1. Introduction
Cutoff lows are typically identified in the mid- to upper-troposphere as cold-core cyclonic circulations associated with a local geopotential height minimum, often developing as closed circulations following from preexisting open troughs in the midlatitude westerlies (e.g., Nieto et al. 2005; Muñoz et al. 2020; Muñoz and Schultz 2021; Kasuga et al. 2021; Grosfeld et al. 2021). In the Northern Hemisphere, 500-hPa cutoff lows are most often identified poleward of 35°N, particularly over northeastern North America and the northern Atlantic Ocean, as well as over eastern Asia and the North Pacific (Muñoz et al. 2020; Kasuga et al. 2021). Cutoff lows generally occur less frequently in the Southern Hemisphere, with a hemispheric maximum frequency of 500-hPa cutoffs over southeastern Australia extending eastward over the southern Pacific Ocean, as well as smaller, regional maxima along the west coast of South America and southern Africa (Reboita et al. 2010; Muñoz et al. 2020; Kasuga et al. 2021).
Cutoff lows can play a crucial role in a variety of societally disruptive weather hazards, such as excessive rainfall (e.g., Brimelow and Reuter 2005; Singleton and Reason 2007; Oakley and Redmond 2014; Abatzoglou 2016; Muñoz and Schultz 2021), severe convection (e.g., NWS Birmingham 2020; Kerr and Alsheimer 2022), downslope winds (e.g., Mass et al. 2021; Abatzoglou et al. 2021), and winter precipitation (e.g., Gurka et al. 1995; Poulos et al. 2002). For example, during 11–13 April 2020, a cutoff low over the southwestern United States preceded the onset of a multiday severe weather event over the southern plains and southeastern United States. Low-level cyclogenesis occurred in association with the eastward progression of the 500-hPa cutoff low across the southern United States and its eventual merging with a larger-scale trough, providing a favorable environment for severe convection and flooding rainfall over the Southeast (NWS Birmingham 2020; Kerr and Alsheimer 2022). As another example, a 500-hPa trough and subsequent cutoff low in a highly amplified flow regime during September 2020 contributed to an outbreak of large wildfires over the Pacific Northwest (e.g., Mass et al. 2021; Abatzoglou et al. 2021). In this event, the early-season cooling over the interior western United States associated with the 500-hPa trough and subsequent cutoff enhanced the low-level pressure gradient across the Cascades, leading to strong northeasterly and easterly downslope winds over much of western Oregon, resulting in the rapid spread of fires over the region (Mass et al. 2021). During the next two days, the same cutoff low was associated with exceptional early-season snowfall over Colorado (Colorado Climate Center 2020) and damaging winds over eastern Idaho and Utah (NWS Pocatello 2020; NWS Salt Lake City 2020; Cappucci 2020).
The timing, location, and occurrence of the sensible weather hazards associated with cutoff lows is naturally dependent on the evolution and track of the relevant upper-level troughs and cutoff lows. In both of the 2020 examples above, forecasters noted uncertainty in the position of upper-level features in medium-range numerical guidance. In particular, forecasters recognized that upper-level troughs and cutoff lows in Global Forecast System (GFS) forecasts were often more progressive than in corresponding forecasts from other numerical guidance—i.e., cutoff lows and troughs in GFS forecasts were advanced farther downstream than in forecasts from other models. For example, a Day 4 Convective Outlook from the Storm Prediction Center (SPC) during the April 2020 multiday severe weather event stated, “Guidance also continues to trend slightly slower, with the GFS still a notably fast outlier” (NWS Storm Prediction Center 2020). Similarly, Area Forecast Discussions issued by the National Weather Service Denver/Boulder office during 2–3 September 2020 noted that medium-range GFS guidance generally failed to produce a cutoff low, instead advancing an open trough more quickly toward the central United States, while concurrent guidance from medium-range European Centre for Medium-Range Weather Forecasts (ECMWF) forecasts more correctly placed a cutoff over the Great Basin region (Table 1).
Excerpts from Area Forecast Discussions from the National Weather Service Denver/Boulder office during the days preceding the September 2020 cutoff low event over the western United States.
Both the April 2020 and September 2020 cases are among a variety of recent impactful events over the CONUS during which cutoff lows were noted to advance downstream too quickly in GFS guidance (cases 8 and 10 in Table 2). Erroneous synoptic progressiveness (the consistent positioning of an upper-level feature too far downstream in successive model runs) is often identified by forecasters as a common error in medium and long-range GFS guidance (Table 2). While climatologies of cutoff lows have been present in existing literature for decades (Muñoz et al. 2020, their Table 1), examinations of forecast distributions of cutoff lows and their long-term error statistics are absent. Therefore, this research develops a model climatology of 0–10-day forecasts of 500-hPa troughs and cutoff lows in operational GFS forecasts and aims to objectively corroborate the often anecdotal impressions of synoptic progressiveness errors in the GFS. Displacement errors of 500-hPa features are computed to identify where synoptic progressiveness errors are common, assess the severity of these errors, and determine how often cutoff lows exhibit these errors in operational GFS forecasts.
List of cases known to display exceptional synoptic progressiveness forecast errors over the CONUS, determined subjectively. Case reference numbers are included in parentheses.
The remainder of this manuscript is arranged as follows: section 2 describes the GFS forecast data used herein, as well as the cutoff low identification and tracking schemes used to examine these features. Position error diagnostics are also initially introduced in section 2. A 7-yr model climatology of Northern Hemisphere 500-hPa cutoff lows and troughs is presented in section 3 and position error characteristics are described in section 4. A comparative examination of Southern Hemisphere cutoff low forecast errors is included in section 5. A concluding discussion and avenues for additional research are finally presented in section 6.
2. Methodology
The 500-hPa cutoff lows and troughs are identified in 0.25° global GFS analyses and forecasts over a 7-yr period from April 2015 to 31 March 2022.1 Troughs and cutoff lows are approximated as isotropic features using a 2D slope function computed for the 500-hPa geopotential height field (e.g., Kasuga et al. 2021) at 6-h forecast intervals between analysis times (forecast hour 0; F000) and 240-h forecasts (F240). The Kasuga et al. (2021) identification scheme is adapted here instead of using other contemporary schemes (e.g., Muñoz et al. 2020) due to several factors, including the relative efficiency of the Kasuga et al. (2021) scheme such that in its basic configuration, only geopotential height at a single level is required, as well as the ability of the scheme to identify both midtropospheric troughs and cutoff lows, which enables the tracking of these features earlier in their lifespans.
Following the identification of cutoff lows and troughs at each time and each forecast hour, feature tracks are computed across successive analysis times as well as through forecast hours. Forecast and analysis tracks are then compared to objectively quantify errors associated with forecast representations of 500-hPa troughs and cutoff lows. Features and tracks computed over analysis times are considered to be the “truth” for verification and error metrics. Since the 7-yr period of study includes a variety of upgrades and changes to the GFS, most notably the change to the GFDL Finite-Volume Cubed-Sphere (FV3) dynamical core in June 2019 (NOAA/Environmental Modeling Center 2022), results in proceeding sections will additionally examine differences in error characteristics before and after the transition to GFS version 15, when the GFS was transitioned from a spectral model to the FV3 dynamical core (NOAA/Environmental Modeling Center 2022).
a. Overview of the Kasuga et al. (2021) algorithm
Kasuga et al. (2021) introduce a feature detection algorithm designed to identify “cutoff lows” and “preexisting troughs” by searching for local maxima in the “average slope” of the geopotential height field. In this context, the average slope of the 2D geopotential height field (Z) at each grid point is computed over a specified range of radii (R) as the average of four slopes between a given point and the four points directed radially outward to the north, south, east, and west from the point at distance R. The radial distance associated with the largest average slope is referred to as the “optimal radius” (Ro), with the average slope at Ro defined as the “optimal slope” (So). An illustration of this process is schematically provided in Fig. 1a for an arbitrary grid point (denoted by Z*), where the 2D average slope is computed over a range of radii R from Rmin ≤ R ≤ Rmax—the smallest and largest specified radii, respectively—with Ro and So found at R = r3 in this example. Additionally, a zonal background slope (BGx) is defined as the slope of the geopotential height field between a point located a distance Ro to the west and a second point located Ro to the east [e.g., (ZW − ZE)/2Ro in Fig. 1a]. A meridional background slope (BGy) is similarly defined [e.g., (ZN − ZS)/2Ro in Fig. 1a]. The magnitude and direction of the full 2D local background slope (BGo) is then defined by the vector described by the BGx and BGy components. Section 2 of Kasuga et al. (2021) provides a complete mathematical description of the 2D slope function, as well as further demonstration of this technique in both 1D and 2D frameworks.
Schematic depiction of the 2D slope calculation and feature identification scheme introduced by Kasuga et al. (2021). (a) The “optimal radius” (Ro) is found at R = r3 (purple ring), with an “optimal slope” (So) equal to the average of four slopes directed radially outward from Z*: [(ZN − Z*)/Ro], [(ZE − Z*)/Ro], [(ZS − Z*)/Ro], and [(ZW − Z*)/Ro]. (b) So is computed at all grid points, and local So maxima are determined where the value of So at a point exceeds that at the immediate surrounding eight grid points (e.g., So0 > So1–8). (c) Local height minima are similarly defined at grid points where the geopotential height is less than that at the surrounding eight points (e.g., Z0 < Z1–8).
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
Following the calculation of So, Ro, and BGo at each grid point, Kasuga et al. (2021) impose several criteria to identify cutoff lows and troughs as approximated isotropic features. First, local slope maxima are identified at grid points where So is greater than that of the adjoining eight grid points (e.g., Fig. 1b). Local maxima are discarded if they correspond to ridges [So ≤ 0 m (100 km)−1], have an ambiguous optimal radius (Ro = Rmin or Ro = Rmax), or are likely associated with small-scale features embedded in strong background gradients (BGo/So ≥ 3). Remaining local maxima are classified as features (cutoff lows or troughs) in the geopotential height field. A feature is classified as a cutoff low if a local height minimum, defined as a grid point with a geopotential height less than that of the adjoining eight grid points (e.g., the magenta-shaded Z0–8 in Fig. 1c), is located within the feature’s Ro, and as a trough if no local height minimum is found within Ro. For feature climatologies, Kasuga et al. (2021) only include cutoff lows if So > 10 m (100 km)−1 or troughs if So > 5 m (100 km)−1.
The present study adapts the above feature identification methodology documented by Kasuga et al. (2021) to identify cutoff lows and troughs in operational GFS forecasts. Modifications to the original scheme are documented in section 2b.
b. Adaptation and implementation of the Kasuga et al. (2021) algorithm
In the present study, Kasuga et al. (2021)’s algorithm is applied to 500-hPa geopotential heights from 0.25° global GFS analyses and forecasts initialized at 0000, 0600, 1200, and 1800 UTC between 1 April 2015 and 31 March 2022 (inclusive) for forecast hours 0–240 h, every 6 h. Before the identification procedure, mesoscale features smaller than those of interest in this study are smoothed by applying a 9-point smoothing filter to the 500-hPa height field. Parameters So, Ro, and BGo are derived at each point over the globe from the average slope of the smoothed 500-hPa heights computed over radii every 100 km from 100 to 2100 km (inclusive).2 Features are first identified independently at all analysis and forecast times following the methodology used by Kasuga et al. (2021); however, additional restrictions are imposed to limit the identification of marginal features and to reduce ambiguity for subsequent feature tracking. In this vein, only local slope maxima with So > 10 m (100 km)−1 and BGo/So < 2.25 are retained.3 Further restrictions are applied to account for multiple identified “features” that may represent a single feature. If two features identified as cutoff lows have overlapping optimal radii and share the same local height minimum, only the cutoff with the larger So is retained. Moreover, if the area of overlap between any two features is greater than 90% of the area ascribed to the smaller feature by its Ro, only the feature with the larger So is retained. For all remaining features following these disambiguation steps, information is saved describing their location, So, Ro, BGo, and height minimum characteristics, as well as 500-hPa geopotential height, temperature, meridional and zonal wind components, and water vapor mixing ratio area averaged over both their Ro and a 600-km radius used for matching in section 2b(2).
While the adapted Kasuga et al. (2021) scheme is able to differentiate between “cutoff lows” and troughs, this scheme does not explicitly ensure that cutoff lows are fully detached from the westerlies; therefore, it is possible that this technique may conflate cutoff lows with embedded closed lows. This is partially ameliorated by the use of a maximum slope ratio (BGo/So) threshold, which limits the identification of features that are relatively weak compared to their background slope, since the background slope (BGo) estimates the strength of the background flow around a feature with radius Ro (Kasuga et al. 2021). Gridded frequencies of cutoff lows identified over the Northern and Southern Hemispheres (described in detail in sections 3a and 5, respectively), are qualitatively similar to those presented by Kasuga et al. (2021) as well as Muñoz et al. (2020), who more explicitly identify cutoff lows as cold-core local height minima associated with a poleward zonal wind reversal and a thickness ridge and frontal zone east of the identified grid point. Thus, we refer to identified features as troughs and cutoff lows to be consistent with previous studies. Regional analyses of features over the Northern and Southern Hemispheres will additionally omit those identified poleward of 70°N and 50°S, and equatorward of 20°N and 20°S to exclude features that are not detached from the polar regions as well as those over the deep tropics, similar to methodologies employed by both Muñoz et al. (2020) and Kasuga et al. (2021).
1) Analysis-time feature tracking
- A0)At the first analysis time (i.e., 0000 UTC 1 April 2015), all features are initialized with unique IDs at the location of their optimal slope. This preliminary step is functionally identical to the subsequent step A8, except with no tracked features present, and is the only step performed at the first analysis time. Step A0 is schematically described in the leftmost column of Fig. 2.
- A1)For a feature at a present time [referred to here as F(t), where F is a feature at present time t], comparisons are made to all features at the previous time [Px(t − Δt); where Δt = 6 h] to determine if any previous feature has an overlapping Ro with F(t). This step is schematically described for a feature F(t) in the center column of Fig. 2.
- A2)If overlapping feature Px(t − Δt) has been tracked for at least two previous analysis times (e.g., P1 in the rightmost column of Fig. 2), a first guess location for the position of Px at the present time (t) is found by extending the most-recent motion vector of Px, as defined by its motion between (t − 2Δt) and (t − Δt), forward to the present time [e.g., if a feature’s most recent Δy = −100 km and Δx = 200 km between (t − 2Δt) and (t − Δt), then it is expected that present-time representation of the feature will be located 100 km south, and 200 km east of its (t − Δt) location, similar to a cyclone tracking methodology used by Wernli and Schwierz 2006]. For feature Px(t − Δt) to be extended to F(t), the implied motion between features Px(t − Δt) and F(t) cannot exceed 700 km in the opposite zonal or meridional direction of the estimated first-guess position change. This direction-change threshold is implemented to maintain track smoothness. Moreover, the distance between feature F(t) and the expected location of feature Px(t) cannot exceed 1200 km, which is the maximum 6-hourly feature motion used in a cutoff low tracking scheme by Muñoz et al. (2020). This test is skipped if feature Px(t − Δt) has not been tracked for at least two prior analysis times.
- A3)Normalized penalty terms for So, Ro, and BGo are computed to ensure diagnostic continuity between the present-time feature F(t) and the candidate prior-time feature Px(t − Δt) (Table 3; index 1–3). For each term, the penalty is computed as a normalized absolute difference:
- A4)If multiple prior-time features Px(t − Δt) overlap the same present-time feature F(t) (e.g., if two or more features merge) and pass the tests in steps A2 and A3, the prior-time feature which minimizes the summed penalty term computed in step A3 is the only prior-time feature extended to F(t) (i.e., feature F is assigned the ID of the prior-time feature associated with the smallest penalty term; see feature 3 in the center panels of Fig. 2). Tracks of the remaining prior-time features with larger penalty terms will terminate at time t unless they overlap a different present time feature and satisfy steps A2 and A3.
- A5)If no prior-time feature Px(t − Δt) is continued to F(t), steps A1–A4 are repeated, except using identified features Qx(t − 2Δt) that were not previously extended to t − Δt.4 This step is included to account for occasions when the feature identification scheme may miss a feature, or if model analysis data are missing for a single time. A feature track is not continued if it is missing at two or more of the most recent four analysis times.
- A6)After steps A1–A5, if multiple present-time features Fx(t) are continuations of the same prior time feature Px(t − Δt) or Qx(t − 2Δt) (e.g., if the prior time feature splits into different features), the feature F(t) which minimizes the summed penalty term (step A3) is retained as the continuation of the prior-time feature. This is similar to step A4, except accounting for multiple present features matching the same prior feature, whereas A4 refers to multiple prior features matching the same present feature. An example of this scenario is depicted in the rightmost panels of Fig. 2, where the leftmost present time features, f and F (5 and 1 in the lower panel), both overlap P1. If f (5) is not excluded due to the direction change criteria (A2), then its penalty with respect to P1 will be compared to the penalty between F and P1.
- A7)Steps A1–A6 are repeated three additional times to attempt to track features Fx(t) that were discarded in step A6, but may also be a candidate feature to continue the track of a different feature from the prior time Px(t − Δt) or Qx(t − 2Δt) that has not yet been successfully tracked to the present time.
- A8)After four passes of steps A1–A6, any remaining present-time features Fx(t) that are not associated with a continuation of a prior-time feature are assigned a new ID.
- A9)Steps A1–A8 are repeated for all analysis times.
Schematic depiction of the adapted analysis-time tracking scheme at the (left) first (0000 UTC 1 Apr 2015), (center) second (0600 UTC 1 Apr 2015), and (right) third (1200 UTC 1 Apr 2015) times in the analysis data. (top) The comparison of a specific feature (F) to multiple prior time features (Px) is demonstrated, and (bottom) the result of the tracking scheme for all present features (f) is provided. Features illustrated using heavy blue lines and gray fill are those represented at the present time. Thin blue lines and thin gray lines represent feature locations at the first prior time (P) and second prior time (Q), respectively. Dashed straight lines indicate the prior-time features to which F is compared, with the best match indicated in magenta, and green arrows in the top-right panel represent the predicted motions of previously tracked prior-time features.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
Normalization value (NX) for each parameter (X) penalty evaluated using Eqs. (1) and (2). Normalization values are derived from a 1-yr test period and represent twice the standard deviation of parameter X for all features during 2020. For indices 5–9, parameter X refers to area-averaged 500-hPa geopotential height (Z), water vapor mixing ratio (qυ), temperature (T), zonal wind speed (U), and meridional wind speed (V) over a 600-km radius surrounding each feature. For tracking, the sum of normalized penalty indices 1–3 cannot exceed 1.5 for a feature to be tracked to a subsequent time step. For matching forecast and analysis features, the sum of 1) the mean of normalized penalty indices 1–3, 2) the mean of normalized penalty indices 5–9, and 3) normalized penalty index 4 cannot exceed 2.0 for a nontracked forecast feature to be matched to an analysis-time feature.
2) Forecast-time feature tracking and matching
While Kasuga et al. (2021) identify and track cutoff lows solely in reanalysis data, the present study identifies and tracks features at both analysis and forecast times to evaluate the position error characteristics of forecast features. In this vein, the analysis-time feature tracking scheme described in the preceding section is paired with a matching scheme that compares features at corresponding forecast and analysis times. The addition of a matching component to the tracking of forecast features is necessary to track features through forecast times when features did not exist at the forecast initialization time. Moreover, matching alone would lack temporal consistency with other forecast hours; thus, the combination of the tracking and matching schemes retains consistency between identified features at successive forecast hours. Analysis-time feature tracking (i.e., steps A0–A9) must be completed prior to forecast tracking and matching to properly assign feature IDs. The matching component is as follows:
- B1)For a feature F at valid time t and forecast hour h [F(t, h)], comparisons are made to all analysis-time (F000) features Ax at the same valid time [Ax(t, 0)] to determine which, if any, analysis-time feature best matches the forecast feature. Specifically, nine normalized penalty terms are computed similar to step A4 [Eq. (1); Table 3] and are combined as a total penalty term:where Xi refers to the ith parameter (Table 3) for a forecast feature F and an analysis time feature Ax at the same valid time t, and N is the normalization value for parameter Xi. The term Ptot is the combined penalty term, defined as the sum of the mean of normalized penalty terms i = 1–3 [derived feature characteristics from the Kasuga et al. (2021) identification algorithm (i.e., So, Ro, and BGo)], the mean of normalized penalty terms i = 5–9 (600-km area-averaged atmospheric characteristics surrounding identified features), and the normalized displacement error between F(t, h) and Ax(t, 0) (penalty term i = 4). As a simple example, two similar features at the same valid time separated by 200 km with an So difference of 1.8 m (100 km)−1, a BGo difference of 2.0 m (100 km)−1, an Ro difference of 300 km, and area-averaged 500-hPa geopotential height, water vapor, temperature, zonal, and meridional wind differences of 50.0 m, 0.2 g kg−1, 3.0 K, 2.2 m s−1, and 2.4 m s−1, respectively, would be associated with a combined matching penalty5 of This penalty function is similar in form to “total interest” functions often used in object-based verification (e.g., Davis et al. 2006a,b, 2009; Flora et al. 2019; Johnson et al. 2020), but unlike previous work, this penalty function incorporates multiple physical fields in determining whether two features “match.”
- B2)If the combined penalty term (Ptot) is less than 2.0, implying that the features F(t, h) and Ax(t, 0) are not spatially disparate and share similar physical attributes, the analysis-time feature is considered a “match” for the forecast-time feature.
- B3)As in step A6 of the analysis-time tracking scheme, if multiple forecast-time features F(t, h) match the same analysis-time feature Ax(t, 0), the feature F(t, h) that minimizes the combined penalty term (step B1) is retained as the best match of the analysis-time feature.
- B4)Similar to step A7 of the analysis-time tracking scheme, steps B1–B3 are repeated three additional times to attempt to match features Fx(t, h) that failed to match in step B3, but may be a candidate feature to match a different analysis-time feature Ax(t, 0) that does not yet have a match at forecast hour h.
- B5)After four passes of steps B1–B4, any remaining forecast features that are not matched to an analysis-time feature are excluded from position error analyses.
- B6)Steps B1–B5 are repeated for all forecast hours, independently, over each verification time.
The matching scheme (B1–B6) is combined with the tracking scheme (A0–A9) for each initialization time. Forecast features are not tracked beyond their final analysis valid time. The generalized procedure for the combined forecast matching-tracking scheme is as follows:
- C1)For features at F006, the tracking scheme described in steps A1–A9 is used to continue feature IDs from the initial time (F000) to F006.
- C2)For features at F006 that have not been tracked from F000 (e.g., if the valid time associated with F006 is the first time a feature is identified in the analysis track data), steps B1–B6 are used to match a nontracked forecast feature to an appropriate feature at the corresponding analysis time (e.g., F000 + 6 h) that is not already represented by a tracked feature from step C1.6
- C3)Any remaining forecast-time features that are not tracked from the prior time or matched to an analysis-time feature are excluded from position error analyses.
- C4)Advance to the next forecast hour (e.g., F012) and repeat steps C1–C3 for F012–F240, every 6 h (e.g., track feature IDs from F006 to F012, including features that were originally tracked from F000 to F006, and features at F006 that were matched to the corresponding analysis).
c. Demonstration of feature identification and tracking
Identification and tracking of features almost certainly is subject to compounding errors associated with data quality, horizontal resolution, and assumptions used to develop the tracking and identification schemes. Moreover, tracking of predicted features is further complicated by forecast errors that grow with time. The configuration of the identification, tracking, and matching schemes used herein may be prone to error; however, manual examination of a variety of identified features and tracks yields satisfactory results, such that nonphysical “jumps” and erroneous termination or extensions of feature tracks are minimized.
Figure 3 provides an illustrative example of the identification of Northern Hemisphere features in the 0000 UTC 9 September 2020 GFS analysis. Twelve cutoff lows and four troughs (Fig. 3c) are identified poleward of 20°N as meeting the criteria described in sections 2a and 2b, all associated with a region where the optimal slope of the 500-hPa geopotential height field is greater than 10 m (100 km)−1 (Fig. 3a). Optimal slopes are largest within cutoff lows and troughs (Fig. 3a), while large values of the background slope (Fig. 3b) coincide with large height gradients.
At 0000 UTC 9 Sep 2020, Northern Hemisphere 0.25° GFS analysis of 500-hPa geopotential height (dam; black contours) and (a) optimal slope [m (100 km)−1; shaded]; (b) 2D background slope at the optimal radius [m (100 km)−1; shaded]; and (c) identified features. In (a), heavy violet contours highlight regions where the optimal slope is at least 10 m (100 km)−1. In (c), the location of identified features is denoted by filled circles shaded according to their optimal slope [m (100 km)−1; lower color bar], feature optimal radii are denoted by radial rings and light red fill, with blue rings denoting features identified as cutoff lows, and green rings denoting those identified as troughs.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
At 0000 UTC 9 September 2020, the cutoff low over the western United States (Fig. 3c) is of particular interest due to its association with exceptional synoptic progressiveness errors (Table 1 and case 10 in Table 2) and considerable societal impacts (e.g., Mass et al. 2021; NWS Salt Lake City 2020; NWS Pocatello 2020), and is thus used as a demonstration of the tracking scheme. This feature is first identified in GFS analyses at 1800 UTC 7 September 2020 (denoted by the green star in Fig. 4) over northern Idaho and moves southeast toward Utah and Colorado during 8 and 9 September (Fig. 4). The feature remains over the western United States through 11 September, before moving northeastward toward Wyoming and South Dakota and eventually eastward toward the Great Lakes region, where the feature dissipates on 13 September (denoted by the red star in Fig. 4). The forecast tracking and matching scheme first identifies this feature in forecasts initialized at 1200 UTC 30 August (a 222-h forecast valid at 1800 UTC 8 September), with forecasts initialized prior to ∼7 September associated with feature tracks (denoted by the colored lines in Fig. 4) that are located east and south of the verification track (black line in Fig. 4). Since this is a case of manually noted synoptic progressiveness errors, it is expected that forecast tracks would be located erroneously far downstream; thus, apparent errors in the forecast position of this feature likely correspond to errors in the forecast system, rather than the matching-tracking scheme. Furthermore, the predicted location of the forecast feature at 0000 UTC 9 September moves to the west with later initialization times, demonstrating that this case is characterized by a progressiveness error that decreases with decreasing forecast lead time (see filled circles in Fig. 4).
Analysis and up to 240-h forecast tracks of a cutoff low over the United States valid during 1800 UTC 7 Sep–1800 UTC 13 Sep 2020. The verification track (provided by GFS analyses) is in black, start (1800 UTC 7 Sep) and end (1800 UTC 13 Sep) points are denoted by a green and red star, respectively, and additional valid-time locations are denoted by black vertical lines every 24 h along the verification track (labels are DDhh; e.g., 0900 means 0000 UTC 9 Sep). The analysis-time location at 0000 UTC 9 Sep (vertical label 0900) is denoted by a black filled circle. Forecast tracks are shaded according to their initialization time (DDhh) as noted along the color bar. The forecast feature location at 0000 UTC 9 Sep 2020 is denoted by color-filled circles with black outlines, shaded as in its corresponding initial time. Note that the filled circle in northeastern Canada is part of a discontinuous forecast track initialized at 1200 UTC 5 Sep, and is not related to the 0000 UTC 9 Sep forecast locations.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
3. Spatial and seasonal distribution of features in GFS analyses and forecasts
a. Analysis climatology
Consistent with existing climatologies of cutoff lows, 500-hPa cutoffs identified in GFS analyses over the Northern Hemisphere between 1 April 2015 and 31 March 2022 were most frequent over the northern Atlantic and Pacific Oceans, where broad, zonally elongated regions of 7-yr feature counts exceed 40–45 cutoff lows between 45° and 65°N (Fig. 5a). Local maxima exceed 65 features over the Gulf of Alaska and along the southeastern coast of Greenland, with a smaller maximum of 45 features of Hudson Bay (Fig. 5a), spatially consistent with the results of Kasuga et al. (2021) (cf. their Fig. 9a).
Number of So > 10 m (100 km)−1 (a) 500-hPa cutoff lows and (b) 500-hPa troughs identified in operational GFS analyses during 1 Apr 2015–31 Mar 2022 every 6 h using the adapted Kasuga et al. (2021) scheme over the Northern Hemisphere. Features are counted in 2° × 2° grid boxes. Dashed circles are plotted at 20°, 45°, and 70°N for geographic reference. During 1 Apr 2015–31 Mar 2022, 117 945 cutoff lows and 39 341 troughs with So > 10 m (100 km)−1 were identified over 20°–70°N.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
The distribution of 500-hPa troughs is also characterized by a maximum frequency band between 45° and 65°N, but with fewer troughs than cutoff lows identified over the 7-yr period (Fig. 5b). Gridded trough frequencies exceeding 15–20 features are present over eastern North America, eastern Europe to central Asia, and the eastern North Pacific (Fig. 5b), mostly consistent with the spatial distribution of cool-season troughs identified by Kasuga et al. (2021) (cf. their Fig. 9c). It is expected that the configuration of the identification algorithm used herein, which only includes features with an optimal slope greater than 10.0 m (100 km)−1 to reduce noise and ambiguity, will yield fewer troughs than Kasuga et al. (2021), who use an optimal slope threshold of 5.0 m (100 km)−1 for troughs. Moreover, the number and scale of identified troughs is generally limited to shortwave and some longwave features by the So and Ro thresholds described in section 2b (e.g., the broad trough south of the Aleutians in Fig. 3 is not classified using this methodology).
Northern Hemisphere (20°–70°N) cutoff lows are most often identified during the spring (MAM; 32 432 features), and least during fall and winter (SON and DJF; 27 795 and 28 846 features, respectively) during 1 April 2015–31 March 2022 (Fig. 6). More specifically, the mean annual peak of Northern Hemisphere cutoff low frequency occurs during late May, with ∼14 cutoff lows present at any time over 20°–70°N, followed by a rapid decrease to ∼11 features by the end of June (Fig. 7). The large decrease in cutoff low frequency during May–June is most prominent over the CONUS, where 7-yr gridded feature counts are <6 over nearly the entire region during JJA (Fig. 6c), but >6–8 during MAM, with maxima over the southwestern United States and central plains in excess of 10 features (Fig. 6b). Muñoz et al. (2020) also demonstrate that the seasonal cycle for 500-hPa cutoff lows is larger over the eastern North Pacific and western North America than for other Northern Hemisphere sectors (e.g., Europe, eastern Asia, and eastern Canada/Greenland) in their study of 1960–2017 cutoff lows in the NCEP–NCAR Reanalysis (Kalnay et al. 1996), and suggest that the seasonality of the polar jet and onset of warm-season midtropospheric subtropical anticyclones are influential in modulating the seasonal cycle of 500-hPa cutoff lows.
As in Fig. 5a, but for 500-hPa Northern Hemisphere cutoff lows during (a) DJF, (b) MAM, (c) JJA, and (d) SON.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
Mean annual cycle (0000 UTC 1 Jan–1800 UTC 31 Dec) of 20°–70°N 500-hPa cutoff lows (solid line) and troughs (dashed line) during 1 Apr 2015–31 Mar 2022. Feature counts are smoothed using a weighted two-week moving average.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
Following the May–June transition, the 20°–70°N cutoff low frequency remains generally consistent through October, reaching an annual minimum of ∼9–10 cutoff lows in early November (Fig. 7). The consistent hemispheric feature counts over this period are likely related to relatively small seasonal variability in cutoff lows identified over mid–high-latitude ocean basins (Fig. 6), and partially related to the identification of features with tropical origins over the western Pacific during JJA and SON (between ∼110° and 150°E; Figs. 6c,d). The annual cycle of identified 20°–70°N troughs is smoother than for cutoff lows, with ∼5 features present during the cool season (NDJFM) and a hemispheric minimum of ∼1 feature during late July (Fig. 7).
b. Forecast distribution errors
In the Northern Hemisphere, both cutoff lows and troughs are generally identified less often in forecasts than in analyses, with this underrepresentation becoming worse at later forecast hours (Fig. 8). For example, the number of cutoff lows and troughs counted over all F006s are only ∼98.5% and ∼96.0% of the total number of features counted over all analysis times, respectively (Fig. 8). Furthermore, the number of total forecast cutoff lows decreases to ∼93% of total analysis time cutoff lows by F240, while the total number of troughs is partially recovered, remaining between ∼95% and 96% through F240, suggesting that verifying cutoff lows may be represented as forecast troughs at later forecast hours. While the root causes of the systematic underrepresentation of both cutoff lows and troughs are not presently clear, we note that this underrepresentation is generally most severe for relatively small, mesoscale features (e.g., Ro < 500 km; not shown).
Total forecast 500-hPa troughs (dashed line) and cutoff lows (solid line) present at forecast hours as the percent of total corresponding analysis time features during 1 Apr 2015–31 Mar 2022 over 20°–70°N. Values < 100% mean there are fewer forecast features than analysis time features; values > 100% mean there are more forecast features than analysis time features.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
Since the 7-yr analysis conducted herein is an examination of operational GFS forecasts—which includes a variety of upgrades to the operational system, such as the upgrade to the FV3 dynamic core in June 2019 (NOAA/Environmental Modeling Center 2022)—it is instructive to examine changes in the forecast characteristics of 500-hPa features with time. Figure 9 depicts the percent of forecast cutoff lows relative to analysis time cutoff lows for each forecast hour and month over the Northern Hemisphere. The underrepresentation of cutoff lows at forecast lead times of 3 days or less is generally worse prior to June 2019, and typically worsens with increasing forecast lead time (Fig. 9). After June 2019, the underrepresentation of short-range forecast cutoff lows is reduced compared to the preceding period, with some months characterized by an overrepresentation of cutoffs; however, medium–long-range forecasts still undercount cutoff lows, particularly during the warm season (∼June–September; Fig. 9). While attributing changes in the forecast representation of cutoff lows to specific modifications during upgrades of the operational GFS is outside the scope of this research, the improved representation of cutoff lows at short–range forecast hours following June 2019 coincides with the upgrade to FV3 GFS (NOAA/Environmental Modeling Center 2022).
Total forecast 500-hPa cutoff lows present at forecast hours as the percent of total corresponding analysis time cutoff lows for each valid month (y axis; time increases downward) and forecast hour (x axis) during 1 Apr 2015–31 Mar 2022 over 20°–70°N. Analysis and forecast cutoff lows are counted as the total number of features present during all valid times over each month. Values < 100% mean there are fewer forecast features than analysis time features during valid times over a given month; values > 100% mean there are more forecast features than analysis time features. A dashed horizontal reference line is plotted at June 2019 to note the transition to FV3 (GFS version 15).
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
To further probe differences before and after the GFS FV3 transition and better understand the climatological forecast errors of cutoff lows, we examine differences in the spatial distribution of forecast and analyzed cutoff lows (Fig. 10). The forecast underrepresentation of cutoff lows is most prominent over continents in long-range forecasts; both before and after the transition to FV3, zonally elongated regions of reduced forecast cutoff low frequencies are present over the CONUS and along 45°N over Europe and Asia by F240 (Figs. 10c,f). Relative increases in forecast cutoff low occurrence compared to analysis times are noted at higher latitudes, such as over the northeastern Pacific and poleward of 50°N over Europe during both periods (Figs. 10b,c,e,f), and along 45°N over North America as well as over Hudson Bay following the transition to FV3 (Figs. 10a–c), suggesting that the forecast distribution of Northern Hemisphere cutoff lows is shifted poleward relative to analysis cutoff lows. At earlier forecast hours, such as F024, the underrepresentation of cutoff lows over Eurasia is more prominent prior to GFS version 15 (Figs. 10a,d). This is not necessarily surprising, since cutoff lows are more severely underrepresented in earlier versions of the GFS (Fig. 9).
Normalized differences between gridded forecast and analysis distributions of 500-hPa cutoff lows over the Northern Hemisphere (number yr−1). Features are counted and gridded as in Fig. 5, and normalized relative to the length of each period in (a)–(c) and (d)–(f). Normalized differences are plotted separately (top) for the period following the transition to the FV3 dynamic core (12 Jun 2019–31 Mar 2022) and (bottom) prior to the transition (1 Apr 2015–11 Jun 2019) for (a),(d) F024; (b),(e) F120; and (c),(f) F240. All identified forecast cutoff lows are represented regardless of their association with a valid-time feature. Dashed circles are plotted at 20°, 45°, and 70°N for geographic reference. Values < 0 indicate that the frequency of forecast cutoff lows in a 2° × 2° grid box is less than the frequency of analysis-time cutoff lows, and values > 0 indicate that the frequency of forecasts cutoff lows is greater than that of analysis-time cutoff lows.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
While the systematic underrepresentation of 500-hPa cutoff lows in ∼0–3-day forecasts over the Northern Hemisphere is improved following the GFS FV3 transition in June 2019, cutoff lows are still undercounted over the Northern Hemisphere midlatitudes at longer forecast lead times (e.g., 5–10 days) between June 2019 and March 2022 (Figs. 10b,c). Over the CONUS, the undercounting of cutoff lows at long forecast lead times is consistent with a component of synoptic progressiveness errors noted by forecasters—specifically, instances where shortwave troughs fail to develop into closed lows in forecasts (e.g., Table 1). This type of error is further emphasized by the difference between hemispheric distributions of F240 and analysis time 500-hPa troughs following transition to FV3. Over the eastern CONUS, forecast troughs are identified more frequently than those at the analysis time, particularly over the Central Plains and Midwest regions (Fig. 11). Since cutoff lows are concurrently underrepresented over a similar region at F240 (Fig. 10c), though at a greater rate than troughs are over represented, these results suggest that some verifying cutoff lows over the CONUS, east of the Rockies, may be represented as troughs in GFS forecasts. These findings are consistent with the difference between total analysis and forecast cutoff lows and troughs over the Northern Hemisphere (Fig. 8), which demonstrate that the underrepresentation of cutoff lows is worse than for troughs in medium to long-range forecasts over the Northern Hemisphere.
Normalized differences between gridded F240 and analysis distributions of 500-hPa troughs over the Northern Hemisphere (number yr−1) during 12 Jun 2019–31 Mar 2022. Note that a smaller contour range is used here compared to Fig. 10c.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
4. Forecast displacement error characteristics
Position error diagnostics are computed separately for each forecast hour and also over forecast windows, including five equal-length periods of F006–F048, F054–F096, F102–F144, F150–F192, and F198–F240. Errors are computed between forecast features tracked using the combined matching-tracking scheme and analysis-time features. Forecast windows corresponding to common operational definitions (e.g., NOAA/NWS/Weather Prediction Center 2022), including short- (F006–F066), medium- (F072–F168), and long- (F174–F240) range forecasts are also examined, and are associated with qualitatively similar results to the corresponding equal-length windows. For brevity, only the five equal-length windows are discussed in this manuscript.
Figure 12 depicts the mean zonal, meridional, and total position errors for cutoff lows verifying between 20° and 70°N for each month and forecast hour. Mean total position errors generally reach 50 km by F012, growing to >900 km after F168 (Fig. 12c). Mean zonal position errors associated with verifying cutoff lows are positive, or eastward, for most months, particularly for medium to long-range forecasts between 2017 and 2021 (Fig. 12a), and meridional position errors become positive (northward, poleward in the Northern Hemisphere) for medium to long-range forecasts during most months (Fig. 12b). The presence of northward meridional position errors is consistent with the apparent poleward shift in the distribution of forecast cutoff lows over the Northern Hemisphere (Fig. 10), while eastward zonal position errors that become larger with longer forecast lead times are consistent with forecasters’ descriptions of synoptic progressiveness errors in GFS forecasts (e.g., Table 1).
Mean (a) zonal, (b) meridional, and (c) total position error (km) for all verifying cutoff lows averaged over each month and at each forecast hour during 1 Apr 2015–31 Mar 2022 between 20° and 70°N. Time increases downward along the y axis, forecast hour increases to the right along the x axis. Positive values in (a) and (b) refer to eastward and northward position errors, respectively, and negative values in (a) and (b) refer to westward and southward position errors, respectively. A dashed horizontal reference line is plotted at June 2019 to note the transition to FV3 (GFS version 15).
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
Examination of the geographic distribution of Northern Hemisphere zonal position errors indicates that predicted features over the CONUS and northern Eurasia are generally located east of their valid-time positions over the 7-yr analysis period (Fig. 13). Gridded mean positive (eastward) zonal position errors develop prior to F048 over the CONUS and central Asia (Fig. 13a), remaining spatially consistent and growing through F144 (Figs. 13b,c). Over the CONUS, these errors are largest for forecast features over the central and southwestern United States, exceeding +90 km over western Texas and eastern New Mexico, while errors in excess of +120 km are prominent over central Russia (Figs. 13a–c). Large eastward errors persist over the two regions through F198–F240 (Figs. 13d,e); however, these errors become more concentrated in location over the CONUS (over the Rocky Mountain region) and Asia (over central and northern Russia) with increasing forecast hour. Gridded mean zonal position errors over midlatitude ocean basins are generally smaller in magnitude and negative (westward) through F150–F192 (Figs. 13a–d), with mean errors over the North Atlantic becoming near-zero or weakly positive (eastward) by F198–F240 (Fig. 13e).
Mean zonal position error of all forecast 500-hPa features valid during 1 Apr 2015–31 Mar 2022 every 6 h present in 2° × 2° grid boxes during (a) F006–F048, (b) F054–F096, (c) F102–F144, (d) F150–F192, and (e) F198–F240. Dashed circles are plotted at 20°, 45°, and 70°N for geographic reference. Positive values indicate mean errors east of corresponding valid-time features, and negative values indicate a westward mean error. Grid boxes containing less than 0.01% of all analysis-time features are masked such that regions where the mean error may be dominated by few features are omitted.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
a. Displacement errors of verifying cutoff lows
Motivated by the spatial differences in zonal position error characteristics of forecast features over the Northern Hemisphere, position error characteristics of verifying Northern Hemisphere cutoff lows are calculated separately over seven Northern Hemisphere regions, including a general Northern Hemisphere latitude band (20°–70°N), North America, CONUS, Atlantic, Europe, Asia, and Pacific sectors (Table 4). An eighth sector encompassing the Southern Hemisphere midlatitudes is further discussed in section 5. Consistent with the gridded mean F102–F144 position errors of all forecast features (Fig. 13c), the mean zonal position errors for F102–F144 of all cutoff lows verifying over both the CONUS and Asia sectors are positive (eastward; Table 4). Mean zonal position errors are also eastward over the European and the general North America sectors; however, the eastward error over these regions is of smaller magnitude than over the CONUS and Asia (Table 4). Cutoff lows over the Atlantic and Pacific sectors—regions characterized by the greatest density of features over the Northern Hemisphere (Fig. 5a)—are generally associated with negative (westward) zonal position errors (Table 4), also consistent with the gridded mean F102–F144 position errors of all forecast features (Fig. 13c). Despite the relatively large influence of westward errors over the feature-dense oceanic sectors on aggregate statistics, the mean F102–F144 zonal position error for cutoff lows over the Northern Hemisphere midlatitudes is still weakly positive (9.44 km to the east) over the 7-yr period (Table 4).
Mean zonal position errors (km) for verifying cutoff lows between F102–F144 over the Northern Hemisphere (NHEM), North America, CONUS, Atlantic, Europe, Asia, Pacific, and Southern Hemisphere (SHEM) sectors during all seasons (All), December–January–February (DJF), March–April–May (MAM), June–July–August (JJA) and September–October–November (SON). Positive and negative values denote eastward and westward mean zonal position errors, respectively. Mean zonal position errors listed in italics are statistically different from zero at the 99% confidence level using a Student’s t test.
Since the frequency and regional distribution of cutoff lows varies by season, forecast position errors of cutoff lows are further examined by individual season. Mean F102–F144 zonal position errors for fall (SON) and winter (DJF) cutoff lows are positive (eastward) for all Northern Hemisphere sectors except for the Atlantic and Pacific regions (Table 4). Similarly, seasonal mean zonal position errors during spring (MAM) are eastward for all regions except the Pacific (Table 4), which is characterized by mean westward zonal errors during all seasons. During boreal summer (JJA), cutoff lows over the Northern Hemisphere are still associated with eastward mean position errors; however, this is likely due to the prevalence of eastward errors over Asia (Table 4), which is characterized by less seasonal variability in the frequency of identified cutoff lows than elsewhere over the Northern Hemisphere (Fig. 6).
Focusing on the distribution of F102–F144 zonal position errors associated with cutoff lows over the CONUS and Asia, where eastward mean errors are largest over the 7-yr period (Table 4 and Fig. 13c), Figs. 14a and 14f demonstrate that eastward errors of a given magnitude are ∼1.1–1.5 times more frequent than westward errors of similar magnitudes over these regions. Mean F102–F144 zonal position errors over Asia are eastward during all seasons and largest during MAM, with eastward position errors counted more frequently than westward position errors in all bins of comparable magnitudes during both MAM and JJA (Figs. 14h,i). Mean F102–F144 zonal errors for cutoff lows over Asia during SON and DJF are still eastward, but larger magnitude westward (negative) errors become more frequent during these seasons (Figs. 14g,j).
Histogram distributions (black line) of medium-range (F102–F144) zonal position errors (km) for (top) the CONUS and (bottom) Asia during (a),(f) all seasons; (b),(g) DJF; (c),(h) MAM; (d),(i) JJA; and (e),(j) SON. Values are binned every 50 km from −1500 to 1500 km. The solid vertical line and red-shaded label along the x axis of each panel refers to the distribution mean. Color shading along the positive x axis denotes the ratio of the number of errors in a >0 km (eastward) bin to the number of errors in a <0 km (westward) bin of the same absolute value bounds [e.g., the ratio of the number of zonal position errors between +(50 and 100 km) to those between −(50 and 100 km)]. Color shading highlights asymmetries in the distribution of position errors about zero. Values > 1 indicate that there are more errors in the eastward bin than the westward bin, while values < 1 denote more frequent errors in the westward bin. Values in the top left of each panel refer to the number of analysis-time cutoff lows identified over a given sector and season (top line) and the number of F102–F144 forecasts (bottom line) corresponding to the analysis-time cutoff lows counted in the top line [i.e., since F102–F144 (inclusive) includes 8 forecast hours, the number of forecast features could be 8 times the number of valid features, at maximum, if all analysis time features were represented in all forecasts]. The bottom value (number of forecasts) is the number of samples included in the distribution in each panel.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
For cutoff lows over the CONUS, mean F102–F144 position errors are eastward during SON, DJF, and MAM, and are associated with the largest seasonal-mean eastward error during SON (Figs. 14b–e). For CONUS cutoff lows during JJA, westward zonal errors during F102–F144 are more common than eastward errors of nearly all magnitudes (Fig. 14d); however, cutoff lows are relatively uncommon over the CONUS during JJA compared to other seasons (Fig. 6). The apparent eastward bias associated with F102–F144 forecasts of cutoff lows over the CONUS outside of JJA, particularly during MAM, does correspond with numerous manually identified cases of synoptic progressiveness where the cutoff low was associated with considerable sensible weather impacts (e.g., cases 2, 3, 4, 6, and 8 in Table 2).
Zonal position errors associated with Northern Hemisphere cutoff lows are further examined by verification month and forecast hour for each Northern Hemisphere sector. Cutoff lows verifying over primarily continental sectors (Figs. 15a,b,d,e) are more strongly associated with eastward (positive) zonal position errors than those verifying over the Atlantic and Pacific sectors (Figs. 15c,f), consistent with the histogram distributions of F102–F144 zonal position errors over the CONUS and Asia (Fig. 14) and mean F102–F144 error characteristics over Northern Hemisphere sectors (Table 4). Between ∼F012–F072, zonal position errors associated with cutoff lows over North America, particularly the CONUS, are generally near-zero or positive (eastward) for most months outside of the warm season (∼JJA; Figs. 15a,b). These eastward errors become large with increasing forecast hour, generally exceeding +100 km between F072–F120 (Fig. 15b). Similar error characteristics are present over the European sector beyond 3-day lead times, particularly for cutoff lows occurring between 2017 and mid-2021 (Fig. 15d), although maximum eastward position errors are smaller than those over the CONUS (Fig. 15b). Over Asia, cutoff lows in nearly all months prior to 2019 are associated with eastward mean zonal position errors by F036–F048 (Fig. 15e). eastward zonal position errors over Asia generally increase with increasing forecast hour; however, similar to the European sector, monthly mean zonal position errors for medium to long-range forecasts are smaller for cutoff lows over Asia than over the CONUS (Figs. 15b,d,e).
As in Fig. 12a, but for the (a) North America, (b) CONUS, (c) Atlantic, (d) Europe, (e) Asia, and (f) Pacific sectors described in Table 4.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
In summary, the displacement error associated with Northern Hemisphere midlatitude 500-hPa cutoff lows in GFS forecasts between April 2015 and March 2022 generally grows with increasing forecast lead time (Fig. 12c). This displacement error appears to be characterized by a poleward bias that increases with forecast hour (Fig. 12b), as well as regionally and seasonally dependent zonal displacement biases, such that cutoff lows over the CONUS and Asia appear to be associated with eastward displacement errors during forecast days 0.25–10, particularly during spring and autumn, as well as summer for cutoff lows over Asia (Figs. 13–15). Over the CONUS, the apparent eastward bias during spring and autumn and the general underrepresentation of cutoff lows described in section 3b are qualitatively consistent with subjective impressions of synoptic progressiveness by operational forecasters (e.g., Tables 1 and 2). While the magnitude of the eastward position errors is largest in medium to long-range forecasts (Figs. 15a,b,d,e), the spatial coherence of these errors appears to be maximized in medium-range forecasts (Fig. 13). As a consequence, the ability to identify synoptic progressiveness errors that are consistent between successive forecast cycles, such as in the April and September 2020 events described in section 1, may be maximized for medium-range forecasts.
b. Displacement error characteristics before and after the transition to FV3 GFS
Following the results presented in section 3b, demonstrating that a systematic undercounting of cutoff lows over the Northern Hemisphere in forecasts was improved following the transition of the GFS to the FV3 dynamic core in June 2019, differences in position error characteristics prior to and following this transition are also considered. This section only summarizes changes in position error characteristics over the 7-yr period of study; it is outside of the scope of this study to directly attribute any changes to specific modifications to the operational model during upgrade cycles.
Averaged over the Northern Hemisphere midlatitude band, zonal and meridional displacement error characteristics of verifying cutoff lows are associated with small changes following transition to FV3 (Fig. 12). Specifically, the eastward mean zonal position error for F102–F144 forecasts of all 20°–70°N cutoff lows decreases by ∼6.3 km following transition to FV3 (Table 5). The relative consistency of hemisphere-averaged zonal position errors between different model versions is likely partially due to the consistency of zonal errors over marine sectors (i.e., Atlantic and Pacific in Figs. 15c,f), where most cutoff lows are identified over the Northern Hemisphere (Fig. 5a).
Mean zonal position errors (km) for verifying 500-hPa cutoff lows between F102–F144 over the Northern Hemisphere (NHEM), CONUS, and Asia sectors during all seasons (All), DJF, MAM, JJA and SON prior to and following the GFS transition to the FV3 dynamic core (12 Jun 2019). The bottom two rows represent the mean zonal position error for verifying features over the CONUS following the transition to FV3 for GFS versions 15 (12 Jun 2019–21 Mar 2021) and 16 (starting on 22 Mar 2021), separately. Positive and negative values denote eastward and westward mean zonal position errors, respectively. Mean zonal position errors listed in italics are statistically different from zero at the 99% confidence level using a Student’s t test.
While zonal position errors evaluated for cutoff lows over the entire Northern Hemisphere midlatitude band are associated with small changes following the transition to GFS version 15 in June 2019, examination of cutoff lows over the CONUS and Asia in isolation demonstrates larger changes in error characteristics over the 7-yr period of study (e.g., Figs. 15b,e). Over Asia, the F102–F144 eastward mean zonal position error bias for cutoff lows during all seasons decreases by nearly 50 km after transition to FV3 (Table 5 and Figs. 16b,d). For cutoff lows over the CONUS during all seasons, conversely, the mean zonal position error at F102–F144 increases by ∼70 km to the east over the same period (Table 5 and Figs. 16a,c), consistent with cases of synoptic progressiveness errors identified by the EMC Model Evaluation Group (Manikin et al. 2019).
As in Figs. 14a and 14f, but for 500-hPa cutoff lows verifying over (a),(c) the CONUS and (b),(d) Asia during (top) 12 Jun 2019–31 Mar 2022, after the upgrade to FV3, and (bottom) 1 Apr 2015–11 Jun 2019, before the upgrade to FV3, separately.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
Changes in F102–F144 mean errors following the transition to FV3 GFS are further examined by individual season over the Northern Hemisphere, Asia, and the CONUS. For cutoff lows over the Northern Hemisphere midlatitudes, the magnitude of the mean zonal position error decreases and becomes westward for DJF and SON, and increases to the east for MAM and JJA (Table 5). Eastward mean F102–F144 zonal position errors for cutoff lows over Asia decrease during all seasons except for JJA, during which season the mean zonal error is characterized by an increase of nearly 20 km to the east (Table 5). The largest change in zonal position errors associated with cutoff lows over Asia following the transition to FV3 GFS occurs during DJF, which is characterized by a change of nearly 160 km to the west (Table 5).
Unlike cutoff lows over Asia, mean F102–F144 zonal position errors for cutoff lows over the CONUS become more eastward following transition to FV3 during all seasons. Mean zonal position errors for cutoff lows over the CONUS during DJF, MAM, JJA, and SON change by ∼+62, ∼+82, ∼+76, and ∼+47 km, respectively (Table 5). During JJA, this change corresponds to a reduction of a mean westward error, while changes in the mean zonal error during all other seasons correspond to an increased eastward mean error for F102–F144 forecasts of cutoff lows over the CONUS after transition to FV3 (Table 5).
In summary, while forecasts of 500-hPa cutoff lows appear to be more frequently associated with eastward position errors over the CONUS following the transition to FV3 GFS, implying a potential worsening of synoptic progressiveness errors, this behavior is not as prominent elsewhere over the Northern Hemisphere. Thus, while it is possible that synoptic progressiveness errors over the CONUS worsen following the upgrade to FV3 GFS, a caveat is that the cases examined over each period, before and after the transition, are inherently different and the two periods are of unequal lengths. Nevertheless, this finding is consistent with individual cases of synoptic progressiveness errors examined by the EMC Model Evaluation Group using concurrent forecasts from GFS version 14 (prior to the upgrade to FV3) and GFS version 15 (FV3; Manikin et al. 2019). Further subsetting CONUS cutoff lows during the FV3 period by those during GFS version 15 and version 16 (NOAA/Environmental Modeling Center 2022, before and after 22 March 2021) suggests that eastward position errors may be considerably reduced following the transition to version 16 of the GFS, becoming more similar to seasonal error characteristics in model versions prior to transition to FV3 (Table 5). However, the period of study incorporating GFS version 16 is only slightly longer than a single year; thus, it is unclear at the time of writing whether the apparent change in seasonal error characteristics during GFS version 16 corresponds to a systematic change in the operational model or is a result of inherently different sets of cutoff low events simulated by each model version.
5. Southern Hemisphere cutoff lows
While examination of the forecast characteristics of Northern Hemisphere cutoff lows is the primary focus of this research, similar evaluation of cutoff lows over the Southern Hemisphere provides a more thorough understanding of forecast position biases in the GFS. To this end, examination of Southern Hemisphere cutoff lows suggests that these features are also associated with a progressive bias and frequency errors. In general, Southern Hemisphere 500-hPa cutoff lows are identified most often between 55° and 70°S (Fig. 17a); however, Muñoz et al. (2020) note that “cutoff lows” identified poleward of 50°S are generally not detached from the polar region, and are thus excluded from their climatology and that of Kasuga et al. (2021), denoted by the heavy-dashed contour in Fig. 17 (fully opaque masking is omitted between 50° and 70°S to highlight large latitudinal differences between forecast and analysis cutoff lows in the subsequent paragraph). Outside of the polar region, Southern Hemisphere cutoff lows are most often identified over the southwest Pacific, along the west coast of midlatitude South America, and to a lesser degree over South Africa (Fig. 17a), consistent with climatologies constructed by Muñoz et al. (2020) and Kasuga et al. (2021).
For the Southern Hemisphere during 1 Apr 2015–31 Mar 2022 every 6 h: (a) number of So > 10 m (100 km)−1 500-hPa cutoff lows, (b) normalized difference between gridded F120 and analysis distributions of 500-hPa cutoff lows (number yr−1), and (c) gridded mean zonal position error (km) of all forecast So > 10 m (100 km)−1 features during F102–F144. Gridded values are in 2° × 2° grid boxes. Values in (c) are masked as in Fig. 13. Dashed circles are plotted at 20°, 45°, and 70°S for geographic reference, and an additional bold-dashed circle is plotted at 50°S to indicate that features poleward of this latitude are excluded from Southern Hemisphere averages and total counts. During 1 Apr 2015–31 Mar 2022, 37 173 cutoff lows with So > 10 m (100 km)−1 were identified over 20°–50°S.
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
Similar to the Northern Hemisphere, the distribution of cutoff lows is generally shifted poleward with increasing forecast hour, such that forecast cutoff lows at F120, for example, near 30°S are underrepresented over nearly the entire hemisphere, particularly near eastern Australia and New Zealand, while cutoff lows between 45° and 70°S, which are generally not detached from the polar region (Muñoz et al. 2020), are overrepresented (Fig. 17b). Additional similarities to the forecast distribution of Northern Hemisphere cutoff lows are noted by examining the occurrence frequency error of 20°–50°S cutoff lows by month and forecast hour, as cutoff lows are generally underrepresented in early forecast hours (∼F006–F048) prior to the transition to GFS version 15 in June 2019 (Fig. 18a). Frequency errors of Southern Hemisphere cutoff lows at later forecast hours are of larger magnitude and less consistent than those associated with Northern Hemisphere cutoff lows, as Northern Hemisphere cutoff lows are underrepresented at long forecast lead times during most months (Fig. 9), while Southern Hemisphere cutoff lows may be over or underrepresented by >20% at forecast hours beyond F120 (Fig. 18a).
For each valid month and forecast hour, (a) total forecast cutoff lows present at forecast hours as the percent of total corresponding analysis time cutoff lows and (b) mean zonal position error (km) for all valid-time cutoff lows. Time increases downward along the y axis, forecast hour increases to the right along the x axis. Only cutoff lows between 20° and 50°S are included. Values < 100% in (a) mean there are fewer forecast features than analysis time features during valid times over a given month, while values > 100% indicate more forecast features than analysis time features. In (b), positive and negative values denote eastward and westward zonal position errors, respectively. A dashed horizontal reference line is plotted at June 2019 to note the transition to FV3 (GFS version 15).
Citation: Weather and Forecasting 38, 10; 10.1175/WAF-D-22-0224.1
Zonal position errors associated with Southern Hemisphere cutoff lows are generally positive, or eastward, over the 7-yr analysis period. For cutoff lows and troughs identified in medium-range forecasts (F102–F144), gridded mean zonal position errors are primarily eastward between ∼30° and 55°S over a broad region of the southern Pacific Ocean, as well as areas of the southern Atlantic and Indian Oceans (Fig. 17c). Examining zonal position errors of only cutoff lows verifying between 20° and 50°S, monthly mean errors generally become large and eastward with increasing forecast hour for nearly all months during the 7-yr period (Fig. 18b). Meridional position errors are generally negative (poleward) over the same region (not shown). Mean seasonal medium-range zonal position errors are similarly positive for all seasons over the Southern Hemisphere (Table 4), with the largest mean eastward error present during the austral spring (SON; 86.97 km) and autumn (MAM; 73.19 km). Thus, while zonal position errors consistent with the descriptions of synoptic progressiveness errors appear to be most prominent over certain regions of the Northern Hemisphere, specifically midlatitude continental regions, this type of error appears to occur more broadly over the Southern Hemisphere, where midlatitude regions are primarily characterized by ocean basins.
6. Summary and conclusions
U.S.-based operational forecasters often note that medium-range GFS forecasts of cutoff lows are too progressive compared to both verifying upper-level features and concurrent numerical guidance from other operational centers. As a consequence, medium-range prediction of impactful weather events, such as severe weather, excessive rainfall, winter precipitation, and downslope winds, may be adversely impacted. Thus, this research examines the frequency and position error characteristics of 500-hPa cutoff lows in 7 years of operational GFS forecasts, with the goal of identifying where synoptic progressiveness errors are common, how often cutoff lows exhibit this error, and the severity of the error.
An objective feature identification scheme based on a method introduced by Kasuga et al. (2021) is adapted to identify and track 500-hPa troughs and cutoff lows in operational GFS forecasts over the globe. Cutoff lows are generally underrepresented in forecasts over the Northern Hemisphere, particularly over midlatitude continents. Furthermore, verifying cutoff lows over Southern Hemisphere midlatitudes, the CONUS, and Asia are generally located too far to the east compared to verifying analyses. These errors are largest at forecast lead times beyond 2 days, particularly during spring and fall in the Northern Hemisphere. While this apparent eastward bias is most prominent over continental regions of the Northern Hemisphere, it is unclear if this bias is directly related to land processes, since eastward mean errors over the Southern Hemisphere are most prominent over midlatitude ocean basins. Overall, our results appear to confirm subjective impressions of synoptic progressiveness errors over the CONUS, at least during certain seasons, and further demonstrate these errors elsewhere over the globe. Operational forecasters should continue to be aware of the potential influence of these biases on GFS forecasts.
Examination of forecast cutoff low characteristics by month over the 7-yr analysis period provides additional insight into the potential impact of model changes on forecast error. Over the Northern Hemisphere, the underrepresentation of cutoff lows in forecasts relative to analyses is improved following the upgrade to GFS version 15 in June 2019 (NOAA/Environmental Modeling Center 2022), particularly for forecast lead times of three days or less. A similar improvement is noted for Southern Hemisphere cutoff lows following transition to FV3 at lead times of two days or less. Furthermore, eastward zonal position errors, consistent with descriptions of synoptic progressiveness errors, appear to become more frequent over the CONUS following the upgrade to GFS version 15, and less frequent over Asia during the same period. As a caveat, the analysis periods before and after the upgrade to GFS version 15 are of unequal lengths and contain inherently different verifying features; however, this conclusion is consistent with the results of experimental forecasts of individual cases using both GFS version 14 and version 15 by the EMC Model Evaluation Group (Manikin et al. 2019). Detailed evaluation of displacement error characteristics for the current GFS configuration at the time of this analysis (GFS version 16), in isolation, is limited by the relatively short period (22 March 2021–31 March 2022) over which operational data are available. While results through March 2022 suggest that eastward zonal displacement errors over the CONUS are reduced coincident with the transition to GFS version 16, additional seasons of operational forecasts from GFS version 16, which is scheduled to be operational until 2024 at the time of writing (Unified Forecast System 2022), should be examined in the future to more robustly evaluate potential improvements over this period. Evaluation of forecasts produced using parallel model versions would be similarly instructive.
While errors in the forecast position of cutoff lows can limit the predictability of a variety of impactful weather events (e.g., Table 2), the apparent seasonality of synoptic progressiveness errors over the CONUS may have a considerable impact on severe weather forecasting during the spring. In the United States, severe weather events frequently occur during the spring and early summer (i.e., ∼March–June) over the Southeast, Midwest, and Great Plains (e.g., Brooks et al. 2019; Taszarek et al. 2020), concurrent with a time of frequent cutoff low events over the CONUS (Fig. 6). Moreover, this region is generally characterized by an underrepresentation of cutoff lows in forecasts (Fig. 10), as well as an eastward bias in the forecast location of cutoff lows (Fig. 14c), consistent with descriptions of synoptic progressiveness errors. Future research should examine the relationship between cutoff low progressiveness errors and the medium to long-range predictability of spring and early-summer severe weather events over the CONUS, such as in the four spring season events over the southern and central CONUS noted in Table 2.
Further research is ongoing and planned which will broaden the scope of these results for operational forecasting. To provide insight on how and when a progressiveness bias may be manifest in GFS forecasts, ongoing work aims to identify environmental flow configurations susceptible to progressiveness errors and to determine how meso- to synoptic-scale forecast errors evolve leading to this kind of feature displacement error. Additional research is also planned to identify and examine deficiencies in processes represented by the GFS, including parameterized physics, which may be instructive for future model development. One possibility is that forecast errors associated with moist processes may contribute to errors in the evolution of cutoff lows as well as amplitude errors in the up- and downstream flow preceding cutoff low formation (e.g., Massacand et al. 2001; Garreaud and Fuenzalida 2007; Knippertz and Martin 2007; Wang et al. 2012). For example, Massacand et al. (2001) and Wang et al. (2012) demonstrate that, for individual case study simulations, cutoff lows failed to develop in the absence of latent heating. Finally, similar examination of subseasonal to seasonal flow configurations associated with prolonged periods of feature under or over representation in forecasts (e.g., Fig. 9) may also be beneficial for operational forecasting.
While outside the scope of this study, which focuses exclusively on cutoff low displacement errors in operational GFS forecasts, comparisons to errors in numerical guidance from other operational centers would likely be beneficial. For example, while anecdotal cases of synoptic progressiveness suggest that this error may be less prominent over the CONUS in ECMWF guidance (e.g., Table 1), it would be useful to objectively document the potential absence of this behavior in a longer-term period of study, as well as to similarly examine displacement errors in ECMWF forecasts of upper-level features over the globe.
The 0.25° global GFS data are available on the NCAR Research Data Archive (RDA; National Centers for Environmental Prediction/National Weather Service/ NOAA/U.S. Department of Commerce 2015) starting 15 January 2015. The choice of 1 April 2015 as a starting date was made to incorporate the longest whole-year date range at the time of analysis.
Maximum radii cannot exceed one-half the circumference of Earth at a given latitude to prevent eastern and western zonal search radii from overlapping near the poles.
BGo/So < 2.25 is chosen here to further limit smaller-scale features that may be present due to finer model resolution than in Kasuga et al. (2021).
In this case, step A2 is amended to use information at t − 2Δt and t − 3Δt.
The total penalty is a unitless value. While units are omitted from individual terms for clarity in this example, these values correspond in order to terms 1–9 in Table 3.
The matching scheme is modified at step C2 to restrict cross-polar matches to prevent subsequent non-representative tracking errors (i.e., matching features cannot be separated by more than 30° of longitude).
Acknowledgments.
This material is based upon work supported by the National Center for Atmospheric Research (NCAR), which is a major facility sponsored by the National Science Foundation under Cooperative Agreement 1852977. Additional funding was provided by NOAA/OAR Weather Program Office [Joint Technology Transfer Initiative (JTTI)] Grant NA21OAR4590184 and NSF (PREEVENTS) Grant ICER-1854966. The authors thank Manda Chasteen (NCAR) for providing a helpful internal review of this paper, as well as Gary Lackmann and two anonymous reviewers for their comments and suggestions.
Data availability statement.
The NCEP GFS 0.25° Global Forecast Grids Historical Archive used herein is freely available to registered users of the NCAR Research Data Archive (RDA; National Centers for Environmental Prediction/National Weather Service/NOAA/U.S. Department of Commerce 2015), available online at https://rda.ucar.edu/datasets/ds084.1/. Archived Area Forecast Discussions are accessible through the Iowa State University–Iowa Environmental Mesonet (2022) website.
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