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  • View in gallery

    Sequence of idealized vertical temperature profiles accompanying a transition from heavy rain to snow at the surface, with account of latent heat absorption via melting. The sequence of panels from top to bottom represents a progression of time, with an increment of roughly 3 h. A saturated atmosphere is assumed. The inset in (a) summarizes terminology relating to the Eta Model, as indicated in the legend at the top of the inset. The locations corresponding to the soil skin temperature, lowest air temperature, and 2-m temperature are also labeled

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    As in Fig. 1 but for idealized vertical temperature profiles accompanying an evolution from sleet to freezing rain and then rain, with account of latent heat absorption (release) via melting (freezing)

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    Synoptic summary based on Eta Model analysis for 12 Feb 2001 for sea level pressure (dashed, contour interval 2 hPa, leading 10 omitted), 500-hPa geopotential height (solid, contour interval 6 dam), and absolute vorticity (shaded, interval 8 × 10−5 s−1 as indicated in legend at lower right): (a) Eta analysis valid 0000 UTC 12 Feb, (b) analysis valid 1200 UTC 12 Feb, and (c) analysis valid 0000 UTC 13 Feb. Subjectively identified frontal locations are included in (b) and (c)

  • View in gallery

    As in Fig. 3 but showing Eta-analyzed sea level pressure (solid, contour interval 2 hPa) and 2-m temperature (dashed and shaded, contour interval 1°C). Shaded regions correspond to temperatures below 0°C

  • View in gallery

    Surface observations and radar mosaic lowest-level base reflectivity for 0900 UTC 12 Feb 2001. Reflectivity values indicated on scale at left

  • View in gallery

    Sensible weather summary for 12 Feb event: (a) maximum temperatures (°F), (b) observed liquid-equivalent precipitation (in.), and (c) frozen precipitation (in.). In (c) T denotes trace. Figure courtesy of the Raleigh National Weather Service Forecast Office

  • View in gallery

    Eta forecast sequence of 2-m temperature (contour interval 1°C, dashed lines with shading below 0°C) and cumulative precipitation (solid contours, interval 0.01, 0.05, and every 0.1 in. thereafter) for 12 Feb: (a) 18-h forecast valid 0600 UTC 12 Feb, (b) 24-h forecast valid 1200 UTC 12 Feb, (c) 30-h forecast valid 1800 UTC 12 Feb, and (d) 36-h forecast valid 0000 UTC 13 Feb

  • View in gallery

    Eta forecast sounding sequence for RDU, with forecast times as in Fig. 7 and in Skew T–logp format. Temperature is plotted as bold solid lines; dewpoint temperature is plotted as bold dashed lines

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    As in Fig. 8 but for a comparison of Eta forecast sounding with GSO rawinsonde data for 1200 UTC 12 Feb 2001: (a) 24-h Eta Model forecast profile for GSO and (b) GSO rawinsonde profile

  • View in gallery

    Eta Model soil temperature analysis (contour interval 1 K) valid 1200 UTC 12 Feb 2001: (a) 0–10-, (b) 10–40-, and (c) 40–100-cm layer

  • View in gallery

    Modified Eta 2-m temperature forecast that includes a correction for latent heat released by freezing rain. Times are as in Fig. 7

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Model Representation of Freezing and Melting Precipitation: Implications for Winter Weather Forecasting

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  • 1 Department of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, North Carolina
  • | 2 NOAA/NWS Forecast Office, Raleigh, North Carolina
  • | 3 NOAA/NWS Forecast Office, Greenville–Spartanburg, South Carolina
  • | 4 NOAA/NWS/NCEP/EMC, Camp Springs, Maryland
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Abstract

During episodes of sustained moderate or heavy precipitation in conjunction with near-freezing temperatures and weak horizontal temperature advection, the latent heat released (absorbed) by the freezing (melting) of falling precipitation may alter thermal profiles sufficiently to affect the type and amount of freezing or frozen precipitation observed at the surface. Representation of these processes by operational numerical weather prediction models is incomplete; forecaster knowledge of these model limitations can therefore be advantageous during winter weather forecasting. The Eta Model employs a sophisticated land surface model (LSM) to represent physical processes at the lower-atmospheric interface. When considering the thermodynamic effect of melting or freezing precipitation at the surface, it is shown that limitations in the current version of the Eta LSM can contribute to biases in lower-tropospheric temperature forecasts. The Eta LSM determines the precipitation type reaching the surface from the air temperature at the lowest model level; subfreezing (above freezing) temperatures are assumed to correspond to snow (rain) reaching the surface. There is currently no requirement for consistency between the LSM and the Eta grid-scale precipitation scheme. In freezing-rain situations, the lowest model air temperature is typically below freezing, and the Eta LSM will therefore determine that snow is falling. As a result, a cold bias develops that is partly caused by the neglected latent heat release accompanying the freezing of raindrops at the surface. In addition, alterations in surface characteristics caused by erroneous snowfall accumulation in the model may also contribute to temperature biases. In an analogous fashion, warm biases can develop in cases with melting snow and above-freezing air temperatures near the surface (the LSM assumes rain). An example case is presented in which model misrepresentation of freezing rain is hypothesized to have contributed to a lower-tropospheric cold bias. A simple temperature correction, based on the first law of thermodynamics, is applied to lower-tropospheric model temperature forecasts; the neglect of latent heat released by freezing rain in the model is shown to contribute substantially to a cold bias in near-surface temperature forecasts. The development of a spurious snow cover likely exacerbated the bias.

Corresponding author address: Gary M. Lackmann, Dept. of Marine, Earth, and Atmospheric Sciences, North Carolina State University, 1125 Jordan Hall, Box 8208, Raleigh, NC 27695-8208. Email: gary@ncsu.edu

Abstract

During episodes of sustained moderate or heavy precipitation in conjunction with near-freezing temperatures and weak horizontal temperature advection, the latent heat released (absorbed) by the freezing (melting) of falling precipitation may alter thermal profiles sufficiently to affect the type and amount of freezing or frozen precipitation observed at the surface. Representation of these processes by operational numerical weather prediction models is incomplete; forecaster knowledge of these model limitations can therefore be advantageous during winter weather forecasting. The Eta Model employs a sophisticated land surface model (LSM) to represent physical processes at the lower-atmospheric interface. When considering the thermodynamic effect of melting or freezing precipitation at the surface, it is shown that limitations in the current version of the Eta LSM can contribute to biases in lower-tropospheric temperature forecasts. The Eta LSM determines the precipitation type reaching the surface from the air temperature at the lowest model level; subfreezing (above freezing) temperatures are assumed to correspond to snow (rain) reaching the surface. There is currently no requirement for consistency between the LSM and the Eta grid-scale precipitation scheme. In freezing-rain situations, the lowest model air temperature is typically below freezing, and the Eta LSM will therefore determine that snow is falling. As a result, a cold bias develops that is partly caused by the neglected latent heat release accompanying the freezing of raindrops at the surface. In addition, alterations in surface characteristics caused by erroneous snowfall accumulation in the model may also contribute to temperature biases. In an analogous fashion, warm biases can develop in cases with melting snow and above-freezing air temperatures near the surface (the LSM assumes rain). An example case is presented in which model misrepresentation of freezing rain is hypothesized to have contributed to a lower-tropospheric cold bias. A simple temperature correction, based on the first law of thermodynamics, is applied to lower-tropospheric model temperature forecasts; the neglect of latent heat released by freezing rain in the model is shown to contribute substantially to a cold bias in near-surface temperature forecasts. The development of a spurious snow cover likely exacerbated the bias.

Corresponding author address: Gary M. Lackmann, Dept. of Marine, Earth, and Atmospheric Sciences, North Carolina State University, 1125 Jordan Hall, Box 8208, Raleigh, NC 27695-8208. Email: gary@ncsu.edu

1. Introduction

As output from operational numerical weather prediction (NWP) models assumes an increasingly important role in the forecast process, additional demands are placed on operational weather forecasters. Few would argue that it is advantageous for forecasters to possess a solid physical and conceptual understanding of atmospheric processes. However, increased reliance on NWP models necessitates that forecasters must also understand how operational models represent atmospheric processes. Furthermore, forecasters are faced with the daunting task of staying abreast of frequent changes to model resolution, physics packages, and data assimilation systems. One specific scenario in which forecaster knowledge of model physics can be advantageous is winter precipitation forecasting.

In many winter weather situations, small changes in the vertical profile of temperature can produce dramatic changes in precipitation type, the amount of freezing or frozen precipitation observed at the surface, and other sensible weather conditions. This circumstance is particularly evident in the Carolinas and Virginia, where multiple precipitation types frequently occur at a single location during winter storms. For example, Moyer (2000) discovered that 86% of the wintry precipitation events at the Greenville–Spartanburg airport in upstate South Carolina consisted of two or more precipitation types. The occurrence of multiple precipitation types across the region is so common that Keeter and Cline (1991) developed a forecast technique to provide guidance regarding the predominant type of precipitation in mixed events at various sites across North Carolina.

These climatological observations and region-specific forecast strategies are indicative of the complex character of the atmosphere's thermal structure during winter precipitation events. Frequent transitions among sleet, snow, freezing rain, and rain may occur as the temperature fluctuates within several degrees of 0°C at some level (or multiple levels) in the lower troposphere. Therefore, an accurate forecast of precipitation type requires an accurate forecast of details of the vertical temperature profile, especially near the surface. Model forecast soundings, which possess high spatial and temporal resolution, provide forecasters with a valuable tool, but the margin for error is so small that one cannot rely on the numerical model temperature profile as the sole predictor of precipitation type. Experience during recent winter storms has demonstrated that a better understanding of physical processes and their representation in the models will provide forecasters with an opportunity to use numerical guidance in the most efficient manner.

When faced with winter precipitation scenarios, forecasters must consider all physical processes that may affect the thermal profile. Although the latent heat associated with melting and freezing precipitation is small relative to that from evaporation and condensation of an equal mass of water substance, it is often concentrated within shallow atmospheric layers and can, therefore, produce locally significant alterations to the temperature profile (Kain et al. 2000). During sustained moderate or heavy precipitation when horizontal temperature advection is weak, melting snow can lead to the development of a near-freezing isothermal layer. These layers have received considerable attention in the meteorological literature (e.g., Findeisen 1940; Wexler et al. 1954; Lumb 1960, 1961, 1963; Atlas et al. 1969; Carbone 1982; Stewart 1984, 1985, 1992; Matsuo et al. 1985; Bosart and Sanders 1991; Fujibe 2001). In a similar way, latent heat release accompanying the freezing of liquid precipitation during sleet and freezing rain can significantly affect the temperature profile, as will be demonstrated herein.

Temperature changes brought about via latent heat release (absorption) accompanying the freezing (melting) of precipitation are difficult to forecast because (i) many NWP models are not configured to adequately account for these processes and (ii) model biases in these situations are linked to quantitative precipitation forecasts (QPF). The challenge to operational forecasters is amplified by the fact that when wintry precipitation threatens there is a heightened demand for information about how much precipitation will fall (in addition to a correct precipitation-type forecast). This demand immediately exposes an oft-noted NWP weakness: QPF. For example, model forecast parameters may indicate an upcoming cold rain event; if actual precipitation is heavier than expected, melting-induced cooling can instead result in a heavy snowfall. Although rare, events of this type are often accompanied by significant disruptions to human activity. McGuire and Penn (1953), Wexler et al. (1954), Lumb (1960), Gedzelman and Lewis (1990), Bosart and Sanders (1991), Ferber et al. (1993), and Kain et al. (2000) have documented cases in which the latent heat of melting affected precipitation type.

This paper advances the hypothesis that substantial temperature biases can arise because of the manner in which the National Centers for Environmental Prediction (NCEP) Eta Model represents phase changes of precipitation reaching the surface. A preliminary test of this hypothesis is provided through consideration of a freezing-rain event from 12 February 2001. The objectives of this research are (i) to alert operational forecasters to potential model biases resulting from the misrepresentation of freezing and melting and (ii) to illustrate how physical understanding of atmospheric processes can be combined with knowledge of model representations to improve interpretation of model output. A brief review of the thermodynamics of freezing and melting and the model representation of these processes is provided in section 2. Section 3 presents an example case. Section 4 follows with suggestions to aid forecasters in addressing model biases.

2. Winter precipitation thermodynamics and model representations

Several earlier studies have documented the dynamical impacts of the melting of precipitation (e.g., Carbone 1982; Marwitz and Toth 1993; Stewart et al. 1990; Szeto and Stewart 1997). Although these studies reveal important feedbacks regarding vertical motion, frontogenesis, and precipitation intensity, in this paper we restrict our focus to the thermodynamics of melting and freezing precipitation without consideration of the ability of operational models to represent melting-induced circulations.

a. Melting and freezing aloft

Although the emphasis in this paper is on model representation of phase changes at the surface, for completeness we will first summarize model representation of melting and freezing aloft. As the sophistication of grid-scale precipitation schemes in operational models has grown, the representation of latent heat released or absorbed during phase changes of falling hydrometeors has now become reasonably complete (e.g., Kain et al. 2000). However, it is important to emphasize two caveats: (i) the adequacy of model representation of these processes is tied to QPF, and (ii) it is not clear that thermodynamic impacts resulting from phase changes of subgrid-scale precipitation are represented adequately.

1) Melting aloft

Consider the idealized situation depicted in Fig. 1a, in which snow is falling into a layer of saturated, above-freezing air near the surface. The melting of falling snowflakes absorbs latent heat, cooling the upper portion of the layer to near 0°C (Fig. 1b). As discussed previously, in some situations this cooling mechanism may completely eradicate the above-freezing layer, producing a deep isothermal layer near 0°C and allowing snow to penetrate to the surface (e.g., Wexler et al. 1954; Lumb 1960, 1961, 1963; Stewart 1985). As latent heat absorption cools the melting layer, convective instability may develop beneath, resulting in downward transport of cold air toward the surface (Wexler et al. 1954). One observational signature of a lowering melting layer that operational forecasters have come to recognize is a constricting radar “bright band” on Weather Surveillance Radar-1988 Doppler (WSR-88D) displays.

The NCEP Eta and Aviation (AVN) Models include sophisticated precipitation physics packages relative to the NCEP Nested Grid Model (NGM). Prior to 27 November 2001, the Eta Model (Rogers et al. 1995, 1996) employed the gridscale precipitation scheme of Zhao and Carr (Zhao and Carr 1997; Zhao et al. 1997). On this date, the precipitation scheme was updated (Rogers et al. 2001, section 3.1). Both the Zhao and Carr scheme and the new scheme account for latent heat absorption accompanying the melting of falling snow (Zhao and Carr 1997, section 2d; Rogers et al. 2001). Prior to 15 May 2001, the AVN did not account for ice processes, but on this date the AVN physics package was upgraded to the Zhao and Carr scheme. The NGM still does not account for any ice processes whatsoever, a limitation that is readily apparent in NGM forecast soundings, which can indicate saturation with respect to liquid water (equal temperature and dewpoint temperature) even at temperatures well below freezing.

2) Freezing aloft

Consider the idealized example depicted in Fig. 2, in which falling snow encounters an above-freezing layer of sufficient strength to produce complete melting (Fig. 2a). Suppose that raindrops falling from this warm layer then enter a subfreezing layer that is sufficiently deep to allow the drops to refreeze completely before they reach the surface as ice pellets. As the falling rain refreezes, latent heat is released. A modified temperature profile that accounts for the action of freezing and melting is depicted in Fig. 2b. Cooling is occurring in the melting layer while warming occurs within the refreezing layer. As the lower subfreezing layer erodes, sleet changes to freezing rain and subsequent latent heat is released at the surface (Fig. 2b). In the absence of a compensating cooling mechanism, this heat release will warm the surface temperature to 0°C; this scenario is discussed in section 2b.

Latent heat released by the freezing of falling rain is neglected in the Zhao and Carr (1997) scheme; this assumption is often justified because vertical velocities on the grid scale are usually too weak to advect hydrometeors above the freezing level (Zhao and Carr 1997, section 2d). However, this assumption is irrelevant when raindrops fall below the freezing level during a sleet (ice pellet) event. The updated Eta grid-scale precipitation scheme does account for latent heat released by freezing aloft (Rogers et al. 2001, section 3.1), although the effective temperature at which raindrops freeze is difficult to parameterize, especially during supercooled freezing-drizzle situations (e.g., Huffman and Norman 1988; B. Ferrier 2001, personal communication). The Zhao and Carr scheme was incorporated into the AVN model on 15 May 2001. Therefore, the neglect of the latent heat released by the freezing of raindrops during sleet contributes a cold bias for the freezing layer in AVN forecasts.

b. Freezing and melting at the surface

A detailed discussion of model land surface representations is beyond the scope of this paper; however, to provide sufficient context for the discussions that follow, a brief summary of the Eta land surface model (LSM) is provided below.

1) The Eta land surface model

As surface process representation in operational NWP models has increased in sophistication, some models now include quasi-independent land surface models to handle communication between the surface and atmosphere. The Eta LSM (Chen et al. 1996, 1997) determines a surface energy balance that incorporates incoming solar and terrestrial radiation, reflected radiation, turbulent fluxes of latent and sensible heat, heat fluxes into or out of the ground, fluxes related to snowmelt and freezing rain, and precipitation–surface fluxes in the presence of a snowpack. The soil heat flux is dependent upon the local vegetation characteristics, soil type, soil moisture, and the soil temperature profile. Based on the surface energy balance, a “skin temperature” (see Fig. 1a inset) is computed by the LSM.

It is through the skin temperature that surface processes are communicated to the overlying atmosphere, via turbulent fluxes of heat, moisture, and momentum, outgoing longwave radiation, and albedo effects in the case of snow. If the LSM detects freezing rain or melting snow at the surface, the impact is not communicated directly to the atmosphere. In other words, there is not a direct representation of surface processes in the temperature tendency equation of the atmospheric model. Rather, these effects are communicated to the atmosphere via surface processes that are linked to the skin temperature.

In cases in which liquid precipitation freezes or solid precipitation melts upon contact with the ground, latent heat release or absorption will be shared between the ground and lowest portion of the atmosphere. The extent to which surface-based thermodynamic alterations are communicated to the overlying atmosphere also depends on near-surface atmospheric stability and the nature of the thermodynamic process in question. Given that precipitation is falling in the model, the Eta LSM determines precipitation type by examining the air temperature at the lowest model level. If the lowest air temperature is above freezing, rain is assumed; if the lowest air temperature is below freezing, snow is assumed. If the soil skin temperature1 is above (below) freezing, and the lowest air temperature is below (above) freezing during precipitation, the model assumes that snow (freezing rain) is falling, and the LSM accounts for the corresponding heat absorbed (released). However, most freezing-rain events are accompanied by subfreezing near-surface air temperatures; therefore, the LSM rarely represents freezing rain correctly (snow is assumed). In a similar fashion, situations in which wet snow is falling with above-freezing near-surface temperatures will not be represented correctly (rain is assumed).

2) Melting at the surface

As demonstrated by Lumb (1961) and others, falling snow may penetrate 400–700 m below the freezing level, depending on the precipitation intensity, the initial temperature lapse rate, and the relative humidity. Situations in which rain changes to wet snow at the surface will therefore be characterized by a period during which wet snow will melt on an above-freezing surface, as depicted in Fig. 1b. The melting absorbs heat, and, if sufficient precipitation intensity persists, the near-surface air temperature may cool to near 0°C (Fig. 1c). Fujibe (2001) found that this occurrence is especially favored under light wind conditions. In these situations, the initial ground temperature can be an important factor in modulating snowfall accumulation. The action of differential latent heat absorption and conduction from the surface will serve to stabilize the near-surface atmospheric layer, which will tend to concentrate the cooling effect of latent heat absorption near the surface [perhaps contributing to the light wind conditions noted by Fujibe (2001) in these circumstances]. The increased near-surface stability would inhibit the upward transport of cooled air because it would serve to suppress turbulent mixing and reduce boundary layer depth.

Consider a situation similar to that depicted in Fig. 1b, with wet snow reaching an above-freezing surface. Recall that if the lowest air temperature is above freezing then rain is assumed by the LSM. In the situation described above (Fig. 1b), the soil skin temperature and lowest air temperature are both above freezing, so the LSM would treat falling precipitation as rain. The neglect of melting snow at the surface would contribute a near-surface warm bias. An additional consideration in this situation would be the failure of the model to account for snow accumulation, which in reality could insulate the lower atmosphere from upward heat flux from the ground and could alter the surface albedo.

3) Freezing at the surface (freezing rain)

In the situation depicted in Fig. 2b, freezing rain is observed at the surface, resulting in the release of latent heat at the surface. The warming from latent heat release affects both the ground and the lower atmosphere; this heat partitioning is complex and will be discussed in greater detail in the following subsection. Owing to the fact that freezing rain typically occurs in the presence of stable2 atmospheric conditions characterized by shallow subfreezing layers, the warming effects of the latent heat are often confined to these shallow layers and can quickly warm the layer to 0°C, with subsequent precipitation running off. Thus, in the absence of a near-surface cooling mechanism, freezing rain is a self-limiting process; the heat released by freezing can eradicate the subfreezing layer (Stewart 1985), as depicted in Fig. 2c. Other processes, including warm advection (Cortinas 2000), downward infrared radiation from a warm cloud base, upward heat flux from the ground, and sensible heat transport by falling rain can also act to limit the longevity or severity of freezing-rain events. In a climatological study of freezing precipitation in the Great Lakes region, Cortinas (2000) found that only 7% of freezing-rain events lasted longer than 5 h. When prolonged freezing rain does occur, it is usually accompanied by one or more of the following: (i) the presence of extremely cold and/or dry air (and/or soil) at the onset of precipitation, (ii) lower-tropospheric cold- and/or dry-air advection, (iii) adiabatic cooling with upslope flow, or (iv) light freezing precipitation (e.g., Forbes et al. 1987; Rauber et al. 1994; Hanesiak and Stewart 1995; Bernstein 2000). In some circumstances, warm-cloud processes can produce light freezing rain or freezing drizzle in a completely subfreezing environment (Huffman and Norman 1988; Rasmussen et al. 1995; Cober et al. 1996). In contrast to the case of melting snow, latent heat released by freezing rain at the surface acts to destabilize the near-surface atmospheric layer, favoring the development of a shallow mixed layer and facilitating the upward transport of heat from the surface.

In cases in which liquid precipitation freezes upon contact with the ground, Eta Model forecasts rely on the LSM, which determines precipitation type by examining the air temperature at the lowest atmospheric model level. In the case depicted in Fig. 2b, the LSM would erroneously determine that snow was falling, owing to the fact that the lower-tropospheric air temperature is below freezing. The resulting neglect of latent heat release would contribute to a near-surface cold bias in the case of freezing rain. A freezing-precipitation event on 12 February 2001 in the Carolinas exhibited these characteristics and will be presented in section 3. The consequences of LSM misrepresentation of freezing rain are not limited to the thermodynamic impact of latent heat release. For example, if the LSM assumes that snow has accumulated at the surface, the communication of soil heat fluxes to the atmosphere, and surface radiative properties (e.g., the local albedo), may be erroneously altered.

c. Quantitative estimates of the impact of melting and freezing

Quantitative estimates of warming or cooling from the release or absorption of latent heat can be obtained via the first law of thermodynamics, which for an air parcel of unit mass can be expressed as
CpdTαdpdq,
where Cp is the specific heat at constant pressure, T is temperature, α is the specific volume, p is pressure, and q is heat. Consider the temperature changes in a saturated air column of unit area near the surface resulting from latent heat released (absorbed) by freezing rain (melting snow). In these situations, we can justify the neglect of the work term [the second left-hand term in (1)] by restricting our consideration to a subfreezing layer trapped near the surface beneath a temperature inversion.3 Utilizing this assumption and expanding consideration to the mass of air (per unit area) over which the latent heat release or absorption is distributed (denoted M), we can rewrite the first law as
i1520-0434-17-5-1016-e2
where ΔQ is the net latent heat released or absorbed in a column of unit area within the layer and ΔT is the corresponding temperature change from latent heat release or absorption. The total quantity of latent heat release (absorption) from a given amount of freezing rain (melting snow) is given by
QLfρRm
where Lf is the latent heat of fusion at 0°C (3.34 × 105 J kg−1), ρ is the density of liquid water, and Rm is the depth of liquid-equivalent precipitation in meters.

Although the development that follows could easily be applied to melting-snow events, for brevity we will restrict consideration from this point forward to the case of freezing rain. The latent heat released by freezing rain is shared between the ground and the air. Precise knowledge of the partition of heat between the air and ground is complex and is a function of land use and other factors. For example, during a freezing-rain event that is taking place in a coniferous forest, more heat would be released above the surface (in the forest canopy) relative to a similar event that is taking place over bare soil. That portion of the latent heat that directly warms the solid earth is not unimportant to the lower-tropospheric air temperature; some of this energy is communicated to the atmosphere through outgoing infrared radiation and conduction. The soil heat flux can also be a critical factor in the surface energy balance in these situations. For instance, in a situation in which the soil temperature was well below freezing, a larger fraction of the latent heat released by freezing rain would go to warming the soil relative to a case in which only a shallow layer of soil was below freezing. During a freezing-rain event that was taking place over a snow-covered surface, the heat flux into or out of the soil would be mitigated by the insulating influence of the snowpack. To provide a quantitative estimate of the importance of latent heat released by freezing rain to near-surface temperatures, we account for the aforementioned partitioning of latent heat between soil and air and denote the fraction of the heat that ultimately warms the atmosphere as FA.

As noted by Kain et al. (2000), condensation partially cancels the cooling from melting; evaporation similarly partially cancels the warming from freezing in the freezing-rain case. Utilizing (3), introducing the fractional atmospheric heating factor, following Kain et al. [see their (4)], and rearranging yields
i1520-0434-17-5-1016-e4
where Lυ is the latent heat of vaporization and qs is saturation specific humidity. Suppose that in the scenario discussed in section 2d (depicted in Fig. 2b), a 50-hPa-deep subfreezing layer with an average temperature of −3°C (26.6°F) is present near the surface. The corresponding mass in a 50-hPa-deep column of unit area is approximately 510 kg. Assume that sufficient above-freezing air is present above the layer to allow precipitation falling into the layer to have melted. Suppose that during a 6-h period, 12.7 mm (0.5 in) of liquid precipitation falls into the layer. If all of the falling precipitation froze, from (3) we see that 4 241 800 J m−2 would be released. In the case study that follows, we employ a more precise method for estimating FA, but for a rough estimate assume that FA = 0.75. The corresponding warming of the layer from (4) is +3.7°C. In reality, this amount of freezing rain would warm the layer to 0°C in less than 6 h, with subsequent precipitation running off. During cases in which the soil temperature was well below freezing, the factor FA would be smaller and the cooling effect of a downward heat flux into the ground may prolong freezing rain (especially in the absence of a snow cover). In converse, when soil temperatures are relatively warm, reduced icing would be expected. While one remains cognizant of the simplifications implicit in this analysis, an estimate of icing in the absence of other atmospheric cooling mechanisms can be provided by grouping the constants in (4) to obtain4
mmF−1ATfzpPlayer_mb
where icingmm is the liquid-water-equivalent ice depth5 expressed in millimeters, ΔPlayer_mb is the depth of subfreezing air over which the latent heat release is distributed [hPa (mb)], and ΔTfzp is the initial layer-average freezing depression (K or °C). Note that if the dewpoint depression is initially nonzero in the layer, the potential for evaporational cooling should be taken into account by using the freezing depression of the wet-bulb temperature rather than the air temperature in (5). The factor FA can vary from almost 1.0 with a shallow layer of subfreezing soil to 0.5 or less with a cold, bare ground.

d. Model biases and forecasting tools

A variety of tools are available to forecasters to assist with precipitation-type forecasting, including automated statistical guidance (e.g., Bocchieri 1979, 1980); partial-thickness techniques (e.g., Murray 1952; Stewart and King 1987; Keeter and Cline 1991; Heppner 1992; Keeter et al. 1995), and sounding-area techniques (e.g., Bourgouin 2000). The biases described in this paper will affect the accuracy of techniques based on model forecast soundings, for which the margin for error is small. For partial-thickness computations, which often include the 1000–850- and 850–700-hPa layers, the bias introduced by the neglect of freezing and melting depends on where these processes occur relative to the 850-hPa level. For example, suppose that in the situation depicted in Figs. 2a or 2b the falling snow melts completely in the 850–700-hPa layer and refreezes at the surface (in the 1000–850-hPa layer). The Eta Model, which accounts for melting, would in principle provide an accurate forecast in the 850–700-hPa layer but would contain a cold bias in the 1000–850-hPa layer owing to the neglect of heat released by freezing at the surface.

3. An example

During the winters of 1999/2000 and 2000/01, we identified several events (in the Carolinas) in which misrepresentation of melting or freezing was suspected of contributing to model errors. Examples involving sleet and freezing rain were observed on 31 January 2000, 12 February 2001, and 22 February 2001. Cases characterized by cooling from melting of snow occurred on 24 January 2000 and 19 November 2000. The 12 February 2001 case was selected as a representative example, although it contained its own peculiarities. This study will focus on the thermodynamics rather than provide a comprehensive model error analysis.

a. Overview and synoptic discussion

Model forecasts from 11 February 2001 indicated the potential for a significant icing event beginning during the early morning hours of 12 February and continuing throughout the day. The Eta Model predicted precipitation amounts in excess of 25.4 mm (1 in.) in conjunction with 2-m temperatures well below freezing across central portions of North and South Carolina. Only limited icing occurred, in part because lower-tropospheric temperatures warmed to above 0°C. We hypothesize that the misrepresentation of precipitation type reaching the surface by the Eta LSM contributed substantially to the Eta cold bias in this case. In this section, we will undertake a preliminary test of this hypothesis. This objective does not necessitate a detailed observational case study; we are most interested in the physical representations in the model that produced the lower-tropospheric cold bias.

At 0000 UTC 12 February, an arctic anticyclone was centered over southern Ontario, with ridging extending southward into the Delmarva Peninsula region (Fig. 3a). At the 500-hPa level, confluent flow and ridging accompanied the surface anticyclone. A classic Appalachian cold-air damming pattern had become established by 1200 UTC 12 February, with a narrow ridge of high pressure extending from Virginia into northern Georgia (Fig. 3b). At this time, precipitation was overspreading cold air near the surface as a westerly flow of warmer air aloft became established over the Carolinas. By 0000 UTC 13 February, the center of the arctic anticyclone had moved offshore, with a weak remnant ridge still extending across the southeastern states (Fig. 3c).

Daytime solar heating under mostly clear skies had warmed temperatures to well above freezing across the Carolinas and southern Virginia by 0000 UTC 12 February (Fig. 4a). Under a thickening cloud shield, temperatures had fallen only slightly below freezing by 1200 UTC 12 February (Fig. 4b). Analyzed temperatures for 0000 UTC 13 February indicated that only a small portion of north-central North Carolina and west-central Virginia remained below freezing (Fig. 4c). Radar and surface observations for 0900 UTC 12 February indicated the presence of dry air over eastern North Carolina (Fig. 5). A mixture of light snow, freezing rain, and rain was observed at this time. Sublimation and evaporation of falling precipitation are evident over the eastern portion of North Carolina, where radar indicated precipitation aloft while surface observations indicated only cloudy skies, with large dewpoint depressions.

The precipitation became light and scattered after 1200 UTC 12 February (not shown), with temperatures warming to near or above freezing across most of the Carolinas during the day. Observed maximum temperatures ranged from 0° to 3°C (32° to 38°F) across central North Carolina (Fig. 6a). Storm-total liquid-equivalent precipitation ranged from 2.5 to 12.7 mm (0.1–0.5 in.) over central and western North Carolina, with values in excess of 12.7 mm (0.5 in.) over southeastern North Carolina (Fig. 6b). Although central North Carolina received between 6 and 12 mm (0.25–0.5 in.) of liquid precipitation equivalent, only trace amounts of frozen precipitation were reported (Figs. 6b,c).

b. Eta Model performance

Figure 7 presents a sequence of Eta Model 2-m temperature and precipitation forecasts at 6-h intervals beginning 0600 UTC 12 February. The 18-h forecast valid 0600 UTC 12 February indicated subfreezing temperatures over much of North Carolina (Fig. 7a). The 24-h forecast valid 1200 UTC 12 February indicated a tongue of subfreezing air covering upstate South Carolina and most of North Carolina, with 2-m temperatures predicted to be colder than −5°C in north-central North Carolina (Fig. 7b). Eta cumulative precipitation forecasts showed totals of up to 15.2 mm (0.6 in.) over the west-central portion of North Carolina and upstate South Carolina by this time. The 30-h forecast maintained a band of subfreezing air across the central Carolinas at 1800 UTC 12 February, with precipitation totals in excess of 25.4 mm (1 in.) over a significant portion of central North Carolina and upstate South Carolina (Fig. 7c). Comparison of Fig. 4b with Fig. 7b reveals a cold bias approaching 5°C over north-central North Carolina. Although some warming had been predicted in the 36-h forecast, a tongue of air colder than −1°C was still forecast to extend from upstate South Carolina northward into central Virginia (Fig. 7d). Storm-total precipitation forecasts exceeded 25.4 mm (1 in.) over southern and southeastern parts of North Carolina; the western portion of this region was collocated with predicted 2-m temperatures well below the freezing mark throughout the precipitation event.

A sequence of Eta forecast soundings for Raleigh–Durham (RDU) suggests precipitation onset between 0600 and 1200 UTC 12 February (Figs. 8a,b). Temperatures are only slightly above freezing between the 850- and 900-hPa levels in the 24-h forecast, with a surface-based subfreezing layer approximately 125 hPa deep beneath (Fig. 8b). By 1800 UTC (Fig. 8c), the 30-h forecast indicates substantial warming aloft and a thermal structure that would certainly be accompanied by freezing rain (if precipitation were in fact falling). By 36 h, the presence of subsaturated layers above the freezing level in the forecast sounding suggests that grid-scale precipitation would have ended in the model, with above-freezing temperatures extending from above the 700-hPa level downward to near the surface (Fig. 8d). Forecast surface temperatures remain near freezing, with near-surface northerly winds predicted. A comparison of 1200 UTC rawinsonde measurements from Greensboro (GSO) with the 24-h Eta forecast is provided in Fig. 9. The near-surface cold bias in the forecast at this time was approximately 3°C. The observed sounding indicates a shallow mixed layer, which is consistent with a surface heat source such as latent heat release from freezing rain or an upward heat flux from the ground. Hourly reports from GSO indicated light freezing rain at 1100 and 1300 UTC, with no precipitation reported at 1200 UTC.

Taken literally, the combination of heavy precipitation, warm air aloft, and near-surface subfreezing temperatures in the Eta Model forecast supported predictions of a major icing event. Indeed, forecasters issued winter-storm warnings, and in fact freezing rain was observed (although amounts did not approach warning criteria). The observed icing was far less than expected based on the Eta forecast, in part because of a pronounced cold bias in the Eta lower-tropospheric temperature forecasts. The Eta Model unrealistically predicted a combination of sustained heavy precipitation and subfreezing temperatures over much of the central Carolinas.

c. Discussion

The Eta temperature biases in this case are likely due to a combination of factors. First, because the lowest model air temperature was below freezing across the central Carolinas, the Eta LSM would have erroneously determined that any model precipitation reaching the surface would be in the form of snow. Therefore, the Eta Model was able to maintain a subfreezing layer near the surface despite heavy precipitation (in the model atmosphere) in part because it did not account for the release of latent heat accompanying freezing rain. Second, the LSM configuration would be consistent with a significant amount of snow accumulating at the surface. This could contribute to a cold bias in several ways, including by altering surface radiative properties, through melting effects, and, perhaps more important, by insulating the lower atmosphere from an upward heat flux from the ground. Figure 10 indicates that the temperature gradient in the soil was directed downward throughout the Carolinas and Virginia, which is consistent with an upward heat flux from the ground to the surface. Later in the forecast cycle, when air temperatures across the region warmed, melting of the spurious snowpack may also have contributed to the near-surface cold bias.

There are also synoptic-scale forecast errors that may be linked to the near-surface temperature bias. There is some evidence that the strength of cold- and dry-air advection into the Carolinas was actually weaker than predicted (e.g., cf. the forecast and observed lower-tropospheric winds in Fig. 9). The model greatly overestimated precipitation amounts across the region (which may also have contributed to the maintenance of the near-surface cold dome). Other Eta Model biases could have played a role, including problems with overestimation of the downward shortwave radiation in cloudy conditions (B. Ferrier 2001, personal communication). However, the presence of temperature biases even before sunrise in the Eta forecast suggests that the LSM-related errors were more significant.

Although a rigorous quantitative diagnosis of the relative importance of the aforementioned errors would require a series of model sensitivity experiments, a crude estimate of the magnitude of the latent heat error is now presented. One can pose the question: If the Eta LSM had correctly identified falling precipitation as freezing rain across the central Carolinas in this event, would the resulting latent heat release have been sufficient to warm the subfreezing layer in the model to the freezing point? To address this question, we applied a “correction” to the model forecast temperature profile. Given that the model temperature profiles depicted in Figs. 8 and 9 would support freezing rain or sleet throughout central North Carolina, we applied a correction at specific grid points to account for the corresponding latent heat release that would have resulted from the model-predicted precipitation. It was assumed that the heat was distributed over a surface-based layer 100 hPa in depth. The choice of a 100-hPa-deep layer is consistent with Fig. 9b, which indicates a mixed layer extending to 925 hPa, with subfreezing temperatures extending to near the 890-hPa level.6 In addition, it was assumed that all model-predicted precipitation would fall in the form of freezing rain or sleet if temperatures aloft exceeded 2°C at some point in the forecast profile and the 2-m temperature was below freezing. The temperature correction was based on the sum of cumulative model precipitation for periods that met the temperature criteria. The temperature correction was not allowed to raise the air temperature above the freezing mark. If the 2-m temperature was above 0°C, then no correction was applied at that grid point.

We now address the partitioning of latent heat between soil and air. Recall that during freezing rain the latent warming of the surface is communicated to the atmosphere through terrestrial radiation and conduction. The resulting near-surface warming is consistent with a reduction in surface-layer stability, an increased buoyant production of turbulence, and an upward heat flux. Inspection of the model soil temperature across the region for the 12 February event (Fig. 10) reveals a downward temperature gradient, consistent with an upward heat flux in the ground. Although the model skin temperatures were not available, the soil temperature in the surface-to-10-cm layer was approximately 2°C, indicating that a warm ground may have helped to preclude significant icing in this event. Based on the temperature of the uppermost soil layer, we estimate that only the top few centimeters of soil were below freezing in this case. Therefore, a relatively small fraction of the latent heat would have gone to warming the soil. A quantitative estimate of FA can be obtained by determining the proportional heating if sufficient heat were released to warm the entire subfreezing mass of soil and air to the freezing mark. Utilizing density estimates for sandy clay soil [1780 kg m−3; Stull (1988, appendix C, p. 643)] and estimating that only the top 3 cm of soil was below freezing, we find that the mass of subfreezing soil per unit area is approximately 54 kg m−2. From the soil density and volumetric heat capacity for this soil type (2.42 × 106 J m−3 K−1), the specific heat of the soil is roughly 1360 J kg−1 K−1. The atmospheric mass per unit area for a 100-hPa-deep layer is 1019 kg, and, by taking the ratio (CsoilMsoil)/(CairMair), it appears that on the order of 10% of the heat would be expended on the soil. In the computations that follow, we therefore estimate that 90% of the heating warms the atmosphere.7

Figure 11 displays the modified temperature forecasts corresponding to the forecasts presented in Fig. 7. Temperature modifications of 1°C or less are evident in the 18-h forecast, owing to the fact that precipitation was only beginning to spread over the cold dome at this time (Fig. 11a). The modified 24-h forecast still indicated subfreezing temperatures over north-central North Carolina, but values in upstate South Carolina and south-central North Carolina were nearly 3°C warmer than in the original forecast because of the latent heat correction and were already approaching the freezing mark (Fig. 11b). Comparison of the modified 24-h forecast to the analysis (Figs. 11b and 4b) indicates that an additional cold bias, beyond what can be attributed to the direct latent heating effect, exists over upstate South Carolina and central North Carolina. In these locations, between 0.3 and 0.5 in. of liquid-equivalent precipitation has already accumulated in the model. The LSM would interpret the falling precipitation as snow, given the subfreezing air temperature. We therefore speculate that the additional cold bias is due in part to the insulating influence of a spurious 3–5-in. model snowpack, which reduces the effect the warm ground has on the lower atmosphere. Melting and albedo effects may also have contributed to the cold bias as the event progressed.

The 0°C isotherm had retreated to the Virginia–North Carolina border by 30 h (Fig. 11c), with further warming over central Virginia by 36 h (Fig. 11d). The latent heat released by the freezing of model-predicted precipitation was sufficient to warm the lowest 100 hPa of the model atmosphere to 0°C across upstate South Carolina and central North Carolina, even without account of the aforementioned development of spurious snow cover in the model forecast cycle.

To summarize, observations and model output are consistent with the hypothesis that the simplified precipitation-type determination in the Eta LSM led to a near-surface cold bias through the neglect of the latent heat of freezing and probably through the introduction of a spurious snow cover over portions of the Carolinas. The computation shown in Fig. 11 supports the hypothesis that if the Eta LSM had correctly assumed that freezing rain was present then the model forecast would not have maintained subfreezing temperatures near the surface across central North Carolina and upstate South Carolina in this case. The relatively warm near-surface temperatures in the real atmosphere were likely due in part to a strong upward heat flux from the ground.

4. Conclusions

In this paper, we have summarized the manner in which the current operational configuration of the Eta Model represents the freezing and melting of precipitation, both aloft and at the surface. The updated Eta Model grid-scale precipitation scheme (as of 27 November 2001) accounts for latent heat absorption (release) from the melting of snow (freezing of rain) aloft. For melting snow or freezing rain at the surface, Eta Model forecasts rely upon the LSM. The current Eta LSM determines precipitation type by examining the air temperature in the lowest model level. If that temperature is above (below) freezing, rain (snow) is assumed. This assumption generally fails in the event of freezing rain and also fails for some wet-snow events, because freezing rain falls with subfreezing near-surface air temperatures and snow may fall with above-freezing near-surface temperatures. The result is a lower-tropospheric cold (warm) bias in the case of freezing rain (melting snow).

One example is presented to illustrate the case of model bias during freezing rain. On 12 February 2001, a cold bias approaching 5°C was observed in Eta Model 2-m temperature forecasts. A temperature correction was applied to the model forecasts to test the hypothesis that the misrepresentation of latent heat release by freezing rain contributed substantially to this bias. These results confirm that the heat released by freezing was capable of explaining a large portion of the cold bias in lower-tropospheric temperature forecasts. The lack of observed freezing rain was likely due to a combination of factors, including only light precipitation and an upward heat flux from the ground. The Eta LSM assumptions are consistent with the spurious generation of snow cover in the model, which likely exacerbated the cold bias by artificially insulating the lower atmosphere from a strong upward heat flux from the soil (and possibly through other surface processes such as melting and albedo effects). The case study analysis highlights the impact of soil temperature and surface characteristics on potential ice accumulation.

Below is a list of some forecast implications that result from model representation of freezing rain.

  • Freezing rain is a self-limiting process owing to the warming associated with the latent heat released by freezing raindrops. This warming process is not correctly represented in most current configurations of the operational forecast models. Prolonged icing events will generally require a compensating near-surface cooling mechanism.
  • One should be suspicious of model forecasts that indicate subfreezing lower-tropospheric temperatures in association with heavy freezing precipitation, especially if there are no obvious near-surface cooling mechanisms (e.g., cold- or dry-air advection, cold soil temperatures, adiabatic upslope cooling, or cooling from evaporation or sublimation).
  • The case study results suggest that upward heat flux from the ground may moderate surface temperatures and mitigate freezing-rain buildup. Examining analyzed soil temperatures will help the forecaster to assess the importance of this effect; temperatures in the uppermost soil layer that are well below freezing constitute a potential cooling mechanism that could offset latent warming.
  • Processes such as thermal advection, adiabatic cooling, cooling from evaporation or sublimation, soil heat fluxes, and radiation must be accurately assessed to ascertain the relative importance of freezing or melting.

It is likely that the Eta Model biases documented in this study will be corrected in the near future. The correction of these biases will necessitate modification of the Eta LSM to determine more accurately the phase of precipitation reaching the surface. Operational forecasters are urged to remain aware of model updates. [Online information regarding model changes (as of winter, 2001/02) was available at http://www.emc.ncep.noaa.gov/mmb/research/eta.log.html; information regarding planned changes could be found at http://www.nco.ncep.noaa.gov/pmb/.] The Cooperative Program for Operational Meteorology, Education, and Training (COMET) has assembled an outstanding summary of operational model characteristics and educational NWP materials (available online at the time of writing at http://meted.ucar.edu/nwp/pcu2/index.htm).

Acknowledgments

This study was inspired by interactions between operational forecasters at the NWSFO in Raleigh, Wilmington, and Newport, North Carolina; Greer, South Carolina; and Wakefield, Virginia; and researchers at North Carolina State University and NCEP/EMC. The NOAA Collaborative Science, Technology, and Applied Research Program (CSTAR), Award NA07WA0206, supported this interaction and research. The first author was also supported by NSF Grant ATM-0079425. Brad Ferrier (NCEP), Rod Gonski (NWSFO Raleigh), Mike Brennan (NCSU), Heather Reeves (NCSU), Allen Riordan (NCSU), and two anonymous reviewers provided valuable comments on earlier drafts of this manuscript. We acknowledge the Unidata program for supplying the data used in this research. Scott Kennedy assisted with graphics. Phil Badgett and Jonathan Blaes (NWSFO Raleigh) contributed Fig. 6.

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Fig. 1.
Fig. 1.

Sequence of idealized vertical temperature profiles accompanying a transition from heavy rain to snow at the surface, with account of latent heat absorption via melting. The sequence of panels from top to bottom represents a progression of time, with an increment of roughly 3 h. A saturated atmosphere is assumed. The inset in (a) summarizes terminology relating to the Eta Model, as indicated in the legend at the top of the inset. The locations corresponding to the soil skin temperature, lowest air temperature, and 2-m temperature are also labeled

Citation: Weather and Forecasting 17, 5; 10.1175/1520-0434(2003)017<1016:MROFAM>2.0.CO;2

Fig. 2.
Fig. 2.

As in Fig. 1 but for idealized vertical temperature profiles accompanying an evolution from sleet to freezing rain and then rain, with account of latent heat absorption (release) via melting (freezing)

Citation: Weather and Forecasting 17, 5; 10.1175/1520-0434(2003)017<1016:MROFAM>2.0.CO;2

Fig. 3.
Fig. 3.

Synoptic summary based on Eta Model analysis for 12 Feb 2001 for sea level pressure (dashed, contour interval 2 hPa, leading 10 omitted), 500-hPa geopotential height (solid, contour interval 6 dam), and absolute vorticity (shaded, interval 8 × 10−5 s−1 as indicated in legend at lower right): (a) Eta analysis valid 0000 UTC 12 Feb, (b) analysis valid 1200 UTC 12 Feb, and (c) analysis valid 0000 UTC 13 Feb. Subjectively identified frontal locations are included in (b) and (c)

Citation: Weather and Forecasting 17, 5; 10.1175/1520-0434(2003)017<1016:MROFAM>2.0.CO;2

Fig. 4.
Fig. 4.

As in Fig. 3 but showing Eta-analyzed sea level pressure (solid, contour interval 2 hPa) and 2-m temperature (dashed and shaded, contour interval 1°C). Shaded regions correspond to temperatures below 0°C

Citation: Weather and Forecasting 17, 5; 10.1175/1520-0434(2003)017<1016:MROFAM>2.0.CO;2

Fig. 5.
Fig. 5.

Surface observations and radar mosaic lowest-level base reflectivity for 0900 UTC 12 Feb 2001. Reflectivity values indicated on scale at left

Citation: Weather and Forecasting 17, 5; 10.1175/1520-0434(2003)017<1016:MROFAM>2.0.CO;2

Fig. 6.
Fig. 6.

Sensible weather summary for 12 Feb event: (a) maximum temperatures (°F), (b) observed liquid-equivalent precipitation (in.), and (c) frozen precipitation (in.). In (c) T denotes trace. Figure courtesy of the Raleigh National Weather Service Forecast Office

Citation: Weather and Forecasting 17, 5; 10.1175/1520-0434(2003)017<1016:MROFAM>2.0.CO;2

Fig. 7.
Fig. 7.

Eta forecast sequence of 2-m temperature (contour interval 1°C, dashed lines with shading below 0°C) and cumulative precipitation (solid contours, interval 0.01, 0.05, and every 0.1 in. thereafter) for 12 Feb: (a) 18-h forecast valid 0600 UTC 12 Feb, (b) 24-h forecast valid 1200 UTC 12 Feb, (c) 30-h forecast valid 1800 UTC 12 Feb, and (d) 36-h forecast valid 0000 UTC 13 Feb

Citation: Weather and Forecasting 17, 5; 10.1175/1520-0434(2003)017<1016:MROFAM>2.0.CO;2

Fig. 8.
Fig. 8.

Eta forecast sounding sequence for RDU, with forecast times as in Fig. 7 and in Skew T–logp format. Temperature is plotted as bold solid lines; dewpoint temperature is plotted as bold dashed lines

Citation: Weather and Forecasting 17, 5; 10.1175/1520-0434(2003)017<1016:MROFAM>2.0.CO;2

Fig. 9.
Fig. 9.

As in Fig. 8 but for a comparison of Eta forecast sounding with GSO rawinsonde data for 1200 UTC 12 Feb 2001: (a) 24-h Eta Model forecast profile for GSO and (b) GSO rawinsonde profile

Citation: Weather and Forecasting 17, 5; 10.1175/1520-0434(2003)017<1016:MROFAM>2.0.CO;2

Fig. 10.
Fig. 10.

Eta Model soil temperature analysis (contour interval 1 K) valid 1200 UTC 12 Feb 2001: (a) 0–10-, (b) 10–40-, and (c) 40–100-cm layer

Citation: Weather and Forecasting 17, 5; 10.1175/1520-0434(2003)017<1016:MROFAM>2.0.CO;2

Fig. 11.
Fig. 11.

Modified Eta 2-m temperature forecast that includes a correction for latent heat released by freezing rain. Times are as in Fig. 7

Citation: Weather and Forecasting 17, 5; 10.1175/1520-0434(2003)017<1016:MROFAM>2.0.CO;2

1

The inset in Fig. 1a clarifies terminology regarding the lowest model air temperature, the soil skin temperature, and the 2-m temperature. The lowest air temperature is obtained from above-surface eta-coordinate surfaces and does not necessarily correspond to a quasi-uniform pressure increment above the ground level, as it would in a sigma-coordinate model.

2

The term stable here refers to the overall thermal profile featuring warm air aloft above colder air in the lower troposphere rather than to the stability characteristics of the cold layer itself.

3

For example, if the sea level pressure changes by 1.5 hPa over a period of time in which the observed temperature change is 4°C, the work term in the first law would be approximately 4% of the internal energy term (assuming a density of ∼1 kg m−3). This example is based on observations during the case study presented in section 3.

4

In (5), the value of ∂qs/∂T was evaluated for 1000 hPa and 0°C, 2.76 × 10−4 K−1.

5

Note that the actual ice depth would be 9% greater because of the slightly lower density of ice relative to liquid water.

6

In reality, the heating was probably confined to a shallower layer, at least initially. However, the goal is to determine how much heat would be required to raise the entire surface-based subfreezing layer to the freezing point.

7

The results here are not highly sensitive to this estimate. Recall that an upper limit is placed on the heating, with the requirement that the corrected air temperature cannot rise above freezing because of latent heat release by freezing rain. The model precipitation in this case is more than sufficient to warm the subfreezing layer to the freezing mark, even if a 50% partition is assumed; the main effect is that the warming is delayed.

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