The Role of Vortex and Environment Errors in Genesis Forecasts of Hurricanes Danielle and Karl (2010)

232 MONTHLY WEATHER REVIEW VOLUME 141

RYAN D. TORN AND DAVID COOK Department of Atmospheric and Environmental Sciences, University at Albany, State University of New York, Albany, New York

(Manuscript received 16 March 2012, in ﬁnal form 2 July 2012)

ABSTRACT

An ensemble of Weather Research and Forecasting Model (WRF) forecasts initialized from a cycling ensemble Kalman filter (EnKF) system is used to evaluate the sensitivity of Hurricanes Danielle and Karl’s (2010) genesis forecasts to vortex and environmental initial conditions via ensemble sensitivity analysis. Both the Danielle and Karl forecasts are sensitive to the 0-h circulation associated with the pregenesis system over a deep layer and to the temperature and water vapor mixing ratio within the vortex over a comparatively shallow layer. Empirical orthogonal functions (EOFs) of the 0-h ensemble kinematic and thermodynamic fields within the vortex indicate that the 0-h circulation and moisture fields covary with one another, such that a stronger vortex is associated with higher moisture through the column. Forecasts of the pregenesis system intensity are only sensitive to the leading mode of variability in the vortex fields, suggesting that only specific initial condition perturbations associated with the vortex will amplify with time. Multivariate regressions of the vortex EOFs and environmental parameters believed to impact genesis suggest that the Karl forecast is most sensitive to the vortex structure, with smaller sensitivity to the upwind integrated water vapor and 200–850-hPa vertical wind shear magnitude. By contrast, the Danielle forecast is most sensitive to the vortex structure during the first 24 h, but is more sensitive to the 200-hPa divergence and vertical wind shear magnitude at longer forecast hours.

1. Introduction Prediction System (NOGAPS) had varied success predicting genesis in the western North Pacific over a 3-yr Despite significant advances in numerical weather period, with many failed predictions tied to large-scale prediction models, tropical cyclone (TC) genesis and features, such as vertical wind shear and humidity. intensity remain a significant challenge for these systems Moreover, Snyder et al. (2010) showed that ensemble (e.g., Rappaport et al. 2009). There are many potential genesis forecasts from the National Centers for Envi- reasons for the lack of improvement in TC genesis ronmental Prediction (NCEP) Global Forecast System forecasts, including that TC genesis is inherently less (GFS) during the National Aeronautics and Space Ad- predictable because of convective dynamics (e.g., Zhang ministration (NASA) African Monsoon Multidisciplin- et al. 2003; Zhang and Sippel 2009) and there is greater ary Analysis (NAMMA) campaign were characterized potential for large initial condition errors over the ocean by varying degrees of predictability, as measured by due to the lack of in situ data. Wang et al. (2012) sur- ensemble variance, which suggests that some forecasts mised that while convective processes may limit the of these systems could be particularly sensitive to initial predictability of TC genesis, the formation of the pro- condition errors. As a consequence, one of the purposes tovortex is largely controlled by synoptic and meso-a of the Pre-Depression Investigation of Cloud-System processes. To that end, Cheung and Elsberry (2002) in the Tropics (PREDICT; Montgomery et al. (2012)) found that the Navy Operational Global Atmospheric experiment was to evaluate the hypothesis that some genesis forecasts are particularly sensitive to initial condition errors by taking additional observations near Corresponding author address: Ryan Torn, University at Albany, State University of New York, ES 351, 1400 Washington Ave., pregenesis systems. Albany, NY 12222. There are multiple theories regarding how clusters of E-mail: [email protected] disorganized convection can develop into an organized

DOI: 10.1175/MWR-D-12-00086.1

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TC, which in turn provide hypotheses on how initial its north. Torn (2010a) and Sippel et al. (2011) found condition errors can influence genesis. Many recent that intensity forecasts associated with African easterly studies argue that genesis is a ‘‘bottom up’’ processes waves that eventually became Hurricane Helene and whereby localized cores of deep convection act to pre- Tropical Storm Debby (2006), respectively, depended condition the atmosphere by warming and moistening on the strength of the initial vortex and to the mid- an embryonic mesoscale vortex, with the circulation tropospheric moisture through which the vortex would forming by merger and axisymmetrization of the con- move through. In addition, Sippel et al. (2011) deter- vectively generated PV anomalies (e.g., Hendricks et al. mined that an ensemble containing a weaker set of storms 2004; Reasor et al. 2005; Montgomery et al. 2006). Other was more sensitive to the nearby moisture field and SST investigations have suggested that it is actually the vor- fields via track differences than an ensemble containing ticity on horizontal scales greater than individual con- stronger storms, suggesting that weaker pregenesis sys- vective updrafts that lead to the vortex buildup (e.g., tems could be more sensitive to their environment. Fang and Zhang 2010, 2011). Dunkerton et al. (2009) This manuscript explores how initial condition errors hypothesized that genesis can only occur in a region of associated with the pregenesis vortex and the surrounding approximately closed Lagrangian circulation, where the environment impact genesis forecasts by applying the embryonic vortex is to some extent isolated from the ensemble-based sensitivity technique (Ancell and Hakim surrounding environmental flow. This dynamical iso- 2007; Torn and Hakim 2008) to ensemble forecasts of lation would allow for the building of vorticity and two different TCs during the PREDICT experiment. gradual moistening of the column that are necessary for The initial conditions for this forecast ensemble are genesis to occur. All of the above theories require some obtained from a cycling ensemble Kalman filter (EnKF) sort of pregenesis synoptic-scale vortex and moistening system coupled to the Weather Research and Fore- of the free troposphere within it, which raises the pos- casting Model (WRF). The two TCs chosen for this sibility that genesis forecasts could be sensitive to the study (Danielle and Karl) were characterized by two initial wind and moisture fields associated with the different types of predecessor systems and locations, vortex. thus providing an opportunity to evaluate the robustness In addition to the pregenesis vortex, there is also ev- of the forecast sensitivities. idence that the genesis process depends on the envi- This manuscript proceeds as follows. Section 2 pro- ronment that the system is moving through; therefore, vides an overview of the data assimilation system and errors associated with these factors could also play a role model. A summary of the two TCs and their forecasts is in genesis prediction or predictability. In general, TC given in section 3. The initial condition sensitivity for genesis is less likely to occur in regions of greater vertical these two forecasts is given in section 4, while section 5 wind shear (e.g., Gray 1998) and low relative humidity tests the results from section 4 by perturbing the initial in the environment (e.g., Nolan 2007; Raymond and conditions in the most sensitive regions. Conclusions are Lopez-Carrillo 2010; Davis and Ahijevych 2012). These given in section 6. two factors are related in that large vertical wind shear acts to reduce the vertical alignment of the pregenesis 2. Model and data assimilation setup vortex, resulting in relative inflow of drier environmental air into the vortex (e.g., Raymond and Lopez- The role of initial condition errors in forecasts of Carrillo 2010; Tang and Emanuel 2010; Rappin et al. genesis for two TCs is evaluated using ensemble analy- 2010; Davis and Ahijevych 2012). This dry air can produce ses and forecasts taken from a cycling ensemble data downdrafts that dry out the boundary layer, produce assimilation system that was run in real time during lower-tropospheric divergence, weaker updrafts, and PREDICT. Much of the data assimilation setup is sim- thus less vortex stretching (e.g., Smith and Montgomery ilar to Torn (2010b) and is summarized here; the in- 2012). terested reader is directed to this paper for greater detail Previous studies have attempted to quantify the role on the methods outlined below. This data assimilation of initial condition errors on individual TC genesis system generates a 96-member analysis ensemble each events. Sippel and Zhang (2008) found that ensemble 6 h from 0000 UTC 1 August to 1800 UTC 7 November members that strengthened a nondeveloping system 2010 by combining observations with a 6-h forecast en- in the Gulf of Mexico were characterized by higher semble initialized at the previous analysis time (i.e., convective available potential energy (CAPE) and deep cycling) over a 36-km resolution domain that covered moisture in the initial conditions. Sippel and Zhang (2010) much of the Atlantic basin (shown in Fig. 1). For each showed that Hurricane Humberto’s (2007) genesis was system that the National Hurricane Center (NHC) is sensitive to similar factors as well as a baroclinic front to tracking at that particular analysis time (both pregenesis

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TC position and minimum SLP, and Constellation Ob- serving System for Meteorology, Ionosphere and Climate (COSMIC) global positioning system (GPS) refractivity profiles (Anthes et al. 2008) using the Data Assimilation Research Testbed (DART; Anderson et al. 2009), which is an implementation of the ensemble adjustment Kalman filter (Anderson 2001). For the dropsonde data, only those profiles that were released within 1 h of the analysis time and located more than 100 km from the center of a TC are considered since 12-km resolution cannot resolve some of the large gradients in the mass and momentum fields near the TC eyewall. Observation preprocessing is FIG. 1. Extent of the 36-km domain used in these forecasts. The thin done using the methods outlined in Torn (2010b), while solid lines are the best-track positions of Danielle (D) and Karl (K), observation errors are obtained from NCEP statistics, including prior to genesis, which are indicated by a dashed line. except for TC position and minimum SLP, which are 3 Each denotes the position of the pregenesis systems at the re- taken from Torn and Snyder (2012). spective forecast initialization times. Latitude and longitude are shown every 108. The severe rank deficiency in the covariance matrix due to the size of the ensemble relative to the number of state variables requires covariance localization and in- investigation or INVEST areas and TCs), the data as- flation techniques. The covariances are localized based similation system also assimilates observations on cycling on three-dimensional distance using Eq. (4.10) of Gaspari 12-km two-way moving nested domain(s) (1000 km 3 and Cohn (1999) where the value reduces to zero 2000 km 1000 km in size) centered on the system of interest. in the horizontal and 8 km in the vertical from the ob- The model is advanced forward in time using version servation location. In regions with dense observations, 3.1 of the Advanced Research Weather Research and the horizontal and vertical covariance length scales are Forecasting Model (ARW-WRF; Skamarock et al. 2005) reduced whenever there are more than 1600 observa- with the following physics parameterizations: WRF tions within the localization ellipsoid as is described in 5-class microphysics scheme (Hong et al. 2004), Rapid Torn (2010b). Covariance inflation is achieved using Radiative Transfer Model (RRTM) longwave radiation the adaptive technique of Anderson (2009), where (Mlawer et al. 1997), Dudhia shortwave scheme (Dudhia the inflation factor is damped by 10% at each assim- 1989), Kain–Fritsch cumulus parameterization (Kain ilation time and the inflation standard deviation is and Fritsch 1990), Yonsei University (YSU) boundary fixed at 0.6. layer scheme (Hong et al. 2006), and similarity theory Ensemble initial conditions for when the ensemble is land surface model (Skamarock et al. 2005) that includes created on 0000 UTC 28 July 2010 and lateral boundary the updated enthalpy and momentum drag formulations conditions for each 6-h forecast are generated using the described in Davis et al. (2010). The movement of each fixed-covariance perturbation (FCP) technique outlined nest is determined by extrapolating the NHC positions in Torn et al. (2006). This method generates a deviation from the previous 6 h (from 26 to 0 h) into the future from the ensemble mean for each ensemble member by (i.e., from 0 to 6 h) assuming a constant propagation drawing random perturbations from the NCEP error vector. This approach is adopted to make sure that all covariances contained in the WRF VAR system (Barker ensemble members would have the same geographical et al. 2004). For the initial ensemble, the perturbations coordinates at the analysis time. Whenever NHC stops are multiplied by 1.7 and added to the 36-h GFS forecast tracking a particular system, data assimilation is dis- valid on 0000 UTC 28 July 2010. Ensemble lateral continued on the corresponding 12-km domain and the boundary conditions are produced in a similar manner, nest is removed from the model. except that the 6-h ensemble mean forecast is the 6-h At each analysis time, observations are assimilated NCEP GFS forecast valid at the appropriate time. from Automated Surface Observing System (ASOS) sta- From 15 August to 30 September, all 96 ensemble tions, ships, buoys, rawinsondes, the Aircraft Communi- analyses are integrated forward to generate 72-h ensem- cations Addressing and Reporting System (ACARS), ble forecasts. Because of time constraints and the focus on cloud motion vectors (Velden et al. 2005), dropsonde pregenesis systems during PREDICT, only the nested do- data from National Oceanic and Atmospheric Admin- main for the pregenesis system closest to the PREDICT istration (NOAA), PREDICT, and NASA Genesis and operations base in St. Croix is retained for these forecast Rapid Intensification Processes (GRIP) aircraft, NHC (i.e., all other nested domains were ‘‘turned off’’). Lateral

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FIG. 2. (a) Ensemble forecasts of pre-Karl’s position initialized at 1200 UTC 12 Sep 2010 (gray lines). The dots indicate the location of each ensemble member at 24-h intervals, while the black circles show a bivariate normal ﬁt to the 24-h positions, similar to Hamill et al. (2011). The thick black line denotes the NHC best-track positions, while the stars indicate the position each 24 h. Latitude and longitude are shown every 58. (b) The ensemble-mean pre-Karl minimum SLP (thin line), the region enclosed by one standard deviation (dark shading), the region spanned by the ensemble (light shading), and the best-track value (thick line) as a function of forecast hour. (c) As in (b), but for the 850-hPa circulation centered on pre-Karl, with radius of 200 km. The thick line represents the 850-hPa circulation computed from the corresponding-time NCEP FNL analyses. (d)–(f) As in (a)–(c), but for the pre-Danielle forecast initialized at 1200 UTC 19 Aug 2010. boundary conditions for each ensemble member are to the north of South America on 8 September. This produced using the FCP technique, where the pertur- system eventually began to move westward across the bation scaling factor linearly increases with time such Windward Islands and into the Caribbean Sea, exhibit- that a 48-h forecast has a perturbation standard devia- ing periodic convection over the course of the next 5 tion that is 55% larger than the 6-h value, which is con- days. By 13 September, the convection became steadier sistent with the RMS error in 48-h GFS forecasts (e.g., and a tropical depression was declared on 1800 UTC 14 Torn and Hakim 2008). The ensemble mean lateral September (Stewart 2010). boundary condition is the comparable-time GFS forecast. The remainder of this manuscript focuses on ensemble forecasts initialized roughly 48 h prior to genesis, 3. Overview of cases and forecasts which gives the initial condition errors enough time to grow, but not become overly nonlinear. Forecasts ini- This study focuses on the genesis of two TCs that tialized 12 h before or after this time show qualitatively overlapped with the PREDICT period, but were char- similar results (not shown), thus the results presented acterized by pregenesis systems of different origin. hereafter are not unique to that particular initialization Hurricane Danielle’s genesis can be traced to a tropical time. Figure 2 shows the ensemble track, minimum SLP, wave that exited the African coast on 18 August 2010 and 850-hPa circulation for a circle of radius 200 km and became stationary within an active phase of an centered on the pregenesis system.1 The latter metric is equatorial Kelvin wave in the eastern Atlantic. Over the employed here because it is proportional to the tan- course of three days, the convection became better or- gential wind and unlike maximum surface wind speed is ganized, particularly around the southwestern side of the system before genesis was declared on 1800 UTC 21 August (Kimberlain 2010). By contrast, the predecessor to 1 Technically, the quantity presented here is circulation per area, Hurricane Karl emerged from a broad cyclonic circulation which by the Stokes’s theorem is equal to area-average vorticity.

Unauthenticated | Downloaded 09/28/21 02:57 AM UTC 236 MONTHLY WEATHER REVIEW VOLUME 141 a dynamical quantity that has a conservation equation. Ancell and Hakim (2007) showed that one can use a M For all times, the center of the pregenesis system is de- member forecast ensemble to determine the sensitivity termined by computing the 800-hPa circulation for a of a forecast metric J to a state variable xi via circle of radius 150 km centered on each grid point, then › cov(J, x ) finding the point with the largest value. This algorithm J 5 i › x , (1) proved to be a very robust method of determining the xi var( i) center compared to finding the minimum in the mass field at any particular level. where J and xi are 1 3 M estimates of the respective WRF ensemble forecasts of Karl’s track forecasts quantities, i is the state variable index, cov denotes the initialized at 1200 UTC 12 September are characterized covariance, and var denotes the variance. Throughout by a slow and slightly south of best-track bias at all lead this manuscript, J will refer to the 850-hPa circulation times, with increasing track variance in the east–west metric described above centered on the vortex in each direction with time (Fig. 2a). The best-track minimum ensemble member. To allow for comparison between SLP is nearly constant during the first 48 h with a 17-hPa initial condition fields of varied units and magnitude, the decrease during 48–72 h, while the ensemble-mean min- values of xi are normalized by the standard deviation imum SLP decreases by 10 hPa over 72 h; at all times, the in that quantity, thus all sensitivities have units of the best-track value is within one standard deviation of the metric per standard deviation of the state variable. mean (Fig. 2b). Over the first 24 h, the ensemble-mean Moreover, the statistical significance of the sensitivity 850-hPa circulation is relatively constant, followed by a values is tested in a manner similar to Torn and Hakim steady increase at longer forecast times while the en- (2008). The null hypothesis of no relationship between semble standard deviation increases by a factor of 3 over the metric and analysis state variable is rejected if the 72 h (Fig. 2c). absolute value of the regression coefficient is greater Similar to Karl, WRF ensemble forecasts of Danielle than its 95% confidence bounds computed from en- are also characterized by track biases, while the intensity semble data (e.g., Wilks 2005, section 6.2.5). forecast shows a tendency to develop the system too a. Karl quickly. In particular, the position forecasts are characterized by a north and west of best-track bias through- Given that previous studies suggest that the largest out with little change in ensemble variance (Fig. 2d).2 initial condition sensitivity for other pregenesis systems Throughout the forecast, the ensemble-mean minimum is associated with the near-storm kinematic and ther- SLP decreases at a relatively steady rate, which is faster modynamic fields (e.g., Sippel and Zhang 2008; Sippel than best track (Fig. 2e), while the ensemble-mean cir- et al. 2011; Torn 2010a), a similar approach is adopted culation increases by a factor of 3 (Fig. 2f). It is worth here. Initial condition sensitivities are computed for noting that both intensity metrics are characterized by the wind, temperature, and moisture fields at numerous a nearly 5 time increase in ensemble standard deviation, vertical levels in a storm-centered framework. In each of representing a fairly wide range of solutions (dissipation the following figures, xi will represent the ensemble es- to category-1 TC) for this forecast. Given that the only timate of a particular field and location relative to the difference between ensemble members in both TCs vortex center, rather than the ensemble estimate of the is due to the initial conditions, the increasing variance field at a particular earth-relative location. For brevity, in the intensity metrics suggest that these two genesis only a subset of those fields with the largest sensitivity forecasts are characterized by a large sensitivity to the are presented hereafter. initial conditions, which is evaluated below. Figure 3a shows the sensitivity of the 48-h 850-hPa circulation associated with the pregenesis system to the 4. Initial condition sensitivity 0-h 850-hPa circulation field; other forecast lead times show similar patterns and are thus not shown. The The following section employs forecast sensitivity largest initial condition sensitivity is associated with analysis to understand how the initial condition differ- the larger ensemble-mean circulation values that char- ences in the kinematic and thermodynamic fields as- acterize pregenesis Karl, such that a one standard de- sociated with the vortex and the environment lead to viation change in the 0-h circulation in this region is 2 2 differences in the genesis forecasts described above. associated with a 1.0 3 10 5 s 1 change in the 48-h circulation forecast (equivalent to a 0.5 standard deviation change). This particular pattern suggests that pre- 2 The verification positions start at 0600 UTC 20 August when genesis systems that are initially strong remain so through NHC began tracking the system. 48 h, thus there is memory of the initial intensity at later

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FIG. 3. Sensitivity of the 48-h forecast of the 850-hPa circulation averaged within 200 km of pre-Karl’s center to the analysis of (a) 850-hPa circulation (averaged within 200 km of each grid point) and (b) 400-hPa equivalent potential 2 2 temperature (shading, 10 5 s 1) on a storm-relative grid for the forecast initialized at 1200 UTC 12 Sep 2010. The 2 2 contours are the ensemble-mean analysis ﬁelds (10 5 s 1 and K, respectively). The center of the 850-hPa vortex is at the center of each plot, while the underlying map provides the geographic location with respect to the ensemble-mean position. Latitude and longitude are shown every 108. (c),(d) As in (a),(b), but for the forecast of pre-Danielle initialized at 1200 UTC 19 Aug 2010. The circle in (a) denotes the area over which the vortex-average quantities described in section 4 are computed. forecast times. In addition, there appears to be a di- motion, rather than a more northwesterly trajectory that pole in sensitivity associated with an east–west-oriented would take the system near land. Below 600 hPa, the strip of positive and negative circulation to the east of sensitivity pattern and magnitude is similar to Fig. 3; the pregenesis Karl, which is associated with a lower- however, above 600 hPa, the magnitude of the sensi- tropospheric easterly jet (not shown), such that in- tivity decreases with height (shown later), which suggests creasing (decreasing) the circulation to the northern that the 850-hPa circulation forecast is most sensitive to (southern) side of this feature is associated with higher the initial-time kinematic ﬁelds below 600 hPa. forecast circulation. Adjusting the initial conditions in In contrast to the 0-h circulation, the largest sensitivity this manner would lead to a more zonally oriented jet, in the equivalent potential temperature ue is in the upper which in turn would be expected to cause more zonal troposphere near the center of the pregenesis system

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(Fig. 3b). Increasing the 0-h 400-hPa ue within the pregenesis system by one standard is associated with a 0.9 3 2 2 10 5 s 1 change in the 48-h circulation, with relatively smaller sensitivity to the ue along the gradients to the north and south of the system. Moreover, the sensitivity is smaller above and below this level, indicating the model is particularly sensitive to the thermodynamic fields at 400 hPa (shown later). Increasing the initial- time equivalent potential temperature would decrease the ue deficit in the midtroposphere, which might be expected to produce less dry air entrainment and more vigorous updrafts, thus allowing convection to efficiently spin up the vortex (e.g., Smith and Montgomery 2012; Wang 2012). It is worth noting that this result is similar to Sippel and Zhang (2008, 2010) and Torn (2010a); however, unlike Sippel and Zhang (2008, 2010), there is little sensitivity to CAPE (not shown). The above results suggest that the largest initial condition sensitivity is associated with the pregenesis system itself, with comparatively smaller sensitivity to the surrounding fields. As a consequence, it is worthwhile to compute the sensitivity of the 850-hPa circulation at various forecast lead times to the 0-h circulation, potential temperature u, and water vapor mixing ratio qy at each model level averaged within 200 km of the vortex center. This particular radius is chosen because it en- compasses the pregenesis vortex that might be expected to have recirculating parcels, and it also encloses the region of high sensitivity in both the kinematic and thermodynamic fields (cf. Fig. 3a). The resulting calculation therefore shows how changes to the 0-h vortex FIG. 4. (a) Sensitivity of the normalized 850-hPa circulation for a structure at each vertical level will impact the subsequent circle of 200-km radius centered on pregenesis Karl at various lead s intensity. To allow for a quantitative comparison be- times (abscissa) to the 0-h circulation at each model level for a circle of 200-km radius centered on pregenesis Karl (ordinate) tween forecast hours, J is normalized by the ensemble for the forecast initialized at 1200 UTC 12 Sep 2010. (b) The 0-h standard deviation in the following calculations. ensemble-mean (solid, lower axis) and ensemble-standard deviation Figure 4a shows that the 850-hPa circulation forecast (dashed; upper axis) circulation at each vertical level. (c),(d) As at all lead times is characterized by a nonzero sensitivity in (a),(b), but for the 0-h potential temperature averaged within to the 0-h circulation over a fairly deep layer of the 200 km of pre-Karl. (e),(f) As in (c),(d), but for the water vapor mixing ratio. troposphere. Over all forecast times, the sensitivity is vertically uniform below s 5 0.6, which corresponds to the highest 0-h ensemble-mean circulation and ensem- Moreover, the sensitivity value itself is smaller than ble standard deviation (Fig. 4b), with smaller sensitivity circulation and fairly consistent over all forecast times, to the circulation at higher vertical levels. In addition, suggesting that while the circulation forecast is less the normalized sensitivity magnitude decreases with sensitive to initial-time u relative to circulation, there forecast time, which suggests that the forecast circula- is a consistent sensitivity to this field at all forecast lead tion retains less memory of the 0-h circulation with in- times. Unlike circulation and u, the normalized sensi- creasing time. Nonetheless, this figure indicates that the tivity to qy is relatively small during the first 12–24 h, forecast circulation is quite sensitive to the 0-h vortex then increases to 0.4 thereafter. This increasing sensi- kinematic structure over a fairly deep layer. tivity suggests that it takes time for initial condition er- In comparison to circulation, the sensitivity to the 0-h rors associated with water vapor field to impact the vortex-average potential temperature u is smaller and forecast circulation, which could support the idea that more vertically localized. For u, the only statistically moistening the atmosphere leads to less dry air entrain- significant sensitivities are between 0.2 , s , 0.4 (Fig. 4c). ment, thus more vigorous updrafts and vortex stretching

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FIG. 5. The ﬁrst three EOFs of the 0-h ensemble (a) circulation, (b) potential temperature, and (c) water vapor mixing ratio averaged within 200 km of the center of pregenesis Karl for the forecast initialized at 1200 UTC 12 Sep 2010.

(e.g., Sippel and Zhang 2008, 2010). Beyond 24 h, the s 5 0.6, a positive u perturbation between 0.2 , s , 0.4, largest sensitivity values are fairly uniform through much and a positive qy perturbation through much of the of the troposphere above s 5 0.9, suggesting that in- troposphere that maximizes near s 5 0.6. This EOF creasing the 0-h moisture over a fairly deep layer within pattern suggests that stronger lower-tropospheric cir- the pregenesis system leads to a more intense vortex. culation at 0 h is associated with higher circulation The previous calculation suggests that the forecast through much of the troposphere, a warmer upper tro- circulation is sensitive to the initial kinematic and mois- posphere, and higher water vapor above the bound- ture fields over a fairly deep vertical layer; however, it ary layer, which is consistent with the pouch ideas of is also possible that some of this sensitivity could be due Dunkerton et al. (2009). By comparison, the second to correlations among the 0-h fields themselves. This and the third EOF (14% and 11% of variance, respec- possibility is evaluated by computing empirical orthog- tively) are characterized by smaller amplitude pertur- onal functions (EOFs) of a state vector that includes the bations to the circulation relative to the first EOF, but ensemble of vortex-average circulation, u, and qy for all comparable or larger amplitude perturbations in the u vertical levels below s 5 0.1. The resulting EOFs thus and qy fields. EOF2 is characterized by a wavenumber-1- show the perturbations that explain the greatest amount like pattern in the qy field and a 0.2-K temperature of variance in the 0-h vortex structure, similar to the perturbation below s 5 0.6 (Fig. 5b). Finally, EOF3 is method outlined by Gombos et al. (2012). To account associated with larger circulation in the midtroposphere, for the differences in units between these fields, all a negative u anomaly in the upper troposphere, and quantities are normalized by the ensemble standard lower qy in the lower troposphere (Fig. 5c). deviation for that particular variable and level. Rather Using (1), it is possible to compute the sensitivity of than presenting the dimensionless EOFs, the following the forecast circulation to the EOF perturbations by

figures show the regression of each EOF’s principle com- replacing xi with the principle components of each EOF. ponents onto the dimensional vortex-average quantities, Figure 6a indicates that the forecast circulation is sen- which has the advantage of showing the typical ampli- sitive to EOF1 at nearly all forecast times, while EOF2 tude of the anomaly for each vertical level and field (e.g., and EOF3 are characterized by nearly zero sensitivity. Thompson and Wallace 2000). This result suggests that only specific initial condition The 0-h vortex EOFs for Karl suggest there is a large errors, related to having higher or lower circulation and vertical and cross-variable correlation among these moisture through the troposphere, project onto the fields (Fig. 5). The first EOF (29% of the variance), cor- amplifying mode within the model that impacts the responds to a positive perturbation in circulation through forecast circulation, while other perturbations, such as much of the troposphere, with the largest values below EOF2 and EOF3 do not.

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FIG. 6. (a) Sensitivity of the 850-hPa circulation forecast for a circle of 200 km centered on pregenesis Karl to the principle components of the analysis EOFs shown in Fig. 5 as a function of forecast hour for the forecast initialized at 1200 UTC 12 Sep 2010. (b) As in (a), but for the Danielle forecast initialized at 1200 UTC 19 Aug 2010.

Although previous calculation suggests that the fore- variable is the 850-hPa circulation of the pregenesis cast circulation is sensitive to EOF1, changes to EOF1 system at a particular forecast hour and the independent only explain 35% of the variance in the 48-h 850-hPa variables are the principle components of the 0-h EOFs circulation forecast; therefore, initial condition errors shown above and the ensemble estimates of the envi- associated with other elements of the state vector must ronmental parameters listed above averaged from 0 h to be contributing to the growth in ensemble variance with the desired forecast time (i.e., for the 48-h circulation time. The success of statistical models, such as the Sta- forecast, the environmental parameters are averaged tistical Hurricane Intensity Prediction Scheme (SHIPS; between 0–48 h). In essence, this calculation is similar to DeMaria et al. 2005) and the Logistical Growth Equa- the part correlations of Sippel and Zhang (2010) and the tion Model (LGEM; DeMaria 2009), in predicting in- regression calculation of Torn (2010a), but with more tensity suggest that the forecast circulation could be predictors. Performing this calculation in a multivariate sensitive to variability in the large-scale environment sense eliminates the possibility of obtaining misleading through which the pregenesis systems move. This pos- results due to cross correlation between predictors. Those sibility can be evaluated by computing the sensitivity factors that have a larger regression coefficient therefore of the 850-hPa circulation to various environmental suggest those dynamical factors that are acting to limit the parameters, such as the nonsatellite-based predictors predictability of the 850-hPa circulation. within the SHIPS rapid intensification model (Kaplan The environmental predictors used here are the 200– et al. 2010), including the 850–200-hPa vertical wind 850-hPa vertical shear computed by taking the average shear, 200-hPa divergence, upshear integrated water 200- and 850-hPa winds within 500 km of the vortex vapor,3 and the potential intensity (PI). Furthermore, center, the 200-hPa divergence averaged within 1000 km the sensitivity to each of these parameters can be com- of the vortex center, the 0–850-hPa integrated qy aver- pared to the sensitivity to EOF1 to evaluate the role of aged within 500 km of the vortex center and within 458 vortex versus environment errors in limiting the pre- upwind of the 200–850-hPa shear vector, and the maxi- dictability of Karl’s genesis forecast. mum potential intensity averaged within 50 km of the To evaluate the role of vortex versus environmental vortex center. Each parameter is computed indepen- errors, multivariate linear regressions are independently dently for each ensemble member from 6-hourly model computed for each forecast hour, where the dependent output based on each member’s vortex position. All variables are normalized by the ensemble standard deviation to account for differences in units between fields, 3 Upshear refers to the quadrant within 458 opposite to the 200– such that the regression coefficients are dimensionless. 850-hPa shear vector. The time averaging of the environmental parameters is

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FIG. 7. Multivariate regression coefficients where the independent variables are the principle components of the 0-h vortex EOFs, time-average 200–850-hPa shear magnitude, upshear integrated water vapor, maximum potential intensity, and 200-hPa divergence; and the dependent variable is the 850-hPa circulation for a circle of radius 200 km centered on pregenesis Karl or Danielle as a function of forecast hour for the forecast initialized at (a) 1200 UTC 12 Sep 2010 and (b) 1200 UTC 19 Aug 2010. All variables are normalized by the ensemble standard deviation. done because it is more likely that the pregenesis system vortex (e.g., Kaplan et al. 2010; Raymond and Lopez- will respond to sustained differences in the environ- Carrillo 2010; Davis and Ahijevych 2012); therefore, this mental parameters relative to the ensemble-mean value, calculation suggests that pregenesis systems that ingest rather than instantaneous changes relative to the en- drier air are weaker, likely through reduced buoyancy semble mean. This statement seems to be supported by and vertical motion. Beyond 12 h, the regression co- computing the regression coefficients with various time- efficient associated with vertical wind shear magnitude averaging intervals for the environmental parameters. becomes increasingly negative, which suggests that higher When the multivariate regression coefficients are com- shear is associated with lower circulation and that puted using smaller averaging intervals (i.e., previous forecast circulation becomes increasingly sensitive to 12 h), the fraction of 850-hPa circulation variance ex- the time-average shear at longer forecast lead times. plained by these predictors is lower than using the time The remaining environmental factors, such as divergence average of environmental parameters from 0 h to the and PI, have near-zero coefficients, which indicates that forecast hour of interest. variations in these quantities have little impact on the The multivariate sensitivity regression for this fore- forecast circulation. The combination of all of these cast suggests that Karl is sensitive to both vortex and predictors explain roughly 50% of the 850-hPa circula- environmental fields. Figure 7a shows that the largest tion forecast variance at all forecast times. regression coefficient, and thus greatest sensitivity, It is noteworthy that the intensity forecast is sensitive at all forecast hours is associated with EOF1, which to the integrated water in the upshear direction; how- suggests that increasing the magnitude of EOF1 (akin ever, it is worth exploring whether this sensitivity is to a stronger initial vortex), is associated with a bigger specific to the upshear quadrant or is reflective of a change in the forecast circulation relative to a comparable sensitivity to the integrated water vapor in all quad- change to the environmental parameters. The second rants. This possibility is evaluated by computing the largest sensitivity at most forecast times is associated correlation between the 850-hPa circulation associated with the upshear moisture, such that more intense vor- with pregenesis Karl at various forecast hours and tices are associated with greater upshear moisture. This the time-average integrated water vapor between metric is meant to roughly approximate the moisture 0–500-km radius averaged over the upshear quadrant content of the midtropospheric air being advected over or averaged over all quadrants (Fig. 8). At all forecast the low-level vortex by the storm-relative flow due to the times, the upshear quadrant integrated water vapor has ambient wind and misalignment of the lower and midlevel a larger correlation, which suggests that the forecast

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FIG. 9. Sensitivity of the normalized 850-hPa circulation associated with pregenesis Karl at various forecast hours (abscissa) to the time-averaged water vapor mixing ratio in the upwind quadrant averaged within 500 km of the center at each model s level (ordinate) for the forecast initialized at 1200 UTC 12 Sep 2010.

sensitivity is related to dry air entrainment within convection (e.g., Fritz and Wang 2013). Having established that the forecast is sensitive to the time-average upwind moisture between roughly 400– FIG. 8. Correlation between the time-average integrated water 600 hPa, it is interesting to evaluate the sensitivity of this vapor averaged over the upshear quadrant (solid) or all quadrands (dashed) within 500 km of pregenesis Karl and the 850-hPa circu- metric to the initial moisture field. For this calculation, lation associated with Karl as a function of forecast hour for the J is each ensemble member’s upwind moisture between forecast initialized at 1200 UTC 12 Sep 2010. 0.4 # s # 0.6 calculated as before and averaged from 0–48 h. Figure 10 indicates that the largest sensitivity for truly is more sensitive to the water vapor in the upshear this metric is southwest of the vortex center along the quadrant. coast of Venezuela at the nose of a region of drier air Although the SHIPS rapid intensification model uses that is subsequently advected along the south side of the the upshear integrated moisture as a predictor, the pregenesis system. Increasing qy here is associated with upshear direction only represents the direction from higher integrated moisture during the 48-h forecast. It which midtropospheric air parcels would enter the is worth noting that two dropsondes deployed during vortex assuming the 850-hPa environmental winds are PREDICT sampled this region, which might explain nearly zero. Moreover, this metric excludes the possi- why many models produced a fairly good genesis forecast at this time; future work will evaluate this hypoth- bility that the model is actually more sensitive to qy in certain layers of the troposphere. These concerns can be esis via targeted data denial experiments. alleviated by computing the sensitivity of the 850-hPa b. Danielle circulation at all forecast hours to the upwind qy at each Initial condition sensitivities for the Danielle forecast model level, where the upwind qy is computed in the same manner as the upshear integrated water vapor, are characterized by some similarities to the Karl fore- except that the upshear direction is replaced by the cast and some intriguing differences. Figure 3c shows storm-relative upwind direction at that model level.4 that the 48-h 850-hPa circulation forecast is most sensitive to the 0-h 850-hPa circulation associated with pregenesis Figure 9 shows that the 850-hPa circulation is sensitive 2 2 Danielle (sensitivity of 1.2 3 10 5 s 1 per standard de- to the upwind qy between 0.4 # s # 0.6, with lower values above and below, which confirms the hypothesis viation), with relatively smaller values surrounding the that changes to the environmental moisture in specific system, which again suggests that the forecast has memory layers has a larger impact on the intensity forecast. It of the initial vortex intensity. At higher vertical levels, the sensitivity magnitude decreases sharply, such that is worth noting that this layer is slightly above the ue minimum in the column, which is similar to the results the forecast circulation is not sensitive to the 0-h circu- obtained by Torn (2010a), and suggests that the forecast lation above 500 hPa (shown later). By contrast, the region of maximum sensitivity for

500-hPa ue is not collocated with the pregenesis system 4 The upwind direction at each forecast hour is determined by (Fig. 3d); instead, the sensitivity pattern is characterized averaging the zonal and meridional winds within 500 km of the by a north–south-oriented dipole across the ensemble- vortex center, then subtracting the vortex motion. mean ue gradient centered on the pregenesis Danielle,

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FIG. 10. (a) Sensitivity of the 0–48-h upwind 400–600-hPa water vapor mixing ratio associated with pregenesis Karl to the 0-h integrated water vapor above 850 hPa (shading; mm per standard deviation) for the forecast initialized at 1200 UTC 12 Sep 2010. The contours are the ensemble-mean integrated water vapor above 850 hPa (mm). (b) Sensitivity of the 48-h 850-hPa circulation associated with pregenesis Danielle to the analysis of 200-hPa divergence 2 2 2 2 (shading, 10 5 s 1 per standard deviation). The contours are the ensemble-mean 200-hPa divergence (10 5 s 1). The dot in both (a) and (b) indicates the 0-h ensemble-mean position of the vortex, while the box denotes the area over

which JIC is computed in section 5.

such that increasing (decreasing) the 0-h ue to the south surface to s 5 0.4, which corresponds to the layer of (north) is associated with a higher forecast circulation. It positive circulation, small differences in u, and higher qy is not clear why this pattern is obtained, though it should below s 5 0.6, which suggests that much like Karl, the be noted that much of the precipitation associated with dominant mode of variability within the 0-h ensemble this system was located along the southern side, thus it is a stronger (weaker) vortex that is characterized by likely reflects the potential for dry air entrainment dis- higher (lower) moisture. By contrast, EOF2 (25% of cussed previously. variance) has a positive peak in circulation at s 5 0.5, The sensitivity of forecast circulation to the vortex- negative perturbation in u at s 5 0.7, and positive per- average circulation, u, and qy suggests that the largest turbation in qy at s 5 0.6, suggesting that a vertically forecast sensitivities are more vertically confined than deeper vortex is associated with colder temperatures, the Karl case (Fig. 11). In particular, the forecast cir- thus lower stability, and higher moisture in the mid- culation is only sensitive to the 0-h circulation below s 5 troposphere. EOF3 (8% of the variance) is associated 0.5, while the magnitude of the sensitivity decreases over with wavenumber-1 variations in these quantities. Sim- the first 24 h, then becomes fairly constant thereafter. ilar to Karl, the forecast circulation is only correlated This result suggests that the forecast does not have as with EOF1, which reinforces the notion that only certain much ‘‘memory’’ of the initial vortex compared to the initial condition perturbations are associated with fore- Karl forecast. Moreover, the rapid falloff of sensitivity cast error growth (Fig. 6b). above s 5 0.5 likely reflects that the pre-Danielle vortex Multivariate regressions for this forecast suggest is a larger vertical gradient in 0-h circulation compared that differences in the environmental parameters have to Karl (cf. Figs. 4b and 11b). The sensitivity to both u a larger impact on the prediction of Danielle’s genesis and qy vortex are lower and more vertically confined (Fig. 7b). During the first 24 h of the forecast, the largest relative to circulation and to the Karl case (Figs. 11c,e). regression coefficients are associated with EOF1 and EOFs of the 0-h ensemble vortex-average quantities EOF2, suggesting that the variability of ,24-h forecasts suggest less correlation between the kinematic and ther- is dominated by differences in the initial vortex struc- modynamic fields for this particular forecast (Fig. 12). ture. Beyond that, the largest regression coefficients are The first EOF (33% of the variance) is associated with associated with the 200-hPa divergence and vertical a positive perturbation in the circulation from the shear, such that greater divergence, or lower shear is

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2 2 2 forecast (1.5 m s 1 and 6.0 3 10 6 s 1, respectively). The higher midtropospheric wind (divergence) could explain the greater sensitivity to the upshear moisture (divergence) in the Karl (Danielle) forecasts; future work will evaluate this possibility by evaluating a larger number of cases. Given the sensitivity to the time-average divergence experienced by the pregenesis system, it is worth in- vestigating whether the 48-h 850-hPa circulation is sensitive to the 0-h divergence. Figure 10b shows that the center of the pregenesis system (denoted by a dot) is located in the northern portion of a large region of 200-hPa divergence5 associated with the convectively active phase of an equatorial Kelvin wave. The sensitivity of the 48-h circulation forecast to this field is maximized to the south of the pregenesis system, such that increasing the 0-h divergence is associated with a stronger forecast cyclone. One possible interpretation of this sensitivity pattern is that the sensitivity is a re- flection of the correlation between the 0-h circulation and 0-h divergence; however, the correlation between the latter two quantities is less than 0.2 during the first 36 h of the forecast, thus they could be considered independent. Finally, there is a suggestion of an east–west- oriented sensitivity dipole, such that moving the region of largest divergence toward the east and/or increasing the overall divergence itself is associated with a more intense system.

5. Perturbed initial condition experiments FIG. 11. As in Fig. 4, but for the forecast of Danielle initialized at 1200 UTC 19 Aug 2010. The sensitivities documented in the previous section are determined via ensemble statistics; therefore, it is possible that the results reflect statistical artifacts, rather associated with a more intense vortex. It is worth noting than how the model actually responds to initial con- that this result is quite different than the Karl forecast, dition errors. To exclude this possibility and test the which suggests that not all genesis forecasts respond to aforementioned hypotheses of how initial condition er- vortex and environmental initial condition errors in the rors impact the predictability of these systems, a series of same way. perturbed initial condition experiments is carried out for The differences in how each forecast responds to the Danielle and Karl forecast where the initial condi- variability in the vortex structure could be related to the tions are modified in a manner consistent with changing differences in the mean vortex structure and environ- the vortex or environmental factors believed to impact ment. For the Karl forecast, the EOFs of the 24-h vortex the intensity of these systems. structure are very similar to the 0-h EOFs, suggesting An ensemble of perturbation initial conditions is that the dominant modes of variability are the same generated using the following procedure, which is simi- at these two times (not shown). By contrast, the 24-h lar to what is used in Torn and Hakim (2009) and Torn forecast EOFs for the Danielle are characterized by (2010b), with some important differences. An ensemble greater vertical extent compared to the 0-h EOFs, indicating that there is little memory of the dominant modes of variability from the initial time. In addition, the Karl forecast has a higher 600-hPa wind averaged 5 In this figure, the divergence at each grid point is ›u/›x 1 ›y/›y 21 from 0–500 km of the center (6 m s ) and smaller di- averaged within 1000 km of each individual grid point, which re- 2 2 vergence (1.5 3 10 6 s 1) compared to the Danielle moves much of the small-scale noise associated with derivatives.

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FIG. 12. As in Fig. 5, but for the forecast of Danielle initialized at 1200 UTC 19 Aug 2010. of perturbed initial conditions for the ith state variable (hereafter ‘‘strong’’). The resulting 48-h circulation xp ( i ) is generated via forecast for the pregenesis system is computed from the perturbed initial condition subensemble and com- ›J xp 5 xa 1 ICa pared to the values from the comparable control mem- i i › a , (2) xi bers to evaluate how well the ensemble predictions matched the model behavior. This procedure is repeated where for various values of a (63 standard deviations in JIC) to test the range over which the sensitivity values are ›J cov(J , xa) linear. IC 5 IC i , ›xa var(xa) i i a. Karl xa 3 where i is the 1 M ensemble estimate of the ith Perturbing the initial conditions based on the princi- control analysis state variable, JIC is the ensemble esti- ple components of EOF1 has the expected impact on the mate of the initial condition parameter that is believed kinematic and thermodynamic ﬁelds at both the initial to impact the forecast circulation, and a is the pertur- and forecast time. Figure 13a shows the ensemble-mean bation amplitude. For the Karl forecasts, JIC is either the 850-hPa circulation for the strong subset of members principle component of EOF1 (vortex structure) or the and the perturbation to the 0-h 850-hPa circulation 400–600-hPa qy averaged over the box in Fig. 10a (up- associated with a one standard deviation decrease in windmoisture),whilefortheDanielleforecast,JIC EOF1. The largest negative differences are collocated is either the principle components of EOF1 (vortex with the vortex itself, suggesting that decreasing the structure) or the 0-h divergence averaged over the box in principle component index has the impact of weakening Fig. 10b. Rather than integrating the entire perturbed the vortex. In addition, there is also a 0.3-K reduction ensemble forward to 48 h, forecasts are produced for a in the 400-hPa ue collocated with the pregenesis system subset of ensemble members, which are chosen based and along its northern periphery (Fig. 13b), which is also on the control ensemble 48-h circulation forecast. For consistent with a negative perturbation associated with a . 0, perturbed initial conditions are integrated for- EOF1. ward for the 10 members with the lowest 48-h circulation Integrating the perturbed ensemble forward 48 h shows in the control ensemble (hereafter ‘‘weak’’). This choice that the initial condition perturbation has the desired shows whether a member with a low forecast circulation impact of reducing the forecast circulation (Fig. 13c). can become stronger through speciﬁc changes to its The difference between the perturbed IC and control initial conditions. Moreover, for a , 0, perturbed initial 48-h 850-hPa circulation suggests that the perturbed IC conditions are integrated forward for the 10 members forecast is farther east relative to the control and has with the largest 48-h circulation in the control ensemble smaller circulation. Moreover, the predicted reduction

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2 in the 48-h 850-hPa circulation of 1.3 3 105 s 1 is similar 2 to the actual change of 1.2 3 105 s 1 and confirms that specific perturbations to the 0-h vortex structure consistent with this EOF can alter the forecast intensity. Repeating the above calculation over multiple values of a indicates that initial condition perturbations consistent with EOF1 have the predicted impact on the forecast intensity. For the strong members, there is good agreement between the predicted and actual change inthe48-hcirculationforuptoatwostandardde- viation reduction in EOF1 (Fig. 14a); beyond that, the response is less, suggesting a limit to the amount of weakening that can occur, similar to the results of Hakim and Torn (2008). Moreover, applying positive perturbations consistent with EOF1 to the weak members produces an increase in the forecast circulation, though the actual response is lower than the prediction (Fig. 14b). Perturbing the initial conditions to increase or decrease the 0-h water vapor in the sensitive region for upwind moisture (box in Fig. 10a) also produces the expected impact on the forecast circulation. Figure 14c shows that decreasing the water vapor in this region actually produces more weakening than is predicted at all values of a, though it is worth noting that a one standard deviation reduction of qy in this region only produces half the reduction in forecast circulation compared to a one standard deviation reduction in EOF1. By contrast, there is better agreement between predicted and actual impact of the perturbations for positive a, which confirms that the forecast circulation is sensitive to the upwind moisture (Fig. 14d). b. Danielle Identical initial condition perturbation experiments

are carried out for the Danielle forecast, except that JIC is the principle components of EOF1 for this particular forecast. For negative a (Fig. 15a), there is a very good agreement between the predicted and actual change in the 48-h 850-hPa circulation; however, the same is not true for a . 0 (Fig. 15b). For perturbations greater than one standard deviation in EOF1, the actual change is below the prediction, suggesting a nonlinear response to large amplitude perturbations. Finally, perturbing the initial conditions in a manner that increases or decreases the 0-h 200-hPa divergence

FIG. 13. (a) Difference between the perturbed initial condition and in Fig. 10b also conﬁrms that changes to this environ- control ensemble-mean 0-h 850-hPa circulation (black contours, mental factor inﬂuences the forecast circulation. While 2 2 dashed negative, 10 5 s 1) for the forecast initialized at 1200 UTC 12 negative a produce a larger response in the forecast Sep 2010. The perturbation is meant to decrease the principle com- circulation relative to the ensemble prediction (Fig. 15c), ponent associated with EOF1 by one standard deviation. The gray the agreement is better for positive perturbations (Fig. contours show the control ensemble-mean 850-hPa circulation. (b) As in (a), but for the 400-hPa equivalent potential temperature. (c) As 15d). This result suggests a nonlinear relationship between in (a), but for the 48-h 850-hPa circulation. the amount of divergence and the strongest members of

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FIG. 14. (a),(b) Difference in 48-h ensemble-mean 850-hPa circulation associated with Karl due to perturbations to the initial conditions based on EOF1 as determined by integrating the WRF (ordinate) against the initial condition perturbation amplitude (abscissa) for the forecast initialized at 1200 UTC 12 Sep 2010. The solid line denotes perfect agreement between the ensemble prediction and model result. (c),(d) As in (a),(b), but for perturbations that will change the 0-h 400–600-hPa integrated water vapor within the box in Fig. 10a. the ensemble, but still confirms that uncertainty in the ensemble forecasts were characterized by track biases amount of divergence is associated with a loss of pre- relative to best track, it generally captured the observed dictability in this case. intensification of these two systems. For both the Karl and Danielle forecasts, the forecast 6. Summary and conclusions circulation, which is used as a proxy for the intensity of the pregenesis system, is most sensitive to the 0-h cir- This manuscript describes the sensitivity of TC genesis culation and thermodynamic fields associated with the forecasts of two different TCs (Danielle and Karl) to the pregenesis system itself, with generally smaller sensi- initial vortex and environmental initial conditions. The initial tivity to the near-system environment fields. Moreover, condition sensitivity was evaluated using the ensemble- the largest sensitivity to the 0-h circulation field is in the based sensitivity technique applied to 96-member en- lower troposphere, close to the location of the maximum semble forecasts from the WRF, with initial conditions in circulation, with smaller values at higher levels, par- taken from a cycling ensemble Kalman filter system that ticularly for the Danielle forecast, which is characterized assimilates conventional in situ data that ran in real time by a shallower vortex. Furthermore, the largest u and qy to support the PREDICT field campaign. Although the sensitivity is in the mid- to upper troposphere, though

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FIG. 15. (a)–(d) As in Fig. 14, but for the Danielle forecast initialized at 1200 UTC 19 Aug 2010. In (c) and (d), the perturbations are meant to change the 0-h 200-hPa divergence in the box shown in Fig. 10b. the vertical extent of the layer of highest sensitivity is The role of vortex versus environmental initial con- different in the two cases. dition errors is evaluated by computing multivariate Given the covariability between fields and vertical levels, regression coefficients, where the independent variables empirical orthogonal functions are computed for the en- are the principle components of the 0-h vortex EOFs semble 0-h vortex-average circulation, u and qy fields at all and environmental parameters believed to impact TC vertical levels to determine the dominant modes of vari- intensity, while the dependent variable is the 850-hPa ability in the vortex structure. The primary mode of vari- circulation associated with the pregenesis system at ability in the 0-h vortex structure is associated with larger various forecast hours. For the Karl forecast, the largest circulation and qy through much of the troposphere, with sensitivity is associated with EOF1, with comparatively little change in the temperature profile, suggesting that smaller sensitivity to theupwindmoisture,andtoa stronger vorticies are characterized by a deeper layer of lesser extent vertical wind shear magnitude. By contrast, moisture, which is consistent with the ideas in Dunkerton the Danielle forecast is most sensitive to the vortex et al. (2009). This mode of variability is characterized by structure for ,24-h forecasts, while longer-term forecasts a large correlation with the forecast circulation at all fore- are characterized by larger sensitivity to the 200-hPa di- cast hours, while EOF2 and EOF3 have small correlations, vergence and the vertical wind shear magnitude. Overall, which indicates that only specific perturbations to the this indicates that not all genesis forecasts react in the vortex initial conditions will result in intensity changes. same way to variations in environmental parameters

Unauthenticated | Downloaded 09/28/21 02:57 AM UTC JANUARY 2013 T O R N A N D C O O K 249 about an ensemble-mean value within a particular re- each case. This issue will be addressed in future studies, gime, which is similar to the weak versus control results which will include carrying out a similar analysis on in Sippel et al. (2011). It is worth noting that although additional cases. a certain environmental factor may not have large sensitivity for a particular forecast, it does not mean that it Acknowledgments. This study benefited from discus- does not affect TC formation generally. sions with Chris Davis, Jason Dunion, Will Komaromi, These results presented here potentially have a Sharan Majumdar, Mike Montgomery, and Brian Tang. number of implications on both the predictability and Jason Sippel, Fuqing Zhang, and an anonymous re- dynamics of TC genesis. First, the lack of correlation viewer provided constructive comments about this between the forecast circulation and the EOFs of the manuscript. Satellite wind data were obtained from vertical vortex structure presented here suggest that not Chris Velden and Dave Stettner (CIMSS/SSEC). ACARS all of the variance associated with the pregenesis vortex data for this study were made available to the Earth projects onto the modes of the model that are associated System Research Laboratory/Global Systems Division with intensity changes; therefore, if one were interested by the following commercial airlines: American, Delta, in deploying targeted observations for TC genesis, these Federal Express, Northwest, United, and United Parcel observations need to project onto something like EOF1 Service. Processed dropsonde data is provided by in the Karl forecast. Future work will test this idea by NOAA/Hurricane Research Division of AOML. This assimilating only those observations that project onto work was supported by NSF Grant ATM-084809. EOF1 and comparing it to the full observation set. It is worth noting that the structure of EOF1 is very similar to the vertical weighting given to shallow vortices within REFERENCES the Hurricane WRF (HWRF; Gopalakrishnan et al. Ancell, B., and G. J. Hakim, 2007: Comparing adjoint and en- 2010) and the Geophysical Fluid Dynamics Laboratory semble sensitivity analysis with applications to observation (GFDL) hurricane model (Bender et al. 2007). These targeting. Mon. Wea. Rev., 135, 4117–4134. results suggest that if the initial vortex projects onto a Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129, 2884–2903. vertical structure similar to EOF1, it might explain why ——, 2009: Spatially and temporally varying adaptive covariance these two models have a tendency to produce erroneous inflation for ensemble filters. 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