Background Error Correlation between Surface Skin and Air

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Background Error Correlation between Surface Skin and Air Temperatures: Estimation and Impact on the Assimilation of Infrared Window Radiances LOUIS GARAND, MARK BUEHNER,

AND

NICOLAS WAGNEUR

Meteorological Service of Canada, Dorval, Quebec, Canada (Manuscript received 23 January 2004, in final form 9 June 2004) ABSTRACT This paper makes use of ensemble forecasts to infer the correlation between surface skin temperature T s and air temperature T a model errors. The impact of this correlation in data assimilation is then investigated. In the process of assimilating radiances that are sensitive to the surface skin temperature, the T s–T a error correlation becomes important because it allows statistically optimal corrections to the background temperature profile in the boundary layer. In converse, through this correlation, surface air temperature data can substantially influence the analysis of skin temperature. One difficulty is that the T s–T a correlation depends on the local static stability conditions that link the two variables. Therefore, a correlation estimate based on spatial or temporal averages is not appropriate. Ensembles of forecasts valid at the analysis time provide a novel means to infer the correlation dynamically at each model grid point. Geostationary Operational Environmental Satellite (GOES)-8 and -10 surface-sensitive imager radiances are assimilated with and without the inferred correlations in a 3D variational analysis system. The impact of the correlation on analyses is assessed using independent radiosonde data. The impact on 6-h forecasts is also evaluated using surface synoptic reports. The influence of the correlation extends from the surface to about 1.5 km. Temperature differences in the resulting analyses on the order of 0.3–0.6 K are typical in the boundary layer and may extend over broad regions. These difference patterns persist beyond 6 h into the forecasts.

1. Introduction Numerical weather prediction (NWP) centers now assimilate microwave and infrared radiances routinely, providing information on temperature and humidity in the atmosphere (e.g., McNally et al. 2000; Ko¨pken et al. 2003). Most of the satellite information used for NWP has sensitivity in the middle and upper troposphere. Progress in using surface-sensitive channels in NWP analyses other than in the form of sea surface temperature analyses has been slow. The assimilation of microwave radiances that are sensitive to the surface represents a major challenge because of the high variability of surface emissivity with soil moisture. Emissivity estimation is also a problem in the infrared (IR) wavelengths, but the problems are much less severe than they are at microwave frequencies. More specifically, the emissivity at 11–12 mm is typically high, above 0.95, and the uncertainty attached to that parameter is on the order of 1% or better for most surface types. Narrow fields of view, on the order of 10 km or less, are preferable to avoid cloud contamination. At the time of this writing, some NWP centers already assimilate surfaceCorresponding author address: Louis Garand, Meteorological Service of Canada, 2121 Trans-Canada Highway, Dorval QC H9P1J3, Canada. E-mail: [email protected]

q 2004 American Meteorological Society

sensitive IR channels over oceans (e.g., McNally 2004) but not over land. This paper explores the use of infrared surface-sensitive IR channels in NWP, with a special focus over land surfaces. To exploit fully these channels, one statistical parameter of interest is the error correlation between surface skin temperature T s and air temperature T a associated with the background estimate used in the data-assimilation process. This correlation is often set to a constant, or even to zero, for lack of better knowledge. In the latter case, increments to T a generated by the assimilation of infrared window channels are typically very small, even if T s increments are large. Eyre (1990) used nonzero, fixed values of the correlation in a one-dimensional variational data assimilation (1DVAR) estimation of T s . Then that T s value was kept as fixed in the subsequent three-dimensional variational data assimilation (3DVAR) analysis (Eyre et al. 1993; Andersson et al. 1994). In the last decade, NWP centers have included T s as a control variable, which in principle allows an analysis of T s directly within 3DVAR/fourdimensional variational data assimilation (4DVAR). The value of the correlation depends on the local static stability in the surface layer, and, therefore, accurately defining this measure is a challenge. The goal of this study is to estimate the T s–T a background error correlation locally and then to demonstrate its impact when

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assimilating surface-sensitive IR channels in a realistic NWP setting. The inversion of radiances into temperature and humidity profiles is a well-known ill-posed problem. A range of solutions exists that can fit the observations equally well. By assimilating radiances directly in the variational system, a statistically optimal solution is obtained in which the optimality depends on the accurate specification of both the observation and background error covariances. The T s–T a covariance is of particular interest in this study. Garand (2000) showed that a positive T s–T a correlation will typically lead to slightly reduced T s analysis increments (corrections to the background) that are compensated for by larger T a increments in the boundary layer. Also, through the correlation, surface T a (1.5 m) observations will result in changes to T s . Because the horizontal coverage of routinely available surface observations is considerable, it is argued that the T s–T a correlation is a very important parameter in the determination of an eventual T s analysis over land. Surface data are available all of the time, whereas only cloud-free infrared radiances can be used. The organization of this paper is as follows. Section 2 briefly describes the data assimilation system, with emphasis on the assimilation of radiances. Section 3 defines the method used to estimate dynamically the Ts–Ta error correlation from ensemble forecasts. Section 4 compares Ts and Ta analysis increments made with and without the correlation. Section 5 presents specific examples of the impact of the correlation on low-level temperature profiles, in comparison with radiosonde profiles excluded from the analysis. The impact on subsequent forecasts is also examined. Section 6 concludes the article. 2. Data assimilation Weather analyses in meteorology are obtained from a statistically optimal mix between observations and a background estimate that is most often a 6-h forecast originating from the previous analysis. This process is called data assimilation. A variational data assimilation system minimizes, by an interative process, the function J(x), where x is the model state: J(x) 5 0.5{(x 2 x b )T B 21 (x 2 x b ) 1 [H(x) 2 y]T O 21 [H(x) 2 y]},

(1)

where superscripts T and 21 denote the transpose and inverse, respectively, x b is the background or first-guess estimate, y represents the observations, and H(x) is the model equivalent of the observations. Thus, in a variational system, observations may be indirectly related to the model variables, allowing, for example, the assimilation of satellite radiances. Matrices B and O are, respectively, the background and observation error covariance matrices. A description of the Meteorological Service of Canada (MSC) 3DVAR system can be found in Gauthier et al. (1999).

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For the assimilation of satellite radiances, H(x) is a radiative transfer model computing radiances from x, with x b used to start the minimization. MSC now assimilates Geostationary Operational Environmental Satellite (GOES)-East and -West radiances from imager (IM) 3 (IM3, 6.7 mm), a channel that is sensitive to upper-tropospheric moisture. In this paper IM4 (11 mm) and IM5 (12 mm) radiances are also assimilated. These are window channels that are sensitive to skin temperature and, to a lesser degree, low-level temperature and moisture. The preparation of the data is described in detail in Garand (2003). This preparation includes the selection of the clear-air pixels, the definition of surface emissivity, the bias-correction procedure applied to brightness temperature (BT), and the error variances associated with each channel BT used to define the diagonal matrix O. The calculation of BT requires vertical profiles of air temperature T a and humidity Q, surface pressure P s and surface skin temperature T s . Climatological values are used for minor or well-mixed gases (e.g., carbon dioxide, ozone, and methane). The MSC Global Environmental Multiscale (GEM) model (Coˆte´ et al. 1998) currently operates on 28 nonstaggered vertical levels from the surface to 10 hPa, and the horizontal resolution is about 100 km. The minimization of Eq. (1), however, operates at the coarser resolution of about 150 km. After convergence of the minimization, analysis increments or corrections to the background are interpolated from the minimization grid to the forecast model grid. The so-called innovations or background minus observed quantities, that is, H(x b ) 2 y, are, however, computed at the resolution of the x b using the forecast model, which is then interpolated to the observation location. Even though the analysis is performed on the 28 model levels, the variables on the vertical level closest to the surface (level 28) are computed diagnostically at every time step during the model integration, using the surface-layer parameterization (Delage and Girard 1992; Delage 1997). The height of this diagnostic level is 1.5 m for T a and Q, whereas the first prognostic level is about 60 m above the surface. The procedure for estimating the background error covariances is described by Gauthier et al. (1998). Vertical correlations for Q are constant in the horizontal direction, whereas for T a they vary with latitude because of variations in the geostrophic constraint imposed on the mass–wind correlations. The error standard deviations are local in the case of T s and are latitude dependent for T a , Q, and P s . The analyzed humidity variable is log(Q), with the T a and log(Q) errors assumed to be uncorrelated. Also, up to now, T s errors are not correlated with those from any other variable. In that scenario, no data other than satellite radiances can influence Ts . 3. T s–T a error correlation a. Determination Ensemble forecasts are used to infer the T s–T a background error correlation as a function of time and lo-

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cation. The forecasts are taken from a recent experiment using the ensemble Kalman filter (EnKF) developed at MSC (Houtekamer et al. 2005). One ensemble consists of 64 six-hour forecasts that are valid at the same time. Each of these forecasts is obtained by integrating the GEM model with initial conditions provided by the members of the analysis ensemble produced by the EnKF. A separate data assimilation cycle is run for each ensemble member. The cycles differ as a result of independent random perturbations made to both the observations and background states to simulate their respective errors. The analysis for each member is performed using background error covariances estimated from the ensemble of background states that are valid at the time of the analyses. The model error perturbations for T s were set equal to those for T a at the lowest level. This T a perturbation is itself correlated with T a perturbations at higher levels. The vertical heat flux at the surface is obtained using a surface-layer parameterization (Delage 1997), whereas the force–restore approach is used to compute tendencies for T s from the surface heat budget (Mailhot et al. 1997). The EnKF is run over a 2-week period, ending on 2 June 2002. This method may appear, at first, to be very expensive. However, ensemble forecasts are developing rapidly at NWP centers, and the EnKF will soon be used to initialize the Canadian operational ensemble prediction system. One of the main reasons for using the EnKF approach is precisely to estimate the complete flowdependent background error covariances for use in NWP data assimilation (Buehner 2004). The T s–T a error correlation used here is just one statistical measure that can be derived from the ensembles. The T s–T a error correlation is obtained from the deviations of T s and T a from their respective 64-member ensemble means. In fact, only the correlation between T s and T a at the lowest prognostic level is calculated. If one knows that value, the correlation between T s and T a at other levels is readily obtained from the T a–T a interlevel error correlation that is used in the 3DVAR system. Because T s remains constant and is not perturbed over oceans in the forecast ensembles of the current ensemble Kalman filter, the correlation can only be derived over land. Figure 1 shows the correlation maps that are valid at 0600, 1200, and 1800 UTC 2 June 2002—the last day of the EnKF experiment. Individual analyses pertaining to these three times are presented in the next section. Because this paper focuses on the assimilation of GOES data, only one-half of the globe is shown. The horizontal resolution of the correlation estimate is the same as that used to compute analysis increments operationally. In general, the T s–T a error correlation is high, often exceeding 0.80. It was verified that the lowest correlations, locally negative, tend to occur at nighttime (e.g., Brazil and Greenland at 0600 UTC) in regions characterized by surface temperature inversions. This characteristic is expected: T s and T a are more decoupled in inversion

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FIG. 1. The T s–T a error correlation derived from ensemble forecasts valid at (a) 0600, (b) 1200, and (c) 1800 UTC 2 Jun 2002.

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situations (with high static stability) than when the boundary layer is well mixed. b. Insertion in the assimilation system The correlation between T s and T a (as shown in Fig. 1) is incorporated in the 3DVAR background error covariance matrix using a balance operator. This same approach is used to represent the mass–wind correlations that result from geostrophy and the correlations between the rotational and divergent wind components that result from the Ekman balance near the surface (Gauthier et al. 1998; Derber and Bouttier 1999). The balance operator relating the T s and T a (at level 27) analysis increments at the same horizontal location is given by DT s 5 DT9s 1 aDT a ,

(2)

where DT9s denotes the unbalanced component of the Ts error (i.e., uncorrelated with the error of other analysis variables). The coefficient a is derived from the Ts–Ta error correlation r for each land grid point, according to

a 5 rs(T s )s(T a ) 21 ,

(3)

where s designates the background error standard deviation. The minimization expressed in Eq. (1) is performed with respect to a set of uncorrelated analysis variables including T9s . Here, the desired increment DT s is obtained from Eq. (2), with the increment DT a itself derived from a balance relationship based on geostrophy. Working with uncorrelated analysis variables is convenient for the 3DVAR system because the B in Eq. (1) becomes block diagonal; that is, the covariances between the various analysis variables are zero. The error associated with T9s is derived from the total T s variance using 2 s(T9) 5 s(T s ) 2 2 a 2 s(T a ) 2 . s

(4)

As a consequence, when r is unity, the balance operator simply scales the T a increment according to the ratio s(T s )s(T a ) 21 , and s(T9s ) and DT9s are zero in that case. 4. Analysis results Analyses were made with (COR) and without (NOCOR, r 5 0) the T s–T a background error correlation as presented in Fig. 1. The background states used to produce these analyses were those produced by the operational 3DVAR. Examination of the results at 0600, 1200, and 1800 UTC clearly shows the diurnal effects. Analyses were also made with and without IM4 and IM5 GOES data to test separately, or in combination, the effect of GOES data and that of the correlation. However, results presented here focus mainly on the impact of the correlation in the case in which IM4 and IM5 brightness temperatures (BT4 and BT5, respectively) are assimilated. Radiosonde data are available at 1200 UTC. For this study, radiosonde observations were

FIG. 2. Location of BT4 pixels assimilated at 0600, 1200, and 1800 UTC. Dark (open) circles are for positive (negative) innovations . 1 s in magnitude, and crosses show magnitude , 1 s.

not assimilated, allowing them to be kept as independent data for the validation presented in section 5. Figure 2 shows the locations of IM4 data that are available for assimilation at the three analysis times (IM5 locations are identical). IM4 and IM5 data are available only in

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FIG. 3. Locations of surface air temperature data used in the 1200 UTC analysis. Synoptic reports are denoted by open circles (human observer) and plus signs (automated), triangles denote buoys, and diamonds indicate ships.

clear air and are thinned at the resolution of 200 km, as is operationally done for the IM3 radiances. Black circles in Fig. 2 denote the BT4 innovations exceeding 1 s in the BT4 innovation distribution (1 s 5 1.09 K). Empty circles denote negative innovations larger than 1 s. It is a striking feature of Fig. 2 that innovations over land tend to be positive in the daytime (1800 UTC) and negative at night (0600 UTC). This pattern is consistent with the result presented in Garand (2003) that there is a significant lack of amplitude in the T s diurnal cycle of the model. Figure 3 shows the location of the surface (1.5 m) observations of T a used in the 1200 UTC analysis. These locations are similar for the analyses at 0600 and 1800 UTC. The reports are not used where the model’s topography differs too much from the real topography (e.g., some areas of the Rockies). For the assimilation experiments, a background error std dev of 3 K was assumed for T s over land. This value was previously identified as representative for the MSC model (Garand 2003), although the error tends to be slightly lower at night (;2.5 K) and higher in the afternoon (;4.0 K). Over oceans, the error std dev varies between 0.8 and 1.5 K, with the larger values occurring over high-gradient regions, such as the Gulf Stream (Brasnett 1997). The horizontal length scale for the background error correlation for T s was arbitrarily set to 100 km, which corresponds to the model resolution. It was judged that a longer length scale lead to increments that extend too far from the observation. The 100km value implies that the influence of a T s observation on the analysis increment of T9s becomes negligible be-

yond ;250 km. However, because the length scale for T a is about 250 km near the surface, the balanced component of T s in COR analyses may be influenced up to a distance of ;600 km through the T a term in Eq. (2). Figure 4 shows the T s analysis increments resulting from the assimilation of the GOES and surface data corresponding to Figs. 2–3. Increments seen on the left panels, without correlation, occur only in regions where GOES data are assimilated. Indeed, no other kind of data can affect the T s analysis, with the exception of the localized influence of some Advanced Microwave Sounding Unit microwave radiances (microwave radiances sensitive to the surface are not used over land). As was expected from Fig. 2, increments tend to be negative at night (0600 UTC) and positive in the daytime (1800 UTC). This tendency is largely corroborated in the analyses with correlation (right panels). Through the T s–T a error correlation, surface data are now allowed to contribute to the T s analysis. Hence, sizable increments are now seen almost everywhere. The dominant negative increments at night and positive increments during the day give the comforting signal that both surface and satellite data tend to modify the background in the same manner. Increments to T s with amplitudes in the range of 3–5 K are not uncommon. To be more precise, BT4 Jacobians (dBT4/dT s ) typically vary between 0.2 and 0.8 K K 21 (Garand 2003), and, as a consequence, BT4 innovations on the order of 1 K typically result in T s increments in the range of 1.3–5.0 K. The sensitivity is higher in dry atmospheres. The left panels of Fig. 5 show the T a increments (at

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FIG. 4. The T s increments (K) at (a), (b) 0600, (c), (d) 1200, and (e), (f ) 1800 UTC 2 Jun 2002 (left) without (NOCOR) and (right) with (COR) T s–T a error correlation.

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FIG. 5. The T a (;60 m) COR increments (K) at (a) 0600, (c) 1200, and (e) 1800 UTC 2 Jun 2002, and (b), (d), (f ) the corresponding T a increment difference COR minus NOCOR.

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;60 m, level 27) from the COR analyses. Again, from the combination of GOES data and surface (at 1.5 m) data, the T a increments are largely negative at night and positive in the daytime. The magnitude of the T a increments is similar to that associated with T s . It can be seen that T a increments are low over southern Brazil at 0600 UTC, despite the fact that satellite data provide large T s corrections in that region (see Fig. 2). This result occurs because the T s–T a correlation is low or negative (Fig. 1). The right panels of Fig. 5 show the corresponding T a increment difference COR minus NOCOR. These differences can only result from the assimilation of GOES data. The impact of the correlation is important, with changes typically on the order of a few tenths of a degree, locally reaching 1.5 K. The correlation acts as expected. Where the correlation is positive and the T s forcing is positive, the T a increment is more positive in the COR analysis than in the NOCOR analysis. A good example of that case can be seen in southern Brazil at 1800 UTC. In a similar way, if the correlation is negative and the T s forcing is negative, the T a increment is again more positive in COR than in NOCOR (same region of southern Brazil, but at 0600 UTC). The other two options lead to more negative T a increments (e.g., positive correlation and negative T s forcing, as seen from the Great Lakes to James Bay at 0600 UTC). In the vertical direction, it can be shown (see next section) that the effect of the correlation remains important up to a typical height of 1.5 km. This result shows that, by including the T s–T a background error correlation, surface channels can contribute in a tangible manner to boundary layer profiling. Without the correlation, the impact of radiances in the boundary layer is much more limited because the air temperature Jacobian typically drops from a weak maximum at the height of about 1 km to nearly zero near the surface. 5. Validation a. Analyses In this section, the results of the data assimilation experiment are compared with observations to validate, at least partially, the impact of the T s–T a error correlation. A more extended validation could eventually be made from an assimilation cycle covering an extended period of time. However, as will be discussed further, it will be better accomplished in the context of the next upgrade of the MSC global model, with the horizontal resolution increasing from 100 to approximately 35 km. As mentioned earlier, the 1200 UTC analysis was made without radiosonde data. Surface data at the radiosonde site were also ignored. Temperature and humidity profiles resulting from the 1200 UTC analysis were interpolated at radiosonde sites for comparison purposes. To illustrate the impact of the correlation, observed and analyzed T a profiles are compared at radiosonde sites

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near which the highest COR–NOCOR differences were found (Fig. 5d). Figure 6 provides four examples of collocated profiles: those at Grand Junction (Colorado), Kelowna (southern British Columbia, Canada), Reno (Nevada), and Kuujjuaq (northern Quebec, Canada). At the first three sites, the effect of the correlation is to make the boundary layer warmer. For completeness, Table 1 provides details on the T s and T a increments for the COR and NOCOR experiments. As expected, the positive correlation at all four sites results in T s and T a increments from the COR analyses that are more similar than the corresponding NOCOR increments. At Kelowna, the NOCOR T s increment is 11.6 K, but the corresponding T a increment is 22.3 K because of three neighboring pixels with large negative innovations (seen in Fig. 2). The COR analysis (T s increment 1.1 K; T a increment 20.3 K) produces a T a that is 2.0 K higher than that of the NOCOR analysis and is much closer to the value observed by the radiosonde. At Grand Junction and Reno, the effect of using the correlation on T a also greatly improves the fit to the radiosonde profile (;1 K). As seen in these plots, the three stations are characterized by considerable differences between the true topography and that of the model because of the coarse horizontal resolution. For Kelowna, located in the Okanagan valley, the model topography is at 1090 m and the true topography is at 456 m. This difference represents a problem for satellite data assimilation based on the observed (satellite footprint near 8 km for GOES data) minus the calculated radiances. It is also a problem for the assimilation of synoptic reports. This situation will be alleviated by the aforementioned future increase in the resolution of the analysis. At Kuujjuaq, the positive correlation coupled with a negative T s forcing had a cooling effect at low levels, with an increment of 20.5 K (COR) as compared with 20.1 K for NOCOR. The increments in the COR analysis, in fact, result from pixels assimilated some distance away. From Fig. 2b, only two satellite pixels are used in the vicinity of Kuujjuaq, and these pixels are as much as 200 km to the north. The two pixels are on the coast, over ice and under clear skies, whereas Kuujjuaq is under overcast skies and the atmosphere is warmer and very moist, with a deep low pressure system centered over eastern Labrador, Canada. Through the background error horizontal correlations, the impact of the assimilated radiances on T a increments spreads over a large radius, on the order of 600 km as seen in Fig. 5d. Avoidance of such negative impacts in transition regions is consequently not trivial to implement, but again higher horizontal resolution would help. Although quality control checks were applied, the possibility that the assimilated pixels are contaminated by clouds cannot be excluded for negative (cold) increments, especially at this high viewing angle and given that the pixels are located on the edge of an extended cloud field. Research is also needed to control locally the length of the horizontal

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FIG. 6. Low-level temperature profiles at Grand Junction, Reno, Kelowna, and Kuujjuaq for the 1200 UTC 2 Jun 2002 analyses made without T s–T a error correlation (NOCOR) and with that correlation (COR). The radiosonde (RAOB) temperature profiles are also shown. Coordinates and height of station above mean sea level are provided. Radiosonde data were not used in the analyses.

correlation of temperature errors in the analysis process. For this problem, the best hope is the definition of flowdependent and nonhomogeneous error statistics for all model variables (Buehner 2004), as exploited here for the T s–T a error correlation. b. Forecasts Forecasts were run starting from the 0600 and 1800 UTC COR and NOCOR analyses. This timing allowed validation of 6-h forecasts at 1200 UTC 2 June and 0000 UTC 3 June using both radiosonde and surface reports. Care was taken to start COR and NOCOR forecasts with their respective T s analyses (as opposed to the current

operational practice in which T s over land is simply set equal to the T a at the level of 1.5 m). Forecasts were run up to 48 h. However, only 6-h-forecast results are presented here. Beyond 6 h, important differences are still noted, but they can hardly be directly related to the differences at initial time. Figure 7 shows the difference between COR and NOCOR 6-h forecasts for T a (;60 m). The main result is that the patterns of differences present in the analyses (Figs. 5b and 5f) are largely maintained 6 h later, with amplitudes on the order of 0.1–0.5 K. Of interest is that a difference of about 0.15 K is also noted over Mauritania (West Africa) at 0000 UTC, a region for which no satellite data were used (Fig. 2). This warming effect is caused by the warmer

TABLE 1. The Ts and Ta (at ;60 m above the surface) increments (K) interpolated at four radiosonde sites for the 1200 UTC 2 Jun NOCOR and COR analyses. The Ts–Ta correlation value is listed next to the name of each station. The difference COR minus NOCOR is provided on the last row. The Ta increments correspond to those of the second lowest level in Fig. 6. Grand Junction (10.56)

NOCOR COR COR 2 NOCOR

Kelowna (10.68)

Kuujjuaq (10.89)

DT s

DT a

DT s

Reno (10.87) DT a

DT s

DT a

DT s

DT a

0.3 20.7 21.0

22.0 21.0 1.0

21.1 21.2 20.1

21.6 20.8 0.8

1.6 1.1 20.5

22.3 20.3 2.0

0.1 20.7 20.8

20.1 20.5 20.4

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FIG. 7. Difference between COR and NOCOR 6-h forecasts of T a (;60 m) valid at (a) 1200 UTC 2 Jun and (b) 0000 UTC 3 Jun 2002.

COR T s analysis relative to the NOCOR analysis (Fig. 4f), resulting from the assimilation of surface reports (Fig. 3). Table 2 provides an objective evaluation using radiosondes and surface reports over North America (the United States and Canada). Two parameters are examined: air temperature and dewpoint depression (T a minus dewpoint temperature). Differences in excess of 0.1 K are highlighted. The COR std dev are generally equal to or marginally lower than corresponding NOCOR values. The most important differences are the lower COR T a (1.5 m) bias by 0.11 K at 1200 UTC and the lower COR dewpoint depression bias in the range of 0.05– 0.14 K at the 700–925-hPa levels at 0000 UTC. These gains are modest but perhaps are to be expected from the magnitude of the differences seen in Fig. 7 (typically less than 0.4 K). The statistics are influenced by large regions in which COR–NOCOR differences are negligible. Regions of the largest differences were examined as in section 5a, and larger signals were noted in them, but this approach limits the number of available refer-

ence data. COR and NOCOR assimilation cycles lasting for several weeks are desirable for a more complete evaluation. 6. Conclusions Ensembles of forecasts are used to infer the T s–T a background error correlation as a function of time and location. As expected, the correlation tends to be generally high, with lower values occurring in situations of surface inversions. This method does not currently allow the estimation of correlations over oceans, because the same sea surface temperature is used in each of the ensemble forecasts. Over oceans, a reasonable estimate of the correlation could perhaps be based on static stability. It was shown that the T s–T a background error correlation has an important impact, in general, on the analysis of both T s and the T a in the boundary layer. COR–NOCOR analysis differences on the order of 0.3– 0.5 K for the air temperature at low levels are often largely maintained in 6-h forecasts. The correlation is

TABLE 2. Air temperature (T a, K) and dewpoint depression (DD, K) error statistics of 6-h NOCOR (NOC) and COR forecasts valid at 1200 UTC 2 Jun and 0000 UTC 3 Jun. Values for the 700–925-hPa levels are based on radiosondes, and 1.5-m values are based on surface reports. Number of samples (N ), standard deviation (std dev), and bias (forecast minus observed) are shown. The region covers North America. Where values differ by at least 0.1 K, the lowest value is boldfaced. 1200 UTC

0000 UTC

Std dev

T a 700 T a 850 T a 925 T a 1.5 m DD 700 DD 850 DD 925 DD 1.5 m

Bias

Std dev

Bias

N

NOC

COR

NOC

COR

N

NOC

COR

NOC

COR

92 79 50 628 93 79 50 593

0.95 1.34 1.43 2.62 4.63 4.62 3.23 3.37

0.94 1.32 1.45 2.62 4.60 4.59 3.24 3.36

20.13 20.34 20.74 0.56 20.54 0.35 20.86 0.44

20.11 20.35 20.82 0.45 20.40 0.44 20.91 0.40

91 77 47 628 91 77 47 594

1.04 1.30 1.27 3.30 4.43 4.37 4.01 4.58

1.04 1.28 1.26 3.28 4.46 4.33 3.99 4.58

20.17 20.03 20.28 21.97 0.31 0.80 0.51 21.81

20.18 20.03 20.27 21.94 0.19 0.66 0.46 21.80

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a prerequisite for an analysis of T s over land because the contribution of infrared radiances is limited to clear regions, whereas synoptic observations of air temperature are available at all times. Using the locally variable T s–T a correlation clearly represents a more appropriate way to assimilate infrared radiances, allowing statistically optimal changes to the background temperature profile, and was the main motivation for this work. This study points to practical problems related to horizontal resolution and the use of stationary and horizontally homogeneous background error correlations. Because of the higher spatial and temporal variability of T s (and low-level T a ) than that of T a in the midtroposphere, and factors such as the difference between the true and model topography, the assimilation of surfacesensitive infrared channels will be best accomplished at resolutions below 50 km. The MSC global model will soon reach that resolution. The EnKF system will also be implemented shortly. These two models will provide an excellent framework to evaluate further the method presented in this paper. REFERENCES Andersson, E., J. Pailleux, J.-N. The´paut, 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. Brasnett, B., 1997: A global analysis of sea surface temperature for numerical weather prediction. J. Atmos. Oceanic Technol., 14, 925–937. Buehner, M., 2004: Ensemble-derived stationary and flow-dependent background error covariances: Evaluation in a quasi-operational NWP setting. Quart. J. Roy. Meteor. Soc., in press. Coˆte´, J., S. Gravel, A. Me´thot, A. Patoine, M. Roch, and A. Staniforth, 1998: The operational CMC-MRB Global Environmental Multiscale (GEM) model. Part I: Design considerations and formulation. Mon. Wea. Rev., 126, 1373–1395. Delage, Y., 1997: Parameterising sub-grid scale vertical transport in atmospheric models under statistically stable conditions. Bound.Layer Meteor., 82, 23–48.

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