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  • View in gallery

    Top-of-atmosphere BT spectra calculated with the offline RT model from typical tropical temperature and WV profiles. The channels shown are those used in the parameterization study.

  • View in gallery

    The BT shift in AMSU-A channel 4 vs frequency shift for an emissivity of (left) 0.6 and (right) 1.0, and for five values of the satellite zenith angle. The BT shift is the mean over the sample of BT shifts obtained from the 52 atmospheric profiles.

  • View in gallery

    The BT shift in MHS channel 4 vs (a) frequency shift, (b) satellite zenith angle, (c) surface emissivity, and (d) total column WV, for discrete realization of these parameters obtained using a line-by-line RT model (stars) and the new parameterization (line).

  • View in gallery

    The BT shift in MHS channel 3 vs (a) frequency shift, (b) satellite zenith angle, (c) surface emissivity, and (d) weighted-average temperature gradient, for discrete realization of these parameters obtained using a line-by-line RT model (stars) and the new parameterization (line).

  • View in gallery

    As in Fig. 4, but for AMSU-A channel 4.

  • View in gallery

    The BT shift in AMSU-A channel 9 vs (a) frequency shift, (b) satellite zenith angle, and (c) weighted-average temperature gradient, for discrete realization of these parameters obtained using a line-by-line RT model (stars) and the new parameterization (line).

  • View in gallery

    Distribution of computed errors in BT (K) for NOAA-15 AMSU-A channel 4 for a single assimilation cycle on 17 Jan 2010 (0000 UTC assimilation window) assuming a fixed frequency shift for this channel of 10 MHz.

  • View in gallery

    Zonal mean differences (perturbed AMSU-A experiments minus the reference experiment; K) in analysis temperature fields averaged over 30 days, for the 1.5-MHz shift experiments using (a) VarBC-set and (b) static-set, and the 20-MHz shift experiments using (c) VarBC-set and (d) static-set.

  • View in gallery

    Zonal mean errors (latitude vs pressure) in temperature analysis over the 30-day period starting 12 Sep 2009, for experiments using VarBC-set (solid line) and static-set (dashed line) and for the frequency shift of 1.5 (red) and 20 MHz (blue).

  • View in gallery

    Normalized RMS forecast error difference in temperature between experiments with perturbed AMSU-A observations and their reference experiment (see text) verified against the operational analyses for the set of experiments using VARBC. Different colors correspond to different frequency shifts: 1.5 (black), 5 (red), 10 (green), and 20 MHz (blue).

  • View in gallery

    As in Fig. 10, but for the geopotential height.

  • View in gallery

    As in Fig. 10, but for the set of experiments using static-set.

  • View in gallery

    As in Fig. 12, but for the geopotential height.

  • View in gallery

    Normalized RMS forecast error difference in temperature between experiments with perturbed AMSU-A observations and their reference experiment (see text) verified against the operational analyses. Two experiments are using VarBC-set with frequency shifts of 1.5 (black) and 5 MHz (red). The two other experiments are using static-set with frequency shifts of 1.5 (green) and 5 MHz (blue).

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The Influence of Frequency Shifts in Microwave Sounder Channels on NWP Analyses and Forecasts

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Abstract

The sensitivity of numerical weather prediction (NWP) analysis and forecast accuracies with respect to frequency shifts in microwave passbands is quantified through a series of observing system experiments using the ECMWF Integrated Forecast System. First, a parameterization is developed to describe the form and magnitude of the brightness temperature errors arising from frequency shifts in Advanced Microwave Sounding Unit-A (AMSU-A) channels 4–10 and Microwave Humidity Sounder (MHS) channels 3–5. Observing system experiments are then run in which realistic synthetic brightness temperature errors are added to AMSU-A observations for various assumptions about the magnitude of a frequency shift, using the parameterization derived previously. A large negative impact on forecast quality is found when a 20-MHz frequency shift is introduced in experiments using a static bias-correction scheme. Although the degradation in forecast scores is reduced by using a variational bias-correction scheme, it remains around 7%–14% (relative) in RMS 6-h forecast errors for temperature and geopotential. Frequency shifts of 5 MHz or greater give rise to a measurable degradation of the forecast even when the variational correction scheme is used. Only low-frequency shifts (of ~1.5 MHz) are found to have a neutral impact on forecasts. Hence, the value of 1.5 MHz can be regarded as an upper limit below which frequency shifts do not degrade forecasts for the key tropospheric and lower-stratospheric temperature sounding channels in a microwave sounding mission. Calculations show that frequency shift is less problematic for 183-GHz humidity sounding channels due to the symmetric positioning of passbands relative to the 183-GHz absorption line. For these channels a passband center frequency stability of 10 MHz is adequate.

Corresponding author address: Carole Peubey, ECMWF, Shinfield Park, Reading RG2 9AX, United Kingdom. E-mail: carole.peubey@ecmwf.int

Abstract

The sensitivity of numerical weather prediction (NWP) analysis and forecast accuracies with respect to frequency shifts in microwave passbands is quantified through a series of observing system experiments using the ECMWF Integrated Forecast System. First, a parameterization is developed to describe the form and magnitude of the brightness temperature errors arising from frequency shifts in Advanced Microwave Sounding Unit-A (AMSU-A) channels 4–10 and Microwave Humidity Sounder (MHS) channels 3–5. Observing system experiments are then run in which realistic synthetic brightness temperature errors are added to AMSU-A observations for various assumptions about the magnitude of a frequency shift, using the parameterization derived previously. A large negative impact on forecast quality is found when a 20-MHz frequency shift is introduced in experiments using a static bias-correction scheme. Although the degradation in forecast scores is reduced by using a variational bias-correction scheme, it remains around 7%–14% (relative) in RMS 6-h forecast errors for temperature and geopotential. Frequency shifts of 5 MHz or greater give rise to a measurable degradation of the forecast even when the variational correction scheme is used. Only low-frequency shifts (of ~1.5 MHz) are found to have a neutral impact on forecasts. Hence, the value of 1.5 MHz can be regarded as an upper limit below which frequency shifts do not degrade forecasts for the key tropospheric and lower-stratospheric temperature sounding channels in a microwave sounding mission. Calculations show that frequency shift is less problematic for 183-GHz humidity sounding channels due to the symmetric positioning of passbands relative to the 183-GHz absorption line. For these channels a passband center frequency stability of 10 MHz is adequate.

Corresponding author address: Carole Peubey, ECMWF, Shinfield Park, Reading RG2 9AX, United Kingdom. E-mail: carole.peubey@ecmwf.int

1. Introduction

This paper aims to quantify the sensitivity of numerical weather prediction (NWP) analysis and forecast accuracy to frequency shifts in microwave channel passbands. Any shift in the center frequency of a passband will change the optical depth characteristics of the atmosphere sampled by this passband. This effect will be largest for passbands that are close to sharp absorption lines, such as the O2 absorption lines used for temperature sounding at 50–60 GHz or the H2O lines at 22 and 183 GHz used for humidity sounding. A shift in passband frequency moves the altitude of the atmospheric layer sampled by the radiometer up or down, depending on the nature of the shift. The resulting error, in terms of measured brightness temperature (BT), depends on the form of the atmospheric temperature profile in the altitude region around the peak of the weighting function. For example, for an observation in the tropics, an upward displacement of a weighting function that peaks in the lower stratosphere where the atmospheric lapse rate is strongly positive will result in an increase in measured brightness temperature. It can also depend on other quantities, such as the surface emissivity for the lower-peaking channels, the satellite zenith angle of the observation or, mostly for channels in the 183-GHz spectral region, the atmospheric water vapor content.

Microwave imager data have been assimilated in NWP models since the early 1980s. A major advance in their use was the direct assimilation of radiances (Eyre et al. 1993). Microwave data have a significant contribution to temperature and impose the dominant constraint on tropospheric humidity over oceans, as demonstrated by a number of studies in the last decade (e.g., Andersson et al. 2007; Kelly et al. 2008). A key component of NWP assimilation systems to date has been data from the Advanced Microwave Sounding Unit (AMSU; Goodrum et al. 2007), a cross-track scanning radiometer that has delivered data since 1998 from both U.S. and European platforms. Long-term continuity of these operational missions should be ensured by future sounder missions currently planned by U.S., European, and Chinese agencies. More recently, much effort has been dedicated to the assimilation of microwave radiances in rainy and cloudy regions (Bauer et al. 2010). Indeed, several preliminary designs for future microwave imager instruments, in the United States and Europe, feature a suite of temperature sounding channels to provide information on clouds, precipitation, and temperature in the lower troposphere.

A crucial step in the preparation of future satellite missions devoted to operational meteorology is to understand the effect of the choice of instrument specifications on the quality of NWP products. The present work is part of a wider effort to define the radiometric and spectral specifications of future microwave sounding and imaging missions that will meet the anticipated needs of NWP users in the 2020 time frame (e.g., Peubey et al. 2011, p. 9).

In this paper, we first derive a parameterization describing the form and magnitude of the BT errors resulting from frequency shifts. This is done by simulating the effect on measured BTs of prescribed frequency shifts (Δν) using a line-by-line radiative transfer model, for a wide range of atmospheric profiles representing global atmospheric variability.

The channels considered are AMSU-A channels 4–10 and Microwave Humidity Sounder (MHS) channels 3–5. These channels have weighting functions peaking from near the surface to around 22 km and are assimilated in the European Centre for Medium-Range Weather Forecasts (ECMWF) operational system. Two independent studies have shown that such microwave sounders are affected by significant uncertainties in on-orbit passband center frequencies (Lu et al. 2011; Zou and Wang 2011). These uncertainties can result from uncertainties in the prelaunch measurements, or a shift that has taken place after launch. Both Lu et al. (2011) and Zou and Wang (2011) strongly suspected the on-orbit frequency shift to be connected to deficiencies of the local oscillator of the instrument. More precisely, the refractive index of the medium filling the resonant cavity used to tune the frequency of the local oscillator could take different values, depending on whether the instrument is in laboratory or space conditions (Lu et al. 2011). More recently, Lu and Bell (2013) found substantial frequency shifts in channels 6–8 of some of the AMSU-A instruments. No significant shifts were found for AMSU-A channels 9–14, which use an on-orbit active frequency locking, which is consistent with the hypothesis that frequency shifts originate from a problem with the local oscillator.

In the second part of this paper, the impact of the frequency shifts on the ECMWF analyses and forecasts is assessed by running observing system experiments (OSEs) in which realistic perturbations to observed BTs are added using the parameterization derived earlier, and the modified observations assimilated in the ECMWF Integrated Forecast System (IFS). A range of plausible frequency shifts are considered: 1.5, 5, 10, and 20 MHz. The perturbations are applied to AMSU-A channels only, as the first part of the study shows that the effect of shifted passbands is mostly an issue for the temperature sounding channels. The experiments are carried out relative to near-full operational configurations to gain realistic estimates of the impact of the frequency shift.

To correctly deal with the effect of a frequency shift in an assimilation system, new radiative transfer parameterizations should be carried out at frequent intervals, taking the (known) frequency shift into account; however, this is impractical in the context of an operational assimilation system. In many operational assimilation systems, the effect of the shifted passbands would be partially dealt with using variational bias correction (VarBC; see Auligné et al. 2007)—a widely used bias-correction scheme. The effectiveness of this form of bias correction for this particular type of error, however, is not clear. Therefore, the impact of frequency shifts is evaluated here by comparing the results of observing system experiments run with a static correction scheme to those run using VarBC.

The line-by-line calculation and the development of the parameterization of the errors in BT induced by frequency shifts are explained in the section 2 of this paper. Section 3 describes the setup and results from the OSEs. Finally, section 4 draws conclusions together with some recommendations for further work.

2. Radiative transfer study

a. Line-by-line calculations

Prior to the development of the parameterization, line-by-line calculations are necessary in order to determine the relationship linking BT and channel frequency and its sensitivity to other parameters (Table 2). Both a line-by-line transmittance model and a radiative transfer model have been used.

The line-by-line model (AMSUTRAN; Saunders et al. 2012) is a version of the Millimeter-Wave Propagation Model (MPM; Liebe et al. 1993). It provides atmospheric water vapor (WV) and mixed gas (dry air) transmittances on 43 pressure levels (1013.25–0.1 hPa). The inputs to the models are channel passbands and atmospheric temperature and water vapor profiles. The mixed gas profiles are taken from a climatology. Ozone absorption can be added when required (for instance for MHS, mainly to improve simulations in the region of the 183-GHz line), in which case the ozone profile is also from a climatology. The computation of the gaseous absorptions is performed with the 1989 version of the Liebe MPM model (Liebe 1989) for water vapor, the 1993 version of the MPM model (MPM-93; Liebe et al. 1993) (with coefficients from the Liebe MPM-92 model; Liebe et al. 1992) for mixed gases, and an adaptation of MPM-93 using High Resolution Transmission (HITRAN) line parameters (Rothman et al. 2009) for ozone. In this study, the frequency resolution of the transmittance computation inside the AMSU channel bands has been adjusted for each channel, so that the error in BT is less than 0.001 K. Transmittances are then averaged over each channel. Calculations are performed for six different atmospheric paths (scan angles).

Transmittances are then passed to the radiative transfer model, which calculates the BT for each of the six paths and each specified channel. The surface emissivity is given as an input to the radiative transfer (RT) model. The top-of-atmosphere brightness temperature spectra covering the AMSU-A and MHS spectral ranges are shown in Fig. 1.

Fig. 1.
Fig. 1.

Top-of-atmosphere BT spectra calculated with the offline RT model from typical tropical temperature and WV profiles. The channels shown are those used in the parameterization study.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

Frequency shifts in the range ±30 MHz have been applied to the calculations for AMSU-A and MHS channels with a frequency step of 1 MHz for AMSU-A and 5 MHz for MHS. The BT calculation was performed at every frequency shift, for different values of the emissivity and for 52 profiles based on a sampling of the ECMWF model (Chevallier 2002). These profiles represent the range of variation in global temperature and water vapor profiles, and were sampled from a large dataset generated using the operational suite of the ECMWF forecasting system.

The BT shift is equal to the difference between the BT calculated for the shifted channel and the BT calculated for the unshifted channel. Table 1 gives some statistics of the BT shifts corresponding to a 10-MHz frequency shift calculated over the set of 52 atmospheric profiles, varying the surface emissivity from 0.6 to 1 and the satellite zenith angle from 0° to 50°, for both AMSU-A and MHS.

Table 1.

Statistics of the shift in BT (K) induced by a frequency shift of 10 MHz for AMSU-A channels 4–14 for the set of 52 atmospheric profiles.

Table 1.

In some cases, on-orbit center frequency uncertainties greater than 30 MHz have been found to affect microwave sounder observations (Lu et al. 2011; Lu and Bell 2013); however, center frequency stability specifications for AMSU-A are typically 5 MHz. In practice, stabilities are expected to be better than 1.5 MHz based on the thermal tuning coefficients and temperature stability of the local oscillator on orbit, although this has yet to be confirmed by careful analysis of on-orbit data. The value of 10 MHz for the frequency shift in Table 1 therefore represents a cautious estimate of the expected errors in BTs and enables us to determine which channels are affected by shifts.

For AMSU-A the median BT error, for shifts of 10 MHz, remains within ±0.2 K for all channels. Channel 6 is most affected by the frequency shift, with a median of −0.178 K and a standard deviation of nearly 0.1 K. This channel is of particular importance for assimilation in NWP, as it is the lowest-peaking channel (400 hPa) that provides information about tropospheric temperature that is not significantly affected by uncertainties in surface emissivity.

For MHS, the 10-MHz frequency shift gives typically much smaller errors, especially for channels 4 and 5, with values in the range ±0.004 K. The BT shift is larger for channel 3 but with most of the values remaining within ±0.02 K. Those low values are largely due to the symmetric alignment of the MHS passbands with respect to the 183-GHz H2O absorption line (Fig. 2), which gives rise to effective compensation for the effect of frequency shift.

Fig. 2.
Fig. 2.

The BT shift in AMSU-A channel 4 vs frequency shift for an emissivity of (left) 0.6 and (right) 1.0, and for five values of the satellite zenith angle. The BT shift is the mean over the sample of BT shifts obtained from the 52 atmospheric profiles.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

NWP assimilation systems combine information from a short-range (typically initial time +6 h) forecast with the new information provided by observations to produce an analysis. Therefore, in order to assess the significance of these errors, the values of the shift-induced BT errors have to be compared with short-range forecast errors mapped into brightness temperatures. These background errors are in the range 0.03–0.1 K for the tropospheric temperature sounding channels. The errors in the AMSU-A channels for a 10-MHz shift are therefore at a level where some measurable negative impact on analyses and forecasts may result. Indeed, it has been established by earlier studies (Bell et al. 2010) that relatively small random errors in measured BTs (of order 0.1 K) can adversely affect analyses and forecast quality. Given that the background errors for the 183-GHz channels are in the range 1–2 K, it seems unlikely that the errors calculated for MHS would give rise to measurable impacts on analyses or forecasts. Nevertheless, the parameterization of the MHS BT shift has been performed and implemented in the ECMWF forecast system to assess the resulting error in BT when considering the entire range of profiles represented in the global NWP model.

As mentioned previously, the BT–frequency relationship can be complex. Figure 2 shows particular examples of this relationship for different satellite zenith angles and emissivities in the case of AMSU-A channel 4 (52.8 GHz). For an emissivity of 1 (right panel), a positive frequency shift lowers the BT. This is a consequence of a decrease in the (warm) surface-to-space transmission. This effect gets stronger with increasing satellite zenith angle. For a surface emissivity of 0.6 (left panel), the impact of the satellite zenith angle is stronger than for an emissivity of 1; while the relationship between the frequency shift and BT is fairly similar to the previous case at high angles, it is of opposite sign at low angles. This is due to the change in the thermal contrast between surface and atmosphere: increasing atmospheric opacity decreases measured brightness temperatures when the surface is radiatively warm (emissivity close to 1, as observed over much land), whereas increasing opacity against a radiatively cold surface results in an increase in measured brightness temperatures. This compensating effect of the emissivity is also observed in MHS channels 4 and 5 (not shown).

b. Parameterization of the shift in brightness temperatures

1) Development of the parameterization

The parameterization of the BT shift involved a linear multivariate regression applied to the BT shifts obtained with the line-by-line model calculations in which the relevant parameters were varied. The physical quantities involved in the parameterization are summarized in Table 2 and explained below. Different sets of parameters have been used for different channels. Cross products between parameters have been used. For example, a BT shift that only depends on Δν up to a power of 2 and the satellite zenith angle θ would be given by
e1
Table 2.

Physical quantities (explained in the text) used in the parameterization of the shift in BT. The asterisk indicates that the quantity is weight averaged by the corresponding channel weighting function.

Table 2.

where the ci are the regression coefficients.

In the present parameterization, Δν are used for MHS, while Δν and Δν2 are used for all AMSU-A channels. Channels 6–10 also use Δν4. The emissivity is used for both AMSU and MHS lower-peaking channels. For the scan angle dependence of the BT shift, the cosine of the satellite zenith angle is used.

To take into account the atmospheric lapse rate, the temperature gradient (T) is an input parameter for all AMSU-A channels and MHS channel 3. Because of the relatively broad vertical resolution of sounding observations, T is averaged over the layer of atmosphere to which each channel is sensitive. This is done by weighting T at every level, where the weight is equal to the value of the weighting function at the same level. The weighted average is then determined as follows:
e2
where W is the weighting function calculated as the derivative of transmittance with respect to height for a given channel and given atmospheric profiles.
Water vapor parameters need to be introduced in the parameterization of MHS BTs. For channel 3, the humidity parameter is a weighted average of the water vapor partial column qi (i.e., the integrated water vapor content in a given atmospheric layer i) calculated in a similar way as in (2). For MHS channels 4 and 5, as the relationship between the BT shift and the logarithm of the total column of water vapor, Q, appears to be well described by the sum of a linear function of Q and a normal distribution N(Q) (Fig. 3), we then have:
e3
where exp(Qm) is equal to 2.0 and 9.0 kg.m−2 for channels 4 and 5, respectively, and σ is equal to 0.6 for both channels.
Fig. 3.
Fig. 3.

The BT shift in MHS channel 4 vs (a) frequency shift, (b) satellite zenith angle, (c) surface emissivity, and (d) total column WV, for discrete realization of these parameters obtained using a line-by-line RT model (stars) and the new parameterization (line).

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

Apart from MHS channel 3 (Fig. 4), the parameterized BT agrees well with those from the RT model over a wide range of values of the different parameters as seen in Figs. 3, 5, and 6, which show the comparison of BTs obtained with the RT model and with the parameterization for a typical atmospheric case. The BT–frequency relationship is well captured by the parameterization. It is fairly linear within the ±10-MHz range except for channels 9 (Fig. 6) and 10 (not shown). The quality of the fit slightly degrades at higher frequency shift, but the differences between the parameterized and calculated errors are still small for a shift of ±30 MHz, which is significantly larger than currently anticipated on-orbit frequency shifts. For MHS channel 3, the parameterized BTs are in some cases affected by significant errors compared to the amplitude of the BT shift (Fig. 4). One of the main difficulties met with this channel is the high scatter of the BT shift versus the temperature gradient or the water vapor column parameters.

Fig. 4.
Fig. 4.

The BT shift in MHS channel 3 vs (a) frequency shift, (b) satellite zenith angle, (c) surface emissivity, and (d) weighted-average temperature gradient, for discrete realization of these parameters obtained using a line-by-line RT model (stars) and the new parameterization (line).

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

Fig. 5.
Fig. 5.

As in Fig. 4, but for AMSU-A channel 4.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

Fig. 6.
Fig. 6.

The BT shift in AMSU-A channel 9 vs (a) frequency shift, (b) satellite zenith angle, and (c) weighted-average temperature gradient, for discrete realization of these parameters obtained using a line-by-line RT model (stars) and the new parameterization (line).

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

To get a better idea of the performance of the parameterization over the whole set of atmospheric cases, the coefficient of determination R2 has been calculated, which indicates the proportion of variance in a dataset that is accounted for by the statistical model. A value of R2 of 1.0 indicates that the regression line perfectly fits the data. Results shown in Table 3 confirm the generally good performance of the parameterization for all the channels with the exception of MHS channel 3. The best performance is found for AMSU-A channel 6 (R2 = 0.96), which is expected to have a relatively strong impact on the model analysis and forecast.

Table 3.

Coefficient of determination R2 for the parameterization of AMSU-A channels 4–10 and MHS channel 3–5. This provides information about the goodness of fit of the parameterization.

Table 3.

2) Implementation in the ECMWF Integrated Forecasting System

The parameterization of the BT shift has been implemented into the ECMWF forecast and assimilation system. It is called during the screening run, that is, the preliminary quality control of the observations prior to assimilation. At this stage, all the parameters required by the parameterization are available and interpolated to the observation position and time. The model transmittances from which the weighting functions are calculated are given by Radiative Transfer for the Television and Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS; RRTOV). The atmospheric profiles used are those of the model background, which is used as the first guess in the ECMWF system. The emissivity is that used in the assimilation. It is calculated with the Fast Emissivity Model, version 2 (FASTEM2; Deblonde and English 2001), over sea and is dynamically retrieved over land (Karbou et al. 2006). The calculated BT shift is then added to the corresponding value of the AMSU observation. As for the case of unperturbed observations, departures from the model first guess are calculated before undergoing further quality control and finally being assimilated in the system.

Figure 7 shows a map of the BT shift added to AMSU-A channel 4 observations for a frequency shift of 10 MHz. The higher values at nadir result from the dependence of the BT shift on scan angle. The land–sea contrast illustrates the surface emissivity dependence of the error. The BT values over land are consistent with maps of the temperature gradient (not shown). In particular, the low values over Australia correspond to strong negative gradients of temperature, while the high values over North Africa and part of Asia correspond to positive temperature gradients as expected in desert regions overnight (Fig. 7 is generated from a 0000 UTC assimilation window).

Fig. 7.
Fig. 7.

Distribution of computed errors in BT (K) for NOAA-15 AMSU-A channel 4 for a single assimilation cycle on 17 Jan 2010 (0000 UTC assimilation window) assuming a fixed frequency shift for this channel of 10 MHz.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

The range of values of the BT shift calculated within the IFS has been found similar to that calculated over the set of 52 profiles used in the development of the parameterization. In particular, the majority of the BT shifts for MHS observations remain far below the error in first-guess temperature, as found in section 2a. For this reason, the decision has been made to concentrate on AMSU-A observations only in the second part of the study, which describes the observing system experiments.

3. Observation system experiments

a. Experimental settings

The experiments were carried out for a 3-month period (from 10 September to 10 December 2009) using the cycle 36r1 version of the ECMWF assimilation system with the forecast model running at the T511 horizontal resolution (approximately 40 km). All of the OSEs assimilated a common observational dataset comprising the full ECMWF observing system (Radnóti et al. 2010) minus all microwave sounding data. AMSU-A observations were additionally assimilated on top of this dataset. The following AMSU-A instruments were used: the National Oceanic and Atmospheric Administration-15 and -19 (NOAA-15 and NOAA-19, respectively) satellites, and the Meteorological Operation-A (MetOp-A) satellite. All the observations underwent the same quality checks as in the operational suite. Channel 6 from NOAA-15 and channel 7 from MetOp-A, considered to be too noisy, were not assimilated.

As stated in the introduction, it was crucial to investigate the ability of VarBC to correct for the errors added to the AMSU-A observations. The impact of VarBC was compared to that of a static bias-correction scheme where the bias-correction coefficients had fixed values equal to the VarBC coefficients from the operational suite taken at the experiment starting date. Two sets of experiments were run, one using VarBC (VarBC-set) and the other one using the static bias correction (static-set).

Each set includes a reference experiment with unperturbed AMSU-A data, and four other experiments for which frequency shifts of 1.5, 5, 10, and 20 MHz were added to channels 4–10. The impact of frequency shifts on analyses and forecasts was then quantified by comparing each perturbed experiment with the corresponding reference experiment.

b. Impact on analysis

The mean difference in analysis temperature fields between the perturbed AMSU-A experiments and their reference experiments for the 1.5- and 20-MHz shifts (Fig. 8) show a systematic warming over the South Pole throughout the troposphere, going from around 0.05 K for the 1.5-MHz shift experiment using VarBC to up to 1 K for the 20-MHz shift experiment using the static bias correction. Elsewhere, the differences appear mostly small scale and random for the 1.5-MHz shift experiment using VarBC. For the other experiments, cooling/warming patterns alternating with height appear over the North Pole. In addition, the experiments that use the static bias correction show a clear cooling at around 100 hPa in the tropics.

Fig. 8.
Fig. 8.

Zonal mean differences (perturbed AMSU-A experiments minus the reference experiment; K) in analysis temperature fields averaged over 30 days, for the 1.5-MHz shift experiments using (a) VarBC-set and (b) static-set, and the 20-MHz shift experiments using (c) VarBC-set and (d) static-set.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

Zonal mean errors in the temperature analysis have been calculated taking the full-resolution (T799, around 25-km resolution) ECMWF operational analysis as a proxy for truth. These errors are thus underestimated, as the operational analysis also has nonzero errors. Comparing the 1.5- and 20-MHz shift experiments with their reference experiments for the two sets (Fig. 9), the larger errors are found for the experiment with the 20-MHz frequency shift using the static bias correction when compared to those of the reference experiment. The error increase in temperature analysis is particularly dramatic over high latitudes, with maximum values of 1 K around 80°S at 700 hPa. Over the tropics and midlatitudes, the analysis error increases are between 0.05 and 0.1 K in the upper troposphere and typically less than 0.1 K in the lower troposphere.

Fig. 9.
Fig. 9.

Zonal mean errors (latitude vs pressure) in temperature analysis over the 30-day period starting 12 Sep 2009, for experiments using VarBC-set (solid line) and static-set (dashed line) and for the frequency shift of 1.5 (red) and 20 MHz (blue).

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

Although these errors are large, Fig. 9 shows that most of them are actually corrected by VarBC. The errors for the 20-MHz shift experiment using VarBC are still detectable, but they remain less than 0.02 K over most of the tropics and midlatitudes and increase above high latitudes. The error increase is higher at the South Pole with a maximum of 0.5 K around 80°. Errors in temperature analysis of the two 1.5-MHz experiments are both very close to their reference experiment.

c. Impact on forecast

The forecast scores are calculated as the normalized difference in root-mean-square errors between each perturbed AMSU-A forecast experiment and the corresponding reference forecast experiment, such that a positive score indicates a degradation of the forecast. Normalization is with respect to the reference experiment errors. Experiments are verified against the operational analysis, which serves as the proxy for truth here. Figures 10 and 11 show the temperature and geopotential forecast scores for the VarBC-set. The scores strongly degrade with increasing frequency shift.

Fig. 10.
Fig. 10.

Normalized RMS forecast error difference in temperature between experiments with perturbed AMSU-A observations and their reference experiment (see text) verified against the operational analyses for the set of experiments using VARBC. Different colors correspond to different frequency shifts: 1.5 (black), 5 (red), 10 (green), and 20 MHz (blue).

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

Fig. 11.
Fig. 11.

As in Fig. 10, but for the geopotential height.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

It is worth pointing out that temperature RMS forecast scores in the tropics at 500 hPa are dominated by small persistent biases in the large-scale temperature fields due to forecast model biases. In principle, the introduction of a biased radiance observation into the analysis that happens to be in better agreement with the biased model state will give better forecast scores than an experiment that assimilates unbiased data. This is likely to be the cause of the apparent improvement in scores for the experiments in which a finite shift has been added.

Overall, the results can be summarized as follows:

  • For the shift of 20 MHz (blue line), the negative impact of the 20-MHz frequency shift is obvious throughout the troposphere, with the worst impact found in the Southern Hemisphere (where the network of conventional observations is less dense; hence, satellite observations play a more important role in determining the analysis) where the degradation of the scores is around 10% at forecast day 1.
  • For the 10-MHz shift (green line), the negative impact of the frequency shift is smaller, yet very clear, with a persistent degradation of the forecast over the Southern Hemisphere and in the upper troposphere.
  • For the 5-MHz frequency shift (red line), a small negative impact at forecast day −1 is measurable but the impact is neutral at other forecast steps.
  • The general impact of the 1.5-MHz frequency shift is neutral for both the temperature and geopotential scores.

This suggests that, with the use of VarBC, the upper limit for a frequency shift that does not affect the forecast is around 1.5 MHz.

Figures 12 and 13 show the temperature and geopotential forecast scores for the static-set. Note the difference of scales on the y axis compared to Figs. 10 and 11. The impact of the 20-MHz shift is much worse than when VarBC is used, especially in the upper troposphere, with values twice as large as those in Figs. 10 and 11 at 500 hPa and more than 3 times larger at 200 hPa. The 10-MHz shift experiment scores are on average worse for the static-set than for the VarBC-set up to forecast days 2 and 3. These results are consistent with those found with the analysis and confirm the ability of VarBC to partially correct the errors added to the AMSU-A observations.

Fig. 12.
Fig. 12.

As in Fig. 10, but for the set of experiments using static-set.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

Fig. 13.
Fig. 13.

As in Fig. 12, but for the geopotential height.

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

To better evaluate the impact of the correction scheme for the lowest frequency shifts, the temperature scores of the two sets of experiments are shown on the same plots (Fig. 14) for the 5- and 1.5-MHz shifts. The differences in the forecast scores are small (less than 2%) for all the experiments shown. For the 5-MHz shift, there is a slight but significant negative impact at day 1 in the SH. On average over the globe, the scores for the 5-MHz shift are worse for the static-set (blue line) than for the VarBC-set (red line) at 200 hPa, but also in the SH and tropics at 1000 hPa. Elsewhere, the two experiments have mostly similar scores. As for the VarBC set, the 1.5-MHz frequency shift with the static bias correction leads to a mostly neutral impact on the forecast scores. Although there are occasional apparently significant positive and negative values, it seems most likely that these are simply statistical fluctuations. These results are consistent with the neutral forecast scores found for the geopotential height.

Fig. 14.
Fig. 14.

Normalized RMS forecast error difference in temperature between experiments with perturbed AMSU-A observations and their reference experiment (see text) verified against the operational analyses. Two experiments are using VarBC-set with frequency shifts of 1.5 (black) and 5 MHz (red). The two other experiments are using static-set with frequency shifts of 1.5 (green) and 5 MHz (blue).

Citation: Journal of Atmospheric and Oceanic Technology 31, 4; 10.1175/JTECH-D-13-00016.1

d. Note on the orbital dependency of the shift

An important motivation for the development of the parameterization was the capability to model orbitally dependent shifts, for example, of the type caused by thermal cycling of the instrument around an orbit. Preliminary estimates of the magnitude of this type of frequency shift error were obtained based on prelaunch test data for NOAA-15 AMSU-A (N. Atkinson 2010, personal communication), which included an assessment of the temperature tuning coefficient of the local oscillators. This, together with on-orbit measurements of the local oscillator temperature, enabled us to estimate the frequency shift, and hence the brightness temperature errors, for AMSU-A channels 4–8.

For a range of atmospheric profiles, the frequency shift associated with the maximum temperature variation of the local oscillator is around ±0.05 MHz, which corresponds to errors in BT in the range ±0.0015 K. The magnitude of this frequency shift is much lower than the 1.5-MHz frequency shift which, as shown in the previous discussion, does not have a significant impact on the forecast. Even in the case where the relationship between the local oscillator temperature and the frequency shift is underestimated by a factor of 10 (as is suspected; N. Atkinson 2010, personal communication), the resulting frequency shifts would still be below the value of 1.5 MHz. It can therefore be anticipated that orbitally dependent (thermally induced) shifts in the local oscillator frequency, for the thermal tuning coefficients measured for AMSU-A, would not affect the forecast.

4. Conclusions and further work

A line-by-line radiative transfer modeling study has been carried out to assess the errors in measured brightness temperatures arising from shifts in the passband center frequencies for AMSU-A channels 4–14 and for MHS channels 3–5. Frequency shifts up to ±30 MHz were simulated. For AMSU-A channels 4–10 (median) errors were in the range ±0.2 K for frequency shifts of 10 MHz. These errors are similar in magnitude to the errors in model fields, projected into radiance space, and are expected to result in measurable negative impacts in forecast quality.

For MHS humidity sounding channels (median), errors are below 0.003 K for a frequency shift of 10 MHz. This weak sensitivity arises from the symmetric alignment of the bands with respect to the absorption line center, which gives rise to an effective cancellation of the shift-induced errors. Given that background errors are in the range 1–2 K for these channels, it is unlikely that errors of 0.003 K would result in a measurable degradation in forecast quality; therefore, the difficulties with the parameterization of MHS channel 3 are not a concern. Although OSEs were not run for MHS, it is reasonable to assume that passband center frequency stabilities of 10 MHz are adequate for these channels.

Observing system experiments were conducted for scenarios that assumed shifts ranging from 1.5 to 20 MHz for a constellation of three AMSU-A instruments. These shifts were applied coherently across all channels and all three satellites. For these scenarios variational bias correction was activated and deactivated to assess the effectiveness of variational bias correction in compensating for this type of bias.

For 3-month OSEs, a very significant negative impact on analyses is detectable for the 20-MHz shift experiments. Errors in temperature at 500 hPa in the northern midlatitudes, for example, are increased from 0.25 to 0.3 K with VarBC deactivated. In the southern midlatitudes, errors are increased from 0.3 to 0.4 K. The error increase is larger still for the southern polar regions, where the analysis error is increased from 0.2 to 0.7 K. The activation of VarBC is effective in significantly reducing the magnitude of these analysis errors, but the residual analysis errors remain larger than those for the reference experiment in most regions. On the other hand, for a shift of 1.5 MHz, the errors are reduced by VarBC to a level close to those of the reference experiment.

The forecast impacts are broadly consistent with the impacts on analyses. For example, for the 20-MHz shift experiments, RMS errors in 500-hPa geopotential forecasts at initial time +24 h are doubled in both (extratropical) hemispheres relative to a shift-free reference experiment when VarBC is deactivated. These errors are greatly reduced, but they still remain significant at 3%–4%, when VarBC is activated. Forecast scores for experiments testing intermediate shifts (5 and 10 MHz) show that frequency shifts equal to or greater than 5 MHz give rise to measurable degradation of the forecast even when VarBC is used. For the 1.5-MHz frequency shift, the impact has been found to be neutral for both VarBC and static bias experiments. Hence, the value of 1.5 MHz can be seen as an upper limit below which frequency shifts do not degrade forecasts in assimilation systems with static or variational bias-correction schemes. The use of a variational bias-correction scheme such as VarBC still partially compensates for larger frequency shifts.

A motivation for the development of the parameterization scheme was to enable the simulation of orbitally dependent frequency shifts, for example, shifts induced by the thermal cycling of the instrument over the course of an orbit. Preliminary calculations, based on local oscillator temperature tuning coefficients from the prelaunch testing of AMSU-A, indicate that such effects would most likely give rise to small frequency shifts (less than 0.5 MHz), corresponding to small errors in brightness temperature (less than 0.015 K), which should not affect forecasts.

Several recent studies have shown that, for some operational microwave sounders, there are significant biases in on-orbit passband center frequencies (up to several tens of MHz). Lu et al. (2011) recently characterized data from the Feng-Yun-3A (FY-3A) Microwave Temperature Sounder and showed that modified passband center frequencies give improved fits to the ECMWF NWP model. Zou and Wang (2011) diagnosed a shift in AMSU-A channel 6 on the NOAA-15 satellite of 36.5 MHz, which is consistent with values found in Lu and Bell (2013). There is therefore an emerging need to evaluate passband shifts for all microwave sounders currently used for operational NWP and, more generally, all sensors that are likely to be used for reanalysis and climate applications. Both Lu et al. (2011) and Zou and Wang (2011) claim to be able to diagnose shifts with uncertainties in the range 1.0–2.5 MHz which, if correct, would be close to sufficient for NWP data assimilation applications.

Acknowledgments

This work was funded by EUMETSAT in support of mission definition for the European Polar System—Second Generation. Peter Bauer (ECMWF), Peter Schluessel (EUMETSAT), Ville Kangas (ESA), and Steve English (ECMWF) are thanked for their keen interest in the study and constructive input.

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