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  • Hou, Y. T., K. A. Campana, K. E. Mitchell, S. K. Yang, and L. L. Stowe, 1993: Comparison of an experimental NOAA AVHRR cloud dataset with other observed and forecast cloud datasets. J. Atmos. Oceanic Technol.,10, 833–849.

  • Janjic, Z. I., 1984: Nonlinear advection schemes and energy cascade on semi-staggered grids. Mon. Wea. Rev.,112, 1234–1245.

  • ——, 1990: The step-mountain coordinate: Physical package. Mon. Wea. Rev.,118, 1429–1443.

  • ——, 1994: The step-mountain eta coordinate model: Further developments of the convection, viscous sublayer, and turbulence closure schemes. Mon. Wea. Rev.,122, 927–945.

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  • Mesinger, F., Z. I. Janjic, S. Nickovic, D. Garilov, and D. G. Deaven, 1988: The step-mountain coordinate: Model description and performance for cases of Alpine lee cyclogenesis and for a case of an Appalachian redevelopment. Mon. Wea. Rev.,116, 1493–1518.

  • Rogers, E., T. L. Black, D. G. Deaven, G. J. DiMego, Q. Zhao, M. E. Baldwin, N. W. Junker, and Y. Lin, 1996: Changes to the operational “early” eta analysis/forecast system at the National Centers for Environmental Prediction. Wea. Forecasting,11, 391–413.

  • Rogers, R. R., 1979: A Short Course in Cloud Physics. 2d ed. Pergamon Press, 235 pp.

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  • Slingo, J. M., 1987: The development and verification of a cloud prediction scheme for the ECMWF model. Quart. J. Roy. Meteor. Soc.,113, 899–927.

  • Sundqvist, H., 1988: Parameterization of condensation and associated clouds in models for weather prediction and general circulation simulation. Physically-Based Modeling and Simulation of Climate and Climatic Change, Part I, M. E. Schlesinger, Ed., Reidel, 433–461.

  • ——, E. Berge, and J. E. Kristjansson, 1989: Condensation and cloud studies with a mesoscale numerical weather prediction model. Mon. Wea. Rev.,117, 1641–1657.

  • Zhao, Q., 1993: The incorporation and initialization of cloud water/ice in an operational forecast model. Ph.D. dissertation, University of Oklahoma, 195 pp. [Available from School of Meteorology, University of Oklahoma, 100 E. Boyd St., Energy Center Room 1310, Norman, OK 73019.].

  • ——, and T. L. Black, 1994: Implementation of the cloud scheme in the eta model at NMC. Preprints, 10th Conf. on Numerical Weather Prediction, Portland, OR, Amer. Meteor. Soc., 331–333.

  • ——, and F. H. Carr, 1997: A prognostic cloud scheme for operational NWP models. Mon. Wea. Rev.,125, 1931–1953.

  • ——, ——, and G. B. Lesins, 1991: Improvement of precipitation forecasts by including cloud water and cloud ice into NMC’s Eta Model. Preprints, Ninth Conf. on Numerical Weather Prediction, Denver, CO, Amer. Meteor. Soc., 50–53.

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    Schematic illustration of the cloud prediction scheme.

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    Distribution of cloud water and cloud ice inside clouds.

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    Microphysical processes simulated in the cloud prediction scheme.

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    The horizontal domain of the 40-km Eta Model.

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    (a) Total cloud fraction (percent, shaded areas) and mean sea level pressure (hPa, contours) at 1200 UTC 13 March 1993 from the 24-h forecasts of the Eta Model with explicit cloud scheme. (b) Satellite cloud picture at 1301 UTC 13 March 1993.

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    Cross section of cloud water–ice mixing ratio (g kg−1) and temperature (°C) at 1200 UTC 13 March 1993 at latitude 33°N.

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    Total cloud fraction (percent, white areas) at 0600 UTC 7 July 1994 from (a) RT-Neph, (b) 18-h forecasts of the Eta Model with explicit cloud scheme, and (c) diagnostic clouds of the Eta Model without explicit cloud scheme. Contour interval is 20%.

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    (Continued)

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    (Continued)

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    Statistical scores of the cloud fraction for both the predicted and diagnostic clouds from the 40-km Eta Model with and without explicit cloud scheme, respectively, at different forecast times starting at 1200 UTC 6 July 1994.

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    Equitable threat scores (a) and biases (b) of the combined 0–24- and 12–36-h precipitation forecasts of the 40-km Eta Model with and without explicit cloud scheme for the parallel tests from 4 September to 18 October 1994.

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    (a) Observed 24-h accumulated precipitation for the period ending at 1200 UTC 19 September 1994. (b) The 36-h forecasts of the 24-h accumulated precipitation from the 40-km Eta Model with explicit cloud scheme for the same period. (c) The same as (b) except from the 40-km Eta Model without explicit cloud scheme. Contour interval is 12.5 mm.

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    Cross section of 24-h specific humidity forecast errors (forecasts minus analyses) from the 40-km Eta Model (a) with explicit cloud scheme and (b) without explicit cloud scheme valid at 1200 UTC 13 March 1993 at latitude 33°N. Contour interval is 0.5 (g kg−1).

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    Root-mean-square errors of the 24-h specific humidity forecasts at pressure levels from the 40-km Eta Model with and without explicit cloud scheme for September 1994.

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Implementation of the Cloud Prediction Scheme in the Eta Model at NCEP

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  • 1 General Sciences Corporation/National Centers for Environmental Prediction, NWS/NOAA, Camp Springs, Maryland
  • 2 National Centers for Environmental Prediction, NWS/NOAA, Washington D.C.
  • 3 General Sciences Corporation/National Centers for Environmental Prediction, NWS/NOAA, Camp Springs, Maryland
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Abstract

An explicit cloud prediction scheme has been developed and incorporated into the Eta Model at the National Centers for Environmental Prediction (NCEP) to improve the cloud and precipitation forecasts. In this scheme, the cloud liquid water and cloud ice are explicitly predicted by adding only one prognostic equation of cloud mixing ratio to the model. Precipitation of rain and snow in this scheme is diagnostically calculated from the predicted cloud fields. The model-predicted clouds are also used in the model’s radiation calculations. Results from the parallel tests performed at NCEP show improvements in precipitation forecasts when prognostic cloud water is included. Compared with the diagnostic clouds, the model-predicted clouds are more accurate in both amount and position. Improvements in specific humidity forecasts have also been found, especially near the surface and above the freezing level.

Corresponding author address: Dr. Qingyun Zhao, NOAA Science Center, Rm. 204, 5200 Auth Road, Camp Springs, MD 20746.

Email: wd20cl@next4.wwb.noaa.gov

Abstract

An explicit cloud prediction scheme has been developed and incorporated into the Eta Model at the National Centers for Environmental Prediction (NCEP) to improve the cloud and precipitation forecasts. In this scheme, the cloud liquid water and cloud ice are explicitly predicted by adding only one prognostic equation of cloud mixing ratio to the model. Precipitation of rain and snow in this scheme is diagnostically calculated from the predicted cloud fields. The model-predicted clouds are also used in the model’s radiation calculations. Results from the parallel tests performed at NCEP show improvements in precipitation forecasts when prognostic cloud water is included. Compared with the diagnostic clouds, the model-predicted clouds are more accurate in both amount and position. Improvements in specific humidity forecasts have also been found, especially near the surface and above the freezing level.

Corresponding author address: Dr. Qingyun Zhao, NOAA Science Center, Rm. 204, 5200 Auth Road, Camp Springs, MD 20746.

Email: wd20cl@next4.wwb.noaa.gov

1. Introduction

For many years, the large-scale saturation adjustment scheme proposed by Hoke et al. (1989) has been used in the parameterization of large-scale condensation and precipitation in the Nested Grid Model (NGM) and the operational Eta Model at the National Centers for Environmental Prediction (NCEP). This scheme treats the complicated processes associated with large-scale precipitation in a simple manner without considering the microphysics in clouds in order to reduce the computational time and memory requirement. While reasonable precipitation forecasts have been produced from these operational models, the lack of realistic depiction of clouds in these models has been one of the major sources of the precipitation forecast errors (Zhao 1993). As computer technology continues to improve, and the quantity and quality of cloud observations increase, an explicit treatment of clouds and microphysics is essential to meet the need of improved cloud and precipitation forecasts from operational NWP models.

Recently, an explicit cloud prediction scheme for NWP models was proposed by Zhao and Carr (Zhao et al. 1991; Zhao and Carr 1997). This scheme explicitly represents cloud liquid water and cloud ice in the model’s prognostic equations and it was incorporated into the Eta Model at NCEP for extensive testing. Results from these tests showed clear improvement in precipitation and moisture forecasts. Statistics from the daily precipitation verification against observations showed an increase of about 12% in threat score for the rain/no-rain threshold and more than 5% for other thresholds. Experimental results also indicated that the impacts of explicit clouds on other large-scale variables such as wind and temperature were relatively small (Zhao 1993; Zhao and Black 1994). Additionally, this scheme produces explicit, three-dimensional forecasts of both cloud fraction and water content, which are used to simulate a better link to the radiation parameterization.

The cloud prediction scheme is currently included in the Eta Model Data Assimilation System version of the Eta Model, which became operational at NCEP on 12 October 1995 (Rogers et al. 1996), and in the Mesoscale Eta Model (Black 1994) to replace the diagnostic cloud scheme (Janjic 1990). The purpose of this paper is to provide the operational forecaster and other model users a description of the explicit cloud prediction scheme that is in operational use by the Eta Model at NCEP. We also investigate the impact of the explicit representation of clouds on the performance of the model. Section 2 will give details of the cloud scheme, while section 3 shows some recent results from the preimplementation tests. Finally, conclusions will be stated in section 4.

2. Description of the cloud prediction scheme

As mentioned earlier, the primary feature of the cloud prediction scheme is the explicit calculation of cloud water and cloud ice content in the large-scale condensation component of the model as illustrated in Fig. 1. Instead of using two separate variables, we use only one predictive variable, the cloud water/ice mixing ratio m, to represent both cloud water and cloud ice. This reduces the model computational time and storage requirements. After incorporation of the cloud scheme, the model predictive equations for temperature, T; specific humidity, q; and cloud water/ice (both cloud liquid water and cloud ice) mixing ratio, m, are
i1520-0434-12-3-697-e2-1
where qnon, Tnon, and mnon are the noncondensation (e.g., advection and turbulence) terms, Cg and Cb are the grid-scale and convective condensation rates, and Ec and Er are the evaporation rates for clouds and precipitation, respectively. Here, Psm is the melting rate of snow below the melting level, P is the precipitation production rate from cloud water/ice mixing ratio, Cp is the specific heat of air at constant pressure, L is the latent heat of condensation and deposition, and Lf is the latent heat of freezing.

a. Large-scale condensation

Equations (2.1) and (2.2) can be rewritten with the form
i1520-0434-12-3-697-e2-4
where
i1520-0434-12-3-697-e2-6
are the changes in q and T caused by all the processes except grid-scale condensation and evaporation. Following Sundqvist et al. (1989), the grid-scale condensation rate is obtained by solving Cg from Eqs. (2.4) and (2.5) together with the Clausius–Clapeyron equation. The final equation for Cg is
i1520-0434-12-3-697-e2-8
where M represents the convergence of available latent heat into the gridbox (s−1); that is,
i1520-0434-12-3-697-e2-9
Here, U is the relative humidity, p is the pressure, qs is the saturation specific humidity, Ec is the evaporation rate of cloud water/ice, R is the gas constant for dry air, and ɛ = 0.622. All terms on the right-hand side of Eqs. (2.8) and (2.9) can be calculated from model dynamical processes (e.g., advection and turbulence) and other physical parameterizations (e.g., cloud and precipitation evaporation, convective adjustment, etc.) except the local change of relative humidity ∂U/∂t. To close the system, an assumption was made by Sundqvist et al. (1989) that the moisture increase in a grid box is divided into two parts: one part goes into the already cloudy portion and condenses, and another part goes into the cloud-free portion and increases the relative humidity there. If we let b represent cloud fraction (the percentage of cloudy area in a grid box), then the equation for ∂U/∂t will be
i1520-0434-12-3-697-e2-10
where Us = 1.0 is the relative humidity in a cloud region, U00 is the critical value of relative humidity for large-scale condensation, and m is the cloud water/ice mixing ratio in Eq. (2.3). According to Sundqvist et al. (1989), cloud fraction b at a grid point can be estimated from relative humidity using the equation
i1520-0434-12-3-697-e2-11
for U > U00 and b = 0 for U < U00. Since both temperature and moisture may vary at scales smaller than model grid scale, it is possible for condensation to occur before the grid-average relative humidity reaches 100%. Therefore U00 needs to be less than 1.0 to account for the subgrid-scale variation of temperature and moisture fields. Based on our sensitivity studies, U00 is set to 0.75 over land. Since condensation can more easily occur over ocean than over land, especially in the lower atmosphere because of the availability of moisture, the value of U00 is set to 0.85 over ocean to avoid excessive condensation.

b. Cloud parameterization

Stratiform clouds are produced from the large-scale condensation scheme. Two three-dimensional cloud fields are calculated: cloud water/ice mixing ratio, which is prognostically computed from Eq. (2.3), and cloud fraction, which is diagnostically estimated from Eq. (2.11). Stratiform clouds in this scheme consist of either liquid water or ice particles, depending on the temperature (T) and the cloud-top temperature (Tp). Figure 2 shows the distribution of liquid water and ice particles inside clouds. In regions where T > 0°C, there is no cloud ice while in regions where T < −15°C, no cloud water is allowed based on the theory that the diffusional growth of ice crystals reaches its maximum at the temperature of −15°C over a wide range of pressure in a water-saturated environment (Rogers 1979) and based on the studies by Golding (1990). In the regions where T is between 0° and −15°C, however, the phase of hydrometeors is determined by the cloud-top temperature Tp. If Tp > −15°C, then the cloud is assumed to consist of supercooled water. If Tp < −15°C, which means there are ice particles above, the cloud should freeze very quickly and is assumed to consist of ice particles because of the seeding effects of ice particles from above.

Evaporation of stratiform clouds is allowed to take place only when the relative humidity U < U00, that is, when there is no condensation occurring. This is most likely to occur when clouds are advected to a drier region or when the relative humidity at a point where cloud already exists drops below the critical value U00. All water vapor from evaporation is used to increase the relative humidity at this point. Evaporation will stop when U00 is reached. Based on the above discussions, the evaporation equation for stratiform clouds is obtained by using the equation q = Uqs:
i1520-0434-12-3-697-e2-12
where Δt is the time step for the precipitation calculation. Since the large-scale precipitation is calculated at every four adjustment time steps (the model’s shortest time steps used in the pressure gradient/gravity wave adjustment calculations) to save computational time, Δt is 480 s for 48-km early eta and 288 s for the 29-km mesoeta. In the case where all clouds will evaporate before U00 is reached, the following equation is used:
i1520-0434-12-3-697-e2-13
where m is the cloud water/ice mixing ratio before evaporation.

The vertical advection of clouds in this scheme is neglected based on the assumption that there is an approximate balance between the small gravitational fall speed of cloud particles and the model’s large-scale vertical motion (Sundqvist et al. 1989). The horizontal advection of cloud water–ice is calculated using the numerical techniques for specific humidity in the Eta Model (Janjic 1984).

Stratiform cloud fractions calculated from Eq. (2.11) are used indirectly in the radiation parameterization (Lacis and Hansen 1974; Fels and Schwarzkopf 1975). Currently, three layers of clouds (low, surface to 642 hPa; middle, 642 to 350 hPa; and high, 350 hPa to the top of model domain) are computed from the cloud fractions in each model layer as input to the radiation calculations. Future improvements will allow direct use of cloud fraction in all model layers.

Parameterization of microphysical processes inside convective clouds was also tested by Zhao and Carr (1997) in the Eta Model. However, this parameterization is not included in the current operational Eta Model since further study is needed to understand the interactions between cloud microphysics and convection. Convective cloud fractions are estimated from convective precipitation rates based on Slingo’s work (Slingo 1987) and used as input to the radiation parameterization. Total cloud fraction is computed from the cloud fraction at each model level using the equation
i1520-0434-12-3-697-e2-14
where LM is the number of the vertical levels of the Eta Model.

c. Precipitation

Precipitation in this scheme is diagnostically calculated from the cloud water/ice mixing ratio; that is, once precipitation is produced from the cloud water/ice, it is assumed to fall to the ground in one precipitation time step. Snow and rain are two components of precipitation produced from ice clouds and liquid clouds, respectively. The interaction between snow and rain is also considered. Six major precipitation processes observed in clouds are used in the parameterization of precipitation production from clouds (see Fig. 3). These processes are autoconversion of cloud water to rain, collection of cloud droplets by the falling rain drops, autoconversion of ice particles to snow, collection of ice particles by the falling snow, melting of snow below the freezing level, and evaporation of precipitation below cloud bases. A brief description of the equations used to calculate the microphysical processes will be given here to provide the basic information about the parameterization of these precipitation processes. Values of all empirical parameters in these equations were taken either from studies by other investigators or determined based on our sensitivity studies. A full description of these equations and their physical meanings can be found in Zhao (1993) and Zhao and Carr (1997).

Following Sundqvist et al. (1989), the autoconversion of cloud water to rain, Praut, can be parameterized from the cloud water mixing ratio m and cloud fraction b; that is,
i1520-0434-12-3-697-e2-15
where constants c0 and mr are 1.0 × 10−4 s−1 and 3.0 × 10−4, respectively. The autoconversion of cloud ice to snow is simulated using the equation from Lin et al. (1983):
Psauta1mmi0
where mi0 is an empirical parameter and is set to 1.0 × 10−4 kg kg−1. According to Lin et al. (1983), a1 is specified as a function of temperature to account for the temperature effects on the rates of growth and shapes of ice particles and is given by
a1−3T
The collection of cloud liquid water by the falling rain is proportional to the cloud water mixing ratio m and the rain rate Pr and can be expressed by
PracwCrmPr
where Cr is the collection coefficient and has a value of 5.0 × 10−4 m2 kg−1 s−1. Similarly, the aggregation process of ice particles by the falling snow is simulated by
PsaciCsmPs
where Ps is the precipitation rate of snow and Cs is the collection coefficient. Unlike Cr, Cs should be a function of temperature since the open structure of ice crystals at relatively warm temperatures increases the likelihood of capture, given a collision, over that for crystals of other shapes (Rogers 1979). Here, Cs is expressed by
Csc1c2T
above the freezing level and zero below, where c1 = 1.25 × 10 −3 m2 kg−1 s−1 and c2 = 0.025 K−1 are two empirical parameters.
The treatment of the melting processes of snow below the melting level is complicated. Two melting processes have to be considered: continuous melting of snow due to the increase in temperature as it falls down through the freezing level, and the immediate melting of melting snow by collection of the cloud liquid water below the freezing level. The former can be parameterized as a function of temperature and snow precipitation rate based on the work by Golding (1990) and Rutledge and Hobbs (1983), that is,
Psm1CsmTaPs
while the latter is given by (Zhao and Carr 1997)
Psm2CwsPsacw
where Psacw is the collection rate of cloud liquid water by the falling snow below the freezing level and is expressed by
PsacwCrmPs
Parameter values of Csm = 5 × 10−8 (m2 kg−1 K−2 s−1), α = 2, and Cws = 0.025 are used to allow the falling snow to be completely melted before it reaches the T = 278.15 K level. All melted snow in both cases becomes rain.
Evaporation of rain as it falls through an unsaturated layer is calculated using the equation (Sundqvist 1988)
ErrkeU00UPrβ
The sublimation of the falling snow is also computed using the equation
i1520-0434-12-3-697-e2-25
The values of the empirical parameters ke, β, Crs1, and Crs2 in Eqs. (2.24) and (2.25) are determined from our experiments and are 2.0 × 10−5m2 kg−1 s−1, 0.5, 5.0 × 10−6 m2 kg−1 s−1, and 6.67 × 10−10 m2 kg−1 K−1 s−1, respectively.
To close the system, the precipitation rates Pr and Ps on the right-hand sides of Eqs. (2.18)–(2.25) need to be determined. In the Eta Model, the first model level is located at the top of the atmosphere. If we let the superscript (n) denote values on model level n, then the precipitation rates on level n are computed by
i1520-0434-12-3-697-e2-26
where ptop and psfc are pressures at the top and bottom of the model atmosphere, respectively; g is gravity; Δη is the depth between model levels n and n −1; and ηs is defined by Mesinger et al. (1988). The difficulty in computing Pr and Ps is that some terms on the right-hand sides of Eqs. (2.26) and (2.27) are functions of Pr and Ps. For simplicity, an explicit computational procedure is used here to solve this problem. In this procedure, all the source and sink terms on the right-hand sides of Eqs. (2.26) and (2.27) are computed from Eqs.(2.15)–(2.25) using the precipitation rates from the level above. Then the precipitation rates on this level are calculated from Eqs. (2.26) and (2.27). This calculation is done level by level, from the top to the surface, by keeping in mind that precipitation rates at the top of the model atmosphere are zero.
At this point, the whole cloud scheme can be closed by using the relationships
i1520-0434-12-3-697-e2-28
where P, Psm, and Er are the precipitation production rate, snow melting rate, and precipitation evaporation rate in Eqs. (2.1)–(2.3), respectively.

There are two important features in the precipitation parameterization. First, snow melts gradually, not immediately, when it falls into the warm cloud regions. This treatment allows the coexistence of snow and rain in some regions just below the melting level, which means that in some areas snow and rain can reach the ground at the same time (see Fig. 2). Second, evaporation of precipitation occurs as it falls through the entire unsaturated layer below cloud base and can reach the ground while it is evaporating.

3. Results

a. Model description and verification procedures

The Eta Model was first developed by Mesinger et al. (1988). A comprehensive physical package has been incorporated into the model by Janjic (1990, 1994). Examples of the Eta Model performance are contained in Black et al. (1993) and Black (1994). Currently, the Eta Model is running at NCEP at several model resolutions. The Eta Model version used for the preimplementation tests of the cloud prediction scheme has a horizontal resolution of 40 km and a vertical resolution of 38 layers. Figure 4 gives the horizontal domain for the 40-km Eta Model and Table 1 lists the main features of the model for both the control and experimental runs.

During the last three years, many interesting cases have been selected for experiments aimed at testing and improving the cloud prediction scheme. In September 1994, a parallel test was established at NCEP for preimplementation testing of the Eta Model with the cloud scheme. These forecasts ran twice daily starting at 0000 and 1200 UTC. Automatic verification of the model forecasts of precipitation and other large-scale variables are carried out daily. Objective verification of precipitation amounts has been done during the parallel tests of the cloud scheme using the National Weather Service Office of Hydrology’s River Forecast Centers database (Black et al. 1993). The 24-h accumulated precipitation amounts from the model forecasts are verified against the analysis of 24-h amounts covering the contiguous United States. Validation of cloud forecasts also is performed for some interesting cases using the Real-Time Nephanalysis (RT-Neph) data from the U.S. Air Force Global Weather Center (AFGWC, Hamill et al. 1992). This data is produced at AFGWC every 3 h and contains cloud amount, cloud type, cloud base, and cloud top of up to four cloud layers in the vertical but was only available at NCEP every 6 h at the time these tests were made. This data was interpolated from the RT-Neph grid to the eta grid using the Barnes scheme (Barnes 1973). The verification results are then compared with those from the control runs at the same time and with the same model resolution.

b. Cloud forecasts

The cloud forecasts from the cloud scheme include the three-dimensional fields of cloud fraction, cloud water/ice mixing ratio and the identification number for cloud ice. Total cloud fraction was also computed from the three-dimensional cloud fraction b using Eq. (2.14). Figure 5a gives an example of the model forecast of total cloud fraction by the cloud scheme, while Fig. 5b shows the cloud image from satellite about one hour later for a major winter storm on the east coast of the United States on 13 March 1993. In this case an extensive cloud system associated with the storm centered in Georgia was well simulated in both structures and locations. To see the three-dimensional structure of the clouds, a vertical cross section of clouds through the center of the storm is given in Fig. 6. The highest clouds associated with the upper-level front were located in the central area of the storm, and the cirrus clouds reached as far as several hundred kilometers away from the storm center in the downwind direction. While the clouds shown in Fig. 6 look realistic, currently there is no data available for directly verifying the three-dimensional structures of the cloud water/ice mixing ratio.

Figure 7a shows an example of the total cloud fraction from the RT-Neph data on the 80-km eta grids at 0600 UTC 7 July 1994. A subjective comparison of the analysis with a satellite image (not shown) at the same time shows good agreement between them, especially over the United States. Figures 7b and 7c give the prognostic clouds from the experiment with the explicit cloud scheme and the diagnostic clouds from the control run without the explicit cloud scheme, respectively. The cloud coverage is clearly underestimated by the diagnostic clouds everywhere. Improvements can be seen in the prognostic clouds in Fig. 7b, although underestimation of total clouds is still apparent. To evaluate the improvements more quantitatively, four statistical scores are calculated: S20 score (the percent of points where the cloud amounts in the two fields differ by less than 20%), correlation, rms error, and bias difference (Hou et al. 1993). The results at every 6 h are given in Fig. 8. In the first 6 h of the model forecasts, little improvement can be found in the prognostic clouds. After that time, however, the prognostic clouds show notable improvement over the diagnostic clouds through the increased S20 score and correlations and decreased bias and rms errors. The “spinup” in the prognostic clouds is very obvious in Fig. 8d, but this should be largely eliminated in the future by initializing the cloud water with values other than zero. The same verification of cloud forecasts against the RT-Neph data were also performed for a period of a week during the parallel tests, and the results showed consistent improvement in total cloud amount by the prognostic cloud scheme (Rogers et al. 1996).

c. Precipitation forecasts

An alternative way to validate the cloud scheme is through verification of the precipitation forecasts, since clouds and precipitation are two directly linked components in the model’s hydrological cycle. For quantitative verification, an equitable threat score (ETS) (Schaefer 1990) and bias are computed using the equations
i1520-0434-12-3-697-e3-1
where F is the number of forecast points above a threshold, O is the number of observed points above a threshold, H is the number of hits (i.e., correct forecasts) above a threshold, and CH is the expected number of hits in a random forecast of F points for O observed points, which is equal to
i1520-0434-12-3-697-e3-3
where M is the number of points to be verified.

The ETS and bias calculations from the parallel tests during the period from 4 September to 18 October 1994 are given in Fig. 9. The cloud scheme has improved the precipitation forecasts skills at all thresholds. As a typical example of the improvements in precipitation forecasts by the cloud scheme, Fig. 10 presents the 24-h accumulated precipitation amounts from the analyses, the model forecasts using the cloud scheme, and the control run without the cloud scheme on 19 September 1994. There was a large area of heavy precipitation in the southeastern United States with a maximum of more than 65 mm in South Carolina. Both the control and the cloud runs predicted the correct area of precipitation, but the maximum in South Carolina was underpredicted in the former. The cloud scheme, however, produced a maximum of about 55 mm, which is much closer to the observed. The increases in the forecasts of both precipitation amounts and areas by the cloud scheme over those in the control can also be seen in Fig. 9b. The bias for each precipitation category from the control runs is less than 1.0, indicating that precipitation was underestimated by the control runs for all precipitation amounts. The cloud scheme, however, increased the bias everywhere. A measure of the overall effect of the cloud scheme on the simulations, was provided by calculating the root-mean-square departure of the bias from one [rms(bias − 1.0)] for simulations with and without the cloud scheme. The results are also given in Fig. 9b. It is obvious that the cloud scheme reduces rms (bias − 1.0) by 25%. Tests of the prognostic cloud scheme for different seasons (Zhao and Carr 1997) reveal that improvement in precipitation forecasts has been achieved for all seasons, with largest improvement during winter. Previous studies (Zhao 1993) also show that the inclusion of cloud ice above the freezing level and the better treatment of precipitation evaporation below cloud bases are both important factors contributing to the increase in precipitation amounts.

For further insight into the relative increase in skill, it would be helpful to compare the improvements in precipitation forecasts by the explicit cloud scheme to the results from other improvements. One comparison has been made between the increases in ETS by the explicit cloud scheme and by doubling the model’s resolution (Black 1994). It turns out that the increases in ETS in Fig. 9a are about the same in magnitude as those in Black’s study. Considering the computational costs of doubling the model’s resolution, the improvements in precipitation forecasts by the explicit cloud scheme are achieved with a relatively small computational cost (about a 10%–15% increase in both CPU time and memory size).

d. Large-scale variable forecasts

Though not shown in this paper, changes in the forecasts of temperature, sea level pressure, and wind fields by the inclusion of cloud water/ice are relatively small. However, the improvements to the forecasts of the specific humidity field, another important component connected to clouds, are apparent. A typical example is from the storm case of 13 March 1993 (see Figs. 5 and 6). Figure 11 shows the cross sections of specific humidity forecast errors through the center of the storm from the control run and the cloud scheme experiment. The control run underpredicted the moisture field in regions ahead of the storm and overpredicted the moisture field in the central part of the storm above 600 hPa and in the area below 700 hPa just behind the storm center. Those errors, however, have been notably reduced by the cloud scheme. The largest differences in the specific humidity forecast, however, are in the areas downstream from the storm. In the forecast without the cloud scheme, the downstream air (right half of the figure) between 500 and 800 hPa is generally too dry by up to 2.5 g kg−1. With cloud scheme, that region has become moister than analyzed but by just 1.5 g kg−1 at most. It was found that cloud particles from the storm were advected by the strong winds and then evaporated downstream resulting in increased moisture in these areas.

Daily verification of moisture profiles from the forecasts has been done by comparing them with the radiosonde data over the continental United States during September 1994. Rms errors were computed at major pressure levels and are given in Fig. 12. Although the vertical distributions of the rms errors from both model runs are basically the same, improvements in moisture forecasts by the explicit cloud scheme can be found at levels below 800 hPa and above 550 hPa. As mentioned previously, the improvement in the specific humidity forecast at levels above 550 hPa could mainly be attributed to the inclusion of cloud ice in the model. On the other hand, the improvements near the surface reflect the effects of the improved parameterization of large-scale condensation of clouds and the better treatment of precipitation evaporation below cloud bases.

4. Conclusions

A description of the cloud prediction scheme in the Eta Model has been provided along with results from recent experiments and parallel tests. As a new predictive variable, cloud water/ice introduced into the model allows a much more realistic description of the hydrological cycle and, hence, should improve moisture and precipitation forecasts. More realistic cloud predictions are important not only because of their effects on the radiation calculations but also because of the consequences of transport and storage of the condensed water substances. The primary microphysical processes associated with precipitation production are also important in transferring water mass from one phase to another. The inclusion of cloud ice, the horizontal advection of clouds, and the better description of precipitation evaporation play an important role in the improved cloud, precipitation, and specific humidity forecasts.

Forecasts using the cloud scheme produced a clear increase in forecast skill of precipitation as measured by the equitable threat score and bias score during test periods over those of forecasts that used only diagnostic clouds. Root-mean-square errors of forecast specific humidity were reduced in the cloud scheme tests during a 1-month period at all pressure levels below 800 hPa and above 500 hPa and were unchanged at intermediate levels. Inspection of individual cases has revealed that cloud cover predicted using the cloud scheme is generally closer to that observed than when using only diagnostic clouds.

It has been found that the lack of initial cloud water/ice content causes spinup of clouds in the first 12 h of the model integration and, as a result, affects the model forecasts of other variables during this period. More effort is needed to incorporate cloud information into the Eta Data Assimilation System at NCEP. Further improvements in model forecasts can be expected from the improved cloud initial conditions.

Acknowledgments

The authors want to thank Dr. Frederick Carr of the University of Oklahoma for his invaluable advice and support during the development of the cloud prediction scheme. Thanks also go to Drs. Eugenia Kalnay and Geoff DiMego for their leadership and continuous support of the implementation of the cloud scheme in the Eta Model. Drs. Kenneth Campana and Yutai Hou are thanked also for providing the new version of the radiation parameterization used in the current Eta Model. The authors are very grateful to Dr. Eric Rogers for his help in the daily verification of the model forecasts during the parallel tests of the cloud scheme. Suggestions from Drs. Fedor Mesinger, Joseph Gerrity, Kenneth Mitchell, and other individuals associated with the development of the Eta Model were also very helpful. The authors also wish to acknowledge the three reviewers whose comments were most useful.

REFERENCES

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Fig. 1.
Fig. 1.

Schematic illustration of the cloud prediction scheme.

Citation: Weather and Forecasting 12, 3; 10.1175/1520-0434(1997)012<0697:IOTCPS>2.0.CO;2

Fig. 2.
Fig. 2.

Distribution of cloud water and cloud ice inside clouds.

Citation: Weather and Forecasting 12, 3; 10.1175/1520-0434(1997)012<0697:IOTCPS>2.0.CO;2

Fig. 3.
Fig. 3.

Microphysical processes simulated in the cloud prediction scheme.

Citation: Weather and Forecasting 12, 3; 10.1175/1520-0434(1997)012<0697:IOTCPS>2.0.CO;2

Fig. 4.
Fig. 4.

The horizontal domain of the 40-km Eta Model.

Citation: Weather and Forecasting 12, 3; 10.1175/1520-0434(1997)012<0697:IOTCPS>2.0.CO;2

Fig. 5.
Fig. 5.

(a) Total cloud fraction (percent, shaded areas) and mean sea level pressure (hPa, contours) at 1200 UTC 13 March 1993 from the 24-h forecasts of the Eta Model with explicit cloud scheme. (b) Satellite cloud picture at 1301 UTC 13 March 1993.

Citation: Weather and Forecasting 12, 3; 10.1175/1520-0434(1997)012<0697:IOTCPS>2.0.CO;2

Fig. 6.
Fig. 6.

Cross section of cloud water–ice mixing ratio (g kg−1) and temperature (°C) at 1200 UTC 13 March 1993 at latitude 33°N.

Citation: Weather and Forecasting 12, 3; 10.1175/1520-0434(1997)012<0697:IOTCPS>2.0.CO;2

Fig. 7.
Fig. 7.

Total cloud fraction (percent, white areas) at 0600 UTC 7 July 1994 from (a) RT-Neph, (b) 18-h forecasts of the Eta Model with explicit cloud scheme, and (c) diagnostic clouds of the Eta Model without explicit cloud scheme. Contour interval is 20%.

Citation: Weather and Forecasting 12, 3; 10.1175/1520-0434(1997)012<0697:IOTCPS>2.0.CO;2

Fig. 8.
Fig. 8.

Statistical scores of the cloud fraction for both the predicted and diagnostic clouds from the 40-km Eta Model with and without explicit cloud scheme, respectively, at different forecast times starting at 1200 UTC 6 July 1994.

Citation: Weather and Forecasting 12, 3; 10.1175/1520-0434(1997)012<0697:IOTCPS>2.0.CO;2

Fig. 9.
Fig. 9.

Equitable threat scores (a) and biases (b) of the combined 0–24- and 12–36-h precipitation forecasts of the 40-km Eta Model with and without explicit cloud scheme for the parallel tests from 4 September to 18 October 1994.

Citation: Weather and Forecasting 12, 3; 10.1175/1520-0434(1997)012<0697:IOTCPS>2.0.CO;2

Fig. 10.
 Fig. 10.

(a) Observed 24-h accumulated precipitation for the period ending at 1200 UTC 19 September 1994. (b) The 36-h forecasts of the 24-h accumulated precipitation from the 40-km Eta Model with explicit cloud scheme for the same period. (c) The same as (b) except from the 40-km Eta Model without explicit cloud scheme. Contour interval is 12.5 mm.

Citation: Weather and Forecasting 12, 3; 10.1175/1520-0434(1997)012<0697:IOTCPS>2.0.CO;2

Fig. 11.
Fig. 11.

Cross section of 24-h specific humidity forecast errors (forecasts minus analyses) from the 40-km Eta Model (a) with explicit cloud scheme and (b) without explicit cloud scheme valid at 1200 UTC 13 March 1993 at latitude 33°N. Contour interval is 0.5 (g kg−1).

Citation: Weather and Forecasting 12, 3; 10.1175/1520-0434(1997)012<0697:IOTCPS>2.0.CO;2

Fig. 12.
Fig. 12.

Root-mean-square errors of the 24-h specific humidity forecasts at pressure levels from the 40-km Eta Model with and without explicit cloud scheme for September 1994.

Citation: Weather and Forecasting 12, 3; 10.1175/1520-0434(1997)012<0697:IOTCPS>2.0.CO;2

Table 1. 

Basic characteristics of the Eta Model in control and experimental runs.

Table 1. 
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