## 1. Introduction

One of the main problems in the numerical prediction of tropical cyclones (TCs) is the difficulty in specifying the dynamical and thermodynamical structures of the atmosphere near the TC center and in the surrounding environment because of sparse conventional observations over the ocean. Even with increased satellite and radar data, the use of bogus vortices in the analysis of an operational numerical TC prediction model is often adopted in order to improve the TC representation. A common method is to construct an initial bogus vortex using other estimated parameters such as minimum sea level pressure near the center and size of the TC and then implant the bogus vortex into the environment (e.g., Ueno 1989; Kurihara et al. 1993; Leslie and Holland 1995; Nuissier et al. 2005).

How to construct a more realistic TC structure and how to combine this bogus vortex with the model state variables are still unsolved problems. Recently, the National Center for Atmospheric Research and Air Force Weather Agency (NCAR–AFWA; Low-Nam and Davis 2001) proposed a scheme (hereafter referred to as the N–A bogussing scheme) for bogussing TCs into the initial conditions of the nonhydrostatic version of the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5). The process they used to detect and extract the inaccurate vortex from the first-guess field distinguishes it from many other approaches. For example, Kurihara et al. (1993) used a sophisticated filtering scheme to remove the erroneous first-guess vortex once it has been located. A year before the N–A scheme was proposed, Zou and Xiao (2000) developed a new bogussing approach using the four-dimensional variational data assimilation (4DVAR) bogus data assimilation (BDA) technique. By assimilating a specified bogus sea level pressure (SLP) distribution, all model fields are adjusted to fit the bogus SLP under the constraint of the forecast model. Although these two schemes produced improvements in different aspects of the bogussing technique, relatively few attempts have been made to study systematically their impacts upon numerical TC forecasts, particularly for those storms in the western North Pacific (WNP).

The objective of this study is therefore to compare the impacts of these two bogussing schemes on track and intensity forecasts of TCs in the WNP. Section 2 gives a brief description of both bogussing schemes. The assimilation methodology and experimental design, as well as the TCs studied, are introduced in section 3. The results and discussion are presented in section 4 while section 5 presents a summary.

## 2. The bogussing schemes

### a. N–A bogussing scheme

The bogussing technique usually includes three main aspects: 1) removal of the inaccurate vortex from the first-guess field; 2) construction of the bogus vortex; and 3) combination of the bogus vortex with the modified analysis field. Because most of the first-guess field is provided by integration of a model with relatively coarse resolution, the vortices are too broad and too weak, and sometimes they are misplaced when interpolated into a higher-resolution forecast model. Therefore, the erroneous vortices have to be removed before the insertion of the bogus vortices; otherwise, there may be two vortices in the background at the same time. The scheme designed by NCAR–AFWA for bogussing TC into the initial conditions of the MM5 uses a new approach in the removal process that departs significantly from the filtering method used by the Geophysical Fluid Dynamics Laboratory (GFDL; Kurihara et al. 1993).

The first step of the extraction is to identify the center of the vortex to be removed in the first-guess field by searching for the maximum vorticity near the surface within a radial distance of 400 km from the best-track location of the TC of interest. Once the first-guess vortex is located, the divergent wind, pressure, geopotential height, and temperature anomalies within a domain of 300-km radius are calculated from a series of Poisson-type equations and the hydrostatic equation. The functions can be seen in detail in Davis and Low-Nam (2001). These anomaly fields are then removed, leaving a first-guess field with only a background wind and temperature where the first-guess vortex was located.

*r*is the distance from the center;

*υ*is the bogus maximum wind, which is assumed to be somewhat lower than the reported maximum wind from the best-track data, considering that the bogus wind is only the axisymmetric part; and

_{m}*r*is the radius of maximum wind (RMW). On a 45-km grid,

_{m}*υ*is specified to be 75% of the reported maximum wind and

_{m}*r*is 90 km. According to the references of Low-Nam and Davis (2001) and Davis and Low-Nam (2001), the tests integrating MM5 on a 45-km grid from initial conditions in which a storm with a radius of about 50 km was inserted suggest that the model is unable to resolve the velocity variation and quickly reestablishes the RMW near 90 km, where it remains. Based on several MM5 simulations of tropical cyclones of varying intensity with varying grid increments, they assume that the maximum azimuthally averaged wind is 0.75

_{m}*V*, where

*V*is the reported maximum wind from the best-track data.

The amplitude and height dependence are contained in *A*(*z*), which is specified to be 1.0 from the surface through 850 hPa, 0.95 at 700 hPA, 0.9 at 500 hPa, 0.7 at 300 hPa, 0.6 at 200 hPa, and 0.1 at 100 hPa. Unlike other studies, where the value of *α* typically is around −0.5 (Riehl 1963), here *α* is specified to be −0.75 to reduce the influence of the TC at large radii (of order 500–1000 km).

Mass and wind fields are assumed to be in nonlinear balance above the planetary boundary layer. Within the planetary boundary layer, where this balance does not hold, we let the model adjust the structure as it integrates, which appears to occur mainly within the first 1–2 h of integration.

From the bogussing process above, there are only three input quantities: the longitude and latitude of the reported TC center and the estimated maximum wind. With fewer quantities to be specified, a more arbitrary decision can be avoided. In addition, compared with the N–A scheme, smoothing in the GFDL bogussing scheme (Kurihara et al. 1993) can have adverse effects on the far fields, and may not remove the entire storm from the first guess, or will likely leave significant imbalances in the modified background field.

### b. BDA scheme

*r*is the distance from the TC center,

*R*

_{out}is the radius of the outermost closed isobar,

*P*is the central SLP of the TC,

_{C}*R*is the radius of the maximum gradient of the SLP, and

*dp*is the difference between

*P*and an estimation of the SLP at an infinite distance. According to the gradient wind relationship,

_{C}*dp*can be adjusted to force the bogus wind toward observations, and, therefore, an SLP distribution matching the observed maximum wind can be constructed. Here,

*ρ*is the density of air (assumed constant at 1.2 kg m

^{−3}), and

*f*is the Coriolis parameter. There are a total of seven input parameters. In addition to the latitude and longitude of the reported TC center and the estimated maximum wind, the central SLP, the first guess of

*dp*, the radii of the outermost closed isobar, and the maximum gradient of the SLP, are needed. However, the parameters

*R*and

*R*

_{out}currently are not provided as observed data for the cases studied here and have to be given empirically.

_{b}being the background partial cost function and 𝗝

_{p}the partial cost function that measures the discrepancy between the model-predicted and bogus SLP. Here, 𝗫

_{0}are the initial conditions, which includes initial wind components

*u*and

*υ*, temperature

*T*, specific humidity

*q*, and pressure perturbation

*p*′; 𝗫

_{b}is the background term and has the same components as 𝗫

_{0}; 𝗕 is an approximated background weighting matrix that relates the MM5 analyses at the initial time and 12 h later; 𝗣

^{i}is the SLP at time

*t*; and 𝗣

_{i}^{i}

_{bogus}is the bogus SLP at this time. The weighting 𝗪

*is treated as being constant and determined empirically and, in all experiments, is 2.5 × 10 hPa*

_{P}^{−2}.

## 3. Experimental design

Experiments in this paper are carried out using the nonhydrostatic version of the MM5 and its 4DVAR system. The model with a single domain has a grid spacing of 45 km, and 85 × 91 grid points. The model center is located at the best-track center of the TC. There are 23 half-*σ* levels in the vertical and the pressure at the model top is 10 hPa. The physics options used for the variational data assimilation system are the same as those for the forecast model, including the Grell et al. (1993) cumulus parameterization, the Blackadar (1979) high-resolution planetary boundary layer parameterization scheme, and the Dudhia (1989) explicit moisture scheme with ice. The first-guess conditions are obtained from the National Centers for Environmental Prediction (NCEP) 12-h forecast.

Forty-one cases are chosen from nine different WNP TCs in 2002 (Table 1). Because the experiments are not performed in real time, the selection of the individual cases is based upon the availability of the NCEP analyses for initializing the model. The model forecast tracks and intensities are verified against the best-track analyses from the Joint Typhoon Warning Center (JTWC). For each case, three experiments are conducted, including a control (CTRL, initial field without bogussing) and integrations with initial fields from the N–A and BDA schemes, respectively.

For the BDA experiments, the main steps are as follows. The tendency of SLP is assumed to be near zero for 30 min from the initial time and the same bogus SLP information is assimilated every 5 min within this 30-min window. The cost function and forcing terms are calculated by integrating the forecast model forward for 30 min. In the course of integrating the adjoint model backward, the forcing term is added at each observing time to obtain the gradient with respect to the initial conditions. According to the gradient, the limited-memory quasi-Newton method is used to calculate the new initial conditions, which can reduce the cost function. All of these steps are repeated for 20 iterations. In Zou and Xiao (2000), about 98% of the total adjustment was completed in seven iterations. According to the experiments of Xiao et al. (2002), the major reductions of the cost function and gradient norm occurred in the first five iterations. Therefore, to save computation time, 20 iterations are carried out in this study.

## 4. Results

### a. Initial TC structure

As an example, consider the case of TC Rusa at 1200 UTC 26 August 2002. The input parameters associated with the bogus vortices of our experiments are specified based on the best-track analyses from the China Meteorological Administration (CMA). At that time, the center of Rusa was located at 22.7°N, 144.5°E, and it was in its mature stage, with a minimum sea level pressure (MSLP) of 950 hPa and a maximum wind of 45 m s^{−1}. It is noted that because of the lack of aircraft reconnaissance, some differences in the best-track intensity nearly always exist among different sources. However, the general trends of intensity change from the CMA and JTWC are similar (Yu and Kwon 2005). The value of the cost function has decreased by 2.5 orders of magnitude before 18 iterations, so 20 iterations were enough for the minimization. In the BDA experiments, the assimilation variable (SLP) was forced toward the bogus information, while all other variables (e.g., temperature, wind, and moisture) were free to be consistent under the dynamical and physical constraints of the forecast model. The improvements in the structure of the initial vortex from bogussing experiments are apparent. Figure 1 shows the distributions of the SLP and wind speed at 850 hPa. The MSLP is deepened from 998 hPa (CTRL) to 951 (BDA) and 969 hPa (N–A), and the wind speed is increased from 22 m s^{−1} (CTRL) to 29 (BDA) and 36 m s^{−1} (N–A). At the same time, the center of the SLP becomes more consistent with that of the minimum wind, and the maximum wind center becomes closer to the vortex center after using the bogussing schemes. In the N–A bogussing scheme, because the parameter used to construct the bogus vortex is the observed maximum wind, the adjusted initial MSLP is much weaker than in the observations. In the BDA scheme, because the bogus SLP is assimilated, the adjusted initial maximum wind speed is much weaker than in the observations. Both bogussing schemes appear to improve significantly upon the intensity of TCs present in first-guess fields from global models, however. At the same time, because of the different scales of the bogus vortices, the SLP gradient distribution in the two bogussing schemes is much different, with a gradual gradient in the BDA scheme and a sharper gradient in the N–A scheme near the TC center.

The vertical structures of the initial vortices also vary considerably after using the bogussing scheme. Figure 2 shows the vertical cross sections through the center of the TC of the temperature, specific humidity, and vertical velocity for the CTRL run and the relative differences between the CTRL and the BDA or N–A initial conditions. The temperature and specific humidity for the CTRL is nearly straight and lacks the warm and wet core of a TC. This is because the CTRL initial conditions is interpolated from a global model, which is unable to produce the realistic structures and gradients of a TC because of the sparse observations over the sea and the coarse resolution. This will be an adverse factor for the development of the TC. Although the vertical motion in the CTRL includes the downward motion near the vortex center and upward motion in the eyewall, obviously the scale is not in agreement with that of a TC. A wet center near the low troposphere and a warm core, which becomes warmer and larger with increasing height until the upper troposphere (near 300 hPa) is adjusted by the BDA scheme, but the scale of the vortex (as measured by the RMW) is much larger than actual TCs. Near the TC center, a broad area of weak subsidence is also adjusted by the BDA scheme. In contrast, the N–A scheme produces a much more realistic TC structure than does the BDA, with a warm, moist core aloft. It also produces an RMW with a more realistic size, and the vertical motion field shows an updraft in the eyewall and a small area of subsidence in the eye.

Figure 3 compares the vertical cross sections of the initial axisymmetric mean tangential and radial winds of BDA and N–A to that of the CTRL run. A more realistic horizontal wind field is obtained by the N–A scheme. The wind speed is increased and the RMW is reduced. However, both bogussing schemes enhance the divergent outflow near the TC center, especially in the BDA scheme. This is mainly because strong divergence in the lower troposphere leads to subsidence, compression, and warming to obtain the bogus low pressure hydrostatically in the BDA scheme.

From the discussion above, we notice that the scale and structure of the N–A initial vortex is closer to more realistic TC vortices compared with that of the CTRL. And in the BDA scheme, the 4DVAR technique can produce an initial vortex that is more consistent with the forecast model. Although only the bogus SLP is assimilated, the additional information contained in the SLP can propagate to other levels and other model variables through integration in the 4DVAR assimilation procedure. Compared with the initial vortex in the CTRL, both bogussing schemes have significant improvements in the location, intensity, and structure of a TC.

### b. TC forecast impact: One case study

As an example, consider the case of TC Rusa at 1200 UTC 26 August 2002. Figure 4 gives the differences between the wind vectors for the CTRL and the two bogussing schemes for the lower and upper troposphere after 1 h of integration. The wind fields including bogussing schemes improve the maintenance and development of the TC. There are obvious cyclonic inflows in the low troposphere, and outflows in the upper troposphere. Compared with the N–A scheme, the inflows and outflows for the BDA scheme are relatively stronger, which cause the intensity in the BDA scheme to become stronger than that in N–A scheme after integrating for some time. This result is similar to that of Park and Zou (2004): in the BDA scheme, at the initial time, strong divergence exists in the lower troposphere and convergence exists in the upper levels. A broad area of downward motion is therefore observed. These adjustments in the model variables at the initial time suggest that the hydrostatic constraint plays a dominant role in generating the desired low pressure system. As the forecast model is integrated forward in time, the pressure gradient force associated with the low pressure system starts to play a dominant role. Strong convergence develops in the lower troposphere and a new divergence center in the upper atmosphere develops and intensifies.

Figure 5 compares the simulated tracks and the temporal variations of the MSLP and maximum winds with the best-track data from JTWC for Rusa. For this case, the results suggest significant improvement in the track forecast when the bogus vortex is introduced into the initial conditions. The 24-h position error is reduced from 283 km to 94 (BDA) and 54 km (N–A), and the 48-h error from 277 km to 192 (BDA) and 104 km (N–A), respectively. The BDA track forecasts before 24 h are slightly better than those from the N–A scheme, and the results of N–A become closer to the observed track after 24 h. One of the possible reasons is that for this strong TC the 4DVAR technique used by the BDA scheme can produce an initial vortex that is more consistent with the forecast model, but the N–A inserted axisymmetric vortex has to adjust to the model by integrating for some time after initialization, and the result of that adjustment is a change in the structure of the vortex that results in a degraded track initially, but then the N–A track improves after the adjustment period. The BDA scheme has a definite advantage over the N–A scheme in the intensity forecast at least at this 45-km resolution. For the BDA experiment, the MSLP errors are generally equal to or less than half of the CTRL errors. Although the adjustment of the BDA initial maximum wind seems to be inadequate, the maximum wind rapidly increases to 40 m s^{−1} within the first 6-h integration, with the subsequent errors equal to or less than half of the CTRL errors. Despite the relatively stronger initial maximum wind of 34 m s^{−1}, a dramatic spindown occurs during the first 6 h of the N–A forecast. This is mainly because of the inconsistency among the adjusted initial variables after using the N–A bogussing scheme. However, after the adjustment for about 6 h, the mass and wind fields become more balanced, and, therefore, TC intensity can be maintained after the first 6 h.

### c. Comparisons for all cases

Figure 6 shows the mean forecast track and intensity errors for the 41 cases. The BDA scheme leads to reductions of 25% and 12% for the 24- and 48-h track forecasts, respectively, compared with the CTRL experiments. The mean 24-h position error is reduced from 158 to 118 km, and the 48-h error from 214 to 189 km. For the N–A scheme, the improvements only occur before the 30-h forecast, and after 36 h, the mean errors become larger than in the CTRL. For intensity forecasts, the BDA scheme has a marked advantage over the N–A scheme. Compared with the CTRL experiments, the BDA forecast MSLP root-mean-square (rms) errors are reduced by 10 hPA at nearly all forecast times and the maximum wind rms errors are reduced by more than 5 m s^{−1}. The N–A scheme seems to have a negative impact on the intensity forecast after 24 h.

A further examination of the individual cases suggests that the N–A scheme has a significant negative impact on the track forecasts for the recurving (turning from an initial path west and poleward to east and poleward) TCs. Among the 41 forecasts, there are 4 recurving TCs and 4 left-turning TCs (turning back toward the left and resuming a west-northwest course instead of recurving to the northwest). The N–A forecast track errors for the four left-turning TCs are smaller than in the CTRL at all forecast times, with error reductions that are much larger than the average value of the 41 cases (Fig. 7). However, among the four recurving TCs, three cases have larger N–A errors. Figure 8 shows that in the BDA scheme, although the vortex is intensified, slight differences in the environmental circulation between the BDA and CTRL experiments exist. On the other hand, in the N–A scheme, associated with the decrease in the scale of the vortex, the western Pacific subtropical ridge strengthens and extends westward, which causes TC Rusa at 1200 UTC 30 August to turn to a more westerly track as the westerly environmental steering flow strengthens. The BDA scheme has small changes in the large-scale environmental circulation because only the bogus vortex is assimilated. In the N–A scheme, before the bogus vortex is inserted, the inaccurate vortex should be removed from the background field. And as a result of the small scale of the bogus vortex, the western Pacific subtropical ridge usually strengthens and extends westward, which causes improvements in the track forecast for the left-turning TCs and negative impacts for the recurving TCs. Figure 7 also suggests that for the N–A scheme, because of the 4 recurving TCs, the mean track errors after 36 h (for the 4 recurving TCs, the recurvatures occur after 24 h) for the 41 cases become larger than CTRL.

## 5. Summary and conclusions

This note assesses the different impacts of two bogussing schemes on the track and intensity predictions of western North Pacific tropical cyclones. One scheme produced by NCAR–AFWA (N–A) uses a relatively new removal process to extract the incorrect vortex in the background and another scheme employs the four-dimensional variational data assimilation technique to blend the bogus vortex with the first-guess fields. The innovations in the two schemes emphasize different aspects of the bogussing technique. To compare the two bogussing schemes, 41 forecasts of TCs from 8 TCs occurring over the western North Pacific in 2002 were studied.

Compared with the CTRL initial fields, significant improvements in the location, intensity, and structure of the vortices were found for both schemes. However, although the initial vortex structure produced by the N–A scheme is more physically realistic, the initial intensity still seems to be somewhat inadequate, and some imbalances are likely left in the modified variables. The adjustment in the BDA initial vortex structure is less realistic, but the four-dimensional variational data assimilation technique will allow the bogus data and background field to be consistent during the dynamical adjusting process and the adjusted initial intensity to be closer to the observed value.

Excluding the recurving TCs, the N–A bogussing scheme has a positive impact on the track forecast. The BDA scheme has better performance in both the track and intensity forecasts. The mean track errors for the 41 cases are reduced by 40 and 25 km for the 24- and 48-h forecasts, respectively, and for the 6–18-h forecasts, even above 50 km. The intensity error reductions at some forecast times are nearly 50%.

It is worth noting some of the limitations of testing both bogussing schemes for intensity forecasts at 45-km grid length. The TC intensity change is closely associated with the inner structure, which requires high resolution for accurate simulations. The Hurricane Weather Research and Forecast (HWRF) model, with an inner-nest resolution of 9 km, was developed at NCEP and began providing operational hurricane forecasts in 2007 (NCEP 2007). Therefore, case studies at higher resolution should be performed in the future to examine whether the improved initial structures in the N–A scheme would yield a greater improvement in TC intensity forecasts. However, at this 45-km resolution at least, the fact that the BDA scheme produces structures that are consistent with the model at the initial time, even though they are less realistic than the N–A scheme, evidently produces a greater benefit to the subsequent track and intensity forecasts, which can be validated to a certain extent by the forecast results.

The implementation of the N–A bogussing scheme is much simpler than that of the BDA scheme. Little additional computational time is needed for the N–A scheme, while the improved results of the BDA scheme entail substantial additional computational expense. Despite the relatively more expensive computational investment required, continuing increases in computing power and the developments of more timesaving and efficient approaches, such as that proposed by Wang and Zhao (2006), should make the BDA an operational possibility.

## Acknowledgments

We thank the National Science Foundation of China for supporting a general project (adjoint sensitivity analyses on the influence factors in the intensity change of typhoon; Grant 40605018), the Chinese Academy of Sciences for an innovation research project (application of nonlinear optimum method to studies of weather and climate predictabilities; Grant KZCX3-SW-230), and the National Science Foundation of China for a general project (mechanism analysis of subseasonal weather and climate characteristics in Yangtze and Huaihe river basins during warm-season; Grant 40475044).

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The name, number of cases, and forecast dates of TCs used for the experiments. All TCs are from 2002.