LI-DISSERTATION-2017.Pdf

c 2017 Weiwei Li TOWARD BETTER SUBSEASONAL-TO-SEASONAL PREDICTION: PHYSICS-ORIENTED MODEL EVALUATION AND PREDICTABILITY OF TROPICAL CYCLONES

WEIWEI LI

DISSERTATION

Submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy in Atmospheric Sciences in the Graduate College of the University of Illinois at Urbana-Champaign, 2017

Urbana, Illinois

Doctoral Committee: Associate Professor Zhuo Wang, Chair Dr. Melinda S. Peng Professor Bob Rauber Professor Donald J. Wuebbles Abstract

Skillful subseasonal-to-seasonal (hereafter S2S; 10 days - 12 weeks) prediction can greatly benefit decision-making on resource management and agricultural planning that falls into the weekly to seasonal time ranges. The S2S prediction, bridging the traditional weather forecasting and climate prediction, remains a challenge for global numerical models. This is mostly because the sources of predictability on S2S timescales are not fully understood and/or not well represented in global models. My Ph.D. thesis research seeks to improve the model performance and the S2S prediction by 1) developing a suite of “physics-oriented” model evaluation metrics that can not only assess how model performs but also help to reveal possible error sources, and 2) investigating sources of predictability of high-impact weather phenomena with a special focus on tropical cyclones (TCs). The analysis is expected to provide useful guidance on model development and improvement. My thesis first evaluated the Madden-Julian oscillation (MJO) - the dominant mode of tropical subseasonal variability and an important source of predictability on S2S timescales. Both the Navy Operational Global Atmo- spheric Prediction System (NOGAPS) and Global Forecasting System (GFS) exhibit relatively low predictive skill when the MJO initiates over the Indian Ocean and when the active convection of the MJO is over the Maritime Con- tinent. Further analyses indicated a dry bias within the marine boundary layer and a misrepresented shallow heating mode in the NOGAPS, suggesting a model deficiency in cumulus parameterization. The diabatic heating biases are associated with weaker trade winds, weaker Hadley and Walker circulations over the Pacific, and weaker cross-equatorial flow over the Indian Ocean. The TC prediction was evaluated in the National Centers for Environmen- tal Prediction (NCEP) Global Ensemble Forecasting System (GEFS) with forecast lead time up to 2 weeks. It shows that the GEFS has large errors

ii of TCs on the regional scale. The negative genesis biases over the western North Pacific are associated with a weaker-than-observed monsoon trough, the erroneous genesis pattern over the eastern North Pacific is related to a southward displacement of the ITCZ, and the positive genesis biases near the Cape Verde islands and negative biases farther downstream over the Atlantic can be attributed to the hyperactive African easterly waves and stronger deep convective heating. The biases are associated with the deficiencies in the cumulus schemes of the GEFS. The precipitation initiates too early with respect to the column water vapor. And there is a dry bias in the column water vapor, which increases with the forecast lead times. The GEFS also underpredicts moderate-to-heavy precipitation. The analyses suggest that improvement in the cumulus parameterization may reduce the model mean state errors and enhance the TC prediction on the regional scale. The predictability of TCs was investigated on interannual, subseasonal, and synoptic timescales using the GEFS reforecasts. It shows that the model skillfully captures the interannual variability of TC activity over the North Pacific and the North Atlantic, which can be attributed to the modulation of TCs by the El Niño-Southern Oscillation (ENSO) and the Atlantic meridional mode. The GEFS has promising skill in predicting the active and inactive periods of TC activity over the Atlantic. The skill, however, has large year- to-year fluctuations. The analyses suggest possible impacts of ENSO, the MJO, and the anticyclonic Rossby wave breaking on the TC subseasonal predictability. Lastly, the predictability associated with different synoptic flow regimes was evaluated using the TC development pathways. It shows that the extratropical influenced TCs have lower predictability than the ones dominantly modulated by tropical atmosphere. Such extratropical influenced storms, when developing near the coast, will pose a challenge for operational forecasts and emergency management.

iii To my family.

iv Acknowledgments

I would like to express my appreciation and gratitude to my advisor Zhuo Wang for her endless guidance and suggestions throughout the course of my doctoral program. Not only has she guided me to overcome all the problems and difficulties, but also her scientific attitude with high integrity truly inspires me to do the same. I profusely thank Dr. Melinda Peng for her continuous support and en- couragement all these years. I especially admire her great personality and positive attitude. I am also grateful to Prof. Bob Rauber for his suggestions on my Ph.D. research and career development, and for being caring, supportive and helpful in numerous ways to everyone in our department. My sincere thanks to Prof. Don Wuebbles for his depth and breadth of knowledge in the area of climate and his interest in my research on operational forecasting. Special thanks to the coauthors of our papers: James Ridout (NRL), Xi- anan Jiang (JPL), Ron McTaggart-Cowan (Environment Canada), Christo- pher Davis (NCAR), and Gan Zhang (UIUC; my group mate and friend). Thanks are extended to Mrs. Tammy Warf and Mrs. Karen Eichelberger. I am always impressed with their willingness to help. Finally, I wish to thank all the friendly people in Champaign-Urbana who have shaped who I am today. This work was supported by the National Oceanic and Atmospheric Ad- ministration (NOAA) Grants NA15NWS4680007 and NA16OAR4310080, the Office of Naval Research(ONR) Grant N00014-11-1-0446, and NavalRe- search Laboratory (NRL) Grant N00173-15-1-G004.

v Table of Contents

Chapter 1 Introduction ...... 1 1.1 Motivation ...... 1 1.1.1 Uncertainty in model initial state ...... 1 1.1.2 Uncertainty in model formulation ...... 2 1.1.3 Identifying sources of predictability ...... 2 1.1.4 Needs of subseasonal-to-seasonal (S2S) prediction . . . 3 1.1.5 Research to Operations (R2O) ...... 3 1.2 Background ...... 4 1.2.1 Physics-oriented model evaluation ...... 4 1.2.2 Sources of predictability ...... 5 1.3 Objectives and scientiﬁc questions ...... 6 1.4 Outcomes and signiﬁcance ...... 7

Chapter 2 Physics-oriented Model Evaluation I: Tropical Subsea- sonal Variability and Moist Processes in the NOGAPS Analysis and Short-Term Forecasts ...... 8 2.1 Introduction ...... 8 2.2 NOGAPS description ...... 10 2.3 Data and Method ...... 11 2.3.1 Data ...... 11 2.3.2 The MJO indices and the MJO metrics ...... 12 2.4 Performance of the NOGAPS analysis in describing the MJO . 13 2.5 Evaluation of the NOGAPS short-term forecasts ...... 19 2.5.1 Precipitation spatial pattern and ITCZ bias ...... 19 2.5.2 Diabatic heating and large-scale circulations ...... 21 2.5.3 Moist processes in the NOGAPS ...... 25 2.5.4 MJO in the NOGAPS forecasts ...... 33 2.6 Summary and discussion ...... 37

Chapter 3 Physics-oriented Model Evaluation II: Tropical Cyclones in the NCEP Global Ensemble Forecasting System (GEFS) Re- forecast Version 2 ...... 39 3.1 Introduction ...... 39 3.2 Data and metrics ...... 41

vi 3.2.1 Global Ensemble Forecasting System Reforecast version- 2...... 41 3.2.2 Detection of TCs ...... 42 3.3 Climatology of TC activity in the GEFS ...... 43 3.4 Impact of environmental condition biases on TC prediction . . 48 3.4.1 Biases in tropical cyclogenesis ...... 48 3.4.2 Possible deﬁciencies in the model physics ...... 57 3.5 Summary and discussion ...... 60

Chapter 4 Predictability of Tropical Cyclones ...... 62 4.1 Introduction ...... 62 4.2 Data and metrics ...... 65 4.2.1 Data ...... 65 4.2.2 Metrics ...... 65 4.3 Interannual timescales ...... 66 4.4 Subseasonal timescales ...... 71 4.4.1 Low-frequency climate modes ...... 71 4.4.2 Impacts of Rossby wave breaking ...... 76 4.5 Synoptic timescales ...... 84 4.5.1 Tropical cyclogenesis pathways ...... 86 4.5.2 Evaluation of tropical cyclogenesis predictability . . . . 89 4.6 Summary and discussion ...... 101

Chapter 5 Conclusions ...... 104

References ...... 107

vii Chapter 1

Introduction

1.1 Motivation

Numerical models are used to routinely predict future weather or climate in major operational centers around the world (WMO, 2015). These models encode the laws of physics (referred to as “dynamical models”), the atmospheric governing equations, and the numerical methods to produce forecasts (e.g., Shuman, 1989; Edwards, 2011). Although forecasting systems have been tremendously improved in recent years, skillful forecasts especially on subseasonal-to-seasonal (hereafter S2S; 10 days - 12 weeks) timescales remain challenging (e.g., Lynch, 2006; Morgan et al., 2007; Smith et al., 2012; NAS, 2016). The problems confronting current-generation forecasts include 1) the model initial uncertainties; 2) uncertainties in the model formulation; 3) lack of an understanding on key physical processes and limits of predictability, especially for high-impact weather/climate phenomena; and 4) more sophisticated and specialized requirement from forecast consumers. As socio-economic activities are becoming increasingly complex and interrelated, the capability of forecasting systems need to be enhanced and persistently improved in order to facilitate decision making across diﬀerent sectors of our society.

1.1.1 Uncertainty in model initial state

Uncertainties associated with the model initial conditions are inevitable, which may arise from inadequate observation sampling (in space, time, and physical quantity), or deﬁciencies in data assimilation and ensemble initialization/perturbation techniques (e.g., Smith et al., 2012; Komaromi and Ma- jumdar, 2014). The chaotic nature of atmosphere imposes that errors in the

1 initial state at a given location may aﬀect the forecasts over a large region and result in useless deterministic forecast in one or two weeks (e.g., Lorenz, 1965, 1996).

1.1.2 Uncertainty in model formulation

Uncertainties in model formulation are mostly the consequences of imperfect model dynamics and physics. Mathematical equations are used to de- scribe the atmospheric fluid dynamics and physical principles, and subgrid- scale processes need to be parameterized using empirical assumptions (e.g., Palmer, 2000; Kirtman et al., 2014). The reliability of a forecasting system can be largely undermined by misrepresented processes especially on scales comparable with or smaller than the truncation scale of a model. In particular, the errors associated with cumulus parameterization remain an outstanding issue (e.g., Cess et al., 1990; Soden and Held, 2006; Bombardi et al., 2015). As a critical component of the model physics, cumulus parameterization has significant impacts. The quality in representing convective processes may affect the predictive skill of mesoscale and large-scale atmospheric circulations (e.g., Li et al., 2014, 2016). Due to the nonlinearity of atmosphere and forecast systems, the errors on mesoscale and convective scale can accumulate and shift to larger scales through upscale error growth and affect the overall performance of a model (e.g., Zhang et al., 2007; Sun and Zhang, 2016). Evaluation of convective processes, such as the coupling between precipitation and moisture, is therefore important to improve the model physics.

1.1.3 Identifying sources of predictability

In addition to optimizing model initialization and formulation, it is a press- ing need to enhance our knowledge of the sources of predictability, especially for high-impact weather phenomena (WMO, 2015). Signiﬁcant progress has been made in identifying the sources of predictability using theoretical and observational analysis. Such type of research usually involves exploiting the physical relationships underlying a phenomenon that yield the predictability (NAS, 2016). Despite the progresses, more work is needed to better under-

2 stand and represent sources of predictability. Taking tropical cyclone (TC) as an example, the predictability of TCs varies case by case, even with the same operational prediction system and during the same hurricane season (Komaromi and Majumdar, 2015; Wang et al., 2017). The forecast bust of the hurricane season in 2013 was because operational models failed predicting the frequent extratropical Rossby wave breaking (Zhang et al., 2016). Such variations of predictability cannot be completely attributed to changes in a prediction system or the heterogeneity of observational data assimilated in a model. Advances in weather prediction are thus closely tied to investigating new sources of predictability and improving their representations in prediction systems.

1.1.4 Needs of subseasonal-to-seasonal (S2S) prediction

A recent emerging forecast challenge is that forecast consumers demand for more sophisticated and specialized weather services (Morgan et al., 2007; NAS, 2016), in particular, S2S prediction. Some high-impact weather phenomena such as TCs, heat waves and cold spells, can cause property damage, economic losses or even high death toll. Before such an event strikes, the more time and more speciﬁc risk information can communities have, the more damages and losses may be prevented. Since weather and climate span a continuum of timescales, skillful S2S prediction may help to optimize different sorts of decision makings, and provide irreplaceable information for disaster preparedness and mitigation. The S2S prediction, however, remains a challenge for global numerical models. This is mostly because the key physical processes and sources of predictability on S2S timescales are not fully understood, and we lack comprehensive evaluation metrics and diagnostic tools for the S2S prediction (NRC, 2010; WMO, 2013; NAS, 2016).

1.1.5 Research to Operations (R2O)

To address the aforementioned forecast issues, we should realize that future model performance largely depends on sustained reduction of model errors and improved understanding of predictability especially on S2S timescales. In facilitating such model development and an eﬀort of the Next Genera-

3 tion Global Prediction system (NGGPS; http://www.nws.noaa.gov/ost/ nggps/), the National Oceanic and Atmospheric Agency’s (NOAA’s) Re- search to Operations (R2O) Initiative appeals collaborative research and development testing, transitioning new scientiﬁc knowledge to operations, and developing in-depth evaluation of model forecasts. The initiative also pro- poses to increase the accuracy of the critical weather forecasting. In light of such imperative needs, my Ph.D. thesis research expects to develop useful model evaluation metrics, obtain a better understanding on the predictability of high-impact weather phenomena, and ultimately contribute to the transition from research to operations.

1.2 Background

1.2.1 Physics-oriented model evaluation

Evaluation of model forecasts is an indispensable component of the model development. Conventionally, performance-oriented metrics [such as anomaly correlation coefficient (ACC) and root-mean square error (RMSE)] are applied to measure the model performance and routinely used in operational centers for forecast verification. The performance-oriented metrics can provide guidance on model development and forecast reliability, but are inca- pable of identifying error sources of a model (Richardson et al., 2013). There is an increasing demand in recent years to adopt “physics-oriented” diagnostics or metrics for model evaluation (NRC, 2010; NAS, 2016). Physics- oriented diagnostics focus on the critical processes or phenomena through evaluating the evolution or distribution of key variables, and can shed light on the deficiency of the model physics such as the physical parameterization or other errors in a model. In brevity, physics-oriented evaluation not only provides information on how well a model performs but also on why a model may fail in a certain aspect. The application of physics-oriented evaluation will be greatly beneficial to the improvement of prediction systems.

4 1.2.2 Sources of predictability

Predictability derives from a series of processes and phenomena across multiple scales (NRC, 2010). Low-frequency climate modes are recognized as sources of predictability. Besides, the initial states including some slowly varying boundary conditions (such as sea surface temperature) and external forcing (such as volcanic eruption) also affect prediction. On the other hand, the major sources of predictability are different for various forecast ranges. Numerical weather predictions (less than 10 days) largely rely on the “memories” of the initial state of the atmosphere, ocean and land (such as sea surface temperature and soil moisture). Due to a relatively slow evolution of these lower boundary conditions, most numerical weather prediction systems are not coupled to an ocean/land model and the atmosphere is affected by the ocean or the land surface (Bender and Ginis, 2000; Koster et al., 2010). Seasonal forecasts (beyond 3 months) that have achieved substantial progresses over years mostly gain skill from the slowly evolving components that are predictable months in advance (Smith et al., 2012). The processes include the lower boundary (oceanic and land) conditions (e.g., Vecchi et al., 2014; Vimont and Kossin, 2007), and the low-frequency climate modes such as El Niño-SouthernOscillation (ENSO) and the North Atlantic Oscillation (NAO; e.g., Brönnimann,2007; Colbert and Soden, 2012). Subseasonal-to-seasonal forecasts (10 days - 12 weeks), bridging a gap between weather and climate, are considered to be challenging because they are too long to use the memory of the initial conditions and too short for the slowly evolving components to influence (Vitart et al., 2017). In addition, the key physical processes on S2S timescales are not fully understood. Although many difficulties remain, previous research have discovered important sources of S2S predictability such as the Madden-Julian oscillation (MJO; Madden and Julian, 1972; Maloney and Hartmann, 2000a; Zhang, 2005). The MJO as the dominant mode of tropical subseasonal variability has a significant impact on the skillful S2S prediction. For example, a model that is more capable of capturing the MJO can skillfully predict TC activity with longer lead times (e.g., Belanger et al., 2010; Vitart, 2009; Elsberry et al., 2014). Although many progresses have been made to improve specific weather and climate phenomena, the sources of predictability, especially on S2S timescales, need to be further investigated. Moreover, continued research is required to

5 advance our understanding of important physical processes involved in atmospheric variability and predictability, and to evaluate the model skill in representing these processes. In summary, advanced prediction of weather or climate events hinges critically on the identiﬁcation of new sources of predictability and the accurate representations of key physical processes in a model.

1.3 Objectives and scientiﬁc questions

The primary objective of this research is to improve the model performance and the S2S prediction by 1) developing a suite of physics-oriented evaluation metrics; 2) identifying possible error sources to provide guidance on the improvement of the model physics; and 3) investigating sources of predictability for high-impact weather phenomena. There is no consensus on the definition of S2S timescales (NAS, 2016). In this Ph.D. thesis, “S2S prediction” refers to the prediction with forecast ranges from 10 days to 12 weeks, which is beyond the range of normal numerical weather predictions (∼10 days) and covers the operational medium-range forecasts (up to 15 days; Vitart et al., 2012, 2017). For completeness, weather forecasts on the timescales shorter than 10 days were also evaluated with the ultimate goal to develop a skillful and seamless weather-climate prediction system. My Ph.D. research covered multiscale processes/systems. For high-impact weather phenomena, this thesis focused on tropical cyclones (TCs). Tropical cyclones are the most destructive storm system on our planet, and skillful TC prediction is critical for improving storm preparedness and mitigating property and life loss. A better understanding on the predictability of TCs will not only help to identify the key processes involved in TC development but may also provide useful information on the reliability of dynamic prediction and thus aid more effective use of forecast products. In addition to TCs, precipitation processes and the MJO were also evaluated. These processes/systems are chosen because i) convection representation is one of the most important components of dynamic models, and precipitation affects atmospheric motions of different scales, and ii) the MJO is the dominant mode of tropical subseasonal variability and an important source of predictability for S2S prediction, and iii) the MJO as a multi-scale process provides an

6 ideal testbed to evaluate the model physics across different spatiotemporal scales and helps to identify the model error sources. This research addressed two overarching thrusts: 1) What physical processes must a model capture for skillful S2S prediction and how well are these processes represented in current global operational models? and 2) How predictable are TCs and what are their sources of predictability on S2S timescales? Through the investigation of these issues, we hope that the research effort will advance our understanding of important physical processes involved in the variability and predictability on S2S timescales, and contribute to the improvements of the S2S prediction. The objective of each chapter in this thesis is listed below: • Chapter 2: To evaluate the tropical subseasonal variability and moist processes in the Navy Operational Global Atmospheric Prediction System (NO- GAPS) analysis and short-term forecasts; • Chapter 3: To evaluate TCs in the National Centers for Environmental Prediction (NCEP)’s Global Ensemble Forecasting System (GEFS) Refore- cast Version-2; • Chapter 4: To investigate the predictability of TCs on different timescales; • Chapter 5: To summarize the thesis.

1.4 Outcomes and signiﬁcance

In collaborations with the NCEP and the Naval Research Laboratory (NRL), we have developed and tested diﬀerent physics-oriented diagnostic tools using the two major operational forecasting systems in the U.S.: the GEFS and the NOGAPS [the predecessor to the Navy Global Environmental Model (NAVGEM)] models. Some diagnostic tools are expected to be incorporated in the global model package by the Developmental Testbed Center (DTC), to be made available to the broad operational and research communities, and to help to advance our weather/climate prediction capabilities. The investigation on the predictability of TCs on diﬀerent timescales will facilitate the improvement of the operational TC forecasts, in particular, the TC prediction on S2S timescales.

7 Chapter 2

Physics-oriented Model Evaluation I: Tropical Subseasonal Variability and Moist Processes in the NOGAPS Analysis and Short-Term Forecasts c 2014 American Meteorological Society1

2.1 Introduction

The Madden-Julian oscillation (MJO) is the dominant subseasonal mode in the tropics (Madden and Julian, 1972, 1994; Lau and Waliser, 2005; Wang, 2005). It has signiﬁcant impacts on the Asian and Australian monsoons as well as the North American and South American monsoons (Yasunari, 1979; Higgins et al., 2000; Kiladis and Weickmann, 1992; Lau and Chan, 1986; Mo, 2000). It plays an active role in the onset and development of ENSO (e.g., Zhang and Gottschalck, 2002) and also modulates tropical convection and tropical cyclone activities over the eastern Paciﬁc and the Atlantic (e.g., Nakazawa, 1988; Chen et al., 1996; Hendon and Salby, 1994; Maloney and Hartmann, 2000a,b). As a low-frequency mode, the MJO serves as an additional source of predictability, besides the lower boundary forcing (SST and land surface conditions), for the atmosphere on subseasonal timescales (e.g., Leroy and Wheeler, 2008; Vitart and Molteni, 2010; Fu and Hsu, 2011). Previous studies have shown that the MJO has remote impacts on the extratropics and modulates the variability and predictability of the midlatitude weather systems (e.g., Liebmann and Hartmann, 1984; Weickmann et al., 1985; Jones et al., 2004; Lau and Phillips, 1986). Realistic simulations of the MJO and its associated teleconnection patterns in a global model are thus important for both weather forecasts and seasonal prediction. Model intercomparison studies (e.g., Slingo et al., 1996; Lin et al., 2006)

1Permission hereby is granted to use ﬁgures, tables, illustrations, and substantial por- tions of text provided that the source is acknowledged: Li, W., Z. Wang, M.S. Peng, and J.A. Ridout, 2014: Evaluation of Tropical Intraseasonal Variability and Moist Processes in the NOGAPS Analysis and Short-Term Forecasts. Wea. Forecasting, 29, 975-995.

8 have shown that general circulation models (GCMs) often have difficulty in simulating the MJO with realistic propagation speed and amplitude. Al- though the exact reason for these deficiencies is not clear, it is generally believed that inadequate representation of cloud processes and multiscale interactions is likely the major culprit (e.g., Tokioka et al., 1988; Wang, 2005). As an intrinsic multiscale system (e.g., Majda and Biello, 2004; Zhang et al., 2010), the MJO serves as an excellent benchmark for evaluating model parameterizations across different spatial and temporal scales. In the present chapter, an evaluation of the MJO-associated tropical subseasonal variability in the analyses and short-term weather forecasts of a global model is presented, in principle offering a look at the development of model forecast errors before the atmospheric state diverges too far from the reality. An ex- amination of more general characteristics of moist processes in the tropics is also presented in an attempt to gain insight into the deficiencies of the model physics on the subseasonal timescales. The forecast system chosen for evaluation in this study is the Navy Op- erational Global Atmospheric Prediction System (NOGAPS). NOGAPS, developed at the Naval Research Laboratory (NRL), had been running operationally at the U.S. Navy’s Fleet Numerical Meteorology and Oceanography Center (FNMOC) since 1982, and was replaced with the Navy Global En- vironmental Model (NAVGEM) in March 2013. NOGAPS produced 6-day forecasts twice daily and, in addition, provided forcing and/or initial and boundary conditions to many other models, including the Navy’s advanced Coupled Ocean-Atmosphere Mesoscale Prediction System (COAMPS2), an ocean wave model, a sea ice model, an ocean circulation model, an ocean thermodynamics model, a tropical cyclone model, and application programs at both FNMOC and the Air Force Weather Agency (AFWA). The products were also used at the Joint Typhoon Warning Center (JTWC) and the Na- tional Hurricane Center (NHC) for tropical cyclone forecasts. Modifications and updates to the model through the years were stringently tested by the NRL and FNMOC before being adopted into operation, but the evaluations mainly focused on the predictive skills of short-term weather forecasts. In this chapter, we will evaluate the representation of tropical subseasonal variability and moist processes in the NOGAPS operational analysis and forecasts

2COAMPS is a trademark of the Naval Research Laboratory.

9 systematically using a suite of diagnostic tools with both performance- and physics-oriented metrics. The NOGAPS evaluation will address the following three aspects with a special focus on the relevant physical processes: (i) the mean states, (ii) the MJO, and (iii) precipitation and moist processes. It is expected that this study will help to guide the diagnostic evaluation of the successor forecast system, NAVGEM, as the development of U.S. Navy atmospheric prediction extends its focus toward longer lead times. This chapter is organized as follows. A description of NOGAPS, in particular the forecast model and its treatment of moist processes, is presented in section 2.2. The data and methods are described in section 2.3. The MJO in the NOGAPS analysis is examined against the Interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim; ERAI) and compared with the Global Forecast System (GFS) analysis in section 2.4. The NOGAPS short-term forecasts are evaluated in section 2.5, including the biases in the thermodynamic ﬁelds and their impacts on large- scale atmospheric circulations and the MJO forecast skill. Section 2.6 oﬀers the summary and discussion.

2.2 NOGAPS description

The NOGAPS forecast system was upgraded to version 4.1 in 2002. It ran operationally at a horizontal resolution of T239 (equivalent to approximately 50 km at the equator) with 30 vertical levels. By the time it was removed from operational use in 2013, the horizontal resolution had been increased to T319, and the model had 42 vertical levels. The NOGAPS data assimilation system in 2002 was a multivariate optimal interpolation (MVOI) analysis scheme. This was replaced in September 2003 by the NRL Atmospheric Variational Data Assimilation System (NAVDAS), and in September 2009 by the NAVDAS-Accelerated Representer (NAVDAS-AR) four-dimensional variational data assimilation (4DVAR) scheme. The physics schemes in the NOGAPS model had been evaluated and updated over the years, particularly the treatment of convection. The convective scheme of Arakawa and Schubert (1974), discretized following Lord (1982), was used until being replaced by a “relaxed” Arakawa-Schubert scheme similar to that described by Moorthi and Suarez (1992). In 2002, the Emanuel convection scheme was

10 adopted. The original Emanuel scheme yielded improvements to tropical cyclone track forecasts, but was found to underpredict heavy precipitation events, overpredict light precipitation, and have unrealistic heating at upper levels. A modiﬁed treatment by Peng et al. (2004) was then adopted. The Emanuel scheme was further improved by increasing the momentum mixing, yielding signiﬁcant improvement in tropical cyclone track forecasts (Hogan and Pauley, 2007). Cloud fractions for deep convective clouds were estimated by a diagnostic cloud scheme (Slingo, 1987). Teixeira and Hogan (2002) im- plemented a new cloud fraction scheme for shallow clouds, which improved the global distributions of the boundary layer clouds and surface shortwave radiation in the model. The adoption of the NAVDAS-AR 4DVAR system, the use of radiance data, and the increase in resolution from T239 to T319 have all contributed to improvements in predictive skill in recent years.

2.3 Data and Method

2.3.1 Data

The NOGAPS analysis and operational forecasts are evaluated against ERAI and compared with the GFS analysis and operational forecasts. ERAI is the latest major undertaking of the ECMWF (Dee et al., 2011). It utilizes 4DVAR and provides a more realistic representation of the atmosphere in both space and time than did earlier versions of the reanalysis. All the datasets are regridded to 1.0 ◦ × 1.0 ◦ resolution, and daily averages are derived from 6-hourly data. The NOGAPS analysis was evaluated for May- November during 2004-10. We focus on the boreal summer because this is the season during which the NOGAPS forecasts are available. The NOGAPS 1-7-day forecasts are available for the following time periods: 7 September-28 November 2008, 14 June-31 October 2009, 4 June-5 November 2010, and 8 July-15 October 2011. Reanalysis and satellite data in the same periods were used to evaluate the NOGAPS forecasts. Two satellite datasets were employed to evaluate precipitation and moist processes. The Climate Prediction Center (CPC) morphing technique precipitation product (CMORPH) is a 3-hourly global precipitation dataset with a spatial resolution of 0.25 ◦ × 0.25 ◦ (Joyce et al., 2004). Precipitation was es-

11 timated from passive microwave precipitation retrievals, and motion vectors derived from geostationary satellite IR data were used to advect the precipitation features. CMORPH thus better represents the spatial structure of precipitation compared to Tropical Rainfall Measuring Mission (TRMM) 3B42. To be consistent with the analysis and forecast data, daily means were derived from the CMORPH precipitation and regridded to the 1.0 ◦ × 1.0 ◦ resolution. Column water vapor (CWV) and precipitation from the version 7 Special Sensor Microwave Imager Sounder (SSM/IS) polar-orbiting dataset were used to evaluate the precipitation-CWV relationship. The SSM/IS data have a spatial resolution of 0.25 ◦ × 0.25 ◦, using a uniﬁed and physically based algorithm to simultaneously retrieve precipitation and CWV (Wentz and Spencer, 1998; Horv´athand Gentemann, 2007). The daily average over the ocean was derived from the F-16 and F-17 satellites for the same periods as the NOGAPS forecasts and interpolated to 1.0 ◦ × 1.0 ◦ resolution.

2.3.2 The MJO indices and the MJO metrics

To evaluate the MJO in the global model analyses and forecasts, we adopted the standardized set in the MJO diagnostics package developed by the U.S. Climate Variability and Predictability (CLIVAR) MJO Working Group (Kim et al., 2009). It objectively evaluates global model simulations of the MJO within a consistent framework (CLIVAR, 2009). Both “global” and “local” MJO indices in this study were used to select the MJO events and construct composites. For the global MJO index, we employed the “All-season Real- time Multivariate MJO Index” (RMM; Wheeler and Hendon, 2004, hereafter WH04). The RMM was derived from the multivariable empirical orthogo- nal functions of outgoing longwave radiation (OLR) and 850- and 200-hPa zonal winds, and was downloaded online (http://cawcr.gov.au/staff/ mwheeler/maproom/RMM). The RMM emphasizes the global structure of the MJO. To examine the MJO-related variability over specific regions, we defined a local MJO index. A space-time filter was applied to the meridionally averaged (10 ◦S-10 ◦N) daily OLR to extract variations with zonal wavenumbers 0-10 and periods between 30 and 91 days (or 4-12 cpy). The data were then normalized by the standard deviation at each grid point. The resultant two-dimensional (longitude and time) OLR array was used to define a local

12 Figure 2.1: Wavenumber-frequency diagrams for the 20-100-day bandpass-ﬁltered 200-hPa zonal winds averaged over 10 ◦S-10 ◦N for (from left to right) the ERAI, NOGAPS, and GFS analyses in boreal summer during 2004-10.

MJO index for a given longitude or longitude range. “Day 0” refers to the peak convection day, when the normalized OLR anomaly reaches a negative minimum and its magnitude exceeds 1.0. Positive (negative) lags indicate the time after (before) the peak convection.

2.4 Performance of the NOGAPS analysis in describing the MJO

As the first step, the MJO signals in the NOGAPS analysis were evaluated against ERAI and compared to the GFS analysis. Figure 2.1 shows the wavenumber-frequency diagrams of 200-hPa zonal wind averaged over 10 ◦S- 10 ◦N from the ERAI, NOGAPS, and GFS analyses. The annual cycle was first removed by subtracting the climatological mean daily data, and then a 20-100-day bandpass filter (Duchon, 1979) was used to extract the subseasonal variations prior to the wave-number-frequency analysis. The NOGAPS analysis captures the MJO signals with a realistic frequency range and spatial scales, that is, eastward-propagating signals are stronger than westward ones, with the maximum power spectra at globally zonal wavenumber 1 and the dominant periods between 40 and 50 days. However, it is discernible that the MJO spectral power in the NOGAPS analysis is weaker than that in the GFS or ERAI simulations. The NOGAPS analysis also slightly overestimates

13 Figure 2.2: (left) The 20-100-day bandpass-filtered NOAA interpolated daily outgoing longwave radiation (OLR; contours) and 850-hPa zonal winds from ERAI (shading) for (from top to bottom) eight MJO phases (by WH04) in boreal summer during 2004-10. The red (blue) contours outline the positive (negative) 6 and 18 W m−2 filtered OLR. (middle),(right) As in (left), but just for the 850-hPa zonal winds from the NOGAPS and GFS analyses, respectively. Spatial pattern correlation coefficients of the zonal winds at 850 hPa (200 hPa) between the NOGAPS-GFS analysis and ERAI at eight MJO phases are marked above each plot. The numbers of composite days for each phase are indicated to the right of each row. the variances at global wavenumbers 2 and 3. The MJO has a baroclinic vertical structure. Convection is closely coupled to the upper- and low-level wind fields over the Indo-Pacific warm pool region. The composites of 20-100-day bandpass-filtered 850-hPa zonal winds were constructed for different MJO phases based on the RMM (Fig. 2.2). To extract prominent MJO events, we only selected the days when the “MJO amplitude” (WH04) exceeded 1.0 (the number of the composite days is indicated to the right of each row). The composites derived from the National Oceanic and Atmospheric Administration (NOAA) daily OLR and the ERAI 850-hPa zonal wind are shown in the left column of Fig. 2.2 to serve as bench- marks for the evaluation, and also to provide a large-scale perspective of the MJO evolution. In phase 1 of the MJO, the MJO convection decays over the

14 central Pacific and is initiated over the Indian Ocean. The easterly anomalies are over the North Indian Ocean and the Maritime Continent. In phase 2, as convection develops over the north Indian Ocean, the easterly anomalies are weakened. In phase 3, enhanced convection is over the Indian Ocean and extends eastward to the Maritime Continent. Meanwhile, the low-level westerlies develop over the central and eastern Indian Ocean, nearly collocated with convection, and the easterly anomalies over the Maritime Continent are also strengthened. From phase 4 to phase 6, convection and westerly anomalies move eastward to the Maritime Continent and then to the western Pacific. A pattern of northward propagation is evident in both fields, which is consistent with previous studies (Kemball-Cook and Wang, 2001; Wheeler and Hendon, 2004; Yang et al., 2013). In phase 7, convection and westerly anomalies are weakened over the western Pacific. The easterly anomalies start prevailing over the Indian Ocean. In phase 8, convection is suppressed (enhanced) over the Maritime Continent and the western (eastern) Pacific. Widespread westerly anomalies cover the tropical Pacific. The composites of filtered 850-hPa zonal wind from the NOGAPS and GFS analyses are shown in the two right columns of Fig. 2.2. Both analyses show a close resemblance with the ERAI. The northward propagation of the westerly anomalies over the western Pacific is captured by both analyses. The spatial correlations of the NOGAPS with the ERAI between 20 ◦S and 20 ◦N remain above 0.97 in all the MJO phases. Similarly strong pattern correlations are also found in the 200-hPa zonal wind. Overall, Figs. 2.1 and 2.2 show that the MJO signals in the dynamic fields of the NOGAPS and GFS analyses are in good agreement with those in the ERAI. The NOGAPS analysis performs better in the lower troposphere, whereas the GFS analysis is somewhat better than the NOGAPS in the upper troposphere, as indicated by the spatial correlations. Previous studies have revealed the complex vertical structure of the MJO in the moisture field: low-level moistening precedes the peak convection and enhanced moisture occurs throughout the troposphere at the time of the peak convection, which is followed by drying in the lower troposphere (Kemball- Cook and Wang, 2001; Kiladis et al., 2005; Tian et al., 2010). The vertical structure of moisture anomalies is consistent with the cloud transition associated with the MJO (Benedict and Randall, 2007; Del Genio et al., 2012; Jiang et al., 2011), and is believed to be critical for the evolution and propa-

15 gation of the MJO (e.g., Zhao et al., 2013). To examine whether this feature is captured by the analyses, the composites of unfiltered daily relative humidity (RH) were constructed using the local MJO index defined over the Indian Ocean (10 ◦S-10 ◦N, 50 ◦E-100 ◦E). The daily climatology derived from the 2004-10 analysis was first removed to exclude the annual cycle. The Indian Ocean was chosen here to examine the premoistening process associated with the MJO initiation. Nineteen prominent MJO events in the boreal summer during 2004-10 were selected. As shown in Fig. 2.3, the ERAI clearly illustrates the evolution of the moisture field. The lower-tropospheric premoistening starts more than 10 days before the peak convection. As the peak convection approaches, the RH increases throughout the troposphere, with a maximum anomaly of up to 9% around 450hPa. The upper-tropospheric moistening persists more than 10 days after the peak convection while the lower-to-middle troposphere dries up earlier, owing to either the stratiform precipitation or the horizontal advection or both (e.g., Benedict and Randall, 2007; Chikira, 2014; Maloney and Hartmann, 1998). The GFS analysis resembles the ERAI except that a weak premoistening occurs more than 20 days prior to the peak convection. Although the NOGAPS captures the premoistening signals, the RH anomalies are about 50% weaker than those in the ERAI or GFS, and the maximum moistening slightly lags the peak convection. A thin layer of negative RH anomalies appears on day -7 and onward around 850 hPa. A similar low- level dry bias is also found in the NOGAPS forecasts and will be discussed in detail in section 2.5. The patterns of evolution of the diabatic heating rate (Q1; Yanai et al., 1973; Yanai and Tomita, 1998) reveal the typical top-heavy heating profiles on “day 0” for all three analyses (Fig. 2.4), which is consistent with many previous studies (e.g., Lin et al., 2004; Morita et al., 2006). But similar to the RH composites, the MJO signals in Q1 in the NOGAPS analysis are weaker (by about 10%) than those in the ERAI or GFS analyses. The shallow heating mode prior to the peak convection is hardly discernible in the NOGAPS analysis. This may be either due to a stronger stratiform process and/or the lack of cumulus congestus (shallow and congestus convection; e.g., Schumacher et al., 2004; Chikira, 2014; Khouider and Majda, 2006). The relatively weak MJO signals in the NOGAPS thermodynamic fields may be attributed to the deficiencies in the model physics, particularly the Emanuel

16 Figure 2.3: (top three rows) Patterns of evolution of RH (%) anomalies from 25 days before to 15 days after the MJO peak convection over the Indian Ocean (10 ◦S-10 ◦N, 50 ◦-100 ◦E), derived from the ERAI, NOGAPS, and GFS analyses, respectively. (bottom) Time series of the space-time-ﬁltered OLR during the same period. Day 0 refers to the peak convection day, and positive (negative) lags indicate the time after (before) the peak convection day.

17 Figure 2.4: As in Fig. 2.3, but for the diabatic heating rate (Q1). Unit is K day−1.

18 cumulus scheme. Compared to some other cumulus schemes, the Emanuel scheme is largely insensitive to the tropospheric moisture and is not well suited to represent cumulus congestus due to untreated subgrid perturbations that tend to enhance vertical development. The insensitivity of convection to free-tropospheric moisture may contribute to weak MJO-like coherences (Grabowski and Moncrieﬀ, 2004).

2.5 Evaluation of the NOGAPS short-term forecasts

As the second part of this chapter, the tropical mean state, thermodynamic fields, and the forecast skill of the MJO in the NOGAPS short-term forecasts are evaluated against the ERAI and satellite data. Previous studies have found that the bias of subseasonal variations is closely related to the mean state bias (e.g., Kim et al., 2011; Yang et al., 2012). Additionally, the tropical- extratropical teleconnections are also sensitive to the mean flow structure (Wang et al., 2005). We will thus first examine the seasonal mean patterns.

2.5.1 Precipitation spatial pattern and ITCZ bias

Skillful precipitation forecasts remain a challenge to the modeling community. Since the observed precipitation data are not directly ingested into the model through data assimilation, precipitation evaluation can reveal the deficiencies in model physics (Trenberth et al., 2003; Dai, 2006; Janowiak et al., 2010). Figure 2.5 shows the average daily precipitation rate in the tropics (15 ◦S- 30 ◦N) during 2008-11 (for the time period when the NOGAPS forecasts are available) derived from CMORPH, the NOGAPS 6-day forecasts, the GFS 6- day forecasts, and the biases of the NOGAPS and GFS forecasts with respect to CMORPH. Comparisons with CMORPH show that both the NOGAPS and GFS forecasts capture the general patterns of tropical precipitation, including the narrow ITCZ band over the central and eastern Pacific and heavy precipitation over the Indo-Pacific warm pool. The NOGAPS 6-day precipitation forecast, however, has a prevailing dry bias over the tropics (Fig. 2.5c). In particular, precipitation is substantially underpredicted over the Indo-Pacific warm pool, the African monsoon and the eastern Atlantic ITCZ regions, and the central Pacific ITCZ region. Wet biases are found over

19 Figure 2.5: The average daily precipitation rate (mm day−1) in the tropics (15 ◦S-30 ◦N, -180 ◦-180 ◦) using all available data in boreal summer during 2008-11 for (a) CMORPH, (b) NOGAPS 6-day forecasts, (c) the difference between (b) and (a); (d) difference between the NOGAPS 6- and 2-day forecasts; and (e)-(g) as in (b)-(d), but for the GFS. the equatorial and southwest Indian Ocean and Central America. The GFS 6-day forecasts have overall wet biases over the tropics, but dry biases appear over the three ascending centers of the global Walker circulation: the Indo- Pacific warm pool, equatorial South America (Amazon basin), and equatorial African regions; precipitation is also overpredicted in other regions, including the Maritime Continent and Southeast Asia. Similar spatial distributions of the precipitation biases are also found in the NOGAPS and GFS forecasts with different forecast lead times (not shown). Figures 2.5d and 2.5g show that the precipitation biases increase with the forecast lead time in most tropical regions in both models. A significant precipitation bias in the NOGAPS forecasts is the northward shift of the ITCZ. Figure 2.6 shows the precipitation averaged over the eastern Pacific (0 ◦-25 ◦N, 100 ◦-85 ◦W) from the NOGAPS and GFS forecasts and CMORPH. Compared to CMORPH, the NOGAPS forecasts capture the magnitude of the ITCZ precipitation, but in the 2-day (4 and 6 day) forecasts the peak precipitation is displaced by about 1 ◦ (2 ◦) northward. GFS captures the latitudinal location of the ITCZ but overpredicts the precipita-

20 Figure 2.6: The average hourly precipitation rate (mm h−1) over the eastern Pacific ITCZ region (0 ◦-25 ◦N, 100 ◦-85 ◦W) with different forecast lead times using all available data in boreal summer during 2008-11: (a) the NOGAPS forecast (colors) and CMORPH (black); and (b) GFS (colors) and CMORPH (black). tion rate, and the wet bias increases with forecast lead time. Precipitation biases are associated with biases in latent heat release. The diabatic heating profiles and their impacts on the large-scale circulations will be examined in the next section. For brevity, we will focus on the NOGAPS forecasts.

2.5.2 Diabatic heating and large-scale circulations

To evaluate the thermodynamic performance of the NOGAPS forecasts, Fig. 2.7 shows the vertical cross sections of the zonally averaged Q1 derived from the ERAI and the NOGAPS 3- and 5-day forecasts over the western Pa- cific (120 ◦-150 ◦E) (top), the eastern Pacific (115 ◦-85 ◦W) (middle), and the Indian Ocean (50 ◦-80 ◦E) (bottom). To examine the connections with the large-scale atmospheric circulations, Fig. 2.8 shows the vertical cross sections of the zonally averaged zonal or meridional winds of the ERAI (left column), the difference between the NOGAPS 3-day forecast and the ERAI (middle column), and the difference between the NOGAPS 5- and 3-day forecasts (right column). The different ocean basins are examined separately as follows. Over the western Pacific (Fig. 2.7, top), the NOGAPS forecasts capture the heating in the lower troposphere and the cooling above in 30 ◦-10 ◦S,

21 Figure 2.7: Vertical cross sections of the zonally averaged diabatic heating rate (Q1; K day−1) using all available data in boreal summer during 2008-11 for (from left to right) ERAI and NOGAPS 3- and 5-day forecasts over the (top) western Paciﬁc (120 ◦E-180 ◦), (middle) eastern Paciﬁc (115 ◦-85 ◦W), and (bottom) Indian Ocean (50 ◦-80 ◦E).

22 Figure 2.8: Vertical cross sections of (top),(middle) the zonally averaged zonal (U) and (bottom) meridional (V) winds using all available data in boreal summer during 2008-11 for (left) ERAI, (middle) the NOGAPS 3-day forecast minus ERAI, and (right) the NOGAPS 5-day minus the NOGAPS 3-day forecasts over the (top) western Paciﬁc (120 ◦-150 ◦E), (middle) eastern Paciﬁc (115 ◦-85 ◦W), and (bottom) Indian Ocean (50 ◦-70 ◦E). Unit is m s−1.

23 which is associated with the marine stratocumulus. Over the western Pacific monsoon regions (10 ◦S-20 ◦N), however, where the NOGAPS forecasts have a dry bias (Fig. 2.5c), the diabatic heating is significantly underproduced, and the maximum heating occurs at an altitude slightly higher than that in the ERAI. The biases in precipitation and heating induce biases in the regional Hadley circulation. Figure 2.8 (top) shows that the tropical easterlies (trade winds) and subtropical westerlies in the Northern Hemisphere are both weaker in the NOGAPS forecasts compared to the ERAI, while the tropical easterlies south of 10 ◦S are stronger. The analysis suggests a weaker northern Hadley cell over the western Pacific. In the eastern Pacific ITCZ region (Figs. 2.7 and 2.8, middle), the lower- tropospheric heating shifts northward and upward with forecast lead time, which is associated with the northward shift of precipitation (or the ITCZ) (Figs. 2.5c and 2.6a). The heating profile in the NOGAPS 5-day forecast is more top heavy compared to the ERAI, which implies a strong stratiform component. Figure 2.8 shows that the westerlies to the south of the ITCZ shift northward with the heating. Due to the resultant changes in the steering flow and vertical shear, the biases in precipitation and diabatic heating may lead to biases in the tropical cyclone frequency, track, and intensity in the NOGAPS forecasts. The NOGAPS forecasts overpredict precipitation over the western south Indian Ocean and underpredict precipitation over the eastern Arabian Sea. Figure 2.7 (bottom) shows that both the diabatic cooling north of 10 ◦N and heating south of 10 ◦N are significantly overpredicted. Similar to the eastern Pacific, the heating over the South Indian Ocean is also more top heavy than that in the ERAI. Figure 2.8 (bottom) reveals weaker cross-equatorial flow (including the Somali jet) over the Indian Ocean in the NOGAPS 5- day forecast (southerlies weakened by more than 30%). This is due to the antisymmetric heating distribution straddling the equator over the Indian Ocean. Weaker cross-equatorial flow implies reduced moisture transport, which may affect the MJO initiation and the monsoon onset over the North Indian Ocean. All the biases in the large-scale atmospheric circulations am- plify with the forecast lead time and are closely related to the biases in the diabatic heating and precipitation fields (Figs. 2.7 and 2.8, right).

24 2.5.3 Moist processes in the NOGAPS

The strong control of CWV on precipitation has been examined in some previous studies (Alaka Jr and Maloney, 2012; Bretherton et al., 2004; Neelin et al., 2009; Zeng, 1999). The relationship between humidity and convection is also a central issue of many cumulus schemes. The sensitivity of the MJO simulations to the model cumulus scheme has been reported previously (e.g., Chao and Lin, 1994; Wang and Schlesinger, 1999; Maloney and Hartmann, 2001). Figure 2.9 shows the average daily precipitation rate stratified with 1-mm-wide bins of the CWV over four tropical ocean basins (20 ◦S-20 ◦N). SSM/IS retrievals of the precipitation rate and CWV plotted in Fig. 2.9 provide an ideal standard for examining the relationship between precipitation rate and the CWV. In addition to the SSM/IS, CMORPH precipitation rates are plotted against the ERAI CWV, and the precipitation rates and CWV from the NOGAPS 1-, 3-, and 5-day forecasts are also shown. All the datasets capture the nonlinear relationship between precipitation rate and the CWV: a low precipitation rate in the presence of less CWV followed by an exponential increase in the precipitation rate with increasing CWV. A close look at the data, however, reveals some quantitative differences. Plots of the CMORPH precipitation versus SSM/IS CWV are quite close to the SSM/IS precipitation rate versus SSM/IS CWV curves for all the basins (not shown), which is expected because the CMORPH results are derived exclusively from passive microwave retrievals. The CMORPH versus ERAI CWV curves, however, are above the SSM/IS precipitation rate versus SSM/IS CWV curves for all the basins, indicating that ERAI underestimates the CWV for a given precipitation rate. For example, the precipitation rate of 15 mm day−1 is associated with 64-mm CWV in the SSM/IS data but with 57-mm CWV in the ERAI data over the Indian Ocean. Compared to other basins, the difference between the CMORPH versus ERAI CWV curve and the SSM/IS curve is relatively small over the Indian Ocean. The precipitation rate versus the CWV curves derived from the NOGAPS forecasts are between the CMORPH versus ERAI CWV curves and the SSM/IS curves for all the basins, and the 3- and 5-day forecasts are closer to the CMORPH versus ERAI CWV curves than to the SSM/IS curves. Similar to ERAI, NOGAPS also underestimates the CWV for a given precipitation rate. Or, in other words, the NOGAPS forecasts and ERAI generate too much precip-

25 Figure 2.9: The average daily precipitation rate (mm day−1) stratified with 1-mm-wide bins of the CWV (mm) using all available data over four tropical ocean basins (20 ◦S-20 ◦N) in boreal summer during 2008-11. Shown are the curves for the (a) Indian Ocean (30 ◦-120 ◦E), (b) western Pacific (120 ◦E-180 ◦), (c) eastern Pacific (180 ◦-80 ◦W), and (d) Atlantic (80 ◦W-30 ◦E). The black solid lines indicate the SSM/IS precipitation rate vs the SSM/IS CWV; black dotted lines show the CMORPH precipitation rate vs the ERAI CWV; red, green, and blue lines show the 1-, 3-, and 5-day precipitation rates, respectively, of the NOGAPS forecast vs the 1-, 3-, and 5-day CWVs of the NOGAPS forecast.

26 itation for the same amount of CWV. This finding indicates that the heavy precipitation may initiate too early in the models in terms of the CWV threshold. The probability distribution functions (PDFs) of the CMORPH precipitation rate with 15-mm-wide precipitation bins (log10%) are shown in Fig. 2.10a. The frequency of occurrence decreases with the precipitation rate. Fig- ure 2.10b shows the percent deviation of the NOGAPS 3-day forecasts from CMORPH. NOGAPS underpredicts light and moderate-to-heavy (13-182 mm day−1) precipitation but overpredicts extremely heavy rainfall (greater than 190 mm day−1). The frequency of the drizzle-like precipitation is captured quite well by the NOGAPS forecasts. Figure 2.10c shows the standardized PDF difference of the precipitation rates between the NOGAPS 5- and 3-day forecasts. As the forecast lead time increases, weak to moderate-to- heavy rainfall (15-150 mm day−1) occurs more frequently, but the occurrence of extremely heavy rainfall (> 200 mm day−1) is reduced by 5%. The reduction of the heavy precipitation is consistent with the amplifying dry bias in the CWV with the forecast lead time, as shown next in Fig. 2.11. The increases in the other types of precipitation with forecast lead time imply that the NOGAPS 5-day forecast exhibits a greater degree of recovery from a biased initial state (Fig. 2.3) toward a realistic state than does the 3-day forecast. The probability distribution of the CWV over each basin is shown in Fig. 2.11. The SSM/IS reveals the different column moisture distributions over different basins. The western Pacific is characterized by a prominent peak between 55 and 60 mm, and low CWV values occur relatively less frequently compared to the other basins. The eastern Pacific has a bimodal distribution, with the primary peak of frequency of occurrence around 30 mm and a secondary one around 57 mm, which reflects dry conditions over the south- eastern Pacific (with prevailing marine stratus) and moist conditions in the ITCZ region. Consistent with Fig. 2.9, Fig. 2.11 shows dry biases in the NOGAPS forecasts. The CWV of the peak frequency of occurrence in the NOGAPS forecasts is more than 5 mm lower than that in the SSM/IS over the Indian Ocean and the western Pacific. Over the eastern Pacific and the Atlantic, the NOGAPS forecasts do not capture the bimodal distribution of the CWV. The CWV of the primary peaking frequency over the Atlantic is up to 10 mm lower than that in the SSM/IS. A weaker dry bias is also

27 Figure 2.10: (a) PDFs (log10%) of the average CMORPH precipitation rate over the tropical ocean basins (20 ◦S-20 ◦N) stratified into 15-mm-wide bins. (b) The relative PDF differences of precipitation rate (%) over the tropical ocean basins between the NOGAPS 3-day forecast and CMORPH. (c) As in (b), but for differences between the NOGAPS 5- and 3-day forecasts. The rainfall types are defined according to the classifications in the Glossary of Meteorology: drizzle (0-12 mm day−1), light (13-60 mm day−1), moderate (61-182 mm day−1), and heavy (>182 mm day−1).

28 Figure 2.11: As in Fig. 2.9, but for the CWV probability distribution (%). The black solid (dotted) lines show the SSM/IS (ERAI) CWV; the faint yellow lines are for the NOGAPS analysis; and the red, green, and blue lines show the 1-, 3-, and 5-day NOGAPS forecasts, respectively.

29 present in the distribution of the CWV from the NOGAPS analysis, which is consistent with our diagnosis of the NOGAPS analysis in section 2.4. A close look shows a small but discernible increase in the dry bias over all the basins from 1- to 5-day forecasts, indicating deficiencies in the model physics. A similar dry bias in the CWV distribution is also found in ERAI, but overall ERAI is more realistic than the NOGAPS forecasts. For example, the ERAI has a smaller dry bias over the Indian Ocean and the western Pa- cific, and it captures the bimodal distribution over the eastern Pacific. The upgrade of the vapor absorption model in the version-7 SSM/IS data partly explains the dry biases in the ERAI and the NOGAPS analyses, because both data assimilation systems ingested an earlier version of SSM/I-SSM/IS. Compared to the earlier versions, the CWV in the version-7 SSM/IS results slightly shifts to higher vapor values (above 55 mm) globally and is in better agreement with the GPS-derived vapor (K. Hilburn 2013, personal communication). To further investigate the moisture biases in the NOGAPS forecasts, we examined the vertical profiles of RH for different CWV thresholds (Fig. 2.12). Although SSM/IS provides a realistic look at the relationship between precipitation rate and CWV, it does not provide information on the vertical distribution of water vapor. The moisture data in the Atmospheric Infrared Sounder (AIRS) suffer from cloud/rain contamination (Fetzer, 2006), and are found to have apparent problems in regions with high precipitation rates (not shown). Despite the dry bias in the CWV and its imperfect relationship with precipitation, ERAI likely provides the best available 3D moisture field, and has a more realistic moisture profile than does NOGAPS. Figure 2.12a illustrates the averaged ERAI RH stratified with 1-mm-wide bins of the CWV over all the tropical ocean basins (20 ◦S-20 ◦N, -180 ◦-180 ◦) It shows that RH exceeds 70% below 900 hPa for all the CWV results between 20 and 65mm. For the smaller CWV, RH decreases sharply above 900 hPa, and a significant dry layer with RH less than 20% is present in the middle troposphere for the CWV less than 30mm. For high CWV values, large RH extends to the upper troposphere, likely due to the convective activities associated with high CWV. While a moist column is favorable for convection, convection transports moisture from the planetary boundary layer and further moistens the free troposphere. Figures 2.12b and 2.12c show that the NOGAPS forecasts broadly resemble

30 Figure 2.12: The RH (%) stratified with 1-mm-wide bins of the CWV (mm) using data in boreal summer during 2008-11 over all the tropical ocean basins (20 ◦S-20 ◦N, -180 ◦-180 ◦), from (a) ERAI; (b) the NOGAPS 3-day forecast; (c) the relative percentage difference between the NOGAPS 3-day forecast and ERAI; and (d) as in (c), but for the difference between the NOGAPS 5- and 3-day forecasts.

31 the ERAI simulations with some quantitative differences. In particular, the NOGAPS forecasts have a dry bias (up to 6%) within the marine boundary layer (MBL) and a moist bias above 800 hPa compared to ERAI. The dry bias in the lower troposphere is particularly large for CWV greater than 33 mm. Since the MBL contains most of the column moisture, the dry bias in the MBL is consistent with the dry bias in the CWV. Additional diagnostics of the moisture tendency terms and cloud fractions in short-term hindcasts show that deep convection increases with forecast lead time for CWV > 50 mm. It is possible that the dry bias in the MBL is due to a hyperactive convection in the NOGAPS model, in which convection is triggered too early in terms of the CWV threshold and moisture does not accumulate as much as it should within the MBL. Hyperactive deep convection may also result in an underrepresentation of shallow convection. Another possibility is the lack of mixing by large eddies in the convective boundary layer. On the other hand, readers should be cautioned about possible biases in the ERAI moisture field. Kishore et al. (2011) compared three reanalysis datasets (ERAI, NCEP- NCAR, and JRA-25) with the six-satellite-based Constellation Observation System for Meteorology Ionosphere and Climate (COSMIC) GPS-based radio occultation (GPS-RO) retrieval. They showed that ERAI is closest to the COSMIC measurements among the three reanalysis datasets but has a dry bias in the free atmosphere and a moist bias at 1.4 km. This suggests that the moisture biases in the NOGAPS forecasts may not be as strong as indicated in Fig. 2.12c. In addition, Pierce et al. (2006) found that it is a common issue for climate models to have a dry bias below 800 hPa and a moist bias in the middle to upper troposphere (between 300 and 600 hPa). The difference between the NOGAPS 3- and 5-day forecasts suggests that the moisture difference between the ERAI and the NOGAPS forecasts is amplified with forecast lead time (Fig. 2.12d). It is instructive to examine the vertical profiles of Q1 in the ERAI and the NOGAPS forecasts. The heating profile of ERAI (Fig. 2.13a) shows a bimodal structure for CWV less than 50 mm, with one maximum around 850 hPa and another around 500 hPa, which correspond to shallow and deep convection, respectively. For CWV > 50 mm, Q1 has a top-heavy heating profile with a peak around 500 hPa. The NOGAPS forecasts have a similar top-heavy profile for high CWV (Fig. 2.13b), but underpredict Q1 below 400 hPa by up to 25% (Fig. 2.13c). The heating maximum around 850 hPa for

32 Figure 2.13: As in Fig. 2.12, but for Q1. Unit is K day−1. low CWV is missing in the NOGAPS forecasts. The weak lower-tropospheric diabatic heating in the NOGAPS forecasts is either due to a stronger stratiform process (which is characterized by condensational heating above and evaporative cooling below the freezing level), or a deﬁciency of cumulus congestus due to untreated subgrid perturbations that tend to enhance vertical development, or both (e.g., Schumacher et al., 2004; Chikira, 2014; Khouider and Majda, 2006). Consistent with the moisture ﬁeld, the negative biases in the lower-tropospheric diabatic heating increase with forecast lead time, whereas deep convective heating increases with forecast lead time for CWV > 50 mm (Fig. 2.13d).

2.5.4 MJO in the NOGAPS forecasts

The errors in the large-scale circulation patterns and the diabatic heating pro- ﬁle as observed in the NOGAPS forecasts may aﬀect the short-term forecast skill of the MJO. Figure 2.14 shows the pattern correlations for the tropical (20 ◦S-20 ◦N, -180 ◦-180 ◦) 200-hPa zonal wind between the NOGAPS-GFS

33 Figure 2.14: Spatial pattern correlations of tropical (20 ◦S-20 ◦N, -180 ◦-180 ◦) zonal winds at 200 hPa between forecasts from: (a) the NOGAPS and ERAI and (b) GFS and ERAI for eight MJO phases (WH04), using all available data in boreal summer during 2008-11. The red lines of decreasing thicknesses show the correlations for 1- to 6-day forecasts.

34 Figure 2.15: (a) Composite anomalies of RH (%) for five MJO events during 2008-11 derived from the NOGAPS 3-day forecasts with respect to the daily average of the NOGAPS analysis during 2004-10. (b) As in (a), but for Q1 (K day−1). (c) The RH profiles (%) on day 0 from ERAI (black), the NOGAPS analysis (faint yellow), and the 3-day (green) and 5-day (blue) NOGAPS forecast. (d) As in (c), but for Q1 (K day−1). forecasts and ERAI in eight MJO phases based on the RMM. The predictability for the MJO drops quickly in phase 2 when the MJO is initiated over the Indian Ocean and in phase 5 when the MJO propagates across the Maritime Continent in both prediction systems, but it drops more quickly in the NO- GAPS forecasts, especially during phase 2. The limited forecast skill of the MJO in phases 2 and 5 is a common issue in GCMs, either because of relatively low intrinsic predictabilities compared with other tropical regions or model deficiencies (Inness and Slingo, 2003; Neale and Slingo, 2003; Slingo et al., 2003). Given the reasonable representation of the MJO in the model initial conditions (i.e., the analysis data), the limited forecast skill implies the strength of NOGAPS in data assimilation and the weakness in the model physics. Also note that the spatial resolution of the NOGAPS model was coarser than that of the GFS during the period of diagnosis. To investigate the possible deficiencies in the model physics that may influence the MJO forecast skill, the composites of RH and Q1 from the NO- GAPS forecasts were constructed based on the local MJO index over the Indian Ocean. Five prominent MJO events in boreal summer during 2008-11 were selected (Fig. 2.15). Due to the gaps in the forecast data, the com-

35 posite anomalies were constructed with respect to the daily mean derived from the 2004-10 NOGAPS analysis (the same as in Figs. 2.3 and 2.4). The composite anomalies thus include both the MJO signals in the NOGAPS forecasts and the difference between the NOGAPS analysis and forecasts. The composite of RH derived from the 3-day NOGAPS forecast is shown in Fig. 2.15a, and is characterized by positive anomalies above 800 hPa and negative anomalies below. The maximum moistening on day 0 at 400 hPa is consistent with Fig. 2.3, but has a larger magnitude. Strong positive RH anomalies are also found around day -15 at 400 hPa, which may be due to the relatively small sample size. The negative anomalies below 800 hPa are consistent with the dry bias identified in Fig. 2.12a. Furthermore, the nearly constant magnitude of the negative RH anomalies at different MJO phases suggests that the RH anomalies in Fig. 2.15a are primarily dominated by the differences between the NOGAPS analysis and forecasts, and that the premoistening and postdrying in the lower troposphere are largely missing in the NOGAPS forecasts. The RH profiles on day 0 from the ERAI, the NOGAPS analysis, and the forecasts are shown in Fig. 2.15c, which further illustrate the positive (negative) biases in the middle and upper (lower) troposphere in the NOGAPS forecasts. The composites of Q1 are shown in Figs. 2.15b and 2.15d. Although the Q1 profiles in the NOGAPS forecasts are close to that derived from ERAI or the NOGAPS analysis (Fig. 2.15d), the temporal evolution of Q1 (Fig. 2.15b) shows no indication of transition from shallow convection to deep convection and then to stratiform precipitation. Again, it shows very weak MJO signals in the diabatic heating fields of the NO- GAPS forecasts. The lack of cloud transitions can probably be attributed to the insensitivity of the Emanuel scheme to the tropospheric moisture (the moisture dependence in the scheme is only through the virtual temperature effect on the parcel buoyancy) and is not well suited to represent cumulus congestus due to untreated subgrid perturbations that tend to enhance vertical development. The weak MJO signals in the NOGAPS forecasts thus imply the deficiency in the RH-dependent formulation for organized deep en- trainment in the model, which has been found to be crucial to an improved simulation of the MJO (e.g., Hirons et al., 2013a,b; Chikira and Sugiyama, 2013; Chikira, 2014).

36 2.6 Summary and discussion

Navy Operational Global Atmospheric Prediction System (NOGAPS) analysis and operational short-term forecasts are evaluated systematically against the ERA-Interim Re-Analysis (ERA-Interim; ERAI) and Global Forecast System (GFS) analysis and forecasts, with a special focus on the following aspects: (i) the mean states, (ii) the Madden-Julian oscillation (MJO), and (iii) the precipitation and moist processes. A suite of diagnostic tools has been developed for the model evaluation using both performance- and physics-oriented metrics. It is found that the MJO signals in the dynamic fields of the NOGAPS and GFS analyses are in good agreement with those in the ERAI. The NOGAPS analysis captures the lower-tropospheric moistening and warming leading to the peak convection of the MJO and the lower- tropospheric drying and cooling following the peak, but the MJO signals in the relative humidity (RH) and diabatic heating rate (Q1) fields are weaker than those in ERAI or in the GFS analysis. The precipitation distributions in the NOGAPS and GFS short-term forecasts are in reasonable agreement with CMORPH. The NOGAPS forecasts have a dry bias over the Indo-Pacific warm pool, the African monsoon region, the eastern Atlantic ITCZ region, and the central Pacific ITCZ region. In particular, the ITCZ shifts northward with forecast lead time in the NO- GAPS over the eastern Pacific where the GFS overpredicts the ITCZ precipitation. In regions with large precipitation biases, the diabatic heating profile is found to be more top heavy in the NOGAPS forecasts than in ERAI. The errors in the diabatic heating field are associated with errors in large-scale circulations, including weaker trade winds and weaker Hadley and Walker circulations over the western Pacific and weaker cross-equatorial flow over the Indian Ocean. The relationship between the precipitation and column water vapor (CWV) in the NOGAPS forecasts is evaluated against SSM/IS, CMORPH, and ERAI. It is found that heavy precipitation develops too early in the NO- GAPS forecasts in terms of the CWV threshold. On the other hand, the NOGAPS forecasts have a dry bias in terms of the probability distribution of the CWV. The vertical profile of RH further shows that the NOGAPS forecasts have a dry bias within the boundary layer and a moist bias in the middle and upper troposphere. The dry biases in the ERAI and NOGAPS

37 analyses can be partly attributed to the old version of SSM/I and/or SSM/IS used in the data assimilation systems. However, a subtle but consistently amplified dry bias with the forecast lead time suggests deficiencies in the model physics. NOGAPS also underpredicts the light to heavy precipitation (13-182 mm day−1), overpredicts extremely heavy rainfall, and reproduces the drizzle-like precipitation quite well. The diagnostic of Q1 shows that the shallow heating mode is missing for CWV<50 mm in the NOGAPS forecasts. The predictive skills of the MJO in the NOGAPS and GFS operational forecasts are evaluated using pattern correlations. It is found that the MJO predictive skill drops quickly with the forecast lead time in both models, especially for phases 2 and 5, and it drops more quickly in NOGAPS for phase 2. The weakest forecast skill levels in phases 2 and 5 of the MJO are consistent with previous findings about the limited predictability of the MJO at its initiation over the Indian Ocean and when its active convection center is near the Maritime Continent. The composite of the RH based on the self- defined local MJO index over the Indian Ocean reveals a dry bias within the boundary layer in the NOGAPS forecasts. The MJO signals are shown to be very weak in both the RH and Q1 fields, similar to the NOGAPS analysis, and cloud transition is also missing in these thermodynamic fields. The moisture biases in the NOGAPS forecasts are possibly due to hyperactive deep convection, a deficiency of cumulus congestus, or/and lack of mixing by large eddies in the convective boundary layer. New cumulus and boundary layer parameterization schemes have been developed and imple- mented in the NAVGEM model, which is expected to better represent moist processes. It is hoped that the diagnostics presented in this study may shed light on future model improvements.

38 Chapter 3

Physics-oriented Model Evaluation II: Tropical Cyclones in the NCEP Global Ensemble Forecasting System (GEFS) Reforecast Version 2 c 2016 American Meteorological Society1

3.1 Introduction

Tropical cyclones (TCs) are among the most destructive weather-related natural disasters. In the past two centuries, TCs have caused approximately 1.9 million deaths worldwide and killed more than 300 000 people in North America and the Caribbean alone (Tobin, 1997; Pielke Jr et al., 2008; Shultz et al., 2005). Meanwhile, property damage from TCs increases because of the growing coastal population and development. Skillful TC prediction is therefore of significant socioeconomic value. On the synoptic timescales, TC track forecasting has been improved significantly in the past decade (WMO, 2007), and progress has also been made over the years toward improving the predictive skill of TCs on seasonal and longer timescales (e.g., Camargo et al., 2007; Goldenberg et al., 2001; Knutson et al., 2010; Vecchi et al., 2011). TC forecasts on the subseasonal timescales provide useful information for early storm preparedness, especially in remote or large communities (Brunet et al., 2010). Statistical and dynamical models have been developed for TC subseasonal prediction. Leroy and Wheeler (2008) and Slade and Maloney (2013) applied logistic regression to predict TC frequency on the subseasonal timescales using the TC climatology, sea surface temperature (SST), El Niño-SouthernOscillation (ENSO), and Madden-Julian oscillation (MJO) indices as predictors, and they showed that skillful prediction can be achieved out to 3 weeks during strong MJO events. Roundy and Schreck III (2009)

39 further considered convectively coupled easterly waves and mixed Rossby- gravity waves to account for the synoptic-scale variability associated with TC development (www.atmos.albany.edu/facstaff/roundy/tcforecast/ tcforecast.html). Dynamical prediction has improved tremendously in recent years as a result of improved model physics, initialization, and increased model resolutions (Klotzbach et al., 2012). Dynamical prediction employs numerical models that generate TC-like disturbances. Such disturbances can be tracked based on the dynamic and thermodynamic features of a TC [e.g., a warm-core structure and strong low-level cyclonic circulation; Gall et al. (2011) and Gopalakrishnan et al. (2012)]. Vitart (2009) showed that the accurate representation of the MJO had a signiﬁcant impact on the subseasonal predictive skill of landfalling TCs over North America and Australia in the European Centre’s Medium-Range Weather Forecasts (ECMWF) 46-days hindcasts. Elsberry et al. (2010) used an objective matching technique and showed that the ECMWF 32-day forecasts can provide useful TC track information on timescales of 10-30 days. Belanger et al. (2010, 2012) found that the TC genesis forecasts from the ECMWF have skill above climatology through 4 weeks over the Atlantic main development region [MDR; between 9◦ and 21.5◦N spanning the Caribbean Sea and tropical Atlantic; Goldenberg et al. (2001)] and the Gulf of Mexico. They found that the regional forecast skill can be attributed to the ability of the model in realistically capturing the large-scale environment and the evolution of the MJO. Some dynamic models demonstrated comparable or better forecast skill than statistical models in some ocean basins (Vitart et al., 2010). In addition, multimodel ensemble techniques produce overall better forecasts than individual models and further improve the skill of dynamical prediction (Sivillo et al., 1997; Vitart, 2006; Kirtman et al., 2014). This chapter will evaluate the dynamical predictive skill of TC activity in the National Centers for Environmental Prediction’s (NCEP) Global En- semble Forecasting System (GEFS) using the GEFS Reforecast version 2 dataset (Hamill et al., 2013). The GEFS reforecasts have a forecast lead time up to 16 days and are available since 1 December 1984. Diﬀerent from most previous studies, we will evaluate the skill of the GEFS from a “climate” perspective. The reasoning is that a skillful model will produce a realistic climatology of TC activity; otherwise, forecast errors may accumulate and

40 manifest in the model climatology. Diagnosis of the long-term statistics will help to identify model error sources and can provide useful information on model improvement. The rest of the chapter is organized as follows. The datasets and methods are described in section 3.2. The TC climatology in the GEFS is examined in section 3.3, and the related model biases and deﬁciencies in the model physics are investigated in section 3.4, followed by a summary and additional discussion in section 3.5.

3.2 Data and metrics

3.2.1 Global Ensemble Forecasting System Reforecast version-2

The GEFS reforecasts were developed by the NOAA’s Earth System Re- search Laboratory (ESRL) using version 9.0.1 of the operational GEFS (ftp: //ftp.cdc.noaa.gov/Projects/Reforecast2). The reforecast is up to 16 days and consists of 11 ensemble members (one control run and 10 perturbed members). The reforecasts were initialized once per day at 0000 UTC with the Climate Forecast System Reanalysis (CFSR) through 20 February 2011 and with the analysis from the Gridpoint Statistical Interpolation (GSI) analysis system afterward (Hamill et al., 2013). We will refer to the initial conditions as the CFSR for brevity. The reforecasts have 42 vertical levels, and the horizontal resolution is T254 (approximately 40 km at 40◦ latitude) for the first week and is degraded to T190 (approximately 54 km at 40◦ latitude) after day 7.5. All reforecast data were saved at 1◦ × 1◦ horizontal resolution. Our analysis focuses on the forecast verification for the time period from January 1985 to December 2012. Such a long time period is critical for establishing robust statistics of weather events like TCs and for identifying possible systematic errors in the mean state. We will evaluate TCs over different ocean basins for different forecast lead times. To exclude the forecast skill directly related to the model initialization, we omitted TC vortices during the first 18 forecast hours. The week-1 reforecasts include the forecast lead time of 24-162 h (days 2-7 with a 6-h interval), and the week-2 reforecasts include the forecast lead time of 168-306

41 h (days 8-13 with a 6-h interval). A TC year is deﬁned as January-December for the Northern Hemisphere and from July to next June for the Southern Hemisphere (McBride and Keenan, 1982; Vitart et al., 1997). To examine the mean state in the GEFS, long-term seasonal ensemble means were derived during 1985-2012, which were evaluated against the interim ECMWF reanalysis [(ERA-Interim (ERAI); Dee et al., 2011)]. The ERAI data, with the original resolution of approximately 0.7◦, were coarsened to 1◦ × 1◦ resolution to facilitate comparison. In addition to the ERAI, the NOAA’s Optimum Interpolation SST version 2 (OISST; Reynolds et al., 2002) data and two satellite datasets were used. The Climate Prediction Center (CPC) morphing technique (CMORPH) derives precipitation estimates from the passive microwave data at a very high spatial and temporal resolution from December 2002 to the present (Joyce et al., 2004). The 3-hourly 0.25◦ × 0.25◦ CMORPH precipitation for the period 2003-12 was mapped to 1.0◦ × 1.0◦, and the daily average was taken to be consistent with the GEFS reforecasts. To evaluate the precipitation and column water vapor (CWV) relationship, we employed the version 7 Special Sensor Microwave Imager/Sounder (SSMIS) polar-orbiting dataset, which had simultaneous retrievals of precipitation and CWV (Horv´athand Gentemann, 2007; Wentz, 2013). Both precipitation and CWV were coarsened to a 1.0◦ × 1.0◦ resolution grid mesh to be consistent with the GEFS reforecasts, and daily averages were taken over the tropical ocean areas for the same period as the CMORPH (2003-12).

3.2.2 Detection of TCs

TCs in the GEFS reforecasts were tracked using the GFDL vortex tracker with an updated warm-core criterion (Gall et al., 2011; Gopalakrishnan et al., 2012). This tracker has been adopted by NCEP for detecting and tracking TC vortices in their operational model since 1998. The scheme evaluates several key parameters, including relative vorticity, geopotential height, and wind speed at 850 and 700 hPa; sea level pressure; and 10-m wind speed. A threshold of 10-m maximum wind speed of 16.5 m s−1 or 32 kt was adopted for TC detection based on the data resolutions (Walsh et al., 2007), and it was also required that a TC had a warm core lasting at least 48 h cumula-

42 tively. The TC center was tracked by searching for the average location of the maximum or minimum of the key parameters, and a genesis was deﬁned as the ﬁrst record of a TC track. To avoid uncertainties due to changes in TC observing systems, short-lived TCs (lifetime less than 48 h) were excluded in both the observation and the GEFS reforecasts (e.g., Villarini et al., 2011; Chen and Lin, 2013). Storms forming poleward of 40◦ latitude were regarded as extratropical cyclones and were excluded. TCs were tracked in individual ensemble members, and the ensemble mean of TCs based on the 11 ensemble members was evaluated against the International Best Track Archive for Cli- mate Stewardship (IBTrACS v03r05; Knapp et al., 2010). Since all ensemble members have a good level of agreement in the TC climatological biases and mean state biases, only the ensemble means will be discussed in the following sections for brevity.

3.3 Climatology of TC activity in the GEFS

We first examined the long-term mean and seasonality of TCs during 1985- 2012 in the GEFS. As shown in Fig. 3.1, the seasonal evolutions of TC genesis frequency over different ocean basins resemble the observed seasonality in both the GEFS week-1 and -2 reforecasts. The GEFS captures the peak storm season from June/July to October over the western and eastern North Pacific, as well as over the North Atlantic. The model also reproduces the bimodal distribution over the Indian Ocean, with a primary (postmonsoon) peak in October-November and a secondary (premonsoon) peak in May-June. In the Southern Hemisphere, TC activity in the GEFS peaks during January- February, same as in the observations. On the other hand, quantitative differences are evident over most ocean basins. For example, negative biases in TC frequency are found over the western and eastern North Pacific, and positive biases are present over the north Indian Ocean and the Southern Hemisphere. The seasonality curves over the Atlantic are nearly perfect, but as shown next, large biases exist at the regional scale. To evaluate the spatial distribution of TC formations, the TC genesis density function (GDF) was derived. It is defined as the total number of TCs per year forming within a 10◦ × 10◦ box centered on each 1.0◦ grid point, and the long-term mean during 1985-2012 is shown in Fig. 3.2. The spatial

43 Figure 3.1: The seasonal variability of tropical cyclogenesis frequency averaged over the period 1985-2012 for (a) the western North Paciﬁc (WP; 105◦E-180◦), (b) the eastern North Paciﬁc (EP; 180◦-85◦W), (c) the North Atlantic (NA; 100◦W-10◦E), (d) the North Indian Ocean (NI; 30◦-105◦E), and (e) the Southern Hemisphere (SH; -180◦-180◦). The black curves are the observed TC counts recorded in IBTrACS, and the red and blue curves show the 11-ensemble mean TC counts in the GEFS week-1 and -2 reforecasts.

44 Figure 3.2: The climatological annual mean TC GDF [number of TCs (10◦ × 10◦)−1 yr−1] during 1985-2012 from (a) IBTrACS, (b) the ensemble mean GEFS week-1 reforecasts, (c) the diﬀerence between the GEFS week-1 reforecasts and IBTrACS, and (d) the diﬀerence between the GEFS week-1 and -2 reforecasts

45 pattern of the GDF in the GEFS week-1 reforecasts qualitatively agrees with that derived from the IBTrACS (Figs. 3.2a,b): most model TCs form equatorward of 20◦ latitude, the GEFS reproduces the GDF maxima over the western and eastern North Pacific, more storms form over the Bay of Bengal than the Arabian Sea, and a nearly zonal band of TC genesis is present along 15◦S. However, large biases exist at the regional scale (Fig. 3.2c). Over the western North Pacific, the GEFS has a strong negative bias in GDF to the east of the Philippines and a weak positive bias over the East China Sea and the northern central Pacific near the date line. Over the eastern North Pacific, a dipole pattern indicates a southeastward shift of the TC genesis center. Over the Atlantic, almost no TCs form over the west Atlantic and the central MDR (west of 40◦W). In contrast, hyperactive cyclogenesis occurs near the Cape Verde islands (off the coast of West Africa). Consistent with the seasonality shown in Fig. 3.1, positive biases are found over the Southern Hemisphere and the north Indian Ocean. The differences in the GDF between the GEFS week-1 and -2 reforecasts suggest that the negative biases in the western North Pacific and the dipole pattern biases in the eastern North Pacific increase with the forecast lead times (Fig. 3.2d). We now examine the spatial distribution of the TC tracks. The track density function (TDF) is defined as the total number of TC days per year within a 10◦ × 10◦ box centered on each 1.0◦ grid point (Fig. 3.3). The TDF depends on both TC genesis frequency and the subsequent storm tracks, and the environmental factors affecting storm tracks and TC formations are not necessarily the same (Mei et al., 2014). The spatial pattern of the TDF in the GEFS week-1 reforecasts is broadly consistent with that in the observations (Figs. 3.3a,b), such as the high track density in the western and eastern North Pacific, the relatively low TDF in the North Atlantic, and the zonally elongated TC tracks in the Southern Hemisphere. The reforecasts also capture the large poleward extension of TC tracks in the western North Pacific and the more latitudinally confined TC activity in the eastern North Pacific. This implies that the GEFS is skillful in reproducing the large-scale steering flows. However, large regional biases exist over all ocean basins. Figure 3.3c shows that the TDF is low in the GEFS over the western North Pacific and the western North Atlantic, which can be at least partially attributed to the negative genesis biases in these regions. The positive biases in the TDF over the central and eastern MDR are consistent with the hyperactive TC

46 Figure 3.3: As in Fig. 3.2, but for the TC TDF [number of TC days (10◦ × 10◦)−1 yr−1].

47 formation near the Cape Verde islands. Over the eastern North Paciﬁc, the dipole-pattern biases in the TDF are consistent with the southeastward shift of the genesis center. In the Southern Hemisphere and the Indian Ocean, the overprediction of the TDF is consistent with the overprediction of genesis. Overall, the track biases can be partly attributed to the genesis biases. Figure 3.3d shows a poleward shift of the TDF in both hemispheres in the week-2 reforecasts compared to the week-1 reforecasts.

3.4 Impact of environmental condition biases on TC prediction

3.4.1 Biases in tropical cyclogenesis

The TC climatology in the GEFS shows some regional biases. Since TC genesis depends on large-scale environmental conditions, it is natural to ask which mean state errors in the model contribute to the genesis biases. We will use the genesis potential index (GPI) to address this question, and we focus on the western North Pacific, the eastern North Pacific, and the North Atlantic during July-October (JASO). GPI is a function of environmental variables and can serve as a proxy for genesis probability. Following Emanuel and Nolan (2004), it is defined as

RH 3PI 3 GP I = |105η|3/2 (1 + 0.1VWS)−2 (3.1) 50 70 where η is 850-hPa absolute vorticity, RH is 700-hPa relative humidity, and VWS is the 850-200-hPa vertical wind shear (vector difference). PI is the potential intensity (Emanuel, 1995), which is a function of the sea surface temperature and the pressure and vertical profiles of temperature and specific humidity, as well as the ratio of the exchange coefficient for enthalpy to the drag coefficient. The monthly mean GPI in the GEFS was calculated from the monthly mean atmospheric fields and SST in the GEFS day-8 reforecast, and the long- term mean GPI was derived by averaging over 1985-2012. The GPI was then calibrated (or rescaled) so that the average TC frequency predicted by the

48 Figure 3.4: (a) The calibrated long-term seasonal mean (JASO) GPI from the ERAI. (b) The calibrated long-term seasonal mean GPI diﬀerences between the GEFS day-8 reforecast and the ERAI. (c) As in Fig. 3.2c, but for JASO from the GEFS day-8 reforecast. (d) The contribution of the 850-hPa relative vorticity (Vort850) to the genesis bias (see the text for details). Results shown are the same as in (d) but for the (e) 700-hPa relative humidity (RH700) and (f) 200-850-hPa VWS.

49 GPI over the North Pacific and the North Atlantic (0◦-40◦N, 100◦-355◦E) was the same as observed. The calibrated long-term seasonal mean GPI derived from the ERAI and the OISST is shown in Fig. 3.4a. It captures the major centers of genesis activity over the western North Pacific, the eastern North Pacific, and the Atlantic, but overpredicts genesis over the central Pacific, which is a common issue with the GPI (Camargo et al., 2014). Figure 3.4b displays the differences in the calibrated seasonal mean GPI between the GEFS day-8 reforecast and the ERAI. The genesis density function differences between the GEFS day-8 reforecast and the IBTrACS are shown in Fig. 3.4c to facilitate comparisons. The negative biases in GPI prevail over both the North Pacific and the North Atlantic (Fig. 3.4b). The broad consistency with the genesis density differences (Fig. 3.4c) suggests that the biases in environmental conditions can to a large extent explain the negative biases over the western and eastern North Pacific and the At- lantic. However, exceptions exist near Central America and the west coast of Africa, suggesting that the positive genesis biases in these two regions cannot be simply attributed to biases in the environmental conditions. The relative contribution of an environmental variable to the genesis biases can be examined by replacing its monthly mean from the GEFS reforecast by the one from the ERAI to recalculate the GPI (with all the other variables from the GEFS reforecast). The GPI derived exclusively from the GEFS were then subtracted from the recalculated GPI, and the resultant differences can indicate how much the correction in a certain variable may affect the biases in GPI. The 850-hPa vorticity, 700-hPa RH, and 850-200-hPa vertical shear were examined in Figs. 3.4d-f, respectively. Readers, however, should be cautioned that these variables may be closely related to each other in some ocean basins. In Fig. 3.4d, a positive difference over the western North Pacific suggests that the correction in the 850-hPa vorticity field reduces the negative genesis bias in this region. In other words, the bias in the GEFS vorticity field makes a large contribution to the negative genesis bias in that region. On the other hand, the correction in the 850-hPa vorticity field enhances the negative biases over the subtropical west Pacific and the subtropical west Atlantic, suggesting errors in the GEFS vorticity field may compensate for the biases in other variables in these regions. Similar diagnoses were carried out by replacing the 700-hPa RH (Fig. 3.4e)

50 and the 850-200-hPa vertical shear (Fig. 3.4f), respectively. Figure 4e suggests that the correction in the 700-hPa RH helps to reduce the negative genesis biases over the South China Sea, the Philippine Sea, and the subtropical west Atlantic (note the partial cancellation between the vorticity and the RH fields in this region). Figure 3.4f shows that the correction in the vertical shear helps to improve the GPI prediction over the subtropical west Pacific, the eastern North Pacific, the subtropical west Atlantic, and the Atlantic MDR. Overall, Fig. 3.4 suggests that TC genesis in the GEFS is more sensitive to the dynamic variables over the western North Pacific and to the thermodynamic ones over the North Atlantic, consistent with the observational analysis by Peng et al. (2012) and Fu et al. (2012). Next, we will examine the environmental biases within the context of large-scale circulations, and also investigate the positive genesis biases near Central America and the west coast of Africa, which the GPI diagnosis fails to explain.

A. WESTERN NORTH PACIFIC

A third of global TCs form over the western North Paciﬁc, 75% of which develop in the monsoon trough environment (Ritchie and Holland, 1999). The dynamic and thermodynamic conditions in the monsoon trough zone are favorable to the growth and development of a TC, such as the low-level convergence and cyclonic vorticity, weak vertical wind shear, high midlevel relative humidity, and warm SST (e.g., Holland, 1995; Chen et al., 1996; Gray, 1998). The successful prediction of a monsoon trough may contribute to the skillful extended-range forecast of tropical cyclogenesis (Nakano et al., 2015). The ERAI shows a northwest-southeast-oriented monsoon trough across 110◦-150◦E (Fig. 3.5a). The low-level monsoonal southwesterlies extend from the Indochina Peninsula to 150◦E. The GEFS day-8 reforecast is broadly consistent with the ERAI results (Fig. 3.5b), but the monsoon trough is much weaker than observed and conﬁned to the South China Sea, while the trade wind easterlies prevail east of the Philippines. The weaker monsoon trough is associated with negative biases in column water vapor and precipitation (Fig. 3.5c), and weaker low-level convergence and cyclonic vorticity (not shown) over the South China Sea and the Philippine Sea (not shown), all

51 Figure 3.5: The monthly average 850-hPa circulations (streamlines) with the 850-hPa zonal winds (shaded) from (a) the ERAI and (b) the GEFS day-8 reforecast in JASO during 1985-2012. (c) The diﬀerence between the long-term mean precipitation rate (mm day−1) for the GEFS day-8 reforecast and the CMORPH (green contours starting at 0 mm day−1 and with intervals of 0.25 mm day−1) in JASO during 2003-12 and the diﬀerence of the long-term mean CWV (mm) between the GEFS day-8 reforecast and the ERAI (shaded) in JASO during 1985-2012.

52 contributing to the underprediction of TC activity in that region (Fig. 3.2c). Also note that the extent (or strength) of the subtropical ridge over East Asia is underpredicted by the GEFS as well, which results in biases in the steering ﬂow and the storm tracks (Fig. 3.3c), as well as overpredicted extratropical cyclogenesis over the East China Sea and Japan (not shown).

B. EASTERN NORTH PACIFIC

The eastern North Pacific is the second most active basin for TC activity (Peduzzi et al., 2012; Jin et al., 2014). TC formation over this basin is more confined in both the longitudinal and latitudinal extents, resulting in the highest genesis density over the globe (Camargo et al., 2008; Davis et al., 2008). TC activity in this region is closely related to the regional Hadley circulation and the intertropical convergence zone (ITCZ; Zhang and Wang, 2015). To evaluate the skill of the GEFS in capturing the ITCZ, precipitation is examined here. Figure 3.6a shows the difference of the long-term mean precipitation rate in JASO during 2003-12 between the GEFS day-8 reforecast and the CMORPH. A dipole pattern in the precipitation difference over the eastern North Pacific indicates a southward displacement (about 2◦) of the ITCZ in the GEFS, along with the overpredicted precipitation in the Central America. Previous studies have suggested that tropical cyclogenesis is sensitive to the meridional displacement of the ITCZ, which is associated with variations in the low-level vorticity, divergence, vertical wind shear, etc. (Molinari and Vollaro, 2000; Merlis et al., 2013). In addition, the ITCZ breakdown is an important mechanism for tropical cyclogenesis over the east Pacific (e.g., Nieto Ferreira and Schubert, 1997; Wang and Mag- nusdottir, 2005). Given that the easternmost tip of the ITCZ is the most unstable region along the vorticity strip (Wang and Magnusdottir, 2006), the southeastward shift of the TC genesis center is consistent with the southward displacement of the ITCZ in the GEFS (Fig. 3.2c). The biases in the 700- hPa RH also contribute to the positive genesis bias over Central America (Fig. 3.4e).

53 Figure 3.6: (a) The diﬀerence of the long-term mean precipitation rate (mm day−1) between the GEFS day-8 reforecast and the CMORPH in JASO during 2003-12. (b) The 700-hPa relative humidity diﬀerence between the GEFS day-8 reforecast and the ERAI in JASO during 1985-2012.

54 C. NORTH ATLANTIC

The ITCZ is also displaced southward over the central MDR of the Atlantic (50◦-15◦W; Fig. 3.6b), which is consistent with the negative genesis biases in this region (Merlis et al., 2013). The GPI diagnosis suggests that the genesis biases over the Atlantic can be mainly attributed to the biases in relative humidity and vertical shear (Figs. 3.4e,f), while it fails to explain the positive genesis bias near the Cape Verde islands (Fig. 3.4c). Most Atlantic TCs (∼ 60%) develop from African easterly waves (AEWs), especially over the MDR (e.g., Landsea et al., 1998; McTaggart-Cowan et al., 2008). Given the role of the AEWs in tropical cyclogenesis, we next examine the representation of the AEWs in the GEFS. The seasonal variances of 2.5- 9-day bandpass-filtered 850-hPa meridional wind along 15◦N were calculated and then averaged over 28 yr (1985-2012) to represent the wave activity. Figure 3.7a shows the variances from the ERAI, the CFSR (i.e., day 0), and the GEFS day-8 reforecast. The ERAI shows a peak in variance (∼ 12.5 m2 s−2) near the West African coastline, and the wave activity over the African continent is much weaker. This is consistent with the observed AEW structure: the AEWs are mainly confined to 600-700 hPa south of the African easterly jet over the land, and become stronger and attain a deeper structure offshore as a result of coastal convection and/or interaction with the northern wave track (Thorncroft and Hodges, 2001; Hankes et al., 2015). Compared to the ERAI, the AEWs in the CFSR are much stronger. Results show a primary peak over the ocean (∼ 18◦W) similar to the ERAI but with larger amplitude, and a secondary peak over the land (∼ 7.5◦W). The synoptic-scale biases in the CFSR can be an error source for the subsequent TC forecasts through downscale cascading (Peters and Roebber, 2014). The positive biases in the variance over the land are even stronger in the GEFS day-8 reforecast, and the wave activity over the land is comparable to or even stronger than that over the ocean, suggesting that the AEWs have an unrealistically deep structure over the land. To further examine the structure of the AEWs, we regressed the 2.5-9-day bandpass-filtered meridional wind and the 2.5-9-day bandpass-filtered diabatic heating rate Q1 (Yanai et al., 1973) at each grid point and each pressure level against the 2.5-9-day bandpass-filtered 850-hPa meridional wind at a reference point (15◦N, 12◦W) over West Africa. Before applying the bandpass

55 Figure 3.7: (a) The mean variance of 2.5-9-day bandpass-filtered 850-hPa meridional wind (V850) along 15◦N in the ERAI (black), the CFSR (day 0; red), and the GEFS day-8 reforecast (green) in JASO for 1985-2012. Longitude-height cross sections of seasonal mean regressions of 2.5-9-day bandpass-filtered meridional wind (shaded) and 2.5-9-day bandpass-filtered Q1 [contours starting at and with intervals of 0.4 K day−1 (m s−1)−1] against the 2.5-9-day bandpass-filtered V850 at a reference point (15◦N, 12◦W; blue plus sign) for (b) ERAI, (c) CFSR, and (d) the GEFS day-8 reforecast.

56 filter and linear regression, the seasonal cycle was removed by subtracting the climatological mean daily data. Figures 3.7b-d show the anomalies in the meridional wind and Q1 fields for one standard deviation of the 850-hPa meridional wind at the reference point. Consistent with previous studies (e.g., Kiladis et al., 2006), the ERAI shows an eastward tilt to the wave structure below 700 hPa and a westward tilt above. The weakening amplitude with height over the land indicates that the wave has a shallow structure in the lower troposphere. The Q1 field shows that shallow heating occurs in the southerly flow west of the trough axis, and the heating near the wave trough is rather weak. Figure 3.7c shows that the CFSR is generally consistent with the ERAI, but the AEWs are slightly stronger at the lower troposphere (∼ 850 hPa). In addition, the Q1 field shows that the heating in the CFSR is stronger, deeper, and closer to the wave trough axis than that in the ERAI. The wave is even stronger in the GEFS day-8 reforecast, with stronger and deeper heating in the vicinity of the 700-hPa trough (Fig. 3.7d). Since a wave of a deeper structure and with active convection is more conducive to TC formation (Raymond and López Carrillo, 2011; Wang, 2012), the biases in the AEWs help to explain the positive TC genesis biases near the Cape Verde islands. Meanwhile, the stronger and deeper waves can be attributed to the stronger deep convective heating associated with the AEWs in the GEFS.

3.4.2 Possible deﬁciencies in the model physics

The biases in the RH and Q1 fields hint at possible deficiencies in the model physics, especially the cumulus scheme. The GEFS (version 9.0.1) employed the simplified Arakawa-Schubert (SAS) deep convection scheme. By deplet- ing the excessive instability in the atmospheric column, the SAS scheme in the GEFS was modified to suppress the grid-scale precipitation and to make the cumulus convection stronger and deeper (Han and Pan, 2011). Figure 3.8a shows the average daily precipitation rate in 1-mm-wide bins of CWV over the tropical ocean areas from the SSMIS and the GEFS day-8 and -16 reforecasts. Consistent with the SSMIS, the GEFS captures the nonlinear relationship between precipitation and CWV and the exponential increase in precipitation for large CWV. However, the GEFS generates too much pre-

57 Figure 3.8: (a) The average daily precipitation rate (mm day−1) in 1-mm-wide bins of the CWV (mm; smoothed by cubic interpolation), (b) the probability distribution of CWV (%), and (c) the relative probability distribution diﬀerences of precipitation rate (%) between the GEFS day-8 and -16 reforecasts and CMORPH over the tropical ocean areas (20◦S-20◦N) for 2003-12. The average daily precipitation rate was stratiﬁed into 15-mm day−1 wide bins. The black solid lines indicate the precipitation rate and CWV of version-7 SSMIS; yellow, red, and green lines (or bars) show the cases in CFSR (day 0), and the GEFS day-8 and -16 reforecasts, respectively.

58 cipitation for a given value of CWV, implying that precipitation may be triggered too early in the model in terms of the CWV accumulation. A similar bias was found by Li et al. (2014) in the operational forecasts of the Navy Operational Global Atmospheric Prediction System (NOGAPS), which also employed the SAS scheme. The difference between day-8 and -16 reforecasts shows an increasing bias with the forecast lead time. Figure 3.8b shows the probability distribution of CWV over the tropical oceans from the SSMIS, the CFSR (day 0), and the GEFS day-8 and -16 reforecasts. The SSMIS depicts a bimodal distribution of CWV with a primary peak around 57 mm and a secondary peak around 34 mm. The CFSR resembles the SSMIS. A dry bias is found in the GEFS reforecasts: the CWV of maximum frequency of occurrence shifts from 56 to 48 mm in the GEFS day-8 reforecast, and to 46 mm in the day-16 reforecast. Given the precipitation-CWV relationship in Fig. 3.8a, the dry bias in CWV indicates the underprediction (overprediction) of heavy (light) precipitation in the GEFS, which is confirmed in Fig. 3.8c. Compared to the CMORPH findings, the GEFS underpredicts moderate-to-heavy precipitation (∼ 30 mm day−1) by over 70%. Consistent with CWV, the negative bias in precipitation increases with the forecast lead times. The frequency of drizzle-to-light (15-30 mm) precipitation is slightly underpredicted in the day-8 reforecast and overpredicted in the day-16 reforecast. The early initiation of precipitation with respect to the CWV is consistent with hyperactive convection over West Africa. This was also confirmed by Bombardi et al. (2015), who found deep convection was triggered too frequently in the SAS scheme. The underprediction of heavy precipitation is consistent with the weaker monsoon trough in the GEFS than observed (Fig. 3.5). A weaker monsoon trough along with negative genesis biases over the western North Pacific was also found in the Model for Prediction Across Scales (MPAS) when using the SAS scheme (C. Davis 2015, personal communication). Overall, it suggests that an improved cumulus parameterization may help to reduce the errors in the model mean state and improve TC predictive skill on the regional scale. In addition to the cumulus scheme, the lack of air-sea interaction and the deficiencies in other model physics, such as the boundary layer and land surface parameterizations (Taylor and Clark, 2001), may also lead to biases in the diabatic heating field and African easterly waves. Further study is warranted to improve our understanding and

59 the model representation of these processes.

3.5 Summary and discussion

The tropical cyclone (TC) predictive skill of the NCEP Global Ensemble Forecasting System (GEFS) Reforecast Version 2 was evaluated against IB- TrACS, the interim ECMWF reanalysis (ERAI), and two satellite datasets with a special focus on tropical cyclogenesis. Different from most previous studies, we assessed the model’s skill from a “climate” perspective. The basic reasoning is that forecast errors may accumulate on longer timescales and the evaluation of climatology can help to identify model error sources. The evaluation of TC activity in the GEFS shows that the GEFS captures the seasonality of TC activity reasonably well and the spatial pattern of TC activity in the GEFS is broadly consistent with the observations, but quantitative errors are present over all ocean basins. Positive biases in genesis frequency are found over the Southern Hemisphere and the Indian Ocean, and negative biases over the western North Pacific and the eastern North Pacific. The genesis center also shifts southeastward over the eastern North Pacific. Although the long-term mean basin-wide TC counts are well captured by the GEFS over the Atlantic, genesis almost exclusively occurs near the Cape Verde islands and is substantially underpredicted over the rest of the Atlantic basin. The biases in TC genesis also lead to large biases in the TC track distribution. Different genesis pathways are dominant over different ocean basins, and genesis biases over different ocean basins are thus associated with errors in different aspects of the large-scale and synoptic-scale circulation patterns. Over the western North Pacific, most TCs develop in the monsoon trough environment, and a weaker monsoon trough in the GEFS and the associated biases in the low-level vorticity and midlevel relative humidity lead to the negative bias in TC genesis. Over the eastern North Pacific, the ITCZ breakdown is an important mechanism for tropical cyclogenesis, and TC activity is modulated by the variability of the regional Hadley circulation. The genesis biases in the GEFS can be largely attributed to the erroneous location of the ITCZ over the eastern North Pacific. Over the Atlantic, most TCs originate from tropical easterly waves. The GEFS overpredicts the wave ac-

60 tivity over West Africa. Compared to the ERAI, the waves in the GEFS are stronger and deeper, and are accompanied by larger diabatic heating around the wave trough axis, which lead to prevailing positive genesis biases (or early TC development) near the coast of West Africa and negative biases farther downstream. The diagnosis of precipitation and column water vapor (CWV) reveals a dry bias in CWV and indicates that precipitation is initiated too early with respect to CWV accumulation in the GEFS. It is suggested that improvement in the cumulus parameterization may reduce the model mean state errors and enhance the TC predictive skill on the regional scale. Al- though some of the biases presented in this study are likely tied to a certain model resolution and the version of the model physics and dynamics, the result can be used to guide future GFS and GEFS development for better TC forecasts.

61 Chapter 4

Predictability of Tropical Cyclones

c 2016 American Meteorological Society1

4.1 Introduction

Skillful prediction of tropical cyclones (TCs) is of signiﬁcant socio-economic value due to the potentially hazardous impacts of the storms. Accurate prediction of the characteristics (genesis, track and intensity) of TCs is critical, in particular, timely and skillful prediction of TCs near the U.S. coast is important for storm preparedness and resource management. Dynamic models are important tools in operational forecasting (e.g., Elsberry et al., 2009; Halperin et al., 2013; Li et al., 2016). Previous studies have shown that the predictive skill of TCs varies from case to case (Komaromi and Majumdar, 2015). The formation of some storms can be predicted by more than one week in advance (e.g., Elsberry et al., 2011; Tsai and Elsberry, 2013; Xiang et al., 2015a), while the 48-hour forecasts of some other storms, such as Hur- ricane Fay (Kimberlain, 2014) and Tropical Storm Hanna (Cangialosi, 2014) in 2014, can be a challenge even for the state-of-the-art operational prediction systems. The predictive skill of an operational model may have substantial variations on the subseasonal and interannual timescales (Komaromi and Ma- jumdar, 2015; Li et al., 2016) and can also vary from basin to basin (Haplerin et al. 2016). Such variations cannot be completely attributed to changes in

1Permission hereby is granted to use ﬁgures, tables, illustrations, and substantial por- tions of text provided that the source is acknowledged: Li, W., Z. Wang, and M.S. Peng, 2016: Evaluating Tropical Cyclone Forecasts from the NCEP Global Ensemble Forecast- ing System (GEFS) Reforecast Version 2: Potential predictive skill on the subseasonal and seasonal timescales. Wea. Forecasting, 31, 895-916. Some excerpts from this chapter are also from: Wang, Z., W. Li, M.S. Peng, X. Jiang, R. McTaggart-Cowan, and C.A. Davis, 2017: Predictive Skill and Predictability of North Atlantic Tropical Cyclogenesis in Diﬀerent Synoptic Flow Regimes. J. Atmos. Sci., submitted.

62 a prediction system or the heterogeneity of observational data assimilated in a model. The spatial and temporal variations of predictive skill often reflect different predictability of TCs. Predictability, the extent to which future states of a system may be predicted based on the knowledge of the current and past states of the system (AMS Glossary), depends on the available observational data and prediction models, and also on the intrinsic dynamic and physical nature of the phenomenon of interest. A better understanding of the predictability of TCs may not only help to identify the key processes involved in TC development, but may also provide useful information on the reliability of dynamic prediction and thus aid more effective use of forecast products. Tropical cyclones involve multi-scale interactions among complex physical processes ranging from the convective scale to the planetary scale (Gray, 1998). It is generally believed that convective processes limit the predictability of TCs, while slowly varying, large-scale processes may serve as important sources of predictability. For example, the Madden-Julian Oscillation (MJO), the dominant mode of subseasonal variability in the tropics (Mad- den and Julian, 1972; Zhang, 2005), is a major source of TC predictability on the subseasonal time scale. The MJO affects TC frequency and intensity via its modulation on vertical wind shear, tropospheric humidity, low-level vorticity and synoptic wave activity (e.g., Camargo et al., 2009; Maloney and Hartmann, 2000b; Jiang et al., 2012; Klotzbach and Oliver, 2015). Ow- ing to its quasi-periodic behavior and strong impacts on TCs, the MJO has been used as an important predictor in many statistical prediction models for tropical cyclogenesis (e.g., Leroy and Wheeler, 2008; Slade and Maloney, 2013). A dynamic model that is more skillful in MJO prediction is often found more skillful in subseasonal TC prediction (Barnston et al., 2015; Xi- ang et al., 2015a,b). It has also been shown that models tend to be more skillful in predicting TC activity during strong MJO periods than during weak MJO periods (e.g., Li et al., 2016). Other sources of predictability for TC genesis include, but are not limited to, the El Niño-SouthernOscillation (ENSO; e.g., Goldenberg and Shapiro, 1996), the Atlantic Meridional Mode (e.g., Kossin and Vimont, 2007) and the Atlantic regional Hadley circulation (Zhang and Wang, 2013), which all strongly modulate Atlantic TCs on the interannual time scale. Li et al. (2016) showed that the subseasonal predictive skill of TCs tends to be higher in El Niñoand La Niñayears than in

63 the ENSO neutral years. Wang et al. (2015) attributed the skillful seasonal prediction of the Atlantic basin-wide hurricane frequency in a global atmospheric model (Chen and Lin, 2013) to the high predictability of the Atlantic regional Hadley circulation. Moving to shorter temporal scales or smaller spatial scales, a pre-existing, cyclonic synoptic disturbance is one of the necessary conditions for TC formation (e.g., Gray, 1968). Tropical cyclones can develop from tropical easterly waves (e.g., Landsea, 1993; Dunkerton et al., 2009), equatorial Rossby waves (Lussier III, 2010), monsoon troughs or monsoon gyres (e.g., Wu et al., 2013), the breakdown of the Intertropical Convergence Zone (ITCZ; e.g., Guinn and Schubert, 1993; Wang and Magnusdottir, 2005), Rossby wave dispersion from a pre-existing cyclone (e.g., Li and Fu, 2006), or originate from subtropical frontal systems (the so-called tropical transition; Davis and Bosart, 2003, 2004). Synoptic-scale precursor disturbances serve as the incubator for the development of a TC (e.g., Dunkerton et al., 2009; Wang, 2012) and control the immediate environmental conditions for genesis. Different types of precursors are characterized by different synoptic-scale environmental states, and their interaction with an incipient TC vortex may be different. It is conceivable that tropical cyclogenesis in different synoptic flow regimes may be associated with different levels of predictability. Although Lorenz (1965) demonstrated, more than 50 years ago, that predictability is dependent on flow regime, predictability of tropical cyclogenesis for different synoptic flow regimes has not been well studied. In this chapter, we will investigate the predictability of TCs on different timescales using the reforecasts dataset. Since a coarse-resolution global model generally has difficulty in predicting TC intensity, we will mainly focus on tropical cyclogenesis and briefly examine TC tracks. We evaluated TCs over different ocean basins around the globe for the interannual timescales, and for the subseasonal and synoptic timescales, we focused on the North Atlantic. This chapter is organized as follows. The datasets and metrics are described in section 4.2. The predictability of TCs on interannual and subseasonal timescales are assessed in section 4.3 and 4.4, respectively. The predictability of tropical cyclogenesis influenced by synoptic-scale flow regimes is presented in section 4.5, followed by a summary and discussion in section 4.6.

64 4.2 Data and metrics

4.2.1 Data

We used the GEFS reforecasts to investigate the predictability of TCs. The data, model description, and TC detection are the same as in section 3.2. To measure the predictive skill of TC formation, we used 2 × 2 contingency table. A hit is defined for a model TC that forms within 120 hours of the observed genesis time and within a 5◦ radius of the observed TC track 2, while the other model TCs are categorized as false alarms. Additionally, a miss is flagged when the model fails to produce a hit for an observed TC, and a non-event or correct negative is identified if neither an observed genesis event nor a predicted one occurs. Several TC indices were used in this study to facilitate quantitative evaluations. “TC counts” is defined as the total number of TCs within a certain period over a certain basin; “TC days” is the sum of the lifetime of all TCs, measured in days; and “accumulated cyclone energy” (ACE; Bell et al., 2000) is calculated by integrating the squares of the 6-hourly maximum sustained surface wind speed (in kt2, where 1 kt = 0.51 m s−1) over the lifetime of a TC for all TCs over a certain basin, which is a function of TC counts, lifetime, and intensity. And “weekly cyclone energy” (WCE) is as ACE but calculated over a week.

4.2.2 Metrics

Several metrics were employed to evaluate the predictive skill of the GEFS reforecasts and to represent predictability in this section. The predictability on subseasonal and interannual timescales will be measured using correlation coeﬃcients. On synoptic timescales, hit rate (H), false alarm rate (F), false alarm ratio (FAR) and critical successful index (CSI) were computed based

2The time window is chosen to include early genesis and late genesis [the predicted genesis time of a storm is too early or too late compared to the observation; see Halperin et al. (2013) and Li et al. (2016)].

65 on the 2 × 2 contingency table as below

a H = (4.1) a + c b F = (4.2) b + d b F AR = (4.3) a + b b CSI = (4.4) a + b + c where a, b, c and d are the numbers of hits, false alarms, misses, and correct negatives, respectively. The hit rate, or the probability of detection, is the proportion of the occurrences that are correctly forecast. The false alarm ratio is the proportion of genesis forecasts that turn out to be false alarms, and the false alarm rate is the ratio of false alarms to the total number of non-occurrences (i.e., b + d). The critical successful index, also known as the threat score, is the number of hits divided by the total number of occasions when the event is forecast and/or observed, which is particularly useful when the occurrence is substantially less frequent than the nonoccurrence (Wilks, 2011). The environmental variables related to TC formations in the GEFS reforecasts were evaluated against the CFSR. The CFSR were mapped to a grid mesh of 1.0◦ × 1.0◦ resolution in keeping with the GEFS. The predictive skill of environmental variables was examined by computing the root mean squared error (RMSE). RMSE was ﬁrst derived for individual ensemble members and then the ensemble mean RMSE was taken. A good agreement was found among ensemble members, and only the ensemble means are discussed below for brevity.

4.3 Interannual timescales

In this section, we will examine the TC interannual variability in the GEFS. The investigations will help to evaluate how well the model reproduces the impacts of some large-scale climate modes on TCs and provide insights into the potential skill of the GEFS in making realtime operational TC forecasts on S2S timescales. The time series of the annual TC counts and ACE from the GEFS week-1

66 Figure 4.1: Time series of the normalized TC counts in IBTrACS (black curves) and the GEFS week-1 (red curves) and -2 (blue curves) reforecasts during 1986-2012 in each basin for (a) WP, (b), EP, (c), NA, (d), NI, and (e) SH. The Spearman rank correlation coeﬃcients between the GEFS week-1 and -2 reforecasts and IBTrACS are marked in the top-left corner of each panel, and the signiﬁcances of correlation are indicated in Table 4.1.

67 Figure 4.2: As in Fig. 4.1, but for the ACE.

68 Table 4.1: The Spearman rank correlation coefficients of the interannual variability of TC counts and ACE between the GEFS and IBTrACS over different basins. The numbers in boldface are the significant coefficients with 95% confidence.

TC counts TC counts ACE ACE Basin Week-1 Week-2 Week-1 Week-2 WP 0.32 0.51 0.82 0.80 EP 0.62 0.71 0.84 0.75 NA 0.51 0.48 0.86 0.75 NI 0.21 0.44 0.11 0.32 SH 0.34 0.28 0.22 0.33

and -2 reforecasts and the IBTrACS are shown in Figs. 4.1 and 4.2. Visual inspection suggests that the GEFS week-1 and -2 reforecasts have a good level of agreement with the IBTrACS over the western North Pacific, the eastern North Pacific, and the Atlantic (Figs. 4.1a-c and 4.2a-c), especially for ACE. The GEFS also captures the out-of-phase relationship of the TC activity between the eastern North Pacific and the Atlantic (Wang and Lee, 2009; Zhang and Wang, 2015). On the other hand, the GEFS fails to skillfully predict the interannual TC variability over the north Indian Ocean and the Southern Hemisphere (Figs. 4.1d,e and 4.2d,e). The Spearman rank correlations with IBTrACS are significant for the GEFS week-1 and -2 reforecasts over the eastern North Pacific and the Atlantic and for the week-2 reforecasts over the western North Pacific (r=0.48; Table 4.1), while the correlations are much weaker over the north Indian Ocean and the Southern Hemisphere. The correlations of ACE are much higher than those of the TC counts over the North Pacific and the North Atlantic (Table 4.1), which can probably be attributed to the strong control of ACE by the SST. It is interesting to note that the rank correlations in the week-2 reforecasts, although still insignificant, are higher than those in the week-1 reforecasts over the north Indian Ocean and the Southern Hemisphere. Previous studies have shown that ENSO impacts the TC activity in various ocean basins, and that the AMM strongly modulates TCs over the North Atlantic (e.g., Gray, 1984; Landsea and Knaff, 2000; Goldenberg et al., 2001;

69 Table 4.2: The Pearson correlations of the Niño-3.4and AMM (July-November mean) indices with the interannual variability of TC counts and ACE in the GEFS and IBTrACS over the WP, EP, and NA during 1986-2012. All coefficients are above the 95% confidence level (0.32) except the correlation between Niño-3.4and the observed TC counts over the WP. The week-2 correlations exceeding the week-1 results are in boldface.

Basin Observed Week-1 Week-2 Observed Week-1 Week-2 TC counts (Ni˜no-3.4) ACE (Ni˜no-3.4) WP 0.25 0.36 0.35 0.72 0.73 0.76 EP 0.48 0.66 0.75 0.38 0.49 0.61 NA -0.42 -0.66 -0.46 -0.48 -0.52 -0.55 TC counts (AMM) ACE (AMM) NA 0.74 0.48 0.52 0.78 0.72 0.60

Jin et al., 2014). Such low-frequency climate modes provide sources of predictability for TC activity on the subseasonal and longer timescales, and it is interesting to examine how well the GEFS represents their impacts. Table 4.2 lists the Pearson correlations of the GEFS’ TC indices with the observed Niño-3.4and the AMM indices (http://www.esrl.noaa.gov/psd) over the western North Pacific, the eastern North Pacific, and the North Atlantic. The correlations with the TC indices derived from IBTrACS are also listed for comparison. Consistent with previous studies (e.g., Lander, 1994; Goldenberg and Shapiro, 1996), IBTrACS shows that the ENSO index is moderately correlated with both TC counts and ACE over the eastern North Pacific and the North Atlantic. Over the western North Pacific, ENSO strongly modulates the interannual variability of ACE (r=0.72) but is weakly correlated with the annual TC counts. Over the North Atlantic, the AMM plays a prominent role in the interannual variability of TC counts (r=0.74) and ACE (r=0.78). The GEFS week-1 and -2 reforecasts capture all the observed significant correlations between ENSO and the TC indices, including a strong correlation with ACE and a weak correlation with the TC counts over the western North Pacific. This is consistent with the relatively low predictive skill of TC counts compared to that of ACE over the western North Pacific. It is also interesting to note that the GEFS overpredicts all the correlations with ENSO,

70 especially for ACE in the week-2 reforecasts. The GEFS captures the positive correlations between the AMM and the Atlantic TC activity, but the correlations are weaker than those observed, which is probably associated with the erroneous location of the ITCZ over the Atlantic.

4.4 Subseasonal timescales

In this section, we will assess how well the inactive/active TC periods are captured by the GEFS. For brevity, we will focus on the North Atlantic basin. The analyses include the impacts of the low-frequency climate modes (including ENSO, the MJO, and AMM) and the extratropical Rossby wave breaking on TC subseasonal variability and predictability.

4.4.1 Low-frequency climate modes

As an example, the time series of the weekly TC days from the GEFS week-1 and -2 reforecasts were compared with that derived from IBTrACS for the hurricane season in 2000 in Fig. 4.3a. The annual cycle has been removed to highlight the subseasonal variability. The Atlantic basin underwent three active periods of TC activity, in mid-August, mid-September, and early to mid-October, respectively. The GEFS captures the peaks in TC days during August and early October but misses a primary peak in mid-September and a small peak in mid-October. The Pearson correlations are 0.79 and 0.53 in the week-1 and -2 reforecasts, respectively. Similar time series were constructed for the weekly cyclone energy (WCE) being deﬁned as the squares of the 6-hourly maximum sustained surface wind speed (in kt2) integrated over all active TCs for the time period of 1 week (Fig. 4.3b). The GEFS shows higher correlations with IBTrACS for WCE than for TC days, especially in the week-1 reforecasts. It is also notable that both the week-1 and -2 reforecasts underpredict the amplitude of the WCE peak in late September- early October. This can be partly attributed to the underpredicted peak in the TC days (Fig. 4.3a) as well as the underpredicted TC intensity in the global model. Other years can be evaluated similarly, and the model skill is summa- rized by the time series of the Pearson correlation between the observed and

71 Figure 4.3: (a) Weekly TC days and (b) WCE from IBTrACS (black curves) and the GEFS week-1 (red curves) and -2 (blue curves) reforecasts from 1 Jul to 30 Nov in 2000 over the Atlantic. In (b), the ordinate for WCE in the GEFS reforecasts is shown on the right. The Pearson correlations with the observations are marked in the top-left corner. All correlations are signiﬁcant with 95% conﬁdence.

72 Figure 4.4: Time series of the Pearson correlation of (a) TC days and (b) WCE computed as in Fig. 4.3, but for each year during 1985-2012 between the GEFS week-1 (red curves) and -2 (blue curves) reforecasts and IBTrACS. The mean correlations during 1985-2012 are marked in the top-left corner of each plot. The gray lines indicate the significance level using a two-tailed t-test with 95% confidence. The degree of freedom was adjusted using a “modified” Chelton method (Pyper and Peterman, 1998).

73 predicted TC days or WCE (Fig. 4.4). The time series of the correlation coefficients for TC days show that the GEFS agrees well with the observation in the week-1 reforecasts, with the correlation coefficient above 0.6 in most years. The correlations for the week-2 reforecasts are weaker compared to the week-1 reforecasts but still above the 95% confidence level in most years. The mean correlations during 1985-2012 are 0.65 for the week-1 reforecasts and 0.44 for the week-2 reforecasts. The correlations for WCE are generally higher than those for TC days, with the mean correlations of 0.75 for the week-1 reforecasts and 0.50 for the week-2 reforecasts. Figure 4.4 suggests that the model has reasonable skill in predicting the active and inactive TC periods with a lead time of 7-14 days. A striking feature in Fig. 4.4 is the large year-to-year variability of the correlation coefficients, especially for the TC days. Since the GEFS reforecasts use a fixed model version, this suggests that intrinsic predictability may vary from year to year. Previous studies have suggested that the low-frequency climate modes such as the ENSO and MJO can enhance the TC subseasonal predictive skill (Leroy and Wheeler, 2008; Slade and Maloney, 2013). It is natural to ask whether TCs are more predictable in some climate conditions, such as during strong ENSO or AMM events or in a year of active MJO. To examine how the predictive skill of TC subseasonal variation is modulated by different climate modes, Fig. 4.5 shows the mean correlations of TC days and WCE with the observations in different climate regimes. The stratification was based on a ±0.5 standard deviation (SD) of the seasonal mean AMM or ENSO index during July-November in each year. Here, the MJO activity is represented by the seasonal mean amplitude of the daily velocity potential MJO indices (VPM; Ventrice et al., 2013), and a larger seasonal mean amplitude indicates stronger MJO activity. The VPM is similar to the all-season real-time multivariate MJO index (RMM; Wheeler and Hendon, 2004), but using 200-hPa velocity potential instead of outgoing longwave radiation. Ventrice et al. (2013) show that the VPM can better represent the MJO activity in the Western Hemisphere than the RMM index. Our analysis also shows a stronger contrast in the stratification using the VPM than using the RMM or a local MJO index defined by the space-time-filtered OLR (not shown). The two-tailed Student’s t-test was applied to explore the statistical significance of the difference in the mean correlations between the neutral group (from -0.5 to 0.5 SD) and an anomalous group (>0.5 or <-0.5 SD).

74 Figure 4.5: The mean correlation coefficients of the (left) TC days and (right) WCE with the observations stratified by different climate indices: (a),(b) the VPM indices, (c),(d) the Niño-3.4index, and (e),(f) the AMM index in July-November during 1985-2012. The red and blue bars indicate the GEFS week-1 and -2 reforecasts, respectively. Plus signs indicate that the difference between an anomalous group and the corresponding neutral group exceeds the 90% confidence level.

75 Figure 4.5 shows that predictive skill tends to be higher (weaker) in years of strong (weak) MJO activity. The model also tends to have better skill during strong ENSO years than in neutral years, especially in strong La Niñayears. The AMM does not seem to impact the predictive skill, except that the correlation of WCE is slightly higher in the positive AMM phase. This may be due to the underpredicted correlation between the AMM and the TC counts in the GEFS (Table 4.2). In addition, most differences in Fig. 4.4 are statistically insignificant, which is probably due to the small sample size and the large fluctuations.

4.4.2 Impacts of Rossby wave breaking

Rossby wave breaking (RWB) is usually manifested as the irreversible overturning of the potential vorticity (PV) contours on isentropic surfaces. The breaking waves can induce mixing of the surrounding air (McIntyre and Palmer, 1985). Thorncroft et al. (1993) illustrated two types of equatorward RWB based on upper-level trough behavior: anticyclonic RWB and cyclonic RWB. Anticyclonic RWB is associated with anticyclonic and equatorward advection of air, while cyclonic RWB is observed as the air cycloni- cally and poleward wraps-up around the jet core. Although synoptic-scale RWB directly stirs up the surrounding air over a finite region, RWB can affect the atmospheric variability across different spatiotemporal scales (e.g., Rivièreand Orlanski, 2007; Martius et al., 2007; Strong and Magnusdottir, 2008). It has been found that RWB not only interacts or reinforces the extratropical low-frequency atmospheric variability and teleconnection patterns, but also facilitates tropical-extratropical interactions by mixing the cold, dry extratropical air with the warm, moist tropical air and influences the subtropical and tropical weather conditions (e.g., Thorncroft et al., 1993; Pelly and Hoskins, 2003; Benedict et al., 2004; Rivière,2009; Moore et al., 2010; MacRitchie and Roundy, 2016). The impact of RWB on TC activity has been examined in some previous studies. On synoptic scales, RWB can occasionally trigger tropical transition (a TC originated from a baroclinic and cold-core system; Davis and Bosart, 2004) by contributing upper-level PV streamers (Galarneau Jr et al., 2015; Bentley et al., 2017). However, an overall negative impact was found on

76 seasonal timescales: anticyclonic RWB was negatively correlated with the seasonal TC activity, which explained the quiet hurricane season in 2013 (Zhang et al., 2016, 2017). Nevertheless, how RWB impacts TC activity on subseasonal timescales has not been well studied despite the growing demand for skillful TC subseasonal forecasts to assist resource management and decision-making. This section will address the following scientific issues: 1) How does RWB affect TC activity on subseasonal timescales? 2) How does RWB affect TC subseasonal predictive skill and predictability? We focus on the North Atlantic and the warm season from July to October (JASO), and only consider the anticyclonic events because they are more active than the cyclonic events equatorward of the jet axis during JASO (Zhang et al., 2016).

A. AWB detection and Indices

An anticyclonic Rossby wave breaking (hereafter AWB) was identified based the PV overturning feature on the 350-K isentropic surface (Abatzoglou and Magnusdottir, 2006; Strong and Magnusdottir, 2008). The AWB activity was represented by the “AWB area”, which was derived as the fraction of the unit spherical surface area of 4π covered by the area of a high-PV tongue (AWB bay area; Strong and Magnusdottir, 2008). Larger AWB area suggests a more active AWB event or a larger area impacted by an AWB. A weekly AWB index was derived based on the areal averaged AWB area anomalies over a domain where the subseasonal variability of AWB area is the largest. To reduce the high-frequency variability, 7-day running mean was take after the seasonal cycle and seasonal mean were removed. A peak of AWB was identified as a maximum of the weekly index anomaly exceeding one standard deviation. And an active episode of AWB was defined as a period of ± 4 days within a peak of AWB. We constructed the time-lagged composites of different atmospheric variables based on the peak or the active episodes of AWB.

B. AWB Climatology

The spatial distribution of the AWB activity was examined by calculating the density function of the AWB area, which was deﬁned as the total AWB area within a 10◦ × 10◦ box centered on each 1.0◦ grid point. Figure 4.6a shows

77 Figure 4.6: (a) the climatological seasonal mean density function of AWB area [shaded; unit: percentage (10◦ × 10◦)−1 (30 days)−1] with the mean 200-hPa circulation scaled by wind speed (streamlines; m s−1), and (b) the standard deviation of the weekly density of AWB area over the North Atlantic in JASO during 1985-2012 from the ERAI.

78 the warm-season AWB climatology overlaid by the 200-hPa streamlines. The AWB maxima occur on the anticyclonic-shear side of the jet (Thorncroft et al., 1993; Martius et al., 2007; MacRitchie and Roundy, 2016). Similar to what was shown in previous studies (e.g., Abatzoglou and Magnusdottir, 2006), strong AWB activity has a southwest-to-northeast elongated pattern across the North Atlantic, especially over the West and Central Atlantic (west of 40◦W), which is nearly collocated with the tropical upper tropospheric trough (TUTT; Postel and Hitchman, 1999). Figure 4.6b shows the standard deviation of the weekly density of the AWB area. The pattern is similar to the seasonal mean distribution, and the strong subseasonal variability of AWB is nearly collocated with the strong seasonal mean AWB. For the following analyses, we derived the weekly AWB index over a region across 85◦-30◦W and from 20◦N to 10◦ south of the 200-hPa jet axis ∼ 35◦N, where AWB is most active and we ﬁnd in this study being associated with larger and more signiﬁcant atmospheric and TC anomalies. Besides, previous studies suggested that TCs over the western North Atlantic are more susceptible to the upper-level forcing of extratropical origin (Bentley et al., 2016; Wang et al., 2017).

C. Impacts of AWB on TC activity

To highlight the impacts of AWB on TCs, we deﬁned the “AWB-related TCs” as all the observed TC vortices that exist during the active RWB episodes (within ± 4 days of the peaks of AWB). The regional TC activity was quantiﬁed by the TC track density function (TDF; the total number of TC vortices forming within a 10◦ × 10◦ box centered on each 1.0◦ grid point). The TDF was normalized by the number of active RWB days and then rescaled to have a unit of “TC days per year”. TDF relies on both tropical cyclogenesis frequency and subsequent TC tracks. The AWB-related regional TC activity was then compared to the climatological TDF. The climatological spatial distribution of the TC activity (Fig. 4.7a) shows that high TDF occurs over the central and western MDR, the Gulf of Mexico and subtropical western North Atlantic, which is associated with both frequent tropical cyclogeneses and prevailing TC tracks in these regions (Holland, 1983). The AWB-related TDF resembles the climatology with one maximum near

79 Figure 4.7: (a) the climatological mean TC track density [number of TC days (10◦ × 10◦)−1 yr−1], (b) the track density of AWB-related TCs normalized by the number of days, and (c) the signiﬁcant track density anomalies with 95% conﬁdence in JASO during 1985-2012 from the IBTrACS

80 the southeast coast and the other one over the central MDR, but the pattern is much patchier (Fig. 4.7b). Signiﬁcant reduced TC activity was found over most of the MDR and the subtropical North Atlantic (east of 75◦W; Fig. 4.7c). The region of reduced TC activity is collocated with the region of strong AWB activity (Fig. 4.6). The negative anomalies are sandwiched by weak positive anomalies near the U.S. east coast and over the central MDR. The reduced TC activity can be explained by the strong VWS and dryness (not shown). It is possible that the suppressed TC genesis or shortened TC lifetime due to the strong vertical wind shear in the MDR lead to the reduced TC activity downstream along the prevailing TC path. Meanwhile, TC activity is slightly increased near the east coast, which may be related to tropical transition (Davis and Bosart, 2004; Galarneau Jr et al., 2015; Bentley et al., 2017) and can be attributed to weak VWS, enhanced wetness and ascent in that region (not shown).

D. Impacts of AWB on TC subseasonal prediction

It has been found that forecast errors grow nonlinearly, and the errors on smaller scale may accumulate and shift to larger scale through upscale error growth (e.g., Lorenz, 1996; Komaromi and Majumdar, 2014; Torn, 2016). As a transient synoptic-scale weather phenomenon, AWB may affects the predictability of large-scale atmospheric environment and TCs (e.g., Fitzpatrick et al., 1995; Davis and Bosart, 2004; Rodwell et al., 2013; Bentley et al., 2016). In this part, we will investigate the impacts of AWB on TC subseasonal predictability by examining the predictive skill of the GEFS reforecasts. The predictive skill of tropical cyclogenesis was investigated by calculating the ensemble mean hit rate. Figure 4.8a shows that the hit rate of AWB- related TCs is much lower than the climatological hit rate by 20% in the week- 1 reforecasts. Although the skill difference decreases with the forecast lead times, the hit rate of AWB-related TCs remains lower than the climatology. The predictive skill of TC tracks was evaluated the average track spread for forecast uncertainty. Previous studies suggested that the optimum steering depth increases with the TC intensity (Velden and Leslie, 1991; Chan, 2005), and a weak TC may be more susceptible to the influence of an upper-level disturbance (Fitzpatrick et al., 1995). We thus examined tropical storms and hurricanes separately. We focused on the Atlantic western basin (west

81 bak n h i aeo W-eae C;tema Cpsto spread position TC mean the TCs; AWB-related of rate hit the and (black) otcsa urcn H)sae ledt niaetesgicne using signiﬁcances the indicate dots Blue stage. (HU) hurricane at vortices emtto etfrpo a n h w-aldtts o lt b n (c) and (b) plots for t-test two-tailed the and (a) plot for test permutation ih9%cndne n h ubro ace ar fT otcswas vortices TC of pairs matched of number the and conﬁdence, 95% with falteT otcsa rpclsom T)saei lmtlg (black) climatology in stage (TS) storms tropical at vortices TC the all of n ot f40 of south and n o h W-eae C rd vrtewsenbsn(eto 70 of (west basin western the over (red) TCs AWB-related the for and iue48 h nebema a i aeo l C nclimatology in TCs all of rate hit (a) mean ensemble The 4.8: Figure akda h otmo ahpnlfrec oeatla time. lead forecast each for panel each of bottom the at marked

Mean position spread [km] Mean position spread [km] H = Hit / (Hit + Miss) 200 400 600 800 200 400 600 800 0.0 0.1 0.2 0.3 0.4 0.5 ◦ D2−3 D2−3 D2−3 )i h eoeat;ad()a n()btfralteTC the all for but (b) in as (c) and reforecasts; the in N) (b) TSstage(W. of70W, S.of40N) (a) HitRate (c) HUstage(W. of70W, S.of40N) 158 732 408 85 ● ● ● active AWB Climatology active AWB Climatology D4−5 D4−5 D4−5 129 550 220 42 Forecast leadtime[day] ● D6−7 D6−7 D6−7 333 119 82 82 24 ● D8−9 D8−9 D8−9 170 D10−11 36 10 38 ● active AWB Climatology D12−13 D10−11 D10−11 15 43 16 ● 6 ◦ W −1 2 6 −1 (a) VWS850−200 [ m s ] (b) PW [ kg m ] (c) Zeta850 [ 10 s ] 10 10 10 active AWB Climatology 5 5 5 0 0 0 Day5 Day10 Day15 Day5 Day10 Day15 Day5 Day10 Day15

−1 −1 (d) Udeep [ m s ] (e) Vdeep [ m s ] 10 10 5 5 0 0 Day5 Day10 Day15 Day5 Day10 Day15

Figure 4.9: Ensemble spread of the ambient (a) vertical wind shear (VWS850−200), (b) 700-hPa relative humidity (RH700), and (c) 850-hPa ◦ ◦ relative vorticity (Zeta850) based on a 20 × 20 box centered at the genesis locations of all TCs in climatology (black bars) and of AWB-related TCs (red bars) in JASO from 1985 to 2012. of 70◦W and south of 40◦N) to emphasize the TC coastal threat. Figures 4.8b-4.8c shows the mean track spread for the TC vortices at the tropical storm (TS) stage and the hurricane (HU) stage, respectively. The track spread is larger (smaller) than the climatology for TS (HU) stage since Day 6, suggesting lower (higher) forecast uncertainty of TC tracks when AWB occurs. It suggests that the track of a weaker storm is more susceptible to the inﬂuence of AWB. The lower predictability of TC activity during the active episodes of AWB can be attributed to the lower predictability of large-scale environmental conditions. We evaluated the ensemble spreads of the TC-related environmental variables including vertical wind shear (VWS850−200), 700-hPa relative hu-

83 midity (RH700), and 850-hPa relative vorticity (Zeta850). For each observed TC genesis, the ensemble spread of each variable was calculated at an observed genesis time over a 20◦ × 20◦ box centered at the genesis location.

We also evaluated the ensemble spreads of the TC-related zonal (Udeep) and meridional (Vdeep) components of steering flow using similar calculation but based on the time and location of each TC vortex. The composite of mean ensemble spread based on all observed tropical cyclogeneses was used as a metric to measure the predictability of each environmental variables. Figure 4.9 shows that all the variables have larger ensemble spread (or lower predictability) than the climatology when TCs were influenced by strong AWB activity. And the differences increase with the forecast lead times. The predictability of TC subseasonal variation was measured by the model skill in capturing the active/inactive TC periods. As in Fig. 4.4, we calculated the subseasonal correlations of the weekly TC indices between the GEFS and the IBTrACS in each year and stratified the years based on the AWB index. Figures 4.10a-4.10b indicate that the GEFS has a reasonable skill in capturing the TC subseasonal variations with lead time up to 2 weeks. The model nevertheless has lower predictive skill of TC subseasonal variations in the years of active AWB for both the week-1 and -2 reforecasts, although only the results of WCE are significant (Fig. 4.10c). The results suggest that AWB is associated with lower predictability of subseasonal TC variation.

4.5 Synoptic timescales

In this section, we will investigate the predictability of tropical cyclogenesis influenced by synoptic flow regimes. Based on the upper-level forcing and low-level baroclinicity of the genesis environment, McTaggart-Cowan et al. (2013) identified five tropical cyclogenesis pathways (or development pathways) that represent different synoptic-scale flow regimes. Built upon this pathway concept, we will test the following hypothesis: tropical cyclogenesis in different synoptic flow regimes is associated with different predictability.

84 Figure 4.10: Subseasonal variations of (a) TC days and (b) WCE in the GEFS reforecasts overlaid by the seasonal mean AWB index (dashed lines), and the mean correlation coefficients of (c) TC days and (d) WCE with the observation stratified by a ± 1.0 standard deviation (SD) of the seasonal mean AWB index for JASO during 1985-2012 are marked in the top-left corner of each plot. The grey lines are the significance level with the white asterisk signs to denote the significant difference between an anomalous group (< -1.0 or > 1.0 SD) and the neutral group (from -1.0 to 1.0 SD) both using two-tailed t-test with 90% confidence. The degree of freedom was adjusted using “modified Chelton” method (Pyper and Peterman, 1998). 85 4.5.1 Tropical cyclogenesis pathways

To distinguish different genesis environmental conditions, McTaggart-Cowan et al. (2013) identified five tropical cyclogenesis pathways, including non- baroclinic (NBC), low-level baroclinic (LBC), trough-induced (TI), weak tropical-transition (WTT) and strong tropical-transition (STT) pathways (Table 4.3). The genesis pathways were categorized via a linear discriminant analysis based on two metrics that represent the environmental atmospheric state for a TC vortex. The Q-metric is defined as the average convergence of the 400-200 hPa Q-vector within 6-degree of the point of interest. To deal with the high-Rossby number flow in the tropics and to reduce noises associated with the irrotational wind component, the Q-vector was calculated using the non-divergent flow. The Q-metric represents the synoptic-scale forcing for ascent, associated with an upper-level trough or a tropical upper tropospheric trough (TUTT) cell. The second metric, T h, represents the low-level baroclinicity, and is defined as the maximum difference in 1000- 700 hPa thickness between two semicircles within 10 degrees of the point of interest. The NBC and LBC pathways are characterized by weak upper- level forcing and represent TC formations in a purely tropical environment. The TI, WTT, and STT pathways are all subject to upper-level forcing, and are characterized by weak, moderate and strong low-level baroclinicity, respectively. The upper-level forcing may be associated with cutoff lows or upper-level troughs (Bentley et al., 2017), which are often of extratropical origin. Additionally, the development of some TI and TT storms is involved with the interaction between an upper-level system and a low-level tropical disturbance (Galarneau Jr et al., 2015). The STT, WTT and TI pathways can thus be regarded as extratropical pathways or hybrid pathways. Figure 4.11 shows the genesis distribution of the Atlantic TCs during 1985- 2012 and distributions associated with different pathways. The NBC pathway is the most frequent genesis pathway and occurs preferentially over the Atlantic Main Development Region (MDR; Goldenberg et al., 2001), where TCs primarily develop from tropical easterly waves and have a larger chance to intensify into hurricanes before moving over land or recurving poleward. Tropical cyclones associated with the LBC pathway cluster near the coast of West Africa (the so-called Cape Verde storms), where the warm, dry Saharan air mass in the north and the cool, moist marine air mass in the south con-

86 Figure 4.11: Genesis distribution for (a) all analyzed Atlantic tropical cyclones and for (b-f) different genesis pathways. The boxes in Fig. 4.11a represent the different regions defined for the Atlantic basin (see text for more details).

87 Figure 4.12: Hit rate as a function of the forecast lead times for diﬀerent genesis pathways (represented by diﬀerent colors as shown in the legend). Closed circles (diamonds) represent hit rate falling below (above) the bottom (top) 5th percentile of random sampling. tribute to the low-level baroclinicity (Hankes et al., 2015). The TI pathway is the least frequent genesis pathway, and the associated geneses scatter over the Central and West Atlantic. The WTT and STT pathways occur more poleward than the TI pathway, in keeping with the stronger low-level baroclinicity. The low-level baroclinicity in the STT and WTT pathways may be associated with strong sea surface temperature gradient or a low-level jet. In addition, remnant cold fronts in the subtropics can enhance low-level baroclinicity and moisture gradients as well (Davis and Bosart, 2004; Zhang et al., 2017). Therefore, the Q-metric and the T h-metric are not completely independent of each other.

88 4.5.2 Evaluation of tropical cyclogenesis predictability

A. Predictability for diﬀerent pathways

The composite mean hit rate3 for each pathway is shown in Fig. 4.12. Boot- strapping was used to test the significance of the differences from random sampling. For example, there are 129 storms associated with the NBC pathway. 10,000 bootstrap samples are constructed, and each sample consists of 129 cases randomly chosen from the 339 storms that include all pathways. Hit rate is then calculated for each sample. If the hit rate value of the NBC pathway is above the top 5th percentile or below the bottom 5th percentile of the 10,000 bootstrap estimates, the hit rate is regarded as significantly different from random sampling. The same test was done for each pathway at different forecast lead times. As shown in Fig. 4.12, the LBC pathway has the highest hit rate among the five pathways, and the hit rate exceeds the top 5th percentile at all forecast lead times. The STT pathway has the lowest hit rate among the five pathways for all forecast lead times. The hit rates of STT and WTT are significantly different from random sampling from Day 2-3 to Day 8-9. The NBC and TI pathways have similar skill and neither is significantly different from random sampling. The different predictive skills of tropical cyclogenesis associated with different pathways can partly be attributed to the different predictive skill of environmental variables. The RMSEs of vertical wind shear (defined as the magnitude of the vector wind difference between 200 and 850 hPa) and 700- hPa relative humidity (RH) were calculated. For each observed storm in the IBTrACS (excluding short-lived storms and those forming poleward of 40◦N), RMSE was evaluated at the observed genesis time over a 20◦ × 20◦ grid box. Since the predicted genesis can occur anywhere within a 5◦ radius of the observed genesis location for a “hit” event, we chose a fixed 20◦ × 20◦ box centered at the observed genesis location in the CFSR, but allowed the center of the 20◦ × 20◦ box in the GEFS reforecasts to move within a 10◦ × 10◦ domain centered at the observed genesis location. RMSE is calculated for each possible location. Given the 1◦ × 1◦ resolution, this yields

3We did not evaluate the false alarm rate or the false alarm ratio for diﬀerent genesis pathways because the model environment may deviate from reality, and the pathways deﬁned based on the observed environment cannot be simply used to categorize false alarm storms.

89 Figure 4.13: RMSE of (a) vertical wind shear and (b) 700-mb relative humidity (see the text for more details). Diﬀerent colors represent diﬀerent genesis pathways.

100 values of RMSE for a given genesis event. The minimum RMSE among the 100 values was chosen to represent a lower bound of the forecast errors. The same calculation was repeated for all GEFS ensemble members, and the ensemble mean of the minimum RMSE was taken to represent the predictive skill of the variable for a genesis event. The composite mean of the RMSE was then calculated for each genesis pathway. Due to the large volume of the dataset, only three representative forecast lead times, 5 days, 10 days and 15 days, were examined. As shown in Fig. 4.13, RMSE increases sharply from t=0 to t=5 days for both vertical wind shear and RH (note that RMSE is nearly zero at t=0). Due to the different error growth rates for the different pathways, the magnitude of the RMSE, of both vertical shear and RH, shows the same sequence at different forecast lead times: STT > WTT > TI > NBC > LBC. A higher RMSE is due to the larger error growth rate and indicates lower predictability. The predictive skill or predictability of the environmental variables is consistent with the genesis predictive skill for different pathways shown in Fig. 4.13 except for the relative order of TI and NBC. Although the largest RMSE of vertical wind shear for the STT pathway may be partly attributed to the strong vertical wind shear that the pathway is subject to

90 Table 4.3: Characteristics and frequency of occurrence of different genesis pathways. Adapted from Table 2 in McTaggart-Cowan et al. (2013). Also shown are the areal mean vertical shear (defined as the magnitude of the zonal wind difference between 200 and 850 hPa) and 700-hPa relative humidity averaged within a 20◦ × 20◦ box centered at the genesis location from IBTrACS.

P athway Non- Low- Trough Weak Strong Upper− Low Low High High High Low− Low High Low Medium High Occur 38% 12% 10% 26% 14% V ertical 3.8 4.7 4.2 6.8 11.7 700hP a 67.4% 67.3% 66.5% 63.6% 54.0%

(Table 4.3), the magnitude of the corresponding mean-state variable does not explain the large RMSE of 700-hPa RH as the STT and WTT pathways occur at higher latitudes and have a lower environmental humidity than the other three pathways (Table 4.3). We also examined column water vapor and 850-hPa relative vorticity. The relative magnitude of the RMSE of column water vapor for the five pathways has the same sequence as that of 700-hPa RH and vertical wind shear. The five pathways, however, are not very well separated in the RMSE of 850-hPa relative vorticity. This is probably due to the lower predictability of relative vorticity than vertical shear or humidity. Komaromi and Majumdar (2014) showed that variables related to large-scale, slowly evolving phenomena are more predictable that those inherently related to small-scale, rapidly evolving features. The different predictive skills suggest different levels of genesis predictability for different pathways, which, from high to low, have the following order, LBC > TI > NBC > WTT > STT. The higher predictability of the LBC pathway than the NBC pathway is probably because the former occurs in a comparatively small region near the Cape Verde Islands (Fig. 4.11). It was a surprise that the hit rate of the NBC pathway is lower than that of the TI pathway, as the real-time wave tracking based on global model forecasts from multiple operational centers in the past several year

91 (http://www.met.nps.edu/~mtmontgo/storms2008.html) gave us the im- pression that TCs originating from tropical easterly waves in the Atlantic MDR are more predictable than those forming farther west in the basin. It is possible that low hit rate of the NBC pathway is due to the negative genesis biases that the GEFS model has over the Central and West MDR (Li et al., 2016). The STT pathway has the lowest predictability, which can be partly attributed to the high vertical wind shear associated with the pathway (Davis and Bosart, 2004). Zhang and Tao (2013), using idealized simulations, showed that environmental vertical shear affects the predictability of tropical cyclone formation and intensity. However, vertical wind shear does not explain the predictability differences among the other pathways because vertical wind shear, averaged over a 20◦ × 20◦ domain centered at the genesis location, is similar among the LBC, NBC, TI and WTT pathways (Table 4.3). On the other hand, it is instructive to note that the STT and WTT pathways, with relatively low predictability, are of hybrid or non-pure tropical nature as they are associated with upper-level troughs or cutoff lows originating from the extratropics. Previous studies have suggested that the extratropical atmosphere has lower predictability than the tropical atmosphere due to baroclinic instability and upscale energy cascade in the extratropics as well as the strong coupling between the atmosphere and the underlying ocean in the tropics (Charney and Shukla, 1981; Metais et al., 1994; Palmer, 1996). More specifically, Komaromi and Majumdar (2014) and Davis et al. (2016) showed that forecast errors grow faster in the subtropics/extratropics than in the tropics for forecast lead time beyond a couple of days. It is conceivable that tropical cyclones developing under strong extratropical influence (as STT and WTT) are less predictable than those developing in a purely tropical environment.

B. Possible extratropical impacts on predictability

The predictability differences among different genesis pathways lead to an interesting question: do stronger extratropical influences imply lower genesis predictability (or lower predictive skill)? The Q-vector can be used as a proxy for extratropical impacts. Although the STT, WTT and TI pathways are separated primarily based on the strength of the low-level baroclinicity

92 (a) Th−Metric (b) Q−Metric

30 Trough−induced (N=34) 30 Trough−induced (N=34) Weak TT (N=87) Weak TT (N=87) Strong TT (N=49) Strong TT (N=49) 25 25 20 20 15 15 Density TC counts 10 10 5 5 0 0

−0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 −3.05 −3.00 −2.95 −2.90 −2.85 −2.80 −2.75

Th−metric (1000−700mb Thickness Asymmetry) Q−metric (Convergence of 400−200mb Q−vector)

Figure 4.14: Histograms of the T h-Metric (low-level baroclinicity) and Q-Metric (upper-level forcing) for the trough-induced, weak TT and strong TT pathways. Note that these are stacked bar charts in which one bar does not go behind the others.

(McTaggart-Cowan et al., 2013), Figure 4.14b shows that stronger upper- level forcing occurs most frequently in the STT pathway and least frequently in the TI pathway. This is consistent with the recent study by Bentley et al. (2017). They showed that the STT pathway is often associated with a stronger upper-level disturbance, such as a cutoff low or a meridional trough. Such upper-level disturbances either extend to the lower troposphere and initiate the low-level cyclonic circulation, or interact with low-level precursor disturbances (Davis and Bosart, 2004; Galarneau Jr et al., 2015). A strong upper-level potential vorticity feature may induce or enhance the low-level baroclinicity (Zhang et al., 2017). To examine further the possible impacts of upper-level features of extratropical origin on tropical cyclogenesis predictability, we combined the STT and WTT storms and separated them into the strong-Q and weak-Q groups by the median of the Q-metric. The two groups have the same sample size of 68. The hit rate was calculated for each group, and the significance of the hit rate difference between the two groups was examined using a permutation test. The permutation test consists of 10,000 drawings. In each drawing,

93 Figure 4.15: Hit rate as a function of the forecast lead times for strong-Q (blue) and weak-Q groups (black) based on (a) the combination of STT and WTT and (b) the combination of STT, WTT and TI. The sample size (N) for each group is indicated in the figure legends. Closed circles represent that the hit rates between the two groups are significantly different from each other based on a permutation test (see text for more information). a group of 68 storms were randomly chosen from the pool of 136 storms, and the remaining storms were treated as another group. The hit rate for each group was calculated, and the difference in the hit rate between the two groups was recorded. The 10,000 drawings thus produced 10,000 outcomes of the hit rate difference. The difference in the hit rate between the strong-Q and weak-Q groups is regarded significant if it exceeds the top 5th percentile of the 10,000 drawings. The same test was repeated for all forecast lead times. As show in Fig. 4.15a, the strong-Q group indeed has a lower hit rate than the weak-Q group, and the difference is significant at all forecast lead times except at Day 12-13. We repeated the same calculation by defining two groups after combining the STT, WTT and TI pathways (Fig. 4.15b). The three-pathway combination has the advantage of a larger sample size (170), but it should be borne in mind that the TI pathway differs from the STT and WTT pathways in many aspects (McTaggart-Cowan et al., 2013). Again, the strong-Q group has a lower hit rate than the weak-Q group, and the difference is significant at all forecast lead times. We also examined the STT and WTT pathways separately. Although a strong-Q group always has

94 a lower hit rate than a weak-Q group, the diﬀerence does not exceed the 5th percentile threshold at some forecast lead times due to the small sample sizes of the pathways (not shown). Overall, the calculations suggest that stronger extratropical impacts imply lower predictability of tropical cyclogenesis.

C. Geographic and seasonal variations of predictability

Previous studies have reported the geographic variations of model forecasting skill for tropical cyclogenesis (e.g., Halperin et al., 2016). In fact, the spatial variations of the model forecast skill are so large in operational models that longitude and latitude, despite of their lack of explicit physical meaning, were selected as two major predictors in a hybrid prediction scheme to reduce the biases of a dynamic model by Halperin et al. (2017). Figure 4.16 shows the hit rate, false alarm rate, false alarm ratio and critical success index for four regions over the Atlantic: the eastern MDR (EMDR), the central and western MDR (CWMDR), the Gulf of Mexico (Gulf), and the subtropical Atlantic (SubAtl; delineated in Fig. 4.11), which are selected based on the geographic distribution of the pathways. The hit rate is clearly separated among the four regions: EMDR > CWMDR > Gulf > SubAtl (Fig. 4.16a). The false alarm rate in the EMDR and CWMDR is much higher than in the other two regions (Fig. 4.16b). This can be attributed to the positive biases in tropical cyclogenesis frequency over the eastern basin in the GEFS reforecasts. On the other hand, the four regions have a similar false alarm ratio beyond 3 days (Fig. 4.16c), or the proportion of forecast events that fail to materialize is about the same in the different regions. Therefore, the higher hit rate over the EMDR and CWMDR does not occur at the expense of a larger false alarm ratio. The CSI shows a sequence similar to the hit rate but the EMDR and CWMDR are less well separated. If evaluated based on the hit rate, tropical cyclogenesis over the EMDR is most predictable, followed by the CWMDR, and tropical cyclogenesis over the subtropical Atlantic region is least predictable. The differences in the hit rate between different regions can be explained by the different relative contributions of each pathway (Fig. 4.17a). Over the EMDR, the LBC pathway accounts for about 70% of tropical cyclogenesis; over the CWMDR, about 70% of tropical cyclones develop via the NBC pathway. In contrast, WTT makes the largest contribution over the Gulf (∼55%), and STT and WTT

95 Figure 4.16: (a) Hit rate, (b) false alarm rate, (c) false alarm ratio and (d) critical success index as a function of the forecast lead times for diﬀerent subregions of the Atlantic.

96 Figure 4.17: (a) The relative contributions of different genesis pathways in different regions of the Atlantic. The relative contribution of a pathway in a region is defined as the storm number for the pathway in the region normalized by the total storm number in the region. (b) Same as (a) except for different seasonal periods over the North Atlantic basin. Note that the trough-induced pathway does not take place over the eastern MDR, and the low-level baroclinic pathway is absent over the Gulf and the subtropical Atlantic. each contribute more than 40% over the subtropical Atlantic. Therefore, the regional difference in tropical cyclogenesis predictive skill is related to the different levels of predictability of the pathways dominating in each region. The relatively low predictive skill of tropical cyclogenesis over the subtropical Atlantic can be attributed to strong extratropical impacts. The seasonal variations of the pathway occurrences also help to explain the differences in genesis predictive skill or predictability between the peak season and the early/late seasons. Since the tropical transition pathways make a larger relative contribution in June-July (JJ) and October-November (ON) than in August-September (AS) (Fig. 4.17b), the hit rate and CSI are higher in the peak season (AS) than in the early season (JJ) or late season (ON) (Figs. 4.18a and 4.18d). Although the GEFS produces a larger number of false alarm storms in AS than in JJ or ON (Fig. 4.18b), the false alarm ratio in AS is close to that in ON and smaller than that in JJ (Fig. 4.18c).

97 Figure 4.18: Same as Fig. 4.16 but for diﬀerent subseasonal time periods over the whole North Atlantic basin.

98 Figure 4.19: Illustrative cases for each genesis pathway in 2010. Black curves represent the observed tracks, and dots of different colors represent forecast genesis locations at different lead times. The insets show the ensemble hit rates at different lead times.

99 D. Illustrative examples

An example of each genesis pathway is selected from the hurricane season of 2010 and shown in Fig. 4.19. Superimposed on the observed track and predicted genesis locations in each plot is an inset showing the ensemble hit rates at different forecast lead times. The ensemble hit rate is defined as the ratio of the number of the ensemble forecasts that produce a hit to the total ensemble size (i.e., 11). The ensemble hit rate is then averaged over different forecast lead periods (i.e., Day 2-5, Day 6-9, and Day 10-13). Hurricane Igor (Fig. 4.19a) is a low-level baroclinic case. It originated from an African easterly wave and formed near the coast of West Africa on September 8th, 2010 (Pasch and Kimberlain, 2011). The ensemble hit rate of the storm is ∼0.6 for Day 2-5 and ∼0.5 for Day 6-9 and drops to ∼0.2 for Day 10-13. The predicted genesis locations are all close to the observed genesis location. Hurricane Danielle (Fig. 9b) is a non-baroclinic case, and genesis occurred on August 21, 2010. Its development involves interaction between an easterly wave and an ITCZ disturbance (Kimberlain, 2010). Although the predicted genesis locations are scattered, most of them fall within the 5◦ radius threshold. The ensemble hit rate is slightly lower than that of Hurricane Igor during Day 2-5 and Day 6-9, but slightly higher during Day 10-13. Tropical Storm Matthew (Fig. 4.19c), falling into the trough-induced cat- egory, formed over the Caribbean Sea on September 23, 2010, and was one of the most destructive storms in history (Brennan, 2011). Although the ensemble hit rate is about 0.7 for Day 2-5, it drops quickly with the forecast lead time. The predicted genesis locations have a large spread, indicating a high fraction of early genesis or late genesis predictions (i.e., incorrect genesis time). If we reduce the radius threshold (5◦) or time window threshold (120 hours) in the ensemble hit rate calculation, the hit rate will be lower. Tropical Storm Bonnie (Fig. 4.19d) and Hurricane Shary (Fig. 4.19e) are weak TT and strong TT storms, respectively. Bonnie developed from the interaction between an African easterly wave and an upper-level low to the north of Hispaniola in late July (Stewart, 2011). Shary formed along the southern portion of a stationary frontal system under the influence of an upper-level low associated with the mid-ocean trough in late October (Avila, 2011). While the ensemble hit rate is low for Bonnie, the predicted genesis

100 locations are very close to that observed. As for Shary, only one ensemble member predicts the formation of a TC during Day 2-5 and the ensemble hit rate is nearly zero, indicating a forecast challenge.

4.6 Summary and discussion

The predictability of TCs on interannual, subseasonal, and synoptic timescales was investigated in this chapter. The predictability was examined by analyz- ing the predictive skill of TC activity in the GEFS. On interannual timescales, the GEFS is able to depict the interannual variability of TC counts and ACE over the North Pacific and the Atlantic, but shows much poorer skill over the Indian Ocean and the Southern Hemisphere than the other basins. The model skill in ACE tends to be higher than that in TC counts, probably due to the control of TC intensity by the SST. The skill of the model over the North Pacific and the North Atlantic is linked to the impacts of the ENSO and/or the AMM. The correlation analysis suggests that the GEFS overpredicts the impacts of ENSO over the North Pacific and the North Atlantic but underpredicts the impacts of the AMM over the North Atlantic. On subseasonal timescales, the subseasonal variability of weekly TC days and cyclone energy was examined over the North Atlantic, and the model skill was evaluated based on the correlation between the observed time series and the forecasts in each year during 1985-2012. The GEFS captures the active and inactive periods of TC activity reasonably well. On the other hand, the large fluctuations in the correlation coefficients from year to year imply that the intrinsic predictability varies. It is found that the active (inactive) MJO events contribute to the higher (lower) predictive skill of the subseasonal TC variations. In addition, the model tends to have better skill during strong ENSO events, especially during the La Niñayears. The GEFS has difficulty in capturing the active/inactive TC periods during the years of strong anticyclonic Rossby wave breaking (AWB), suggesting AWB is associated with lower predictability of subseasonal TC variation. In addition, the GEFS shows a lower hit rate and larger track spread than climatology during the active episodes of AWB up to 2 weeks, which is attributable to the lower predictability of ambient vertical wind shear, mid-level humidity, and low-level vorticity.

101 On synoptic timescales, the predictability of tropical cyclogenesis over the North Atlantic was examined in different synoptic flow regimes. Flow regimes were identified objectively by five tropical cyclogenesis pathways that were categorized based on the upper-level forcing and low-level baroclinicity of the background atmospheric state (McTaggart-Cowan et al., 2013). Among them, the NBC and LBC pathways have negligible upper-level forcing and can be regarded as purely tropical pathways; TI, WTT and STT pathways are associated with strong upper-level forcing and have weak, moderate and strong low-level baroclinicity, respectively, and can be regarded as hybrid or extratropical pathways. Since the conventional ensemble spread metric cannot be readily applied to the dichotomy between genesis and non-genesis, the dependence of tropical cyclogenesis predictability on flow regimes is estimated by comparing the hit rate for different genesis pathways in the way that a lower hit rate represents lower predictability. The hit rate of the pathways has the following order: LBC > TI > NBC > WTT > STT. Further analysis showed that the RMSEs of vertical wind shear and RH helped to explain the different predictive skill for different pathways. The different predictive skill of tropical cyclogenesis reflects different levels of predictability for different pathways. In brevity, the tropical transition pathways, STT and WTT, have lower predictability than the other pathways, which is consistent with the general perception that the extratropical atmosphere is less predictable than the tropical atmosphere for forecast lead time beyond a few days. We further examined whether stronger extratropical impacts imply lower genesis predictability, and the Q-vector (i.e., upper-level forcing) was used as a proxy for extratropical impacts. Although the STT, WTT and TI pathways are categorized based on the low-level baroclinicity, they are associated with upper-level forcing of different strengths. Strong upper-level forcing occurs more frequently in the STT pathway and least frequently in the TI pathway. When strong-Q and weak-Q groups are defined based on the Q-metric for the STT, WTT and TI pathways, a strong-Q group always has a lower hit rate than the corresponding weak-Q group, suggesting that stronger (weaker) extratropical impacts may lead to lower (higher) genesis predictability. Previous studies have reported that the predictive skill of a model in tropical cyclogenesis varies from region to region and from month to month (see the introduction). Large spatial variations of the hit rate are also found: the

102 MDR region has a higher hit rate than the Gulf of Mexico or the subtropical Atlantic (the false alarm ratio is similar and very large in all the regions). The spatial variations can be explained by the different relative contributions of the pathways in different regions. The relatively frequent occurrence of TT pathways over the Gulf of Mexico and the subtropical Atlantic contributes to the lower genesis predictability in these regions. In addition, the purely tropical pathways (NBC and LBC) occur more frequently in August and September, and this contributes to a relatively high hit rate in the peak hurricane season compared to the early/late seasons. This chapter aims to provide a systematic investigation of TC predictability on different timescales. However, there are some admitted limitations. First, our analyses were based on only one reforecast dataset. It is possible that some results are model-dependent. Second, the dependence of predictability on flow regimes was estimated based on the hit rate. A sin- gle metric may not provide a complete picture of how predictable tropical cyclones are. Further research is required to shed light on the interactions among the sources of predictability, and relevant questions may be asked such as: How predictable are TCs when the Rossby wave breaking is active during a strong MJO or ENSO year? Our research also suggests that storms developing near the North American coast, which are more likely subject to strong extratropical impacts, may pose a particular challenge for operational forecasts and emergency management. Knowledge of the predictability of such coastal storms can assist decision making by providing useful information on predictive skill before forecast validation becomes available.

103 Chapter 5

Conclusions

My Ph.D. thesis research aims to improve the model performance and the subseasonal-to-seasonal (S2S; 10 days - 12 weeks) prediction by developing “physics-oriented” evaluation metrics and investigating the predictability of high-impact weather phenomena with a special focus on tropical cyclones (TCs). This study is motivated by an imperative need of persistently improving global forecasting systems. The scientific outcome of this research is two-fold: 1) a suite of physics-oriented model evaluation metrics, and 2) in-depth understanding on the predictability of TCs. The physics-oriented evaluation metrics were developed using the data from the Navy Operational Global Atmospheric Prediction System (NO- GAPS), the Global Forecasting System (GFS), and the Global Ensemble Forecasting System (GEFS) Reforecast Version-2. The evaluations include the Madden-Julian oscillation (MJO; a dominant mode of tropical subseasonal variability and a major source of predictability on S2S timescales), TCs (significant social-economic impacts), and precipitation and convective processes (critical indicators of deficiencies in a cumulus parameterization). It has been found that both the NOGAPS and the GFS have relatively low predictive skill when the MJO initiates over the Indian Ocean or when the active convection of the MJO is over the Maritime Continent. It is likely associated with deficiencies in the model cumulus schemes, which results in a dry bias within the boundary layer and misrepresented shallow heating mode. The diabatic heating biases are associated with weaker trade winds, weaker Hadley and Walker circulations over the Pacific, and weaker cross-equatorial flow over the Indian Ocean. The evaluation of TCs in the GEFS shows that large errors exist on the regional scale. Since different tropical cyclogenesis pathways are dominant over different basins, genesis biases are related to the biases in different large- and synoptic-scale circulations over different oceanic basins. The negative

104 genesis biases over the western North Pacific are associated with a weaker- than-observed monsoon trough in the GEFS, the erroneous genesis pattern over the eastern North Pacific is related to a southward displacement of the ITCZ, and the positive genesis biases near the Cape Verde islands and negative biases farther downstream over the Atlantic can be attributed to the hyperactive African easterly waves and stronger deep convective heating in the GEFS. Further analyses show that precipitation initiates too early with respect to the column water vapor, and there is a dry bias in the column water vapor increasing with the forecast lead times. The model also underpredicts moderate-to-heavy precipitation. All suggest a deficiency in the cumulus schemes of the GEFS. To obtained in-depth understanding on the predictability of TCs, we investigated the predictability of TCs on the interannual, subseasonal, and synoptic timescales using the GEFS reforecasts. It has been found that the GEFS skillfully captures the interannual variability of TC activity over the North Pacific and the North Atlantic, which can be attributed to the modulation of TCs by the El Niño-SouthernOscillation (ENSO) and the Atlantic meridional mode (AMM). The GEFS shows promising skill in predicting the active/inactive periods of TC activity over the Atlantic. The skill, however, has large fluctuations from year to year. The analysis suggests that the model tends to have better skill in predicting the TC subseasonal variations during strong ENSO years than in neutral years, especially in strong La Niñayears. The GEFS has difficulty in capturing the active/inactive TC periods during the years of strong anticyclonic Rossby wave breaking (AWB), suggesting AWB is associated with lower predictability of subseasonal TC variation. These analyses help to better understand the variability and predictability of the Atlantic TCs on S2S timescales. Lastly, we investigated the impacts of synoptic flow regimes on the TC predictability, particularly the predictability associated with different TC cyclogenesis pathways over the North Atlantic. A previous study defined five tropical cyclogenesis pathways based on the low-level baroclinicity and upper-level forcing of the genesis environmental state: non-baroclinic, low- level baroclinic, trough-induced, weak tropical transition (TT) and strong TT pathways. Our results show that the strong TT and weak TT pathways have a lower predictability than the other pathways. The lower predictive skill of TCs can be explained by the lower predictability of vertical wind shear,

105 mid-level humidity, and lower-level relative vorticity in the vicinity of genesis associated with the TT pathways. The diﬀerent levels of predictability help to explain the regional and subseasonal variations of the GEFS’ predictive skill in TCs. It is expected that the physics-oriented diagnostic package will be dissemi- nated with general applicability across models, and transitioned to modeling and testbed centers for a systematic physics-oriented model evaluation. The diagnostic tools will also be made available to the general research community to facilitate studies on the variability and predictability of high-impact weather phenomena. The investigation of TC predictability will help to improve TC forecasts, especially on S2S timescales, and contribute to the National Oceanic and Atmospheric Administration (NOAA)’s goal to extend skillful forecasts over a longer time and the development of the NOAA’s Next Generation Global Prediction System (NGGPS) under the Research to Operations (R2O) Initiative.

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