WHAT ARE THE BEST THERMODYNAMIC QUANTITY AND FUNCTION TO DEFINE A FRONT IN GRIDDED MODEL OUTPUT?
Defining automated fronts requires quantities (e.g., potential temperature, equivalent potential temperature, wind shifts) and kinematic functions (e.g., gradient, thermal front parameter, and frontogenesis). Which are the most appropriate to use in different applications remains an open question. This question is investigated using two quantities (potential temperature and equivalent potential temperature) and three functions (magnitude of the horizontal gradient, thermal front parameter, and frontogenesis) from both the context of real-time surface analysis and climatologies from 38 years of reanalyses. The strengths of potential temperature to identify fronts are that it represents the thermal gradients and its direct association with the kinematics and dynamics of fronts. Although climatologies using potential temperature show features associated with extratropical cyclones in the storm tracks, climatologies using equivalent potential temperature include moisture gradients within air masses, most notably at low latitudes that are unrelated to the traditional definition of a front, but may be representative of a broader definition of an airmass boundary. These results help to explain previously published frontal climatologies featuring maxima of fronts in the subtropics and tropics. The best function depends upon the purpose of the analysis, but Petterssen frontogenesis is attractive, both for real-time analysis and long-term climatologies, in part because of its link to the kinematics and dynamics of fronts. Finally, this study challenges the conventional definition of a front as an airmass boundary and suggests that a new, dynamically based definition would be useful for some applications.
Careful consideration is required in choosing diagnostic quantities and functions to identify fronts.
Fronts have been controversial from the time that the concept was first introduced (e.g., Henry 1922; Douglas 1952, p. 6; Namias 1981, p. 493; Thompson 1985, p. 1291; Friedman 1989; Volkert 1999). Although discontinuities in the temperature (or density) field were previously recognized as critical features for forecasting (e.g., Gold 1935; Volkert 1999), the conceptual model of a front that synthesized these observations with a theory of extratropical cyclones was developed by what has come to be called the Bergen School or Norwegian School of Meteorology [e.g., Bjerknes (1919), as described in Friedman (1989), Jewell (2017), and Schultz et al. (2019)]. The Bergen School considered a front to be the boundary between two air masses, which are regions of near-surface air with nearly homogeneous properties of temperature, moisture, and stability. Although adoption by British and American forecasters was not immediate (e.g., Douglas 1952; Namias 1981,1983; Sutcliffe 1982; Ashford 1992; Newton and Rodebush Newton 1999; Schultz 2008), eventually the Norwegian methods became widespread.
As years of surface frontal analyses began to accumulate, researchers realized that they could use these maps for computing climatologies of fronts. For example, Petterssen (1939) used the thrice-daily weather maps produced in Bergen for the three Januaries during 1933-35 to create a climatology of occluded and nonoccluded fronts over the eastern North Atlantic Ocean. There were maxima of fronts over the central ocean basin and between Britain and Norway. Several other climatologies also showed the potential of the synthesis of a large number of surface maps (Table la).
Once the Norwegian methods were officially adopted by other weather services and a wonderful panoply of weather systems from around the world was analyzed, maintaining consistency between different analysts and determining common criteria for frontal analysis became important issues (e.g., Fig. 1 of Renard and Clarke 1965). For example, Taljaard et al. (1961, p. 26) lamented, "Wherever meteorologists gather to discuss problems of circulation and analysis, dissatisfaction is expressed with frontal analysis as practised at present," and textbooks offered prescriptions for analyzing fronts (e.g., chapter 9 in Saucier 1955; chapter 11 in Petterssen 1956). Of course, none of this was new. Once in the 1930s, Carl-Gustaf Rossby was "distressed at finding such inconsistency in the frontal analyses [drawn by four different operational forecasting offices] for the current synoptic time that they could hardly be recognized as being based on the same set of data" [Beckwith (1976), as reported in Persson and Phillips (2001)]. In another anecdote, Jacob Bjerknes once told C. K. M. Douglas (Douglas 1952, p. 9) that "some of the published monstrosities which were supposed to be fronts made him quite ashamed, as he felt some responsibility owing to his international propaganda in favor of marking fronts on the charts."
In the United States, the situation with the quality of frontal analysis came to a head in the late 1980s and early 1990s when the lack of mesoscale analysis approaches (Young and Fritsch 1989) and perceived problems with frontal analysis on the National Weather Service (NWS) charts (Mass 1991) led to a workshop on surface analysis at the National Meteorological Center (NMC; now NCEP) [Uccellini et al. (1992), and reported on in Science by Kerr (1991)]. At the NMC workshop, national experts in synoptic meteorology and analysis, when faced with the same data and pressures as NWS forecasters, produced a collective spaghetti of fronts, similar to the one produced by Renard and Clarke (1965, their Fig. 1) 26 years earlier. The NMC workshop eventually spawned the creation of official unified surface analyses and guidance for their construction (Berg et al. 2007; NOAA 2013).
Also as a result of the NMC workshop, Fred Sanders took up the mantle for frontal analysis, producing a series of papers laying out his principles for frontal analysis (e.g., Sanders and Doswell 1995; Sanders and Kessler 1999; Sanders 1999a,b, 2005, 2008). Sanders argued that many baroclinic zones (regions of locally enhanced horizontal temperature gradient) were not fronts, and that fronts were characterized by both temperature gradients and "considerable" wind shifts (e.g., Sanders 1999a, p. 948). His work gained some traction in the United States, but was less influential abroad. Even after all this intellectual effort directed toward frontal analysis, if the experts could not agree, would there be any hope for surface analysis?
Enter the modern era of gridded analyses and fast computers. In 1965, Renard and Clarke (1965, p. 547) declared, "the time has come when fields of data containing frontal information are numerically produced in such a manner as to lend themselves to an objective frontal analysis." A few efforts at automated fronts were tried, but none seemed to catch on (e.g., Table 1 in Hewson 1998). The most successful effort was Hewson (1998), who revived the quantity created by Renard and Clarke (1965) and Clarke and Renard (1966) involving the derivative of the temperature gradient and called it the thermal front parameter. Through Hewson's considerable efforts--and not without some implementation issues (McCann and Whistler 2001)--automated fronts produced by the thermal front parameter were eventually adopted in real-time surface analyses and ensemble model output by NCEP's Aviation Weather Center (McCann and Whistler 2001), European Centre for Medium-Range Weather Forecasts (ECMWF; Hewson 2009), and the Met Office (Hewson and Titley 2010; as described by Mulqueen and Schultz 2015, p. 102). Other automated approaches have been applied at Meteo-France (Santurette and Joly 2002). Now, frontal analysis can readily be automated and computed for large global datasets. Here, we avoid the word "objective" to refer to such automated approaches because of the subjective nature of the criteria applied for even so-called objective approaches (section 18.2 in Schultz 2009), as will be discussed later.
As global reanalysis datasets have become more widely used, synoptic meteorologists have ushered in a new era of automated synoptic climatologies (Table lb). In addition, more sophisticated questions have been asked, including:
* How has the climatology of fronts changed over time (Berry et al. 2011b; Rudeva and Simmonds 2015)?
* How will the climatology of fronts change in the future (Catto et al. 2014)?
* How much precipitation is associated with fronts, and how will that change in the future (Catto et al. 2012,2013,2014; Catto and Pfahl 2013; Henin et al. 2019)?
* How can fronts in regions of topography be analyzed in high-resolution model output (Jenkner et al. 2010)?
* What fraction of cyclones are attended by fronts (Schemm et al. 2018)?
The number and depth of interesting and provocative questions that can be asked because of automated frontal analysis of global gridded data, which would have been immensely time consuming to address by hand, make it a great time to work as a synoptic meteorologist. Yet, the specific definition of a front chosen may determine the answers to these questions. Thus, this article addresses some aspects of how these automated frontal analyses are created and how the choices made in their creation determine their resulting interpretation. Specifically, this article first provides a brief review of automated frontal analysis with respect to various choices of thermodynamic quantity and function. Then, this article develops annual climatologies based on gridded reanalyses for combinations of meteorological quantity and mathematical function to understand how these choices affect the resulting climatologies and their interpretation. As a result, some of the strengths and weaknesses of these various automated approaches will be discussed for various applications.
HOW TO CREATE AN AUTOMATED FRONTAL ANALYSIS. Because there is no single definition of a front, different automated methods have been developed (Table lb). Methods range from the relatively simple [e.g., mapping where the surface potential temperature gradient exceeds a fixed magnitude as in Sanders and Hoffman (2002)] to the increasingly complicated [e.g., the method of Hewson and Titley (2010, their Table IA) uses a function of wet-bulb equivalent potential temperature [[theta].sub.w] followed by three different masking functions of [[theta].sub.w] to identify their fronts]. The choice of method is typically related to the philosophy of the user and the application, with research-oriented approaches favoring the simpler approaches and operational applications designed to mimic manually analyzed fronts on surface charts favoring the more complicated approaches.
With the variety of diagnostics available, researchers have occasionally intercompared the various methods to show their strengths and weaknesses, but such practice is not widespread. Indeed, Table lb shows that only the climatologies of Berry et al. (2011b) and Schemm et al. (2015) have performed intercomparisons on two different frontal diagnostics, with Simmonds et al. (2012) performing an intercomparison of the same diagnostic on two different vertical levels. Hope et al. (2014) compared six different methods, but on only one case study. Because of the variety of different approaches for producing automated fronts and the relative lack of intercomparisons performed, we investigate how they are typically produced in a little more detail. To produce one of the simpler automated analyses, at least five choices are typically needed:
1) a quantity (usually a thermodynamic quantity) that is used to analyze the front (multiple quantities may also be considered in more complicated approaches; e.g., Hewson and Titley 2010),
2) a mathematical function (or functions) that operates upon the quantity to create the field for identifying the front,
3) a vertical level at which the analysis is performed (usually the surface or 850 hPa),
4) a minimum tolerance or threshold in the magnitude of the field for the feature to be considered a front (multiple thresholds may also be considered in some more complicated approaches), and
5) an algorithm to either draw a line to represent a front or identify a region representing the frontal zone along the field at a given tolerance, and also possibly classifying the front as a warm or cold front.
Although a comprehensive intercomparison of the different methods is needed, the focus of this article is to examine the utility of specific options for the first two choices only: the quantity and function. The other three choices are interesting in their own right, but are not the subject of this article. In one attempt to address the level and the threshold choices, Thomas and Schultz (2019) explore the effect of these two choices on global frontal climatologies.
As will be shown later in this article, different approaches for identifying fronts focus upon different characteristics. Whereas some diagnostics identify contours specifying a frontal zone, others follow synoptic convention and draw the front at the warm edge of the frontal zone. Other approaches that identify fronts in three dimensions identify frontal volumes. For simplicity, internal consistency, and consistency with other authors, we refer to all these different types of identified features as fronts. Frontal zones will necessarily be wider than lines identifying the warm edge of the frontal zone, so this needs to be taken into consideration in this study.
THE CHOICE OF QUANTITY. Different choices of the quantity can be made: air temperature, potential temperature, virtual potential temperature, wet-bulb potential temperature, equivalent potential temperature, and wind. The advantages and disadvantages of some of these quantities are developed further in this section and summarized in Table 2a.
Although surface analysis of a thermodynamic quantity is not officially generated by the NWS, a common approach for manual frontal analysis in the United States is to use temperature Tor potential temperature [theta] (NOAA 2013, p. 6), perhaps because surface temperature gradients tend to be stronger over continents than over oceans. On a constant-pressure surface, there is a one-to-one relationship between air temperature and potential temperature, so these two are functionally equivalent. Potential temperature is typically better than temperature at identifying surface temperature gradients in regions of complex terrain because the variation in temperature due to different elevations has been accounted for intrinsically by adjusting to a common pressure (e.g., Sanders 1999a). In addition, the virtual potential temperature includes the effect of moisture on air density. Even in the most humid air masses, the virtual-temperature effect adds only a few degrees Celsius to the air temperature (e.g., Doswell and Rasmussen 1994).
Our experimentation reveals that including the virtual temperature correction does not change the interpretation of our results, so we stick with more common usage and only plot potential temperature.
A strength of potential temperature is that the kinematics and dynamics of fronts are derived in terms of potential temperature. For example, the Sawyer-Eliassen equation for the secondary circulation of fronts is expressed as a function of potential temperature (e.g., Sawyer 1956; Eliassen 1962; summarized in Eliassen 1990). Foundational dynamical studies of fronts--both dry (e.g., Hoskins and Bretherton 1972; Keyser and Anthes 1982) and moist (e.g., Joly and Thorpe 1990; Xu 1990; Montgomery and Farrell 1991)--all use potential temperature. Thus, use of the gradient in potential temperature (and its changes in direction and magnitude; i.e., frontogenesis) directly links to the ascent that is responsible for the clouds and precipitation along fronts. If the aspect of a front that makes it worth diagnosing is its secondary circulation, then a gradient in potential temperature is a sensible defining characteristic of a front.
Potential temperature has two disadvantages however. Use of potential temperature can often identify a nearly stationary ring around warm continental regions, which would generally not constitute a front (Hoffman 2008; G. Berry 2012, personal communication). Also, potential temperature may highlight gradients in temperature on the upwind sides of foehns, which many would also not consider fronts (e.g., Heimann 1992; Hewson 1998).
On the other hand, analysts in the United Kingdom and Europe generally favor quantities that incorporate both temperature and humidity: equivalent potential temperature [[theta].sub.e] or wet-bulb potential temperature [[theta].sub.w] (e.g., Hewson 1998; Santurette and Joly 2002; Joly and Santurette 2002). The equivalent potential temperature and wet-bulb potential temperature are determined by the pressure, temperature, and moisture content of the air, and so have a one-to-one relationship (Bindon 1940). For simplicity, we choose [[theta].sub.e].
The rationale for including moisture in the definition of a front is usually one of two reasons. First, many authors (e.g., Hewson 1998, p. 54; de la Torre et al. 2008, p. 238; Schemm et al. 2018) argue that [[theta].sub.e] and [[theta].sub.w] are preferred because they are better conserved during moist processes, whereas [theta] is not. Thus, these authors claim [[theta].sub.e] and [[theta].sub.w] are better tracers of an air mass. This argument is not quite correct. Air masses are defined by their source region (e.g., continental, maritime, tropical, polar), a result of extensive modification by surface heat and moisture fluxes over time. The only process that is conserved for [[theta].sub.e] or [[theta].sub.w] is condensation or evaporation through reversible processes. Because automated fronts are calculated on a quasi-horizontal surface, the advantage in including moist processes that are occurring in conjunction with vertical velocities is unclear. Also, all the other diabatic processes (e.g., sensible heat flux, latent heat flux, deposition, sublimation, radiation) can still change [[theta].sub.e] or [[theta].sub.w]. Thus, there is little advantage to using [[theta].sub.e] or [[theta].sub.w] over [theta] as these fluxes would produce nonconservative changes in any of these three quantities. As a result, [[theta].sub.e] and [[theta].sub.w] would not seem to be substantially better than [theta] at tracing air masses.
Second, because both the temperature and moisture fields usually change in the same direction across fronts (e.g., most cold air masses also tend to be lower in moisture content), gradients of [[theta].sub.e] and [[theta].sub.w] tend to be stronger across fronts than gradients in 8. In fact, Thorpe and Clough (1991, 921-923) showed that gradients of [[theta].sub.e] across wintertime North Atlantic fronts are attributed to roughly equal gradients in humidity and temperature. Using [[theta].sub.e] or [[theta].sub.w] to identify fronts produces stronger gradients of [[theta].sub.e] and [[theta].sub.w] across fronts, which may help better diagnose weaker fronts (e.g., Jenkner et al. 2010), especially those over the ocean where temperature gradients are often weaker (e.g., McCann and Whistler 2001, p. 197).
However, not all fronts may have this typical cross-frontal correlation between temperature and moisture. Consider the following scenario. The utility of gradients in [[theta].sub.e] to identify a front is limited when hot dry air masses have a similar [[theta].sub.e] to cool moist air masses. For example, air with a temperature of 29[degrees]C and dewpoint of 15[degrees]C would have the same [[theta].sub.e] (328 K) as saturated air at 1000 hPa with a temperature of 20[degrees]C. Thus, compared to temperature, gradients in [[theta].sub.e] may be weakened, as well as enhanced, because of moisture gradients.
As an illustration of just such a front, consider Fig. 1, which is a northwest-southeast-oriented cross section through a dryline and a cold front parallel to it in Kansas from Murphey et al. (2006). The nearsurface air between the cold front and dryline reaches a maximum of virtual potential temperature of 321 K (Fig. la). However, the pre-cold-frontal air is drier than the post-cold-frontal air (mixing ratios of about 7 versus 11 g [kg.sup.-1]). Thus, [[theta].sub.e] increases behind the cold front (340 K in the prefrontal air versus 350 K in the postfrontal air; Fig. lb). Consequently, analysts using [[theta].sub.e] would incorrectly identify this feature as a warm front. Another similar case was published by Koch and Clark (1999, their Figs. 6a and 6c). A similar concern regarding the lack of similarity in [theta] and [[theta].sub.e] for frontal analysis has been noted by Heimann (1992) in the case of a prefrontal foehn. The western European prefrontal convergence lines associated with north African air masses (Dahl and Fischer 2016) may also have this behavior, although maps of surface [[theta].sub.e] were not presented. Thus, in some situations where the prefrontal air is particularly dry (illustrated here with situations from the Great Plains and prefrontal foehn, but not limited to those), using [[theta].sub.e] in frontal analyses might misrepresent the situation.
Another disadvantage of using [[theta].sub.e] is that, because [[theta].sub.e] is a function of moisture content, gradients in [[theta].sub.e] may also indicate moisture gradients that would not otherwise be considered fronts (e.g., Figs, le, le, and 2c in Schemm et al. 2015). One example is what Hewson (1998, pp. 54,56) termed warm-conveyor-belt fronts, or gradients in moisture at the eastward edge of the warm conveyor belt inside the warm sector. Such humidity gradients were detected in 55% of cold fronts in a sample detected over a region of the North Atlantic (Hewson 1998); thus, they are a common occurrence and can potentially inflate the number of actual fronts in climatologies over the North Atlantic. (1) Indeed, these warm-conveyor-belt fronts may explain some of the multiple-front cyclones identified by Mulqueen and Schultz (2015) on Met Office charts (T. Hewson 2015, personal communication). Finally, the humidity field is not necessarily coincident with the temperature field across fronts, with this distance increasing with height above the surface as in the case of split fronts and katafronts, for example (e.g., Browning 1986; Thorpe and Clough 1991; Mass and Schultz 1993; Hewson 1998). For these reasons, we recommend examining the temperature and moisture fields separately when analyzing frontal structures for understanding how fronts are identified (e.g., Sanders and Doswell 1995).
Fronts are also commonly associated with abrupt wind changes, so wind could be a sensible choice to diagnose fronts. Simmonds et al. (2012) defined fronts as wind shifts, specifically the 6-h change in meridional wind. A disadvantage of using winds, however, is that the wind may shift for more reasons than just a frontal passage (e.g., lee troughs, surface convergence lines) or the wind shift of a front may be separated from its temperature gradient (e.g., Hutchinson and Bluestein 1998; Schultz 2004,2005), a point that is illustrated through a comparison of the thermodynamic- and wind-based automated fronts in Schemm et al. (2015, their Figs. 1 and 2). Furthermore, wind-based approaches perform poorly in identifying warm fronts compared to thermodynamic-based quantities (e.g., Schemm et al. 2015). For example, Hewson (1998, p. 38) wrote, "A trough-line on a surface chart, for example, may be characterised by a vorticity strip, a cloud band and a precipitation band but would not, if there were no thermal contrast, be classified as a front." Diagnostics have been developed for the automated detection of airstream boundaries due to changes in wind (e.g., Cohen and Kreitzberg 1997; Cohen and Schultz 2005). However, a wind shift lacks a thermal gradient, which is a fundamental property of a front (e.g., Godson 1951; Petterssen 1956, p. 189; Taljaard et al. 1961; Sanders and Doswell 1995; Sanders 1999a), so wind shifts are not considered further in this article.
THE CHOICE OF FUNCTION. The second choice is the function, which operates upon the quantity to produce a field that defines a front. The advantages and disadvantages of these different functions are developed further in this section and summarized in Table 2b. For this article, we choose three functions to calculate.
The first and simplest measure of a front is the magnitude of the horizontal gradient of the thermodynamic quantity [tau]:
G([tau]) = [absolute value of [[nabla][tau]],
[nabla] = i(partial derivative]/[partial derivative]x) + j([partial derivative]/[partial derivative]y).
The magnitude of the horizontal gradient is commonly used by meteorologists in their manual analyses of fronts (e.g., NOAA 2013, p. 6). Gridded analyses of the magnitude of the horizontal gradient of the surface temperature data over the United States were used to perform climatologies of baroclinic zones (Sanders and Hoffman 2002; Hoffman 2008). Quantitatively, Sanders (1999a) defined magnitudes of the gradient of the surface potential temperature of 4 K [(110 km).sup.-1] for moderate baroclinic zones and 8 K [(110 km).sup.-1] for strong baroclinic zones.
One disadvantage with the gradient is that it depends upon the resolution of the gridded data. High-resolution data with lots of structure will produce large magnitudes of gradients, so a unique threshold for such baroclinic zones independent of resolution is challenging. This issue becomes even more significant when using higher-order derivatives, as will be seen for subsequent diagnostics (e.g., Hewson and Titley 2010; Jenkner et al. 2010).
Another disadvantage with the magnitude of the horizontal gradient for frontal analysis is that its location does not necessarily correspond to where a meteorologist would draw the line on the map. By synoptic convention, the line on the map representing a front is drawn along the warm edge of the thermal gradient. So, the region of maximum gradient in temperature would be colder than the location of the front. Instead, the magnitude of the gradient corresponds to the frontal zone, the finite width of the front over which the temperature decreases.
The second diagnostic function attempts to rectify this weakness in the gradient. The thermal front parameter (TFP; e.g., Renard and Clarke 1965; Clarke and Renard 1966; Hewson 1998) is defined as the directional derivative of the horizontal gradient of the thermodynamic quantity t along its gradient:
TFP([tau]) = -[nabla] [absolute value of [[nabla][tau]] [[nabla].sub.]/[absolute value of [nabla][tau]]. (1)
By taking the gradient of the magnitude of the temperature gradient, the thermal front parameter determines the warm and cold edges of the frontal zone. The negative sign on the right-hand side of (1) ensures that the warm side of the frontal zone has TFP > 0 (e.g., Fig. 3 in Hewson 1998). Hewson (1998) discusses the thermal front parameter, including the computation of its directional derivative and how to plot the result. Some implementations of the thermal front parameter do not identify the warm-air edge of the gradient of the thermal parameter as the front, but where TFP = 0, which places their fronts outside of the sea level pressure trough (e.g., Figs. la,c,e, 2a,c,e, and 3a,c,e in Schemm et al. 2015; Fig. 2 in Schemm et al. 2018). (2) This implementation both violates synoptic convention and defeats the purpose of using the thermal front parameter to draw fronts along the warm edge of the frontal zone.
In contrast to the first two diagnostic functions that were based only on a thermodynamic quantity, the third diagnostic function not only requires a thermodynamic quantity, but also requires the wind field. Frontogenesis was originally defined by Petterssen (1936) as the Lagrangian rate of change of the magnitude of the horizontal gradient of temperature (or equivalently on a constant-pressure surface, potential temperature [theta]):
[mathematical expression not reproducible]. (2)
When (2) was applied to a scalar other than air temperature or potential temperature, Saucier (1955, p. 363) termed it accumulation, although other researchers simply referred to it as frontogenesis of the scalar (e.g., Buban et al. 2007). Later, Miller (1948) developed a three-dimensional formulation, and Keyser et al. (1988) developed a vector formulation. Schultz (2015) described some of the other mathematical forms of frontogenesis and discussed their utility, but, for the purposes of this study, Petterssen's form is sufficient.
The strength of Petterssen frontogenesis F([theta]) as a frontal diagnostic is that it directly links to the process by which a front forms, the strengthening of the horizontal gradient in temperature by the wind field, yet is a kinematic quantity calculated at a single time. If the wind field is uniform, then Petterssen frontogenesis will be zero. If the wind field used in the total derivative is the geostrophic wind, then Petterssen frontogenesis is also related to the forcing for quasigeostrophic vertical velocity associated with the divergence of the component of the Q-vector normal to the isentropes (e.g., Keyser et al. 1988). In other words, the field of frontogenesis is related to the frontal-scale quasigeostrophic ascent. Thus, the advantage of frontogenesis is its association with both the kinematics and the dynamics of the front itself. Generalizations of the frontogenesis function to other scalars such as [[theta].sub.e] lose those properties that make Petterssen frontogenesis attractive as a frontal diagnostic. Nevertheless, expressions such as F([[theta].sub.e]) can be useful for quantifying the rate of change of the magnitude of the horizontal gradient in [[theta].sub.e] due to the horizontal wind field.
The frontogenesis function can be either positive or negative, and some analyzed synoptic frontal zones may experience positive frontogenesis along some parts and negative frontogenesis (i.e., frontolysis) along other parts, as in the bent-back frontal zone of the Shapiro-Keyser model (e.g., Takayabu 1986; Shapiro and Keyser 1990; Schultz et al. 1998; Schultz and Sienkiewicz 2013). Because Petterssen frontogenesis is a Lagrangian quantity, even weakening frontal zones may experience positive Petterssen frontogenesis. As with the magnitude of the gradient and thermal front parameter, additional derivatives would be required to identify the warm edge of the frontogenesis region as the front, although this is not implemented in this article. Petterssen frontogenesis has not been used in any global climatology of fronts, so we test it out in this article.
One issue that is not addressed in our study is the length of the front, a metric that some climatologies have included (e.g., Berry et al. 201 la,b; Catto et al. 2013, 2014; Schemm et al. 2015), but we and others have not (e.g., Serreze et al. 2001; Sanders and Hoffman 2002; Hoffman 2008; de la Torre et al. 2008; Simmonds et al. 2012). Our decision not to include a length criterion is because our primary purpose is not to replicate manual frontal analyses, but to explore the sensitivity of choices of thermodynamic quantity and function to the climatology of fronts. This purpose does not require a minimum-length criterion, and we would argue that doing so would inhibit fair comparison between different analyses and climatologies by introducing another level of subjectivity. Furthermore, the kinematics and dynamics are the same regardless of the length of the front. What is clear is that climatologies produced using frontal zones (i.e., determined by the area exceeding a threshold) are likely to produce maxima that are wider than those detected as lines (e.g., fronts determined by a maximum in TFP); otherwise, we believe that climatologies produced through approaches that do not draw lines are just as valid as those that do.
DATA AND METHODS. For the reasons discussed above, interpretation of automated fronts in both weather maps and climatologies can be ambiguous because of the two choices of quantity (or quantities) and function (or functions). In this article, we investigate the differences between two different quantities ([theta] and [[theta].sub.e]) and three functions (magnitude of the horizontal gradient, thermal front parameter, and frontogenesis) based on global reanalyses using a gridpoint-based method of identifying fronts described below. By computing fronts using these six different approaches, we can see the differences in the analysis of weather systems and frontal climatologies that result.
Similar to many previous researchers, we use the ECMWF interim reanalysis (ERA-Interim) during 1979-2016 (Dee et al. 2011). ERA-Interim is obtained on a 0.75[degrees] x 0.75[degrees] latitude-longitude grid four times daily, a higher resolution than has been used previously (Table lb). Frontal analysis has traditionally been performed near the surface because of the abundance of hourly surface data. However, boundary layer effects may create frontal-like temperature gradients at the surface or obscure deeper tropospheric fronts (e.g., Sanders and Kessler 1999; Doswell and Haugland 2007; Lackmann 2011, 132-133) that may not be resolved in the reanalysis. Using lower-tropospheric thickness might avoid these situations (e.g., McCann and Whistler 2001), although few authors have adopted this quantity. Thus, many previous studies analyze fronts at 850 hPa (Table lb; Table 1 in Hewson 1998), which would typically be above the boundary layer and be largely immune from these issues. Later, Hewson (2009) advocated a height of 1 km above the surface because "surface processes and sub-surface extrapolation would have had a contaminating effect around high topography." The problem is that this quantity would be plotted for a range of heights on a single map from 1 km above sea level to several kilometers in altitude above major mountain ranges, complicating interpretation of these fields. Despite these tradeoffs, we stick with analyzing fronts at 850 hPa. The difference between the surface and 850-hPa fronts is examined by Thomas and Schultz (2019).
Each grid point is searched for each 6-h period during the 38-yr period for values of the frontal diagnostics that exceed a minimum intensity threshold. The threshold is set to a value to produce enough fronts to reveal the climatology of the relevant features and to compare them to previously published climatologies (Table 1). The specific thresholds used for each quantity will be stated in the figure captions for the upcoming Figs. 3-7 and 9, and they generally are at about the 10th-percentile level of the distribution of all values of that quantity. In other words, about 10% of any given global map would be identified as a frontal zone. This value of 10% is the result of the threshold being selected so that the regions along the analyzed fronts are as continuous as possible. This choice is to negate the potential criticism that the numeric values of the diagnostics involving [theta] are smaller than those involving [[theta].sub.e] (e.g., Jenkner et al. 2010). A deeper investigation into the effect of the threshold on the climatologies can be found in Thomas and Schultz (2019).
EXAMPLE OF FRONTAL QUANTITIES FOR A CASE STUDY. To illustrate these quantities in action on real weather systems, we calculate them for a specific case chosen at random: 0000 UTC 24 January 2014. Surface analyses over the North Atlantic Ocean and western Europe are presented from three different national forecast agencies: the U.S. NOAA/NCEP/Weather Prediction Center, Germany's Deutscher Wetterdienst (DWD), and the U.K. Met Office (Fig. 2). These three analyses show the variety of interpretations of the fronts at that time. A strong surface occluded cyclone of about 960 hPa was south of Greenland (Figs. 2a-c), and a high-pressure system of about 1035 hPa was located over northeastern Europe and Russia (Figs. 2b,c). These two large pressure systems were separated by a quasi-stationary front (Figs. 2a-c). A smaller and weaker low was centered over Italy (Figs. 2b,c). The major pressure centers are nearly the same across all three maps, and the frontal analyses from NOAA and DWD are similar, perhaps because the pressure centers are quite strong. In contrast, the Met Office chart has many more fronts analyzed, which is typical of their analyses (e.g., Mulqueen and Schultz 2015; Owens 2016). Although no special consideration was given to selecting this time and date, Fig. 2 is typical of the differences between the agencies from our experiences.
Because the ERA-Interim reanalyses (about 80-km horizontal grid spacing) are at too coarse a resolution for comparison to operational analyses of fronts, some caution must be expressed when trying to compare to small-scale features and weak fronts. Indeed, an archived image from the real-time Advanced Research version of the Weather Research and Forecasting Model (WRF-ARW)-based forecasting system ManUniCast at 20-km grid spacing (Schultz et al. 2015) shows a separation between the gradients of 850-hPa moisture and temperature along the cold front in the North Atlantic cyclone, as well as considerably more detail, particularly along the coastlines (http://manunicast.seaes .manchester.ac.uk/view.php?t=20l40124&d=d01 &p =27,30,21,14,24&1=2,2,2,0,2). Nevertheless, we use ERA-Interim to demonstrate what the application of the various frontal diagnostics looks like on the same dataset used for the climatologies in the next section.
For this time period, the plotted quantities that use G([theta]) and G([[theta].sub.e]) best replicate the frontal analyses by NOAA and DWD (cf. Figs. 2a,b with Figs. 3a and 4a). This result is perhaps not too surprising as the magnitude of the gradient is one of the primary quantities that analysts use to identify fronts at these two organizations (e.g., NOAA 2013; W. Jacobs 2017, personal communication). Because of its second derivative of the temperature field, the thermal front parameter field shows more structure (Figs. 3b, 4b), much of which is unrelated to the analyzed fronts. Some of this structure can be eliminated through a more restrictive plotting threshold, different finite-differencing approaches, and other approaches (e.g., Hewson 1998), but not all of it can. Although the fields of F([theta]) and F([[theta].sub.e]) are smoother than the thermal front parameter fields, the maxima are less continuous along the fronts, with a large number of nonfrontal regions shaded red (Figs. 3c, 4c).
There is much similarity between the fields calculated with [theta] and those calculated with [[theta].sub.e] (cf. Figs. 3 and 4), perhaps indicating the strength of the fronts on this day and that the moisture in [[theta].sub.e] has little additional effect. To help visualize the importance of the moisture in the diagnostic fields involving [[theta].sub.e] without the influence of the temperature field, we compute the same three functions (magnitude of the gradient, thermal front parameter, and frontogenesis) using the specific humidity q at 850 hPa (Fig. 5). Where the moisture effect has its largest impact on potential frontal analysis is in situations where the variability of specific humidity is in the warm sector of the North Atlantic cyclone, which shows up in the [[theta].sub.e] diagnostics (cf. Figs. 4 and 5). Here, where the amount of moisture is much greater than in the colder air farther north, the magnitude of the gradient also tends to be larger, and hence tends to have a greater influence on the [[theta].sub.e] diagnostics (e.g., Schemm et al. 2015). In this case, this variability does not seem to result in additional fronts analyzed on the Met Office chart (cf. Figs. 2b and 4b).
Because this section presents just one case study, our conclusions will not necessarily generalize to all situations. Nevertheless, the conclusion from this case study is that all quantities can detect features that are consistent with frontal analyses. There are many other places on the map that meet our minimum threshold criteria, and raising the thresholds would cause at least some of the frontal regions to break up into segments. Whether these segments would be worthy of identification of fronts in the eyes of an analyst is a different question, which gets to the purpose of surface frontal analysis (e.g., Young and Fritsch 1989; Mass 1991; Sanders and Doswell 1995; Bosart 2003) and is a topic for elsewhere.
GLOBAL CLIMATOLOGIES OF FRONTS.
Climatologies are constructed for the six different frontal diagnostics discussed earlier: magnitude of the gradient, thermal front parameter, and frontogenesis for 850-hPa potential temperature and equivalent potential temperature (Figs. 6 and 7). The most prominent features in the climatologies constructed from functions of potential temperature (magnitude of the gradient, thermal front parameter, frontogenesis) are the maxima in the percentage occurrence of fronts associated with the storm tracks over the oceans at middle and high latitudes (Figs. 6a,b,c). Maxima in the frequencies of fronts associated with the storm tracks would be expected due to the frequent passage of extratropical cyclones and are consistent with previous frontal climatologies (e.g., Petterssen 1939; Schumann and van Rooy 1951; Reed and Kunkel 1960; Serreze et al. 2001; de la Torre et al. 2008; Berry et al. 201 la; Catto et al. 2014; Schemm et al. 2015) and the climatology of frontogenesis in the midlatitudes (Satyamurty and de Mattos 1989, their Fig. 7a). The maximum in frontal occurrence over and downstream of the Alps in Flocas (1984) also occurs, but is smaller in areal extent in Fig. 6. Frequent fronts are also identified at lower latitudes with G([theta]) compared to TFP([theta]) or F([theta]). Fewer fronts may be identified by TFP([theta]) at lower latitudes because the warm edge of the frontal zone may be poorly defined or weak when fronts reach lower latitudes.
The largest values quantitatively, for G([theta]) and TFP([theta]), in particular, occur over and near regions of high terrain such as the Tibetan Plateau, western North America, Alps, Atlas Mountains, Andes, Cape Fold Mountains of South Africa, eastern Africa, and Antarctica (Figs. 6a,b). Such maxima near topography were also recognized by Berry et al. (2011a) and Schemm et al. (2015). These maxima are more subdued in the climatology of F([theta]) (Fig. 6c), perhaps because the 850-hPa winds are weaker over the higher terrain due to underground extrapolation but enhanced along the terrain edges (as suggested by an anonymous reviewer).
By comparison, the climatologies constructed from [[theta].sub.e] have, at first glance, many similarities with those from [theta] (cf. Figs. 6 and 7). Fronts in association with the oceanic storm tracks are more frequent when using [[theta].sub.e], even with the higher threshold, consistent with the frequent occurrence of warm conveyor belt fronts in warm sectors, as was found for the North Atlantic (Hewson 1998). Closer inspection, however, particularly for G([[theta].sub.e]) and TFP([[theta].sub.e]), reveals not only maxima in the midlatitudes, but larger maxima in the subtropics and occasionally the tropics, including west of Mexico and Central America, west of South America, west of Africa, South Pacific Ocean, equatorial Pacific Ocean, India, and northern Australia (Figs. 7a,b) that are either not present in or enhanced relative to the climatologies for [theta] (Figs. 6a,b). Fronts, particularly those associated with extratropical cyclones, would not be expected to occur frequently in these regions, so these maxima are unexpected. These maxima of fronts exist in low-latitude regions in part because they are associated with airmass changes near the subsidence of the subtropical anticyclones, which produce strong horizontal gradients in moisture and temperature. Maxima of frontal occurrence in these regions are consistent with climatological frontogenetic regions in Satyamurty and de Mattos (1989) (3) and also show up in other climatologies of fronts that use TFP([[theta].sub.w]) or TFP([[theta].sub.e]) (e.g., de la Torre et al. 2008; Berry et al. 2011a; Catto et al. 2013, 2014; Schemm et al. 2015; Spensberger and Sprenger 2018). Interestingly, these other climatologies using [[theta].sub.e] or [[theta].sub.w] often restrict the latitudes at which their analysis is performed, so these low-latitude features are either absent or cut in half because they fall outside or on the edge of their plotting domains. Specifically, both de la Torre et al. (2008, their Figs. 3 and 4) and Schemm et al. (2015, their Fig. 6c) do not plot equatorward of 20[degrees] latitude, cutting off maxima of their identified fronts that are shown through our analysis. Explaining their choice to not plot equatorward of 20[degrees] latitude, Schemm et al. (2015) argue that their method "should be used with care if applied outside midlatitudes."
As further evidence that the moisture field is affecting the climatologies involving [[theta].sub.e], we compute the differences between the fields computed with [theta] and [[theta].sub.e] from Figs. 6 and 7, respectively (Fig. 8). For the thresholds used in this article, fewer fronts are identified at higher latitudes when using [[theta].sub.e] compared to [theta] (Fig. 8). Also, local maxima of the difference fields occur along the midlatitude storm tracks and over Africa, again indicating that including moisture in the quantities used for identifying fronts results in the identification of fronts more frequently in these regions. As a caveat, the quantitative values of this difference field will depend upon the thresholds used to identify fronts, as previously discussed by other authors (e.g., Hewson and Titley 2010; Jenkner et al. 2010). Nevertheless, the qualitative difference between the fields would be the same: more fronts identified at middle and lower latitudes than at higher latitudes when using [[theta].sub.e] compared to [theta].
Another way to show that the moisture field is affecting the climatologies involving [[theta].sub.e] is to compute the same three functions (magnitude of the gradient, thermal front parameter, and frontogenesis) using the specific humidity q at 850 hPa (Fig. 9). All three functions have maxima at low to midlatitudes (Fig. 9). The most prominent maxima in G(q) and TFP(q) occur primarily in low latitudes because of the Clausius-Clapeyron relationship. Interestingly, F(q) shows maxima across the South Pacific and South Atlantic, as well as in the storm tracks of the Northern Hemisphere, because the frontogenesis field combines the wind field and the moisture field. Also, a local maximum in F(q)--and also to some extent in F([theta]) and F([[theta].sub.e])--exists in the lee of the Rocky Mountains because of frontogenesis associated with lee troughs and drylines (e.g., Steenburgh and Mass 1994; Keshishian et al. 1994; Castle et al. 1996; Schultz et al. 2007; Buban et al. 2007; Bosart et al. 2008).
Revisiting the climatologies using [[theta].sub.e] (Fig. 7), the existence of the maxima can now be recognized to be due in part to the fronts associated with the temperature fields (Fig. 6) and the airmass boundaries associated with moisture (Fig. 9). These effects are most apparent in the magnitude of the gradient (cf. Figs. 6a, 7a, and 9a) and thermal front parameter (cf. Figs. 6b, 7b, and 9b). Airmass boundaries derived from the TFP([[theta].sub.e]) (Fig. 7b) would be expected to be similar to airstream boundaries that lie along the edges of the airmass source regions. From a climatological perspective, the edges of source regions for air masses defined by Wendland and Bryson (1981, their Fig. 10) for the Northern Hemisphere bear a rough resemblance to these airmass boundaries derived from TFP([[theta].sub.e]), particularly in low latitudes. For example, similar regions occur in the Northern Hemisphere over the North Atlantic storm track, North Pacific storm track, and southern North Pacific (Wendland and Bryson 1981, their Figs. 1-4). Similarities in the Southern Hemisphere are harder to identify (e.g., Wendland and McDonald 1986, their Fig. 9), but this may be in part due to the more sparse data in the Southern Hemisphere at the time their analysis was performed. These results suggest that TFP([[theta].sub.e]) may not only represent airmass boundaries in the middle latitudes that constitute fronts, but also airmass boundaries from the subtropics and tropics where humidity is important.
CONCLUSIONS. Manual surface-chart analysis provides the operational forecaster the opportunity to interact and become familiar with the data, identifying the relevant weather phenomena in today's weather, marking them as important lines, and tracking them over time (e.g., Sanders and Doswell 1995; Bosart 2003). The downside is that different analysts will produce somewhat different analyses (e.g., Fig. 1 of Renard and Clarke 1965; Uccellini et al. 1992). Although automated frontal analysis on gridded data might seem to solve that problem by providing less subjectivity, choices are still required for the thermodynamic quantity or quantities, function(s), contouring threshold(s), and line-drawing algorithm. Hence, automated fronts are not objective--they reflect the choices and the objectives of the person who created the automated algorithm and reflect the ultimate application of the frontal analysis.
This article explored the choices of thermodynamic quantity and function in producing climatologies of fronts using ERA-Interim. The principal results from this study include the following:
* The advantages and disadvantages of two thermodynamic quantities ([theta] and [[theta].sub.e]) and three functions (magnitude of the horizontal gradient, thermal front parameter, and frontogenesis) were reviewed in the text and summarized in Table 2.
* Functions that used [theta] produced climatologies that more closely represented features commonly associated with lower-tropospheric fronts associated with extratropical cyclones in the midlatitudes.
* In contrast, functions that used [[theta].sub.e] produced maxima in the subtropics and tropics, including many features that were primarily associated with humidity gradients.
* The Petterssen frontogenesis function using [theta] was effective for identifying midlatitude fronts, although may have quite a bit of alongfront variability in individual cases.
Given that Petterssen frontogenesis represents the process of frontal formation (i.e., isotherms being concentrated in the horizontal by the horizontal wind), it can be a useful tool for the analysis of fronts in operational forecasting and climatological analysis, as well as for research where its usage is already common (e.g., Keyser et al. 1986,1988; Prenosil et al. 1995; Sanders 2000; Harr and Elsberry 2000; Trapp et al. 2001; Schultz 2004; Schultz and Zhang 2007; Novak et al. 2009; Steenburgh et al. 2009; Galarneau et al. 2010,2013; Moore et al. 2012,2013; Schultz and Sienkiewicz 2013; Catto 2018).
The results of this study invite continued community discussion on the definition of a front versus an airmass boundary. Commonly defined as a boundary between air masses (e.g., Bluestein 1993, p. 239), in practice, fronts are only applied to boundaries between air masses associated with a temperature gradient (e.g., Lackmann 2011, p. 132). Drylines, lee troughs, Southern Hemisphere convergence zones over the oceans (e.g., Vincent 1994), and the edges of subtropical anticyclones are not generally considered fronts, although they may be worth identifying and analyzing on surface maps. If the community requires fronts to have temperature gradients as the synoptic-dynamic literature and synoptic experience imply, then fronts should be a subset of airmass boundaries with a requisite thermal gradient and possibly also Petterssen frontogenesis along it. This distinction is consistent with previous discussions of nonfrontal airstream boundaries by Cohen and Kreitzberg (1997) and Cohen and Schultz (2005) and with discussions of what constitutes a front by Sanders and Doswell (1995), Sanders (1999a, 2005), and Schultz and Blumen (2015).
Moreover, how fronts are defined affects the conclusions that can be drawn about how they may change over time, perhaps as a result of climate change (e.g., Berry et al. 201 lb). If moisture content in the atmosphere changes as a result of global warming (e.g., Pall et al. 2007; Sherwood et al. 2010a,b; Pendergrass 2018), secular trends in fronts may appear that would be distinct from those caused by changes in temperature. Although [[theta].sub.e] and its gradients are another metric of such changes, the difficulty arises in trying to separate the distinct effects of temperature and moisture. Indeed, the increase in fronts between 1989 and 2009 determined from TFP([[theta].sub.e]) compared to TFP([theta]) in the subtropics and in the South Pacific convergence zone (e.g., Berry et al. 2011b, their Figs. 2, 4c,d) may illustrate just such an effect.
ACKNOWLEDGMENTS. Funding for Thomas was provided by the U.K. Natural Environment Research Council through the Manchester-Liverpool Doctoral Training Programme Grant NE/L002469/1. Partial funding for Schultz was provided by the Natural Environment Research Council Grants NE/1026545/1 and NE/ N003918/1 to the University of Manchester. We thank Callum Thompson (University of Manchester) for his assistance with the research, Wilfried Jacobs (DWD) for insights into the DWD frontal-analysis process, Gareth Berry for discussions about his research, Jeff Waldstreicher (NOAA/NWS) for providing surface analyses by NOAA, wetter3.de for making the DWD and Met Office maps available online, and Chuck Doswell for enlightening the second author to the fact that so-called objective approaches are fundamentally subjective. We thank Roger Wakimoto for providing Fig. 1. We gratefully acknowledge the time and effort by Editor Jeff Waldstreicher, Sebastian Schemm, and three anonymous reviewers towards improving this article.
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AFFILIATIONS: Thomas*--School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom; Schultz-- Centre for Atmospheric Science, School of Earth and Environmental Sciences, University of Manchester, Manchester, United Kingdom
* CURRENT AFFILIATION: Department of Physics, Imperial College, London, United Kingdom
CORRESPONDING AUTHOR: Prof. David Schultz; email@example.com
The abstract for this article can be found in this issue, following the table of contents.
(1) Hewson and Titley (2010, p. 362) eliminate warm-conveyor-belt fronts from their frontal analysis by applying a mask based in part on the magnitude of the gradient of [theta]. We note the incongruity of the need for an additional [theta]-based mask to eliminate moisture-based features from a climatology based on [[theta].sub.e]. Regardless, others studies that use the thermal front parameter and [[theta].sub.e] do not appear to apply this mask (e.g., Berry et al. 2011a,b; Catto et al. 2014; Schemm et al. 2015), which would appear to admit warm-conveyor-belt fronts into their climatologies.
(2) To distinguish fronts represented by lines running down the middle of the thermal gradient (i.e., Schemm et al. 2018) from fronts represented by lines running along the warm edge of the thermal gradient (i.e., traditional synoptic approach), Schemm et al. (2018) refer to these as "frontal markers" in two locations within that article. This terminology, however, is not used elsewhere in that article nor in other publications where they use this dataset (e.g., Schemm et al. 2015; Sprenger et al. 2017).
(3) Satyamurty and de Mattos (1989) is not considered in this study because they use the climatological wind and temperature fields to produce their climatological frontogenesis fields. Instead, our approach is to construct the 6-h maps of frontogenesis and then add them up to produce an annual average of percentage occurrence of fronts.
Caption: Fig. 1. Northwest-southeast cross section of winds, mixing ratio (gray lines), and (a) virtual potential temperature and (b) equivalent potential temperature across a cold front and dryline on 19 Jun 2002 based on a series of dropsondes deployed from an aircraft in northwest Kansas. The release times of the dropsondes are shown above each panel. Black dots represent the positions of the penetrations through the cross section by the Naval Research Laboratory's P-3 aircraft. Mixing ratio values greater than 7 g [kg.sup.-1] are shaded gray. Wind vectors are plotted with the full and half barb representing 5 and 2.5 m [s.sup.-1], respectively. Figure and caption from Murphey et al. (2006, their Fig. 5). Note that I mb = I hPa.
Caption: Fig. 2. Surface frontal analyses over the North Atlantic and Europe for 0000 UTC 24 Jan 2014 from (a) NOAA, (b) DWD, and (c) Met Office.
Caption: Fig. 3. The 850-hPa (a) magnitude of the gradient, (b) thermal front parameter, and (c) Petterssen frontogenesis calculated using 6 for 0000 UTC 24 Jan 2014, colored according to the respective scales with minimum shaded values starting at (a) 1.5 K [(100 km).sup.-1], (b) 0.5 K [(100 km).sup.-2], and (c) 0.25 K [(100 km).sup.-1] [(3 h).sup.-1]. Black solid lines are 6 contoured every 4 K; green dashed lines are sea level pressure contoured every 4 hPa.
Caption: Fig. 4. The 850-hPa (a) magnitude of the gradient, (b) thermal front parameter, and (c) Petterssen frontogenesis calculated using [[theta].sub.e] for 0000 UTC 24 Jan 2014, colored according to the respective scales with minimum shaded values starting at (a) 3 K [(100 km).sup.-1], (b) I K [(100 km).sup.-2], and (c) 0.25 K [(100 km).sup.-1] [(3 h).sup.1]. Black solid lines are [[theta].sub.e] contoured every 8 K; green dashed lines are sea level pressure contoured every 4 h Pa.
Caption: Fig. 5. The 850-hPa (a) magnitude of the gradient, (b) thermal front parameter, and (c) Petterssen frontogenesis calculated using specific humidity q for 0000 UTC 24 Jan 2014, colored according to the respective scales with minimum shaded values starting at (a) 0.25 g [kg.sup.-1] [(100 km).sup.-1], (b) 0.2 g [kg.sup.-1] [(100 km).sup.-2], and (c) 0.1 g [kg.sup.-1] [(100 km).sup.-1] [(3 h).sup.-1]. Black solid lines are specific humidity contoured every 2 g [kg.sup.-1]; green dashed lines are sea level pressure contoured every 4 hPa.
Caption: Fig. 6. Annual average percentage of time of occurrence of 850-hPa (a) G([theta]) exceeding 2 K [(100 km).sup.-1], (b) TFP([theta]) exceeding I K [(100 km).sup.-2], and (c) F([theta]) exceeding 0.3 K [(100 km).sup.-1] [(3 h).sup.-1] from ERA-lnterim (1979-2016).
Caption: Fig. 7. Annual average percentage of time of occurrence of 850-hPa (a) G([[theta].sub.e]) exceeding 4 K [(100 km).sup.-1], (b) TFP([[theta].sub.e]) exceeding 2K [(100 km).sup.-2], and (c) F([[theta].sub.e]) exceeding 0.5 K [(100 km).sup.-1] [(3 h).sup.-1] from ERA-Interim (1979-2016).
Caption: Fig. 8. Annual average percentage of time of occurrence of 850-hPa (a) G(q) exceeding 4 g[ kg.sup.-1] [(100 km).sup.-1], (b) TFP(q) exceeding 0.5 g [kg.sup.-1] [(100 km).sup.-1], and (c) F(q) exceeding 0.1 g [kg.sup.-1] [(100 km).sup.-1] [(3 h).sup.-1] from ERA-Interim (1979-2016).
Caption: Fig. 9. Annual average difference in the percentage of time of occurrence of 850-hPa (a) G([[theta].sub.e]) - G([theta]), (b) TFP([[theta].sub.e]) - TFP([theta]), and (c) F([[theta].sub.e]) - F([theta]) from ERA-Interim 1979-2016. These difference fields were constructed by subtracting the fields in Figs. 6 and 7.
Table 1. Climatologies of fronts and baroclinic zones based on (a) manual synoptic analyses and (b) gridded data. (a) Manual synoptic analyses Reference Location Petterssen (1939) Eastern North Atlantic and western Europe Schumann and van Rooy (1951) Northern Hemisphere Reed and Kunkel (i960) 20[degrees]-90[degrees]N Morgan et al. (1975) United States and southern Canada Flocas (1984) Europe Utsumi et al. (2014) Western Pacific around Japan Reference Data source Petterssen (1939) Bergen synoptic maps Schumann and van Rooy (1951) U.S. Daily Historical Weather Maps Reed and Kunkel (i960) U.S. Weather Bureau Daily Series Synoptic Weather Maps Morgan et al. (1975) U.S. Daily Weather Maps Flocas (1984) Daily synoptic charts from three sources Utsumi et al. (2014) Asia Surface Analysis Charts Reference Years Petterssen (1939) Januaries 1933-35 Schumann and van Rooy (1951) 1928-38 Reed and Kunkel (i960) 1952-56 Morgan et al. (1975) 1961-70 Flocas (1984) 1971-79 Utsumi et al. (2014) 2000-10 (b) Gridded data Reference Location Serreze et al. (2001) 30[degrees]-90[degrees]N Sanders and Hoffman (2002) Contiguous United States Hoffman (2008) Contiguous United States de la Torre et al. (2008) 20[degrees]-70[degrees]N Berry et al. (2011a) 80[degrees]S-80[degrees]N Berry et al. (2011b) Global Simmonds et al. (2012) 20[degrees]-90[degrees]S Catto et al. (2013) 60[degrees]S-60[degrees]N Catto et al. (2014) 80[degrees]S-80[degrees]N Schemm et al. (2015) 20[degrees]-90[degrees]N, 20[degrees]-90[degrees]S Spensberger and Global Sprenger (2018) Present study Global Reference Data source Grid spacing Serreze et al. (2001) NCEP-NCAR Reanalysis 2.5[degrees] Sanders and Hoffman (2002) Gridded surface data 0.5[degrees] Hoffman (2008) Gridded surface data 0.5[degrees] de la Torre et al. (2008) NCEP-NCAR Reanalysis 2.5[degrees] Berry et al. (2011a) ERA-40 2.5[degrees] Berry et al. (2011b) Reanalyses: ERA-Interim, 2.5[degrees] NCEP-DOE 2, JMA, MERRA Simmonds et al. (2012) ERA-Interim 1.5[degrees] Catto et al. (2013) ERA-Interim, ACCESS 1.3 2.5[degrees] Catto et al. (2014) ERA-Interim, I8CMIP5 2.5[degrees] models Schemm et al. (2015) ERA-Interim 1.0[degrees] Spensberger and ERA-Interim 1.0[degrees] Sprenger (2018) Present study ERA-Interim 0.75[degrees] Reference Years Minimum length or volume Serreze et al. (2001) 1979-98 None Sanders and Hoffman (2002) Aug 1999-Jul 2000 None Hoffman (2008) Aug 1999-Jul 2000 None de la Torre et al. (2008) Dec 1957-Feb 2006 None Berry et al. (2011a) 1958-2001 5[degrees] lat-lon Berry et al. (2011b) 1989-2009 5[degrees] lat-lon Simmonds et al. (2012) Jan 1989-Feb 2009 None Catto et al. (2013) 1997-2008 5[degrees] lat-lon Catto et al. (2014) 1980-2005 5[degrees] lat-lon Schemm et al. (2015) 1979-2012 500 km Spensberger and 1979-2014 75,000 [km.sup.2] Sprenger (2018) x 250 hPa Present study 1979-2016 None Reference Quantity and level Serreze et al. (2001) 850-hPa TFP(T) Sanders and Hoffman (2002) [absolute value of [nabla][[theta]. sub.surface]] Hoffman (2008) [absolute value of [nabla][[theta]. sub.surface]] de la Torre et al. (2008) 850-hPa TFP([[theta].sub.e]) Berry et al. (2011a) 850-hPa TFP([[theta].sub.w]) Berry et al. (2011b) 850-hPa TFP([[theta].sub.w]) and TFP([theta]) Simmonds et al. (2012) 10-m and 850-hPa wind speed and direction changes Catto et al. (2013) 850-hPa TFP([[theta].sub.w]) Catto et al. (2014) 850-hPa TFP([[theta].sub.w]) Schemm et al. (2015) 850-hPa TFP([[theta].sub.e]), 10-m wind Spensberger and 850-hPa [[absolute value of [nabla] Sprenger (2018) [[theta].sub.e]] Present study 850-hPa [absolute value of [nabla]], TFP, F for [theta], ([[theta].sub.e]), q Table 2. Advantages and disadvantages to automated frontal analysis of different (a) thermodynamic quantities and (b) functions. (a) Thermodynamic quantities Advantages Disadvantages Potential temperature * Reflects the kinematics and * Conserved only for dry dynamics of fronts adiabatic motion * Can change due to surface sensible heat flux, radiative heating, and all types of latent heat release * Nonfrontal gradients are possible * Identifies foehn phenomena (Heimann 1992; Hewson 1998) Equivalent potential temperature * Enhances weak gradients across * Humidity and temperature the front when temperature and field sometimes vary moisture both change in the same independently direction across the front * Better conserved than potential * Conserved for reversible temperature moist adiabatic motion (i.e., condensation), not surface fluxes * Can change due to surface sensible heat flux, radiative heating, and all irreversible latent heat release * Identifies so-called warm- conveyor-belt fronts in the warm sector (Hewson 1998) * Nonfrontal gradients are possible * Fronts vary in intensity depending on the moisture gradient as well as the temperature gradient (i.e., airmass boundaries can also be identified) (b) Functions Advantages Disadvantages Magnitude of the gradient * Function most consistent with * Algorithms do not draw fronts synoptic experience on the warm-air side of the frontal zone Thermal front parameter * Identifies the warm-air side of * Second derivative makes for the frontal zone noisy field, unless suitably addressed through filtering Petterssen frontogenesis * Is the kinematic process by which * Less continuous along the a front forms front in the case study * Direct link to the dynamics of * Algorithms do not draw fronts fronts through the secondary on the warm-air side of the circulation frontal zone
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|Author:||Thomas, Carl M.; Schultz, David M.|
|Publication:||Bulletin of the American Meteorological Society|
|Date:||May 1, 2019|
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