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    (left) TRMM 3B42 3-h precipitation (shaded, mm h−1) averaged from 5°S to 5°N from 0000 UTC 21 Nov to 1800 UTC 30 Nov. TRMM precipitation averaged from 5° to 20°N is shown in the black contours (contour interval of 0.5 mm h−1, values below 1.0 mm h−1 not shown). (right) The ECMWF-analyzed 10-m zonal wind (shaded, m s−1) averaged from 5°S to 5°N. The 10-m vorticity averaged from 5° to 20°N is shown in the black contours (contour interval of 10−5 s−1). In both panels, the longitude of TC05 as given in the JTWC best track archive is shown by black circles with red centers, the longitudinal range of the TC05 response function is given by the brown lines, and the longitudinal range of the KW response function is given by the black lines.

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    Infrared imagery over the Indian Ocean from the Indian Meteorological Department (IMD) Kalpana-1 satellite. The red numbers indicate the corresponding dates and hours. “KW” denotes the convection associated with the KW, and CV and TC05 denote the cyclonic vortex that becomes TC05, and TC05 itself.

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    Vertically averaged total energy of the optimal initial perturbation (shading, m2 s−2) with the 850-hPa analyzed wind vectors based on the 18-h adjoint sensitivity centered on TC05 and its precursor circulation for forecasts started every 12 h from (top left) 0000 UTC 23 Nov to (bottom right) 1200 UTC 26 Nov 2011. Location of TC05 (and precursor circulation) denoted by black circles, and location of the leading edge of the low-level westerlies associated with the first and second KWs denoted by black and red boxes, respectively.

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    As in Fig. 3, but with the response function centered on the westerlies associated with the first KW.

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    Domain-averaged absolute sensitivity as a function of pressure level for (left) TC05 and (right) the KW for (top) wind [m2 s−2 (m s−1)−1], (middle) temperature (m2 s−2 K−1), and (bottom) water vapor [m2 s−2 (g kg−1)−1]. Individual sensitivity calculations from different analysis times are given by the color curves and indicated in key in top-right panel. The average for all 12 cases is given by the solid black curve.

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    Domain-averaged sensitivity as a function of pressure level for (left) TC05 and (right) the KW for (top) temperature (m2 s−2 K−1) and (bottom) water vapor [m2 s−2 (g kg−1)−1]. Individual sensitivity calculations from different analysis times are given by the color curves and indicated in key in top-right panel. The average for all 12 cases is given by the solid black curve.

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    Vertically averaged magnitude of the zonal and meridional wind components of the TC05 adjoint sensitivity (shading, m2 s−2) with the 850-hPa-analyzed wind vectors based on the (top) 18-h adjoint sensitivity, (middle) 36-h adjoint sensitivity, and (bottom) 36-h sensitivity based on the dry adjoint for forecasts started from (left) 0000 UTC 23 Nov and (right) 0000 UTC 25 Nov 2011. The location of TC05 (and precursor circulation) is denoted by black circles, and location of first and second KWs is denoted by black and red boxes, respectively.

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    The 850-hPa U component of the optimal perturbation (shaded m s−1) at forecast (top left) tau = 0 for TC05, (top right) tau = 0 for the KW, and (bottom left) tau = 18 for TC05. (bottom right) The 18-h nonlinear perturbation for TC05 is shown. All panels show the control forecast 850-hPa wind vectors. Forecasts from 1200 UTC 23 Nov 2011. The TC05 response function region is denoted by the black square.

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    Vertical cross sections for the TC05 case from 1200 UTC 23 Nov 2011. (left) Zonal wind optimal perturbations at (top) 0 h [contour interval (ci) = 0.01 m s−1], (middle) 9 h (ci = 0.5 m s−1), and (bottom) 18 h (ci = 4 m s−1), and the control forecast zonal wind (shading, m s−1). (right) Water vapor optimal perturbation (shading, g kg−1) at 0, 9, and 18 h, with optimal perturbation divergence in black contours, optimal perturbation temperature in green contours, and optimal perturbation cloud water in blue contours. Divergence contour intervals are 1 × 10−7, 1 × 10−5, and 5 × 10−5 s−2 at 0, 9, and 18 h, respectively. Temperature contour interval at 0 h is 0.03 K. Contour intervals for cloud water are 0.06 and 0.3 g kg−1 at 9 and 18 h, respectively. Solid contours are positive values and dashed contours are negative values. The 0- and 9-h fields are averaged from 2°S to 2°N. The 18-h fields are averaged from 0° to 4°N.

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    The 850-hPa horizontal wind speed (shaded, m s−1) and 850-hPa wind vectors at forecast tau = 18 h for (top left) the control forecast, (top right) the control forecast with the linear perturbation, and (bottom left) the control forecast with the nonlinear perturbation for the TC05 case. Forecast is from 1200 UTC 23 Nov 2011.

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    Domain-averaged optimal perturbation magnitude as a function of pressure level for TC05 (solid curves) and the KW (dashed curves) for (top) wind (m s−1), (middle) temperature (K), and (bottom) water vapor (g kg−1) for the 18-h forecast started at 1200 UTC 23 Nov. The mark, circle, square, and diamond represent the optimal perturbations at 0-, 6-, 12-, and 18-h integration times, respectively. The 0-h wind curve values are increased by an order of magnitude for clarity.

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    The analyzed SST (shaded, K) and initial-time SST sensitivity (contour interval of 0.05 m2 s−2 K−1 with positive contours solid and negative contours dashed) for (left) the TC05 case and (right) the KW case. Forecast is from 1200 UTC 23 Nov 2011.

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    Domain-averaged 1000–850-hPa kinetic energy (m2 s−2) as a function of forecast time for the optimal perturbations for the TC05 (solid) and KW (dashed) cases from 1200 UTC 23 Nov 2011. Linearly evolved perturbations associated with the full initial perturbations (black), moist-only initial perturbations (blue), dry-only initial perturbations (red), and constant SST perturbations (green) are shown. The 3–18-h growth rates (day−1) are given in parentheses in key.

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Examining Tropical Cyclone–Kelvin Wave Interactions Using Adjoint Diagnostics

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  • 1 Naval Research Laboratory, Monterey, California
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Abstract

The initial-state sensitivity and interactions between a tropical cyclone and atmospheric equatorial Kelvin waves associated with the Madden–Julian oscillation (MJO) during the DYNAMO field campaign are explored using adjoint-based tools from the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS). The development of Tropical Cyclone 5 (TC05) coincided with the passage of an equatorial Kelvin wave (KW) and westerly wind burst associated with an MJO that developed in the Indian Ocean in late November 2011. COAMPS 18-h adjoint sensitivities of low-level kinetic energy to changes in initial state winds, temperature, and water vapor are analyzed for both TC05 and the KW to document when the evolution of each system is sensitive to the other. Time series of sensitivity patterns confirm that TC05 and the KW low-level westerlies are sensitive to each other when the KW is to the southwest and south of TC05. While TC05 is not sensitive to the KW after this, the KW low-level westerlies remain sensitive to TC05 until it enters the far eastern Indian Ocean. Vertical profiles of both TC05 and KW sensitivity indicate lower-tropospheric maxima in temperature, wind, and moisture, with KW sensitivity typically 20% smaller than TC05 sensitivity. The magnitude of the sensitivity for both systems is greatest just prior to, and during, their closest proximity. A case study examination reveals that adjoint-based optimal perturbations grow and expand quickly through a dynamic response to decreased static stability. The evolution of moist-only and dry-only initial perturbations illustrates that the moist component is primarily responsible for the initial rapid growth, but that subsequent growth rates are similar.

Corresponding author address: Carolyn Reynolds, Marine Meteorology Division, Naval Research Laboratory, 7 Grace Hopper Ave., Monterey, CA 93943-5502. E-mail: carolyn.reynolds@nrlmry.navy.mil

Abstract

The initial-state sensitivity and interactions between a tropical cyclone and atmospheric equatorial Kelvin waves associated with the Madden–Julian oscillation (MJO) during the DYNAMO field campaign are explored using adjoint-based tools from the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS). The development of Tropical Cyclone 5 (TC05) coincided with the passage of an equatorial Kelvin wave (KW) and westerly wind burst associated with an MJO that developed in the Indian Ocean in late November 2011. COAMPS 18-h adjoint sensitivities of low-level kinetic energy to changes in initial state winds, temperature, and water vapor are analyzed for both TC05 and the KW to document when the evolution of each system is sensitive to the other. Time series of sensitivity patterns confirm that TC05 and the KW low-level westerlies are sensitive to each other when the KW is to the southwest and south of TC05. While TC05 is not sensitive to the KW after this, the KW low-level westerlies remain sensitive to TC05 until it enters the far eastern Indian Ocean. Vertical profiles of both TC05 and KW sensitivity indicate lower-tropospheric maxima in temperature, wind, and moisture, with KW sensitivity typically 20% smaller than TC05 sensitivity. The magnitude of the sensitivity for both systems is greatest just prior to, and during, their closest proximity. A case study examination reveals that adjoint-based optimal perturbations grow and expand quickly through a dynamic response to decreased static stability. The evolution of moist-only and dry-only initial perturbations illustrates that the moist component is primarily responsible for the initial rapid growth, but that subsequent growth rates are similar.

Corresponding author address: Carolyn Reynolds, Marine Meteorology Division, Naval Research Laboratory, 7 Grace Hopper Ave., Monterey, CA 93943-5502. E-mail: carolyn.reynolds@nrlmry.navy.mil

1. Introduction

Many previous studies have shown that tropical cyclone (TC) formation is strongly related to equatorial wave activity (e.g., Frank and Roundy 2006; Bessafi and Wheeler 2006; Schreck and Molinari 2011; Schreck et al. 2012; Ventrice et al. 2012a; Shen et al. 2012). These waves, including mixed Rossby–gravity waves, equatorial Rossby waves, Kelvin waves, and the Madden–Julian oscillation (MJO; Zhang 2005) appear to enhance the local circulations by increasing the organized upward vertical motion, as well as the low-level vorticity at the genesis location, and modulate the vertical shear (Frank and Roundy 2006). An example of the interactions between tropical waves and a TC occurred during the Dynamics of the Madden–Julian Oscillation (DYNAMO) period from November to December 2011. Several observational studies have reported on the co-occurrences of Kelvin waves (KWs) and the Indian Ocean TC 05A (TC05) during this period (Gottschalck et al. 2013; Johnson and Ciesielski 2013; Moum et al. 2014). In this study, we use adjoint sensitivity diagnostics to examine when the development of TC05 influences the development of the KW and vice versa.

Previous studies have suggested mechanisms through which KWs may promote TC genesis and have also suggested that TCs may project onto equatorial KWs. Roundy (2008) found that diabatically generated potential vorticity (PV) appeared as cyclonic gyres in composites of Indian Ocean atmospheric KWs, which he hypothesized could act as TC precursors. Schreck and Molinari (2011) examine the role of KWs in the development of twin TCs Rammasun and Chatann in the western Pacific during June 2002. The TCs developed during periods when the MJO and embedded KWs enhanced cyclonic PV and equatorial westerlies. Ventrice et al. (2012a) find a statistically significant increase in Atlantic tropical cyclogenesis 2 days after the passage of the active phase of convectively coupled KWs. Ventrice et al. (2012b) relate this enhanced TC activity to the KW modulation of the wind shear, moisture, and lower-tropospheric vorticity. Schreck (2015) used the Modern-Era Retrospective Analysis for Research and Applications (MERRA; Rienecker et al. 2011) and the International Best Track Archive for Climate Stewardship (IBTrACS) to establish relationships between KWs and tropical cyclogenesis over all basins. He found that TC genesis is inhibited for approximately 3 days before the KW peak rainfall, and enhanced for 3 days after. The low-level equatorial westerlies enhance cyclonic vorticity while the upper-tropospheric easterlies enhance outflow. He found that the north Indian Ocean had the largest percent increase in genesis (83% at +2.5 days) for any basin. The KWs may contribute to the initiation of the pregenesis disturbances. Sobel and Camargo (2005), through lag regression analysis of large-scale atmospheric variables and TC accumulated cyclone energy, suggest the reverse influence; that is, TCs forming at low-latitudes may project onto atmospheric KWs. This lack of consensus regarding TC interactions with KWs provides further motivation for our study.

Aspects of TC evolution and predictability have been studied using adjoint-related techniques in many previous studies. An adjoint, or transpose, of the forecast model linearized about a trajectory allows for the efficient calculation of the sensitivity of a particular forecast measure, or response function, to changes in the initial state (Errico 1997). Adjoint and the related singular vector techniques have been applied to TCs in the context of targeted observations (e.g., Majumdar et al. 2006; Wu et al. 2009); dynamics (e.g., Yamaguchi et al. 2011; Peng and Reynolds 2006); influences and processes during recurvature and extratropical transition (e.g., Reynolds et al. 2009; Kim and Jung 2009; Lang et al. 2012); and observation impact (Jung et al. 2013). Doyle et al. (2011, 2012) used the same forecast and adjoint system employed here to study the predictability and sensitivity of tropical cyclones and tropical cyclogenesis. They found that tropical disturbances are most sensitive to perturbations in the moisture and temperature fields in the lower to middle troposphere, and that adjoint-based optimal perturbations grow more rapidly for disturbances that develop into TCs than for disturbances that do not develop. They found the rapid extension in the vertical of initial low-level perturbations to be consistent with a bottom-up development process, but secondary midlevel sensitivity was also present. These adjoint based sensitivity studies are complementary to ensemble-based sensitivity analysis (Torn and Hakim 2008) applied to TCs such as in Torn and Hakim (2009), Sippel and Zhang (2010), Munsell et al. (2015), and references therein.

While there are numerous adjoint-based studies focused on TCs, much less attention has been given to adjoint-based sensitivity studies of equatorial waves. An exception is the study by Cornforth and Hoskins (2009), who apply moist singular vector diagnostics using the ECMWF system to study African easterly waves. They found that while the moist singular vectors were able to capture the essence of African easterly wave structure and geographic distribution, interpreting the mechanisms for the singular vector growth was not straightforward, with barotropic, baroclinic, and moist processes all appearing to be important. Singular vector and optimal perturbation analyses have been applied extensively to El Niño–Southern Oscillation and low-frequency tropical ocean–atmosphere modes (e.g., Moore et al. 2003, 2006 and references therein), and singular value decomposition techniques have been applied to ocean equatorial waves (Susanto et al. 1998). However, aside from the Cornforth and Hoskins study, the authors are not aware of adjoint-based sensitivity studies applied to higher-frequency atmospheric equatorial waves or the relationship between TCs and these waves.

In this study, we investigate the interaction between the KWs and TC05 using the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS)1 forecast and adjoint system. Although TC05 was not an especially strong TC, it did result in extensive damage and loss of life in Sri Lanka, where the storm was linked with heavy rains and flooding, which caused at least 19 deaths, mostly fishermen at sea (Moum et al. 2014), and damage to 5700 homes (http://reliefweb.int/report/sri-lanka/sri-lanka-storm-kills-19-damages-5700-homes).

The methodology is described in section 2, results are presented in section 3, and a summary and conclusions are given in section 4.

2. Methodology

a. Adjoint sensitivity and optimal perturbations

The adjoint sensitivity and optimal perturbation methodologies are detailed in Doyle et al. (2012) and are described briefly here. As noted in the introduction, an adjoint model provides the sensitivity of a forecast metric J (for model state xt at time t) to each component of an earlier model state (xt0):
e1
where J is the response function and M is the nonlinear model. The gradient of J with respect to the initial model state is defined as
e2
where is the tangent linear model of M and superscript T denotes the transpose. ∂J/∂xt is computed through differentiation of J with respect to the model state at time t. Term J must be a continuous and differentiable function.
Adjoint-derived optimal initial perturbations (Errico and Raeder 1999; Rabier et al. 1996; Oortwijn and Barkmeijer 1995) are produced in the same manner as described in Doyle et al. (2012) and Doyle et al. (2014). The optimization problem we are solving is to find the smallest perturbation that maximizes the change in a response function. Perturbations to the response function J are expressed as follows:
e3
where is the gradient of the response function with respect to the jth component of the initial state. The jth component of the perturbation vector is optimal when defined such that
e4
for weights wj. The smallest initial perturbation (in a norm measured by the weights wj) is found such that (3) is satisfied. The method for obtaining the scaling parameter s and the weights is detailed in Doyle et al. (2014). The scaling, s (same units as J−1), is chosen such that the largest perturbation of the potential temperature, water vapor, or zonal wind speed does not exceed 1 K, 1 g kg−1, or 1 m s−1, respectively. These perturbation magnitudes are comparable to errors assigned to radiosonde and dropwindsonde observations in the data assimilation system [1 K, 1.8 m s−1, and 10% relative humidity at 925 hPa (~1–1.5 g kg−1)]. The optimal perturbations are calculated for all wind components (zonal, meridional, and vertical), potential temperature, the Exner pressure perturbation, mixing ratio, and microphysical species.

b. Forecast and adjoint system

COAMPS forecast and adjoint systems used in this study are described very briefly here. The reader is referred to Doyle et al. (2012) for a more in-depth description of the systems. COAMPS (Hodur 1997) is the nonhydrostatic mesoscale model used for the U.S. Navy operational forecasting as well as many diverse research applications. The physical parameterizations in the atmospheric component of the model used here include a modified version of Rutledge and Hobbs (1983) cloud microphysical processes, a linearized Kuo convective parameterization (Molinari 1985), a prognostic TKE equation (Hodur 1997), and a surface-layer parameterization (Louis et al. 1982).

The COAMPS tangent linear and adjoint models are described in Amerault et al. (2008). Identical physical parameterizations are used in the nonlinear, adjoint, and tangent linear models. Radiative effects are ignored and only warm-rain processes are considered in order to avoid highly nonlinear components of the physics. The COAMPS forecast and adjoint system have been used for several different applications, including the study of TC predictability (Doyle et al. 2011, 2012), targeted observing for TCs (Reynolds et al. 2010), predictability studies of severe extratropical cyclones (Doyle et al. 2014), and most recently in support of the DEEPWAVE field project (Fritts et al. 2016).

c. Experimental design

COAMPS 18-h forecasts are run from Navy Operational Global Atmospheric Prediction System (NOGAPS) analyses every 6 h for the period of interest, starting at 0000 UTC 23 November through 1800 UTC 26 November 2011. The domain, with lateral boundaries at 25°S–25°N and 37°E–112°W covers the tropical and subtropical Indian Ocean. Lateral boundary conditions are provided by NOGAPS forecasts. Two sets of adjoint sensitivity calculations are performed for each of the forecasts. In one set, the response function is the kinetic energy in the lowest 2000 m of the atmosphere in a 13° latitude by 13° longitude box centered on the forecast position of TC05, or the center of the circulation that evolves into TC05. This response function is chosen to reflect storm intensity and potential impacts associated with low-level winds. Tests with the response function set to 200 and 1000 m produced qualitatively similar results. For simplicity, we will refer to all of these sensitivity calculations as TC05 calculations, even for time periods before the storm is named TC05 and the sensitivity corresponds to the precursor circulation. In another set, the response function is the kinetic energy in the lowest 2000 m in a 13° × 13° box centered on the low-level westerlies associated with the KW.

An optimal perturbation is constructed from each adjoint sensitivity field as described in section 2a. This optimal perturbation is propagated forward in time using the tangent linear model of COAMPS. It is also added to the initial conditions from which a nonlinear COAMPS forecast is produced. The difference between the control COAMPS forecast and this perturbed COAMPS forecast gives the nonlinear perturbation. Comparison of the nonlinear perturbation with the perturbation evolved using the tangent linear model allows for an assessment of the appropriateness of the tangent linear assumption. Results based on 15-km horizontal resolution forecast and adjoint simulations indicated that the perturbation growth becomes substantially nonlinear over an 18-h forecast period. In contrast, the linear and nonlinear perturbation growth for 18-h, 45-km simulations is similar (an example will be shown in section 3c). Therefore, results presented here are for 45-km simulations. Extending the optimization time to 36 h results in a significant degradation of the linear approximation, but examples are shown to enable consideration of TC–KW interactions over longer time scales. While this relatively coarse-resolution setup obviously cannot represent the finescale features of the TC, it can represent the broader scales of the KW and the interactions between the TC and KWs on these synoptic scales. It is also of comparable resolution to that used in Doyle et al. (2012) and Jung et al. (2013) and finer than the O(100) km resolution or larger used in several previous studies on TC sensitivity (e.g., Peng and Reynolds 2006; Kim and Jung 2009; Lang et al. 2012).

3. Results

After a brief description of the tropical conditions during late November 2011, we present an overview of the sensitivity results calculated for the entire time period of interest. This is followed by a detailed examination of one case during the time when the sensitivity of both TC05 and the KW is particularly strong.

a. Description of the environmental conditions

The late November 2011 MJO and concurrent TC05 have been examined and described in detail in several studies (e.g., Johnson and Ciesielski 2013; Moum et al. 2014; Gottschalck et al. 2013; Xu and Rutledge 2014), and thus only a brief overview of events will be given here.

The left panel of Fig. 1 shows the Tropical Rainfall Measuring Mission (TRMM; Huffman et al. 2007) 3B42 precipitation (shaded) averaged from 5°S to 5°N from 0000 UTC 21 November to 1800 UTC 30 November. The right panel of Fig. 1 shows the 10-m zonal wind from the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim; Dee et al. 2011), averaged from 5°S to 5°N for the same time period. The two eastward-propagating precipitation events, accompanied by enhanced low-level westerlies are clearly evident. These are identified as KWs through Wheeler and Weickmann (2001) filtering applied to OLR in Johnson and Ciesielski (2013), although the propagation speed of approximately 8 m s−1 is relatively slow. Johnson and Ciesielski also note that trailing poleward-moving low-level cyclones are associated with these events. Moum et al. (2014) and Gottschalck et al. (2013) note that these convectively coupled KWs are associated with strong westerly winds and precipitation events. Oh et al. (2015) describe the first westerly wind event as likely due to the superposition of Rossby and KW westerlies, and the second westerly wind event due to the supposition of equatorial Kelvin, Rossby, and mixed Rossby–gravity wave westerly phases. Also shown in Fig. 1 is the TRMM precipitation and ECMWF 10-m vorticity (contours in left and right panels, respectively) averaged from 5° to 20°N. The enhanced precipitation and vorticity that propagates westward is associated with TC05 [the longitude positions of TC05 as given by the Joint Typhoon Warning Center (JTWC) best track are indicated by the dots]. The cyclonic vortex that becomes TC05 is first noted as a tropical depression in the JTWC best track at 1200 UTC 25 November with 25-kt (12.9 m s−1) maximum winds, is first designated TC05 with 30-kt (15.4 m s−1) maximum winds at 0000 UTC 26 November, and is upgraded to a tropical storm with 35-kt (18 m s−1) maximum winds at 0600 UTC 28 November. Enhanced precipitation associated with the precursor cyclonic circulation is also evident about 2 days prior to when the storm is first named a tropical depression.

Fig. 1.
Fig. 1.

(left) TRMM 3B42 3-h precipitation (shaded, mm h−1) averaged from 5°S to 5°N from 0000 UTC 21 Nov to 1800 UTC 30 Nov. TRMM precipitation averaged from 5° to 20°N is shown in the black contours (contour interval of 0.5 mm h−1, values below 1.0 mm h−1 not shown). (right) The ECMWF-analyzed 10-m zonal wind (shaded, m s−1) averaged from 5°S to 5°N. The 10-m vorticity averaged from 5° to 20°N is shown in the black contours (contour interval of 10−5 s−1). In both panels, the longitude of TC05 as given in the JTWC best track archive is shown by black circles with red centers, the longitudinal range of the TC05 response function is given by the brown lines, and the longitudinal range of the KW response function is given by the black lines.

Citation: Monthly Weather Review 144, 11; 10.1175/MWR-D-16-0174.1

Horizontal bars are included in both panels of Fig. 1 to indicate the longitudinal extent of the adjoint response function boxes (the latitudinal extent, not indicated in the figure, varies with time). The brown bars indicate the TC05 (and precursor) response function locations. These bars are not always centered on the observed location of the TC, being centered instead on the COAMPS forecast location of the storm. However, the observed location is always contained within the response function box. The black bars show the longitudinal extent of the KW response functions, which are centered on the enhanced precipitation and low-level westerlies associated with the KW.

Infrared imagery over the Indian Ocean taken from the Indian Meteorological Department (IMD) Kalpana-1 satellite valid at 1200 UTC 23, 24, 25, and 26 November (Fig. 2) provides another perspective. Magenta lettering indicates the approximate position of the cyclonic vortex (CV) over the Bay of Bengal that propagates westward into the Arabian Sea and evolves into TC05. Also indicated is the eastward-propagating area of enhanced convection along the equator associated with the first convectively coupled KW.

Fig. 2.
Fig. 2.

Infrared imagery over the Indian Ocean from the Indian Meteorological Department (IMD) Kalpana-1 satellite. The red numbers indicate the corresponding dates and hours. “KW” denotes the convection associated with the KW, and CV and TC05 denote the cyclonic vortex that becomes TC05, and TC05 itself.

Citation: Monthly Weather Review 144, 11; 10.1175/MWR-D-16-0174.1

Moum et al. (2014) note that as the first westerly wind burst was propagating eastward across the position of the Research Vessel (R/V) Roger Revelle (part of the DYNAMO observing array) at 80.5°E, a cyclonic vortex was present directly north centered at 4°N. Gottschalck et al. (2013) have shown the interaction of the convective phases of an equatorial Rossby wave, a KW, and the MJO over the DYNAMO array on 27 November based on time–longitude diagrams of filtered anomalies of OLR and precipitation. They suggested that the superposition of modes likely led to the genesis of TC05. However, since the enhanced convection is largely confined to the Northern Hemisphere, this implies that the precursor circulation may be more akin to a tropical depression–type disturbance.

b. Sensitivity overview

We first show the dry total energy of the optimal perturbation in order to give an inclusive overview of the sensitivity fields. Dry total energy, following Ehrendorfer et al. (1999) and Errico et al. (2004), is defined as follows:
e5
where i, j, and k are horizontal and vertical gridpoint indices; N is the number of layers; u and υ are the wind components; T is the temperature; R = 287.04 J kg−1 K−1 is the gas constant; Cp = 1005.7 J kg−1 K−1 is the specific heat of air at constant pressure; Tr = 300 K and psr = 1000 hPa are reference T and ps values, respectively; and a prime indicates a perturbation. The factor Δσ accounts for the normalized mass in each layer.

Figure 3 shows the vertically integrated dry total energy of the optimal initial perturbation corresponding to the 18-h adjoint sensitivity for TC05 for forecasts started every 12 h from 0000 UTC 23 November to 1200 UTC 26 November. Superimposed on the total energy fields are the 850-hPa vector winds from the analyses. The black circles and boxes represent, respectively, the approximate position of TC05 (and its precursor cyclonic vortex) and the leading-edge low-level westerlies associated with the first KW. The red second box that appears at 65°E at 0000 UTC 25 November gives the location of the second KW feature apparent in Fig. 1. At 0000 UTC 23 November, the strongest sensitivity is centered on the northern part of the TC precursor circulation itself, but a secondary maximum associated with the KW low-level westerlies to the southwest is also apparent. Twelve hours later, the sensitivity has contracted from the southwest closer to the storm, but still includes the leading edge of the KW westerlies. By 0000 UTC 24 November, when the TC and the KW are in closest proximity, the sensitivity pattern is at its most localized for the whole period. TC05 ceases to show sensitivity to the KW westerlies after the KW moves into the central Bay of Bengal and farther east.

Fig. 3.
Fig. 3.

Vertically averaged total energy of the optimal initial perturbation (shading, m2 s−2) with the 850-hPa analyzed wind vectors based on the 18-h adjoint sensitivity centered on TC05 and its precursor circulation for forecasts started every 12 h from (top left) 0000 UTC 23 Nov to (bottom right) 1200 UTC 26 Nov 2011. Location of TC05 (and precursor circulation) denoted by black circles, and location of the leading edge of the low-level westerlies associated with the first and second KWs denoted by black and red boxes, respectively.

Citation: Monthly Weather Review 144, 11; 10.1175/MWR-D-16-0174.1

These sensitivity patterns show that the evolution of the precursor of TC05 is sensitive to initial perturbations in the vicinity of the KW westerlies when these are within 1300 km to the southwest and south of the storm. While TC05 no longer exhibits sensitivity to the first KW once the TC moves into the Arabian Sea and the two features become separated by more than 1000 km, remote influences still occur, in particular in the region of equatorial westerlies between 65° and 70°E at 1200 UTC 25 November and 1200 UTC 26 November. This indicates that TC05 exhibits sensitivity to the westerlies associated with the second KW apparent in Fig. 1. Adjoint calculations using the second KW as a response function (not shown), indicate that this KW is also sensitive to TC05.

Figure 4 is analogous to Fig. 3, except that the optimal perturbation total energy is from the sensitivity of the forecast of the KW low-level westerlies, rather than TC05. The forecast of the KW is, as expected, sensitive to changes in the initial state in the vicinity of the KW itself. In addition, the sensitivity patterns clearly extend to TC05 and its precursor circulation until the KW has reached the far eastern Indian Ocean and TC05 is in the Arabian Sea on 26 November. Specifically, the KW low-level westerlies are sensitive to changes in the initial state in the region of low-level easterly winds to the north and northwest of TC05 while TC05 is to the northeast, and sensitive to the changes in the region of westerlies to the south of TC05 while TC05 is to the north or northwest. These adjoint diagnostics confirm, respectively, that the evolution of TC05 is sensitive to changes in the initial state KW westerly region, and the evolution of the KW westerlies are sensitive to changes in the initial state TC. In this sense, the sensitivity results are in agreement with the findings of Roundy (2008), Ventrice et al. (2012a), and Schreck and Molinari (2011) who find that equatorial waves influence the development of TCs, as well as Sobel and Camargo (2005), who hypothesize that TCs may influence KWs. It does appear that the influence of the TC on the KW is longer lived than the influence of the KW on the TC. In general, remote sensitivity appears in regions where flow is toward the feature of interest. However, there is not a one-to-one correspondence between the strength of flow toward the feature and sensitivity, as illustrated by counter examples such as the lack of TC05 sensitivity to the strong easterly flow northeast of the storm at 0000 UTC 24 November. While the local sensitivity is usually substantially larger than the remote sensitivity, there are cases where the remote and local sensitivities are of comparable magnitude (e.g., the KW sensitivity from 1200 UTC 23 November).

Fig. 4.
Fig. 4.

As in Fig. 3, but with the response function centered on the westerlies associated with the first KW.

Citation: Monthly Weather Review 144, 11; 10.1175/MWR-D-16-0174.1

As a complement to the vertically integrated fields shown in Figs. 3 and 4, Fig. 5 shows the average absolute magnitude of the different sensitivity components (wind, temperature, and water vapor) as a function of height for the 16 different forecasts for both the TC05 (left) and KW (right) response functions. The panels in Fig. 5 show pronounced maxima in the lower troposphere (below 700 hPa) for both wind and temperature sensitivities. While the moisture sensitivities also have maxima in the lower troposphere, in several cases there appears to be secondary maxima in the middle troposphere (around 500 hPa). These results are consistent with those found in the tropical cyclogenesis study of Doyle et al. (2012). In that study, Doyle et al. found that TCs were most sensitive to moisture and temperature, followed by winds, and had sensitivity maxima in the lower troposphere. Comparison of the left and right panels in Fig. 5 indicates that the magnitude of the TC sensitivity is larger than the magnitude of the KW sensitivity for winds, temperature, and moisture, typically by about 20%. This indicates that a similarly sized initial optimal perturbation can result in a larger difference to the low-level kinetic energy associated with TC05 then to the low-level kinetic energy associated with the KW westerlies. In addition, as the curves corresponding to the initial dates are color coded, one can see that both TC05 and KW sensitivities are considerably larger during forecasts started on 23 and 24 November (red and purple curves), when the KW westerlies are southwest and then south of the TC, than for forecasts started on 25 and 26 November (green and blue curves), when the KW has moved east of the TC. Thus, the adjoint calculations indicate that the evolution of both TC05 and the KW is most sensitive to changes in the initial state (and perhaps least predictable) when the KW low-level westerlies and TC05 are approaching each other and subsequently in close proximity. The westerlies associated with the KW and TC05 precursor circulation are in closest proximity on 24 November. JTWC starts tracking the storm at 1200 UTC 25 November and denotes it as TC05 at 0600 UTC 26 November. This timing is roughly consistent with, though faster than, the results of Schreck (2015), who finds that genesis, as defined when the storm first appears in the IBTrACS database, is most likely to occur 2.5 days after the passage of a KW in the Indian Ocean. Schreck (2015) did find an increased likelihood of genesis 1.5 days after the KW passage as well, although this was much less prominent than the 2.5-day peak and was not statistically significant. More cases would be needed to determine if the adjoint-based studies suggest a systematically different time lag in maximum sensitivity than the time lag between the KW passage and TC genesis found in previous studies.

Fig. 5.
Fig. 5.

Domain-averaged absolute sensitivity as a function of pressure level for (left) TC05 and (right) the KW for (top) wind [m2 s−2 (m s−1)−1], (middle) temperature (m2 s−2 K−1), and (bottom) water vapor [m2 s−2 (g kg−1)−1]. Individual sensitivity calculations from different analysis times are given by the color curves and indicated in key in top-right panel. The average for all 12 cases is given by the solid black curve.

Citation: Monthly Weather Review 144, 11; 10.1175/MWR-D-16-0174.1

In addition to the domain-averaged sensitivity magnitudes shown in Fig. 5, we have also calculated the domain-averaged values for the temperature and water vapor sensitivities shown in Fig. 6. For both TC05 and KW calculations, the temperature sensitivity is positive on average in the lowest levels of the troposphere (approximately below 850 hPa), but negative in the mid- to lower troposphere (from approximately 850 to 500 hPa). This is consistent with convective destabilization of the column resulting in larger near-surface kinetic energy. The water vapor sensitivity domain averages are also largest in the lower troposphere, although unlike the temperature domain averages, the water vapor domain averages usually remain positive through the depth of the troposphere. Note that the average values are small compared to the average magnitude of the values shown in Fig. 5, reflecting substantial compensation between regional positive and negative values at any particular level.

Fig. 6.
Fig. 6.

Domain-averaged sensitivity as a function of pressure level for (left) TC05 and (right) the KW for (top) temperature (m2 s−2 K−1) and (bottom) water vapor [m2 s−2 (g kg−1)−1]. Individual sensitivity calculations from different analysis times are given by the color curves and indicated in key in top-right panel. The average for all 12 cases is given by the solid black curve.

Citation: Monthly Weather Review 144, 11; 10.1175/MWR-D-16-0174.1

As discussed in the previous section, an 18-h optimization time was chosen because the match between linear and nonlinear perturbation growth degrades at longer lead times due to inherent nonlinearities in moist processes. However, the choice of such a short optimization time limits our ability to diagnose more remote influences. Therefore, it may be instructive to examine longer optimization times and consider sensitivity calculations performed without the inclusion of moist processes to find what remote influences might occur under more linear conditions. Figure 7 shows the vertically integrated magnitude of the sensitivity to the wind field for the TC05 case for forecasts started at 0000 UTC 23 November and 0000 UTC 25 November. The top panels are the wind sensitivity for the 18-h optimization cases discussed previously. The middle panels are the wind sensitivity for 36-h optimization cases. The bottom panels are wind sensitivity for 36-h optimization cases in which the adjoint calculation is performed without the inclusion of moist processes (dry adjoint). We show the wind sensitivity to emphasize remote influences. Water vapor and total energy sensitivities in the 36-h case (not shown) are similar to the 18-h case and remain fairly close to the storm. In both the 36-h moist and dry adjoint cases, the sensitivity to the wind field extends considerably farther to the southwest (and somewhat farther to the northeast) than in the 18-h cases. The 36-h wind sensitivity extends more than 10° farther west and almost 10° farther south than the 18-h wind sensitivity for the 0000 UTC 25 November case. Comparison between the 36-h moist and dry adjoint results illustrate how moist processes facilitate large wind sensitivity in the immediate vicinity and just to the east of the TC, which are absent in the dry case. While care must be taken in interpreting these results given the limitations of the tangent linear approximation, it would be interesting to see if similar sensitivities are found in techniques that may be somewhat less constrained by these assumptions, such as ensemble-based sensitivity calculations.

Fig. 7.
Fig. 7.

Vertically averaged magnitude of the zonal and meridional wind components of the TC05 adjoint sensitivity (shading, m2 s−2) with the 850-hPa-analyzed wind vectors based on the (top) 18-h adjoint sensitivity, (middle) 36-h adjoint sensitivity, and (bottom) 36-h sensitivity based on the dry adjoint for forecasts started from (left) 0000 UTC 23 Nov and (right) 0000 UTC 25 Nov 2011. The location of TC05 (and precursor circulation) is denoted by black circles, and location of first and second KWs is denoted by black and red boxes, respectively.

Citation: Monthly Weather Review 144, 11; 10.1175/MWR-D-16-0174.1

c. Case study

We now examine in some detail the case for the TC05 response function for the forecast beginning at 1200 UTC 23 November. This is the time period when the KW low-level westerlies are approaching the TC precursor circulation from the west. At the final forecast time (0600 UTC 24 November) the KW westerlies are just south of, and in close proximity to, the TC. It is also in the middle of the time period where the sensitivities for the KW and the TC are both relatively large. Figure 8 shows the 850-hPa zonal wind component of the initial-time TC05 optimal perturbation, and its tangent linear evolution and nonlinear evolution after 18 h. Only the subdomain in the vicinity of the features of interest is shown. Also shown is the initial-time optimal perturbation calculated for the KW response function. Superimposed on these fields are the 850-hPa wind vectors associated with the control analysis and forecast. The box shows the location of the TC response function at final time. The perturbation structure indicates that enhancing initial-time low-level easterlies to the north and northeast of the storm, and enhancing low-level westerlies to the southwest of the storm, will increase the low-level kinetic energy associated with the storm at the 18-h forecast time. At final time (18 h), as expected, the wind perturbations are shown to enhance westerlies to the south of the center of the storm, and easterlies to the north, although the pattern does show some complexity. Comparison of the nonlinear perturbation with the linear perturbation indicates a fairly good correspondence between the two, especially inside the response function region. However, the magnitude of the nonlinear perturbation is about 30% smaller than the expected linear perturbation. Quantitatively, in terms of the response function, the increase in low-level kinetic energy in the response region is 46.6% of that expected from the linear calculation. The initial-time zonal wind perturbations corresponding to the KW response function are similar to those for the TC05 response function, although the easterly perturbations to the north of the circulation are weaker and less extensive, and the westerly perturbations along the equator are stronger and extend farther westward. The similarity of the KW and TC05 patterns at this time is not surprising, given the proximity of these two features and the overlap in the response function regions.

Fig. 8.
Fig. 8.

The 850-hPa U component of the optimal perturbation (shaded m s−1) at forecast (top left) tau = 0 for TC05, (top right) tau = 0 for the KW, and (bottom left) tau = 18 for TC05. (bottom right) The 18-h nonlinear perturbation for TC05 is shown. All panels show the control forecast 850-hPa wind vectors. Forecasts from 1200 UTC 23 Nov 2011. The TC05 response function region is denoted by the black square.

Citation: Monthly Weather Review 144, 11; 10.1175/MWR-D-16-0174.1

To provide more insight into the mechanisms responsible for perturbation evolution, Fig. 9 shows vertical cross sections of the TC05 optimal perturbations at 0, 9, and 18 h. The control forecast zonal wind (shading) and zonal wind optimal perturbations (contours) are shown in the left panels. The right panels show the optimal perturbation water vapor (shaded), divergence (black contours), temperature at 0 h (green contours), and cloud water at 9 and 18 h (blue contours). The quantities are averaged between 2°S and 2°N at 0 and 9 h, to highlight the role of the equatorial westerlies, and between 0° and 4°N at 18 h, to include the large perturbations to the south of the TC. At initial time, the wind perturbations primarily act to enhance the low-level westerlies associated with the westerly wind burst. Positive low-level moisture and temperature perturbations are centered at 83°E, in the low-level convergence region of the KW. After 9 h, the positive moisture anomaly extends up to 500 hPa with enhanced cloud water centered at 450 hPa, accompanied by low-level convergence and midlevel divergence. By 18 h, the positive moisture anomaly is centered between 400 and 500 hPa, accompanied again by increased cloud water. The convergence/divergence couplet, in response to the moisture perturbation, shifts to higher altitudes as well. These perturbations illustrate the dynamic response to the initial low-level positive buoyancy perturbations, which decrease static stability and result in increased cloud water formation. Note that values of the initial optimal perturbations are quite small (less than 1 m s−1 and 1 g kg−1) while the resulting changes in the evolved wind fields reach values above 28 m s−1. This figure illustrates how initial low-level perturbations can amplify and extend in the vertical very rapidly over 18 h, consistent with adjoint-based studies of TCs such as Doyle et al. (2012). The expansion in the vertical from the initial low-level peaks in temperature and water vapor are consistent with the results of Tulich and Mapes (2010), who find low-tropospheric temperature and moisture perturbations are effective at producing vertically nonlocal responses in a cloud-resolving model of the tropical environment, while responses to mid- and upper-tropospheric perturbations are mostly local in the vertical.

Fig. 9.
Fig. 9.

Vertical cross sections for the TC05 case from 1200 UTC 23 Nov 2011. (left) Zonal wind optimal perturbations at (top) 0 h [contour interval (ci) = 0.01 m s−1], (middle) 9 h (ci = 0.5 m s−1), and (bottom) 18 h (ci = 4 m s−1), and the control forecast zonal wind (shading, m s−1). (right) Water vapor optimal perturbation (shading, g kg−1) at 0, 9, and 18 h, with optimal perturbation divergence in black contours, optimal perturbation temperature in green contours, and optimal perturbation cloud water in blue contours. Divergence contour intervals are 1 × 10−7, 1 × 10−5, and 5 × 10−5 s−2 at 0, 9, and 18 h, respectively. Temperature contour interval at 0 h is 0.03 K. Contour intervals for cloud water are 0.06 and 0.3 g kg−1 at 9 and 18 h, respectively. Solid contours are positive values and dashed contours are negative values. The 0- and 9-h fields are averaged from 2°S to 2°N. The 18-h fields are averaged from 0° to 4°N.

Citation: Monthly Weather Review 144, 11; 10.1175/MWR-D-16-0174.1

Figure 10 shows the 850-hPa horizontal wind speed and wind vectors for the 18-h control forecast, the control forecast to which the TC05 linear perturbations have been added, and the nonlinear forecast run from the perturbed analysis. As designed, the linear perturbation increases the wind speed (and kinetic energy) in the vicinity of the storm. The peak winds, which occur in the northern part of the storm, have increased from 23.8 m s−1 in the control run to 32.7 m s−1 in the linear perturbed run. While the peak winds in the nonlinear perturbed forecast have not increased much over the control run (24.3 m s−1), the wind speeds in the southern part of the storm have increased substantially (from 17.9 m s−1 in the control case, to 23.7 m s−1 in the linear perturbed case and 21.9 m s−1 in the nonlinear perturbed case). This increase in the westerly winds to the south of the storm corresponds to enhanced westerlies associated with the KW, consistent with the composites in Schreck (2015).

Fig. 10.
Fig. 10.

The 850-hPa horizontal wind speed (shaded, m s−1) and 850-hPa wind vectors at forecast tau = 18 h for (top left) the control forecast, (top right) the control forecast with the linear perturbation, and (bottom left) the control forecast with the nonlinear perturbation for the TC05 case. Forecast is from 1200 UTC 23 Nov 2011.

Citation: Monthly Weather Review 144, 11; 10.1175/MWR-D-16-0174.1

While the response function is defined as the kinetic energy in the lowest 2000 m of the atmosphere in a box surrounding the feature of interest, the evolved tangent linear perturbations are not constrained to exist only within the lower atmosphere, as illustrated by the cross sections in Fig. 9. To examine how the full vertical profiles of the optimal perturbations evolve with time, Fig. 11 shows the area-averaged optimal perturbation magnitudes at 0, 6, 12, and 18-h integration times for the TC05 case (solid lines) and KW case (dashed lines) for the forecast started at 1200 UTC 23 November. For TC05, the wind perturbation maximum starts out in the lower troposphere, but after 18 h, the greatest perturbation is at 350 hPa followed by a secondary maximum at 850 hPa. For temperature and moisture, the vertical structures evolve from a peak in the lower troposphere to a fairly broad peak in the middle troposphere for temperature, and the middle and lower troposphere for water vapor. The vertical profiles for the KW optimal perturbation are similar in structure to those for TC05 for wind and temperature, although the perturbation growth is slower. For water vapor, the KW 18-h optimal perturbation has a pronounced peak in the lower troposphere, lacking the deep perturbation growth in moisture that is seen for TC05. Taken together, Figs. 9 and 11 illustrate the rapid amplification and vertical extension of low-level temperature and moisture perturbations consistent with both earlier adjoint studies (e.g., Doyle et al. 2012) and theoretical studies such as Tulich and Mapes (2010).

Fig. 11.
Fig. 11.

Domain-averaged optimal perturbation magnitude as a function of pressure level for TC05 (solid curves) and the KW (dashed curves) for (top) wind (m s−1), (middle) temperature (K), and (bottom) water vapor (g kg−1) for the 18-h forecast started at 1200 UTC 23 Nov. The mark, circle, square, and diamond represent the optimal perturbations at 0-, 6-, 12-, and 18-h integration times, respectively. The 0-h wind curve values are increased by an order of magnitude for clarity.

Citation: Monthly Weather Review 144, 11; 10.1175/MWR-D-16-0174.1

The COAMPS adjoint calculation also includes sensitivity to a fixed sea surface temperature (SST) perturbation. Figure 12 shows the SST sensitivity for the TC05 and KW response functions for the 1200 UTC 23 November forecast superimposed upon the analyzed SSTs. The relatively warm temperatures ahead of the KW and relatively cool temperatures behind it are apparent in the analyzed SST field. Both TC05 and KW sensitivities indicate that warming SSTs in two specific areas—one along the relatively cold waters under the northeasterly winds on the northwest side of the circulation and one near the convergence region of the KW—will enhance the low-level kinetic energy associated with both features. The KW sensitivity is very similar to the TC05 sensitivity, although it is weaker, and lacks the negative sensitivity centered at 5°N, 88°E. In TC05, the negative sensitivity lobe (collocated with negative 850-hPa moisture sensitivity, not shown) indicates that drying to the east of the TC will result in a stronger TC after 18 h, but would not impact the strength of the KW low-level westerlies.

Fig. 12.
Fig. 12.

The analyzed SST (shaded, K) and initial-time SST sensitivity (contour interval of 0.05 m2 s−2 K−1 with positive contours solid and negative contours dashed) for (left) the TC05 case and (right) the KW case. Forecast is from 1200 UTC 23 Nov 2011.

Citation: Monthly Weather Review 144, 11; 10.1175/MWR-D-16-0174.1

To examine the relative importance of the dry and moist components of the initial perturbations, we set the nonmoisture components of the initial optimal perturbation to zero and evolve this moisture-only initial perturbation linearly in time. Likewise, we set the moisture components of the initial perturbation to zero and evolve the dry-only initial perturbation in time. The only difference in these cases is in the initial perturbations. The forecast trajectory and linear propagator are identical and both include moist process. Figure 13 shows the domain-averaged low-level (1000–850 hPa) kinetic energy of the full initial-perturbation, moist-only initial perturbation, and dry-only initial perturbation as a function of forecast time for the 1200 UTC 23 November case. Also included is the perturbation growth due to the fixed SST perturbation. As temperature and wind perturbations are set to zero for the moist case at initial time, and all perturbations aside from the SST perturbation are set to zero at initial time for the SST case, both of these experiments have zero perturbation kinetic energy at initial time. These quantities are plotted on a log-linear axis such that the slope of the curve is proportional to the growth rate. The average growth rate (day−1) from 3 to 18 h is given by the numbers in the key. The energy associated with the moist case is much closer to that of the full perturbation case than the dry case after 3 h, indicating that most of the rapid growth that occurs early in the forecast time period is due to the moisture component of the initial perturbation. However, after 3 h, the growth rates for the full, moist, and dry cases are all comparable. It is interesting to note that the growth rate for the SST is actually greater than that for any of the initial perturbations. Of course, the nature of the forcing for the initial perturbations, which evolve in time, and the SST perturbation, which in this uncoupled framework is fixed through the integration, are different. Nevertheless, it points to the potential importance of SST influence on the evolution of these phenomena. The relationships between the different curves for the TC05 and KW cases are very similar, but the growth rates are smaller for the KW case, consistent with the results shown in Fig. 11.

Fig. 13.
Fig. 13.

Domain-averaged 1000–850-hPa kinetic energy (m2 s−2) as a function of forecast time for the optimal perturbations for the TC05 (solid) and KW (dashed) cases from 1200 UTC 23 Nov 2011. Linearly evolved perturbations associated with the full initial perturbations (black), moist-only initial perturbations (blue), dry-only initial perturbations (red), and constant SST perturbations (green) are shown. The 3–18-h growth rates (day−1) are given in parentheses in key.

Citation: Monthly Weather Review 144, 11; 10.1175/MWR-D-16-0174.1

4. Summary and conclusions

We use the COAMPS atmospheric forecast and adjoint system to characterize the sensitivity of an Indian Ocean TC and the low-level westerlies associated with an equatorial KW that occurred during the same time period, and establish when the evolution of one is sensitive to the evolution of the other. While adjoint sensitivity and related SV diagnostics have been applied in several previous studies to extratropical and tropical cyclones, and to more slowly varying atmosphere–ocean coupled phenomena such as El Niño, the only previous application of these techniques to fast atmospheric equatorial waves that the authors are aware of is an African easterly wave study by Cornforth and Hoskins (2009). The particular case considered here is that of TC05 and an equatorial KW that was part of an MJO event that occurred during the DYNAMO field phase in late November 2011 (Johnson and Ciesielski 2013; Moum et al. 2014; Gottschalck et al. 2013; Xu and Rutledge 2014). Adjoint sensitivity is calculated using response functions centered on TC05 and its precursor circulation, and the enhanced low-level westerlies associated with the concurrent KW, for 18-h forecasts started every 6 h, from 0000 UTC 23 November to 1800 UTC 26 November 2011.

The vertically integrated sensitivity patterns (Figs. 3 and 4) indicate that both the TC and the KW low-level westerlies always exhibit local sensitivity. This means that, as expected, the 18-h forecast of TC05 or the KW is sensitive to changes in the initial state in the immediate vicinity of the TC or the KW. In addition to the local sensitivity, the results here clearly establish that the evolution of one is sensitive to the evolution of the other, particularly when the KW westerlies are southwest and south of TC05. After TC05 moves into the Arabian Sea and the KW moves into the eastern Indian Ocean, TC05 is no longer sensitive to the KW (although there is evidence that TC05 is sensitive to low-level westerlies associated with a second KW while it is in the Arabian Sea). The KW westerlies remain sensitive to TC05 until it reaches the far eastern Indian Ocean. While the local sensitivity is usually substantially larger than the remote sensitivity, there are cases where the remote and local sensitivities are of comparable magnitude (e.g., the KW sensitivity from 1200 UTC 23 November). These results support previous studies that find that atmospheric KWs can promote TC genesis (e.g., Roundy 2008; Schreck and Molinari 2011; Ventrice et al. 2012b; Schreck 2015) as well as the findings of Sobel and Camargo (2005) that suggest TCs may project onto atmospheric KWs.

Vertical profiles of TC and KW sensitivity (Fig. 5) indicate that both phenomena are most sensitive to initial perturbations in the mid- to lower troposphere. On average, the magnitude of the TC05 sensitivity is about 20% larger than the magnitude of the KW sensitivity, indicating that the KW forecast would be somewhat less sensitive to initial errors than TC forecasts, at least for the examples considered here. The sensitivity of both TC05 and the KW westerlies are largest when the KW westerlies are southwest and south of the TC, indicating that the period before and during the closest proximity of the two systems is less predictable than the following period. Examination of the sensitivity for 36-h forecasts (Fig. 7) suggests that more remote connections between the KW and the TC exist on longer time scales, but care must be taken when interpreting these results, given the limitations of the tangent linear assumption.

A case study during this sensitive period (Figs. 813) demonstrates how very small initial perturbations in the mid- to lower troposphere can evolve rapidly to become deep perturbations that strengthen both the low-level westerlies of the KW and the TC. In addition to a direct enhancement of the low-level westerlies associated with the KW (Fig. 8), initial-time low-level positive moisture and temperature perturbations in the convergence region of the KW decrease static stability, and thereby, increase deep convection and enhance lower-tropospheric convergence and upper-tropospheric divergence (Fig. 9). These perturbations strengthen the developing TC05 through enhancement, in particular, of the westerlies along the south side of the storm that coincide with the KW westerlies (Fig. 10). Vertical profiles of the evolving optimal perturbations indicate that the vertical structures for the KW and TC05-based perturbations are quite similar, although the KW growth rate is smaller, and the evolved KW perturbation does not contain the substantial midtropospheric moisture signature apparent in the TC05 evolved perturbation (Fig. 11). Examination of the evolution of the moist-only and dry-only initial perturbations (Fig. 13) indicates that the moist component is mostly responsible for the initial rapid growth, but that subsequent growth rates are similar. The fixed SST growth rate is actually larger than the initial perturbation growth rate and points to the potential influence of SST uncertainty on forecast errors.

This study has successfully established that forecasts of the KW and TC that occurred in late November 2011 are sensitive to each other when the KW low-level westerlies are southwest and south of the TC. It has also established that the sensitivity of both phenomena peak during this period of interaction, indicative of heightened potential for initial error growth. However, it remains uncertain how general these sensitivity patterns may be for other cases. Studies that consider more cases, as well as studies focusing on other types of tropical waves, would help further establish these relationships. It would also be interesting to consider simulations at finer resolution, although the commensurate decrease in optimization time to satisfy the linear constraints of the adjoint tools may limit understanding of remote influences.

Acknowledgments

This research is supported by Office of Naval Research through the Departmental Research Initiative Predictability of Seasonal and Intraseasonal Oscillations and the Chief of Naval Research through the NRL Base Program, PE 0601153N. Computational resources were supported in part by a grant of HPC time from the Department of Defense Major Shared Resource Centers, Stennis Space Center, Mississippi. We acknowledge Dr. Clark Amerault for the development of the COAMPS TLM and Adjoint system. We acknowledge the comments of two anonymous reviewers, which helped us to improve the manuscript.

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