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  • View in gallery

    Flowchart describing the interaction between the linearized moist parameterization schemes and the optical depth scheme in the context of the standard 4DVAR minimization problem. See text for explanations.

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    Probability distribution functions of first-guess departures in logarithmic optical depth (unitless): (a) before bias correction and (b) after bias correction.

  • View in gallery

    Bias in logarithmic optical depth as a function of the model logarithmic optical depth. See text for explanations.

  • View in gallery

    Scatterplot of (a) first guess before applying bias correction, (b) first guess after bias correction was applied, and (c) analysis vsobservations of logarithmic optical depth (unitless). The color bar represents the population in each bin of logarithmic optical depth.

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    Zonal differences in (left) temperature (K) and (right) specific humidity (g kg−1) analyses between experimental and reference run averaged over the month and plotted as a function of pressure (hPa).

  • View in gallery

    Horizontal maps of the differences (kg m−2) of integrated (a) liquid water path and (b) ice water path between experimental and reference run averaged over the month. (c), (d) Zoom over the warm pool area corresponding to (a) and (b), respectively. Shading with solid lines represents positive values.

  • View in gallery

    Maps of ice water content at 215 hPa: (top) MLS retrievals, (left) reference run, and (right) cloud assimilation experiment. Units of IWC are mg m−3. (bottom) The relative percentage error with respect to the MLS retrievals of the reference run and the cloud assimilation experiment, respectively. Plots are courtesy of Frank Li, Jet Propulsory Laboratory.

  • View in gallery

    Statistics for Meteosat Tb observations in the water vapor channel over the tropics. Reference run is in gray and experiment in black. Statistics for the (left) background departure and (right) analysis departure. Statistical values are displayed for the reference run (in brackets) and for the experiment on the top of each panel.

  • View in gallery

    (left) Standard deviation and (right) bias of the background (solid line) and analysis (dotted line) departures from the HIRS brightness temperature observations in the tropics. Reference run is in gray and experiment in black. Dashed black and gray lines indicate the estimated bias correction for the HIRS observations for the cloud assimilation experiment and the reference run, respectively.

  • View in gallery

    Same as Fig. 9, but for SSM/I clear-sky Tb observations.

  • View in gallery

    Same as Fig. 9, but for relative humidity based on TEMP temperature and humidity measurements.

  • View in gallery

    The RMS errors of (top) 500- and (bottom) 850-hPa temperature for a set of 30 forecasts compared to the observations. Control experiment based on the operational cycle (gray dashed line) and experiment with 4DVAR of cloud optical depth (black solid line). Areas shown are (left) Northern Hemisphere, (middle) Southern Hemisphere, and (right) tropics.

  • View in gallery

    Same as Fig. 12, but for the RMS errors of 700- and 850-hPa vector wind.

  • View in gallery

    Significance of the impact coming from the assimilation of MODIS cloud optical depths in 4DVAR system for the period of April 2006 in the tropics. The forecasts are compared with respect to the observations for 30 cases and significance is based on RMS error differences. The significance is displayed for (top) 850- and 500-hPa temperature and (bottom) 850- and 700-hPa vector wind. The y axis shows the RMS change (the difference between RMS of the reference run minus RMS of the experimental run) normalized by the mean RMS of two experiments (range from −30% to 30%).

  • View in gallery

    One-day forecasts produced from the reference run (black dotted line) and from the run with assimilation of cloud optical depths (black solid line) compared to the observations (gray line), all averaged over the tropical belt between 20°N and 20°S for April 2006. Comparisons of the TOA (a) shortwave and (b) longwave cloud forcings to the CERES products and (c) surface precipitation to the GPCP Version 2 dataset.

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Assimilation of MODIS Cloud Optical Depths in the ECMWF Model

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Abstract

At the European Centre for Medium-Range Weather Forecasts (ECMWF), a large effort has recently been devoted to define and implement moist physics schemes for variational assimilation of rain- and cloud-affected brightness temperatures. This study expands on the current application of the new linearized moist physics schemes to assimilate cloud optical depths retrieved from the Moderate Resolution Imaging Spectroradiometer (MODIS) on board the Aqua platform for the first time in the ECMWF operational four-dimensional assimilation system. Model optical depths are functions of ice water and liquid water contents through established parameterizations. Linearized cloud schemes in turn link these cloud variables with temperature and humidity. A bias correction is applied to the optical depths to minimize the differences between model and observations. The control variables in the assimilation are temperature, humidity, winds, and surface pressure. One-month assimilation experiments for April 2006 demonstrated an impact of the assimilated MODIS cloud optical depths on the model fields, particularly temperature and humidity. Comparison with independent observations indicates a positive effect of the cloud information assimilated into the model, especially on the amount and distribution of the ice water content. The impact of the cloud assimilation on the medium-range forecast is neutral to slightly positive. Most importantly, this study demonstrates that global assimilation of cloud observations in ECMWF four-dimensional variational assimilation system (4DVAR) is technically doable but a continued research effort is necessary to achieve clear positive impacts with such data.

Corresponding author address: Marta Janisková, European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, RG2 9AX, United Kingdom. Email: marta.janiskova@ecmwf.int

Abstract

At the European Centre for Medium-Range Weather Forecasts (ECMWF), a large effort has recently been devoted to define and implement moist physics schemes for variational assimilation of rain- and cloud-affected brightness temperatures. This study expands on the current application of the new linearized moist physics schemes to assimilate cloud optical depths retrieved from the Moderate Resolution Imaging Spectroradiometer (MODIS) on board the Aqua platform for the first time in the ECMWF operational four-dimensional assimilation system. Model optical depths are functions of ice water and liquid water contents through established parameterizations. Linearized cloud schemes in turn link these cloud variables with temperature and humidity. A bias correction is applied to the optical depths to minimize the differences between model and observations. The control variables in the assimilation are temperature, humidity, winds, and surface pressure. One-month assimilation experiments for April 2006 demonstrated an impact of the assimilated MODIS cloud optical depths on the model fields, particularly temperature and humidity. Comparison with independent observations indicates a positive effect of the cloud information assimilated into the model, especially on the amount and distribution of the ice water content. The impact of the cloud assimilation on the medium-range forecast is neutral to slightly positive. Most importantly, this study demonstrates that global assimilation of cloud observations in ECMWF four-dimensional variational assimilation system (4DVAR) is technically doable but a continued research effort is necessary to achieve clear positive impacts with such data.

Corresponding author address: Marta Janisková, European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, RG2 9AX, United Kingdom. Email: marta.janiskova@ecmwf.int

1. Introduction

The new frontier for improvement in weather forecasts and climate models from the point of view of defining the model initial state is the full use of available satellite and ground-based data, including cloud and precipitation-affected observations. Current satellite-based observations are rich in global cloud-related information. New sensors such as the Moderate Resolution Imaging Spectroradiometer (MODIS) on board the Terra and Aqua satellites, the cloud profiling radar (CPR) on board CloudSat, and the cloud–aerosol lidar with orthogonal polarization (CALIOP) on board CALIPSO are revealing the complex two-dimensional and three-dimensional structures of clouds (Stephens et al. 2002). The challenge now is to extract the largest amount of information about the cloudy atmosphere from this wealth of data by using state-of-the-art modeling and assimilation systems.

The assimilation of cloud observations, using global numerical weather prediction (NWP) systems, has been hampered by several factors: (i) the inherent nonlinearities and discontinuities in the cloud parameterization schemes, particularly those treating convection (Fillion and Mahfouf 2003); (ii) the lack of suitable linearized cloud schemes for the minimization that could combine a description of the cloud fields close to the nonlinear model with the computational efficiency of a linearized scheme, which is particularly important in an operational context (Janisková et al. 1999; Mahfouf 1999); (iii) the complexity of the observation operators, for example, the radiative transfer schemes for cloudy atmospheres especially in the presence of scattering (Greenwald et al. 2002, 2004; Matricardi 2005); (iv) the definition of the bias for these observation operators; (v) the deviations from Gaussian distribution in the error statistics; and (vi) the difficulties in defining error background statistics for cloud control variables. Most of these problems are also common to the assimilation of rain-related measurements. The latter has received more attention in global NWP models (Županski and Mesinger 1995; Tsuyuki 1997; and Bauer et al. 2006a, b; to mention a few studies), while cloud assimilation has been successfully implemented in limited-area models based on nudging technique (MacPherson et al. 1996; Lipton and Modica 1999; Bayler et al. 2000), mostly outside the operational context.

Initial cloud assimilation studies have focused on cloud retrievals from radar data, either in the context of one-dimensional variational schemes (1DVAR) (Benedetti et al. 2003a, b) or with fully-blown mesoscale models in 3D-Var (Hu et al. 2006a, b) and 4DVAR (Sun and Crook 1998; Wu et al. 2000). Chevallier et al. (2004) investigated the capability of a 4DVAR system in assimilating cloud-affected satellite infrared radiances using observations from the narrowband Advanced Infrared Sounder (AIRS). An attempt at exploiting visible and infrared cloudy satellite radiances in 4DVAR has been made by Vukićević et al. (2004). In that study, the authors used the Regional Atmospheric Modeling and Data Assimilation System (RAMDAS) 4DVAR to estimate the cloud state from Geostationary Operational Environmental Satellite 9 (GOES-9) observations. Their findings show an improvement in the model cloud forecast through both enhanced vertical mixing and the coupling between initial conditions and observed state by the model dynamics. However, they also note that observations that are more directly related to local temperature and humidity are also needed to better constrain the system and reduce the errors. Lopez et al. (2006) also noted that behavior in their 2DVAR of Atmospheric Radiation Measurement (ARM) cloud radar retrievals.

To date, a large percentage of satellite observations affected by clouds are not included in global analysis systems mainly because of the lack of suitable schemes to describe cloud processes in the assimilation with the necessary accuracy. Moist physics schemes for variational data assimilation that permit the treatment of complex cloud systems, while retaining the simplicity of being diagnostic and linearized, have been developed and are now operational in the European Centre for Medium-Range Weather Forecasts (ECMWF) 4DVAR (Tompkins and Janisková 2004; Lopez and Moreau 2005). These developments have allowed the operational implementation of the 1D+4DVAR of rain and cloud-affected brightness temperatures from the Special Sensor Microwave Imager (SSM/I; Bauer et al. 2006a, b). Results show a positive impact of these observations, especially in the redistribution of relative humidity in the tropics, and consequently in the location of the precipitating systems. Despite this major achievement, a large percentage of the satellite data (75% to 80% depending on instruments, channels, and sensitivity to clouds) that are ingested in the ECMWF 4DVAR system is still screened for cloud and rain contamination, except for a few microwave and infrared channels whose sensitivity peaks in the upper troposphere/stratosphere. As a result, cloudy areas are still less constrained by observations than cloud-free areas.

In this study we attempt to demonstrate that the ECMWF 4DVAR system is technically ready to assimilate cloud observations, thanks to the development of the new linearized moist physics schemes. As a first step, the visible cloud optical depths from the MODIS instrument onboard Aqua are used as observations. While it is recognized that dealing with the raw radiance measurements through the appropriate observation operators allows for both a more consistent treatment of the observations within the model framework and a full utilization of the model sensitivity to observations (Vukićević et al. 2004; Moreau et al. 2004), the use of preprocessed cloud optical depths for testing purposes is more practical and less computationally demanding. Observational operators for visible radiances and their corresponding adjoints have been developed and applied in research contexts (Greenwald et al. 2002, 2004). However, to be used in an operational context, the operators need to be made more efficient (as has happened over the years for infrared radiative transfer codes; Matricardi 2005). It is envisaged that cloud retrievals will be replaced by the cloudy radiance observations for assimilation purposes, but for the time being the cloud retrievals represent a good, largely untapped source of information on the cloud and the atmospheric state.

The outline of the paper is as follows: Section 2 describes the general methodology and briefly provides details about the operational ECMWF 4DVAR system and the observation operators (cloud optical depth parameterizations and moist parameterization schemes). The main section, 3, describes the setup for one-month assimilation experiments with a brief introduction to the MODIS data and the discussion of the first-guess departures, the bias correction, and the observation and representativeness errors. Section 4 presents the outcome of the cloud assimilation experiment with respect to a reference run. Several measures of analysis performance are presented, including the standard assessment of an improved model fit to the assimilated observations, and the validation against independent observations. The impact of the assimilation of cloud optical depth on key atmospheric parameters such as temperature, humidity, and ice water content (IWC) is also shown. Some issues with the analysis of humidity are highlighted via comparisons with other assimilated observations that are sensitive to moisture. Section 5 discusses the effect of the assimilation of cloud data on the medium-range forecast using standard meteorological scores and comparisons with independent radiation and precipitation observations. The closing section, 6, summarizes the main findings and presents open questions and future perspectives of this line of work.

2. Methodology

a. The ECMWF operational 4DVAR

The ECMWF 4DVAR system is based on an incremental formulation that ensures a good compromise between operational feasibility and a physically consistent four-dimensional analysis (Courtier et al. 1994). The cost function in the incremental approach is formulated as follows:
i1520-0493-136-5-1727-e1
In this formulation, Jb(δx0) is the background cost function which measures the distance between the initial state of the model x0 and the background xb0 obtained from a short-range forecast valid at the initial time of the assimilation period; Jo(δx0) is the observation cost function measuring the distance between the model trajectory and corresponding observations. A constraint cost function Jc(δx0) is used to include all the physical constraints one wants to impose on the model solution (Gauthier and Thépaut 2001). In Eq. (1), δxi = xixbi is the analysis increment and represents the departure of the model state (x) with respect to the background (xb) at any time ti; H′ is the linearized observation operator and di = yoiHi(xbi) is the departure of the model background equivalent from the observation (yoi). The matrix 𝗥i is the observation error covariance matrix, while 𝗕 represents the background error covariance matrix, formulated according to the “wavelet–Jb” method of Fisher (2003, 2004). A nonlinear integration provides the linearization state trajectory in the vicinity of which the model is linearized. The departures are computed during the nonlinear integration at high resolution using complex nonlinear physics (as used by the forecast model).

Using the incremental approach, 4DVAR can be approximated to the first order by finding analysis increments δxa0 that minimize the cost function J. The minimization requires an estimation of the gradient of the cost function. The gradient with respect to δx0 is computed efficiently using the adjoint model. The minimization is solved using an iterative algorithm based on the Lanczos conjugate gradient algorithm with appropriate preconditioning. To reduce the computational costs in the operational 4DVAR system, the perturbations δxi are computed with a tangent-linear model using simplified physics (Mahfouf 1999; Janisková et al. 2002; Tompkins and Janisková 2004; Lopez and Moreau 2005) at a lower resolution than the trajectory. The gradient of the cost function is computed with the low-resolution adjoint model, which also includes simplified physics. After the minimization, the trajectory and the departures are recomputed and a second minimization at a higher horizontal resolution is run. The model and observation operators are linearized again around the current state (Andersson et al. 2005; Radnóti et al. 2005). For this study we use a resolution of T511 (corresponding to approximately 40 km) for the forecast, while the two minimizations are run at T95 (∼215 km) and T159 (∼120 km). To decrease the computational cost, the first minimization is run with the vertical diffusion scheme and moist physics and other physical processes are only activated in the second minimization of the operational configuration used in 4DVAR. However, in our configuration it was necessary to turn on the linearized moist physics schemes in both minimizations. On average, 70 iterations in the first minimization and 35–40 iterations in the second minimization are required to reach a satisfactory convergence of the minimization. Convergence criteria and a detailed description of the incremental 4DVAR can be found in Fisher (1998) and Trémolet (2005).

The current assimilation window is 12 h. Observations are ingested over the window and subdivided into half-hour time slots. The model fields, including cloud cover and cloud liquid and ice water contents, that are required by the operators are interpolated at the observation location. This interpolation introduces a representativeness error that increases the error variance of the observations. This component of the error should not be neglected and may be quite large for heterogeneous variables such as cloud fields. In this study we addressed this issue by artificially increasing the observation error as described in section 3f. However, this is not an entirely satisfying solution. Recent efforts at ECMWF have shown that the representativeness error, in particular error related to interpolation of nonhomogenous fields such as precipitation and clouds to the observation location, can dominate the observation error. An alternative to the interpolation would be a weighted nearest-neighbor approach within a certain radius of distance between model grid point and observation location. This approach is currently under development at ECMWF for the assimilation of rainy brightness temperatures and could be adapted to the assimilation of cloud-related observations.

b. Observational operators

The core of the observation operator for the cloud optical depth is the diagnostic linearized cloud scheme (Tompkins and Janisková 2004) combined with the linearized convection scheme (Lopez and Moreau 2005), which provides detrained convective cloud water as input to the convective contribution of the cloud scheme. These schemes allow for a full representation of cloud systems in the context of the linearization approximations, and are tuned to match the full nonlinear parameterization schemes. Regularizations in the linearized version of the schemes had to be implemented to ensure numerical stability and avoid development of spurious noise. The accuracy of the linearization was tested against two sets of nonlinear results, that is, the difference between two forecasts, one started from the analysis and one from the background. These tests are discussed in great length in the references provided. The main advantage of the linearized schemes is the possibility of representing complex cloud and precipitation systems while retaining the computational efficiency required to run the several iterations during the minimization of the cost function. The schemes were first applied in the 1D+4DVAR of SSM/I brightness temperatures and are currently fully operational in the ECMWF 4DVAR.

The main outputs of the linearized schemes, liquid water and ice water contents, are passed to the optical depth routine that computes the model equivalent of the observed optical depth at the observation location. This routine uses the Slingo (1989) parameterization for the optical properties of liquid water clouds and Fu (1996) for those of ice clouds. For liquid water clouds, the effective radius (re) is derived from the cloud liquid water content following Martin et al. (1994), with the concentration of cloud condensation nuclei fixed at 50 cm−3 over the oceans and 900 cm−3 over the continents. For ice clouds, the effective size of the particles is a function of temperature following Ou and Liou (1995). A detailed description of the cloud optical depth parameterization is provided in the appendix. Since all necessary regularizations were applied to the moist parameterization schemes, the linearized version of the cloud optical depth scheme did not require any special adjustment.

Figure 1 illustrates the flow between the linearized moist parameterization schemes and the optical depth routines in 4DVAR computation. During the minimization, the linearized cloud scheme with input from the convection scheme provides the perturbations in cloud liquid and ice water content, which are then passed to the tangent linear version of the optical depth routine to compute the perturbation of optical depth. In the backward calculation, the gradient of the cost function with respect to the control variables is calculated by first using the adjoint of the optical depth routine to obtain the gradient with respect to the cloud liquid and ice water contents. The gradient is then passed to the adjoint of the cloud and convection schemes and used to compute the cloud contribution to the gradient with respect to temperature and specific humidity, and through the convection scheme also to the gradient with respect to the wind components. The final gradient of the observation cost function with respect to the model state variables is transformed to the control vector variables and passed together with the gradient of the background cost function to the minimization algorithm. The minimization provides analysis increments δxa0 to be added to the background xb0 in order to obtain the model analysis.

As can be seen from the flow diagram of Fig. 1, the control variables in the 4DVAR are temperature, humidity, vorticity, divergence, and surface pressure. The cloud gradients computed by the adjoint of the moist parameterizations contribute directly to the gradients in temperature and humidity and indirectly to the gradients in the other control variables (such as wind) through the coupling that takes place in the 4DVAR. The use of a moist control variable that is unable to take cloud increments directly into account could constitute a major limitation of the current system. As a consequence, the cloud-related observations can only impact the model indirectly and in a way that is largely determined by the local, regime-dependent cloud Jacobians (Fillion and Mahfouf 2003). Recognizing this limitation, Sharpe has implemented a total water control variable in the Met Office assimilation system (M. Sharpe 2006, personal communication) to allow for a more effective assimilation of cloud observations. This variable is used to analyze moisture increments representing changes in total water substance defined as water vapor plus cloud liquid and ice water. More recently, an incrementing operator for cloud fraction has also been included (M. Sharpe 2006, personal communication). It is envisaged that a similar approach might be taken at ECMWF to increase the benefits of the assimilation of cloud-related observations, and improve background error statistics in cloudy and rainy areas.

3. Data and description of experimental setup

a. MODIS observations

The data used in this assimilation study is the cloud optical depth product from the MODIS instrument flying onboard Aqua. The cloud optical depth is retrieved from simultaneous cloud reflectance measurements in various solar spectral bands. Specifically, the water-absorbing bands (1.6, 2.1, and 3.7 μm) provide an estimate of the particle size while the nonabsorbing bands (0.65, 0.86, and 1.2 μm) are chosen to minimize the effect of surface reflectance and mainly provide information on the visible optical thickness (Platnick et al. 2003; King et al. 2003). Most cloud level 2 products are provided at a resolution of 1 km. However, here we used the latest release, collection 5, that also provides a summary file that contains both cloud- and aerosol-retrieved products at a resolution of 5 km at the standard reference wavelength of 0.55 μm (King et al. 2006). Before entering the assimilation, the MODIS cloud optical depth observations are further averaged to a resolution of 25 km. This is done to minimize the mismatch between observations and model resolution (T511, approximately 40 km). The model equivalent optical depths are calculated at 0.55 μm using the observation operator described in the appendix.

b. Experimental setup

The experimental setup is similar to that of a former operational run at a resolution of T511. The incremental 4DVAR is initialized with a short forecast and all standard observations (conventional and satellite-based) are used in the minimization. During each 12-h assimilation cycle, over three million observations that have passed the screening process are ingested in the 4DVAR. Some of this data are screened and/or thinned according to the system requirements. Since data acquisition for MODIS optical depth is not automated as it is for other observations, we processed only Aqua measurements for the month of April 2006. The data volume of these observations amounts to approximately 100 000 optical depth data points per cycle. A prescreening is applied when the trajectory is run, and model optical depths smaller than 0.025 and larger than 100 are not included in the minimization as those are also the lower and upper limits, respectively, in the MODIS files. We also screen observations at high latitudes, that is, above 60°, to avoid spurious optical depth retrievals over sea ice. No further screening or thinning is applied to the averaged data. The minimization is run with the linearized moist physics in both the lower (T95) and higher (T159) resolution inner loops. The cloud optical depths are included in the minimization via the observational database (ODB) as a special class of observations. All statistics about the first-guess and analysis departures are collected in the ODB as for all other observations. The initial investigation was performed using the optical depth; it was then decided to assimilate the decimal logarithm of the optical depth instead to limit the range of increments and to obtain a more Gaussian distribution. Two sets of experiments were conducted with the logarithm cloud optical depth variable: one with and one without bias correction. Below is the rationale for these choices.

c. Logarithmic optical depth

One of the main underlying assumptions for a well-behaved incremental variational assimilation is the existence of Gaussian error statistics for the background and observational errors, as this implies that the cost function is quadratic and does not have multiple minima. This assumption translates into the requirement for a Gaussian distribution of the departures, which represent the differences between the observations and their model equivalents. For variables such as precipitation and optical depth, however, it is observed that the departure statistics diverge from the Gaussian shape and are often skewed. The range of values that these departures can take is also wide, and implies even larger deviations from Gaussian behavior. Some authors suggest using a change of variables to reduce the range of departures and improve their distribution. One of the most common choices for positive-definite variables is to use the logarithm in decimal base of the model and observed quantities, as in Hou et al. (2004) for the assimilation of precipitation. In light of these considerations, we decided to use this approach and develop the cloud assimilation in terms of logarithmic optical depth. Note that the errors in the logarithmic variables need also to be expressed in that form. Following Cohn (1997), we reassigned errors in logarithmic optical depth according to the formula
i1520-0493-136-5-1727-e2
where rlog is the error variance of the logarithmic optical depth and ϵr is the relative error on physical optical depth.

d. Monitoring of the first-guess departures

When a new observation is introduced in the 4DVAR, a preliminary monitoring is performed by looking at the first-guess departures that represent the difference between the observations and the model background in observation space. In an ideal system, the distribution of these departures should be centered around zero (unbiased model/observations) and Gaussian in shape. However, the most likely scenario is that the observations or the model or both present biases. For the observations, the most common sources of bias are calibration errors of the instrument, scanning angle errors, and/or errors in the radiative transfer models that translate the atmospheric signal in radiances as measured by the spaceborne instruments. All of the above sources of bias introduce biases in the retrieved cloud optical parameters. Model systematic errors are more difficult to describe, as they can stem from a number of reasons ranging from inaccurate model parameterizations to errors introduced by the numerics. The weak-constraint 4DVAR addresses the problem of the inclusion of model error as part of the estimation problem (Trémolet 2005). The discussion of this aspect of 4DVAR is, however, beyond the scope of the current study.

The assumption for the strong-constraint 4DVAR assimilation is that the first-guess departures are unbiased; hence, diagonal elements of the observation error covariance matrix describe only the random component of the error. This is why a lot of effort is generally put either toward eliminating the biases at the preprocessing stage or toward developing a bias model for the different sets of measurements that can be used to remove those biases in the 4DVAR context. This is the approach taken at ECMWF where a variational bias correction is implemented, and the coefficients describing the bias model are estimated as part of the minimization problem (Dee 2004; Auligné et al. 2007). In our study, however, we could not make use of this method, as defining a bias model for cloud observations such as optical depth is not a trivial task. We then decided to run an experiment without bias correction and to investigate the first-guess departure statistics with the purpose of modeling the optical depth bias. The first result that emerged was that observations over land had a much larger bias than the observations over ocean. This different behavior could be due to the differences between the optical depth parameterization over land and over ocean. This aspect can be tested by choosing another set of parameterizations to see whether the bias is reduced and also by applying a tuning that is appropriate for the assimilation; these possibilities will be explored in future studies. As a first step, however, we decided to assimilate cloud optical depth observations over ocean only.

e. Bias correction

Figure 2a illustrates the nature of the bias problem. It shows the bias over ocean for over two million points accumulated during a two-week period (1–15 April 2006) from the monitoring run. As shown in the picture, the distribution of the first-guess departures (i.e., the differences between observation and first guess) is not perfectly Gaussian (note the tail on the right-hand side of the histogram) and the mean is not zero. It was decided to apply a simple bias correction as a function of the model optical depth in logarithmic space. The range of logarithmic optical depth (−1.6 to 2.0) was divided into eighteen bins and for each bin the average of the corresponding first-guess departures was calculated. These averages were subsequently subtracted from the model optical depths falling in the specific bin. As a consequence, the bias-corrected departures have a lower mean bias and the shape of their distribution is more Gaussian, as shown in Fig. 2b. The bias as a function of optical depth is shown in Fig. 3. Note that negative optical depths in logarithmic space are synonymous with optical depth smaller than unity in physical space. The shape of the bias curve is rather smooth. On average, the model has a positive bias for low optical depths (i.e., it underestimates the cloud optical depth) whereas it has a negative bias for large optical depths (i.e., it overestimates the optical depth with respect to observations). In what follows, the term optical depth will signify logarithmic optical depth, unless otherwise stated.

f. Observation and representativeness errors

Although MODIS collection 5 cloud optical depths come with a pixel-by-pixel uncertainty (King et al. 2006), initial assimilation tests were performed using an assumed value of 20% error on optical depth, which was then translated by means of Eq. (2) into an error in logarithmic optical depth. This value was chosen as inclusive of various error sources such as the spectral albedo uncertainty (15%) and the calibration and radiative transfer model uncertainty (5%), as suggested in King et al. (2006). Additionally, the error was increased to 50% to partially account for representativeness errors deriving from the interpolation to observation location as well as those inherent to the optical depth observation operator and the parameters that describe it. For points where the model optical depth differed from the observed one by more than 50, an extra 50% was added to the error to restrain the model within the assumptions of the incremental formulation, which assumes small departures from the model state. The total relative error was in this case 100%. By increasing the errors in such a way, large departures in optical depth were greatly penalized. We also increased to 150% the error for observed values of optical depths greater than 25 in an attempt to account for errors due to instrument saturation.

4. Assimilation results for April 2006

This section describes in detail the results for an assimilation run that included the bias correction for cloud optical depth. Various measures of the performance of the analysis are presented and discussed, including comparisons of resulting analyses with independent observations.

a. Overview of the fit to observations

The first comparison that we made can be described as a sanity check: the analyzed optical depths are plotted as a function of the observations and compared with the first guess. In a successful analysis, the departures are smaller than in the first guess, hence the analysis better matches the observations. Figure 4 shows scatterplots of first guess and analysis plotted against observations. Because of the large data volume, we used only fifteen days in the middle of April to produce this figure. In Fig. 4a all data points are included in the first-guess statistics, prior to the bias correction discussed in section 3e. Figure 4b shows the first-guess statistics after application of the bias correction. It is possible to notice a large residual bias, which indicates that the bias correction was not as effective as hoped for. This could be due to the fact that when the number of first-guess optical depth values in a specific bin is low, the mean for that particular bin is not representative, hence a correction based on that estimated mean may not be suitable for all optical depth values. A different bias estimator needs to be implemented for better results. However, the total bias after the correction is 0.22 as opposed to a value of 0.35 prior to the correction. This indicates that the correction worked to a certain degree. Also, root-mean-square (RMS) error and correlation with observations are improved, suggesting that the simple bias correction that has been implemented is somehow effective in reducing systematic errors in the model optical depth. However, the persistence of the residual bias indicates that refinements to this correction are necessary. The analysis is shown in Fig. 4c. The correlation with observations is much improved in the analysis. A small reduction in bias and RMS with respect to the first-guess departures is also noticeable. However, these improvements in bias and RMS are small, consistent with the fact that the analysis is not supposed to correct for biases, and thus confirm the need for a better a priori bias correction. Overall this scatterplot confirms that the analysis draws closer to the observations.

b. Impact of cloud assimilation on temperature, humidity, and cloud parameters

In parallel with one month of cloud assimilation for April 2006, a reference run of the same length was also performed with a setup identical to the cloud assimilation experiment (except for the use of MODIS data) to provide a benchmark for the impact of the introduction of cloud optical depths. Figure 5 shows the mean zonal differences between experiment and reference for temperature and specific humidity analyses. These were averaged over the month of April and are shown as a function of pressure. The differences in specific humidity have a distinct vertical structure with a tendency for the experiment to be drier at upper- and lower-tropospheric levels and moister than the reference at middle levels across all latitudes up to ±40°S/N. Above this latitude, the prevalent pattern is that of larger moisture values in the experiment with respect to the reference. The pattern in temperature is more noisy but there is a distinct dipolar structure in the experiment of cooling at upper levels down to 750 hPa and warming below 750 hPa. Based on these impact plots, it appears that any changes induced by the cloud observations above 600 hPa reflect mainly a balance between a decrease in temperature that favors cloud formation and a reduction in specific humidity that opposes cloud formation. Between ∼600 and 750 hPa, temperature and moisture changes seem to be more in phase, enhancing cloud formation, whereas at lower levels the situation is similar to that at upper levels.

As a response to these changes in temperature and specific humidity in the analysis, there is a noticeable redistribution in ice water path (IWP) and liquid water path (LWP) at all latitudes, which can be observed in the maps of monthly averages of the differences between experimental and reference run, as shown in Fig. 6. Note especially the increase in LWP along the storm tracks and the decrease over the extratropical Pacific Ocean. IWP changes appear to have a more varied structure.

From these figures we can conclude that the assimilation of cloud optical depths has a large impact on the temperature, moisture, and cloud fields in the tropics, low-level polar regions, and upper-tropospheric regions at all latitudes. To ascertain whether this impact is positive, negative, or neutral we compare both the reference run and experiment with other assimilated observations in the 4DVAR or, when possible, with independent observations.

c. Comparisons with independent cloud observations

Comparisons in ice water content (IWC) between the reference run and the experiment were carried out using independent data retrieved from the Microwave Limb Sounder (MLS) onboard Aura (Li et al. 2005, 2007). The MLS, operational since August 2004, has five radiometers measuring microwave emissions from the earth’s atmosphere in a limb-scanning configuration to retrieve chemical composition, water vapor, temperature, and cloud ice. The retrieved parameters consist of vertical profiles on fixed-pressure surfaces having near-global (82°N–82°S) coverage. The MLS IWCs are derived from cloud-induced radiance (CIR) using modeled CIR–IWC relations based on the MLS 240-GHz measurements. The IWCs have a vertical resolution of ∼3.5 km and a horizontal along-track resolution of ∼160 km for a single MLS measurement along an orbital track. This study uses MLS version 1.51 IWCs (Livesey et al. 2005), which are similar to the IWCs discussed in Li et al. (2005). In this version, the estimated precision for the IWC measurements is approximately 0.4, 1.0, and 4.0 mg m−3 at 100, 147, and 215 hPa, respectively. These values account for combined instrument plus algorithm uncertainties associated with a single observation.

Figure 7 shows a global map of the MLS IWC field at 215 hPa and the corresponding fields from the reference run and the cloud assimilation experiment. Percentage differences between MLS retrievals and model fields are also shown. From these it is possible to see qualitatively that the IWC from the cloud assimilation experiment is closer to the MLS observations than the reference run, particularly over the equatorial west Pacific. In general, assimilation of MODIS optical depths tends to reduce the values of 215-hPa IWC where these were high in the reference run. The signature of the intertropical convergence zone (ITCZ) is improved in the Atlantic and the Indian Oceans and, to a lesser extent, over the central Pacific.

This result indicates that the cloud observations are effective in modifying the distribution of total tropospheric condensate in a manner that appears consistent with the MLS observations. Note, for example, the pattern of mostly decrease in LWP and IWP in the experimental run between 5° and 10°N over Indonesia in Fig. 6 where the reference run showed a positive bias in IWC at 215 hPa with respect to the MLS observations (Fig. 7).

d. Comparisons with temperature and moisture-related observations

This section shows a series of plots that compare the reference and the experiment analyses with observations. The comparison focuses on the tropics as this region appears to be greatly affected by the cloud assimilation (see impact plots of section 4b). However, similar trends are also seen for other regions.

Figure 8 shows statistics for Meteosat brightness temperature (Tb) observations over the tropics in the water vapor channel. These observations are not included in the minimization and can be considered an independent source of validation for the first guess and analysis. The shape of the first-guess and analysis departures for this Meteosat channel shows a positive impact of the inclusion of cloud data. The mean of the first-guess departures for the reference is 0.626 as opposed to 0.533 for the cloud assimilation experiment, indicating a better agreement of the background with the observations. For the analysis, this mean value of departures is still lower for the cloud assimilation experiment (0.723 versus 0.806 for the reference). However, these mean values are larger than those of the first-guess departures indicating a slight shift of both analyses from these observations that were not assimilated.

Figure 9 displays comparisons of the first-guess (background) and analysis departures averaged over the whole month with respect to High-Resolution Infrared Radiation Sounder (HIRS) Tb observations in the tropics. These observations were included in the assimilation. Bias with respect to HIRS observations is lower in the cloud assimilation experiment, particularly for channels 14 and 15. The bias correction applied to the observations and now estimated on-line within the 4DVAR assimilation (Dee 2004; Auligné et al. 2007) is also reduced for most of the channels. This reduction is more significant for channels 11 and 12 in the case of cloud assimilation experiment with respect to the reference run (black and gray dashed lines in the plot), indicating that the model configuration with assimilated cloud data had a lower bias with respect to the HIRS observations. However, the standard deviation with respect to HIRS observations is not particularly improved in the humidity channels (11 and 12).

The adjustments in humidity induced by the cloud assimilation also have an impact on the clear-sky Tb by providing information on the total column water vapor (TCWV). This impact, however, is not always positive, as shown in Fig. 10. In this figure, bias and standard deviation with respect to the SSM/I clear-sky Tb observations in the tropics are displayed. In this case, it is the reference run that performs slightly better than the cloud assimilation experiment and the standard deviation of the reference run is smaller than that of the cloud assimilation experiment. The bias correction for the observations is smaller in the reference for some channels, indicating an overall better agreement between observations and first guess. However, the two analyses are almost identical in terms of final bias. Comparisons with TCWV derived from rain-affected SSM/I Tb largely confirm the same behavior.

However, we observed that there are virtually no differences of bias and standard deviation between the reference and the experimental runs when looking at a sensor that is more sensitive to temperature [e.g., the Advanced Microwave Sounding Unit (AMSU-A)].

The performance of two experiments is also compared in terms of relative humidity to radiosonde (“TEMP”) observations. Figure 11 shows bias and standard deviation of first guess and analysis for the control and the cloud assimilation experiment with respect to relative humidity based on temperature and humidity measurements. The analysis obtained from the experiment shows a lower bias with respect to the reference run, especially in the lower troposphere (1000 to 700 hPa). This happens, however, at the expense of the standard deviation, which is degraded in the analysis from the cloud assimilation experiment with respect to the reference run.

Overall these results show that the assimilation of cloud observations tends to affect the moisture balance in a slightly negative way. The assimilation experiment performs neutrally or worse than the reference run when compared with other assimilated observations from moisture-sensitive instruments, except for the positive impact shown in the comparison with the Meteosat data. The behavior in temperature is mostly neutral.

5. Impact of the cloud assimilation on the forecast

a. Standard meteorological scores

The root-mean-square error, computed with respect to observations, is used as a measure to quantitatively compare the ten-day forecast from the reference run to that from the experiment that included cloud observations in the analysis. Figure 12 shows the mean RMS, averaged over the whole month of April, as a function of forecast day for temperature at two levels, 500 and 850 hPa respectively, for the Northern Hemisphere, Southern Hemisphere, and tropics. The impact of the assimilated cloud data on the Northern Hemispheric temperature is neutral, with the two lines almost overlapping both at 500 and 850 hPa. For the Southern Hemisphere, the impact on temperature at 850 hPa is neutral up to forecast day 6. After that, the control run shows a lower RMS than the cloud assimilation experiment. A similar behavior is observed in the tropics at 850 hPa with a slightly negative impact of the cloud assimilation on the forecasts. At 500 hPa and for short-term forecasts (day 1 to 4), the cloud assimilation experiment shows an overall lower RMS than the control.

A similar impact of the assimilated cloud data on the forecast is shown in Fig. 13, but this time for the wind variable at 700 and 850 hPa. The impact of the assimilation is neutral in the Northern Hemisphere, slightly positive in the tropics, and neutral to negative in the Southern Hemisphere.

Generally, the tropics appear to be more influenced by the assimilation of cloud data than other areas, as already emphasized. The significance of this impact in the tropics is shown in Fig. 14 for temperature and wind RMS errors at the selected pressure levels over the period of 10 days. Statistical significance tells us how likely we would be to get differences between the groups that are being sampled (in our case, the difference between RMS errors of two different experiments) that are as large as or larger than those we observe. The chosen confidence level 90% indicates that the probability of the observed behavior being due to pure chance is less than 10% (or there is 90% chance of observed behavior being true). The difference between two samples is computed as RMS of the reference run minus RMS of the experimental run, so a positive impact coming from the assimilation of cloud observations is marked by positive values, while the opposite is true for negative values. An inspection of the significance plots indicates that the impact of the cloud assimilation in the tropics is: 1) positive for tropical mid-troposphere (500 hPa) temperature at the beginning of the forecast period, and neutral for later in the forecast, 2) slightly negative for lower troposphere (850 hPa) temperature over the whole period, and 3) neutral for wind.

b. Comparisons with independent radiation and precipitation observations

One-day forecasts produced from the reference run and from the run with assimilation of cloud optical depths were compared to sets of different independent observations. Figure 15 shows some of the results for the shortwave and longwave cloud forcings (SWCF and LWCF, respectively) at the top of atmosphere (TOA) and for precipitation averaged over the tropical belt between 20°N and 20°S for April 2006. The TOA radiative forcings obtained from the model runs were compared against the Clouds and the Earth’s Radiant Energy System (CERES) products (Wielicki et al. 1996). The surface precipitation was compared to the version 2 of combined precipitation dataset of the Global Precipitation Climatology Project (GPCP). There is an obvious improvement in the cloud forcing of shortwave radiation (Fig. 15a), which is more significant over the Indian and Pacific Oceans where improvements in IWC were also observed (Fig. 7). Impact of the cloud assimilation on the TOA longwave cloud forcing (Fig. 15b) is close to neutral or very slightly negative in some areas. This suggests that the assimilation of cloud optical depths led to modifications of the cloud thickness rather than the cloud height. It is apparent that surface precipitation accumulated over the first day of forecast (Fig. 15c) obtained from the experimental run is overall closer to the observations than in the case of the reference run. The largest positive impact is observed over the Pacific Ocean.

6. Discussion and conclusions

In this study, we used the ECMWF 4DVAR system to assimilate, for the first time on a global scale, MODIS cloud optical depth observations. The version of the 4DVAR included new linearized moist physics schemes that allow the treatment of cloud fields in the minimization. As the cloud variables are not part of the control vector, the increments that come from the cloud departures are translated into increments in temperature and specific humidity via the adjoints of the moist physics schemes. MODIS optical depths over ocean were added to the ECMWF observation database for the month of April 2006. Experiments were conducted to assert the technical feasibility of the cloud assimilation, to monitor the optical depth bias in the background fields, and to find the most suitable model configuration for this type of exercise. A bias correction as a function of optical depth was implemented and a logarithmic variable was used to limit the range of optical depth departures. Results show that this bias correction worked only partially and needs to be revised in future studies. Despite the residual first-guess bias, the analysis is shown to draw closer to the observations and to improve slightly the correlation between model and observed optical depth.

Results for the month of April 2006 show a positive impact of the cloud observations on the distribution of the ice water content, particularly in the tropics, as shown by comparisons with the Microwave Limb Sounder retrievals. However, comparisons with other assimilated observations show that the changes in specific humidity and TCWV induced by the assimilation of MODIS cloud optical depth retrievals do not always improve the analysis fit to the observations. For sensors such as SSM/I, the reference run performs better than the cloud assimilation experiment, indicating an imbalance in TCWV caused by the introduction of the cloud observations. The impact on temperature appears to be more neutral. This behavior is not entirely inconsistent with the improvements in IWC described above. In fact, especially at the tropics, at upper-tropospheric levels, changes in the cloud fields can be achieved by small changes in temperature. Hence, even if the moisture field is affected in a slightly negative way, the cloud fields are better forecast when the cloud observations are assimilated because of temperature changes.

The impact of the cloud assimilation on the ten-day forecast, as investigated using the RMS and the significance plots, appears to be positive for upper-level temperature in the tropics, more significantly at the beginning of the forecast period. The impact is neutral for the model winds.

These results show that the ECMWF 4DVAR is approaching the level of technical maturity that is necessary for global assimilation of cloud-related information. Crucial ingredients like efficient and accurate linearized moist parameterization schemes and improved dynamically and physically dependent vertical motion in the background error covariances are necessary. In addition, improvements in several areas are still required. For example, alternatives to the current interpolation method could ensure a better representativeness of the model cloud optical depths. At present, the cloud IWC and LWC are interpolated to the observation locations as usually done in the operational data assimilation system. While this procedure might be satisfactory for more homogenous fields such as temperature, it might be less appropriate for cloud variables. In acknowledgment of this problem, an interpolation method for the assimilation of rainy radiances, based on weighing the contributions from all observations within a specific radius according to the distance from the model grid point, is under investigation. This solution might also be beneficial for the cloud optical depth.

Improved parameterizations for the optical depth observation operator will allow better use of the data, especially over land. In the current study, it was found that the optical depth bias over land was larger than over ocean. It is known that cloud optical depth parameterizations take into account the fact that effective particle size is larger and number concentration is smaller over ocean than over land due to the presence of fewer cloud condensation nuclei. To account for this, two sets of parameters for land and ocean are used in the cloud optical depth parameterization. These parameters could still be tuned to better match the observed optical depths. This could be addressed in a future study.

Developments in the inclusion of a total water variable in the control vector will also help in exploiting the information contained in the cloud observations. The current assimilation system uses humidity in the form of normalized relative humidity (Hólm et al. 2002), temperature, surface pressure, vorticity, and divergence as control variables. The linearized large-scale and convection schemes transfer increments derived from cloud observations into increments in the control variables. In this way, the contribution from cloud observations is included only indirectly in the 4DVAR. With the introduction of a total water variable, the link between cloud-related observations and control variables will become more direct, possibly avoiding problems in the redistribution of moisture increments between saturated and subsaturated regions and hence improving the impact of the cloud data.

Furthermore, the use of weak-constraint 4DVAR to account for model systematic errors could also help with the problems emphasized in the changes in moisture induced by the cloud observations. At present the model is assumed to be error-free and in the context of the incremental 4DVAR only small departures from the model state are allowed (Andersson et al. 2005). Moreover, the whole 4DVAR system is somewhat “tuned” to clear-sky observations, which represent the vast majority of observations integrated in the assimilation. When cloud observations are introduced the model background is perturbed and large increments in the control variables might occur. However, since there is no inclusion of model error, the system is not designed to deal with these large departures that are in contrast with the underlying assumption of the incremental 4DVAR. The lack of treatment of model error in the 4DVAR is highlighted by the introduction cloud observations, as model error is likely to be larger for this type of model field rather than for more homogenous fields such as temperature and humidity.

Improvements notwithstanding, this study demonstrates the feasibility of global cloud assimilation in a numerical weather prediction model. The technical developments described in this paper pave the way for future assimilation of cloudy radiances, which in turn will allow a more comprehensive exploitation of satellite data.

Acknowledgments

Thanks to Philippe Lopez and Jean-Jacques Morcrette (ECMWF) for their invaluable contributions to this study. Peter Bauer and Erik Andersson (ECMWF) are acknowledged for providing suggestions for improvement of earlier versions of the manuscript. We are grateful to Allegra B. Korch for her patience when working on this paper. Many thanks also to Duane Waliser and Frank Li (Jet Propulsory Laboratory, USA) for providing the comparison plots for the MLS data. The monitoring plots were kindly provided by Gerald Vander Grijn (ECMWF). We also would like to thank the two anonymous reviewers for instructive suggestions. We would like to acknowledge Steve Platnick (NASA) for his help with MODIS data. Data for MODIS optical depth collection 5 were downloaded from the LAADS distribution site (http://ladsweb.nascom.nasa.gov). The GPCP combined precipitation data were developed and computed by the NASA Goddard Space Flight Center’s Laboratory for Atmosphere as a contribution to the GEWEX Global Precipitation Climatology Project.

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APPENDIX

Parameterization of Cloud Optical Depth

The optical depth of liquid water clouds is computed following Slingo (1989) as
i1520-0493-136-5-1727-ea1
where LWP is the liquid water path in g m−2 and reLC (μm) is the droplet effective radius. For 0.55 μm, the value of coefficient a is 2.838 × 10−2 m2 g−1 and b is equal to 1.3 μm m2 g−1. The effective radius of cloud droplets is parameterized as in Martin et al. (1994),
i1520-0493-136-5-1727-ea2
and it is constrained to be in the interval between 4 and 16 μm. In the above equation, LWC is the liquid water content in g m−3, ρw is the density of liquid water (106 g m−3), and NTOT (cm−3) is the total droplet concentration, while k is defined as (1 + d2)3/(1 + 3d2)2. In maritime areas, d = 0.33 and NTOT is defined as
i1520-0493-136-5-1727-ea3
with A representing number concentration of cloud condensation nuclei and being set to 50 cm−3. In the continental areas, d = 0.43 and
i1520-0493-136-5-1727-ea4
where A has the value of 900 cm−3.
For ice clouds, the parameterization of Fu (1996) is used for the optical depth,
i1520-0493-136-5-1727-ea5
where IWP is the ice water path in g m−2 and Dge (μm) is the generalized effective size. The values of coefficients a1 = −0.303 108 × 10−4 and a2 = 2.518 05 are used for the spectral limit of 0.55 μm, and Dge is related to the ice particle effective radius as
i1520-0493-136-5-1727-ea6
The effective dimension of the cloud ice particles is diagnosed from temperature using a revision of the formulation of Ou and Liou (1995). The following parameterized polynomial relationship derived from a statistical procedure is used:
i1520-0493-136-5-1727-ea7
where c0 = 326.3, c1 = 12.42, c2 = 0.197, and c3 = 0.0012. The value of reIC is restricted to an interval of 〈30, 60〉 μm, and TC (°C) is defined as TC = min(−23, T − 273.16), with T being air temperature in K.

Fig. 1.
Fig. 1.

Flowchart describing the interaction between the linearized moist parameterization schemes and the optical depth scheme in the context of the standard 4DVAR minimization problem. See text for explanations.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 2.
Fig. 2.

Probability distribution functions of first-guess departures in logarithmic optical depth (unitless): (a) before bias correction and (b) after bias correction.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 3.
Fig. 3.

Bias in logarithmic optical depth as a function of the model logarithmic optical depth. See text for explanations.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 4.
Fig. 4.

Scatterplot of (a) first guess before applying bias correction, (b) first guess after bias correction was applied, and (c) analysis vsobservations of logarithmic optical depth (unitless). The color bar represents the population in each bin of logarithmic optical depth.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 5.
Fig. 5.

Zonal differences in (left) temperature (K) and (right) specific humidity (g kg−1) analyses between experimental and reference run averaged over the month and plotted as a function of pressure (hPa).

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 6.
Fig. 6.

Horizontal maps of the differences (kg m−2) of integrated (a) liquid water path and (b) ice water path between experimental and reference run averaged over the month. (c), (d) Zoom over the warm pool area corresponding to (a) and (b), respectively. Shading with solid lines represents positive values.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 7.
Fig. 7.

Maps of ice water content at 215 hPa: (top) MLS retrievals, (left) reference run, and (right) cloud assimilation experiment. Units of IWC are mg m−3. (bottom) The relative percentage error with respect to the MLS retrievals of the reference run and the cloud assimilation experiment, respectively. Plots are courtesy of Frank Li, Jet Propulsory Laboratory.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 8.
Fig. 8.

Statistics for Meteosat Tb observations in the water vapor channel over the tropics. Reference run is in gray and experiment in black. Statistics for the (left) background departure and (right) analysis departure. Statistical values are displayed for the reference run (in brackets) and for the experiment on the top of each panel.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 9.
Fig. 9.

(left) Standard deviation and (right) bias of the background (solid line) and analysis (dotted line) departures from the HIRS brightness temperature observations in the tropics. Reference run is in gray and experiment in black. Dashed black and gray lines indicate the estimated bias correction for the HIRS observations for the cloud assimilation experiment and the reference run, respectively.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 10.
Fig. 10.

Same as Fig. 9, but for SSM/I clear-sky Tb observations.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 11.
Fig. 11.

Same as Fig. 9, but for relative humidity based on TEMP temperature and humidity measurements.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 12.
Fig. 12.

The RMS errors of (top) 500- and (bottom) 850-hPa temperature for a set of 30 forecasts compared to the observations. Control experiment based on the operational cycle (gray dashed line) and experiment with 4DVAR of cloud optical depth (black solid line). Areas shown are (left) Northern Hemisphere, (middle) Southern Hemisphere, and (right) tropics.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 13.
Fig. 13.

Same as Fig. 12, but for the RMS errors of 700- and 850-hPa vector wind.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 14.
Fig. 14.

Significance of the impact coming from the assimilation of MODIS cloud optical depths in 4DVAR system for the period of April 2006 in the tropics. The forecasts are compared with respect to the observations for 30 cases and significance is based on RMS error differences. The significance is displayed for (top) 850- and 500-hPa temperature and (bottom) 850- and 700-hPa vector wind. The y axis shows the RMS change (the difference between RMS of the reference run minus RMS of the experimental run) normalized by the mean RMS of two experiments (range from −30% to 30%).

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

Fig. 15.
Fig. 15.

One-day forecasts produced from the reference run (black dotted line) and from the run with assimilation of cloud optical depths (black solid line) compared to the observations (gray line), all averaged over the tropical belt between 20°N and 20°S for April 2006. Comparisons of the TOA (a) shortwave and (b) longwave cloud forcings to the CERES products and (c) surface precipitation to the GPCP Version 2 dataset.

Citation: Monthly Weather Review 136, 5; 10.1175/2007MWR2240.1

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