation, split into the contributions from the synoptic advection terms, the convective heating term, and the boundary condition, as well as the reanalysis ω for the flood event6. Shown are point-in-time profiles at May 24 0000 (which was the time of maximum vertical velocity for the event) and a four-day average over the whole event from May 23 to May 26. The time-averaged solution matches the reanalysis profile remarkably well, while the point-in-time solution matches the shape and magnitude in the lower troposphere well and underestimates the reanalysis ω by roughly 20% in the upper troposphere.

(a) 4-day avg: 5/23 - 5/26 (b) 05-24-15 0000 100 100

200 200

300 300

400 400

500 500

600 600 Pressure (hPa) Pressure (hPa) 700 700

800 800

900 900

1000 1000 -4 -3 -2 -1 0 1 -20 -15 -10 -5 0 5 ω (hPa/hr) ω (hPa/hr) Advection Terms Heating Boundary Condition All Terms Reanalysis

Figure 3.5: Area average pressure vertical velocity, ω, profiles from inverting the omega equation. Shown are the contribution from the advection terms (blue), the heating term (red), the boundary condition (yellow), the sum of all terms (purple), and the Reanalysis vertical velocity (black). (a) Four-day average during the flood. (b) Peak of the flood: 05-24-15 0000

For the time-averaged solution, the heating term component is much larger than the advection terms in the middle and upper troposphere, while the component of the advection terms is larger in the lower troposphere. The relatively large component of the advection terms in the lower troposphere is intriguing when thinking

6I am plotting ω here as opposed to w (which was used in chapter 2). Negative ω corresponds to rising motion. CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 46 about the triggering of convection, because convection has been shown to be more sensitive to temperature and moisture perturbations in the lower troposphere than to perturbations in the upper troposphere (Tulich and Mapes, 2010). For the point- in-time solution, the heating term component is roughly twice as large as advection terms. In contrast to the India/Pakistan study in chapter 2, the boundary condition component is negligible. Figure 3.6 shows daily-averaged profiles of ω, similar to figure 3.5. The shape and magnitude of the QG solution matches the reanalysis profile fairly well for all days. Just before and during the onset of the event (May 22 and 23) the heating component is small and the advection terms component is largest, with a maximum in the lower troposphere. The convection commences on May 24, which is by far the day of the strongest ω and the heating term component is largest. This sequence further strengthens the hypothesis that low-level forcing from the advection terms leads to the triggering of convection. May 25 has only weak vertical motion consistent with a pause in the precipitation (figures 3.2 and 3.4). On the final day of the event, May 26, ω is solely driven by heating, with the advection term component near zero. Figure 3.7 shows the time evolution of the ω profiles from inverting the omega equation and the reanalysis. Shown are the sum of the contributions from the two advection terms (which captures the effect of the large scale circulation), the contribution of the heating term, the sum of all terms, and the reanalysis. The total QG solution matches the reanalysis very well in both time and vertical structure. Both the advection terms component and the heating component are significant during the flood event as well as during the previous periods of upward motion (May 17 and May 20). Additionally, the peaks in the advection terms component appear to lead the peaks in the heating component, which further suggests a triggering of convection by the advection terms forcing. Analogously to the decomposition of ω, it is possible to decompose the precipitation. Making the approximation that adiabatic cooling due to ascent is balanced by latent heating due to condensation, I can estimate the precipitation associated CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 47

5/22 5/23 5/24 100 100 100 200 200 200 300 300 300 400 400 400 500 500 500 600 600 600 700 700 700 Pressure (hPa) Pressure (hPa) Pressure (hPa) 800 800 800 900 900 900 1000 1000 1000 -10 -5 0 -10 -5 0 -10 -5 0 ω (hPa/hr) ω (hPa/hr) ω (hPa/hr)

5/25 5/26 5/27 100 100 100 200 200 200 300 300 300 400 400 400 500 500 500 600 600 600 700 700 700 Pressure (hPa) Pressure (hPa) Pressure (hPa) 800 800 800 900 900 900 1000 1000 1000 -10 -5 0 -10 -5 0 -10 -5 0 ω (hPa/hr) ω (hPa/hr) ω (hPa/hr)

Advection Terms Heating Boundary Condition All Terms Reanalysis

Figure 3.6: Daily and area averaged pressure vertical velocity, ω, profiles from inverting the omega equation. The colors are the same as in figure 3.5 with the components of ω: c Z σp P ≈ − p ωdp (3.4) gLc R where cp is the specific heat at constant pressure, g is the acceleration due to gravity, and Lc is the latent heat of condensation. Equation 3.4 permits negative values of precipitation for positive (descending) ω, which I ignore. Precipitation associated with each component of ω is calculated using equation 3.4 with the appropriate ω component. The precipitation decomposition is shown in figure 3.8 along with the reanalysis precipitation. The precipitation estimated with the total QG ω solution matches the reanalysis precipitation reasonably well, though it overestimates on May 20 and May 23 and underestimates on May 26. It also overestimates on May 29, which is a day where the rain gauge precipitation was higher than the reanalysis. The precipitation forced by the advection terms and the precipitation forced by the heating are both significant during the flood event, with the precipitation forced CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 48

(a) Advection Terms 200 400 600 800

Pressure (hPa) 1000 05/16 05/18 05/20 05/22 05/24 05/26 05/28 05/30 (b) Heating 200 400 600 800

Pressure (hPa) 1000 05/16 05/18 05/20 05/22 05/24 05/26 05/28 05/30 (d) All Terms 200 400 600 800

Pressure (hPa) 1000 05/16 05/18 05/20 05/22 05/24 05/26 05/28 05/30 (e) Reanalysis 200 400 600 800

Pressure (hPa) 1000 05/16 05/18 05/20 05/22 05/24 05/26 05/28 05/30

-10 -8 -6 -4 -2 0 2 4 6 8 10 hPa/hr

Figure 3.7: Area average vertical velocity through time from inverting the omega equation. Shown are the contribution from (a) the advection terms , (b) the heating term, (c) the sum of all terms, and (d) the Reanalysis vertical velocity. The black lines bound the time of the ﬂood event. by the heating being somewhat higher. Similar to the case of the ω proﬁles, the precipitation forced by the boundary condition is negligible.

3.5 Column model simulations

In section 2.4, it was possible to decompose the vertical motion into components forced by the large-scale motion and by convective heating. The convective heating rate was taken as a given and while it could be suggested that the upper-level PV forcing might have led to the triggering of convection, it is not possible to deﬁnitively establish this fact. A model which simulates convection is needed to demonstrate CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 49

40 P(ω ) PV 35 P(ω ) Q P(ω ) 30 BC P(ω ) total 25 Precip

15 Precip (mm/day) 10

0 05/18 05/20 05/22 05/24 05/26 05/28 05/30

Figure 3.8: Time series of precipitation estimated from each ω component using equation 3.4 and the reanalysis precipitation (black). this convective triggering. The Column Quasi-Geostrophic (CQG) modeling framework, introduced in Nie and Sobel (2016) and applied to the 2010 Pakistan flood in Nie et al. (2016), can be used to explore the coupling between large-scale dynamics and convection. The CQG framework parameterizes large-scale vertical motion, including components due to both the large-scale motion and convective heating, using the QG omega equation. A numerical model of convection is combined with the omega equation to explore the interaction of the forcings and to attribute precipitation events to specific forcings. Nie et al. (2016) used the CQG framework to show that the convection and precipitation during the 2010 Pakistan flood analyzed in chapter 2 was mainly driven by orographic forced lifting. The CQG framework is described in Nie and Sobel (2016) and I briefly outline it here. The temperature (T ) and moisture (q) equations for a column of air in pressure coordinates are: ∂T σp = Adv + ω + Q (3.5) ∂t T R ∂q ∂q = Adv + ω + Q (3.6) ∂t q ∂p q where AdvT and Advq are the large-scale horizontal advection of T and q and Q and

Qq are the heating and moistening tendencies due to sub-column scale processes CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 50

(e.g. convection and radiation). In CQG, the large-scale dynamics are parameterized using the QG omega equation. Since the CQG framework models a one-dimensional column, it is not possible to use the three-dimensional omega equation that was used in section 3.4. I therefore must make an assumption about the horizontal structure to reduce equation 3.1 to a one-dimensional form. I assume the horizontal structure of the disturbance of interest has a single horizontal wavenumber (k, with an equivalent wavelength 2π L = k ) and equation 3.1 becomes:

∂2ω k 2 1 ∂ R k 2 R k 2 2 − σ ω = − Advζ + AdvT + Q (3.7) ∂p f0 f0 ∂p p f0 p f0 where ζ = 1 ∇2Φ+f is the geostrophic absolute vorticity and Adv is the large-scale f0 ζ horizontal advection of ζ. CQG is a framework for modeling a convecting air column using equations 3.5 and 3.6 with either a Single Column Model (SCM),which has a convective parameterization for simulating convection, or a Cloud Resolving Model (CRM), which explicitly simulates the convection. The omega equation is used to parameterize the large-scale dynamics and generates a large-scale ω that depends on the convection as well as forces the convection. At each time step, Q from the SCM or CRM along with ﬂood-domain averaged Advζ and AdvT computed from the reanalysis are used to calculate ω using equation 3.7. Flood-domain averaged AdvT and Advq computed from the reanalysis are then used with this calculated ω to calculate the T and q proﬁles using equations 3.5 and 3.6. As just described, equations 3.5, 3.6, and 3.7 require the large-scale horizontal

advection terms (AdvT , Advq, and Advζ ) to be specified. These advection terms were calculated from the ERA-Interim reanalysis, averaged over the flood region, and are shown in figure 3.9. The moistening of the flood region prior to the start of the event from May 22-24 can be seen at low levels in the moisture advection.

Additionally, large forcing of Advζ during the ﬂood event can be seen at high levels near the tropopause. Similar to section 2.4, the CQG ω can be decomposed into components forced CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 51

(a) Adv (g/kg/day) q 200 5 400 600 0

800 -5 Pressure (hPa) 1000 05/18 05/20 05/22 05/24 05/26 05/28 05/30

(b) Adv (10-4/s/day) Vort 2 200 1 400 600 0 800 -1 Pressure (hPa) 1000 -2 05/18 05/20 05/22 05/24 05/26 05/28 05/30 (c) Adv (K/day) T 15 200 10 400 5 600 0 -5 800 -10 Pressure (hPa) 1000 -15 05/18 05/20 05/22 05/24 05/26 05/28 05/30

Figure 3.9: Area averaged quantities to force the SCM. (a) speciﬁc humidity advection, (b) vorticity avection, and (c) temperature advection. The black lines bound the time of the ﬂood event. by PV, diabatic heating, and the lower boundary condition:

ω = ωPV + ωQ + ωBC (3.8)

In CQG, Q is a prognostic variable, so now ωQ is predicted by the model while ωPV

and ωBC are imposed. In this section, I consider three large-scale forcings of the model:

7 • PV forcing (Advζ and AdvT applied to equation 3.7)

• Horizontal moisture advection (Advq applied to equation 3.6)

7 AdvT is also used in equation 3.5 CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 52

• Surface lifting (ω0 from the reanalysis used as a lower boundary condition in equation 3.7)

As explained in Nie et al. (2016), an important limitation of this type of imple- mentation of CQG is that the large-scale forcings are specified and are not allowed to be altered by convection. This is a trade-off that is necessary to simplify and reduce a three-dimensional system to one dimension. Despite this limitation, the results in Nie et al. (2016) (as well as the results in this section) which demonstrate good agreement between one-dimensional CQG simulated ω and precipitation and observations lend confidence to the usefulness of the CQG system. In this section I describe simulations with the CQG framework using two models: a simulation of the flood event and ω decomposition with an SCM in section 3.5.1 and a CRM in section 3.5.2. Section 3.5.2 also describes a climate attribution application of the flood event with a CRM.

3.5.1 Single Column Model

The SCM used is the MIT SCM (Emanuel and Zivkovic-Rothman, 1999) which uses the convective parameterization of Emanuel (1991), which represents an ensemble of convective clouds, and the stratiform cloud parameterization of Bony and Emanuel (2001). The effects of interactive radiation are not considered, instead a constant radiative cooling of -1.5 K/day is applied. The lower boundary is set to an ocean surface with a fixed sea-surface temperature of 27 C. The vertical resolution was set to 25 hPa and the time step used is 5 minutes. The omega equation (3.7) is solved for ω at each time step. The upper boundary condition is a rigid lid (ω = 0) at the tropopause (150 hPa) and the lower boundary condition at 1000 hPa is set to the reanalysis ω at 1000 hPa. The characteristic wavelength, L, in equation 3.7 is set to 2500 km. Nie and Sobel (2016) showed that, in the CQG system, the strength of the convective feedback depends on the choice of L. This choice of L is justified below by comparing the modeled ω to the reanalysis ω.8

8Simulations were also run with diﬀerent values of L. 2500 km resulted in the best agreement CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 53

Similar to Nie et al. (2016), the temperature and moisture profiles are initialized with profiles from a radiative-convective equilibrium (RCE) simulation performed over the same surface temperature and first run to equilibrium with the omega equation coupled, but with no externally imposed large-scale forcing. This RCE state has a time mean ω equal to zero and a mean precipitation rate of 4 mm/day (which is determined by the imposed radiative cooling rate). The model is then

forced with the large-scale forcings (Advζ , AdvT , Advq, and ω0) from the reanalysis, starting from May 1, 2015. The first ten days of the simulation are considered a spin-up time and are not considered. Figure 3.10(a) shows a comparison of the precipitation from the SCM control case (forced by all the large-scale forcings) with the reanalysis and rain gauge precipitation. The SCM simulates the time variation of precipitation quite well when compared to observations, both during the flood event as well as before the event, though over predicts the peak of May 24. After the event, the SCM over predicts the reanalysis precipitation, but is close to the rain gauge precipitation on May 29. Figure 3.10(b) shows a comparison of the precipitable water from the SCM control case with the reanalysis. There is good agreement prior to the peak of the event on May 24, but afterwards the SCM over predicts the precipitable water by up to 40%. A comparison of the decomposition of the ω profiles between the reanalysis and the SCM is shown in figure 3.11. (a) and (b) are the three-dimensional inversions that were shown in figure 3.5. (c) and (d) are the one-dimensional inversions of the SCM. For the four-day average, the shape and magnitude of the total SCM ω profile in figure 3.11(c) matches fairly well the reanalysis profile in figure 3.11(a), with the maximum of the SCM ω located 50 hPa below the maximum of the reanalysis ω. The relative magnitudes of the ω components of the SCM are similar to the reanalysis components. The profile shapes of the ω components are also similar, with the heating ω peaking at the same height as the total ω and the advection with observations. CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 54

(a) Precipitation 40 Reanalysis Gauge 30 SCM

10 Precip (mm/day)

0 05/18 05/20 05/22 05/24 05/26 05/28 05/30

(b) Precipitable Water 45

30 PW (mm) 25

20 05/18 05/20 05/22 05/24 05/26 05/28 05/30

Figure 3.10: Time series comparison of reanalysis quantities with SCM simulation. (a) Precipitation and (b) precipitable water. terms ω having a maximum in the lower troposphere. The boundary condition ω is negligible in both inversions. Similarly, for the point-in-time plots, the shape of the total SCM ω profile in figure 3.11(d) matches the reanalysis profile figure 3.11(b) well, now with the maximum of the SCM ω located 100 hPa below the maximum of the reanalysis ω. The magnitude of the total SCM ω profile is greater than the three-dimensional solution, but matches the magnitude of the actual reanalysis ω. Again, the relative magnitudes of the ω components of the SCM are similar to the reanalysis components. Figure 3.12 shows the time evolution of the ω profiles from the SCM and the reanalysis. Shown are the sum of the contributions from the two advection terms, the contribution of the heating term, the sum of all terms, and the reanalysis. Com- paring figure 3.12 with figure 3.7 shows the decomposition of the SCM simulation is very similar to the three-dimensional decomposition of the reanalysis. The total SCM ω in figure 3.12(d) matches the reanalysis ω in figure 3.12(e) during the time CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 55

(a) Reanalysis: 3D Inversion. 4-day avg (b) Reanalysis: 3D Inversion. 05-24-15 0000 100 100 200 200 300 300 400 400 500 500 600 600 700 700 Pressure (hPa) Pressure (hPa) 800 800 900 900 1000 1000 -5 -4 -3 -2 -1 0 1 -20 -15 -10 -5 0 5 ω (hPa/hr) ω (hPa/hr)

(c) SCM: 1D Inversion. 4-day avg (d) SCM: 1D Inversion. 05-24-15 0000 100 100 200 200 300 300 400 400 500 500 600 600 700 700 Pressure (hPa) Pressure (hPa) 800 800 900 900 1000 1000 -5 -4 -3 -2 -1 0 1 -20 -15 -10 -5 0 5 ω (hPa/hr) ω (hPa/hr)

Advection Terms Heating Boundary Condition All Terms Reanalysis

Figure 3.11: Comparison of pressure vertical velocity, ω, profiles from inverting the omega equation between the reanalysis and the SCM simulation. (a) Four-day average during the flood, ERA: 3D inversion, (b) peak of the flood: 05-24-15 0000 , ERA: 3D inversion, (c) four-day average during the flood, SCM: 1D inversion, and (d) peak of the flood: 05-24-15 0000, SCM: 1D inversion. The colors are the same as in figure 3.5 period simulated, including during the flood event. One exception is the SCM ω is greater than the reanalysis ω after the flood event, which is consistent with the SCM simulation producing greater precipitation than the reanalysis during this time (figure 3.10). The SCM ω components in figure 3.12(a) and (b) show a similar pattern to the reanalysis components in figure figure 3.7(a) and (b), except for an absence of SCM heating ω on May 17 and greater SCM heating ω after the flood event during the time of the precipitation discrepancy between the TRMM and SCM and the reanalysis. Additionally, the higher temporal resolution of the SCM compared to the reanalysis allows a clearer picture of the advection term component peaks leading the heating CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 56

(a) Advection Terms 200 400 600 800

Pressure (hPa) 1000 05/16 05/18 05/20 05/22 05/24 05/26 05/28 05/30 (b) Heating 200 400 600 800

Pressure (hPa) 1000 05/16 05/18 05/20 05/22 05/24 05/26 05/28 05/30 (d) All Terms 200 400 600 800

Pressure (hPa) 1000 05/16 05/18 05/20 05/22 05/24 05/26 05/28 05/30 (e) Reanalysis 200 400 600 800

Pressure (hPa) 1000 05/16 05/18 05/20 05/22 05/24 05/26 05/28 05/30

-10 -8 -6 -4 -2 0 2 4 6 8 10 hPa/hr

Figure 3.12: Area average vertical velocity through time from the SCM simulation. Shown are the contribution from (a) the advection terms , (b) the heating term, (c) the sum of all terms, and (d) the Reanalysis vertical velocity. The black lines bound the time of the flood events. component peaks, once again suggesting that the advection terms forcing could be triggering the convection. A decomposition of the SCM precipitation into components forced by individual ω components using equation 3.4 is shown in figure 3.13(b). The decomposition of the SCM precipitation is similar to the reanalysis decomposition, with the contributions of the advection terms and the heating term both being significant, with the heating term contribution being slightly larger during the event. The precipitation estimated with equation 3.4 using the total ω for the SCM matches well with the modeled SCM precipitation for most of the time period. The exception is for the period after the event, where the estimated precipitation from ω is significantly CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 57

(a) Reanalysis 40 P(ω ) 35 PV P(ω ) 30 Q P(ω ) BC 25 P(ω ) total 20 Precip 15 10 Precip (mm/day) 5 0 05/18 05/20 05/22 05/24 05/26 05/28 05/30

(b) SCM 40 35 30 25 20 15 10 Precip (mm/day) 5 0 05/18 05/20 05/22 05/24 05/26 05/28 05/30

Figure 3.13: Time series of precipitation estimated from each ω component using equation 3.4. (a) Reanalysis (also shown in ﬁgure 3.8) and (b) SCM. The black line in (a) represents the reanalysis precipitation and the black line in (b) represents the SCM precipitation. lower than the modeled precipitation. The SCM estimated precipitation from ω for this period is similar to the reanalysis precipitation estimated from ω because of the well matched ω proﬁles of the SCM and reanalysis, and this estimation removes much of the discrepancy between the reanalysis and SCM precipitation. It has been repeatedly suggested in this chapter that the convection during the event could have been triggered by the advection terms forcing. In order to demonstrate this triggering, I performed thee separate SCM simulations forced solely by: (1) the PV forcing, (2) the advection of q, and (3) the lower boundary condition. The simulation with all forcings discussed above will be referred to as the “control case”. Note that while the omega equation (3.7) is linear, so the components of ω CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 58 must sum up to the total ω, the precipitation from these individual forcing experiments will not necessarily sum up to the precipitation from the control case, because the simulated convection does not have to be a linear function of the forcings.

(a) Precip sum (b) to (d) (b) Precip forced by PV 40 40 Control Control 35 Sum (b)-(d) 35 PV Forcing 30 No Feedback 30 25 25 20 20 15 15

Precip (mm/day) 10 Precip (mm/day) 10 5 5 0 0 05/18 05/20 05/22 05/24 05/26 05/28 05/30 05/18 05/20 05/22 05/24 05/26 05/28 05/30

(c) Precip forced by q Adv (d) Precip forced by BC 40 40 Control Control 35 q Adv Forcing 35 BC Forcing 30 30 25 25 20 20 15 15

Precip (mm/day) 10 Precip (mm/day) 10 5 5 0 0 05/18 05/20 05/22 05/24 05/26 05/28 05/30 05/18 05/20 05/22 05/24 05/26 05/28 05/30

Figure 3.14: Precipitation time-series for SCM model simulations with only a single forcing applied. The black curve in all panels represents the control case (with all forcings) precipitation. The red curves in (b)-(d) represent the precipitation from the SCM forced solely by: (b) the PV advection terms, (c) q advection, and (d) the boundary conditions. The red curve in (a) represents the sum of the red curves in (b)-(d) minus 8 mm/day as multiple-counted mean precipitation. The blue curve in (a) represents the precipitation of the SCM with all forcings applied, but without the convective feedback on ω.

The precipitation from these simulations with individual forcings is shown in figure 3.14. The simulation with just the PV forcing captures much of the precipitation during the event (figure 3.14(b)). It captures about half of the precipitation during the first peak of the event on May 24 and all of the precipitation during the second peak of the event on May 26. The simulation with just the q advection shows that q advection was a significant contributor to the first peak of the event, but not the second peak (figure 3.14(c)). The simulation with just the lower boundary condition CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 59 shows just the background precipitation rate and was not a contributor to the event. I compare the sum of the precipitation from the single-forcing simulations with the control case precipitation in figure 3.14(a). The time-mean precipitation that balances the radiative cooling imposed (corresponding to a precipitation rate of 4 mm/day) is present in all of the single-forcing simulations. To account for this multiple counting of the time-mean precipitation, 8 mm/day was subtracted from the sum of the single-forcing simulation precipitations9. As noted before, the sum of the single-forcing simulations precipitation need not match the control case precipitation because the system may not be linear. During the event, the two match fairly well except that the peak in the sum of the single-forcing simulations is half a day later than the peak in the control case. This close match indicates that the strong dynamical forcings account for most of the precipitation during the event (Nie et al., 2016). Nie et al. (2016) found that the diabatic heating feedback of convection to the large-scale dynamics as parameterized in CQG was essential during the 2010 Pak- istan floods analyzed in chapter 2. To test if this feedback was also essential for this event, I also performed an SCM simulation with all forcings, but without the convective feedback on ω by setting the Q term in equation 3.7 to zero. The precipitation from this no-feedback simulation is shown by the blue curve in figure 3.14(a). The precipitation from the no-feedback simulation is much weaker during the event than in the control case. Similar to the 2010 Pakistan floods, without the positive feedback of diabatic heating on the large-scale dynamics, the convection only produces enough heating to balance the imposed large-scale forcings.

3.5.2 Cloud Resolving Model

Section 3.5.1 presented CQG simulations from an SCM, which uses a parameterization of convection. It is also useful to compare these results to simulations from a CRM, which explicitly resolves convection. CRM simulations were performed for

9I am adding the precipitation from three simulations, so I need to subtract twice the amount of time-mean precipitation, or 8 mm/day. CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 60 the Texas/Oklahoma event, again using the CQG framework to parameterize the large-scale vertical velocity. These CRM simulations were run by Ji Nie. The CRM used is the System for Atmospheric Modeling (Khairoutdinov and Randall, 2003). The model has a spatial domain of 128 km x 128 km with a horizontal grid spacing of 2 km and doubly periodic boundaries. There are 64 vertical levels with vertical grid spacing ranging from 75 m near the surface to 500 m in the free troposphere. For simplicity, the boundary condition (which had a negligible effect on the SCM results) was set to zero for the CRM simulation. All other parameters are the same as the SCM described in section 3.5.1. The CRM simulation described in this section will be used as the control case in the attribution analysis described in section 3.5.2.1 and is run slightly differ- ently than the SCM described in section 3.5.1. The CRM is first run to radiative- convective equilibrium (RCE) without the horizontal T and q advection in equations 3.5 and 3.6 while nudging the T and q profiles to the time-averaged profiles from the reanalysis with a nudging time-scale of one day.

The time-averaged nudging tendencies for temperature and moisture, NT and

Nq, during the RCE run were recorded and then used in the control run as large-scale background forcings. For the control run, equations 3.5 and 3.6 become

∂T σp = Adv + ω + Q + N (3.9) ∂t T R T ∂q ∂q = Adv + ω + Q + N (3.10) ∂t q ∂p q q where as in the SCM the horizontal advections, AdvT and Advq, are taken from the reanalysis and the large-scale vertical velocity, ω, is from equation 3.710. Figure 3.15(a) shows a comparison of the precipitation from the CRM with the reanalysis and rain gauge precipitation, similar to ﬁgure 3.10(a) for the SCM. Similar to the SCM, the CRM simulates the time variation of precipitation quite well when compared to observations, both during the ﬂood event as well as before the event.

10The CRM was also run with a conﬁguration similar to the SCM and without the nudging procedure. The results from that run are qualitatively the same as the results in this section. CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 61

In contrast to the SCM, after the event the CRM has very little precipitation with an exception being a spike in CRM precipitation on May 29.

(a) Precipitation 40 Reanalysis Gauge 30 CRM

10 Precip (mm/day)

0 05/18 05/20 05/22 05/24 05/26 05/28 05/30

(b) Precipitable Water 45

30 PW (mm)

20 05/18 05/20 05/22 05/24 05/26 05/28 05/30

Figure 3.15: Time series comparison of reanalysis quantities with CRM simulation. (a) Precipitation and (b) precipitable water.

Figure 3.15(b) shows a comparison of the precipitable water from the CRM with the reanalysis, similar to figure 3.10(b) for the SCM. As was the case with the SCM, the there is good agreement between the model and reanalysis, including a much better agreement after the event when the SCM overpredicted the PW by up to 40%. A comparison of the decomposition of the ω profiles between the reanalysis and the CRM is shown in figure 3.16, similar to figure 3.16 for the SCM. (a) and (b) are the three-dimensional inversions that were shown in figure 3.5. (c) and (d) are the one-dimensional inversions of the CRM. For the four-day average, the peak of the total CRM ω profile in figure 3.16(c) is 25% larger than the peak in the reanalysis ω profile in figure 3.16(a). This CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 62

(c) CRM: 1D Inversion. 4-day avg (d) CRM: 1D Inversion. 05-24-15 0000 100 100 200 200 300 300 400 400 500 500 600 600 700 700 Pressure (hPa) Pressure (hPa) 800 800 900 900 1000 1000 -5 -4 -3 -2 -1 0 1 -20 -15 -10 -5 0 5 ω (hPa/hr) ω (hPa/hr) Advection Terms Heating Boundary Condition All Terms Reanalysis

Figure 3.16: Comparison of pressure vertical velocity, ω, profiles from inverting the omega equation between the reanalysis and the CRM simulation. (a) Four-day average during the flood, ERA: 3D inversion, (b) peak of the flood: 05-24-15 0000 , ERA: 3D inversion, (c) four-day average during the flood, CRM: 1D inversion, and (d) peak of the flood: 05-24-15 0000, CRM: 1D inversion. The colors are the same as in figure 3.5 discrepancy is coming from the heating term; the advection terms component of the CRM is close in magnitude to the reanalysis, while the peak of the heating term component is about 35% larger in the CRM than the reanalysis. This discrepancy may be caused by the choice of characteristic wavelength, L, for use in equation 3.7. Nie and Sobel (2016) showed that the choice of L determines the strength of the convective feedback. Despite this discrepancy, there is still a relatively good qualitative match between the CRM and reanalysis ω profiles and decomposition. Additionally, the good agreement between the CRM and reanalysis precipitation CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 63 time-series described above and the point-in-time ω decomposition described below lends confidence to using this CRM simulation in the attribution analysis carried out in section 3.5.2.1. For the point-in-time plots, the shape and magnitude of the total CRM ω profile in figure 3.16(c) matches very well with the reanalysis profile in figure 3.16(a), with the maximum of the CRM ω located slightly below the maximum of the reanalysis ω, which was also the case for the SCM. The relative magnitudes and shapes of the ω components of the CRM are also similar to the reanalysis components.

3.5.2.1 Attribution analysis

As discussed previously, attribution studies attempt to quantify the impact that climate change had on a weather event. In this section I describe a highly-conditional attribution analysis using the CRM introduced in section 3.5.2. The simulated precipitation of the event using the CRM described in section 3.5.2 is compared to two additional CRM simulations: one for a past climate and one for a future warmer climate. These climate scenarios were defined using the output of the models from the fifth phase of the Couple Model Intercomparison Project 5 (CMIP5) (Taylor et al., 2012). An average of 39 models and 79 runs was used. The past climate was defined using an average of the years 1900-1909 from the historical CMIP5 runs and the future climate is defined using an average of the years 2090-2999 from the Representative Concentration Pathways 8.5 (RCP8.5) scenario CMIP5 runs. The RCP8.5 scenario is the pathway with the highest greenhouse gas emissions (Riahi et al., 2011). A current climate is also defined to compute anomalies. It is defined using an average of the years 2010-2019 from the RCP8.5 CMIP5 runs. Temperature and moisture profile anomalies for the past and future climates are computed as differences of the flood-domain averaged profiles between the current and past runs and the future and current runs, respectively. These anomalies are added to the reanalysis profiles and the resulting perturbed profiles are used for the two perturbed CRM runs. As described in section 3.5.2, the CRM is first run to CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 64

Table 3.1: Four-day total area-average precipitation during the ﬂood for diﬀerent climate scenarios.

Scenario Precip (mm) Past Climate 35.6 Control 37.0 Future Climate 46.2

RCE with no horizontal advection while nudging to the perturbed proﬁles of T and q just described with a nudging time-scale of one day. The time-averaged nudging tendencies from the perturbed RCE runs are then used for the perturbed CRM runs, again using equations 3.9 and 3.10. Similarly, surface temperature anomalies for the past and future perturbed runs were taken from diﬀerences between the current and past runs and the future and current runs, respectively. These anomalies were added to the surface temperature from the control run for use in the perturbed runs. Table 3.1 shows the area-averaged total four-day accumulated precipitation for the three simulations. These simulations show that there was a modest climate- change contribution to the intensity of the event; the total precipitation is slightly higher (4%) in the control simulation than in the past simulation. Looking towards the future, the simulations predict a large (25%) increase in total precipitation for the warmer climate.

3.6 Conclusions

Record breaking floods occurred in Texas and Oklahoma in late May 2015 as the result of an extreme precipitation event. This chapter has attempted to describe the factors that supported the flooding event, specifically the source of moisture and the driving factors of upward motion and convection that led to the precipitation. The low-level wind field advected moisture from the Gulf of Mexico into the flood CHAPTER 3. THE MAY 2015 FLOOD IN TEXAS AND OKLAHOMA 65 region before and during the event. The vertical motion was analyzed through inverting the quasi-geostrophic omega equation, which allowed for the contribution of the large-scale circulation forcing to be quantified. The omega equation solution matched the reanalysis vertical motion well, lending confidence to this approach. Similar to the India/Pakistan floods considered in chapter 2, the heating term component of ω was dominant during the event. In contrast to the India/Pakistan flood, where topographic forced upward motion was found to be the main triggering factor of the convection, for the Texas/Oklahoma flood the main triggering factor of convection was found to be the forcing of the advection terms in the omega equation from upper-level PV disturbances. In addition to applying the omega equation to the reanalysis data, CQG model simulations were performed to explicitly attribute the convection to specific forcings. Unlike in the reanalysis inversion, the CQG models are able to simulate convection and thus it is possible to directly demonstrate the effect of an applied forcing to the convection. It was found that the large-scale PV forcing and advection of moisture into the flood region were both essential in producing the extreme amounts of rainfall during the event. Finally, the CQG model simulations were used for a climate attribution analysis. It was found that the event was 4% more intense due to climate change and that this event would potentially be 25% more intense in a warmer climate in the future. 66

Part II

Tropical Cyclones in climate models 67

Introduction

Tropical cyclones (TCs) are intense storms that originate over warm tropical oceans and are referred to as hurricanes and typhoons in various parts of the world. TCs are characterized by strong surface winds and a low-pressure and warm core in their center. The energetics of TCs can be thought of as a Carnot heat engine (Emanuel, 1986). TCs are among the most destructive natural disasters on the planet (Emanuel, 2003). TCs that make landfall produce heavy rain as well as strong winds that and can lead to damaging storm surge. They are currently estimated to cause 19,000 deaths per year and produce $26 billion per year in worldwide damages (Mendelsohn et al., 2012). Because of their large societal impacts, it is important to understand any possible changes to TCs in a warmer future climate. A natural tool to study TC changes are General Circulation Models (GCMs). A GCM is a numerical model that simulates the global atmosphere and consists of a dynamical core that numerically solves the equations of motion for the resolved component of the flow on some discretized grid as well as parameterizations of the subgrid scale unresolved processes (e.g. radiation, convection, surface fluxes). GCMs are used for short term simulations for numerical weather forecasting as well as long term simulations of climate change. TCs have long been found in GCMs, even those run at relatively low resolution. An early example is Manabe et al. (1970) which found that a GCM with a resolution of around 400 km was able to generate TC-like disturbances. Low resolution GCMs have been shown to be able to generate TC-like disturbances, but the simulated TCs are biased with weaker intensity and larger spatial scale than observed TCs (Hamilton, 2008). More recently, atmospheric GCMs have been able to be run with a much higher resolution over prescribed Sea Surface Temperatures (SSTs) (e.g. Bengtsson et al. 2007a; LaRow et al. 2008; Zhao et al. 2009). These high-resolution models have demonstrated the ability to simulate more realistic TCs. The U.S. CLIVAR Hurricane Working Group (HWG) (Walsh et al., 2015) was 68 formed to study the ability of modern high-resolution atmospheric GCMs to simulate global TCs and project how TCs might change in a warmer climate. Experiments were performed using climatological SSTs as well as a future warmer climate scenario with SSTs that are uniformly 2 K warmer than the climatology.11 As a first step in considering a projection of TC changes, it is first necessary to evaluate the models’ ability to simulate the characteristics of TCs in the present climate. These characteristics include the climatological spatial, temporal, and intensity distributions as well as the interannual variability of TCs. This part consists of chapter 4 in which I present an intercomparison of the ability of the 9 high- resolution GCMs that were part of the HWG experiments to simulate TCs in the present climate. This analysis is mostly contained in Shaevitz et al. (2014).

11There were also experiments that studied the eﬀect of doubling carbon dioxide, both with and without SST changes. CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 69

Chapter 4

Characteristics of tropical cyclones in high-resolution models in the present climate

4.1 Introduction

The impact of tropical cyclones (TCs) on society makes it important to understand how their characteristics might change in the future. Global climate models, also known as General Circulation Models (GCMs), are important tools for studying this problem. In a GCM, one has the ability to simulate the climate organically; if the model has suﬃcient resolution and physics to provide a plausible simulation of TCs as well, then one can use the model to examine how climate controls the statistical properties of TCs. One can explore, in particular, the behavior of TCs under diﬀerent climate scenarios. Many studies (e.g. Manabe et al. 1970; Bengtsson et al. 1982; Vitart et al. 1997; Camargo et al. 2005) have shown that GCMs, even at relatively low resolution, are capable of generating storms that have similar characteristics as observed TCs. More recently, studies that have used higher resolution atmospheric GCMs forced with prescribed sea surface temperatures (SSTs) (e.g. Bengtsson et al. 2007a; CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 70

LaRow et al. 2008; Zhao et al. 2009) have demonstrated these high-resolution models’ remarkable ability to simulate realistic distributions of TCs. In order to use GCMs for projections of possible future changes in TC activity, it is first necessary to assess their ability to reproduce the characteristics of observed TCs in the present climate. These characteristics include the climatological spatial, temporal, and intensity distributions as well as the interannual variability of TCs. The analysis in this chapter is an intercomparison of the ability of 9 high-resolution GCMs to simulate TCs. The models have resolutions that vary from 28 to 130 km, with different parameterizations. Two of the models have done simulations at multiple resolutions, while a single resolution is available for my analysis of the other models. The simulations analyzed were performed for the U.S. CLIVAR Hurricane Work- ing Group (Walsh et al., 2015). The objective of this working group was to have a better understanding of the differences among high-resolution models in simulating TC activity, in the present climate as well as in warmer climate scenarios. In order to do that, a set of common experiments with the same forcings and fixed SST was performed by all modeling groups. Here I analyze the characteristics of TC activity in the simulations of climate produced by the working group over SST distributions derived from observations taken in the late 20th century (1981-2005 for the climatology simulations and 1981-2009 for the interannual simulations). Observed TC tracks and intensities are derived from atmospheric measurements — in situ and remote — by human forecasters. With climate models, it is necessary to apply objective tracking schemes to the model output fields to obtain the tracks and intensities. The criteria applied to the models can be different than those applied to observations; a model storm is not necessarily required to meet the same thresholds for intensity as an observed one would be in order to be classified as a TC. It has been found that when allowance is made for the fact that model TCs are weaker and larger than those observed, the resulting spatio-temporal distributions of TC tracks resemble those observed enough to be useful — for example, in seasonal forecasting — even in quite low-resolution models (Camargo and Barnston, 2009; CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 71

Camargo et al., 2010). In the present study, I examine the TCs derived from each model’s output by the group who ran that particular model, using their own preferred tracking scheme1.I consider the combination of model and tracking scheme to be a “modeling system” and compare the outputs from each system. In the interests of brevity, I will refer to these modeling systems below simply as “models”, taking the tracking scheme as implicit, though my expectations about the sensitivities of the results to tracking schemes are discussed in several points. This approach implicitly makes allowances for the different resolutions and physics of each model, resulting in different TC intensities. It is consistent with the way each model has been used in previous single-model studies. Using each group’s own tracks also allows each model to be seen in the best light, to the extent that tracking schemes have tunable parameters whose adjustment can allow some gross aspects of the statistics to be brought closer to those observed. It is also of interest to compare the different models using the same tracking scheme, so that the differences in results are purely attributable to the differences in the models themselves. This comparison was carried out in Horn et al. (2014) which ran multiple tracking schemes on the same model outputs. They found that the differences between the thresholds used in different tracking schemes can have a moderate impact on the genesis frequency of TCs, but some of these differences could be removed by adjusting the detection thresholds in the tracking schemes. This chapter is organized as follows. The data, models, and experiments are discussed in section 4.2. Results from the climatological and historical forced simulations are described in section 4.3. Finally, conclusions are given in section 4.4.

1I was responsible for producing the tracks for the GISS model using the Camargo and Zebiak (2002) tracking scheme. CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 72

4.2 Models and data

The data used for this study consists of TC tracks from nine GCMs. The models were forced with two different SST boundary conditions, climatologically averaged SSTs and monthly interannually varying SSTs. The SSTs were obtained from the Hadley Centre Sea Ice and Sea Surface Temperature (HadISST) data set (Rayner et al., 2003). Each group used the output of their simulations to detect and track the model TCs, using their own tracking algorithm. Tracks for these TCs were generated and their characteristics were analyzed here. The sensitivity of the models to the different tracking schemes was analyzed in Horn et al. (2014). Output from nine GCMs were analyzed in this study, as summarized in table 4.1, namely: Community Atmosphere Model version 5.1, or CAM5.1 (Wehner et al., 2014); European Centre for Medium-Range Weather Forecasting - Hamburg, or ECHAM5 (Roeckner, 2003; Scoccimarro et al., 2011); Florida State University, or FSU (LaRow et al., 2008); NASA Goddard Earth Observing System Model version 5, or GEOS-5 (Rienecker et al., 2008); National Centers for Environmental Prediction Global Forecasting System, or GFS (Saha et al., 2013); NASA Goddard Institute for Space Studies, or GISS (Schmidt, 2013); Met Office Hadley Centre Model version 3 - Global Atmosphere 3.0 (GA3) configuration, or HadGEM3 (Walters et al., 2011); Geophysical Fluid Dynamics Laboratory High Resolution Atmosphere Model, or HiRAM (Zhao et al., 2009); and Meteorological Research Institute, or MRI (Mizuta et al., 2012; Murakami et al., 2012). The model resolutions vary from 28 to 130 km. The models have different tracking schemes, most of them with very similar characteristics, based on the original tracking schemes in Bengtsson et al. (1982) and Vitart et al. (2007). These tracking schemes look for vortices with a minimum of sea level pressure, a maximum of low-level vorticity and a warm core (Camargo and Zebiak, 2002; Walsh, 1997; Vitart et al., 2003; Zhao et al., 2009; Murakami et al., 2012). The main difference among the schemes is how they define the warm core and the thresholds used to define the model TC. An exception is the HadGEM3, which uses a tracking scheme originally developed for extra-tropical (cold core) cyclones (Hodges, 1995) and modified to track warm core vortices (Bengtsson et al., 2007a; CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 73

Strachan et al., 2013). I compare the model TC characteristics with the observed TC data. For the North Atlantic and eastern and central North Paciﬁc the best- track datasets from the National Hurricane Center is used (Landsea and Franklin, 2013; NHC, 2013). In the case of the western North Paciﬁc, North Indian Ocean and southern hemisphere, the TC data is from the best-track datasets from the Joint Typhoon Warning Center (Chu et al., 2002; JTWC, 2013).

Table 4.1: Table of model parameters. LR: Low Resolution, MR: Medium Reso- lution, HR: High Resolution. Roeckner/Scoccimarro: Roeckner (2003) and Scocci- marro et al. (2011). Hodges/Bengtsson: Hodges (1995) and Bengtsson et al. (2007b). Mizuta/Murakami: Mizuta et al. (2012) and Murakami et al. (2012)

Model Resolution Approx Res (km) Reference Tracking Scheme LR CAM5.1 100 km 100 Wehner et al. (2014) Prabhat et al. (2012) HR CAM5.1 1/4◦ 28 Wehner et al. (2014) Prabhat et al. (2012) ECHAM5 T159 84 Roeckner/Scoccimarro Walsh (1997) FSU T126 106 LaRow et al. (2008) Vitart et al. (2003) GEOS-5 1/2◦ 56 Rienecker et al. (2008) Vitart et al. (2003) GFS T126 106 Saha et al. (2013) Zhao et al. (2009) GISS 1◦ 111 Schmidt (2013) Camargo and Zebiak (2002) LR HadGEM3 N96 130 Walters et al. (2011) Hodges/Bengtsson MR HadGEM3 N216 60 Walters et al. (2011) Hodges/Bengtsson HR HadGEM3 N320 40 Walters et al. (2011) Hodges/Bengtsson HiRAM 50 km 50 Zhao et al. (2009) Zhao et al. (2009) MRI TL319 60 Mizuta/Murakami Murakami et al. (2012)

4.3 Results

4.3.1 Climatology

4.3.1.1 TC Frequency

There are on average approximately 80 TCs observed every year across the globe (Emanuel, 2003). Figure 4.1 shows the distribution of the number of TCs per year for CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 74 all models along with the observations. There are large differences in the number of TCs between the different models. Different models run at approximately the same resolution do not have similar mean numbers of TCs (e.g. the LR CAM5.1, FSU, GFS, and GISS models all have resolutions of roughly 100 km, but the mean number of TCs per year varies from about 10 to over 100.)

120

100

Number of TCs Per Year 40

0 CAML CAMH ECHAM5 FSU GEOS−5 GFS GISS HadL HadM HadH HiRAM Obs

Figure 4.1: Distributions of the number of TCs per year for models and observations. The horizontal line inside the boxes shows the median number of TCs per year, the top and bottom of the boxes represent the 75th and 25th percentiles respectively, with the whiskers extending to the maximum and minimum number of TCs per year in each case. CAML: Low-resolution CAM5.1, CAMH: High-resolution CAM5.1, HadL: Low-resolution HadGEM3, HadM: Medium-resolution HadGEM3, HadH: High-resolution HadGEM3.

At the same time, the absolute number of TCs in each model is somewhat dependent on the tracking scheme applied; higher thresholds result in fewer TCs. This is particularly evident in the CAM5.1 models, where the same thresholds were used for both the low resolution and high resolutions simulations, resulting in a very low number of TCs in the LR CAM5.1 model. Application of strictly uniform tracking schemes, with no allowance for the diﬀerent intensities in diﬀerent models CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 75

(whether due to resolution or other factors) would almost certainly produce even larger differences in the total numbers of TCs from model to model. By using each group’s own tracking scheme, I allow some compensation for the different TC intensities, in order to allow more productive comparison between other aspects of the results, such as the spatial and seasonal distributions of TC genesis and tracks, in the way that they would be shown in single-model studies by the individual groups. The three resolutions of the HadGEM3 model show an increase in the number of TCs with increasing resolution, though it does not increase linearly. The tracking algorithm for all resolutions of the HadGEM3 model use the same threshold for the 850-hPa relative vorticity after being filtered to a standard spectral resolution of T42 as described in Strachan et al. (2013). Thus, the increase in the number of TCs with increasing resolution is not an artifact of the tracking scheme. Figure 4.2 shows the mean number of TCs formed per year in each ocean basin. The total number of TCs formed in each basin per year is shown at the top of the figure and the percentage of all TCs that formed in each basin is shown at the bottom. Due to the large differences in the total numbers of global TCs reported by each model, it is more illustrative to compare the percentages of the TCs that form in each basin, rather than the total number of TCs, to the observations. There are clear differences between the models in the distribution of TCs across all basins, particularly in the North Atlantic and Pacific. Several of the models (ECHAM5, GISS, and all resolutions of the HadGEM) have percentages much lower than that observed in the North Atlantic. Three of the models (ECHAM5, FSU, and GISS) have a significantly lower percentage than that observed in the Eastern North Pacific, while the CAM5.1 (at both resolutions) and the GEOS-5 model have a much higher percentage than observed in the Eastern North Pacific. In the Western North Pacific, the CAM5.1 models have smaller percentages than observed, and the ECHAM5 and GISS models have larger percentages than observed. This is consistent with previous studies that have found that low-resolution models tend to have a large percentage of TCs in the Western North Pacific and very few TCs in the North Atlantic (Camargo et al., 2005; Camargo, 2013). Also of note is that the CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 76

CAML 20 CAMH ECHAM5 10 FSU

Number of TCs per Year GEOS−5 0 SI AUS SP NI WNP ENP NATL GFS GISS HadL 0.5 HadM 0.4 HadH HiRAM 0.3 Obs 0.2

Fraction of TCs 0.1

0 SI AUS SP NI WNP ENP NATL

Figure 4.2: Mean number of TCs formed in each basin for models and observations. The top panel shows the total number of TCs, while the bottom panel shows the percentage of TCs in each basin. The basins are defined as: SI (South Indian), AUS (Australian), SP (South Pacific), NI (North Indian), WNP (Western North Pacific), ENP (Easter North Pacific), NATL (North Atlantic). The model names follow the definitions in Fig. 4.1. discrepancies in the partitioning between the Western and Eastern North Pacific in the CAM5.1 models are partially linked to a bias for the tendency of too many TCs in the Central North Pacific. One interesting observation is that there is a larger difference in TC distributions among the different models, than among different resolutions of the same model. The TC distributions of the different resolutions of the CAM5.1 and HadGEM3 models are very similar. This suggests that the global and regional distributions of TCs is mainly determined by the characteristics of the models (e.g. parameterizations, convection scheme), with model resolution not being as important. While CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 77 the tracking schemes are also different, my expectation is that the usage of different tracking schemes reduces the apparent differences between models, particularly in overall TC frequency. As will be seen below, the intensities of the simulated TCs are quite different in different models, and the different thresholds in the tracking schemes adjust for this to a large degree. If the same tracking scheme (including the specific thresholds) used to detect TCs in HiRAM were applied to the GISS model, for example, very few TCs would be detected. In order to study the geographic patterns of TC occurrence, I will use track density, defined as the total number of TCs that pass through a 5◦ x 5◦ box per year. Figure 4.3 shows the track density distributions for all models and observations. The distribution of observed track density shows a region of very high density off the western coast of Central America and the eastern coast of Asia, along with regions of high density in the North Atlantic, South Indian, and off the eastern coasts of Australia and India. Consistent with the basin averages, the models have different patterns of track density. The GISS model has a similar pattern to the observations, with some key differences. The most striking difference is the lack of a region of high track density off the eastern coast of Central America, which is notoriously difficult to simulate with lower resolution GCMs (Camargo et al., 2005). Other differences include a higher density around India, the region of high density off the eastern coast of Asia extending further to the east, and a lower density in the North Atlantic. The HiRAM model has a remarkably similar pattern to the observations globally. The FSU model has higher density in the North Atlantic and South Indian along with lower density off the eastern coast of Central America. The ECHAM5 model has very low density in the North Atlantic and South Indian, but similar density patterns to the observations in the Western Pacific and South Pacific. The ECHAM5 model also has a localized region of very high density directly on the eastern coast of India. The high resolution CAM5.1 model has a region of very high density off the western coast of Central America that extends too far westward and has much lower density off the eastern coast of Asia than the observations. The low resolution CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 78

LR CAM5.1 HR Cam5.1 ECHAM5 50

−50 FSU GEOS−5 GFS 50

−50 GISS LR HadGEM3 MR HadGEM3 50

−50 HR HadGEM3 HiRAM Obs 50

−50 0 100 200 300 0 100 200 300 0 100 200 300

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Figure 4.3: TC track density in models and observations. Track density is deﬁned as the mean number of TC transits per 5◦ x 5◦ box per year.

HadGEM3 model has small regions of high density in the correct locations. The higher resolution HadGEM3 models have higher density in these regions, which expand covering larger areas. The global mean densities in the lower resolution CAM5.1, GEOS-5, and GFS models are much lower than observed. These results are consistent with the ﬁndings of Strazzo et al. (2013) which examined track densities of the FSU and HiRAM simulations and also found that the HiRAM density distribution is very similar to the observed distribution and the FSU model had higher density in the North Atlantic than the observations. In addition to track density, it is useful to study where the simulated TCs form, or genesis density, and end, or lysis density. Figures 4.4 and 4.5 shows the genesis and lysis densities of all the models and observations. Genesis (lysis) density is deﬁned as the total number of TCs that form (die) in a 5◦ x 5◦ box per year. The CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 79

LR CAM5.1 HR Cam5.1 ECHAM5 50

−50 FSU GEOS−5 GFS 50

−50 GISS LR HadGEM3 MR HadGEM3 50

−50 HR HadGEM3 HiRAM Obs 50

−50 0 100 200 300 0 100 200 300 0 100 200 300

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 4.4: TC genesis density in models and observations. Genesis density is deﬁned as mean TC formation per 5◦ x 5◦ box per year.

overall diﬀerences in the patterns of the genesis and lysis densities between the models and observations are similar to the diﬀerences in the track density described above. Consistent with the observations, all the models have narrower meridional bands of high genesis density as compared to track density. This occurs because the TCs tend to form in low-latitudes and travel poleward, causing the track density to have a greater meridional spread than the genesis density. It can be easier to distinguish patterns in the distributions by examining certain spatial or temporal dimensions. The top panel of Fig.4.6 shows the genesis as a function of latitude of each model and the observations. For the CAM5.1 and HadGEM3 models, only the highest resolution simulations are shown. The observations have a large peak at 10◦ north, a smaller peak at 10◦ south, and no TC formation directly at the equator. All of the models have peaks at roughly the same CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 80

LR CAM5.1 HR Cam5.1 ECHAM5

FSU GEOS−5 GFS

GISS LR HadGEM3 MR HadGEM3

HR HadGEM3 HiRAM Obs

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 4.5: TC lysis density in models and observations. Lysis density is deﬁned as mean TC lysis per 5◦ x 5◦ box per year. latitudes as the observations, with the exception of the FSU model, whose peaks are closer to the equator, and the ECHAM5 model, whose peaks are further poleward than the observations. In addition, the FSU model is the only model that has significant non-zero genesis at the equator. The ECHAM5 model’s southern hemisphere peak has a fatter tail and has non-zero genesis extending to higher latitudes than the observations and all other models. Although the GEOS-5 and GFS models have fewer TCs than in observations, but the maxima in genesis location occur at roughly the same latitudes and with similar relative magnitude as the observations. The middle panel of Fig.4.6 shows the genesis as a function of longitude for the models and observations. The observations have two sharp peaks at roughly 90◦ and 250◦ (corresponding to the maxima in the South Indian and western coast of Central America in Fig. 4.4), a broader peak at roughly 150◦ (corresponding to the CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 81

20 NTC 10

0 40S 30S 20S 10S Eq 10N 20N 30N 40N Latitude (deg) 6

4 NTC 2

0 0 50 100 150 200 250 300 350 Longitude (deg)

10 NTC 5

0 J F M A M J J A S O N D Month

HR Cam5.1 ECHAM5 FSU GEOS−5 GFS GISS HR HadGEM3 HiRAM Obs

Figure 4.6: Mean number of TC genesis per year in models and observations as a function of latitude (top panel), longitude (middle panel), and month (bottom panel). maxima off the eastern coast of Asia in Fig. 4.4), and near-zero genesis near the dateline. Three of the models (GISS, FSU, and ECHAM5) have much lower Central American 250◦ peak than the observations, with the GISS model producing virtually no TCs. The FSU model has peaks at 55◦ (off the eastern coast of Africa) and 310◦ (North Atlantic) that are not present in any other model or the observations. The ECHAM5 model has a very strong peak at 85◦ (off the eastern coast of India). The HiRAM model exhibits a pattern remarkably similar to the observations. Another metric of interest is the seasonal cycle of TC formation. The bottom panel of Fig. 4.6 shows global genesis as a function of month for models and observations. The observations show a fairly smooth seasonal cycle with a clear maximum between August and September and a minimum around April. In gen- CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 82 eral, the models have a significantly weaker seasonal cycle than the observations, i.e. the difference between the number of TCs in the second half of the year and the first half of the year is less than the difference in the observations. The TC seasonal cycle varies in the different basins, so I examine the seasonal cycle in each basin individually in Fig. 4.72. The basins in the northern hemisphere typically have a broad peak in the second half of the year and few TCs in the first half of the year, with exception of the North Indian Ocean. In the Western North Pacific, the GISS, HiRAM, FSU, HR HadGEM3, and ECHAM5 models are able to roughly reproduce the peak in the second half of the year, while the other models have no peak. In the Eastern North Pacific, the HiRAM3, HR HadGEM3, HR CAM5.1, and GFS models are able to reproduce the August peak while the other models have very low density throughout the year in this basin. In the North Atlantic, the HiRAM3, FSU, HR CAM5.1, and GFS models reproduce the second half of the year peak. Also of note is that the FSU model has a peak in the Western North Pacific that is roughly three months later than in observations, while it has a peak in the North Atlantic roughly one month earlier than observed. Most models are able to capture the bimodal distribution in the North Indian Ocean, with exception of the ECHAM5. All models are able to reproduce the observed peak in the early part of the year in the South Pacific and Australian basins. In contrast, in the South Indian basin, the CAM5.1 and FSU models have the wrong seasonality with a peak in the second half of the year.

4.3.1.2 TC Intensity

Along with the frequency of TCs, it is important to examine TC intensity. Although the global climate models here are considered “high-resolution”, it is not expected that they would be able to reproduce the most intense TCs (category 4 and 5 hurricanes), which would require even higher resolution to be able to simulate those intensities (see e.g. Bender et al. (2010)). A signiﬁcant fraction of the models here

2The HadGEM3 models only tracked TCs for speciﬁc seasons (May-November for the Northern Hemisphere and October-May for the Southern Hemisphere). CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 83

NATL ENP WNP 6 6 10

4 4 5

NTC 2 NTC 2 NTC

0 0 0 J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D NI SP AUS 3 3 3

2 2 2

NTC 1 NTC 1 NTC 1

0 0 0 J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D SI 4

2 NTC

0 J F M A M J J A S O N D

HR Cam5.1 ECHAM5 FSU GEOS−5 GFS GISS HR HadGEM3 HiRAM Obs

Figure 4.7: Mean TC genesis per year and month in models and observation in various basins (as defined in Fig. 4.2) do not come anywhere near those intensities. The accumulated cyclone energy (ACE) of a TC is the sum of the squares of the TC’s maximum wind speed, sampled at 6-hourly intervals whenever the maximum wind speed is at least tropical storm strength (35 kt). Adding the ACE of individual TCs can produce a total ACE for a spatial or temporal region, e.g. a basin ACE or a seasonal ACE. Thus, a larger value of total ACE could correspond to stronger TCs, more TCs, and/or TCs that last longer. Figure 4.8 shows the total ACE (averaged per year) for each basin. The top panel shows the total ACE of each basin and the bottom panel shows the percentage of the global ACE that occur in each basin. The observations have large values of ACE in the western North Pacific (40%), followed by the eastern North Pacific, North Atlantic, and South Indian Ocean (15%), with the Australian and South Pacific contributing with about 5% of the global ACE and a very low value of ACE in the North Indian Ocean. All models are able to reproduce the large ACE percentage in the western North CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 84

Pacific, with the ECHAM5 and FSU models having a very low ACE percentage in the eastern North Pacific. The ECHAM5 and GISS models have a relatively large ACE percentage in the South Pacific, while the HadGEM3 models (all resolutions) have an anomalously high ACE percentage in the South Indian Ocean.

x 105 10

6 CAML 4 CAMH

Total ACE ECHAM5 2 FSU 0 GEOS−5 SI AUS SP NI WNP ENP NATL GFS GISS

0.5 HadL HadM 0.4 HadH HiRAM 0.3 Obs 0.2

0.1 Fraction of Total ACE 0 SI AUS SP NI WNP ENP NATL

Figure 4.8: Total accumulated cyclone energy (ACE) for models and observations (top panel). The bottom panel shows the percentage of the total ACE in each basin for models and observations. Basins and models are deﬁned as in previous ﬁgures.

The top panel of Fig. 4.9 shows the distribution of the maximum wind speed achieved by each TC in all models and the observations. The vertical lines represent boundaries of the Saffir-Simpson hurricane intensity scale (Saffir, 1977). The models seem to separate into four regimes of intensities. The HR CAM5.1 has an intensity distribution similar to observations, with a significant number of category 2 hurricanes and even the ability to produce the most intense TCs, i.e. categories 4 and 5 storms. The HiRAM, FSU, and HR HadGEM3 models have many tropical storms and category 1 TCs and some category 2 TCs. The ECHAM5, GEOS-5, and CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 85

GFS models have mostly tropical storms. The GISS model’s TCs are almost all of tropical depression intensity, with only a very small number of weak tropical storms. The difference between the intensity distributions among the models can not simply be a result of the models’ resolution. For example, the GEOS-5 model has a horizontal resolution similar to the HiRAM model, but has significantly weaker TCs. On the other hand, the FSU model has some of the strongest TCs, but does not have one of the highest resolutions among the models. In order to better understand the effect of model resolution on simulated TC intensities, it is instructive to examine the differences in the intensity distributions of the models in multiple horizontal resolutions. Histograms of the maximum wind speeds for the CAM5.1 and HadGEM3 models in various resolutions are shown in the middle and bottom panels of Fig. 4.9. As expected, both the CAM5.1 and HadGEM3 models show an increase in the mean TC intensity with higher resolution. The increase in intensity of the HR HadGEM3 and HR CAM5.1 models can be also seen as an elongation of the tails of the distributions into higher TC categories.

4.3.1.3 TC life-time

TC life-time distributions in models and observations are shown in Fig. 4.10, with the TC life-time histograms of the CAM5.1 and HadGEM3 models in different resolution given in the middle and bottom panels, respectively. There is a large variation in the TC life-time among the models. The ECHAM5, GISS, and HR HadGEM3 models have TCs lasting longer than 40 days, while the GEOS-5 and GFS models have very few TCs lasting more than 10 days. This is most likely due to the different tracking schemes used, as they consider different criteria for when to form and end a TC. Of particular note is that for the models with simulations in multiple resolutions, the TCs in the higher resolution simulations have a slightly longer average duration than in the low-resolution ones. CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 86

TD TS C1 C2 C3 C4 C5 CAMH ECHAM5 FSU GEOS−5 GFS GISS HadH HiRAM Obs 0 10 20 30 40 50 60 70 80 90 Max wind speed (m/s)

CAM5.1 0.4 TD TS C1 C2 C3 C4

LR 0.2 HR Fraction

0 0 10 20 30 40 50 60 70 Max wind speed (m/s) HadGEM3 0.4 TD TS C1 C2 0.3 LR 0.2 MR

Fraction HR 0.1

0 0 10 20 30 40 50 Max wind speed (m/s)

Figure 4.9: Distributions of TC maximum intensity in models and observations (top panel). The horizontal line shows the median of each distribution, the left and right edges of the box represent the 75th and 25th percentiles respectively, and the whiskers extend to the maximum and minimum values in each case. Histograms of TC maximum intensity for two horizontal resolutions of the CAM5.1 model (middle panel) and three model resolutions of the HadGEM1 model (bottom panel). The vertical lines show the boundaries of the Saﬃr-Simpson hurricane classiﬁcation scale. TD: Tropical Depression, TS: Tropical Storm, C1-C5: Category 1-5 hurricanes. LR: Low resolution, MR: Medium resolution, HR: High resolution. CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 87

CAMH ECHAM5 FSU GEOS−5 GFS GISS HadH HiRAM Obs 0 10 20 30 40 50 Duration (days)

CAM5.1

LR 0.4 HR

0.2 Fraction

0 0 5 10 15 20 25 Duration (days) HadGEM3

LR MR 0.2 HR

Fraction 0.1

0 0 5 10 15 20 25 30 35 Duration (days)

Figure 4.10: Distributions of TC life-time (or duration) for models and observations. The horizontal line shows the median of each distribution, the left and right edges of the box represent the 75th and 25th percentiles respectively, and the whiskers extend to the maximum and minimum values in each case. The histograms of TC durations in the CAM5.1 and HadGEM3 models for diﬀerent resolutions are shown in the middle and bottom panel, respectively. LR: Low resolution, MR: Medium resolution, HR: High resolution. CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 88

4.3.2 Interannual variability

In the previous section, I analyzed the model simulations forced with climatological SSTs, which characterizes the typical TC properties in the models, but does not simulate the TC interannual variability. Well known modes of climate variability in the atmosphere and ocean, most notably the El-Ni˜noSouthern Oscillation (ENSO), have been shown to aﬀect the frequency and characteristics of TCs (Camargo et al., 2010; Iizuka and Matsuura, 2008; Bell et al., 2014). In order to evaluate the ability of the models to accurately simulate the interannual variability of TCs, the models were also run while forced with historical monthly varying SST, as opposed to climatological mean SSTs. The number of ensemble members and years of the simulations are shown in Table 4.2.

Table 4.2: Models that performed interannual simulations.

Model Number of Ensembles Years FSU 3 1982-2009 GEOS-5 2 1982-2009 GISS 3 1981-2009 HiRAM 3 1981-2009 MRI 1 1981-2003

Figure 4.11 shows the total number of TCs globally per year for the models and observations (top panel), as well as for the Western North Paciﬁc, Eastern North Paciﬁc, and North Atlantic, separately3,4. The global number of TCs in the models is similar to the observed numbers in all the models, but the global interannual

3The FSU model interannual simulation was only performed between June and November of each year and the tracking scheme was only done in the North Atlantic and North Paciﬁc basins.

4The GEOS-5 model used different physical parametrizations (minimum entrainment threshold for parameterized deep convection in the modified Relaxed Arakawa-Schubert convection scheme, as well as a different time step) in the climatological and interannual simulations, which led a very different TC global frequency between those runs. CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 89 variability is not well captured by the models. The three individual basins shown here present a greater similarity between the observations and model results, with the exception of the GISS model which has very few TCs in the North Atlantic and Eastern North Pacific and the FSU model which has very few TCs in the Eastern North Pacific.

Global 150

100 NTC

50 1985 1990 1995 2000 2005 Western North Pacific 60

NTC 20

0 1985 1990 1995 2000 2005 Eastern North Pacific 40

20 NTC

0 1985 1990 1995 2000 2005 North Atlantic 30

NTC 10

0 1985 1990 1995 2000 2005

FSU GEOS−5 GISS HiRAM MRI Observations

Figure 4.11: Number of TCs per year (top panel) in the globe and in a few of the Northern Hemipshere basins (Western North Paciﬁc, Eastern North Paciﬁc, and North Atlantic). For the models, when more than one ensemble simulation was available, the ensemble mean number of TCs in each year is shown.s

In order to quantify the ability of the models to reproduce the interannual variability of observed TCs in different basins, I calculate the correlation coefficient between the models and observations ACE per year in each basin in Table 4.3. Since the GISS model’s TCs have very weak intensities that seldom exceed the ACE CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 90 threshold of 35 kt, I define another metric, the model-ACE (MACE), as the sum of the squares of the TC’s maximum wind speed, sampled at 6-hourly intervals without any intensity threshold (as was done in Camargo et al. (2005) for low-resolution models). The correlations of the models’ yearly MACE in each basin with the yearly ACE of the observations are also shown in Table 4.3. The correlations in the North Atlantic and Pacific basins are much higher than the other basins. In particular, the FSU and HiRAM models have a correlation coefficient of 0.7 in the North Atlantic and the GEOS-5 model has a correlation coefficient of 0.7 in the Western North Pacific basin.

Table 4.3: Correlation of yearly ACE and model-ACE (MACE) in each basin and the yearly observed ACE, shown as ACE / MACE. Asterisks denote correlations that are statistically significant. Basins are defined as: SI (South Indian), AUS (Australian), SP (South Pacific), NI (North Indian), WNP (Western North Pacific), ENP (Easter North Pacific), NATL (North Atlantic).

Model SI AUS SP NI WNP ENP NATL FSU - - - - 0/0 0.5*/0.5* 0.7*/0.7* GEOS-5 0/0 -0.1/-0.2 0.5*/0.4* -0.2/-0.2 0.7*/0.7* 0.4*/0.5* 0.6*/0.6* GISS 0/0 -0.3/0 -0.2/-0.2 -0.2/0.2 0.3/0.2 0/0.7* 0/0.4 HiRAM 0.2/0.2 0.4*/0.4* 0.1/0.1 -0.1/-0.1 0.5*/0.5* 0.6*/0.6* 0.7*/0.7* MRI 0.2/0.2 -0.4*/-0.4* 0.1/0.1 -0.1/-0.1 0.3/0.3 0.4*/0.4* 0.6*/0.6*

Figure 4.12 shows the difference of genesis density for El Niñoand La Niñayears. El Niñoand La Niñaseasons are defined for the northern and southern Hemispheres in Table 4.45. The observations have a larger and stronger peak in genesis density off of the western coast of Central America in El Niñomonths than La Niñamonths.

5Using the warm and cold ENSO (El Ni˜noSouthern Oscillations) deﬁnitions of the Climate Prediction Center, available at http://www.cpc.ncep.noaa.gov/products/analysis_monitoring/ ensostuff/ensoyears.shtml. CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 91

As the GISS and FSU models have very few TCs in this region, they are unable to reproduce this diﬀerence, while the HiRAM and GEOS-5 models are able to reproduce the diﬀerence.

Table 4.4: El Niñoand La Niñaseasons for the northern and southern hemispheres, using the warm and cold ENSO (El NiñoSouthern Oscillations) definitions of Cli- mate Prediction Center. The northern (southern) hemisphere seasons definitions as based on the state of ENSO in the August - October (January - March) seasons. Note that the southern hemisphere TC seasons are defined from July to June, encompassing 2 calendar years.

Northern Hemisphere El Ni˜no 1982, 1986, 1987, 1991, 1994, 1997, 2002, 2004, 2006, 2009 La Ni˜na 1983, 1985, 1988, 1995, 1998, 1999, 2000, 2007

Southern Hemisphere El Ni˜no 1982/83, 1986/87, 1987/88, 1991/92, 1994/95, 1997/98, 2002/03 La Ni˜na 1980/81, 1984/85, 1988/89, 1995/96, 1998/99, 1999/00, 2000/01, 2005/06, 2007/08, 2008/09

A well known impact of ENSO on TC development is for average formation location to shift to the south and east in the Western North Pacific and to shift to the south and west in the Eastern North Pacific during El Niñoyears (Chia and Ropelewski, 2002). Figure 4.13 shows the mean position of TC formation in the Western and Eastern North Pacific, split between La Niñaand El Niñoyears. In the Western North Pacific, the models are able to reproduce the southwest shift in El Niñoyears, with exception of the FSU model which has an eastern shift. In the Eastern North Pacific, all the models are able to simulate the southwest shift in El Niñoyears.

4.4 Conclusions

This chapter has described an intercomparison of several high-resolution atmospheric models of the present climate, forced with both climatological and historical CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 92

FSU GEOS−5 50

−50

GISS HiRAM 50

−50

MRI Observations 50

−50 0 100 200 300 0 100 200 300

−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5

Figure 4.12: Difference of TC genesis density in El Niñoand La Niñaseasons in models and observations. The genesis density is defined as the mean TC formation per 5◦ x 5◦ box per year. CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 93

Western North Pacific

Latitude 10

8 120 125 130 135 140 145 150 155 160 165 170 Longitude

Eastern North Pacific

Latitude 10

210 215 220 225 230 235 240 245 250 255 260 Longitude

FSU GEOS−5 GISS HiRAM MRI Observations

Figure 4.13: Mean TC genesis location in the western and eastern North Pacific in El Niño(triangles) and La Niña(circles) years in models and observations. CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 94

SSTs, in their ability to simulate the characteristics of TCs seen in observations. Model TCs were compared to observational TCs in terms of frequency as well as spatial, temporal, and intensity distributions. A range of tracking schemes were applied by each individual group to derive TC tracks and intensities for all models, consistent with the way in which results from these models have been shown previously in single-model studies. Overall the models were able to reproduce the geographic distribution of TC track density in the observations, with the HiRAM model, in particular, demonstrating the most similarity to observations. TC formation off the eastern coast of Central America was the most difficult region to correctly simulate, with the HiRAM, HR CAM5.1, and HadGEM3 models demonstrating superior performance. All models have a weaker seasonal cycle than observations, with relatively too few TCs in the second half of the year and relatively too many TCs in the first half of the year. The models reproduce the observational seasonal cycle to varying degrees in each basin, with the HiRAM model showing arguably the best match to observations overall. There is a wide range in TC intensities between the different models. Some, but not all, of this difference can be seen as a consequence of resolution, with higher resolution models being able to simulate stronger TCs. This effect can be most readily seen in the CAM5.1 and HadGEM3 models which were run at multiple resolutions. Many previous studies have predicted a decrease in TC frequency and an increase in TC intensity in a warmer climate (Knutson et al., 2010). The prediction of a decrease in TC frequency is mainly from modeling studies, where GCM simulations of a warmer climate produce fewer TCs than the present climate, with a few notable exceptions (e.g. Emanuel 2013). Given that this study has found a large range of TC frequency between these high-resolution models, it raises concerns about the reliability of GCM driven predictions of future TC frequency. However, some of the models (especially HiRAM) are able to simulate the TC climatology remarkably well and demonstrate the usefulness of GCM modeling studies of TC characteristics. CHAPTER 4. CHARACTERISTICS OF TROPICAL CYCLONES IN HIGH-RESOLUTION MODELS IN THE PRESENT CLIMATE 95

In the simulations forced with historical SSTs, the models were able to reproduce the interannual variability of TC frequency in the North Pacific and Atlantic basins, with the HiRAM and GEOS-5 models showing particularly high correlation with observations in those basins. All models were also able to reproduce the general geographic shift in TC formation location during El Niñoand La Niñayears. CHAPTER 5. CONCLUSIONS 96

Chapter 5

Conclusions

In this thesis I have focused on two types of extreme weather events: subtropical floods and tropical cyclones (TCs). Because of their impact on society, it is important to understand these extreme events and how they may change with a warming climate due to greenhouse gas emissions. In the previous chapters, I analyzed these events in both models and observations. In part I, I focused on subtropical floods and the interaction of large-scale dynamics with convection. I first examined the 2010 and 2014 floods in India and Pakistan in chapter 2 using reanalysis data. It was found that the source of the high levels of moisture in the flood region was advection from the Bay of Bengal or Arabian Sea caused by a combination of high pressure systems and monsoon depressions traveling over India. The quasi-geostrophic (QG) omega equation was used to decompose the vertical velocity into components due to the synoptic forcing of the large-scale dynamics, the surface forcing of orographically forced mechanical ascent due to low-level winds, and the heating. It was found that the orographic forcing was the dominant trigger of convection and that the synoptic forcing due to vorticity and temperature advection was relatively weak. These results are consistent with the results from the modeling study of Nie et al. (2016) using the Column QG (CQG) framework, which uses the QG omega equation to parameterize the large-scale dynamics. The conclusion drawn from these events was further supported by an examination of historical data of this region which demonstrated that CHAPTER 5. CONCLUSIONS 97 topographic forced ascent and moisture content are the main drivers of extreme precipitation in this region. By identifying common features among the events in this region and highlighting the two most relevant environmental factors which regulate their occurrence, the conclusions of chapter 2 could inspire future work that investigates potential future changes of flooding in this region. Next, in chapter 3 I apply a similar analysis to the 2015 flood in Texas and Oklahoma. Again, the QG omega equation was applied to reanalysis data to decompose the vertical velocity and similar to the India/Pakistan events, the heating term component was found to be dominant during the event. In contrast to the India/Pakistan events, the dominant triggering mechanism of convection during the Texas/Oklahoma event was found to be the synoptic forcing of the advection terms in the omega equation from upper-level PV disturbances. Additionally, CQG model simulations using a Single Column Model and a Cloud Resolving Model (CRM) were used to further examine the interaction between the large-scale dynamics with convection. It was found that the large-scale PV forcing and the advection of moisture into the flood region were both essential in producing the extreme amounts of rainfall during the event. I also used CQG model simulations to conduct a climate attribution analysis. It was found that the event was 4% more intense due to climate change and that this event would potentially be 25% more intense in a warmer future climate. Finally, part II consisted of chapter 4, in which I detailed an intercomparison of the ability of several high-resolution models to simulate the characteristics of TCs in the present climate. TCs from the models were compared to observational TCs in terms of frequency as well as spatial, temporal, and intensity distributions. Overall the models were able to reproduce the geostrophic distribution of TCs reasonably well. All of the models had a weaker seasonal cycle of TCs than the observations and there was a wide range of TC intensities between the models. Some, but not all, of the intensity difference can be seen as a consequence of resolution, with higher resolution models producing stronger TCs. When forced with historical Sea Surface Temperatures, the models were able to reproduce the internal variability CHAPTER 5. CONCLUSIONS 98 of TC frequency in the North Pacific and Atlantic basins. Some of the models (especially HiRAM) were able to simulate the TC climatology remarkably well and lend confidence to the use of modeling studies to project future changes in TC characteristics. The methods and results of this thesis could lead to several avenues of future work. The application of the QG omega equation detailed in part I can be applied to any number of other extreme precipitation events. While I was focused on subtropical events, where dry QG dynamics and moist convection were expected to both be important, this approach is quite general and could be used to examine any event outside of the deep tropics. In particular, the CQG framework using a CRM could be a valuable tool for highly-conditional climate attribution studies. It may prove to be a useful complement to other highly-conditional attribution studies which use more complicated models. For example, Meredith et al. (2015) conducted a highly-conditional attribution study of an extreme precipitation event near the Black Sea town of Krymsk using a nested-grid regional atmospheric model where the higher resolution grids were run at convection-permitting resolution. While this type of model is capable of very accurate simulations of an event, its complexity makes it harder to conceptually understand. A CQG model that parameterizes the large-scale circulation while still explicitly representing the convection allows for an easier understanding of the interaction between the dynamics and convection during the event and can be used to augment the more realistic model’s simulations. I highlighted the strength and weaknesses of several high resolution models in simulating the characteristics of TCs in part II. These models were also used to project future changes in TCs in a warmer climate scenario. The results in part II were important in putting these projections in context and help to understand how much faith to put into the projections of certain TC characteristics from the different models. These projections were summarized in Walsh et al. (2015). The majority of models predict a decrease in TC frequency and an increase in the total rainfall associated with global TCs. BIBLIOGRAPHY 99

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