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Application of AVHRR Data to a One-Dimensional Variational Retrieval Scheme for Cloudy TOVS Data CHIEN-BEN CHOU Central Weather Bureau, Taipei, Taiwan
HUEI-PING HUANG NOAA–CIRES Climate Diagnostics Center, Boulder, Colorado (Manuscript received 19 October 1999, in final form 13 March 2000) ABSTRACT The use of the Advanced Very High Resolution Radiometer (AVHRR) data in a one-dimensional variational scheme is examined to retrieve cloud parameters and atmospheric profiles. The variational scheme used TIROS Operational Vertical Sounder radiance data for retrieval. The AVHRR data were used in the partly cloudy and cloudy cases to provide initial guesses for cloud parameters in the iterative scheme, to detect the presence of cirrus clouds, and to determine the sea surface temperature used in retrieval. Sensitivity tests showed that the error in the initial guesses of cloud parameters has substantial impact on the accuracy of the retrieved fields; this sensitivity increases with increased cloudiness. Cloud parameters deduced from AVHRR data are nearly optimal, in terms of maximizing the efficiency of convergence, as the initial guesses for the retrieval scheme. In the absence of cirrus cloud, a retrieval procedure incorporating AVHRR initial guesses produced temperature and humidity profiles for partly cloudy cases that are about as accurate as those for clear cases. In both cases the maximum improvement made in the retrieval procedure over background error was about 0.2 K in the temperature profile, and 0.05 (in logarithm of mixing ratio) in the humidity profile. For partly cloudy cases, best retrieval results were obtained for a low cloud top, or a middle cloud top but with small cloud fraction. Cirrus cloud remains a problem, as its presence generally degrades the quality of retrieval.
1. Introduction A variational method for retrieving temperature and humidity of the atmosphere from Television Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS) data has been developed in the past decade (Eyre and Lorenc 1989; Eyre 1989; Thepaut and Moll 1990; Eyre et al. 1993). Based on a similar principle, the variational approach has been applied to full three-dimensional forecast fields in the three- and fourdimensional data assimilation schemes. In these schemes satellite-measured radiances are assimilated with other conventional observations and forecast fields. For example, a direct use of TOVS cloud-cleared radiances in a three-/four-dimensional data assimilation scheme was developed at the European Centre for Medium-Range Weather Forecasts (Andersson et al. 1994). Progress has also been reported by the National Centers for Environmental Prediction on assimilation of cloudcleared radiance into an analysis system for spectral
Corresponding author address: Chien-Ben Chou, Satellite Center, Central Weather Bureau, 64 Kung-Yuan Road, Taipei, Taiwan. E-mail:
[email protected]
q 2000 American Meteorological Society
statistical interpolation (Derber and Wu 1998). In principle, the variational method enables simultaneous retrieval of surface temperature, cloud parameters, and temperature and humidity profiles. It can incorporate raw satellite data that are not subject to cloud clearing and other preprocessing procedures in retrieving atmospheric parameters from cloudy TOVS observations. As cloud-detecting and-clearing processes contribute to errors in the final results of retrieval, a variational method may assist in avoiding such errors when accurate first guesses of cloud parameters are provided. Uses of accurate cloud parameters may also improve the overall quality of retrieval in the variational method. For instance, the relationship between observed and retrieved quantities is generally nonlinear; this nonlinearity increases as cloud parameters are included in the retrieval scheme. The increased nonlinearity hinders the convergence of the iterative procedure in the retrieval scheme. Eyre (1989) suggested that using more accurate initial cloud parameters in a retrieval procedure may accelerate convergence and, in some cases, may even be essential for the procedure to achieve convergence. The presence of cirrus clouds is usually a problem for retrieval due to the complicated radiative properties of cirrus and the
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TABLE 1. Standard deviation of the error (K) in the measurements and radiative transfer model used in this work.
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TABLE 2. Standard deviation of the background error used in this work.
Channel
Error
Channel
Error
Pressure (hPa)
Temperature (K)
Humidity ln (g/Kg)
HIRS 2 HIRS 3 HIRS 4 HIRS 5 HIRS 6 HIRS 7 HIRS 8 MSU 2 MSU 3 MSU 4
1.45 1.12 0.58 0.55 0.69 1.04 1.40 0.66 0.51 0.90
HIRS HIRS HIRS HIRS HIRS HIRS HIRS
1.10 3.01 4.06 0.47 0.39 0.36 1.12
100 150 200 250 300 400 500 700 850 1000
0.89 1.06 1.00 0.81 0.73 0.66 0.66 0.73 1.00 1.45
0.121 0.095 0.086 0.058 0.054 0.047
10 11 12 13 14 15 16
uncertainty in the observed or model-specified emissivity. A retrieval procedure may benefit from a preprocessing quality control scheme in which the presence of cirrus is detected. To provide more accurate initial cloud parameters and detect the presence of cirrus, here we consider the use of the Advanced Very High Resolution Radiometer (AVHRR) data collocated onto the High-Resolution Infrared Radiation Sounder (HIRS) fields of view in the retrieval procedure. The AVHRR data, with their complement of visible and infrared window channels, also offer promise in determining the surface skin temperature used in retrieval. In this paper we investigate a one-dimensional variational retrieval scheme and its results from cloudy TOVS data, when the initial cloud parameters and sea surface temperature are estimated from AVHRR data. 2. Method and data
Surface skin temperature: sea, 1.57 K; land, 4.0 K; Cloud amount: 0.15; Cloud top: 70 hPa.
error covariance matrix was generated from the statistics of the differences between analyses and NWP forecasts. Standard deviations of the background error are listed in Table 2. Note that the analysis 2 forecast differences might sometimes underestimate the true error. To analyze the cloud parameters from AVHRR data, we used Aoki’s (1985) algorithm to collocate the HIRS field of view on higher-resolution AVHRR images and extracted AVHRR data from every HIRS field of view. The accuracy of collocation was established on comparing values from HIRS channel 8 with averaged and collocated counterparts from AVHRR channel 4, as illustrated in the scatter diagram in Fig. 1. The data used in this diagram included pixels located from the midlatitude (the vicinity of Japan) to the subtropics. In Fig. 1 a straight line with a slope of 1.0 was drawn to guide
A variational method for assimilating satellite data into a numerical weather prediction system has been discussed by many authors (e.g., Lorenc 1986; Le Dimet and Talagrand 1986). In this method one tries to minimize a cost function J(x) with respect to an atmospheric state x, with J(x) measuring the degree of fit to the radiances and background statistical constraints and optionally other observational and dynamical/physical constraints [see, e.g., Eyre et al. (1993); the last two terms are not included here]. If the error involved has a Gaussian distribution, the cost function can be written as J(x) 5 (x 2 x b )T C21 (x 2 x b ) 1 [y m 2 y(x)]T E21 [y m 2 y(x)],
(1)
where x b is a background state with estimated error covariance matrix C, y m is an observation and y(x) is a (forward) radiative transfer operator with x as its input, and E is the expected error covariance matrix of the combined observation and forward model error. To minimize the cost function, we applied a Newtonian iteration method and an iteration formula developed by Eyre (1989). The covariance matrix for measurement errors of TOVS channels was estimated by the method of Eyre (1992). The measurement errors of the TOVS channels used here are listed in Table 1. The background
FIG. 1. Scatter diagram comparing AVHRR measurements at 11 mm averaged over a collocated HIRS field of view with HIRS 11mm measurements for one NOAA-12 pass at 2229 UTC 3 Sep 1996 over Taiwan. Values are brightness temperature in K.
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the eyes. A linear regression between the HIRS and AVHRR data points gives a slope of 1.03 (AVHRR is slightly colder than HIRS in the low-temperature end). The scatter in Fig. 1 is generally comparable to previous work, for example, Baum et al. (1992) and Kim and Chou (1995). It is useful to note that a greater degree of scatter occurred in the low-temperature end in Fig. 1, which may be understandable since many points in the low-temperature end were contributed by smallscale deep convective clouds (mostly located in the lower latitudes) that were better resolved by AVHRR than by HIRS. In cloud analysis we adopted the method of Saunders and Kriebel (1988) to classify each AVHRR pixel into clear or cloudy condition. This procedure consisted of five daytime or nighttime tests applied to each individual AVHRR pixel to determine whether it is cloud free or cloud contaminated. These lengthy but straightforward tests are detailed in Saunders and Kriebel (1988). In this process, we also attempted to detect cirrus cloud by using a bispectral threshold method. This method is based on the assumption that the difference in brightness temperature between two AVHRR channels is expected to be small under a clear sky condition and large in the presence of cirrus, due to the spectral dependence of the emissivity of cirrus cloud (e.g., Inoue 1985; Saunders and Kriebel 1988). In our procedure, if the difference between the AVHRR channel 4 (11 mm) and channel 5 (12 mm) brightness temperature exceeds a certain threshold value, then we assume the presence of cirrus. Here, the ‘‘threshold’’ is determined from the expected value of the difference of brightness temperature between the two channels in the absence of clouds. It is a function of the satellite zenith angle and the channel 4 brightness temperature (Saunders and Kriebel 1988). Next, we used AVHRR data to test whether a HIRS field of view contains a uniform layer or multiple layers of clouds, using the method of Taylor et al. (1985). In this method a large number of samples of AVHRR data within the HIRS field of view are used to determine the uniformity by simple statistical tests applied to channel 4. First, the scatter of the AVHRR data determines whether the HIRS field of view contains a single or multiple temperature scenes, with a standard deviation (SD) of 4 mW m22 sr21 as the threshold. If SD , 4 mW m22 sr21 , a uniform cloud is assumed and an average scene brightness temperature is given. Otherwise, the AVHRR pixels are further divided into 3 3 3 subarrays. The mean radiance and standard deviation of each subarray is calculated. A histogram with class interval of two radiance units is assembled from the sample of subarrays. Each contribution to a class interval is weighted according to its standard deviation, w i 5 0.25(4 2 SD i ), where the subscript i is the index of the subarray and w i is the weight that is set to zero if SD i exceeds 4. A running mean filter of two intervals is passed over the final histogram. A final cold or warm value is determined by averaging over two class inter-
FIG. 2. (a) A histogram of AVHRR radiances within one HIRS field of view. A dashed line represents the original data, and a solid line the data analyzed with Taylor’s method. (b) AVHRR image in this HIRS field of view.
vals on either side of each peak. A sample of the histogram of AVHRR radiance in one HIRS field of view is shown in Fig. 2a; the corresponding AVHRR image in that field of view is shown in Fig. 2b. Combining the above information, each HIRS field of view is classified as clear, partly cloudy, cloudy, or multiple cloud condition. In the ‘‘partly cloudy’’ case the fraction of cloud is further estimated from A c 5 (I 2 I s )/(I c 2 I s ),
(2)
in which A c is the ‘‘effective’’ cloud fraction, I s is the clear sky radiance, I c is the cloudy sky radiance, and I is the mean radiance. The pressure at the cloud top was obtained by comparing the brightness temperature of AVHRR channel 4 with atmospheric vertical temperature profile.
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When an AVHRR observation is made over the ocean and is cloud free, it can be used to estimate the sea surface temperature, for which purpose we adopted the formula of McClain et al. (1985), based on the brightness temperature of AVHRR channels 4 and 5. The TOVS and AVHRR data from July to September 1996 were used in our study. The data from July and August were used to estimate the measurement errors of TOVS channels, whereas those from September were used for retrieval experiments. The TOVS data consisted of HIRS, Microwave Sounding Unit (MSU), and Stratospheric Sounding Unit observations. In this work the HIRS channels 2–8 and 10–16, and MSU channels 2–4 were included in our experiments. These data were not subject to limb correction and cloud clearing. The AVHRR data contain two visible and three infrared channels; they were used for analysis of cloud parameters in each HIRS field of view. In the 3-month period (Jul–Sep 1996) we accumulated 12-h NWP forecasts and analyses produced by the Central Weather Bureau in Taiwan. [For an overview of the forecast system used, see Liou et al. (1997) and Jeng et al. (1991).] The forecasts and analyses from July and August were used to determine the error covariance matrix of vertical temperature and humidity profiles of 12-h forecasts. The matrix thus determined is called the ‘‘background error covariance matrix,’’ as 12-h forecasts served as initial guesses (background) in the retrieval scheme. Radiosonde data and routine analyses were used to verify the accuracy of retrieval results. 3. Results a. Impact of the background error of cloud parameters on retrieval Several sensitivity experiments were conducted following the approach of Eyre (1989). The background profile x b was calculated by adding a perturbation, generated with a random combination of eigenvectors of forecast error covariance matrix C, to the ‘‘true’’ profile x t . The ‘‘simulated’’ measured radiances were obtained by adding random Gaussian noise, through the covariance matrix E, to the true radiances calculated from the true profile using a forward radiative transfer model. We examine the effects of varying background errors of cloud parameters on the results of retrieval. Reference values of the background errors of cloud parameters were set to 0.15 for cloud fraction and 70 hPa for cloudtop pressure. In the following two sets of sensitivity tests the background errors of cloud parameters with 13, 23, and 33 reference values were used. In the first set of experiments the true value of the cloud amount was set to 0.2, and the cloud-top pressure to 500 hPa. When the background errors of cloud parameters were set to 13 reference values, there were 886 successfully converged samples from 1000 retrieval cases. The number of successfully converged samples
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FIG. 3. Retrieval errors of cloud parameters with 13, 23, and 33 reference values, shown as histograms in the lower, middle, and upper panels: (a) cloud amount and (b) cloud-top pressure in hPa.
decreased to 879 and 811 as the background errors of cloud parameters were increased to 23 and 33 reference values. The root-mean-square errors of retrieved cloud parameters were 55.78, 104.09, and 152.60 hPa for cloud top and 0.056, 0.104, and 0.134 for cloud amount when the error of cloud parameters with 13, 23, and 33 reference values were used. Figure 3 shows the errors of retrieved cloud parameters for all successfully converged cases, with three different settings (13, 23, and 33 reference values) of background errors of cloud parameters. Their root-mean-square errors in retrieved temperature and humidity profiles are shown in Fig. 4. Figures 3 and 4 demonstrate that a more accurate first guess (i.e., a smaller background error) of cloud parameters improves the chance of convergence and the quality of the final results of retrieval. The second set of experiments was performed with the true cloud amount fixed to 0.8 (and with other details unchanged from the first set). The number of successfully converged samples was 865 from 1000 retrieval cases when the background errors of cloud parameters were set to 13 reference values. This number decreased to 736 and 564 as the background errors of cloud parameters were increased to 23 and 33 reference values. The root-mean-square errors of the retrieved cloud parameters were 29.69, 39.62, and 67.31 hPa for cloudtop pressure and 0.04, 0.054, and 0.069 for cloud amount for the 13, 23, and 33 cases. The errors of the retrieved cloud parameters for the converged sam-
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FIG. 5. Same as Fig. 3 except that the true cloud amount is 0.8.
FIG. 4. Root-mean-square error of retrieved atmospheric profiles with varied background errors of cloud parameters. (a) Error in temperature in K. (b) Error in water vapor in natural logarithm of mixing ratio. The dotted, dotted–dashed, and dashed lines represent the retrieval cases with 13, 23, and 33 reference values of background error. The solid line represents the background error.
ples are shown in Fig. 5. Their root-mean-square errors in the retrieved temperature and humidity profiles are shown in Fig. 6. From both sets of experiments, an accurate first guess of cloud parameters generally improves the efficiency of convergence and the accuracy of the retrieved atmospheric profiles and cloud parameters. The improvement in atmospheric profiles is more significant with a larger true cloud amount. We have further confirmed this point by varying the true cloud amount over a wide range (not shown). In the extreme cases under a clear condition (cloud amount 5 0), almost no impact was found on the retrieved temperature profiles when the background errors were altered from 13 to 33 reference values. (However, the sensitivity of the retrieved cloud parameters seems to increase with a decreasing true cloud amount. The reason for this dependence remains to be investigated.) In the simulation study in this section we have considered a single-layer cloud with emissivity 51.0. In principle, more complicated tests could be conducted
FIG. 6. Same as Fig. 4 except that the true cloud amount is 0.8.
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with more sophisticated multilayer radiation models with spectral dependence of cloud emissivity. We hope to explore this aspect in future work. b. The use of AVHRR data The TOVS data used here contained 14 National Oceanic and Atmospheric Administration Satellite-12 (NOAA-12) passes over an area from Japan to the Philippines in the period 3–22 September 1996. All passes occurred at around 0000 UTC each day. The background profiles used in retrievals were NWP forecast fields produced by the Central Weather Bureau in Taiwan. The retrieved profiles were compared with analyzed fields that incorporated radiosonde measurements. For a meaningful comparison, the analyzed values were interpolated onto the locations where the retrieval was done. Statistics of the differences between retrieved and analyzed values were estimated from only those samples with the ‘‘retrieval’’ and ‘‘radiosonde’’ sites less than 200 km apart. The background errors were estimated by using the differences between the forecast background profiles used in retrievals and analysis. The statistics of the background versus retrieval errors in temperature and humidity profiles, from 507 samples under clear condition, are shown in Fig. 7. In these clear sky cases we gained an improvement (over background errors) of about 0.2 K in temperature in the lower to middle troposphere, and 0.05 in the natural logarithm of mixing ratio (g kg21 ) in the upper troposphere, from the retrieval procedure. Figures 8a and 8b show the background and retrieved 500-hPa humidity fields for a pass at 2229 UTC 3 September, with an HIRS channel 8 image superimposed in the background. Encouragingly, a dry area in the retrieved humidity (Fig. 8b), which is not evident in the background humidity (Fig. 8a), coincides closely with an area of clear sky in the HIRS channel 8 image. We next considered partly cloudy cases that incorporated AVHRR data. As shown in Table 3, the averaged required number of iterations in the retrieval procedure increases with an increased fraction of cirrus cloud (deduced from AVHRR) in the total cloud field. (Here, the ‘‘fraction of cirrus’’ is defined as the area covered by cirrus cloud divided by the area covered by all types of clouds. Thus, if the total cloud cover is 0.5 and total cirrus cloud cover is 0.4, then the fraction of cirrus is 0.4/0.5 5 0.8.) Figure 9 shows the scatter between the retrieved and AVHRR cloud fractions (panel a) and cloud-top pressure (panel b) when the fraction of cirrus exceeds 0.8. Figure 10 is similar to Fig. 9 but pertains to cases with fraction of cirrus less than 0.2. Figures 9 and 10 show that the presence of cirrus clouds can cause substantial differences between retrieved and original AVHRR cloud parameters. Figures 11 and 12 show the rms errors in the retrieved temperature and humidity profiles when the fractions of cirrus cloud are greater than 0.8 and less than 0.2, respectively. They further
FIG. 7. Root-mean-square error for background (solid) and retrieval (dashed) from 507 clear cases. (a) Temperature in K. (b) Water vapor in natural logarithm of mixing ratio.
show that the presence of cirrus clouds degrades the quality of the retrieved fields. It is useful to mention that the negative impact of cirrus clouds on retrieval in the above experiments may be due to the fact that the forward radiation model and the retrieval scheme used did not contain enough sophisticated treatments for cirrus. For example, the radiative transfer operator was designed for liquid cloud instead of thin ice cloud. As a result, the estimates of the expected error in the forward radiative transfer operator [which is included in the E matrix in Eq. (1)] may not be very good for the cases with cirrus. This may explain why the results of retrieval could be worse than the background error in Fig. 11, in which a large amount of cirrus was present. As a more specific example of the cirrus problem, in our procedure we have assumed emissivity 51 even though the actual emissivity of cirrus cloud can be less than 1. Thus, in the case with cirrus, or cirrus cloud overlapping lower-level cloud, there can be an overestimate of the temperature of the cirrus cloud and underestimate the altitude of the cloud top. It is, however, far from trivial to determine, either empirically or theoretically, the correct value of emissivity to be used in the procedure. Unless these
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FIG. 8. The 500-hPa humidity [in natural logarithm of mixing ratio (g kg 21 )] contours superimposed on a HIRS channel 8 image for a 2229 UTC pass on 3 Sep 1996: (a) background and (b) retrieval. Contour interval is 0.1.
difficulties could be overcome with more future research, the presence of cirrus will remain a problem for retrieval. When the cloud field is less contaminated by cirrus, the retrieved cloud parameters become closer to those estimated from AVHRR data in each HIRS field of view. (Here, without more reliable observations, we regarded the AVHRR values as the closest to reality.) In this case, the retrieval procedure was able to improve the temperature and humidity profiles from their first guesses. Eyre (1989) suggested that a good initial guess of cloud parameters may help to accelerate convergence in retrieval; in some cases a good initial guess could be even essential for the retrieval scheme to convergence. In the following experiments we first defined reference values of initial cloud parameters as those obtained from TABLE 3. Relationship between the fraction of cirrus in the total cloud and the number of iterations for the retrieval procedure. Fraction of cirrus
No. of samples
No. of iterations
1.0–0.8 0.8–0.6 0.6–0.4 0.4–0.2 0.2–0.0 Total
404 246 235 211 615 1701
5.685 5.047 4.702 4.677 4.312 4.843
AVHRR. Then, initial guesses of cloud parameters were tuned away from these reference values in the sensitivity tests. Figure 13 shows the dependence of the required number of iterations and the percentage of successfully converged samples as functions of the difference between the perturbed initial guesses and the reference (AVHRR) values. In Fig. 13, the difference is defined by the cloud fraction, with a fixed cloud-top pressure. Figure 14 is similar to Fig. 13 but with a fixed cloud fraction and varied cloud-top pressure. Both figures show that AVHRR cloud parameters as initial guesses yield nearly an optimal efficiency for convergence and produce nearly a maximum percentage of converged samples. AVHRR data may hence be considered good choices as initial guesses of cloud parameters. In the absence of cirrus cloud, the retrieval scheme with AVHRR initial guesses produced promising results for the partly cloudy cases. Figure 15 shows the rms errors in the retrieved temperature and humidity profiles from the cases with cloud-top pressure greater than 800 hPa. Figure 16 is similar to Fig. 15 but for the cases with cloud-top pressure between 600 and 800 hPa, and cloud fraction less than 0.3. In these cases, even with clouds present, the uses of the AVHRR initial guesses produced retrieval results (in terms of the improvement in atmospheric profiles over background errors) that are
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FIG. 9. Scatter diagram of AVHRR vs retrieved cloud parameters, for (a) cloud amount and (b) cloud-top pressure. Cases considered are those with fraction of cirrus exceeding 0.8.
FIG. 11. Same as Fig. 7 but for partly cloudy cases with a fraction of cirrus exceeding 0.8. Statistics are from 151 samples.
FIG. 10. Same as Fig. 9 but for partly cloudy cases with a fraction of cirrus less than 0.2.
comparable to the clear sky cases shown in Fig. 7. These results demonstrate the potential for using AVHRR data to improve retrieval procedures. When the sky is completely cloudy, results of retrieval showed no clear improvements over background profiles, except that favorable results were still obtained from retrieval when the cloud top is below 900 hPa; an example of the rms errors for this ‘‘low cloud top’’ case is shown in Fig. 17. When the HIRS fields of view are identified as having multilevel clouds, they are not processed by the retrieval procedure. The reason is that the (forward) radiative transfer operator used here only simulates the singlelayer cloud situation. To overcome this limitation we should in the future improve the radiative transfer operator to incorporate multilevel cloud conditions. Note that in the case with multilevel clouds, the AVHRR data can be used to determine the brightness temperature for each level of cloud using the method of Taylor et al. (1985). Thus, it can be used to estimate the initial cloud height of each cloud level for the multilevel cloud situation. However, the cloud fraction for each level cannot be simply evaluated from Eq. (2) in section 2 when the number of cloud level exceeds two. A detailed ‘‘counting’’ of the AVHRR data for each level, as discussed
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FIG. 12. Same as Fig. 7 but for partly cloudy cases with a fraction of cirrus less than 0.2. Statistics are from 263 samples.
by Kim and Chou (1995), may provide a way to estimate the initial cloud fraction. These aspects need to be investigated in conjunction with the development of a multilevel radiative transfer operator. With the current radiative transfer operator we use, a compromised way to process multilevel cloud scenes is to force them to be treated as having an equivalent single-level cloud [use HIRS channels 7 and 8 to first determine cloud parameters, e.g., Eyre (1989)]. For our purpose, we did not consider this approach since it would return unrealistic cloud parameters for multilevel cloud conditions. In some of our experiments the accuracy of the retrieved profiles appears to be even greater in the partly cloudy case (Fig. 15) than the clear case (Fig. 7). However, these are statistics from only the period 3–22 September 1996. Statistics from extended records of data may be needed to determine the relative accuracy that can be achieved in retrieval under clear and partly cloudy conditions. Extensive experiments in this direction are suggested for future work. The improvement in the temperature profile in retrieval is generally confined to the lower troposphere, particularly between 850 and 500 hPa (e.g., Figs. 7, 15). The reason might be that the HIRS channels 2, 3, 4, and 5 included in our experiments have relatively large biases in the upper tro-
FIG. 13. (a) Percentage of samples that achieved convergence. (b) Average number of iterations, as a function of the difference between the initial guess of cloud fraction and ‘‘reference’’ AVHRR values. Zero on the abscissa corresponds to the case in which the AVHRR cloud fraction served as the initial guess. The vertical bars indicate the standard deviations estimated from the data in a 2-week period. In this experiment the first guess of cloud top was fixed as that estimate from AVHRR.
posphere. The bias of HIRS channel 2 is about 3.0 K and biases of HIRS channels 3, 4, and 5 are around 1.5 K. The maxima of their weighting functions are located above 500 hPa. Near the surface, the retrieved profiles of temperature and humidity often do not show significant improvement over the background error. This might be due to the fact that the vertical gradients of temperature and humidity are large near the surface, such that the TOVS channels might not provide enough resolution as compared with analysis or radiosonde measurements (e.g., Stephens 1994, chapter 7). One may also speculate that the fluctuation of water vapor is rel-
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FIG. 15. Same as Fig. 7 but for partly cloudy cases with cloud top below 800 hPa. Statistics are from 145 samples.
FIG. 14. Same as Fig. 13 but with the cloud fraction fixed (at the AVHRR value) and cloud-top pressure tuned away from the AVHRR value. Zero on the abscissa corresponds to the case in which the AVHRR cloud-top pressure was used as the initial guess.
atively large near the surface over the ocean (because evaporation rate depends on the surface wind and temperature/humidity, which can fluctuate strongly within the boundary layer). Thus, near the surface the background error of humidity might not follow a perfect Gaussian distribution as assumed in the variational method. It may be useful to investigate these points in future work. 4. Conclusions In this paper we demonstrated the use of AVHRR data in a one-dimensional variational scheme to retrieve the cloud parameters and atmospheric profiles. Besides providing useful initial cloud guesses for a retrieval scheme, AVHRR data were used to detect cirrus clouds
and determine the sea surface temperature. Sensitivity tests showed that errors in the initial guess of cloud parameters (background error in the tests in section 3a) affect the efficiency of convergence and the accuracy of the final results of retrieval. This sensitivity increases with an increased cloudiness. Cloud parameters deduced from AVHRR data were shown to be nearly optimal choices for the initial guesses, in the sense that they maximized the efficiency of convergence in the retrieval scheme. In the absence of cirrus clouds, the retrieval procedure incorporating AVHRR initial guesses produced temperature and humidity profiles for partly cloudy cases with an accuracy comparable to those from clear sky cases. In both cases the improvement made by the retrieval procedure over the background error was about 0.2 K in the temperature profile in the lower to middle troposphere, and 0.05 in the natural logarithm of mixing ratio in the upper troposphere. The partly cloudy cases that show particular promise for application of AVHRR data are those with a low cloud top, or a middle cloud top but with small cloud fraction. As our experiments were restricted to data obtained from the period of July–September 1996, and the region near Taiwan, we look forward to future research with more
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FIG. 16. Same as Fig. 7 but for partly cloudy cases with cloud top located between 800 and 600 hPa and cloud amount less than 0.3. Statistics are from 55 samples.
extensive data to investigate the use of AVHRR data in retrieval and data assimilation. Quality control is important for the application of any data in a data assimilation process for weather and climate prediction. The one-dimensional variational retrieval scheme performs quality control. Only those satellite radiances that are successfully processed in the one-dimensional variational retrieval scheme may be passed on to the three-dimensional variational data assimilation system (Eyre et al. 1993). Here, we found that the use of AVHRR data allows us to detect cloud type and to provide accurate estimates for cloud parameters in a one-dimensional variational scheme and, consequently, improve retrieval results in many cases. Thus, the procedure described in this paper may be used as a quality control function when raw satellite data are directly used in a data assimilation system. Acknowledgments. The first author thanks Drs. Stanley G. Benjamin, John M. Brown, and Dongsoo Kim of NOAA/Forecast Systems Laboratory (FSL) for their helpful discussion and instruction during his past visits to FSL. He also thanks the administrations of the Central Weather Bureau of Taiwan for their support of this pro-
FIG. 17. Same as Fig. 7 but for cloudy cases with cloud top below 900 hPa. Statistics are based on 1353 samples.
ject. We appreciate constructive comments from three anonymous reviewers. REFERENCES Andersson, E., J. Pailleux, J.-N. Thepaut, J. R. Eyre, A. P. McNally, G. A. Kelly, and P. Courtier, 1994: Use of cloud-cleared radiances in three/four-dimensional variational data assimilation. Quart. J. Roy. Meteor. Soc., 120, 627–653. Aoki, T., 1985: A method for matching the HIRS/2 and AVHRR pictures of TIROS-N satellites. Tech. Proc. Second Int. TOVS Study Conf., Igls, Austria, Cooperative Institute for Meteorological Satellite Studies, 308–318. Baum, B. A., B. A. Wielicki, P. Minnis, and L. Parker, 1992: Cloudproperty retrieval using merged HIRS and AVHRR data. J. Appl. Meteor., 31, 351–369. Derber, J. C., and W. S. Wu, 1998: The use of TOVS cloud-cleared radiances in the NCEP SSI analysis system. Mon. Wea. Rev., 126, 2287–2299. Eyre, J. R., 1989: Inversion of cloudy satellite sounding radiances by nonlinear optimal estimation. I: Theory and simulation for TOVS. Quart. J. Roy. Meteor. Soc., 115, 1001–1026. , 1992: A bias correction scheme from simulated TOVS brightness temperature. ECMWF Tech. Memo. 186, 28 pp. , and A. C. Lorenc, 1989: Direct use of satellite sounding radiances in numerical weather prediction. Meteor. Mag., 118, 13– 16. , G. A. Kelly, A. P. McNally, E. Anderson, and A. Persson, 1993: Assimilation of TOVS radiance information through one-di-
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