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    Mean and standard deviation of the fractional refractivity differences between GPS RO and model simulations as a function of geometric height for the NH winter campaign for (a) NH (north of 20°N), (b) TR (between 20°S and 20°N), and (c) SH (south of 20°S).

  • View in gallery

    As in Fig. 2, but for the NH summer campaign.

  • View in gallery

    Total observation error of the refractivity.

  • View in gallery

    Mean and standard deviation of fractional normalized refractivity differences between GPS RO and model simulations as a function of geometric height for (a) NH (north of 20°N), (b) TR (between 20°S and 20°N), and (c) SH (south of 20°S). A two-term refractivity expression has been used to simulate the observations from model variables. Only the observations that passed the QC procedures are shown. The current QC process and observation error characterization have been used.

  • View in gallery

    As in Fig. 4, but with the use of the new QC procedure and observation error characterization, and a three-term expression for refractivity with the B94 coefficients.

  • View in gallery

    Anomaly correlation scores as a function of the forecast length for the geopotential heights at 250 hPa for the SH (20°–80°S).

  • View in gallery

    Time series of the 3-day geopotential height bias (in m) for the NH (20°–80°N) at 500 hPa verified against (a) own analysis and (b) consensus analysis for the different experiments: PRCNT (dashes), PREXP (triangles), PREXPB (x), and PREXPC (plus symbols, on top of PREXP).

  • View in gallery

    Time series of the 1-day temperature bias (K) for the SH (20°–80°S) at 700 hPa verified against (a) own analysis and (b) consensus analysis for the different experiments: PRCNT (dashes), PREXP (triangles), PREXPB (x), and PREXPC (plus symbols, on top of PREXP).

  • View in gallery

    Zonal cross section of the temperature differences between PREXPB and PREXP for (a) analyses and (b) 3-day forecasts. The differences have been averaged over the campaign period.

  • View in gallery

    Temperature differences (K) between the PREXPB and PREXP analyses on 20 Mar 2008, where (a) all the observations and (b) only GPS RO data are assimilated into the system. The differences are shown for the lowest model level.

  • View in gallery

    RMS difference at day 3 for the tropical (20°S–20°N) wind vector component (m s−1) at (a) 850 and (b) 200 hPa for the different experiments: PRCNT (dashes), PREXP (triangles), PREXPB (x), and PREXPC (plus symbols, on top of PREXP).

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    AC scores as a function of the forecast length for the geopotential heights at 500 hPa for the SH (20°–80°S). The results are filtered to represent the structures with total wavenumbers 1–20.

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Improvement in the Use of an Operational Constellation of GPS Radio Occultation Receivers in Weather Forecasting

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  • 1 NOAA/NESDIS/STAR, and Joint Center for Satellite Data Assimilation, Washington, D.C
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Abstract

As of May 2007, the National Centers for Environmental Prediction (NCEP) implemented a new Global Data Assimilation System. This system incorporated the assimilation of global positioning system (GPS) radio occultation (RO) profiles from the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) mission, which was launched in April 2006. Since then, this new type of observation has been shown to provide additional information on the thermodynamic state of the atmosphere, resulting in a significant increase in the model skill.

Recent updates of the analysis and modeling codes have required a revision of the algorithm that assimilates GPS RO data. In addition, some modifications in the processing of the observations have further enhanced the need for a revisiting of the assimilation code. Better characterizations of the quality control procedures, observation error structure, and forward modeling for the GPS RO observations are described. The updated system significantly improves the data usage, in particular in the tropics. Different sets of the atmospheric refractive indices are also evaluated in this study. The model performance is proven to be quite sensitive to the chosen coefficients and a reevaluation of these constants is recommended within the GPS community.

The new assimilation configuration results in an improvement in the anomaly correlation scores for the Southern Hemisphere extratropics (∼4.5 h for the 500-mb geopotential heights at day 7) and a reduction of the high- and low-level tropical wind errors. Overall, the benefits of using COSMIC on top of all the other observations used in the operational system are still very significant. The loss in model skill when COSMIC is removed from the observing system is remarkable at day 4 (∼8 h) and steadily increases beyond 12 h with the extended forecast range.

Corresponding author address: L. Cucurull, NOAA Science Center, 5200 Auth Rd., Camp Springs, MD 20746. Email: lidia.cucurull@noaa.gov

Abstract

As of May 2007, the National Centers for Environmental Prediction (NCEP) implemented a new Global Data Assimilation System. This system incorporated the assimilation of global positioning system (GPS) radio occultation (RO) profiles from the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) mission, which was launched in April 2006. Since then, this new type of observation has been shown to provide additional information on the thermodynamic state of the atmosphere, resulting in a significant increase in the model skill.

Recent updates of the analysis and modeling codes have required a revision of the algorithm that assimilates GPS RO data. In addition, some modifications in the processing of the observations have further enhanced the need for a revisiting of the assimilation code. Better characterizations of the quality control procedures, observation error structure, and forward modeling for the GPS RO observations are described. The updated system significantly improves the data usage, in particular in the tropics. Different sets of the atmospheric refractive indices are also evaluated in this study. The model performance is proven to be quite sensitive to the chosen coefficients and a reevaluation of these constants is recommended within the GPS community.

The new assimilation configuration results in an improvement in the anomaly correlation scores for the Southern Hemisphere extratropics (∼4.5 h for the 500-mb geopotential heights at day 7) and a reduction of the high- and low-level tropical wind errors. Overall, the benefits of using COSMIC on top of all the other observations used in the operational system are still very significant. The loss in model skill when COSMIC is removed from the observing system is remarkable at day 4 (∼8 h) and steadily increases beyond 12 h with the extended forecast range.

Corresponding author address: L. Cucurull, NOAA Science Center, 5200 Auth Rd., Camp Springs, MD 20746. Email: lidia.cucurull@noaa.gov

1. Introduction

The National Centers for Environmental Prediction (NCEP) has been assimilating observations from the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) mission (Cheng et al. 2006; Anthes et al. 2008) into their operational global data assimilation (Kleist et al. 2009) system since 1 May 2007. The use of global positioning system (GPS) radio occultation (RO) data required the coding of new numerical algorithms and the implementation of quality control (QC) procedures and observation errors according to this data type. The infrastructure necessary to assimilate GPS RO observations at NCEP was developed within the Joint Center for Satellite Data Assimilation (JCSDA) (Cucurull et al. 2007, 2008). The incorporation of COSMIC into the operational assimilation system was shown to produce a significant improvement in model skill (Cucurull and Derber 2008). For a detailed description of the processing of the GPS RO products, the reader is referred to Melbourne et al. (1994), Rocken et al. (1997), and Kursinski et al. (1997).

The JCSDA has recently updated the quality control procedures and error characterization for the COSMIC observations. This work has been done in order to address the final satellite orbit configuration, not reached until late 2007, and to perform QC procedures in a more optimal way. The original QC structure that assimilates RO data in the operational code is based on the statistics for November 2006, when the number of RO observations was lower and the cluster of satellites had not reached its final orbit yet. In addition, a better representation of the forward operator for the refractivity has been evaluated, tested, and implemented in the analysis code.

In this paper, the methodology followed to set up the new QC procedures and error characterization to improve the operational assimilation of COSMIC observations into the NCEP’s Global Data Assimilation System is described. In addition, the implementation of a more accurate forward operator for refractivity is described. For this purpose, different sets of atmospheric refractive indices are evaluated. The benefits of using this upgraded configuration for the assimilation of GPS RO observations at NCEP are evaluated, taking into account all of the other observations being assimilated operationally. In the Northern Hemisphere extratropics, the results are, in general, consistent with the earlier impact studies. However, an improvement in anomaly correlation scores for the Southern Hemisphere extratropics and a reduction of the root-mean-square (rms) tropical winds error are found with the use of the new assimilation algorithm. The significant positive benefits of using COSMIC on top of all the other observations used operationally are also presented in this paper. The changes described in this study were implemented operationally at NCEP in December 2009.

The paper is organized as follows. Section 2 describes the procedure used to upgrade the algorithm used to assimilate COSMIC refractivities, including QC procedures, forward operators, and observation errors. Evaluation of the performance of the new code versus the current (operational) version is presented in section 3. The section also analyzes the pros and cons of using different sets of refractive coefficients. The benefits of assimilating COSMIC observations on top of more conventional observations are discussed in section 4. Finally, the main conclusions are summarized in section 5.

2. Assimilation of GPS RO observations

a. Quality control checks

The QC procedure for the COSMIC observations in the current Global Data Assimilation System is based on the statistics of the comparison between observations and model simulations for November 2006 (Cucurull et al. 2007). The QC procedure is applied to each observation based on its altitude and latitude values (see Table 1). However, the transition between the different latitude ranges and vertical heights is not a smooth function of these values. In addition, the statistics were computed when the COSMIC satellites had not reached their final orbit configuration and did not take into account the seasonal dependence of the model skill.

The JCSDA has recently updated the QC procedures applied to the GPS RO observations. The new QC procedure is based on the statistics of the model and data comparison for two different seasons. Results of the statistics for the Northern Hemisphere (NH, latitudes above 20°N), tropics (TR, latitudes between 20°S and 20°N), and Southern Hemisphere (SH, latitudes below 20°S) are shown in Figs. 1 and 2 for the NH winter and NH summer campaigns, respectively. In both Figs. 1 and 2, the data have been binned to layers of 1 km. The mean difference between the observations of refractivity and the model first guess (a 6-h forecast), as well as the standard deviation of the differences, are shown in percentages of fractional refractivity. Model variables are interpolated in time and space to the location of the observations before simulating the refractivity value (Cucurull et al. 2007). The NH winter campaign (Fig. 1) shows counts above 40 km while the NH summer campaign (Fig. 2) does not because the Cosmic Data Analysis and Archive Center (CDAAC) extended the altitude of the profiles of refractivity to ∼60 km between the periods.

The main differences between the two seasons are located at altitudes above ∼25 km and below ∼10 km. Between 10 and 25 km, there is not an apparent seasonal dependence and the standard deviation of the differences in refractivity is found to be a function of the latitude only. In fact, a plot of the standard deviation of differences between the observations and their model counterparts as a function of the latitude shows good symmetry around the equator, so we can fit the standard deviation function with a cosine function. Within this altitude range (∼10–25 km), the GPS RO observations show their higher accuracy, and the “cutoff” (or threshold) for rejecting an observation is set to 3 times the standard deviation value.

Ionospheric residuals and climatological weighting reduce the accuracy of the retrieved refractivities above ∼25 km. In addition, refractivity errors might be vertically correlated due to the use of an Abel transform inversion when converting bending angles to refractivities (Kursinski et al. 1997). These effects might vary with the state of the atmosphere; thus, some differences in the statistics between the two seasons might be expected. Furthermore, CDAAC reported a bug in the processing of the data that affected the stratospheric profiles during the NH summer campaign. Due to all of these reasons, and although there is a larger standard deviation value at these higher altitudes, the cutoff value for the observations between 25 and 30 km is set to the same value and it is given by the same cosine function as used for the 10–25-km range. Even if CDAAC now provides observations up to 60 km, observations above 30 km are not used at NCEP because of limitations in our assimilation system (Cucurull et al. 2008).

Between 5 and 10 km, the differences between the observations and model simulations in Figs. 1 and 2 manifest clear latitudinal and seasonal dependences. Since within this altitude range the GPS RO data are still shown to have good accuracy (Kuo et al. 2004), the differences in the statistics can likely be attributed to the model. A plot of the differences between the model simulations and observations as a function of the temperature at the observation location (not shown) reveals similar statistical patterns regardless of the season or latitude range being evaluated. Consequently, the QC procedure within this altitude range is set to be dependent on the model temperature interpolated at the observation location. A value of 3 times the standard deviation of the differences is used as a cutoff.

Below 5 km, a systematic negative difference and an increase in the standard deviation are evident in Figs. 1 and 2. The larger values are found in the tropical latitudes, where the assumption of spherical symmetry of the atmosphere (always assumed in the processing of the observations) is less valid. In addition, superrefraction and other unknown conditions might affect the quality of the observations. For this altitude range, we averaged both seasons and set the QC to be latitude dependent. A cosine function was used to approximate the standard deviation of the differences as a function of latitude. Then, a value of one standard deviation was selected for the cutoff. By averaging the seasons, we allow a few more observations in winter than in summer. This is desirable as the observations are less likely to be affected by superrefraction and horizontal refractivity inhomogeneities (mainly caused by gradients of water vapor) in winter than in summer.

A summary of the QC structures for the four different altitude ranges discussed above is provided in Table 2. In the code, the transition between the altitude ranges has been smoothed, so the cutoff is now a continuous function of the height.

b. Forward operator for refractivity

The total refractivity (N) of moist air in the neutral atmosphere at microwave wavelengths is given by the following three-term expression (Thayer 1974, hereafter T74):
i1520-0434-25-2-749-e1
where Pd is the pressure of the dry air, Pw is the pressure of the water vapor, and T is the absolute temperature. Here, k1, k2, and k3 are the atmospheric refractivity constants, and Zd−1 and Zw−1 are the compressibility factors that take into account small departures from the behavior of an ideal gas. The first two terms in (1) are dry and wet density terms and represent the ability of the dry and wet molecules, respectively, to be polarized by an electromagnetic field. The third term is due to the permanent dipole moment of the water vapor molecules. The nonideal behavior of air is often ignored in (1), from the original expression, which introduces an error of 0.04 ppm in the dry term Nd [first term in (1)] and 0.1 ppm in the wet term Nw [second and third terms in (1)] at high humidity. The error introduced in the dry component by the omission of the compressibility factors is of the same order of magnitude as the accuracy of the dry term, while the error introduced in the wet component is much lower than the accuracy of the wet term.
Traditionally, the three-term expression has been simplified to a two-term expression which uses the total pressure P, where P = Pd + Pw, and where the refractivity constants are usually given by Smith and Weintraub (1953)
i1520-0434-25-2-749-e2
In the equation above, P and Pw are given in millibars and T in kelvins. This expression is missing the second term on the right-hand side of (1) and has widely been used within the GPS RO meteorological community. This is also the equation that describes the forward operator used in the current system at NCEP. Since the simplified two-term expression for refractivity is numerically and physically less accurate than the three-term equation, we have replaced (2) by (1) in the assimilation algorithm.

One of the key components of (1) is the specification of the k1, k2, and k3 coefficients, which have been determined empirically. There is a long list of published values and uncertainties associated with these indices for frequencies in the microwave range of the spectrum. A review of the different values is discussed in detail in Rüeger (2002, hereafter R02) and here we summarize only some of the most quoted values within the GPS community.

Early experimental measurements were provided, for instance, by Smith and Weintraub (1953), Boudouris (1963), and Hasegawa and Stokesbury (1975). An alternate approach was given by T74, where the value k2 was extrapolated from the visible wavelengths. This approach has been disputed by Hill et al. (1982) on the basis that one cannot extrapolate k2 from the visible to the microwave range. Unfortunately, because the value for k2 provided by T74 has a much higher precision than other values found in the literature, his coefficients have been largely used.

In an attempt to determine the coefficients from direct measurements, Bevis et al. (1994, hereafter B94) reevaluated the experimental values used by Hasegawa and Stokesbury (1975) and recomputed a new set of k1, k2, and k3 coefficients. However, as pointed out by R02, the new set of coefficients was derived without considering the high correlation between the k2 and k3 refractive indices. Consequently, the standard error associated with the Nw claimed by B94 should be treated with caution.

More recently, additional determinations of the radio wave refractivity of air led to a new reevaluation of the coefficients used in the refractivity equation [(1)]. R02 presents two expressions for the calculation of refractivity based on the “best available” and “best average” coefficients, respectively. The latter is roughly a reevaluation of the refractive indices used by B94 after omission of some inadequate measurements. It also uses a more precise conversion between degrees Celsius and kelvin, which leads to slightly larger values for the dry air and water vapor refractive coefficients. R02 recommends the use of the best average rather than the best available values for being more robust and more reliable.

The best average coefficients suggested by R02 also assume a more realistic content of 375 ppm (in volume) of CO2 in the atmosphere. Traditionally, a value of 300 ppm of carbon dioxide has been used. The effects of using a carbon dioxide content of 300 ppm instead of 375 ppm results in an error in the refractivity of ∼0.005%. Earlier studies (e.g., B94) did not seem to include carbon dioxide in the determination of k1, although some experimental measurements used to estimate this coefficient might have been corrected to account for the carbon dioxide content of the dry air. The omission of the carbon dioxide contribution to the dry-air coefficient leads to an error in refractivity of ∼0.02%.

Conservative values for the accuracy of the dry-air refractivity and water vapor components with the use of R02 coefficients are 0.02% of Nd and 0.2% of Nw, respectively. Differences between (1) and (2) are of the order of 0.1%, if R02 values are used in (1). This is a consequence of the ∼0.1% larger refractive index of dry air reported by R02, as compared to other authors (see Table 3). Instead, if the T74 and B94 coefficients are used, the systematic difference between (1) and (2) is negligible.

To choose the more appropriate forward operator for refractivity, we will evaluate the sensitivity of our model forecast skill to the value of the refractivity constants. For this purpose, we select the use of the coefficients provided by T74, B94, and R02 to conduct sensitivity tests in section 3. A list of the different values analyzed in this study is given in Table 3. Although the compressibility factors have been omitted in (1), some authors might have adjusted the refractive coefficients to account for the nonideal behavior of air.

Another improvement in the forward operator has been a better treatment when locating observations within the model vertical grid in areas of complex topography. This is of particular importance in steep coastal areas, such as Antarctica. In fact, soon after assimilating COSMIC operationally, it was seen that the assimilation of some profiles over continental coastlines with steep topography occasionally showed larger differences between the observations and model simulations, as well as larger than expected analysis increments. This was found to be caused by the way an observation was interpolated in the model’s vertical grid, manifesting some deficiencies in the design of the forward operator. As described in Cucurull et al. (2007), the computation of model geopotential heights is a necessary step toward the simulation of an observation of refractivity. Because geopotential heights are referenced with respect to the sea level geoid, and the model topography is only a coarse representation of reality, an observation might have been treated in the model differently whether the observation was located over land or over sea. This is because over land, the model topography has a fixed value (zland). On the other hand, the atmosphere is allowed to compress or expand over sea, so the height over the sea level, zsea, might differ from that of the corresponding nearby land zland. In other words, there was an inconsistency in terms of how the reference (surface) height was defined depending on if the model located the observation over sea or over land. The forward operator would treat the two situations differently. As a measurement profile might drift ∼400 km in the horizontal direction, this condition might not affect an entire profile, but a subset of observations within it.

This problem was overcome by referencing the geopotential heights with respect to the model topography rather than with respect to the sea level. In addition, observations located within the first model layer were rejected from the assimilation system. This approach alleviated situations where a sea level observation was misrepresented in the model as a land observation, thus enabling a thinner atmospheric layer between the observation and the model surface to be adjusted. This new definition of geopotential heights also prevents negative heights due to Gibbs effects associated with spectral models. This fix was already implemented in the operational model late in 2007 and, as a result, the model skill improved over areas such as Antarctica.

c. Observation error characterization

The observation errors assigned to the RO data in the current system are currently based on the errors provided in Kuo et al. (2004) and empirically tuned to account for the representativeness error associated with our model. To characterize the RO observation error in a more optimal way, we have followed the methodology described in Desroziers et al. (2005) to better represent the error structure of the profiles of refractivity. The authors describe how a set of diagnostics based on combinations of departures between the observations and background simulations, along with differences between the observations and analyses, can be used to optimize the observation errors. In the linear estimation theory, the variance of the observations errors can be diagnosed from the observation value and their corresponding background and analysis simulations as follows:
i1520-0434-25-2-749-e3
where nRO is the number of observations, yiRO is the value of the observation i, and yia and yib are their analysis and background counterparts, respectively. The variable ERO is the diagnosed observation error for an RO observation. Following this procedure, we have used (3) to estimate the errors for refractivities as a function of the vertical height and latitude range. The superobs factor was then removed from the diagnosed error to recover the total contribution of the instrument and representativeness errors. This factor penalizes observations within a layer that contains more than one GPS RO observation, and it is intended to partially account for the different vertical resolutions between the observations and model layers [refer to Cucurull et al. (2007) for a detailed description of this factor]. Because the errors using (3) are a function of the background and analyzed values, which in turn depend on the observation error, a few iterations were performed in order to retrieve a value close to the optimal error configuration. In the assimilation system, the new QC procedure (see section 2b) was used.

Errors of refractivity estimated using (3) are shown in Fig. 3 as a function of the geometric height. The new estimated observational errors are, in general, smaller in the NH and SH than in the tropical latitudes. To evaluate the differences with the current error characterization, the current observation errors are also plotted in Fig. 3. In this case, the errors in the extratropics are larger than in the tropics around 8–12 km and above ∼26 km, while with the new configuration this situation occurs in a more limited altitude range (∼10 km). Comparing the current and new error structures, the current configuration underestimates the errors above the upper troposphere globally, and in particular in the tropics, while the errors in tropical latitudes are overestimated for heights <8 km. A penalization of the observations above ∼25 km with the current error structure is also evident from Fig. 3.

Figure 4 shows the normalized difference between the observations of refractivity and the model simulations with the current observation error structure. Only observations that passed the current QC procedures (see Table 1) were used to plot the statistics. If the observation and model errors were unbiased and uncorrelated, the variance of the differences normalized by the total error (observation and background) would be approximately one. However, because the normalization in Fig. 4 does not include the background error, this value should usually range between one and two. We see that in the NH (Fig. 4a) and SH (Fig. 4c) this stays true for most of the vertical range of the atmosphere. However, there is large penalization in the upper atmosphere (above ∼25 km), and in the mid- to upper troposphere, which is consistent with the current observation error structure in Fig. 3. The assumed a priori observation errors in the upper atmosphere were empirically tuned to be large to avoid larger unrealistic increments in the top layers when assimilating relatively more accurate RO data. On the other hand, Fig. 3 seems to indicate that the lower ratio of the normalized differences between the observations and the model simulations in Figs. 4a and 4c in the mid- to upper troposphere might be partially a result of an inadequate tuning of the errors within this vertical range (errors are too large).

In the tropical latitudes (Fig. 4b), a larger ratio of normalized refractivity differences is evident in the tropopause, which indicates that the current estimated observation errors are too small. This is also evident from Fig. 3, when comparing the current and new observation errors. In addition, Fig. 3 also shows an inappropriate tuning of the current low-level observations in the tropics (errors are too large), which results in lower ratios of normalized refractivity differences in Fig. 4b. The fewer observations that passed the QC procedure, as compared to the NH and SH, might also partially justify the lower ratios of the normalized refractivity differences found in the lower tropical troposphere. In general, there are, overall, a lower number of observations being assimilated in the TR as compared to the other latitude ranges.

Plots for the statistics of the normalized differences between the observations and model simulations with errors derived using (3), B94 coefficients in the forward operator, and the new QC procedures described in section 2a are displayed in Figs. 5a–c for the NH, TR, and SH, respectively. It is noticeable from Fig. 5 that the new QC enables many more observations to be assimilated for all latitude ranges and heights. In the NH and SH, the current existing QC procedure (Figs. 4a and 4c) shows a decrease in the number of counts with decreasing height, while with the modified QC procedure (Figs. 5a and 5c) this number is essentially constant until it reaches the midtroposphere, where the rejection of the observations increases. In addition, we now penalize the high-level observations less, due to a better estimation of the observation errors. In general, the normalized error structure is smoother when the new observation errors and QC procedures are used, mostly due to better characterization of the observation errors.

The tropical tropopause (Fig. 5b) shows lower ratios of normalized refractivity differences than with the current assimilation configuration (Fig. 4b). This is a result of better specification of the observation errors (Fig. 3) and the larger number of observations that pass the new QC procedure. Furthermore, smaller observation errors and larger counts result in better normalized differences in the lower troposphere. In general, as was found in the NH and SH, the structure is smoother and the counts are larger when the new assimilation algorithm is used. Note that in this case the number of observations that pass the QC procedure in the tropics (Fig. 5b) is much larger than with the current QC approach (Fig. 4b). A quick look at Figs. 4b and 5b indicates, for example, that the number of observations assimilated is now two orders or magnitude higher around the tropopause. The main reason for this is that the current QC configuration is highly penalizing observations in the TR. This was done in order to avoid an increase in the high-level tropical wind errors with the assimilation of COSMIC observations in a preoperational test. However, this degradation was later shown to not be caused by the use of COSMIC observations, but by the verification method being used. Unfortunately, by the time this was discovered, it was too late and the assimilation of COSMIC at NCEP became operational with the tighter QC procedure in the tropics. With the new assimilation configuration described in this paper, we allow more tropical observations into the system. It is worth mentioning that plots similar to those in Figs. 4 and 5, but not shown here, present a slight negative bias when the R02 refractivity constants are used. However, the standard deviations of the results look the same; thus, the QC procedures we have implemented behave similarly regardless of the refractive constants being chosen.

3. Trial experiments with a new assimilation configuration

We conducted several experiments to assess the benefits of using the diagnosed error structure and the updated QC procedure for the COSMIC observations. In addition, the gain obtained by using a three-term expression for the refractivity was evaluated by testing different refractive indices. B94 coefficients were used in experiment PREXP, T74 constants (with compressibility factors set to unity) in PREXPC, and values from R02 were tested in PREXPB (see Table 3). To evaluate the benefits of the new assimilation algorithm, we also ran a control experiment (PRCNT) where the QC, observation error, and forward operator were the same as in the current (operational) configuration. All of the experiments started on 20 March 2008 and finished on 30 April 2008.

Anomaly correlation (AC) scores for the 250-mb geopotential heights as a function of the forecast day are shown in Fig. 6 (top) for the SH. Differences for each of the experiments (PREXP, PREXPB, and PREXPC) with respect to the control (PRCNT) are shown in the bottom panel of Fig. 6. AC differences outside the outline bars are significant at the 95% confidence level. If model skill is lost below AC = 0.6, the use of B94 coefficients (PREXP) results in ∼10 h of improvement in forecast skill w.r.t. PRCNT and gives the best AC scores for the extended forecast range (gain of 0.03 points at day 8). Higher AC scores with the use of B94 coefficients are also found at other pressure levels. In general and for the period being evaluated in this study, all the experiments showed better model skill than the control in the SH, and neutral impacts in the NH.

The model bias in the NH at day 3 with the different sets of refractivity constants is shown in Fig. 7a for the 500-mb geopotential heights. In Fig. 7, each experiment is verified against its own analysis. From all the trials, only PREXPB shows a slight reduction of the model bias as compared to PRCNT. However, when the verification is performed against a consensus analysis between the NCEP, European Centre for Medium-Range Weather Forecasts (ECMWF), and Met Office analyses, the results are completely different. Figure 7b shows the same experiments as in Fig. 7a, but where the model forecasts haven been verified against the consensus analysis. With the new verification analysis, PREXP and PREXPC slightly reduce the model bias but it actually increases (∼2 m) when R02 coefficients are used in PREXPB. This larger bias is already evident in the analysis field and it remains when forecasting. The increase in the bias in PREXPB as compared to the other experiments is also found for other latitudes and vertical ranges of the atmosphere. Similar results are found when verifying against radiosondes. Since the moisture fields in PREXPB do not show a larger bias as compared to the other runs, the negative bias in the geopotential heights found in PREXPB must come from a bias in the temperature field.

In fact, a close look into the temperature field reveals characteristics that are similar to the geopotential heights. For example, Figs. 8a and 8b show the temperature bias at day 1 in the SH at 700 mb verified against its own analysis and the consensus analysis, respectively. Again, the use of R02 coefficients in PREXPB slightly decreases the model bias when forecasts are verified against their own analysis, but the bias increases (−0.14 K) when the consensus analysis is used for verification. The larger negative temperature bias in PREXPB as compared to the other experiments, when the verification is done against the consensus analysis, is found globally for the lower and midtroposphere. This larger bias does not decrease to similar values compared to the other experiments until day ∼6, probably due to a drift of the model with respect to its own climatology.

Above the midtroposphere, all experiments show similar bias characteristics when verified against their own analysis. However, a reduction of the model bias is found in PREXPB in the upper troposphere and lower stratosphere when the consensus analysis is used. The reason for this is that, in general, the use of R02 coefficients produces cooler temperatures in the analysis. Since the NCEP model is already too cold in the lower troposphere, PREPXB accentuates the cold bias of the model. On the other hand, the NCEP model has a warm bias in the upper troposphere and stratosphere. Consequently, the tendency to reduce temperatures in PREXPB compensates partly for the bias, producing slightly better results. Verification of temperature values in PREXPB against a consensus analysis and radiosondes confirms that the model bias decreases in the upper troposphere and lower stratosphere when compared to PRCNT only when R02 coefficients are used. Similar results are found for other latitude ranges.

We did some tests by modifying the observation error structure and tightening the QC procedure in PREXPB, but the lower temperatures and geopotential heights in the analysis field remained. This seems to indicate that there are some deficiencies in the forward operator in PREXPB, associated with the use of the R02 refractive indices. In particular, our results seem to indicate that the value of the constant k1 is slightly too high, which in turn produces slightly higher refractivity differences between the observations and model simulations (the modeled values being higher). Given an observation of refractivity at a given geometric height, the larger the coefficient k1 and the smaller the equivalent observed air density. In response, to compensate for the larger differences in the air density, the analysis algorithm will reduce the air density at the location of the observation. As this situation occurs globally, it will lead to a reduction in the geopotential heights, producing cooler temperatures and enabling a better fit of the analysis variables to the observations. This is shown in Fig. 9a, where the zonal cross section of the differences in temperature between the PREXPB and PREXP analyses are displayed. The lower temperatures in PREXPB are global, being more significant in the mid- and lower troposphere in the NH and SH. These results are consistent with the fit to the radiosondes. The differences in temperature remain with the forecast range. In particular, some high-latitude areas still show significant differences at day 3 (Fig. 9b).

To understand where the larger differences occur, a horizontal plot of the differences between the PREXPB and PREXP analyses is shown in Fig. 10a for the first analysis cycle. From the figure, the larger differences between them are in areas of complex topography (e.g., Antarctica, Greenland, and central Asia). We conducted several experiments where observations within a profile were rejected if they were within a few kilometers of the model’s complex topography. This QC step was aimed at disabling the assimilation of observations far from the surface but erroneously misplaced close to the surface in the model, thus allowing larger (and unrealistic) surface increments. These changes improved things a bit but did not fix the problem, which supports the theory of the coefficient k1 being too large.

One might think that the larger bias in PREXPB might be a consequence of an inappropriate bias correction of the other satellite data. Within this context, the bias correction of the nadir infrared and microwave sounders would not respond quickly enough to the changes introduced by the assimilation of GPS RO data in PREXPB. However, we should see a reduction in the bias over the period being tested, which is not what the results indicate (see, e.g., Fig. 8b). In addition, a plot similar to Fig. 10a, but where only GPS RO observations are assimilated, still shows an overall cooling pattern in the same areas (Fig. 10b). This indicates that the interaction with the assimilation of other satellite data cannot justify the lower temperatures found in PREXPB.

All three experiments being evaluated in this study result in a reduction of the tropical wind errors. This is most likely due to the increase in the number of observations being assimilated in the tropics in PREXP, PREXPB, and PREXPC as compared to PRCNT. Figure 11 shows the rms errors for the low- (Fig. 11a) and high-level (Fig. 11b) tropical winds. The lowest wind errors are found for experiment PREXP. In Fig. 11, model forecasts are verified against the consensus analysis. Verification of the experiments against their own analyses shows similar results.

Based on the results described in this section, and provided that T74 coefficients should not be used (see, e.g., Hill et al. 1982), we chose the configuration used in PREXP as the most appropriate available configuration for operational implementation.

4. Impacts of COSMIC

The benefits of adding a new instrument to the observing system can diminish over time (or even disappear) due to several factors such as changes in the analysis and model configuration. This in general is due to a lack of parallel work on the observation component side of the data assimilation. To avoid this situation, it is important to monitor the gain obtained from any instrument over several periods of time so additional tuning can be done in the assimilation algorithm if results are found to be suboptimal. Unfortunately, the necessary resources needed for continuously assessing the impacts of a new observation type are not always available. In this study, we wanted to evaluate if COSMIC is still a key component of the observing system, providing additional information on the true state of the atmosphere. With this goal in mind, we ran a third experiment (EXPX), where the COSMIC observations were not assimilated. This experiment started at and covered the same period as the other experiments. The results of EXPX should be compared with PRCNT and PREXP.

AC scores for the 500-mb geopotential heights as a function of the forecast day are shown in Fig. 12 for EXPX, PRCNT, and PREXP for the SH. The benefits of using COSMIC in PREXP are already obvious in the short-range forecast. The steady decrease in model skill when COSMIC is removed from the observing system (EXPX) extends to the long-range forecast. There is ∼8 h of loss in forecast skill starting at day 4 and this loss extends to ∼15 h at day 7 if COSMIC data are removed. Results are statistically significant at the 95% confidence level.

Overall, PREXP is performing better than PRCNT, gaining ∼4.5 h in forecast skill at day 7. The differences between PREXP and PRCNT are statistically significant at the 95% confident level starting at day 5. For the period evaluated in this study, the impacts of COSMIC were found to be neutral in the NH, probably due to the larger number of observations being already assimilated. To provide a rough estimate of the percentage of COSMIC observations being assimilated into the operational suite (run similarly to PRCNT), from the 6 321 520 observations of total satellite dataset that were globally assimilated in April 2008, COSMIC only accounted for 3.6% of this amount.

One could argue that the larger number of observations being assimilated in PREXP versus PRCNT does not result in significant improvements in the model skill in the short- and medium-range forecasts (Fig. 12) and that there is no need for deploying more RO satellites. This would be an erroneous conclusion because the improved QC procedure in PREXP allows more observations to be assimilated within a profile, as compared to PRCNT. However, we are not increasing the number of profiles, so the horizontal observation density of the RO data does not necessarily increase. Only the deployment of new satellites will increase this horizontal observation density, which would be expected to provide ongoing forecasting improvements.

5. Conclusions

The algorithm that assimilates GPS RO observations at NCEP has been updated. The changes include a better characterization of the observation error and QC procedures, and a more accurate representation of the forward operator for refractivity. As a result, the data usage has significantly improved, in particular in the tropical latitudes where the counts have increased by two orders of magnitude.

The results of this study also show that the model’s skill depends on the specification of the refractivity coefficients more than what one would initially expect. The uncertainty associated with these constants is not negligible and a more robust determination of these values within the GPS community is needed. Until then, we can only test the available sets of atmospheric refractivity constants. From the different configurations being assessed in this study and given that T74 coefficients are not recommended for use, employing the coefficients estimated by B94 seems to be the more appropriate configuration at the moment.

The additional contribution of the carbon dioxide content cannot explain the larger refractive index of dry air in R02, as this gas only accounts for ∼0.02% and the differences in k1 between B94 and R02 are of ∼0.1%. A more precise conversion in the recovery of the k1 measured values, the omission of some doubtful experimental data, and the addition of some other larger values in the average result, altogether, in a larger k1 in R02. On top of a robust determination of the refractive indices for the microwave range of the spectrum, the use of appropriate compressibility factors in (1) is also desirable. In general, a reevaluation of the equation of refractivity is needed.

Overall, the value gained with the new assimilation algorithm is significant in the SH and tropical latitudes. AC scores for the mass fields are improved in the long-term forecast (4.5 h at day 7 for the 500-hPa geopotential heights). The larger number of observations being assimilated in the tropical latitudes with the new QC procedures results in an improvement in the high- and low-level winds.

We have shown that COSMIC remains a key component of the global observing system, providing information on the state of the atmosphere that is not contained in other satellite observations. The fact that GPS RO is minimally affected by clouds and precipitation, and provides equal accuracy over land as well as over oceans, are a few of the main reasons for the high value of the GPS RO data. In addition, because GPS RO provides limb-type soundings, profiles of refractivity are provided at a much higher vertical resolution than those of many other satellite data sources and, thus, are capable of resolving smaller structures. We believe that both nadir and limb-sounding instruments are complementary technologies, and a combination of both systems should provide the most optimal results in weather forecasting.

Finally, the configuration for the assimilation of COSMIC observations described in this study were implemented operationally in NCEP’s Global Data Assimilation System in late 2009.

Acknowledgments

The author thanks Dr. John Derber for valuable discussions and Dr. Rüeger for providing a copy of the manuscript on the revision of the refractive indices. I am also thankful to Drs. Louis Uccellini, Steve Lord, and John Ward for providing computer resources. I also acknowledge Mr. Dave Ector for careful proofreading, and Taiwan’s National Space Organization (NSPO) and UCAR for providing the COSMIC data. Finally, the author would like to thank both anonymous reviewers for their comments and suggestions that have significantly helped to improve the manuscript. The paper’s contents are solely the opinions of the author and do not constitute a statement of policy, decision, or position on behalf of NOAA or the U.S. government.

REFERENCES

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Fig. 1.
Fig. 1.

Mean and standard deviation of the fractional refractivity differences between GPS RO and model simulations as a function of geometric height for the NH winter campaign for (a) NH (north of 20°N), (b) TR (between 20°S and 20°N), and (c) SH (south of 20°S).

Citation: Weather and Forecasting 25, 2; 10.1175/2009WAF2222302.1

Fig. 2.
Fig. 2.

As in Fig. 2, but for the NH summer campaign.

Citation: Weather and Forecasting 25, 2; 10.1175/2009WAF2222302.1

Fig. 3.
Fig. 3.

Total observation error of the refractivity.

Citation: Weather and Forecasting 25, 2; 10.1175/2009WAF2222302.1

Fig. 4.
Fig. 4.

Mean and standard deviation of fractional normalized refractivity differences between GPS RO and model simulations as a function of geometric height for (a) NH (north of 20°N), (b) TR (between 20°S and 20°N), and (c) SH (south of 20°S). A two-term refractivity expression has been used to simulate the observations from model variables. Only the observations that passed the QC procedures are shown. The current QC process and observation error characterization have been used.

Citation: Weather and Forecasting 25, 2; 10.1175/2009WAF2222302.1

Fig. 5.
Fig. 5.

As in Fig. 4, but with the use of the new QC procedure and observation error characterization, and a three-term expression for refractivity with the B94 coefficients.

Citation: Weather and Forecasting 25, 2; 10.1175/2009WAF2222302.1

Fig. 6.
Fig. 6.

Anomaly correlation scores as a function of the forecast length for the geopotential heights at 250 hPa for the SH (20°–80°S).

Citation: Weather and Forecasting 25, 2; 10.1175/2009WAF2222302.1

Fig. 7.
Fig. 7.

Time series of the 3-day geopotential height bias (in m) for the NH (20°–80°N) at 500 hPa verified against (a) own analysis and (b) consensus analysis for the different experiments: PRCNT (dashes), PREXP (triangles), PREXPB (x), and PREXPC (plus symbols, on top of PREXP).

Citation: Weather and Forecasting 25, 2; 10.1175/2009WAF2222302.1

Fig. 8.
Fig. 8.

Time series of the 1-day temperature bias (K) for the SH (20°–80°S) at 700 hPa verified against (a) own analysis and (b) consensus analysis for the different experiments: PRCNT (dashes), PREXP (triangles), PREXPB (x), and PREXPC (plus symbols, on top of PREXP).

Citation: Weather and Forecasting 25, 2; 10.1175/2009WAF2222302.1

Fig. 9.
Fig. 9.

Zonal cross section of the temperature differences between PREXPB and PREXP for (a) analyses and (b) 3-day forecasts. The differences have been averaged over the campaign period.

Citation: Weather and Forecasting 25, 2; 10.1175/2009WAF2222302.1

Fig. 10.
Fig. 10.

Temperature differences (K) between the PREXPB and PREXP analyses on 20 Mar 2008, where (a) all the observations and (b) only GPS RO data are assimilated into the system. The differences are shown for the lowest model level.

Citation: Weather and Forecasting 25, 2; 10.1175/2009WAF2222302.1

Fig. 11.
Fig. 11.

RMS difference at day 3 for the tropical (20°S–20°N) wind vector component (m s−1) at (a) 850 and (b) 200 hPa for the different experiments: PRCNT (dashes), PREXP (triangles), PREXPB (x), and PREXPC (plus symbols, on top of PREXP).

Citation: Weather and Forecasting 25, 2; 10.1175/2009WAF2222302.1

Fig. 12.
Fig. 12.

AC scores as a function of the forecast length for the geopotential heights at 500 hPa for the SH (20°–80°S). The results are filtered to represent the structures with total wavenumbers 1–20.

Citation: Weather and Forecasting 25, 2; 10.1175/2009WAF2222302.1

Table 1.

Fit to the standard deviation of the differences between the observations and model simulations, and threshold for rejection, in the current assimilation configuration. The fit is given in percentages of fractional refractivity, and it depends on the geometric height (z, km) and latitudinal range (NH, TR, and SH) of the observation. The QC process has been tuned by rejecting all the data in a profile below an observation that failed the QC process.

Table 1.
Table 2.

Fit to the standard deviation of the differences between the observations and model simulations, and threshold for rejection, in the new assimilation configuration. The fit is given in percentages of fractional refractivity, and it depends on the geometric height, latitude (λ), and temperature (T, K) of the observation. The transition between the different height levels has been smoothed so that the QC process is a continuous function of the height. The QC system has been tuned by rejecting all the data in a profile below an observation with altitude <5 km that failed the QC process.

Table 2.
Table 3.

Refractive indices k1, k2, and k3 provided by different authors and evaluated in this study. Uncertainties (in parentheses) are provided for k1. (Precision results for k2 and k3 are not given in the table because information on their correlations and how the errors are propagated to compute the total moisture refractivity should be discussed as well). T74’s coefficients have not been adjusted to take into account the compressibility factors. The refractive indices in R02 are the best-average values (see text). The dry-air coefficient, k1, in R02 contains the contribution of 375 ppm (by volume) of carbon dioxide, while the values reported by the other authors do not. (If the carbon dioxide content is omitted in Rüeger, the value for k1 is 77.6681.) The uncertainty in k1 from R02 does not contain the uncertainty associated with the carbon dioxide contribution. The coefficient for the dependence of refractivity with respect to Pc/T reported by R02, with Pc being the partial pressure or CO2, is 133.4800 ± 0.022.

Table 3.
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