1. Introduction
The extratropical transition (ET) of a warm-core tropical cyclone (TC) into a cold-core baroclinic system is often associated with large forecast errors produced by numerical weather prediction (NWP) models. For example, Jones et al. (2003) showed that Navy Operational Global Atmospheric Prediction System (NOGAPS) forecasts during August 1996 were characterized by lower 500-hPa geopotential height anomaly correlation scores when three TCs underwent transition. During each ET event, 72-h forecasts initialized at the onset of transition were no more skillful than climatology. By comparing the forecast with the verifying-time analysis, Jones et al. (2003) determined that the large forecast errors were related to the position of major midlatitude circulation features, including upper-tropospheric troughs that interacted with the TC during transition. Similarly, Ma et al. (2003) found that the Canadian Meteorological Center’s ensemble forecast skill during ET events is proportional to the quality of the upstream midlatitude analysis. These results reflect the importance of the midlatitude troughs in the reintensification of the TC as a baroclinic storm (e.g., Harr and Elsberry 2000). Furthermore, Harr et al. (2008) and Anwender et al. (2008) found that much of the variability associated with ensemble forecasts of ET can be explained by a few synoptic patterns.
Errors in ET forecasts also relate to the structure of the transitioning TC in the initial conditions. Evans et al. (2006) applied the cyclone phase-space diagram of Hart (2003) to evaluate the National Centers for Environmental Prediction (NCEP) Global Forecasting System (GFS) and NOGAPS forecasts of TCs before, during, and after transition. Their results indicate that forecasts initialized at the onset of transition (defined by cyclone phase space coordinates) have the largest errors, which they attribute to deficiencies in the analysis of the transitioning TC. Because of inadequacies in quasi-fixed error covariance models, operational forecast models often perform data assimilation in the vicinity of a TC via vortex bogusing (e.g., Kurihara et al. 1995) or vortex repositioning (e.g., Liu et al. 2000). These schemes assume an axisymmetric vortex, which is not appropriate for ET because of developing asymmetries in wind and temperature.
One method of improving ET forecasts involves evaluating the relationship between initial condition errors and a forecast metric through sensitivity analysis. Browning et al. (2000) computed singular vectors for the midlatitude cyclone that resulted from Hurricane Lili’s (1996) extratropical transition. The leading initial time singular vectors that maximize growth in total energy had the largest magnitude near two tropopause-based disturbances that subsequently interacted with the remnant TC. Shifting the initial position of one upper-level trough, in a manner consistent with the initial time singular vectors, improved both the cyclone track and minimum sea level pressure (SLP) forecasts. Rabier et al. (1996) explored initial condition sensitivity for several high-impact events in Europe, including the extratropical cyclone resulting from the ET of Hurricane Floyd (1993) using singular vector analysis. For this storm, the largest growth in squared energy was associated with the upstream flow and a precursor low-level circulation in the Atlantic Ocean. While these studies addressed mainly the latter stages of ET, the goals here are to understand the initial condition sensitivity of ET forecasts at the onset of transition and the impact of observations on ET predictability.
Ensemble-based sensitivity (Ancell and Hakim 2007; Hakim and Torn 2008) is employed here to evaluate the predictability of two western Pacific tropical cyclones undergoing ET. This technique uses an ensemble of equally likely analyses and forecasts produced by an ensemble Kalman filter (EnKF) to compute statistical estimates of initial condition sensitivity and observation impact. The flow-dependent error statistics used by the EnKF may be particularly useful for ET forecasts because transition often occurs in regions of sparse in situ data and is characterized by rapidly evolving dynamics. Moreover, the EnKF produces an ensemble of equally likely analyses that are available for ensemble forecasting, without resorting to methods that perturb deterministic analyses, which may suffer from a lack of variance near the TC (e.g., Anwender et al. 2006).
This paper proceeds as follows. Section 2 provides details on the model and data assimilation method. An overview of the two ET cases and the skill of the ensemble forecasts are presented in section 3. Sections 4 and 5 describe the sensitivity of the transitioning TC forecasts to the initial conditions and the impact of diagnostic corrections to the initial conditions on forecasts, respectively. The impact of observations on the ET forecast is shown in section 6. A concluding summary is given in section 7.
2. Experiment setup
Two extratropical transition cases are selected for investigation based on the performance of operational models: one where baroclinic reintensification was poorly predicted and characterized by greater variability in ensemble forecasts, Typhoon Tokage (2004), and one where the baroclinic development was well forecast and characterized by smaller variability in ensemble forecasts, Typhoon Nabi (2005). Analyses are produced every 6 h by cycling an EnKF system on a 45-km grid that includes eastern Asia and the western Pacific Ocean. Table 1 gives the observation cycling period for each case, while Fig. 1 shows the computational domain. The analysis ensemble is advanced in time using version 2.1 of the Advanced Research (ARW) version of the Weather Research and Forecasting (WRF) model, with the WRF three-class microphysics scheme (Hong et al. 2004), the Kain–Fritsch cumulus parameterization scheme (Kain and Fritsch 1990), the Yonsei University (YSU) boundary layer scheme (Hong et al. 2006), and the Noah land surface model (Ek et al. 2003).
Lateral boundary conditions for each ensemble member are obtained using the fixed covariance perturbation technique of Torn et al. (2006). This technique generates independent ensemble boundary condition perturbations for 6-h forecasts by adding random draws from a fixed covariance model [WRF VAR; Barker et al. 2004] to the 6-h NCEP GFS forecast initialized at the same time. These perturbations are scaled by 1.7, which gives ensemble variance that is consistent with errors in the GFS 6-h forecast. Moreover, the perturbations are constructed to have a temporal autocorrelation of 0.4, which is roughly consistent with the observed value for this location.
Observations are assimilated every 6 h from automated surface stations, ships, fixed and drifting buoys, rawinsondes, the Aircraft Communications Addressing and Reporting System (ACARS), and cloud motion vectors (Velden et al. 2005) serially using a square root version of the EnKF (Whitaker and Hamill 2002) for a 90-member ensemble. Observation errors are assumed to be uncorrelated and are obtained from European Centre for Medium-Range Weather Forecasts (ECMWF) statistics. In addition to conventional observations, tropical cyclone best-track latitude and longitude from the Joint Typhoon Warning Center (JTWC) are assimilated in a manner similar to Chen and Snyder (2007). Since the western Pacific is characterized by few in situ observations, assimilating TC position data ensures that the TC is in a reasonable location.
Small ensembles, such as the one used here, often contain spurious long-distance covariances and underestimate covariance magnitudes (e.g., Houtekamer and Mitchell 1998; Anderson and Anderson 1999). Two conventional techniques are employed to address problems due to sampling statistics from a small ensemble. First, the influence of observations is limited in the horizontal direction by a localization function [Gaspari and Cohn 1999, their Eq. (4.10)], where the covariance magnitude reduces to zero 2500 km from the observation; vertical localization is not used. Second, to ensure that the ensemble does not lose variance over time, deviations from the ensemble mean at each analysis time are inflated by averaging the prior and posterior deviations from the ensemble mean with a 0.75 and 0.25 weighting, respectively (Zhang et al. 2004). These weighting factors are determined by cycling the EnKF system during Tokage’s transition and comparing the mean-squared error in ensemble-mean 6-h forecasts (computed with respect to rawinsondes) against the innovation variance; these two quantities are equal for a well-calibrated ensemble system (Houtekamer et al. 2005).
The initial ensemble for each cycling period is generated by adding fixed covariance perturbations from the WRF VAR system to the 36-h GFS forecast valid at the initialization time. These perturbations are scaled by 1.8 so that the ensemble variance is greater than the ensemble-mean error; this setup has been shown to shorten the development time for flow-dependent error statistics (Dirren et al. 2007). After assimilating observations for two days (eight analysis cycles), the ensemble-mean error and the ensemble standard deviation become statistically consistent (not shown).
For the TCs studied here, 48-h ensemble forecasts at the onset of transition are generated by integrating the 90-member analysis ensemble using WRF. The onset of transition (given in Table 1) is objectively defined from WRF EnKF ensemble-mean analysis data to occur when the 900–600-hPa thickness averaged over a semicircle of radius 500 km to the left of the cyclone track is 10 m less than the thickness averaged over a semicircle of radius 500 km to the right of the cyclone track; Hart (2003) showed that this difference corresponds well to ET onset. Lateral boundary conditions for each ensemble member are obtained as described previously, except that the scaling factor for the perturbations increases linearly in time to a value of 2.4 for a 48-h forecast. The scaling factor for the 48-h forecast perturbations is determined by matching the RMS error in 48-h GFS forecasts to the standard deviation of the WRF VAR perturbations.
3. Case overview
Prior to describing how initial condition errors affect the predictability of the two selected ET forecasts, we first provide an overview of each case including forecast performance. In addition, the skill of the WRF EnKF forecast is compared with the corresponding GFS forecast and to a WRF forecast using GFS initial and boundary conditions (denoted WRF-GFS). The WRF-GFS and WRF EnKF forecasts employ the same model configuration, and since the ensemble-mean lateral boundary conditions for the WRF EnKF are nearly identical to the WRF-GFS (the ensemble perturbations do not exactly average to zero), differences between these solutions are due, almost exclusively, to the initial conditions.
Figure 1 shows the WRF EnKF ensemble mean and ensemble standard deviation SLP and 500-hPa geopotential height forecast during Tokage’s transition. During this 48-h period, the WRF EnKF forecast shows Tokage moving northeastward toward Japan, weakening over land, and reintensifying into a baroclinic cyclone upon moving over the Pacific Ocean east of Japan (Figs. 1a,c,e). In this forecast, reintensification occurs when a 500-hPa trough, which is initially located over Mongolia (Fig. 1b), moves just upstream of the remnant TC (Fig. 1f). Coincident with Tokage’s transition, another midlatitude cyclone, initially over far southeastern Russia (hereinafter called the SER cyclone), translates eastward and either deepens into a 988-hPa cyclone, or is absorbed into the transitioning TC, depending on the particular ensemble member. By 1200 UTC 21 October (hour 48), the ensemble standard deviation in SLP (500-hPa height) exceeds 8 hPa (48 m) over a large region northeast of Japan, indicating diverging forecast trajectories as a result of sensitivity to the initial state.
Despite differences in models and initial conditions, Figs. 2a,c show that all forecasts had difficulty predicting the track and minimum SLP of the cyclone. The GFS solution has the smallest track errors, while errors for the EnKF and WRF-GFS are similar. For intensity, the GFS and WRF-GFS forecast a deepening cyclone during transition, whereas the best-track data shows substantial weakening while the storm is over land.1 Although the WRF EnKF ensemble captures the weakening trend, it is much smaller than observed. Furthermore, members that have large intensity errors move farther poleward, corresponding to large track errors.
In comparison with Tokage, WRF EnKF forecasts of Nabi’s ET are characterized by lower forecast variance (Fig. 3). WRF EnKF forecasts initialized at 0000 UTC 6 September show Nabi moving poleward into the Sea of Japan and deepening into a 964-hPa cyclone by 0000 UTC 8 September. During reintensification, the remnant TC interacts with a slowly moving 500-hPa trough initially located along the southern border of Siberia (Fig. 3b). Unlike the Tokage transition forecast, the region of large ensemble standard deviation in the 48-h SLP and 500-hPa height forecast is confined to the area immediately around the cyclone (Figs. 3e,f).
Model forecasts of Nabi’s transition are more accurate relative to Tokage at short lead times, but errors at 48 h are comparable (Figs. 2b,d). All forecasts underestimate the weakening of Nabi over land during the first 24 h of the forecast. While in reality the storm maintains its intensity after entering the Sea of Japan at forecast hour 24, the EnKF deepens the storm, resulting in ensemble-mean minimum SLP errors of nearly 30 hPa by hour 48. The GFS and WRF-GFS forecasts have smaller errors by 10 and 15 hPa, respectively, although the storm was over 20 hPa too weak in the initial conditions. We note that Nabi deepened into a 970-hPa cyclone by 1200 UTC 8 September, so that errors in the EnKF forecasts could be due to a timing error.
4. Forecast sensitivity
Initial condition sensitivity is evaluated for two different forecast metrics: the cyclone minimum SLP and the RMS error in the SLP field near the TC. For each ensemble member, the minimum SLP value is determined by finding the grid point of lowest SLP near the TC. An ensemble of SLP RMS error values is obtained by verifying each ensemble member’s SLP forecast against the appropriate WRF EnKF ensemble-mean analysis averaged over a circle with a radius of 600 km, centered on the best-track position. Directional ambiguities in TC position errors lead to statistically insignificant sensitivity values; therefore, this metric is not considered. For brevity, the remainder of this section focuses on the sensitivity of these two metrics to 500-hPa geopotential height analyses; results for other upper-tropospheric analysis fields (e.g., meridional winds and temperature) are qualitatively consistent (not shown).
a. Cyclone minimum SLP
Figures 4a,b show the sensitivity of Tokage’s 24- and 48-h minimum SLP forecast to the analysis of 500-hPa geopotential height. Rather than describe the sensitivity gradient, as expressed in (1), we instead multiply the gradient by the initial condition error as approximated by the ensemble standard deviation. This quantity, which we shall hereinafter refer to as sensitivity, describes the change in the forecast metric resulting from state-dependent initial condition errors in all variables, accounts for the intrinsic difference in error variance in the tropics and midlatitudes, and allows for comparison among fields and forecast hours since the units are of the forecast metric. Regions of positive (negative) sensitivity indicate that increasing the analyzed height produces an increase (decrease) in the forecast cyclone minimum SLP.
At shorter lead times, (<24 h, Fig. 4a), the region of largest sensitivity (2.5 hPa per analysis standard deviation) is associated with the TC, with smaller values to the northwest and northeast. This pattern of sensitivity appears to be a superposition of position and intensity changes, such that a position shift in the TC across-track direction to the southeast (i.e., away from land), or a decrease in geopotential height near the vortex center, is associated with a deeper cyclone in the forecast.
For the 48-h forecast, midlatitude initial condition errors have equal importance to those near the TC (Fig. 4b). The sensitivity near the TC is oriented in a dipole centered on Tokage: decreasing (increasing) the heights to the southwest (northeast) of the TC by one standard deviation, consistent with shifting the storm in the along-track direction to the southwest, leads to a 3-hPa increase in the forecast minimum SLP. In the extratropics, sensitivity is located mainly near two 500-hPa troughs: one over Mongolia and the second over Siberia. Considering first the Siberian trough, the sensitivity dipole centered on the trough indicates that shifting the phase of the trough to the east is associated with an increase in the 48-h forecast cyclone minimum SLP.
To further illustrate how initial condition errors associated with this Siberian trough relate to Tokage’s ET, two outlier ensemble forecasts are compared: one where Tokage evolves into a 953-hPa cyclone by hour 48 (denoted “strong”) and another where Tokage remains a 985-hPa storm (denoted “weak”). In the weak member analysis (Fig. 5a), the Siberian trough is located east of the ensemble mean position. As this trough reaches the Sea of Okhotsk, a surface cyclone develops from the SER storm (Fig. 5b) and redistributes the low-level temperature field so that after 36 h, 850-hPa temperatures are approximately 10 K cooler in the region where Tokage undergoes transition (not shown). In contrast, the strong member forecast shows the Siberian trough merging with another trough initially over Mongolia (Figs. 5c,d). As a result, the SER cyclone does not form in advance of Tokage, but rather is absorbed into the ET cyclone.
For the Mongolian trough, the positive (negative) sensitivity values to the east (west) of this trough indicate that displacing this feature to the west leads to a higher minimum SLP 48 h later. Moving this trough to the west delays the interaction with the TC, thus hindering reintensification. The results for this lead time point to the importance of the phasing between the trough and TC during ET, which is similar to the conclusions on ET predictability reached by Klein et al. (2002), McTaggert-Cowan et al. (2003), and Ritchie and Elsberry (2007). It is worth noting that the region of large sensitivity surrounding this trough is characterized by few rawinsonde observations, which could explain the lower skill and predictability in this forecast; this point will be revisited in section 6.
Ensemble forecasts of Tokage’s transition are also considered for initialization times 12 h before and after the onset of transition. The ensemble standard deviation in the TC track and intensity forecasts valid at 1200 UTC 21 October is about 5% larger (20% smaller) for the forecast initialized 12 h prior (after) the onset of ET as compared to the forecast described above. The improvement in later forecasts may relate to improved initialization for the upstream trough as it moved into the denser Chinese rawinsonde network. This deduction is consistent with the findings of Harr et al. (2008) and Anwender et al. (2008), who show that the predictability of downstream midlatitude forecasts increases closer to the onset of ET, defined as the point where the storm is declared extratropical. Initial condition sensitivity for the minimum SLP forecast valid at 1200 UTC 21 October reveals that forecasts initialized 12 h before and after transition exhibit patterns similar to those shown in Fig. 4b, though the sensitivity magnitude decreases for later initialization times. In particular, the largest sensitivity is associated with the TC and the two aforementioned troughs (not shown). For brevity, we restrict the discussion of the Tokage transition to the previously described forecast initialization time.
Forecasts of Nabi’s transition exhibit initial condition sensitivity that is qualitatively similar to the Tokage forecast, especially for short lead times. The 24-h cyclone minimum SLP forecast is most sensitive to the 500-hPa height field near the TC (Fig. 4c). Similar to the 24-h forecast for Tokage, this sensitivity pattern is a superposition of a dipole centered on the TC and a storm-centered maximum, suggesting that a weaker cyclone shifted in the along-track direction (i.e., northeast) in the analysis corresponds to a weaker cyclone in the forecast. Smaller sensitivity values are located within an upstream trough.
For 48-h forecasts, the largest sensitivity is located in phase with an upper-level trough over Siberia, while there is relative little sensitivity to the region near the TC (Fig. 4d). Large sensitivity in phase with the trough indicates that the minimum SLP depends on the amplitude of the trough, rather than its position. Recall from section 3 that this trough interacts with Nabi’s remnants during ET, suggesting that a stronger upstream trough leads to a more intense baroclinic cyclone. This result is qualitatively similar to Ritchie and Elsberry (2003), who found that the initial trough amplitude regulated the rate of intensification and the minimum SLP in idealized simulations of ET.
b. RMS error in SLP forecasts
Here we consider the sensitivity of RMS errors in the SLP field to initial condition errors by averaging the SLP over a circle of radius 600 km centered on the storm. This metric provides an a posteriori diagnostic of how initial condition errors impact forecast errors at a particular lead time. Positive (negative) sensitivity values in this metric indicate that higher (lower) 500-hPa height values in the analysis at a select location are associated with larger SLP errors near the cyclone.
Comparison of the results for both cases (Fig. 6) reveals similar patterns to the minimum SLP forecast sensitivity pattern (Fig. 4), indicating a strong correlation between sensitivity and error. Specifically, the largest sensitivity values for 24-h forecast error are oriented mainly in a dipole around the TC and in a broad area to the north, indicating that the RMS error at short lead times is dominated by TC initial position errors (Fig. 6a). The expected response to a one standard deviation change in the 500-hPa height field in these areas is approximately a 1-hPa (17%) reduction in the area-averaged RMS forecast error. For the 48-h forecast, the RMS error in SLP is most sensitive to the 500-hPa height near the TC and to the two previously described midlatitude troughs. Decreasing (increasing) 500-hPa height to the west (east) of the Mongolian trough, east (west) of the Siberian trough, and southwest (northeast) of the TC is associated with a reduction in RMS error. These regions are similar to the areas of large sensitivity for 48-h minimum SLP forecasts (cf. Fig. 4b) indicating that, for this case, initial condition errors associated with these features have a significant impact on forecast errors near the ET cyclone.
Results for Nabi’s ET forecast are qualitatively similar to those for Tokage’s forecast. Initial condition sensitivity for 24-h RMS SLP forecast error is maximized in a dipole centered on the TC (Fig. 6c), where a one standard deviation change to the 500-hPa height field reduces the area-mean RMS SLP error by 0.8 hPa (15%). For 48-h forecasts (Fig. 6d), the largest reductions in RMS error are achieved by increasing the heights in the base of the Siberian trough, which is collocated with the maximum sensitivity for the 48-h minimum SLP forecast (cf. Fig. 4d). These results show that improved forecasts of Nabi’s ET can be achieved by decreasing the amplitude of the Siberian trough.
5. Perturbed initial condition experiments
Results in the previous section suggest that initial condition errors in sensitive regions can have a large impact on the ET forecasts for Typhoons Tokage and Nabi. This idea is tested here by objectively applying perturbations to the analysis ensemble in the most sensitive regions and evaluating the impact on cyclone minimum SLP 48-h forecasts and the RMS error in SLP near the cyclone. These experiments test whether the ensemble-derived predictions are quantitatively consistent with model simulations for perturbed initial conditions.
For both the Tokage and Nabi forecasts, perturbations based on initial condition sensitivity are added to the analysis ensemble using the linear regression procedure described in appendix A, where the independent variable is the forecast metric and the dependent variables are the analysis state variables, including moisture and cloud fields. After integrating the ensemble forward 48 h, the ensemble-mean forecast metric value is compared to the control value. This process is repeated for a range of initial condition perturbation amplitudes α. These experiments are similar to adjoint-based experiments for midlatitude cyclones conducted by Rabier et al. (1996), Zou et al. (1998), and Langland et al. (2002).
Figures 7a,b show the control SLP and 500-hPa height analysis, respectively, and the initial condition perturbation that is predicted to increase Tokage’s 48-h cyclone minimum SLP forecast by 18 hPa. The perturbed TC is shifted southwest, resulting in SLP perturbations of up to 12 hPa, with smaller differences near the extratropical cyclone located in the Bering Sea (Fig. 7a). A similar pattern is found at 500 hPa, with perturbation geopotential height values up to 100 m higher near the TC (Fig. 7b). The geopotential height on the eastern side of the Siberian (Mongolian) trough is 30 m lower (50 m higher) in the perturbed initial condition, which produces an eastward (westward) shift in the trough location. For both SLP and 500-hPa height fields, the largest perturbations are roughly equivalent to a two standard deviation change in the analysis.
After 48 h, differences between the control and perturbed forecasts have increased in magnitude and are maximized near the ET cyclone. In the perturbed forecast, the SLP is 40 hPa higher near the control forecast cyclone and 25 hPa lower to the north and south (Fig. 7c). This difference pattern results from the perturbed forecast having a weaker ET cyclone, which is farther south, and a Siberian cyclone that remains independent. Consistent with a weaker baroclinic cyclone, the 500-hPa geopotential height near the ET cyclone is 300 m higher in the perturbed forecast (Fig. 7d). In addition, the perturbed forecast has lower (higher) geopotential height in the downstream ridge (trough), which implies less downstream amplification. The cyclone minimum SLP in the perturbed forecast is 12 hPa higher than the control forecast, which compares with the predicted change of 18 hPa.
The above process is repeated for a range of perturbation amplitude (α) to evaluate the assumption of linear dynamics over the 48-h time interval. Figure 8a shows that for α between −5 and 10 hPa, there is good agreement between the predicted change in the 48-h minimum SLP forecast and the actual difference obtained from WRF model integrations. Outside this range of α, the ensemble prediction falls below the main diagonal, which indicates that the magnitude of the WRF response is less than the prediction and linear perturbation dynamics are violated. As a consequence, it is not possible to modify the initial conditions using forecast sensitivity in a way that will eliminate the 18-hPa error in the 48-h cyclone minimum SLP forecast without applying an iterative procedure.
For Nabi’s transition forecast, perturbations predicted to change the metric in the range −8 hPa ≤ α ≤ 8 hPa compare well with WRF solutions. Outside this range, the actual change is smaller than the predicted change (Fig. 8b). The significant asymmetry between positive and negative perturbations indicates that the linear approximation applies to weakening the storm by more than 20 hPa, whereas the approximation breaks down for strengthening the storm beyond 10 hPa.
Finally, we test the possibility of reducing the RMS error in 48-h SLP forecasts near the TC by modifying the initial conditions for both the Tokage and Nabi forecasts using the same procedure described above, except that J is taken now as the RMS error in 48-h SLP forecasts. Recall from section 4 that decreasing J (negative α) corresponds to smaller errors.
Forecasts for both storms exhibit considerable agreement between the predicted reduction in forecast error and the actual change obtained from the model, for α up to 6 hPa (i.e., 60% of error; Fig. 9). Increasing the amplitude of the perturbations beyond this value does not lead to further forecast error reductions. Nevertheless, the results indicate that these a posteriori corrections provide accurate estimates of 48-h forecast error reduction.
6. Observation impact
Given that ensemble sensitivity is able to accurately predict how analysis perturbations affect cyclone minimum SLP, and that observation assimilation leads to initial condition changes, we use ensemble sensitivity to determine the observation set at the analysis time that has the largest impact on the WRF EnKF minimum SLP forecast valid 48 h later. The procedure used to diagnose the largest-impact observations is similar to that of Torn and Hakim (2008) and is completely described in appendix B. Essentially, ensemble sensitivity is used in the Kalman filter equations to predict how the sequential assimilation of individual observations changes the mean and variance of a forecast metric, conditioned upon the assimilation of other observations. This procedure, which is similar to that of Langland and Baker (2004), identifies the 32 (42) statistically significant observations that have the largest impact on the Tokage (Nabi) 48-h minimum SLP forecast, which is roughly 0.3% of the total observations assimilated.
Figure 10 shows the estimated change in the expected value and standard deviation of the 48-h cyclone minimum SLP forecast due to assimilating specific observations, while Table 2 gives a summary for each observation type. For the metric expected value, the ensemble-based estimate of observation impact is similar to the actual difference obtained from taking the difference between two model integrations. For the metric standard deviation, the agreement between predicted and actual impact is not as good (Table 2). We hypothesize that excessive prediction in metric variance reduction is due to our choice of covariance inflation, which alters the analysis covariance after data assimilation is completed.
For both the Tokage and Nabi forecasts, the largest changes in the metric’s expected value are associated with rawinsondes in China and Japan, while cloud winds, ACARS, and surface observations are typically associated with smaller changes. Whereas the observations with the largest impact on Tokage forecasts are collocated with regions of large initial condition sensitivity, the correspondence is less clear for Nabi. The most sensitive observation for the Tokage forecast is the rawinsonde in eastern Mongolia (Ulaan-Baator, WMO ID 44292), which corresponds to a 3-hPa increase in the 48-h forecast of cyclone minimum SLP; other observations lead to less than 2-hPa changes (Fig. 10a). In contrast, Nabi’s 48-h minimum SLP forecast is affected less by observation assimilation. The greatest impact is also associated with the Ulaan-Baator, Mongolia, rawinsonde and the TC position observation, which are both associated with a 2-hPa reduction in the 48-h cyclone minimum SLP forecast (Fig. 10b).
While there is generally good correspondence between observations that produce large changes in the expected value and standard deviation (Figs. 10c,d), a few observations lead to large reductions in the metric variance without producing a large change in the expected value. This results from the fact that the change in the metric expected value depends on the observation innovation, [y −
To demonstrate that the high-impact observations actually produce a large change on the forecast, we perform two additional WRF forecasts of Tokage’s transition that are initialized from the ensemble-mean background forecast valid at 1200 UTC 19 October 2004. For the “assimilation” forecast, the 250-hPa zonal wind observation from the Mongolian rawinsonde is assimilated using the procedure described in section 2, while in the control case, no observations are assimilated. This observation is characterized by a sensitivity of 0.81 hPa (m s−1)−1 (first term on the right hand side of B1), and an innovation of 3.8 m s−1. All other model settings and boundary conditions are the same, so that differences between the two forecasts are due solely to assimilating the single observation.
Figure 11 shows that this observation initially has a relatively small impact on the initial SLP and 500-hPa height fields near the Mongolian trough; however, the differences rapidly grow in the vicinity of transitioning cyclone. At hour 0, the difference between the assimilation and control SLP is less than 1 hPa, while the 500-hPa heights are 20 m smaller (larger) than the control on the west (east) side of the trough, corresponding to a westward shift (Figs. 11a,b). Forty-eight hours later, the difference between the control and assimilation forecast is greater than 10 hPa (60 m) in SLP (500-hPa height) in a region surrounding Tokage’s ET (Figs. 11c,d). Assimilating this observation leads to a cyclone minimum central pressure that is 2.5 hPa higher than the 48-h control forecast, which compares with the ensemble prediction of a 3.0-hPa change.
7. Summary and conclusions
This paper describes the impact of initial condition errors on extratropical transition for two typhoons in the western Pacific region, one of which became a strong baroclinic cyclone (Nabi) and another that did not (Tokage), using data from cycling an EnKF with the WRF model. The EnKF system assimilates conventional in situ observations from surface stations, rawinsondes, ACARS, cloud motion vectors, and TC position data each 6 h. For the analysis time closest to the onset of transition, all 90 ensemble members are integrated forward 48 h to provide a forecast sample for initial condition sensitivity and observation impact studies. These forecasts are compared to those from the GFS and a WRF forecast initialized with the GFS analysis. Although this WRF EnKF system assimilates only a small fraction of the observations available to the GFS, forecasts of cyclone track and intensity have skill similar to the operational GFS forecast and the WRF forecast initialized from the GFS analysis.
The sensitivity of the cyclone minimum SLP forecast to the initial conditions is determined from WRF EnKF analysis and forecast ensemble data. For short lead times, cyclone minimum SLP forecasts are most sensitive to TC intensity and position. At longer lead times, the minimum SLP forecast is equally sensitive to midlatitude troughs that interact with the TC, indicating that the forecast depends on the interaction between the TC and trough. Moreover, the RMS error in the SLP field surrounding the cyclone shows large sensitivity to the analysis in the same locations, supporting the hypothesis that initial condition errors associated with the TC or midlatitude troughs have a large impact on ET forecasts. In contrast to previous studies of ET (e.g., Klein et al. 2002; McTaggert-Cowan et al. 2003; Ritchie and Elsberry 2007), the importance of the phasing between the TC and trough is established by objective means, rather than subjective adjustments to the trough and/or TC.
Although it is well established that the ET is sensitive to the interaction between the TC and midlatitude troughs, this study quantifies less obvious sensitivity to multiple troughs in the upstream analysis. Specifically, Tokage’s transition forecast is sensitive to the location of a midlatitude 500-hPa trough that phases with a downstream surface cyclone; when the trough is closer to this surface cyclone, Tokage does not deepen significantly. Comparing two outlier forecasts indicates that surface cyclogenesis downstream of Tokage alters the temperature distribution in the area where Tokage undergoes reintensification. This result suggests that accurate ET forecasts may require accurate midlatitude analyses both upstream and downstream of the TC.
Improved cyclone minimum SLP forecasts and lower SLP errors are obtained by applying diagnostic perturbations to the initial conditions based on initial condition sensitivity. Forecast differences compare closely to the ensemble prediction of the 48-h cyclone minimum SLP forecast for changes up to about 8 hPa. Beyond this value, nonlinearity becomes important as the perturbation amplitude saturates below the linear prediction. Furthermore, a posteriori adjustments to the initial conditions reduce the RMS error in SLP fields near the TC by up to 60%. We note that since WRF is an imperfect model, these initial condition perturbations, which are up to two analysis standard deviations in the most sensitive regions, may also correct for model deficiencies in addition to initial condition errors.
The value of individual observations on the 48-h cyclone minimum SLP is evaluated by combining ensemble sensitivity with the ensemble data assimilation system. This method identifies the approximately 40 observations that have the biggest impact on the forecast minimum SLP variance. In general, rawinsonde observations near the regions of large initial condition sensitivity lead to the largest changes in this metric’s expected value and variance; however, high-impact observations for Nabi are spread around the main region of sensitivity. The Tokage forecast is characterized by large sensitivity in regions of sparse in situ data, which probably contributed to the large variance in ensemble forecasts and a large forecast change due to assimilating a single observation from the Ulaan-Baator rawinsonde.
During the transition of Typhoon Tokage (Nabi), the minimum SLP forecast is more (less) sensitive to initial condition errors, and features within the upper-tropospheric westerlies move comparatively faster (slower). Klein et al. (2002), McTaggart-Cowan et al. (2001), and Ritchie and Elsberry (2007) all show that the relative phasing between the TC and midlatitude trough, rather than the amplitude, acts as a strong constraint on whether the TC evolves into a baroclinic system. Based on these two cases and the aforementioned previous studies, we speculate that when the midlatitude trough is located within relatively fast westerly flow, small errors in the trough’s initial position can lead to large errors in the orientation of the trough and TC in the forecast, resulting in poor forecasts for storm intensity (i.e., baroclinic reintensification or continued decay). In contrast, forecasts of ET events in relatively slower westerly flow are more likely to correctly predict the phasing between the TC and upstream trough, so that the intensity of the extratropical cyclone depends more on the initial amplitude of the TC and trough. This hypothesis that the predictability of the ET storm is proportional to the speed of the midlatitude flow requires testing with a larger sample of ET events and is the subject of future work.
Acknowledgments
We thank Pat Harr (NPS) for suggesting the Tokage case, Rolf Langland (NRL) for discussions on sensitivity and observation impact, and Chris Velden and Dave Stettner (CIMSS/SSEC) for providing the cloud motion vector data. Two anonymous reviewers provided helpful comments that improved this manuscript. ACARS observations used in this study were made available to the Earth System Research Laboratory/Global Systems Division by the following commercial airlines: American, Delta, Federal Express, Northwest, United, and United Parcel Service. This work was supported by NSF Grant ITR-0205648, NOAA CSTAR Grant NA17RJ1232, and ONR Grant N00014-06-1-0510.
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APPENDIX A
Initial Condition Perturbations
This procedure is repeated for a range of α to assess the accuracy of the ensemble sensitivity estimate. For the minimum SLP forecast metric, the maximum value of α is the error in the ensemble-mean 48-h minimum SLP forecast (computed with respect to best-track data), while the maximum α for the RMS error metric is the ensemble-mean error value.
APPENDIX B
Observation Impact
Several caveats apply to the ensemble-based observation impact calculations. First, the impact of observations is considered only for those that have a statistically significant sensitivity value; performing this calculation for statistically insignificant observations leads to larger errors (Torn and Hakim 2008). The values of δJ and δσ for each observation depend on the order of assimilation since nearby observations can produce similar analysis increments and changes to the forecast metric. If previously assimilated observations are not accounted for, this technique will overestimate the impact of individual observations (Torn and Hakim 2008). Observation ordering is objectively determined based on the predicted reduction in forecast metric variance. This contrasts with the method of Langland and Baker (2004) and Liu and Kalnay (2008), which allows for observation impact calculations for all observations.
WRF EnKF ensemble-mean (contours) and ensemble standard deviation (shading) (left) SLP (hPa) and (right) 500-hPa height (m) forecasts of Typhoon Tokage’s transition initialized at 1200 UTC 19 Oct 2004: (a,b) initial time, (c,d) 24-h forecast, and (e,f) 48-h forecast.
Citation: Monthly Weather Review 137, 10; 10.1175/2009MWR2879.1
(a,b) Cyclone position errors (km) and (c,d) cyclone minimum SLP (hPa) as a function of forecast hour for (left) the Tokage forecast initialized at 1200 UTC 19 Oct 2004 and (right) the Nabi forecast initialized at 0000 UTC 6 Sep 2005. The thin black lines denote the ensemble-mean error, dashed lines are the corresponding GFS forecast, the dotted–dashed line is a WRF forecast on the same domain initialized from the GFS analysis, and the thick line is the verification JMA best-track intensity. The dark shading indicates the area within one standard deviation of the ensemble mean, while the light shading denotes the span of the ensemble.
Citation: Monthly Weather Review 137, 10; 10.1175/2009MWR2879.1
As in Fig. 1, but for the Typhoon Nabi forecast initialized at 0000 UTC 6 Sep 2005.
Citation: Monthly Weather Review 137, 10; 10.1175/2009MWR2879.1
Sensitivity patterns for (left) 24- and (right) 48-h cyclone minimum SLP forecasts to the analysis of 500-hPa height (shading; hPa). Field represents the sensitivity gradient multiplied by the analysis standard deviation at each grid point for (a,b) the Tokage forecast initialized at 1200 UTC 19 Oct 2004 and (c,d) the Nabi forecast initialized at 0000 UTC 6 Sep 2005. Contours denote the ensemble-mean 500-hPa height analysis; the squares denote the location of rawinsonde stations. TC best-track data is denoted by the dashed line.
Citation: Monthly Weather Review 137, 10; 10.1175/2009MWR2879.1
SLP (dashed; hPa) and 500-hPa heights (solid; m) for the (top) weak and (bottom) strong ensemble member forecast initialized at 1200 UTC 19 Oct 2004: (a,c) the analysis and (b,d) the 36-h forecast.
Citation: Monthly Weather Review 137, 10; 10.1175/2009MWR2879.1
As in Fig. 4, but for the RMS error in SLP forecasts within 600 km of the best-track cyclone position. The circle, which is centered on the best-track position and has a radius of 600 km, denotes the region over which the SLP errors are computed.
Citation: Monthly Weather Review 137, 10; 10.1175/2009MWR2879.1
(a) Difference between the perturbed initial condition ensemble-mean SLP and the control ensemble-mean analysis SLP at 1200 UTC 19 Oct 2004 (shading; hPa). The control ensemble-mean SLP analysis is given by the solid lines (hPa). The perturbation added to the control analysis is predicted to increase the 48-h cyclone minimum SLP forecast by 18 hPa. (b) As in (a), but for the 500-hPa height field. (c),(d) As in (a),(b), but for the 48-h forecast of SLP and 500-hPa height, respectively.
Citation: Monthly Weather Review 137, 10; 10.1175/2009MWR2879.1
48-h ensemble-mean cyclone minimum SLP differences (hPa) as determined by perturbed integrations of the WRF model (ordinate) against the differences predicted by ensemble sensitivity analysis (abscissa) for forecasts initialized at (a) 1200 UTC 19 Oct 2004 (Tokage) and (b) 0000 UTC 6 Sep 2005 (Nabi). The solid line indicates perfect agreement between the predicted and WRF model integrations, while the error bars denote one standard deviation.
Citation: Monthly Weather Review 137, 10; 10.1175/2009MWR2879.1
As in Fig. 8, but for the difference in the RMS error in 48-h minimum SLP forecasts within 600 km of the best-track cyclone position.
Citation: Monthly Weather Review 137, 10; 10.1175/2009MWR2879.1
Change (hPa) in the (a,b) expected value and (c,d) ensemble standard deviation of the 48-h cyclone minimum central pressure forecast due to sequentially assimilating observations that have a statistically significant observation sensitivity at (left) 1200 UTC 19 Oct 2004 (Tokage) and (right) 0000 UTC 6 Sep 2005 (Nabi). The shape of the symbol indicates the observation platform, and the size denotes the magnitude. The shaded region denotes locations where the absolute value of the 500-hPa height sensitivity exceeds 1.5 hPa (0.7 hPa) for the Tokage (Nabi) forecast.
Citation: Monthly Weather Review 137, 10; 10.1175/2009MWR2879.1
(a) Difference in analysis SLP (shading; hPa) between a test case where the initial condition is perturbed by assimilating a single 250-hPa zonal-wind radiosonde observation from Ulaan-Baator and the control case. The control SLP is given by the solid lines (hPa). The dot denotes the location of Ulaan-Baator. (b) As in (a), but for the 500-hPa height field. (c),(d) As in (a),(b), but for the 48-h forecast.
Citation: Monthly Weather Review 137, 10; 10.1175/2009MWR2879.1
Analysis and forecast initialization times for the Tokage and Nabi simulations.
Ensemble-based estimate of the impact of assimilating observations on the expected value (δJ) and standard deviation (δ
The JTWC does not provide best-track data after the cyclone is classified as extratropical; therefore, the Japan Meteorological Agency (JMA) best-track minimum SLP data is used during these time periods.
