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  • View in gallery

    (a) Observed SST from TMI and AMSR-E optimally interpolated by the RSS1 on 25 Jun 2005, (b) COAMPS analysis SST at 0000 UTC 25 Jun 2005, and (c) the difference between the COAMPS analysis and observed SST. All in °C.

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    Ensemble mean sea level pressure (hPa), 2-m air temperature (°C), and 10-m wind at 0000 UTC 25 Jun 2005. One full wind barb represents 10 m s−1 and a half barb 5 m s−1. (Note that this figure has a correct map aspect ratio. All other map figures have exaggerated aspect ratios to allow for more convenient comparison of three plots.)

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    (a) Mean rain rate (mm h−1) computed from TMI, AMSR-E, the Special Sensor Microwave Imager (SSM/I) on board the F-13 and F-15 satellites on 20 Jun 2005. (b) COAMPS ensemble means of geopotential height (gpm; contours) and wind barbs (as in Fig. 1) at 500 hPa at 0000 UTC 25 Jun 2005. The thick 5880-m contour line indicates the western edge of the WNPSH. (c) As in (a), but for 25 Jun 2005.

  • View in gallery

    (a) Perturbed COAMPS analysis SSTs (°C) for ensemble member 005, and difference to the observed SST for ensemble members (b) 015 and (c) 025.

  • View in gallery

    COAMPS 48-h ensemble mean field (contoured) and ensemble spread (shaded) for 850-hPa geopotential height (gpm) valid at 0000 UTC 27 Jun 2005 for (a) perturbed and (b) nonperturbed SSTs, and (c) the ensemble mean difference between the 850-hPa geopotential height (contour) and the absolute difference of the ensemble spread for perturbed minus nonperturbed SSTs (shaded). The thick 1480-m contour lines in (a) and (b) indicate the western positions of the WNPSH. The dotted line in (a) indicates the 1480-m contour for the nonperturbed SST case. The dashed red lines in (a) and (b) are the approximated climatological mean 1480-m positions from Lu (2002).

  • View in gallery

    COAMPS ensemble mean field (shaded) and ensemble spread (contour) for 48-h accumulated precipitation (kg m−2) valid at 0000 UTC 27 Jun 2005 for (a) perturbed and (b) nonperturbed SSTs. The ensemble mean difference (contour) and the absolute difference of the ensemble spread (shaded) between the two cases are shown in (c).

  • View in gallery

    Rain rate (mm h−1) from (a) perturbed and (b) nonperturbed SSTs, and (c) the mean AMSR-E, TMI, SSM/I F-13 and F-15 passive radiometer data on 27 Jun 2005.

  • View in gallery

    COAMPS 48-h ensemble mean field of vertically integrated moisture transport flux (vector, kg m−1 s−1) and moisture flux divergence (shaded, kg m−2 s−1) valid at 0000 UTC 27 Jun 2005 for (a) perturbed and (b) nonperturbed SSTs. The divergence values are scaled by 10−3. The ensemble mean difference of the moisture flux transport (contour) and the absolute ensemble spread difference (shaded) between the two cases is shown in (c).

  • View in gallery

    COAMPS 48-h ensemble mean (barbs as in Fig. 1) and ensemble spread (shaded) for the 850-hPa wind valid at 0000 UTC 27 Jun 2005 for (a) perturbed and (b) nonperturbed SSTs, and (c) the ensemble mean difference of the 850-hPa wind speed (contoured) and the absolute difference of the ensemble spread for the perturbed minus nonperturbed SST (shaded). The contour lines in (a) and (b) correspond to the wind speeds of 10 and 20 m s−1, respectively.

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    RMSDs of the 48-h ensemble mean forecast from the perturbed and nonperturbed SSTs for (a) 850-hpa wind, (b) integrated moisture flux, and (c) 36-h accumulated precipitation.

  • View in gallery

    Scatter diagram of the bin-mean ensemble variance and bin-mean squared error for 48-h forecasts of the (a) sea level pressure, (b) 2-m air temperature, (c) u-wind component, and (d) υ-wind component.

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Impacts of Sea Surface Temperature Uncertainty on the Western North Pacific Subtropical High (WNPSH) and Rainfall

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  • 1 Marine Meteorology Division, Naval Research Laboratory, Monterey, California
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Abstract

This paper examines the sensitivity of short-term forecasts of the western North Pacific subtropical high (WNPSH) and rainfall to sea surface temperature (SST) uncertainty using the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS). A comparison of analyzed SSTs with satellite observations of SST indicates that SST analysis errors are particularly pronounced on horizontal scales from 100 to 200 km, similar to the mesoscale eddy scales in the Kuroshio region. Since significant oceanic variations occur on these scales, it is of interest to examine the effects of representing this small-scale uncertainty with random, scale-dependent perturbations. An SST ensemble perturbation generation technique is used here that enables temporal and spatial correlations to be controlled and produces initial SST fields comparable to satellite observations. The atmospheric model develops large uncertainty in the Korea and Japan area due to the fluctuation in the horizontal pressure gradient caused by the location of the WNPSH. This, in turn, increases the variance of the low-level jet (LLJ) over southeast China, resulting in large differences in the moist transport flux from the tropical ocean and subsequent rainfall. Validation using bin-mean statistics shows that the ensemble forecast with the perturbed SST better distinguishes large forecast error variance from small forecast error variance. The results suggest that using the SST perturbation as a proxy for the ocean ensemble in a coupled atmosphere and ocean ensemble system is feasible and computationally efficient.

Corresponding author address: Xiaodong Hong, Naval Research Laboratory, 7 Grace Hopper Ave., Monterey, CA 93943. E-mail: xd.hong@nrlmry.navy.mil

Abstract

This paper examines the sensitivity of short-term forecasts of the western North Pacific subtropical high (WNPSH) and rainfall to sea surface temperature (SST) uncertainty using the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS). A comparison of analyzed SSTs with satellite observations of SST indicates that SST analysis errors are particularly pronounced on horizontal scales from 100 to 200 km, similar to the mesoscale eddy scales in the Kuroshio region. Since significant oceanic variations occur on these scales, it is of interest to examine the effects of representing this small-scale uncertainty with random, scale-dependent perturbations. An SST ensemble perturbation generation technique is used here that enables temporal and spatial correlations to be controlled and produces initial SST fields comparable to satellite observations. The atmospheric model develops large uncertainty in the Korea and Japan area due to the fluctuation in the horizontal pressure gradient caused by the location of the WNPSH. This, in turn, increases the variance of the low-level jet (LLJ) over southeast China, resulting in large differences in the moist transport flux from the tropical ocean and subsequent rainfall. Validation using bin-mean statistics shows that the ensemble forecast with the perturbed SST better distinguishes large forecast error variance from small forecast error variance. The results suggest that using the SST perturbation as a proxy for the ocean ensemble in a coupled atmosphere and ocean ensemble system is feasible and computationally efficient.

Corresponding author address: Xiaodong Hong, Naval Research Laboratory, 7 Grace Hopper Ave., Monterey, CA 93943. E-mail: xd.hong@nrlmry.navy.mil

1. Introduction

The western North Pacific subtropical high (WNPSH) is one of the most difficult systems to forecast due to its nonlinear, complex, and highly variable characteristics. It is an important weather system for East Asia since the variation of its zonal position can greatly influence the transport of water vapor along its northwestern edge and the resultant rainfall (Zhou and Yu 2005; Yang and Sun 2005). The WNPSH’s movement in the north–south direction is also strongly related to the shift of the summer monsoon rainband from central China to Japan (Zhou and Yu 2005; Wang et al. 2008). Previous studies have shown that the relocation of the WNPSH is significantly correlated with the sea surface temperature (SST) anomaly in the tropical region (Zhou et al. 2009; Yang and Sun 2005), the Kuroshio, and the Kuroshio Extension region (Geng et al. 1996; Sawada and Handa 1997).

The Kuroshio is a warm and energetic western boundary current beginning off the east coast of Taiwan and flowing northeastward past Japan. The Kuroshio Extension is the eastward continuation of the Kuroshio, a free jet leaving the Japanese coast and entering the open basin of the North Pacific (Sverdrup et al. 1942; Kawai 1972). The mean circulation feature of the Kuroshio Extension has been presented using the sea surface dynamic height maps constructed from historical hydrographic data (e.g., Wyrtki 1975; Qu et al. 2001). There is high mesoscale anticyclonic and cyclonic eddy activity along the vigorous meandering (Kawai 1972; Yasuda et al. 1992; Qiu et al. 2007; Itoh and Yasuda 2010) due to highly nonlinear transport of vortices (Wyrtki et al. 1976; Chelton et al. 2007). These eddies are called warm-core rings and cold-core rings and are routinely observed from satellites. Their abundance, variability of scale, amplitude, and propagation play important roles in the interannual trend in the Kuroshio Extension’s transport–path (Qiu 2000) and the property changes in North Pacific Subtropical Mode Water (Qiu et al. 2007). The mean eddy diameters decrease from about 200 km in the eddy-rich low- and middle-latitude regions to about 100 km at high latitudes (Chelton et al. 2007). In the Kuroshio–Oyashio Extension region, the radii of dense distributed anticyclonic eddies and cyclonic eddies are as small as 60 km (larger than the first baroclinic Rossby radius of deformation, 30 km). One can identify an average of 75 anticyclonic eddies (warm-core rings) and 80 cyclonic eddies (cold-core rings) each week in this region using the sea surface height anomaly data during the available period of 790 weeks (Itoh and Yasuda 2010). The anticyclonic and cyclonic eddies are located on the crests and troughs of SST, respectively. These eddies interact between different scales actively. Many of these eddies have life spans of more than 12 weeks with propagation speeds at 1–5 cm s−1 with directions ranging from westward to poleward. Studies using satellite altimetry data have revealed that there is evidence for an upscale nonlinear cascade of kinetic energy with an arrest scale similar to the large eddy diameters (Scott and Wang 2005).

Representing these small-scale eddies through an accurate SST analysis from a data assimilation system is important so that the atmospheric model has an accurate lower boundary condition. However, most interpolation algorithms have difficulty in obtaining small spatial scale disturbances of SST (Wang and Xie 2007). A comparison of satellite observed SSTs (Fig. 1a) and Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) analyzed SSTs (Fig. 1b) indicates that SST analysis errors (Fig. 1c) are particularly pronounced on the horizontal scales from 100 to 200 km, similar to the mesoscale eddy scales in this region (see Fig. 1 in Chelton et al. 2007). These random errors in the SST specification will cause forecast errors to amplify in space and time via both linear and nonlinear processes (Auclair et al. 2003). The analysis error is related to the limitations in the assimilation system associated with data observation and quality control, systematic model error and bias, and error covariance that define both the analysis and forecasting problem. Even though the grid resolutions are increased, the analysis may still fail to resolve the small-scale features due to the broad error correlation scale from the resolution limitation of the input observations, satellite data availability during cloudy periods, and persistency of small-scale features (Reynolds and Chelton 2010). Hence, an accurate representation of these SST errors in an ensemble forecast could help quantify the effects of these unresolved variations on the forecast. Such quantification of the uncertainty in the surface boundary condition is difficult but important for the coupled system since the error can propagate between adjacent boundaries of the atmosphere and the ocean and can be amplified by chaotic dynamics through a complex response even when the uncertainty is small at the initial time (Chu and Ivanov 2002; Lorenz 2005). Numerical studies have shown that surface wind uncertainty can cause ocean forecast errors not only in the surface current, elevation, and temperature fields (Chu et al. 1999), but also is strongest at the top of the thermocline, as a consequence of the vertical displacement of the mixed-layer base, horizontal advection, and surface heat flux fluctuation (Burillo et al. 2002).

Fig. 1.
Fig. 1.

(a) Observed SST from TMI and AMSR-E optimally interpolated by the RSS1 on 25 Jun 2005, (b) COAMPS analysis SST at 0000 UTC 25 Jun 2005, and (c) the difference between the COAMPS analysis and observed SST. All in °C.

Citation: Weather and Forecasting 26, 3; 10.1175/WAF-D-10-05007.1

To promote ensemble forecasting (EF) as a means to enhance Department of Defense (DoD) operations from weather prediction, the Fleet Numerical Meteorology and Oceanography Center (FNMOC) and Air Force Weather Agency (AFWA) conducted a Joint Ensemble Forecast System (JEFS) project. The multiyear pilot project with a comprehensive use of EF promises substantial benefits but entails a challenging transition from deterministic to stochastic processes. The ultimate goals of this project are to produce a robust ensemble prediction system and provide analysis and application of EF data and products to DoD weather forecasting and decision making (Eckel 2011). JEFS consists of two separate ensembles, the Joint Global Ensemble (JGE) for medium-range, large-scale stochastic forecasting from global model runs, and the Joint Mesoscale Ensemble (JME) for short-range, small-scale stochastic forecasting from limited-area model runs. The JME consists of members from both the Advanced Research module of Weather Research and Forecasting model (WRF-ARW) and the COAMPS. East Asia was chosen by the Committee for Operational Processing Centers (COPC) since it is a region of high geopolitical interest that contains challenging weather and a wide assortment of DoD assets. It is an excellent region to prove the value of ensembles to DoD operations. This paper makes use of the JME framework to examine SST uncertainty impacts in the WNPSH region.

The details of the mesoscale ensemble forecast system, including SST ensemble generation, are given in section 2. The numerical model configuration and the case study are described in section 3. The sensitivity of WNPSH and rainfall forecasts to the SST uncertainty is discussed in section 4. Section 5 presents the effects of the perturbed SST on the forecast error. Section 6 gives the discussion and conclusions.

2. The mesoscale ensemble forecast system

a. COAMPS ensemble forecast system

The mesoscale EF system used in this study is composed of three components: (i) a 3D variational data assimilation system [Naval Research Laboratory (NRL) Atmospheric Variational Data Assimilation System (NAVDAS; Daley and Barker 2001)], (ii) a nonhydrostatic atmospheric forecast model (COAMPS; Hodur 1997), and (iii) an ensemble transform (ET) scheme for generating high-resolution initial perturbations (Bishop et al. 2009).

The ET scheme provides initial perturbations that (i) have an initial variance that is consistent with the best available estimates of the initial condition error variance, (ii) are dynamically conditioned by a process similar to that used in the breeding technique (Toth and Kalnay 1993, 1997), (iii) add to zero at the initial time, (iv) are quasi-orthogonal and equally likely, and (v) partially respect the mesoscale balance constraints by ensuring that each initial perturbation is a linear sum of the forecast perturbations from the preceding forecast. The analysis error variance from NAVADAS is used to constrain the magnitude of the initial perturbations that represent transformations or linear combinations of ensemble forecast perturbations, so-called ET perturbations (Bishop and Toth 1999; Bishop et al. 2009). A complete description of the ET technique and the detailed steps to creating an ET ensemble can be found in Bishop et al. (2009).

The ensemble of the lateral boundary conditions is obtained from the Navy Operational Global Atmospheric Prediction System (NOGAPS) ET ensemble system described in McLay et al. (2008). The ensemble mean used to initialize the ensemble is obtained from NAVDAS as are the analysis error variance estimates. The inconsistencies between the temporal evolution and dynamical balance of NOGAPS fields and COAMPS fields are handled by prescribing the tendencies of COAMPS fields to be a weighted average of NOGAPS and COAMPS tendencies within seven grid points from the lateral boundaries following Davies (1976).

This paper presents results from the initial testing of the mesoscale EF system. As such, NAVDAS has not been fully implemented for COAMPS. Therefore, the system uses a multivariate optimal interpolation (MVOI) scheme for analyses using the 12-h COAMPS forecast fields blended with available observations from upper-air soundings, and observations from the surface, commercial aircraft, and satellites (Barker 1992). An incremental update data assimilation procedure is used in conjunction with the MVOI, which enables mesoscale phenomena to be retained in the analysis increment fields. We approximate the analysis error variance with an estimate obtained using the volume-based method described in Daley and Barker (2001). This analysis error variance method has been implemented for the global NAVDAS data assimilation scheme and not for the regional scheme. Hence, an estimate of the analysis error variance on the regional model grid is obtained by simply interpolating the analysis error variances from the global model grid to the regional model grid. This estimate differs from the true error variance of the analysis on the regional model grid because of the assumptions of Daley and Barker’s method and because one would expect the error variances of the regional model analysis to be somewhat different from the global model analysis. Nevertheless, since it is the best estimate available to us, we used it.

b. SST ensemble generation

The ensemble of ocean-surface lower boundary conditions for the atmosphere is generated by adding small perturbations to an initial best-guess unperturbed state of SST to represent the inherent uncertainty in the analysis SST. The COAMPS analysis SST is obtained from the Navy Coupled Ocean Data Assimilation (NCODA) using an optimum interpolation (OI) of surface observations, mostly from satellite (Cummings 2005). For these uncoupled COAMPS simulations, the analyzed SST field is held fixed in time over the forecast period. Therefore, the temporal evolution of SST is missing and the coupling of propagating mesoscale ocean features to overlying atmospheric properties (like wind, moisture flux, etc.) is neglected. The analyzed SST is sensitive to satellite data availability and cloud cover and the evolution of the atmosphere and ocean. The SST errors associated with these sensitivities are modeled by adding random but smooth perturbations to the analyzed SST field. The amplitude of the perturbations is chosen to be small enough to ensure that the perturbed field lies within the error bounds of the analysis.

To control the amplitude and horizontal correlation length scale of the random perturbations, the covariance matrix of the vector x′ for all variables defining the SST perturbation is prescribed as
e1
where is a diagonal matrix of the variances we wish to assign to the random process at each grid point and defines a correlation matrix whose diagonal values are all equal to 1. For simplicity, we chose the columns of to be the two-dimensional sinusoids and cosinusoids that define a basis for the two-dimensional domain upon which the ocean state is defined. Let a be a random normal vector with zero mean and covariance 〈aaT〉 = Λ. Now consider random vectors y obtained using . Note that since the columns of are the sinusoidal basis used in the inverse Fourier transform, the operation is simply an inverse Fourier transform. To ensure that our random SST perturbations satisfy Eq. (1), we generate each perturbation using
e2
In other words, a random SST perturbation is created by
  1. Creating a vector b of n normally, independently, and identically distributed numbers, each of which has a mean of 0 and a variance of 1;

  2. letting a = Λ1/2b;

  3. performing the inverse Fourier transform implied by ; and

  4. performing the operation .

To see that this process creates random perturbations that satisfy (1), we note that
e3
The scales and magnitudes of the random perturbations are thus determined by the user’s specification of and Λ. Here, we chose so that the constant α gives the variance at each point and we let the diagonal elements λii of Λ be given by the Gaussian function of the total wavenumber to which they pertain, which is given by
e4
where k and l are wavenumbers, L controls the horizontal correlation length scale in spectral space, and C is an amplitude factor that is used to ensure that is a correlation matrix. The values of C, L, and α used in our experiments are 0.5, 10, and 0.5, respectively. Once K SST perturbations have been generated using the above procedure, their mean is removed and then the resulting perturbations are added to the analyzed SST to create an ensemble of K SST distinct SST fields whose mean is precisely equal to the analyzed SST.

On an IBM SP4 computer for the current domain setting with 16 processes, running a three-dimensional ocean analysis using MVOI (NCODA) requires 25 s of CPU time and running an ocean model (NCOM) for a 12-h background field requires 125 s of CPU. The total CPU time to complete one ocean data assimilation cycle, then, is about 150 s. This means it will cost 4200 s to complete one ocean data assimilation cycle for 28 ensemble members to obtain an SST ensemble. The SST perturbation technique used here, in contrast, requires much less CPU time since the calculation is essentially algebra, which is much easier and faster than three-dimensional ocean model calculations. The cost is only 20 s to generate SST ensembles for equivalent members from a single control SST.

3. Numerical experiments

a. Model configuration

The COAMPS ensemble configuration used here is identical to that of the JME project. The system is configured for a 29-member (including 1 control member), single-nest (45 km × 45 km horizontal resolution) ET ensemble cycle with 29 initial states from a T119L30 global NOGAPS ET ensemble at 0000 UTC 20 June 2005. To begin the ET cycle, each member of the COAMPS ensemble is initialized with the initial conditions from the corresponding NOGAPS ensemble. The global model states are interpolated onto the COAMPS grid (116 × 110 grid points in the horizontal and 30 vertical levels). The ET ensemble is spun up using a 6-h analysis–forecast cycle until 0000 UTC 25 June 2005 following the procedure described in Bishop et al. (2009) and Holt et al. (2009). The ensemble means of 2-m air temperature, sea level pressure, and 10-m wind at 0000 UTC 25 June 2005 are displayed in Fig. 2.

Fig. 2.
Fig. 2.

Ensemble mean sea level pressure (hPa), 2-m air temperature (°C), and 10-m wind at 0000 UTC 25 Jun 2005. One full wind barb represents 10 m s−1 and a half barb 5 m s−1. (Note that this figure has a correct map aspect ratio. All other map figures have exaggerated aspect ratios to allow for more convenient comparison of three plots.)

Citation: Weather and Forecasting 26, 3; 10.1175/WAF-D-10-05007.1

After the spinup period, a series of six 48-h forecasts are performed every 12 h, each using the data assimilation and ET technique described in section 2. Two ensemble experiments are designed to evaluate the impacts of SST uncertainty on the atmospheric boundary layer. The control experiment uses the COAMPS-analyzed SST (nonperturbed SST) so that the lower boundary is fixed for each ensemble member. The second experiment uses the COAMPS-analyzed SST with the addition of a small perturbation, as described in section 2 (perturbed SST). All other conditions are kept the same so that the effects of SST perturbation could be evaluated. Since the atmospheric forecast model used here is not coupled with the ocean model, the effects of temporal evolution of SST on overlying atmospheric properties are neglected in this study.

b. Case study

From 17 to 24 June 2005, long-lived torrential rain fell on southern China, causing among other things, flash floods. The rain was associated with the north–south and east–west movement of the WNPSH (Bao 2008; Wang et al. 2008). Compared to its climatological position, the WNPSH had extended westward with a low trough in northeast China and formed a confluence of northwesterly cold air in the midlatitudes with southwesterly warm and moist flow in the westward portion of the subtropical high (Fig. 3 in Wang et al. 2008). This flow resulted from flow merging from the south of the subtropical high and southwest of the equatorial Indian Ocean. Substantial moisture was transported into southern China and induced torrential rainfall from 17 to 24 June 2005. The rainband extended to the east and south of Japan and was oriented northeast–southwest with the maximum rain rate reaching over 8 mm h−1 on 20 June 2005 as shown from mean satellite observations (Fig. 3a).

Fig. 3.
Fig. 3.

(a) Mean rain rate (mm h−1) computed from TMI, AMSR-E, the Special Sensor Microwave Imager (SSM/I) on board the F-13 and F-15 satellites on 20 Jun 2005. (b) COAMPS ensemble means of geopotential height (gpm; contours) and wind barbs (as in Fig. 1) at 500 hPa at 0000 UTC 25 Jun 2005. The thick 5880-m contour line indicates the western edge of the WNPSH. (c) As in (a), but for 25 Jun 2005.

Citation: Weather and Forecasting 26, 3; 10.1175/WAF-D-10-05007.1

The WNPSH shifted northward on 25 June 2005 with the 5880-gpm contour line (denoting the northern extent of the WNPSH) having retreated eastward and advanced northward (Fig. 3b) as compared to previous heavy rain days (not shown). A ridge extending from the northwest edge of the WNPSH reached the Korea and Japan area. There was no upper-air trough in the northeast China area as seen in the previous days; therefore, there was no upper-level convergence (Fig. 3b) and no precipitation (Fig. 3c).

Perturbed COAMPS analysis SSTs (Fig. 4a) show major hydrographic features of the subtropical gyre, Kuroshio, Kuroshio Extension, subarctic front, Oyashio currentand subarctic gyre also evident in the satellite observations (Fig. 1a) and nonperturbed analysis field (Fig. 1b). In addition to the COAMPS analysis’s SSTs with smooth and larger scale oceanic features, the perturbed ensemble SSTs give more varying eddy distributions. The difference between the perturbed and satellite-observed SSTs provides uncertainty for each ensemble member (e.g., Figs. 4b and 4c). At the initial time, the ensemble mean of the perturbed SSTs (not shown) is the same as the control because the ensemble perturbations have zero ensemble mean. However, later in the forecast, the ensemble mean will not, in general, be equal to the control forecast because of nonlinearity (Auclair et al. 2003).

Fig. 4.
Fig. 4.

(a) Perturbed COAMPS analysis SSTs (°C) for ensemble member 005, and difference to the observed SST for ensemble members (b) 015 and (c) 025.

Citation: Weather and Forecasting 26, 3; 10.1175/WAF-D-10-05007.1

4. Results

a. Sensitivity in the WNPSH and rainfall forecast

The position of the WNPSH as indicated by the 48-h 850-hpa geopotential height 1480-m contour ensemble mean forecast valid at 0000 UTC 27 June 2005 shows a western displacement in the case with SST perturbation (Fig. 5a) compared to the nonperturbed SST case (Fig. 5b). The June climatological position of the 1480-m contour from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis dataset is located west of Taiwan as shown in Lu (2002). The perturbed SST case extends the subtropical high westward, positioning the 1480-m contour line closer to its climatological mean position as indicated by the dashed red contours in Figs. 5a and 5b. The maximum displacement from climatology is about 200 km for the perturbed SST case and is about 800 km for the nonperturbed SST case. The maximum displacement between the perturbed and nonperturbed SST cases is about 600 km. This westward movement is crucial to the monsoon rainfall as it will affect the distribution of water vapor transported from the Pacific. The westward shift also strengthens the south China quasi-stationary front, which will induce abundant precipitation in south China (Yang and Sun 2005; Kripalani et al. 2005). The difference in geopotential height between the two cases (Fig. 5c) depicts a stronger WNPSH and larger gradient between the high and the low over the North Korean area for the perturbed SST case. The low over the North Korea area deepens with the smallest geopotential height contour (1360 m) covering a larger area. A noticeable positive change of the height field appears in northeast China (Fig. 5c), indicating that the atmosphere’s response to the SST uncertainty can extend well inland. The SST perturbations change the flux of moisture, heat, and momentum off the surface of the ocean. The changed air mass can then affect the atmosphere over the land by either being advected over the land or creating a changed stability profile near the front, which in turn could alter the frontogenetically induced vertical motion over the land.

Fig. 5.
Fig. 5.

COAMPS 48-h ensemble mean field (contoured) and ensemble spread (shaded) for 850-hPa geopotential height (gpm) valid at 0000 UTC 27 Jun 2005 for (a) perturbed and (b) nonperturbed SSTs, and (c) the ensemble mean difference between the 850-hPa geopotential height (contour) and the absolute difference of the ensemble spread for perturbed minus nonperturbed SSTs (shaded). The thick 1480-m contour lines in (a) and (b) indicate the western positions of the WNPSH. The dotted line in (a) indicates the 1480-m contour for the nonperturbed SST case. The dashed red lines in (a) and (b) are the approximated climatological mean 1480-m positions from Lu (2002).

Citation: Weather and Forecasting 26, 3; 10.1175/WAF-D-10-05007.1

The western edge of the WNPSH is a highly sensitive area, as indicated by the large difference in the ensemble spread between the perturbed and nonperturbed SST cases (Fig. 5c). This implies that a forecast of the western position of the WNPSH has higher uncertainty and lower predictability. A slightly larger uncertainty response corresponding to the perturbed SST is located in the Korea–Japan area due to an increased pressure gradient between the strengthened subtropical high and the deeper low over North Korea.

In corresponding to the position of the WNPSH, the precipitation is influenced by the inclusion of SST uncertainty. Both cases generate a strong precipitation band in the southwest–northeast direction passing through the Korean Peninsula with precipitation along the western edge of the WNPSH (Figs. 6a and 6b). In general, the areas of large ensemble spread correspond to the areas of large precipitation, indicating high uncertainty for quantitative precipitation forecasts. There is slightly more precipitation over the Japan Sea for the perturbed SST case (Fig. 6c). The difference in the ensemble spread for both cases shows that greater dispersion of precipitation is also from the perturbed SST case.

Fig. 6.
Fig. 6.

COAMPS ensemble mean field (shaded) and ensemble spread (contour) for 48-h accumulated precipitation (kg m−2) valid at 0000 UTC 27 Jun 2005 for (a) perturbed and (b) nonperturbed SSTs. The ensemble mean difference (contour) and the absolute difference of the ensemble spread (shaded) between the two cases are shown in (c).

Citation: Weather and Forecasting 26, 3; 10.1175/WAF-D-10-05007.1

Rain rates on 27 June 2005 show larger value along the convergence zone in the Korea–Japan area and over the northern Philippines from the perturbed SST case (Fig. 7a) than from the nonperturbed SST case (Fig. 7b). This is comparable to the mean precipitation rate from satellite observations (Fig. 7c). However, the observation shows larger rain rates along the west coast of Japan, on the eastern side of Japan, and north of Japan. Smaller-scale features along the east coast of Japan in the observations may be associated with coastal topography, implying that higher resolution is needed for the model simulation.

Fig. 7.
Fig. 7.

Rain rate (mm h−1) from (a) perturbed and (b) nonperturbed SSTs, and (c) the mean AMSR-E, TMI, SSM/I F-13 and F-15 passive radiometer data on 27 Jun 2005.

Citation: Weather and Forecasting 26, 3; 10.1175/WAF-D-10-05007.1

Additional comparisons are discussed in section 5 by comparing pairs of bin-mean ensemble variance and squared forecast error for the perturbed and nonperturbed SST cases. All available observational data used in the analysis of the control run are accounted for in the bin-averaged comparison to evaluate the ensemble forecast skill.

b. Mechanism for rainfall

The main source of rainfall in East Asia is associated with the position of the western edge of the WNPSH and the associated strong tropical water vapor transport (Zhou and Yu 2005). The tropical water transport can come directly from the Bay of Bengal and the South China Sea with a southwestward extension of the WNPSH or from the East China Sea with a northwestward extension of the WNPSH. It is essentially a convergence of the tropical or subtropical southwest water vapor transport with the midlatitude water vapor transport.

Moisture transport flux is a useful quantity to determine the possible sources of water vapor for East Asia (Zhou and Yu 2005; M. Chen et al. 2005) and other regions (Smirnov and Moore 2001). The vertically integrated moisture transport flux vector Q (kg m−1 s−1) is expressed as
e5
e6
e7
where Qy and Qx are the moisture transport flux in the zonal and meridional directions, respectively; q is the specific humidity; u and υ are the zonal and meridional components of the horizontal wind vector V; p is the pressure; ps is the surface pressure; pT is the top pressure of integrated layer; and g is the gravity acceleration. The vertically integrated moisture flux divergence F (kg m−2 s−1) is computed from
e8
where is the isobaric gradient operator.

The moisture transport flux integrated from 1000 to 300 hPa indicates two major water vapor paths (Figs. 8a and 8b). One of them transports warm and moist air easterly from the tropical Pacific through the south side of the WNPSH. Another one transports warm and moist air southwesterly from the equatorial Indian Ocean. The two water transport paths merge over south China and become one strong water vapor transport toward the northeast. Strong convergence of the moisture flux appears in the Korea and Japan area. Larger moisture transport flux is evident in the perturbed SST case, especially in the Korea and Japan area (Fig. 8c). This type of convergence is usually associated with a southwestward extension of the WNPSH and a southward shift of the upper East Asian jet stream (Zhou and Yu 2005). The most sensitive area of moisture transport flux corresponding to the uncertainty of SST lies between Korea and Japan and has a maximum ensemble spread reaching 120 kg m−1 s−1.

Fig. 8.
Fig. 8.

COAMPS 48-h ensemble mean field of vertically integrated moisture transport flux (vector, kg m−1 s−1) and moisture flux divergence (shaded, kg m−2 s−1) valid at 0000 UTC 27 Jun 2005 for (a) perturbed and (b) nonperturbed SSTs. The divergence values are scaled by 10−3. The ensemble mean difference of the moisture flux transport (contour) and the absolute ensemble spread difference (shaded) between the two cases is shown in (c).

Citation: Weather and Forecasting 26, 3; 10.1175/WAF-D-10-05007.1

The moisture transport flux is dynamically driven by the flow pattern at the northwestern edge of the WNPSH; an LLJ carries large amounts of warm and moist vapor from the tropics into East Asia (Kripalani et al. 2005). The LLJ often forms at the southern edge of a quasi-stationary front, called a mei-yu front, and extends from south China to southern Japan. Active cumulus convection along the mei-yu front can lead to the development of the LLJ through low-level convergence and induced secondary circulation by Coriolis acceleration (Chou et al. 1990; Chen et al. 2003). The level of maximum wind speed of the LLJ is generally between 850 and 700 hPa.

The LLJ is strongly correlated with heavy rainfall since it enhances the mesoscale convective systems by feeding the convection and conditioning the environment (Chen and Yu 1988; G. T.-J. Chen et al. 2005). G. T.-J. Chen et al. (2005) indicate that there is a ~94% likelihood that an LLJ of at least 12.5 m s−1 would be present at 850 hPa and an ~88% chance at 850 hPa before and near the onset of the more severe heavy rain events (100 mm in 24 h) in northern Taiwan. Therefore, it is necessary to examine the sensitivity response of the LLJ to the rainfall due to the inclusion of SST uncertainty.

The strength of the low-level jet is increased in the perturbed SST case because of the increased westward extension of the WNPSH and the deepened cyclone between Korea and Japan (Figs. 9a and 9c). The maximum wind speed is located over the Korea and Japan area, at the northwest region of the subtropical high. The increased zonal wind speed reaches about 8 m s−1. A slightly increased wind speed is also evident in the southwest branch of the subtropical high.

Fig. 9.
Fig. 9.

COAMPS 48-h ensemble mean (barbs as in Fig. 1) and ensemble spread (shaded) for the 850-hPa wind valid at 0000 UTC 27 Jun 2005 for (a) perturbed and (b) nonperturbed SSTs, and (c) the ensemble mean difference of the 850-hPa wind speed (contoured) and the absolute difference of the ensemble spread for the perturbed minus nonperturbed SST (shaded). The contour lines in (a) and (b) correspond to the wind speeds of 10 and 20 m s−1, respectively.

Citation: Weather and Forecasting 26, 3; 10.1175/WAF-D-10-05007.1

The locations of higher uncertainty in the 850-hPa wind for both cases are similar with the largest value in the Korea–Japan area and the secondary maximum at the western edge of the WNPSH (Figs. 9a and 9b). A stronger response is apparent in the perturbed SST case. Larger wind speeds from the perturbed SST case are coincident with higher values of spread (Fig. 9c), as it is also related to the stronger pressure gradient.

5. Effects of the perturbed SST on forecast errors

The uncertainty of the two ensemble forecasts (using all available forecasts) is analyzed using the root mean of the squared ensemble mean differences (rmsd):
e9
where represents the ensemble mean from the perturbed SST, from the nonperturbed SST, and n is the number of forecasts. Larger values of RMSD indicate greater forecast uncertainty and a more sensitive response to small SST perturbations (Chu et al. 1999; Langland et al. 2008).

The impacts of SST-induced errors are displayed in Fig. 10. The largest response of the 850-hPa wind (Fig. 10a) is located in the Korea–Japan area and northeast China due to the increased gradient between the WNPSH and the low along northeast China, which strengthens the low-level jet at the northwestern edge of the WNPSH and increases the uncertainty in the moisture transport flux (Fig. 10b) and precipitation (Fig. 10c).

Fig. 10.
Fig. 10.

RMSDs of the 48-h ensemble mean forecast from the perturbed and nonperturbed SSTs for (a) 850-hpa wind, (b) integrated moisture flux, and (c) 36-h accumulated precipitation.

Citation: Weather and Forecasting 26, 3; 10.1175/WAF-D-10-05007.1

This implies that inclusion of SST uncertainty as a lower boundary condition for the ensemble forecast is important. Air–sea interaction is directly affected by the SST uncertainty, which can lead to inaccurate air–sea fluxes in the coupled system and decrease forecast accuracy. The error that propagates from the ocean surface to the atmosphere is nonlinear and is not only confined to the surface layer but also propagates into the upper layer via dynamics and physics. The case study shows that the effects can be profound in active East Asia precipitation areas during the rainy season.

The predicted errors from an ensemble of possible initial states of a numerical model can be determined by the variance of the forecasted ensemble since, during the time integration of the different states, the forecast may drift away from the forecasted mean state. The variance of the distribution determines the uncertainty of the initial state and the probability decreases when one moves away from the mean (Evensen 1994).

Pairs of bin-mean ensemble variance and squared forecast error (forecast-verifying analysis) are used to assess the ensemble forecast skill due to SST with and without perturbations. Here the “true” state is the analysis fields from the control run with all available data assimilated. The binning approach follows the procedure of Wang and Bishop (2003) and Bishop et al. (2009). Ensemble variance and squared forecast error are ordered from smallest to the largest, and then the ordered list is divided into approximately equally populated bins. The bin-averaged squared error is plotted against the bin-averaged ensemble variance for SST with and without perturbations as shown in Fig. 11. Values along the 45° line indicate that the forecast error variance is approximately equal to the ensemble variance. In general, the results from the perturbed SST case lie closer to the 45° line than those from the unperturbed case. This indicates that the perturbed SST ensemble forecast is able to better distinguish large forecast error variance from small forecast error variance compared to the case without perturbed SSTs. The atmospheric ensemble, however, is still underdispersive, indicating that further research and validation for tuning the parameters such as the correlation length scale and amplitude of perturbation for the SST ensemble generation are needed.

Fig. 11.
Fig. 11.

Scatter diagram of the bin-mean ensemble variance and bin-mean squared error for 48-h forecasts of the (a) sea level pressure, (b) 2-m air temperature, (c) u-wind component, and (d) υ-wind component.

Citation: Weather and Forecasting 26, 3; 10.1175/WAF-D-10-05007.1

6. Discussion and conclusions

The impacts of sea surface temperature (SST) uncertainty on the ensemble mean forecast error of the ensemble forecasts of the evolution of the western North Pacific subtropical high (WNPSH) and related rainfall are investigated using ensemble simulations. The SST uncertainty associated with small-scale anticyclonic and cyclonic eddies is quantitatively produced using a perturbation technique to smoothly add a spatial correlation function and random noise to the background COAMPS-analyzed SST field from NCODA. Error propagation from the lower boundary SSTs to the atmospheric model prediction, focusing on the WNPSH and rainfall in the East Asia region, is discussed by comparing the results from the ensemble simulations with the perturbed and nonperturbed SST cases.

The case study suggests that the additional SST perturbations produced by our technique lends realistic small-scale SST fluctuations in the Kuroshio and western North Pacific region, as is evident in the comparison of the perturbed and nonperturbed (control) SST fields with Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) SST observations. The SST perturbations are constrained to sum to zero.

The COAMPS atmospheric ensemble forecast responds to the perturbed SST ensemble by extending the position of the WNPSH to the west, a position similar to climatology and responsible for a rainy event in late June 2005 in East Asia. The inclusion of SST perturbations also leads to larger ensemble spread on the northwestern side of the WNPSH, is in itself highly sensitive to the inclusion of SST perturbations, and has large uncertainty for the forecast. The greater ensemble mean rainfall that occurs for the perturbed SST case is closer to satellite observations of rain. The increased ensemble variances of accumulated precipitation found in the perturbed SST case are consistent with Sloughter et al.'s (2007) finding that rainfall prediction error variance is proportional to the mean rainfall amount.

The mechanism responsible for the rainfall in East Asia is a merged larger water vapor transport over south China easterly from the tropical Pacific Ocean through the south side of the WNPSH and southwesterly from the equatorial Indian Ocean. Stronger convergence of moisture flux appears in the Korea and Japan area in the perturbed SST case due to the stronger LLJ, which is enhanced by the larger pressure gradient between the westward extension of the WNPSH and the deepened cyclone over the North Korea area. The most sensitive area to the SST uncertainty for the moisture transport flux and the LLJ is consistent with the rainfall.

Surface verification using the bin-mean ensemble variance and squared forecast error shows that the atmospheric ensemble variance from the perturbed SST case is larger than the nonperturbed SST case. The statistical analysis also shows that the atmospheric ensemble is still slightly underdispersive, indicating the need for the representation of error due to model error in the ensemble.

The atmospheric model response to SST perturbation can be profound, causing large ensemble variance in the case studied for the WNPSH, LLJ, and resultant rainfall. In the absence of a fully coupled model, the stochastic SST ensemble perturbation generation technique presented in this paper can be used to estimate how SST errors of any prescribed scale affect the error growth and the ensemble mean. Computational time also can be saved when one uses the SST perturbation as an alternative for the ocean ensemble.

Acknowledgments

The support of the sponsor, the Space and Naval Warfare System Command (SPAWAR), through Program Element 75927210, is gratefully acknowledged. Computations were performed on the IBM P4+ at the Naval Oceanographic Office (NAVO) Major Shared Resource Center (MSRC) at Stennis Space Center, Mississippi.

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1

TMI and AMSRE-E data are produced by Remote Sensing Systems (RSS) and sponsored by the National Aeronautics and Space Administration’s (NASA) Making Earth Science Data Records for Use in Research Environments (MEaSUREs) Distributed Information Services for Climate and Ocean Products and Visualizations for Earth Research (DISCOVER) Project and the AMSR-E Science Team. The SST is optimally interpolated by the RSS at ¼° (~25 km) resolution to avoid missing data due to orbital gaps or environmental conditions precluding SST retrieval. Data are available online (www.remss.com).

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