Ice Phase Parameterization in a Numerical Weather ... - AMS Journals

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Ice Phase Parameterization in a Numerical Weather Prediction Model VIEL ØDEGAARD Norwegian Meteorological Institute, Oslo, Norway (Manuscript received 31 October 1995, in final form 24 September 1996) ABSTRACT This article presents the implementation of simple parameterization schemes for ice phase microphysics, with snow as a diagnostic variable. The microphysical schemes are used within a standard parameterization scheme for stratiform and convective precipitation in a numerical weather prediction model with a 50-km mesh width. The aim is to improve precipitation forecasts, improve forecasts of temperature changes due to latent heat transfer, and to supply the weather service with a tool for prediction of snow. Another objective is to determine to what extent the simplifications of the parameterization are affecting the model’s forecast. The schemes are compared to a condensation scheme with no ice phase included. Parallel runs show that the impact on the general dynamics is limited compared to control runs. Precipitation from the ice phase parameterization model has larger maximum intensity and is often of less horizontal extent than the fields in the control runs. Prediction of snow is improved. Introducing cloud ice as a prognostic variable has an insignificant effect on the development of the forecast as compared to a scheme when cloud ice is diagnosed. Introduction of a probability function for ice gives small changes in distribution of snow and rain, but the scale of the changes is beyond the resolution of the observational network.

1. Introduction The presence of ice in the atmosphere is important for condensation processes on scales ranging from synoptic to cloud drop size. Most of the precipitation reaching the earth’s surface at high and middle latitudes has its origin as ice. The ice particles initiate the Bergeron– Findeisen process, which effectively enhances the seeder–feeder process and thus the release and increase of precipitation. Microphysical processes depending on air temperature, relative humidity, precipitation intensity, and fall speed are of the most important in determining surface precipitation type. Rutledge and Hobbs (1983) presented a model for the seeder–feeder process in frontal rainbands and showed model results to be in agreement with observations. During recent years the parameterization of condensation in numerical weather prediction has been taking the ice phase into account. In HIRLAM (high-resolution limited area model—European cooperation project), a Sundqvist condensation scheme has detailed ice phase parameterization including modeling of the Bergeron– Findeisen effect (Sundqvist 1993), and Deutscher Wetterdienst is running a high-resolution model with ice phase parameterization (DWD 1995). Golding suggested in 1989 (Golding 1989) a simple parameterization scheme for two-phase precipitation for use in numerical weather prediction models. The scheme Corresponding author address: Viel Ødegaard, Norwegian Meteorological Institute, P.O. Box 43, Blindern, Oslo N-0313, Norway. E-mail: [email protected]

q 1997 American Meteorological Society

carries snow as the only supplementary variable, and cloud-top temperature is used to diagnose condensate phase. The scheme was implemented and tested in the Norwegian limited area model in a 3-month parallel run in 1993. After a new parallel run in 1994 with extensive daily verification, the model was implemented in the operational routine in August 1994. Verification of parallel runs will show if the ice phase parameterization has a positive impact on the scores in precipitation and temperature forecast, if it gives reliable information about precipitation type, and how model dynamics is affected. The model without ice phase parameterizations is referred to as LAM25S/LAM50S; the model with ice phase condensation scheme is referred to as ICE25S/ ICE50S. The horizontal mesh size of the model is 25 or 50 km, respectively, at 608N. In addition to the general verification, special interest is given to the study of the impact of microphysical parameterizations on selected variables, such as 2-m temperature in situations where snow is melting close to the surface, development of an isothermal layer due to melting of ice, increase in vertical velocity due to freezing of cloud water, and distribution of rain and snow due to how the model discriminates between water and ice. The impact on model dynamics by extending the scheme with a cloud ice variable to calculate latent heat transfer by conversion of cloud water to ice in the Bergeron–Findeisen process is investigated in a case study. In contrast to the simple diagnosis of cloud water’s phase in the tested scheme, more sophisticated functions are used to determine the distribution of ice

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in the atmosphere in other parameterizations. A probability function suggested by Sundqvist (1993) is tested in one case. Section 2 gives a description of the parameterization scheme and the microphysical formulations, and the verification results are given in section 3. In section 4 the microphysical aspect is studied closer in order to find out how comprehensive the description of microphysical processes has to be to describe the effects of ice in the atmosphere that is resolved in the present model. Summary and conclusions are given in section 5. 2. Ice phase parameterization Ice phase microphysics is characterized by numerous processes—including aggregation, riming or vapor deposition, evaporation, and melting of hydrometeors— creating a large variability of ice crystal formations. These processes lead to different kinds of precipitation particles with implications for the weather as it is experienced on the earth’s surface, for example, light or heavy precipitation, precipitation in the form of rain, sleet, snow, hail, and supercooled water. The impact of cloud microphysics on atmospheric circulation is mainly due to the spatial distribution and varying rates of latent heat transfer, redistribution of atmospheric water, and water loading. The contributions from ice phase microphysics are the additional heat of sublimation compared to condensation/evaporation and the freezing and melting of water. In addition the formation of ice crystals triggers the growth of hydrometeors and release of precipitation. The downdrafts in precipitation depend on fall speed and mass of precipitation, which in turn are influenced by ice phase microphysics. The circulation systems are on a large variability of scales, of which some are resolved in numerical weather prediction models. The role of latent heat transfer by condensation/evaporation is undoubtedly important for the development of synoptic-scale low pressure systems and fronts, and is documented in studies by, for example, Sundqvist et al. (1989) and Grøna˚s et al. (1994). In stratiform precipitation, melting of precipitation is concentrated to a shallow layer and frequently stable isothermal layers are produced. Under certain conditions there might develop isothermal layers as deep as 1 km (Atlas et al. 1969; Marwitz 1983). In widespread frontal precipitation, significant wind perturbations near the melting layer have been observed by Doppler radar. The typical scale of the largest structure in this perturbation is 80 km (Atlas et al. 1969). Marwitz (1983) has also shown that melting contributes to downdrafts in wintertime orographic cloud systems. Radar observations of the melting layer also show more contrast or structure below the melting layer than above, indicating that convection can be triggered by the development of an isothermal layer. The melting-layer convection will be favored in situations when the lapse rate is large, as the

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atmosphere then shows less resistance to vertical motion (Fabry and Zawadzki 1995). Parameterization scheme 1) CONDENSATION–PRECIPITATION PARAMETERIZATION

The control condensation scheme treats condensation and precipitation, from large-scale (model resolved) and subgrid-scale convective processes. Convection is parameterized according to a modified version of the Kuo scheme, including modeling of large-scale instability processes. Rain is a diagnostic variable, while cloud liquid water and water vapor are prognostic variables. The scheme is described in Nordeng (1986). The extensions in ICE50S and ICE25S are based on Golding (1989) and include snow as a supplementary diagnostic variable. Latent heat of phase transitions becomes a function of temperature, and water vapor pressure at saturation is a function of temperature and phase of condensate. Parameterization of cloud microphysics is more comprehensive than in LAM50S/LAM25S, and the formulas used are documented in section 2a (2)–(6). 2) CONDENSATION

AND EVAPORATION OF CLOUD

LIQUID WATER

The amount of vapor to condense in supersaturated air and the amount of cloud liquid water to evaporate in subsaturated air is determined from the implicit equations, q9v 1dq9v 5 qsat (T 1 dT)

(1)

cpdT 1Ldq9v 5 0,

(2)

and the Clausius–Clapeyron equation, where dq9v is the necessary change in specific humidity and dT the change in temperature in order to end up with an exactly saturated state. The first equation ensures that the air is exactly saturated after condensation/evaporation; the second equation is the first law of thermodynamics. The amount to evaporate is taken from cloud water/ice and is limited by the available amount of cloud water/ice. Specific humidity is q9v , temperature is T, and cp is specific heat at constant pressure. The saturation vapor pressure is assumed to be saturation pressure over ice if the temperature is below 2128C or if the cloud is an ice cloud. If temperature is above melting level, saturation vapor pressure is saturation pressure over water. For temperatures between 2128 and 08C a linear interpolation between the two is used. Similarly the latent heat constant is the latent heat constant for sublimation if temperature is below 2128C, the latent heat constant for vaporization/condensation if temperature is above 08C, and a linear interpolation between the two for temperatures between 2128 and 08C.

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3) DIAGNOSIS

OF CLOUD

If temperature in a grid point is less than 2128C, the condensate is assumed to be ice. If the temperature in the grid point is less than 08C, the condensate is assumed to be supercooled water, but if snow from cloud layer above is entering the layer of supercooled cloud water, the whole cloud above the 08C isotherm is glaciated in one time step. In the real atmosphere, heterogeneous ice crystal formation is most common and is a function of ice condensation nuclei among other variables. The distribution of condensation nuclei is not exactly known, but investigations of clouds show that ice is likely to appear when the cloud-top temperature is 2128C or below. The transport of ice crystals to lower levels with supercooled water is important for the glaciation of the entire cloud (Cotton and Anthes 1989). Glaciation in stratiform clouds can thus be parameterized on the basis of this assumption, but convective clouds should be treated differently. 4) PRECIPITATION In the model, local production of snow in an ice cloud is due to the empirical formulas derived from the work of Heymsfield (1977): ]Psloc ] 5 (rVm) (kg m23s21 ), ]z ]z

(3)

where Ps and Pr is the sedimentation mass flux of, respectively, snow and rain; r is the density of the air; m is mixing ratio of nonprecipitating condensate (water or ice); and V is the fall speed of the snow, given as V 5 3.23(rm)0.17 (m s21).

(4)

This release of precipitation is very effective, except in cirrus clouds, where fall speeds are low. The local production of rain in water clouds is described with the Sundqvist formula ]Prloc 5 c Lrm{1 2 exp[2(m/cm ) 2 ]} (kg m23s21 ), ]z

(5)

where cL is a rate constant and cm controls the humidity mixing ratio of liquid water required to give significant precipitation (Sundqvist et al. 1989). Enhancement of precipitation by coalescence/accretion is described in the formula ]Prcoa 5 rm(Pr 1 Ps ) (kg m23s21 ), ]z

(6)

which is a simplification of Kessler (1969) and produces rain much more efficiently than the formula for initiation of rain. 5) MELTING

AND EVAPORATION

Because the snowflakes are chilled by evaporation from their surface while falling through subsaturated

air, melting of snow starts when wet-bulb temperature (Tw) exceeds 08C (Matsuo and Sasyo 1981b). The melted water is shown to be absorbed by the snowflakes; therefore, the snow and the melted snow are added in Eq. (7) (Matsuo and Sasyo 1981a). The melting equation is based on Rutledge and Hobbs (1983): ]Ps ]P 5 2 r 5 20.0028Tw (Pr ]z ]z 1 Ps ) (kg m23s21 ).

(7)

Evaporation of snow is modeled as a slow process, limited to temperatures above 2308C and assumed a constant fall speed velocity of 1 m s21. Golding uses a simplified evaporation equation based on Rutledge and Hobbs (1983): ]Ps 5 xPs (S i 2 1) (kg m23s21 ). ]z

(8)

Here x is 3 3 1023 1 1024T, where T is temperature in degrees Celsius, and Si 5 q/qsi, where q is the specific vapor content and qsi is specific humidity by saturation over ice. The formula controlling evaporation from rain has been used in the European Centre for Medium– Range Weather Forecasts model and is based on Kessler (1969): ÏPr ]Pr 5 2k E rg 2 (q s 2 q) (kg m23s21 ). ]z p

(9)

Here the rate constant kE is 4.8 3 106, r is the density of the air, g is gravity force, p is pressure, and qs is saturation humidity over water. 6) CALCULATION

OF MELTING LEVELS

For most practical purposes the accumulation of snow and rain at station level is of greater interest than the phase of precipitation at the lowest model layer. The topography of LAM50S is normally different from the real terrain, and the difference between model height and real height above sea level is particularly large in valleys, where people mainly live. The difference springs mainly from the resolution of the model but also from the envelope orography of the model, which is higher than the mean orography within a grid square. The enveloped orography is used to describe flow blocking and stagnant air within valleys, which do not contribute to the free atmospheric flow. To calculate precipitation type below the model orography, we assume that the wet-bulb temperature increases with 0.68C/100 m below the lowest model layer and that precipitation rate is unchanged. In addition the wet-bulb temperature gradient is assumed to be a linear function within each model layer. Precipitation type is then determined from the calculated levels where snow starts melting and where all snow is melted. It can easily be shown that below the lowest model layer these assumptions lead to a constant melting layer of 244-m thickness.

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Long-term radar measurements of the brightband show characteristics of the melting layer of wintertime stratiform precipitation that correspond well to this parameterization. The brightband is an increase in reflectivity associated with melting of precipitation and shows the dependence of melting-layer characteristics, precipitation intensity, and melting-layer top. The brightband top is proportional to the height of the 08C isotherm, and the brightband thickness shows a good correlation with precipitation intensity. The melting-layer thickness is also slightly correlated with the brightband height. The melting-layer thickness curve is increased about 100 m when the brightband top increases from 1–2-km height in winter situations to 3–4 km in summer situations (Fabry and Zawadzki 1995). In winter this parameterization frequently calculates melting below model orography. 3. Parallel runs The scheme is implemented into a primitive equation, limited area model with horizontal mesh size 25 km by 50 km on a polar stereographic map. The vertical coordinate is s 5 (p 2 pT)/(ps 2 pT), and there are 31 layers in the vertical. A description of the model is found in Grøna˚s and Hellevik (1982). Complete references to the model may be found in Nordeng and Rasmussen (1992). a. The model physics Diabatic processes in the model include parameterization of clouds and radiation, turbulent vertical diffusion of heat, momentum, and moisture, in addition to large-scale and convective precipitation. Soil heat and moisture is parameterized in three soil layers, and several classes of surface are treated separately (vegetation, ice, snow, sea, etc.). The diabatic effects of the physical processes are added to the governing equations each physical time step. Prognostic equations for water vapor [Eq. (10)], cloud water/ice [Eq. (11)], and heat [Eq. (12)] are ]q v C E 5 A(q v ) 2 p 1 p 1 F q v , ]t L L

(10)

where qv is specific water vapor content, A(qv) represents the horizontal and the vertical advection, and the second and the third terms represent the rate of change in latent heat of condensation and evaporation with p as the Exner function and L as the latent heat of vaporization. The last term is the vertical turbulent flux of water vapor. For cloud water/ice,

1

2

]m C E gr ]Prloc ]Psloc ]Prcoa 5p 2p 2 1 1 . ]t L L p s 2 p t ]s ]s ]s

(11)

Specific cloud water/ice content is m, P is sedimentation mass flux, and subscripts rloc, sloc, and rcoa mean local

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production of rain and snow, and local enhancement of rain due to coalescence processes. Cloud water/ice is not advected in the model. For heat, ]u 5 A (u) 1 C 2 E 2 M 1 S 1 R 1 Fu , ]t

(12)

where u is potential temperature, M represents latent heat of melting, R is net radiation heating, S is latent heat of sublimation, and Fu is turbulent heat flux. b. Validation The scheme is tested in a 3-month parallel run in 1993 in a limited-area model with horizontal mesh size 25 km (LAM25S), for validation of precipitation amount, precipitation type, and 2-m temperature. Encouraged by the results of precipitation-type forecasts, the model was tested for operational implementation in another parallel run in 1994. Extensive validation of the models against daily observations of mean sea level pressure, 2-m temperature, windspeed at 10-m and in the free atmosphere, and geopotential height for an area covering northwestern Europe was carried out. In this second parallel run, we used the model with 50-km horizontal mesh size, since this was what was used operationally. 1) VALIDATION

OF PRECIPITATION AMOUNT

Precipitation forecasts from numerical models with mesh size 50 km or coarser are in general too smooth and are not able to capture the maximum precipitation amounts. Precipitation is also distributed over too large areas. To some extent, inclusion of the ice phase in ICE50S can contribute to improvement of such forecasts, given that the precipitation pattern is perfectly forecasted. Figure 1 shows a case from the models with 50-km mesh size. Precipitation from ICE50S has higher maximum values and less horizontal extent, and this difference was pronounced in many cases during the parallel run. 2) VERIFICATION

OF MODEL PRECIPITATION TYPE

The most complete investigation of model precipitation phase is made with the data from the 3-month parallel run in 1993 (i.e., with horizontal mesh size 25 km). The data used for the verification are observed precipitation phase at 594 stations. The observations express the observers validation of precipitation phase during the whole observation period, which is 6 h long. The instantaneously calculated melting levels from the model are not directly comparable to these observations. However the amount of data is large, and we assume that the cases when precipitation type change, during the observation period, will be nearly equally distributed on cases of correct forecasts and cases of unsuccessful forecasts.

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TABLE 1. Values given to a precipitation type category in order to calculate bias. Precipitation category

Value

Snow Sleet Rain

1 0 21

means that forecast is rain while observation is snow, 21 that forecast is sleet/rain while observation is snow/ sleet, and 0 is a correct forecast. Positive bias is calculated correspondingly. The geographical distribution of station bias averaged over the verification cases is shown in Fig. 2. The plots are created with interpolation of bias at stations based on kriging (Journel and Huijbregts 1978) and cover southern Norway, where the difference between the two models is largest. 3) VERIFICATION

OF DAILY FORECASTS AGAINST OBSERVATIONS

FIG. 1. (a) Accumulated precipitation (12 h) in ICE50S from 0600 to 1800UTC 13 September 1994. Forecast started at 0000 UTC 13 September 1994. Shaded areas represent 0.5, 6, 8, and 10 mm/12 h. 1(b) Same as in a Fig. 1(a) but for LAM50S.

Verification of precipitation phase from ICE25S is not directly comparable to verification results from LAM25S, which do not explicitly calculate melting of ice. The forecasters mainly use the 2-m temperature from the models as a basis for precipitation-type forecasts. Temperature forecasts from LAM25S are compared to observed precipitation types in about 7300 cases. The best correlation was found when snow was forecasted at model temperatures below 08C, and sleet at model temperatures between 08 and 1.58C, else rain was forecasted. The 2-m temperature in LAM25S is corrected with 0.68C/100 m from lowest model level to station level, to give a relevant comparison with the melting level forecasts from ICE25S. LAM25S is expected to have an error in temperature forecasts in cases when precipitation is melting close to the ground. Precipitation type is a categorical parameter, and the numerical bias value is calculated by giving each case in a category the value of a number related to precipitation type (Table 1). The bias is calculated by comparing the category of forecast and observation in each case, and is a number varying from 22 to 2, where 22

For mean sea level pressure, 10-m windspeed, and 2-m temperature, daily observations from synoptic stations over northwestern Europe are compared to model calculations. Bias of 2-m temperature is reduced, and standard deviation of error is reduced for mean sea level pressure (MSLP) and 2-m temperature (Fig. 3). Bias of 10-m windspeed and standard deviation of error of MSLP and 10-m windspeed show no impact from the ice phase parameterization. During the parallel run there appeared to be a need for tuning of the model. The verification presented here is the result of the final tuned version of the model. The condensation scheme interacts with the models dynamics by releasing latent heat. Radio sounding data from northwestern Europe are also compared to model calculations of windspeed and geopotential height. For these parameters the differences in standard deviation of error and bias are insignificant in the 10-week run, and it seems as if the model dynamics is not too sensitive to the changes in the cloud/condensation parameterization. 4. The influence of ice phase microphysics on model performance Numerical weather prediction models are now on a large range of scales, from about 100 km down to 5-km horizontal mesh size. Many meteorological institutes are running a main model with horizontal mesh size of approximately 0.58 and additional model(s) with higher resolution covering a smaller area and integrating a shorter forecast time. Operational forecasts are often based on the main model, and experiences in using the very high resolution models for daily weather forecasting are limited.

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A system to be resolved in a numerical model must have an extent or scale of at least four times that of the grid distance, which means approximately 200 km for many NWP models. The ice phase is documented to have a significant influence on the development of a number of meteorological systems, but these systems are in most cases too small to be resolved in the present numerical model. Atlas et al. (1969) documented a case where mesoscale oscillations in the wind near the melting layer are produced by pressure perturbations due to horizontal variation of cooling by melting of snow associated with the precipitation pattern. Marwitz (1983) showed that the isothermal layer produced by melting was changing the circulation in stable orographic clouds and displacing the maximum precipitation upwind of the mountain crest. Braun and Houze (1995) calculated the magnitude of cooling and heating rates due to melting and freezing, respectively, in a mesoscale convective system. Since the conversion of cloud water to ice and the melting of snow are features of widespread frontal precipitation systems as well, the remainder of this section will concentrate on the dynamical feedback of improved microphysical parameterization in an NWP model. a. The melting layer A significant melting layer is often difficult to discover in the model fields. The latent heat consumed by melting is only about 10% of the latent heat released by condensation, and as condensation in frontal situations often occurs close to the ground, the melting term is overridden by the condensation term. Some melting can be seen below cloud base when a front is approaching, but as condensation is developing close to the earth’s surface, the signature of an isothermal melting layer rapidly disappears. Figure 4 shows a forecasted low near Spitsbergen with connected precipitation over most of the Norwegian west coast. The following experiments are run on this situation, and vertical cross sections are made through the front on the line BB. In Fig. 5 a comparison is made between the temperature profile from ICE50S and LAM50S in a time cross section from the Station Bodø (point A in Fig. 4) at the west coast of northern Norway. From 1200 to 2100 UTC the isotherms below 273 K are forced relatively closer to the ground in ICE50S. This coincides with the period ← FIG. 2. (a) Bias in precipitation-type forecasts for southern Norway from ICE25S, covering the period February–May 1993 and about 400 stations. Heavy black contour is land contour, black contour is bias 5 0, light-shaded red areas are 20.5 . bias . 21, dark-shaded red areas are 21 . bias . 21.5 (forecasted precipitation type is too warm), light-shaded blue areas are 0.5 , bias , 1, dark-shaded blue areas are 1 , bias , 1.5, solid blue areas are 1.5 , bias , 2, and green area is bias 5 $2 (forecasted precipitation type is too cold). (b) Same as in Fig. 2a, but for LAM25S.

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FIG. 3. Bias and standard deviation of error in forecasts of surface parameters from ICE50S (legend lam503) and LAM50S. Verification against synops in northwestern Europe for the period 14 May–24 June 1994. Horizontal axis is forecast length in hours; vertical axis are, respectively, hPa (upper two panels) and 8C (lower panels).

when latent heat of melting is consumed (Fig. 6) but release of latent heat of condensation has not reached its maximum value (Fig. 7). Later the differences between the models start to disappear as the condensation term completely dominates and snow reaches the ground. The resulting 2-m temperature fields in the two

models contain the temperature difference in the same period (as in Fig. 5) as precipitation starts as rain and gradually changes to snow (Fig. 8). Given the condition that melting is occurring below cloud base, the melting of precipitation is able to produce an isothermal layer in the model. The melting layer

FIG. 4. Mean sea level pressure (hPa, heavy lines) and 3-h accumulated precipitation (0.5, 1, 2, 4, 6 mm, thin lines). The 12-h forecast started at 0000 UTC 11 October 1994.

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FIG. 5. Time cross section at point A of Fig. 4. The 24-h forecast started at 0000 UTC 11 October 1994. Temperature in kelvins; ICE50S, solid lines; LAM50S, dotted lines.

FIG. 7. Time cross section as in Fig. 5. Released heat by condensation in joules accumulated in the model layers over the last 3 h in ICE50S.

is stable and might have some dynamical implications, but the model is not able to resolve the mesoscale perturbations in the wind fields as described by Atlas (1969) and Marwitz (1983). b. Latent heat released by condensation

FIG. 6. Time cross section as in Fig 5. Consumed heat by melting in joules accumulated in the model layers over the last 3 h in ICE50S.

The latent heat released by condensation is an important source of buoyancy for the air parcel, and in extratropical cyclones it is sometimes crucial for the development (Sundqvist et al. 1989; Grøna˚s et al. 1994). The latent heat released is balanced by the adiabatic cooling by expansion, and thus the vertical velocity will reflect the condensation process. When the condensation process goes from vapor to ice, the released heat is about 10% larger than when it goes from vapor to water. In the model this increased heat release will occur in the whole column down to the 08C isotherm as long as the model cloud top is higher than the 2128C isotherm. The latent heat released in the condensation/sublimation process in ICE50S is shown in vertical cross section BB (Fig. 9) through the front in Fig. 4. A reference run with LAM50S (Fig. 10) shows significantly reduced heat re-

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FIG. 8. (Upper panel) The 3 h accumulated precipitation rain (solid) and snow (dotted) in ICE50S at point A in Fig. 4. (Lower panel) The 2-m temperature in ICE50S (solid) and LAM50S (dotted) at the same point.

lease in low levels. The specific humidity fields in Fig. 11 explain the observed changes in distribution of latent heat release. Because the ice phase microphysics is valid all the way down to the 08C isotherm in ICE50S, the saturation vapor pressure is lower than in LAM50S and the removal of vapor by condensation is more effective. The specific humidity has its maximum values near the surface. In higher levels the difference in saturation vapor pressure over ice and over water is substantially larger. The humidity in ICE50S is effectively removed by condensation, but in LAM50S it is carried to higher

levels before it is removed. The vertical velocity fields (Fig. 12) show that upward motion is stronger at low levels in ICE50S and at higher levels in LAM50S because the latter tends to release its latent heat at higher levels. This effect in general may have some importance for cyclone development. It is known that for cyclone spinup it is important to have latent heat release at low levels to maximize growth. We have not however noticed this in our study. In the parameterization of the ice phase, snow and cloud ice are assumed to be indistinguishable except in

FIG. 9. Vertical cross section along line BB in Fig. 4 and the same forecast. Temperature is in K, and 3-h accumulated released heat of condensation is in joules. Vertical axis hPa; horizontal axis latitude–longitude.

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FIG. 10. Same as in Fig. 9 but for LAM50S.

terms of fall speed, and the cloud ice variable is therefore omitted. In the initiation of a precipitation process, when the cloud cover gradually builds up, the condensate is water or supercooled water. In the scheme, when the cloud top eventually reaches the 2128C level, the Bergeron–Findeisen process is assumed to start. The ice particles grow at the expense of water droplets and the net result is release of latent heat of freezing. This is not calculated when the cloud ice variable is absent in the model. An experimental run where the model is extended with a prognostic cloud ice variable in order to quantify the error of this simplification has been performed. The cloud ice is prognostic in the same sense as the cloud water: it is not advected but it is stored in the grid box from one time step to the next. The sinks and source terms are assumed to be substantially larger than the advection term, which therefore is omitted. The

latent heat released by freezing cloud water at temperatures between 08 and 2128C is added to the condensation heating. The experiment showed an increase in latent heat release due to the cloud ice variable, but the difference is small compared to the difference due to introduction of the ice phase itself. The vertical velocity fields show no response to these small amounts of heat. c. Probability of ice The cloud-top temperature 2128C is chosen to distinguish between cloud ice and cloud water, assuming that the two are mutually exclusive. For homogenous freezing of cloud water a temperature of 2408C is needed, but heterogeneous freezing on ice condensation nuclei (IN) is common in clouds. However, the concentration of ice crystals is not always represented by the

FIG. 11. Vertical cross section as in Fig. 9. Specific humidity in kg vapor/kg air from ICE50S (solid) and LAM50S (dotted).

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FIG. 12. Vertical cross section as in Fig. 9. Omega in hPa s21 from ICE50S (solid) and LAM50S (dotted).

concentration of IN measured or expected to be activated in the cloud. Temperature, drop size spectrum, and microphysical processes in connection with the detailed dynamics of the cloud are all important (Cotton and Anthes 1989). For the numerical weather prediction model in question, the only possible parameterization of probability of ice is in terms of temperature. The IN concentration is not available for daily forecasting, drop size spectrum is not parameterized in the model, and detailed cloud dynamics is not resolved. Alternatively to the cloud-top temperature criterion, the probability of ice can be calculated as a function of temperature and precipitation type in each grid point. A probability function suggested by Sundqvist (1993) is applied: fice 5 1 2 A[1 2 exp(2x2)],

(13)

with fice 5 0 for T $ T1, T1 5 273 K, and fice 5 1 for T $ Tci, Tci 5 232 K. x5

(T 2 T ci ) (T2 2 T ci )

(13a)

1 ]T 2 .

and T2 5 max

] fice

(13b)

Here, T2 is chosen to be 258 K and A determines the rate of change of ice mixing ratio with decreasing temperature and is dependent on the choice of T2. Probability of ice is modified by the function (mod) f ice 5 fice 1 (1 2 fice )

Pice Ptot

(14)

to calculate for snow falling from layers aloft: Pice is precipitating snow and Ptot is total precipitation. Probability of ice as function of temperature and precipitation type is shown in Fig. 13.

The probability of ice is expected to affect the distribution of rain and snow at the model surface. A test run for case of 11 October 1994 is performed, and the distribution of snow at the model surface is compared to ICE50S. The distribution of snow using the two different probability functions is shown in Fig. 14. The differences are too small to be captured by the available observational network in these areas, although there is a large area of discrepancy in the Norwegian Sea; this is only a 0.5-mm contour line accumulated over 6 h. It is not surprising that the results are very similar, as the Sundqvist’s probability function can be looked upon as a smoother version of the one proposed by Golding, and it will have a tendency to give small amounts of ice over a larger area. The introduction of the ice phase is shown to have significant influence on distribution of latent heating in the model. The discrimination between water and ice on the basis of a threshold temperature contains an uncertainty, as the model does not carry all the variables that determine condensate phase in real clouds. It is of importance, then, to see that the model is not too sensitive to how ice and water are distributed, because we do not want the feedback from the ice phase to be introduced on the basis of an erroneous diagnosis of ice. 5. Conclusions Motivated by the need for a description of the ice phase in the condensation scheme of numerical weather prediction models, a condensation scheme developed by Golding (1989) has been implemented and tested in the Norwegian limited area model (LAM50S). The importance of the ice phase in cloud microphysics and formation of precipitation is well known and documented, for example, by Rutledge and Hobbs (1983). The scheme is fairly simple to implement in the mod-

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FIG. 13. (Upper-left panel) Modified probability of ice as function of probability of ice and fraction of snow in the grid box. Probability lines are 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 with the lowest value down and to the left. (Upper-right panel) Probability of ice as function of temperature in the grid box and fraction of snow; T2 is 249 K. (Lower-left panel) Probability of ice as function of temperature and fraction of snow; T2 is 258 K. (Lower-right panel) Probability of ice as function of temperature and fraction of snow; T2 is 299 K. Line for probability 1.0 is to the upper-left edge; probability 0.1 is in the lower-right corner.

FIG. 14. Distribution of 6-h accumulated snow at 1800 UTC 11 October 1994 from ICE50S (solid) and ICE50S extended with the probability function of Sundqvist to discriminate between water and ice (dotted).

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el. It requires only the supplementary variable snow in addition to the variables used in the condensation scheme of LAM50S. The crucial assumption in the scheme is that water clouds and ice clouds are mutually exclusive, so there is a need for a method to diagnose the cloud type. The present scheme diagnoses the cloud on basis of cloud-top temperature, where 2128C is taken to be the criterion for ice clouds. The scheme also includes more detailed parameterization of cloud microphysics than the scheme used in LAM50S. The scheme is tested against the Norwegian limited area model and its two-phase condensation scheme (water vapor and liquid water) in parallel runs of two time series of 3 and 4 months each. Validation of precipitation, precipitation type, 2-m temperature, and some dynamical variables against surface observations are shown in this article. Two experiments with an extended scheme are performed: the first by introducing a cloud ice variable to calculate latent heat release by freezing of cloud water to cloud ice when snow from aloft is entering a layer of supercooled cloud water. The second experiment is to test a probability function of ice suggested by Sundqvist (1993) replacing the cloud top below the2128C criterion. Comparison between the two schemes shows that precipitation type is well forecasted by the Golding scheme and is better than we achieved with the 2-m temperature as a predictor for snow or rain, which is often used by the forecasters. Precipitation amount is about equally in the two models, but tuning of the Golding scheme has led to changes in precipitation fields that fit well with the observed systematic errors in precipitation forecasts. Precipitation amount is increased in areas of heavy precipitation, and the horizontal extent of the areas is reduced. The difference between the schemes obtained in the forecast of 2-m temperature is connected to certain winter situations with melting of precipitating snow near the ground. Forecast of mean sea level pressure, height of pressure surfaces, and windspeed turned out to have the same magnitude of error in verification of the two schemes. The testing of extended microphysics in the Golding scheme shows that the main impact on model behavior is due to the introduction of the ice phase. Under the condition that condensation is not taking place in the melting layer, the model will develop an isothermal melting layer, but melting-layer wind perturbations are not resolved. Further extension of the scheme by a cloud ice variable seems not to be necessary at the scale of the present model. The probability function of ice suggested by Sundqvist is changing the distribution of snow and rain on a scale that is not resolved by the observational network and is therefore difficult to verify. The practical conclusion was that the scheme was implemented into the operational numerical weather prediction model at the Norwegian Meteorological Institute because it competes satisfactorily with the original scheme and provides a suitable tool for prediction of snow.

Acknowledgments. I would like to thank Professor Thor Erik Nordeng at the Norwegian Meteorological Institute for supervising the work with implementation of the Golding scheme into the numerical weather prediction model from the very beginning and for valuable discussions and comments on the manuscript. I am also grateful to two anonymous reviewers who have helped to improve the clarity of the paper with their critical questions and comments. REFERENCES Atlas, D., R. Tatehira, T. C. Srivastava, W. Marker, and R. E. Carbone, 1969: Precipitation-induced mesoscale wind perturbations in the melting layer. Quart. J. Roy. Meteor. Soc., 95, 544–560. Braun, S. A., and R. A. Houze Jr., 1995: Melting and freezing in a mesoscale convective system. Quart. J. Roy. Meteor. Soc., 121, 55–79. Cotton, W. R., and R. A. Anthes, 1989: Storm and Cloud Dynamics. International Geophysics Series, Vol. 44, Academic Press, 883 pp. Fabry, F., and I. Zawadzki, 1995: Long-term radar observations of the melting layer of precipitation and their interpretation. J. Atmos. Sci., 52, 838–851. Golding, B. W., 1989: A simple two phase precipitation scheme for use in numerical weather prediction models. U.K. Meteorological Office Science Note 13, 18 pp. [Available from U.K. Meteorological Office, London Road, Bracknell, Berkshire RG12 2SZ, United Kingdom.] Grøna˚s, S., and O. E. Hellevik, 1982: A limited area prediction model at the Norwegian Meteorological Institute. Norwegian Meteorological Institute Tech. Rep. 61, 75 pp. [Available from Norwegian Meteorological Institute, P.O. Box 43, Blindern, N-0313 Oslo, Norway.] , N. G. Kvamstø, and E. Raustein, 1994: Numerical simulation of the northern Germany storm of 27–28 August 1989. Tellus, 46A, 635–650. Heymsfield, A., 1977: Precipitation development in stratiform ice clouds: A microphysical and dynamical study. J. Atmos. Sci., 34, 367–381. Journel, A. G., and C. J. Huijbregts, 1978: Mining Geostatistics. Academic Press, 600 pp. Kessler, E., 1969: On the Distribution and Continuity of Water Substance in Atmospheric Circulation. Meteor. Monogr., No. 32, Amer. Meteor. Soc., 84 pp. Marwitz, J. D., 1983: The kinematics of orographic airflow during Sierra storms. J. Atmos. Sci., 40, 1218–1227. Matsuo, T., and Y. Sasyo, 1981a: Empirical formula for the melting rate of snowflakes. J. Meteor. Soc. Japan, 59, 1–9. , and , 1981b: Non-melting phenomena of snowflakes observed in subsaturated air below freezing level. J. Meteor. Soc. Japan, 59, 26–32. Nordeng, T. E., 1986: Parameterization of physical processes in a three-dimensional numerical weather prediction model. Norwegian Meteorological Institute Tech. Rep. 65, 61 pp. [Available from Norwegian Meteorological Institute, P.O. Box 43, Blindern, N-0313 Oslo, Norway.] , and E. A. Rasmussen, 1992: A most beautiful polar low. Tellus, 44A, 81–99. Rutledge, S. A., and P. V. Hobbs, 1983: The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. VIII: A model for the ‘‘seeder-feeder’’ process in warm-frontal rainbands. J. Atmos. Sci., 40, 1185–1206. Sundqvist, H., 1993: Inclusion of ice phase of hydrometeors in cloud parameterization for mesoscale and large-scale models. Contrib. Atmos. Phys., 66, 137–147. , E. Berge, and J. E. Kristjansson, 1989: Condensation and cloud parameterization studies with a mesoscale numerical weather prediction model. Mon. Wea. Rev., 117, 1641–1657.