1. Introduction
Most climate models have warm and dry summer biases in the central United States (CUS) that persist after decades of physics improvements and resolution increases, diminishing their reliability of climate predictions and scenario projections in the region [see a comprehensive analysis in the companion paper Sun and Liang (2023, hereafter referred to as S&L)]. A recent project for Clouds Above the United States and Errors at the Surface (CAUSES) was established to search for the causes of CUS summer warm biases, and a viable solution (Morcrette et al. 2018; Van Weverberg et al. 2018; Zhang et al. 2018). The project’s existing hypotheses categorized the warm biases into three major causes: underestimating precipitation, underestimating low clouds, and misrepresenting land–atmosphere interactions. Since precipitation has a cooling effect (Lin et al. 2017), models that underestimate precipitation may overpredict surface temperature. Most models underestimate clouds in midlatitudes (Cheruy et al. 2014), which leads to overpredicting surface solar radiation and hence temperature. Misrepresenting land processes and interactions with the atmosphere may result in model underestimation of evapotranspiration, which is a leading cause of the warm-and-dry biases (Mueller and Seneviratne 2014; Ma et al. 2018).
While these hypotheses are not in full agreement with one another, they are closely linked by how well models simulate convective processes. Unskillful cumulus parameterization may underestimate both precipitation and cloud amounts. Deficit precipitation leads to a drier surface and smaller evapotranspiration, causing model overestimation of Bowen ratio, so more sensible heat flux to the atmosphere (Van Weverberg et al. 2018). Meanwhile, inadequate clouds lead to an overestimation of surface downwelling shortwave radiation. Both effects collaborate to induce summer warm-and-dry biases in CUS. Furthermore, models rely on a skillful cumulus scheme to realistically simulate the land–atmosphere coupling strength (Guo et al. 2006). Taken together, the model representation of the convective process is the central argument connecting the three hypotheses on the warm-and-dry biases.
Current cumulus parameterization schemes still suffer many difficulties in capturing convection characteristics in CUS (Liang et al. 2004a; Klein et al. 2006; Qiao and Liang 2015, 2016, 2017; Gao et al. 2017; Sun and Liang 2020a,b). Two unique summer climate features of CUS may challenge skillful cumulus parameterization. First, considerable convection activities can occur in CUS under weak large-scale forcing conditions and even unfavorable environments (Song et al. 2019). Early observational studies recognized those weakly forced yet highly impactful convections (e.g., the northwest-flow severe weather outbreaks) as the preexisting synoptic circulation for MCSs to occur (Johns 1993; Stensrud and Fritsch 1994). More recent observations showed that small-scale upward motions could form in the left exit region of the Great Plains low-level jets (LLJ) or ahead of subsynoptic-scale midtropospheric perturbations to overcome existing convective inhibitions (CIN) and hence trigger mesoscale convective systems (MCS) in unfavorable environments (Augustine and Caracena 1994; Moore et al. 2003; Wang et al. 2009, 2011; Wang and Clark 2010; Marsham et al. 2011; Geerts et al. 2017; Pokharel et al. 2019; Chasteen et al. 2019; Parish et al. 2020). These MCSs may be associated with more than half of total precipitation in CUS (Wang et al. 2009; Feng et al. 2019, 2021; Hu et al. 2020, 2021). Thus, neglecting the lifting effect of these subgrid updrafts can cause a cumulus parameterization scheme to significantly underpredict convective precipitation in CUS.
Second, cirrus clouds are the most frequent cloud type observed in summer CUS (Kollias et al. 2007). They significantly reduce outgoing longwave radiation (Hartmann et al. 2001) and modulate precipitation through diabatic cooling changes (Muller and O’Gorman 2011). They can form a persistent upper cloud ice shield to increase the static stability, which is a crucial negative feedback suppressing convective activity (Fowler and Randall 1994). Climate models may underestimate these high-level clouds in summer over CUS (e.g., Joos et al. 2008; Kay et al. 2012; Evans et al. 2017), although their bias evaluation was still very limited, lacking regional specification or by large observational uncertainty (Zhang et al. 2005; Tselioudis et al. 2021). The underestimation of high thin clouds may imply that the modeled cirrus lifetime is too short, preventing them from being advected to have a downstream effect, or cirrus clouds may also be quickly burned off by strong absorption of upwelling longwave radiation from below unless they lie above lower cloudy layers (Hartmann et al. 2001). Thus, anvils that coexist with deep convective towers can be expected to be more effective for changes in diabatic cooling. In both cases, underestimated cirrus clouds and their consequences on surface climate may indicate cumulus parameterization deficiencies.
This study aims to understand and reduce the warm-and-dry summer biases in CUS through improving the cumulus parameterization (for deep convection) by incorporating the two overlooked climate features discussed above. Section 2 articulates the improvements to the cumulus scheme in the regional Climate–Weather Research and Forecasting Model (CWRF; Liang et al. 2012). Section 3 describes the model experiments, observational data, and analysis methods. Section 4 compares the results of CWRF using the cumulus scheme with and without the improvements. Section 5 explores the physics mechanisms for the improved cumulus parameterization to reduce the warm-and-dry biases. Section 6 gives the summary and conclusions.
2. Cumulus parameterization improvements
This study used CWRF (Liang et al. 2012) as the test bed for improving cumulus parameterization to reduce the dry-and-warm biases in CUS (see Table 1 for the list of key acronyms). The CWRF has incorporated an ensemble cumulus parameterization (ECP) based on Grell and Dvénéyi (2002) with major improvements detailed in Qiao and Liang (2015, 2016, 2017). The ECP has demonstrated reliable performance over ocean (Qiao and Liang 2016), land (Qiao and Liang 2017), other climate regimes (Liang et al. 2019; Li et al. 2021; Jiang et al. 2021), and for extreme precipitation (Qiao and Liang 2015; Sun and Liang 2020a). The ECP has built-in parameterization for both deep and shallow convections. This study used ECP only for deep convection and the parameterization developed by Park and Bretherton (2009) for shallow convection.
Summary of key acronyms used in this study.
This study improved the ECP scheme [hereafter referred to as the new cumulus parameterization (NCP)] by incorporating three major changes: 1) the convection trigger function, 2) the entrainment rate constraint, and 3) the cloud water conversion rate. While the specific formulations for these changes are presented in the online supplemental material, their rationale and principles are outlined below.
As discussed earlier, LLJs and midtropospheric perturbations can induce subgrid updrafts that overcome the negative buoyancy barrier of CIN and thus lift parcels to the level of free convection (LFC), triggering MCS in unfavorable environments. Some attempts to parameterize the effect of unresolved updrafts were to define the cloud base at the level of condensation (LCL) (Donner 1993; Hong and Pan 1998). In particular, Jakob and Siebesma (2003) developed a new parcel ascent model-based trigger function that explicitly predicts the updraft vertical velocity and defines the cloud base at the LCL. (Note that these subgrid parcels or updrafts are represented as a collective ensemble and parameterized in terms of resolved quantities.) This function, hereafter referred to as the JS trigger, was tested with the Tiedtke (1983) cumulus parameterization that led to an overall improved ECMWF forecast performance (Bechtold et al. 2008).
This study incorporated into ECP the JS trigger, which decides whether a convection occurs and where its cloud base and top are located (following the implementation by Zhang and Wang 2017). The original ECP defines the cloud base at LFC, which is estimated as follows. It first searches upward for the layer with the maximum moist static energy. If this layer is higher than 4000 m above the surface, no convection occurs. Otherwise, it sets the cloud base to this layer for a deep convection. The cloud top is located at the layer of zero buoyancy.
The JS trigger uses an entraining plume model to predict the updraft vertical velocity wu in the convective boundary layer depending on buoyancy and near-surface perturbations. It defines the cloud base at the discrete model level closest to LCL at which wu > 0 and the cloud top at which wu vanishes. The first parcel departure level is set at the second layer for deep convections. At this level, turbulent perturbations parameterized in terms of surface sensible and latent heat fluxes are added to the parcel’s temperature and humidity, respectively. A deep convection occurs if the cloud depth is thicker than 200 hPa. Otherwise, it tests sequentially the parcels departing from higher levels (below ∼500 hPa) with constant perturbations (0.2 K, 10−4 kg kg−1) until finding deep convection.
The JS trigger thus assumes that the updraft induced by turbulent perturbations serves as the pseudobuoyancy to overcome existing CIN, lifting the parcel to penetrate through LCL and further LFC. In addition, we adopted the constraint of Tokioka et al. (1988) to prevent deep penetrative convection if the PBL is too shallow, that is, set wu = 0 so no convection occurs if the entrainment rate of environmental air is smaller than a threshold inverse of the PBL height. While the PBL height is provided by the CAM PBL scheme (improved Holtslag and Boville 1993), the entrainment rate is parameterized following Bechtold et al. (2008).
Anvil cirrus clouds typically accompany deep convections. An essential but often underappreciated parameter in cumulus parameterization is the cloud-to-rainwater conversion rate C0 (Emanuel and Živković-Rothman 1999), which generally increases with air temperature for the ice phase microphysical process (Fletcher 1962). Neglecting this dependency tends to underestimate water detrainment to form sufficient cirrus clouds (Lim et al. 2014; Han et al. 2017; Goswami et al. 2020). We adopted the C0 increase with temperature from Han et al. (2016), except replacing the exponential dependence with a sigmoid function for a more gradual slope (see appendix A).
3. Model experiments, observational data, and analysis methods
This study conducted two 40-yr continuous CWRF integrations from 1 October 1979 to 1 January 2020 at 30-km grid spacing over the well-tested North American domain, including the contiguous United States (Liang et al. 2012). The control simulation (CTL) used the CWRF default physics configuration [see Sun and Liang (2020a) for details], including ECP for cumulus parameterization. The second simulation (NCP) used the identical configuration except incorporating into ECP all the improvements presented in section 2. To understand the physical mechanisms causing the improved model results, four additional branch runs were made, each of which was a warm start from the CTL simulation conditions on 1 May for a 4-month integration that ended on 1 September each year between 1980 and 2020. One run adopted both the JS trigger and the Tokioka constraint to determine the combined convection activation (JST), while the others included separately one of the two activations and the temperature-dependent autoconversion parameter C0 (C0T). The warm start helped remedy the complication by soil memory effects to focus on the ECP changes. All CWRF simulations were driven by lateral boundary conditions derived from the latest European Centre for Medium-Range Weather Forecasts reanalysis (version 5, hereafter ERA5), with 6-hourly data available at a grid spacing of 0.25° (Hersbach et al. 2020). The analyses below were based on summer (1 June–31 August) during 1980–2019.
Table 2 summarizes the observational data used in this study, including their source, period, resolution, and mapping method onto the CWRF 30-km grid. In particular, daily precipitation and surface air temperature data were from the high-resolution (4-km) gridded surface meteorological analysis of Abatzoglou (2013), available from 1979 onward. Other data include surface downwelling shortwave and longwave radiation fluxes, cloud amounts in categorical bins of pressure and optical depth, and atmospheric circulation variables (geopotential height, wind, air temperature, and specific humidity).
Observations, resolutions, available years, and their references.
The major characteristic regions affected by changing ECP to NCP include CUS defined in the CAUSES project and the Midwest, North-Central, South, and Southeast typically used as the key U.S. climate regions. These are illustrated in Fig. 1 along with the terrain distribution and used below to elaborate the result comparison and process understanding.
Characteristic climate regions (colored boundaries with names) along with the CUS key area (blue dotted outline enclosing 31°–52°N, 89°–98°W) where the warm-and-dry bias is most significant as defined in the CAUSES project. The color contour map shows the terrain height distribution.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0254.1
To facilitate the physical understanding of the results by various changes to ECP, two decomposition analyses were performed. First, following Zhang et al. (2018) and Van Weverberg et al. (2018), the net surface shortwave or longwave radiation biases were decomposed into contributions from the surface (shortwave reflection or longwave emission), total cloud, and integrated water vapor. Comparison of these component differences helped identify whether the ECP changes reduced model biases in a physically consistent manner and which key processes induced these bias reductions. Second, following Muller and O’Gorman (2011), the precipitation-related latent heat release was separated into the column-integrated dry static energy divergence and total diabatic cooling that consists of the atmospheric net radiative loss minus the gain from surface sensible heat flux. This separation helped quantify the radiative contribution to the precipitation change associated with the ECP improvements.
The CWRF has a unique Conjunctive Surface–Subsurface Process model (CSSP) to realistically capture the detailed terrestrial hydrology and land–atmosphere interaction (Dai et al. 2003, 2004; Liang et al. 2005a; Choi et al. 2007, 2013; Choi and Liang 2010; Yuan and Liang 2011; Liang et al. 2012; Xu et al. 2014; Gan et al. 2015; Ji et al. 2017). This facilitates the present study to focus on cumulus parameterization improvements, assuming that the CSSP coupling well represents the interactions between surface and convection processes. In addition, CWRF has implemented the latest satellite Cloud Feedback Model Intercomparison Project Observation Simulator Package version 2 (COSP; Bodas-Salcedo et al. 2011; Swales et al. 2018) to simulate cloud characteristics that are consistent with satellite retrievals. The COSP allows a direct comparison with satellite observations, which is needed to evaluate how our proposed ECP changes affect coupling convection, cloud, and radiation processes.
4. Reduction of CUS warm-and-dry biases
Figure 2 compares the 1980–2019 averaged summer biases in surface air temperature, precipitation, surface downwelling shortwave radiation, and top-of-the-atmosphere outgoing longwave radiation (OLR) between the CWRF using the control (CTL) and new (NCP) cumulus parameterization. Similar to the Coupled Model Intercomparison Project (CMIP) result, CTL simulated significant warm biases in CUS, most prominent (>2°C) in the Midwest and North-Central (see Fig. 1 for the specification of the key climatic regions). It also had warm biases of ∼2°C over the Rocky Mountain regions, resembling high-resolution CMIP results (Fig. 1 in S&L). In contrast, NCP largely eliminated the warm biases around CUS, with most areas reduced to <1°C. The reduction is evident on the NCP − CTL map concentrated in the Midwest.
Summer biases in surface air temperature (°C), precipitation (mm day−1), and surface downwelling shortwave and top outgoing longwave radiation fluxes (W m−2) simulated by CWRF using the control (CTL) and new (NCP) cumulus parameterization. The temperature and precipitation biases are averaged over the whole integration period (1980–2019), while the radiation bias over a shorter period (1984–2007) as limited by available observations.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0254.1
For precipitation, CTL simulated significant dry biases (≤−1 mm day−1) in CUS and some areas of the southern Rocky and the Appalachian Mountains. Meanwhile, it had wet biases over the Gulf states, most pronounced in south Texas. NCP mostly eliminated the dry biases over CUS and the southern Rocky Mountains region. It also largely suppressed the overestimation in the Gulf states, albeit overdone so in some areas away from the coast. This suppression is clearly seen on the NCP − CTL map to occur over broad regions across the Southeast, mainly due to the constraint of Tokioka et al. (1988). As shown in Fig. S1 in the online supplemental material, this constraint significantly reduced the number of rainy days over the Great Plains and Southeast, led to locally less precipitation and drier soil moisture with deficit water available for surface evaporation, and so caused a drier and deeper PBL under similar surface sensible heating, that is, elevated PBL height (Troen and Mahrt 1986). Remotely, more abundant water vapor was transported downstream to yield more precipitation in the Midwest and northern Southeast. On the other hand, NCP slightly enhanced the wet biases in the northern states, which may be related to rainfall overestimation by cloud microphysics processes. It also produced more excessive precipitation on many spots in Wyoming and Colorado, mostly along the windward slope of local terrain peaks east of the Rocky Mountains. This amplification was mainly due to the JS trigger (Fig. S2). It may suggest that some constraint is needed to prevent the JS trigger from activating convection too easily because of local orographic lifting. The role of lower tropospheric perturbations that induce small-scale updrafts to trigger MCS may be overestimated as they are relatively rare on the windward of the Rocky Mountains (Wang et al. 2009).
For surface shortwave radiation, CTL produced substantial overestimates in the Midwest and Northeast (20–60 W m−2), with a spatial pattern highly correlated with that of temperature biases. It had smaller overestimates in the North-Central, which did not correspond well to the center of warm biases. Weak correspondences were also simulated in the western states, especially in the Southwest, where excessive radiation happened with warm or small temperature biases. NCP essentially eliminated the radiation biases in most areas across the North-Central, Midwest to Northeast, generally below 10 W m−2 or within observational uncertainty. As clearly shown on the NCP − CTL map, the systematic insolation reduction (by 20–40 W m−2) extended to also cover the entire South to Southeast. This reduction was somewhat overdone to cause underestimates (by 10–20 W m−2) in some areas of the Southeast, coincident with slightly colder biases along the Gulf coast. It was a combined result of the Tokioka constraint and C0T effect (Fig. S2), increasing total cloud amount (Fig. S3).
For OLR, CTL simulated substantial overestimates across the southern to central Great Plains and the western part of the Midwest (15–30 W m−2), indicating that high-level clouds were significantly underestimated. NCP eliminated the biases in most areas across the region. As shown on the NCP − CTL map, the systematic OLR reduction (by 10–30 W m−2) extended to also cover the entire eastern United States. As designed, C0T significantly increased high–middle clouds (Fig. S3), which overcame the large underestimate in CTL and further reduction by the Tokioka constraint eliminating convection occurrences from shallow PBL (Fig. S1). The OLR reduction was overdone to cause underestimates (by 15–20 W m−2) in the South to Southeast coastal regions, coincident with drier biases.
Figure 3 compares summer composite biases of total precipitable water and vertically integrated moisture transport flux when daily precipitation averaged over a key region (i.e., the Midwest, North-Central, South, and Southeast) exceeds its climatological median. Observations showed a southerly LLJ prevailing over the Great Plains along the western flank of the Bermuda high. The LLJ and its associated moisture transport were much stronger in the composites for the above-median precipitation events in the Midwest and North-Central than those in the South and Southeast. This is consistent with the observed interannual teleconnection pattern in which westward extension of the Bermuda high enhances the Great Plains LLJ that transports more moisture northward to cause precipitation increases in the Midwest and decreases in the Gulf states (Zhu and Liang 2013). For all composites, CTL produced systematically less precipitable water (i.e., drier atmosphere) over the Gulf of Mexico, Southeast, and CUS, while transporting more moisture toward New England through the channel over the western North Atlantic. NCP largely eliminated all these regional circulation biases.
Summer composites of total precipitable water (kg m−2; color fill), mean sea level pressure (hPa; color contour lines) and vertically integrated moisture flux (kg m−1 s−1; vectors) when daily precipitation averaged over a key region (enclosed in a thick black outline) exceeds its climatological (1980–2019) median. (left) The NARR reference overlaid with sea level pressure (hPa; color contours), and (center),(right) CWRF CTL and NCP biases from NARR. (top to bottom) Our key composite regions: the Midwest, North-Central, South, and Southeast.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0254.1
Figure S4 compares the latitude–pressure cross-section composites of specific humidity, and meridional–vertical wind biases averaged across the longitudinal span of CUS for the same above-median precipitation events in the four regions. CTL simulated stronger upward motions over the Gulf of Mexico and coastal states, driving locally more convective precipitation while causing remotely larger subsidence over the central Great Plains. Both effects depleted more moisture from the column between 800 and 500 hPa, resulted in a drier lower troposphere across 22°–40°N. Again, NCP largely corrected these regional circulation biases.
Given their critical role in linking CUS warm and dry biases as revealed from the CWRF NCP sensitivity (Fig. 2), the net (downwelling minus upwelling) surface shortwave and longwave radiation flux biases were decomposed into the contributions from the column (vertically integrated) cloud and water vapor as well as surface reflection or emission, following the method of Zhang et al. (2018) and Van Weverberg et al. (2018). Figure 4 compares these bias compositions between CTL and NCP, while Fig. S5 shows the NCP minus CTL differences in the net fluxes and their relative changes to the observed means. The net shortwave biases were mostly positive in CTL and about twice the magnitude of the net longwave biases, which were positive in CUS and eastern coast states but negative in the western states. NCP significantly reduced the biases for both shortwave and longwave fluxes over most areas from the central to eastern states. [Note that the bias reduction relative to the observed mean is larger in the longwave than shortwave flux (Fig. S5).] Small changes were simulated in the western states, where the Rocky Mountains play a dominant role in the prevailing weather patterns.
CWRF summer surface net (a) shortwave and (b) longwave radiation (W m−2) biases from SRB observations during 1984–2007, comparing CTL and NCP. (left to right) Total biases and their contributions to induced column cloud and water vapor as well as surface reflection or emission biases.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0254.1
For shortwave, cloud biases dominated most regions while water vapor biases play a second important role in eastern United States. Insufficient low clouds (see below) reflected less while inadequate water vapor amounts (Fig. 3) absorbed less, both of which led to more insolation to the surface. The contribution from surface reflection biases was relatively small, likely because CWRF incorporates a realistic albedo parameterization (Liang et al. 2005b), which was not changed between NCP and CTL. Minor reflection changes might occur as wetter soil from more precipitation has lower albedo. For longwave, cloud biases dominated the Rocky Mountains while water vapor biases played a more important role in CUS. Insufficient clouds emitted less, causing negative downwelling radiation biases over the Rockies. In contrast, inadequate water vapor amounts were identified with positive radiation biases in CUS and also, albeit weaker, in the Midwest and Northeast. This occurred because the water vapor effect on longwave radiation is considerably stronger when it is wet than dry—the less frequent wetter conditions may cause excessive radiation in total even in a drier atmosphere on average (Van Weverberg et al. 2018). Note that surface emission biases mainly reflected ground temperature biases, which were closely related to surface air temperature biases (S&L).
For both shortwave and longwave radiation biases, the most remarkable improvement by NCP over CTL was the significant reduction of cloud underestimates. The NCP − CTL maps reveal close correspondences of increased low and mid–high clouds (Fig. S3) with, respectively, decreased surface downwelling shortwave and top outgoing longwave fluxes (Fig. 2). Given their importance, cloud biases were further separated by their top pressures and optical depths. Figure 5 compares these statistics averaged over the four key regions. CTL underestimated optically thin and thick clouds in both low and high layers over all regions except for overestimated thick low clouds in the Southeast. CTL also underestimated thin but overestimated thick middle clouds over all regions. Thus, in CTL, insufficient low and high cloud amounts contributed most to the cloud-induced radiation biases. In the Midwest, North-Central, and Southeast, NCP systematically improved both thin and thick low and middle clouds as well as thick high clouds. Exceptions occurred in the South, where NCP underestimated thin middle clouds but overestimated thick low clouds. Therefore, NCP simulated overall more realistic cloud amounts in both vertical distribution and optical depth to largely reduce surface radiation budget biases and essentially eliminate CUS warm-and-dry biases.
CWRF summer cloud amount biases from MODIS averaged 2002–19 in each bin of joint pressure (vertical) and optical depth (horizontal) over the four key regions, comparing biases (denoted by a prime) of (left) CTL and (center) NCP as well as (right) relative differences of their absolute biases (%; |NCP′| minus |CTL′| over the observed mean of MODIS). The actual bias value (×100) is listed with a warmer (cooler) color for a larger overestimation (underestimation). A cooler (warmer) color for the relative difference indicates improvement (deterioration).
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0254.1
An important question is how NCP changed (from CTL) the frequency and intensity between convective (parameterized) and large-scale (resolved) precipitation events. As shown in Fig. S3, NCP significantly increased convective rainy days over two major clusters. One cluster extended across the Great Plains and the neighboring western states, where more frequent deep convections (starting from high elevations) produced more cirrus clouds to mostly eliminate the OLR overestimates in CTL, with little effect on surface shortwave radiation. Another cluster extended across the Midwest and Southeast, where more deep convections (starting from low elevations) produced more low–midlevel clouds to significantly reduce both surface insolation and OLR overestimates in CTL. Meanwhile, more frequent triggering of convections removed instability energy and water vapor (by rainout) more quickly so to reduce convective rainfall intensity, especially in the downstream regions (such as eastern Great Plains). On the other hand, weaker convective precipitation allowed the air to be more saturated and hence increased large-scale rainy days, especially in the downstream regions of the two clusters. For the same reason, large-scale rainfall intensity was generally enhanced over most regions.
5. Physical mechanisms on the CWRF bias reduction
This section explores the physical mechanisms through which NCP eliminated the warm and dry biases in CUS. The previous section compared the results from the three major changes to the ECP cumulus parameterization (CTL)—the Tokioka constraint, the JS trigger, and C0T autoconversion—separately as well as their total effects (NCP). We showed that the resulting temperature and precipitation changes had complex relationships with cloud, radiation, and other fields. The effects were neither local nor linear. It is thus challenging to gain physical insights from local and isolated comparisons. Below we performed two decomposition analyses to address the issues from the surface radiation budget and atmospheric diabatic cooling perspectives in the coupled climate system. Since the Tokioka constraint was built directly into the JS trigger as an additional limiting condition for convection to occur and produced some compensating results, we focused on their combined effects (JST).
a. Effects of the JS trigger and Tokioka constraint
Figure 6 compares the composite vertical profiles (cloud fraction and base/top pressure frequency, convective temperature, and water vapor tendencies) and relative differences due to incorporating the JS trigger plus the Tokioka constraint (i.e., JST minus CTL). The composite was done on all grids over each of the four key regions when convections took place. The JST simulated systematically much lower cloud bases than CTL (Fig. 6a and Fig. S6), mainly because the JS trigger defines the cloud base at LCL that is generally lower than LFC. The CTL used LFC, which caused a systematic overestimation of cloud-base heights. Besides, the CTL cloud-base frequency had a pronounced zigzag distribution, while the JST profile was quite smooth (Fig. S6). This is because CTL using the default ECP located the cloud base simply at the discrete model level of LFC, while JST adopting the JS trigger located that at the closest model level to the exact pressure of LCL (Jakob and Siebesma 2003).
Summer composite JST minus CTL changes over the four key regions (Midwest, North-Central, South, Southeast) separated by (a)–(e) colors and (f)–(i) titles. (a)–(e) The changes in the vertical profiles of the (a) cloud-base and (b) cloud-top pressure frequency, the convective (c) temperature (°C day−1) and (d) water vapor (g kg−1 day−1) tendency, and (e) the cloud fraction (%). (f)–(i) The relative changes in the cumulus characteristic terms (F′/F), where the prime denotes for the change, and F for any feature among cloud pressure depth (D), cloud-base mass flux (mb), downdraft mass flux (md), and ε = md/mb.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0254.1
The composite analysis also shows that JST simulated systematically higher cloud tops than CTL (Fig. 6b). Thus, on average, coincident with a lower cloud base was a deeper cloud depth in the Midwest, North-Central, and South, albeit a slightly shallower depth in the Southeast (Fig. 6i). A cloud-base change may have important consequences on other cumulus characteristics, such as the downdraft mass flux (md) that determines convective effects on large-scale environments (Grell et al. 1994). To the first-order approximation (see appendix B for the derivation), the relative change in md can be estimated by the negative relative change in cloud pressure depth (D) and in the downdraft over (updraft) cloud-base mass flux ratio (ε),
The North-Central differs from other three regions in that its mass flux ratio (ε) was enhanced by JST, causing a weaker reduction in the downdraft than updraft. It was also identified with a much wider peak of the cloud-base frequency between 850 and 650 hPa than other regions, each with a distinct narrow peak around 900 hPa. The changes in the North-Central were more evident for the increased midlevel clouds, but relatively small in the low- and high-level clouds. In contrast, the Midwest, South, and Southeast were all evident with significantly increased low and reduced high clouds. This contrast is likely because the precipitable water is much less abundant in the North-Central, inadequate to support deep convections. Therefore, it was not the cloud-induced shortwave biases, but the water vapor induced longwave biases, that dominated the warm biases in the North-Central (Figs. 2 and 4).
Figure 7 compares the atmospheric diabatic cooling compositions associated with the latent heat released due to precipitation changes when switching the CTL to JST parameterization. Following Muller and O’Gorman (2011), the decomposition links the changes in precipitation with cloud radiative forcing from an energetic perspective (ignoring the energy exchange outside the analysis region). The JST simulated large precipitation increases from CTL in the Midwest, North-Central, and South, but small reductions in the Southeast. On average, the surface sensible heat reduction (more diabatic cooling) contributed the most to support more precipitation latent heat release, while the surface longwave emission reduction (again more diabatic cooling) played a secondary role. In all cases, the atmospheric total (surface downwelling minus top upwelling, i.e., SWtot in Fig. 7) shortwave adiabatic cooling changed little between JST and CTL, while the surface insolation reduction (SWd) was canceled by the atmospheric top reflection (
(a) The summer mean JST minus CTL diabatic cooling changes as decomposed into the contributions from the surface downwelling and negative upwelling shortwave (SWd, −SWd) and longwave (LWd, −LWd) radiation, the top-of-the-atmosphere outgoing shortwave (
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0254.1
One exception was in the Southeast, where a large increase in the diabatic cooling from less surface sensible heat and longwave emission accompanied a small reduction in precipitation (Fig. 7). The long-term average may mask important relationships as complicated by other feedbacks. Hence, a linear regression was made between the composite changes in precipitation and the sum of two dominant diabatic cooling terms, that is, surface sensible heat plus longwave emission, from all individual years (Table 3). Strong positive correlations occurred in the Midwest, South, and Southeast, where the surface diabatic cooling changes explained the precipitation interannual differences between JST and CTL by, respectively, 62%, 80%, and 67% of the total variance. Now, the North-Central became exceptional, with the variance explained by only 42%. As discussed earlier, the North-Central is unique with more evident increases in mid- rather than low-level clouds. Together with terrain-induced precipitation anomalies, these bias characteristics may indicate different feedback mechanisms in North-Central. On the other hand, the regression intercepts in the South and Southeast were much larger, indicating an important systematic contribution from the dry-static energy flux divergence missed in the long-term average. Nevertheless, through interactions with land surface processes, low- to midlevel cloud increases induced by deeper convections significantly reduced the warm and dry biases and strongly controlled precipitation interannual variations.
The variance of the JST minus CTL changes in precipitation (PR) and temperature (T2) that can be explained by the key diabatic cooling terms (LWu + SH, SWd, PR) and a combined regression (SWd, PR). It is shown as the coefficient of determinant R2 using 40 data samples and identified as statistically significant at the confidence level of 95% (*) or 99% (**).
Interannual temperature differences between JST and CTL in the four regions (Midwest, North-Central, South, Southeast) were correlated with those of both surface insolation (positive) and precipitation (negative), respectively explaining (15%, 41%, 47%, 48%) and (45%, 31%, 72%, 48%) of the total variance. Notice the relatively small correlation with insolation in the Midwest and with precipitation in the North-Central. In all four regions, a simple linear regression with both insolation and precipitation led to overall larger correlations, explaining most of the T2 variance (45%, 50%, 75%, 54%). Thus, the JST induced insolation reduction and precipitation increase collaborated to significantly diminish the regional warm biases. The key mechanisms and physical processes underlying this bias reduction were elaborated in S&L.
b. Effects of the temperature-dependent autoconversion
Figure 6 shows that JST reduced high-level clouds from CTL, which is not beneficial to overestimation of OLR in CTL (Fig. S2). This motivated improving cirrus clouds associated with deep convections to counter back the JST-caused OLR errors. Figure 8 compares the composite vertical profiles (convective water vapor and temperature tendencies, cloud fraction) between C0T and CTL. Overall changes from CTL to C0T were similar for all fields among the four regions. Most notably, C0T simulated a wetter tendency (up to 0.5 g kg−1 day−1) in the upper troposphere between 300 and 150 hPa. Our derivation in appendix A (A10) explains this positive anomaly in water vapor tendency was due to the vertical gradient of C0. A higher moisture tendency led to more cirrus clouds with less OLR, which caused a temperature decrease above the cloud and increase below. Thus, the environmental temperature change is a direct effect from the water vapor tendency perturbation. The enhanced vertical temperature gradient near the tropopause (∼200 hPa) reduced the upper tropospheric convective warming—an indirect effect of the water vapor tendency change. More cirrus led to larger warming at a higher altitude than near the surface and hence enhanced the column stability. Those extra water vapor near the tropopause subsided to further increase midlevel clouds.
Summer composite vertical profiles change (C0T minus CTL) over the four key regions. (a) Temperature (°C), the convective tendency in (b) temperature (°C day−1) and (c) water vapor (g kg−1 day−1), and (d) cloud fraction (%). The shaded area indicates where anvil cirrus occurs.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0254.1
As an additional benefit, C0T produced a convective cold top, a prevalent mesoscale phenomenon observed in midlatitude summer (Fritsch and Brown 1982). To simulate this cold top in a Boussinesq model, the hydrostatic pressure perturbation created by the low-troposphere cumulus warming must be balanced by the pressure perturbation above (Holloway and Neelin 2007). Apparently, the CTL result shows that this balance is not warranted in a nonhydrostatic model. Instead, the indirect effect from the diabatic cooling due to cumulus turrets (anvil cirrus) offers a viable explanation. Both JST (Fig. 6) and C0T (Fig. 8) captured this convective cold top.
Figure 9 compares the atmospheric diabatic cooling compositions associated with the latent heat released due to precipitation changes when switching the CTL to C0T parameterization. In all four regions, C0T produced systematically more cirrus clouds and so reduced OLR. On average, this OLR reduction dominated the total diabatic cooling change to allow less condensation heating and thus slightly less precipitation (with large uncertainty), which is consistent with the enhanced tropospheric stability (Fig. 8b). Both surface sensible heat increase and net shortwave radiation decrease were much smaller, while surface upwelling and atmospheric downwelling emission changes canceled each other. Hence, a linear regression was made between the interannual composite changes in precipitation and OLR (Table 4). Negative correlations were significant in the Midwest, but became weaker in the North-Central, South, and Southeast where the OLR changes explained the precipitation interannual differences between C0T and CTL by, respectively, 44%, 12%, 22%, and 24% of the total variance. These relationships agreed with observations that correlations between OLR and precipitation were positive for the annual cycle but negative for interannual anomalies, depicting the relative roles of surface temperature and deep convection in the extratropics (Xie and Arkin 1998). On the other hand, the C0T induced insolation and precipitation changes still dominated surface temperature interannual differences, jointly explaining 54%, 53%, 82%, and 37% of the total variance.
As in Fig. 7a, but for C0T minus CTL changes.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0254.1
Figure 10 summarizes the major physical processes and underlying mechanisms that explain how the new cumulus parameterization incorporating JST and C0T reduced the summer warm-and-dry biases in CUS. First, the JS trigger defines the cloud base at LCL, which reduces the cloud-base height and increases its depth. A deeper cloud reduces the mass flux at its base and so weakens its downdraft [Eq. (B5)], which decreases the convective drying and warming in the low- to midtroposphere and subsequently increases low to midlevel clouds (Fig. 6). Hence, less solar insolation reaches the surface so to cool the ground, which reduces sensible heat and longwave emission. This reduced surface forcing enhances the atmospheric diabatic cooling, which is associated with more condensation heating from heavier precipitation (Fig. 7). Second, the Tokioka entrainment constraint prevents penetrative convection when the PBL is too shallow, which reduces the number of rainy days and total precipitation over warm oceans and coasts (Fig. 2 and Fig. S1). Third, the temperature dependence (and so vertical gradient) of the cloud-to-rainwater conversion rate produces a wetter upper troposphere and so more cirrus clouds (Fig. 8), which reduce OLR and thus the diabatic cooling to allow less condensation heating from lighter precipitation (Fig. 9). In all cases, any reduced insolation and/or increased precipitation result in a colder surface air temperature, although the strength of the responses depends on regions due to other feedbacks. S&L further elaborated the key feedback pathways involving both temperature and precipitation biases among CMIP models.
The conceptual summary explaining the physics processes (pathways) through which the new cumulus parameterization (NCP) reduces the summer warm-and-dry biases in CUS. The upper-left and lower-right ovals represent, respectively, the NCP incorporation of the convection trigger function and cloud water-to-rain conversion rate, while the boxes are their corresponding physics processes. The black (red) arrows indicate the positive (negative) forcing.
Citation: Journal of Climate 36, 7; 10.1175/JCLI-D-22-0254.1
The CTL largely underestimated both low- and high-level clouds to cause substantial compensating errors between too much surface warming and too much OLR cooling (Fig. 2). On the other hand, JST simulated sufficient low-level clouds to significantly reduce the warm and dry biases in CUS. However, it still produced inadequate high-level clouds, breaking CTL’s error compensation, to overestimate precipitation and OLR in broad regions around CUS (Fig. S2). Meanwhile, C0T systematically increased cirrus clouds and so reduced OLR. Together NCP (JST + C0T), through the robust physical mechanisms outlined above (Fig. 10), essentially eliminated the biases in CUS.
6. Summary and conclusions
This study aimed to use CWRF incorporating cumulus parameterization improvements to understand and reduce the long-lasting warm and dry summer biases in CUS that are common to global and regional climate models. The bias attribution and reduction are challenging because of the complex nonlinear land–atmosphere coupling feedbacks. To disentangle the complexity, we considered two unique summer climate features prevailing in CUS: convective activities under weak large-scale forcing conditions and cirrus clouds, both of which are associated with cumulus parameterization. We thus incorporated into CWRF ECP 1) the trigger function of Jakob and Siebesma (2003) to represent the lifting effect of small-scale rising motions associated with LLJ activities and midtropospheric perturbations to overcome CIN for MCS to occur in unfavorable environments, 2) the entrainment constraint of Tokioka et al. (1988) to prevent deep convection in case of shallow PBL to remedy the overestimation of precipitation frequency, and 3) the temperature-dependent cloud-to-rainwater conversion rate modified from Han et al. (2016) to increase water detrainment to form sufficient cirrus clouds. To facilitate the physical understanding, we conducted CWRF 1980–2019 simulations driven by ERA5 and decomposition analyses of the resulted surface radiation budget (Zhang et al. 2018; Van Weverberg et al. 2018) and precipitation heat budget (Muller and O’Gorman 2011). We found that the new ECP produced overall more realistic cloud amounts in both vertical distribution and optical depth, especially increased low- and high-level clouds, to largely reduce biases in the surface radiation budget and OLR, and through the robust physical mechanisms (Fig. 10) essentially eliminate CUS warm-and-dry biases.
Significant summer bias reductions from the new ECP also occurred in other key regions, including the Midwest, Southeast, Northeast, and the southern and eastern U.S. coastal oceans. In some regions and other seasons, a large room exists for further model improvements. In particular, pronounced biases in the western United States throughout the year involve different processes and need more detailed investigation. Nevertheless, the bias identification and process diagnosis procedures established in this study offer a practical guidance to detect the critical formulation deficiencies and understand the underlying physical mechanisms. For each region, it is vital to first identify the bias characteristics and their governing climate processes, and then detect the key model formulation deficiencies in representing these observed processes. Only after the signals are diagnosed and the processes understood can one develop and institute viable solutions to eliminate the regional biases in a physically consistent manner. Some of the findings from this study were applied in our companion paper S&L to identify the model deficiencies that may likely explain CUS warm and dry biases among CMIP models. We confirmed that the models defining the cloud base at LCL rather than LFC reduce the warm-and-dry biases and that the regional temperature and precipitation biases among all models are more generally explained by errors in surface shortwave insolation, longwave emission, and sensible heat. These results will be beneficial to seeking specific solutions based on individual models.
An important question is whether NCP improved precipitation diurnal cycle simulation. Figures S7 and S8 compare observed and CWRF simulated summer rainfall diurnal cycle in the eastward propagation for the 36°–42°N averaged amount and the geographical distribution of the phase or timing, respectively. The NCP showed noticeable improvement over CTL with an enhanced amplitude of the nocturnal precipitation across the Great Plains to Midwest, whereas the phase changed insignificantly. Improving the precipitation diurnal cycle warrants further investigation from both cumulus parameterization and convection-permitting modeling perspectives (Liang et al. 2004b; Gao et al. 2017).
Acknowledgments.
The research was supported by the U.S. National Science Foundation Innovations at the Nexus of Food, Energy and Water Systems under Grant EAR1639327 and the U.S. Department of Agriculture–National Institute of Food and Agriculture under Grant 20206801231674 for developing the Dashboard for Agricultural Water use and Nutrient management at the University of Maryland and Grant 2015-34263-24070 for the UV-B Monitoring and Research Program at Colorado State University. The simulations and analyses were conducted on computers in the National Center for Atmospheric Research Computational and Information Systems Lab and the Maryland Advanced Research Computing Center under Grant EES210017.
Data availability statement.
All CWRF experiment outcomes used to generate the results in the manuscript are available from the corresponding author upon reasonable request.
APPENDIX A
Derivation of the Temperature-Dependent Cloud-to-Rain Autoconversion Effect
APPENDIX B
Approximation of the Cloud Depth and Downdraft Mass-Flux Perturbation Relationship
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