A brief description of GOES-8 satellite data

The new series of Geostationary Operational Environmental Satellites beginning with GOES-8 was launched on 13 April 1994. It has been designed with separate imaging and sounding instruments to support the requirements of the modernized National Weather Service. It is three-axis stabilized to improve instrument performance and to enable more efficient data gathering by both the imager and sounder. The GOES-8 sounder includes 18 thermal infrared bands plus a low-resolution visible band. The spectral bands are sensitive to temperature, moisture, and ozone. Significant improvements in data quality and information content, with respect to previous geostationary satellites, encourage the use of these data in many areas of research (Smith and Lee 1995).

The potential use of satellite data to contribute significantly to hurricane forecasting, for which models are initialized mostly over oceanic regions, needs to be assessed fully. However, the “optimal” use of satellite data faces many challenges. Among these are (i) the quality control of the observed brightness temperatures to remove potentially cloud-contaminated or erroneous data and (ii) the direct use of brightness temperature data instead of the retrieval products. The latter requires a computationally efficient radiative transfer model that computes the brightness temperatures from the meteorological variables. One such radiative transfer model for the use of GOES-8 brightness temperatures is briefly illustrated in the following section.

Radiative transfer model

In this research, we adopted a radiative transfer model similar to that of Eyre and Woolf (1988) and Eyre (1991), with some modifications made to fit the GOES-8 sensor observation. The input variables of our radiative transfer model are temperature and relative humidity profiles, surface pressure, and surface skin temperature. The forward model consists of 40 layers ranging from 0.1 to 1000 hPa (Table 1). Because the radiative-transfer model layers are not necessarily consistent with the model layers for which values of temperature and humidity are available, interpolation or extrapolation of pressure p is needed. In this study, a linear interpolation (extrapolation) scheme in log(p) is adopted to generate temperature and humidity in the 40 radiative-transfer model layers from the 27 σ-layer model analysis and/or forecast, where σ = (p − p_t)/(p_s − p_t), with p_s being surface pressure and p_t being pressure at the model top.

The fast transmittance model developed by Eyre and Woolf (1988) is used to calculate the transmittance of the atmosphere. For GOES-8, every individual field of view (IFOV) has a unique zenith angle. The transmittance coefficients are found by multiple regression, which fits to the line-by-line radiative transfer model (LBLRTM; see Clough et al. 1992), and are supplied as constant quantities to our radiative transfer model.

The contribution of direct atmospheric upward emission is obtained as a sum of the contributions from all emitting layers:

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where T_k is the temperature at atmospheric level k and τ_α,k is the transmittance in channel α from level k to space. The brightness temperature is converted from radiance using the inverse Planck function.

Data quality control and error statistics

Infrared satellite data were collected at the Air Force Research Laboratory (AFRL) from the sounder aboard the GOES-8 satellite using the AFRL Interactive Meteorological System facility. The GOES-8 sounder data were cloud cleared to correct for the complicating effects that hydrometeors have on the interpretation of infrared brightness temperatures. Cloudy GOES-8 IFOVs were identified using a person–computer interactive cloud–clear discrimination program that operated on images made with data from the visible channel and from the infrared channels at 3.7 and 11.0 μm. To create a single sounding field of view (SFOV), a set of IFOVs were averaged horizontally. The purpose of the averaging is to compensate for data noise. We used the method outlined in Lipton (1998) to select a set of averaging areas that would minimize the gaps in coverage caused by clouds. Data were averaged from 3 × 3 boxes of GOES-8 IFOVs, resulting in SFOVs that represent an area of approximately 30 × 30 km². At least four clear IFOVs were required to make an SFOV, and an isolation limit of nine clear IFOVs was used.

After the cloud- and precipitation-clearing steps outlined above, the satellite data were further processed by removing the bias between the satellite brightness temperatures and those calculated from collocated radiosonde observations. For this step, we used a shrinkage estimator (Fleming et al. 1991), which is a modified regression technique. In our application of the shrinkage estimation technique, we used the satellite sounder channels, the latitude, and the satellite zenith angle of the satellite observations as predictors. The radiosonde–GOES-8 observation pairs were taken from 1200 UTC 15 and 0000 UTC 16 August 1995. The approximate region was from about 24.56° to 42.59°N and 72.66° to 89.31°W. Table 2 gives the GOES-8 instrument noise errors E_ins and the forward model errors E_fwd. Values of E_ins were computed using a statistical data analysis method (Hillger and Vonder Haar 1988). The forward model errors E_fwd were evaluated from comparison between the“fast” forward model and the slow LBLRTM. The error variances of GOES-8 radiance for each channel are then calculated by

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where n is the number of samples averaged for the given IFOV. The error variance of brightness temperature is computed by multiplying the radiance error variance by (dT_b/dR)², which is the derivative of the brightness temperature T_b with respect to radiance based on the Planck function.

Cost function formulation and the two BDA experiments

There were 12 time levels when GOES-8 brightness temperature observations were available in the 6-h window from 1200 UTC to 1800 UTC 15 August 1995. Specifically, the GOES-8 observations were collected at time t_n = t₀ + Δt_n, where Δt_n = 0, 46, 88, 107, 148, 167, 208, 226, 268, 287, 328, and 346 min and t₀ corresponds to 1200 UTC 15 August 1995. Figure 3a plots the locations of all the brightness temperature observations that were available over the assimilation domain during the 6-h time window, for incorporation into the BDA procedure. Satellite data were available over most areas except the initial vortex region. To assess the effect of these satellite data on the 2–3-day prediction of the hurricane, an initial bogus vortex was needed to compensate for the satellite data void over the initial vortex region as mentioned earlier. We thus developed, as the first step, a variational bogus data assimilation scheme that makes use of a bogus surface low. The BDA scheme and its numerical performance on the initialization of Hurricane Felix at a mature stage and the subsequent prediction were presented in Zou and Xiao (2000). In the study reported here, we included the satellite data into the BDA procedure. The bogus surface low was specified using the Fujita formula with the observed central value of SLP and the estimated radius of maximum low-level wind as the input to the axisymmetric vortex.

The four-dimensional variational data assimilation experiments were carried out by minimizing two cost functions: one is J_bg, which measures the discrepancy between the model-predicted and specified sea level pressures representing the bogus surface low, and the other is J_bgsat, in which an additional term is added to J_bg to minimize also the distance between model-predicted and GOES-8 observed brightness temperatures. A simple background term J_b is included in both cost functions. Mathematically, they can be expressed as

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where

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Here, the summation over t_m in (9) was carried out over a one-half-hour window at 5-min intervals starting from t₀ (1200 UTC 15 August 1999). Here, R is a two-dimensional circular domain of 300-km radius centered at the hurricane center, and (i, j) represent model horizontal grid points within R at the lowest σ level (σ = 0.995). The cost function J_bgsat was calculated over a 6-h window. The summation in (10) was carried out at t_n, which represents the 12 observational times t_n = t₀ + Δt_n, where Δt_n = 0, 46, 88, 107, 148, 167, 208, 226, 268, 287, 328, and 346 min. The vector r_k represents the physical locations of all GOES-8 brightness temperatures at time t_n. Variables P and T_b represent the sea level pressure and brightness temperature, respectively. Here, J_b is a simple background term measuring the distance between the model state (x₀) and the MM5 analysis based on the large-scale NCEP analysis (x_b). Both J_bg and J_bgsat are functions of the model initial condition x₀. During the minimization procedure, x₀ is adjusted to fit the model solution to the bogus surface low and/or the GOES-8 brightness temperatures as closely as possible. The values W_P, W_bt, and W_b are diagonal weighting matrices approximating the error variances of the bogus surface low, the brightness temperature data, and the background estimate of the model state, respectively. The value of W_P was taken simply as a constant and was determined empirically by assuming a 1-hPa pressure error. Here, W_bt was calculated based on the error statistics of the GOES-8 brightness temperatures, the error variance of which was computed by multiplying the radiance error variance [see (4) and Table 2] by (dT/dR)², where dT/dR is the derivative of the temperature with respect to the Planck function. The value of W_bt is the inverse of the brightness temperature error variance Var. For the background term, the value of the weighting W_b was calculated as the inverse of the maximum differences at each vertical level of two MM5 analyses 12 h apart.

All the data assimilation experiments were carried out at 30-km horizontal spacing using the adjoint modeling system of MM5 described by Zou et al. (1997, 1998). The physical parameterizations included in the minimization program of the model were (i) a bulk aerodynamic formulation of the planetary boundary layer, (ii) a dry convective adjustment, (iii) grid-resolvable large-scale precipitation, and (iv) the Kuo cumulus parameterization scheme.

The forecast model

A version of the MM5 nonhydrostatic, movable, and triply nested grid model version was used for the 3.5-day numerical simulation of Hurricane Felix. The grid system contained the triply nested meshes and 27 σ layers for all grid meshes, with horizontal spacing of 90 km for the coarse domain A, 30 km for the intermediate domain B, and 10 km for the fine-mesh domain C (see Fig. 3b for the domain configuration). The 27-layer σ values are 0.025, 0.070, 0.110, 0.150, 0.190, 0.230, 0.270, 0.310, 0.350, 0.390, 0.430, 0.470, 0.510, 0.550, 0.590, 0.630, 0.670, 0.710, 0.750, 0.790, 0.830, 0.870, 0.910, 0.945, 0.970, 0.985, and 0.995. The horizontal dimensions for domains A, B, and C were 45 × 51, 76 × 85, and 121 × 121, respectively. Domains A and B were fixed throughout the simulation, and the 10-km domain C_i moved along the hurricane track, with domains C₁, C₂, C₃, and C₄ used for the forecast periods of 0–18 h, 18–42 h, 42–55 h, and 55–84 h, respectively.

The model’s moist processes included parameterization of shallow convection for all domains, Grell cumulus parameterization and stable precipitation scheme for domain A, Grell cumulus parameterization and Dudhia’s simple-ice explicit moisture scheme for domain B, and Kain–Fritsch cumulus parameterization and mixed-phase explicit moisture processes for domains C₁, C₂, C₃, and C₄. The high-resolution planetary boundary layer parameterization scheme (Blackadar scheme) was used for all the domains. The land surface temperature was calculated using surface energy budget equations. For a more detailed description of MM5, see Dudhia (1993) and Grell et al. (1994).

Experiment design

We conducted four forecast experiments, all initialized at 1200 UTC 15 August 1995 (Fig. 4). This time period is when Hurricane Felix was approaching the Outer Banks of North Carolina. The National Hurricane Center official operational track forecast indicated that Felix would make a landfall in 72 h from the initial time.

The same model configuration, described in section 4b, was used for all four forecast experiments. Only the initial conditions were different. The initial condition obtained by the standard preprocessing procedure of MM5 (Grell et al. 1994) was used as the initial condition for the control experiment CTRL. The initial condition obtained with the use of bogus surface data through minimizing J_bg was used as the initial condition for the BG experiment. The initial conditions obtained with the use of both bogus surface data and satellite brightness temperature data through minimizing J_bgsat were used as the initial conditions for the two experiments BGSAT and BGSAT2. Only those GOES-8 brightness temperatures with values that differed from that of the large-scale analysis by less than 2°C (4°C) were included in the data assimilation procedures of BGSAT (BGSAT2).

The bogus and satellite data assimilation experiments were carried out on a single domain, domain B, at 30-km spacing over one-half-hour (for BG) and 6-h (for BGSAT and BGSAT2) windows, respectively. The initial conditions on domain C₁ at 10-km spacing were obtained from the initial conditions at 30 km by a linear interpolation. The initial conditions for domain A at 90 km were obtained from the NCEP large-scale analysis.

The fit to data

To see how well the model fits to the GOES-8 brightness temperature data, we plot in Fig. 5 the mean errors and the rms errors between the simulated and the observed GOES-8 brightness temperatures for CTRL (dashed line), BG (dotted line), and BGSAT (solid line). The mean errors and the rms errors were calculated for all the GOES-8 observations available in the 6-h time window (from 1200 to 1800 UTC 15 August 1995). The mean errors were reduced for all channels after data assimilation (Fig. 5a). Large error reductions in terms of distance of the analysis of BGSAT to the satellite observations occur mainly in the channels 5–8 and 10–15. As we know from the sensitivity profile (Fig. 2), large sensitivities of the brightness temperatures at channels 5–8 and 13–14 are found in the low troposphere for both the temperature and the specific humidity fields. The brightness temperatures at channels 10–12 and 15 are more sensitive to the temperature and specific humidity in the mid- and upper troposphere. The fit of the model state to observations at channels 9 and 16 is slightly degraded after data assimilation. The problem of the satellite data assimilation at channels 9 and 16 is found to be linked to the large observational error variances at these two channels (see the dash–dotted line in Fig. 5b). During the model fit to the specified bogus surface low, adjustments occurred outside the vortex region that resulted in larger rms errors for the BG analysis than for the background field in comparison with the GOES-8 observations.

It is logical to expect error reductions of the model solution when comparing it with data that were assimilated. What will be the fit of the model forecasts of, say BGSAT, to observations that are available beyond the assimilation time period? For Hurricane Felix, GOES-8 brightness temperature data were also made available during the next 6-h period following the 6-h data assimilation window. These data exist at 10 time levels, with a total number of observations of 837, 140, 796, 148, 916, 151, 841, 106, 72, and 850 available, respectively, at 1846, 1928, 1947, 2028, 2047, 2129, 2147, 2229, 2328, and 2346 UTC 15 August 1995. At a few times when the available satellite data are less than 200 observations, the satellite data were located in the northeast corner of domain B, whereas at other times (5 out of 10) the data covered only the western half of domain B. Because the purpose is to assess the effect of upstream conditions on Hurricane Felix’s track prediction, we calculated in Table 3 the fit of model forecasts to data at 1846, 1947, 2047, 2147, and 2346 UTC 15 August, when not only were the observations located upstream, but the number of observations was significantly larger (near or above 800). The brightness temperatures derived from the BGSAT model solution gave the best overall fit to the GOES-8 satellite data. It is surprising to find that the fit of the BG forecast was generally slightly better than that of CTRL for the environmental flow prediction. Improvements in different channels for data at all the five time levels are shown in Fig. 6. Error reductions occurred for both BG and BGSAT for most channels during the forecast period from 6 to 12 h. The error reduction in the BG forecast indicates a positive effect of the BDA-generated hurricane on the simulation of environmental flow over the east coast and the eastern United States.

Model prediction contains errors of two kinds: errors in the initial condition and errors due to the imperfection of the forecast model. The fact that the forecast from BGSAT fits the GOES-8 data better than does that of the BG beyond the assimilation window indicates that important adjustments in the model initial condition errors were made through satellite data assimilation, and these adjustments were significant enough to result in an improvement to the model simulation of Hurricane Felix beyond the assimilation window. Numerical results will be shown in more detail in the following two subsections.

Differences in the initial conditions with and without the use of GOES-8 brightness temperatures

As mentioned in sections 2 and 3, GOES-8 brightness temperature information is directly sensitive to the atmospheric temperature and moisture fields. Figure 7 shows the mean and rms differences of the initial temperature and specific humidity fields between BGSAT and BG. The largest changes in the initial temperature field with the use of GOES-8 brightness temperatures were near the surface and the top of the model (see solid line in Fig. 7b), with an increase of temperature in the low troposphere and a decrease of temperature in the mid- and upper troposphere (Fig. 7a). The relatively large changes in the temperature field near the model top, indicated by the rms difference, were found to be mainly over the vortex region. The mean and rms differences of the initial temperature fields between BGSAT and BG outside the vortex region (see the thick-line circle in Fig. 3a), shown in Fig. 7 as dash lines, confirm this result. The largest change in the initial moisture field was at σ = 0.75 (model level 19, near 800 hPa), with a dry bias below model level 14 and a small moist bias above level 14 but below level 7. Therefore, large changes to the initial condition describing the environmental flow outside the initial vortex region are found in all model levels for the temperature field and mostly in the low levels for the specific humidity field. A large difference between BG and BGSAT at a certain height implies that either the model is better fitted to brightness temperatures at those wave bands where the large sensitivity occurs at that height or the discrepancies between the background and the observations at these wave bands are larger than those at other wave bands. The former appears to be the case if we combine the results in Figs. 2 and 5. The fit of the model state to observations was best achieved for the brightness temperatures in channels 5–14 (Fig. 5b, solid curve) and the maximum sensitivities for the brightness temperatures at most of these channels are in the low troposphere (Fig. 2). The latter probably is not true, because the fit of the CTRL analysis to the observations (dashed line in Fig. 5b) does not show an absolute peak at the wave bands of 5–8 and 10–15.

In the following we first examine modifications made to the environmental flow by the assimilation of the GOES-8 brightness temperatures and then examine the differences of the initial vortices obtained in BG and BGSAT. Comparing the surface temperature fields in BG and BGSAT (Fig. 8), we find that the two thermal ridges, one over the continent and the other over the ocean, are intensified after the assimilation of GOES-8 brightness temperatures. The enhanced thermal ridges, as highlighted by 299- and 300-K contours, reflect the temperature adjustments to the initial condition as a direct result of fitting satellite brightness temperatures. The warm air to the west of the hurricane was allowed to penetrate farther north from the south. In the 850-hPa specific humidity field, the modification made to the background moisture field by satellite data was mostly negative to the west of the hurricane, indicating a reduced amount of moisture content after the assimilation (Fig. 9). The air to the west of the storm is drier in BGSAT by as much as 4 g kg⁻¹ in comparison with that in BG.

The low-level temperature increase, corresponding to the intensified thermal ridge over the continent, was found to be associated with downward motions, which may have caused the subsidence warming. The region of maximum temperature increase is located to the west side of the Appalachian mountain ridge (Fig. 10). The representativeness of the real atmosphere is difficult to verify because of (i) very little or no independent observations over these regions and (ii) the possible inclusion of model errors in the initial adjustments. During the fit to all brightness temperature observations in the 6-h assimilation window, errors may result from sources such as the imperfect forecast model, the approximated observation error variances, and the neglect of the observation error correlations. Nevertheless, we compared the model-derived profiles of temperature after the 12-h forecast with two radiosonde soundings that were available over these regions. The geographical locations of these two stations are shown in Fig. 10. Figure 11 shows the vertical profiles of the differences in temperature between the 12-h model results interpolated to the radiosonde stations A (at 38.4°N, 82.6°W: Huntington, West Virgina) and B (at 40.5°N, 80.2°W: Pittsburgh, Pennsylvania) and the radiosonde observations themselves (i.e., T^BG − T^OBS) for both BG and BGSAT. We find that the 12-h forecast errors are significantly reduced at most vertical levels because of the use of satellite data. The vertically averaged rms errors are shown in Table 4, including variables of temperature, zonal wind, meridional wind, and specific humidity. The assimilation of satellite brightness temperatures reduces the 12-h forecast errors of temperature and wind fields. Results for the specific humidity field are mixed at the two stations. We also compared the 12-h model forecasts to all of the radiosonde data in the forecasting domain B (a total of 23 stations), and an improvement in the 12-h forecast fit to data is observed (see Table 5).

Although there were no satellite observations over the vortex region at any time, differences in the initial conditions over the vortex region with and without GOES-8 satellite data resulted from the interaction of the bogus surface low and the background flow, the latter being modified by the satellite data. For example, the low-level wind (σ = 0.995) distribution in the BG vortex is different from in the BGSAT vortex (Fig. 12). The maximum low-level winds are 36.7 and 53.6 m s⁻¹ in BG and BGSAT, respectively. The latter may be too strong to be verified by observations. The maximum low-level winds in the BGSAT initial condition were located to the north of the vortex center, but they were located to the east-northeast of the vortex center for BG. Differences arising from variations in the initial vortices of BG and BGSAT are also found in the other model fields (temperature, specific humidity, pressure perturbation, and vertical velocity). Because their distributions are mostly axisymmetric, we show in Fig. 13 a cross-section cutting through the initial vortex centers from west to east (along the line CD in Fig. 12). The adjustments of the temperature, specific humidity, pressure perturbation, and vertical velocity in BGSAT show more reasonable magnitudes than those from the BG assimilation. For example, the maximum temperature increase in the upper level of the BG vortex was as high as 26.3°C, but it was 14.7°C in the BGSAT vortex. The pressure increases in the upper levels above the surface low were 11.8 and 5.5 hPa for BG and BGSAT vortices, respectively. The vertical velocity on the east side of the BG vortex was greater than 600 cm s⁻¹; it was 135 cm s⁻¹ in the BGSAT vortex. A temperature adjustment of 26.3°C and a vertical velocity of 600 cm s⁻¹ in BG are difficult to verify through observations. The temperature increase seems to be related to the adiabatic warming associated with the descent in the eye. In addition, the air in the eye of the initial BGSAT vortex was drier than that in the BG vortex. The hurricane eye was generated in both BDA experiments, with descending warm and dry air in the center of the hurricane and ascending moist air around the eye throughout the entire layer of the model atmosphere. However, the BGSAT vortex is quantitatively more realistic than that of the BG vortex, except for too strong a surface wind in BGSAT.

Seeing the differences in both the environmental flow and the initial vortex described by the BG and BGSAT initial conditions, one compelling question would be what effect these differences have on the forecasts, or are they significant enough to make a difference in the subsequent 2–3 day prediction of Hurricane Felix? Results of the three model simulations using the NCEP analysis (CTRL), the BG initial condition, and the BGSAT initial condition are shown in the following section. Emphasis is placed on comparing numerical forecast results from BG and BGSAT.