Estimating the Correlated Observation-Error Characteristics of the Chinese FengYun Microwave Temperature Sounder and Microwave Humidity Sounder

Ting WANG,Jianfang FEI,Xiaoping CHENG?,Xiaogang HUANG,and Jian ZHONG

1College of Meteorology and Oceanography,National University of Defense Technology,Nanjing 211101,China

2China Satellite Maritime Tracking and Control Department,Jiangyin 214431,China

ABSTRACT In operational data assimilation systems,observation-error covariance matrices are commonly assumed to be diagonal.However,inter-channel and spatial observation-error correlations are inevitable for satellite radiances.The observation errors of the Microwave Temperature Sounder(MWTS)and Microwave Humidity Sounder(MWHS)onboard the FengYun-3A(FY-3A)and FY-3B satellites are empirically assigned and considered to be uncorrelated when they are assimilated into the WRF model’s Community Variational Data Assimilation System(WRFDA).To assimilate MWTS and MWHS measurements optimally,a good characterization of their observation errors is necessary.In this study,background and analysis residuals were used to diagnose the correlated observation-error characteristics of the MWTS and MWHS.It was found that the error standard deviations of the MWTS and MWHS were less than the values used in the WRFDA.MWTS had small inter-channel errors,while MWHS had significant inter-channel errors.The horizontal correlation length scales of MWTS and MWHS were about 120 and 60 km,respectively.A comparison between the diagnosis for instruments onboard the two satellites showed that the observation-error characteristics of the MWTS or MWHS were different when they were onboard different satellites.In addition,it was found that the error statistics were dependent on latitude and scan positions.The forecast experiments showed that using a modified thinning scheme based on diagnosed statistics can improve forecast accuracy.

Key words:data assimilation, correlated observation errors, MWTS (Microwave Temperature Sounder),MWHS(Microwave Humidity Sounder)

1.Introduction

In data assimilation,prior errors are used to describe the uncertainty in observations and background states,and they are specified as observation-error and background-error covariance matrices. Together with assigned background errors,observation errors provide the weighting of observations in a data assimilation system and determine the impact of observations on analyses and forecasts.Therefore,to improve the accuracies of analyses and forecasts,it is important to obtain an accurate observation-error covariance matrix.

Observation errors are not only caused by the observations themselves but are also related to the operator,due to projection from the background to the observation space.For many satellite radiances,instrument noise is uncorrelated spatially or between channels.The errors arising from the observation operator include preprocessing errors,errors of the forward operator,and representativeness errors.These sources contribute to the inter-channel and spatial correlation of the errors.Due to the uneven and sparse distributions of conventional observations,spatially correlated errors can be ignored.However,both inter-channel and spatially correlated errors have been shown to exist in some satellite observations due to errors from observation operators(Bormann and Bauer,2010;Bormann et al.,2010;Waller et al.,2016a;Cordoba et al.,2017).In general,instrument noise is easy to obtain,but the other components of observation errors are more complex and difficult to estimate.Thus,the observation-error covariance matrix has often been assumed to be diagonal in data assimilation.This assumption leads to an inefficient use of observations and a sub-optimal assimilation system.Some approaches,such as variance inflation,observation thinning,and “superobbing”,have been conducted to mitigate for the deficiency of considering uncorrelated observation errors,but they are still not the optimal way to assimilate observations.Miyoshi et al.(2013)reported that error-correlated observations could provide better analysis when the non-diagonal observation-error covariance matrix was explicitly considered in data assimilation.Previous studies have demonstrated that considering the observation-error correlations could significantly reduce small-scale errors(Rainwater et al.,2015;Fowler et al.,2018)and improve the accuracy of forecasts(Weston et al.,2014;Bormann et al.,2016;Campbell et al.,2017).Therefore,considering the correlated observation error could be an efficient way to further improve the use of observations and analysis accuracy.

Because the correlations of observation errors cannot be directly calculated,statistical methods are used to evaluate them.A widely used approach was proposed by Desroziers et al.(2005).The basic principle of this approach is to estimate an observation-error covariance matrix by averaging the outer product of the background and analysis residuals.In theory,this method can obtain exact results if the weightings applied during the assimilation are consistent with the true weightings.Desroziers et al.(2005)showed that statistics can still be used to estimate an observation-error covariance matrix with imperfect prior observation and background errors.Desroziers et al.(2005)and M′enard(2016)argued that improved error covariance statistics can be obtained following several iterations of the diagnostic tool.This method repeats the process using the statistical result of the last iteration until it converges.However,due to its large computational requirement,its use is not practical in operational systems.The Desroziers method calculated by one iteration is currently used to diagnose observation-error variances and correlations in both the ECMWF(Bormann and Bauer,2010;Bormann et al.,2010)and Met Office(Stewart et al.,2014;Weston et al.,2014;Waller et al.,2016a,2016c)variational assimilation system.The method has also been used to evaluate observation errors in ensemble data assimilation systems(Li et al.,2010;Miyoshi et al.,2013;Waller et al.,2014a).These studies described the inter-channel and spatial correlation characteristics of microwave,infrared,and visible sounding data,and radar data.They revealed that the error correlation features of the specific instrument differ in the different assimilation systems.It is therefore necessary to estimate the error covariance for specific satellite sensors in certain assimilation systems.

FengYun-3(FY-3)is the Chinese second-generation polar orbiting meteorological satellite series.The first three satellites(FY-3A/B/C)were launched in May 2008,November 2010,and September 2013,respectively.The main goal of the satellite series was to achieve global,all-weather,threedimensional,quantitative and multi-spectral remote sensing to fulfill the requirements of modern meteorological services(Dong et al.,2009).There are two microwave vertical sensors onboard FY-3A/B,the Microwave Temperature Sounder(MWTS)and the Microwave Humidity Sounder(MWHS),which are similar to the Microwave Sounding Unit(MSU)and the Microwave Humidity Sounder(MHS)onboard the NOAA satellites.Lu et al.(2011)revealed significant biases in the MWTS that were consistent with the post-launch shifts in the frequency of channel pass-bands and an inadequate nonlinearity correction during instrument calibration.After these deficiencies were properly accounted for,the qualities of MWTS and MWHS were found to be comparable with similar instruments(Guan et al.,2011;Zou et al.,2011,2012;Chen et al.,2015).Studies have shown that the forecast could be improved by assimilating MWTS and MWHS observations(Lu,2011;Lu et al.,2011,2012).Bormann and Bauer(2010)found the existence of a spatial and inter-channel observation-error correlation in the Advanced Microwave Sounding Unit-A(AMSU-A)and MHS.Because these instruments have channels similar to those of the MWTS and MWHS,it is likely that the observation errors of the MWTS and MWHS are also correlated.Currently used assimilation systems do not consider the correlated observation errors of FY-3A/B atmospheric sounding data directly;rather,they use variance inflation and observation thinning to weaken the influence of neglecting the correlated errors.This limits the effectiveness of FY-3 data in producing accurate forecasts.

With the successive launch of the FY-3 series satellites,FY-3 satellite data have played an increasingly important role in numerical weather prediction.Therefore,how to accurately define the observation errors is an important scientific problem in the application of FY-3 satellite data.In that context,the present study is the first to consider the interchannel and spatial observation-error correlations for MWTS and MWHS observations assimilated in the WRF model’s Community Variational/Ensemble Data Assimilation System(WRFDA)using the Desroziers method.Unlike previous studies,we compared the observation-error characteristics for the same instrument onboard different satellites.In addition,the relationship between observation errors and both scan positions and geographical location were analyzed.It was found that the MWHS channels were significantly correlated,with both the MWTS and MWHS having certain spatial correlation errors that were related to their observing resolution.The statistical results suggest that to better assimilate MWTS and MWHS data we need to consider observation error correlation.These results also provide valuable information for quality control and data thinning.It was found that the same instrument had different error characteristics for different satellites.In addition,we found that the error standard deviations and correlations of the MWTS and MWHS were dependent on scan positions and latitudes.These findings can help us further understand the observation-error characteristics of the MWTS and MWHS and provide guidance to specify observation errors.

The structure of the paper is as follows:Section 2 details the sources of observation errors,the Desroziers method,and the MWTS and MWHS observations.Section 3 describes the experimental design.The observation-error statistics of the MWTS and MWHS and forecast experiments using the diagnosed results are presented in section 4.Conclusions and discussion are presented in section 5.

2.Theory and method

2.1.Desroziers method

Observation errors play a vital role in a data assimilation system.According to the best linear unbiased estimate,the analysis xxxaderived by the assimilation system can be expressed as the combination of the information from the background xxxband observations yyy:

where RRR is the observation-error covariance matrix, BBB is the background-error covariance matrix,H is the observation operator that projects the background to observation space,and HHH is the linearized observation operator.It is obvious that RRR and BBB are used to determine the weighting of the observation and background in the analysis.

In practice,the observation errors include systematic errors and random errors.Systematic errors refer to the biases in the data,and there are usually significant biases in satellite observations.To assimilate biased observations,a bias correction procedure is applied to correct them.Random errors are introduced by both the observations themselves and the observation operators.The main sources of random errors associated with the observation operator can be categorized as the forward model error,representativeness error,and preprocessing error.Detailed discussions of these error types can be found in Daley(1991)and Janji′c et al.(2017).All of these error sources may result in a correlation between the different observation positions and channels(Weston et al.,2014).Therefore,we need to study the possible structure of the off-diagonal observation-error covariance matrix to ensure that the observations are assimilated in an optimal way.

Because the true state is impossible to obtain,the covariance matrix of the observation errors is usually obtained by statistical methods.Posterior diagnostics can be used to estimate the observation-error covariance matrix(Desroziers et al.,2005).The diagnosed posterior observation-error covariance matrixcan be expressed as

where dddo,a= yyy ? HHH( xxxa)is the difference between the observation and analysis, dddo,b= yyy ? HHH( xxxb)is the difference between observations and background.When the observation and background errors are independent and RRR and BBB in Eq.(1)are exactly correct,the posterior RRR? is equal to the prior RRR.

The diagnostic results cannot be an exact representation of the true error characteristics,leading to an inaccurate observation-and background-error covariance matrix.Waller et al.(2016b)reported that the diagnostics will underestimate the correlation length scale when the correlated errors are treated as uncorrelated.Additionally,the estimated correlation length scale will be overestimated when the assumed observation-error standard deviations are inflated.Because uncorrelated and inflated observation errors are used,the diagnostic deficiency will be partly offset.Bormann(2015)demonstrated that background-error dependence was relatively weak in estimating correlated errors.We also conducted experiments with different background-error specifications and found that the differences in the diagnosed results were rather small.Therefore,although the diagnostic has some limitations,it can still reflect the characteristics of observation-error correlation when the results are carefully interpreted.

In Eq.(2), dddo,aand dddo,bare assumed to be unbiased.Because a satellite data bias correction was performed in the assimilation system,this assumption was considered reasonable.However,we still subtracted the mean of the difference[as in Eq.(4.3)of Stewart(2010)]to ensure an unbiased result.Waller et al.(2016a)suggested that the diagnostics were unaffected by biases in the observations when the mean residual values were subtracted.In addition,the matrix obtained by the diagnostic does not guarantee symmetry,and therefore we usedto ensure a symmetrical result.

2.2.FY-3A/B microwave sounders

Fig.1.Weighting functions of MWTS channels 1–4(red lines)and MWHS channels 1–5(blue lines).The pressure levels(gray horizontal lines)for the background are shown.

The radiance data from the MWTS and MWHS onboard FY-3A/B were used in this study.The MWTS and MWHS instruments were placed on FY-3A with an equatorial local crossing time of 1015(descending),and on FY-3B with an equatorial local crossing time of 1340(ascending).Figure 1 displays the weighting functions of the channels of the two sensors.These instruments can obtain the vertical atmospheric temperature and humidity in different layers.The MWTS channels are similar to those of the MSU channels and channels 3,5,7 and 9 of the AMSU-A.Table 1 lists the channel characteristics of the MTWS,including the frequency,main absorber,and peak weighting function height.Channel 1 is the window channel used to obtain the surface temperature and emissivity.The other channels are used to detect atmospheric temperature in the troposphere and lower stratosphere.The MWHS and MHS have five similar channels,with the MWHS also including a dual-polarization channel at 150 GHz(channels 1 and 2),while channels 1 and 2 of the MHS are at 89 and 150 GHz.Channels 3–5 of the MWHS can provide information on mid-to upper tropospheric humidity.The MWTS has 15 fields of view(FOVs)per scan line,a swath width of 2250 km,and a spatial resolution of 50 km at the nadir view.The MWHS has 98 FOVs,each with a swath width of 2700 km,and a spatial resolution of 15 km at the nadir view.The channel characteristics of the MWHS are shown in Table 2.The satellite data used in this paper were derived from the China Meteorological Data Service Center(CMDC,http://data.cma.cn).

2.3.WRFDA three-dimensional variational assimilation system

The three-dimensional variational assimilation system(3DVar)provided by the WRFDA(version 3.8.1)(Barker et al.,2012)was used to assimilate all non-window channels of the MWTS and MWHS(channels 2–4 for MWTS and channels 3–5 for MWHS).The radiative transfer model used to simulate brightness temperature was RTTOV(version 11.3)(Hocking et al.,2013).The assumed observation errors of the MWTS and MWHS were determined empirically by referring to the AMSU-A and MHS assumed observation errors.The back ground at each time was interpolated using NCEP final(FNL)analysis data with a horizontal resolution of 1°×1°for the same time.Because FNL data are observational data collected from many sources(but not FY-3A/B),only the MWTS and MWHS non-window channels were assimilated in the experiments.The background-error covariance was estimated by the National Meteorological Center method(Parrish and Derber,1992)using the differences of the 12 and 24 h forecasts valid at 0000 and 1200 UTC over a period of one month.All assimilated observations passed through quality control procedures,including a limb check(reject observations at limb scan positions),cloud check,gross check,first-guess check,and others.Observations strongly affected by cloud and precipitation were eliminated by rejecting observations for which the absolute value of the window channel innovation exceeded a threshold(3 and 5 K for channel 1 of the MWTS and MWHS,respectively).Only observations over sea were assimilated(as shown in Fig.2).A variational bias correction was applied to remove systematic errors before the radiance data were assimilated,in which a constant component and seven state-dependent predictors(1000–300 hPa thickness,200–50 hPa thickness,surface skin temperature,total column precipitable water,scan position,and the square and cube of scan position)and their coefficients were included.The WRFDA started running two days before the experiment was initiated.The updated bias correction coefficients were used as the input coefficients for the next cycle.Twenty cycles per analysis time were conducted to spin up these coefficients.The initial coefficients at the beginning of the cycles were provided by the statistics of the initial MWTS and MWHS data.Figure 3 shows that the overall bias was close to zero after variational bias correction.Scandependent biases and geographical biases were also effectively removed(not shown).It has been shown that the assimilation of the MWTS and MWHS in the WRFDA with a similar set-up can have a positive impact on a forecast(Dong et al.,2014;Xu et al.,2016).

Table 1.Channel characteristics of the MWTS.

Table 2.Channel characteristics of the MWHS.

2.4.Experimental design

To diagnose the inter-channel and spatial correlation of the MWTS and MWHS observations,we selected observations and background data from 0000 UTC 10 February 2012 to 1800 UTC 24 February 2012(four times per day).The domain used for the experiments(as shown in Fig.2)consisted of 360×300 horizontal grids,with a grid spacing of 30 km and 40 vertical levels up to 10 hPa(Fig.1).

In the WRFDA,the default thinning distance is 120 km for all satellite radiance data.Because the horizontal resolutions of the two instruments used in this study were both greater than 120 km,the thinning process prevented the estimation of correlations at distances of less than 120 km.This process had little effect on the diagnosed observation-error characteristics,although it resulted in a sub-optimal analysis(Waller et al.,2016a).As a result,the experiments were performed using unthinned data to obtain a complete understanding of the correlation structure.We also conducted the experiments using thinned data,and similar statistics were obtained.

Fig.2.Observation departures after bias correction for assimilated MWHS channel 4 observations onboard(a)FY3-A and(b)FY3-B located in the statistical domain on 10 February 2012.Histograms means show the distribution of sample numbers in the range of observation departures after bias correction.The binning width is 0.25 K.

Fig.3.Distribution of sample number in the range of observation departures before and after bias correction for the FY-3A(a–c)MWTS and(d–f)MWHS.The binning width is 0.25 K.

3.Results

We considered the observation-error characteristics of both the MWTS and MWHS.Although the instruments onboard FY-3A and FY-3B were identical,there were still differences in the statistical results.Therefore,we report individual statistics for each of the two satellites.

3.1.MWTS

Figure 4 shows the diagnosed observation-error standard deviations along with the assumed error standard deviations in the WRFDA.The statistical results show that the error standard deviations of the MWTS were all smaller than those of the WRFDA and were assigned as values greater than 0.25 K for all assimilated channels.Because an artificial inflation was conducted for the observation-error standard deviations to account for the unconsidered correlated errors,it was expected that the standard deviations of the observation-error used in the assimilation system would be much larger than the statistical results.The same sensor onboard different satellites may still have different error characteristics.Although FY-3A and FY-3B use the same microwave temperature sensor,the error standard deviations of the FY-3A MWTS differed from that of the FY-3B MWTS.It was apparent that the observation-error standard deviations of the FY-3B MWTS were greater than that of the FY-3A MWTS,especially for channel 3.

Figure 5 shows the diagnosed inter-channel correlation for the FY-3A and FY-3B MWTS assimilated channels.The absolute values of all the correlation coefficients were less than 0.2,except for the correlation between channels 2 and 3 on FY-3B,which had a coefficient of?0.28.The interchannel correlations may be caused by a combination of the radiative transfer model,representativeness error,and quality control procedures.Because the same sensor had the same parameters in the radiative transfer model and also the same representativeness error,the difference in the inter-channel correlations for different satellites may be related to the quality control procedures.

Fig.4.Diagnosed and original observation-error standard deviations for assimilated MWTS channels.

Fig.5.Diagnosed inter-channel correlation for assimilated MWTS channels.

Fig.6.Diagnosed spatial observation-error correlation(lines)and the number of observation samples(bars)for the MWTS onboard(a–c)FY-3A and(d–f)FY-3B.

Figure6 shows the spatial correlation of the MWTS channels and the number of observations used to calculate them.The amount of assimilated radiance data varied because of the omissions during the quality control process,with channel 4 having more observations assimilated than others.To better reflect the spatial correlation,the observation samples were binned with an interval of 60 km,which was close to the horizontal resolution of the MWTS.Although the spatial correlation of FY-3A and FY-3B was clearly different,all channels had a strong correlation(＞0.2)within 120 km.The correlation length scale of some channels reached 180 km(FY-3A channel 3 and FY3B channel 2).The spatial correlation length scale was greatest for channel 3,with a value up to 300 km.This was very different from the spatial error correlation for AMSU-A reported by Bormann and Bauer(2010),which was less than 0.2 even at the least distance.There were two likely reasons for this.One was the difference between the AMSU-A and MWTS observations and the other was the use of different assimilation systems,which would lead to differences in the quality control process and radiative transfer model.The correlation length scales of the MWTS were consistent with the default thinning distance of 120 km.This suggests that it is reasonable to use this thinning distance to offset the spatial observation-error correlation.

3.2.MWHS

The standard deviations of the MWHS observation-error are shown in Fig.7.The observation-error standard deviations of channels 3 and 5 for FY-3A/B were similar at about 1.3 and 1.1 K,respectively.The difference for channel 4 was large,with a standard deviation of 1.35 K for FY-3A,while it was less than 1.05 K for FY-3B.As with the results for the MWTS,due to the use of the inflated error standard deviations in the assimilation system,the statistical error standard deviations were less than the assumed errors in the assimilation system.Because the MWHS channels had larger instrumental noises than those of the MWTS,the error standard deviations of the MWHS were much larger.

Fig.7.As in Fig.4 but for the MWHS.

The inter-channel correlation of the MWHS is shown in Fig.8.The figure shows that the channels of the MWHS had significantly correlated errors,especially between adjacent channels(i.e.,channels 3 and 4,and channels 4 and 5).The correlations between the two satellites were also different.For adjacent channels,the correlations for FY-3B were greater than those for FY-3A,which were 0.6 and 0.4,respectively.Figure 9 shows the MWHS spatial observation error correlations calculated with an interval of 15 km and the observation samples used.Because the MWHS had a higher spatial resolution and a larger scanning angle than the MWTS,it had many more assimilated observations than the MWTS.The MWHS had a significant spatial error correlation when the distance of separation was within 60 km;the distance was about four times the length of the observing resolution.The default thinning distance of the MWHS in the WRFDA system is 120 km,which is greater than the spatial observation-error correlation length scales of the MWHS.This thinning distance will reject many uncorrelated observations;thus,the amount of data used was reduced and the information contained in the observations was lost.This suggests that it may well improve the present data thinning scheme.For example,using a smaller thinning distance or combining the present thinning scale with a suitable observation-error inflation may be a more reasonable approach.

3.3.Scan position and latitudinal dependence of error statistics

Fig.8.As in Fig.5 but for the MWHS.

Fig.9.As in Fig.6 but for the MWHS.

Bormann and Bauer(2010)showed that the error statistics obtained by the Desroziers method had an anisotropic characteristic at different scan positions and scan lines.Waller et al.(2016a)found that the inter-channel observation error statistics varied spatially,but their research domain was so small that it could not reveal the relationship between error statistics and the geographical locations of the observations.The anisotropy on different scan lines identified by Bormann and Bauer(2010)may also be due to the different latitude of the observing location.Therefore,it is necessary to study the difference in the statistical results in scanning position and geographical location.

Fig.10.Statistical results at different scan positions for the FY-3B(a,b)MWTS and(c,d)MWHS.Panels(a,c)are the observation-error standard deviations for different channels,and(b,d)are the inter-channel observation-error correlations.

Figure 10 shows the differences in the statistical results of the instruments in different scan positions.Except for some small changes in parts of the diagnosed results(error standard deviation of MWTS channel 2,and the inter-channel correlation of MWHS channels 3 and 4),the other error statistics,including the observation-error standard deviations,and interchannel correlations,displayed a clear scan position dependence,especially for the MWTS.The error standard deviations in the limb position were larger than those near the nadir point.The inter-channel correlations showed a pronounced asymmetry and the correlations on the left of the nadir point differed from those on the right.MWTS channels 3 and 4 exhibited strong inter-channel error correlations at the beginning of several scan positions,but only a very small correlation in other positions.This oscillatory distribution of the diagnostic results was similar to the striped distribution of the statistics found by Bormann and Bauer(2010).It should be noted that the limb observations of each scan line were removed during the quality control process,and the limb observations in this study were not the observations made at the scan boundary.The scan position dependence of error standard deviations was mainly attributed to the design of the instruments,but the scan position dependence of error correlations may be due to the different performance of the radiative transfer model at different scan positions.The deficiency in the scan bias correction may also be the reason for this phenomenon.In addition,the results for FY-3A were slightly different from the results for FY-3B,which indicates that the scan position dependence of the error features was satellite specific.To check the comparability,similar experiments using data from10–25August2012were conducted and similar characteristics were found.

To determine the performance of the statistical results ob-tained at different geographical locations,the research domain was divided into three regions:Northern Hemisphere(＞ 10°N);Southern Hemisphere(＜ 10°S);and equatorial zone(＜ 10°N and ＞ 10°S).Figure 11 shows the difference in the diagnostics at different latitudinal bands.In terms of the observation-error statistics,the two sensors performed differently in the different areas.For the MWTS,the error standard deviations and spatial error correlation were similar in each region,but the inter-channel errors were latitudeand channel-specific.For the MWHS,the error standard deviations and inter-channel correlation of the Northern Hemisphere were significantly different from those of the Southern Hemisphere and equatorial regions.This may be due to the differences in weather conditions at different latitudes,because the time period we used to calculate the error characteristics was in the winter of the Northern Hemisphere and summer of the Southern Hemisphere.Waller et al.(2014b)also found that the representativeness error was sensitive to the synoptic situation.To further verify the relationship between the statistical results and the weather conditions,we used the data from 10–25 August 2012 to recalculate the error correlations.During this period,the seasons in the Northern Hemisphere and Southern Hemisphere were the opposite of those in the previous experiment.The statistical results for all domains obtained by the data for this time period were basically the same as previous results(not shown),but the performance of the error statistics in different latitudinal bands was very different from the original results(Fig.12).The inter-channel correlation between MWTS channel 3 and the other channels was very different from that of the original experiment in the equatorial region and Southern Hemisphere.The MWHS results changed slightly in the equatorial region,but the distribution in the Northern Hemisphere and Southern Hemisphere was almost the opposite of that in the original experiment.This further suggested that the latitudinal dependence of the error statistics was related to the difference in weather conditions.The observation error was associated with the nonlinear observation operator,which indicated that the observation error could be attributed to the initial state.In different seasons,the dominant synoptic situation in specific latitudinal bands was different.For example,in the summer,the subtropical high over the Northwest Pacific was the main synoptic situation in the Northern Hemisphere area of the domain.In this situation,the field was more homogeneous,and the atmosphere was relatively stable.However,in the winter,the atmosphere over the Northwest Pacific was more varied and less homogeneous.This difference may influence the representativeness errors because different weather conditions may contain different scales or features and processes that were represented in the observations and not in the background.The different behaviors of the Desroziers diagnostic could be an alternative explanation.For example,the reliability of the assigned background errors may be situation dependent.

Fig.11.Statistical results at different latitudinal bands for the FY-3B(a–c)MWTS and(d–f)MWHS.Panels(a,d)are the observation-error standard deviations,(b,e)are the inter-channel observation-error correlations,and(c,f)are the spatial observation-error correlation of MWTS channel 4 and MWHS channel 5,respectively.

Fig.12.As in Fig.11,but for the statistics obtained using the data for August.

3.4.Forecast experiments using a modified thinning scheme

The above results suggested that an improved thinning scheme was needed to improve the assimilation of the MWTS and MWHS.To test the forecast impact of the improved thinning scheme,we performed the following two data assimilation experiments:(1)using a default thinning scheme(the thinning distances were 120 km for both the MWTS and MWHS);(2)using a modified thinning scheme(the thinning distances were 120 km for MWTS and 60 km for MWHS).A five-day forecast was made after data assimilation for both experiments using WRF V3.7.

Figure 13 shows the forecast verification of the two experiments against the analysis.More than 94%of the verification metrics were improved,with reductions in the forecast root-mean-square error of between 0.3%and 1.5%compared to the analysis.This indicates that using a modified thinning scheme improved the forecast accuracy for most variables and levels at different forecast lead times.Some verification metrics,such as the temperature and relative humidity at 500 hPa for the equatorial zone,showed degradations for the modified thinning scheme compared with the default scheme.This may be because the smaller thinning distance meant some poor-quality observations were assimilated.Another aspect to note was that the contribution from analysis errors may be significant and the forecast impact evaluated against analyses may not be an accurate indicator of forecast accuracy.

4.Conclusions

In data assimilation,the specification of observation errors is crucial to the data assimilation system.The true observation errors are likely to be correlated for many kinds of observations,due to the existence of representativeness and forward operator errors and other types of errors.The correlation of observation errors cannot be directly calculated and usually needs to be obtained by various diagnostic methods,of which the Desroziers method is one of the most commonly used.In this study,the Desroziers method was used to evaluate the inter-channel and spatial observation-error correlation of the MWTS and MWHS onboard FY-3A/B in the WRFDA.At the same time,the relationship between the statistics and scan position and latitudinal position was explored.

It was found that the observation-error standard deviations were less than the given values in the WRFDA,which was consistent with the assumption that the observation-error standard deviations were artificially inflated in the data assimilation.Otherwise,the diagnosed results were related to the specification of observation and background errors(Waller et al.,2016b).Therefore,the misspecification of observation and background-error covariance matrixes may result in underestimated observation-error standard deviations.

Fig.13.Normalized differences of forecast root-mean-square errors between cases using the modified thinning and default thinning schemes at different latitudinal bands.The verification metrics used are geopotential height(H),temperature(T),and relative humidity(R)at(a)850 hPa,(b)500 hPa and(c)200 hPa for 1–5-day forecasts.Negative values mean an improvement using the modified thinning scheme compared with the default.

The inter-channel observation-error correlation of the MWTS was weak.In contrast,there were strong interchannel observation-error correlations for the MWHS,especially between adjacent channels.There were significant spatial correlations for both the MWTS and MWHS,but the correlation length scales of the MWTS and MWHS were very different at about 120 and 60 km,respectively.Because the representativeness errors in temperature and humidity detection data were very different(Waller et al.,2014b),the different correlations for the MWTS and MWHS may be responsible for the differences in representativeness errors.The spatial observation-error correlation length scale is an important criterion for determining the thinning distance of an instrument during data assimilation.We suggest that a specific thinning scheme should be conducted for a specific instrument according to the length scale of the spatial observation-error correlation.The use of a modified thinning scheme based on diagnosed statistics was tested in forecast experiments.Improvements in forecast accuracy were realized using a modified thinning scheme.This proved that the diagnostic results were reasonable.

For the same instrument,the observation-error standard deviation and correlation statistics were satellite-specific.The main source of the difference in error standard deviations may have been the differences in the performance of the instrument itself.The correlated errors were mainly caused by the errors related to the observation operator.The parameters for one sensor were the same in the radiative transfer model and the representativeness error was also the same.Therefore,the difference in the correlated errors among different satellites may have been caused by the quality control procedures.The errors associated with quality control procedures were due to imperfections in the preparation and selection of the observation and the failure in cloud detection could be the main source of quality control errors in the clearsky radiance assimilation.We used the window channels of the MWTS and MWHS to construct cloud identification indexes to achieve cloud screening.It is therefore likely that the different performances of the quality control procedures can be attributed to the differences in the window channels of the sensors onboard different satellites.Because the differences in the window channels were related to different calibration or instrument issues,the differences in the statistics were likely due to different calibration or instrument issues.Thus,differences in the raw data could partly explain the different statistics.

The error statistics had a dependence on the scan position of the satellite radiance data.The large error standard deviations at the limb positions indicated that there were some shortcomings in the selection of the limb observation in the quality control process,and therefore it was necessary to determine a more accurate quality control process for the specific channels.There was a large difference between the inter-channel correlations in different scan positions,and the distributions on the two sides of the nadir position were distinctly asymmetric.The scan position dependence of the error characteristics can be accounted for by the design of the instruments and the deficiency in the scan bias correction.The error statistics also had a latitudinal position dependence,especially for the MWHS.The error performance of this instrument was different in the Northern Hemisphere and Southern Hemisphere,and this difference changed season-ally.This phenomenon could be attributed to the differences in representativeness errors in different weather conditions.The different behaviors of the Desroziers diagnostic could be an alternative explanation.However,to determine the exact causes of these phenomena,a meteorological investigation is required,which is beyond the scope of this work.These conclusions suggest that when using the correlated observation errors in data assimilation,it is reasonable to consider the scan position and latitudinal dependence of the inter-channel observation-error correlation.

The results suggest that there may be benefits from considering the correlated observation-error correlation when assimilating the MWTS and MWHS observations to improve observation utilization and analysis accuracy.The results provide useful guidance for improving the assimilation of FY-3 satellite data in terms of data thinning and quality control procedures.This study,however,only analyzed the error characteristics of two microwave sensors,and tested the impact on forecasts using a modified thinning scheme.Further work is needed to determine the reason for these error features and validate the performances of the diagnosed error covariance matrix.In addition,the MWTS and MWHS onboard FY-3C have been upgraded to the MWTS-2 and MWHS-2,with more channels.These upgraded instruments will also be configured onboard FY-3D and other satellites launched in the future,and it is therefore necessary to explore the observation error correlation features of MWTS-2 and MWHS-2.

Acknowledgements.This work was funded by the National Basic Research(973)Program of China(Grant No.2015CB452802)and the National Natural Science Foundation of China(Grant Nos.41230421,41605075,and 41675058).We thank the CMDC for providing the FY-3A/B MWTS and MWHS data and the NCAR/UCAR Research Data Archive for providing the FNL data.