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  • View in gallery
    Fig. 1.

    COAMPS nesting domains of 81-, 27-, and 9-km grids, centered on the ARM SGP site. The 81-km grid is also the 18-km grid domain for the CONUS simulation in section 5.

  • View in gallery
    Fig. 2.

    Scatterplots of shortwave downward fluxes at surface of the 9-km grid vs observation at ARM SGP site, 20 to 27 Sep 2002 at 3-min intervals: (a) Fu–Liou 8-day simulation; (b) standard model 8-day simulation; (c) Fu–Liou 120-h forecast; and (d) standard model 120-h forecast.

  • View in gallery
    Fig. 3.

    Same as Fig. 2, but for longwave downward fluxes.

  • View in gallery
    Fig. 4.

    Charts of (a) bias errors and (b) RMS errors for COAMPS surface radiative fluxes on the 9-km grid by Fu–Liou model with cloud effective radii from FL01 to FL09 and COAMPS STD from 21 Oct to 4 Nov 2002 at ARM SGP site. Red dashed circles mark the smallest errors and black dashed ovals mark the largest errors of each category.

  • View in gallery
    Fig. 5.

    Bias error profiles for (a) January and (b) July of air temperature on standard pressure levels at 0-, 24-, 48-, and 72-h forecasts in 18-km CONUS domain verified with raob soundings: dashed lines for STD, heavy solid lines for FL4, and light solid lines for FL2.

  • View in gallery
    Fig. 6.

    Same as Fig. 5, but for RMS error.

  • View in gallery
    Fig. 7.

    Profiles of modeled (a) cloud water content and (b) radiative heating rates, averaged over the 18-km CONUS grid for July for the 24-, 48-, and 72-h forecasts.

  • View in gallery
    Fig. 8.

    Same as Fig. 5, but for dewpoint temperature bias error.

  • View in gallery
    Fig. 9.

    Same as Fig. 5, but for dewpoint temperature RMS.

  • View in gallery
    Fig. 10.

    (a) Bias error and (b) RMS error of the 2-m air temperature from the STD, FL4, and FL2 from 0- to 72-h forecasts on the 18-km CONUS grid; (c) bias error and (d) RMS error of sea level pressure from STD, FL4, and FL2. All plots are valid for January.

  • View in gallery
    Fig. 11.

    Same as Fig. 10, but for July.

  • View in gallery
    Fig. 12.

    Modeled shortwave and longwave radiative heating rates for the surface air layer by STD and FL4 for the 6–72-h forecasts, averaged over the 18-km CONUS domain in (a) January and (b) July.

  • View in gallery
    Fig. 13.

    Modeled IWP and LWP by STD and FL4 for the 0–72-h forecasts, averaged over the 18-km CONUS domain in (a) January and (b) July. The 6–72-h averages of IWP and LWP are also listed, with reductions by FL4 as 19% of IWP and 28% of LWP in (a) and 21% of IWP and 44% of LWP in (b).

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On the Improvement of COAMPS Weather Forecasts Using an Advanced Radiative Transfer Model

Ming LiuNaval Research Laboratory, Monterey, California

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Jason E. NachamkinNaval Research Laboratory, Monterey, California

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Douglas L. WestphalNaval Research Laboratory, Monterey, California

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Abstract

Fu–Liou’s delta-four-stream (with a two-stream option) radiative transfer model has been implemented in the U.S. Navy’s Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) to calculate solar and thermal infrared fluxes in 6 shortwave and 12 longwave bands. The model performance is evaluated at high resolution for clear-sky and overcast conditions against the observations from the Southern Great Plains of the Atmospheric Radiation Measurement Program. In both cases, use of the Fu–Liou model provides significant improvement over the operational implementation of the standard Harshvardhan radiation parameterization in both shortwave and longwave fluxes. A sensitivity study of radiative flux on clouds reveals that the choices of cloud effective radius schemes for ice and liquid water are critical to the flux calculation due to the effects on cloud optical properties. The sensitivity study guides the selection of optimal cloud optical properties for use in the Fu–Liou parameterization as implemented in COAMPS. The new model is then used to produce 3-day forecasts over the continental United States for a winter and a summer month. The verifications of parallel runs using the standard and new parameterizations show that Fu–Liou dramatically reduces the model’s systematic warm bias in the upper troposphere in both winter and summer. The resultant cooling modifies the atmospheric stability and moisture transport, resulting in a significant reduction in the upper-tropospheric wet bias. Overall ice and liquid water paths are also reduced. At the surface, Fu–Liou reduces the negative temperature and sea level pressure biases by providing more accurate radiative heating rates to the land surface model. The error reductions increase with forecast length as the impact of improved radiative fluxes accumulates over time. A combination of the two- and four-stream options results in major computational efficiency gains with minimal loss in accuracy.

Corresponding author address: Ming Liu, Naval Research Laboratory, 7 Grace Hopper Ave., Stop 2, Monterey, CA 94943. Email: ming.liu@nrlmry.navy.mil

Abstract

Fu–Liou’s delta-four-stream (with a two-stream option) radiative transfer model has been implemented in the U.S. Navy’s Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS) to calculate solar and thermal infrared fluxes in 6 shortwave and 12 longwave bands. The model performance is evaluated at high resolution for clear-sky and overcast conditions against the observations from the Southern Great Plains of the Atmospheric Radiation Measurement Program. In both cases, use of the Fu–Liou model provides significant improvement over the operational implementation of the standard Harshvardhan radiation parameterization in both shortwave and longwave fluxes. A sensitivity study of radiative flux on clouds reveals that the choices of cloud effective radius schemes for ice and liquid water are critical to the flux calculation due to the effects on cloud optical properties. The sensitivity study guides the selection of optimal cloud optical properties for use in the Fu–Liou parameterization as implemented in COAMPS. The new model is then used to produce 3-day forecasts over the continental United States for a winter and a summer month. The verifications of parallel runs using the standard and new parameterizations show that Fu–Liou dramatically reduces the model’s systematic warm bias in the upper troposphere in both winter and summer. The resultant cooling modifies the atmospheric stability and moisture transport, resulting in a significant reduction in the upper-tropospheric wet bias. Overall ice and liquid water paths are also reduced. At the surface, Fu–Liou reduces the negative temperature and sea level pressure biases by providing more accurate radiative heating rates to the land surface model. The error reductions increase with forecast length as the impact of improved radiative fluxes accumulates over time. A combination of the two- and four-stream options results in major computational efficiency gains with minimal loss in accuracy.

Corresponding author address: Ming Liu, Naval Research Laboratory, 7 Grace Hopper Ave., Stop 2, Monterey, CA 94943. Email: ming.liu@nrlmry.navy.mil

1. Introduction

Solar and thermal infrared radiation is a fundamental mechanism for driving the energy exchange among air mass, clouds, aerosols, and land surface to maintain the thermal and dynamic systems in the atmosphere. The accurate prediction of atmospheric radiative processes, particularly cloud–radiation interaction, highly depends on the accurate calculation of radiative transfer fluxes (i.e., radiative transfer parameterizations). It has been well recognized that radiation modeling is not only a major component of global circulation and climate models, where long-term radiative balance affects the general circulation, but also in regional weather forecasting models, where substantial spatial and temporal variations of clouds and aerosols make the effects of radiative interactions critical to weather changes.

The U.S. Navy maintains an operational mesoscale model known as the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS1) developed by the Naval Research Laboratory (NRL; Hodur 1997). The Fleet Numerical Meteorology and Oceanography Center (FNMOC) conducts operational COAMPS forecasts for dissemination to the general defense community (https://www.fnmoc.navy.mil). COAMPS currently employs an explicit microphysical scheme based on the Rutledge and Hobbs (1983) parameterization. Radiation is calculated from the high-speed radiative transfer model developed by Harshvardhan et al. (1987, 1989). COAMPS forecasts frequently exhibit positive temperature and moisture biases in the upper troposphere and negative temperature biases near the surface for many of the operational regions around the world. Factors contributing to the formation of these biases may include cloud–radiation interactions, bulk microphysics, vertical moisture advection, subgrid-scale turbulent mixing, and the land surface model. Since radiative transfer is involved in many of these processes, this paper presents an examination of the COAMPS standard radiation parameterization (Harshvardhan 1987, 1989) and an evaluation of a new advanced radiation parameterization in an effort to improve COAMPS. The standard model uses a two-stream scattering-absorption approximation for solar radiation, but neglects cloud scattering for thermal infrared (IR) radiation. The cloud optical property parameterization has no size dependence. This simplification increases the computational efficiency for weather forecasts and climate studies by speeding up flux calculations with a simplified cloud–radiation interaction and a coarse spectral resolution.

Computational power has grown rapidly in terms of the number of clustered processors, internal memory, and processor speed, and computational limits are becoming less stringent to the operational forecasting environment. As such, use of a higher-order accurate radiative transfer model has become more practical. Furthermore, a fully coupled in-line mineral dust aerosol module with multiple size bins and comprehensive microphysics using a high-resolution dust source database (Liu et al. 2003) has been developed for COAMPS. The coupled system is currently used for operational dust forecasting in southwest Asia at FNMOC as a part of the weather forecasts (Liu et al. 2007). The inclusion of aerosol particles in COAMPS requires the modeling of aerosol–radiation interactions in order to account for the direct and semidirect impacts of aerosols on dynamics changes. An advanced radiative transfer model that is capable of calculating the optical properties of aerosol species in addition to clouds has become necessary for COAMPS. The standard Harshvardhan radiation package lacks such a capability.

In response to these needs, a high-order accurate broadband radiative transfer model was recently implemented into COAMPS. The model details can be found in Liou et al. (1988) and Fu and Liou (1992, 1993). The new radiation parameterization or model is named Fu–Liou in the following discussions to distinguish it from the COAMPS standard model. Fu–Liou uses a four-stream (with a two-stream option) scattering-absorption approximation for both the solar and IR radiation with a delta function to correct strong forward scattering from large cloud and aerosol particles. It calculates spectral-dependent and species-dependent optical properties to achieve accurate radiative fluxes in clear, cloudy, and aerosol-laden atmospheres. Fu–Liou’s model has been extensively used and upgraded in many radiation studies (Tegen and Lacis 1996; Fu 1996; Fu et al. 1997, 1998b; Kratz and Rose 1999; Rose and Charlock 2002; Gu et al. 2003; Kato et al. 2005).

The objective of the present research is to improve COAMPS forecasts, in particular by reducing the air temperature and moisture biases, through the implementation of the Fu–Liou radiation model. We also wish to explore its potential for operational applications. In section 2, COAMPS is briefly described along with the new radiation model. In section 3, the new radiation model is verified against observations in a clear-sky case. In section 4, it is evaluated in cloudy and overcast conditions using various parameterizations of cloud optical properties. In section 5, bias reduction is studied using 3-day forecasts for the conterminous U.S. (CONUS) domain in a winter and a summer month. Section 6 presents a summary including a discussion of the computational costs. In these sections, the Fu–Liou model is always compared with the standard COAMPS radiation scheme.

2. Model description

COAMPS is a state-of-the-art dynamical model with multiple grid nests and two-way nest interaction. It is nonhydrostatic and compressible, and applied in a terrain-following sigma vertical coordinate with staggered grids in both horizontal and vertical directions. It predicts turbulent kinetic energy (TKE) to obtain eddy exchange coefficients for subgrid-scale diffusion, and uses a force-restore method in the surface energy budget to calculate boundary fluxes. It contains explicit cloud microphysics to predict five cloud species: liquid water, ice, rain, snow, and graupel, with each species simulated in a bulk-size approach. The Kain–Fritsch convective parameterization (Kain and Fritsch 1993) is applied to grids with horizontal spacing over 10 km. Ozone mixing ratio is prescribed as a function of latitude, height, and time based on climate data. The complete details of the model structure, dynamics, and physics can be found in Hodur (1997) and Chen et al. (2003). Operationally, data assimilation is performed at 6-h intervals using the 6-h forecast as a first guess. Lateral boundary conditions are supplied from the Navy Operational Global Atmospheric Prediction System (NOGAPS; Hogan and Rosmond 1991).

The COAMPS standard Harshvardhan radiation model has a coarse spectral resolution of three shortwave bands (wavelength 0.2–4.0 μm) and five longwave bands (4–50 μm). Solar scattering by clouds is prescribed with a constant single scattering albedo of 1.0 in the nonabsorbing spectrum (wavelengths <0.9 μm) and 0.99 elsewhere. A constant asymmetry factor of 0.85 is assumed over the entire spectrum. Cloud optical depth is linearly proportional to the pressure thickness of cloud layer and the mean cloud-layer temperature (Platt and Harshvardhan 1988), while the cloud longwave emissivity depends on the optical depth of cloud layer. Therefore, the cloud–radiation interaction is modeled based on a simple droplet size independent parameterization.

The newly implemented Fu–Liou radiative transfer model calculates nongray gaseous absorption in the multiple-scattering inhomogeneous atmosphere using a correlated-k distribution method of probability integration developed by Fu and Liou (1992). The principal absorbing gases are H2O, CO2, CH4, N2O, and O3. The solar and IR spectra are divided into 18 bands according to the locations of the absorption: 6 solar wavelength bands (0.2–0.7, 0.7–1.3, 1.3–1.9, 1.9–2.5, 2.5–3.5, and 3.5–4.0 μm) and 12 thermal IR wavenumber bands (2200–1900, 1900–1700, 1700–1400, 1400–1250, 1250–1100, 1100–980, 980–800, 800–670, 670–540, 540–400, 400–280, and 280–10 cm−1). The cloud particle optical properties used to solve the radiative transfer equation are volume extinction coefficient (βext), scattering coefficient (βsca), single scattering albedo (ω), and asymmetry factor (g). These parameters are defined as
i1520-0434-24-1-286-e21
i1520-0434-24-1-286-e22
i1520-0434-24-1-286-e23
i1520-0434-24-1-286-e24
where r is particle radius, k = 2πλ−1, λ is the wavelength, n(r) is the cloud droplet size distribution, and Qext and Qsca are the extinction and scattering efficiencies calculated from Mie theory by integrating over the particle sizes of interest. The parameter μ is the cosine of the scattering angle, p(μ) is the phase function, and g represents the particle average scattering direction. Another important parameter is cloud effective radius Re, theoretically defined as the ratio of the third to the second moment of the size distribution. Also, β (e.g., βext), ω, and g can be calculated empirically as functions of cloud water and effective radius Re. Following Fu and Liou (1993), the optical parameters of ice crystals are parameterized using ice water content (IWC), cloud weighting factor (frc), and ice effective radius (Rice) in the forms
i1520-0434-24-1-286-e25
i1520-0434-24-1-286-e26
i1520-0434-24-1-286-e27
where coefficients an, bn, and cn are determined by numerically fitting the detailed calculations of scattering and absorption for a range of ice crystal shape and size distributions in an effective range of Rice from 10 to 120 μm. Here, N = 2 is sufficient. For cloud water droplets in the shortwave spectrum, β, ω, and g are parameterized with liquid water content (LWC) and cloud effective radius (Rcld) for liquid water following Hu and Stamnes (1993):
i1520-0434-24-1-286-e28
i1520-0434-24-1-286-e29
i1520-0434-24-1-286-e210
where coefficients a1, a2, a3, b1, b2, b3, c1, c2, and c3 are constants at a given wavelength obtained by a least squares fit to the Mie scattering from cloud droplets with explicit gamma size distributions. In the longwave spectrum, eight water cloud types are defined based on cloud droplet shapes, sizes, and refraction indices (Fu 1996; Fu et al. 1998b). Each cloud type is characterized by the mean optical properties for a spectral band. Then β, ω, and g are obtained by interpolating the mean scattering values from the eight cloud types as weighted by LWC and Rcld.

The weighting factor frc in Eqs. (2.5) and (2.8) of cloud optical depth calculation is a cloud coverage fraction (e.g., the percentage of cloud volume in a grid box). It is used to scale the grid-resolved cloud water contents LWC and IWC to account for subgrid-scale cloud effects in the cloud optical properties. The fraction calculation follows Slingo (1987): nonconvective cloud fraction is a function of relative humidity, temperature, and pressure, while convective cloud fraction is a function of convective rainfall. Using such cloud fractions is a simple and easy method, but does not address the highly detailed complexity of cloud geometry and phase. Clouds are assumed to randomly overlap in the vertical in this study. This assumption has been used in the standard radiation model of COAMPS because COAMPS has relatively high resolutions and it resolves cloud physics. The alternative maximum-random overlap will be tested in the future along with cloud verifications. LWC and IWC are explicitly predicted in COAMPS, while Rcld and Rice are prescribed by cloud parameterizations as functions of LWC, IWC, and temperature. The importance of the Rcld and Rice schemes in the Fu–Liou model performance will be discussed in section 4.

To quantitatively compare the Fu–Liou model with the standard model, the bias and root-mean-square (RMS) error are calculated:
i1520-0434-24-1-286-e211
and
i1520-0434-24-1-286-e212
where F represents the model values, O represents the observations, and N is the number of data pairs, different from the one in (2.5). Bias error indicates the mean linear difference between the model and the observations. RMS error indicates the dispersion of modeled data about the observations, giving a magnitude that is quadratically weighted, thus emphasizing large errors. Another error measurement used in the scatterplots below is the linear correlation coefficient:
i1520-0434-24-1-286-e213
where F and O represent the mean values of model and observation data. The correlation determines the extent of the linear relationship between the model and the observations and ranges from −1.0 to +1.0.

3. Evaluation of Fu–Liou model for clear-sky conditions

The surface observational data from the Southern Great Plains (SGP) Atmospheric Radiation Measurement (ARM) Program, supported by U.S. Department of Energy, are used to verify the Fu–Liou model in COAMPS. The SGP site is located at 36°37′N, 97°30′W, southeast of Lamont, Oklahoma. The data consist of broadband upwelling and downwelling components of the shortwave and longwave radiative fluxes (W m−2) measured at 1-min intervals. By examining the weather reports, cloud fractions, and temporal variations in solar and IR fluxes at this site, an 8-day period from 20 to 27 September 2002 was found to have clear sky prevailing over 95% of the period. The clear-sky evaluation isolates the basic shortwave and longwave transfers for Rayleigh scattering and nongray gaseous absorption with minimal cloud influence. During this clear-sky period, the observed visibility was high and both PM10 and PM2.5 levels were low in the area. The distributions of observed downward solar fluxes over time were smooth curves, indicating little attenuation of solar radiation in the sky. The radiative effect of aerosols is therefore considered insignificant. For the cloudy–overcast sensitivity test in the next section, the radiative effect of cloud was the dominant forcing, and clouds became an aerosol scavenger. Hence, the impact of aerosols on radiation is neglected in this study.

The COAMPS model domain extends vertically to an altitude of 35 km with 51 layers ranging in thickness from 10 m at the surface to 4 km at the top. In the horizontal, the model has three nested grid meshes with the SGP site located at the center (Fig. 1). The 81-km domain (61 × 51 points) is purposely chosen to cover the upstream and downstream weather systems that might cross the SGP site. The 27-km nest (85 × 73) is a transition from the coarse grid to the fine grid. The 9-km nest (91 × 91) covers the area of interest around the SGP site. This combination of nested grids allows COAMPS to capture the multiscale features of dynamical systems. Both the Fu–Liou and standard radiation parameterizations are executed at 3-min intervals on all three nests in the following parallel COAMPS runs (sections 3 and 4) in order to maximize the use of the observational data and to verify model output at 3-min intervals. The surface radiative fluxes from the 9-km nest are verified against the SGP observations. The observed fluxes are obtained from the Solar and Infrared Radiation Station (SIRS) in the central facility, consisting of four components: longwave broadband downwelling flux, longwave broadband upwelling flux, shortwave broadband total downwelling flux, and shortwave broadband upwelling flux.

Two parallel 8-day simulations with 12-h update cycles were run from 0000 UTC 20 to 0000 UTC 28 September. Additionally, two parallel 120-h forecasts initiated at 0000 UTC 23 September and ending at 0000 UTC 28 September were generated to show the absence of drift of the model over long integration times. The modeled solar downward fluxes from the six shortwave bands for all four simulations are compared with the observations in Figs. 2a–d. The plots are created from the 3-min interval data and contain 3840 pairs for the 8-day simulation and 2400 pairs for the 120-h forecast. The statistical scores are also listed. Overall, the Fu–Liou outperforms the standard model: it produces much smaller biases and RMS errors, about 50% lower than the standard in the 8-day simulation and 40% lower in the 120-h forecast. The standard model tends to generate larger fluxes during the noon hours (Figs. 2b,d). Both models produce slightly larger errors at 120 h. However, Fu–Liou is still more accurate than the standard. On the other hand, both models show good correlation coefficients, indicating high extents of linear relationships between the models and the observations.

The downward clear-sky longwave fluxes are compared in Fig. 3. Both models predict smaller fluxes than the observations on average (negative biases) and the correlation coefficients are not as good as those of the solar fluxes in Fig. 2. The negative biases become even larger in the 120-h forecast. These flux errors result from the dependence on the analyzed and predicted temperature and water vapor fields on other physical processes in addition to the radiative transfer algorithms. The RMS errors of the longwave fluxes, however, are much smaller than those of the shortwave fluxes due to the different magnitudes of the fluxes. Again in the downward components, Fu–Liou significantly outperforms the standard: its bias and RMS errors are one-half those for the standard in both the 8-day simulation and the 120-h forecast. The improved scores can be largely attributed to the high spectral resolution of the Rayleigh scattering and nongray gas absorption in the solar and thermal IR broad bands, as well as the high-order accurate four-stream approximation in the Fu–Liou model. In contrast, the standard parameterization uses only three shortwave and five longwave bands, and uses a two-stream approximation. Since the radiative fluxes impact the model dynamics, the two parallel 120-h forecasts diverge as differences in temperature and moisture accumulate. In contrast, the 8-day runs utilize data assimilation every 12 h and therefore differences between temperature and moisture fields are lessened.

The modeled upward fluxes of both shortwave and longwave radiation at the surface not only depend on the downward fluxes of incoming radiation but also on the surface conditions. The verification against the observations becomes complicated due to the uncertainties at the surface in the model and at the observation site. The bias and RMS errors listed in Table 1 reveal that Fu–Liou exhibits improved scores compared to the standard in the 8-day simulation and the 120-h forecast. The model physical domain terminates at 35-km altitude, above which the radiative fluxes are neglected. Such flux truncations may contribute to the flux errors at the surface.

4. Evaluation in cloud–overcast conditions—Sensitivity of radiative fluxes to cloud effective radius

As described in section 2, the cloud effective radius is a key cloud parameter used to calculate cloud radiative properties: optical depth, single-scattering albedo, and asymmetry factor [Eqs. (2.5)(2.10)]. The COAMPS bulk microphysics does not output explicit particle size distributions and number concentrations, but only the cloud water contents. An appropriate effective radius parameterization scheme is therefore needed for the Fu–Liou radiative transfer model. A number of approaches are listed below. To understand the impact of the cloud optical parameters on the radiative flux calculation, we conduct sensitivity tests using various combinations of parameterized cloud and ice optical properties. Verification is done using fluxes observed at the ARM SGP site. These comparisons are used to guide the selection of the optical properties.

For cloud liquid water droplets, a 1/3 power universal law has been found to represent the relationship of cloud effective radius (Rcld) to liquid water content (Bower et al. 1994; Liu and Hallett 1997, Reid et al. 1999). According to Bower’s formula, Rcld (μm) is proportional to the ratio of LWC (g m−3) to droplet number concentration Nd (cm−3):
i1520-0434-24-1-286-e41
where Nd = 100 over ocean and Nd = 400–600 over land. In some weather and climate models, a constant Rcld is also assumed (Min and Harrison 1998; Gu et al. 2003; Black 1994; Gultepe and Isaac 2004). However, due to the irregular shapes and structures of ice crystals and their irregular size distributions, many different parameterizations for ice effective radius (Rice) have been derived from various field experiments using various methods. Following the selections of Rice schemes examined in the cloud–radiation study by Iacobellis et al. (2003), the same parameterizations are also tested with the Fu–Liou model within COAMPS:
  1. McFarlane et al. (1992), a function of ice water content only:
    i1520-0434-24-1-286-e42
  2. Suzuki et al. (1993), a function of temperature (T) only:
    i1520-0434-24-1-286-e43
  3. Ou and Liou (1995), also a function of T only:
    i1520-0434-24-1-286-e44
  4. Wyser (1998), a function of both T and IWC:
    i1520-0434-24-1-286-e45
  5. McFarquhar (2001), also a function of both T and IWC:
    i1520-0434-24-1-286-e46

A close look at these ice schemes reveals a wide variety of formulations. Sensitivity tests will be used to tell which of these approaches is more suitable to the Fu–Liou within COAMPS and to compare with the standard radiation scheme (STD) that has no cloud size dependence as described in section 2 of the model description.

Table 2 lists nine combinations of the effective size parameterizations for liquid and ice water as well as some constant Rcld and Rice parameterizations. Denoted as FL01–FL09, these combinations are used to calculate the cloud optical parameters defined in Eqs. (2.5)(2.10). In combinations FL06–FL08, Bower’s Rcld scheme is tested with cloud droplet number concentrations of 200, 400, and 600 m−3. Gultepe and Isaac (2004) found in their aircraft observational studies that cloud droplet concentration is another major parameter affecting the cloud physical and optical characteristics. A range of droplet concentrations have been applied when using Bower’s formula (Del Genio et al. 1996; Lee et al. 1997). Thus it is meaningful to examine cloud radiative effects with differing number concentrations.

The evaluation trial consists of a 15-day period of continuous cloudy–overcast skies at the SGP site from 21 October to 4 November 2002. (These results are specific to this region and season. A broader comparison is done in section 5.) Surface radiative flux measurements and the cloud fraction observations (not shown) indicate that each day was overcast or nearly so over the area. COAMPS also predicted total cloud water paths of 50–500 g m−2 throughout the period (not shown). The COAMPS horizontal and vertical domain configuration was identical to that used for the tests in section 3 (Fig. 1). Ten parallel 15-day simulations are conducted, nine of which test the Fu–Liou model with the combined cloud schemes in Table 2, with the tenth employing the standard radiation. In all simulations the radiation was called at 3-min intervals. Radiative fluxes on the 9-km grid are verified against the SGP surface flux observations at 3-min intervals for a total of 7200 measurements in 15 days. The observed fluxes are obtained from the SGP central facility, the same type of datasets as used in the clear-sky verification. Bias and RMS scores are calculated for each simulation. Downwelling and upwelling components of the solar and IR fluxes, as well as the net radiative flux, are scored for day (solar zenith angle >0.0) and night separately. The statistical scores are grouped in a total of 16 categories shown in Fig. 4: 8 bias and 8 RMS categories with red dashed circles marking the smallest errors and black dashed ovals marking the largest errors of each category.

We assume that negative and positive biases are equally detrimental to cloud radiation physics. Figure 4 reveals that the FL02 (Bower Rcld and constant Rice in Table 2) produces the greatest number of minimum errors: three in the bias and three in the RMS, all during the daytime. That implies that this combination best represents the cloud scattering for solar radiation. Combination FL03 (Bower Rcld and McFarlane Rice functions of LWC only) is the most disputable, as it receives four minimum errors for the nighttime longwave radiation but five maximum errors for the daytime, implying that McFarlane Rice fails in COAMPS. The STD scheme, which neglects cloud effective radius and cloud scattering in the longwave bands, received 10 maximum errors out of the 16 categories. As in the clear-sky cases, STD overestimates the downward solar flux. The large positive bias in the net surface solar flux of STD, calculated as (SW down daytime) − (SW up daytime) in Fig. 4, implies that STD generates extra heating in the daytime, whereas the negative bias in the net surface IR flux of STD [e.g., (LW down night) − (LW up night)] implies that STD generates extra cooling at night.

A normalized error score (based on the statistics in Fig. 4) is calculated to obtain a comprehensive assessment of the 16 error types. Each type defines a relative error as
i1520-0434-24-1-286-e47
where errormin is the minimum error in a type. Then a normalized error is derived by averaging the relative errors from each combination in Table 2:
i1520-0434-24-1-286-e48
where N = 16 types. Equation (4.8) gives equal weighting to upwelling and downwelling fluxes of shortwave and longwave radiation, and equal weighting to the bias and RMS errors of fluxes in the daytime and nighttime. The normalized errors are listed in Table 3. It is clear that FL07 receives the best score (e.g., the smallest normalized error) while the STD gets the worst score as expected. FL07 maximally reduces the error of the STD by 73% [=(STD − FL07)/STD].

The results presented in Fig. 4 and Table 3 indicate that cloud effective radius schemes for ice and liquid water are critical to the flux calculation due to the effects on cloud optical properties. Constant effective radii, which are used in some models, are not always suitable but the parameterizations, as functions of LWC for Rcld and of IWC and T for Rice should be considered. Therefore, the best-scored combination scheme FL07 is chosen to be used in the Fu–Liou radiation model in the 3-day forecast evaluation in the CONUS domain described next, whose center is located at the ARM SGP site (Fig. 1). These results are valid in this particular region and this particular time period. Similar assessments of the new radiation model are being conducted at NRL for other regions of the world and different periods.

5. Evaluation of 3-day forecasts for CONUS in winter and summer months

In this section, the Fu–Liou model is tested extensively over the CONUS domain. Three-day forecasts initialized at 0000 UTC and 1200 UTC each day for the months of January and July 2006 are used to show the impact of Fu–Liou. The domain consists of two nested grids with a horizontal space of 54 km (135 × 87) and 18 km (316 × 172). The inner nest is about the size and location of the 81-km domain shown in Fig. 1, while the outer mesh covers a much larger area from 45° to 150°W and 15° to 60°N (not shown). Vertical grid spacing consists of 30 stretched layers ranging from 10 m near the surface to 6 km near domain top (∼32 km). Such grid spacing has been used at FNMOC for many years, and has achieved reliable forecasts at minimal computational expense. In keeping with operational constraints, the radiation is calculated at 1-h intervals. To spin up the model, a cold start forecast (initialized with NOGAPS background fields) begins 2 days prior to the first of each month. Thereafter, data assimilation using COAMPS 12-h forecasts as a first guess continues to the end of each month.

Fu–Liou is evaluated in two separate configurations: four-stream solar and four-stream IR radiation (FL4), and four-stream solar and two-stream IR radiation (FL2). Considering the relatively minor effects of cloud scattering compared to absorption in the longwave, Fu–Liou’s two-stream IR radiation can be a practical approach. However, due to the dominant nature of cloud scattering of direct solar radiation, the two-stream solar option is not recommended. Fu et al. (1998a) have shown that the use of two-stream solar radiative transfer causes a significant loss of accuracy in the radiative fluxes compared to the four-stream option. In summary, three parallel COAMPS forecasts using STD, FL4, and FL2 are conducted for the winter and summer months.

COAMPS forecasts of air temperature and dewpoint temperature on the inner gird of 18-km resolution at the standard pressure levels, as well as 2-m air temperature and sea level pressure, are directly compared with synoptic observations: upper-air radiosonde data (raob), available at 0000 and 1200 UTC, and surface station data, available at 0000, 0600, 1200, and 1800 UTC each day. Profiles of bias and RMS errors are calculated for the 0-, 24-, 48-, and 72-h forecasts throughout each month to illustrate the vertical dependence of these errors. (The statistical scores from forecasts initialized at 0000 UTC were very similar to those initialized at 1200 UTC, both showing opposite phased diurnal variations in the lower atmosphere and near the surface. Hence, only the forecasts from 0000 UTC, or 1600–1900 LST, are discussed below.)

a. Evaluation of the vertical distribution of air temperature

Figure 5 shows the vertical profiles of temperature bias at 0, 24, 48, and 72 h. It is clear that for all of the radiation models, COAMPS generates a warm bias in the upper troposphere reaching a maximum at 300 hPa in January. In July the warm bias is twice as large and centered near 250 hPa. A cold bias maximum is found at 150 hPa in January and at 100 hPa in July. Another cold bias is found at 925 hPa in January, but is near zero in July. Overall, FL4 and FL2 reduce the temperature bias on almost every pressure level except 700 hPa in January (Fig. 5a), and 400–500 hPa in July (Fig. 5b). The reductions by FL4 and FL2 increase with forecast length and the most significant reductions are achieved in the upper-atmospheric warm bias layers.

To further quantify the changes made by the new radiation model, the error reductions are evaluated with two linear quantities:
i1520-0434-24-1-286-e51
i1520-0434-24-1-286-e52
Table 4 shows the bias reductions on the most significant bias error levels of 300 hPa in January and 250 hPa in July from 12- to 72-h forecasts. Here we assume positive and negative biases are equally unwanted. In January, FL4 results in a 0.6° warm bias reduction or a relative reduction of 48% at 72 h. Much greater reduction is found in July as FL4 brings up to a 1.4° warm bias reduction to the error of STD.

Figure 6 is the same as Fig. 5 except that RMS errors are displayed for January and July and the RMS error reductions are also listed in Table 4. Both FL4 and FL2 produce smaller RMS errors than STD on almost all pressure levels except 500 hPa in July. FL4 achieves a maximum RMS reduction of 0.6° on 300 hPa. Still much greater RMS reductions are found in July in the upper deep warm bias layer, reaching a maximum 1.1° reduction or a relative reduction of 32% at 72 h on 250 hPa. Similar to the bias distributions, overall, the upper-air RMS reductions in FL4 and FL2 increase with forecast length in both winter and summer months, indicating that the impact of the radiation accumulates over time.

Comparing the statistical scores from FL4 and FL2 in Figs. 5 and 6, it can be seen that in January FL4 is about the same as or slightly outperforms FL2 above 700 hPa, but slightly underperforms FL2 below 700 hPa. In July, FL4 appears to be noticeably better than FL2 above 500 hPa, especially at 250 hPa, while below 500 hPa there is little difference except near 850 hPa. The slightly better performance by FL2 in very few places implies that Fu–Liou is sensitive to the cloud input between the four-stream and the two-stream algorithms. The noticeable differences in July over the high deep warm bias layer arise from the predominance of upper-tropospheric ice clouds in the summer. Optically thick clouds increase the importance of longwave scattering, and the four-stream scattering-absorption algorithm is more accurate than the two stream one. Generally speaking, the differences between FL2 and FL4 are minor compared to those from STD. The computational costs of FL4 and FL2 will be discussed in the next section.

To understand the distributions of temperature bias and RMS in the Fu–Liou and the standard parameterizations, Fig. 7 shows the profiles of cloud IWC and LWC as well as the corresponding heating rates at 24, 48, and 72 forecast hours. The profiles are obtained by averaging over the 18-km domain throughout the month of July. (January displays similar correlations between clouds and heating rate and is not presented). There are two main cloud layers: low-level clouds below 700 hPa containing liquid water only and high-level clouds from 400 to 100 hPa containing ice water only. Strong warm biases were found in the middle part of high-level cloud whereas strong cold biases were found at the top of the high cloud layer in Fig. 5b. It appears that the cloud–radiation interaction in FL4 results in less ice and liquid water content at most pressure levels. Both FL4 and STD produce radiative cooling in the upper half of the high-level cloud layer and radiative warming in the lower half of the cloud, resulting from net divergence of radiative flux gradients within the cloud. However, FL4 produces much smaller cooling and heating rates than STD does, due to the smaller vertical gradients in ice water, and this likely explains how Fu–Liou reduces the bias and RMS errors from 400 to 100 hPa (Figs. 5, 6). Furthermore, the reduced cloud water in FL4 results in a reduced cloud albedo that further reduces cooling at 150–100 hPa. In the lower atmosphere and near the surface, FL4 produces much stronger warming rates than STD (Fig. 7b), which helps to reduce the cold bias below 850 hPa in Fig. 5b as FL4 shows smaller errors than STD there.

b. Evaluation of vertical distribution of dewpoint temperature

Dewpoint temperature is directly compared with the observations in this part of the evaluation, rather than relative humidity, which is temperature dependent. Radiative transfer processes can modify the moisture distribution through direct and indirect circulations resulting from heating or cooling of the air. Additionally, the modified atmospheric stability alters the vertical turbulent transport of moisture. All processes influence moisture redistribution and can thus change the bias and RMS.

Figures 8a,b show the bias profiles of dewpoint temperature at 0, 24, 48, and 72 h for January and July, respectively. Table 5 lists the dewpoint error reductions by FL4 on the most significant bias error levels at these lead times. COAMPS predicts a positive bias at most heights, especially in the upper troposphere where large warm ambient temperature biases exist (Fig. 5). But FL4 and FL2 generate much smaller wet biases than STD particularly from 400 to 150 hPa. In January, the largest reduction is achieved at 250 hPa for FL4 reducing the moist bias by up to 31% or 0.9° from STD. In July, the moist bias is further reduced with the largest reduction at 200 hPa, being a 1.6° drop at 72 h. Comparing Figs. 5 and 8 and Tables 4 and 5, the maximum wet bias reductions in both January and July all occur at one pressure level above the maximum warm temperature bias reduction. The reduction in the warm bias by Fu–Liou may be stabilizing the surrounding atmosphere and suppressing the upward moisture transport and mixing. The bias distributions of Fu–Liou and STD are similar below 500 hPa in both January and July.

Figure 9 is the same as Fig. 8 but for RMS error profiles being displayed. In contrast to the winter (Fig. 9a), all the experiments in (Fig. 9b) exhibit large RMS errors in the upper troposphere corresponding to the large bias errors in Fig. 8. Both FL4 and FL2 generate smaller RMS errors at most heights. The maximum improvements occur at 250 hPa in January and 200 hPa in July: FL4 reduces RMS by 8%–10%, or a 0.5°–0.6° drop in January, and reduces RMS by up to 13% or 1.1° drop in July for the 3-day forecasts (Table 5).

Similar to the temperature field, the overall differences in dewpoint bias and RMS between FL4 and FL2 are slightly larger in July than January. It reveals again that the radiative interaction with water vapor and clouds is more evident in the shortwave and longwave transfer during summer than winter. At upper levels FL4 outperforms FL2 consistently throughout the deep moist layers, which demonstrates the advantage of the high-order accurate algorithm. However, the differences between FL4 and FL2 are always relatively minor compared to those of the standard model.

c. Evaluation of 2-m temperature and sea level pressure

Air temperature and sea level pressure are the primary surface meteorological parameters in numerical weather forecasts by which many phenomena are inferred, including wind. The 2-m air temperature and sea level pressure are directly and indirectly influenced by the radiative transfer calculation through vertical integration, and are thus particularly relevant in the Fu–Liou evaluation.

Figure 10 displays the 2-m air temperature and sea level pressure biases and RMS for the 0–72-h forecasts at 6-h intervals for January. Also presented are the average bias and RMS for the 0–72-h forecasts from STD, FL4, and FL2. All versions of COAMPS generate cold biases and large RMS in January with the strongest cold bias occurring at 18, 42, and 66 h, or approximately midday. FL4 and FL2 exhibit consistently smaller temperature bias and RMS errors than STD throughout the 3-day forecasts. FL2 even outperforms FL4 by reducing STD’s cold bias by 0.6°C (26% reduction) and reducing RMS by 0.5°C (11% reduction). Such reductions imply that Fu–Liou predicts more accurate solar and IR radiative fluxes in the surface energy budget calculation, and therefore improve the surface temperature prediction. The sea level pressure from STD is consistently lower than the observations and the RMS error increases with forecast length (Figs. 10c,d). FL4 and FL2 generate much smaller pressure biases than STD does (FL4 average bias = −0.046 hPa, or an 88% reduction). The average improvement by FL4 and FL2 to the RMS score in 0–72 h is small (2%–3% reduction) but the difference increases with forecast length.

The temperature bias and RMS error in July (Fig. 11) are small compared to January for all experiments. Still, FL4 and FL2 outperform STD with FL4 reaching a nearly perfect bias score (= −0.013°, 96% reduction), though reductions in the RMS are small. Similar to January, the sea level pressure bias of STD is prevailingly negative, but FL4 achieves a 75% bias error reduction while FL2 exhibits a 51% reduction. RMS scores also improve with an average 7% reduction, and these improvements increase with forecast length. Comparing Figs. 10 and 11, it is reasonable to conclude that FL4 outperforms FL2 consistently during the cloudier month of July, whereas FL4 and FL2 randomly outperform one another in January.

To help understand the temperature bias differences between the standard and Fu–Liou, modeled surface radiative heating rates are shown in Figs. 12a,b for January and July, being averaged over the 18-km domain for each month. In both months, the solar heating rates are much smaller than the longwave rates during most daylight hours, as longwave warming–cooling dominates both day and night. In January, longwave warming is much stronger in FL4 than STD, especially during midday [e.g., 18, 42, and 66 h (starting from 0000 UTC)]. These coincide with the largest cold biases in Fig. 10a: the surface air in FL4 is not as cold due to the added radiative warming, hence, the cold bias is reduced. In July, FL4 produces stronger longwave warming during the day and stronger longwave cooling during the night, but the daytime warming exceeds the nighttime cooling. So on the average FL4 generates a smaller cold bias than STD in Fig. 11a. Overall the surface air is less cold in FL4 than STD because of stronger radiative warming. Figure 12 also illustrates that the variations of shortwave and longwave heating rates from FL4 and STD are closely aligned to each other in time (no phase dislocations). That partially explains why Fu–Liou primarily improves the bias scores as opposed to the RMS. Large cold biases remain in January despite radiative transfer improvement. Errors could exist in the many other processes that are involved.

d. The impact of Fu–Liou on clouds

The significant impact of the radiative transfer fluxes in the atmosphere is on the formation and variation of cloud species. These impacts are achieved through direct changes in the air temperature and indirect changes in air temperature and moisture due to transport and mixing. To quantify the cloud comparison between FL4 and STD, Fig. 13 shows the modeled cloud water paths produced in both experiments. The ice water path (IWP) is mainly located in the upper troposphere and liquid water path (LWP) mainly in the lower troposphere (Fig. 7a). The total cloud optical depth is directly related to these water paths [Eqs. (2.5) and (2.8)]. In both the winter and summer months, FL4, through cloud–radiation interactions, generates smaller IWP and LWP than STD. Over the average of the 6–72-h forecasts, FL4 reduces IWP by 19% and LWP by 28% in January, and reduces IWP by 21% and LWP by 44% in July, indicating that FL4 is more effective in summer at correcting the cloud water distribution than in winter through the process of cloud–radiation interaction. Nachamkin et al. (2007) verified COAMPS cloud forecasts over the eastern Pacific, which partially overlaps the CONUS domain, using the Harshvardhan standard radiation. It was found that COAMPS predicted more cloud cover in the upper troposphere than the cloud satellite measurements indicated. Since Fu–Liou reduces cloud water contents and water paths from the standard model (Figs. 7a, 13), it is reasonable to expect that the clouds predicted by Fu–Liou would compare more favorably to the observations. It has been found in this study that the use of Fu–Liou results in a reduced precipitation during the 3-day forecasts by an average of 5% in winter and 19% in summer. Precipitation is another important weather product in the operational forecasts and will be further examined and verified along with COAMPS clouds in an ongoing cloud modeling study at NRL using the Fu–Liou radiation parameterization.

6. Summary

A more accurate radiative transfer model developed by Fu and Liou that accounts for the wavelength dependence of gaseous and particular absorption–scattering has been implemented in COAMPS, the Navy’s operational mesoscale weather prediction system, and transitioned to FNMOC. Fu–Liou calculates solar spectral fluxes in 6 bands and thermal IR fluxes in 12 bands through a delta-four-stream approximation or a delta-two-stream approach. Nongray gas absorption in the multiscattering atmosphere is modeled by a correlated-k distribution method. The cloud extinction coefficient, single-scattering albedo, and asymmetry factor are parameterized in terms of cloud effective radius and cloud liquid and ice water contents, of which only cloud water contents are explicitly predicted in COAMPS.

The Fu–Liou model is first evaluated in a clear-sky case over an 8-day period using the surface radiation measurements at the ARM SGP site and against the standard COAMPS Harshvardhan radiation parameterization. Fu–Liou outperforms the standard model for both shortwave and longwave radiative fluxes, exhibiting bias and RMS scores 40%–50% of the standard model. The Fu–Liou also demonstrates stable performance over a 5-day forecast and significantly surpasses the standard model in the verification.

The new model is then evaluated in a cloudy case consisting of a 15-day period at the ARM SGP site. Nine combinations of cloud droplet and ice crystal effective radius schemes are tested in the Fu–Liou model, verified against the flux observations, and compared to the standard model. These tests reveal that modeled radiative fluxes are sensitive to cloud effective radius. An appropriate cloud Re scheme is critical for modeling cloud–radiation interactions. Bower’s Re scheme for cloud water and Wyser’s Re scheme for ice water scored the best over the 16 error categories. The standard model, which uses prescribed constants for cloud optical parameters at coarse spectral resolution, underperforms Fu–Liou with any of the cloud Re schemes.

Fu–Liou is further evaluated over CONUS using output from 3-day forecasts during a winter and a summer month. The four-stream shortwave–four-stream longwave (FL4) and the four-stream shortwave–two-stream longwave (FL2) options were verified against the observations. Both FL4 and FL2 significantly improve COAMPS forecasts over the standard radiation as shown by the statistical analysis. The systematic warm bias in regions of upper-tropospheric cloudiness was reduced by 40%–50% and the corresponding temperature RMS was reduced by 20%–30%. The cold bias and corresponding RMS errors at the top of the high-level clouds are also greatly reduced. The error reductions increase with forecast length, indicating that the impact of more accurate radiative fluxes accumulates over time, resulting in a 30% reduction in dewpoint bias and a 13% reduction in the RMS at upper levels by 72 h. Fu–Liou reduces the 2-m cold bias by 0.3°–0.5°C by providing more accurate heating rates to the COAMPS land surface model. The sea level pressure statistical scores are also improved, achieving a near-zero bias on average. Fu–Liou also results in smaller ice and liquid water paths than those in the standard model, and a slight reduction in precipitation.

The evaluation over CONUS reveals little difference between FL4 and FL2 in less cloudy conditions, but FL4 appears to perform better in heavy or deep clouds. This indicates that cloud scattering in the longwave spectrum is still important for cloud–radiation interactions. Such interactions are completely neglected in the Harshvardhan model. The computational cost for FL4 is 20% greater than that for the standard when radiation is calculated hourly during the 3-day CONUS forecasts, while the FL2 option requires a 10% increase over the standard model. These increases in computational cost are worthwhile for the improvements in the physics as well as the scores. Considering both accuracy and efficiency, the combination of Fu–Liou four-stream shortwave and Fu–Liou two-stream longwave (e.g., FL2) is the most practical choice for operational forecasting.

Acknowledgments

We sincerely thank Dr. Allen Zhao and Dr. Hao Jin for inspirational discussions on radiation modeling and help in the data analysis. We are also thankful for the support from Principal Investigators Dr. Shouping Wang and Dr. Jerome Schmidt. The support of the Office of Naval Research and the Naval Research Laboratory through programs PE-061153N and PE-0602435N is gratefully acknowledged.

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Fig. 1.
Fig. 1.

COAMPS nesting domains of 81-, 27-, and 9-km grids, centered on the ARM SGP site. The 81-km grid is also the 18-km grid domain for the CONUS simulation in section 5.

Citation: Weather and Forecasting 24, 1; 10.1175/2008WAF2222137.1

Fig. 2.
Fig. 2.

Scatterplots of shortwave downward fluxes at surface of the 9-km grid vs observation at ARM SGP site, 20 to 27 Sep 2002 at 3-min intervals: (a) Fu–Liou 8-day simulation; (b) standard model 8-day simulation; (c) Fu–Liou 120-h forecast; and (d) standard model 120-h forecast.

Citation: Weather and Forecasting 24, 1; 10.1175/2008WAF2222137.1

Fig. 3.
Fig. 3.

Same as Fig. 2, but for longwave downward fluxes.

Citation: Weather and Forecasting 24, 1; 10.1175/2008WAF2222137.1

Fig. 4.
Fig. 4.

Charts of (a) bias errors and (b) RMS errors for COAMPS surface radiative fluxes on the 9-km grid by Fu–Liou model with cloud effective radii from FL01 to FL09 and COAMPS STD from 21 Oct to 4 Nov 2002 at ARM SGP site. Red dashed circles mark the smallest errors and black dashed ovals mark the largest errors of each category.

Citation: Weather and Forecasting 24, 1; 10.1175/2008WAF2222137.1

Fig. 5.
Fig. 5.

Bias error profiles for (a) January and (b) July of air temperature on standard pressure levels at 0-, 24-, 48-, and 72-h forecasts in 18-km CONUS domain verified with raob soundings: dashed lines for STD, heavy solid lines for FL4, and light solid lines for FL2.

Citation: Weather and Forecasting 24, 1; 10.1175/2008WAF2222137.1

Fig. 6.
Fig. 6.

Same as Fig. 5, but for RMS error.

Citation: Weather and Forecasting 24, 1; 10.1175/2008WAF2222137.1

Fig. 7.
Fig. 7.

Profiles of modeled (a) cloud water content and (b) radiative heating rates, averaged over the 18-km CONUS grid for July for the 24-, 48-, and 72-h forecasts.

Citation: Weather and Forecasting 24, 1; 10.1175/2008WAF2222137.1

Fig. 8.
Fig. 8.

Same as Fig. 5, but for dewpoint temperature bias error.

Citation: Weather and Forecasting 24, 1; 10.1175/2008WAF2222137.1

Fig. 9.
Fig. 9.

Same as Fig. 5, but for dewpoint temperature RMS.

Citation: Weather and Forecasting 24, 1; 10.1175/2008WAF2222137.1

Fig. 10.
Fig. 10.

(a) Bias error and (b) RMS error of the 2-m air temperature from the STD, FL4, and FL2 from 0- to 72-h forecasts on the 18-km CONUS grid; (c) bias error and (d) RMS error of sea level pressure from STD, FL4, and FL2. All plots are valid for January.

Citation: Weather and Forecasting 24, 1; 10.1175/2008WAF2222137.1

Fig. 11.
Fig. 11.

Same as Fig. 10, but for July.

Citation: Weather and Forecasting 24, 1; 10.1175/2008WAF2222137.1

Fig. 12.
Fig. 12.

Modeled shortwave and longwave radiative heating rates for the surface air layer by STD and FL4 for the 6–72-h forecasts, averaged over the 18-km CONUS domain in (a) January and (b) July.

Citation: Weather and Forecasting 24, 1; 10.1175/2008WAF2222137.1

Fig. 13.
Fig. 13.

Modeled IWP and LWP by STD and FL4 for the 0–72-h forecasts, averaged over the 18-km CONUS domain in (a) January and (b) July. The 6–72-h averages of IWP and LWP are also listed, with reductions by FL4 as 19% of IWP and 28% of LWP in (a) and 21% of IWP and 44% of LWP in (b).

Citation: Weather and Forecasting 24, 1; 10.1175/2008WAF2222137.1

Table 1.

The bias error and RMS error (W m−2) of modeled upward fluxes of shortwave and longwave radiation in the 8-day simulation and 120-h forecast tests.

Table 1.
Table 2.

List of nine combinations of cloud droplet and ice crystal effective radius parameterizations from FL01 to FL09 tested in the Fu–Liou model and the standard model (“fn” means “function of”).

Table 2.
Table 3.

Normalized statistical errors in COAMPS with FL01 to FL09 and STD, obtained from the 16 types of errors shown in Fig. 4. FL07 has the lowest normalized error.

Table 3.
Table 4.

Absolute error reductions and relative error reduction rates of temperature bias and RMS by FL4 to STD on the maximum bias error levels of 300 hPa in January and 250 hPa in July at 12-, 24-, 36-, 48-, 60-, and 72-forecast hours.

Table 4.
Table 5.

Same as in Table 4, but for dewpoint temperature on the maximum bias error levels of 250 hPa in January and 200 hPa in July.

Table 5.

1

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