Including Uncertainties of Sea Surface Temperature in an Ensemble Kalman Filter: A Case Study of Typhoon Sinlaku (2008)

Masaru Kunii Department of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland

Search for other papers by Masaru Kunii in
Current site
Google Scholar
PubMed
Close
and
Takemasa Miyoshi Department of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland

Search for other papers by Takemasa Miyoshi in
Current site
Google Scholar
PubMed
Close
Full access

Abstract

Sea surface temperature (SST) plays an important role in tropical cyclone (TC) life cycle evolution, but often the uncertainties in SST estimates are not considered in the ensemble Kalman filter (EnKF). The lack of uncertainties in SST generally results in the lack of ensemble spread in the atmospheric states near the sea surface, particularly for temperature and moisture. In this study, the uncertainties of SST are included by adding ensemble perturbations to the SST field, and the impact of the SST perturbations is investigated using the local ensemble transform Kalman filter (LETKF) with the Weather Research and Forecasting Model (WRF) in the case of Typhoon Sinlaku (2008). In addition to the experiment with the perturbed SST, another experiment with manually inflated ensemble perturbations near the sea surface is performed for comparison. The results indicate that the SST perturbations within EnKF generally improve analyses and their subsequent forecasts, although manually inflating the ensemble spread instead of perturbing SST does not help. Investigations of the ensemble-based forecast error covariance indicate larger scales for low-level temperature and moisture from the SST perturbations, although manual inflation of ensemble spread does not produce such structural effects on the forecast error covariance. This study suggests the importance of considering SST perturbations within ensemble-based data assimilation and promotes further studies with more sophisticated methods of perturbing SST fields such as using a fully coupled atmosphere–ocean model.

Corresponding author address: Masaru Kunii, Dept. of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, MD 20742. E-mail: kunii@atmos.umd.edu

Abstract

Sea surface temperature (SST) plays an important role in tropical cyclone (TC) life cycle evolution, but often the uncertainties in SST estimates are not considered in the ensemble Kalman filter (EnKF). The lack of uncertainties in SST generally results in the lack of ensemble spread in the atmospheric states near the sea surface, particularly for temperature and moisture. In this study, the uncertainties of SST are included by adding ensemble perturbations to the SST field, and the impact of the SST perturbations is investigated using the local ensemble transform Kalman filter (LETKF) with the Weather Research and Forecasting Model (WRF) in the case of Typhoon Sinlaku (2008). In addition to the experiment with the perturbed SST, another experiment with manually inflated ensemble perturbations near the sea surface is performed for comparison. The results indicate that the SST perturbations within EnKF generally improve analyses and their subsequent forecasts, although manually inflating the ensemble spread instead of perturbing SST does not help. Investigations of the ensemble-based forecast error covariance indicate larger scales for low-level temperature and moisture from the SST perturbations, although manual inflation of ensemble spread does not produce such structural effects on the forecast error covariance. This study suggests the importance of considering SST perturbations within ensemble-based data assimilation and promotes further studies with more sophisticated methods of perturbing SST fields such as using a fully coupled atmosphere–ocean model.

Corresponding author address: Masaru Kunii, Dept. of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, MD 20742. E-mail: kunii@atmos.umd.edu

1. Introduction

For atmospheric and oceanic data assimilation studies, the ensemble Kalman filter (EnKF; Evensen 1994; 2003) has been widely used and explored. After the traditional EnKF methods (Houtekamer and Mitchell 1998; Keppenne 2000), various alternatives to the EnKF have been developed during the past decade (e.g., Anderson 2001; Bishop et al. 2001; Whitaker and Hamill 2002; Hunt et al. 2007). The EnKF has become the choice of operational numerical weather prediction (NWP) systems at the Meteorological Service of Canada (Houtekamer et al. 2005; Houtekamer and Mitchell 2005) and the Met Office (Bowler et al. 2008).

The EnKF has also been applied with mesoscale limited-area models for regional NWP (e.g., Snyder and Zhang 2003; Dowell et al. 2004; Miyoshi and Aranami 2006; Dirren et al. 2007; Bonavita et al. 2008; Zhang et al. 2009; Torn 2010; Meng and Zhang. 2011; Miyoshi and Kunii 2012). In EnKF applications with limited-area models, including ensemble perturbations in the boundary conditions has been a major issue. Using identical boundary conditions for all ensemble members yields generally insufficient ensemble spread near the boundaries, which would lead to systematic underestimation of the weight of the observations on the analyses. Some of the previous studies applied ensemble perturbations to the boundary conditions (e.g., Barker 2005; Torn et al. 2006), whereas other studies used identical boundary conditions with large enough domains (e.g., Snyder and Zhang 2003; Dowell et al. 2004; Bonavita et al. 2008; Miyoshi and Kunii 2012). Torn et al. (2006) proposed several methods to perturb lateral boundary conditions and showed promising results. However, these previous studies focused only on the lateral boundary conditions and, to the best of the authors’ knowledge, no research has been published thus far that investigates in detail the impact of perturbing the lower boundary conditions with an EnKF, such as ground temperature and moisture, and sea surface temperature (SST).

The significant impact of SST on NWP has long been perceived, particularly in the tropical cyclone (TC) life cycle evolution. Studies have shown that SST plays an important role in the generation stage and the subsequent intensification stage of TCs (Palmen 1948; Tuleya and Kurihara 1981; Emanuel 1986). TCs are strengthened or maintained through heat and moisture fluxes from the warm upper ocean, which leads to further intensification of TCs as the evaporation rate is enhanced by the increasing wind speed. The intensifying winds in turn enhance mixing in the upper ocean, contributing to cooling SSTs beneath the TCs (Price 1981). Lowering SST then results in the reduction of sensible and latent heat fluxes into the atmosphere from the ocean surface and leads to a decrease in storm intensity (Ginis 2002). These positive and negative feedback processes have nonlinear interactions and introduce complexities into the TC intensity forecasts. Hence, for the simulation focused on TC life cycle evolution, it is essential to consider the air–sea interaction processes appropriately.

Although many studies have been published thus far investigating the air–sea coupling effects in the TC forecasts (Bender et al. 1993; Schade and Emanuel 1999; Bender and Ginis 2000; Chan et al. 2001; Emanuel et al. 2004; Bender et al. 2007), data assimilation studies that consider the air–sea interactions are still at an early stage. Some recent studies found it important to consider the uncertainties of SST in ensemble forecasting (Eckel and Mass 2005; Vialard et al. 2005). However, the uncertainties of SST are usually ignored in an EnKF, and it is unknown what impact perturbing SST may have on ensemble-based data assimilation cycles, particularly on TC analyses and forecasts that are generally sensitive to SST. The present study aims at investigating the impact of SST perturbations on EnKF data assimilation cycles with a limited-area atmospheric forecast model. Section 2 describes the experimental system and settings. The results are presented in section 3. Finally, conclusions are provided in section 4.

2. Experimental settings

a. The WRF-LETKF system

Miyoshi and Kunii (2012, hereafter MK12) developed the local ensemble transform Kalman filter (LETKF; Hunt et al. 2007) system with the Weather Research and Forecasting Model (WRF; Skamarock et al. 2005), and obtained promising results with the analyses and forecasts of Typhoon Sinlaku in September 2008. Sinlaku formed as a tropical depression east of the Philippines at 0000 UTC 8 September, and intensified into a tropical storm at 1800 UTC that day. Moving northward with steady intensification, Sinlaku reached its peak intensity with a minimum central pressure of 935 hPa at 1200 UTC 10 September after a relatively rapid intensification with the minimum mean sea level pressure (MSLP) dropping by 40 hPa in the previous 24 h. After making landfall on Taiwan, it recurved in the north of Taiwan and passed south of Japan after a slight reintensification. The best track of Sinlaku from the Regional Specialized Meteorological Center (RSMC) Tokyo-Typhoon Center is shown in Fig. 1.

Fig. 1.
Fig. 1.

Model domains for the WRF-LETKF analysis (D01, 60-km grid spacing) and the WRF model simulations (D02, 20-km grid spacing), along with the best track of Typhoon Sinlaku from 0000 UTC 8 Sep (0800) to 0000 UTC 20 Sep (2000) 2008.

Citation: Weather and Forecasting 27, 6; 10.1175/WAF-D-11-00136.1

In the present study, the WRF-LETKF data assimilation cycle is initiated at 1200 UTC 6 August 2008 with 27 ensemble initial conditions from the National Centers for Environmental Prediction (NCEP) Final Analysis (FNL) fields on randomly chosen dates during August 2007 and 2008, and continues until 0000 UTC 20 September 2008. The spinup period of more than a month before Sinlaku’s generation is long enough for the ensemble-based error covariance in the LETKF to stabilize. The lateral boundary conditions are derived from the NCEP FNL in all ensemble members; that is, the perturbations of the lateral boundary conditions are not considered in this study. MK12 investigated the effect of the unperturbed lateral boundary conditions and found it not essential to the analyses and forecasts of Sinlaku (2008).

The ensemble size of 27 is chosen based on the verification results of MK12. They compared the LETKF performance with different ensemble sizes (20, 27, 34, and 41 members) in terms of accuracy and computational efficiency, and found that the ensemble size of 27 was a reasonably balanced choice. The covariance localization parameters follow MK12: 400 km in the horizontal, 0.4 in the logp coordinate in the vertical, and 3 h in time; the equivalent radii of influence are about 1460 km and 1.46 in the logp coordinate. The adaptive covariance inflation scheme (Miyoshi 2011) is employed, so that the inflation factors are estimated adaptively at each grid point. MK12 showed that adaptive inflation outperformed fixed multiplicative inflation with this WRF-LETKF system using real observations in the case of Sinlaku. The data assimilation cycle interval is 6 h, in which observations separated into hourly bins are assimilated using the 4D-LETKF (Hunt et al. 2004).

Version 3.2.1 of the Advanced Research core of the WRF (ARW; Skamarock et al. 2005) is set up in the northwestern Pacific region (D01 in Fig. 1) at 60-km resolution (137 × 109 horizontal grid points) and with 40 vertical levels up to 10 hPa. The Kain–Fritsch cumulus parameterization scheme (Kain and Fritsch 1993) is used, along with the WRF single-moment five-class (WSM5) microphysics scheme (Hong et al. 2004). Other parameterization schemes include the Yonsei University (YSU) planetary boundary layer scheme (Hong et al. 2006), the Rapid Radiative Transfer Model (RRTM) long-wave radiation scheme (Mlawer et al. 1997), and the Dudhia shortwave radiation scheme (Dudhia 1989). Initialized by the 60-km analysis, one-way-nested forecasts at 20-km resolution are also performed (D02 in Fig. 1).

As for the observation data, the real observations used in the NCEP Global Data Assimilation System (GDAS), including upper-air sounding data from radiosondes and dropsondes, surface stations, ships, buoys, aircrafts, wind profilers, and satellite-based winds are assimilated. These observation data are available through the University Corporation for Atmospheric Research (UCAR) data server in the PREPBUFR format (Keyser 2010). The satellite radiances are not used in this study.

b. SST perturbations

This study aims to reveal the impact of SST perturbations on the WRF-LETKF cycles, and basically performs two experiments. The CTRL experiment employs no SST perturbations (i.e., the original settings of the WRF-LETKF as in MK12). All ensemble members in CTRL have the same SST fields as in the NCEP FNL data. The other experiment, SSTP, employs SST perturbations, while all other settings are the same as in CTRL; in particular, the ensemble-mean SST fields are the same as in CTRL.

The SST perturbations are derived from random draws of SST analyses. Specifically, 27 SST fields are randomly selected from the SST fields of the NCEP FNL data during August and September 2008, and the ensemble average of the 27 SST fields is subtracted to generate 27 SST perturbation fields. These perturbation fields are added to the SST analysis in every cycle, so that the ensemble-mean SST remains the same for both the CTRL and SSTP experiments. Here, each ensemble member has the temporally fixed SST perturbations throughout the experimental period, in order to avoid abrupt changes in the SST fields at every 6 h. The SST fields are not updated by the observations through the LETKF analysis, since this would involve ocean data assimilation, which is beyond the scope of this study. Although these SST perturbations are temporally constant and are chosen independently from the atmospheric fields, they would represent general climatological uncertainties of SST fields with spatial variations. Since the SST perturbations are derived from the SST analyses during the experimental period, these perturbations are not available in real-time applications. Despite these limitations, this study aims to explore the potential impact of SST perturbations on atmospheric ensemble data assimilation.

Figure 2a shows the time series of SST averaged over the entire model domain. The maximum amplitude of the SST perturbations is about 0.2 K, and the distribution appears to be positively skewed with longer tail in the upper end. Although this would not be ideal, this issue is not considered further in the present study. Figure 2b shows the horizontal pattern of the SST perturbation field for a randomly chosen member, indicating relatively broad structures in contrast to smaller scales of atmospheric variables. Figure 2c shows the ensemble spread of SST, in which we find local maxima of about 0.2 K over the region 10°–30°N, 110°–140°E, where Sinlaku existed in its generation and intensification stages. This probably corresponds to the SST changes due to Sinlaku’s passage. The horizontally averaged SST over that region exceeds 29°C (302 K), indicating a generally favorable environment for the development of TCs. The averaged ensemble spread of SST in the whole domain, or the SST perturbation size, is approximately 0.32 K.

Fig. 2.
Fig. 2.

(a) Time series of SST averaged over the entire domain D1 during September 2008, for the NCEP analysis (ANAL, solid line) and each ensemble member (MEM, dashed lines). Horizontal distributions (K) of (b) a single ensemble member of the SST perturbation field and (c) the ensemble spread of SST.

Citation: Weather and Forecasting 27, 6; 10.1175/WAF-D-11-00136.1

3. Results

a. General verifications

First, general verification measures are investigated to find the overall impact of perturbed SST in the WRF-LETKF system. Figure 3 shows the verifications of 6-h forecasts relative to radiosonde observations averaged over 19 days from 0000 UTC 1 September to 0000 UTC 20 September, including the whole life cycle of Sinlaku. Only very small portions of radiosonde data exist around Sinlaku over the ocean, so that this verification measure does not specifically represent the forecast errors of Sinlaku but does represent the forecast errors mostly over land where most radiosonde data exist. The root-mean-square errors (RMSE) of the zonal wind component are improved in the lower and upper troposphere due to the SST perturbations (Fig. 3a). In addition, the wind forecast error biases are reduced consistently below 250 hPa in the SSTP experiment. This is also true of the meridional wind component (not shown). For temperature, no significant difference is found between CTRL and SSTP (Fig. 3b). The RMSEs and biases for moisture show the slight but consistent advantage of perturbing SST, especially at lower levels (Fig. 3c). Overall, the statistical significance of these verification results seems to be low, as we often see in operational system developments.

Fig. 3.
Fig. 3.

The 6-h forecast verifications relative to radiosonde observations for (a) zonal wind component (U, m s−1), (b) temperature (T, K) and (c) water vapor mixing ratio (QV, g kg−1), averaged over 19 days from 0000 UTC 1 Sep to 0000 UTC 20 Sep 2008. The forecast model resolution is 60 km. Dashed, solid, and dotted lines correspond to the CTRL, SSTP, and INFL experiments, respectively, and thick and thin lines indicate RMSEs and biases, respectively.

Citation: Weather and Forecasting 27, 6; 10.1175/WAF-D-11-00136.1

To account for data-scarce regions such as over the ocean, we verify the analysis fields relative to the NCEP FNL. NCEP FNL has an advantage of including additional satellite radiance data that are important over the ocean. Figure 4 shows the time series of the RMSE for the wind components (U, V), temperature (T), and relative humidity (RH). SST perturbations improve the RMSEs of U850 and U500 during most of the experimental period, especially before the generation of Sinlaku, from 5 to 8 September (Figs. 4a and 4b). As for temperature, although there was no significant difference in Fig. 3b, the RMSE of SSTP is generally smaller than that of CTRL most of the time (Figs. 4e and 4f). In addition, the improvement in the RH at 850 hPa is large and consistent (Fig. 4h). These results suggest that the SST perturbations bring significant advantages for temperature and relative humidity analyses over the ocean.

Fig. 4.
Fig. 4.

Time series of analysis RMS differences from NCEP FNL for zonal wind components (U and V, m s−1), temperature (T, K), and relative humidity (RH, %) at 925, 850, and 500 hPa averaged over the entire model domain. The variables (a) U850, (b) U500, (c) V850, (d) V500, (e) T850, (f) T500, (g) RH925 and (h) RH850 are shown for CTRL (dashed), SSTP (solid), and INFL (dotted).

Citation: Weather and Forecasting 27, 6; 10.1175/WAF-D-11-00136.1

b. TC forecast verifications

We now focus on the verification of the TC analyses and their subsequent forecasts. Here, since the forecasts are single deterministic runs from the ensemble-mean analyses, no SST perturbations are involved in the forecasts; that is, the difference between CTRL and SSTP is purely from the initial conditions of the atmosphere. The MSLP analyses of all experiments are generally weaker than the best-track data mainly due to the insufficient model resolution of 60 km (Fig. 5a). However, the overall pattern of behavior of the strengthening and weakening tendencies seems to be relatively well captured with a small time lag. Although Fig. 5a shows no significant difference among the TC intensity analyses due to the SST perturbations, Fig. 5b indicates a consistent advantage in the forecast track error averaged over 16 initial times from 0000 UTC 9 September to 1800 UTC 12 September. The improvement due to the SST perturbations in the WRF-LETKF cycles becomes apparent after 18-h forecasts and grows as large as 50 km in 48-h forecasts.

Fig. 5.
Fig. 5.

(a) Time series of Sinlaku’s central pressure analyses of CTRL (dashed), SSTP (solid), and INFL (dotted), along with the best-track data (dotted–dashed). The resolution of the analysis is 60 km. (b) Time-mean forecast track errors of Sinlaku over 16 initial times from 9 to 12 September for the deterministic WRF forecasts initialized by the CTRL (dashed), SSTP (solid), and INFL (dotted) analyses. In each forecast, the same SST is used.

Citation: Weather and Forecasting 27, 6; 10.1175/WAF-D-11-00136.1

To investigate the impact of SST perturbations on the TC intensity forecast, one-way-nested WRF forecasts with a horizontal resolution of 20 km (D02 in Fig. 1) are performed for the same 16 initial times. Here, single deterministic runs are initiated by the ensemble-mean analyses, so that there are no SST perturbations involved in the forecasts. Figure 6 depicts the results of a single case; the initial time of the experiment is 0000 UTC 9 September, so that the 72-h forecast period includes Sinlaku’s rapid intensification stage, in which the MSLP of Sinlaku dropped by 40 hPa (24 h)−1. The results show that the forecast MSLP initiated from the SSTP analysis successfully captures the rapid intensification with a relatively small time lag, showing the pressure drop of about 39 hPa from 1200 UTC 9 September to 1200 UTC 10 September (Fig. 6a). The forecast from the CTRL analysis also represents the remarkable development of Sinlaku, but the drop in MSLP during the 24-h period is about 28 hPa. Notable differences are also found in the TC track forecasts (Fig. 6b). Although the forecast from the CTRL analysis shows a better track than that from the SSTP analysis in the early stage up to 12-h forecasts, the discrepancy between the CTRL forecast and the best track becomes larger as the forecast proceeds, reaching more than 500 km after 72 h of forecast time. By contrast, the SSTP forecast shows much better agreement with the best track throughout the forecast period. Other initial times also show the advantages of the SST perturbations, especially in Sinlaku’s rapid intensification stage. The track forecast errors averaged over 16 initial times using the 20-km experiments are almost identical to Fig. 5b of the 60-km experiments.

Fig. 6.
Fig. 6.

(a) Evolution of the central pressure and (b) the forecast tracks of Sinlaku, simulated in the 20-km one-way-nested WRF forecasts up to 72 h, initialized at 0000 UTC 9 Sep 2008 by the analyses of the CTRL (blue) and SSTP (red) experiments. The best track is shown by the black lines.

Citation: Weather and Forecasting 27, 6; 10.1175/WAF-D-11-00136.1

Figure 7 illustrates the analysis and 12-h forecast of geopotential height at 500 hPa for each experiment along with the NCEP FNL analysis at the corresponding time. Here, the NCEP-FNL analysis is used as a reference, which is useful for verifying the 12-h forecasts (Figs. 7c and 7d). In the CTRL experiment, the stronger subtropical high is analyzed to be farther east of Sinlaku than that in the NCEP FNL (Fig. 7a), which would cause the northwestward shift of the TC track in the 12-h forecast (Fig. 7c). By contrast, the subtropical high in the SSTP experiment is relatively similar to that in the NCEP FNL although no significant difference is found in the TC structures between CTRL and SSTP. The 12-h forecast of geopotential height in SSTP has better correspondence with that in the NCEP FNL. As a result, the large improvement of the TC track forecasts in longer leads implies that the SST perturbations may contribute to improving the large-scale environment in the analysis rather than the TC structure itself.

Fig. 7.
Fig. 7.

The 500-hPa geopotential height analyses (m) at 0000 UTC 9 Sep 2008 for (a) CTRL and (b) SSTP (thick black contours), superimposed on the NCEP FNL analysis (gray coutours). (c),(d) As in (a),(b), but for the 12-h forecasts at 1200 UTC 9 Sep 2008. The cyclone weather symbols indicate the observed TC positions.

Citation: Weather and Forecasting 27, 6; 10.1175/WAF-D-11-00136.1

c. Ensemble spread analysis

The ensemble spread is investigated; Fig. 8 shows the vertical profiles averaged over the entire model domain for 16 analyses from 9 to 12 September. Not surprisingly, the SST perturbations yield larger ensemble spread, especially for lower-level temperature and specific humidity (Figs. 8b and 8c). Wind ensemble spread shows almost no impact from the SST perturbations (Fig. 8a). In CTRL, the ensemble spread of temperature and humidity may be underestimated at the lower levels since all ensemble members use identical SSTs. In fact, Fig. 3b shows an increase in temperature error near the surface, although Fig. 8b shows a decrease in temperature ensemble spread near the surface for CTRL. By contrast, the SSTP shows increasing temperature ensemble spread near the surface, being consistent with the error.

Fig. 8.
Fig. 8.

Vertical profiles of the ensemble spread for (a) zonal wind component (m s−1), (b) temperature (K), and (c) water vapor mixing ratio (g kg−1), averaged over the entire model domain D1 under z = 20 for 16 analyses from 9 to 12 Sep 2008, in CTRL (dashed line), SSTP (solid line), and INFL (dotted line).

Citation: Weather and Forecasting 27, 6; 10.1175/WAF-D-11-00136.1

In the present study, the adaptive covariance inflation method of Miyoshi (2011) is applied to find optimal multiplicative inflation factors at each grid point. The inflation factors are estimated by using the observation-minus-forecast innovation statistics based on Desroziers et al. (2005) and Li et al. (2009). Since a large number of satellite-based wind observations such as the Quick Scatterometer (QuikSCAT) and the Special Sensor Microwave Imager (SSM/I) retrieval winds are assimilated, far more wind observations contribute to the analyses near the surface than temperature and moisture observations. Therefore, the inflation factors are optimized mainly for winds. This may be why adaptive inflation is suboptimal for temperature and moisture in CTRL.

To investigate whether the benefits from the SST perturbations may simply come from the large ensemble spread for lower-level temperature and humidity, an additional experiment named INFL is performed, with manual inflation of the ensemble spread for lower-level temperature and humidity but without perturbing SST. In INFL, additional inflation up to about 40% is applied to the lower-level temperature and humidity, on top of the regular adaptive inflation.

As intended, INFL shows large ensemble spread for lower-level temperature and moisture (Fig. 8), so that the ensemble spread of INFL is much closer to SSTP than CTRL. However, Fig. 5 shows no advantage of INFL. Namely, the manually inflated ensemble spread does not help improve the TC forecasts and can even degrade the results at times. Similar results are consistently found in the verifications relative to the NCEP GDAS (Fig. 4), indicating that the brute enforcement of larger ensemble spread for lower-level temperature and humidity has no essential influence toward improvement of analyses and forecasts. This implies that perturbing SST has a physically meaningful impact on the use of observations in the LETKF.

d. Structure of the error covariance

The results from the previous subsection motivated us to further investigate the structure of the error covariance estimated from the ensemble perturbations. The ensemble-based error covariance is responsible for the way in which observations are assimilated in the LETKF. Figure 9 shows horizontal error covariance maps of temperature and moisture fields at the fifth model level (~925 hPa) at 1200 UTC 10 September. Here, the same localization function as is used in the LETKF is considered, but in the model space rather than the observation space. This simulates approximately the analysis increments from a temperature or humidity observation at the center (cross marks).

Fig. 9.
Fig. 9.

Horizontal error covariance maps of temperature at the fifth model level (~925 hPa) estimated from the forecast ensemble perturbations of the (a) CTRL and (b) SSTP experiments at 1200 UTC 10 Sep 2008. (c),(d) As in (a),(b), but for specific humidity. The center of the region (denoted by the cross marks) is the base point of the covariance. Localization is applied by multiplying localization factors by the error covariance.

Citation: Weather and Forecasting 27, 6; 10.1175/WAF-D-11-00136.1

In general, the estimated error correlations have significantly broader structures in SSTP than those in CTRL for low-level temperature and moisture (Fig. 9). This is probably because of the spatially and temporally larger correlation scales of the SST perturbation fields. In addition, the covariant directions for temperature are different between CTRL and SSTP. The temperature correlations of CTRL (Fig. 9a) are oriented in the north-northwest to south-southeast direction, whereas those of SSTP (Fig. 9b) are aligned in the southwest to northeast direction. The low-level temperature error correlations are strongly affected by the correlations of SST perturbations. Humidity correlations show smaller differences between CTRL and SSTP, but larger-scale features appear in the correlations of SSTP. The difference in the forecast error correlations is not found in an additional sensitivity experiment where the SST perturbations are given by independent random numbers at each grid point with the same standard deviation as in the SSTP experiment. The broad temperature correlations in the SSTP experiment would be physically meaningful and play an essential role.

These differences in forecast error correlations result in a qualitative difference in the use of observations. The NCEP PREPBUFR observation dataset contains conventional observations as well as satellite-based wind data. Since satellite radiances or temperature–humidity retrievals are not included, observation instruments that measure temperature and moisture profiles near the sea surface are limited to radiosondes, dropsondes, ships, and buoys. The broad covariance structure of SSTP contributes to broadening the impact of these sparse observations, which would have caused the difference in the analyses and subsequent forecasts.

e. SST perturbations drawn from the previous year (SSTP2007)

So far, the SST perturbations were derived from a single realization of random draws from SST analyses during August and September 2008. Although this could address the potential impact of including SST uncertainties, this approach is not applicable in real time and may lead to erroneous implications. Namely, the promising results may have been simply a product of chance due to the particular random draws, or may have been overestimated by using the samples from the same year as the experimental period (2008). To address these issues, different SST perturbations are randomly chosen from the SST fields from the previous year (2007). This approach can be applied in real time and also addresses the robustness of the method with another realization of random draws. We call this additional experiment SSTP2007.

The SST perturbations drawn from the previous year also help improve Sinlaku’s analyses and forecasts, although not as much as in the previous SSTP experiment. Figure 10a shows the horizontal pattern of the SST ensemble spread, which is similar to that in Fig. 2c. We find a generally similar pattern, with larger spread in the midlatitudes (30°–50°N) and smaller spread in the tropical Pacific east of 140°E, although the peak locations shift southward in SSTP2007. Figure 10b shows the forecast track errors of Sinlaku over 16 initial times from 9 to 12 September. SSTP2007 shows consistent improvement over CTRL, although the results are slightly worse than those of SSTP after 30-h forecasts. These results of SSTP2007 are consistent with those of SSTP, suggesting that the general conclusions are robust for the choice of random draws, particularly the year of the sampled SST analyses, although SSTP would have slightly overestimated the impact of including SST perturbations.

Fig. 10.
Fig. 10.

(a) As in Fig. 2c, but for the perturbations randomly chosen from the SST fields in 2007. (b) As in Fig. 5b, but including the experiment with SST perturbations derived from SSTs in 2007 (SSTP2007).

Citation: Weather and Forecasting 27, 6; 10.1175/WAF-D-11-00136.1

4. Summary and discussions

In this study, the influence of SST perturbations on ensemble-based data assimilation was investigated with the WRF-LETKF system. With the SST perturbations, the analysis fields and the subsequent model forecasts were improved, particularly in Sinlaku’s forecasts. Since the SST perturbations increased the ensemble spread for lower-level temperature and moisture, an additional experiment with a brute enforcement of large ensemble spread through manual inflation was performed. The manually inflated ensemble spread did not contribute to the improvement of TC analyses or forecasts, implying that the physically meaningful perturbations caused by SST perturbations were essential in the EnKF simulations. The estimated error correlations for low-level temperature and moisture showed horizontally broader structures due to the SST perturbations. This structural change in the ensemble-based error covariance would have played an essential role in ensemble-based data assimilation and may be the reason for the improvement due to perturbing SST.

This study investigated only Sinlaku’s case. To investigate the case dependence of the results, similar experiments were repeated for the case of Typhoon Jangmi (2008). Figure 11 shows the time-mean forecast track errors for Jangmi, similar to Fig. 5b, indicating the consistent advantage of SSTP. Namely, the advantage of using climatological SST perturbations on the TC track forecast is not limited to the case of Sinlaku. Further studies on the robustness and significance with more cases remain as a subject of future research.

Fig. 11.
Fig. 11.

As in Fig. 5b, bur for Typhoon Jangmi (2008), averaged over 16 initial times from 24 to 26 Sep 2008.

Citation: Weather and Forecasting 27, 6; 10.1175/WAF-D-11-00136.1

The method of perturbing SST in this study was apparently primitive, fixed in time, and drawn from random dates within the experimental period; therefore, further studies are desired with more sophisticated approaches to perturbing SST. Saha et al. (2010) used an air–sea coupled global model (NCEP Climate Forecasting System), but employed separate data assimilation systems for ocean and atmosphere. For the seasonal-to-decadal climate predictions, Zhang et al. (2007) developed an atmosphere–ocean fully coupled data assimilation system using an EnKF scheme with the Geophysical Fluid Dynamics Laboratory (GFDL) global atmosphere–ocean coupled climate model. These previous studies explicitly considered the effect of the SST variations on the long-term climate simulations. The results obtained in this study indicate that the influence of SST perturbations would be significant even with the relatively short-range data assimilation cycles. For further improvement of limited-area forecasts, particularly for TCs that are generally sensitive to SST, developing and investigating air–sea coupled data assimilation with the explicit consideration of the error covariance between atmospheric and oceanic variables would be an important subject of future research.

Acknowledgments

The authors thank the members of the UMD Weather-Chaos Group for fruitful discussions. The NCEP PREPBUFR observation data were obtained from the UCAR data server, while several missing files were kindly provided by Daryl Kleist of NCEP. The authors are grateful to the three anonymous reviewers for their valuable comments, which helped improve the manuscript significantly. This study was supported by the Office of Naval Research (ONR), through Grant N000141010149, under the National Oceanographic Partnership Program (NOPP).

REFERENCES

  • Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129, 28842903.

  • Barker, D. M., 2005: Southern high-latitude ensemble data assimilation in the Antarctic Mesoscale Prediction System. Mon. Wea. Rev., 133, 34313449.

    • Search Google Scholar
    • Export Citation
  • Bender, M. A., and Ginis I. , 2000: Real-case simulations of hurricane–ocean interaction using a high-resolution coupled model: Effects on hurricane intensity. Mon. Wea. Rev., 128, 917946.

    • Search Google Scholar
    • Export Citation
  • Bender, M. A., Ginis I. , and Kurihara Y. , 1993: Numerical simulations of tropical cyclone-ocean interaction with a high-resolution coupled model. J. Geophys. Res., 98 (D12), 23 24523 263.

    • Search Google Scholar
    • Export Citation
  • Bender, M. A., Ginis I. , Tuleya R. , Thomas B. , and Marchok T. , 2007: The operational GFDL coupled hurricane–ocean prediction system and a summary of its performance. Mon. Wea. Rev., 135, 39653989.

    • Search Google Scholar
    • Export Citation
  • Bishop, C. H., Etherton B. J. , and Majumdar S. J. , 2001: Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon. Wea. Rev., 129, 420436.

    • Search Google Scholar
    • Export Citation
  • Bonavita, M., Torrisi L. , and Marcucci F. , 2008: The ensemble Kalman filter in an operational regional NWP system: Preliminary results with real observations. Quart. J. Roy. Meteor. Soc., 134, 17331744.

    • Search Google Scholar
    • Export Citation
  • Bowler, N. E., Arribas A. , Mylne K. R. , Robertson K. B. , and Beare S. E. , 2008: The MOGREPS short-range ensemble prediction system. Quart. J. Roy. Meteor. Soc., 134, 703722.

    • Search Google Scholar
    • Export Citation
  • Chan, J. C. L., Duan Y. , and Shay L. K. , 2001: Tropical cyclone intensity change from a simple ocean–atmosphere coupled model. J. Atmos. Sci., 58, 154172.

    • Search Google Scholar
    • Export Citation
  • Desroziers, G., Berre L. , Chapnik B. , and Poli P. , 2005: Diagnosis of observation, background and analysis-error statistics in observation space. Quart. J. Roy. Meteor. Soc., 131, 33853396.

    • Search Google Scholar
    • Export Citation
  • Dirren, S., Torn R. D. , and Hakim G. J. , 2007: A data assimilation case study using a limited-area ensemble Kalman filter. Mon. Wea. Rev., 135, 14551473.

    • Search Google Scholar
    • Export Citation
  • Dowell, D. C., Zhang F. , Wicker L. J. , Snyder C. , and Crook N. A. , 2004: Wind and temperature retrievals in the 17 May 1981 Arcadia, Oklahoma, supercell: Ensemble Kalman filter experiments. Mon. Wea. Rev., 132, 19822005.

    • Search Google Scholar
    • Export Citation
  • Dudhia, J., 1989: Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 30773107.

    • Search Google Scholar
    • Export Citation
  • Eckel, F. A., and Mass C. F. , 2005: Aspects of effective mesoscale, short-range ensemble forecasting. Wea. Forecasting, 20, 328350.

  • Emanuel, K. A., 1986: An air–sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585604.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., DesAutels C. , Holloway C. , and Korty R. , 2004: Environmental control of tropical cyclone intensity. J. Atmos. Sci., 61, 843858.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99 (C5), 10 14310 162.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 2003: The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dyn., 53, 343367.

  • Ginis, I., 2002: Tropical cyclone–ocean interactions. Atmosphere–Ocean Interactions, W. Perrie, Ed., Advances in Fluid Mechanics Series, Vol. 33, WIT Press, 83–114.

  • Hong, S.-Y., Dudhia J. , and Chen S.-H. , 2004: A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation. Mon. Wea. Rev., 132, 103120.

    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., Noh Y. , and Dudhia J. , 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., and Mitchell H. L. , 1998: Data assimilation using an ensemble Kalman filter technique. Mon. Wea. Rev., 126, 796811.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., and Mitchell H. L. , 2005: Ensemble Kalman filtering. Quart. J. Roy. Meteor. Soc., 131, 32693289.

  • Houtekamer, P. L., Mitchell H. L. , Pellerin G. , Buehner M. , Charron M. , Spacek L. , and Hansen B. , 2005: Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations. Mon. Wea. Rev., 133, 604620.

    • Search Google Scholar
    • Export Citation
  • Hunt, B. R., and Coauthors, 2004: Four-dimensional ensemble Kalman filtering. Tellus, 56A, 273277.

  • Hunt, B. R., Kostelich E. J. , and Szunyogh I. , 2007: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Physica D, 230, 112126.

    • Search Google Scholar
    • Export Citation
  • Kain, J., and Fritsch J. , 1993: Convective parameterization for mesoscale models: The Kain–Fritsch scheme. The Representation of Cumulus Convection in Numerical Models, Meteor.Monogr., No. 46, Amer. Meteor. Soc., 165–170.

  • Keppenne, C. L., 2000: Data assimilation into a primitive-equation model with a parallel ensemble Kalman filter. Mon. Wea. Rev., 128, 19711981.

    • Search Google Scholar
    • Export Citation
  • Keyser, D., cited 2010: PREPBUFR processing at NCEP. [Available online at http://www.emc.ncep.noaa.gov/mmb/data_processing/prepbufr.doc/document.htm.]

  • Li, H., Kalnay E. , and Miyoshi T. , 2009: Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter. Quart. J. Roy. Meteor. Soc., 135, 523533, doi:10.1002/qj.371.

    • Search Google Scholar
    • Export Citation
  • Meng, Z., and Zhang F. , 2011: Limited-area ensemble-based data assimilation. Mon. Wea. Rev., 139, 20252045.

  • Miyoshi, T., 2011: The Gaussian approach to adaptive covariance inflation and its implementation with the local ensemble transform Kalman filter. Mon. Wea. Rev., 139, 15191535.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., and Aranami K. , 2006: Applying a four-dimensional local ensemble transform Kalman filter (4D-LETKF) to the JMA nonhydrostatic model (NHM). SOLA, 2, 128131, doi:10.2151/sola.2006-033.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., and Kunii M. , 2012: The local ensemble transform Kalman filter with the Weather Research and Forecasting model: Experiments with real observations. Pure Appl. Geophys., 169, 321333, doi:10.1007/s00024-011-0373-4.

    • Search Google Scholar
    • Export Citation
  • Mlawer, E. J., Taubman S. J. , Brown P. D. , Iacono M. J. , and Clough S. A. , 1997: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102 (D14), 16 66316 682.

    • Search Google Scholar
    • Export Citation
  • Palmen, E., 1948: On the formation and structure of tropical cyclones. Geophysics, 3, 2638.

  • Price, J. F., 1981: Upper-ocean response to a hurricane. J. Phys. Oceanogr., 11, 153175.

  • Saha, S., and Coauthors, 2010: The NCEP Climate Forecast System reanalysis. Bull. Amer. Meteor. Soc., 91, 10151057.

  • Schade, L. R., and Emanuel K. A. , 1999: The ocean’s effect on the intensity of tropical cyclones: Results from a simple coupled atmosphere–ocean model. J. Atmos. Sci., 56, 642651.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., Klemp J. B. , Dudhia J. , Gill D. O. , Barker D. M. , Wang W. , and Powers J. G. , 2005: A description of the Advanced Research WRF version 2. NCAR Tech. Note TN-468+STR, 88 pp.

  • Snyder, C., and Zhang F. , 2003: Assimilation of simulated Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 131, 16631677.

    • Search Google Scholar
    • Export Citation
  • Torn, R. D., 2010: Performance of a mesoscale ensemble Kalman filter (EnKF) during the NOAA high-resolution hurricane test. Mon. Wea. Rev., 138, 43754392.

    • Search Google Scholar
    • Export Citation
  • Torn, R. D., Hakim G. J. , and Snyder C. , 2006: Boundary conditions for limited-area ensemble Kalman filters. Mon. Wea. Rev., 134, 24902502.

    • Search Google Scholar
    • Export Citation
  • Tuleya, R. E., and Kurihara Y. , 1981: A numerical study on the effects of environmental flow on tropical storm genesis. Mon. Wea. Rev., 109, 24872506.

    • Search Google Scholar
    • Export Citation
  • Vialard, J., Vitart F. , Balmaseda M. A. , Stockdale T. N. , and Anderson D. T. L. , 2005: An ensemble generation method for seasonal forecasting with an ocean–atmosphere coupled model. Mon. Wea. Rev., 133, 441453.

    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., and Hamill T. M. , 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130, 19131924.

  • Zhang, F., Weng Y. , Meng Z. , Sippel J. A. , and Bishop C. H. , 2009: Cloud-resolving hurricane initialization and prediction through assimilation of Doppler radar observations with an ensemble Kalman filter: Humberto (2007). Mon. Wea. Rev., 137, 21052125.

    • Search Google Scholar
    • Export Citation
  • Zhang, S., Harrison M. J. , Rosati A. , and Wittenberg A. T. , 2007: System design and evaluation of coupled ensemble data assimilation for global oceanic climate studies. Mon. Wea. Rev., 135, 35413564.

    • Search Google Scholar
    • Export Citation
Save
  • Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129, 28842903.

  • Barker, D. M., 2005: Southern high-latitude ensemble data assimilation in the Antarctic Mesoscale Prediction System. Mon. Wea. Rev., 133, 34313449.

    • Search Google Scholar
    • Export Citation
  • Bender, M. A., and Ginis I. , 2000: Real-case simulations of hurricane–ocean interaction using a high-resolution coupled model: Effects on hurricane intensity. Mon. Wea. Rev., 128, 917946.

    • Search Google Scholar
    • Export Citation
  • Bender, M. A., Ginis I. , and Kurihara Y. , 1993: Numerical simulations of tropical cyclone-ocean interaction with a high-resolution coupled model. J. Geophys. Res., 98 (D12), 23 24523 263.

    • Search Google Scholar
    • Export Citation
  • Bender, M. A., Ginis I. , Tuleya R. , Thomas B. , and Marchok T. , 2007: The operational GFDL coupled hurricane–ocean prediction system and a summary of its performance. Mon. Wea. Rev., 135, 39653989.

    • Search Google Scholar
    • Export Citation
  • Bishop, C. H., Etherton B. J. , and Majumdar S. J. , 2001: Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon. Wea. Rev., 129, 420436.

    • Search Google Scholar
    • Export Citation
  • Bonavita, M., Torrisi L. , and Marcucci F. , 2008: The ensemble Kalman filter in an operational regional NWP system: Preliminary results with real observations. Quart. J. Roy. Meteor. Soc., 134, 17331744.

    • Search Google Scholar
    • Export Citation
  • Bowler, N. E., Arribas A. , Mylne K. R. , Robertson K. B. , and Beare S. E. , 2008: The MOGREPS short-range ensemble prediction system. Quart. J. Roy. Meteor. Soc., 134, 703722.

    • Search Google Scholar
    • Export Citation
  • Chan, J. C. L., Duan Y. , and Shay L. K. , 2001: Tropical cyclone intensity change from a simple ocean–atmosphere coupled model. J. Atmos. Sci., 58, 154172.

    • Search Google Scholar
    • Export Citation
  • Desroziers, G., Berre L. , Chapnik B. , and Poli P. , 2005: Diagnosis of observation, background and analysis-error statistics in observation space. Quart. J. Roy. Meteor. Soc., 131, 33853396.

    • Search Google Scholar
    • Export Citation
  • Dirren, S., Torn R. D. , and Hakim G. J. , 2007: A data assimilation case study using a limited-area ensemble Kalman filter. Mon. Wea. Rev., 135, 14551473.

    • Search Google Scholar
    • Export Citation
  • Dowell, D. C., Zhang F. , Wicker L. J. , Snyder C. , and Crook N. A. , 2004: Wind and temperature retrievals in the 17 May 1981 Arcadia, Oklahoma, supercell: Ensemble Kalman filter experiments. Mon. Wea. Rev., 132, 19822005.

    • Search Google Scholar
    • Export Citation
  • Dudhia, J., 1989: Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 30773107.

    • Search Google Scholar
    • Export Citation
  • Eckel, F. A., and Mass C. F. , 2005: Aspects of effective mesoscale, short-range ensemble forecasting. Wea. Forecasting, 20, 328350.

  • Emanuel, K. A., 1986: An air–sea interaction theory for tropical cyclones. Part I: Steady-state maintenance. J. Atmos. Sci., 43, 585604.

    • Search Google Scholar
    • Export Citation
  • Emanuel, K. A., DesAutels C. , Holloway C. , and Korty R. , 2004: Environmental control of tropical cyclone intensity. J. Atmos. Sci., 61, 843858.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99 (C5), 10 14310 162.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 2003: The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dyn., 53, 343367.

  • Ginis, I., 2002: Tropical cyclone–ocean interactions. Atmosphere–Ocean Interactions, W. Perrie, Ed., Advances in Fluid Mechanics Series, Vol. 33, WIT Press, 83–114.

  • Hong, S.-Y., Dudhia J. , and Chen S.-H. , 2004: A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation. Mon. Wea. Rev., 132, 103120.

    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., Noh Y. , and Dudhia J. , 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., and Mitchell H. L. , 1998: Data assimilation using an ensemble Kalman filter technique. Mon. Wea. Rev., 126, 796811.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., and Mitchell H. L. , 2005: Ensemble Kalman filtering. Quart. J. Roy. Meteor. Soc., 131, 32693289.

  • Houtekamer, P. L., Mitchell H. L. , Pellerin G. , Buehner M. , Charron M. , Spacek L. , and Hansen B. , 2005: Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations. Mon. Wea. Rev., 133, 604620.

    • Search Google Scholar
    • Export Citation
  • Hunt, B. R., and Coauthors, 2004: Four-dimensional ensemble Kalman filtering. Tellus, 56A, 273277.

  • Hunt, B. R., Kostelich E. J. , and Szunyogh I. , 2007: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Physica D, 230, 112126.

    • Search Google Scholar
    • Export Citation
  • Kain, J., and Fritsch J. , 1993: Convective parameterization for mesoscale models: The Kain–Fritsch scheme. The Representation of Cumulus Convection in Numerical Models, Meteor.Monogr., No. 46, Amer. Meteor. Soc., 165–170.

  • Keppenne, C. L., 2000: Data assimilation into a primitive-equation model with a parallel ensemble Kalman filter. Mon. Wea. Rev., 128, 19711981.

    • Search Google Scholar
    • Export Citation
  • Keyser, D., cited 2010: PREPBUFR processing at NCEP. [Available online at http://www.emc.ncep.noaa.gov/mmb/data_processing/prepbufr.doc/document.htm.]

  • Li, H., Kalnay E. , and Miyoshi T. , 2009: Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter. Quart. J. Roy. Meteor. Soc., 135, 523533, doi:10.1002/qj.371.

    • Search Google Scholar
    • Export Citation
  • Meng, Z., and Zhang F. , 2011: Limited-area ensemble-based data assimilation. Mon. Wea. Rev., 139, 20252045.

  • Miyoshi, T., 2011: The Gaussian approach to adaptive covariance inflation and its implementation with the local ensemble transform Kalman filter. Mon. Wea. Rev., 139, 15191535.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., and Aranami K. , 2006: Applying a four-dimensional local ensemble transform Kalman filter (4D-LETKF) to the JMA nonhydrostatic model (NHM). SOLA, 2, 128131, doi:10.2151/sola.2006-033.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., and Kunii M. , 2012: The local ensemble transform Kalman filter with the Weather Research and Forecasting model: Experiments with real observations. Pure Appl. Geophys., 169, 321333, doi:10.1007/s00024-011-0373-4.

    • Search Google Scholar
    • Export Citation
  • Mlawer, E. J., Taubman S. J. , Brown P. D. , Iacono M. J. , and Clough S. A. , 1997: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102 (D14), 16 66316 682.

    • Search Google Scholar
    • Export Citation
  • Palmen, E., 1948: On the formation and structure of tropical cyclones. Geophysics, 3, 2638.

  • Price, J. F., 1981: Upper-ocean response to a hurricane. J. Phys. Oceanogr., 11, 153175.

  • Saha, S., and Coauthors, 2010: The NCEP Climate Forecast System reanalysis. Bull. Amer. Meteor. Soc., 91, 10151057.

  • Schade, L. R., and Emanuel K. A. , 1999: The ocean’s effect on the intensity of tropical cyclones: Results from a simple coupled atmosphere–ocean model. J. Atmos. Sci., 56, 642651.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., Klemp J. B. , Dudhia J. , Gill D. O. , Barker D. M. , Wang W. , and Powers J. G. , 2005: A description of the Advanced Research WRF version 2. NCAR Tech. Note TN-468+STR, 88 pp.

  • Snyder, C., and Zhang F. , 2003: Assimilation of simulated Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 131, 16631677.

    • Search Google Scholar
    • Export Citation
  • Torn, R. D., 2010: Performance of a mesoscale ensemble Kalman filter (EnKF) during the NOAA high-resolution hurricane test. Mon. Wea. Rev., 138, 43754392.

    • Search Google Scholar
    • Export Citation
  • Torn, R. D., Hakim G. J. , and Snyder C. , 2006: Boundary conditions for limited-area ensemble Kalman filters. Mon. Wea. Rev., 134, 24902502.

    • Search Google Scholar
    • Export Citation
  • Tuleya, R. E., and Kurihara Y. , 1981: A numerical study on the effects of environmental flow on tropical storm genesis. Mon. Wea. Rev., 109, 24872506.

    • Search Google Scholar
    • Export Citation
  • Vialard, J., Vitart F. , Balmaseda M. A. , Stockdale T. N. , and Anderson D. T. L. , 2005: An ensemble generation method for seasonal forecasting with an ocean–atmosphere coupled model. Mon. Wea. Rev., 133, 441453.

    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., and Hamill T. M. , 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130, 19131924.

  • Zhang, F., Weng Y. , Meng Z. , Sippel J. A. , and Bishop C. H. , 2009: Cloud-resolving hurricane initialization and prediction through assimilation of Doppler radar observations with an ensemble Kalman filter: Humberto (2007). Mon. Wea. Rev., 137, 21052125.

    • Search Google Scholar
    • Export Citation
  • Zhang, S., Harrison M. J. , Rosati A. , and Wittenberg A. T. , 2007: System design and evaluation of coupled ensemble data assimilation for global oceanic climate studies. Mon. Wea. Rev., 135, 35413564.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Model domains for the WRF-LETKF analysis (D01, 60-km grid spacing) and the WRF model simulations (D02, 20-km grid spacing), along with the best track of Typhoon Sinlaku from 0000 UTC 8 Sep (0800) to 0000 UTC 20 Sep (2000) 2008.

  • Fig. 2.

    (a) Time series of SST averaged over the entire domain D1 during September 2008, for the NCEP analysis (ANAL, solid line) and each ensemble member (MEM, dashed lines). Horizontal distributions (K) of (b) a single ensemble member of the SST perturbation field and (c) the ensemble spread of SST.

  • Fig. 3.

    The 6-h forecast verifications relative to radiosonde observations for (a) zonal wind component (U, m s−1), (b) temperature (T, K) and (c) water vapor mixing ratio (QV, g kg−1), averaged over 19 days from 0000 UTC 1 Sep to 0000 UTC 20 Sep 2008. The forecast model resolution is 60 km. Dashed, solid, and dotted lines correspond to the CTRL, SSTP, and INFL experiments, respectively, and thick and thin lines indicate RMSEs and biases, respectively.

  • Fig. 4.

    Time series of analysis RMS differences from NCEP FNL for zonal wind components (U and V, m s−1), temperature (T, K), and relative humidity (RH, %) at 925, 850, and 500 hPa averaged over the entire model domain. The variables (a) U850, (b) U500, (c) V850, (d) V500, (e) T850, (f) T500, (g) RH925 and (h) RH850 are shown for CTRL (dashed), SSTP (solid), and INFL (dotted).

  • Fig. 5.

    (a) Time series of Sinlaku’s central pressure analyses of CTRL (dashed), SSTP (solid), and INFL (dotted), along with the best-track data (dotted–dashed). The resolution of the analysis is 60 km. (b) Time-mean forecast track errors of Sinlaku over 16 initial times from 9 to 12 September for the deterministic WRF forecasts initialized by the CTRL (dashed), SSTP (solid), and INFL (dotted) analyses. In each forecast, the same SST is used.

  • Fig. 6.

    (a) Evolution of the central pressure and (b) the forecast tracks of Sinlaku, simulated in the 20-km one-way-nested WRF forecasts up to 72 h, initialized at 0000 UTC 9 Sep 2008 by the analyses of the CTRL (blue) and SSTP (red) experiments. The best track is shown by the black lines.

  • Fig. 7.

    The 500-hPa geopotential height analyses (m) at 0000 UTC 9 Sep 2008 for (a) CTRL and (b) SSTP (thick black contours), superimposed on the NCEP FNL analysis (gray coutours). (c),(d) As in (a),(b), but for the 12-h forecasts at 1200 UTC 9 Sep 2008. The cyclone weather symbols indicate the observed TC positions.

  • Fig. 8.

    Vertical profiles of the ensemble spread for (a) zonal wind component (m s−1), (b) temperature (K), and (c) water vapor mixing ratio (g kg−1), averaged over the entire model domain D1 under z = 20 for 16 analyses from 9 to 12 Sep 2008, in CTRL (dashed line), SSTP (solid line), and INFL (dotted line).

  • Fig. 9.

    Horizontal error covariance maps of temperature at the fifth model level (~925 hPa) estimated from the forecast ensemble perturbations of the (a) CTRL and (b) SSTP experiments at 1200 UTC 10 Sep 2008. (c),(d) As in (a),(b), but for specific humidity. The center of the region (denoted by the cross marks) is the base point of the covariance. Localization is applied by multiplying localization factors by the error covariance.

  • Fig. 10.

    (a) As in Fig. 2c, but for the perturbations randomly chosen from the SST fields in 2007. (b) As in Fig. 5b, but including the experiment with SST perturbations derived from SSTs in 2007 (SSTP2007).

  • Fig. 11.

    As in Fig. 5b, bur for Typhoon Jangmi (2008), averaged over 16 initial times from 24 to 26 Sep 2008.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 325 191 3
PDF Downloads 137 34 2