1. Introduction
Quantitative precipitation forecasts (QPF) are of high socioeconomic value and the topic of much research. During the past decade, many convection-allowing models have been developed, primarily to predict mesoscale and convective scale precipitation systems. In addition to deterministic models, convection-allowing ensemble prediction systems are widely used to measure forecast uncertainty for precipitation events. Since convective-scale moist processes have faster forecast error growth than synoptic-scale weather systems, it is challenging to predict the timing, location, and intensity of convective precipitation. A further complication is that convection is strongly influenced by its meteorological environment. Done et al. (2006) and Zimmer et al. (2011) have demonstrated the use of a diagnostic metric called the “convective adjustment time scale” for effectively characterizing this coupling.
Since different convective regimes generally possess different degrees of precipitation predictability (Jankov and Gallus 2004; Duda and Gallus 2013; Surcel et al. 2015), an objective measure to classify varying convective weather situations is of considerable value. The aim of this paper is to investigate the climatology of convective regimes, as measured by the convective adjustment time scale, over the contiguous United States (CONUS), including regional and seasonal dependences. Its relationship with forecast skill is also considered to assess the utility of this measure to identify regime dependent differences.
In broad terms, the coupling of convection to its environment can be viewed as a continuum with two extremes: equilibrium and nonequilibrium convection. For equilibrium convection, the properties of precipitation (e.g., timing and intensity) are controlled by large-scale destabilization. For this to occur, there should be little collocation between convective available potential energy (CAPE) and convection inhibition (CIN) so that convection is free to act immediately in response to CAPE (Done et al. 2006). For example, large-scale uplift can cool air masses and create large amounts of CAPE, which is then rapidly exhausted by convective precipitation and a fast return to equilibrium. Since the CAPE is immediately converted to upward motion, equilibrium convection is typically associated with small CAPE values throughout its life cycle. In most cases, equilibrium convection is more predictable since it is more constrained by environmental forcing (Flack et al. 2018; Keil et al. 2014; Done et al. 2012). In contrast, nonequilibrium convection is primarily triggered by local processes such as boundary layer turbulence, radiative heating, orography, and cold pool lifting. This type of convection occurs mostly in summer, partially due to strong radiative heating. For nonequilibrium convection, CAPE is often collocated with CIN and thus can build up until convection is triggered by overcoming the CIN threshold. Therefore, the properties of nonequilibrium convection largely depend on local processes, such as surface and boundary layer variability, and tend to be less predictable.
The distinction between equilibrium and nonequilibrium regimes is not identical to the strong versus weak forcing of convection. There is no standard quantitative definition of strong or weak forcing, but the terms generally reflect the rate at which the atmospheric flow creates instability, for example, through the dynamical forcing of synoptic and mesoscale ascent. Ascent generates CAPE, but also decreases CIN. This makes it easy to trigger convection, which can increase rapidly in response to the creation of CAPE, leading to a rapid adjustment to equilibrium. In contrast, afternoon convection occurring in response to surface heating can be accompanied by a strong temperature inversion at the top of the boundary layer giving a large CIN. Triggering convection is difficult, and the response to increasing CAPE is delayed in a nonequilibrium situation. There is thus a tendency for equilibrium to occur in the presence of strong dynamical forcing, but it is also possible that the convection is, for some time, unable to respond to strong forcing, and the instability rapidly increases. Similarly, there is a tendency for nonequilibrium to prevail when dynamical forcing is weak. However, if surface processes are not dominant, weak equilibrium convection can occur in response to weak forcing.
The convective adjustment time scale was first proposed by Done et al. (2006) as a metric to objectively classify convective weather according to the degree of equilibrium between the convection and the forcing processes. Since this metric reflects the strength of coupling of the convection to its environment, it may be of value in distinguishing regimes with different convective behavior and predictability. The concept is based on estimating the time scale at which convective instability is consumed by convective heating, which can be compared with the time scale of the processes that create instability. Processes that create CAPE, such as large-scale uplift, evolve significantly over periods of 6–12 h. A small convective adjustment time scale of a few hours indicates equilibrium convection: convective instability is removed quickly by convective heating, and the atmosphere returns rapidly to equilibrium. A large convective adjustment time scale of a day or more indicates that convection is acting too slowly to follow the evolution of the forcing processes and is indicative of nonequilibrium convection.
The convective adjustment time scale can serve as a valuable tool in NWP. Numerous applications demonstrate the potential benefits of using the convective adjustment time scale to assess multiple facets of convective-scale modeling during different weather conditions. One illustrative application is the ability to objectively classify midlatitude weather situations across a wide range of model forecasts into distinct scenarios to effectively demonstrate the flow-dependent impact of certain model components to forecast performance. Recently, Puh et al. (2023) have demonstrated a systematic benefit of using a physically based stochastic perturbation scheme for convection-allowing forecasts of convection covering a 3-month period. In particular, there is increased ensemble spread of precipitation during weak synoptic forcing conditions, which is much more difficult to detect in statistics that contains all weather regimes.
More generally, different sources of uncertainty represented in ensemble forecasting systems, namely, initial, boundary, and model physics uncertainty respond differently under different convective regimes. In the context of convective-scale data assimilation different formulations of the model error behave differently in different flow situations. Using the convective adjustment time scale to delineate the flow situations, Zeng et al. (2018) find that the representation of model error using additive noise is more beneficial during strongly forced weather conditions. Craig et al. (2012) point out that the impact of radar data assimilation lasts longer in weak forcing regimes. Lateral boundary perturbations grow faster in strongly forced environments, while the response to model perturbations is more pronounced under weak forcing conditions (Keil et al. 2014). Kühnlein et al. (2014) consider the response of convection to different perturbation strategies for an entire warm season and show that model physics perturbations had a greater impact on total precipitation spread during weakly forced conditions than during strongly forced situations. The relative importance of microphysical uncertainties in ensemble forecasts crucially depends on the control of convection synoptic coupling (Matsunobu et al. 2022; Keil et al. 2019; Surcel et al. 2017). During weak synoptic control, the relative impact of microphysical uncertainty on daily area-averaged precipitation is twice as large as in strong forcing and accounts for about one-third of the variability caused by operational initial and lateral boundary condition uncertainty (Matsunobu et al. 2022). Thus, this metric can aid in interpreting the forecast sensitivity of midlatitude convective precipitation to different sources of uncertainty, which is valuable for the ensemble NWP community.
The convective adjustment time scale can be used as a measure to delineate different levels of predictability of convective precipitation. Bachmann et al. (2020), Keil et al. (2020), and Schwartz and Sobash (2019) demonstrate above-average predictability of total area-averaged precipitation in weather situations controlled by synoptic forcing.
So far, the convective adjustment time-scale diagnostic has been mostly used as a categorical measure to classify certain weather situations into equilibrium or nonequilibrium flow regimes. However, the exact threshold value depends on the geographical region, the season, and the intricacies of its computation (e.g., hourly or 3-hourly rainfall accumulations, the exact CAPE calculation, horizontal smoothing of input fields, mean or maximum daily values). Studies over Europe have applied threshold values of 3 h (e.g., Keil et al. 2020; Flack et al. 2016; Keil et al. 2014) and 6 h (e.g., Grazzini et al. 2020; Kühnlein et al. 2014; Molini et al. 2011). The choice of these values concurs with the results of Zimmer et al. (2011), who use observations in central Europe and find a continuous distribution of these time scales and conclude that a value somewhere between 3 and 12 h clearly distinguishes between different regimes. However, it is not necessary to make a categorical distinction, and the convective adjustment time scale can also be directly correlated with metrics related to forecast skill (Schwartz and Sobash 2019; Surcel et al. 2017) or used in a relative sense, choosing the upper or lower 20% of its distribution throughout a summer season (Puh et al. 2023).
In this study, we construct a convective adjustment time-scale climatology for warm-season precipitation using the National Oceanic and Atmospheric Administration (NOAA) High-Resolution Rapid Refresh (HRRR) forecast dataset. This is the first time the convective adjustment time-scale climatology is computed over CONUS using a convection-allowing model with a horizontal grid spacing of 3 km. To account for geographical variances, the domain is partitioned into multiple subdomains, and the climatology of convective equilibrium and nonequilibrium regimes are studied regionally. The timing and amount of precipitation are linked with the convective adjustment time scale to examine if the classification is physically meaningful, and the relation to forecast skill of convective precipitation is investigated.
The paper is organized as follows. Section 2 describes the methodology, including the definition of the convective adjustment time scale, details of subdomains, and forecast dataset. Section 3 and section 4 present the convective adjustment time-scale climatology and investigate its relation to forecast skill, respectively. Conclusions are given in section 5.
2. Method
a. Definition of the convective adjustment time scale
There are multiple definitions of CAPE, which include the influence of different depths, such as surface CAPE, mixed-layer CAPE, and most unstable CAPE. After comprehensive sensitivity tests, we chose to use the instantaneous surface CAPE directly from the model output since it is most closely linked to the 24-h QPF skill over CONUS. While τc ought to represent local features, it should be smooth enough not to capture variability on scales smaller than the spacing between convective clouds (Craig et al. 2012). In this study, we adopt the same smoothing method as Keil and Craig (2011) and Flack et al. (2016), namely, a Gaussian kernel with a half-width of 15 km that is applied to both precipitation and CAPE fields. In general, the regime classification is insensitive to the details of the smoothing methods, as would be expected as long as the smoothing scale is large enough to average out the effects of individual clouds while not being so large that synoptic forcing features are significantly smoothed. To neglect the impact of very light rainfall and avoid abnormal jumps between convective regimes, we further introduce a precipitation threshold of 1 mm h−1 after smoothing (following Keil and Craig 2011).
In this study, we utilized hourly τc values to establish the τc climatology for each respective subdomain. The hourly τc values represent domain averages for each subdomain and are reported only if more than a hundred grid points have a valid τc value according to the defined criteria. For each case, the daily τc values were obtained by averaging the hourly τc values, and their correlation with the skill of precipitation forecasts is subsequently investigated.
b. Description of subdomains, forecast, and observation dataset
The τc values computed across the entire CONUS domain generally fall within the range of 1 to 10 h, with rare occurrences of extreme values (not shown). This behavior is primarily caused by averaging over the continental scale CONUS domain generally encompassing various weather systems simultaneously. For this reason, we partition CONUS into several subdomains to account for regional differences. Guided by the 14 verification regions defined by NOAA (https://www.wpc.ncep.noaa.gov/rgnscr/verify.html), we combined several small subdomains with similar climatology. This leaves us with four northern and four southern subdomains roughly divided by the 40°N latitude (Fig. 1).
Verification and diagnostic subdomains used in NOAA model QPF verification by regions (color shades) and this study (thick borders). The black numbers denote the subdomain indices.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0108.1
This study uses historical forecast datasets from NOAA’s operational High-Resolution Rapid Refresh (HRRR; Dowell et al. 2022) system, which forecast covers the CONUS domain (3177 km × 5397 km). This convection-allowing HRRR system has been operational since 2014 to provide forecast guidance for rapidly evolving weather. It is built on the nonhydrostatic Weather Research and Forecasting (WRF; Skamarock et al. 2008) Model with a 3-km horizontal grid spacing that explicitly resolves convective storms. It has 51 vertical levels covering from near the surface (∼8 m) up to 15 hPa. It assimilates observations on an hourly basis using the Gridpoint Statistical Interpolation (GSI) Hybrid 3DEnVar and with enhancements for radar, land and cloud assimilation, all described in Dowell et al. (2022). Note that the model is running without a deep convective parameterization, which is crucial for this study since such schemes often prescribe a convective adjustment time scale determining how quickly CAPE is consumed.
In this study, the warm season [May–August (MJJA)] τc climatology is derived from data covering the period of 2019–22. The 4-yr period is chosen since HRRRV3 (operational in 2019 and 2020) and HRRRV4 (operational in 2021 and 2022) provide forecasts of up to 36 h. In this study, the HRRR forecasts were retrieved from the NOAA open data platform (https://console.cloud.google.com/marketplace/details/noaa-public/hrrr?pli=1). The 1200 UTC run is selected since we aim to cover the whole life cycle of summertime convection. The first 3-h forecasts are excluded from τc computation to mitigate the impact of model spinup. That is, the 4-yr MJJA hourly forecast dataset was composed of a forecast from +3 to +27 h initialized at 1200 UTC daily. The 3-h forecast from the 1200 UTC run corresponds to 1100 eastern daylight time (UTC − 4 h) at the East Coast of CONUS to 0800 Pacific daylight time (UTC − 7 h) at the West Coast of CONUS.
To ensure that the HRRR system produces a realistic rainfall climatology, we first compare the 3–27-h precipitation forecast with observed precipitation derived from the National Centers for Environmental Prediction (NCEP) Stage-IV quantitative precipitation estimates (QPEs, Nelson et al. 2016). As shown in Figs. 2 and 3, the composed monthly forecast dataset captures the precipitation amount and structure realistically [cf. also with Liu et al. (2017)]. Heavy precipitation (>200 mm) covering much of the Great Plains is apparent in May on average over this 4-yr period in both observations and in the HRRR forecast precipitation. In June, the intensity of precipitation systems decreases and shifts toward the east of CONUS, particularly toward the southeast coast. Here, the rainfall associated with hurricanes is excluded by masking precipitation within 350 km from the hurricane center (defined by best track) partly since hurricanes can bring long-lasting heavy rainfall that is not related to the convective rainfall studied here. In this study, we have identified 18 tropical systems and excluded associated precipitation, primarily over eastern CONUS. Note that this method assumes that the model forecasts have a realistic hurricane track in comparison with the best track.
Monthly total precipitation (shading; mm) in May and June from 2019 to 2022 derived from the HRRR 3–27-h forecasts (denoted as F) and NCEP Stage-IV products (denoted as O). Rows are the result of different years, and columns are the result of forecasts (the first and third columns) and observations (the second and fourth columns) at different months. Thick black borders are the subdomain boundaries used in this study.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0108.1
As in Fig. 2, but for July and August.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0108.1
3. Convective regime classification
a. Cases illustrating equilibrium and nonequilibrium convection
Two cases are selected to illustrate the link between convective precipitation, synoptic forcing, and the resulting convective adjustment time scale for different weather regimes. The first case, initialized at 1200 UTC 1 July 2021, features precipitation events with clear synoptic forcing, where equilibrium behavior is expected (Fig. 4). The 24-h accumulated precipitation shows that there is an elongated precipitation system located across subdomains 4, 6, and 7 (Fig. 4b). This precipitation system is located downstream of a 500-hPa trough (Fig. 4a), associated with temperature, moisture, and vorticity advection providing a favorable environment for precipitation since it is conducive to synoptic scale ascent (Doswell 2001). Precipitation within subdomains 1 and 8 is more scattered and weakly forced when compared with the major rainband.
(a) The 500-hPa geopotential height (contours; m) and wind speed (shading; m s−1) valid at 1200 UTC 1 Jul 2021. (b) The 24-h accumulated precipitation (shading; mm) beginning at 1200 UTC 1 Jul 2021. Thick black borders are subdomain boundaries. (c) Time series of hourly (top) precipitation (mm), (middle) CAPE (J kg−1), and (bottom) convective adjustment time scale τc (h) averaged over different subdomains. The dashed line in the τc plot marks the 6-h threshold between equilibrium and nonequilibrium convection.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0108.1
The precipitation time series (Fig. 4c) shows that precipitation continues for 24 h in subdomains 4, 6, 7, and 8. In contrast, precipitation in subdomain 1 occurs at around 1600 LT, exhibiting the lowest intensity among all the subdomains considered. The major rainband initially develops within subdomain 7 and subsequently moves in subdomain 4. While being part of the major rainband, the precipitation is less intense in subdomain 6 than in subdomains 4 and 7. In contrast, precipitation in subdomain 8 exhibits a clear diurnal pattern, implying a thermally forced trigger mechanism. Since low-level moisture is generally higher in southern subdomains, these regions typically attain larger CAPE values than the northern subdomains. The instability in this case is modest, with CAPE ≲ 1000 J kg−1. The CAPE values do not vary strongly throughout the forecast period, suggesting that CAPE does not accumulate and is converted immediately to convective heating. For subdomains 4, 6, and 7 the τc values remain low, consistent with equilibrium convection in a strong forcing environment. In contrast, subdomains 1 and 8 have initially larger τc values suggesting they are situated within weaker synoptic flow, which agrees with the general flow situation depicted in Fig. 4a and the precipitation texture shown in Fig. 4b. The rapid decrease of τc in these cases would indicate an adjustment to equilibrium. Note that there are no τc values in the beginning of the forecast due to low precipitation rates (see section 2a). In conclusion, this case illustrates an equilibrium rainband that is tightly coupled to the governing flow, showing low τc values within affected subdomains. Also, this case gives an example for the simultaneous presence of various weather situations across the entire CONUS domain that are only distinguishable by their τc values when splitting CONUS into subdomains.
The second case, initialized at 1200 UTC 27 July 2021, features convective precipitation under weak synoptic forcing (Fig. 5). In contrast to the trough pattern in the previous example, this day is dominated by a high pressure system, which corresponds to sinking drier air and thus a more stable atmosphere (Fig. 5a). We focus on the four southern subdomains (5–8) that are far from the synoptic wave pattern to the north. These regions feature rather scattered precipitation, which is likely forced by surface heating, and indeed show a clear maximum in precipitation rates in the afternoon (Fig. 5c). In subdomain 8, the influence of land–sea breezes is apparent, leading to stronger, more organized precipitation that starts in the early morning. The combination of broad subsidence in the high pressure area, combined with surface heating, leads to a strong CIN that inhibits convective initiation and large CAPE values build up (Fig. 5c). CAPE increases until convection starts to remove the instability. The τc values reflect the buildup and slow removal of CAPE, with values exceeding 6 h for almost all subdomains and times. This is the behavior expected for nonequilibrium convection, where convection is inhibited and cannot act fast enough to remove CAPE. The exception is subdomain 5, where strong orography is present and CAPE and τc values remain low. In this mountainous region, even relatively weak convection is sufficient to remove the instability as fast as it is created, leading to equilibrium conditions.
As in Fig. 4, but valid at 2000 UTC 27 Jul 2021 in (a) and beginning at 1200 UTC 27 Jul 2021 in (b).
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0108.1
The two days highlighted in this section show examples of equilibrium convection, with strong forcing by Rossby waves facilitating favorable conditions for convection that removes CAPE as fast as it is produced, and nonequilibrium convection, with precipitation following the diurnal cycle and convection that is unable to remove CAPE. However, the examples of orographic convection show that simply looking for strong synoptic forcing is not a reliable indication of convective behavior.
b. Convective adjustment time-scale climatology over the CONUS domain
The climatological frequencies of convective adjustment time scales are separately shown for all subdomains in Fig. 6. The frequency distribution follows roughly two power law lines with a scale break between 3 and 12 h. The distributions can be divided into three different categories. The convection in the northern subdomains (1–4) is characterized by a smooth distribution with a high occurrence of small τc, indicating that equilibrium convection is relatively common in the northern part of CONUS. In comparison, τc values larger than 6 h occur more often in the southern subdomains (5–8), indicating that nonequilibrium convection is dominant. In subdomain 8, τc values shorter than about 6 h are much rarer than in other subdomains.
Frequency distributions of the convective adjustment time scale shown annually (colors) and for the 4-yr mean (black) for each subdomain. The frequency is computed with a bin size of 0.2 h, and lines are smoothed by a Gaussian filter. The dashed vertical lines indicate 3, 6, and 12 h, respectively, from left to right.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0108.1
Previous work investigated the existence of a scale break in the frequency distributions, which would be a clear indication of two distinct convection regimes. While Flack et al. (2016) identified a distinct scale break at 3 h over the British Isles, Zimmer et al. (2011) find a continuous distribution and propose τc = 6 h, a value somewhere between 3 and 12 h to distinguish both weather situations. The results in Fig. 6 show strong evidence of a scale break between 6 and 12 h. Notably, this is the time scale for which the frequency distributions in subdomain 8 peaks. While the convective regimes should be regarded as a continuum with two extremes, we use a τc value of 6 h as threshold to categorize equilibrium and nonequilibrium convection in this study. To get a sense of the statistical robustness of our results, Fig. 6 also shows the frequency distribution for each of the 4 years 2019 to 2022. While there is some year-to-year variability–especially for the southern domains—all findings hold qualitatively.
The fraction of cases attaining τc values smaller than certain cumulative thresholds represents another test of robustness (Fig. 7). Applying a threshold of τc = 6 h classifies 53% of the cases as equilibrium convection for the northern subdomains versus 22% equilibrium for the southern subdomains. This is consistent with the case studies presented earlier, where the northern part of CONUS is frequently under the influence of Rossby waves. The prevalence of equilibrium conditions in the northern subdomains closely aligns with the fraction observed in Germany. During the summer months (June, July, August), approximately 52% of convective precipitation cases in Germany were classified as an equilibrium regime (Zimmer et al. 2011).
Cumulative percentage of convective cases with τc less than 1, 3, 6, 12, and 24 h for each subdomain. All τc not meeting the thresholding criteria in section 2a are excluded. The red dashed lines indicate the percentage of equilibrium cases (τc < 6 h) averaged over all subdomains. The blue dashed line in the top and bottom panel indicates the percentage of equilibrium cases (τc < 6 h) averaged over northern and southern subdomains, respectively.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0108.1
Next, we investigate the monthly variation of τc for warm-season convection (Fig. 8). In all subdomains, May is characterized by shorter τc than JJA, leading to a higher proportion of equilibrium conditions. There is a transition in the precipitation pattern over the central plains and southeast coastal region from May to June (see Fig. 2). The increase in rainfall over the central Plains in late spring is primarily driven by the Great Plains low-level jet (Wang and Chen 2009) and the passage of eastward moving systems (Carbone and Tuttle 2008). Accordingly, the convection in May is predominantly forced by synoptic flow and contributes to a high percentage of small τc values, particularly in the central four subdomains 2, 3, 6, and 7. In June, the total precipitation in the central plains is reduced due to the development of an upper-level anticyclone (Wang and Chen 2009).
Frequency distributions of convective adjustment time scale stratified by calendar month. All other details as in Fig. 6.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0108.1
In the North the climatology of convective regimes is similar throughout JJA. In the South, in contrast, there is a strong monthly variation in the frequency of equilibrium conditions, with short τc values more common in May and June, and particularly rare in July. Much of this variability may be associated with changes in the mean latitude of the jet stream where synoptic waves propagate, but the seasonal cycle of solar heating may also play a role. For example, the increase in coastal precipitation from May to June is primarily due to the seasonal transition of thermodynamic forcing (Rickenbach et al. 2015).
c. Diurnal cycle of precipitation under different convective regimes
To further corroborate that our classification mirrors the underlying basic dynamics, we classify all forecasts within each subdomain into two types: equilibrium and nonequilibrium regimes. This classification is done using a τc threshold of 6 h. Next, we analyze the subdomain-averaged rainfall time series to determine the presence of a diurnal cycle. Our hypothesis is that nonequilibrium convection should exhibit a higher proportion of diurnal precipitation. This is based on the assumption that under weak forcing conditions, convection relies more on diurnal solar heating as the triggering mechanism.
To objectively identify diurnal and nondiurnal precipitation systems, we use a supervised learning algorithm, namely, the linear support vector machine (SVM), which has been applied to real-world applications and is reported to have significant accuracy (Cortes and Vapnik 1995). In particular, the SVM algorithm is suitable for solving data regression and classification problems. For data classification, an SVM classifier functions by identifying the optimal decision boundary that maximizes the separation between classes. Since supervised learning is possible only if data are labeled, a hundred diurnal and a hundred nondiurnal precipitation time series are labeled subjectively in this study. The 200 samples with subjectively assigned labels are drawn from the eight subdomains, with an effort to distribute them as evenly as possible. For the SVM classifier, we chose to reduce the number of features by employing a 2-h precipitation interval. This feature reduction helps maintain a more manageable classifier dimensionality while retaining valuable information capable of capturing time series patterns. As shown in Fig. 9, the time series labeled as diurnal precipitation exhibit precipitation maxima primarily during the afternoon hours. In contrast, the time series labeled as nondiurnal precipitation do not display a distinct peak in precipitation timing. Among the sampled dataset, 70% are utilized for training the model, while the remaining 30% are used for testing purposes. The final SVM classifier used in this study has an accuracy of 0.94, a precision (1− false alarm ratio) of 0.95, and a recall (probability of detection) of 0.96. As shown in Fig. 10, the classification result supports the effectiveness of the SVM classifier. Overall, the identified diurnal precipitation time series have precipitation maxima in the afternoon to the early evening. In contrast, the precipitation maxima of identified nondiurnal precipitation time series tend to distribute across various hours.
Probability of precipitation maxima in a hundred precipitation time series subjectively labeled as (a) diurnal precipitation and (b) nondiurnal precipitation. The dataset used in this figure consists of 200 time series data.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0108.1
Probability of precipitation maxima in precipitation time series classified as (a) diurnal precipitation and (b) nondiurnal precipitation for each subdomain. The figure contains a complete 4-yr MJJA dataset, excluding those associated with tropical systems, resulting in slight variations in the exact number across different subdomains.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0108.1
As shown in Fig. 11, the statistical results support that about 61.9% of nonequilibrium convection is associated with a diurnal cycle in precipitation, while only about 33.8% of equilibrium cases. This is consistent with our expectation that the nonequilibrium convection should encompass more diurnal precipitation than equilibrium convection. As the partition between equilibrium and nonequilibrium cases was determined using a τc threshold of 6 h, these results provide evidence that the convective adjustment time scale, along with the 6-h threshold, can yield a classification that aligns with our physical understanding of the underlying dynamics. While somewhat less conclusive, it is evident that the nonequilibrium precipitation maxima tend to be confined within a shorter timeframe of a few hours (Fig. 11). Based on our examination, one explanation for the noon peak in equilibrium cases is that precipitation often intensifies in the afternoon during summertime, even under strong synoptic forcing.
Identification of diurnal precipitation pattern in subdomain-averaged rainfall time series. The (a) equilibrium convection and (b) nonequilibrium convection are classified by a τc threshold of 6 h. Bars represent probabilities of precipitation maxima, and annotations correspond to fractions of cases identified as having a diurnal pattern. The figure contains a complete 4-yr MJJA dataset, excluding those associated with tropical systems, resulting in slight variations in the exact number across different subdomains.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0108.1
4. Convective adjustment time scale as a predictor of forecast skill
One central aim of this study is to assess if the convective adjustment time scale derived from HRRR forecasts provides some indication on their quantitative precipitation forecast (QPF) skill over CONUS, as suggested by Keil et al. (2014) and Keil and Craig (2011) for central Europe. To avoid the double penalty problem of rainfall, in which the predicted storms are realistic but in a slightly wrong location, we complement the Gilbert skill score (GSS; Doswell et al. 1990) with a neighborhood-based skill score, the fractions skill score (FSS; Roberts and Lean 2008), to assess the forecast quality of 24-h accumulated precipitation. The GSS, also called equitable threat score (ETS), is modified from the threat score (TS) to account for the correct hits due to random chance. This verification is performed using the Model Evaluation Tools (MET; Brown et al. 2021) developed by the U.S. Developmental Testbed Center (https://dtcenter.org).
Figure 12 shows the FSS for a neighborhood of 25 grid points and an absolute threshold of 5 mm in 24 h against τc values, where the hourly convective time scale is averaged over 24 h to cover the accumulation window. In general, the FSS and τc are negatively correlated with coefficients between 0.4 and 0.7, depending on the region. Since the FSS cannot distinguish between false alarms and misses, we use the GSS as a second skill metric. Again, we see a distinct anticorrelation between GSS and convective time scale of similar amplitude (Fig. 13).
Scatterplots of convective adjustment time scale (h) and fractional skill score for the eight subdomains. Annotations denote the correlation coefficient computed for each subdomain. The FSS presented here used a squared neighborhood of 25 grid points and a binary threshold of 5 mm (24 h)−1.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0108.1
As in Fig. 12, but for Gilbert skill score.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0108.1
The sensitivity to different neighborhood sizes and thresholds was also investigated. While there is sensitivity, especially for high precipitation thresholds, our findings hold qualitatively across a large range of neighborhood sizes and thresholds. In this paper, we present correlations between the FSS of 24-h accumulated precipitation and the 24-h average τc. Reducing the window to 12- or 6-h windows yields similar conclusions. These results consistently demonstrate that forecast skill is reduced for nonequilibrium convection and decreases with increasing values of τc.
5. Conclusions
Previous work proposed the use of the convective adjustment time scale τc to classify convective weather regimes over different parts of Europe and link them to various properties like forecast skill and predictability of precipitation. The hypothesis is that equilibrium convection (small τc) is governed by more predictable synoptic flow conditions and therefore is expected to have higher skill and above average predictability of convective systems. In contrast, nonequilibrium convection (large τc) is assumed to be less predictable since it is subject to local variations (e.g., topography and cold pools).
This study identifies the climatological frequency of equilibrium and nonequilibrium convection in different parts of the CONUS domain. Here, we apply these concepts to operational forecasts from the convection-allowing High-Resolution Rapid Refresh (HRRR) Model to see if these findings also hold over CONUS. Since this domain is much larger and often contains various weather systems simultaneously, we develop a τc climatology over eight subdomains north and south of ∼40°N latitude and focus on precipitation systems during May, June, July, and August from 2019 to 2022.
The results show that τc is a good measure for identifying equilibrium (synoptically forced) and nonequilibrium (locally forced) convection. Unlike Flack et al. (2016), which point out a distinct scale break at 3 h, the climatological frequency of τc generally has a scale break between 6 and 12 h across the CONUS domain. In general, the northern domains exhibit more equilibrium convection than the southern domains. Synoptically, this reflects the fact that the North is dominated by a trough–ridge pattern of the Rossby waveguide, while the South is dominated by the subtropical anticyclone with descending air masses leading to a more stable stratification and build-up of CAPE. These results collectively support that τc can provide a physically meaningful regime classification. For the southern regions, a scale break of the distribution allows for a clear classification into two distinct regimes, while it is more continuous in the North. In this study, we apply a τc of 6 h as the threshold to categorize equilibrium and nonequilibrium convection.
One hypothesis of this study is that the precipitation of equilibrium convection depends on the propagation and intensity of synoptic weather systems. In contrast, nonequilibrium convection is expected to follow the diurnal cycle since it depends more on radiative heating and local dynamic processes. Using a supervised learning algorithm, we find that precipitation patterns with a diurnal cycle are about twice as likely to be identified in nonequilibrium regimes based on τc values.
We investigate whether the convective adjustment time scale can be used as a predictor of forecast skill for precipitation systems over CONUS, as suggested by Keil et al. (2014) and Keil and Craig (2011) for a domain over Germany. To this extent, we examine the relationship between the neighborhood skill score FSS and the traditional GSS for 24-h accumulated precipitation and τc values and find negative correlations between 0.4 and 0.7 for the different subdomains. Regional factors like maritime versus continental conditions suggest why previous studies chose different thresholds for the convective adjustment time scale. Convection over the British Isles and Germany is characterized by synoptic flow, more like the northern CONUS domain that has, on average, 55% of quasi-equilibrium convection. In contrast, only 22% of convection is classified as strongly forced in southern CONUS.
This is the first study to derive a climatology of the convective adjustment time scale over the CONUS domain using data from a convection-allowing forecast model. By studying convective systems over a number of subdomains and for a wide range of synoptic situations, our conclusions largely confirm previous work conducted on much smaller domains. Our results indicate that the convective adjustment time scale is an effective objective measure to classify equilibrium and nonequilibrium convection regimes enabling the flow-dependent assessment of the relative impact of different sources of uncertainty as well as various aspects of predictability. Ultimately, this study offers guidance on how to utilize the convective adjustment time scale to classify weather regimes across the CONUS domain.
Acknowledgments.
We gratefully acknowledge the National Oceanic and Atmospheric Administration (NOAA) Open Data Dissemination (NODD) Program for providing a robust dataset of high quality. The availability of this valuable data has greatly contributed to the success of our research. We express our gratitude to the University Corporation for Atmospheric Research (UCAR) Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) Program for funding and supporting author I-Han Chen’s visit to UCAR. All computations were performed on the National Center for Atmospheric Research (NCAR) Cheyenne supercomputer. NCAR is sponsored by the National Science Foundation. This work was conducted as part of Project A6 within the Collaborative Research Centre “Waves to Weather” funded by the (Deutsche Forschungsgemeinschaft under Grant SFB/TR165.
Data availability statement.
The dataset from NOAA High-Resolution Rapid Refresh (HRRR) Model is accessible online (https://registry.opendata.aws/noaa-hrrr-pds).
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