1. Introduction
Previous studies of the relative importance of synoptic-scale features and processes to tropical cyclone (TC) steering in a numerical weather prediction (NWP) model have used adjoint models to calculate singular vectors, which determine regions where perturbations will grow most rapidly (Langland 2005; Buizza et al. 2007; Cardinalli et al. 2007; Peng and Reynolds 2006; Chen et al. 2009). A more useful application of adjoint models to dynamical sensitivity analysis of TC steering is the calculation of sensitivity of TC steering itself, which requires a response function that describes the steering of the TC. Dynamical sensitivity gradients of TC steering with respect to model initial conditions provide valuable a priori information about where perturbations to the initial conditions of an NWP model will have the strongest effect on TC steering specifically. In addition, the inner product of the sensitivity gradient and any hypothetical perturbation to the initial conditions provides an estimate for how large an impact on TC steering can be expected.
Tropical cyclone motion is primarily caused by advection of the TC by the flow of the surrounding environment (Chan and Gray 1982; Flatau et al. 1994; Chan 2005). While mechanisms exist that cause the TC to move independent of this environmental “steering flow” (Fiornio and Elsberry 1989; Carr and Elsberry 1990; Wu and Emanuel 1993), the steering of the TC by its environment is the dominant contribution, especially for steady TC motion (Chan et al. 2002). Moreover, ambiguities exist in the designation of what constitutes the “environment” of a TC that makes its definition nonunique (Flatau et al. 1994). The relationship of a TC with respect to a complexly evolving environment and how the environment steers the TC has been a subject of modeling research for many years (e.g., Holland 1983; Shapiro 1992; Wu and Wang 2000; Chan et al. 2002).
By providing high-resolution, four-dimensional, nearly dynamically consistent datasets, NWP model simulations can provide insight into the relative importance (steering wise) of various synoptic-scale features in the environment of the TC. To this end, much of the research using NWP models comes in the form of impact studies, which involve comparing a simulation in which the initial conditions have been perturbed to a “control” run in order to diagnose the importance of specific weather phenomena on a verifying forecast. These impact studies can usually be phrased as “what if?” experiments, such as “what if the potential vorticity (PV) of an upper trough (Fehlmann and Davies 1997) or a tropical cyclone (McTaggart-Cowan et al. 2004) were removed or altered in the initial model state?” Often these impact studies are characterized as a more robust “sensitivity study” by perturbing the initial conditions in multiple ways in order to keep the results from seeming anecdotal. The major drawback of this methodology is that it is usually not known a priori what kinds of perturbations will have the most impact; as a result, the study must include many perturbations to many variables in many locations in order to be considered a sensitivity study—an expensive proposition both in terms of time and computational resources.
Alternatively, robust sensitivity analysis can be performed with the adjoint of a NWP model. The adjoint of an NWP model is the transpose of the tangent-linear model, linearized about a full-physics, nonlinear trajectory from the NWP model. A sensitivity study can be performed by defining some specific aspect of the forecast as a response function [R(xf)], which must be first-order differentiable with respect to the model forecast verification state (xf). The gradient of R with respect to the model forecast verification state is integrated backward through time using the adjoint model to compute the gradient of that same response function (still defined at forecast verification) with respect to the model state at earlier times. Most often, these gradients are computed with respect to the model initial conditions; with these “sensitivity gradients,” the adjoint model provides an economical means by which to determine how small perturbations to the initial conditions would impact the chosen response function (Errico 1997).
While these sensitivity gradients have practical application to tasks such as four-dimensional variational data assimilation (Lewis and Derber 1985), adjoint models provide valuable a priori information about the dynamical sensitivity of any aspect of the model verification state with respect to past states that is difficult or impossible to derive otherwise. Attempts have been made to reconcile calculated sensitivity gradients with the large-scale dynamics of the model simulation (Langland et al. 1995; Kleist and Morgan 2005), and several studies have used adjoint models alongside NWP models to evaluate the relative importance of synoptic-scale features in the basic state to the development of extratropical cyclones (Vukicevic and Raeder 1995; Langland et al. 1995).
While some work has been done to produce sensitivity gradients of TC steering (Wu et al. 2007, 2009a), the methodology employed has suffered due to lack of rigorous testing and dynamical interpretation of the resultant sensitivity gradients (Hoover 2009; Hoover and Morgan 2010); it is important to keep in mind that sensitivity gradients provide information on how changes to the initial conditions will result in changes to the response function, and the results cannot be used explicitly to determine if a particular aspect of the initial conditions contributes most to the response function in the basic state (Langland et al. 1995; Langland and Errico 1996).
This study focuses on dynamical interpretation of adjoint-derived sensitivity gradients for the steering of simulated TCs. Small perturbations to the initial conditions of an NWP model can change the evolution of the TC environment, having a substantial impact on how the environment steers the TC. An NWP model and its adjoint are employed to analyze the sensitivity of the steering of a TC to the initial conditions from this perspective. Several cases of west Pacific TCs in a variety of environments are employed to produce some generalized evaluations of the synoptic features in the environment to which TC steering is most sensitive.
Section 2 provides a description of the model and cases used in the study. A description of the methodology is provided in section 3. An analysis of sensitivity gradients is provided and tested in section 4. Directions for future study are provided in section 5.
2. Model simulations
a. The model
We employ the Navy Operational Global Atmospheric Prediction System (NOGAPS) global spectral model (Hogan and Rosmond 1991; Rosmond et al. 2002) at T159 resolution and 30 vertical (sigma) levels to establish the basic state around which the NOGAPS adjoint model (Rosmond 1997) is linearized. The adjoint model is initialized with sensitivity gradients given a response function defined as a measure of the environmental flow that steers the TC (see section 3) and run at the same resolution.
The NOGAPS model was chosen for several reasons. The study of synoptic-scale influences on TC steering necessarily means we are focusing on large-scale, even global-scale, features. The use of a global spectral model eliminates the influence of boundary conditions that could plague a regional gridpoint model. Many adjoint models do not make use of moisture-physics schemes used in the nonlinear, full-physics NWP model, because the adjoint of these routines is difficult to produce (Errico 1997); however, the NOGAPS adjoint model employs the physics schemes responsible for large-scale precipitation. This feature, combined with the information concerning moisture physics provided by the full-physics basic state (Kleist and Morgan 2005), makes the NOGAPS adjoint model attractive for sensitivity studies focusing on tropical environments.
b. Cases
Four cases of west Pacific TCs were chosen, which describe a variety of environments and synoptic-scale interactions that produce widely varying TC tracks. The cases can be separated into three categories. Simulations of Typhoon Meari (2004) and Typhoon Choi-Wan (2009) describe environments under which the TC experiences significant recurvature, with meridional or nearly meridional tracks caused by interaction with a midlatitude trough. A simulation of Typhoon Longwang (2005), on the other hand, provides a case of a steady, zonal track. Finally, a simulation of Typhoon Parma (2009) provides a peculiar case wherein the TC remains essentially motionless for 108 h; this case also appears to include a binary interaction between Typhoon Parma and Typhoon Melor to its east.
For each case, a 36-h simulation is performed with the NOGAPS model, and sensitivity gradients are integrated backward 36 h to model initialization. The 108-h simulation of Typhoon Parma (2009) is cut into three 36-h sections, and sensitivity gradients are calculated for steering of the TC at the end of each section with respect to the model state at the beginning of each section. Table 1 is a list of the beginning and ending times for each model simulation. The model is initialized with 1° × 1° Fleet Numerical Meteorological and Oceanographic Center (FNMOC) analyses. [Data for this project are from the FNMOC and the U. S. Global Data Assimilation Experiment (USGODAE) and are available online at http://www.usgodae.org/ftp/outgoing/fnmoc/models/nogaps.]
Beginning and ending time for each 36-h simulation. The 108-h simulation of Typhoon Parma (2009) is divided into three 36-h sections for the purposes of calculating TC steering sensitivities for the end of each 36-h section.
3. Methodology
A modified version of the adjoint-derived sensitivity steering vector (ADSSV; Wu et al. 2007, 2009a,b) technique is employed to determine how small perturbations to the initial conditions of the model simulation will impact the steering of the TC 36 h in the future. We wish to isolate the asymmetric flow over the TC attributed to the environment that steers the TC; this is usually done by averaging the horizontal winds over some horizontal domain centered on the TC and over some vertical depth (Chan and Gray 1982; Velden and Leslie 1991) to remove the symmetric circulation of the TC, leaving the residual to constitute the “environmental flow.” However, since the adjoint model can only determine how changes to the initial conditions will produce changes to the response function, and the average flow in this domain can be greatly changed by perturbing the model so as to cause a (small) displacement of the TC from the center of the domain, this technique will not adequately produce sensitivities to TC steering by the environment (Hoover 2009).
4. Analysis
a. Typhoon Meari (2004): Typhoon–midlatitude trough interaction
Figure 1a is a plot of the position of Typhoon Meari (2004) every 6 h in a 36-h NOGAPS simulation initialized at 0000 UTC 24 September 2004, with the NHC best-track analysis overlaid. The model appears to capture the direction and speed of Meari quite accurately, maintaining a track that takes Meari northwest toward mainland China. The reason for the recurvature is clear; Meari appears to be steered by a midlatitude trough just upstream and a weak subtropical high to the east for the entirety of the model simulation (Figs. 1b–d).
(a) Track of Typhoon Meari (2004) in 36-h simulation initialized at 0000 UTC 24 Sep 2004. Black dots indicate the location of minimum sea level pressure every 6 h. White dots indicate TC location according to NHC best-track analysis. Geopotential height (black contours every 30 m) and absolute vorticity (shaded every 5 × 10−5 s−1) at 500 hPa at (b) model initialization, (c) 18 h, and (d) 36 h.
Citation: Monthly Weather Review 139, 9; 10.1175/MWR-D-10-05084.1
Sensitivities are computed with respect to vorticity; Fig. 2 is a plot of 
Sensitivity of steering of Typhoon Meari (2004) with respect to vorticity at the 0.2740σ level, corresponding roughly to the 300-hPa level assuming a sea level pressure of 1000 hPa. (a) Sensitivity of the zonal component of steering with respect to vorticity (shaded, cool colors negative), and basic-state vorticity (black contours every 4 × 10−5 s−1, negative contours dashed) in the forecast with unperturbed initial conditions. (b) Sensitivity of the meridional component of steering with respect to vorticity. (c) ADSSV representing the magnitude and direction of perturbation steering with respect to vorticity. All sensitivities are computed for steering by the environmental flow in a response function box (red) 36 h into the model simulation.
Citation: Monthly Weather Review 139, 9; 10.1175/MWR-D-10-05084.1
A very strong region of sensitivity of meridional steering is found west of the TC, upstream of the midlatitude trough (Fig. 2b). In fact, the vorticity ADSSV appears to be strong in this region (Fig. 2c), indicating that a small perturbation to the vorticity in this region would have a large impact on the steering of the TC; in this case, a positive (negative) perturbation would add a southerly (northerly) component to the steering of the TC 36 h in the future.
Similar results were found by Wu et al. (2009a) when using their ADSSV technique to investigate the role of TC–trough interaction with Typhoon Shanshan (2006). While it was intimated in that study that the coincidence of these features indicates that the midlatitude trough is of great importance to the steering of Shanshan, it is important to remember what these sensitivity gradients actually mean. Sensitivity gradients valid at model initialization only describe how the response function will change as a result of perturbations added to a model’s initial conditions. While it may be seductive to conclude a synoptic-scale feature must be important to the steering in the basic state because of the coincidence of that feature (such as the vorticity of the midlatitude trough) and sensitivity of steering to vorticity, this is not necessarily the case. A feature of the basic state may be in a region of high sensitivity that would exist in that location whether that particular feature of the basic state were present or not; Langland et al. (1995) found that sensitivity of cyclone intensity to temperature in an idealized channel model appeared very similar regardless of whether a cyclone actually developed in the basic state. It should also be noted that while the sensitivity is near the trough, and may be within the trough when looking at geopotential height, the sensitivity is actually slightly upstream of the vorticity of the trough.
The sensitivity in this region may in fact correspond to important interactions between Meari and the midlatitude trough. Alternatively, the sensitivity may be due to some other process that takes place near the trough but is not directly related to the strength of the trough. The only way to be sure is to perturb the vorticity in the initial conditions and observe the result. Small perturbations to the vorticity in the initial conditions where the sensitivity is positive in this region show an interesting result (Fig. 3). The initial perturbation vorticity (Fig. 3a) is advected downstream and is stretched when it enters the subsidence in the lee of the midlatitude trough (Fig. 4), creating a strong vortex that appears just west of the response function box at model verification (Fig. 3b).
Perturbation experiment for Typhoon Meari (2004) simulation. (a) Initial condition perturbation vorticity (shaded every 5 × 10−6 s−1, cool colors negative), perturbation winds, and basic-state geopotential height (black contours every 45 m) and basic-state isotachs (magenta contours every 12 m s−1 ≥24 m s−1) at 300 hPa. (b) 36-h perturbation vorticity (shaded every 1 × 10−5 s−1), perturbation winds, and basic-state heights and isotachs at 300 hPa. (c) 36-h perturbation environmental winds, streamfunction (shaded), and basic-state geopotential height and isotachs. (d) Cross section from A to B of perturbation environmental vorticity (contour every 1 × 10−5 s−1, negative contours dashed) and perturbation environmental meridional flow (shaded every 0.5 m s−1). The red boxes correspond to the response function box location.
Citation: Monthly Weather Review 139, 9; 10.1175/MWR-D-10-05084.1
Perturbation experiment for Typhoon Meari (2004) simulation. (a) Perturbation vorticity (shaded every 2 × 10−5 s−1), basic-state vertical motion (solid contours every 0.5 μbar s−1, and basic-state convergence (dashed contours every 1 × 10−5 s−1) at 300 hPa valid 24 h into the simulation. (b) Cross section from A to B of perturbation vorticity (shaded every 2 × 10−5 s−1), basic-state vertical motion (solid contours every 0.5 μbar s−1, and basic-state convergence (dashed contours every 1 × 10−5 s−1) valid 24 h into the simulation.
Citation: Monthly Weather Review 139, 9; 10.1175/MWR-D-10-05084.1
If one were to compute the vorticity and divergence of the environment and invert it to recover the environmental flow, a vortex appears just west of the response function box, inducing a strong southerly component to the environmental flow in the box (Fig. 3c). A cross section through the box (Fig. 3d) shows that this positive contribution to the meridional steering extends from the midtroposphere to the top of the response function box.
b. Typhoon Choi-Wan (2009): Typhoon–midlatitude trough interaction
The interaction of Typhoon Choi-Wan (2009) with a midlatitude trough creates a recurving track that steers the TC northward to northeastward for the entire simulation; the track and speed of motion are well represented by the model (Fig. 5a). Choi-Wan has a synoptic environment very similar to Meari, with a midlatitude trough initialized north and upstream of the TC, and a subtropical ridge to the east at 0000 UTC 18 September 2009 (Fig. 5b). Unlike with Meari, the midlatitude trough largely stays north of the TC for the entire simulation, with very little direct contact with the TC itself (Figs. 5c,d). The subtropical ridge is stronger in this case, steering the TC northward and eventually eastward as the TC enters midlatitude westerly flow. An examination of ADSSVs for the Choi-Wan case is provided in order to verify the conclusions drawn from the Meari case (e.g., one would expect that the similar set of circumstances in the basic state found in the Choi-Wan simulation should yield similar results in sensitivity), as well as investigate if any of the subtle differences between these cases yields any significant differences in sensitivity.
As in Fig. 1, but for Typhoon Choi-Wan (2009) initialized at 0000 UTC 18 Sep 2009.
Citation: Monthly Weather Review 139, 9; 10.1175/MWR-D-10-05084.1
Sensitivity of steering with respect to vorticity near tropopause level (Fig. 6) reveals similar characteristics to those found for Meari. Although 
As in Fig. 2, but for Typhoon Choi-Wan (2009).
Citation: Monthly Weather Review 139, 9; 10.1175/MWR-D-10-05084.1
c. Typhoon Longwang (2005): Steady zonal track
Typhoon Longwang (2005) is provided as an example of a TC that undergoes steady, zonal steering for the entirety of the simulation (Fig. 7a). Steered primarily by a dominating subtropical ridge to the north (Figs. 7b–d), the ridge prevents Longwang from experiencing any meaningful interaction with passing midlatitude systems. We therefore may expect that sensitivities to steering may be of smaller magnitude, and localized to the immediate environment of the TC and the subtropical ridge. One can imagine that any small perturbation to the vorticity upstream of the TC would be caught up in the westerly flow of the midlatitudes, be carried north of the subtropical ridge, and have little if any impact on the steering of Longwang.
As in Fig. 1, but for Typhoon Longwang (2005) initialized at 0000 UTC 30 Sep 2005.
Citation: Monthly Weather Review 139, 9; 10.1175/MWR-D-10-05084.1
Steering sensitivity near the tropopause level appears to have all of these qualities (Fig. 8). Zonal steering sensitivity (Fig. 8a) shares many characteristics of zonal steering sensitivity for the case of an idealized, barotropic vortex (Hoover and Morgan 2010) embedded in a mean easterly steering flow. Maximum positive (negative) sensitivity appears northeast (southwest) of the TC, localized near the TC, where vorticity perturbations of the same polarity can be advected to be situated just north (south) of the response function box and provide a westerly environmental current. Strong negative sensitivity also appears within and south of the subtropical ridge. ADSSV outside of this small, localized region is very weak (Fig. 8c).
As in Fig. 2, but for Typhoon Longwang (2005).
Citation: Monthly Weather Review 139, 9; 10.1175/MWR-D-10-05084.1
d. Typhoon Parma (2009): No TC motion–binary interaction
Typhoon Parma (2009) is an abnormal case wherein the TC began a southeasterly track across the northern Philippines, but quickly stalled and remained essentially stationary for several days (Fig. 9a). Flanked on either side by a ridge, there is little in Parma’s environment to advect the cyclone away from this position (Fig. 9b). While a passing midlatitude trough could provide a means to force Parma to recurve and move northeastward, Parma also appears to interact with Typhoon Melor (2009) as the two cyclones move closer to each other between 36 and 72 h into the 108-h simulation (Figs. 9d–f), which would induce a binary interaction opposing the advection of Parma by the midlatitude trough. As Melor recurves and moves into the midlatitudes (Figs. 9g,h), Parma again finds itself between two ridges and does not move from its position.
(a) Track of Typhoon Parma (2009) in 108-h simulation initialized at 1200 UTC 2 Oct 2009. Black dots indicate the location of minimum sea level pressure every 6 h. White dots indicate TC location according to NHC best-track analysis. Geopotential height (black contours every 30 m) and absolute vorticity (shaded every 5 × 10−5 s−1) at 500 hPa at (b) model initialization, (c) 18, (d) 36, (e) 54, (f) 72, (g) 90, and (h) 108 h.
Citation: Monthly Weather Review 139, 9; 10.1175/MWR-D-10-05084.1
The 108-h basic-state trajectory provided by the NOGAPS model is divided into three 36-h-long pieces, and a sensitivity analysis is performed for the steering at the end of each piece (36, 72, and 108 h, respectively) with respect to model conditions 36 h previous (model initialization, 36 h, and 72 h, respectively). This is done for two reasons. First, a 108-h trajectory is far too long to allow for the assumption of linearity required to use the adjoint model, while small perturbations can behave linearly in a moist, nonlinear NWP model simulation for upward of 36 h (Errico and Vukicevic 1992). Second, Parma appears to experience three environmental regimes throughout the 108-h simulation: an initial stall after moving to the northwest over the northern Philippines (0–36 h), binary interaction with Typhoon Melor (36–72 h), and post-interaction with Melor (72–108 h). Evaluating the sensitivity of the steering of Parma at these different times provides a survey of information about the relative influence of the major synoptic features near Parma on TC steering for the entirety of the 108-h simulation.
A comparison of ADSSV in the midtroposphere at these three times (Fig. 10) shows the relative sensitivity of Parma to the vorticity of Melor, the midlatitude trough, and the two flanking ridges throughout the simulation. Note that ADSSV in the first two time periods (Figs. 10a,b) diverge over Melor, with northerly ADSSV south of Melor and southerly ADSSV to the north. From this it can be deduced that small perturbations in vorticity around Melor (or the position of Melor itself, which would manifest as a dipole of perturbation vorticity) have a substantial impact on the meridional portion of Parma’s steering, with the strongest sensitivities appearing for steering at 72 h into the simulation (when Melor and Parma are closest to one another and the binary interaction is likely strongest).
Vorticity ADSSV at the 0.4718σ level, corresponding roughly to the 500-hPa level. Basic-state vorticity contoured every 4 × 10−5 s−1 (negative contours dashed). The red box is the location of the response function. Computed for a 108-h simulation of Typhoon Parma (2009) initialized at 1200 UTC 2 Oct 2009 and valid at (a) model initialization, (b) 36 h, and (c) 72 h corresponding to sensitivities derived for the steering of the TC 36 h in the future.
Citation: Monthly Weather Review 139, 9; 10.1175/MWR-D-10-05084.1
The physical interpretation of these ADSSV is relatively simple. Parma and Melor exist at or very nearly at the same latitude; any contribution to Parma’s steering through a binary interaction with Melor will therefore be in the (negative) meridional direction. A southerly component, for example, can be induced by placing a positive (negative) vorticity perturbation north (south) of Melor 36 h earlier (Fig. 10b). The effect of these perturbations would be to induce westerly flow over Melor, increasing the distance between Parma and Melor, and therefore decreasing the strength of their binary interaction. Since Parma is positioned west of Melor, this would decrease the strength of the northerly winds from Melor that would steer Parma, resulting in a positive perturbation to the meridional steering of Parma relative to the unperturbed (control) run. These ADSSVs suggest that the zonal steering of Melor modulates the meridional steering of Parma at this time. ADSSVs from the 36-h period before (Fig. 10a) or after (Fig. 10c) show that the steering of Parma is not as sensitive to this effect during these times and sensitivities are localized about Parma or upstream of the TC.
e. Comparisons
ADSSVs of Meari (2004) and Choi-Wan (2009) in the midtroposphere (Fig. 11) provide another perspective. Large differences between ADSSV for Typhoon Meari (2004) (Fig. 11a) and Typhoon Choi-Wan (2009) (Fig. 11b) are observed, despite the similarities in track and environment. While the upstream trough is clearly visible in both plots, it appears to only be barely significant to the steering of Meari at this level, while for Choi-Wan the strongest sensitivity again exists just in the lee of the trough. Significant subsidence exists upstream of the trough in both simulations.
As in Fig. 10, but valid at model initialization for 36 h simulations of (a) Typhoon Meari (2004) initialized at 0000 UTC 24 Sep 2004 and (b) Typhoon Choi-Wan (2009) initialized at 0000 UTC 18 Sep 2009.
Citation: Monthly Weather Review 139, 9; 10.1175/MWR-D-10-05084.1
The difference may have to do with the location of the trough. In the Meari simulation, the trough interacts directly with Meari, and even at model initialization, the vorticity of the trough is well within the response function box. The trough in the Choi-Wan simulation, on the other hand, is outside of the response function box. Recall that the response function presupposes that vorticity within the response function box is considered vorticity associated with the TC. This vorticity is removed when calculating the vorticity of the environment. Any perturbation just in the lee of the trough in the initial conditions of the Meari simulation would most likely end up in the response function box by model verification and have no impact. Perturbations placed in the lee of the trough in the Choi-Wan simulation do not experience this effect.
What is being observed is an effective “blind spot” in the sensitivities that arises as a result of how the response function is defined. Sensitivities are also likely to vary depending on the size of the response function box because perturbations that yield the largest effect on steering will most likely create perturbation vortices that exist just outside of the response function box at model verification, where they can impose the maximum amount of influence on the flow in the box. Repeating the calculation of sensitivities for Meari (2004) using an 11° × 11° box results in a slight eastward shift in the meridional steering sensitivity with respect to vorticity, putting it just to the west of the midlatitude trough (not shown).
5. Conclusions
Through careful choice of response functions representing the steering of a TC, adjoint models can provide valuable a priori information about the sensitivity of TC steering to features in all previous model states. While these sensitivity gradients cannot explicitly determine the importance of a particular feature of the model state in terms of its contribution to the response function in the basic state, sensitivity information provides insight into how small perturbations of the model state will change the response function, and which features of the basic-state perturbations would be of greatest import.
It is found in this study that the ADSSV technique is able to effectively describe the speed and direction change of TC steering given perturbations of vorticity in the initial conditions over a trajectory length of 36 h. Furthermore, a dynamical interpretation of these sensitivities is possible; the rule established by Langland et al. (1995) can be applied here: features of the basic state are “important” if they are found in regions of strong sensitivity to the model state x and are responsible for large time tendencies of the model state. In this study, the subsidence region in the lee of a passing midlatitude trough is found to be a region of significant sensitivity with respect to vorticity. In addition, it is found that the reason for this sensitivity is the ability for a small vorticity perturbation to be stretched by the subsidence, leading to a large growth of the perturbation vortex over time. We can therefore employ this rule to identify this subsidence region as an important feature of the basic state to the steering of a TC. Likewise, the ADSSV technique is able to distinguish when a binary interaction is significant in a simulation of Typhoon Parma (2009) and Typhoon Melor (2009).
The most practical application of this technique is in the deployment of targeted observations for the explicit purpose of improving TC track prediction. Owing to the dearth of in situ observations of TCs and their surrounding environment, NWP forecasts of TC track suffer from poorly defined initial conditions with large uncertainties. Track errors can be mitigated by deployment of targeted observations in the TC’s environment to reduce error in the initial conditions near the TC (Aberson 2003). However, lacking any a priori information concerning the potential impact of an observation on TC steering, it is not clear where these observations should be taken. The addition of good observational data into the model’s initial conditions would not necessarily lead to a significant forecast improvement if those observations were taken in the wrong places (Aberson 2002), or improperly assimilated. A strategy for defining optimal targets for observation is required to ensure that the effort and expense in obtaining these observational data improves the TC forecast in a significant way.
Adjoint-derived sensitivity gradients clearly show where small perturbations to the model initial conditions can have the largest impact on the steering of the TC; this information is vital if one wishes to objectively deploy observations that have the (desired) effect of making small but meaningful innovations (meaningful from the perspective of TC track forecasting) to a model background state. While this sensitivity information says nothing about the uncertainty in the model background state, which clearly modulates the impact of deployed observations (Buizza et al. 2007), that information can be provided through the application of the adjoint of the observation assimilation system, a method known as “observation-space targeting” (Langland 2005), which also provides valuable information on the impact of a single observation based on how the information from that observation is assimilated into the initial conditions (Langland and Baker 2004).
Starting with the firm foundation established in this study, it is hoped that dynamical sensitivity information provided by the adjoint of an NWP model can be combined with information about initial condition uncertainty and the assimilation of observational data provided by the adjoint of an assimilation system to provide a fully comprehensive, more objective targeting strategy for the improvement of TC track prediction. Furthermore, response functions can be developed for the purpose of defining sensitivities for a variety of other forecast challenges, such as TC intensity prediction. The development of such a technique would provide an objective, robust method for defining flight plans and target locations for reconnaissance aircraft, as well as valuable dynamical information for researchers and forecasters who wish to better understand the physical processes at work in TC steering and intensity change.
Acknowledgments
The authors wish to thank Dr. Rolf Langland at the Naval Research Laboratory for his help with the NOGAPS model and its adjoint. The first author is supported by the Office of Naval Research under Grants N000141610563 and N000141110609. Additional funding was supplied by the National Science Foundation under Grant 0950349.
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Initial-time ADSSV are computed at each grid point for each variable; the ADSSV of a particular variable (e.g., temperature) at a point intends to describe the vector change in steering a TC will experience at the time the steering response function is defined given a unit perturbation to that variable in the initial state. The total vector change is represented by the inner product of the sensitivity with the total initial-time perturbation across all variables and grid points: 
